b,transcrib]'s notes_/b3 ,! text ( ?is book has be5 pres]v$ z closely z practicable to its orig9al =m4 ,h[ev]1 ! au?or us$ "s unusual symbols1 & ,i h tak5 ! lib]ty ( us+ ,unicode *>act]s ) simil> appe>ance 7 7 z sub/itutes1 disreg>d+ _! (ficial mean+ & aw>e t !y might n display on all devices4 ,an ar*aic symbol us$ by ! au?or to indicate ! ma!matical #8factorial' function has be5 replac$ by ! mod]n equival5t1 viz4 6 ,unusual placem5ts ( v>i\s sub- & sup]script$ symbols rema9 z 9 ! orig9al text4 ,9 ?is pla9-text v]sion1 italic text is d5ot$ by 99a/]isks992 sup]script$ & subscript$ *>act]s are enclos$ )9 curly brackets prec$$ by a c>et 77 or und]l9e 77 respectively4 ,inconsi/5cies ( punctuation h be5 correct$ sil5tly1 b inconsi/5t spell+s su* z 99,roem]1 ,rm]1 ,rm]99 h n be5 alt]$4 ,a li/ ( correct$ spell+s is app5d$ at ! end ( ! book4 ,footnotes h be5 r5umb]$ consecutively & position$ bel[ ! relevant p>agraphs4 ,a miss+ footnote m>k] has be5 ins]t$ on p4#gea aft] track+ d[n ! orig9al docum5t4 ,a miss+ negative symbol has be5 add$ to an expon5t 9 a =mula on p4#cbg4 ,!re is a mislead+ calculation on p4#aid & ! table t foll[s1 reg>d+ progressive p[]s ( two3 77#bb7b7b is equival5t to 7#af7b :i* equals #bef n #fe1cef z /at$1 b #baf does equal #fe1cef4 sic has be5 ins]t$ on p4#agi alongside a /atem5t t ! alphabet conta9s #bd lett]s2 h[ev]1 ! /atem5t may well be correct giv5 t x 0 writt5 9 #agjd by a ,flemi% au?or & ! language is n specifi$4 ,a l>ge ari?metic triangle on p4#ahd _c be display$ optimally 9 ?is pla9-text v]sion = lack ( space ,,! ,,pr9ciples ,,( ,,sci5ce4 ,illu/ration ,illu/ration3 ,,! ,,logical ,,ma*9e4 ,,! ,,pr9ciples ,,( ,,sci5ce3 99,a ,,treatise ,,on ,,logic99 99,,&99 99,,sci5tific ,,me?od499 ,,by ,w4 ,,/anley ,,jevons1 ,,ll4,d4 7,,ed9b471 ,m4,a4 7,,lond471 ,f4,r4,s4 ,london3 ,,macmillan ,,& ,,co4 #ahhc4 99,! ,"r ( ,translation & ,reproduction is ,res]v$499 ,,london3 ,r4 ,clay1 ,sons1 ,taylor1 ,pr9t]s1 ,,bread ,,/reet ,,hill4 ,/]eotyp$ ,edition4 ,,preface 99,,to ,,! ,,fir/ ,,edition994 ,x may be truly ass]t$ t ! rapid progress ( ! physical sci5ces dur+ ! la/ ?ree c5turies has n be5 accompani$ by a correspond+ advance 9 ! !ory ( reason+4 ,physici/s speak famili>ly ( ,sci5tific ,me?od1 b !y c\ld n readily describe :at !y mean by t expression4 ,pr(\ndly engag$ 9 ! /udy ( p>ticul> classes ( natural ph5om5a1 !y are usually too mu* engross$ 9 ! imm5se & ev]-accumulat+ details ( _! special sci5ces to g5]alise ^u ! me?ods ( reason+ :i* !y unconsci\sly employ4 ,yet few w d5y t ^! me?ods ( reason+ ought to be /udi$1 especially by ^? :o endeav\r to introduce sci5tific ord] into less successful & me?odical bran*es ( k4 ,! application ( ,sci5tific ,me?od _c be re/rict$ to ! sph]e ( lifeless objects4 ,we mu/ soon] or lat] h /rict sci5ces ( ^? m5tal & social ph5om5a1 :i*1 if comp>ison be possible1 are ( m int]e/ to u ?an purely mat]ial ph5om5a4 ,b x is ! prop] c\rse ( reason+ to proce$ f ! kn[n to ! unkn[n--f ! evid5t to ! obscure--f ! mat]ial & palpable to ! subtle & ref9$4 ,! physical sci5ces may !re=e be prop]ly made ! practice-gr\nd ( ! reason+ p[]s1 because !y furni% u ) a great body-( precise & successful inve/igations4 ,9 ^! sci5ces we meet ) happy in/ances ( unque/ionable d$uctive reason+1 ( ext5sive g5]alisation1 ( happy pr$iction1 ( satisfactory v]ification1 ( nice calculation ( probabilities4 ,we c note h[ ! slighte/ analogical clue has be5 foll[$ up to a glori\s discov]y1 h[ a ra% g5]alisation has at l5g? be5 expos$1 or a conclusive 99exp]im5tum crucis99 has decid$ ! long-cont9u$ /rife betwe5 two rival !ories4 ,9 foll[+ out my design ( detect+ ! g5]al me?ods ( inductive inve/igation1 ,i h f\nd t ! m elaborate & int]e/+ processes ( quantitative induction h _! necess>y f\ndation 9 ! simpl] sci5ce ( ,=mal ,logic4 ,! e>li]1 & probably by f> ! lea/ attractive "p ( ?is "w1 consi/s1 !re=e1 9 a /atem5t ( ! s-call$ ,fundam5tal ,laws ( ,?\ght1 & ( ! all-important ,pr9ciple ( ,sub/itution1 ( :i*1 z ,i ?9k1 all reason+ is a developm5t4 ,! :ole proc$ure ( inductive inquiry1 9 its mo/ complex cases1 is =e%ad[$ 9 ! comb9ational view ( ,logic1 :i* arises directly f ^! fundam5tal pr9ciples4 ,incid5tally ,i h describ$ ! me*anical arrangem5ts by :i* ! use ( ! important =m call$ ! ,logical ,alphabet1 & ! :ole work+ ( ! comb9ational sy/em ( ,=mal ,logic1 may be r5d]$ evid5t to ! eye1 & easy to ! m9d & h&4 ,! /udy bo? ( ,=mal ,logic & ( ! ,!ory ( ,probabilities has l$ me to adopt ! op9ion t !re is no su* ?+ z a di/9ct me?od ( induction z contra/$ ) d$uction1 b t induction is simply an inv]se employm5t ( d$uction4 ,)9 ! la/ c5tury a reaction has be5 sett+ 9 aga9/ ! purely empirical proc$ure ( ,francis ,bacon1 & physici/s h le>nt to advocate ! use ( hypo!ses4 ,i take ! extreme view ( hold+ t ,francis ,bacon1 al?\gh he correctly insi/$ ^u con/ant ref]5ce to exp]i5ce1 _h no correct notions z to ! logical me?od by :i* f p>ticul> facts we educe laws ( nature4 ,i endeav\r to %[ t hypo!tical anticipation ( nature is an ess5tial "p ( inductive inquiry1 & t x is ! ,newtonian me?od ( d$uctive reason+ comb9$ ) elaborate exp]im5tal v]ification1 :i* has l$ to all ! great triumphs ( sci5tific rese>*4 ,9 attempt+ to give an explanation ( ?is view ( ,sci5tific ,me?od1 ,i h fir/ to %[ t ! sci5ces ( numb] & quantity repose ^u & spr+ f ! simpl] & m g5]al sci5ce ( ,logic4 ,! ,!ory ( ,probability1 :i* enables u to e/imate & calculate quantities ( k1 is !n describ$1 & especial att5tion is drawn to ! ,inv]se ,me?od ( ,probabilities1 :i* involves1 z ,i conceive1 ! true pr9ciple ( inductive proc$ure4 ,no inductive conclusions are m ?an probable1 & ,i adopt ! op9ion t ! !ory ( probability is an ess5tial "p ( logical me?od1 s t ! logical value ( e inductive result mu/ be det]m9$ consci\sly or unconsci\sly1 accord+ to ! pr9ciples ( ! inv]se me?od ( probability4 ,! ph5om5a ( nature are commonly manife/$ 9 quantities ( "t1 space1 =ce1 en]gy1 c41 & ! obs]vation1 measurem5t1 & analysis ( ! v>i\s quantitative conditions or results involv$1 ev5 9 a simple exp]im5t1 dem& mu* employm5t ( sy/ematic proc$ure4 ,i devote a book1 !re=e1 to a simple & g5]al description ( ! devices by :i* exact measurem5t is effect$1 errors elim9at$1 a probable mean result atta9$1 & ! probable error ( t mean asc]ta9$4 ,i !n proce$ to ! pr9cipal1 & probably ! mo/ int]e/+1 subject ( ! book1 illu/rat+ successively ! conditions & precautions requisite = accurate obs]vation1 = successful exp]im5t1 & = ! sure detection ( ! quantitative laws ( nature4 ,z x is impossible to compreh5d aright ! value ( quantitative laws )\t con/antly be>+ 9 m9d ! degree ( quantitative approximation to ! tru? probably atta9$1 ,i h devot$ a special *apt] to ! ,!ory ( ,approximation1 & h[ev] imp]fectly ,i may h treat$ ?is subject1 ,i mu/ look ^u x z a v ess5tial "p ( a "w on ,sci5tific ,me?od4 ,x !n rema9s to illu/rate ! s\nd use ( hypo!sis1 to di/+ui% betwe5 ! portions ( k :i* we owe to empirical obs]vation1 to accid5tal discov]y1 or to sci5tific pr$iction4 ,int]e/+ que/ions arise conc]n+ ! accordance ( quantitative !ories & exp]im5ts1 & ,i po9t out h[ ! successive v]ification ( an hypo!sis by di/9ct me?ods ( exp]im5t yields conclusions approximat+ to b nev] atta9+ c]ta9ty4 ,additional illu/rations ( ! g5]al proc$ure ( inductive inve/igations are giv5 9 a *apt] on ! ,"* ( ! ,exp]im5tali/1 9 :i* ,i endeav\r to %[1 moreov]1 t ! inv]se use ( d$uction 0 really ! logical me?od ( su* great ma/]s ( exp]im5tal inquiry z ,newton1 ,huygh5s1 & ,f>aday4 ,9 treat+ ,g5]alisation & ,analogy1 ,i consid] ! precautions requisite 9 inf]r+ f "o case to ano!r1 or f "o "p ( ! univ]se to ano!r "p2 ! validity ( all su* inf]5ces re/+ ultimately ^u ! inv]se me?od ( probabilities4 ,! treatm5t ( ,exceptional ,ph5om5a appe>$ to af=d an int]e/+ subject = a fur!r *apt] illu/rat+ ! v>i\s modes 9 :i* an out/&+ fact may ev5tually be expla9$4 ,! =mal "p ( ! book closes ) ! subject ( ,classification1 :i* is1 h[ev]1 v inadequately treat$4 ,i h1 9 fact1 almo/ re/rict$ myself to %[+ t all classification is fundam5tally c>ri$ out ^u ! pr9ciples ( ,=mal ,logic & ! ,logical ,alphabet describ$ at ! outset4 ,9 c]ta9 conclud+ rem>ks ,i h express$ ! conviction :i* ! /udy ( ,logic has by degrees =c$ ^u my m9d1 t s]i\s misconceptions are ent]ta9$ by "s sci5tific m5 z to ! logical value ( our k ( nature4 ,we h he>d mu* ( :at has be5 aptly call$ ! ,reign ( ,law1 & ! necessity & uni=mity ( natural =ces has be5 n uncommonly int]pret$ z involv+ ! non-exi/5ce ( an intellig5t & b5evol5t ,p[]1 capable ( int]f]+ ) ! c\rse ( natural ev5ts4 ,fe>s h be5 express$ t ! progress ( ,sci5tific ,me?od mu/ !re=e result 9 dissipat+ ! fonde/ beliefs ( ! human he>t4 ,ev5 ! #8,utility ( ,religion' is s]i\sly propos$ z a subject ( discussion4 ,x seem$ to be n out ( place 9 a "w on ,sci5tific ,me?od to allude to ! ultimate results & limits ( t me?od4 ,i fe> t ,i h v imp]fectly succe$$ 9 express+ my /rong conviction t be=e a rigor\s logical scrut9y ! ,reign ( ,law w prove to be an unv]ifi$ hypo!sis1 ! ,uni=mity ( ,nature an ambigu\s expression1 ! c]ta9ty ( our sci5tific inf]5ces to a great ext5t a delusion4 ,! value ( sci5ce is ( c\rse v high1 :ile ! conclusions are kept well )9 ! limits ( ! data on :i* !y are f\nd$1 b x is po9t$ out t our exp]i5ce is ( ! mo/ limit$ "* comp>$ ) :at !re is to le>n1 :ile our m5tal p[]s seem to fall inf9itely %ort ( ! task ( compreh5d+ & expla9+ fully ! nature ( any "o object4 ,i draw ! conclusion t we mu/ int]pret ! results ( ,sci5tific ,me?od 9 an affirmative s5se only4 ,ours mu/ be a truly positive philosophy1 n t false negative philosophy :i*1 build+ on a few mat]ial facts1 presumes to ass]t t x has compass$ ! b\nds ( exi/5ce1 :ile x nev]!less ignores ! mo/ unque/ionable ph5om5a ( ! human m9d & feel+s4 ,x is approximately c]ta9 t 9 freely employ+ illu/rations drawn f _m diff]5t sci5ces1 ,i h frequ5tly fall5 into errors ( detail4 ,9 ?is respect ,i mu/ ?r[ myself ^u ! indulg5ce ( ! read]1 :o w be> 9 m9d1 z ,i hope1 t ! sci5tific facts are g5]ally m5tion$ purely = ! purpose ( illu/ration1 s t inaccuracies ( detail w n 9 ! majority ( cases affect ! tru? ( ! g5]al pr9ciples illu/rat$4 99,decemb] #ae1 #ahgc499 ,,preface 99,,to ,,! ,,second ,,edition994 ,few alt]ations ( importance h be5 made 9 prep>+ ?is second edition4 ,nev]!less1 advantage has be5 tak5 ( ! opportunity to revise v c>efully bo? ! language & ! matt] ( ! book4 ,correspond5ts & critics hav+ po9t$ out inaccuracies ( m or less importance 9 ! fir/ edition1 suitable corrections & em5dations h be5 made4 ,i am "u obligations to ,mr4 ,c4 ,j4 ,monro1 ,m4,a41 ( ,b>net1 & to ,mr4 ,w4 ,h4 ,brew]1 ,m4,a41 "o ( ,h] ,maje/y's ,inspectors ( ,s*ools1 = num]\s corrections4 ,among sev]al additions :i* h be5 made to ! text1 ,i may m5tion ! ab/ract 7p4 #adc7 ( ,pr(essor ,clif=d's rem>kable inve/igation into ! numb] ( types ( comp\nd /atem5t involv+ f\r classes ( objects4 ,?is inquiry c>ries =w>d ! inv]se logical problem describ$ 9 ! prec$+ sections4 ,aga91 ! ne$ ( "s bett] logical me?od ?an ! old ,b>b>a ,cel>5t1 c41 is /rik+ly %[n by ,mr4 ,v5n's logical problem1 describ$ at p4 #ij4 ,a great numb] ( c&idates 9 logic & philosophy 7 te/$ by ,mr4 ,v5n ) ?is problem1 :i*1 ?\gh simple 9 reality1 0 solv$ by v few ( ^? :o 7 ignorant ( ,boole's ,logic4 ,o!r evid5ce c\ld be adduc$ by ,mr4 ,v5n ( ! ne$ = "s bett] means ( logical tra9+4 ,to enable ! logical /ud5t to te/ 8 skill 9 ! solution ( inductive logical problems1 ,i h giv5 7p4 #abg7 a s]ies ( t5 problems graduat$ 9 difficulty4 ,to prev5t misappreh5sion1 x %\ld be m5tion$ t1 ?r\gh\t ?is edition1 ,i h sub/itut$ ! "n 99,logical ,alphabet99 = 99,logical ,abec$>ium991 ! "n appli$ 9 ! fir/ edition to ! exhau/ive s]ies ( logical comb9ations repres5t$ 9 t]ms ( 99,a991 99,b991 99,c991 99,d99 7p4 #id74 ,x 0 object$ by "s read]s t 99,abec$>ium99 is a long & unfamili> "n4 ,to ! *apt] on ,units & ,/&>ds ( ,measurem5t1 ,i h add$ two sections1 "o 7p4 #cbe7 conta9+ a brief /atem5t ( ! ,!ory ( ,dim5sions1 & ! o!r 7p4 #cai7 discuss+ ,pr(essor ,cl]k ,maxwell's v orig9al sugge/ion ( a ,natural ,sy/em ( ,/&>ds = ! measurem5t ( space & "t1 dep5d+ ^u ! l5g? & rapidity ( waves ( light4 ,9 my description ( ! ,logical ,ma*9e 9 ! 99,philosophical ,transactions99 7vol4 #afj1 p4 #dih71 ,i said--8,x is r>ely inde$ t any inv5tion is made )\t "s anticipation be+ soon] or lat] discov]$2 b up to ! pres5t "t ,i am totally unaw>e ( ev5 a s+le previ\s attempt to devise or con/ruct a ma*9e :i* %\ld p]=m ! op]ations ( logical inf]5ce2 & x is only1 ,i believe1 9 ! satirical writ+s ( ,swift t an allusion to an actual reason+ ma*9e is to be f\nd40 ,be=e ! pap] 0 pr9t$1 h[ev]1 ,i 0 able to ref] 7p4 #eah7 to ! +5i\s designs ( ! late ,mr4 ,alfr$ ,smee z attempts to repres5t ?\ght me*anically4 ,mr4 ,smee's ma*9es inde$ 7 nev] con/ruct$1 &1 if con/ruct$1 w\ld n h p]=m$ actual logical inf]5ce4 ,x has n[ j come to light1 h[ev]1 t ! celebrat$ ,"l ,/anhope actually did con/ruct a me*anical device1 capable ( repres5t+ syllogi/ic inf]5ces 9 a concrete =m4 ,x appe>s t logic 0 "o ( ! fav\rite /udies ( ?is truly orig9al & +5i\s nobleman4 ,!re rema9 fragm5ts ( a logical "w1 pr9t$ by ! ,e>l at 8 own press1 :i* %[ t he _h arriv$1 be=e ! ye> #ahjj1 at ! pr9ciple ( ! quantifi$ pr$icate4 ,he puts =w>d ?is pr9ciple 9 ! mo/ explicit mann]1 & proposes to employ x ?r\gh\t 8 syllogi/ic sy/em4 ,moreov]1 he conv]ts negative propositions into affirmative ones1 & repres5ts ^! by means ( ! copula 8is id5tic )40 ,?us he anticipat$1 probably by ! =ce ( 8 own unaid$ insight1 ! ma9 po9ts ( ! logical me?od orig9at$ 9 ! works ( ,george ,b5?am & ,george ,boole1 & develop$ 9 ?is "w4 ,/anhope1 inde$1 has no claim to priority ( discov]y1 because he seems nev] to h publi%$ 8 logical writ+s1 al?\gh !y 7 put into pr9t4 ,!re is no trace ( !m 9 ! ,briti% ,museum ,libr>y1 nor 9 any o!r libr>y or logical "w1 s f> z ,i am aw>e4 ,bo? ! pap]s & ! logical contrivance h be5 plac$ by ! pres5t ,e>l ,/anhope 9 ! h&s ( ! ,rev4 ,rob]t ,h>ley1 ,f4,r4,s41 :o w1 ,i hope1 soon publi% a description ( !m4#a #a ,s9ce ! above 0 writt5 ,mr4 ,h>ley has read an acc\nt ( ,/anhope's logical rema9s at ! ,dubl9 ,meet+ 7#ahgh7 ( ! ,briti% ,association4 ,! pap] w be pr9t$ 9 99,m9d994 7,note add$ ,novemb]1 #ahgh47 ,by ! k9dness ( ,mr4 ,h>ley1 ,i h be5 able to exam9e ,/anhope's logical contrivance1 call$ by him ! ,demon/rator4 ,x consi/s ( a squ>e piece ( bay-wood ) a squ>e depression 9 ! c5tre1 across :i* two slides c be pu%$1 "o be+ a piece ( r$ glass1 & ! o!r consi/+ ( wood col\r$ gray4 ,! ext5t to :i* ea* ( ^! slides is pu%$ 9 is indicat$ by scales & figures along ! edges ( ! ap]ture1 & ! simple rule ( inf]5ce adopt$ by ,/anhope is3 8,to ! gray add ! r$ & subtract ! 99holon9910 mean+ by holon 77 ! :ole wid? ( ! ap]ture4 ,?is rule ( inf]5ce is a curi\s anticipation ( ,de ,morgan's num]ically def9ite syllogism 7see bel[1 p4 #afh71 & ( inf]5ces f\nd$ on :at ,hamilton call$ 8,ultra-total di/ribution40 ,ano!r curi\s po9t ab\t ,/anhope's device is1 t "o slide c be drawn out & pu%$ 9 aga9 at "r angles to ! o!r1 & ! ov]lapp+ "p ( ! slides !n repres5ts ! probability ( a conclusion1 d]iv$ f two premises ( :i* ! probabilities are respectively repres5t$ by ! project+ p>ts ( ! slides4 ,?us x appe>s t ,/anhope _h /udi$ ! logic ( probability z well z t ( c]ta9ty1 "h aga9 anticipat+1 h[ev] obscurely1 ! rec5t progress ( logical sci5ce4 ,x w be se51 h[ev]1 t betwe5 ,/anhope's ,demon/rator & my ,logical ,ma*9e !re is no resemblance beyond ! fact t !y bo? p]=m logical inf]5ce4 ,9 ! fir/ edition ,i ins]t$ a section 7vol4 i4 p4 #be71 on 8,anticipations ( ! ,pr9ciple ( ,sub/itution10 & ,i h repr9t$ t section un*ang$ 9 ?is edition 7p4 #ba74 ,i rem>k !re9 t1 8,9 su* a subject z logic x is h>dly possible to put =? any op9ions :i* h n be5 9 "s degree previ\sly ent]ta9$4 ,! g]m at lea/ ( e doctr9e w be f\nd 9 e>li] writ+s1 & novelty mu/ arise *iefly 9 ! mode ( h>monis+ & develop+ ideas40 ,i po9t out1 z ,pr(essor ,t4 ,m4 ,l9dsay _h previ\sly done1 t ,b5eke _h employ$ ! "n & pr9ciple ( sub/itution1 & t doctr9es closely approximat+ to sub/itution 7 /at$ by ! ,port ,royal ,logicians m ?an #bjj ye>s ago4 ,i h n be5 at all surpris$ to le>n1 h[ev]1 t o!r logicians h m or less di/9ctly /at$ ?is pr9ciple ( sub/itution dur+ ! la/ two c5turies4 ,z my fri5d & successor at ,ow5s ,college1 ,pr(essor ,adamson1 has discov]$1 ?is pr9ciple c be trac$ back to no less a philosoph] ?an ,leibnitz4 ,! rem>kable tract ( ,leibnitz1#b entitl$ 8,non inelegans ,specim5 ,demon/r&i 9 ,ab/ractis10 comm5ces at once ) a def9ition correspond+ to ! pr9ciple3-- 8,eadem sunt quorum unum pote/ sub/itui alt]i salva v]itate4 ,si s9t 99,a99 et 99,b991 et 99,a99 +r$iatur aliquam propositionem v]am1 et ibi 9 aliquo loco ipsius 99,a99 pro ipso sub/itu5do 99,b99 fiat nova propositio que itidem v]a1 idque semp] succ$at 9 quacunque tali propositione1 99,a99 et 99,b99 dicuntur esse eadem2 et contra1 si eadem s9t 99,a99 et 99,b991 proc$et sub/itutio quam dixi40 #b ,leibnitii 99,op]a ,philosophica qu extant994 ,erdmann1 ,p>s ,i4 ,b]ol9i1 #ahdj1 p4 #id4 ,leibnitz1 !n1 explicitly adopts ! pr9ciple ( sub/itution1 b he puts x 9 ! =m ( a def9ition1 say+ t ^? ?+s are ! same :i* c be sub/itut$ "o = ! o!r1 )\t affect+ ! tru? ( ! proposition4 ,x is only aft] hav+ ?us te/$ ! sam5ess ( ?+s t we c turn r\nd & say t 99,a99 & 99,b991 be+ ! same1 may be sub/itut$ "o = ! o!r4 ,x w\ld seem z if we 7 "h 9 a vici\s circle2 = we are n all[$ to sub/itute 99,a99 = 99,b991 unless we h asc]ta9$ by trial t ! result is a true proposition4 ,! difficulty does n seem to be remov$ by ,leibnitz' proviso1 8idque semp] succ$at 9 quacunque tali propositione40 ,h[ c we le>n t because 99,a99 & 99,b99 may be mutually sub/itut$ 9 "s propositions1 !y may !re=e be sub/itut$ 9 o!rs2 & :at is ! crit]ion ( lik5ess ( propositions express$ 9 ! ^w 8tali08 ,:e!r ! pr9ciple ( sub/itution is to be reg>d$ z a po/ulate1 an axiom1 or a def9ition1 is j "o ( ^? fundam5tal que/ions :i* x seems impossible to settle 9 ! pres5t position ( philosophy1 b ?is unc]ta9ty w n prev5t our mak+ a consid]able /ep 9 logical sci5ce4 ,leibnitz proce$s to e/abli% 9 ! =m ( a !orem :at is usually tak5 z an axiom1 ?us 799,op]a991 p4 #ie73 8,!orema ,i4 ,qu sunt eadem uni t]tio1 eadem sunt int] se4 ,si 99,a99 99,b99 et 99,b99 99,c991 erit 99,a99 99,c994 ,nam si 9 propositione 99,a99 99,b99 7v]a ea hypo!si7 sub/ituitur 99,c99 9 locum 99,b99 7quod fac]e licet p] ,def4 ,i4 quia 99,b99 99,c99 ex hypo!si7 fiet 99,a99 99,c994 ,q4 ,e4 ,dem40 ,?us ,leibnitz precisely anticipates ! mode ( treat+ inf]5ce ) two simple id5tities describ$ at p4 #ea ( ?is "w4 ,ev5 ! ma!matical axiom t #8equals add$ to equals make equals1' is d$uc$ f ! pr9ciple ( sub/itution4 ,at p4 #ie ( ,erdmann's edition1 we f9d3 8,si eidem addantur co9cid5tia fiunt co9cid5tia4 ,si 99,a99 99,b991 erit 99,a99 99,c99 99,b99 99,c994 ,nam si 9 propositione 99,a99 99,c99 99,a99 99,c99 7qu e/ v]a p] se7 pro 99,a99 semel sub/ituas 99,b99 7quod fac]e licet p] ,def4 ,i4 quia 99,a99 99,b997 fiet 99,a99 99,c99 99,b99 99,c99 ,q4 ,e4 ,dem40 ,?is is unque/ionably ! mode ( d$uc+ ! sev]al axioms ( ma!matical reason+ f ! high] axiom ( sub/itution1 :i* is expla9$ 9 ! section on ma!matical inf]5ce 7p4 #afb7 9 ?is "w1 & :i* _h be5 previ\sly /at$ 9 my 99,sub/itution ( ,simil>s991 p4 #af4 ,!re are "o or two o!r brief tracts 9 :i* ,leibnitz anticipates ! mod]n views ( logic4 ,?us 9 ! eighte5? tract 9 ,erdmann's edition 7p4 #ib71 call$ 8,fundam5ta ,calculi ,ratioc9atoris01 he says3 8,int] ea quorum unum alt]i sub/itui pote/1 salvis calculi legibus1 dicetur esse quipoll5tiam40 ,!re is evid5ce1 also1 t he _h arriv$ at ! quantification ( ! pr$icate1 & t he fully und]/ood ! r$uction ( ! univ]sal affirmative proposition to ! =m ( an equation1 :i* is ! key to an improv$ view ( logic4 ,?us1 9 ! tract entitl$ 8,difficultates ,qudam ,logic10#c he says3 8,omne 99,a99 e/ 99,b992 id e/ quival5t 99,,ab99 et 99,a991 seu 99,a99 non 99,b99 e/ non-ens40 #c ,erdmann1 p4 #ajb4 ,x is curi\s to f9d1 too1 t ,leibnitz 0 fully acqua9t$ ) ! ,laws ( ,commutativ5ess & 8,simplicity0 7z ,i h call$ ! second law7 atta*+ to logical symbols4 ,9 ! 8,add5da ad ,specim5 ,calculi ,univ]salis0 we read z foll[s4#d 8,transpositio lit]>um 9 eodem t]m9o nihil mutat1 ut 99ab99 co9cidet cum 99ba991 seu animal rationale et rationale animal40 8,repetitio ejusdem lit] 9 eodem t]m9o e/ inutilis1 ut 99b99 e/ 99aa992 vel 99bb99 e/ 99a992 homo e/ animal animal1 vel homo homo e/ animal4 ,sufficit enim dici 99a99 e/ 99b991 seu homo e/ animal40 #d ,ibid4 p4 #ih4 ,comp>+ ?is ) :at is /at$ 9 ,boole's 99,ma!matical ,analysis ( ,logic991 pp4 #ag-ah1 9 8 99,laws ( ,?\ght991 p4 #bi1 or 9 ?is "w1 pp4 #cb-ce1 we f9d t ,leibnitz _h arriv$ two c5turies ago at a cle> p]ception ( ! bases ( logical notation4 ,:5 ,boole po9t$ out t1 9 logic1 99xx99 99x991 ?is seem$ to ma!maticians to be a p>adox1 or 9 any case a :olly new discov]y2 b "h we h x pla9ly /at$ by ,leibnitz4 ,! read] mu/ n assume1 h[ev]1 t because ,leibnitz correctly appreh5d$ ! fundam5tal pr9ciples ( logic1 he left no?+ = mod]n logicians to d4 ,on ! contr>y1 ,leibnitz obta9$ no useful results f 8 def9ition ( sub/itution4 ,:5 he proce$s to expla9 ! syllogism1 z 9 ! pap] on 8,def9itiones ,logic10#e he gives up sub/itution altoge!r1 & falls back ^u ! notion ( inclusion ( class 9 class1 say+1 8,includ5s includ5tis e/ includ5s inclusi1 seu si 99,a99 includit 99,b99 et 99,b99 includit 99,c991 etiam 99,a99 includet 99,c9940 ,he proce$s to make out c]ta9 rules ( ! syllogism involv+ ! di/9ction ( subject & pr$icate1 & 9 no important respect bett] ?an ! old rules ( ! syllogism4 ,leibnitz' logical tracts are1 9 fact1 little m ?an brief memor&a ( inve/igations :i* seem nev] to h be5 foll[$ out4 ,!y rema9 z evid5ce ( 8 wond]ful sagacity1 b x w\ld be difficult to %[ t !y h _h any influ5ce on ! progress ( logical sci5ce 9 rec5t times4 #e ,erdmann1 p4 #ajj4 ,i %\ld l to expla9 h[ x happ5$ t ^! logical writ+s ( ,leibnitz 7 unkn[n to me1 until )9 ! la/ twelve mon?s4 ,i am s sl[ a read] ( ,lat9 books1 inde$1 t my ov]look+ a few pages ( ,leibnitz' works w\ld n h be5 9 any case surpris+4 ,b ! fact is t ! copy ( ,leibnitz' works ( :i* ,i made occasional use1 0 "o ( ! edition ( ,dut5s1 conta9$ 9 ,ow5s ,college ,libr>y4 ,! logical tracts 9 "q 7 n pr9t$ 9 t edition1 & ) "o exception1 !y rema9$ 9 manuscript 9 ! ,royal ,libr>y at ,hanov]1 until edit$ by ,erdmann1 9 #ahci-dj4 ,! tract 8,difficultates ,qudam ,logic10 ?\gh n kn[n to ,dut5s1 0 publi%$ by ,raspe 9 #agfe1 9 8 collection call$ 99uvres ,philosophiques de feu ,mr4 ,leibnitz992 b ?is "w _h n come to my notice1 nor does ! tract 9 "q seem to conta9 any explicit /atem5t ( ! pr9ciple ( sub/itution4 ,x is1 ,i presume1 ! comp>atively rec5t publication ( ,leibnitz' mo/ rem>kable logical tracts :i* expla9s ! app>5t ignorance ( logicians z reg>ds _! cont5ts & importance4 ,! mo/ le>n$ logicians1 su* z ,hamilton & ,ueb]weg1 ignore ,leibnitz' pr9ciple ( sub/itution4 ,9 ! ,app5dix to ! f\r? volume ( ,hamilton's 99,lectures on ,metaphysics & ,logic991 is giv5 an elaborate comp5dium ( ! views ( logical writ]s conc]n+ ! ultimate basis ( d$uctive reason+4 ,leibnitz is briefly notic$ on p4 #cai1 b )\t any h9t ( sub/itution4 ,he is "h quot$ z say+1 8,:at are ! same ) ! same ?ird1 are ! same ) ea* o!r2 t is1 if 99,a99 be ! same ) 99,b991 & 99,c99 be ! same ) 99,b991 x is necess>y t 99,a99 & 99,c99 %\ld also be ! same ) "o ano!r4 ,= ?is pr9ciple fl[s imm$iately f ! pr9ciple ( contradiction1 & is ! gr\nd & basis ( all logic2 if t fail1 !re is no long] any way ( reason+ ) c]ta9ty40 ,?is view ( ! matt] seems to be inconsi/5t ) t :i* he adopt$ 9 8 po/hum\s tract4 ,dr4 ,?omson1 inde$1 0 acqua9t$ ) ,leibnitz' tracts1 & ref]s to !m 9 8 99,outl9e ( ! ,necess>y ,laws ( ,?\ght994 ,he calls !m valuable2 nev]!less1 he seems to h miss$ ! really valuable po9t2 = 9 mak+ two brief quotations1#f he omits all m5tion ( ! pr9ciple ( sub/itution4 #f ,fif? ,edition1 #ahfj1 p4 #aeh4 ,ueb]weg is probably consid]$ ! be/ au?ority conc]n+ ! hi/ory ( logic1 & 9 8 well-kn[n 99,sy/em ( ,logic & ,hi/ory ( ,logical ,doctr9es991#g he gives "s acc\nt ( ! pr9ciple ( sub/itution1 especially z x is implicitly /at$ 9 ! 99,port ,royal ,logic994 ,b he omits all ref]5ce to ,leibnitz 9 ?is connection1 nor does he else:]e1 s f> z ,i c f9d1 supply ! omission4 ,8 ,engli% editor1 ,pr(essor ,t4 ,m4 ,l9dsay1 9 ref]r+ to my 99,sub/itution ( ,simil>s991 po9ts out h[ ,i 0 anticipat$ by ,b5eke2 b he also ignores ,leibnitz4 ,x is ?us app>5t t ! mo/ le>n$ logicians1 ev5 :5 writ+ especially on ! hi/ory ( logic1 display$ ignorance ( ,leibnitz' mo/ valuable logical writ+s4 #g ,section #abj4 ,x has be5 rec5tly po9t$ out to me1 h[ev]1 t ! ,rev4 ,rob]t ,h>ley did draw att5tion1 at ! ,nott+ham ,meet+ ( ! ,briti% ,association1 9 #ahff1 to ,leibnitz' anticipations ( ,boole's laws ( logical notation1#h & ,i am in=m$ t ,boole1 ab\t a ye> aft] ! publication ( 8 99,laws ( ,?\ght991 0 made acqua9t$ ) ^! anticipations by ,r4 ,leslie ,ellis4 #h ,see 8 8,rem>ks on ,boole's ,ma!matical ,analysis ( ,logic40 99,report ( ! #cf? ,meet+ ( ! ,briti% ,association1 ,transactions ( ! ,sections991 pp4 #c-f4 ,!re seems to h be5 at lea/ "o o!r ,g]man logician :o discov]$1 or adopt$1 ! pr9ciple ( sub/itution4 ,reus*1 9 8 99,sy/ema ,logicum991 publi%$ 9 #agcd1 lab\r$ to give a broad] basis to ! 99,dictum de ,omni et ,nullo994 ,he argues1 t 8! :ole bus9ess ( ord9>y reason+ is accompli%$ by ! sub/itution ( ideas 9 place ( ! subject or pr$icate ( ! fundam5tal proposition4 ,?is "s call ! 99equation ( ?\ghts9940 ,b1 9 ! h&s ( ,reus*1 sub/itution does n seem to lead to simplicity1 s9ce x has to be c>ri$ on accord+ to ! rules ( ,equipoll5ce1 ,reciprocation1 ,subord9ation1 & ,co-ord9ation4#i ,reus* is else:]e spok5 (#aj z ! 8celebrat$ ,reus*02 nev]!less1 ,i h n be5 able to f9d a copy ( 8 book 9 ,london1 ev5 9 ! ,briti% ,museum ,libr>y2 x is n m5tion$ 9 ! pr9t$ catalogue ( ! ,bodleian ,libr>y2 ,messrs4 ,a%] h fail$ to obta9 x = me by adv]tisem5t 9 ,g]many2 & ,pr(essor ,adamson has be5 equally unsuccessful4 ,f ! way 9 :i* ! pr9ciple ( sub/itution is m5tion$ by ,reus*1 x w\ld seem likely t o!r logicians ( ! e>ly "p ( ! eighte5? c5tury 7 acqua9t$ ) x2 b1 if s1 x is /ill m curi\s t rec5t hi/orians ( logical sci5ce h ov]look$ ! doctr9e4 #i ,hamilton's ,lectures1 vol4 iv4 p4 #cai4 #aj ,ibid4 p4 #cbf4 ,x is a /range & disc\rag+ fact1 t true views ( logic %\ld h be5 discov]$ & discuss$ f "o to two c5turies ago1 & yet %\ld h rema9$1 l ,george ,b5?am's "w 9 ?is c5tury1 )\t influ5ce on ! subsequ5t progress ( ! sci5ce4 ,x may be reg>d$ z c]ta9 t none ( ! discov]]s ( ! quantification ( ! pr$icate1 ,b5?am1 ,hamilton1 ,?omson1 ,de ,morgan1 & ,boole1 7 9 any way assi/$ by ! h9ts ( ! pr9ciple conta9$ 9 previ\s writ]s4 ,z to my own views ( logic1 !y 7 orig9ally m\ld$ by a c>eful /udy ( ,boole's works1 z fully /at$ 9 my fir/ logical essay4#aa ,z to ! process ( sub/itution1 x 0 n le>nt f any "w on logic1 b is simply ! process ( sub/itution p]fectly famili> to ma!maticians1 & ) :i* ,i necess>ily became famili> 9 ! c\rse ( my long-cont9u$ /udy ( ma!matics "u ! late ,pr(essor ,de ,morgan4 #aa 99,pure ,logic1 or ! ,logic ( ,quality ap>t f ,quantity2 ) ,rem>ks on ,boole's ,sy/em1 & on ! ,relation ( ,logic & ,ma!matics499 ,london1 #ahfd1 p4 #c4 ,i f9d t ! ,!ory ( ,numb]1 :i* ,i expla9$ 9 ! eigh? *apt] ( ?is "w1 is also p>tially anticipat$ 9 a s+le s*olium ( ,leibnitz4 ,he fir/ gives z an axiom ! n[ well-kn[n law ( ,boole1 z foll[s3-- 8,axioma ,i4 ,si idem secum ipso sumatur1 nihil con/ituitur novum1 seu 99,a99 99,a99 99,a9940 ,!n foll[s ?is rem>kable s*olium3 8,equidem 9 num]is #d #d facit #h1 seu b9i nummi b9is additi faciunt quatuor nummos1 s$ tunc b9i additi sunt alii a prioribus2 si iidem ess5t nihil novi prodiret et p]9de esset ac si joco ex tribus ovis fac]e vellemus sex num]&o1 primum #c ova1 de9de uno sublato residua #b1 ac d5ique uno rursus sublato residuum40 ,translat$ ?is w\ld read z foll[s3-- 8,axiom ,i4 ,if ! same ?+ is tak5 toge!r ) itself1 no?+ new arises1 or 99,a99 99,a99 99,a994 8,s*olium4 ,9 numb]s1 inde$1 #d #d makes #h1 or two co9s add$ to two co9s make f\r co9s1 b !n ! two add$ are diff]5t f ! =m] ones2 if !y 7 ! same no?+ new w\ld be produc$1 & x w\ld be j z if we tri$ 9 joke to make six eggs out ( ?ree1 by c\nt+ fir/ly ! ?ree eggs1 !n1 "o be+ remov$1 c\nt+ ! rema9+ two1 & la/ly1 "o be+ aga9 remov$1 c\nt+ ! rema9+ egg40 ,comp>e ! above ) pp4 #aef to #afb ( ! pres5t "w4 ,m4 ,littr has q rec5tly po9t$ out#ab :at he ?9ks is an analogy betwe5 ! sy/em ( =mal logic1 /at$ 9 ! foll[+ pages1 & ! logical devices ( ! celebrat$ ,raymond ,lully4 ,lully's me?od ( inv5tion 0 describ$ 9 a great numb] ( m$ival books1 b is be/ /at$ 9 8 99,ars ,comp5diosa ,inv5i5di ,v]itatem1 seu ,ars ,magna et ,major994 ,?is me?od consi/$ 9 plac+ v>i\s names ( ?+s 9 ! sectors ( conc5tric circles1 s t :5 ! circles 7 turn$1 e possible comb9ation ( ! ?+s 0 easily produc$ by me*anical means4 ,x might1 p]haps1 be possible to discov] 9 ?is me?od a vague & rude anticipation ( comb9ational logic2 b x is well kn[n t ! results ( ,lully's me?od 7 usually ( a fanciful1 if n absurd "*4 #ab 99,la ,philosophie ,positive991 ,mai-,ju91 #ahgg1 tom4 xviii4 p4 #def4 ,a mu* clos] analogue ( ! ,logical ,alphabet is probably to be f\nd 9 ! ,logical ,squ>e1 inv5t$ by ,john ,*ri/ian ,lange1 & describ$ 9 a r>e & unnotic$ "w by him :i* ,i h rec5tly f\nd 9 ! ,briti% ,museum4#ac ,?is squ>e involv$ ! pr9ciple ( bifurcate classification1 & 0 an improv$ =m ( ! ,ramean & ,porphyrian tree 7see bel[1 p4 #gjb74 ,lange seems1 inde$1 to h work$ out 8 ,logical ,squ>e into a me*anical =m1 & he sugge/s t x might be employ$ some:at 9 ! mann] ( ,napi]'s ,bones 7p4 #fe74 ,!re is mu* analogy betwe5 8 ,squ>e & my ,abacus1 b ,lange _h n arriv$ at a logical sy/em enabl+ him to use 8 inv5tion = logical inf]5ce 9 ! mann] ( ! ,logical ,abacus4 ,ano!r "w ( ,lange is said to conta9 ! fir/ publication ( ! well kn[n ,eul]ian diagrams ( proposition & syllogism4#ad #ac 99,inv5tum ,novum ,quadrati ,logici991 c41 ,giss ,hassorum1 #agad1 #hvo4 #ad ,see 99,ueb]weg's ,sy/em ( ,logic991 c41 translat$ by ,l9dsay1 p4 #cjb4 ,s9ce ! fir/ edition 0 publi%$1 an important "w by ,mr4 ,george ,lewes has appe>$1 namely1 8 99,problems ( ,life & ,m9d991 :i* to a great ext5t treats ( sci5tific me?od1 & =mulates ! rules ( philosophis+4 ,i %\ld h lik$ to discuss ! be>+ ( ,mr4 ,lewes's views ^u ^? "h prop\nd$1 b ,i h felt x to be impossible 9 a book already fill+ ne>ly #hjj pages1 to ent] ^u ! discussion ( a yet m ext5sive book4 ,= ! same reason ,i h n be5 able to comp>e my own treatm5t ( ! subject ( probability ) ! views express$ by ,mr4 ,v5n 9 8 99,logic ( ,*ance994 ,) ,mr4 ,j4 ,j4 ,murphy's pr(\nd & rem>kable works on 99,habit & ,intellig5ce991 & on 99,! ,sci5tific ,basis ( ,fai?991 ,i 0 un=tunately unacqua9t$ :5 ,i wrote ! foll[+ pages4 ,!y _c safely be ov]look$ by any "o :o wi%es to compreh5d ! t5d5cy ( philosophy & sci5tific me?od 9 ! pres5t day4 ,x seems desirable t ,i %\ld endeav\r to answ] "s ( ! critics :o h po9t$ out :at !y consid] defects 9 ! doctr9es ( ?is book1 especially 9 ! fir/ "p1 :i* treats ( d$uction4 ,"s ( ! notices ( ! "w 7 inde$ r /atem5ts ( its cont5ts ?an critiques4 ,?us1 ,i am mu* indebt$ to ,m4 ,l\is ,li>d1 ,pr(essor ( ,philosophy at ,bordeaux1 = ! v c>eful exposition#ae ( ! sub/itutional view ( logic :i* he gave 9 ! excell5t 99,revue ,philosophique991 edit$ by ,m4 ,ribot4 7,m>s1 #ahgg1 tom4 iii4 p4 #bgg47 ,an equally c>eful acc\nt ( ! sy/em 0 giv5 by ,m4 ,riehl1 ,pr(essor ( ,philosophy at ,graz1 9 8 article on 8,die ,englis*e ,logik d] ,geg5w>t10 publi%$ 9 ! 99,vi]teljahrss*rift fr wiss5s*aftli*e ,philosophie994 7#a ,heft1 ,leipzig1 #ahgf47 ,i %\ld l to ackn[l$ge also ! c>eful & able mann] 9 :i* my book 0 review$ by ! 99,new ,york ,daily ,tribune99 & ! 99,new ,york ,times994 #ae ,s9ce ! above 0 writt5 ,m4 ,li>d has republi%$ ?is exposition z "o *apt] ( an int]e/+ & admirably lucid acc\nt ( ! progress ( logical sci5ce 9 ,engl&4 ,aft] a brief b cle> introduction1 treat+ ( ! views ( ,h]s*el1 ,mill1 & o!rs conc]n+ ,inductive ,logic1 ,m4 ,li>d describes 9 succession ! logical sy/ems ( ,george ,b5?am1 ,hamilton1 ,de ,morgan1 ,boole1 & t conta9$ 9 ! pres5t "w4 ,! title ( ! book is z foll[s3--99,les ,logici5s ,anglais ,contempora9s994 ,p> ,l\is ,li>d1 ,pr(esseur de ,philosophie la ,facult des ,lettres de ,bordeaux4 ,p>is3 ,librairie ,g]m] ,baillire4 #ahgh4 7,note add$ ,novemb]1 #ahgh47 ,! mo/ s]i\s objections :i* h be5 br\ght aga9/ my treatm5t ( logic h reg>d to my failure to ent] into an analysis ( ! ultimate nature & orig9 ( ! ,laws ( ,?\ght4 ,! 99,spectator991#af = in/ance1 9 ! c\rse ( a c>eful review1 says ( ! pr9ciple ( sub/itution1 8,surely x is a great omission n to discuss :5ce we get ?is great pr9ciple itself2 :e!r x is a pure law ( ! m9d1 or only an approximate lesson ( exp]i5ce2 & if a pure product ( ! m9d1 :e!r !re are any o!r products ( ! same k9d1 furni%$ by our kn[+ faculty itself40 ,pr(essor ,rob]tson1 9 8 v acute review1#ag likewise objects to ! want ( psy*ological & philosophical analysis4 8,if ! book really correspond$ to its title1 ,mr4 ,jevons c\ld h>dly h pass$ s lightly ov] ! "q1 :i* he does n omit to raise1 conc]n+ ^? und\bt$ pr9ciples ( k commonly call$ ! ,laws ( ,?\ght4444 ,ev]y:]e1 inde$1 he appe>s lea/ at ease :5 he t\*es on que/ions prop]ly philosophical2 nor is he satisfactory 9 8 psy*ological ref]5ces1 z on pp4 #d1 #e1 :]e he _c commit himself to a /atem5t )\t an accompanim5t ( #8probably1' #8almo/1' or #8h>dly4' ,res]vations are (t5 v mu* 9 place1 b !re are fundam5tal que/ions on :i* x is prop] to make up "o's m9d40 #af 99,spectator991 ,septemb] #ai1 #ahgd1 p4 #aagh4 ,a second portion ( ! review appe>$ 9 ! same j\rnal = ,septemb] #bf1 #ahgd1 p4 #abjd4 #ag 99,m9d993 a ,qu>t]ly ,review ( ,psy*ology & ,philosophy4 ,no4 ,,ii4 ,april #ahgf4 ,vol4 ,i4 p4 #bjf4 ,^! rem>ks appe> to me to be well f\nd$1 & ,i mu/ /ate :y x is t ,i h v5tur$ to publi% an ext5sive "w on logic1 )\t prop]ly mak+ up my m9d z to ! fundam5tal nature ( ! reason+ process4 ,! fault aft] all is "o ( omission r ?an ( commission4 ,x is op5 to me on a future occasion to supply ! defici5cy if ,i %\ld ev] feel able to und]take ! task4 ,b ,i d n conceive x to be an ess5tial "p ( any treatise to ent] into an ultimate analysis ( its subject matt]4 ,analyses mu/ always end some:]e4 ,!re 7 good treatises on light :i* describ$ ! laws ( ! ph5om5on correctly be=e x 0 kn[n :e!r light consi/$ ( undulations or ( project$ p>ticles4 ,n[ we h treatises on ! ,undulatory ,!ory :i* are v valuable & satisfactory1 al?\gh !y leave u 9 almo/ complete d\bt z to :at ! vibrat+ m$ium really is4 ,s ,i ?9k t1 9 ! pres5t day1 we ne$ a correct & sci5tific exhibition ( ! =mal laws ( ?\ght1 & ( ! =ms ( reason+ bas$ on !m1 al?\gh we may n be able to ent] into any complete analysis ( ! nature ( ^? laws4 ,:at w\ld ! sci5ce ( geometry be l n[ if ! ,greek geomet]s _h decid$ t x 0 improp] to publi% any propositions be=e !y _h decid$ on ! nature ( an axiom8 ,:]e w\ld ! sci5ce ( ari?metic be n[ if an analysis ( ! nature ( numb] itself 7 a necess>y prelim9>y to a developm5t ( ! results ( its laws8 ,9 rec5t times !re h be5 enorm\s additions to ! ma!matical sci5ces1 b v few attempts at psy*ological analysis4 ,9 ! ,alex&rian & e>ly m$ival s*ools ( philosophy1 mu* att5tion 0 giv5 to ! nature ( unity & plurality *iefly call$ =? by ! "q ( ! ,tr9ity4 ,9 ! la/ two c5turies :ole sci5ces h be5 creat$ out ( ! notion ( plurality1 & yet speculation on ! nature ( plurality has dw9dl$ away4 ,?is pres5t treatise conta9s1 9 ! eigh? *apt]1 "o ( ! few rec5t attempts to analyse ! notion ( numb] itself4 ,if fur!r illu/ration is ne$$1 ,i may ref] to ! diff]5tial calculus4 ,nobody calls 9 "q ! =mal tru? ( ! results ( t calculus4 ,all ! m exact & successful p>ts ( physical sci5ce dep5d ^u its use1 & yet ! ma!maticians :o h creat$ s great a body ( exact tru?s h nev] decid$ ^u ! basis ( ! calculus4 ,:at is ! nature ( a limit or ! nature ( an inf9itesimal8 ,/>t ! "q among a knot ( ma!maticians1 & x w be f\nd t h>dly two agree1 unless x is 9 reg>d+ ! "q itself z a trifl+ "o4 ,"s hold t !re are no su* ?+s z inf9itesimals1 & t x is all a "q ( limits4 ,o!rs w\ld argue t ! inf9itesimal is ! necess>y outcome ( ! limit1 b v>i\s %ades ( int]m$iate op9ion spr+ up4 ,n[ x is j ! same ) logic4 ,if ! =ms ( d$uctive & inductive reason+ giv5 9 ! e>li] "p ( ?is treatise are correct1 !y con/itute a def9ite addition to logical sci5ce1 & x w\ld h be5 absurd to decl9e to publi% su* results because ,i c\ld n at ! same "t decide 9 my own m9d ab\t ! psy*ology & philosophy ( ! subject4 ,x comes 9 %ort to ?is1 t my book is a book on ,=mal ,logic & ,sci5tific ,me?od1 & n a book on psy*ology & philosophy4 ,x may be object$1 inde$1 z ! 99,spectator99 objects1 t ,mill's ,sy/em ( ,logic is p>ticul>ly /rong 9 ! discussion ( ! psy*ological f\ndations ( reason+1 s t ,mill w\ld appe> to h successfully treat$ t :i* ,i feel myself to be incapable ( attempt+ at pres5t4 ,if ,mill's analysis ( k is correct1 !n ,i h no?+ to say 9 excuse = my own defici5cies4 ,b x is well to d "o ?+ at a "t1 & !re=e ,i h n occupi$ any consid]able "p ( ?is book ) controv]sy & refutation4 ,:at ,i h to say ( ,mill's logic w be said 9 a sep>ate "w1 9 :i* 8 analysis ( k w be some:at m9utely analys$4 ,x w !n be %[n1 ,i believe1 t ,mill's psy*ological & philosophical treatm5t ( logic has n yield$ su* satisfactory results z "s writ]s seem to believe4#ah #ah ,portions ( ?is "w h already be5 publi%$ 9 my articles1 entitl$ 8,john ,/u>t ,mill's ,philosophy ,te/$10 pr9t$ 9 ! 99,contempor>y ,review99 = ,decemb]1 #ahgg1 vol4 xxxi4 p4 #afg1 & = ,janu>y & ,april1 #ahgh1 vol4 xxxi4 p4 #bef1 & vol4 xxxii4 p4 #hh4 7,note add$ 9 ,novemb]1 #ahgh47 ,v>i\s m9or b /ill important criticisms 7 made by ,pr(essor ,rob]tson1 a few ( :i* h be5 notic$ 9 ! text 7pp4 #bg1 #aja74 ,9 o!r cases 8 objections h>dly admit ( any o!r answ] ?an su* z consi/s 9 ask+ ! read] to judge betwe5 ! "w & ! criticism4 ,?us ,mr4 ,rob]tson ass]ts#ai t ! mo/ complex logical problems solv$ 9 ?is book 7up to p4 #ajb ( ?is edition7 might be m easily & %ortly dealt ) ^u ! pr9ciples & ) ! recognis$ me?ods ( ! traditional logic4 ,! burd5 ( pro( "h lies ^u ,mr4 ,rob]tson1 & 8 only pro( consi/s 9 a s+le case1 :]e he is able1 z x seems to me accid5tally1 to get a special conclusion by ! old =m ( dilemma4 ,x w\ld be a long lab\r to te/ ! old logic ^u e result obta9$ by my notation1 & ,i mu/ leave su* read]s z are well acqua9t$ ) ! syllogi/ic logic to pron\nce ^u ! comp>ative simplicity & p[] ( ! new & old sy/ems4 ,= o!r acute objections br\ght =w>d by ,mr4 ,rob]tson1 ,i mu/ ref] ! read] to ! article 9 "q4 #ai 99,m9d991 vol4 i4 p4 #bbb4 ,"o po9t 9 my la/ *apt]1 t on ! ,results & ,limits ( ,sci5tific ,me?od1 has be5 criticis$ by ,pr(essor ,w4 ,k4 ,clif=d 9 8 lecture#bj on 8,! ,fir/ & ! ,la/ ,cata/rophe40 ,9 vol4 ii4 p4 #dch ( ! fir/ edition 7p4 #gdd ( ?is edition7 ,i ref]r$ to c]ta9 inf]5ces drawn by em95t physici/s z to a limit to ! antiquity ( ! pres5t ord] ( ?+s4 8,accord+ to ,sir ,w4 ,?omson's d$uctions f ,f\ri]'s 99!ory ( heat991 we c trace d[n ! dissipation ( heat by conduction & radiation to an inf9itely di/ant "t :5 all ?+s w be uni=mly cold4 ,b we _c simil>ly trace ! ,heat-hi/ory ( ! ,univ]se to an inf9ite di/ance 9 ! pa/4 ,= a c]ta9 negative value ( ! "t1 ! =mul give impossible values1 indicat+ t !re 0 "s initial di/ribution ( heat :i* c\ld n h result$1 accord+ to kn[n laws ( nature1 f any previ\s di/ribution40 #bj 99,=tnightly ,review991 ,new ,s]ies1 ,april #ahge1 p4 #dhj4 ,lecture repr9t$ by ! ,sunday ,lecture ,society1 p4 #bd4 ,n[ accord+ to ,pr(essor ,clif=d ,i h "h mis/at$ ,?omson's results4 8,x is n accord+ to ! kn[n laws ( nature1 x is accord+ to ! kn[n laws ( conduction ( heat1 t ,sir ,william ,?omson is speak+4444 ,all ^! physical writ]s1 kn[+ :at !y 7 writ+ ab\t1 simply drew su* conclusions f ! facts :i* 7 be=e !m z c\ld be reasonably drawn4 ,!y say1 "h is a /ate ( ?+s :i* c\ld n h be5 produc$ by ! circum/ances we are at pres5t inve/igat+4 ,!n y\r speculator comes1 he reads a s5t5ce & says1 #8,"h is an opportunity = me to h my fl+4' ,& he has 8 fl+1 & makes a purely baseless !ory ab\t ! necess>y orig9 ( ! pres5t ord] ( nature at "s def9ite po9t ( "t1 :i* might be calculat$40 ,pr(essor ,clif=d proce$s to expla9 t ,?omson's =mul only give a limit to ! heat hi/ory (1 say1 ! e>?'s cru/ 9 ! solid /ate4 ,we are l$ back to ! "t :5 x became solidifi$ f ! fluid condition4 ,!re is discont9uity 9 ! hi/ory ( ! solid matt]1 b /ill discont9uity :i* is )9 our compreh5sion4 ,/ill fur!r back we %\ld come to discont9uity aga91 :5 ! liquid 0 =m$ by ! cond5sation ( heat$ gase\s matt]4 ,beyond t ev5t1 h[ev]1 !re is no ne$ to suppose fur!r discont9uity ( law1 = ! gase\s matt] might consi/ ( molecules :i* _h be5 fall+ toge!r f diff]5t p>ts ( space ?r\gh inf9ite pa/ "t4 ,z ,pr(essor ,clif=d says 7p4 #dha7 ( ! bodies ( ! univ]se1 8,:at !y h actually done is to fall toge!r & get solid4 ,if we %\ld rev]se ! process we %\ld see !m sep>at+ & gett+ cool1 & z a limit to t1 we %\ld f9d t all ^! bodies w\ld be resolv$ into molecules1 & all ^! w\ld be fly+ away f ea* o!r4 ,!re w\ld be no limit to t process1 & we c\ld trace x z f> back z ev] we lik$ to trace x40 ,assum+ t ,i h err$1 ,i %\ld l to po9t out t ,i h err$ 9 ! be/ company1 or m /rictly1 be+ a speculator1 ,i h be5 l$ into error by ! be/ physical writ]s4 ,pr(essor ,tait1 9 8 99,sket* ( ,!rmodynamics991 speak+ ( ! laws discov]$ by ,f\ri] = ! motion ( heat 9 a solid1 says1 8,_! ma!matical expressions po9t also to ! fact t a uni=m di/ribution ( heat1 or a di/ribution t5d+ to become uni=m1 mu/ h aris5 f "s primitive di/ribution ( heat ( a k9d n capable ( be+ produc$ by kn[n laws f any previ\s di/ribution40 ,9 ! latt] words x w be se5 t !re is no limitation to ! laws ( conduction1 &1 al?\gh ,i _h c>efully ref]r$ to ,sir ,w4 ,?omson's orig9al pap]1 x is n unnatural t ,i %\ld take ,pr(essor ,tait's int]pretation ( its mean+4#ba #ba ,sir ,w4 ,?omson's words are z foll[s 799,cambridge ,ma!matical ,j\rnal991 ,nov4 #ahdb1 vol4 iii4 p4 #agd74 8,:5 99x99 is negative1 ! /ate repres5t$ _c be ! result ( any 99possible99 di/ribution ( temp]ature :i* has previ\sly exi/$40 ,!re is no limitation 9 ! s5t5ce to ! laws ( conduction1 b1 z ! :ole pap] treats ( ! results ( conduction 9 a solid1 x may no d\bt be und]/ood t !re is a 99tacit99 limitation4 ,see also a second pap] on ! subject 9 ! same j\rnal = ,febru>y1 #ahdd1 vol4 iv4 p4 #fg1 :]e aga9 !re is no express$ limitation4 ,9 8 new "w 99,on "s ,rec5t ,advances 9 ,physical ,sci5ce991 ,pr(essor ,tait has recurr$ to ! subject z foll[s3#bb 8,a pr(\nd lesson may be le>n$ f "o ( ! e>lie/ little pap]s ( ,sir ,w4 ,?omson1 publi%$ :ile he 0 an und]graduate at ,cambridge1 :]e he %[s t ,f\ri]'s magnific5t treatm5t ( ! conduction ( heat 9 a solid body leads to =mul = its di/ribution :i* are intelligible 7& ( c\rse capable ( be+ fully v]ifi$ by exp]im5t7 = all "t future1 b :i*1 except 9 p>ticul> cases1 :5 ext5d$ to "t pa/1 rema9 intelligible = a f9ite p]iod only1 & 99!n99 indicate a /ate ( ?+s :i* c\ld n h result$ "u kn[n laws f any conceivable previ\s di/ribution ( heat 9 ! body4 ,s f> z heat is conc]n$1 mod]n inve/igations h %[n t a previ\s di/ribution ( ! 99matt]99 involv$ may1 by its pot5tial en]gy1 be capable ( produc+ su* a /ate ( ?+s at ! mom5t ( its aggregation2 b ! example is n[ adduc$ n = its be>+ on heat alone1 b z a simple illu/ration ( ! fact t all portions ( our ,sci5ce1 especially t beautiful "o1 ! ,dissipation ( ,en]gy1 po9t unanim\sly to a beg9n+1 to a /ate ( ?+s incapable ( be+ d]iv$ by pres5t laws ( tangible matt] & its en]gy f any conceivable previ\s arrangem5t40 ,z ?is 0 publi%$ ne>ly a ye> aft] ,pr(essor ,clif=d's lecture1 x may be inf]r$ t ,pr(essor ,tait adh]es to 8 orig9al op9ion t ! !ory ( heat does give evid5ce ( 8a beg9n+40 #bb ,pp4 #be-bf4 ,! p>5!ses are 9 ! orig9al1 & %[ ,pr(essor ,tait's corrections 9 ! v]batim reports ( 8 lectures4 ,! subject is treat$ aga9 on pp4 #afh-i4 ,i may add t ,pr(essor ,cl]k ,maxwell's words seem to c\nt5ance ! same view1 = he says1#bc 8,?is is only "o ( ! cases 9 :i* a consid]ation ( ! dissipation ( en]gy leads to ! det]m9ation ( a sup]ior limit to ! antiquity ( ! obs]v$ ord] ( ?+s40 ,! expression 8obs]v$ ord] ( ?+s0 is op5 to mu* ambiguity1 b 9 ! abs5ce ( qualification ,i %\ld take x to include ! aggregate ( ! laws ( nature kn[n to u4 ,i %\ld int]pret ,pr(essor ,maxwell z mean+ t ! !ory ( heat indicates ! occurr5ce ( "s ev5t ( :i* our sci5ce _c give any fur!r explanation4 ,! physical writ]s ?us seem n to be s cle> ab\t ! matt] z ,pr(essor ,clif=d assumes4 #bc 99,!ory ( ,heat99 #ahga1 p4 #bde4 ,s f> z ,i may v5ture to =m an indep5d5t op9ion on ! subject1 x is to ! effect t ,pr(essor ,clif=d is "r1 & t ! kn[n laws ( nature d n enable u to assign a 8beg9n+40 ,sci5ce leads u backw>ds into inf9ite pa/ duration4 ,b t ,pr(essor ,clif=d is "r on ?is po9t1 is no reason :y we %\ld suppose him to be "r 9 8 o!r op9ions1 "s ( :i* ,i am sure are wrong4 ,nor is x a reason :y o!r p>ts ( my la/ *apt] %\ld be wrong4 ,! "q only affects ! s+le p>agraph on pp4 #gdd-e ( ?is book1 :i* might1 ,i believe1 be /ruck out )\t necessitat+ any alt]ation 9 ! re/ ( ! text4 ,x is always to be rememb]$ t ! failure ( an argum5t 9 fav\r ( a proposition does n1 g5]ally speak+1 add mu*1 if any1 probability to ! contradictory proposition4 ,i _c conclude )\t express+ my ackn[l$gm5ts to ,pr(essor ,clif=d = 8 k9d expressions reg>d+ my "w z a :ole4 #b1 ,! ,*e/nuts1 ,we/ ,hea?1 ,hamp/ead1 ,n4 ,w4 99,augu/ #ae1 #ahgg499 ,,cont5ts4 ,,book ,i4 ,,=mal ,,logic1 ,,d$uctive ,,& ,,inductive4 ,,*apt] ,i4 ,,introduction4 ,,section ,,page #a4 ,introduction #a #b4 ,! ,p[]s ( ,m9d conc]n$ 9 ! ,creation ( ,sci5ce #d #c4 ,laws ( ,id5tity & ,diff]5ce #e #d4 ,! ,nature ( ! ,laws ( ,id5tity & ,diff]5ce #f #e4 ,! ,process ( ,inf]5ce #i #f4 ,d$uction & ,induction #aa #g4 ,symbolic ,expression ( ,logical ,inf]5ce #ac #h4 ,expression ( ,id5tity & ,diff]5ce #ad #i4 ,g5]al ,=mula ( ,logical ,inf]5ce #ag #aj4 ,! ,propagat+ ,p[] ( ,simil>ity #bj #aa4 ,anticipations ( ! ,pr9ciple ( ,sub/itution #ba #ab4 ,! ,logic ( ,relatives #bb ,,*apt] ,,ii4 ,,t]ms4 #a4 ,t]ms #bd #b4 ,tw(old mean+ ( ,g5]al ,names #be #c4 ,ab/ract ,t]ms #bg #d4 ,sub/antial ,t]ms #bh #e4 ,collective ,t]ms #bi #f4 ,syn!sis ( ,t]ms #cj #g4 ,symbolic ,expression ( ! ,law ( ,contradiction #ca #h4 ,c]ta9 ,special ,conditions ( ,logical ,symbols #cb ,,*apt] ,,iii4 ,,propositions4 #a4 ,propositions #cf #b4 ,simple ,id5tities #cg #c4 ,p>tial ,id5tities #dj #d4 ,limit$ ,id5tities #db #e4 ,negative ,propositions #dc #f4 ,conv]sion ( ,propositions #df #g4 ,tw(old ,int]pretation ( ,propositions #dg ,,*apt] ,,iv4 ,,d$uctive ,,reason+4 #a4 ,d$uctive ,reason+ #di #b4 ,imm$iate ,inf]5ce #ej #c4 ,inf]5ce ) ,two ,simple ,id5tities #ea #d4 ,inf]5ce ) a ,simple & a ,p>tial ,id5tity #ec #e4 ,inf]5ce ( a ,p>tial f ,two ,p>tial ,id5tities #ee #f4 ,on ! ,ellipsis ( ,t]ms 9 ,p>tial ,id5tities #eg #g4 ,inf]5ce ( a ,simple f ,two ,p>tial ,id5tities #eh #h4 ,inf]5ce ( a ,limit$ f ,two ,p>tial ,id5tities #ei #i4 ,miscellane\s ,=ms ( ,d$uctive ,inf]5ce #fj #aj4 ,fallacies #fb ,,*apt] ,v4 ,,disjunctive ,,propositions4 #a4 ,disjunctive ,propositions #ff #b4 ,expression ( ! ,alt]native ,relation #fg #c4 ,nature ( ! ,alt]native ,relation #fh #d4 ,laws ( ! ,disjunctive ,relation #ga #e4 ,symbolic ,expression ( ! ,law ( ,duality #gc #f4 ,v>i\s ,=ms ( ! ,disjunctive ,proposition #gd #g4 ,inf]5ce by ,disjunctive ,propositions #gf ,,*apt] ,,vi4 ,,! ,,indirect ,,me?od ,,( ,,inf]5ce4 #a4 ,! ,indirect ,me?od ( ,inf]5ce #ha #b4 ,simple ,illu/rations #hc #c4 ,employm5t ( ! ,contrapositive ,proposition #hd #d4 ,contrapositive ( a ,simple ,id5tity #hf #e4 ,miscellane\s ,examples ( ! ,me?od #hh #f4 ,mr4 ,v5n's ,problem #ij #g4 ,abbreviation ( ! ,process #ia #h4 ,! ,logical ,alphabet #id #i4 ,! ,logical ,slate #ie #aj4 ,ab/raction ( ,indiff]5t ,circum/ances #ig #aa4 ,illu/rations ( ! ,indirect ,me?od #ih #ab4 ,second ,example #ii #ac4 ,?ird ,example #ajj #ad4 ,f\r? ,example #aja #ae4 ,fif? ,example #aja #af4 ,fallacies ,analys$ by ! ,indirect ,me?od #ajb #ag4 ,! ,logical ,abacus #ajd #ah4 ,! ,logical ,ma*9e #ajg #ai4 ,! ,ord] ( ,premises #aad #bj4 ,! ,equival5ce ( ,propositions #aae #ba4 ,! ,nature ( ,inf]5ce #aah ,,*apt] ,,vii4 ,,induction4 #a4 ,induction #aba #b4 ,induction an ,inv]se ,op]ation #abb #c4 ,inductive ,problems = ,solution by ! ,read] #abf #d4 ,induction ( ,simple ,id5tities #abg #e4 ,induction ( ,p>tial ,id5tities #acj #f4 ,solution ( ! ,inv]se or ,inductive ,problem1 involv+ ,two ,classes #acd #g4 ,! ,inv]se ,logical ,problem1 involv+ ,?ree ,classes #acg #h4 ,pr(essor ,clif=d on ! ,types ( ,comp\nd ,/atem5t involv+ ,f\r ,classes #adc #i4 ,di/9ction betwe5 ,p]fect & ,imp]fect ,induction #adf #aj4 ,transition f ,p]fect to ,imp]fect ,induction #adi ,,book ,,ii4 ,,numb]1 ,,v>iety1 ,,& ,,probability4 ,,*apt] ,,viii4 ,,pr9ciples ,,( ,,numb]4 #a4 ,pr9ciples ( ,numb] #aec #b4 ,! ,nature ( ,numbe #aef #c4 ,( ,num]ical ,ab/raction #aeh #d4 ,concrete & ,ab/ract ,numb] #aei #e4 ,analogy ( ,logical & ,num]ical ,t]ms #afj #f4 ,pr9ciple ( ,ma!matical ,inf]5ce #afb #g4 ,reason+ by ,inequalities #afe #h4 ,ari?metical ,reason+ #afg #i4 ,num]ically ,def9ite ,reason+ #afh #aj4 ,num]ical mean+ ( ,logical ,conditions #aga ,,*apt] ,,ix4 ,,! ,,v>iety ,,( ,,nature1 ,,or ,,! ,,doctr9e ,,( ,,comb9ations ,,& ,,p]mutations4 #a4 ,! ,v>iety ( ,nature #agc #b4 ,di/9ction ( ,comb9ations & ,p]mutations #agg #c4 ,calculation ( ,numb] ( ,comb9ations #ahj #d4 ,! ,ari?metical ,triangle #ahb #e4 ,connexion betwe5 ! ,ari?metical ,triangle & ! ,logical ,alphabet #ahi #f4 ,possible ,v>iety ( ,nature & ,art #aij #g4 ,high] ,ord]s ( ,v>iety #aib ,,*apt] ,x4 ,,!ory ,,( ,,probability4 #a4 ,!ory ( ,probability #aig #b4 ,fundam5tal ,pr9ciples ( ! ,!ory #bjj #c4 ,rules = ! ,calculation ( ,probabilities #bjc #d4 ,! ,logical ,alphabet 9 que/ions ( ,probability #bje #e4 ,comp>ison ( ! ,!ory ) ,exp]i5ce #bjf #f4 ,probable ,d$uctive ,argum5ts #bji #g4 ,difficulties ( ! ,!ory #bac ,,*apt] ,,xi4 ,,philosophy ,,( ,,inductive ,,inf]5ce4 #a4 ,philosophy ( ,inductive ,inf]5ce #bah #b4 ,v>i\s ,classes ( ,inductive ,tru?s #bai #c4 ,! ,relation ( ,cause & ,effect #bbj #d4 ,fallaci\s ,use ( ! ,t]m ,cause #bba #e4 ,confusion ( ,two ,que/ions #bbb #f4 ,def9ition ( ! ,t]m ,cause #bbd #g4 ,di/9ction ( ,inductive & ,d$uctive ,results #bbf #h4 ,! ,gr\nds ( ,inductive ,inf]5ce #bbh #i4 ,illu/rations ( ! ,inductive ,process #bbi #aj4 ,geometrical ,reason+ #bcc #aa4 ,discrim9ation ( ,c]ta9ty & ,probability #bce ,,*apt] ,,xii4 ,,! ,,inductive ,,or ,,inv]se ,,application ,,( ,,! ,,!ory ,,( ,,probability4 #a4 ,! ,inductive or ,inv]se ,application ( ! ,!ory #bdj #b4 ,pr9ciple ( ! ,inv]se ,me?od #bdb #c4 ,simple ,applications ( ! ,inv]se ,me?od #bdd #d4 ,! ,!ory ( ,probability 9 ,a/ronomy #bdg #e4 ,! ,g5]al ,inv]se ,problem #bej #f4 ,simple ,illu/ration ( ! ,inv]se ,problem #bec #g4 ,g5]al ,solution ( ! ,inv]se ,problem #bee #h4 ,rules ( ! ,inv]se ,me?od #beg #i4 ,=tuit\s ,co9cid5ces #bfa #aj4 ,summ>y ( ! ,!ory ( ,inductive ,inf]5ce #bfe ,,book ,,iii4 ,,me?ods ,,( ,,measurem5t4 ,,*apt] ,,xiii4 ,,! ,,exact ,,measurem5t ,,( ,,ph5om5a4 #a4 ,! ,exact ,measurem5t ( ,ph5om5a #bgj #b4 ,division ( ! ,subject #bgd #c4 ,cont9u\s quantity #bgd #d4 ,! ,fallaci\s ,indications ( ! ,s5ses #bgf #e4 ,complexity ( ,quantitative ,que/ions #bgh #f4 ,! ,me?ods ( ,accurate ,measurem5t #bhb #g4 ,conditions ( ,accurate ,measurem5t #bhb #h4 ,measur+ ,in/rum5ts #bhd #i4 ,! ,me?od ( ,repetition #bhh #aj4 ,measurem5ts by ,natural ,co9cid5ce #bib #aa4 ,modes ( ,indirect ,measurem5t #bif #ab4 ,comp>ative ,use ( ,measur+ ,in/rum5ts #bii #ac4 ,sy/ematic ,p]=mance ( ,measurem5ts #cjj #ad4 ,! ,p5dulum #cjb #ae4 ,atta9able ,accuracy ( ,measurem5t #cjc ,,*apt] ,,xiv4 ,,units ,,& ,,/&>ds ,,( ,,measurem5t4 #a4 ,units & ,/&>ds ( ,measurem5t #cje #b4 ,/&>d ,unit ( ,"t #cjg #c4 ,! ,unit ( ,space & ! ,b> ,/&>d #cab #d4 ,! ,t]re/rial ,/&>d #cad #e4 ,! ,p5dulum ,/&>d #cae #f4 ,unit ( ,d5sity #caf #g4 ,unit ( ,mass #cag #h4 ,natural ,sy/em ( ,/&>ds #cai #i4 ,subsidi>y ,units #cbj #aj4 ,d]iv$ ,units #cba #aa4 ,provisional ,units #cbc #ab4 ,!ory ( ,dim5sions #cbe #ac4 ,natural ,con/ants #cbh #ad4 ,ma!matical ,con/ants #ccj #ae4 ,physical ,con/ants #cca #af4 ,a/ronomical ,con/ants #ccb #ag4 ,t]re/rial ,numb]s #ccc #ah4 ,organic ,numb]s #ccc #ai4 ,social ,numb]s #ccd ,,*apt] ,,xv4 ,,analysis ,,( ,,quantitative ,,ph5om5a4 #a4 ,analysis ( ,quantitative ,ph5om5a #cce #b4 ,illu/rations ( ! ,complication ( ,effects #ccf #c4 ,me?ods ( ,elim9at+ ,error #cci #d4 ,me?od ( ,avoidance ( ,error #cdj #e4 ,diff]5tial ,me?od #cdd #f4 ,me?od ( ,correction #cdf #g4 ,me?od ( ,comp5sation #cej #h4 ,me?od ( ,rev]sal #ced ,,*apt] ,,xvi4 ,,! ,,me?od ,,( ,,means4 #a4 ,! ,me?od ( ,means #ceg #b4 ,sev]al ,uses ( ! ,mean ,result #cei #c4 ,! ,mean & ! ,av]age #cfj #d4 ,on ! ,av]age or ,fictiti\s ,mean #cfc #e4 ,! ,precise ,mean ,result #cfe #f4 ,det]m9ation ( ! ,z]o ,po9t #cfh #g4 ,det]m9ation ( ,maximum ,po9ts #cga ,,*apt] ,,xvii4 ,,! ,,law ,,( ,,error4 #a4 ,! ,law ( ,error #cgd #b4 ,e/abli%m5t ( ! ,law ( ,error #cge #c4 ,h]s*el's ,geometrical ,pro( #cgg #d4 ,laplace's & ,quetelet's ,pro( ( ! ,law #cgh #e4 ,logical ,orig9 ( ! ,law ( ,error #chc #f4 ,v]ification ( ! ,law ( ,error #chc #g4 ,! ,probable ,mean ,result #che #h4 ,! ,probable ,error ( ,results #chf #i4 ,rejection ( ! ,mean ,result #chi #aj4 ,me?od ( ,lea/ ,squ>es #cic #aa4 ,works ^u ! ,!ory ( ,probability #cid #ab4 ,detection ( ,con/ant ,errors #cif ,,book ,,iv4 ,,inductive ,,inve/igation4 ,,*apt] ,,xviii4 ,,obs]vation4 #a4 ,obs]vation #cii #b4 ,di/9ction ( ,obs]vation & ,exp]im5t #djj #c4 ,m5tal ,conditions ( ,correct ,obs]vation #djb #d4 ,in/rum5tal & ,s5sual ,conditions ( ,correct ,obs]vation #djd #e4 ,ext]nal ,conditions ( ,correct ,obs]vation #djg #f4 ,app>5t ,sequ5ce ( ,ev5ts #dji #g4 ,negative ,argum5ts f ,non-,obs]vation #daa ,,*apt] ,,xix4 ,,exp]im5t4 #a4 ,exp]im5t #daf #b4 ,exclusion ( ,indiff]5t ,circum/ances #dai #c4 ,simplification ( ,exp]im5ts #dbb #d4 ,failure 9 ! ,simplification ( ,exp]im5ts #dbd #e4 ,removal ( ,usual ,conditions #dbf #f4 ,int]f]5ce ( ,unsuspect$ ,conditions #dbh #g4 ,bl9d or ,te/ ,exp]im5ts #dcc #h4 ,negative ,results ( ,exp]im5t #dcd #i4 ,limits ( ,exp]im5t #dcg ,,*apt] ,,xx4 ,,me?od ,,( ,,v>iations4 #a4 ,me?od ( ,v>iations #dci #b4 ,! ,v>iable & ! ,v>iant #ddj #c4 ,measurem5t ( ! ,v>iable #dda #d4 ,ma9t5ance ( ,simil> ,conditions #ddc #e4 ,collective ,exp]im5ts #dde #f4 ,p]iodic ,v>iations #ddg #g4 ,comb9$ ,p]iodic ,*anges #dej #h4 ,pr9ciple ( ,=c$ ,vibrations #dea #i4 ,integrat$ ,v>iations #deb ,,*apt] ,,xxi4 ,,!ory ,,( ,,approximation4 #a4 ,!ory ( ,approximation #def #b4 ,sub/itution ( ,simple ,hypo!ses #deh #c4 ,approximation to ,exact ,laws #dfb #d4 ,successive ,approximations to ,natural ,conditions #dfe #e4 ,discov]y ( ,hypo!tically ,simple ,laws #dgj #f4 ,ma!matical ,pr9ciples ( ,approximation #dga #g4 ,approximate ,indep5d5ce ( ,small ,effects #dge #h4 ,f\r ,mean+s ( ,equality #dgi #i4 ,ari?metic ( ,approximate ,quantities #dha ,,*apt] ,,xxii4 ,,quantitative ,,induction4 #a4 ,quantitative ,induction #dhc #b4 ,probable ,connexion ( ,v>y+ ,quantities #dhd #c4 ,empirical ,ma!matical ,laws #dhg #d4 ,discov]y ( ,rational ,=mul #dhi #e4 ,! ,graphical ,me?od #dib #f4 ,int]polation & ,extrapolation #die #g4 ,illu/rations ( ,empirical ,quantitative ,laws #dii #h4 ,simple ,proportional ,v>iation #eja ,,*apt] ,,xxiii4 ,,! ,,use ,,( ,,hypo!sis4 #a4 ,! ,use ( ,hypo!sis #ejd #b4 ,requisites ( a good ,hypo!sis #eaj #c4 ,possibility ( ,d$uctive ,reason+ #eaa #d4 ,consi/5cy ) ! ,laws ( ,nature #ead #e4 ,con=mity ) ,facts #eaf #f4 ,exp]im5tum ,crucis #eah #g4 ,descriptive ,hypo!ses #ebb ,,*apt] ,,xxiv4 ,,empirical ,,k1 ,,explanation ,,& ,,pr$iction4 #a4 ,empirical ,k1 ,explanation & ,pr$iction #ebe #b4 ,empirical ,k #ebf #c4 ,accid5tal ,discov]y #ebi #d4 ,empirical ,obs]vations subsequ5tly ,expla9$ #ecb #e4 ,ov]look$ ,results ( ,!ory #ecd #f4 ,pr$ict$ ,discov]ies #ecf #g4 ,pr$ictions 9 ! ,sci5ce ( ,light #ech #h4 ,pr$ictions f ! ,!ory ( ,undulations #edj #i4 ,pr$iction 9 o!r ,sci5ces #edb #aj4 ,pr$iction by ,inv]sion ( ,cause & ,effect #ede #aa4 ,facts kn[n only by ,!ory #edg ,,*apt] ,,xxv4 ,,accordance ,,( ,,quantitative ,,!ories4 #a4 ,accordance ( ,quantitative ,!ories #eea #b4 ,empirical ,measurem5ts #eeb #c4 ,quantities indicat$ by ,!ory1 b ,empirically ,measur$ #eec #d4 ,expla9$ ,results ( ,measurem5t #eed #e4 ,quantities det]m9$ by ,!ory & v]ifi$ by ,measurem5t #eee #f4 ,quantities det]m9$ by ,!ory & n v]ifi$ #eef #g4 ,discordance ( ,!ory & ,exp]im5t #eeh #h4 ,accordance ( ,measurem5ts ( ,a/ronomical ,di/ances #efj #i4 ,selection ( ! be/ ,mode ( ,measurem5t #efc #aj4 ,agreem5t ( ,di/9ct ,modes ( ,measurem5t #efd #aa4 ,residual ,ph5om5a #efi ,,*apt] ,,xxvi4 ,,"* ,,( ,,! ,,exp]im5tali/4 #a4 ,"* ( ! ,exp]im5tali/ #egd #b4 ,error ( ! ,baconian ,me?od #egf #c4 ,fre$om ( ,!oris+ #egg #d4 ,! ,newtonian ,me?od1 ! ,true ,organum #eha #e4 ,c&\r & ,c\rage ( ! ,philosophic ,m9d #ehf #f4 ,! ,philosophic ,"* ( ,f>aday #ehg #g4 ,res]vation ( ,judgm5t #eib ,,book ,v4 ,,g5]alisation1 ,,analogy1 ,,& ,,classification4 ,,*apt] ,,xxvii4 ,,g5]alisation4 #a4 ,g5]alisation #eid #b4 ,di/9ction ( ,g5]alisation & ,analogy #eif #c4 ,two ,mean+s ( ,g5]alisation #eig #d4 ,value ( ,g5]alisation #eii #e4 ,comp>ative ,g5]ality ( ,prop]ties #fjj #f4 ,uni=m ,prop]ties ( all ,matt] #fjc #g4 ,v>iable ,prop]ties ( ,matt] #fjf #h4 ,extreme ,in/ances ( ,prop]ties #fjg #i4 ,! ,detection ( ,cont9uity #faj #aj4 ,! ,law ( ,cont9uity #fae #aa4 ,failure ( ! ,law ( ,cont9uity #fai #ab4 ,negative ,argum5ts on ! ,pr9ciple ( ,cont9uity #fba #ac4 ,t5d5cy to ,ha/y ,g5]alisation #fbc ,,*apt] ,,xxviii4 ,,analogy4 #a4 ,analogy #fbg #b4 ,analogy z a ,guide 9 ,discov]y #fbi #c4 ,analogy 9 ! ,ma!matical ,sci5ces #fca #d4 ,analogy 9 ! ,!ory ( ,undulations #fce #e4 ,analogy 9 ,a/ronomy #fch #f4 ,failures ( ,analogy #fda ,,*apt] ,,xxix4 ,,exceptional ,,ph5om5a4 #a4 ,exceptional ,ph5om5a #fdd #b4 ,imag9>y or ,false ,exceptions #fdg #c4 ,app>5t b ,congru5t ,exceptions #fdi #d4 ,s+ul> ,exceptions #feb #e4 ,div]g5t ,exceptions #fee #f4 ,accid5tal ,exceptions #feh #g4 ,novel & ,unexpla9$ ,exceptions #ffa #h4 ,limit+ ,exceptions #ffc #i4 ,real ,exceptions to ,suppos$ ,laws #fff #aj4 ,unclass$ ,exceptions #ffh ,,*apt] ,,xxx4 ,,classification4 #a4 ,classification #fgc #b4 ,classification involv+ ,induction #fge #c4 ,multiplicity ( ,modes ( ,classification #fgg #d4 ,natural & ,artificial ,sy/ems ( ,classification #fgi #e4 ,correlation ( ,prop]ties #fha #f4 ,classification 9 ,cry/allography #fhe #g4 ,classification an ,inv]se & ,t5tative ,op]ation #fhi #h4 ,symbolic ,/atem5t ( ! ,!ory ( ,classification #fib #i4 ,bifurcate ,classification #fid #aj4 ,! ,five ,pr$icates #fih #aa4 ,summum ,g5us & ,infima ,species #gja #ab4 ,! ,tree ( ,porphyry #gjb #ac4 ,does ,ab/raction imply ,g5]alisation8 #gjd #ad4 ,discov]y ( ,m>ks or ,*>act]i/ics #gjh #ae4 ,diagno/ic ,sy/ems ( ,classification #gaj #af4 ,index ,classifications #gad #ag4 ,classification 9 ! ,biological ,sci5ces #gah #ah4 ,classification by ,types #gbb #ai4 ,natural ,g5]a & ,species #gbd #bj4 ,unique or ,exceptional ,objects #gbh #ba4 ,limits ( ,classification #gcj ,,book ,,vi4 ,,*apt] ,,xxxi4 ,,reflections ,,on ,,! ,,results ,,& ,,limits ,,( ,,sci5tific ,,me?od4 #a4 ,reflections on ! ,results & ,limits ( ,sci5tific ,me?od #gce #b4 ,! ,mean+ ( ,natural ,law #gcg #c4 ,inf9it5ess ( ! ,univ]se #gch #d4 ,! ,indet]m9ate ,problem ( ,creation #gdj #e4 ,hi]>*y ( ,natural ,laws #gdb #f4 ,! ,ambigu\s ,expression--8,uni=mity ( ,nature0 #gde #g4 ,possible ,/ates ( ! ,univ]se #gdi #h4 ,speculations on ! ,reconc5tration ( ,en]gy #gea #i4 ,! ,div]g5t ,scope = ,new ,discov]y #geb #aj4 ,inf9ite ,incomplet5ess ( ! ,ma!matical ,sci5ces #ged #aa4 ,! ,reign ( ,law 9 ,m5tal & ,social ,ph5om5a #gei #ab4 ,! ,!ory ( ,evolution #gfa #ac4 ,possibility ( ,div9e ,int]f]5ce #gfe #ad4 ,conclusion #gff ,,index #ggc ,,! ,,pr9ciples ,,( ,,sci5ce4 ,,*apt] ,i4 ,,introduction4 ,sci5ce arises f ! discov]y ( ,id5tity amid/ ,div]sity4 ,! process may be describ$ 9 diff]5t words1 b our language mu/ always imply ! pres5ce ( "o common & necess>y elem5t4 ,9 e act ( inf]5ce or sci5tific me?od we are engag$ ab\t a c]ta9 id5tity1 sam5ess1 simil>ity1 lik5ess1 resemblance1 analogy1 equival5ce or equality app>5t betwe5 two objects4 ,x is d\btful :e!r an entirely isolat$ ph5om5on c\ld pres5t itself to our notice1 s9ce !re mu/ always be "s po9ts ( simil>ity betwe5 object & object4 ,b 9 any case an isolat$ ph5om5on c\ld be /udi$ to no useful purpose4 ,! :ole value ( sci5ce consi/s 9 ! p[] :i* x conf]s ^u u ( apply+ to "o object ! k acquir$ f l objects2 & x is only s f>1 !re=e1 z we c discov] & regi/] resemblances t we c turn our obs]vations to acc\nt4 ,nature is a spectacle cont9ually exhibit$ to our s5ses1 9 :i* ph5om5a are m+l$ 9 comb9ations ( endless v>iety & novelty4 ,wond] fixes ! m9d's att5tion2 memory /ores up a record ( ea* di/9ct impression2 ! p[]s ( association br+ =? ! record :5 ! l is felt aga94 ,by ! high] faculties ( judgm5t & reason+ ! m9d comp>es ! new ) ! old1 recognises ess5tial id5tity1 ev5 :5 disguis$ by div]se circum/ances1 & expects to f9d aga9 :at 0 be=e exp]i5c$4 ,x mu/ be ! gr\nd ( all reason+ & inf]5ce t 99:at is true ( "o ?+ w be true ( its equival5t991 & t "u c>efully asc]ta9$ conditions 99,nature repeats h]self994 ,7 ?is inde$ a ,*aotic ,univ]se1 ! p[]s ( m9d employ$ 9 sci5ce w\ld be useless to u4 ,did ,*ance :olly take ! place ( ord]1 & did all ph5om5a come out ( an 99,inf9ite ,lott]y991 to use ,condorcet's expression1 !re c\ld be no reason to expect ! l result 9 l circum/ances4 ,x is possible to conceive a _w 9 :i* no two ?+s %\ld be associat$ m (t51 9 ! long run1 ?an any o!r two ?+s4 ,! frequ5t conjunction ( any two ev5ts w\ld !n be purely =tuit\s1 & if we expect$ conjunctions to recur cont9ually1 we %\ld be disappo9t$4 ,9 su* a _w we might recognise ! same k9d ( ph5om5on z x appe>$ f "t to "t1 j z we might recognise a m>k$ ball z x 0 occasionally drawn & re-drawn f a ballot-box2 b ! approa* ( any ph5om5on w\ld be 9 no way indicat$ by :at _h gone be=e1 nor w\ld x be a sign ( :at 0 to come aft]4 ,9 su* a _w k w\ld be no m ?an ! memory ( pa/ co9cid5ces1 & ! reason+ p[]s1 if !y exi/$ at all1 w\ld give no clue to ! nature ( ! pres5t1 & no presage ( ! future4 ,happily ! ,univ]se 9 :i* we dwell is n ! result ( *ance1 & :]e *ance seems to "w x is our own defici5t faculties :i* prev5t u f recognis+ ! op]ation ( ,law & ( ,design4 ,9 ! mat]ial framework ( ?is _w1 sub/ances & =ces pres5t !mselves 9 def9ite & /able comb9ations4 ,?+s are n 9 p]petual flux1 z anci5t philosoph]s held4 ,elem5t rema9s elem5t2 iron *anges n into gold4 ,) suitable precautions we c calculate ^u f9d+ ! same ?+ aga9 end[$ ) ! same prop]ties4 ,! con/itu5ts ( ! globe1 inde$1 appe> 9 almo/ endless comb9ations2 b ea* comb9ation be>s its fix$ "*1 & :5 resolv$ is f\nd to be ! comp\nd ( def9ite sub/ances4 ,misappreh5sions mu/ cont9ually occur1 ow+ to ! limit$ ext5t ( our exp]i5ce4 ,we c nev] h exam9$ & regi/]$ possible exi/5ces s ?or\ghly z to be sure t no new ones w occur & fru/rate our calculations4 ,! same outw>d appe>ances may cov] any am\nt ( hidd5 diff]5ces :i* we h n yet suspect$4 ,to ! v>iety ( sub/ances & p[]s diffus$ ?r\gh nature at its creation1 we %\ld n suppose t our brief exp]i5ce c assign a limit1 & ! necess>y imp]fection ( our k mu/ be ev] borne 9 m9d4 ,yet !re is mu* to give u confid5ce 9 ,sci5ce4 ,! wid] our exp]i5ce1 ! m m9ute our exam9ation ( ! globe1 ! great] ! accumulation ( well-reason$ k1--! few] 9 all probability w be ! failures ( inf]5ce comp>$ ) ! successes4 ,exceptions to ! preval5ce ( ,law are gradually r$uc$ to ,law !mselves4 ,c]ta9 deep simil>ities h be5 detect$ among ! objects ar\nd u1 & h nev] yet be5 f\nd want+4 ,z ! means ( exam9+ di/ant p>ts ( ! univ]se h be5 acquir$1 ^? simil>ities h be5 trac$ !re z "h4 ,o!r worlds & /ell> sy/ems may be almo/ incompreh5sively diff]5t f ours 9 magnitude1 condition & disposition ( p>ts1 & yet we detect !re ! same elem5ts ( :i* our own limbs are compos$4 ,! same natural laws c be detect$ 9 op]ation 9 e "p ( ! univ]se )9 ! scope ( our in/rum5ts2 & d\btless ^! laws are obey$ irrespective ( di/ance1 "t1 & circum/ance4 ,x is ! pr]ogative ( ,intellect to discov] :at is uni=m & un*ang+ 9 ! ph5om5a ar\nd u4 ,s f> z object is diff]5t f object1 k is useless & inf]5ce impossible4 ,b s f> z object resembles object1 we c pass f "o to ! o!r4 ,9 proportion z resemblance is deep] & m g5]al1 ! comm&+ p[]s ( k become m wond]ful4 ,id5tity 9 "o or o!r ( its phases is ?us always ! bridge by :i* we pass 9 inf]5ce f case to case2 & x is my purpose 9 ?is treatise to trace out ! v>i\s =ms 9 :i* ! "o same process ( reason+ pres5ts itself 9 ! ev]-gr[+ a*ievem5ts ( ,sci5tific ,me?od4 99,! ,p[]s ( ,m9d conc]n$ 9 ! ,creation ( ,sci5ce499 ,x is no "p ( ! purpose ( ?is "w to inve/igate ! nature ( m9d4 ,p n uncommonly suppose t logic is a bran* ( psy*ology1 because reason+ is a m5tal op]ation4 ,on ! same gr\nd1 h[ev]1 we might argue t all ! sci5ces are bran*es ( psy*ology4 ,z w be fur!r expla9$1 ,i adopt ! op9ion ( ,mr4 ,h]b]t ,sp5c]1 t logic is really an objective sci5ce1 l ma!matics or me*anics4 ,only 9 an incid5tal mann]1 !n1 ne$ ,i po9t out t ! m5tal p[]s employ$ 9 ! acquisition ( k are probably ?ree 9 numb]4 ,!y are sub/antially z ,pr(essor ,ba9 has /at$ !m#bd3-- #bd 99,! ,s5ses & ! ,intellect991 ,second ,ed41 pp4 #e1 #cbe1 c4 #a4 ,! ,p[] ( ,discrim9ation4 #b4 ,! ,p[] ( ,detect+ ,id5tity4 #c4 ,! ,p[] ( ,ret5tion4 ,we ex]t ! fir/ p[] 9 e act ( p]ception4 ,h>dly c we h a s5sation or feel+ unless we discrim9ate x f some?+ else :i* prec$$4 ,consci\sness w\ld almo/ seem to consi/ 9 ! break betwe5 "o /ate ( m9d & ! next1 j z an induc$ curr5t ( electricity arises f ! beg9n+ or ! end+ ( ! prim>y curr5t4 ,we are always engag$ 9 discrim9ation2 & ! rudim5t ( ?\ght :i* exi/s 9 ! l[] animals probably consi/s 9 _! p[] ( feel+ diff]5ce & be+ agitat$ by x4 ,yet _h we ! p[] ( discrim9ation only1 ,sci5ce c\ld n be creat$4 ,to "k t "o feel+ diff]s f ano!r gives purely negative in=mation4 ,x _c tea* u :at w happ54 ,9 su* a /ate ( intellect ea* s5sation w\ld /& out di/9ct f e o!r2 !re w\ld be no tie1 no bridge ( aff9ity betwe5 !m4 ,we want a unify+ p[] by :i* ! pres5t & ! future may be l9k$ to ! pa/2 & ?is seems to be accompli%$ by a diff]5t p[] ( m9d4 ,"l ,bacon has po9t$ out t diff]5t m5 possess 9 v diff]5t degrees ! p[]s ( discrim9ation & id5tification4 ,x may be said inde$ t discrim9ation necess>ily implies ! action ( ! opposite process ( id5tification2 & s x d\btless does 9 negative po9ts4 ,b !re is a r>e prop]ty ( m9d :i* consi/s 9 p5etrat+ ! disguise ( v>iety & seiz+ ! common elem5ts ( sam5ess2 & x is ?is prop]ty :i* furni%es ! true measure ( intellect4 ,! "n ( 8intellect0 expresses ! int]lac+ ( ! g5]al & ! s+le1 :i* is ! peculi> prov9ce ( m9d4#be ,to 99cogitate99 is ! ,lat9 99coagit>e991 re/+ on a l metaphor4 ,logic1 also1 is b ano!r "n = ! same process1 ! peculi> "w ( reason2 = is d]iv$ f 1 :i* l ! ,lat9 99leg]e99 meant orig9ally to ga!r4 ,plato said ( ?is unify+ p[]1 t if he met ! man :o c\ld detect 99! "o 9 ! _m991 he w\ld foll[ him z a god4 #be ,max ,mll]1 99,lectures on ! ,sci5ce ( ,language991 ,second ,s]ies1 vol4 ii4 p4 #fc2 or ,six? ,edition1 vol4 ii4 p4 #fg4 ,! view ( ! etymological mean+ ( 8intellect0 is giv5 above on ! au?ority ( ,pr(essor ,max ,mll]4 ,x seems to be oppos$ to ! ord9>y op9ion1 accord+ to :i* ! ,lat9 99intellig]e99 means to *oose betwe51 to see a diff]5ce betwe51 to discrim9ate1 in/ead ( to unite4 99,laws ( ,id5tity & ,diff]5ce499 ,at ! base ( all ?\ght & sci5ce mu/ lie ! laws :i* express ! v nature & conditions ( ! discrim9at+ & id5tify+ p[]s ( m9d4 ,^! are ! s-call$ ,fundam5tal ,laws ( ,?\ght1 usually /at$ z foll[s3-- #a4 ,! ,law ( ,id5tity4 99,:atev] is1 is499 #b4 ,! ,law ( ,contradiction4 99,a ?+ _c bo? be & n be499 #c4 ,! ,law ( ,duality4 99,a ?+ mu/ ei!r be or n be499 ,! fir/ ( ^! /atem5ts may p]haps be reg>d$ z a description ( id5tity itself1 if s fundam5tal a notion c admit ( description4 ,a ?+ at any mom5t is p]fectly id5tical ) itself1 &1 if any p]son 7 unaw>e ( ! mean+ ( ! ^w 8id5tity10 we c\ld n bett] describe x ?an by su* an example4 ,! second law po9ts out t contradictory attributes c nev] be jo9$ toge!r4 ,! same object may v>y 9 its diff]5t p>ts2 "h x may be black1 & !re :ite2 at "o "t x may be h>d & at ano!r "t s(t2 b at ! same "t & place an attribute _c be bo? pres5t & abs5t4 ,ari/otle truly describ$ ?is law z ! fir/ ( all axioms--"o ( :i* we ne$ n seek = any demon/ration4 ,all tru?s _c be prov$1 o!rwise !re w\ld be an endless *a9 ( demon/ration2 & x is 9 self-evid5t tru?s l ?is t we f9d ! simple/ f\ndations4 ,! ?ird ( ^! laws completes ! o!r two4 ,x ass]ts t at e /ep !re are two possible alt]natives--pres5ce or abs5ce1 affirmation or negation4 ,h5ce ,i propose to "n ?is law ! ,law ( ,duality1 = x gives to all ! =mul ( reason+ a dual "*4 ,x ass]ts also t betwe5 pres5ce & abs5ce1 exi/5ce & non-exi/5ce1 affirmation & negation1 !re is no ?ird alt]native4 ,z ,ari/otle said1 !re c be no mean betwe5 opposite ass]tions3 we mu/ ei!r affirm or d5y4 ,h5ce ! inconv5i5t "n by :i* x has be5 kn[n--,! ,law ( ,exclud$ ,middle4 ,x may be all[$ t ^! laws are n ?ree indep5d5t & di/9ct laws2 !y r express ?ree diff]5t aspects ( ! same tru?1 & ea* law d\btless presupposes & implies ! o!r two4 ,b x has n hi!rto be5 f\nd possible to /ate ^! *>act]s ( id5tity & diff]5ce 9 less ?an ! ?reefold =mula4 ,! read] may p]haps desire "s in=mation z to ! mode 9 :i* ^! laws h be5 /at$1 or ! way 9 :i* !y h be5 reg>d$1 by philosoph]s 9 diff]5t ages ( ! _w4 ,abundant in=mation on ?is & _m o!r po9ts ( logical hi/ory w be f\nd 9 ,ueb]weg's 99,sy/em ( ,logic991 ( :i* an excell5t translation has be5 publi%$ by ,pr(essor ,t4 ,m4 ,l9dsay 7see pp4 #bbh-bha74 99,! ,nature ( ! ,laws ( ,id5tity & ,diff]5ce499 ,i mu/ at lea/ allude to ! pr(\ndly difficult "q conc]n+ ! nature & au?ority ( ^! ,laws ( ,id5tity & ,diff]5ce4 ,are !y ,laws ( ,?\ght or ,laws ( ,?+s8 ,d !y belong to m9d or to mat]ial nature8 ,on ! "o h& x may be said t sci5ce is a purely m5tal exi/5ce1 & mu/ !re=e con=m to ! laws ( t :i* =m$ x4 ,sci5ce is 9 ! m9d & n 9 ! ?+s1 & ! prop]ties ( m9d are !re=e all important4 ,x is true t ^! laws are v]ifi$ 9 ! obs]vation ( ! ext]ior _w2 & x w\ld seem t !y might h be5 ga!r$ & prov$ by g5]alisation1 _h !y n already be5 9 our possession4 ,b on ! o!r h&1 x may well be urg$ t we _c prove ^! laws by any process ( reason+ or obs]vation1 because ! laws !mselves are presuppos$1 z ,leibnitz acutely rem>k$1 9 ! v notion ( a pro(4 ,!y are ! prior conditions ( all ?\ght & all k1 & ev5 to "q _! tru? is to all[ !m true4 ,h>tley +5i\sly ref9$ ^u ?is argum5t1 rem>k+ t if ! fundam5tal laws ( logic be n c]ta91 !re mu/ exi/ a logic ( a second ord] :]eby we may det]m9e ! degree ( unc]ta9ty3 if ! second logic be n c]ta91 !re mu/ be a ?ird2 & s on 99ad inf9itum994 ,?us we mu/ suppose ei!r t absolutely c]ta9 laws ( ?\ght exi/1 or t !re is no su* ?+ z c]ta9ty :atev]4#bf #bf ,h>tley on ,man1 vol4 i4 p4 #cei4 ,logicians1 inde$1 appe> to me to h paid insuffici5t att5tion to ! fact t mi/akes 9 reason+ are always possible1 & ( n unfrequ5t occurr5ce4 ,! ,laws ( ,?\ght are (t5 call$ necess>y laws1 t is1 laws :i* _c b be obey$4 ,yet z a matt] ( fact1 :o is !re t does n (t5 fail to obey !m8 ,!y are ! laws :i* ! m9d ought to obey r ?an :at x always does obey4 ,our ?\ghts _c be ! crit]ion ( tru?1 = we (t5 h to ackn[l$ge mi/akes 9 argum5ts ( mod]ate complexity1 & we sometimes only discov] our mi/akes by collision betwe5 our expectations & ! ev5ts ( objective nature4 ,mr4 ,h]b]t ,sp5c] holds t ! laws ( logic are objective laws1#bg & he reg>ds ! m9d z be+ 9 a /ate ( con/ant education1 ea* act ( false reason+ or miscalculation lead+ to results :i* are likely to prev5t simil> mi/akes f be+ aga9 committ$4 ,i am q incl9$ to accept su* +5i\s views2 b at ! same "t x is necess>y to di/+ui% betwe5 ! accumulation ( k1 & ! con/itution ( ! m9d :i* all[s ( ! acquisition ( k4 ,be=e ! m9d c p]ceive or reason at all x mu/ h ! conditions ( ?\ght impress$ ^u x4 ,be=e a mi/ake c be committ$1 ! m9d mu/ cle>ly di/+ui% ! mi/ak5 conclusion f all o!r ass]tions4 ,are n ! ,laws ( ,id5tity & ,diff]5ce ! prior conditions ( all consci\sness & all exi/5ce8 ,mu/ !y n hold true1 alike ( ?+s mat]ial & immat]ial8 & if s1 c we say t !y are only subjectively true or objectively true8 ,i am incl9$1 9 %ort1 to reg>d !m z true bo? 89 ! nature ( ?\ght & ?+s10 z ,i express$ x 9 my fir/ logical essay2#bh & ,i hold t !y belong to ! common basis ( all exi/5ce4 ,b ?is is "o ( ! mo/ difficult que/ions ( psy*ology & metaphysics :i* c be rais$1 & x is h>dly "o = ! logician to decide4 ,z ! ma!matician does n inquire into ! nature ( unity & plurality1 b develops ! =mal laws ( plurality1 s ! logician1 z ,i conceive1 mu/ assume ! tru? ( ! ,laws ( ,id5tity & ,diff]5ce1 & occupy himself 9 develop+ ! v>iety ( =ms ( reason+ 9 :i* _! tru? may be manife/$4 #bg 99,pr9ciples ( ,psy*ology991 ,second ,ed41 vol4 ii4 p4 #hf4 #bh 99,pure ,logic1 or ! ,logic ( ,quality ap>t f ,quantity991 #ahfd1 pp4 #aj1 #af1 #bb1 #bi1 #cf1 c4 ,aga91 ,i ne$ h>dly dwell ^u ! "q :e!r logic treats ( language1 notions1 or ?+s4 ,z reasonably might we debate :e!r a ma!matician treats ( symbols1 quantities1 or ?+s4 ,a ma!matician c]ta9ly does treat ( symbols1 b only z ! in/rum5ts :]eby to facilitate 8 reason+ conc]n+ quantities2 & z ! axioms & rules ( ma!matical sci5ce mu/ be v]ifi$ 9 concrete objects 9 ord] t ! calculations f\nd$ ^u !m may h any validity or utility1 x foll[s t ! ultimate objects ( ma!matical sci5ce are ! ?+s !mselves4 ,9 l mann] ,i conceive t ! logician treats ( language s f> z x is ess5tial = ! embodim5t & exhibition ( ?\ght4 ,ev5 if reason+ c take place 9 ! inn] consci\sness ( man )\t ! use ( any signs1 :i* is d\btful1 at any rate x _c become ! subject ( discussion until by "s sy/em ( mat]ial signs x is manife/$ to o!r p]sons4 ,! logician !n uses words & symbols z in/rum5ts ( reason+1 & leaves ! nature & peculi>ities ( language to ! gramm>ian4 ,b signs aga9 mu/ correspond to ! ?\ghts & ?+s express$1 9 ord] t !y %all s]ve _! int5d$ purpose4 ,we may !re=e say t logic treats ultimately ( ?\ghts & ?+s1 & imm$iately ( ! signs :i* /& = !m4 ,signs1 ?\ghts1 & ext]ior objects may be reg>d$ z p>allel & analog\s s]ies ( ph5om5a1 & to treat any "o ( ! ?ree s]ies is equival5t to treat+ ei!r ( ! o!r s]ies4 99,! ,process ( ,inf]5ce499 ,! fundam5tal action ( our reason+ faculties consi/s 9 inf]r+ or c>ry+ to a new in/ance ( a ph5om5on :atev] we h previ\sly kn[n ( its l1 analogue1 equival5t or equal4 ,sam5ess or id5tity pres5ts itself 9 all degrees1 & is kn[n "u v>i\s names2 b ! great rule ( inf]5ce embraces all degrees1 & affirms t 99s f> z !re exi/s sam5ess1 id5tity or lik5ess1 :at is true ( "o ?+ w be true ( ! o!r994 ,! great difficulty d\btless consi/s 9 asc]ta9+ t !re does exi/ a suffici5t degree ( lik5ess or sam5ess to w>rant an int5d$ inf]5ce2 & x w be our ma9 task to inve/igate ! conditions "u :i* reason+ is valid4 ,9 ?is place ,i wi% to po9t out t !re is some?+ common to all acts ( inf]5ce1 h[ev] diff]5t _! app>5t =ms4 ,! "o same rule l5ds itself to ! mo/ div]se applications4 ,! simple/ possible case ( inf]5ce1 p]haps1 occurs 9 ! use ( a 99patt]n991 99example991 or1 z x is commonly call$1 a 99sample994 ,to prove ! exact simil>ity ( two portions ( commodity1 we ne$ n br+ "o portion beside ! o!r4 ,x is suffici5t t we take a sample :i* exactly repres5ts ! texture1 appe>ance1 & g5]al nature ( "o portion1 & accord+ z ?is sample agrees or n ) ! o!r1 s w ! two portions ( commodity agree or diff]4 ,:atev] is true z reg>ds ! col\r1 texture1 d5sity1 mat]ial ( ! sample w be true ( ! goods !mselves4 ,9 su* cases lik5ess ( quality is ! condition ( inf]5ce4 ,exactly ! same mode ( reason+ holds true ( magnitude & figure4 ,to comp>e ! sizes ( two objects1 we ne$ n lay !m beside ea* o!r4 ,a /aff1 /r+1 or o!r k9d ( measure may be employ$ to repres5t ! l5g? ( "o object1 & accord+ z x agrees or n ) ! o!r1 s mu/ ! two objects agree or diff]4 ,9 ?is case ! proxy or sample repres5ts l5g?2 b ! fact t l5g?s c be add$ & multipli$ r5d]s x unnecess>y t ! proxy %\ld always be z l>ge z ! object4 ,any /&>d ( conv5i5t size1 su* z a common foot-rule1 may be made ! m$ium ( comp>ison4 ,! height ( a *ur* 9 "o t[n may be c>ri$ to t 9 ano!r1 & objects exi/+ immovably at opposite sides ( ! e>? may be vic>i\sly measur$ aga9/ ea* o!r4 ,we obvi\sly employ ! axiom t :atev] is true ( a ?+ z reg>ds its l5g?1 is true ( its equal4 ,to e o!r simple ph5om5on 9 nature ! same pr9ciple ( sub/itution is applicable4 ,we may comp>e weights1 d5sities1 degrees ( h>dness1 & degrees ( all o!r qualities1 9 l mann]4 ,to asc]ta9 :e!r two s\nds are 9 unison we ne$ n comp>e !m directly1 b a ?ird s\nd may be ! g-betwe54 ,if a tun+-=k is 9 unison ) ! middle ,c ( ,york ,m9/] organ1 & we aft]w>ds f9d x to be 9 unison ) ! same note ( ! organ 9 ,we/m9/] ,abbey1 !n x foll[s t ! two organs are tun$ 9 unison4 ,! rule ( inf]5ce n[ is1 t :at is true ( ! tun+-=k z reg>ds ! tone or pit* ( its s\nd1 is true ( any s\nd 9 unison ) x4 ,! skilful employm5t ( ?is sub/itutive process enables u to make measurem5ts beyond ! p[]s ( our s5ses4 ,no "o c c\nt ! vibrations1 = in/ance1 ( an organ-pipe4 ,b we c con/ruct an in/rum5t call$ ! 99sir5991 s t1 :ile produc+ a s\nd ( any pit*1 x %all regi/] ! numb] ( vibrations con/itut+ ! s\nd4 ,adju/+ ! s\nd ( ! sir5 9 unison ) an organ-pipe1 we measure indirectly ! numb] ( vibrations belong+ to a s\nd ( t pit*4 ,to measure a s\nd ( ! same pit* is z good z to measure ! s\nd itself4 ,sir ,david ,brew/]1 9 a some:at simil> mann]1 succe$$ 9 measur+ ! refractive indices ( irregul> fragm5ts ( transp>5t m9]als4 ,x 0 a tr\blesome1 & sometimes impracticable "w to gr9d ! m9]als into prisms1 s t ! p[] ( refract+ light c\ld be directly obs]v$2 b he fell ^u ! +5i\s device ( comp\nd+ a liquid possess+ ! same refractive p[] z ! transp>5t fragm5t "u exam9ation4 ,! mom5t :5 ?is equality 0 atta9$ c\ld be kn[n by ! fragm5ts ceas+ to reflect or refract light :5 imm]s$ 9 ! liquid1 s t !y became almo/ invisible 9 x4 ,! refractive p[] ( ! liquid be+ !n measur$ gave t ( ! solid4 ,a m beautiful in/ance ( repres5tative measurem5t1 dep5d+ imm$iately ^u ! pr9ciple ( inf]5ce1 c\ld n be f\nd4#bi #bi ,brew/]1 99,treatise on ,new ,philosophical ,in/rum5ts991 p4 #bgc4 ,conc]n+ ?is me?od see also ,:ewell1 99,philosophy ( ! ,inductive ,sci5ces991 vol4 ii4 p4 #cee2 ,toml9son1 99,philosophical ,magaz9e991 ,f\r? ,s]ies1 vol4 xl4 p4 #cbh2 ,tyndall1 9 ,y\mans' 99,mod]n ,culture991 p4 #af4 ,?r\gh\t ! v>i\s logical processes :i* we are ab\t to consid]--,d$uction1 ,induction1 ,g5]alisation1 ,analogy1 ,classification1 ,quantitative ,reason+--we %all f9d ! "o same pr9ciple op]at+ 9 a m or less disguis$ =m4 99,d$uction & ,induction499 ,! processes ( inf]5ce always dep5d on ! "o same pr9ciple ( sub/itution2 b !y may nev]!less be di/+ui%$ accord+ z ! results are inductive or d$uctive4 ,z g5]ally /at$1 d$uction consi/s 9 pass+ f m g5]al to less g5]al tru?s2 induction is ! contr>y process f less to m g5]al tru?s4 ,we may h[ev] describe ! diff]5ce 9 ano!r mann]4 ,9 d$uction we are engag$ 9 develop+ ! consequ5ces ( a law4 ,we le>n ! mean+1 cont5ts1 results or inf]5ces1 :i* atta* to any giv5 proposition4 ,induction is ! exactly inv]se process4 ,giv5 c]ta9 results or consequ5ces1 we are requir$ to discov] ! g5]al law f :i* !y fl[4 ,9 a c]ta9 s5se all k is inductive4 ,we c only le>n ! laws & relations ( ?+s 9 nature by obs]v+ ^? ?+s4 ,b ! k ga9$ f ! s5ses is k only ( p>ticul> facts1 & we require "s process ( reason+ by :i* we may collect out ( ! facts ! laws obey$ by !m4 ,exp]i5ce gives u ! mat]ials ( k3 induction dige/s ^? mat]ials1 & yields u g5]al k4 ,:5 we possess su* k1 9 ! =m ( g5]al propositions & natural laws1 we c usefully apply ! rev]se process ( d$uction to asc]ta9 ! exact in=mation requir$ at any mom5t4 ,9 its ultimate f\ndation1 !n1 all k is inductive--9 ! s5se t x is d]iv$ by a c]ta9 inductive reason+ f ! facts ( exp]i5ce4 ,x is nev]!less true1--& ?is is a po9t to :i* insuffici5t att5tion has be5 paid1 t all reason+ is f\nd$ on ! pr9ciples ( d$uction4 ,i call 9 "q ! exi/5ce ( any me?od ( reason+ :i* c be c>ri$ on )\t a k ( d$uctive processes4 ,i %all endeav\r to %[ t 99induction is really ! inv]se process ( d$uction994 ,!re is no mode ( asc]ta9+ ! laws :i* are obey$ 9 c]ta9 ph5om5a1 unless we h ! p[] ( det]m9+ :at results w\ld foll[ f a giv5 law4 ,j z ! process ( division necessitates a prior k ( multiplication1 or ! integral calculus re/s ^u ! obs]vation & remembrance ( ! results ( ! diff]5tial calculus1 s induction requires a prior k ( d$uction4 ,an inv]se process is ! undo+ ( ! direct process4 ,a p]son :o ent]s a maze mu/ ei!r tru/ to *ance to lead him out aga91 or he mu/ c>efully notice ! road by :i* he ent]$4 ,! facts furni%$ to u by exp]i5ce are a maze ( p>ticul> results2 we might by *ance obs]ve 9 !m ! fulfilm5t ( a law1 b ?is is sc>cely possible1 unless we ?or\ghly le>n ! effects :i* w\ld atta* to any p>ticul> law4 ,accord+ly1 ! importance ( d$uctive reason+ is d\bly supreme4 ,ev5 :5 we ga9 ! results ( induction !y w\ld be ( no use unless we c\ld d$uctively apply !m4 ,b be=e we c ga9 !m at all we mu/ und]/& d$uction1 s9ce x is ! inv]sion ( d$uction :i* con/itutes induction4 ,our fir/ task 9 ?is "w1 !n1 mu/ be to trace out fully ! nature ( id5tity 9 all its =ms ( occurr5ce4 ,hav+ giv5 any s]ies ( propositions we mu/ be prep>$ to develop d$uctively ! :ole mean+ embodi$ 9 !m1 & ! :ole ( ! consequ5ces :i* fl[ f !m4 99,symbolic ,expression ( ,logical ,inf]5ce499 ,9 develop+ ! results ( ! ,pr9ciple ( ,inf]5ce we require to use an appropriate language ( signs4 ,x w\ld inde$ be q possible to expla9 ! processes ( reason+ by ! use ( words f\nd 9 ! diction>y4 ,special examples ( reason+1 too1 may seem to be m readily appreh5d$ ?an g5]al symbolic =ms4 ,b x has be5 %[n 9 ! ma!matical sci5ces t ! atta9m5t ( tru? dep5ds greatly ^u ! inv5tion ( a cle>1 brief1 & appropriate sy/em ( symbols4 ,n only is su* a language conv5i5t1 b x is almo/ ess5tial to ! expression ( ^? g5]al tru?s :i* are ! v s\l ( sci5ce4 ,to appreh5d ! tru? ( special cases ( inf]5ce does n con/itute logic2 we mu/ appreh5d !m z cases ( m g5]al tru?s4 ,! object ( all sci5ce is ! sep>ation ( :at is common & g5]al f :at is accid5tal & diff]5t4 ,9 a sy/em ( logic1 if any:]e1 we %\ld e/eem ?is g5]ality1 & /rive to exhibit cle>ly :at is simil> 9 v div]se cases4 ,h5ce ! great value ( 99g5]al symbols99 by :i* we c repres5t ! =m ( a reason+ process1 dis5tangl$ f any consid]ation ( ! special subject to :i* x is appli$4 ,! signs requir$ 9 logic are ( a v simple k9d4 ,z sam5ess or diff]5ce mu/ exi/ betwe5 two ?+s or notions1 we ne$ signs to indicate ! ?+s or notions comp>$1 & o!r signs to d5ote ! relations betwe5 !m4 ,we ne$1 !n1 7#a7 symbols = t]ms1 7#b7 a symbol = sam5ess1 7#c7 a symbol = diff]5ce1 & 7#d7 "o or two symbols to take ! place ( conjunctions4 ,ord9>y n\ns sub/antive1 su* z 99,iron991 99,metal991 99,electricity991 99,undulation991 might s]ve z t]ms1 b1 = ! reasons expla9$ above1 x is bett] to adopt blank lett]s1 devoid ( special signification1 su* z ,a1 ,b1 ,c1 c4 ,ea* lett] mu/ be und]/ood to repres5t a n\n1 &1 s f> z ! conditions ( ! argum5t all[1 99any n\n994 ,j z 9 ,algebra1 99x991 99y991 99z991 99p991 99q991 c4 are us$ = 99any quantities991 undet]m9$ or unkn[n1 except :5 ! special conditions ( ! problem are tak5 into acc\nt1 s w our lett]s /& = undet]m9$ or unkn[n ?+s4 ,^! lett]-t]ms w be us$ indiff]5tly = n\ns sub/antive & adjective4 ,betwe5 ^! two k9ds ( n\ns !re may p]haps be diff]5ces 9 a metaphysical or grammatical po9t ( view4 ,b grammatical usage sanctions ! conv]sion ( adjectives into sub/antives1 & 99vice v]s992 we may avail ourselves ( ?is latitude )\t 9 any way prejudg+ ! metaphysical difficulties :i* may be involv$4 ,"h1 z ?r\gh\t ?is "w1 ,i %all devote my att5tion to tru?s :i* ,i c exhibit 9 a cle> & =mal mann]1 believ+ t 9 ! pres5t condition ( logical sci5ce1 ?is c\rse w lead to great] advantage ?an discussion ^u ! metaphysical que/ions :i* may und]lie any "p ( ! subject4 ,e n\n or t]m d5otes an object1 & usually implies ! possession by t object ( c]ta9 qualities or circum/ances common to all ! objects d5ot$4 ,!re are c]ta9 t]ms1 h[ev]1 :i* imply ! abs5ce ( qualities or circum/ances atta*+ to o!r objects4 ,x w be conv5i5t to employ a special mode ( indicat+ ^! 99negative t]ms991 z !y are call$4 ,if ! g5]al "n ,a d5otes an object or class ( objects possess+ c]ta9 def9$ qualities1 !n ! t]m ,n ,a w d5ote any object :i* does n possess ! :ole ( ^? qualities2 9 %ort1 ,n ,a is ! sign = any?+ :i* diff]s f ,a 9 reg>d to any "o or m ( ! assign$ qualities4 ,if ,a d5ote 8transp>5t object10 ,n ,a w d5ote 8n transp>5t object40 ,brevity & facility ( expression are ( no slight importance 9 a sy/em ( notation1 & x w !re=e be desirable to sub/itute = ! negative t]m ,n ,a a brief] symbol4 ,de ,morgan repres5t$ negative t]ms by small ,roman lett]s1 or sometimes by small italic lett]s2#cj z ! latt] seem to be highly conv5i5t1 ,i %all use 99a991 99b991 99c991 444 99p991 99q991 c41 z ! negative t]ms correspond+ to ,a1 ,b1 ,c1 444 ,p1 ,q1 c4 ,?us if ,a means 8fluid10 99a99 w mean 8n fluid40 #cj 99,=mal ,logic991 p4 #ch4 99,expression ( ,id5tity & ,diff]5ce499 ,to d5ote ! relation ( sam5ess or id5tity ,i unhesitat+ly adopt ! sign 1 s long us$ by ma!maticians to d5ote equality4 ,?is symbol 0 orig9ally appropriat$ by ,rob]t ,recorde 9 8 99,:et/one ( ,wit991 to avoid ! t$i\s repetition ( ! words 8is equal to20 & he *ose a pair ( p>allel l9es1 because no two ?+s c be m equal4#ca ,! mean+ ( ! sign has h[ev] be5 gradually ext5d$ beyond t ( equality ( quantities2 ma!maticians h !mselves us$ x to indicate equival5ce ( op]ations4 ,! =ce ( analogy has be5 s great t writ]s 9 mo/ o!r bran*es ( sci5ce h employ$ ! same sign4 ,! philologi/ uses x to indicate ! equival5ce ( mean+ ( words3 *emi/s adopt x to signify id5tity 9 k9d & equality 9 weight ( ! elem5ts :i* =m two diff]5t comp\nds4 ,n a few logicians1 = in/ance ,lamb]t1 ,drobits*1 ,george ,b5?am1#cb ,boole1#cc h employ$ x z ! copula ( propositions4 ,de ,morgan decl9$ to use x = ?is purpose1 b /ill fur!r ext5d$ its mean+ s z to include ! equival5ce ( a proposition ) ! premises f :i* x c be inf]r$2#cd & ,h]b]t ,sp5c] has appli$ x 9 a l mann]4#ce #ca ,hallam's 99,lit]ature ( ,europe991 ,fir/ ,ed41 vol4 ii4 p4 #ddd4 #cb 99,outl9e ( a ,new ,sy/em ( ,logic991 ,london1 #ahbg1 pp4 #acc1 c4 #cc 99,an ,inve/igation ( ! ,laws ( ,?\ght991 pp4 #bg1 c4 #cd 99,=mal ,logic991 pp4 #hb1 #ajf4 ,9 8 lat] "w1 99,! ,syllabus ( a ,new ,sy/em ( ,logic991 he discont9u$ ! use ( ! sign4 #ce 99,pr9ciples ( ,psy*ology991 ,second ,ed41 vol4 ii4 pp4 #ed1 #ee4 ,_m p]sons may ?9k t ! *oice ( a symbol is a matt] ( slight importance or ( m]e conv5i5ce2 b ,i hold t ! common use ( ?is sign 9 s _m diff]5t mean+s is really f\nd$ ^u a g5]alisation ( ! wide/ "* & ( ! greate/ importance--"o inde$ :i* x is a pr9cipal purpose ( ?is "w to expla94 ,! employm5t ( ! same sign 9 diff]5t cases w\ld be unphilosophical unless !re 7 "s real analogy betwe5 its div]se mean+s4 ,if su* analogy exi/s1 x is n only all[able1 b highly desirable & ev5 imp]ative1 to use ! symbol ( equival5ce ) a g5]ality ( mean+ correspond+ to ! g5]ality ( ! pr9ciples involv$4 ,accord+ly ,de ,morgan's refusal to use ! symbol 9 logical propositions indicat$ 8 op9ion t !re 0 a want ( analogy betwe5 logical propositions & ma!matical equations4 ,i use ! sign because ,i hold ! contr>y op9ion4 ,i conceive t ! sign z commonly employ$1 always d5otes "s =m or degree ( sam5ess1 & ! p>ticul> =m is usually indicat$ by ! nature ( ! t]ms jo9$ by x4 ,?us 8#f1gbj p\nds #c tons0 is evid5tly an equation ( quantities4 ,! =mula - - expresses ! equival5ce ( op]ations4 8,exog5s ,dicotyl$ons0 is a logical id5tity express+ a pr(\nd tru? conc]n+ ! "* & orig9 ( a mo/ important gr\p ( plants4 ,we h great ne$ 9 logic ( a di/9ct sign = ! copula1 because ! little v]b 99is99 7or 99are9971 hi!rto us$ bo? 9 logic & ord9>y disc\rse1 is ?or\ghly ambigu\s4 ,x sometimes d5otes id5tity1 z 9 8,/4 ,paul's is ! 99*ef-d'uvre99 ( ,sir ,*ri/oph] ,wr520 b x m commonly indicates inclusion ( class )9 class1 or p>tial id5tity1 z 9 8,bi%ops are memb]s ( ! ,h\se ( ,lords40 ,?is latt] relation involves id5tity1 b requires c>eful discrim9ation f simple id5tity1 z w be %[n fur!r on4 ,:5 ) ?is sign ( equality we jo9 two n\ns or logical t]ms1 z 9 ,hydrog5 ,! lea/ d5se elem5t1 we signify t ! object or gr\p ( objects d5ot$ by "o t]m is id5tical ) t d5ot$ by ! o!r1 9 ev]y?+ except ! names4 ,! g5]al =mula ,a ,b mu/ be tak5 to mean t ,a & ,b are symbols = ! same object or gr\p ( objects4 ,?is id5tity may sometimes arise f ! m]e imposition ( names1 b x may also arise f ! deepe/ laws ( ! con/itution ( nature2 z :5 we say ,gravitat+ matt] ,matt] possess+ in]tia1 ,exog5\s plants ,dicotyl$on\s plants1 ,plagih$ral qu>tz cry/als ,qu>tz cry/als caus+ ! plane ( pol>isation ( light to rotate4 ,we %all ne$ c>efully to di/+ui% betwe5 relations ( t]ms :i* c be modifi$ at our own w & ^? :i* are fix$ z express+ ! laws ( nature2 b at pres5t we are consid]+ only ! mode ( expression :i* may be ! same 9 ei!r case4 ,sometimes1 b mu* less frequ5tly1 we require a symbol to indicate diff]5ce or ! abs5ce ( complete sam5ess4 ,= ?is purpose we may g5]alise 9 l mann] ! symbol 1 :i* 0 introduc$ by ,wallis to signify diff]5ce betwe5 quantities4 ,! g5]al =mula ,b ,c d5otes t ,b & ,c are ! names ( two objects or gr\ps :i* are n id5tical ) ea* o!r4 ,?us we may say ,acrog5s ,fl[]+ plants4 ,sn[don ,! highe/ m\nta9 9 ,great ,brita94 ,i %all also occasionally use ! sign to signify 9 ! mo/ g5]al mann] ! exi/5ce ( any relation betwe5 ! two t]ms connect$ by x4 ,?us might mean n only ! relations ( equality or inequality1 sam5ess or diff]5ce1 b any special relation ( "t1 place1 size1 causation1 c4 9 :i* "o ?+ may /& to ano!r4 ,by ,a ,b ,i mean1 !n1 any two objects ( ?\ght relat$ to ea* o!r 9 any conceivable mann]4 99,g5]al ,=mula ( ,logical ,inf]5ce499 ,! "o supreme rule ( inf]5ce consi/s1 z ,i h said1 9 ! direction to affirm ( any?+ :atev] is kn[n ( its l1 equal or equival5t4 ,! 99,sub/itution ( ,simil>s99 is a phrase :i* seems aptly to express ! capacity ( mutual replacem5t exi/+ 9 any two objects :i* are l or equival5t to a suffici5t degree4 ,x is matt] = fur!r inve/igation to asc]ta9 :5 & = :at purposes a degree ( simil>ity less ?an complete id5tity is suffici5t to w>rant sub/itution4 ,= ! pres5t we ?9k only ( ! exact sam5ess express$ 9 ! =m ,a ,b4 ,n[ if we take ! lett] ,c to d5ote any ?ird conceivable object1 & use ! sign 9 its /at$ mean+ ( 99indef9ite relation991 !n ! g5]al =mula ( all inf]5ce may be ?us exhibit$3-- ,f ,a ,b ,c we may inf] ,a ,c or1 9 words--99,9 :atev] relation a ?+ /&s to a second ?+1 9 ! same relation x /&s to ! l or equival5t ( t second ?+499 ,! id5tity betwe5 ,a & ,b all[s u indiff]5tly to place ,a :]e ,b 01 or ,b :]e ,a 02 & !re is no limit to ! v>iety ( special mean+s :i* we c be/[ ^u ! signs us$ 9 ?is =mula consi/5tly ) its tru?4 ,?us if we fir/ specify only ! mean+ ( ! sign 1 we may say t if 99,c is ! weight ( ,b991 !n 99,c is also ! weight ( ,a994 ,simil>ly ,if ,c is ! fa!r ( ,b1 ,c is ! fa!r ( ,a2 ,if ,c is a fragm5t ( ,b1 ,c is a fragm5t ( ,a2 ,if ,c is a quality ( ,b1 ,c is a quality ( ,a2 ,if ,c is a species ( ,b1 ,c is a species ( ,a2 ,if ,c is ! equal ( ,b1 ,c is ! equal ( ,a2 & s on 99ad inf9itum994 ,we may also end[ ) special mean+s ! lett]-t]ms ,a1 ,b1 & ,c1 & ! process ( inf]5ce w nev] be false4 ,?us let ! sign mean 8is height (10 & let ,a ,sn[don1 ,b ,highe/ m\nta9 9 ,engl& or ,wales1 ,c #c1eij feet2 !n x obvi\sly foll[s s9ce 8#c1eij feet is ! height ( ,sn[don10 & 8,sn[don ! highe/ m\nta9 9 ,engl& or ,wales10 t1 8#c1eij feet is ! height ( ! highe/ m\nta9 9 ,engl& or ,wales40 ,"o result ( ?is g5]al process ( inf]5ce is t we may 9 any aggregate or complex :ole replace any "p by its equival5t )\t alt]+ ! :ole4 ,to alt] is to make a diff]5ce2 b if 9 replac+ a "p ,i make no diff]5ce1 !re is no alt]ation ( ! :ole4 ,_m inf]5ces :i* h be5 v imp]fectly includ$ 9 logical =mulas at once foll[4 ,i rememb] ! late ,pr(4 ,de ,morgan rem>k+ t all ,ari/otle's logic c\ld n prove t 8,because a horse is an animal1 ! head ( a horse is ! head ( an animal40 ,i conceive t ?is am\nts m]ely to replac+ 9 ! complete notion 99head ( a horse991 ! t]m 8horse10 by its equival5t 99"s animal99 or 99an animal994 ,simil>ly1 s9ce ,! ,"l ,*ancellor ,! ,speak] ( ! ,h\se ( ,lords1 x foll[s t ,! dea? ( ! ,"l ,*ancellor ,! dea? ( ! ,speak] ( ! ,h\se ( ,lords2 & any ev5t1 circum/ance or ?+1 :i* /&s 9 a c]ta9 relation to ! "o w /& 9 l relation to ! o!r4 ,milton reasons 9 ?is way :5 he says1 9 8 ,areopagitica1 8,:o kills a man1 kills a reasonable creature1 ,god's image40 ,if we may suppose him to mean ,god's image man "s reasonable creature1 x foll[s t 8,! kill] ( a man is ! kill] ( "s reasonable creature10 & also 8,! kill] ( ,god's image40 ,?is replacem5t ( equival5ts may be repeat$ ov] & ov] aga9 to any ext5t4 ,?us if 99p]son99 is id5tical 9 mean+ ) 99individual991 x foll[s t ,meet+ ( p]sons meet+ ( individuals2 & if 99assemblage99 99meet+991 we may make a new replacem5t & %[ t ,meet+ ( p]sons assemblage ( individuals4 ,we may 9 fact f\nd ^u ?is pr9ciple ( sub/itution a mo/ g5]al axiom 9 ! foll[+ t]ms#cf3-- #cf 99,pure ,logic1 or ! ,logic ( ,quality991 p4 #ad4 99,same p>ts samely relat$ make same :oles499 ,if1 = in/ance1 exactly simil> bricks & o!r mat]ials be us$ to build two h\ses1 & !y be simil>ly plac$ 9 ea* h\se1 ! two h\ses mu/ be simil>4 ,!re are millions ( cells 9 a human body1 b if ea* cell ( "o p]son 7 repres5t$ by an exactly simil> cell simil>ly plac$ 9 ano!r body1 ! two p]sons w\ld be undi/+ui%able1 & w\ld be only 99num]ically99 diff]5t4 ,x is ^u ?is pr9ciple1 z we %all see1 t all accurate processes ( measurem5t dep5d4 ,if = a weight 9 a scale ( a balance we sub/itute ano!r weight1 & ! equilibrium rema9s entirely un*ang$1 !n ! weights mu/ be exactly equal4 ,! g5]al te/ ( equality is sub/itution4 ,objects are equally bright :5 on replac+ "o by ! o!r ! eye p]ceives no diff]5ce4 ,objects are equal 9 dim5sions :5 te/$ by ! same gauge !y fit 9 ! same mann]4 ,g5]ally speak+1 two objects are alike s f> z :5 sub/itut$ "o = ano!r no alt]ation is produc$1 & 99vice v]s99 :5 alike no alt]ation is produc$ by ! sub/itution4 99,! ,propagat+ ,p[] ( ,simil>ity499 ,! relation ( simil>ity 9 all its degrees is reciprocal4 ,s f> z ?+s are alike1 ei!r may be sub/itut$ = ! o!r2 & ?is may p]haps be consid]$ ! v mean+ ( ! relation4 ,b x is well wor? notice t !re is 9 simil>ity a peculi> p[] ( ext5d+ itself among all ! ?+s :i* are simil>4 ,to r5d] a numb] ( ?+s simil> to ea* o!r we ne$ only r5d] !m simil> to "o /&>d object4 ,ea* co9 /ruck f a pair ( dies n only resembles ! matrix or orig9al patt]n f :i* ! dies 7 /ruck1 b resembles e o!r co9 manufactur$ f ! same orig9al patt]n4 ,among a million su* co9s !re are n less ?an #dii1iii1ejj1jjj 99pairs ( co9s99 resembl+ ea* o!r4 ,simil>s to ! same are simil>s to all4 ,x is "o great advantage ( pr9t+ t all copies ( a docum5t /ruck f ! same type are necess>ily id5tical ea* ) ea*1 & :atev] is true ( "o copy w be true ( e copy4 ,simil>ly1 if fifty r[s ( pipes 9 an organ be tun$ 9 p]fect unison ) "o r[1 usually ! ,pr9cipal1 !y mu/ be 9 unison ) ea* o!r4 ,simil>ity c also reproduce or propagate itself 99ad inf9itum993 = if a numb] ( tun+-=ks be adju/$ 9 p]fect unison ) "o /&>d =k1 all in/rum5ts tun$ to any "o =k w agree ) any in/rum5t tun$ to any o!r =k4 ,/&>d measures ( l5g?1 capacity1 weight1 or any o!r measurable quality1 are propagat$ 9 ! same mann]4 ,s f> z copies ( ! orig9al /&>d1 or copies ( copies1 or copies aga9 ( ^? copies1 are accurately execut$1 !y mu/ all agree ea* ) e o!r4 ,x is ! capability ( mutual sub/itution :i* gives su* great value to ! mod]n me?ods ( me*anical con/ruction1 accord+ to :i* all ! p>ts ( a ma*9e are exact facsimiles ( a fix$ patt]n4 ,! rifles us$ 9 ! ,briti% army are con/ruct$ on ! ,am]ican int]*angeable sy/em1 s t any "p ( any rifle c be sub/itut$ = ! same "p ( ano!r4 ,a bullet fitt+ "o rifle w fit all o!rs ( ! same bore4 ,sir ,j4 ,:itwor? has ext5d$ ! same sy/em to ! screws & screw-bolts us$ 9 connect+ toge!r ! p>ts ( ma*9es1 by e/abli%+ a s]ies ( /&>d screws4 99,anticipations ( ! ,pr9ciple ( ,sub/itution499 ,9 su* a subject z logic x is h>dly possible to put =? any op9ions :i* h n be5 9 "s degree previ\sly ent]ta9$4 ,! g]m at lea/ ( e doctr9e w be f\nd 9 e>li] writ]s1 & novelty mu/ arise *iefly 9 ! mode ( h>monis+ & develop+ ideas4 ,:5 ,i fir/ employ$ ! process & "n ( 99sub/itution99 9 logic1#cg ,i 0 l$ to d s f analogy ) ! famili> ma!matical process ( sub/itut+ = a symbol its value z giv5 9 an equation4 ,9 writ+ my fir/ logical essay ,i _h a mo/ imp]fect conception ( ! importance & g5]ality ( ! process1 & ,i describ$1 z if !y 7 ( equal importance1 a numb] ( o!r laws :i* n[ seem to be b p>ticul> cases ( ! "o g5]al rule ( sub/itution4 #cg 99,pure ,logic991 pp4 #ah1 #ai4 ,my second essay1 8,! ,sub/itution ( ,simil>s10 0 writt5 %ortly aft] ,i _h become aw>e ( ! great simplification :i* may be effect$ by a prop] application ( ! pr9ciple ( sub/itution4 ,i 0 n !n acqua9t$ ) ! fact t ! ,g]man logician ,b5eke _h employ$ ! pr9ciple ( sub/itution1 & _h us$ ! ^w itself 9 =m+ a !ory ( ! syllogism4 ,my imp]fect acqua9tance ) ! ,g]man language _h prev5t$ me f acquir+ a complete k ( ,b5eke's views2 b !re is no d\bt t ,pr(essor ,l9dsay is "r 9 say+ t he1 & probably o!r logicians1 7 9 "s degree famili> ) ! pr9ciple4#ch ,ev5 ,ari/otle's dictum may be reg>d$ z an imp]fect /atem5t ( ! pr9ciple ( sub/itution2 &1 z ,i h po9t$ out1 we h only to modify t dictum 9 accordance ) ! quantification ( ! pr$icate 9 ord] to arrive at ! complete process ( sub/itution4#ci ,! ,port-,royal logicians appe> to h ent]ta9$ ne>ly equival5t views1 = !y consid]$ t all moods ( ! syllogism might be r$uc$ "u "o g5]al pr9ciple4#dj ,( two premises !y reg>d "o z ! 99conta9+ proposition99 7propositio cont95s71 & ! o!r z ! 99applicative proposition994 ,! latt] proposition mu/ always be affirmative1 & repres5ts t by :i* a sub/itution is made2 ! =m] may or may n be negative1 & is t 9 :i* a sub/itution is effect$4 ,!y also %[ t ?is me?od w embrace c]ta9 cases ( complex reason+ :i* _h no place 9 ! ,ari/otelian syllogism4 ,_! views probably con/itute ! greate/ improvem5t 9 logical doctr9e made up to t "t s9ce ! days ( ,ari/otle4 ,b a true re=m 9 logic mu/ consi/1 n 9 expla9+ ! syllogism 9 "o way or ano!r1 b 9 do+ away ) all ! n>r[ re/rictions ( ! ,ari/otelian sy/em1 & 9 %[+ t !re exi/s an inf9ite v>iety ( logical argum5ts imm$iately d$ucible f ! pr9ciple ( sub/itution ( :i* ! anci5t syllogism =ms b a small & n ev5 ! mo/ important "p4 #ch ,ueb]weg's 99,sy/em ( ,logic991 transl4 by ,l9dsay1 pp4 #ddb-ddf1 #ega1 #egb4 ,! anticipations ( ! pr9ciple ( sub/itution to be f\nd 9 ! works ( ,leibnitz1 ,reus*1 & p]haps o!r ,g]man logicians1 w be notic$ 9 ! preface to ?is second edition4 #ci 99,sub/itution ( ,simil>s99 7#ahfi71 p4 #i4 #dj 99,port-,royal ,logic991 transl4 by ,sp5c] ,baynes1 pp4 #bab-bai4 ,"p ,,iii4 *ap4 x4 & xi4 99,! ,logic ( ,relatives499 ,!re is a difficult & important bran* ( logic :i* may be call$ ! ,logic ( ,relatives4 ,if ,i argue1 = in/ance1 t because ,daniel ,b]n\lli 0 ! son ( ,john1 & ,john ! bro!r ( ,james1 !re=e ,daniel 0 ! nephew ( ,james1 x is n possible to prove ?is conclusion by any simple logical process4 ,we require at any rate to assume t ! son ( a bro!r is a nephew4 ,a simple logical relation is t :i* exi/s betwe5 prop]ties & circum/ances ( ! same object or class4 ,b objects & classes ( objects may also be relat$ accord+ to all ! prop]ties ( "t & space4 ,i believe x may be %[n1 inde$1 t :]e an inf]5ce conc]n+ su* relations is drawn1 a process ( sub/itution is really employ$ & an id5tity mu/ exi/2 b ,i w n und]take to prove ! ass]tion 9 ?is "w4 ,! relations ( "t & space are logical relations ( a complicat$ "* dem&+ mu* ab/ract & difficult inve/igation4 ,! subject has be5 treat$ ) su* great ability by ,peirce1#da ,de ,morgan1#db ,ellis1#dc & ,h>ley1 t ,i w n 9 ! pres5t "w attempt any review ( _! writ+s1 b m]ely ref] ! read] to ! publications 9 :i* !y are to be f\nd4 #da 99,description ( a ,notation = ! ,logic ( ,relatives1 result+ f an ,amplification ( ! ,conceptions ( ,boole's ,calculus ( ,logic499 ,by ,c4 ,s4 ,peirce4 99,memoirs ( ! ,am]ican ,academy991 vol4 ix4 ,cambridge1 ,u4,s41 #ahgj4 #db 99,on ! ,syllogism ,no ,,iv41 & on ! ,logic ( ,relations499 ,by ,augu/us ,de ,morgan4 99,transactions ( ! ,cambridge ,philosophical ,society991 vol4 x4 "p ii41 #ahfj4 #dc 99,obs]vations on ,boole's ,laws ( ,?\ght499 ,by ! late ,r4 ,leslie ,ellis2 communicat$ by ! ,rev4 ,rob]t ,h>ley1 ,f4,r4,s4 99,report ( ! ,briti% ,association991 #ahgj4 99,report ( ,sections991 p4 #ab4 ,also1 99,on ,boole's ,laws ( ,?\ght994 ,by ! ,rev4 ,rob]t ,h>ley1 ,f4,r4,s41 99ibid499 p4 #ad4 ,,*apt] ,,ii4 ,,t]ms4 ,e proposition expresses ! resemblance or diff]5ce ( ! ?+s d5ot$ by its t]ms4 ,z inf]5ce treats ( ! relation betwe5 two or m propositions1 s a proposition expresses a relation betwe5 two or m t]ms4 ,9 ! portion ( ?is "w :i* treats ( d$uction x w be conv5i5t to foll[ ! usual ord] ( exposition4 ,we w consid] 9 succession ! v>i\s k9ds ( t]ms1 propositions1 & argum5ts1 & we comm5ce 9 ?is *apt] ) t]ms4 ,! simple/ & mo/ palpable mean+ :i* c belong to a t]m consi/s ( "s s+le mat]ial object1 su* z ,we/m9/] ,abbey1 ,/oneh5ge1 ! ,sun1 ,sirius1 c4 ,x is probable t 9 e>ly /ages ( intellect only concrete & palpable ?+s are ! objects ( ?\ght4 ,! y\nge/ *ild kn[s ! diff]5ce betwe5 a hot & a cold body4 ,! dog c recognise 8 ma/] among a hundr$ o!r p]sons1 & animals ( mu* l[] intellig5ce "k & discrim9ate _! haunts4 ,9 all su* acts !re is judgm5t conc]n+ ! lik5ess ( physical objects1 b !re is little or no p[] ( analys+ ea* object & reg>d+ x z a gr\p ( qualities4 ,! dignity ( intellect beg9s ) ! p[] ( sep>at+ po9ts ( agreem5t f ^? ( diff]5ce4 ,comp>ison ( two objects may lead u to p]ceive t !y are at once l & unlike4 ,two fragm5ts ( rock may diff] entirely 9 outw>d =m1 yet !y may h ! same col\r1 h>dness1 & texture4 ,fl[]s :i* agree 9 col\r may diff] 9 od\r4 ,! m9d le>ns to reg>d ea* object z an aggregate ( qualities1 & acquires ! p[] ( dwell+ at w ^u "o or o!r ( ^? qualities to ! exclusion ( ! re/4 ,logical ab/raction1 9 %ort1 comes into play1 & ! m9d becomes capable ( reason+1 n m]ely ab\t objects :i* are physically complete & concrete1 b ab\t ?+s :i* may be ?\ght ( sep>ately 9 ! m9d ?\gh !y exi/ n sep>ately 9 nature4 ,we c ?9k ( ! h>dness ( a rock1 or ! col\r ( a fl[]1 & ?us produce ab/ract notions1 d5ot$ by ab/ract t]ms1 :i* w =m a subject = fur!r consid]ation4 ,at ! same "t arise g5]al notions & classes ( objects4 ,we _c fail to obs]ve t ! quality 99h>dness99 exi/s 9 _m objects1 = in/ance 9 _m fragm5ts ( rock2 m5tally jo9+ ^! toge!r1 we create ! class 99h>d object991 :i* w include1 n only ! actual objects exam9$1 b all o!rs :i* may happ5 to agree ) !m1 z !y agree ) ea* o!r4 ,z our s5ses _c possibly report to u all ! cont5ts ( space1 we _c usually set any limits to ! numb] ( objects :i* may fall into any su* class4 ,at ?is po9t we beg9 to p]ceive ! p[] & g5]ality ( ?\ght1 :i* enables u 9 a s+le act to treat ( indef9itely or ev5 inf9itely num]\s objects4 ,we c safely ass]t t :atev] is true ( any "o object com+ "u a class is true ( any ( ! o!r objects s f> z !y possess ! common qualities impli$ 9 _! belong+ to ! class4 ,we mu/ n place a ?+ 9 a class unless we are prep>$ to believe ( x all t is believ$ ( ! class 9 g5]al2 b x rema9s a matt] ( important consid]ation to decide h[ f> & 9 :at mann] we c safely und]take ?us to assign ! place ( objects 9 t g5]al sy/em ( classification :i* con/itutes ! body ( sci5ce4 99,tw(old ,mean+ ( ,g5]al ,names499 ,etymologically ! 99mean+99 ( a "n is t :i* we are caus$ to ?9k ( :5 ! "n is us$4 ,n[ e g5]al "n causes u to ?9k ( "s "o or m ( ! objects belong+ to a class2 x may also cause u to ?9k ( ! common qualities possess$ by ^? objects4 ,a "n is said to 99d5ote99 ! object ( ?\ght to :i* x may be appli$2 x 99implies99 at ! same "t ! possession ( c]ta9 qualities or circum/ances4 ,! objects d5ot$ =m ! 99ext5t99 ( mean+ ( ! t]m2 ! qualities impli$ =m ! 99int5t99 ( mean+4 ,cry/al is ! "n ( any sub/ance ( :i* ! molecules are arrang$ 9 a regul> geometrical mann]4 ,! sub/ances or objects 9 "q =m ! ext5t ( mean+2 ! circum/ance ( hav+ ! molecules s arrang$ =ms ! int5t ( mean+4 ,:5 we comp>e g5]al t]ms toge!r1 x may (t5 be f\nd t ! mean+ ( "o is includ$ 9 ! mean+ ( ano!r4 ,?us all 99cry/als99 are includ$ among 99mat]ial sub/ances991 & all 99opaque cry/als99 are includ$ among 99cry/als992 "h ! inclusion is 9 ext5sion4 ,we may also h inclusion ( mean+ 9 reg>d to int5sion4 ,=1 z all cry/als are mat]ial sub/ances1 ! qualities impli$ by ! t]m mat]ial sub/ance mu/ be among ^? impli$ by cry/al4 ,aga91 x is obvi\s t :ile 9 ext5sion ( mean+ opaque cry/als are b a "p ( cry/als1 9 int5sion ( mean+ cry/al is b "p ( opaque cry/al4 ,we increase ! int5t ( mean+ ( a t]m by jo9+ to x adjectives1 or phrases equival5t to adjectives1 & ! removal ( su* adjectives ( c\rse decreases ! int5sive mean+4 ,n[1 conc]n+ su* *anges ( mean+1 ! foll[+ all-important law holds univ]sally true3--99,:5 ! int5t ( mean+ ( a t]m is increas$ ! ext5t is decreas$2 &99 vice v]s1 99:5 ! ext5t is increas$ ! int5t is decreas$994 ,9 %ort1 z "o is increas$ ! o!r is decreas$4 ,?is law ref]s only to logical *anges4 ,! numb] ( /eam-eng9es 9 ! _w may be und]go+ a rapid increase )\t ! int5sive mean+ ( ! "n be+ alt]$4 ,! law w only be v]ifi$1 aga91 :5 !re is a real *ange 9 ! int5sive mean+1 & an adjective may (t5 be jo9$ to a n\n )\t mak+ a *ange4 99,elem5t>y metal99 is id5tical ) 99metal992 99mortal man99 ) 99man992 x be+ a 99prop]ty99 ( all metals to be elem5ts1 & ( all m5 to be mortals4 ,!re is no limit to ! am\nt ( mean+ :i* a t]m may h4 ,a t]m may d5ote "o object1 or _m1 or an inf9ite numb]2 x may imply a s+le quality1 if su* !re be1 or a gr\p ( any numb] ( qualities1 & yet ! law connect+ ! ext5sion & int5sion w infallibly apply4 ,tak+ ! g5]al "n 99planet991 we increase its int5sion & decrease its ext5sion by prefix+ ! adjective 99ext]ior992 & if we fur!r add 99ne>e/ to ! e>?991 !re rema9s b "o planet1 99,m>s991 to :i* ! "n c !n be appli$4 ,s+ul> t]ms1 :i* d5ote a s+le individual only1 come "u ! same law ( mean+ z g5]al names4 ,!y may be reg>d$ z g5]al names ( :i* ! mean+ 9 ext5sion is r$uc$ to a m9imum4 ,logicians h errone\sly ass]t$1 z x seems to me1 t s+ul> t]ms are devoid ( mean+ 9 int5sion1 ! fact be+ t !y exce$ all o!r t]ms 9 t k9d ( mean+1 z ,i h else:]e tri$ to %[4#dd #dd ,jevons' 99,elem5t>y ,lessons 9 ,logic991 pp4 #da-dc2 99,pure ,logic991 p4 #f4 ,see also ,j4 ,s4 ,mill1 99,sy/em ( ,logic991 ,book ,i4 *ap4 ii4 section #e1 & ,%$d5's 99,elem5ts ( ,logic991 ,london1 #ahfd1 pp4 #ad1 c4 ,pr(essor ,rob]tson objects 799,m9d991 vol4 i4 p4 #baj7 t ,i confuse 99s+ul>99 & 99prop]99 names2 if s1 x is because ,i hold t ! same rem>ks apply to prop] names1 :i* d n seem to me to diff] logically f s+ul> names4 99,ab/ract ,t]ms499 ,comp>ison ( objects1 & analysis ( ! complex resemblances & diff]5ces :i* !y pres5t1 lead u to ! conception ( 99ab/ract qualities994 ,we le>n to ?9k ( "o object z n only diff]5t f ano!r1 b z diff]+ 9 "s p>ticul> po9t1 su* z col\r1 or weight1 or size4 ,we may !n conv]t po9ts ( agreem5t or diff]5ce into sep>ate objects ( ?\ght :i* we call qualities & d5ote by 99ab/ract t]ms994 ,?us ! t]m 99r$ness99 means some?+ 9 :i* a numb] ( objects agree z to col\r1 & 9 virtue ( :i* !y are call$ r$4 ,r$ness =ms1 9 fact1 ! int5sive mean+ ( ! t]m r$4 ,ab/ract t]ms are /rongly di/+ui%$ f g5]al t]ms by possess+ only "o k9d ( mean+2 = z !y d5ote qualities !re is no?+ :i* !y _c 9 addition imply4 ,! adjective 8r$0 is ! "n ( r$ objects1 b x implies ! possession by !m ( ! quality 99r$ness992 b ?is latt] t]m has "o s+le mean+--! quality alone4 ,?us x arises t ab/ract t]ms are incapable ( plurality4 ,r$ objects are num]ically di/9ct ea* f ea*1 & !re are multitudes ( su* objects2 b r$ness is a s+le quality :i* runs ?r\gh all ^? objects1 & is ! same 9 "o z x is 9 ano!r4 ,x is true t we may speak ( 99r$nesses991 mean+ diff]5t k9ds or t9ts ( r$ness1 j z we may speak ( 99col\rs991 mean+ diff]5t k9ds ( col\rs4 ,b 9 di/+ui%+ k9ds1 degrees1 or o!r diff]5ces1 we r5d] ! t]ms s f> concrete4 ,9 t !y are m]ely r$ !re is b a s+le nature 9 r$ objects1 & s f> z ?+s are m]ely col\r$1 col\r is a s+le indivisible quality4 ,r$ness1 s f> z x is r$ness m]ely1 is "o & ! same ev]y:]e1 & possesses absolute on5ess4 ,9 virtue ( ?is unity we acquire ! p[] ( treat+ all in/ances ( su* quality z we may treat any "o4 ,we possess1 9 %ort1 g5]al k4 99,sub/antial ,t]ms499 ,logicians appe> to h tak5 little notice ( a class ( t]ms :i* p>take 9 c]ta9 respects ( ! "* ( ab/ract t]ms & yet are und\bt$ly ! names ( concrete exi/+ ?+s4 ,^! t]ms are ! names ( sub/ances1 su* z gold1 c>bonate ( lime1 nitrog51 c4 ,we _c speak ( two golds1 tw5ty c>bonates ( lime1 or a hundr$ nitrog5s4 ,!re is no su* di/9ction betwe5 ! p>ts ( a uni=m sub/ance z w all[ ( a discrim9ation ( num]\s individuals4 ,! qualities ( col\r1 lu/re1 malleability1 d5sity1 c41 by :i* we recognise gold1 ext5d ?r\gh its sub/ance irrespective ( p>ticul> size or %ape4 ,s f> z a sub/ance is gold1 x is "o & ! same ev]y:]e2 s t t]ms ( ?is k9d1 :i* ,i propose to call 99sub/antial t]ms991 possess ! peculi> unity ( ab/ract t]ms4 ,yet !y are n ab/ract2 = gold is ( c\rse a tangible visible body1 entirely concrete1 & exi/+ indep5d5tly ( o!r bodies4 ,x is only :51 by actual me*anical division1 we break up ! uni=m :ole :i* =ms ! mean+ ( a sub/antial t]m1 t we introduce numb]4 99,piece ( gold99 is a t]m capable ( plurality2 = !re may be a great _m pieces discrim9at$ ei!r by _! v>i\s %apes & sizes1 or1 9 ! abs5ce ( su* m>ks1 by simultane\sly occupy+ diff]5t p>ts ( space4 ,9 sub/ance !y are "o2 z reg>ds ! prop]ties ( space !y are _m4#de ,we ne$ n fur!r pursue ?is "q1 :i* involves ! di/9ction betwe5 unity & plurality1 until we consid] ! pr9ciples ( numb] 9 a subsequ5t *apt]4 #de ,pr(essor ,rob]tson has criticis$ my introduction ( 8,sub/antial ,t]ms0 799,m9d991 vol4 i4 p4 #baj71 & objects1 p]haps correctly1 t ! di/9ction if valid is extra-logical4 ,i am incl9$ to ?9k1 h[ev]1 t ! doctr9e ( t]ms is1 /rictly speak+1 = ! mo/ "p extra-logical4 99,collective ,t]ms499 ,we mu/ cle>ly di/+ui% betwe5 ! 99collective99 & ! 99g5]al mean+s99 ( t]ms4 ,! same "n may be us$ to d5ote ! :ole body ( exi/+ objects ( a c]ta9 k9d1 or any "o ( ^? objects tak5 sep>ately4 8,man0 may mean ! aggregate ( exi/+ m51 :i* we sometimes describe z 99mank9d992 x is also ! g5]al "n apply+ to any man4 ,! vegetable k+dom is ! "n ( ! :ole aggregate ( 99plants991 b 8plant0 itself is a g5]al "n apply+ to any "o or o!r plant4 ,e mat]ial object may be conceiv$ z divisible into p>ts1 & is !re=e collective z reg>ds ^? p>ts4 ,! animal body is made up ( cells & fibres1 a cry/al ( molecules2 :]ev] physical division1 or z x has be5 call$ 99p>tition991 is possible1 !re we deal 9 reality ) a collective :ole4 ,?us ! great] numb] ( g5]al t]ms are at ! same "t collective z reg>ds ea* individual :ole :i* !y d5ote4 ,x ne$ h>dly be po9t$ out t we mu/ n inf] ( a collective :ole :at we "k only ( ! p>ts1 nor ( ! p>ts :at we "k only ( ! :ole4 ,! relation ( :ole & "p is n "o ( id5tity1 & does n all[ ( sub/itution4 ,!re may nev]!less be qualities :i* are true alike ( ! :ole & ( its p>ts4 ,a numb] ( organ-pipes tun$ 9 unison produce an aggregate ( s\nd :i* is ( exactly ! same pit* z ea* sep>ate s\nd4 ,9 ! case ( sub/antial t]ms1 c]ta9 qualities may be pres5t equally 9 ea* m9ute/ "p z 9 ! :ole4 ,! *emical nature ( ! l>ge/ mass ( pure c>bonate ( lime is ! same z ! nature ( ! smalle/ p>ticle4 ,9 ! case ( ab/ract t]ms1 aga91 we _c draw a di/9ction betwe5 :ole & "p2 :at is true ( r$ness 9 any case is always true ( r$ness1 s f> z x is m]ely r$4 99,syn!sis ( ,t]ms499 ,we cont9ually comb9e simple t]ms toge!r s z to =m new t]ms ( m complex mean+4 ,?us1 to increase ! int5sion ( mean+ ( a t]m we write x ) an adjective or a phrase ( adjectival nature4 ,by jo9+ 8brittle0 to 8metal10 we obta9 a comb9$ t]m1 8brittle metal10 :i* d5otes a c]ta9 portion ( ! metals1 namely1 su* z are select$ on acc\nt ( possess+ ! quality ( 99brittl5ess994 ,z we h already se51 8brittle metal0 possesses less ext5sion & great] int5sion ?an metal4 ,n\ns1 prepositional phrases1 p>ticipial phrases & subord9ate propositions may also be add$ to t]ms s z to increase _! int5sion & decrease _! ext5sion4 ,9 our symbolic language we ne$ "s mode ( indicat+ ?is junction ( t]ms1 & ! mo/ conv5i5t device w be ! juxtaposition ( ! lett]-t]ms4 ,?us if ,a mean brittle1 & ,b mean metal1 !n ,,ab w mean brittle metal4 ,nor ne$ !re be any limit to ! numb] ( lett]s ?us jo9$ toge!r1 or ! complexity ( ! notions :i* !y may repres5t4 ,?us if we take ! lett]s ,p metal1 ,q :ite1 ,r monoval5t1 ,s ( specific gravity #aje1 ,t melt+ above #ajjj ,c41 ,v good conductor ( heat & electricity1 !n we c =m a comb9$ t]m ,,pqr/v1 :i* w d5ote 8a :ite monoval5t metal1 ( specific gravity #aje1 melt+ above #ajjj ,c41 & a good conductor ( heat & electricity40 ,!re are _m grammatical usages conc]n+ ! junction ( words & phrases to :i* we ne$ pay no att5tion 9 logic4 ,we c nev] say 9 ord9>y language 8( wood table10 mean+ 8table ( wood20 b we may consid] 8( wood0 z logically an exact equival5t ( 8wood502 s t if ,x ( wood1 ,y table1 !re is no reason :y1 9 our symbols1 ,,xy %\ld n be j z correct an expression = 8table ( wood 0 z ,,yx4 ,9 ?is case inde$ we might sub/itute = 8( wood 0 ! correspond+ adjective 8wood510 b we %\ld (t5 fail to f9d any adjective answ]+ exactly to a phrase4 ,!re is no s+le ^w by :i* we c\ld express ! notion 8( specific gravity #aje30 b logically we may consid] ^! words z =m+ an adjective2 & d5ot+ ?is by ,s & metal by ,p1 we may say t ,,sp means 8metal ( specific gravity #aje40 ,x is "o ( _m advantages 9 ^! blank lett]-symbols t !y enable u completely to neglect all grammatical peculi>ities & to fix our att5tion solely on ! purely logical relations involv$4 ,inve/igation w probably %[ t ! rules ( gramm> are ma9ly f\nd$ ^u traditional usage & h little logical signification4 ,?is inde$ is suffici5tly prov$ by ! wide grammatical diff]5ces :i* exi/ betwe5 languages1 ?\gh ! logical f\ndation mu/ be ! same4 99,symbolic ,expression ( ! ,law ( ,contradiction499 ,! syn!sis ( t]ms is subject to ! all-important ,law ( ,?\ght1 describ$ 9 a previ\s section 7p4 #e7 & call$ ! ,law ( ,contradiction1 ,x is self-evid5t t no quality c be bo? pres5t & abs5t at ! same "t & place4 ,?is fundam5tal condition ( all ?\ght & ( all exi/5ce is express$ symbolically by a rule t a t]m & its negative %all nev] be all[$ to come into comb9ation4 ,su* comb9$ t]ms z ,a99a991 ,b99b991 ,c99c991 c41 are self-contradictory & devoid ( all intelligible mean+4 ,if !y c\ld repres5t any?+1 x w\ld be :at _c exi/1 & _c ev5 be imag9$ 9 ! m9d4 ,!y c !re=e only ent] into our consid]ation to suff] imm$iate exclusion4 ,! crit]ion ( false reason+1 z we %all f9d1 is t x involves self-contradiction1 ! affirm+ & d5y+ ( ! same /atem5t4 ,we might repres5t ! object ( all reason+ z ! sep>ation ( ! consi/5t & possible f ! inconsi/5t & impossible2 & we _c make any /atem5t except a truism )\t imply+ t c]ta9 comb9ations ( t]ms are contradictory & exclud$ f ?\ght4 ,to ass]t t 8all ,a's are ,b's0 is equival5t to ! ass]tion t 8,a's :i* are n ,b's _c exi/40 ,x w be conv5i5t to h ! means ( indicat+ ! exclusion ( ! self-contradictory1 & we may use ! famili> sign = 99no?+991 ! ciph] #j4 ,?us ! second law ( ?\ght may be symbolis$ 9 ! =ms ,a99a99 #j ,,ab99b99 #j ,,abc99a99 #j ,we may v>i\sly describe ! mean+ ( #j 9 logic z ! 99non-exi/5t991 ! 99impossible991 ! 99self-inconsi/5t991 ! 99inconceivable994 ,close analogy exi/s betwe5 ?is mean+ & its ma!matical signification4 99,c]ta9 ,special ,conditions ( ,logical ,symbols499 ,9 ord] t we may argue & inf] truly we mu/ treat our logical symbols accord+ to ! fundam5tal laws ( ,id5tity & ,diff]5ce4 ,b 9 ?us us+ our symbols we %all frequ5tly meet ) comb9ations ( :i* ! mean+ w n at fir/ sight be app>5t4 ,if 9 "o case we le>n t an object is 8yell[ & r\nd10 & 9 ano!r case t x is 8r\nd & yell[10 !re arises ! "q :e!r ^! two descriptions are id5tical 9 mean+ or n4 ,aga91 if we prov$ t an object 0 8r\nd r\nd10 ! mean+ ( su* an expression w\ld be op5 to d\bt4 ,accord+ly we mu/ take notice1 be=e proce$+ fur!r1 ( c]ta9 special laws :i* gov]n ! comb9ation ( logical t]ms4 ,9 ! fir/ place ! comb9ation ( a logical t]m ) itself is )\t effect1 j z ! repetition ( a /atem5t does n alt] ! mean+ ( ! /atem5t2 8a r\nd r\nd object0 is simply 8a r\nd object40 ,:at is yell[ yell[ is m]ely yell[2 metallic metals _c diff] f metals1 nor circul> circles f circles4 ,9 our symbolic language we may simil>ly hold t ,,aa is id5tical ) ,a1 or ,a ,,aa ,,aaa c4 ,! late ,pr(essor ,boole is ! only logician 9 mod]n times :o has drawn att5tion to ?is rem>kable prop]ty ( logical t]ms2#df b 9 place ( ! "n :i* he gave to ! law1 ,i h propos$ to call x ,! ,law ( ,simplicity4#dg ,its high importance w only become app>5t :5 we attempt to det]m9e ! relations ( logical & ma!matical sci5ce4 ,two symbols ( quantity1 & only two1 seem to obey ?is law2 we may say t #a #a #a1 & #j #j #j 7tak+ #j to mean absolute z]o or #a - #a72 !re is app>5tly no o!r numb] :i* comb9$ ) itself gives an un*ang$ result4 ,i %all po9t out1 h[ev]1 9 ! *apt] ^u ,numb]1 t 9 reality all num]ical symbols obey ?is logical pr9ciple4 #df 99,ma!matical ,analysis ( ,logic991 ,cambridge1 #ahdg1 p4 #ag4 99,an ,inve/igation ( ! ,laws ( ,?\ght991 ,london1 #ahed1 p4 #ca4 #dg 99,pure ,logic991 p4 #ae4 ,x is curi\s t ?is ,law ( ,simplicity1 ?\gh almo/ unnotic$ 9 mod]n times1 0 kn[n to ,bo?ius1 :o makes a s+ul> rem>k 9 8 treatise 99,de ,tr9itate et ,unitate ,dei99 7p4 #iei74 ,he says3 8,if ,i %\ld say sun1 sun1 sun1 ,i %\ld n h made ?ree suns1 b ,i %\ld h nam$ "o sun s _m times40#dh ,anci5t discussions ab\t ! doctr9e ( ! ,tr9ity drew m att5tion to subtle que/ions conc]n+ ! nature ( unity & plurality ?an has ev] s9ce be5 giv5 to !m4 #dh 8,velut si dicam1 ,sol1 ,sol1 ,sol1 non tres soles effec]im1 s$ uno toties prdicav]im40 ,x is a second law ( logical symbols t ord] ( comb9ation is a matt] ( indiff]5ce4 8,ri* & r>e gems0 are ! same z 8r>e & ri* gems10 or ev5 z 8gems1 ri* & r>e40 ,grammatical1 rhetorical1 or poetic usage may give consid]able significance to ord] ( expression4 ,! limit$ p[] ( our m9ds prev5ts our grasp+ _m ideas at once1 & ?us ! ord] ( /atem5t may produce "s effect1 b n 9 a simply logical mann]4 ,all life proce$s 9 ! succession ( "t1 & we are oblig$ to write1 speak1 or ev5 ?9k ( ?+s & _! qualities "o aft] ! o!r2 b betwe5 ! ?+s & _! qualities !re ne$ be no su* relation ( ord] 9 "t or space4 ,! sweetness ( sug> is nei!r be=e nor aft] its weight & solubility4 ,! h>dness ( a metal1 its col\r1 weight1 opacity1 malleability1 electric & *emical prop]ties1 are all coexi/5t & coext5sive1 p]vad+ ! metal & e "p ( x 9 p]fect community1 none be=e nor aft] ! o!rs4 ,9 our words & symbols we _c obs]ve ?is natural condition2 we mu/ "n "o quality fir/ & ano!r second1 j z "s "o mu/ be ! fir/ to sign a petition1 or to walk =emo/ 9 a procession4 ,9 nature !re is no su* prec$5ce4 ,i f9d t ! op9ion "h /at$1 to ! effect t relations ( space & "t d n apply to _m ( our ideas1 is cle>ly adopt$ by ,hume 9 8 celebrat$ 99,treatise on ,human ,nature99 7vol4 i4 p4 #daj74 ,he says3#di--8;,an object may be said to be no :]e1 :5 its p>ts are n s situat$ ) respect to ea* o!r1 z to =m any figure or quantity2 nor ! :ole ) respect to o!r bodies s z to answ] to our notions ( contiguity or di/ance4 ,n[ ?is is evid5tly ! case ) all our p]ceptions & objects1 except ^? ( sight & feel+4 ,a moral reflection _c be plac$ on ! "r h& or on ! left h& ( a passion1 nor c a smell or s\nd be ei!r ( a circul> or a squ>e figure4 ,^! objects & p]ceptions1 s f> f requir+ any p>ticul> place1 are absolutely incompatible ) x1 & ev5 ! imag9ation _c attribute x to !m40 #di ,book i41 ,"p iv41 ,section #e4 ,a little reflection w %[ t k 9 ! highe/ p]fection w\ld consi/ 9 ! 99simultane\s99 possession ( a multitude ( facts4 ,to compreh5d a sci5ce p]fectly we %\ld h e fact pres5t ) e o!r fact4 ,we mu/ write a book & we mu/ read x successively ^w by ^w1 b h[ inf9itely high] w\ld be our p[]s ( ?\ght if we c\ld grasp ! :ole 9 "o collective act ( consci\sness6 ,comp>$ ) ! brutes we d possess "s slight approximation to su* p[]1 & x is conceivable t 9 ! indef9ite future m9d may acquire an increase ( capacity1 & be less re/rict$ to ! piecemeal exam9ation ( a subject4 ,b ,i wi% "h to make pla9 t !re is no logical f\ndation = ! successive "* ( ?\ght & reason+ unavoidable "u our pres5t m5tal conditions4 99,we are logically weak & imp]fect 9 respect ( ! fact t we are oblig$ to ?9k ( "o ?+ aft] ano!r499 ,we mu/ describe metal z 8h>d & opaque10 or 8opaque & h>d10 b 9 ! metal itself !re is no su* diff]5ce ( ord]2 ! prop]ties are simultane\s & coext5sive 9 exi/5ce4 ,sett+ aside all grammatical peculi>ities :i* r5d] a sub/antive less moveable ?an an adjective1 & disreg>d+ any mean+ indicat$ by emphasis or m>k$ ord] ( words1 we may /ate1 z a g5]al law ( logic1 t ,,ab is id5tical ) ,,ba1 or ,,ab ,,ba4 ,simil>ly1 ,,abc ,,acb ,,bca c4 ,boole fir/ drew att5tion 9 rec5t ye>s to ?is prop]ty ( logical t]ms1 & he call$ x ! prop]ty ( ,commutativ5ess4#ej ,he n only /at$ ! law ) ! utmo/ cle>ness1 b po9t$ out t x is a ,law ( ,?\ght r ?an a ,law ( ,?+s4 ,i %all h 9 v>i\s p>ts ( ?is "w to %[ h[ ! necess>y imp]fection ( our symbols express$ 9 ?is law cl+s to our modes ( expression1 & introduces complication into ! :ole body ( ma!matical =mul1 :i* are really f\nd$ on a logical basis4 #ej 99,laws ( ,?\ght991 p4 #bi4 ,x is po9t$ out 9 ! preface to ?is ,second ,edition t ,leibnitz 0 acqua9t$ ) ! ,laws ( ,simplicity & ( ,commutativ5ess4 ,x is ( c\rse app>5t t ! p[] ( commutation belongs only to t]ms relat$ 9 ! simple logical mode ( syn!sis4 ,no "o c confuse 8a h\se ( bricks0 ) 8bricks ( a h\se10 8twelve squ>e feet0 ) 8twelve feet squ>e10 8! wat] ( cry/allization0 ) 8! cry/allization ( wat]40 ,all relations :i* involve diff]5ces ( "t & space are inconv]tible2 ! high] mu/ n be made to *ange places ) ! l[]1 nor ! fir/ ) ! la/4 ,= ! p>ties conc]n$ !re is all ! diff]5ce 9 ! _w betwe5 ,a kill+ ,b & ,b kill+ ,a4 ,! law ( commutativ5ess simply ass]ts t diff]5ce ( ord] does n atta* to ! connection betwe5 ! prop]ties & circum/ances ( a ?+--to :at ,i call 99simple logical relation994 ,,*apt] ,,iii4 ,,propositions4 ,we n[ proce$ to consid] ! v>iety ( =ms ( propositions 9 :i* ! tru?s ( sci5ce mu/ be express$4 ,i %all endeav\r to %[ t1 h[ev] div]se ^! =ms may be1 !y all admit ! application ( ! "o same pr9ciple ( inf]5ce t :at is true ( a ?+ is true ( ! l or same4 ,?is pr9ciple holds true :atev] be ! k9d or mann] ( ! lik5ess1 provid$ prop] reg>d be _h to its nature4 ,propositions may ass]t an id5tity ( "t1 space1 mann]1 quantity1 degree1 or any o!r circum/ance 9 :i* ?+s may agree or diff]4 ,we f9d an in/ance ( a proposition conc]n+ "t 9 ! foll[+3--8,! ye> 9 :i* ,newton 0 born1 0 ! ye> 9 :i* ,galileo di$40 ,?is proposition expresses an approximate id5tity ( "t betwe5 two ev5ts2 h5ce :atev] is true ( ! ye> 9 :i* ,galileo di$ is true ( t 9 :i* ,newton 0 born1 & 99vice v]s994 8,t[] ,hill is ! place :]e ,raleigh 0 execut$0 expresses an id5tity ( place2 & :atev] is true ( ! "o spot is true ( ! spot o!rwise def9$1 b 9 reality ! same4 ,9 ord9>y language we h _m propositions obscurely express+ id5tities ( numb]1 quantity1 or degree4 8,s _m m51 s _m m9ds10 is a proposition conc]n+ numb]1 t is to say1 an equation2 :atev] is true ( ! numb] ( m5 is true ( ! numb] ( m9ds1 & 99vice v]s994 8,! d5sity ( ,m>s is 7ne>ly7 ! same z t ( ! ,e>?10 8,! =ce ( gravity is directly z ! product ( ! masses1 & inv]sely z ! squ>e ( ! di/ance10 are propositions conc]n+ magnitude or degree4 ,logicians h n paid adequate att5tion to ! great v>iety ( propositions :i* c be /at$ by ! use ( ! little conjunction 99z991 toge!r ) 99s994 8,z ! home s ! p10 is a proposition express+ id5tity ( mann]2 & a great numb] ( simil> propositions all indicat+ "s k9d ( resemblance might be quot$4 ,:atev] be ! special k9d ( id5tity1 all su* expressions are subject to ! great pr9ciple ( inf]5ce2 b z we %all 9 lat] p>ts ( ?is "w treat m p>ticul>ly ( inf]5ce 9 cases ( numb] & magnitude1 we w "h conf9e our att5tion to logical propositions :i* involve only notions ( quality4 99,simple ,id5tities499 ,! mo/ important class ( propositions consi/s ( ^? :i* fall "u ! =mula ,a ,b1 & may be call$ 99simple id5tities994 ,i may in/ance1 9 ! fir/ place1 ^? mo/ elem5t>y propositions :i* express ! exact simil>ity ( a quality enc\nt]$ 9 two or m objects4 ,i may comp>e ! col\r ( ! ,pacific ,ocean ) t ( ! ,atlantic1 & decl>e !m id5tical4 ,i may ass]t t 8! smell ( a rott5 egg is l t ( hydrog5 sulphide20 8! ta/e ( silv] hyposulphite is l t ( cane sug>20 8! s\nd ( an e>?quake resembles t ( di/ant artill]y40 ,su* are propositions /at+1 accurately or o!rwise1 ! id5tity ( simple physical s5sations4 ,judgm5ts ( ?is k9d are necess>ily pre-suppos$ 9 m complex judgm5ts4 ,if ,i decl>e t 8?is co9 is made ( gold10 ,i mu/ base ! judgm5t ^u ! exact lik5ess ( ! sub/ance 9 sev]al qualities to o!r pieces ( sub/ance :i* are und\bt$ly gold4 ,i mu/ make judgm5ts ( ! col\r1 ! specific gravity1 ! h>dness1 & ( o!r me*anical & *emical prop]ties2 ea* ( ^! judgm5ts is express$ 9 an elem5t>y proposition1 8! col\r ( ?is co9 is ! col\r ( gold10 & s on4 ,ev5 :5 we e/abli% ! id5tity ( a ?+ ) itself "u a diff]5t "n or aspect1 x is by di/9ct judgm5ts conc]n+ s+le circum/ances4 ,to prove t ! ,hom]ic is copp] we mu/ %[ ! id5tity ( ea* quality record$ ( ) a quality ( copp]4 ,to e/abli% ,deal z ! l&+-place ( ,cs> all mat]ial circum/ances mu/ be %[n to agree4 ,if ! mod]n ,wroxet] is ! anci5t ,uriconium1 !re mu/ be ! l agreem5t ( all features ( ! c\ntry n subject to alt]ation by "t4 ,su* id5tities mu/ be express$ 9 ! =m ,a ,b4 ,we may say ,col\r ( ,pacific ,ocean ,col\r ( ,atlantic ,ocean4 ,smell ( rott5 egg ,smell ( hydrog5 sulphide4 ,9 ^! & simil> propositions we ass]t id5tity ( s+le qualities or causes ( s5sation4 ,9 ! same =m we may also express id5tity ( any gr\p ( qualities1 z 9 ,copp]4 ,deal ,l&+-place ( ,cs>4 ,a multitude ( propositions involv+ s+ul> t]ms fall into ! same =m1 z 9 ,! ,pole /> ,! sl[e/-mov+ />4 ,jupit] ,! greate/ ( ! planets4 ,! r+$ planet ,! planet hav+ sev5 satellites4 ,! ,que5 ( ,engl& ,! ,empress ( ,india4 ,! numb] two ,! ev5 prime numb]4 ,hone/y ,! be/ policy4 ,9 ma!matical & sci5tific !ories we (t5 meet ) simple id5tities capable ( expression 9 ! same =m4 ,?us 9 me*anical sci5ce 8,! process = f9d+ ! resultant ( =ces ! process = f9d+ ! resultant ( simultane\s velocities40 ,!orems 9 geometry (t5 give results 9 ?is =m1 z ,equilat]al triangles ,equiangul> triangles4 ,circle ,f9ite plane curve ( con/ant curvature4 ,circle ,curve ( lea/ p]imet]4 ,! m pr(\nd & important laws ( nature are (t5 expressible 9 ! =m ( simple id5tities2 9 addition to "s in/ances :i* h already be5 giv51 ,i may sugge/1 ,cry/als ( cubical sy/em ,cry/als n possess+ ! p[] ( d\ble refraction4 ,all def9itions are necess>ily ( ?is =m1 :e!r ! objects def9$ be _m1 few1 or s+ul>4 ,?us we may say1 ,common salt ,sodium *loride4 ,*lorophyl ,gre5 col\r+ matt] ( leaves4 ,squ>e ,equal-sid$ rectangle4 ,x is an extraord9>y fact t propositions ( ?is elem5t>y =m1 all-important & v num]\s z !y are1 _h no recognis$ place 9 ,ari/otle's sy/em ( ,logic4 ,accord+ly _! importance 0 ov]look$ until v rec5t times1 & logic 0 ! mo/ de=m$ ( sci5ces4 ,b x is impossible t ,ari/otle or any o!r p]son %\ld avoid con/antly us+ !m2 n a t]m c\ld be def9$ )\t _! use4 ,9 "o place at lea/ ,ari/otle actually notices a proposition ( ! k9d4 ,he obs]ves3 8,we sometimes say t t :ite ?+ is ,socrates1 or t ! object approa*+ is ,callias40#ea ,"h we c]ta9ly h simple id5tity ( t]ms2 b he consid]$ su* propositions purely accid5tal1 & came to ! un=tunate conclusion1 t 8,s+ul>s _c be pr$icat$ ( o!r t]ms40 #ea 99,prior ,analytics991 i4 cap4 xxvii4 #c4 ,propositions may also express ! id5tity ( ext5sive gr\ps ( objects tak5 collectively or 9 "o connect$ :ole2 z :5 we say1 ,! ,que51 ,lords1 & ,commons ,! ,legislature ( ! ,unit$ ,k+dom4 ,:5 ,black/one ass]ts t 8,! only true & natural f\ndation ( society are ! wants & fe>s ( individuals10 we mu/ int]pret him z mean+ t ! :ole ( ! wants & fe>s ( individuals 9 ! aggregate =m ! f\ndation ( society4 ,b _m propositions :i* might seem to be collective are b gr\ps ( s+ul> propositions or id5tities4 ,:5 we say 8,potassium & sodium are ! metallic bases ( pota% & soda10 we obvi\sly mean1 ,potassium ,metallic base ( pota%2 ,sodium ,metallic base ( soda4 ,x is ! "w ( grammatical analysis to sep>ate ! v>i\s propositions (t5 comb9$ into a s+le s5t5ce4 ,logic _c be prop]ly requir$ to int]pret ! =ms & devices ( language1 b only to treat ! mean+ :5 cle>ly exhibit$4 99,p>tial ,id5tities499 ,a second highly important k9d ( proposition is t :i* ,i propose to call 99a p>tial id5tity994 ,:5 we say t 8,all mammalia are v]tebrata10 we d n mean t mammalian animals are id5tical ) v]tebrate animals1 b only t ! mammalia =m a 99"p ( ! class v]tebrata994 ,su* a proposition 0 reg>d$ 9 ! old logic z ass]t+ ! inclusion ( "o class 9 ano!r1 or ( an object 9 a class4 ,x 0 call$ a univ]sal affirmative proposition1 because ! attribute 99v]tebrate99 0 affirm$ ( ! :ole subject 99mammalia992 b ! attribute 0 said to be 99undi/ribut$991 because n all v]tebrata 7 ( necessity involv$ 9 ! proposition4 ,ari/otle1 ov]look+ ! importance ( simple id5tities1 & inde$ almo/ d5y+ _! exi/5ce1 un=tunately f\nd$ 8 sy/em ^u ! notion ( inclusion 9 a class1 in/ead ( adopt+ ! basis ( id5tity4 ,he reg>d$ inf]5ce z re/+ ^u ! rule t :at is true ( ! conta9+ class is true ( ! conta9$1 9 place ( ! va/ly m g5]al rule t :at is true ( a class or ?+ is true ( ! l4 ,?us he n only r$uc$ logic to a fragm5t ( its prop] self1 b de/roy$ ! deep analogies :i* b9d toge!r logical & ma!matical reason+4 ,h5ce a cr[d ( defects1 difficulties & errors :i* w long disfigure ! fir/ & simple/ ( ! sci5ces4 ,x is surely evid5t t ! relation ( inclusion re/s ^u ! relation ( id5tity4 ,mammalian animals _c be includ$ among v]tebrates unless !y be id5tical ) "p ( ! v]tebrates4 ,cab9et ,m9i/]s are includ$ almo/ always 9 ! class ,memb]s ( ,p>liam5t1 because !y are id5tical ) "s :o sit 9 ,p>liam5t4 ,we may indicate ?is id5tity ) a "p ( ! l>g] class 9 v>i\s ways2 z = in/ance1 ,mammalia "p ( ! v]tebrata4 ,diatomace a class ( plants4 ,cab9et ,m9i/]s "s memb]s ( ,p>liam5t4 ,iron a metal4 ,9 ord9>y language ! v]bs 99is99 & 99are99 express m]e inclusion m (t5 ?an n4 99,m5 are mortals991 means t 99m599 =m a "p ( ! class 99mortal992 b great confusion exi/s betwe5 ?is s5se ( ! v]b & t 9 :i* x expresses id5tity1 z 9 8,! sun is ! c5tre ( ! planet>y sy/em40 ,! introduction ( ! indef9ite article 99a99 (t5 expresses p>tiality2 :5 we say 8,iron is a metal0 we cle>ly mean t iron is 99"o only99 ( sev]al metals4 ,c]ta9 rec5t logicians h propos$ to avoid ! indef9it5ess 9 "q by :at is call$ ! ,quantification ( ! ,pr$icate1 & !y h g5]ally us$ ! little ^w 99"s99 to %[ t only a "p ( ! pr$icate is id5tical ) ! subject4 99,"s99 is an 99indet]m9ate adjective992 x implies unkn[n qualities by :i* we might select ! "p 9 "q if ! qualities 7 kn[n1 b x gives no h9t z to _! nature4 ,i might make use ( su* an indet]m9ate sign to express p>tial id5tities 9 ?is "w4 ,?us1 tak+ ! special symbol ,v ,"s1 ! g5]al =m ( a p>tial id5tity w\ld be ,a ,,vb1 & 9 ,boole's ,logic expressions ( ! k9d 7 mu* us$4 ,b ,i believe t indet]m9ate symbols only introduce complexity1 & de/roy ! beauty & simple univ]sality ( ! sy/em :i* may be creat$ )\t _! use4 ,a vague ^w l 99"s99 is only us$ 9 ord9>y language by 99ellipsis991 & to avoid ! tr\ble ( atta9+ accuracy4 ,we c always employ m def9ite expressions if we l2 b :5 once ! indef9ite 99"s99 is introduc$ we _c replace x by ! special description4 ,we d n "k :e!r 99"s99 col\r is r$1 yell[1 blue1 or :at x is2 b on ! o!r h& 99r$99 col\r is c]ta9ly 99"s99 col\r4 ,?r\gh\t ?is sy/em ( logic ,i %all disp5se ) su* indef9ite expressions2 & ?is c readily be done by sub/itut+ "o ( ! o!r t]ms4 ,to express ! proposition 8,all ,a's are "s ,b's0 ,i %all n use ! =m ,a ,,vb1 b ,a ,,ab4 ,?is =mula /ates t ! class ,a is id5tical ) ! class ,,ab2 & z ! latt] mu/ be a "p at lea/ ( ! class ,b1 x implies ! inclusion ( ! class ,a 9 t ( ,b4 ,we might repres5t our =m] example ?us1 ,mammalia ,mammalian v]tebrata4 ,?is proposition ass]ts id5tity betwe5 a "p 7or x may be ! :ole7 ( ! v]tebrata & ! mammalia4 ,if x is ask$ ,:at "p8 ! proposition af=ds no answ]1 except t x is ! "p :i* is mammalian2 b ! ass]tion 8mammalia "s v]tebrata0 tells u no m4 ,x is q likely t "s read]s w ?9k ?is mode ( repres5t+ ! univ]sal affirmative proposition artificial & complicat$4 ,i w n und]take to conv9ce !m ( ! opposite at ?is po9t ( my exposition4 ,ju/ification = x w be f\nd1 n s mu* 9 ! imm$iate treatm5t ( ?is proposition1 z 9 ! g5]al h>mony :i* x w enable u to disclose betwe5 all p>ts ( reason+4 ,i h no d\bt t ?is is ! critical difficulty 9 ! relation ( logical to o!r =ms ( reason+4 ,grant ?is mode ( d5ot+ t 8all ,a's are ,b's10 & ,i fe> no fur!r difficulties2 refuse x1 & we f9d want ( analogy & endless anomaly 9 e direction4 ,x is on g5]al gr\nds t ,i hope to %[ ov]:elm+ reasons = seek+ to r$uce e k9d ( proposition to ! =m ( an id5tity4 ,i may add t n a few logicians h accept$ ?is view ( ! univ]sal affirmative proposition4 ,leibnitz1 9 8 99,difficultates ,qudam ,logic991 adopts x1 say+1 8,omne ,a e/ ,b2 id e/ quival5t ,,ab et ,a1 seu ,a non ,b e/ non5s40 ,boole employ$ ! logical equation 99x99 99xy99 concurr5tly ) 99x99 99vy992 & ,spald+#eb di/9ctly says t ! proposition 8all metals are m9]als0 might be describ$ z an ass]tion ( 99p>tial id5tity99 betwe5 ! two classes4 ,h5ce ! "n :i* ,i h adopt$ = ! proposition4 #eb 99,encyclopdia ,britannica991 ,eigh? ,ed4 art4 ,logic1 sect4 #cg1 note4 #hvo4 repr9t1 p4 #gi4 99,limit$ ,id5tities499 ,an important class ( propositions h ! =m ,,ab ,,ac1 express+ ! id5tity ( ! class ,,ab ) ! class ,,ac4 ,9 o!r words1 8,)9 ! sph]e ( ! class ,a1 all ! ,b's are all ! ,c's20 or aga91 8,! ,b's & ,c's1 :i* are ,a's1 are id5tical40 ,b x w be obs]v$ t no?+ is ass]t$ conc]n+ ?+s :i* are outside ( ! class ,a2 & ?us ! id5tity is ( limit$ ext5t4 ,x is ! proposition ,b ,c limit$ to ! sph]e ( ?+s call$ ,a4 ,?us we may say1 ) "s approximation to tru?1 t 8,l>ge plants are plants devoid ( locomotive p[]40 ,a b>ri/] may make numb]s ( mo/ g5]al /atem5ts conc]n+ ! relations ( p]sons & ?+s 9 ! c\rse ( an argum5t1 b x is ( c\rse to be und]/ood t he speaks only ( p]sons & ?+s "u ! ,engli% ,law4 ,ev5 ma!maticians make /atem5ts :i* are n true ) absolute g5]ality4 ,!y say t imag9>y roots ent] into equations by pairs2 b ?is is only true "u ! tacit condition t ! equations 9 "q %all n h imag9>y coeffici5ts4#ec ,! univ]se1 9 %ort1 )9 :i* !y habitually disc\rse is t ( equations ) real coeffici5ts4 ,^! impli$ limitations =m "p ( t great mass ( tacit k :i* accompanies all special argum5ts4 #ec ,de ,morgan1 99,on ! ,root ( any ,function994 ,cambridge ,philosophical ,transactions1 #ahfg1 vol4 xi4 p4 #be4 ,to ,de ,morgan is due ! rem>k1 t we d usually ?9k & argue 9 a limit$ univ]se or sph]e ( notions1 ev5 :5 x is n expressly /at$4#ed #ed 99,syllabus ( a propos$ ,sy/em ( ,logic991 #abb1 #abc4 ,x is wor?y ( inquiry :e!r all id5tities are n really limit$ to an impli$ sph]e ( mean+4 ,:5 we make su* a pla9 /atem5t z 8,gold is malleable0 we obvi\sly speak ( gold only 9 its solid /ate2 :5 we say t 8,m]cury is a liquid metal0 we mu/ be und]/ood to exclude ! froz5 condition to :i* x may be r$uc$ 9 ! ,arctic regions4 ,ev5 :5 we take su* a fundam5tal law ( nature z 8,all sub/ances gravitate10 we mu/ mean by sub/ance1 mat]ial sub/ance1 n includ+ t basis ( heat1 light1 & electrical undulations :i* occupies space & possesses _m wond]ful me*anical prop]ties1 b n gravity4 ,! proposition !n is really ( ! =m ,mat]ial sub/ance ,mat]ial gravitat+ sub/ance4 99,negative ,propositions499 ,9 e act ( intellect we are engag$ ) a c]ta9 id5tity or diff]5ce betwe5 ?+s or s5sations comp>$ toge!r4 ,hi!rto ,i h treat$ only ( id5tities2 & yet x might seem t ! relation ( diff]5ce mu/ be inf9itely m common ?an t ( lik5ess4 ,"o ?+ may resemble a great _m o!r ?+s1 b !n x diff]s f all rema9+ ?+s 9 ! _w4 ,div]sity may almo/ be said to con/itute life1 be+ to ?\ght :at motion is to a riv]4 ,! p]ception ( an object involves its discrim9ation f all o!r objects4 ,b we may nev]!less be said to detect resemblance z (t5 z we detect diff]5ce4 ,we _c1 9 fact1 ass]t ! exi/5ce ( a diff]5ce1 )\t at ! same "t imply+ ! exi/5ce ( an agreem5t4 ,if ,i comp>e m]cury1 = in/ance1 ) o!r metals1 & decide t x is 99n solid991 "h is a diff]5ce betwe5 m]cury & solid ?+s1 express$ 9 a negative proposition2 b !re mu/ be impli$1 at ! same "t1 an agreem5t betwe5 m]cury & ! o!r sub/ances :i* are n solid4 ,z x is impossible to sep>ate ! v[els ( ! alphabet f ! consonants )\t at ! same "t sep>at+ ! consonants f ! v[els1 s ,i _c select z ! object ( ?\ght 99solid ?+s991 )\t !reby ?r[+ toge!r into ano!r class all ?+s :i* are 99n solid994 ,! v fact ( n possess+ a quality1 con/itutes a new quality :i* may be ! gr\nd ( judgm5t & classification4 ,9 ?is po9t ( view1 agreem5t & diff]5ce are ev] ! two sides ( ! same act ( intellect1 & x becomes equally possible to express ! same judgm5t 9 ! "o or o!r aspect4 ,betwe5 affirmation & negation !re is accord+ly a p]fect equilibrium4 ,e affirmative proposition implies a negative "o1 & 99vice v]s994 ,x is ev5 a matt] ( indiff]5ce1 9 a logical po9t ( view1 :e!r a positive or negative t]m be us$ to d5ote a giv5 quality & ! class ( ?+s possess+ x4 ,if ! ord9>y /ate ( a man's body be call$ 99good heal?991 !n 9 o!r circum/ances he is said 99n to be 9 good heal?992 b we might equally describe him 9 ! latt] /ate z 99sickly991 & 9 8 normal condition he w\ld be 99n sickly994 ,animal & vegetable sub/ances are n[ call$ 99organic991 s t ! o!r sub/ances1 =m+ an imm5sely great] "p ( ! globe1 are describ$ negatively z 99inorganic994 ,b we might1 ) at lea/ equal logical correctness1 h describ$ ! prepond]at+ class ( sub/ances z 99m9]al991 & !n vegetable & animal sub/ances w\ld h be5 99non-m9]al994 ,x is pla9 t any positive t]m & its correspond+ negative divide betwe5 !m ! :ole univ]se ( ?\ght3 :atev] does n fall into "o mu/ fall into ! o!r1 by ! ?ird fundam5tal ,law ( ,?\ght1 ! ,law ( ,duality4 ,x foll[s at once t !re are two modes ( repres5t+ a diff]5ce4 ,suppos+ t ! ?+s repres5t$ by ,a & ,b are f\nd to diff]1 we may indicate 7see p4 #ag7 ! result ( ! judgm5t by ! notation ,a ,b4 ,we may n[ repres5t ! same judgm5t by ! ass]tion t ,a agrees ) ^? ?+s :i* diff] f ,b1 or t ,a agrees ) ! n-,b's4 ,us+ our notation = negative t]ms 7see p4 #ad71 we obta9 ,a ,a99b99 z ! expression ( ! ord9>y negative proposition4 ,?us if we take ,a to mean quicksilv]1 & ,b solid1 !n we h ! foll[+ proposition3-- ,quicksilv] ,quicksilv] n-solid4 ,!re may also be sev]al o!r classes ( negative propositions1 ( :i* no notice 0 tak5 9 ! old logic4 ,we may h cases :]e all ,a's are n-,b's1 & at ! same "t all n-,b's are ,a's2 !re may1 9 %ort1 be a simple id5tity betwe5 ,a & n-,b1 :i* may be express$ 9 ! =m ,a 99b994 ,an example ( ?is =m w\ld be ,conductors ( electricity non-electrics4 ,we %all also frequ5tly h to deal z results ( d$uction1 ) simple1 p>tial1 or limit$ id5tities betwe5 negative t]ms1 z 9 ! =ms 99a99 99b991 99a99 99a9999b991 99a99,c 99b99,c1 etc4 ,x w\ld be possible to repres5t affirmative propositions 9 ! negative =m4 ,?us 8,iron is solid10 might be express$ z 8,iron is n n-solid10 or 8,iron is n fluid20 or1 tak+ ,a & 99b99 = ! t]ms 8iron10 & 8n-solid10 ! =m w\ld be ,a 99b994 ,b !re are v /rong reasons :y we %\ld employ all propositions 9 _! affirmative =m4 ,all inf]5ce proce$s by ! sub/itution ( equival5ts1 & a proposition express$ 9 ! =m ( an id5tity is ready to yield all its consequ5ces 9 ! mo/ direct mann]4 ,z w be m fully %[n1 we c inf] 99999 a negative proposition1 b n 99by99 x4 ,diff]5ce is incapable ( becom+ ! gr\nd ( inf]5ce2 x is only ! impli$ agreem5t ) o!r diff]+ objects :i* admits ( d$uctive reason+2 & x w always be f\nd advantage\s to employ propositions 9 ! =m :i* exhibits cle>ly ! impli$ agreem5ts4 99,conv]sion ( ,propositions499 ,! old books ( logic conta9 _m rules conc]n+ ! conv]sion ( propositions1 t is1 ! transposition ( ! subject & pr$icate 9 su* a way z to obta9 a new proposition :i* w be true :5 ! orig9al proposition is true4 ,! r$uction ( e proposition to ! =m ( an id5tity r5d]s all su* rules & processes ne$less4 ,id5tity is ess5tially reciprocal4 ,if ! col\r ( ! ,atlantic ,ocean is ! same z t ( ! ,pacific ,ocean1 t ( ! ,pacific mu/ be ! same z t ( ! ,atlantic4 ,sodium *loride be+ id5tical ) common salt1 common salt mu/ be id5tical ) sodium *loride4 ,if ! numb] ( w9d[s 9 ,salisbury ,ca!dral equals ! numb] ( days 9 ! ye>1 ! numb] ( days 9 ! ye> mu/ equal ! numb] ( ! w9d[s4 ,"l ,*e/]field 0 n wrong :5 he said1 8,i w give anybody _! *oice ( ^! two tru?s1 :i* am\nt to ! same ?+2 ,he :o loves himself be/ is ! hone/e/ man2 or1 ,! hone/e/ man loves himself be/40 ,scotus ,erig5a exactly expresses ?is reciprocal "* ( id5tity 9 say+1 8,!re are n two /udies1 "o ( philosophy & ! o!r ( religion2 true philosophy is true religion1 & true religion is true philosophy40 ,a ma!matician w\ld n ?9k x wor? :ile to m5tion t if 99x99 99y99 !n also 99y99 99x994 ,he w\ld n consid] ^! to be two equations at all1 b "o equation accid5tally writt5 9 two diff]5t mann]s4 ,9 writt5 symbols "o ( two names mu/ come fir/1 & ! o!r second1 & a l succession mu/ p]haps be obs]v$ 9 our ?\ghts3 b 9 ! relation ( id5tity !re is no ne$ = succession 9 ord] 7see p4 #cc71 ea* is simultane\sly equal & id5tical to ! o!r4 ,^! rem>ks w hold true bo? ( logical & ma!matical id5tity2 s t ,i %all consid] ! two =ms ,a ,b & ,b ,a to express exactly ! same id5tity diff]5tly writt54 ,all ne$ = rules ( conv]sion disappe>s1 & !re w be no s+le proposition 9 ! sy/em :i* may n be writt5 ) ei!r end =emo/4 ,?us ,a ,,ab is ! same z ,,ab ,a1 99a99,c 99b99,c is ! same z 99b99,c 99a99,c1 & s =?4 ,! same rem>ks are p>tially true ( diff]5ces & inequalities1 :i* are also reciprocal to ! ext5t t "o ?+ _c diff] f a second )\t ! second diff]+ f ! fir/4 ,m>s diff]s 9 col\r f ,v5us1 & ,v5us mu/ diff] f ,m>s4 ,! ,e>? diff]s f ,jupit] 9 d5sity2 !re=e ,jupit] mu/ diff] f ! ,e>?4 ,speak+ g5]ally1 if ,a ,b we %all also h ,b ,a1 & ^! two =ms may be consid]$ expressions ( ! same diff]5ce4 ,b ! relation ( diff]+ ?+s is n :olly reciprocal4 ,! d5sity ( ,jupit] does n diff] f t ( ! ,e>? 9 ! same way t t ( ! ,e>? diff]s f t ( ,jupit]4 ,! *ange ( s5sation :i* we exp]i5ce 9 pass+ f ,v5us to ,m>s is n ! same z :at we exp]i5ce 9 pass+ back to ,v5us1 b j ! opposite 9 nature4 ,! col\r ( ! sky is light] ?an t ( ! ocean2 !re=e t ( ! ocean _c be light] ?an t ( ! sky1 b d>k]4 ,9 ^! & all simil> cases we ga9 a notion ( 99direction99 or "* ( *ange1 & results ( imm5se importance may be %[n to re/ on ?is notion4 ,= ! pres5t we %all be conc]n$ ) ! m]e fact ( id5tity exi/+ or n exi/+4 99,tw(old ,int]pretation ( ,propositions499 ,t]ms1 z we h se5 7p4 #be71 may h a mean+ ei!r 9 ext5sion or int5sion2 & accord+ z "o or ! o!r mean+ is attribut$ to ! t]ms ( a proposition1 s may a diff]5t int]pretation be assign$ to ! proposition itself4 ,:5 ! t]ms are ab/ract we mu/ read !m 9 int5sion1 & a proposition connect+ su* t]ms mu/ d5ote ! id5tity or non-id5tity ( ! qualities respectively d5ot$ by ! t]ms4 ,?us if we say ,equality ,id5tity ( magnitude1 ! ass]tion means t ! circum/ance ( be+ equal exactly corresponds ) ! circum/ance ( be+ id5tical 9 magnitude4 ,simil>ly 9 ,opacity ,incapability ( transmitt+ light1 ! quality ( be+ incapable ( transmitt+ light is decl>$ to be ! same z ! int5d$ mean+ ( ! ^w opacity4 ,:5 g5]al names =m ! t]ms ( a proposition we may apply a d\ble int]pretation4 ,?us ,exog5s ,dicotyl$ons means ei!r t ! qualities :i* belong to all exog5s are ! same z ^? :i* belong to all dicotyl$ons1 or else t e individual fall+ "u "o "n falls equally "u ! o!r4 ,h5ce x may be said t !re are two di/9ct fields ( logical ?\ght4 ,we may argue ei!r by ! qualitative mean+ ( names or by ! quantitative1 t is1 ! ext5sive mean+4 ,e argum5t involv+ concrete plural t]ms might be conv]t$ into "o involv+ only ab/ract s+ul> t]ms1 & 99vice v]s994 ,b !re are reasons = believ+ t ! int5sive or qualitative =m ( reason+ is ! prim>y & fundam5tal "o4 ,x is suffici5t to po9t out t ! ext5sive mean+ ( a "n is a *angeable & fleet+ ?+1 :ile ! int5sive mean+ may nev]!less rema9 fix$4 ,v num]\s additions h be5 lately made to ! ext5sive mean+s bo? ( planet & elem5t4 ,e iron /eam-%ip :i* is made or de/roy$ adds to or subtracts f ! ext5sive mean+ ( ! "n /eam-%ip1 )\t necess>ily affect+ ! int5sive mean+4 ,/age coa* means z mu* z ev] 9 "o way1 b 9 ext5sion ! class is ne>ly ext9ct4 ,*9ese railway1 on ! o!r h&1 is a t]m repres5t$ only by a s+le in/ance2 9 tw5ty ye>s x may be ! "n ( a l>ge class4 ,,*apt] ,,iv4 ,,d$uctive ,,reason+4 ,! g5]al pr9ciple ( inf]5ce hav+ be5 expla9$ 9 ! previ\s *apt]s1 & a suitable sy/em ( symbols provid$1 we h n[ be=e u ! comp>atively easy task ( trac+ out ! mo/ common & important =ms ( d$uctive reason+4 ,! g5]al problem ( d$uction is z foll[s3--99,f "o or m propositions call$ premises to draw su* o!r propositions z w necess>ily be true :5 ! premises are true499 ,by d$uction we inve/igate & unfold ! in=mation conta9$ 9 ! premises2 & ?is we c d by "o s+le rule--99,= any t]m occurr+ 9 any proposition sub/itute ! t]m :i* is ass]t$ 9 any premise to be id5tical ) x499 ,to obta9 c]ta9 d$uctions1 especially ^? involv+ negative conclusions1 we %all require to br+ into use ! second & ?ird ,laws ( ,?\ght1 & ! process ( reason+ w !n be call$ 99,indirect ,d$uction994 ,9 ! pres5t *apt]1 h[ev]1 ,i %all conf9e my att5tion to ^? results :i* c be obta9$ by ! process ( 99,direct ,d$uction991 t is1 by apply+ to ! premises !mselves ! rule ( sub/itution4 ,x w be f\nd t we c comb9e into "o h>moni\s sy/em1 n only ! v>i\s moods ( ! anci5t syllogism b a great numb] ( equally important =ms ( reason+1 :i* _h no recognis$ place 9 ! old logic4 ,we c at ! same "t disp5se entirely ) ! elaborate app>atus ( logical rules & mnemonic l9es1 :i* 7 requisite s long z ! vital pr9ciple ( reason+ 0 n cle>ly express$4 99,imm$iate ,inf]5ce499 ,probably ! simple/ ( all =ms ( inf]5ce is t :i* has be5 call$ 99,imm$iate ,inf]5ce991 because x c be p]=m$ ^u a s+le proposition4 ,x consi/s 9 jo9+ an adjective1 or o!r qualify+ clause ( ! same nature1 to bo? sides ( an id5tity1 & ass]t+ ! equival5ce ( ! t]ms ?us produc$4 ,= in/ance1 s9ce ,conductors ( electricity ,non-electrics1 x foll[s t ,liquid conductors ( electricity ,liquid non-electrics4 ,if we suppose t ,plants ,bodies decompos+ c>bonic acid1 x foll[s t ,microscopic plants ,microscopic bodies decompos+ c>bonic acid4 ,9 g5]al t]ms1 f ! id5tity ,a ,b we c inf] ! id5tity ,,ac ,,bc4 ,?is is b a case ( pla9 sub/itution2 = by ! fir/ ,law ( ,?\ght x mu/ be admitt$ t ,,ac ,,ac1 & if1 9 ! second side ( ?is id5tity1 we sub/itute = ,a its equival5t ,b1 we obta9 ,,ac ,,bc4 ,9 l mann] f ! p>tial id5tity ,a ,,ab we may obta9 ,,ac ,,abc by an exactly simil> act ( sub/itution2 & 9 e o!r case ! rule w be f\nd capable ( v]ification by ! pr9ciple ( inf]5ce4 ,! process :5 p]=m$ z "h describ$ w be q free f ! liability to error :i* ,i h %[n#ee to exi/ 9 8,imm$iate ,inf]5ce by add$ ,det]m9ants10 z describ$ by ,dr4 ,?omson4#ef #ee 99,elem5t>y ,lessons 9 ,logic991 p4 #hf4 #ef 99,outl9e ( ! ,laws ( ,?\ght991 #hg4 99,inf]5ce ) ,two ,simple ,id5tities499 ,"o ( ! mo/ common =ms ( inf]5ce1 & "o to :i* ,i %all especially direct att5tion1 is practis$ ) two simple id5tities4 ,f ! two /atem5ts t 8,london is ! capital ( ,engl&0 & 8,london is ! mo/ popul\s city 9 ! _w10 we in/antane\sly draw ! conclusion t 8,! capital ( ,engl& is ! mo/ popul\s city 9 ! _w40 ,simil>ly1 f ! id5tities ,hydrog5 ,sub/ance ( lea/ d5sity1 ,hydrog5 ,sub/ance ( lea/ atomic weight1 we inf] ,sub/ance ( lea/ d5sity ,sub/ance ( lea/ atomic weight4 ,! g5]al =m ( ! argum5t is exhibit$ 9 ! symbols ,b ,a 7#a7 ,b ,c 7#b7 h5ce ,a ,c4 7#c7 ,we may describe ! result by say+ t t]ms id5tical ) ! same t]m are id5tical ) ea* o!r2 & x is impossible to ov]look ! analogy to ! fir/ axiom ( ,euclid t 8?+s equal to ! same ?+ are equal to ea* o!r40 ,x has be5 v commonly suppos$ t ?is is a fundam5tal pr9ciple ( ?\ght1 incapable ( r$uction to any?+ simpl]4 ,b ,i ent]ta9 no d\bt t ?is =m ( reason+ is only "o case ( ! g5]al rule ( inf]5ce4 ,we h two propositions1 ,a ,b & ,b ,c1 & we may = a mom5t consid] ! second "o z affirm+ a tru? conc]n+ ,b1 :ile ! =m] "o in=ms u t ,b is id5tical ) ,a2 h5ce by sub/itution we may affirm ! same tru? ( ,a4 ,x happ5s 9 ?is p>ticul> case t ! tru? affirm$ is id5tity to ,c1 & we might1 if we pref]r$ x1 h consid]$ ! sub/itution z made by means ( ! second id5tity 9 ! fir/4 ,hav+ two id5tities we h a *oice ( ! mode 9 :i* we w make ! sub/itution1 ?\gh ! result is exactly ! same 9 ei!r case4 ,n[ comp>e ! ?ree foll[+ =mul1 7#a7 ,a ,b ,c1 h5ce ,a ,c 7#b7 ,a ,b ,c1 h5ce ,a ,c 7#c7 ,a ,b ,c1 no inf]5ce4 ,9 ! second =mula we h an id5tity & a diff]5ce1 & we are able to inf] a diff]5ce2 9 ! ?ird we h two diff]5ces & are unable to make any inf]5ce at all4 ,because ,a & ,c bo? diff] f ,b1 we _c tell :e!r !y w or w n diff] f ea* o!r4 ,! fl[]s & leaves ( a plant may bo? diff] 9 col\r f ! e>? 9 :i* ! plant gr[s1 & yet !y may diff] f ea* o!r2 9 o!r cases ! leaves & /em may bo? diff] f ! soil & yet agree ) ea* o!r4 ,:]e we h diff]5ce only we c make no inf]5ce2 :]e we h id5tity we c inf]4 ,?is fact gives great c\nt5ance to my ass]tion t inf]5ce proce$s always ?r\gh id5tity1 b may be equally well effect$ 9 propositions ass]t+ diff]5ce or id5tity4 ,def]r+ a m complete discussion ( ?is po9t1 ,i w only m5tion n[ t argum5ts f d\ble id5tity occur v frequ5tly1 & are usually tak5 = grant$1 ow+ to _! extreme simplicity4 ,9 reg>d to ! equival5ce ( words ?is =m ( inf]5ce mu/ be con/antly employ$4 ,if ! anci5t ,greek is our 99copp]991 !n x mu/ be ! ,fr5* 99cuivre991 ! ,g]man 99kupf]991 ! ,lat9 99cuprum991 because ^! are words1 9 "o s5se at lea/1 equival5t to copp]4 ,:5ev] we c give two def9itions or expressions = ! same t]m1 ! =mula applies2 ?us ,s5ior def9$ weal? z 8,all ^? ?+s1 & ^? ?+s only1 :i* are transf]able1 are limit$ 9 supply1 & are directly or indirectly productive ( pleasure or prev5tive ( pa940 ,weal? is also equival5t to 8?+s :i* h value 9 ex*ange20 h5ce obvi\sly1 8?+s :i* h value 9 ex*ange all ^? ?+s1 & ^? ?+s only1 :i* are transf]able1 c40 ,two expressions = ! same t]m are (t5 giv5 9 ! same s5t5ce1 & _! equival5ce impli$4 ,?us ,?omson & ,tait say1#eg 8,! naturali/ may be cont5t to "k matt] z t :i* c be p]ceiv$ by ! s5ses1 or z t :i* c be act$ ^u by or c ex]t =ce40 ,i take ?is to mean-- ,matt] :at c be p]ceiv$ by ! s5ses2 ,matt] :at c be act$ ^u by or c ex]t =ce4 #eg 99,treatise on ,natural ,philosophy991 vol4 i4 p4 #afa4 ,= ! t]m 8matt]0 9 ei!r ( ^! id5tities we may sub/itute its equival5t giv5 9 ! o!r def9ition4 ,else:]e !y (t5 employ s5t5ces ( ! =m exemplifi$ 9 ! foll[+3#eh 8,! integral curvature1 or :ole *ange ( direction ( an arc ( a plane curve1 is ! angle ?r\gh :i* ! tang5t has turn$ z we pass f "o extremity to ! o!r40 ,?is s5t5ce is c]ta9ly ( ! =m-- ,! integral curvature ! :ole *ange ( direction1 c4 ! angle ?r\gh :i* ! tang5t has turn$1 c4 #eh 99,treatise on ,natural ,philosophy991 vol4 i4 p4 #f4 ,disguis$ cases ( ! same k9d ( inf]5ce occur ?r\gh\t all sci5ces1 & a rem>kable in/ance is f\nd 9 algebraic geometry4 ,ma!maticians readily %[ t e equation ( ! =m 99y99 99mx99 99c99 corresponds to or repres5ts a /raight l9e2 x is also easily prov$ t ! same equation is equival5t to "o ( ! g5]al =m ,a99x99 ,b99y99 ,c #j1 & 99vice v]s994 ,h5ce x foll[s t e equation ( ! =m 9 "q1 t is to say1 e equation ( ! fir/ degree1 corresponds to or repres5ts a /raight l9e4#ei #ei ,todhunt]'s 99,plane ,co-ord9ate ,geometry991 *ap4 ii4 pp4 #aa-ad4 99,inf]5ce ) a ,simple & a ,p>tial ,id5tity499 ,a =m ( reason+ some:at diff]5t f t la/ consid]$ consi/s 9 inf]5ce-betwe5 a simple & a p>tial id5tity4 ,if we h two propositions ( ! =ms ,a ,b1 ,b ,,bc1 we may !n sub/itute = ,b 9 ei!r proposition its equival5t 9 ! o!r1 gett+ 9 bo? cases ,a ,,bc2 9 ?is we may if we l make a second sub/itution = ,b1 gett+ ,a ,,ac4 ,?us1 s9ce 8,! ,mont ,blanc is ! highe/ m\nta9 9 ,europe1 & ! ,mont ,blanc is deeply cov]$ ) sn[10 we inf] by an obvi\s sub/itution t 8,! highe/ m\nta9 9 ,europe is deeply cov]$ ) sn[40 ,^! propositions :5 rigor\sly /at$ fall into ! =ms above exhibit$4 ,?is mode ( inf]5ce is con/antly employ$ :5 = a t]m we sub/itute its def9ition1 or 99vice v]s994 ,! v purpose ( a def9ition is to all[ a s+le n\n to be employ$ 9 place ( a long descriptive phrase4 ,?us1 :5 we say 8,a circle is a curve ( ! second degree10 we may sub/itute a def9ition ( ! circle1 gett+ 8,a curve1 all po9ts ( :i* are at equal di/ances f "o po9t1 is a curve ( ! second degree40 ,! real =ms ( ! propositions "h giv5 are exactly ^? %[n 9 ! symbolic /atem5t1 b 9 ?is & _m o!r cases x w be suffici5t to /ate !m 9 ord9>y elliptical language = sake ( brevity4 ,9 sci5tific treatises a t]m & its def9ition are (t5 bo? giv5 9 ! same s5t5ce1 z 9 8,! weight ( a body 9 any giv5 locality1 or ! =ce ) :i* ! e>? attracts x1 is proportional to its mass40 ,! conjunction 99or99 9 ?is /atem5t gives ! =ce ( equival5ce to ! p>5!tic phrase1 s t ! propositions really are ,weight ( a body =ce ) :i* ! e>? attracts x4 ,weight ( a body weight1 c4 proportional to its mass4 ,a slightly diff]5t case ( inf]5ce consi/s 9 sub/itut+ 9 a proposition ( ! =m ,a ,,ab1 a def9ition ( ! t]m ,b4 ,?us f ,a ,,ab & ,b ,c we get ,a ,,ac4 ,= in/ance1 we may say t 8,metals are elem5ts0 & 8,elem5ts are incapable ( decomposition40 ,metal metal elem5t4 ,elem5t :at is incapable ( decomposition4 ,h5ce ,metal metal incapable ( decomposition4 ,x is almo/ ne$less to po9t out t ! =m ( ^! argum5ts does n suff] any real modification if "s ( ! t]ms happ5 to be negative2 inde$ 9 ! la/ example 8incapable ( decomposition0 may be treat$ z a negative t]m4 ,tak+ ,a metal ,b elem5t ,c capable ( decomposition 99c99 incapable ( decomposition2 ! propositions are ( ! =ms ,a ,,ab ,b 99c99 :5ce1 by sub/itution1 ,a ,a99c994 99,inf]5ce ( a ,p>tial f ,two ,p>tial ,id5tities499 ,h[ev] common be ! cases ( inf]5ce already notic$1 !re is a =m occurr+ almo/ m frequ5tly1 & :i* des]ves mu* att5tion1 because x occupi$ a prom95t place 9 ! anci5t syllogi/ic sy/em4 ,t sy/em /rangely ov]look$ all ! k9ds ( argum5t we h z yet consid]$1 & select$1 z ! type ( all reason+1 "o :i* employs two p>tial id5tities z premises4 ,?us f ! propositions ,sodium is a metal 7#a7 ,metals conduct electricity1 7#b7 we may conclude t ,sodium conducts electricity4 7#c7 ,tak+ ,a1 ,b1 ,c to repres5t ! ?ree t]ms respectively1 ! premises are ( ! =ms ,a ,,ab 7#a7 ,b ,,bc4 7#b7 ,n[ = ,b 9 7#a7 we c sub/itute its expression z giv5 9 7#b71 obta9+ ,a ,,abc1 7#c7 or1 9 words1 f ,sodium sodium metal1 7#a7 ,metal metal conduct+ electricity1 7#b7 we inf] ,sodium sodium metal conduct+ electricity1 7#c7 :i*1 9 ! elliptical language ( common life1 becomes 8,sodium conducts electricity40 ,! above is a syllogism 9 ! mood call$ ,b>b>a#fj 9 ! truly b>b>\s language ( anci5t logicians2 & ! fir/ figure ( ! syllogism conta9$ ,b>b>a & ?ree o!r moods :i* 7 e/eem$ di/9ct =ms ( argum5t4 ,b x is wor?y ( notice t1 )\t any real *ange 9 our =m ( inf]5ce1 we readily include ^! ?ree o!r moods "u ,b>b>a4 ,! negative mood ,cel>5t w be repres5t$ by ! example #fj ,an explanation ( ?is & o!r te*nical t]ms ( ! old logic w be f\nd 9 my 99,elem5t>y ,lessons 9 ,logic991 ,six? ,edition1 #ahgf2 ,macmillan4 ,neptune is a planet1 7#a7 ,no planet has retrograde motion2 7#b7 ,h5ce ,neptune has n retrograde motion4 7#c7 ,if we put ,a = ,neptune1 ,b = planet1 & ,c = 8hav+ retrograde motion10 !n by ! correspond+ negative t]m c1 we d5ote 8n hav+ retrograde motion40 ,! premises n[ fall into ! =ms ,a ,,ab 7#a7 ,b ,b99c991 7#b7 & by sub/itution = ,b1 exactly z be=e1 we obta9 ,a ,,ab99c994 7#c7 ,:at is call$ 9 ! old logic a p>ticul> conclusion may be d$uc$ )\t any real v>iation 9 ! symbols4 ,p>ticul> quantity is indicat$1 z be=e m5tion$ 7p4 #da71 by jo9+ to ! t]m an indef9ite adjective ( quantity1 su* z 99"s991 99a "p (991 99c]ta9991 c41 mean+ t an unkn[n "p ( ! t]m ent]s into ! proposition z subject4 ,consid]able d\bt & ambiguity arise out ( ! "q :e!r ! "p may n 9 "s cases be ! :ole1 & 9 ! syllogism at lea/ x mu/ be und]/ood 9 ?is s5se4#fa ,n[1 if we take a lett] to repres5t ?is indef9ite "p1 we ne$ make no *ange 9 our =mul to express ! syllogisms ,d>ii & ,f]io4 ,consid] ! example-- #fa 99,elem5t>y ,lessons 9 ,logic991 pp4 #fg1 #gi4 ,"s metals are ( less d5sity ?an wat]1 7#a7 ,all bodies ( less d5sity ?an wat] w float ^u ! surface ( wat]2 h5ce 7#b7 ,"s metals w float ^u ! surface ( wat]4 7#c7 ,let ,a "s metals1 ,b body ( less d5sity ?an wat]1 ,c float+ on ! surface ( wat] !n ! propositions are evid5tly z be=e1 ,a ,,ab1 7#a7 ,b ,,bc2 7#b7 h5ce ,a ,,abc1 7#c7 ,?us ! syllogism ,d>ii does n really diff] f ,b>b>a4 ,if ! read] pref] x1 we c readily employ a di/9ct symbol = ! indef9ite sign ( quantity4 ,let ,p "s1 ,q metal1 ,b & ,c hav+ ! same mean+s z be=e4 ,!n ! premises become ,,pq ,,pqb1 7#a7 ,b ,,bc2 7#b7 h5ce1 by sub/itution1 z be=e1 ,,pq ,,pqbc4 7#c7 ,except t ! =mul look a little m complicat$ !re is no diff]5ce :atev]4 ,! mood ,f]io is ( exactly ! same "* z ,d>ii or ,b>b>a1 except t x involves ! use ( a negative t]m4 ,take ! example1 ,bodies :i* are equally ela/ic 9 all directions d n d\bly refract light2 ,"s cry/als are bodies equally ela/ic 9 all directions2 !re=e1 "s cry/als d n d\bly refract light4 ,assign+ ! lett]s z foll[s3-- ,a "s cry/als1 ,b bodies equally ela/ic 9 all directions1 ,c d\bly refract+ light1 99c99 n d\bly refract+ light4 ,our argum5t is ( ! same =m z be=e1 & may be concisely /at$ 9 "o l9e1 ,a ,,ab ,,ab99c994 ,if x is pref]r$ to put ,,pq = ! indef9ite 99"s cry/als991 we h ,,pq ,,pqb ,,pqb99c994 ,! only diff]5ce is t ! negative t]m c takes ! place ( ,c 9 ! mood ,d>ii4 99,ellipsis ( ,t]ms 9 ,p>tial ,id5tities499 ,! read] w probably h notic$ t ! conclusion :i* we obta9 f premises is (t5 m full ?an t drawn by ! old ,ari/otelian processes4 ,?us f 8,sodium is a metal10 & 8,metals conduct electricity10 we inf]r$ 7p4 #ee7 t 8,sodium sodium1 metal1 conduct+ electricity10 :]eas ! old logic simply concludes t 8,sodium conducts electricity40 ,symbolically1 f ,a ,,ab1 & ,b ,,bc1 we get ,a ,,abc1 :]eas ! old logic gets at ! mo/ ,a ,,ac4 ,x is !re=e well to %[ t )\t employ+ any o!r pr9ciples ( inf]5ce ?an ^? already describ$1 we may inf] ,a ,,ac f ,a ,,abc1 ?\gh we _c inf] ! latt] m full & accurate result f ! =m]4 ,we may %[ ?is mo/ simply z foll[s3-- ,by ! fir/ ,law ( ,?\ght x is evid5t t ,,aa ,,aa2 & if we h giv5 ! proposition ,a ,,abc1 we may sub/itute = bo? ! ,a's 9 ! second side ( ! above1 obta9+ ,,aa ,,abc 4 ,,abc4 ,b f ! prop]ty ( logical symbols express$ 9 ! ,law ( ,simplicity 7p4 #cc7 "s ( ! repeat$ lett]s may be made to coalesce1 & we h ,a ,,abc 4 ,c4 ,sub/itut+ aga9 = ,,abc its equival5t ,a1 we obta9 ,a ,,ac1 ! desir$ result4 ,by a simil> process ( reason+ x may be %[n t we c always drop out any t]m appe>+ 9 "o memb] ( a proposition1 provid$ t we sub/itute = x ! :ole ( ! o!r memb]4 ,?is process 0 describ$ 9 my fir/ logical ,essay1#fb z 99,intr9sic ,elim9ation991 b x might p]haps be bett] entitl$ ! 99,ellipsis ( ,t]ms994 ,x enables u to get rid ( ne$less t]ms by /rict sub/itutive reason+4 #fb 99,pure ,logic991 p4 #ai4 99,inf]5ce ( a ,simple f ,two ,p>tial ,id5tities499 ,two t]ms may be connect$ toge!r by two p>tial id5tities 9 yet ano!r mann]1 & a case ( inf]5ce !n arises :i* is ( ! highe/ importance4 ,9 ! two premises ,a ,,ab 7#a7 ,b ,,ab 7#b7 ! second memb] ( ea* is ! same2 s t we c by obvi\s sub/itution obta9 ,a ,b4 ,?us1 9 pla9 geometry we readily prove t 8,e equilat]al triangle is also an equiangul> triangle10 & we c ) equal ease prove t 8,e equiangul> triangle is an equilat]al triangle40 ,!nce by sub/itution1 z expla9$ above1 we pass to ! simple id5tity1 ,equilat]al triangle equiangul> triangle4 ,we ?us prove t "o class ( triangles is entirely id5tical ) ano!r class2 t is to say1 !y diff] only 9 our way ( nam+ & reg>d+ !m4 ,! great importance ( ?is process ( inf]5ce arises f ! fact t ! conclusion is m simple & g5]al ?an ei!r ( ! premises1 & conta9s z mu* in=mation z bo? ( !m put toge!r4 ,x is on ?is acc\nt con/antly employ$ 9 inductive inve/igation1 z w aft]w>ds be m fully expla9$1 & x is ! natural mode by :i* we arrive at a conviction ( ! tru? ( simple id5tities z exi/+ betwe5 classes ( num]\s objects4 99,inf]5ce ( a ,limit$ f ,two ,p>tial ,id5tities499 ,we h consid]$ "s argum5ts :i* are ( ! type treat$ by ,ari/otle 9 ! fir/ figure ( ! syllogism4 ,b !re exi/ two o!r types ( argum5t :i* employ a pair ( p>tial id5tities4 ,if our premises are z %[n 9 ^! symbols1 ,b ,,ab 7#a7 ,b ,,cb1 7#b7 we may sub/itute = ,b ei!r by 7#a7 9 7#b7 or by 7#b7 9 7#a71 & by bo? modes we obta9 ! conclusion ,,ab ,,cb1 7#c7 a proposition ( ! k9d :i* we h call$ a limit$ id5tity 7p4 #db74 ,?us1 = example1 ,potassium potassium metal 7#a7 ,potassium potassium capable ( float+ on wat]2 7#b7 h5ce ,potassium metal potassium capable ( float+ on wat]4 7#c7 ,?is is really a syllogism ( ! mood ,d>apti 9 ! ?ird figure1 except t we obta9 a conclusion ( a m exact "* ?an ! old syllogism gives4 ,f ! premises 8,potassium is a metal0 & 8,potassium floats on wat]10 ,ari/otle w\ld h inf]r$ t 8,"s metals float on wat]40 ,b if inquiry 7 made :at ! 8"s metals0 are1 ! answ] w\ld c]ta9ly be 8,metal :i* is potassium40 ,h5ce ,ari/otle's conclusion simply leaves out "s ( ! in=mation af=d$ 9 ! premises4 ,x ev5 leaves u op5 to int]pret ! 99"s metals99 9 a wid] s5se ?an we are w>rant$ 9 do+4 ,f ^! di/9ct defects ( ! old syllogism ! process ( sub/itution is free1 & ! new process only incurs ! possible objection ( be+ t$i\sly m9ute & accurate4 99,miscellane\s ,=ms ( ,d$uctive ,inf]5ce499 ,! m common =ms ( d$uctive reason+ hav+ be5 exhibit$ & demon/rat$ on ! pr9ciple ( sub/itution1 !re /ill rema9 _m1 9 fact an indef9ite numb]1 :i* may be expla9$ ) ne>ly equal ease4 ,su* z involve ! use ( disjunctive propositions w be describ$ 9 a lat] *apt]1 & sev]al ( ! syllogi/ic moods :i* include negative t]ms w be m conv5i5tly treat$ aft] we h introduc$ ! symbolic use ( ! second & ?ird laws ( ?\ght4 ,we sometimes meet ) a *a9 ( propositions :i* all[ ( repeat$ sub/itution1 & =m an argum5t call$ 9 ! old logic a ,sorites4 ,take1 = in/ance1 ! premises ,iron is a metal1 7#a7 ,metals are good conductors ( electricity1 7#b7 ,good conductors ( electricity are useful = telegraphic purposes4 7#c7 ,x obvi\sly foll[s t ,iron is useful = telegraphic purposes4 7#d7 ,n[ if we take our lett]s ?us1 ,a ,iron1 ,b metal1 ,c good conductor ( electricity1 ,d useful = telegraphic purposes1 ! premises w assume ! =ms ,a ,,ab1 7#a7 ,b ,,bc1 7#b7 ,c ,,cd4 7#c7 ,= ,b 9 7#a7 we c sub/itute its equival5t 9 7#b7 obta9+1 z be=e1 ,a ,,abc4 ,sub/itut+ = ,c 9 ?is int]m$iate result its equival5t z giv5 9 7#c71 we obta9 ! complete conclusion ,a ,,abcd4 7#d7 ,! full int]pretation is t 99,iron is iron1 metal1 good conductor ( electricity1 useful = telegraphic purposes991 :i* is abridg$ 9 common language by ! ellipsis ( ! circum/ances :i* are n ( imm$iate importance4 ,in/ead ( all ! propositions be+ exactly ( ! same k9d z 9 ! la/ example1 we may h a s]ies ( premises ( v>i\s "*2 = in/ance1 ,common salt is sodium *loride1 7#a7 ,sodium *loride cry/allizes 9 a cubical =m1 7#b7 ,:at cry/allizes 9 a cubical =m does n possess ! p[] ( d\ble refraction2 7#c7 x w foll[ t ,common salt does n possess ! p[] ( d\ble refraction4 7#d7 ,tak+ our lett]-t]ms ?us1 ,a ,common salt1 ,b ,sodium *loride1 ,c ,cry/alliz+ 9 a cubical =m1 ,d ,possess+ ! p[] ( d\ble refraction1 we may /ate ! premises 9 ! =ms ,a ,b1 7#a7 ,b ,,bc1 7#b7 ,c ,c99d994 7#c7 ,sub/itut+ by 7#c7 9 7#b7 & !n by 7#b7 z ?us alt]$ 9 7#a7 we obta9 ,a ,,bc99d991 7#d7 :i* is a m precise v]sion ( ! common conclusion4 ,we (t5 meet ) a s]ies ( propositions describ+ ! qualities or circum/ances ( ! "o same ?+1 & we may comb9e !m all into "o proposition by ! process ( sub/itution4 ,?is case is1 9 fact1 t :i* ,dr4 ,?omson has call$ 8,imm$iate ,inf]5ce by ! sum ( sev]al pr$icates10 & 8 example w s]ve my purpose well4#fc ,he describes copp] z 8,a metal--( a r$ col\r--& disagreeable smell--& ta/e--all ! prep>ations ( :i* are poison\s--:i* is highly malleable--ductile--& t5aci\s--) a specific gravity ( ab\t #h4hc40 ,if we assign ! lett] ,a to copp]1 & ! succe$+ lett]s ( ! alphabet 9 succession to ! s]ies ( pr$icates1 we h n9e di/9ct /atem5ts1 ( ! =m ,a ,,ab 7#a7 ,a ,,ac 7#b7 ,a ,,ad 7#c7 444 ,a ,,ak 7#i74 ,we c readily comb9e ^! propositions into "o by sub/itut+ = ,a 9 ! second side ( 7#a7 its expression 9 7#b74 ,we ?us get #fc 99,an ,outl9e ( ! ,necess>y ,laws ( ,?\ght991 ,fif? ,ed4 p4 #afa4 ,a ,,abc1 & by repeat+ ! process ov] & ov] aga9 we obvi\sly get ! s+le proposition ,a ,,abcd 444 ,,jk4 ,b ,dr4 ,?omson is mi/ak5 9 suppos+ t we c obta9 9 ?is mann] a 99def9ition99 ( copp]4 ,/rictly speak+1 ! above proposition is only a 99description99 ( copp]1 & all ! ord9>y descriptions ( sub/ances 9 sci5tific works may be summ$ up 9 ?is =m4 ,?us we may ass]t ( ! organic sub/ances call$ ,p>aff9s t !y are all saturat$ hydroc>bons1 incapable ( unit+ ) o!r sub/ances1 produc$ by heat+ ! alcoholic iodides ) z9c1 & s on4 ,x may be %[n t no am\nt ( ord9>y description c be equival5t to a def9ition ( any sub/ance4 99,fallacies499 ,i h hi!rto be5 engag$ 9 %[+ t all ! =ms ( reason+ ( ! old syllogi/ic logic1 & an indef9ite numb] ( o!r =ms 9 addition1 may be readily & cle>ly expla9$ on ! s+le pr9ciple ( sub/itution4 ,x is n[ desirable to %[ t ! same pr9ciple w prev5t u fall+ into fallacies4 ,s long z we exactly obs]ve ! "o rule ( sub/itution ( equival5ts x w be impossible to commit a 99p>alogism991 t is to break any "o ( ! elaborate rules ( ! anci5t sy/em4 ,! "o new rule is ?us prov$ to be z p[]ful z ! six1 eight1 or m rules by :i* ! correctness ( syllogi/ic reason+ 0 gu>d$4 ,x 0 a fundam5tal rule1 = in/ance1 t two negative premises c\ld give no conclusion4 ,if we take ! propositions ,granite is n a s$im5t>y rock1 7#a7 ,basalt is n a s$im5t>y rock1 7#b7 we ought n to be able to draw any inf]5ce conc]n+ ! relation betwe5 granite & basalt4 ,tak+ our lett]-t]ms ?us3 ,a granite1 ,b s$im5t>y rock1 ,c basalt1 ! premises may be express$ 9 ! =ms ,a ,b1 7#a7 ,c ,b4 7#b7 ,we h 9 ?is =m two /atem5ts ( diff]5ce2 b ! pr9ciple ( inf]5ce c only "w ) a /atem5t ( agreem5t or id5tity 7p4 #fc74 ,?us our rule gives u no p[] :atev] ( draw+ any inf]5ce2 ?is is exactly 9 accordance ) ! fif? rule ( ! syllogism4 ,x is to be rememb]$1 inde$1 t we claim ! p[] ( always turn+ a negative proposition into an affirmative "o 7p4 #de72 & x might seem t ! old rule aga9/ negative premises w\ld ?us be circumv5t$4 ,let u try4 ,! premises 7#a7 & 7#b7 :5 affirmatively /at$ take ! =ms ,a ,a99b99 7#a7 ,c ,c99b994 7#b7 ,! read] w f9d x impossible by ! rule ( sub/itution to discov] a relation betwe5 ,a & ,c4 ,?ree t]ms occur 9 ! above premises1 namely ,a1 99b991 & ,c2 b !y are s comb9$ t no t]m occurr+ 9 "o has its exact equival5t /at$ 9 ! o!r4 ,no sub/itution c !re=e be made1 & ! pr9ciple ( ! fif? rule ( ! syllogism holds true4 ,fallacy is impossible4 ,x w\ld be a mi/ake1 h[ev]1 to suppose t ! m]e occurr5ce ( negative t]ms 9 bo? premises ( a syllogism r5d]s !m incapable ( yield+ a conclusion4 ,! old rule in=m$ u t f two negative premises no conclusion c\ld be drawn1 b x is a fact t ! rule 9 ?is b>e =m does n hold univ]sally true2 & ,i am n aw>e t any precise explanation has be5 giv5 ( ! conditions "u :i* x is or is n imp]ative4 ,consid] ! foll[+ example3 ,:atev] is n metallic is n capable ( p[]ful magnetic influ5ce1 7#a7 ,c>bon is n metallic1 7#b7 ,!re=e1 c>bon is n capable ( p[]ful magnetic influ5ce4 7#c7 ,"h we h two di/9ctly negative premises 7#a7 & 7#b71 & yet !y yield a p]fectly valid negative conclusion 7#c74 ,! syllogi/ic rule is actually falsifi$ 9 its b>e & g5]al /atem5t4 ,9 ?is & _m o!r cases we c conv]t ! propositions into affirmative ones :i* w yield a conclusion by sub/itution )\t any difficulty4 ,to %[ ?is let ,a c>bon1 ,b metallic1 ,c capable ( p[]ful magnetic influ5ce4 ,! premises readily take ! =ms 99b99 99bc991 7#a7 ,a ,a99b991 7#b7 & sub/itution = 99b99 9 7#b7 by means ( 7#a7 gives ! conclusion ,a ,a99bc994 7#c7 ,our pr9ciple ( inf]5ce !n includes ! rule ( negative premises :5ev] x is true1 & discrim9ates correctly betwe5 ! cases :]e x does & does n hold true4 ,! p>alogism1 anci5tly call$ 99! ,fallacy ( ,undi/ribut$ ,middle991 is also easily exhibit$ & infallibly avoid$ by our sy/em4 ,let ! premises be ,hydrog5 is an elem5t1 7#a7 ,all metals are elem5ts4 7#b7 ,accord+ to ! syllogi/ic rules ! middle t]m 8elem5t0 is "h undi/ribut$1 & no conclusion c be obta9$2 we _c tell !n :e!r hydrog5 is or is n a metal4 ,repres5t ! t]ms z foll[s ,a hydrog51 ,b elem5t1 ,c metal4 ,! premises !n become ,a ,,ab1 7#a7 ,c ,,cb4 7#b7 ,! read] w "h1 z 9 a =m] page 7p4 #fb71 f9d x impossible to make any sub/itution4 ,! only t]m :i* occurs 9 bo? premises is ,b1 b x is diff]5tly comb9$ 9 ! two premises4 ,= ,b we mu/ n sub/itute ,a1 :i* is equival5t to ,,ab1 n to ,b4 ,nor mu/ we confuse toge!r ,,cb & ,,ab1 :i*1 ?\gh !y conta9 "o common lett]1 are diff]5t aggregate t]ms4 ,! rule ( sub/itution gives u no "r to decompose comb9ations2 & if we adh]e rigidly to ! rule1 t if two t]ms are /at$ to be equival5t we may sub/itute "o = ! o!r1 we _c commit ! fallacy4 ,x is app>5t t ! =m ( premises /at$ above is ! same z t :i* we obta9$ by translat+ two negative premises into ! affirmative =m4 ,! old fallacy1 te*nically call$ ! 99,illicit ,process ( ! ,major ,t]m991 is m easy to commit & m difficult to detect ?an any o!r brea* ( ! syllogi/ic rules4 ,9 our sy/em x c\ld h>dly occur4 ,f ! premises ,all planets are subject to gravity1 7#a7 ,fix$ />s are n planets1 7#b7 we might inadv]t5tly b fallaci\sly inf] t1 8,fix$ />s are n subject to gravity40 ,to r$uce ! premises to symbolic =m1 let ,a planet ,b fix$ /> ,c subject to gravity2 !n we h ! propositions ,a ,,ac 7#a7 ,b ,b99a994 7#b7 ,! read] w try 9 va9 to produce f ^! premises by legitimate sub/itution any relation betwe5 ,b & ,c2 he c\ld n !n commit ! fallacy ( ass]t+ t ,b is n ,c4 ,!re rema9 two o!r k9ds ( p>alogism1 commonly kn[n z ! fallacy ( ,f\r ,t]ms & ! ,illicit ,process ( ! ,m9or ,t]m4 ,!y are s evid5tly impossible :ile we obey ! rule ( ! sub/itution ( equival5ts1 t x is n necess>y to give any illu/rations4 ,:5 !re are f\r di/9ct t]ms 9 two propositions z 9 ,a ,b & ,c ,d1 !re c\ld evid5tly be no op5+ = sub/itution4 ,z to ! ,illicit ,process ( ! ,m9or ,t]m x consi/s 9 a flagrant sub/itution = a t]m ( ano!r wid] t]m :i* is n kn[n to be equival5t to x1 & :i* is !re=e n all[$ by our rule to be sub/itut$ = x4 ,,*apt] ,v4 ,,disjunctive ,,propositions4 ,9 ! previ\s *apt] ,i h exhibit$ v>i\s cases ( d$uctive reason+ by ! process ( sub/itution1 avoid+ ! introduction ( disjunctive propositions2 b we _c long def] ! consid]ation ( ?is m complex class ( id5tities4 ,g5]al t]ms arise1 z we h se5 7p4 #bd71 f classify+ or m5tally unit+ toge!r all objects :i* agree 9 c]ta9 qualities1 ! value ( ?is union consi/+ 9 ! fact t ! p[] ( k is multipli$ !reby4 ,9 =m+ su* classes or g5]al notions1 we ov]look or ab/ract ! po9ts ( diff]5ce :i* exi/ betwe5 ! objects jo9$ toge!r1 & fix our att5tion only on ! po9ts ( agreem5t4 ,b e process ( ?\ght may be said to h its inv]se process1 :i* consi/s 9 undo+ ! effects ( ! direct process4 ,j z division undoes multiplication1 & evolution undoes involution1 s we mu/ h a process :i* undoes g5]alization1 or ! op]ation ( =m+ g5]al notions4 ,?is inv]se process w consi/ 9 di/+ui%+ ! sep>ate objects or m9or classes :i* are ! con/itu5t p>ts ( any wid] class4 ,if we m5tally unite toge!r c]ta9 objects visible 9 ! sky & call !m planets1 we %all aft]w>ds ne$ to di/+ui% ! cont5ts ( ?is g5]al notion1 :i* we d 9 ! disjunctive proposition-- ,a planet is ei!r ,m]cury or ,v5us or ! ,e>? or 444 or ,neptune4 ,hav+ =m$ ! v wide class 8v]tebrate animal10 we may specify its subord9ate classes ?us3--8,a v]tebrate animal is ei!r a mammal1 bird1 reptile1 or fi%40 ,nor is !re any limit to ! numb] ( possible alt]natives4 8,an exog5\s plant is ei!r a ranunculus1 a poppy1 a crucif]1 a rose1 or x belongs to "s "o ( ! o!r sev5ty natural ord]s ( exog5s at pres5t recogniz$ by botani/s40 ,a ca!dral *ur* 9 ,engl& mu/ be ei!r t ( ,london1 ,cant]bury1 ,w9*e/]1 ,salisbury1 ,man*e/]1 or ( "o ( ab\t tw5ty-f\r cities possess+ su* *ur*es4 ,& if we 7 to attempt to specify ! mean+ ( ! t]m 8/>10 we %\ld require to enum]ate z alt]natives1 n only ! _m ?\s&s ( />s record$ 9 catalogues1 b ! _m millions unnam$4 ,:5ev] we ?us di/+ui% ! p>ts ( a g5]al notion we employ a disjunctive proposition1 9 at lea/ "o side ( :i* are sev]al alt]natives jo9$ by ! s-call$ disjunctive conjunction or1 a contract$ =m ( 99o!r994 ,!re mu/ be "s relation betwe5 ! p>ts ?us connect$ 9 "o proposition2 we may call x ! 99disjunctive99 or 99alt]native99 relation1 & we mu/ c>efully inquire into its nature4 ,?is relation is t ( ignorance & d\bt1 giv+ rise to *oice4 ,:5ev] we classify & ab/ract we mu/ op5 ! way to su* unc]ta9ty4 ,by fix+ our att5tion on c]ta9 attributes to ! exclusion ( o!rs1 we necess>ily leave x d\btful :at ^? o!r attributes are4 ,! t]m 8mol> too?0 be>s ^u ! face ( x t x is a "p ( ! wid] t]m 8too?40 ,b if we meet ) ! simple t]m 8too?0 !re is no?+ to indicate :e!r x is an incisor1 a can9e1 or a mol> too?4 ,?is d\bt1 h[ev]1 may be resolv$ by fur!r in=mation1 & we h to consid] :at are ! appropriate logical processes = treat+ disjunctive propositions 9 connection ) o!r propositions disjunctive or o!rwise4 99,expression ( ! ,alt]native ,relation499 ,9 ord] to repres5t disjunctive propositions ) conv5i5ce we require a sign ( ! alt]native relation1 equival5t to "o mean+ at lea/ ( ! little conjunction 99or99 s frequ5tly us$ 9 common language4 ,i propose to use = ?is purpose ! symbol 4 ,9 my fir/ logical essay ,i foll[$ ! practice ( ,boole & adopt$ ! sign 2 b ?is sign %\ld n be employ$ unless !re exi/s exact analogy betwe5 ma!matical addition & logical alt]nation4 ,we %all f9d t ! analogy is imp]fect1 & t !re is su* pr(\nd diff]5ce betwe5 logical & ma!matical t]ms z %\ld prev5t our unit+ !m by ! same symbol4 ,accord+ly ,i h *os5 a sign 1 :i* seems aptly to sugge/ :atev] degree ( analogy may exi/ )\t imply+ m4 ,! exact mean+ ( ! symbol we w n[ proce$ to inve/igate4 99,nature ( ! ,alt]native ,relation499 ,be=e treat+ disjunctive propositions x is indisp5sable to decide :e!r ! alt]natives mu/ be consid]$ exclusive or unexclusive4 ,by 99exclusive alt]natives99 we mean ^? :i* _c conta9 ! same ?+s4 ,if we say 8,ar*es are circul> or po9t$10 x is c]ta9ly to be und]/ood t ! same ar* _c be describ$ z bo? circul> & po9t$4 ,_m examples1 on ! o!r h&1 c readily be sugge/$ 9 :i* two or m alt]natives may hold true ( ! same object4 ,?us ,lum9\s bodies are self-lum9\s or lum9\s by reflection4 ,x is und\bt$ly possible1 by ! laws ( optics1 t ! same surface may at "o & ! same mom5t give (f light ( its own & reflect light f o!r bodies4 ,we speak famili>ly ( 99deaf or dumb99 p]sons1 kn[+ t ! majority ( ^? :o are deaf f bir? are also dumb4 ,!re c be no d\bt t 9 a great _m cases1 p]haps ! great] numb] ( cases1 alt]natives are exclusive z a matt] ( fact4 ,any "o numb] is incompatible ) any o!r2 "o po9t ( "t or place is exclusive ( all o!rs4 ,rog] ,bacon di$ ei!r 9 #abhd or #abib2 x is c]ta9 t he c\ld n die 9 bo? ye>s4 ,h5ry ,field+ 0 born ei!r 9 ,dubl9 or ,som]set%ire2 he c\ld n be born 9 bo? places4 ,!re is s mu* m precision & cle>ness 9 ! use ( exclusive alt]natives t we ought d\btless to select !m :5 possible4 ,old works on logic accord+ly conta9$ a rule direct+ t ! 99,membra divid5tia991 ! p>ts ( a division or ! con/itu5t species ( a g5us1 %\ld be exclusive ( ea* o!r4 ,x is no d\bt ow+ to ! great preval5ce & conv5i5ce ( exclusive divisions t ! majority ( logicians h held x necess>y to make e alt]native 9 a disjunctive proposition exclusive ( e o!r "o4 ,aqu9as consid]$ t :5 ?is 0 n ! case ! proposition 0 actually 99false991 & ,kant adopt$ ! same op9ion4#fd ,a multitude ( /atem5ts to ! same effect might readily be quot$1 & if ! "q 7 to be det]m9$ by ! weight ( hi/orical evid5ce1 x w\ld c]ta9ly g aga9/ my view4 ,among rec5t logicians ,hamilton1 z well z ,boole1 took ! exclusive side4 ,b !re are au?orities to ! opposite effect4 ,:ately1 ,mansel1 & ,j4 ,s4 ,mill h all po9t$ out t we may (t5 treat alt]natives z 99,compossible991 or true at ! same "t4 ,:ately gives u an example1#fe 8,virtue t5ds to procure u ei!r ! e/eem ( mank9d1 or ! fav\r ( ,god10 & he adds--8,"h bo? memb]s are true1 & consequ5tly f "o be+ affirm$ we are n au?oriz$ to d5y ! o!r4 ,( c\rse we are left to conjecture 9 ea* case1 f ! context1 :e!r x is meant to be impli$ t ! memb]s are or are n exclusive40 ,mansel says1#ff 899,we may happ5 to "k99 t two alt]natives _c be true toge!r1 s t ! affirmation ( ! second necessitates ! d5ial ( ! fir/2 b ?is1 z ,boe?ius obs]ves1 is a 99mat]ial991 n a 99=mal99 consequ5ce40 ,mill has also po9t$ out ! absurdities :i* w\ld arise f always int]pret+ alt]natives z exclusive4 8,if we ass]t10 he says1#fg 8t a man :o has act$ 9 "s p>ticul> way mu/ be ei!r a knave or a fool1 we by no means ass]t1 or int5d to ass]t1 t he _c be bo?40 ,aga91 8to make an entirely unselfi% use ( despotic p[]1 a man mu/ be ei!r a sa9t or a philosoph]4444 ,does ! disjunctive premise necess>ily imply1 or mu/ x be con/ru$ z suppos+1 t ! same p]son _c be bo? a sa9t & a philosoph]8 ,su* a con/ruction w\ld be ridicul\s40 #fd ,mansel's 99,aldri*991 p4 #ajc1 & 99,prolegom5a ,logica991 p4 #bba4 #fe 99,elem5ts ( ,logic991 ,book ,,ii4 *ap4 iv4 sect4 #d4 #ff ,aldri*1 99,artis ,logic ,rudim5ta991 p4 #ajd4 #fg 99,exam9ation ( ,sir ,w4 ,hamilton's ,philosophy991 pp4 #deb-ded4 ,i discuss ?is subject fully because x is really ! po9t :i* sep>ates my logical sy/em f t ( ,boole4 ,9 8 99,laws ( ,?\ght99 7p4 #cb7 he expressly says1 8,9 /rictness1 ! words #8&1' #8or1' int]pos$ betwe5 ! t]ms descriptive ( two or m classes ( objects1 imply t ^? classes are q di/9ct1 s t no memb] ( "o is f\nd 9 ano!r40 ,?is ,i altoge!r dispute4 ,9 ! ord9>y use ( ^! conjunctions we d n jo9 di/9ct t]ms only2 & :5 t]ms s jo9$ d prove to be logically di/9ct1 x is by virtue ( a 99tacit premise991 some?+ 9 ! mean+ ( ! names & our k ( !m1 :i* tea*es u t !y are di/9ct4 ,if our k ( ! mean+s ( ! words jo9$ is defective x w (t5 be impossible to decide :e!r t]ms jo9$ by conjunctions are exclusive or n4 ,9 ! s5t5ce 8,rep5tance is n a s+le act1 b a habit or virtue10 x _c be impli$ t a virtue is n a habit2 by ,ari/otle's def9ition x is4 ,milton has ! expression 9 "o ( 8 sonnets1 8,un/a9'd by gold or fee10 :]e x is obvi\s t if ! fee is n always gold1 ! gold is meant to be a fee or bribe4 ,t5nyson has ! expression 8wrea? or anadem40 ,mo/ read]s w\ld be q unc]ta9 :e!r a wrea? may be an anadem1 or an anadem a wrea?1 or :e!r !y are q di/9ct or q ! same4 ,f ,d>w9's 99,orig9 ( ,species991 ,i take ! expression1 8,:5 we see any 99"p or organ99 develop$ 9 a rem>kable 99degree or mann]9940 ,9 ?is1 99or99 is us$ twice1 & nei!r "t exclusively4 ,= if 99"p99 & 99organ99 are n synonym\s1 at any rate an organ is a "p4 ,& x is obvi\s t a "p may be develop$ at ! same "t bo? 9 an extraord9>y degree & an extraord9>y mann]1 al?\gh su* cases may be comp>atively r>e4 ,f a c>eful exam9ation ( ord9>y writ+s1 x w ?us be f\nd t ! mean+s ( t]ms jo9$ by 8&10 8or0 v>y f absolute id5tity up to absolute contr>iety4 ,!re is no logical condition ( di/9ctness at all1 & :5 we d *oose exclusive alt]natives1 x is because our subject dem&s x4 ,! matt]1 n ! =m ( an expression1 po9ts out :e!r t]ms are exclusive or n4#fh ,9 bills1 policies1 & o!r k9ds ( legal docum5ts1 x is sometimes necess>y to express v di/9ctly t alt]natives are n exclusive4 ,! =m &_/or is !n us$1 &1 z ,mr4 ,j4 ,j4 ,murphy has rem>k$1 ?is =m co9cides exactly 9 mean+ ) ! symbol 4 #fh 99,pure ,logic991 pp #gf1 #gg4 ,9 ! fir/ edition ( ?is "w 7vol4 i41 p4 #ha71 ,i took ! disjunctive proposition 8,matt] is solid1 or liquid1 or gase\s10 & treat$ x z an in/ance ( exclusive alt]natives1 rem>k+ t ! same portion ( matt] _c be at once solid & liquid1 prop]ly speak+1 & t /ill less c we suppose x to be solid & gase\s1 or solid1 liquid1 & gase\s all at ! same "t4 ,b ! exp]im5ts ( ,pr(essor ,&rews %[ t1 "u c]ta9 conditions ( temp]ature & pressure1 !re is no abrupt *ange f ! liquid to ! gase\s /ate4 ,! same sub/ance may be 9 su* a /ate z to be indiff]5tly describ$ z liquid & gase\s4 ,9 _m cases1 too1 ! transition f solid to liquid is gradual1 s t ! prop]ties ( solidity are at lea/ p>tially jo9$ ) ^? ( liquidity4 ,! proposition !n1 in/ead ( be+ an in/ance ( exclusive alt]natives1 seems to af=d an excell5t in/ance to ! opposite effect4 ,:5 su* d\bts c arise1 x is evid5tly impossible to treat alt]natives z absolutely exclusive by ! logical nature ( ! relation4 ,x becomes purely a "q ( ! matt] ( ! proposition4 ,! "q1 z we %all aft]w>ds see m fully1 is "o ( ! greate/ !oretical importance1 because x conc]ns ! true di/9ction betwe5 ! sci5ces ( ,logic & ,ma!matics4 ,x is ! f\ndation ( numb] t e unit %all be di/9ct f e o!r unit2 b ,boole import$ ! conditions ( numb] into ! sci5ce ( ,logic1 & produc$ a sy/em :i*1 ?\gh wond]ful 9 its results1 0 n a sy/em ( logic at all4 99,laws ( ! ,disjunctive ,relation499 ,9 consid]+ ! comb9ation or syn!sis ( t]ms 7p4 #cj71 we f\nd t c]ta9 laws1 ^? ( ,simplicity & ,commutativ5ess1 mu/ be obs]v$4 ,9 unit+ t]ms by ! disjunctive symbol we %all f9d t ! same or closely simil> laws hold true4 ,! alt]natives ( ei!r memb] ( a disjunctive proposition are c]ta9ly commutative4 ,j z we _c prop]ly di/+ui% betwe5 99ri* & r>e gems99 & 99r>e & ri* gems991 s we mu/ consid] z id5tical ! expression 99ri* or r>e gems991 & 99r>e or ri* gems994 ,9 our symbolic language we may say ,a ,b ,b ,a4 ,! ord] ( /atem5t1 9 %ort1 has no effect ^u ! mean+ ( an aggregate ( alt]natives1 s t ! ,law ( ,commutativ5ess holds true ( ! disjunctive symbol4 ,z we h admitt$ ! possibility ( jo9+ z alt]natives t]ms :i* are n really diff]5t1 ! "q arises1 ,h[ %all we treat two or m alt]natives :5 !y are cle>ly %[n to be ! same8 ,if we h x ass]t$ t ,p is ,q or ,r1 & x is aft]w>ds prov$ t ,q is b ano!r "n = ,r1 ! result is t ,p is ei!r ,r or ,r4 ,h[ %all we int]pret su* a /atem5t8 ,:at w\ld be ! mean+1 = in/ance1 ( 8wrea? or anadem0 if1 on ref]r+ to a diction>y1 we f\nd 99anadem99 describ$ z a wrea?8 ,i take x to be self-evid5t t ! mean+ w\ld !n become simply 8wrea?40 ,accord+ly we may affirm ! g5]al law ,a ,a ,a4 ,any numb] ( id5tical alt]natives may always be r$uc$ to1 & are logically equival5t to1 any "o ( ^? alt]natives4 ,?is is a law :i* di/+ui%es ma!matical t]ms f logical t]ms1 because x obvi\sly does n apply to ! =m]4 ,i propose to call x ! 99,law ( ,unity991 because x mu/ really be involv$ 9 any def9ition ( a ma!matical unit4 ,?is law is closely analog\s to ! ,law ( ,simplicity1 ,,aa ,a2 & ! nature ( ! connection is wor?y ( att5tion4 ,few or no logicians except ,de ,morgan h adequately notic$ ! close relation betwe5 comb9$ & disjunctive t]ms1 namely1 t e disjunctive t]m is ! negative ( a correspond+ comb9$ t]m1 & 99vice v]s994 ,consid] ! t]m ,malleable d5se metal4 ,h[ %all we describe ! class ( ?+s :i* are n malleable-d5se-metals8 ,:atev] is includ$ "u t t]m mu/ h all ! qualities ( malleability1 d5s5ess1 & metallicity4 ,:]ev] any "o or m ( ! qualities is want+1 ! comb9$ t]m w n apply4 ,h5ce ! negative ( ! :ole t]m is ,n-malleable or n-d5se or n-metallic4 ,9 ! above ! conjunction 99or99 mu/ cle>ly be int]pret$ z unexclusive2 = !re may readily be objects :i* are bo? n-malleable1 & n-d5se1 & p]haps n-metallic at ! same "t4 ,if 9 fact we 7 requir$ to use 99or99 9 a /rictly exclusive mann]1 x w\ld be requisite to specify sev5 di/9ct alt]natives 9 ord] to describe ! negative ( a comb9ation ( ?ree t]ms4 ,! negatives ( f\r or five t]ms w\ld consi/ ( fifte5 or ?irty-"o alt]natives4 ,?is consid]ation alone is suffici5t to prove t ! mean+ ( 99or99 _c be always exclusive 9 common language4 ,express$ symbolically1 we may say t ! negative ( ,,abc is n-,a or n-,b or n-,c2 t is1 99a99 99b99 99c994 ,reciprocally ! negative ( ,p ,q ,r is 99pqr994 ,e disjunctive t]m1 !n1 is ! negative ( a comb9$ t]m1 & 99vice v]s994 ,apply ?is result to ! comb9$ t]m ,,aaa1 & its negative is 99a99 99a99 99a994 ,s9ce ,,aaa is by ! ,law ( ,simplicity equival5t to ,a1 s 99a99 99a99 99a99 mu/ be equival5t to 99a991 & ! ,law ( ,unity holds true4 ,ea* law ?us necess>ily presupposes ! o!r4 99,symbolic expression ( ! ,law ( ,duality499 ,we may n[ employ our symbol ( alt]nation to express 9 a cle> & =mal mann] ! ?ird ,fundam5tal ,law ( ,?\ght1 :i* ,i h call$ ! ,law ( ,duality 7p4 #f74 ,tak+ ,a to repres5t any class or object or quality1 & ,b any o!r class1 object or quality1 we may always ass]t t ,a ei!r agrees ) ,b1 or does n agree4 ,?us we may say ,a ,,ab ,a99b994 ,?is is a =mula :i* w h5ce=? be con/antly employ$1 & x lies at ! basis ( reason+4 ,! read] may p]haps wi% to "k :y ,a is ins]t$ 9 bo? alt]natives ( ! second memb] ( ! id5tity1 & :y ! law is n /at$ 9 ! =m ,a ,b 99b994 ,b if he w consid] ! cont5ts ( ! la/ section 7p4 #gc71 he w see t ! latt] expression _c be correct1 o!rwise no t]m c\ld h a correspond+ negative t]m4 ,= ! negative ( ,b 99b99 is 99b99,b1 or a self-contradictory t]m2 ?us if ,a 7 id5tical ) ,b 99b991 its negative 99a99 w\ld be non-exi/5t4 ,to say ! lea/1 ?is result w\ld 9 mo/ cases be an absurd "o1 & ,i see mu* reason to ?9k t 9 a /rictly logical po9t ( view x w\ld always be absurd4 ,9 all probability we ought to assume z a fundam5tal logical axiom t 99e t]m has its negative 9 ?\ght994 ,we _c ?9k at all )\t sep>at+ :at we ?9k ab\t f o!r ?+s1 & ^! ?+s necess>ily =m ! negative notion4#fi ,x foll[s t any proposition ( ! =m ,a ,b 99b99 is j z self-contradictory z "o ( ! =m ,a ,b99b994 #fi 99,pure ,logic991 p4 #fe4 ,see also ! criticism ( ?is po9t by ,de ,morgan 9 ! 99,a!num991 ,no4 #ahib1 #cj? ,janu>y1 #ahfd2 p4 #aee4 ,x is conv5i5t to recapitulate 9 ?is place ! ?ree ,laws ( ,?\ght 9 _! symbolic =m1 ?us ,law ( ,id5tity ,a ,a4 ,law ( ,contradiction ,a99a99 #j4 ,law ( ,duality ,a ,,ab ,a99b994 99,v>i\s ,=ms ( ! ,disjunctive ,proposition499 ,disjunctive propositions may occur 9 a great v>iety ( =ms1 ( :i* ! old logicians took insuffici5t notice4 ,!re may be any numb] ( alt]natives1 ea* ( :i* may be a comb9ation ( any numb] ( simple t]ms4 ,a proposition1 aga91 may be disjunctive 9 "o or bo? memb]s4 ,! proposition ,solids or liquids or gases are electrics or conductors ( electricity is an example ( ! d\bly disjunctive =m4 ,! mean+ ( su* a proposition is t :atev] falls "u any "o or m alt]natives on "o side mu/ fall "u "o or m alt]natives on ! o!r side4 ,f :at has be5 said be=e1 x is app>5t t ! proposition ,a ,b ,c ,d w correspond to 99ab99 99cd991 ea* memb] ( ! latt] be+ ! negative ( a memb] ( ! =m] proposition4 ,z an in/ance ( a complex disjunctive proposition ,i may give ,s5ior's def9ition ( weal?1 :i*1 briefly /at$1 am\nts to ! proposition 8,weal? is :at is transf]able1 limit$ 9 supply1 & ei!r productive ( pleasure or prev5tive ( pa940#gj #gj ,boole's 99,laws ( ,?\ght991 p4 #ajf4 ,jevons' 99,pure ,logic991 p4 #fi4 ,let ,a weal? ,b transf]able ,c limit$ 9 supply ,d productive ( pleasure ,e prev5tive ( pa94 ,! def9ition takes ! =m ,a ,,bc7,d ,e72 b if we develop ! alt]natives by a me?od to be aft]w>ds m fully consid]$1 x becomes ,a ,,bcde ,,bcd99e99 ,,bc99d99,e4 ,an example ( a /ill m complex proposition is f\nd 9 ,de ,morgan's writ+s1#ga z foll[s3--8,he mu/ h be5 ri*1 & if n absolutely mad 0 weakness itself1 subject$ ei!r to bad advice or to mo/ unfav\rable circum/ances40 #ga 99,on ! ,syllogism991 ,no4 iii4 p4 #ab4 ,camb4 ,phil4 ,trans4 vol4 x1 "p i4 ,if we assign ! lett]s ( ! alphabet 9 succession1 ?us1 ,a he ,b ri* ,c absolutely mad ,d weakness itself ,e subject$ to bad advice ,f subject$ to mo/ unfav\rable circum/ances1 ! proposition w take ! =m ,a ,,ab,c ,d 7,e ,f71 & if we develop ! alt]natives1 express+ "s ( ! diff]5t cases :i* may happ51 we obta9 ,a ,,abc ,,ab99c99,,def ,,ab99c99,,de99f99 ,,ab99c99,d99e99,f4 ,! above gives ! /rict logical int]pretation ( ! s5t5ce1 & ! fir/ alt]native ,,abc is capable ( developm5t into eight cases1 accord+ z ,d1 ,e & ,f are or are n pres5t4 ,al?\gh f our k ( ! matt]1 we may inf] t weakness ( "* _c be ass]t$ ( a p]son absolutely mad1 !re is no explicit /atem5t to ?is effect4 99,inf]5ce by ,disjunctive ,propositions499 ,be=e we c make a free use ( disjunctive propositions 9 ! processes ( inf]5ce we mu/ consid] h[ disjunctive t]ms c be comb9$ toge!r or ) simple t]ms4 ,9 ! fir/ place1 to comb9e a simple t]m ) a disjunctive "o1 we mu/ comb9e x ) e alt]native ( ! disjunctive t]m4 ,a vegetable1 = in/ance1 is ei!r a h]b1 a %rub1 or a tree4 ,h5ce an exog5\s vegetable is ei!r an exog5\s h]b1 or an exog5\s %rub1 or an exog5\s tree4 ,symbolically /at$1 ?is process ( comb9ation is z foll[s1 ,a7,b ,c7 ,,ab ,,ac4 ,secondly1 to comb9e two disjunctive t]ms ) ea* o!r1 comb9e ea* alt]native ( "o ) ea* alt]native ( ! o!r4 ,s9ce fl[]+ plants are ei!r exog5s or endog5s1 & are at ! same "t ei!r h]bs1 %rubs or trees1 x foll[s t !re are altoge!r six alt]natives--namely1 exog5\s h]bs1 exog5\s %rubs1 exog5\s trees1 endog5\s h]bs1 endog5\s %rubs1 endog5\s trees4 ,?is process ( comb9ation is %[n 9 ! g5]al =m 7,a ,b7 7,c ,d ,e7 ,,ac ,,ad ,,ae ,,bc ,,bd ,,be4 ,x is h>dly necess>y to po9t out t1 h[ev] num]\s ! t]ms comb9$1 or ! alt]natives 9 ^? t]ms1 we may effect ! comb9ation1 provid$ ea* alt]native is comb9$ ) ea* alt]native ( ! o!r t]ms1 z 9 ! algebraic process ( multiplication4 ,"s processes ( d$uction may be at once exhibit$4 ,we may always1 = in/ance1 unite ! same qualify+ t]m to ea* side ( an id5tity ev5 ?\gh "o or bo? memb]s ( ! id5tity be disjunctive4 ,?us let ,a ,b ,c4 ,n[ x is self-evid5t t ,,ad ,,ad1 & 9 "o side ( ?is id5tity we may = ,a sub/itute its equival5t ,b ,c1 obta9+ ,,ad ,,bd ,,cd4 ,s9ce 8a gase\s elem5t is ei!r hydrog51 or oxyg51 or nitrog51 or *lor9e1 or fluor9e10 x foll[s t 8a free gase\s elem5t is ei!r free hydrog51 or free oxyg51 or free nitrog51 or free *lor9e1 or free fluor9e40 ,?is process ( comb9ation w lead to mo/ useful inf]5ces :5 ! qualify+ adjective comb9$ ) bo? sides ( ! proposition is a negative ( "o or m alt]natives4 ,s9ce *lor9e is a col\r$ gas1 we may inf] t 8a col\rless gase\s elem5t is ei!r 7col\rless7 hydrog51 oxyg51 nitrog51 or fluor9e40 ,! alt]native *lor9e disappe>s because col\rless *lor9e does n exi/4 ,aga91 s9ce 8a too? is ei!r an incisor1 can9e1 bicuspid1 or mol>10 x foll[s t 8a n-incisor too? is ei!r can9e1 bicuspid1 or mol>40 ,! g5]al rule is t f ! d5ial ( any ( ! alt]natives ! affirmation ( ! rema9d] c be inf]r$4 ,n[ ?is result cle>ly foll[s f our process ( sub/itution2 = if we h ! proposition ,a ,b ,c ,d1 & we ins]t ?is expression = ,a on "o side ( ! self-evid5t id5tity ,a99b99 ,a99b991 we obta9 ,a99b99 ,,ab99b99 ,a99b99,c ,a99b99,d2 &1 z ! fir/ ( ! ?ree alt]natives is self-contradictory1 we /rike x out accord+ to ! law ( contradiction3 !re rema9s ,a99b99 ,a99b99,c ,a99b99,d4 ,?us our sy/em fully includes & expla9s t mood ( ! ,disjunctive ,syllogism te*nically call$ ! 99modus toll5do pon5s994 ,b ! read] mu/ c>efully obs]ve t ! ,disjunctive ,syllogism ( ! mood 99pon5do toll5s991 :i* affirms "o alt]native1 & !nce inf]s ! d5ial ( ! re/1 _c be held true 9 ?is sy/em4 ,if ,i say1 inde$1 t ,wat] is ei!r salt or fre% wat]1 x seems evid5t t 8wat] :i* is salt is n fre%40 ,b ?is inf]5ce really proce$s f our k t wat] _c be at once salt & fre%4 ,?is inconsi/5cy ( ! alt]natives1 z ,i h fully %[n1 w n always hold4 ,?us1 if ,i say ,gems are ei!r r>e /ones or beautiful /ones1 7#a7 x w obvi\sly n foll[ t ,a r>e gem is n a beautiful /one1 7#b7 nor t ,a beautiful gem is n a r>e /one4 7#c7 ,our symbolic me?od gives only true conclusions2 = if we take ,a gem ,b r>e /one ,c beautiful /one1 ! proposition 7#a7 is ( ! =m ,a ,b ,c h5ce ,,ab ,b ,,bc & ,,ac ,,bc ,c2 b ^! inf]5ces are n equival5t to ! false ones 7#b7 & 7#c74 ,we c readily repres5t disjunctive reason+ by ! 99modus pon5do toll5s991 :5 x is valid1 by express+ ! inconsi/5cy ( ! alt]natives explicitly4 ,?us if we resort to our in/ance ( ,wat] is ei!r salt or fre%1 & take ,a ,wat] ,b salt ,c fre%1 !n ! premise is app>5tly ( ! =m ,a ,,ab ,,ac2 b 9 reality !re is an unexpress$ condition t 8:at is salt is n fre%10 f :i* foll[s1 by a process ( inf]5ce to be aft]w>ds describ$1 t 8:at is fre% is n salt40 ,we h !n1 9 lett]-t]ms1 ! two propositions ,b ,b99c99 ,c 99b99,c4 ,if we sub/itute ^! descriptions 9 ! orig9al proposition1 we obta9 _/99 ,a ,,ab99c99 ,a99b99,c2 99_/ unit+ ,b to ea* side we inf] ,,ab ,,ab99c99 ,,ab99b99,c or ,,ab ,,ab99c992 t is1 ,wat] :i* is salt is wat] salt & n fre%4 ,i %\ld we>y ! read] if ,i attempt$ to illu/rate ! multitude ( =ms :i* disjunctive reason+ may take2 & z 9 ! next *apt] we %all be con/antly treat+ ! subject1 ,i mu/ "h re/rict myself to a s+le in/ance4 ,a v common process ( reason+ consi/s 9 ! det]m9ation ( ! "n ( a ?+ by ! successive exclusion ( alt]natives1 a process call$ by ! old "n 99abscissio inf9iti994 ,take ! case3 ,r$-col\r$ metal is ei!r copp] or gold 7#a7 ,copp] is dissolv$ by nitric acid 7#b7 ,?is specim5 is r$-col\r$ metal 7#c7 ,?is specim5 is n dissolv$ by nitric acid 7#d7 ,!re=e1 ?is specim5 consi/s ( gold 7#e7 ,let u assign ! lett]-symbols ?us-- ,a ?is specim5 ,b r$-col\r$ metal ,c copp] ,d gold ,e dissolv$ by nitric acid4 ,assum+ t ! alt]natives copp] or gold are int5d$ to be exclusive1 z j expla9$ 9 ! case ( fre% & salt wat]1 ! premises may be /at$ 9 ! =ms ,b ,,bc99d99 ,b99c99,d 7#a7 ,c ,,ce 7#b7 ,a ,,ab 7#c7 ,a ,a99e99 7#d7 ,sub/itut+ = ,c 9 7#a7 by means ( 7#b7 we get ,b ,,bc99d99,e ,b99c99,d ,f 7#c7 & 7#d7 we may inf] likewise ,a ,,ab99e99 & if 9 ?is we sub/itute = ,b its equival5t j /at$1 x foll[s t ,a ,,abc99d99,e99e99 ,,ab99c99,d99e99 ,! fir/ ( ! alt]natives be+ contradictory ! result is ,a ,,ab99c99,d99e99 :i* conta9s a full description ( 8?is specim510 z furni%$ 9 ! premises1 b by ellipsis ass]ts t x is gold4 ,x w be obs]v$ t 9 ! symbolic expression 7#a7 ,i h explicitly /at$ :at is c]ta9ly impli$1 t copp] is n gold1 & gold n copp]1 )\t :i* condition ! inf]5ce w\ld n hold good4 ,,*apt] ,,vi4 ,,! ,,indirect ,,me?od ,,( ,,inf]5ce4 ,! =ms ( d$uctive reason+ z yet consid]$1 are mo/ly cases ( ,direct ,d$uction z di/+ui%$ f ^? :i* we are n[ ab\t to treat4 ,! me?od ( ,indirect ,d$uction may be describ$ z t :i* po9ts out :at a ?+ is1 by %[+ t x _c be any?+ else4 ,we c def9e a c]ta9 space ^u a map1 ei!r by col\r+ t space1 or by col\r+ all except ! space2 ! fir/ mode is positive1 ! second negative4 ,! diff]5ce1 x w be readily se51 is exactly analog\s to t betwe5 ! direct & indirect modes ( pro( 9 geometry4 ,euclid (t5 %[s t two l9es are equal1 by %[+ t !y _c be unequal1 & ! pro( re/s ^u ! kn[n numb] ( alt]natives1 great]1 equal or less1 :i* are alone conceivable4 ,9 o!r cases1 z = in/ance 9 ! sev5? proposition ( ! fir/ book1 he %[s t two l9es mu/ meet 9 a p>ticul> po9t1 by %[+ t !y _c meet else:]e4 ,9 logic we c always def9e ) c]ta9ty ! utmo/ numb] ( alt]natives :i* are conceivable4 ,! ,law ( ,duality 7pp4 #f1 #gd7 enables u always to ass]t t any quality or circum/ance :atsoev] is ei!r pres5t or abs5t4 ,:atev] may be ! mean+ ( ! t]ms ,a & ,b x is c]ta9ly true t ,a ,,ab ,a99b99 ,b ,,ab 99a99,b4 ,^! are univ]sal tacit premises :i* may be employ$ 9 ! solution ( e problem1 & :i* are su* inv>iable & necess>y conditions ( all ?\ght1 t !y ne$ n be specially laid d[n4 ,! ,law ( ,contradiction is a fur!r condition ( all ?\ght & ( all logical symbols2 x enables1 & 9 fact obliges1 u to reject f fur!r consid]ation all t]ms :i* imply ! pres5ce & abs5ce ( ! same quality4 ,n[1 :5ev] we br+ bo? ^! ,laws ( ,?\ght into explicit action by ! me?od ( sub/itution1 we employ ! ,indirect ,me?od ( ,inf]5ce4 ,x w be f\nd t we c treat n only ^? argum5ts already exhibit$ accord+ to ! direct me?od1 b we c include an inf9ite multitude ( o!r argum5ts :i* are incapable ( solution by any o!r means4 ,"s philosoph]s1 especially ^? ( ,france1 h held t ! ,indirect ,me?od ( ,pro( has a c]ta9 inf]iority to ! direct me?od1 :i* %\ld prev5t our us+ x except :5 oblig$4 ,b !re are _m tru?s :i* we c prove only indirectly4 ,we c prove t a numb] is a prime only by ! purely indirect me?od ( %[+ t x is n any ( ! numb]s :i* h divisors1 & ! rem>kable process kn[n z ,erato/h5es' ,sieve is ! only mode by :i* we c select ! prime numb]s4#gb ,x be>s a /rong analogy to ! indirect me?od "h to be describ$4 ,we c prove t ! side & diamet] ( a squ>e are incomm5surable1 b only 9 ! negative or indirect mann]1 by %[+ t ! contr>y supposition inevitably leads to contradiction4#gc ,_m o!r demon/rations 9 v>i\s bran*es ( ! ma!matical sci5ces proce$ ^u a l me?od4 ,n[1 if !re is only "o important tru? :i* mu/ be1 & c only be1 prov$ indirectly1 we may say t ! process is a necess>y & suffici5t "o1 & ! "q ( its comp>ative excell5ce or usefulness is n wor? discussion4 ,z a matt] ( fact ,i believe t ne>ly half our logical conclusions re/ ^u its employm5t4 #gb ,see ,horsley1 99,philosophical ,transactions991 #aggb2 vol4 lxii4 p4 #cbg4 ,montucla1 99,hi/oire des ,ma!matiques991 vol4 i4 p4 #bci4 99,p5ny ,cyclopdia991 article 8,erato/h5es40 #gc ,euclid1 ,book x4 ,prop4 #aag4 99,simple ,illu/rations499 ,9 trac+ out ! p[]s & results ( ?is me?od1 we w beg9 ) ! simple/ possible in/ance4 ,let u take a proposition ( ! common =m1 ,a ,,ab1 say1 99,a ,metal is an ,elem5t199 & let u inve/igate its full mean+4 ,any p]son :o has _h ! lea/ logical tra9+1 is aw>e t we c draw f ! above proposition an app>5tly diff]5t "o1 namely1 99,a ,n-elem5t is a ,n-metal499 ,:ile "s logicians1 z = in/ance ,de ,morgan1#gd h consid]$ ! relation ( ^! two propositions to be purely self-evid5t1 & nei!r ne$+ nor all[+ analysis1 a great _m m p]sons1 z ,i h obs]v$ :ile tea*+ logic1 are at fir/ unable to p]ceive ! close connection betwe5 !m4 ,i believe t a true & complete sy/em ( logic w furni% a cle> analysis ( ?is process1 :i* has be5 call$ 99,contrapositive ,conv]sion992 ! full process is z foll[s3-- #gd 99,philosophical ,magaz9e991 ,decemb] #aheb2 ,f\r? ,s]ies1 vol4 iv4 p4 #dce1 8,on ,indirect ,demon/ration40 ,fir/ly1 by ! ,law ( ,duality we "k t 99,n-elem5t is ei!r ,metal or ,n-metal499 ,if x be metal1 we "k t x is by ! premise 99an elem5t992 we %\ld ?us be suppos+ t ! same ?+ is an elem5t & a n-elem5t1 :i* is 9 opposition to ! ,law ( ,contradiction4 ,accord+ to ! only o!r alt]native1 !n1 ! n-elem5t mu/ be a n-metal4 ,to repres5t ?is process ( inf]5ce symbolically we take ! premise 9 ! =m ,a ,,ab4 7#a7 ,we obs]ve t by ! ,law ( ,duality ! t]m n-,b is ?us describ$ 99b99 ,a99b99 99ab994 7#b7 ,= ,a 9 ?is proposition we sub/itute its description z giv5 9 7#a71 obta9+ 99b99 ,,ab99b99 99ab994 ,b accord+ to ! ,law ( ,contradiction ! t]m ,,ab99b99 mu/ be exclud$ f ?\ght1 or ,,ab99b99 #j4 ,h5ce x results t 99b99 is ei!r no?+ at all1 or x is 99ab992 & ! conclusion is 99b99 99ab994 ,z x w (t5 be necess>y to ref] to a conclusion ( ?is k9d ,i %all call x1 z is usual1 ! 99,contrapositive ,proposition99 ( ! orig9al4 ,! read] ne$ h>dly be caution$ to obs]ve t f all ,a's are ,b's x does n foll[ t all n-,a's are n-,b's4 ,= by ! ,law ( ,duality we h 99a99 99a99,b 99ab991 & x w n be f\nd possible to make any sub/itution 9 ?is by our orig9al premise ,a ,,ab4 ,x /ill rema9s d\btful1 !re=e1 :e!r n-metal is elem5t or n-elem5t4 ,! pro( ( ! ,contrapositive ,proposition giv5 above is exactly ! same z t :i* ,euclid applies 9 ! case ( geometrical notions4 ,de ,morgan describes ,euclid's process z foll[s#ge3--8;,f e n-,b is n-,a he produces ,e ,a is ,b1 ?us3 ,if x be possible1 let ?is ,a be n-,b1 b e n-,b is n-,a1 !re=e ?is ,a is n-,a1 :i* is absurd3 :5ce e ,a is ,b40 ,n[ ,de ,morgan ?9ks t ?is pro( is entirely ne$less1 because common logic gives ! inf]5ce )\t ! use ( any geometrical reason+4 ,i conceive h[ev] t logic gives ! inf]5ce only by an indirect process4 ,de ,morgan claims 8to see id5tity 9 ,e ,a is ,b & e n-,b is n-,a1 by a process ( ?\ght prior to syllogism40 ,:e!r prior to syllogism or n1 ,i claim t x is n prior to ! laws ( ?\ght & ! process ( sub/itutive inf]5ce1 by :i* x may be und\bt$ly demon/rat$4 #ge 99,philosophical ,magaz9e991 ,dec4 #aheb2 p4 #dcg4 99,employm5t ( ! ,contrapositive ,proposition499 ,we c frequ5tly employ ! contrapositive =m ( a proposition by ! me?od ( sub/itution2 & c]ta9 moods ( ! anci5t syllogism1 :i* we h hi!rto pass$ ov]1 may ?us be satisfactorily compreh5d$ 9 our sy/em4 ,take = in/ance ! foll[+ syllogism 9 ! mood ,came/res3-- 8,:ales are n true fi%2 = !y d n respire wat]1 :]eas true fi% d respire wat]40 ,let u take ,a :ale ,b true fi% ,c respir+ wat] ,! premises are ( ! =ms ,a ,a99c99 7#a7 ,b ,,bc 7#b7 ,n[1 by ! process ( contraposition we obta9 f ! second premise 99c99 99bc99 & we c sub/itute ?is expression = 99c99 9 7#a71 obta9+ ,a ,a99bc99 or 8,:ales are n true fi%1 n respir+ wat]40 ,! mood ,ces>e does n really diff] f ,came/res except 9 ! ord] ( ! premises1 & x c\ld be exhibit$ 9 an exactly simil> mann]4 ,! mood ,b>oko gave mu* tr\ble to ! old logicians1 :o c\ld n 99r$uce99 x to ! fir/ figure 9 ! same mann] z ! o!r moods1 & 7 oblig$ to inv5t1 specially = x & = ,bok>do1 a me?od ( ,indirect ,r$uction closely analog\s to ! indirect pro( ( ,euclid4 ,n[ ^! moods require no exceptional treatm5t 9 ?is sy/em4 ,let u take z an in/ance ( ,b>oko1 ! argum5t ,all heat$ solids give cont9u\s spectra 7#a7 ,"s nebul d n give cont9u\s spectra 7#b7 ,!re=e1 "s nebul are n heat$ solids 7#c7 ,treat+ ! little ^w "s z an indet]m9ate adjective ( selection1 to :i* we assign a symbol l any o!r adjective1 let ,a "s ,b nebul ,c giv+ cont9u\s spectra ,d heat$ solids ,! premises !n become ,d ,,dc 7#a7 ,,ab ,,ab99c99 7#b7 ,n[ f 7#a7 we obta9 by ! indirect me?od ! contrapositive proposition 99c99 99cd99 & if we sub/itute ?is expression = 99c99 9 7#b7 we h ,,ab ,,ab99cd99 ! full mean+ ( :i* is t 8"s nebul d n give cont9u\s spectra & are n heat$ solids40 ,we might simil>ly apply ! contrapositive 9 _m o!r in/ances4 ,take ! argum5t1 8,all fix$ />s are self-lum9\s2 b "s ( ! heav5ly bodies are n self-lum9\s1 & are !re=e n fix$ />s40 ,tak+ our t]ms ,a fix$ />s ,b self-lum9\s ,c "s ,d heav5ly bodies we h ! premises ,a ,,ab1 7#a7 ,,cd 99b99,,cd 7#b7 ,n[ f 7#a7 we c draw ! contrapositive 99b99 99ab99 & sub/itut+ ?is expression = 99b99 9 7#b7 we obta9 ,,cd 99ab99,,cd :i* expresses ! conclusion ( ! argum5t t "s heav5ly bodies are n fix$ />s4 99,contrapositive ( a ,simple ,id5tity499 ,! read] %\ld c>efully note t :5 we apply ! process ( ,indirect ,inf]5ce to a simple id5tity ( ! =m ,a ,b we may obta9 fur!r results4 ,if we wi% to "k :at is ! t]m n-,b1 we h z be=e1 by ! ,law ( ,duality1 99b99 ,a99b99 99ab99 & sub/itut+ = ,a we obta9 99b99 ,b99b99 99ab99 99ab994 ,b we may n[ also draw a second contrapositive2 = we h 99a99 99a99,b 99ab991 & sub/itut+ = ,b its equival5t ,a we h 99a99 99a99,a 99ab99 99ab994 ,h5ce f ! s+le id5tity ,a ,b we c draw ! two propositions 99a99 99ab99 99b99 99ab991 & obs]v+ t ^! propositions h a common t]m 99ab99 we c make a new sub/itution1 gett+ 99a99 99b994 ,?is result is 9 /rict accordance ) ! fundam5tal pr9ciples ( inf]5ce1 & x may be a "q :e!r x is n a self-evid5t result1 indep5d5t ( ! /eps ( d$uction by :i* we h rea*$ x4 ,= :]e two classes are co9cid5t l ,a & ,b1 :atev] is true ( ! "o is true ( ! o!r2 :at is exclud$ f ! "o mu/ be exclud$ f ! o!r simil>ly4 ,n[ z 99a99 be>s to ,a exactly ! same relation t 99b99 be>s to ,b1 ! id5tity ( ei!r pair foll[s f ! id5tity ( ! o!r pair4 ,9 e id5tity1 equality1 or simil>ity1 we may argue f ! negative ( ! "o side to ! negative ( ! o!r4 ,?us at ord9>y temp]atures ,m]cury liquid-metal1 h5ce obvi\sly ,n-m]cury n liquid-metal2 or s9ce ,sirius brighte/ fix$ />1 x foll[s t :atev] /> is n ! brighte/ is n ,sirius1 & 99vice v]s994 ,e correct def9ition is ( ! =m ,a ,b1 & may (t5 require to be appli$ 9 ! equival5t negative =m4 ,let u take z an illu/ration ( ! mode ( us+ ?is result ! argum5t foll[+3 ,v[els are lett]s :i* c be s\nd$ alone1 7#a7 ,! lett] 99w99 _c be s\nd$ alone2 7#b7 ,!re=e ! lett] 99w99 is n a v[el4 7#c7 ,"h we h a def9ition 7#a71 & a comp>ison ( a ?+ ) t def9ition 7#b71 lead+ to exclusion ( ! ?+ f ! class def9$4 ,tak+ ! t]ms ,a v[el1 ,b lett] :i* c be s\nd$ alone1 ,c lett] 99w991 ! premises are pla9ly ( ! =ms ,a ,b1 7#a7 ,c 99b99,c4 7#b7 ,n[ by ! ,indirect me?od we obta9 f 7#a7 ! ,contrapositive 99b99 99a991 & ins]t+ 9 7#b7 ! equival5t = 99b99 we h ,c 99a99,c1 7#c7 or 8! lett] 99w99 is n a v[el40 99,miscellane\s ,examples ( ! ,me?od499 ,we c apply ! ,indirect ,me?od ( ,inf]5ce h[ev] _m may be ! t]ms involv$ or ! premises conta9+ ^? t]ms4 ,z ! work+ ( ! me?od is be/ le>nt f examples1 ,i w take a case ( two premises =m+ ! syllogism ,b>b>a3 ?us ,iron is metal 7#a7 ,metal is elem5t4 7#b7 ,if we want to asc]ta9 :at inf]5ce is possible conc]n+ ! t]m 99,iron991 we develop ! t]m by ! ,law ( ,duality4 ,iron mu/ be ei!r metal or n-metal2 iron :i* is metal mu/ be ei!r elem5t or n-elem5t2 & simil>ly iron :i* is n-metal mu/ be ei!r elem5t or n-elem5t4 ,!re are !n altoge!r f\r alt]natives among :i* ! description ( iron mu/ be conta9$2 ?us ,iron1 metal1 elem5t1 77 ,iron1 metal1 n-elem5t1 77 ,iron1 n-metal1 elem5t1 77 ,iron1 n-metal1 n-elem5t4 77 ,our fir/ premise in=ms u t iron is a metal1 & if we sub/itute ?is description 9 77 & 77 we %all h self-contradictory comb9ations4 ,our second premise likewise in=ms u t metal is elem5t1 & apply+ ?is description to 77 we aga9 h self-contradiction1 s t !re rema9s only 77 z a description ( iron--our inf]5ce is ,iron iron1 metal1 elem5t4 ,to repres5t ?is process ( reason+ 9 g5]al symbols1 let ,a iron ,b metal ,c elem5t1 ,! premises ( ! problem take ! =ms ,a ,,ab 7#a7 ,b ,,bc4 7#b7 ,by ! ,law ( ,duality we h ,a ,,ab ,a99b99 7#c7 ,a ,,ac ,a99c994 7#d7 ,n[1 if we ins]t = ,a 9 ! second side ( 7#c7 its description 9 7#d71 we obta9 :at ,i %all call ! 99developm5t ( ,a ) respect to ,b & ,c991 namely ,a ,,abc ,,ab99c99 ,a99b99,c ,a99bc994 7#e7 ,:]ev] ! lett]s ,a or ,b appe> 9 ! second side ( 7#e7 sub/itute _! equival5ts giv5 9 7#a7 & 7#b71 & ! results /at$ at full l5g? are ,a ,,abc ,,abc99c99 ,,ab99b99,c ,,ab99b99,c99c994 ,! la/ ?ree alt]natives break ! ,law ( ,contradiction1 s t ,a ,,abc #j #j #j ,,abc4 ,?is conclusion is1 inde$1 no m ?an we c\ld obta9 by ! direct process ( sub/itution1 t is by sub/itut+ = ,b 9 7#a71 its description 9 7#b7 z 9 p4 #ee2 x is ! *>act]i/ic ( ! ,indirect process t x gives all possible logical conclusions1 bo? ^? :i* we h previ\sly obta9$1 & an imm5se numb] ( o!rs or :i* ! anci5t logic took little or no acc\nt4 ,f ! same premises1 = in/ance1 we c obta9 a description ( ! class 99n-elem5t99 or 99c994 ,by ! ,law ( ,duality we c develop 99c99 into f\r alt]natives1 ?us 99c99 ,,ab99c99 ,a99bc99 99a99,b99c99 99abc994 ,if we sub/itute = ,a & ,b z be=e1 we get 99c99 ,,abc99c99 ,,ab99bc99 99a99,,bc99c99 99abc991 &1 /rik+ out ! t]ms :i* break ! ,law ( ,contradiction1 !re rema9s 99c99 99abc991 or :at is n elem5t is also n iron & n metal4 ,?is ,indirect ,me?od ( ,inf]5ce ?us furni%es a complete solution ( ! foll[+ problem--99,giv5 any numb] ( logical premises or conditions1 requir$ ! description ( any class ( objects1 or ( any t]m1 z gov]n$ by ^? conditions499 ,! /eps ( ! process ( inf]5ce may ?us be concisely /at$-- #a4 ,by ! ,law ( ,duality develop ! utmo/ numb] ( alt]natives :i* may exi/ 9 ! description ( ! requir$ class or t]m z reg>ds ! t]ms involv$ 9 ! premises4 #b4 ,= ea* t]m 9 ^! alt]natives sub/itute its description z giv5 9 ! premises4 #c4 ,/rike out e alt]native :i* is !n f\nd to break ! ,law ( ,contradiction4 #d4 ,! rema9+ t]ms may be equat$ to ! t]m 9 "q z ! desir$ description4 99,mr4 ,v5n's ,problem499 ,! ne$ ( "s logical me?od m p[]ful & compreh5sive ?an ! old logic ( ,ari/otle is /rik+ly illu/rat$ by ,mr4 ,v5n 9 8 mo/ int]e/+ & able article on ,boole's logic4#gf ,an easy example1 orig9ally got1 z he says1 by ! aid ( my me?od z simply describ$ 9 ! 99,elem5t>y ,lessons 9 ,logic991 0 propos$ 9 exam9ation & lecture-rooms to "s hundr$ & fifty /ud5ts z a problem 9 ord9>y logic4 ,x 0 answ]$ by1 at mo/1 five or six ( !m4 ,x 0 aft]w>ds set1 z an example on ,boole's me?od1 to a small class :o _h att5d$ a few lectures on ! nature ( ^! symbolic me?ods4 ,x 0 readily answ]$ by half or m ( _! numb]4 #gf 99,m9d992 a ,qu>t]ly ,review ( ,psy*ology & ,philosophy2 ,octob]1 #ahgf1 vol4 i4 p4 #dhg4 ,! problem 0 z foll[s3--8,! memb]s ( a bo>d 7 all ( !m ei!r bondhold]s1 or %>ehold]s1 b n bo?2 & ! bondhold]s z x happ5$1 7 all on ! bo>d4 ,:at conclusion c be drawn80 ,! conclusion want$ is1 8,no %>ehold]s are bondhold]s40 ,n[1 z ,mr4 ,v5n says1 no?+ c look simpl] ?an ! foll[+ reason+1 99:5 /at$993--8,!re c be no bondhold]s :o are %>ehold]s2 = if !re 7 !y mu/ be ei!r on ! bo>d1 or (f x4 ,b !y are n on x1 by ! fir/ ( ! giv5 /atem5ts2 nor (f x1 by ! second40 ,yet f ! want ( any sy/ematic mode ( treat+ su* a "q only five or six ( "s hundr$ & fifty /ud5ts c\ld succe$ 9 s simple a problem4 ,by symbolic /atem5t ! problem is in/antly solv$4 ,tak+ ,a memb] ( bo>d ,b bondhold] ,c %>ehold] ! premises are evid5tly ,a ,,ab99c99 ,a99b99,c ,b ,,ab4 ,! class ,c or %>ehold]s may 9 respect ( ,a & ,b be develop$ into f\r alt]natives1 ,c ,,abc ,a99b99,c 99a99,,bc 99ab99,c4 ,b sub/itut+ = ,a 9 ! fir/ & = ,b 9 ! ?ird alt]native we get ,c ,,abc99c99 ,,ab99b99,c ,a99b99,c 99a99,,abc 99ab99,c4 ,! fir/1 second1 & f\r? alt]natives 9 ! above are self-contradictory comb9ations1 & only ^!2 /rik+ !m out !re rema9 ,c ,a99b99,c 99ab99,c 99b99,c1 ! requir$ answ]4 ,?is symbolic reason+ is1 ,i believe1 ! exact equival5t ( ,mr4 ,v5n's reason+1 & ,i d n believe t ! result c be atta9$ 9 a simpl] mann]4 ,mr4 ,v5n adds t he c\ld adduce o!r simil> in/ances1 t is1 in/ances %[+ ! necessity ( a bett] logical me?od4 99,abbreviation ( ! ,process499 ,be=e proce$+ to fur!r illu/rations ( ! use ( ?is me?od1 ,i mu/ po9t out h[ mu* its practical employm5t c be simplifi$1 & h[ mu* m easy x is ?an w\ld appe> f ! description4 ,:5 we want to effect at all a ?or\gh solution ( a logical problem x is be/ to =m1 9 ! fir/ place1 a complete s]ies ( all ! comb9ations ( t]ms involv$ 9 x4 ,if !re be two t]ms ,a & ,b1 ! utmo/ v>iety ( comb9ations 9 :i* !y c appe> are ,,ab 99a99,b ,a99b99 99ab994 ,! t]m ,a appe>s 9 ! fir/ & second2 ,b 9 ! fir/ & ?ird2 99a99 9 ! ?ird & f\r?2 & 99b99 9 ! second & f\r?4 ,n[ if we h any premise1 say ,a ,b1 we mu/ asc]ta9 :i* ( ^! comb9ations w be r5d]$ self-contradictory by sub/itution2 ! second & ?ird w h to be /ruck out1 & !re w rema9 only ,,ab 99ba994 ,h5ce we draw ! foll[+ inf]5ces ,a ,,ab1 ,b ,,ab1 99a99 99ab991 99b99 99ab994 ,exactly ! same me?od mu/ be foll[$ :5 a "q involves a great] numb] ( t]ms4 ,?us by ! ,law ( ,duality ! ?ree t]ms ,a1 ,b1 ,c1 give rise to eight conceivable comb9ations1 namely ,,abc 77 99a99,,bc 77 ,,ab99c99 77 99a99,b99c99 77 ,a99b99,c 77 99ab99,c 77 ,a99bc99 77 99abc994 77 ,! developm5t ( ! t]m ,a is =m$ by ! fir/ f\r ( ^!2 = ,b we mu/ select 771 771 771 772 ,c consi/s ( 771 771 771 772 99b99 ( 771 771 771 771 & s on4 ,n[ if we want to inve/igate completely ! mean+ ( ! premises ,a ,,ab 7#a7 ,b ,,bc 7#b7 we exam9e ea* ( ! eight comb9ations z reg>ds ea* premise2 77 & 77 are contradict$ by 7#a71 & 77 & 77 by 7#b71 s t !re rema9 only ,,abc 77 99a99,,bc 77 99ab99,c 77 99abc994 77 ,to describe any t]m "u ! conditions ( ! premises 7#a7 & 7#b71 we h simply to draw out ! prop] comb9ations f ?is li/2 ?us1 ,a is repres5t$ only by ,,abc1 t is to say ,a ,,abc1 simil>ly 99c99 99abc994 ,= ,b we h two alt]natives ?us /at$1 ,b ,,abc 99a99,,bc2 & = 99b99 we h 99b99 99ab99,c 99abc994 ,:5 we h a problem involv+ f\r di/9ct t]ms we ne$ to d\ble ! numb] ( comb9ations1 & z we add ea* new t]m ! comb9ations become twice z num]\s4 ,?us ,a1 ,b produce f\r comb9ations ,a1 ,b1 ,c1 eight ,a1 ,b1 ,c1 ,d sixte5 ,a1 ,b1 ,c1 ,d1 ,e ?irty-two ,a1 ,b1 ,c1 ,d1 ,e1 ,f sixty-f\r & s on4 ,i propose to call any su* s]ies ( comb9ations ! 99,logical ,alphabet994 ,x holds 9 logical sci5ce a position ! importance ( :i* _c be exagg]at$1 & z we proce$ f logical to ma!matical consid]ations1 x w become app>5t t !re is a close connection betwe5 ^! comb9ations & ! fundam5tal !orems ( ma!matical sci5ce4 ,= ! conv5i5ce ( ! read] :o may wi% to employ ! 99,alphabet99 9 logical que/ions1 ,i h _h pr9t$ on ! next page a complete s]ies ( ! comb9ations up to ^? ( six t]ms4 ,at ! v comm5cem5t1 9 ! fir/ column1 is plac$ a s+le lett] ,x1 :i* might seem to be sup]flu\s4 ,?is lett] s]ves to d5ote t x is always "s high] class :i* is divid$ up4 ,?us ! comb9ation ,,ab really means ,,abx1 or t "p ( "s l>g] class1 say ,x1 :i* has ! qualities ( ,a & ,b pres5t4 ,! lett] ,x is omitt$ 9 ! great] "p ( ! table m]ely = ! sake ( brevity & cle>ness4 ,9 a lat] *apt] on ,comb9ations x w become app>5t t ! introduction ( ?is unit class is requisite 9 ord] to complete ! analogy ) ! ,ari?metical ,triangle !re describ$4 ,! read] ought to be> 9 m9d t ?\gh ! ,logical ,alphabet seems to give m]e li/s ( comb9ations1 ^! comb9ations are int5d$ 9 e case to con/itute ! developm5t ( a t]m ( a proposition4 ,?us ! f\r comb9ations ,,ab1 ,a99b991 99a99,b1 99ab99 really mean t any class ,x is describ$ by ! foll[+ proposition1 ,x ,,xab ,,xa99b99 ,x99a99,b ,x99ab994 ,if we select ! ,a's1 we obta9 ! foll[+ proposition ,,ax ,,xab ,,xa99b994 ,?us :atev] gr\p ( comb9ations we treat mu/ be conceiv$ z "p ( a high] class1 99summum g5us99 or univ]se symbolis$ 9 ! t]m ,x2 b1 be>+ ?is 9 m9d1 x is ne$less to complicate our =mul by always introduc+ ! lett]4 ,all inf]5ce consi/s 9 pass+ f propositions to propositions1 & comb9ations 99p] se99 h no mean+4 ,!y are consequ5tly to be reg>d$ 9 all cases z =m+ p>ts ( propositions4 ,,! ,,logical ,,alphabet4 ,i4 ,,ii4 ,,iii4 ,,iv4 ,v4 ,,vi4 ,,vii4 ,x ,,ax ,,ab ,,abc ,,abcd ,,abcde ,,abcdef 99a99,x ,a99b99 ,,ab99c99 ,,abc99d99 ,,abcd99e99 ,,abcde99f99 99a99,b ,a99b99,c ,,ab99c99,d ,,abc99d99,e ,,abcd99e99,f 99ab99 ,a99bc99 ,,ab99cd99 ,,abc99de99 ,,abcd99ef99 99a99,,bc ,a99b99,,cd ,,ab99c99,,de ,,abc99d99,,ef 99a99,b99c99 ,a99b99,c99d99 ,,ab99c99,d99e99 ,,abc99d99,e99f99 99ab99,c ,a99bc99,d ,,ab99cd99,e ,,abc99de99,f 99abc99 ,ab99cd99 ,,ab99cde99 ,,abc99def99 99a99,,bcd ,a99b99,,cde ,,ab99c99,,def 99a99,,bc99d99 ,a99b99,,cd99e99 ,,ab99c99,,de99f99 99a99,b99c99,d ,a99b99,c99d99,e ,,ab99c99,d99e99,f 99a99,b99cd99 ,a99b99,c99de99 ,,ab99c99,d99ef99 99ab99,,cd ,a99bc99,,de ,,ab99cd99,,ef 99ab99,c99d99 ,a99bc99,d99e99 ,,ab99cd99,e99f99 99abc99,d ,a99bcd99,e ,,ab99cde99,f 99abcd99 ,a99bcde99 ,,ab99cdef99 99a99,,bcde ,a99b99,,cdef 99a99,,bcd99e99 ,a99b99,,cde99f99 99a99,,bc99d99,e ,a99b99,,cd99e99,f 99a99,,bc99de99 ,a99b99,,cd99ef99 99a99,b99c99,,de ,a99b99,c99d99,,ef 99a99,b99c99,d99e99 ,a99b99,c99d99,e99f99 99a99,b99cd99,e ,a99b99,c99de99,f 99a99,b99cde99 ,a99b99,c99def99 99ab99,,cde ,a99bc99,,def 99ab99,,cd99e99 ,a99bc99,,de99f99 99ab99,c99d99,e ,a99bc99,d99e99,f 99ab99,cd99e99 ,a99bc99,d99ef99 99abc99,,de ,a99bcd99,,ef 99abc99,d99e99 ,a99bcd99,e99f99 99abcd99,e ,a99bcde99,f 99abcde99 ,a99bcdef99 99a99,,bcdef 99a99,,bcde99f99 99a99,,bcd99e99,f 99a99,,bcd99ef99 99a99,,bc99d99,,ef 99a99,,bc99d99,e99f99 99a99,,bc99de99,f 99a99,,bc99def99 99a99,b99c99,,def 99a99,b99c99,,de99f99 99a99,b99c99,d99e99,f 99a99,b99c99,d99ef99 99a99,b99cd99,,ef 99a99,b99cd99,e99f99 99a99,b99cde99,f 99a99,b99cdef99 99ab99,,cdef 99ab99,,cde99f99 99ab99,,cd99e99,f 99ab99,,cd99ef99 99ab99,c99d99,,ef 99ab99,c99d99,e99f99 99ab99,c99de99,f 99ab99,c99def99 99abc99,,def 99abc99,,de99f99 99abc99,d99e99,f 99abc99,d99ef99 99abcd99,,ef 99abcd99,e99f99 99abcde99,f 99abcdef99 ,9 a !oretical po9t ( view we may conceive t ! ,logical ,alphabet is inf9itely ext5d$4 ,e new quality or circum/ance :i* c belong to an object1 subdivides ea* comb9ation or class1 s t ! numb] ( su* comb9ations1 :5 unre/rict$ by logical conditions1 is repres5t$ by an inf9itely high p[] ( two4 ,! extremely rapid increase 9 ! numb] ( subdivisions obliges u to conf9e our att5tion to a few qualities at a "t4 ,:5 contemplat+ ! prop]ties ( ?is ,alphabet ,i am (t5 incl9$ to ?9k t ,py?agoras p]ceiv$ ! deep logical importance ( duality2 = :ile unity 0 ! symbol ( id5tity & h>mony1 he describ$ ! numb] two z ! orig9 ( contra/s1 or ! symbol ( div]sity1 division & sep>ation4 ,! numb] f\r1 or ! 99,tetractys991 0 also reg>d$ by him z "o ( ! *ief elem5ts ( exi/5ce1 = x repres5t$ ! g5]at+ virtue :5ce come all comb9ations4 ,9 "o ( ! gold5 v]ses ascrib$ to ,py?agoras1 he conjures 8 pupil to be virtu\s3#gg 8,by him :o /ampt 99,! ,f\r99 ^u ! ,m9d1 99,! ,f\r991 ! f\nt ( ,nature's endless /ream40 #gg ,:ewell1 99,hi/ory ( ! ,inductive ,sci5ces991 vol4 i4 p4 #bbb4 ,n[ f\r & ! high] p[]s ( duality d repres5t 9 ?is logical sy/em ! numb]s ( comb9ations :i* c be g5]at$ 9 ! abs5ce ( logical re/rictions4 ,! foll[]s ( ,py?agoras may h %r\d$ _! ma/]'s doctr9es 9 my/]i\s & sup]/iti\s notions1 b 9 _m po9ts ^! doctr9es seem to h "s basis 9 logical philosophy4 99,! ,logical ,slate499 ,to a p]son :o has once compreh5d$ ! extreme significance & utility ( ! ,logical ,alphabet ! indirect process ( inf]5ce becomes r$uc$ to ! repetition ( a few uni=m op]ations ( classification1 selection1 & elim9ation ( contradictories4 ,logical d$uction1 ev5 9 ! mo/ complicat$ que/ions1 becomes a matt] ( m]e r\t9e1 & ! am\nt ( lab\r requir$ is ! only imp$im5t1 :5 once ! mean+ ( ! premises is r5d]$ cle>4 ,b ! am\nt ( lab\r is (t5 f\nd to be consid]able4 ,! m]e writ+ d[n ( sixty-f\r comb9ations ( six lett]s ea* is no small task1 &1 if we _h a problem ( five premises1 ea* ( ! sixty-f\r comb9ations w\ld h to be exam9$ 9 connection ) ea* premise4 ,! requisite comp>ison is (t5 ( a v t$i\s "*1 & consid]able *ance ( error int]v5es4 ,i h giv5 mu* att5tion1 !re=e1 to less5+ bo? ! manual & m5tal lab\r ( ! process1 & ,i %all describe sev]al devices :i* may be adopt$ = sav+ tr\ble & risk ( mi/ake4 ,9 ! fir/ place1 z ! same sets ( comb9ations occur ov] & ov] aga9 9 diff]5t problems1 we may avoid ! lab\r ( writ+ !m out by hav+ ! sets ( lett]s ready pr9t$ ^u small %eets ( writ+-pap]4 ,x has also be5 sugge/$ by a correspond5t t1 if any "o s]ies ( comb9ations 7 m>k$ ^u ! m>g9 ( a %eet ( pap]1 & a slit cut betwe5 ea* pair ( comb9ations1 x w\ld be easy to fold d[n any p>ticul> comb9ation1 & ?us /rike x out ( view4 ,! comb9ations consi/5t ) ! premises w\ld !n rema9 9 a brok5 s]ies4 ,?is me?od answ]s suffici5tly well = occasional use4 ,a m conv5i5t mode1 h[ev]1 is to h ! s]ies ( lett]s %[n on p4 #id1 engrav$ ^u a common s*ool writ+ slate1 ( su* a size1 t ! lett]s may occupy only ab\t a ?ird ( ! space on ! left h& side ( ! slate4 ,! conditions ( ! problem c !n be writt5 d[n on ! unoccupi$ "p ( ! slate1 & ! prop] s]ies ( comb9ations be+ *os51 ! contradictory comb9ations c be /ruck out ) ! p5cil4 ,i h us$ a slate ( ?is k9d1 :i* ,i call a 99,logical ,slate991 = m ?an twelve ye>s1 & x has sav$ me mu* tr\ble4 ,x is h>dly possible to apply ?is process to problems ( m ?an six t]ms1 ow+ to ! l>ge numb] ( comb9ations :i* w\ld require exam9ation4 99,ab/raction ( ,indiff]5t ,circum/ances499 ,!re is a simple b highly important process ( inf]5ce :i* enables u to ab/ract1 elim9ate or disreg>d all circum/ances indiff]5tly pres5t & abs5t4 ,?us if ,i 7 to /ate t 8a triangle is a ?ree-sid$ rectil9e> figure1 ei!r l>ge or n l>ge10 ^! two alt]natives w\ld be sup]flu\s1 because1 by ! ,law ( ,duality1 ,i "k t ev]y?+ mu/ be ei!r l>ge or n l>ge4 ,to add ! qualification gives no new k1 s9ce ! exi/5ce ( ! two alt]natives w be und]/ood 9 ! abs5ce ( any in=mation to ! contr>y4 ,accord+ly1 :5 two alt]natives diff] only z reg>ds a s+le compon5t t]m :i* is positive 9 "o & negative 9 ! o!r1 we may r$uce !m to "o t]m by /rik+ out _! indiff]5t "p4 ,x is really a process ( sub/itution :i* enables u to d ?is2 = hav+ any proposition ( ! =m ,a ,,abc ,,ab99c991 7#a7 we "k by ! ,law ( ,duality t ,,ab ,,abc ,,ab99c994 7#b7 ,z ! second memb] ( ?is is id5tical ) ! second memb] ( 7#a7 we may sub/itute1 obta9+ ,a ,,ab4 ,?is process ( r$uc+ useless alt]natives may be appli$ aga9 & aga92 = x is pla9 t ,a ,,ab 7,,cd ,c99d99 99c99,d 99cd997 communicates no m in=mation ?an t ,a is ,b4 ,ab/raction ( indiff]5t t]ms is 9 fact ! conv]se process to t ( developm5t describ$ 9 p4 #hi2 & x is "o ( ! mo/ important op]ations 9 ! :ole sph]e ( reason+4 ,! read] %\ld obs]ve t 9 ! proposition ,,ac ,,bc we _c ab/ract ,c & inf] ,a ,b2 b f ,,ac ,a99c99 ,,bc ,b99c99 we may ab/ract all ref]5ce to ! t]m ,c4 ,x ought to be c>efully rem>k$1 h[ev]1 t alt]natives :i* seem to be )\t mean+ (t5 imply important k4 ,?us if ,i say t 8a triangle is a ?ree-sid$ rectil9e> figure1 ) or )\t ?ree equal angles10 ! la/ alt]natives really express a prop]ty ( triangles1 namely1 t "s triangles h ?ree equal angles1 & "s d n h !m4 ,if we put ,p 8,"s10 mean+ by ! indef9ite adjective 8,"s10 "o or m ( ! undef9$ prop]ties ( triangles ) ?ree equal angles1 & take ,a triangle ,b ?ree-sid$ rectil9e> figure ,c ) ?ree equal angles1 !n ! k impli$ is express$ 9 ! two propositions ,,pa ,,pbc 99p99,a 99p99,b99c994 ,^! may also be ?r[n into ! =m ( "o proposition1 namely1 ,a ,,pbc 99p99,b99c992 b ^! alt]natives _c be r$uc$1 & ! proposition is q diff]5t f ,a ,,bc ,b99c994 99,illu/rations ( ! ,indirect ,me?od499 ,a great v>iety ( argum5ts & logical problems might be introduc$ "h to %[ ! compreh5sive "* & p[]s ( ! ,indirect ,me?od4 ,we c treat ei!r a s+le premise or a s]ies ( premises4 ,take 9 ! fir/ place a simple def9ition1 su* z 8a triangle is a ?ree-sid$ rectil9e> figure40 ,let ,a triangle ,b ?ree-sid$ ,c rectil9e> figure1 !n ! def9ition is ( ! =m ,a ,,bc4 ,if we take ! s]ies ( eight comb9ations ( ?ree lett]s 9 ! ,logical ,alphabet 7p4 #id7 & /rike out ^? :i* are inconsi/5t ) ! def9ition1 we h ! foll[+ result3-- ,,abc 99a99,b99c99 99ab99,c 99abc499 ,= ! description ( ! class ,c we h ,c ,,abc 99ab99,c1 t is1 8a rectil9e> figure is ei!r a triangle & ?ree-sid$1 or n a triangle & n ?ree-sid$40 ,= ! class 99b99 we h 99b99 99ab99,c 99abc994 ,to ! second side ( ?is we may apply ! process ( simplification by ab/raction describ$ 9 ! la/ section2 = by ! ,law ( ,duality 99ab99 99ab99,c 99abc992 & z we h two propositions id5tical 9 ! second side ( ea* we may sub/itute1 gett+ 99b99 99ab991 or :at is n ?ree-sid$ is n a triangle 7:e!r x be rectil9e> or n74 99,second ,example499 ,let u treat by ?is me?od ! foll[+ argum5t3-- 8,bl5de is n an elem5t>y sub/ance2 elem5t>y sub/ances are ^? :i* are undecomposable2 bl5de1 !re=e1 is decomposable40 ,tak+ our lett]s ?us-- ,a bl5de1 ,b elem5t>y sub/ance1 ,c undecomposable1 ! premises are ( ! =ms ,a ,a99b991 7#a7 ,b ,c4 7#b7 ,no imm$iate sub/itution c be made2 b if we take ! contrapositive ( 7#b7 7see p4 #hf71 namely 99b99 99c991 7#c7 we c sub/itute 9 7#a7 obta9+ ! conclusion ,a ,a99c994 ,b ! same result may be obta9$ by tak+ ! eight comb9ations ( ,a1 ,b1 ,c1 ( ! ,logical ,alphabet2 x w be f\nd t only ?ree comb9ations1 namely1 ,a99bc99 99a99,,bc 99abc991 are consi/5t ) ! premises1 :5ce x results t ,a ,a99bc991 or by ! process ( ,ellipsis be=e describ$ 7p4 #eg7 ,a ,a99c994 99,?ird ,example499 ,z a some:at m complex example ,i take ! argum5t ?us /at$1 "o :i* c\ld n be ?r[n into ! syllogi/ic =m3-- 8,all metals except gold & silv] are opaque2 !re=e :at is n opaque is ei!r gold or silv] or is n-metal40 ,!re is m impli$ 9 ?is /atem5t ?an is di/9ctly ass]t$1 ! full mean+ be+ z foll[s3 ,all metals n gold or silv] are opaque1 7#a7 ,gold is n opaque b is a metal1 7#b7 ,silv] is n opaque b is a metal1 7#c7 ,gold is n silv]4 7#d7 ,tak+ our lett]s ?us-- ,a metal ,c silv] ,b gold ,d opaque1 we may /ate ! premises 9 ! =ms ,a99bc99 ,a99bc99,d 7#a7 ,b ,,ab99d99 7#b7 ,c ,,ac99d99 7#c7 ,b ,b99c994 7#d7 ,to obta9 a complete solution ( ! "q we take ! sixte5 comb9ations ( ,a1 ,b1 ,c1 ,d1 & /rik+ out ^? :i* are inconsi/5t ) ! premises1 !re rema9 only ,,ab99cd99 ,a99b99,c99d99 ,a99bc99,d 99abc99,d 99abcd994 ,! expression = n-opaque ?+s consi/s ( ! ?ree comb9ations conta9+ 99d991 ?us 99d99 ,,ab99cd99 ,a99b99,c99d99 99abcd991 or 99d99 ,a99d99 7,b99c99 99b99,c7 99abcd994 ,9 ord9>y language1 :at is n-opaque is ei!r metal :i* is gold1 & !n n-silv]1 or silv] & !n n-gold1 or else x is n-metal & nei!r gold nor silv]4 99,f\r? ,example499 ,a good example = ! illu/ration ( ! ,indirect ,me?od is to be f\nd 9 ,de ,morgan's 99,=mal ,logic99 7p4 #abc71 ! premises be+ sub/antially z foll[s3-- ,f ,a foll[s ,b1 & f ,c foll[s ,d2 b ,b & ,d are inconsi/5t ) ea* o!r2 !re=e ,a & ,c are inconsi/5t4 ,! mean+ no d\bt is t :]e ,a is1 ,b w be f\nd1 or t e ,a is a ,b1 & simil>ly e ,c is a ,d2 b ,b & ,d _c occur toge!r4 ,! premises !re=e appe> to be ( ! =ms ,a ,,ab1 7#a7 ,c ,,cd1 7#b7 ,b ,b99d994 7#c7 ,on exam9+ ! s]ies ( sixte5 comb9ations1 only five are f\nd to be consi/5t ) ! above conditions1 namely1 ,,ab99cd99 99a99,b99cd99 99ab99,,cd 99abc99,d 99abcd994 ,9 ^! comb9ations ! only ,a :i* appe>s is jo9$ to 99c991 & simil>ly ,c is jo9$ to 99a991 or ,a is inconsi/5t ) ,c4 99,fif? ,example499 ,a m complex argum5t1 also giv5 by ,de ,morgan1#gh conta9s five t]ms1 & is z /at$ bel[1 except t ! lett]s are alt]$4 ,e ,a is "o only ( ! two ,b or ,c2 ,d is bo? ,b & ,c1 except :5 ,b is ,e1 & !n x is nei!r2 !re=e no ,a is ,d4 #gh 99,=mal ,logic991 p4 #abd4 ,z ,pr(essor ,croom ,rob]tson has po9t$ out to me1 ! second & ?ird premises may be ?r[n into a s+le proposition1 ,d ,d99e99,,bc ,,de99bc994 ,! mean+ ( ! above premises is difficult to int]pret1 b seems to be capable ( expression 9 ! foll[+ symbolic =ms-- ,a ,,ab99c99 ,a99b99,c1 7#a7 ,de ,d99e99,,bc1 7#b7 ,,de ,,de99bc994 7#c7 ,z five t]ms ent] into ^! premises x is requisite to treat _! ?irty-two comb9ations1 & x w be f\nd t f\rte5 ( !m rema9 consi/5t ) ! premises1 namely ,,ab99cd99,e 99a99,,bcd99e99 99ab99,c99d99,e ,,ab99cde99 99a99,,bc99d99,e 99ab99,c99de99 ,a99b99,c99d99,e 99a99,,bc99de99 99abc99,,de ,a99b99,c99de99 99a99,b99cd99,e 99abcd99,e 99a99,b99cde99 99abcde994 ,if we exam9e ! fir/ f\r comb9ations1 all ( :i* conta9 ,a1 we f9d t !y none ( !m conta9 ,d2 or aga91 if we select ^? :i* conta9 ,d1 we h only two1 ?us-- ,d 99a99,,bcd99e99 99abc99,,de4 ,h5ce x is cle> t no ,a is ,d1 & 99vice v]s99 no ,d is ,a4 ,we might draw _m o!r conclusions f ! same premises2 = in/ance-- ,,de 99abc99,,de1 or ,d & ,e nev] meet b 9 ! abs5ce ( ,a1 ,b1 & ,c4 99,fallacies analys$ by ! ,indirect ,me?od499 ,x has be5 suffici5tly %[n1 p]haps1 t we c by ! ,indirect ,me?od ( ,inf]5ce extract ! :ole tru? f a s]ies ( propositions1 & exhibit x anew 9 any requir$ =m ( conclusion4 ,b x may also ne$ to be %[n by examples t s long z we foll[ correctly ! almo/ me*anical rules ( ! me?od1 we _c fall into any ( ! fallacies or p>alogisms :i* are (t5 committ$ 9 ord9>y discussion4 ,let u take ! example ( a fallaci\s argum5t1 previ\sly treat$ by ! ,me?od ( ,direct ,inf]5ce 7p4 #fb71 ,granite is n a s$im5t>y rock1 7#a7 ,basalt is n a s$im5t>y rock1 7#b7 & let u asc]ta9 :e!r any precise conclusion c be drawn conc]n+ ! relation ( granite & basalt4 ,tak+ z be=e ,a granite1 ,b s$im5t>y rock1 ,c basalt1 ! premises become ,a ,a99b991 7#a7 ,c ,c99b994 7#b7 ,( ! eight conceivable comb9ations ( ,a1 ,b1 ,c1 five agree ) ^! conditions1 namely ,a99b99,c 99a99,b99c99 ,a99bc99 99ab99,c 99abc994 ,select+ ! comb9ations :i* conta9 ,a1 we f9d ! description ( granite to be ,a ,a99b99,c ,a99bc99 ,a99b997,c 99c9971 t is1 granite is n a s$im5t>y rock1 & is ei!r basalt or n-basalt4 ,if we want a description ( basalt ! answ] is ( l =m ,c ,a99b99,c 99ab99,c 99b99,c7,a 99a9971 t is basalt is n a s$im5t>y rock1 & is ei!r granite or n-granite4 ,z x is already p]fectly evid5t t basalt mu/ be ei!r granite or n1 & 99vice v]s991 ! premises fail to give u any in=mation on ! po9t1 t is to say ! ,me?od ( ,indirect ,inf]5ce saves u f fall+ into any fallaci\s conclusions4 ,?is example suffici5tly illu/rates bo? ! fallacy ( ,negative premises & t ( ,undi/ribut$ ,middle ( ! old logic4 ,! fallacy call$ ! ,illicit ,process ( ! ,major ,t]m is also incapable ( commission 9 foll[+ ! rules ( ! me?od4 ,our example 0 7p4 #fe7 ,all planets are subject to gravity1 7#a7 ,fix$ />s are n planets4 7#b7 ,! false conclusion is t 8fix$ />s are n subject to gravity40 ,! t]ms are ,a planet ,b fix$ /> ,c subject to gravity4 ,& ! premises are ,a ,,ac1 7#a7 ,b 99a99,b4 7#b7 ,! comb9ations :i* rema9 uncontradict$ on comp>ison ) ^! premises are ,a99b99,c 99a99,b99c99 99a99,,bc 99ab99,c 99abc994 ,= fix$ /> we h ! description ,b 99a99,,bc 99a99,b99c991 t is1 8a fix$ /> is n a planet1 b is ei!r subject or n1 z ! case may be1 to gravity40 ,"h we h no conclusion conc]n+ ! connection ( fix$ />s & gravity4 99,! ,logical ,abacus499 ,! ,indirect ,me?od ( ,inf]5ce has n[ be5 suffici5tly describ$1 & a c>eful exam9ation ( its p[]s w %[ t x is capable ( giv+ a full analysis & solution ( e "q involv+ only logical relations4 ,! *ief difficulty ( ! me?od consi/s 9 ! great numb] ( comb9ations :i* may h to be exam9$2 n only may ! requisite lab\r become =midable1 b a consid]able *ance ( mi/ake arises4 ,i h !re=e giv5 mu* att5tion to modes ( facilitat+ ! "w1 & h succe$$ 9 r$uc+ ! me?od to an almo/ me*anical =m4 ,x soon appe>$ obvi\s t if ! conceivable comb9ations ( ! ,logical ,alphabet1 = any numb] ( lett]s1 in/ead ( be+ pr9t$ 9 fix$ ord] on a piece ( pap] or slate1 7 m>k$ ^u light movable pieces ( wood1 me*anical arrangem5ts c\ld readily be devis$ = select+ any requir$ class ( ! comb9ations4 ,! lab\r ( comp>ison & rejection might ?us be imm5sely r$uc$4 ,?is idea 0 fir/ c>ri$ out 9 ! ,logical ,abacus1 :i* ,i h f\nd useful 9 ! lecture-room = exhibit+ ! complete solution ( logical problems4 ,a m9ute description ( ! con/ruction & use ( ! ,abacus1 toge!r ) figures ( ! p>ts1 has already be5 giv5 9 my essay call$ 99,! ,sub/itution ( ,simil>s991#gi & ,i w "h give only a g5]al description4 #gi ,pp4 #ee-ei1 #ha-hf4 ,! ,logical ,abacus consi/s ( a common s*ool black-bo>d plac$ 9 a slop+ position & furni%$ ) f\r horizontal & equi-di/ant l$ges4 ,! comb9ations ( ! lett]s %[n 9 ! fir/ f\r columns ( ! ,logical ,alphabet are pr9t$ 9 some:at l>ge type1 s t ea* lett] is ab\t an in* f ! neighb\r+ "o1 b ! lett]s are plac$ "o above ! o!r in/ead ( be+ 9 horizontal l9es z 9 p4 #id4 ,ea* comb9ation ( lett]s is sep>ately fix$ to ! surface ( a ?9 slip ( wood "o in* broad & ab\t "o-eigh? in* ?ick4 ,%ort /eel p9s are !n driv5 9 an incl9$ position into ! wood4 ,:5 a lett] is a l>ge capital repres5t+ a positive t]m1 ! p9 is fix$ 9 ! upp] "p ( its space2 :5 ! lett] is a small italic repres5t+ a negative t]m1 ! p9 is fix$ 9 ! l[] "p ( ! space4 ,n[1 if "o ( ! s]ies ( comb9ations be rang$ ^u a l$ge ( ! black-bo>d1 ! %>p edge ( a flat rule c be ins]t$ b5ea? ! p9s belong+ to any "o lett]--say ,a1 s t all ! comb9ations m>k$ ,a c be lift$ out & plac$ ^u a sep>ate l$ge4 ,?us we h repres5t$ ! act ( ?\ght :i* sep>ates ! class ,a f :at is n-,a4 ,! op]ation c be repeat$2 out ( ! ,a's we c 9 l mann] select ^? :i* are ,b's1 obta9+ ! ,,ab's2 & 9 l mann] we may select any o!r classes su* z ! 99a99,b's1 ! 99ab99's1 or ! 99abc99's4 ,if n[ we take ! s]ies ( eight comb9ations ( ! lett]s ,a1 ,b1 ,c1 99a991 99b991 99c991 & wi% to analyse ! argum5t anci5tly call$ ,b>b>a1 hav+ ! premises ,a ,,ab 7#a7 ,b ,,bc1 7#b7 we proce$ z foll[s--,we raise ! comb9ations m>k$ 99a991 leav+ ! ,a's beh9d2 out ( ^! ,a's we move to a l[] l$ge su* z are 99b99's1 & to ! rema9+ ,,ab's we jo9 ! 99a99's :i* h be5 rais$4 ,! result is t we h divid$ all ! comb9ations into two classes1 namely1 ! ,a99b99's :i* are incapable ( exi/+ consi/5tly ) premise 7#a71 & ! comb9ations :i* are consi/5t ) ! premise4 ,turn+ n[ to ! second premise1 we raise out ( ^? :i* agree ) 7#a7 ! 99b99's1 !n we l[] ! ,b99c99's2 la/ly we jo9 ! 99b99's to ! ,,bc's4 ,we n[ f9d our comb9ations arrang$ z bel[4 -------------------------------------- ,a 99a99 99a99 99a99 ,b ,b 99b99 99b99 ,c ,c ,c 99c99 -------------------------------------- ,a ,a ,a 99a99 ,b 99b99 99b99 ,b 99c99 ,c 99c99 99c99 -------------------------------------- ,! l[] l9e conta9s all ! comb9ations :i* are inconsi/5t ) ei!r premise2 we h c>ri$ out 9 a me*anical mann] t exclusion ( self-contradictories :i* 0 =m]ly done ^u ! slate or ^u pap]4 ,accord+ly1 f ! comb9ations rema9+ 9 ! upp] l9e we c draw any inf]5ce :i* ! premises yield4 ,if we raise ! ,a's we f9d only "o1 & t is ,c1 s t ,a mu/ be ,c4 ,if we select ! 99c99's we aga9 f9d only "o1 :i* is 99a99 & also 99b992 ?us we prove t n-,c is n-,a & n-,b4 ,:5 a disjunctive proposition occurs among ! premises ! requisite movem5ts become r m complicat$4 ,take ! disjunctive argum5t ,a is ei!r ,b or ,c or ,d1 ,a is n ,c & n ,d1 ,!re=e ,a is ,b4 ,! premises are repres5t$ accurately z foll[s3-- ,a ,,ab ,,ac ,,ad 7#a7 ,a ,a99c99 7#b7 ,a ,a99d994 7#c7 ,z !re are f\r t]ms1 we *oose ! s]ies ( sixte5 comb9ations & place !m on ! highe/ l$ge ( ! bo>d b "o4 ,we raise ! 99a99's & out ( ! ,a's1 :i* rema91 we l[] ! 99b99's4 ,b we are n to reject all ! ,a99b99's z contradictory1 because by ! fir/ premise ,a's may be ei!r ,b's or ,c's or ,d's4 ,accord+ly out ( ! ,a99b99's we mu/ select ! 99c99's1 & out ( ^! aga9 ! 99d99's1 s t only ,a99bcd99 w rema9 to be reject$ f9ally4 ,jo9+ all ! o!r fifte5 comb9ations toge!r aga91 & proce$+ to premise 7#b71 we raise ! 99a99's & l[] ! ,,ac's1 & ?us reject ! comb9ations inconsi/5t ) 7#b72 simil>ly we reject ! ,,ad's :i* are inconsi/5t ) 7#c74 ,x w be f\nd t !re rema91 9 addition to all ! eight comb9ations conta9+ 99a991 only "o conta9+ ,a1 namely ,,ab99cd991 :5ce x is app>5t t ,a mu/ be ,b1 ! ord9>y conclusion ( ! argum5t4 ,9 my 8,sub/itution ( ,simil>s0 7pp4 #ef-ei7 ,i h describ$ ! work+ ^u ! ,abacus ( two o!r logical problems1 :i* x w\ld be t$i\s to repeat 9 ?is place4 99,! ,logical ,ma*9e499 ,al?\gh ! ,logical ,abacus consid]ably r$uc$ ! lab\r ( us+ ! ,indirect ,me?od1 x 0 n free f ! possibility ( error4 ,i ?\ght moreov] t x w\ld af=d a conspicu\s pro( ( ! g5]ality & p[] ( ! me?od if ,i c\ld r$uce x to a purely me*anical =m4 ,logicians _h long be5 accu/om$ to speak ( ,logic z an ,organon or ,in/rum5t1 & ev5 ,"l ,bacon1 :ile he reject$ ! old syllogi/ic logic1 _h insi/$1 9 ! second aphorism ( 8 8,new ,in/rum5t10 t ! m9d requir$ "s k9d ( sy/ematic aid4 ,9 ! k9dr$ sci5ce ( ma!matics me*anical assi/ance ( "o k9d or ano!r _h long be5 employ$4 ,orr]ies1 globes1 me*anical clocks1 & su* l in/rum5ts1 are really aids to calculation & are ( consid]able antiquity4 ,! ,ari?metical ,abacus is /ill 9 common use 9 ,russia & ,*9a4 ,! calculat+ ma*9e ( ,pascal is m ?an two c5turies old1 hav+ be5 con/ruct$ 9 #afdb-de4 ,m4 ,?omas ( ,colm> manufactures an ari?metical ma*9e on ,pascal's pr9ciples :i* is employ$ by eng9e]s & o!rs :o ne$ frequ5tly to multiply or divide4 ,to ,babbage & ,s*eutz is due ! m]it ( embody+ ! ,calculus ( ,diff]5ces 9 a ma*9e1 :i* ?us became capable ( calculat+ ! mo/ complicat$ tables ( figures4 ,x seem$ /range t 9 ! m intricate sci5ce ( quantity me*anism %\ld be applicable1 :]eas 9 ! simple sci5ce ( qualitative reason+1 ! syllogism 0 only call$ an in/rum5t by a figure ( spee*4 ,x is true t ,swift satirically describ$ ! ,pr(essors ( ,laputa z 9 possession ( a ?9k+ ma*9e1 & 9 #ahea ,mr4 ,alfr$ ,smee actually propos$ ! con/ruction ( a ,relational ma*9e & a ,diff]5tial ma*9e1 ! fir/ ( :i* w\ld be a me*anical diction>y & ! second a mode ( comp>+ ideas2 b ) ^! exceptions ,i h n yet met ) s mu* z a sugge/ion ( a reason+ ma*9e4 ,x may be add$ t ,mr4 ,smee's designs1 ?\gh highly +5i\s1 appe> to be impracticable1 & 9 any case !y d n attempt ! p]=mance ( logical inf]5ce4#hj #hj ,see 8 "w call$ 99,! ,process ( ,?\ght adapt$ to ,words & ,language1 toge!r ) a ,description ( ! ,relational & ,diff]5tial ,ma*9es994 ,also 99,philosophical ,transactions991 #ahgj vol4 #afj1 p4 #eah4 ,! ,logical ,abacus soon sugge/$ ! notion ( a ,logical ,ma*9e1 :i*1 aft] two unsuccessful attempts1 ,i succe$$ 9 con/ruct+ 9 a comp>atively simple & effective =m4 ,! details ( ! ,logical ,ma*9e h be5 fully describ$ by ! aid ( plates 9 ! ,philosophical ,transactions1#ha & x w\ld be ne$less to repeat ! acc\nt ( ! some:at intricate movem5ts ( ! ma*9e 9 ?is place4 #ha 99,philosophical ,transactions99 #ahgj1 vol4 #afj1 p4 #dig4 99,proce$+s ( ! ,royal ,society991 vol4 xviii4 p4 #aff1 ,jan4 #bj1 #ahgj4 99,nature991 vol1 i4 p4 #cdc4 ,! g5]al appe>ance ( ! ma*9e is %[n 9 a plate fac+ ! title-page ( ?is volume4 ,x some:at resembles a v small upright piano or organ1 & has a keybo>d conta9+ tw5ty-"o keys4 ,^! keys are ( two k9ds1 sixte5 ( !m repres5t+ ! t]ms or lett]s ,a1 99a991 ,b1 99b991 ,c1 99c991 ,d1 99d991 :i* h s (t5 be5 employ$ 9 our logical notation4 ,:5 lett]s occur on ! left-h& side ( a proposition1 =m]ly call$ ! subject1 ea* is repres5t$ by a key on ! left-h& half ( ! keybo>d2 b :5 !y occur on ! "r-h& side1 or z x us$ to be call$ ! pr$icate ( ! proposition1 ! lett]-keys on ! "r-h& side ( ! keybo>d are ! prop] repres5tatives4 ,! five o!r keys may be call$ op]ation keys1 to di/+ui% !m f ! lett] or t]m keys4 ,!y /& = ! /ops1 copula1 & disjunctive conjunctions ( a proposition4 ,! middle key ( all is ! copula1 to be press$ :5 ! v]b 99is99 or ! sign is met4 ,! key to ! extreme "r-h& is call$ ! ,full ,/op1 because x %\ld be press$ :5 a proposition is complet$1 9 fact 9 ! prop] place ( ! full /op4 ,! key to ! extreme left-h& is us$ to t]m9ate an argum5t or to re/ore ! ma*9e to its initial condition2 x is call$ ! ,f9is key4 ,! la/ keys b "o on ! "r & left complete ! :ole s]ies1 & repres5t ! conjunction 99or99 9 its unexclusive mean+1 or ! sign :i* ,i h employ$1 accord+ z x occurs 9 ! "r or left h& side ( ! proposition4 ,! :ole keybo>d is arrang$ z %[n on ! next page-- ---------------------------------------- ----------------------------------- ,c ,f ,left-h& side ( ,proposition4 o ,"r-h& side ( ,proposition4 ,f ,s i p u t n---------------------------u----------- ----------------l o i l l p s99d99 ,d 99c99 ,c 99b99 ,b 99a99 ,a a ,a 99a99 ,b 99b99 ,c 99c99 ,d 99d99 4 4,or 4 ,or ---------------------------------------- ------------------- ,to "w ! ma*9e x is only requisite to press ! keys 9 succession z indicat$ by ! lett]s & signs ( a symbolical proposition4 ,all ! premises ( an argum5t are suppos$ to be r$uc$ to ! simple notation :i* has be5 employ$ 9 ! previ\s pages4 ,tak+ !n su* a simple proposition z ,a ,,ab1 we press ! keys ,a 7left71 copula1 ,a 7"r71 ,b 7"r71 & full /op4 ,if !re be a second premise1 = in/ance ,b ,,bc1 we press 9 l mann] ! keys-- ,b 7left71 copula1 ,b 7"r71 ,c 7"r71 full /op4 ,! process is exactly ! same h[ev] num]\s ! premises may be4 ,:5 !y are complet$ ! op]ator w see indicat$ on ! face ( ! ma*9e ! exact comb9ations ( lett]s :i* are consi/5t ) ! premises accord+ to ! pr9ciples ( ?\ght4 ,z %[n 9 ! figure opposite ! title-page1 ! ma*9e exhibits 9 front a ,logical ,alphabet ( sixte5 comb9ations1 exactly l t ( ! ,abacus1 except t ! lett]s ( ea* comb9ation are sep>at$ by a c]ta9 int]val4 ,aft] ! above problem has be5 work$ ^u ! ma*9e ! ,logical ,alphabet w h be5 modifi$ s z to pres5t ! foll[+ appe>ance-- ---------------------------------------- --------------- ---------------------------------------- ,a ,a 99a9999a99 99a9999a9999a9999a99 ---------------------------------------- ---------------------------------------- ,b ,b ,b ,b 99b9999b9999b9999b99 ---------------------------------------- ---------------------------------------- ,c ,c ,c ,c ,c ,c 99c9999c99 ---------------------------------------- ---------------------------------------- ,d 99d99 ,d 99d99 ,d 99d99 ,d 99d99 ---------------------------------------- ---------------------------------------- --------------- ,! op]ator w readily collect ! v>i\s conclusions 9 ! mann] describ$ 9 previ\s pages1 z1 = in/ance t ,a is always ,c1 t n-,c is n-,b & n-,a2 & n-,b is n-,a b ei!r ,c or n-,c4 ,! results are ?us to be read (f exactly z 9 ! case ( ! ,logical ,slate1 or ! ,logical ,abacus4 ,disjunctive propositions are to be treat$ 9 an exactly simil> mann]4 ,?us1 to "w ! premises ,a ,,ab ,,ac ,b ,c ,,bd ,,cd1 x is only necess>y to press 9 succession ! keys ,a 7left71 copula1 ,a 7"r71 ,b1 1 ,a1 ,c1 full /op4 ,b 7left71 1 ,c1 copula1 ,b 7"r71 ,d1 1 ,c1 ,d1 full /op4 ,! comb9ations !n rema9+ w be z foll[s ,,abcd 99a99,,bcd 99abc99,d ,,ab99c99,d 99a99,b99c99,d 99abcd499 ,a99c99,,cd 99ab99,,cd ,on press+ ! left-h& key ,a1 all ! possible comb9ations :i* d n conta9 ,a w disappe>1 & ! description ( ,a may be ga!r$ f :at rema91 namely t x is always ,d4 ,! full-/op key re/ores all comb9ations consi/5t ) ! premises & any o!r selection may be made1 z say n-,d1 :i* w be f\nd to be always n-,a1 n-,b1 & n-,c4 ,at ! end ( e problem1 :5 no fur!r que/ions ne$ be address$ to ! ma*9e1 we press ! ,f9is key1 :i* has ! effect ( br++ into view ! :ole ( ! conceivable comb9ations ( ! alphabet4 ,?is key 9 fact oblit]ates ! conditions impress$ ^u ! ma*9e by mov+ back into _! ord9>y places ^? comb9ations :i* _h be5 reject$ z inconsi/5t ) ! premises4 ,be=e beg9n+ any new problem x is requisite to obs]ve t ! :ole sixte5 comb9ations are visible4 ,aft] ! ,f9is key has be5 us$ ! ma*9e repres5ts a m9d end[$ ) p[]s ( ?\ght1 b :olly devoid ( k4 ,x w\ld n 9 t condition give any answ] b su* z w\ld consi/ 9 ! prim>y laws ( ?\ght !mselves4 ,b :5 any proposition is work$ ^u ! keys1 ! ma*9e analyses & dige/s ! mean+ ( x & becomes *>g$ ) ! k embodi$ 9 t proposition4 ,accord+ly x is able to return z an answ] any description ( a t]m or class s f> z furni%$ by t proposition 9 accordance ) ! ,laws ( ,?\ght4 ,! ma*9e is ?us ! embodim5t ( a true logical sy/em4 ,! comb9ations are classifi$1 select$ or reject$1 j z !y %\ld be by a reason+ m9d1 s t at ea* /ep 9 a problem1 ! ,logical ,alphabet repres5ts ! prop] condition ( a m9d exempt f mi/ake4 ,x _c be ass]t$ inde$ t ! ma*9e entirely sup]s$es ! ag5cy ( consci\s ?\ght2 m5tal lab\r is requir$ 9 int]pret+ ! mean+ ( grammatical expressions1 & 9 correctly impress+ t mean+ on ! ma*9e2 x is fur!r requir$ 9 ga!r+ ! conclusion f ! rema9+ comb9ations4 ,nev]!less ! true process ( logical inf]5ce is really accompli%$ 9 a purely me*anical mann]4 ,x is wor?y ( rem>k t ! ma*9e c detect any self-contradiction exi/+ betwe5 ! premises pres5t$ to x2 %\ld ! premises be self-contradictory x w be f\nd t "o or m ( ! lett]-t]ms disappe>s entirely f ! ,logical ,alphabet4 ,?us if we "w ! two propositions1 ,a is ,b1 & ,a is n-,b1 & !n inquire = a description ( ,a1 ! ma*9e w refuse to give x by exhibit+ no comb9ation at all conta9+ ,a4 ,?is result is 9 agreem5t ) ! law1 :i* ,i h expla9$1 t e t]m mu/ h its negative 7p4 #gd74 ,accord+ly1 :5ev] any "o ( ! lett]s ,a1 ,b1 ,c1 ,d1 99a991 99b991 99c991 99d991 :olly disappe>s f ! alphabet1 x may be safely inf]r$ t "s act ( self-contradiction has be5 committ$4 ,x ought to be c>efully obs]v$ t ! logical ma*9e _c receive a simple id5tity ( ! =m ,a ,b except 9 ! d\ble =m ( ,a ,b & ,b ,a4 ,to "w ! proposition ,a ,b1 x is !re=e necess>y to press ! keys-- ,a 7left71 copula1 ,b 7"r71 full /op2 ,b 7left71 copula1 ,a 7"r71 full /op4 ,! same d\ble op]ation w be necess>y :5ev] ! proposition is n ( ! k9d call$ a p>tial id5tity 7p4 #dj74 ,?us ,,ab ,,cd1 ,,ab ,,ac1 ,a ,b ,c1 ,a ,b ,c ,d1 all require to be read f bo? ends sep>ately4 ,! prop] rule = us+ ! ma*9e may 9 fact be giv5 9 ! foll[+ way3--7#a7 99,read ea* proposition z x /&s1 & play ! correspond+ keys993 7#b7 99,conv]t ! proposition & read & play ! keys aga9 9 ! transpos$ ord] ( ! t]ms499 ,s long z ?is rule is obs]v$ ! true result mu/ always be obta9$4 ,!re c be no mi/ake4 ,b x w be f\nd t 9 ! case ( p>tial id5tities1 & "s o!r simil> =ms ( propositions1 ! transpos$ read+ has no effect ^u ! comb9ations ( ! ,logical ,alphabet4 ,"o read+ is 9 su* cases all t is practically ne$ful4 ,aft] "s exp]i5ce has be5 ga9$ 9 ! use ( ! ma*9e1 ! work] naturally saves himself ! tr\ble ( ! second read+ :5 possible4 ,x is no d\bt a rem>kable fact t a simple id5tity _c be impress$ ^u ! ma*9e except 9 ! =m ( two p>tial id5tities1 & ?is may be ?\ght by "s logicians to militate aga9/ ! equational mode ( repres5t+ propositions4 ,be=e leav+ ! subject ,i may rem>k t ^! me*anical devices are n likely to possess mu* practical utility4 ,we d n require 9 common life to be con/antly solv+ complex logical que/ions4 ,ev5 9 ma!matical calculation ! ord9>y rules ( ari?metic are g5]ally suffici5t1 & a calculat+ ma*9e c only be us$ ) advantage 9 peculi> cases4 ,b ! ma*9e & abacus h nev]!less two important uses4 ,9 ! fir/ place ,i hope t ! "t is n v f> di/ant :5 ! pr$om9ance ( ! anci5t ,ari/otelian ,logic w be a matt] ( hi/ory only1 & :5 ! tea*+ ( logic w be plac$ on a foot+ m wor?y ( its supreme importance4 ,x w !n be f\nd t ! solution ( logical que/ions is an ex]cise ( m9d at lea/ z valuable & necess>y z ma!matical calculation4 ,i believe t ^! me*anical devices1 or some?+ ( ! same k9d1 w !n become useful = exhibit+ to a class ( /ud5ts a cle> & visible analysis ( logical problems ( any degree ( complexity1 ! nature ( ea* /ep be+ r5d]$ pla9 to ! eyes ( ! /ud5ts4 ,i (t5 us$ ! ma*9e or abacus = ?is purpose 9 my class lectures :ile ,i 0 ,pr(essor ( ,logic at ,ow5s ,college4 ,secondly1 ! m imm$iate importance ( ! ma*9e seems to consi/ 9 ! unque/ionable pro( :i* x af=ds t correct views ( ! fundam5tal pr9ciples ( reason+ h n[ be5 atta9$1 al?\gh !y 7 unkn[n to ,ari/otle & 8 foll[]s4 ,! "t mu/ come :5 ! inevitable results ( ! admirable inve/igations ( ! late ,dr4 ,boole mu/ be recognis$ at _! true value1 & ! pla9 & palpable =m 9 :i* ! ma*9e pres5ts ^? results w1 ,i hope1 ha/5 ! "t4 ,und\bt$ly ,boole's life m>ks an era 9 ! sci5ce ( human reason4 ,x may seem /range t x _h rema9$ = him fir/ to set =? 9 its full ext5t ! problem ( logic1 b ,i am n aw>e t anyone be=e him _h treat$ logic z a symbolic me?od = evolv+ f any premises ! description ( any class :atsoev] z def9$ by ^? premises4 ,9 spite ( sev]al s]i\s errors into :i* he fell1 x w probably be all[$ t ,boole discov]$ ! true & g5]al =m ( logic1 & put ! sci5ce sub/antially into ! =m :i* x mu/ hold = ev]more4 ,he ?us effect$ a re=m ) :i* !re is h>dly any?+ comp>able 9 ! hi/ory ( logic betwe5 8 "t & ! remote age ( ,ari/otle4 ,nev]!less1 ,boole's quasi-ma!matical sy/em c\ld h>dly be reg>d$ z a f9al & unexceptionable solution ( ! problem4 ,n only did x require ! manipulation ( ma!matical symbols 9 a v intricate & p]plex+ mann]1 b ! results :5 obta9$ 7 devoid ( demon/rative =ce1 because !y turn$ ^u ! employm5t ( un9telligible symbols1 acquir+ mean+ only by analogy4 ,i h also po9t$ out t he import$ into 8 sy/em a condition conc]n+ ! exclusive nature ( alt]natives 7p4 #gj71 :i* is n necess>ily true ( logical t]ms4 ,i %all h to %[ 9 ! next *apt] t logic is really ! basis ( ! :ole sci5ce ( ma!matical reason+1 s t ,boole inv]t$ ! true ord] ( pro( :5 he propos$ to inf] logical tru?s by algebraic processes4 ,x is wond]ful evid5ce ( 8 m5tal p[] t by me?ods fundam5tally false he %\ld h succe$$ 9 rea*+ true conclusions & wid5+ ! sph]e ( reason4 ,! me*anical p]=mance ( logical inf]5ce af=ds a demon/ration bo? ( ! tru? ( ,boole's results & ( ! mi/ak5 nature ( 8 mode ( d$uc+ !m4 ,conclusions :i* he c\ld obta9 only by pages ( intricate calculation1 are exhibit$ by ! ma*9e aft] "o or two m9utes ( manipulation4 ,& n only are ^? conclusions easily rea*$1 b !y are demon/ratively true1 because e /ep ( ! process involves no?+ m obscure ?an ! ?ree fundam5tal ,laws ( ,?\ght4 99,! ,ord] ( ,premises499 ,be=e quitt+ ! subject ( d$uctive reason+1 ,i may rem>k t ! ord] 9 :i* ! premises ( an argum5t are plac$ is a matt] ( logical indiff]5ce4 ,mu* discussion has tak5 place at v>i\s times conc]n+ ! arrangem5t ( ! premises ( a syllogism2 & x has be5 g5]ally held1 9 accordance ) ! op9ion ( ,ari/otle1 t ! s-call$ major premise1 conta9+ ! major t]m1 or ! pr$icate ( ! conclusion1 %\ld /& fir/4 ,?is di/9ction h[ev] falls to ! gr\nd 9 our sy/em1 s9ce ! proposition is r$uc$ to an id5tical =m1 9 :i* !re is no di/9ction ( subject & pr$icate4 ,9 a /rictly logical po9t ( view ! ord] ( /atem5t is :olly devoid ( significance4 ,! premises are simultane\sly coexi/5t1 & are n relat$ to ea* o!r accord+ to ! prop]ties ( space & "t4 ,j z ! qualities ( ! same object are nei!r be=e nor aft] ea* o!r 9 nature 7p4 #cc71 & are only ?\ght ( 9 "s "o ord] ow+ to ! limit$ capacity ( m9d1 s ! premises ( an argum5t are nei!r be=e nor aft] ea* o!r1 & are only ?\ght ( 9 succession because ! m9d _c grasp _m ideas at once4 ,! comb9ations ( ! logical alphabet are exactly ! same 9 :atev] ord] ! premises be treat$ on ! logical slate or ma*9e4 ,"s diff]5ce may d\btless exi/ z reg>ds conv5i5ce to human memory4 ,! m9d may take 9 ! results ( an argum5t m easily 9 "o mode ( /atem5t ?an ano!r1 al?\gh !re is no real diff]5ce 9 ! logical results4 ,b 9 ?is po9t ( view ,i ?9k t ,ari/otle & ! old logicians 7 cle>ly wrong4 ,x is m easy to ga!r ! conclusion t 8all ,a's are ,c's0 f 8all ,a's are ,b's & all ,b's are ,c's10 ?an f ! same propositions 9 inv]t$ ord]1 8all ,b's are ,c's & all ,a's are ,b's40 99,! ,equival5ce ( ,propositions994 ,"o great advantage :i* arises f ! /udy ( ?is ,indirect ,me?od ( ,inf]5ce consi/s 9 ! cle> notion :i* we ga9 ( ! ,equival5ce ( ,propositions4 ,! old] logicians %[$ h[ f c]ta9 simple premises we might draw an inf]5ce1 b !y fail$ to po9t out :e!r t inf]5ce conta9$ ! :ole1 or only a "p1 ( ! in=mation embodi$ 9 ! premises4 ,any "o proposition or gr\p ( propositions may be class$ ) respect to ano!r proposition or gr\p ( propositions1 z #a4 ,equival5t1 #b4 ,inf]rible1 #c4 ,consi/5t1 #d4 ,contradictory4 ,tak+ ! proposition 8,all m5 are mortals0 z ! orig9al1 !n 8,all immortals are n m50 is its equival5t2 8,"s mortals are m50 is inf]rible1 or capable ( inf]5ce1 b is n equival5t2 8,all n-m5 are n mortals0 _c be inf]r$1 b is consi/5t1 t is1 may be true at ! same "t2 8,all m5 are immortals0 is ( c\rse contradictory4 ,"o suffici5t te/ ( equival5ce is capability ( mutual inf]5ce4 ,?us f ,all electrics all non-conductors1 ,i c inf] ,all non-electrics all conductors1 & 99vice v]s99 f ! latt] ,i c pass back to ! =m]4 ,9 %ort1 ,a ,b is equival5t to 99a99 99b994 ,aga91 f ! union ( ! two propositions1 ,a ,,ab & ,b ,,ab1 ,i get ,a ,b1 & f ?is ,i might z easily d$uce ! two ) :i* ,i />t$4 ,9 ?is case "o proposition is equival5t to two o!r propositions4 ,!re are 9 fact no less ?an f\r modes 9 :i* we may express ! id5tity ( two classes ,a & ,b1 namely1 ,,fir/ ,,mode4 ,,second ,,mode4 ,,?ird ,,mode4 ,,f\r? ,,mode4 ,a ,b 99a99 99b99 ,a ,,ab 99a99 99ab99 ,b ,,ab 99b99 99ab99 ,! ,indirect ,me?od ( ,inf]5ce furni%es a univ]sal & cle> crit]ion z to ! relation%ip ( propositions4 ,! import ( a /atem5t is always to be measur$ by ! comb9ations ( t]ms :i* x de/roys4 ,h5ce two propositions are equival5t :5 !y remove ! same comb9ations f ! ,logical ,alphabet1 & nei!r m nor less4 ,a proposition is inf]rible b n equival5t to ano!r :5 x removes "s b n all ! comb9ations :i* ! o!r removes1 & none except :at ?is o!r removes4 ,aga91 propositions are consi/5t provid$ t !y jo9tly all[ ea* t]m & ! negative ( ea* t]m to rema9 some:]e 9 ! ,logical ,alphabet4 ,if aft] all ! comb9ations inconsi/5t ) two propositions are /ruck out1 !re /ill appe>s ea* ( ! lett]s ,a1 99a991 ,b1 99b991 ,c1 99c991 ,d1 99d991 :i* 7 !re be=e1 !n no inconsi/5cy betwe5 ! propositions exi/s1 al?\gh !y may n be equival5t or ev5 inf]rible4 ,f9ally1 contradictory propositions are ^? :i* tak5 toge!r remove any "o or m lett]-t]ms f ! ,logical ,alphabet4 ,:at is true ( s+le propositions applies also to gr\ps ( propositions1 h[ev] l>ge or complicat$2 t is to say1 "o gr\p may be equival5t1 inf]rible1 consi/5t1 or contradictory z reg>ds ano!r1 & we may simil>ly comp>e "o proposition ) a gr\p ( propositions4 ,to give 9 ?is place illu/rations ( all ! f\r k9ds ( relation w\ld require mu* space3 z ! examples giv5 9 previ\s sections or *apt]s may s]ve m or less to expla9 ! relations ( inf]5ce1 consi/5cy1 & contradiction1 ,i w only add a few in/ances ( equival5t propositions or gr\ps4 ,9 ! foll[+ li/ ea* proposition or gr\p ( propositions is exactly equival5t 9 mean+ to ! correspond+ "o 9 ! o!r column1 & ! tru? ( ?is /atem5t may be te/$ by work+ out ! comb9ations ( ! alphabet1 :i* ought to be f\nd exactly ! same 9 ! case ( ea* pair ( equival5ts4 ,a ,a99b99 4 4 4 4 4 4 4 ,b 99a99,b ,a 99b99 4 4 4 4 4 4 4 4 99a99 ,b ,a ,,bc 4 4 4 4 4 4 4 4 99a99 99b99 99c99 ,a ,,ab ,,ac 4 4 4 4 4 4 99b99 99ab99 ,a99b99,c ,a ,b ,c ,d 4 4 4 4 4 4 4 99ab99 99cd99 ,a 99c99 ,b 99d99 4 4 4 4 4 4 99a99,c 99b99,d ,a ,,ab99c99 ,a99b99,c 4 4 4 ,a ,,ab ,,ac ,,ab ,,ab99c99 ,a ,b ,a ,b ,b ,c 4 4 4 4 4 4 4 4 4 ,a ,c ,a ,,ab ,a ,,ac ,b ,,bc 4 4 4 4 4 4 4 4 4 ,b ,a 99a99,,bc ,al?\gh 9 ^! & _m o!r cases ! equival5ts ( c]ta9 propositions c readily be giv51 yet ,i believe t no uni=m & infallible process c be po9t$ out by :i* ! exact equival5ts ( premises c be asc]ta9$4 ,ord9>y d$uctive inf]5ce usually gives u only a portion ( ! conta9$ in=mation4 ,x is true t ! comb9ations consi/5t ) a set ( premises may always be ?r[n into ! =m ( a proposition :i* mu/ be logically equival5t to ^? premises2 b ! difficulty consi/s 9 detect+ ! o!r =ms ( propositions :i* w be equival5t to ! premises4 ,! task is "h ( a diff]5t "* f any :i* we h yet attempt$4 ,x is 9 reality an inv]se process1 & is j z mu* m tr\blesome & unc]ta9 ?an ! direct process1 z seek+ is comp>$ ) hid+4 ,n only may sev]al diff]5t answ]s equally apply1 b !re is no me?od ( discov]+ any ( ^? answ]s except by repeat$ trial4 ,! problem :i* we h "h met is really t ( induction1 ! inv]se ( d$uction2 &1 z ,i %all soon %[1 induction is always t5tative1 &1 unless conduct$ ) peculi> skill & insight1 mu/ be exce$+ly labori\s 9 cases ( complexity4 ,de ,morgan 0 un=tunately l$ by ?is equival5ce ( propositions into ! mo/ s]i\s error ( 8 +5i\s sy/em ( ,logic4 ,he held t because ! proposition 8,all ,a's are all ,b's10 is b ano!r expression = ! two propositions 8,all ,a's are ,b's0 & 8,all ,b's are ,a's10 x mu/ be a composite & n really an elem5t>y =m ( proposition4#hb ,b on tak+ a g5]al view ( ! equival5ce ( propositions su* an objection seems to h no weight4 ,logicians h1 ) few exceptions1 p]si/5tly upheld ! orig9al error ( ,ari/otle 9 reject+ f _! sci5ce ! "o simple relation ( id5tity on :i* all m complex logical relations mu/ really re/4 #hb 99,syllabus ( a propos$ sy/em ( ,logic991 #eg1 #aba1 c4 99,=mal ,logic991 p4 #ff4 99,! ,nature ( ,inf]5ce499 ,! "q1 ,:at is ,inf]5ce8 is involv$1 ev5 to ! pres5t day1 9 z mu* unc]ta9ty z t anci5t "q1 ,:at is ,tru?8 ,i %all 9 m ?an "o "p ( ?is "w endeav\r to %[ t inf]5ce nev] does m ?an explicate1 unfold1 or develop ! in=mation conta9$ 9 c]ta9 premises or facts4 ,nei!r 9 d$uctive nor inductive reason+ c we add a tittle to our implicit k1 :i* is l t conta9$ 9 an unread book or a seal$ lett]4 ,sir ,w4 ,hamilton has well said1 8,reason+ is ! %[+ out explicitly t a proposition n grant$ or suppos$1 is implicitly conta9$ 9 some?+ diff]5t1 :i* is grant$ or suppos$40#hc #hc ,lectures on ,metaphysics1 vol4 iv4 p4 #cfi4 ,pr(essor ,b[5 has expla9$#hd ) mu* cle>ness t ! conclusion ( an argum5t /ates explicitly :at is virtually or implicitly ?\ght4 8,! process ( reason+ is n s mu* a mode ( evolv+ a new tru?1 z x is ( e/abli%+ or prov+ an old "o1 by %[+ h[ mu* 0 admitt$ 9 ! concession ( ! two premises tak5 toge!r40 ,x is true t ! :ole mean+ ( ^! /atem5ts re/s ^u t ( su* words z 8explicit10 8implicit10 8virtual40 ,t is implicit :i* is wrapp$ up1 & we r5d] x explicit :5 we unfold x4 ,j z ! conception ( a circle involves a hundr$ important geometrical prop]ties1 all foll[+ f :at we "k1 if we h acut5ess to unfold ! results1 s e fact & /atem5t involves m mean+ ?an seems at fir/ sight4 ,reason+ explicates or br+s to consci\s possession :at 0 be=e unconsci\s4 ,x does n create1 nor does x de/roy1 b x transmutes & ?r[s ! same matt] into a new =m4 #hd ,b[51 99,treatise on ,logic991 ,cambridge1 ,u4,s41 #ahff2 p4 #cfb4 ,! difficult "q /ill rema9s1 ,:]e does novelty ( =m beg98 ,is x a case ( inf]5ce :5 we pass f 8,s9c]ity is ! p>5t ( tru?0 to 8,! p>5t ( tru? is s9c]ity80 ,! old logicians w\ld h call$ ?is *ange 99conv]sion991 "o case ( imm$iate inf]5ce4 ,b z all id5tity is necess>ily reciprocal1 & ! v mean+ ( su* a proposition is t ! two t]ms are id5tical 9 _! signification1 ,i fail to see any diff]5ce betwe5 ! /atem5ts :atev]4 ,z well might we say t 99x99 99y99 & 99y99 99x99 are diff]5t equations4 ,ano!r po9t ( difficulty is to decide :5 a *ange is m]ely grammatical & :5 x involves a real logical trans=mation4 ,betwe5 a 99table ( wood99 & a 99wood5 table99 !re is no logical diff]5ce 7p4 #ca71 ! adjective be+ m]ely a conv5i5t sub/itute = ! prepositional phrase4 ,b x is unc]ta9 to my m9d :e!r ! *ange f 8,all m5 are mortal0 to 8,no m5 are n mortal0 is purely grammatical4 ,logical *ange may p]haps be be/ describ$ z consi/+ 9 ! det]m9ation ( a relation betwe5 c]ta9 classes ( objects f a relation betwe5 c]ta9 o!r classes4 ,?us ,i consid] x a truly logical inf]5ce :5 we pass f 8,all m5 are mortal0 to 8,all immortals are n-m510 because ! classes 99immortals99 & 99n-m599 are diff]5t f 99mortals99 & 99m5991 & yet ! propositions conta9 at ! bottom ! v same tru?1 z %[n 9 ! comb9ations ( ! ,logical ,alphabet4 ,! passage f ! qualitative to ! quantitative mode ( express+ a proposition is ano!r k9d ( *ange :i* we mu/ discrim9ate f true logical inf]5ce4 ,we /ate ! same tru? :5 we say t 8mortality belongs to all m510 z :5 we ass]t t 8all m5 are mortals40 ,"h we d n pass f class to class1 b f "o k9d ( t]m1 ! ab/ract1 to ano!r k9d1 ! concrete4 ,b inf]5ce probably ent]s :5 we pass f ei!r ( ! above propositions to ! ass]tion t ! class ( immortal m5 is z]o1 or conta9s no objects4 ,x is ( c\rse a "q ( words to :at processes we %all or %all n apply ! "n 8inf]5ce10 & ,i h no wi% to cont9ue ! trifl+ discussions :i* h already tak5 place ^u ! subject4 ,:at we ne$ to d is to def9e accurately ! s5se 9 :i* we use ! ^w 8inf]5ce10 & to di/+ui% ! relation ( inf]rible propositions f o!r possible relations4 ,x seems to be suffici5t to recognise f\r modes 9 :i* two app>5tly diff]5t propositions may be relat$4 ,?us two propositions may be-- #a4 99,tautolog\s99 or 99id5tical991 involv+ ! same relation betwe5 ! same t]ms & classes1 & only diff]+ 9 ! ord] ( /atem5t2 ?us 8,victoria is ! ,que5 ( ,engl&0 is tautolog\s ) 8,! ,que5 ( ,engl& is ,victoria40 #b4 99,grammatically relat$991 :5 ! classes or objects are ! same & simil>ly relat$1 & ! only diff]5ce is 9 ! words2 ?us 8,victoria is ! ,que5 ( ,engl&0 is grammatically equival5t to 8,victoria is ,engl&'s ,que540 #c4 99,equival5ts99 9 qualitative & quantitative =m1 ! classes be+ ! same1 b view$ 9 a diff]5t mann]4 #d4 99,logically inf]rible991 "o f ! o!r1 or x may be 99equival5t991 :5 ! classes & relations are diff]5t1 b involve ! same k ( ! possible comb9ations4 ,,*apt] ,,vii4 ,,induction4 ,we ent] 9 ?is *apt] ^u ! second great dep>tm5t ( logical me?od1 t ( ,induction or ! ,inf]5ce ( g5]al f p>ticul> tru?s4 ,x _c be said t ! ,inductive process is ( great] importance ?an ! ,d$uctive process already consid]$1 because ! latt] process is absolutely ess5tial to ! exi/5ce ( ! =m]4 ,ea* is ! complem5t & c\nt]p>t ( ! o!r4 ,! pr9ciples ( ?\ght & exi/5ce :i* und]lie !m are at ! bottom ! same1 j z subtraction ( numb]s necess>ily re/s ^u ! same pr9ciples z addition4 ,induction is1 9 fact1 ! inv]se op]ation ( d$uction1 & _c be conceiv$ to exi/ )\t ! correspond+ op]ation1 s t ! "q ( relative importance _c arise4 ,:o ?9ks ( ask+ :e!r addition or subtraction is ! m important process 9 ari?metic8 ,b at ! same "t mu* diff]5ce 9 difficulty may exi/ betwe5 a direct & inv]se op]ation2 ! integral calculus1 = in/ance1 is inf9itely m difficult ?an ! diff]5tial calculus ( :i* x is ! inv]se4 ,simil>ly1 x mu/ be all[$ t inductive inve/igations are ( a f> high] degree ( difficulty & complexity ?an any que/ions ( d$uction2 & x is ?is fact no d\bt :i* l$ "s logicians1 su* z ,francis ,bacon1 ,locke1 & ,j4 ,s4 ,mill1 to errone\s op9ions conc]n+ ! exclusive importance ( induction4 ,hi!rto we h be5 engag$ 9 consid]+ h[ f c]ta9 conditions1 laws1 or id5tities gov]n+ ! comb9ations ( qualities1 we may d$uce ! nature ( ! comb9ations agree+ ) ^? conditions4 ,our "w has be5 to unfold ! results ( :at is conta9$ 9 any /atem5ts1 & ! process has be5 "o ( 99,syn!sis994 ,! t]ms or comb9ations ( :i* ! "* has be5 det]m9$ h usually1 ?\gh by no means always1 involv$ m qualities1 & !re=e1 by ! relation ( ext5sion & int5sion1 few] objects ?an ! t]ms 9 :i* !y 7 describ$4 ,! tru?s inf]r$ 7 ?us usually less g5]al ?an ! tru?s f :i* !y 7 inf]r$4 ,9 induction all is inv]t$4 ,! tru?s to be asc]ta9$ are m g5]al ?an ! data f :i* !y are drawn4 ,! process by :i* !y are rea*$ is 99analytical991 & consi/s 9 sep>at+ ! complex comb9ations 9 :i* natural ph5om5a are pres5t$ to u1 & det]m9+ ! relations ( sep>ate qualities4 ,giv5 ev5ts obey+ c]ta9 unkn[n laws1 we h to discov] ! laws obey$4 ,in/ead ( ! comp>atively easy task ( f9d+ :at effects w foll[ f a giv5 law1 ! effects are n[ giv5 & ! law is requir$4 ,we h to int]pret ! w by :i* ! conditions ( creation 7 laid d[n4 99,induction an ,inv]se ,op]ation99 ,i h already ass]t$ t induction is ! inv]se op]ation ( d$uction1 b ! diff]5ce is "o ( su* great importance t ,i mu/ dwell ^u x4 ,!re are _m cases 9 :i* we c easily & infallibly d a c]ta9 ?+ b may h mu* tr\ble 9 undo+ x4 ,a p]son may walk into ! mo/ complicat$ labyr9? or ! mo/ ext5sive catacombs1 & turn hi!r & ?i!r at 8 w2 x is :5 he wi%es to return t d\bt & difficulty comm5ce4 ,9 ent]+1 any pa? s]v$ him2 9 leav+1 he mu/ select c]ta9 def9ite pa?s1 & 9 ?is selection he mu/ ei!r tru/ to memory ( ! way he ent]$ or else make an exhau/ive trial ( all possible ways4 ,! explor] ent]+ a new c\ntry makes sure 8 l9e ( return by b>k+ ! trees4 ,! same difficulty arises 9 _m sci5tific processes4 ,giv5 any two numb]s1 we may by a simple & infallible process obta9 _! product2 b :5 a l>ge numb] is giv5 x is q ano!r matt] to det]m9e its factors4 ,c ! read] say :at two numb]s multipli$ toge!r w produce ! numb] #h1faf1dfj1gii8 ,i ?9k x unlikely t anyone b myself w ev] "k2 = !y are two l>ge prime numb]s1 & c only be r$iscov]$ by try+ 9 succession a long s]ies ( prime divisors until ! "r "o be fall5 ^u4 ,! "w w\ld probably occupy a good comput] = _m weeks1 b x did n occupy me _m m9utes to multiply ! two factors toge!r4 ,simil>ly !re is no direct process = discov]+ :e!r any numb] is a prime or n2 x is only by exhau/ively try+ all inf]ior numb]s :i* c\ld be divisors1 t we c %[ !re is none1 & ! lab\r ( ! process w\ld be intol]able 7 x n p]=m$ sy/ematically once = all 9 ! process kn[n z ! ,sieve ( ,erato/h5es1 ! results be+ regi/]$ 9 tables ( prime numb]s4 ,! imm5se difficulties :i* are enc\nt]$ 9 ! solution ( algebraic equations af=d ano!r illu/ration4 ,giv5 any algebraic factors1 we c easily & infallibly arrive at ! product2 b giv5 a product x is a matt] ( inf9ite difficulty to resolve x into factors4 ,giv5 any s]ies ( quantities h[ev] num]\s1 !re is v little tr\ble 9 mak+ an equation :i* %all h ^? quantities z roots4 ,let 99a991 99b991 99c991 99d991 c41 be ! quantities2 !n 799x99 - 99a997799x99 - 99b997799x99 - 99c997799x99 - d7 444 #j is ! equation requir$1 & we only ne$ to multiply out ! expression on ! left h& by ord9>y rules4 ,b hav+ giv5 a complex algebraic expression equat$ to z]o1 x is a matt] ( exce$+ difficulty to discov] all ! roots4 ,ma!maticians h exhau/$ _! highe/ p[]s 9 c>ry+ ! complete solution up to ! f\r? degree4 ,9 e o!r ma!matical op]ation ! inv]se process is f> m difficult ?an ! direct process1 subtraction ?an addition1 division ?an multiplication1 evolution ?an involution2 b ! difficulty increases va/ly z ! process becomes m complex4 ,diff]5tiation1 ! direct process1 is always capable ( p]=mance by fix$ rules1 b z ^! rules produce consid]able v>iety ( results1 ! inv]se process ( integration pres5ts imm5se difficulties1 & 9 an inf9ite majority ( cases surpasses ! pres5t res\rces ( ma!maticians4 ,!re are no infallible & g5]al rules = its accompli%m5t2 x mu/ be done by trial1 by guesswork1 or by rememb]+ ! results ( diff]5tiation1 & us+ !m z a guide4 ,com+ m ne>ly to our own imm$iate subject1 exactly ! same difficulty exi/s 9 det]m9+ ! law :i* c]ta9 ?+s obey4 ,giv5 a g5]al ma!matical expression1 we c infallibly asc]ta9 its value = any requir$ value ( ! v>iable4 ,b ,i am n aw>e t ma!maticians h ev] attempt$ to lay d[n ! rules ( a process by :i*1 hav+ giv5 c]ta9 numb]s1 "o might discov] a rational or precise =mula f :i* !y proce$4 ,! read] may te/ 8 p[] ( detect+ a law1 by contemplation ( its results1 if he1 n be+ a ma!matician1 w attempt to po9t out ! law obey$ by ! foll[+ numb]s3 #a_/f1 #a_/cj1 #a_/db1 #a_/cj1 #e_/ff1 #fia_/bgcj1 #g_/f1 #cfag_/eaj1 #dchfg_/gih1 etc4 ,^! numb]s are sometimes 9 l[ t]ms1 b unexpect$ly spr+ up to high t]ms2 9 absolute magnitude !y are v v>iable4 ,!y seem to set all regul>ity & me?od at defiance1 & x is h>dly to be suppos$ t anyone c\ld1 f contemplation ( ! numb]s1 h detect$ ! relations betwe5 !m4 ,yet !y are d]iv$ f ! mo/ regul> & symmetrical laws ( relation1 & are ( ! highe/ importance 9 ma!matical analysis1 be+ kn[n z ! numb]s ( ,b]n\lli4 ,comp>e aga9 ! difficulty ( decyph]+ ) t ( cyph]+4 ,anyone c inv5t a secret language1 & ) a little /eady lab\r c translate ! longe/ lett] into ! "*4 ,b to decyph] ! lett]1 hav+ no key to ! signs adopt$1 is a :olly diff]5t matt]4 ,z ! possible modes ( secret writ+ are inf9ite 9 numb] & exce$+ly v>i\s 9 k9d1 !re is no direct mode ( discov]y :atev]4 ,repeat$ trial1 guid$ m or less by k ( ! cu/om>y =m ( cyph]1 & re/+ entirely on ! pr9ciples ( probability & logical induction1 is ! only res\rce4 ,a peculi> tact or skill is requisite = ! process1 & a few m51 su* z ,wallis or ,:eat/one1 h atta9$ great success4 ,induction is ! decyph]+ ( ! hidd5 mean+ ( natural ph5om5a4 ,giv5 ev5ts :i* happ5 9 c]ta9 def9ite comb9ations1 we are requir$ to po9t out ! laws :i* gov]n ^? comb9ations4 ,any laws be+ suppos$1 we c1 ) ease & c]ta9ty1 decide :e!r ! ph5om5a obey ^? laws4 ,b ! laws :i* may exi/ are inf9ite 9 v>iety1 s t ! *ances are imm5sely aga9/ m]e r&om guess+4 ,! difficulty is mu* increas$ by ! fact t sev]al laws w usually be 9 op]ation at ! same "t1 ! effects ( :i* are complicat$ toge!r4 ,! only modes ( discov]y consi/ ei!r 9 exhau/ively try+ a great numb] ( suppos$ laws1 a process :i* is exhau/ive 9 m s5ses ?an "o1 or else 9 c>efully contemplat+ ! effects1 endeav\r+ to rememb] cases 9 :i* l effects foll[$ f kn[n laws4 ,9 :atev] mann] we accompli% ! discov]y1 x mu/ be done by ! m or less consci\s application ( ! direct process ( d$uction4 ,! ,logical ,alphabet illu/rates induction z well z d$uction4 ,9 consid]+ ! ,indirect ,process ( ,inf]5ce we f\nd t f c]ta9 propositions we c\ld infallibly det]m9e ! comb9ations ( t]ms agree+ ) ^? premises4 ,! inductive problem is j ! inv]se4 ,hav+ giv5 c]ta9 comb9ations ( t]ms1 we ne$ to asc]ta9 ! propositions ) :i* ! comb9ations are consi/5t1 & f :i* !y may h proce$$4 ,n[1 if ! read] contemplates ! foll[+ comb9ations1 ,,abc 99ab99,c 99a99,,bc 99abc991 he w probably rememb] at once t !y belong to ! premises ,a ,,ab1 ,b ,,bc 7p4 #ib74 ,if n1 he w require a few trials be=e he meets ) ! "r answ]1 & e trial w consi/ 9 assum+ c]ta9 laws & obs]v+ :e!r ! d$uc$ results agree ) ! data4 ,to te/ ! facility ) :i* he c solve ?is inductive problem1 let him casually /rike out any ( ! comb9ations ( ! f\r? column ( ! ,logical ,alphabet1 7p4 #id71 & say :at laws ! rema9+ comb9ations obey1 obs]v+ t e "o ( ! lett]-t]ms & _! negatives ought to appe> 9 ord] to avoid self-contradiction 9 ! premises 7pp4 #gd1 #aaa74 ,let him say1 = in/ance1 :at laws are embodi$ 9 ! comb9ations ,,abc 99a99,,bc ,a99bc99 99ab99,c4 ,! difficulty becomes mu* great] :5 m t]ms ent] into ! comb9ations4 ,x w\ld require "s little exam9ation to asc]ta9 ! complete conditions fulfill$ 9 ! comb9ations ,,ac99e99 99ab99,c99e99 99a99,,bc99e99 99abc99,e4 99a99,b99cd99,e ,! read] may discov] easily en\gh t ! pr9cipal laws are ,c 99e991 & ,a ,a99e992 b he w\ld h>dly discov] )\t "s tr\ble ! rema9+ law1 namely1 t ,,bd ,,bd99e994 ,! difficulties enc\nt]$ 9 ! inductive inve/igations ( nature1 are ( an exactly simil> k9d4 ,we seldom obs]ve any law 9 un9t]rupt$ & undisguis$ op]ation4 ,! acut5ess ( ,ari/otle & ! anci5t ,greeks did n enable !m to detect t all t]re/rial bodies t5d to fall t[>ds ! c5tre ( ! e>?4 ,a few nights ( obs]vation might h conv9c$ an a/ronom] view+ ! sol> sy/em f its c5tre1 t ! planets travell$ r\nd ! sun2 b ! fact t our place ( obs]vation is "o ( ! travell+ planets1 s complicates ! app>5t motions ( ! o!r bodies1 t x requir$ all ! sagacity ( ,cop]nicus to prove ! real simplicity ( ! planet>y sy/em4 ,x is ! same ?r\gh\t nature2 ! laws may be simple1 b _! comb9$ effects are n simple1 & we h no clue to guide u ?r\gh _! intricacies4 8,x is ! glory ( ,god10 said ,solomon1 8to conceal a ?+1 b ! glory ( a k+ to se>* x out40 ,! laws ( nature are ! invaluable secrets :i* ,god has hidd51 & x is ! k+ly pr]ogative ( ! philosoph] to se>* !m out by indu/ry & sagacity4 99,inductive ,problems = ,solution by ! ,read]499 ,9 ! fir/ edition 7vol4 ii4 p4 #cgj7 ,i gave a logical problem involv+ six t]ms1 & reque/$ read]s to discov] ! laws gov]n+ ! comb9ations giv54 ,i receiv$ satisfactory replies f read]s bo? 9 ! ,unit$ ,/ates & 9 ,engl&4 ,i =m$ ! comb9ations d$uctively f f\r laws ( correction1 b my correspond5ts f\nd t ?ree simpl] laws1 equival5t to ! f\r m complex ones1 7 ! be/ answ]2 ^! laws are z foll[s3 99a99 99ac991 99b99 99cd991 99d99 ,e99f994 ,9 case o!r read]s %\ld l to te/ _! skill 9 ! inductive or inv]se problem1 ,i give bel[ sev]al s]ies ( comb9ations =m+ problems ( graduat$ difficulty4 ,,problem ,i4 ,a ,b 99c99 ,a 99b99 ,c 99a99 ,b ,c ,,problem ,,ii4 ,a ,b ,c ,a 99b99 ,c 99a99 ,b ,c 99a99 ,b 99c99 ,,problem ,,iii4 ,a ,b ,c ,a 99b99 ,c 99a99 ,b ,c 99a99 ,b 99c99 99a99 99b99 99c99 ,,problem ,,iv4 ,a ,b ,c ,d ,a 99b99 99c99 ,d 99a99 ,b 99c99 99d99 99a99 99b99 ,c 99d99 ,,problem ,v4 ,a ,b ,c ,d ,a ,b ,c 99d99 ,a ,b 99c99 99d99 ,a 99b99 ,c ,d ,a 99b99 99c99 ,d 99a99 ,b ,c ,d 99a99 ,b 99c99 ,d 99a99 ,b 99c99 99d99 99a99 99b99 ,c 99d99 ,,problem ,,vi4 ,a ,b ,c ,d ,e ,a ,b ,c 99d99 99e99 ,a ,b 99c99 ,d ,e ,a ,b 99c99 99d99 99e99 ,a 99b99 ,c ,d ,e 99a99 ,b ,c ,d ,e 99a99 ,b ,c 99d99 99e99 99a99 99b99 ,c ,d ,e 99a99 99b99 99c99 99d99 99e99 ,,problem ,,vii4 ,a 99b99 99c99 ,d 99e99 99a99 ,b ,c 99d99 ,e 99a99 99b99 ,c 99d99 ,e ,,problem ,,viii4 ,a ,b ,c ,d ,e ,a ,b ,c ,d 99e99 ,a ,b ,c 99d99 99e99 ,a ,b 99c99 99d99 99e99 ,a 99b99 ,c ,d ,e ,a 99b99 99c99 99d99 ,e ,a 99b99 99c99 99d99 99e99 99a99 ,b ,c ,d 99e99 99a99 ,b ,c 99d99 99e99 99a99 ,b 99c99 ,d 99e99 99a99 99b99 ,c ,d 99e99 99a99 99b99 ,c 99d99 ,e 99a99 99b99 99c99 ,d 99e99 99a99 99b99 99c99 99d99 ,e ,,problem ,,ix4 ,a ,b 99c99 ,d ,e ,f ,a ,b 99c99 ,d 99e99 ,f ,a 99b99 ,c ,d 99e99 99f99 ,a 99b99 99c99 ,d ,e 99f99 ,a 99b99 99c99 ,d 99e99 99f99 ,a 99b99 99c99 99d99 ,e ,f ,a 99b99 99c99 99d99 99e99 ,f 99a99 ,b 99c99 ,d ,e ,f 99a99 ,b 99c99 ,d 99e99 ,f 99a99 ,b 99c99 99d99 ,e ,f 99a99 99b99 ,c ,d ,e ,f 99a99 99b99 ,c ,d 99e99 ,f 99a99 99b99 ,c ,d 99e99 99f99 99a99 99b99 99c99 ,d 99e99 99f99 99a99 99b99 99c99 ,d ,e 99f99 99a99 99b99 99c99 99d99 99e99 ,f ,,problem ,x4 ,a ,b ,c ,d 99e99 ,f ,a ,b 99c99 ,d ,e 99f99 ,a 99b99 ,c ,d ,e ,f ,a 99b99 ,c ,d 99e99 ,f ,a 99b99 99c99 ,d 99e99 ,f 99a99 ,b ,c ,d ,e 99f99 99a99 ,b 99c99 ,d ,e 99f99 99a99 99b99 ,c ,d 99e99 ,f 99a99 99b99 ,c 99d99 99e99 ,f 99a99 99b99 99c99 ,d 99e99 99f99 99a99 99b99 99c99 99d99 99e99 99f99 99,induction ( ,simple ,id5tities994 ,_m important laws ( nature are expressible 9 ! =m ( simple id5tities1 & ,i c at once adduce !m z examples to illu/rate :at ,i h said ( ! difficulty ( ! inv]se process ( induction4 ,two ph5om5a are conjo9$4 ,?us all gravitat+ matt] is exactly co9cid5t ) all matt] possess+ in]tia2 :]e "o prop]ty appe>s1 ! o!r likewise appe>s4 ,all cry/als ( ! cubical sy/em1 are all ! cry/als :i* d n d\bly refract light4 ,all exog5\s plants are1 ) "s exceptions1 ^? :i* h two cotyl$ons or se$-leaves4 ,a little reflection w %[ t !re is no direct & infallible process by :i* su* complete co9cid5ces may be discov]$4 ,natural objects are aggregates ( _m qualities1 & any "o ( ^? qualities may prove to be 9 close connection ) "s o!rs4 ,if ea* ( a num]\s gr\p ( objects is end[$ ) a hundr$ di/9ct physical or *emical qualities1 !re w be no less ?an 7#a_/b77ajj #ii7 or #diej pairs ( qualities1 :i* may be connect$1 & x w evid5tly be a matt] ( great intricacy & lab\r to asc]ta9 exactly :i* qualities are connect$ by any simple law4 ,"o pr9cipal s\rce ( difficulty is t ! f9ite p[]s ( ! human m9d are n suffici5t to comp>e by a s+le act any l>ge gr\p ( objects ) ano!r l>ge gr\p4 ,we _c hold 9 ! consci\s possession ( ! m9d at any "o mom5t m ?an five or six diff]5t ideas4 ,h5ce we mu/ treat any m complex gr\p by successive acts ( att5tion4 ,! read] w p]ceive by an almo/ individual act ( comp>ison t ! words 99,roma99 & 99,mora99 conta9 ! same lett]s4 ,he may p]haps see at a glance :e!r ! same is true ( 99,causal99 & 99,casual991 & ( 99,logica99 & 99,caligo994 ,to assure himself t ! lett]s 9 99,a/ronom]s99 make 99,no m />s991 t 99,s]p5s 9 akuleo99 is an anagram ( 99,joannes ,kepl]us991 or 99,great gun d u a sum99 an anagram ( 99,augu/us de ,morgan991 x w c]ta9ly be necess>y to break up ! act ( comp>ison into sev]al successive acts4 ,! process w acquire a d\ble "*1 & w consi/ 9 asc]ta9+ t ea* lett] ( ! fir/ gr\p is among ! lett]s ( ! second gr\p1 & 99vice v]s991 t ea* lett] ( ! second is among ^? ( ! fir/ gr\p4 ,9 ! same way we c only prove t two long li/s ( names are id5tical1 by %[+ t ea* "n 9 "o li/ occurs 9 ! o!r1 & 99vice v]s994 ,?is process ( comp>ison really consi/s 9 e/abli%+ two p>tial id5tities1 :i* are1 z already %[n 7p4 #eh71 equival5t 9 conjunction to "o simple id5tity4 ,we fir/ asc]ta9 ! tru? ( ! two propositions ,a ,,ab1 ,b ,,ab1 & we !n rise by sub/itution to ! s+le law ,a ,b4 ,!re is ano!r process1 x is true1 by :i* we may get to exactly ! same result2 = ! two propositions ,a ,,ab1 99a99 99ab99 are also equival5t to ! simple id5tity ,a ,b4 ,if !n we c %[ t all objects includ$ "u ,a are includ$ "u ,b1 & also t all objects n includ$ "u ,a are n includ$ "u ,b1 our purpose is effect$4 ,by ?is process we %\ld usually comp>e two li/s if we are all[$ to m>k !m4 ,= ea* "n 9 ! fir/ li/ we %\ld /rike (f "o 9 ! second1 & if1 :5 ! fir/ li/ is exhau/$1 ! second li/ is also exhau/$1 x foll[s t all names abs5t f ! fir/ mu/ be abs5t f ! second1 & ! co9cid5ce mu/ be complete4 ,^! two modes ( prov+ an id5tity are s closely alli$ t x is d\btful h[ f> we c detect any diff]5ce 9 _! p[]s & in/ances ( application4 ,! fir/ me?od is p]haps m conv5i5t :5 ! ph5om5a to be comp>$ are r>e4 ,?us we prove t all ! musical concords co9cide ) all ! m simple num]ical ratios1 by %[+ t ea* concord arises f a simple ratio ( undulations1 & !n %[+ t ea* simple ratio gives rise to "o ( ! concords4 ,to exam9e all ! possible cases ( discord or complex ratio ( undulation w\ld be impossible4 ,by a happy /roke ( induction ,sir ,john ,h]s*el discov]$ t all cry/als ( qu>tz :i* cause ! plane ( pol>ization ( light to rotate are precisely ^? cry/als :i* h plagih$ral faces1 t is1 oblique faces on ! corn]s ( ! prism unsymmetrical ) ! ord9>y faces4 ,?is s+ul> relation w\ld be prov$ by obs]v+ t all plagih$ral cry/als possess$ ! p[] ( rotation1 & 99vice v]s99 all cry/als possess+ ?is p[] 7 plagih$ral4 ,b x might at ! same "t be notic$ t all ord9>y cry/als 7 devoid ( ! p[]4 ,!re is no reason :y we %\ld n detect any ( ! f\r propositions ,a ,,ab1 ,b ,,ab1 99a99 99ab991 99b99 99ab991 all ( :i* foll[ f ,a ,b 7p4 #aae74 ,sometimes ! t]ms ( ! id5tity may be s+ul> objects2 ?us we obs]ve t diamond is a combu/ible gem1 & be+ unable to discov] any o!r t is1 we affirm-- ,diamond combu/ible gem4 ,9 a simil> mann] we asc]ta9 t ,m]cury metal liquid at ord9>y temp]atures1 ,sub/ance ( lea/ d5sity sub/ance ( lea/ atomic weight4 ,two or ?ree objects may occasionally ent] into ! induction1 z :5 we le>n t ,sodium potassium metal ( less d5sity ?an wat]1 ,v5us ,m]cury ,m>s major planet devoid ( satellites4 99,induction ( ,p>tial ,id5tities994 ,we f\nd 9 ! la/ section t ! complete id5tity ( two classes is almo/ always discov]$ n by direct obs]vation ( ! fact1 b by fir/ e/abli%+ two p>tial id5tities4 ,!re are also a multitude ( cases 9 :i* ! p>tial id5tity ( "o class ) ano!r is ! only relation to be discov]$4 ,?us ! mo/ common ( all inductive inf]5ces consi/s 9 e/abli%+ ! fact t all objects hav+ ! prop]ties ( ,a h also ^? ( ,b1 or t ,a ,,ab4 ,to asc]ta9 ! tru? ( a proposition ( ?is k9d x is m]ely necess>y to assemble toge!r1 m5tally or physically1 all ! objects includ$ "u ,a1 & !n obs]ve :e!r ,b is pres5t 9 ea* ( !m1 or1 :i* is ! same1 :e!r x w\ld be impossible to select f among !m any n-,b4 ,?us1 if we m5tally assemble toge!r all ! heav5ly bodies :i* move ) app>5t rapidity1 t is to say1 ! planets1 we f9d t !y all possess ! prop]ty ( n sc9tillat+4 ,we _c analyse any vegetable sub/ance )\t discov]+ t x conta9s c>bon & hydrog51 b x is n true t all sub/ances conta9+ c>bon & hydrog5 are vegetable sub/ances4 ,! great mass ( sci5tific tru?s consi/s ( propositions ( ?is =m ,a ,,ab4 ,?us 9 a/ronomy we le>n t all ! planets are sph]oidal bodies2 t !y all revolve 9 "o direction r\nd ! sun2 t !y all %9e by reflect$ light2 t !y all obey ! law ( gravitation4 ,b ( c\rse x is n to be ass]t$ t all bodies obey+ ! law ( gravitation1 or %9+ by reflect$ light1 or revolv+ 9 a p>ticul> direction1 or be+ sph]oidal 9 =m1 are planets4 ,9 o!r sci5ces we h imm5se numb]s ( propositions ( ! same =m1 z1 = in/ance1 all sub/ances 9 becom+ gase\s absorb heat2 all metals are elem5ts2 !y are all good conductors ( heat & electricity2 all ! alkal9e metals are monad elem5ts2 all =am9if]a are m>9e organisms2 all p>asitic animals are non-mammalian2 lightn+ nev] issues f /rat\s cl\ds2 pumice nev] occurs :]e only ,labrador felsp> is pres5t2 milkmaids d n suff] f small-pox2 &1 9 ! works ( ,d>w91 sci5tific importance may atta* ev5 to su* an app>5tly trifl+ obs]vation z t 8:ite tom-cats hav+ blue eyes are deaf40 ,! process ( inf]5ce by :i* all su* tru?s are obta9$ may readily be exhibit$ 9 a precise symbolic =m4 ,we mu/ h "o premise specify+ 9 a disjunctive =m all ! possible individuals :i* belong to a class2 we resolve ! class1 9 %ort1 into its con/itu5ts4 ,we !n ne$ a numb] ( propositions1 ea* ( :i* affirms t "o ( ! individuals possesses a c]ta9 prop]ty4 ,?us ! premises mu/ be ( ! =ms ,a ,b ,c ,d 4444 ,p ,q ,b ,,bx ,c ,,cx 444 444 444 444 ,q ,,qx4 ,n[1 if we sub/itute = ea* alt]native ( ! fir/ premise its description z f\nd among ! succe$+ premises1 we obta9 ,a ,,bx ,,cx 4444 ,,px ,,qx or ,a 7,b ,c 4444 ,q7,x ,b = ! aggregate ( alt]natives we may n[ sub/itute _! equival5t z giv5 9 ! fir/ premise1 namely ,a1 s t we get ! requir$ result3 ,a ,,ax4 ,we %\ld h rea*$ ! same result if ! fir/ premise _h be5 ( ! =m ,a ,,ab ,,ac 4444 ,,aq4 ,we c always prove a proposition1 if we f9d x m conv5i5t1 by prov+ its equival5t4 ,to ass]t t all n-,b's are n-,a's1 is exactly ! same z to ass]t t all ,a's are ,b's4 ,accord+ly we may asc]ta9 t ,a ,,ab by fir/ asc]ta9+ t 99b99 99ab994 ,if we obs]ve1 = in/ance1 t all sub/ances :i* are n solids are also n capable ( d\ble refraction1 x foll[s necess>ily t all d\ble refract+ sub/ances are solids4 ,we may conv9ce ourselves t all electric sub/ances are nonconductors ( electricity1 by reflect+ t all good conductors d n1 & 9 fact _c1 reta9 electric excitation4 ,:5 we come to que/ions ( probability x w be f\nd desirable to prove1 z f> z possible1 bo? ! orig9al proposition & its equival5t1 z !re is !n an increas$ area ( obs]vation4 ,! numb] ( alt]natives :i* may arise 9 ! division ( a class v>ies greatly1 & may be any numb] f two upw>ds4 ,?us x is probable t e sub/ance is ei!r magnetic or diamagnetic1 & no sub/ance c be bo? at ! same "t4 ,! division !n mu/ be made 9 ! =m ,a ,,ab99c99 ,a99b99,c4 ,if n[ we c prove t all magnetic sub/ances are capable ( pol>ity1 say ,b ,,bd1 & also t all diamagnetic sub/ances are capable ( pol>ity1 ,c ,,cd1 x foll[s by sub/itution t all sub/ances are capable ( pol>ity1 or ,a ,,ad4 ,we commonly divide ! class sub/ance into ! ?ree subclasses1 solid1 liquid1 & gas2 & if we c %[ t 9 ea* ( ^! =ms x obeys ,c>not's !rmodynamic law1 x foll[s t all sub/ances obey t law4 ,simil>ly we may %[ t all v]tebrate animals possess r$ blood1 if we c %[ sep>ately t fi%1 reptiles1 birds1 m>supials1 & mammals possess r$ blood1 !re be+1 z f> z is kn[n1 only five pr9cipal subclasses ( v]tebrata4 ,our inductions w (t5 be emb>rass$ by exceptions1 real or app>5t4 ,we might affirm t all gems are incombu/ible 7 n diamonds und\bt$ly combu/ible4 ,no?+ seems m evid5t ?an t all ! metals are opaque until we exam9e !m 9 f9e films1 :5 gold & silv] are f\nd to be transp>5t4 ,all plants absorb c>bonic acid except c]ta9 fungi2 all ! bodies ( ! planet>y sy/em h a progressive motion f we/ to ea/1 except ! satellites ( ,uranus & ,neptune4 ,ev5 "s ( ! pr(\nde/ laws ( matt] are n q univ]sal2 all solids exp& by heat except india-rubb]1 & possibly a few o!r sub/ances2 all liquids :i* h be5 te/$ exp& by heat except wat] bel[ #d ,c4 & fus$ bismu?2 all gases h a coeffici5t ( expansion increas+ ) ! temp]ature1 except hydrog54 ,9 a lat] *apt] ,i %all consid] h[ su* anomal\s cases may be reg>d$ & classifi$2 "h we h only to express !m 9 a consi/5t mann] by our notation4 ,let u take ! case ( ! transp>5cy ( metals1 & assign ! t]ms ?us3-- ,a metal ,d iron ,b gold ,e1 ,f1 c4 copp]1 lead1 c4 ,c silv] ,x opaque4 ,our premises w be ,a ,b ,c ,d ,e1 c4 ,b ,b99x99 ,c ,c99x99 ,d ,,dx ,e ,,ex1 & s on = ! re/ ( ! metals4 ,n[ evid5tly ,a99bc99 7,d ,e ,f 444799bc991 & by sub/itution z be=e we %all obta9 ,a99bc99 ,a99bc99,x1 or 9 words1 8,all metals n gold nor silv] are opaque20 at ! same "t we h ,a7,b ,c7 ,,ab ,,ac ,,ab99x99 ,,ac99x99 ,a7,b ,c799x991 or 8,metals :i* are ei!r gold or silv] are n opaque40 ,9 "s cases ! problem ( induction assumes a mu* high] degree ( complexity4 ,if we exam9e ! prop]ties ( cry/alliz$ sub/ances we may f9d "s prop]ties :i* are common to all1 z cleavage or fracture 9 def9ite planes2 b x w\ld soon become requisite to break up ! class into sev]al m9or ones4 ,we %\ld divide cry/als accord+ to ! sev5 accept$ sy/ems--& we %\ld !n f9d t cry/als ( ea* sy/em possess _m common prop]ties4 ,?us cry/als ( ! ,regul> or ,cubical sy/em exp& equally by heat1 conduct heat & electricity ) uni=m rapidity1 & are ( l ela/icity 9 all directions2 !y h b "o index ( refraction = light2 & e facet is repeat$ 9 l relation to ea* ( ! ?ree axes4 ,cry/als ( ! sy/em hav+ "o pr9cipal axis w be f\nd to possess ! v>i\s physical p[]s ( conduction1 refraction1 ela/icity1 c41 uni=mly 9 directions p]p5dicul> to ! pr9cipal axis2 9 o!r directions _! prop]ties v>y accord+ to complicat$ laws4 ,! rema9+ sy/ems 9 :i* ! cry/als possess ?ree unequal axes1 or h incl9$ axes1 exhibit /ill m complicat$ results1 ! effects ( ! cry/al ^u light1 heat1 electricity1 c41 v>y+ 9 all directions4 ,b :5 we pursue induction into ! intricacies ( its application to nature we really ent] ^u ! subject ( classification1 :i* we mu/ take up aga9 9 a lat] "p ( ?is "w4 99,solution ( ! ,inv]se or ,inductive ,problem1 involv+ ,two ,classes994 ,x is n[ pla9 t ,induction consi/s 9 pass+ back f a s]ies ( comb9ations to ! laws by :i* su* comb9ations are gov]n$4 ,! natural law t all metals are conductors ( electricity really means t 9 nature we f9d ?ree classes ( objects1 namely-- #a4 ,metals1 conductors2 #b4 ,n-metals1 conductors2 #c4 ,n-metals1 n-conductors4 ,x comes to ! same ?+ if we say t x excludes ! exi/5ce ( ! class1 8metals n-conductors40 ,9 ! same way e o!r law or gr\p ( laws w really mean ! exclusion f exi/5ce ( c]ta9 comb9ations ( ! ?+s1 circum/ances or ph5om5a gov]n$ by ^? laws4 ,n[ 9 logic1 /rictly speak+1 we treat n ! ph5om5a1 nor ! laws1 b ! g5]al =ms ( ! laws2 & a little consid]ation w %[ t = a f9ite numb] ( ?+s ! possible numb] ( =ms or k9ds ( law gov]n+ !m mu/ also be f9ite4 ,us+ g5]al t]ms1 we "k t ,a & ,b c be pres5t or abs5t 9 f\r ways & no m--?us3 ,,ab1 ,a99b991 99a99,b1 99ab992 !re=e e possible law :i* c exi/ conc]n+ ! relation ( ,a & ,b mu/ be m>k$ by ! exclusion ( "o or m ( ! above comb9ations4 ,! numb] ( possible laws !n _c exce$ ! numb] ( selections :i* we c make f ^! f\r comb9ations4 ,s9ce ea* comb9ation may be pres5t or abs5t1 ! numb] ( cases to be consid]$ is #b #b #b #b1 or sixte52 & ^! cases are all %[n 9 ! foll[+ table1 9 :i* ! sign #j indicates abs5ce or non-exi/5ce ( ! comb9ation %[n at ! left-h& column 9 ! same l9e1 & ! m>k #a its pres5ce3-- #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af 99 99 99 99 99 99 99 ,,ab #j #j #j #j #j #j #j #j #a #a #a #a #a #a #a #a ,a99b99 #j #j #j #j #a #a #a #a #j #j #j #j #a #a #a #a 99a99,b #j #j #a #a #j #j #a #a #j #j #a #a #j #j #a #a 99ab99 #j #a #j #a #j #a #j #a #j #a #j #a #j #a #j #a ,?us 9 column sixte5 we f9d t all ! conceivable comb9ations are pres5t1 :i* means t !re are no special laws 9 exi/5ce 9 su* a case1 & t ! comb9ations are gov]n$ only by ! univ]sal ,laws ( ,id5tity & ,diff]5ce4 ,! example ( metals & conductors ( electricity w\ld be repres5t$ by ! twelf? column2 & e o!r mode 9 :i* two ?+s or qualities might pres5t !mselves is %[n 9 "o or o!r ( ! columns4 ,m ?an half ! cases may inde$ be at once reject$1 because !y involve ! entire abs5ce ( a t]m or its negative4 ,x has be5 %[n to be a logical pr9ciple t e t]m mu/ h its negative 7p4 #aaa71 & :5 ?is is n ! case1 inconsi/5cy betwe5 ! conditions ( comb9ation mu/ exi/4 ,?us if we laid d[n ! two foll[+ propositions1 8,graphite conducts electricity10 & 8,graphite does n conduct electricity10 x w\ld am\nt to ass]t+ ! impossibility ( graphite exi/+ at all2 or 9 g5]al t]ms1 ,a is ,b & ,a is n ,b result 9 de/roy+ altoge!r ! comb9ations conta9+ ,a1 a case %[n 9 ! f\r? column ( ! above table4 ,we !re=e re/rict our att5tion to ^? cases :i* may be repres5t$ 9 natural ph5om5a :5 at lea/ two comb9ations are pres5t1 & :i* correspond to ^? columns ( ! table 9 :i* ea* ( ,a1 99a991 ,b1 99b99 appe>s4 ,^! cases are %[n 9 ! columns m>k$ ) an a/]isk4 ,we f9d t sev5 cases rema9 = exam9ation1 ?us *>act]is$-- ,f\r cases exhibit+ ?ree comb9ations1 ,two cases exhibit+ two comb9ations1 ,"o case exhibit+ f\r comb9ations4 ,x has already be5 po9t$ out t a proposition ( ! =m ,a ,,ab de/roys "o comb9ation1 ,a99b991 s t ?is is ! =m ( law apply+ to ! twelf? column4 ,b by *ang+ "o or m ( ! t]ms 9 ,a ,,ab into its negative1 or by int]*ang+ ,a & ,b1 99a99 & 99b991 we obta9 no less ?an eight diff]5t v>ieties ( ! "o =m2 ?us-- #ab? case4 #h? case4 #ae? case4 #ad? case4 ,a ,,ab ,a ,a99b99 99a99 99a99,b 99a99 99ab99 99b99 99ab99 ,b 99a99,b 99b99 ,a99b99 ,b ,,ab ,! read] ( ! prec$+ sections w see t ea* proposition 9 ! l[] l9e is logically equival5t to1 & is 9 fact ! contrapositive (1 t above x 7p4 #hc74 ,?us ! propositions ,a ,a99b99 & ,b 99a99,b bo? give ! same comb9ations1 %[n 9 ! eigh? column ( ! table1 & trial %[s t ! twelf?1 eigh?1 fifte5? & f\rte5? columns are ?us acc\nt$ =4 ,we come to ?is conclusion !n--99,! g5]al =m ( proposition99 ,a ,,ab 99admits ( f\r logically di/9ct v>ieties1 ea* capable ( expression 9 two modes994 ,9 two columns ( ! table1 namely ! sev5? & t5?1 we obs]ve t two comb9ations are miss+4 ,n[ a simple id5tity ,a ,b r5d]s impossible bo? ,a99b99 & 99a99,b1 acc\nt+ = ! t5? case2 & if we *ange ,b into 99b99 ! id5tity ,a 99b99 acc\nts = ! sev5? case4 ,!re may inde$ be two o!r v>ieties ( ! simple id5tity1 namely 99a99 99b99 & 99a99 ,b2 b x has already be5 %[n repeat$ly t ^! are equival5t respectively to ,a ,b & ,a 99b99 7p4 #aae74 ,z ! sixte5? column has already be5 acc\nt$ = z gov]n$ by no special conditions1 we come to ! foll[+ g5]al conclusion3--,! laws gov]n+ ! comb9ations ( two t]ms mu/ be capable ( expression ei!r 9 a p>tial id5tity or a simple id5tity2 ! p>tial id5tity is capable ( only f\r logically di/9ct v>ieties1 & ! simple id5tity ( two4 ,e logical relation betwe5 two t]ms mu/ be express$ 9 "o ( ^! six =ms ( law1 or mu/ be logically equival5t to "o ( !m4 ,9 %ort1 we may conclude t 9 treat+ ( p>tial & complete id5tity1 we h exhau/ively treat$ ! modes 9 :i* two t]ms or classes ( objects c be relat$4 ,( any two classes x c be said t "o mu/ ei!r be includ$ 9 ! o!r1 or mu/ be id5tical ) x1 or a l relation mu/ exi/ betwe5 "o class & ! negative ( ! o!r4 ,we h ?us completely solv$ ! inv]se logical problem conc]n+ two t]ms4#he #he ,! cont5ts ( ?is & ! foll[+ section ne>ly correspond ) ^? ( a pap] read be=e ! ,man*e/] ,lit]>y & ,philosophical ,society on ,decemb] #bf?1 #ahga4 ,see ,proce$+s ( ! ,society1 vol4 xi4 pp4 #fe-fh1 & ,memoirs1 ,?ird ,s]ies1 vol4 v4 pp4 #aai-acj4 99,! ,inv]se ,logical ,problem involv+ ,?ree ,classes499 ,no soon] d we introduce into ! problem a ?ird t]m ,c1 ?an ! inve/igation assumes a f> m complex "*1 s t "s read]s may pref] to pass ov] ?is section4 ,?ree t]ms & _! negatives may be comb9$1 z we h frequ5tly se51 9 eight diff]5t comb9ations1 & ! effect ( laws or logical conditions is to de/roy any "o or m ( ^! comb9ations4 ,n[ we may make selections f eight ?+s 9 #bh or #bef ways2 s t we h no less ?an #bef diff]5t cases to treat1 & ! complete solution is at lea/ fifty times z tr\blesome z ) two t]ms4 ,_m s]ies ( comb9ations1 inde$1 are contradictory1 z 9 ! simpl] problem1 & may be pass$ ov]1 ! te/ ( consi/5cy be+ t ea* ( ! lett]s ,a1 ,b1 ,c1 99a991 99b991 99c991 %all appe> some:]e 9 ! s]ies ( comb9ations4 ,my mode ( solv+ ! problem 0 z foll[s3--,hav+ writt5 out ! :ole ( ! #bef s]ies ( comb9ations1 ,i exam9$ !m sep>ately & /ruck out su* z did n fulfil ! te/ ( consi/5cy4 ,i !n *ose "s =m ( proposition involv+ two or ?ree t]ms1 & v>i$ x 9 e possible mann]1 bo? by ! circul> int]*ange ( lett]s 7,a1 ,b1 ,c into ,b1 ,c1 ,a & !n into ,c1 ,a1 ,b71 & by ! sub/itution = any "o or m ( ! t]ms ( ! correspond+ negative t]ms4 ,= in/ance1 ! proposition ,,ab ,,abc c be fir/ v>i$ by circul> int]*ange s z to give ,,bc ,,bca & !n ,,ca ,,cab4 ,ea* ( ^! ?ree c !n be ?r[n into eight v>ieties by negative *ange4 ,?us ,,ab ,,abc gives 99a99,b 99a99,,bc1 ,a99b99 ,a99b99,c1 ,,ab ,,ab99c991 99ab99 99ab99,c1 & s on4 ,?us !re may possibly exi/ no less ?an tw5ty-f\r v>ieties ( ! law hav+ ! g5]al =m ,,ab ,,abc1 mean+ t :atev] has ! prop]ties ( ,a & ,b has ^? also ( ,c4 ,x by no means foll[s t "s ( ! v>ieties may n be equival5t to o!rs2 & trial %[s1 9 fact1 t ,,ab ,,abc is exactly ! same 9 mean+ z ,a99c99 ,a99bc99 or ,b99c99 ,b99ca994 ,?us ! law 9 "q has b eight v>ieties ( di/9ct logical mean+4 ,i n[ asc]ta9 by actual d$uctive reason+ :i* ( ! #bef s]ies ( comb9ations result f ea* ( ^! di/9ct laws1 & m>k !m (f z soon z f\nd4 ,i !n proce$ to "s o!r =m ( law1 = in/ance ,a ,,abc1 mean+ t :atev] has ! qualities ( ,a has ^? also ( ,b & ,c4 ,i f9d t x admits ( tw5ty-f\r v>iations1 all ( :i* are f\nd to be logically di/9ct2 ! comb9ations be+ work$ out1 ,i am able to m>k (f tw5ty-f\r m ( ! li/ ( #bef s]ies4 ,i proce$ 9 ?is way to "w out ! results ( e =m ( law :i* ,i c f9d or inv5t4 ,if 9 ! c\rse ( ?is "w ,i obta9 any s]ies ( comb9ations :i* _h be5 previ\sly m>k$ (f1 ,i le>n at once t ! law giv+ ^! comb9ations is logically equival5t to "s law previ\sly treat$4 ,x may be safely inf]r$ t e v>iety ( ! app>5tly new law w co9cide 9 mean+ ) "s v>iety ( ! =m] expression ( ! same law4 ,i h suffici5tly v]ifi$ ?is assumption 9 "s cases1 & h nev] f\nd x lead to error4 ,?us z ,,ab ,,abc is equival5t to ,a99c99 ,a99bc991 s we f9d t 99ab99 99ab99,c is equival5t to 99ac99 99ac99,b4 ,among ! laws treat$ 7 ! two ,a ,,ab & ,a ,b :i* involve only two t]ms1 because x may ( c\rse happ5 t among ?ree ?+s two only are 9 special logical relation1 & ! ?ird indep5d5t2 & ! s]ies ( comb9ations repres5t+ su* cases ( relation are sure to occur 9 ! complete enum]ation4 ,all s+le propositions :i* ,i c\ld inv5t hav+ be5 treat$1 pairs ( propositions 7 next inve/igat$4 ,?us we h ! relations1 8,all ,a's are ,b's1 & all ,b's are ,c's10 ( :i* ! old logical syllogism is ! developm5t4 ,we may also h 8all ,a's are all ,b's1 & all ,b's are ,c's10 or ev5 8all ,a's are all ,b's1 & all ,b's are all ,c's40 ,all su* premises admit ( v>iations1 great] or less 9 numb]1 ! logical di/9ctness ( :i* c only be det]m9$ by trial 9 detail4 ,disjunctive propositions ei!r s+ly or 9 pairs 7 also treat$1 b 7 (t5 f\nd to be equival5t to o!r propositions ( a simpl] =m2 ?us ,a ,,abc ,a99bc99 is exactly ! same 9 mean+ z ,,ab ,,ac4 ,?is mode ( exhau/ive trial be>s "s analogy to t anci5t ma!matical process call$ ! ,sieve ( ,erato/h5es4 ,hav+ tak5 a long s]ies ( ! natural numb]s1 ,erato/h5es is said to h calculat$ out 9 succession all ! multiples ( e numb]1 & to h m>k$ !m (f1 s t at la/ ! prime numb]s alone rema9$1 & ! factors ( e numb] 7 exhau/ively discov]$4 ,my problem ( #bef s]ies ( comb9ations is ! logical analogue1 ! *ief po9ts ( diff]5ce be+ t !re is a limit to ! numb] ( cases1 & t prime numb]s h no analogue 9 logic1 s9ce e s]ies ( comb9ations corresponds to a law or gr\p ( conditions4 ,b ! analogy is p]fect 9 ! po9t t !y are bo? inv]se processes4 ,!re is no mode ( asc]ta9+ t a numb] is prime b by %[+ t x is n ! product ( any assignable factors4 ,s !re is no mode ( asc]ta9+ :at laws are embodi$ 9 any s]ies ( comb9ations b try+ exhau/ively ! laws :i* w\ld give !m4 ,j z ! results ( ,erato/h5es' me?od h be5 work$ out to a great ext5t & regi/]$ 9 tables = ! conv5i5ce ( o!r ma!maticians1 ,i h endeav\r$ to "w out ! inv]se logical problem to ! utmo/ ext5t :i* is at pres5t practicable or useful4 ,i h ?us f\nd t !re are altoge!r fifte5 conditions or s]ies ( conditions :i* may gov]n ! comb9ations ( ?ree t]ms1 =m+ ! premises ( fifte5 ess5tially diff]5t k9ds ( argum5ts4 ,! foll[+ table conta9s a /atem5t ( ^! conditions1 toge!r ) ! numb]s ( comb9ations :i* are contradict$ or de/roy$ by ea*1 & ! numb]s ( logically di/9ct v>iations ( :i* ! law is capable4 ,!re might be also add$1 z a sixte5? case1 t case :]e no special logical condition exi/s1 s t all ! eight comb9ations rema94 ---------------------------------------- ----------------------- ,numb] ( ,numb] ( ,ref]5ce ,propositions express+ ! di/9ct comb9ations ,numb]4 g5]al type ( ! logical logical contradict$ conditions4 v>iations4 by ea*4 ---------------------------------------- ----------------------- ,i4 ,a ,b #f #d ,,ii4 ,a ,,ab #ab #b ,,iii4 ,a ,b1 ,b ,c #d #f ,,iv4 ,a ,b1 ,b ,,bc #bd #e ,v4 ,a ,,ab1 ,b ,,bc #bd #d ,,vi4 ,a ,,bc #bd #d ,,vii4 ,a ,,abc #bd #c ,,viii4 ,,ab ,,abc #h #a ,,ix4 ,a ,,ab1 99a99,b 99a99,b99c99 #bd #c ,x4 ,a ,,abc1 99ab99 99ab99,c #h #d ,,xi4 ,,ab ,,abc1 99ab99 99abc99 #d #b ,,xii4 ,,ab ,,ac #ab #b ,,xiii4 ,a ,,bc ,a99bc99 #h #c ,,xiv4 ,a ,,bc 99bc99 #b #d ,,xv4 ,a ,,abc1 99a99 ,b99c99 99b99,c #h #e ---------------------------------------- ----------------------- ,!re are sixty-?ree s]ies ( comb9ations d]iv$ f self-contradictory premises1 :i* ) #aib1 ! sum ( ! numb]s ( di/9ct logical v>iations /at$ 9 ! ?ird column ( ! table1 & ) ! "o case :]e !re are no conditions or laws at all1 make up ! :ole conceivable numb] ( #bef s]ies4 ,we le>n f ?is table1 = in/ance1 t two propositions ( ! =m ,a ,,ab1 ,b ,,bc1 :i* are su* z con/itute ! premises ( ! old syllogism ,b>b>a1 exclude z impossible f\r ( ! eight comb9ations 9 :i* ?ree t]ms may be unit$1 & t ^! propositions are capable ( tak+ tw5ty-f\r v>iations by transpositions ( ! t]ms or ! introduction ( negatives4 ,?is table !n pres5ts ! results ( a complete analysis ( all ! possible logical relations aris+ 9 ! case ( ?ree t]ms1 & ! old syllogism =ms b "o out ( fifte5 typical =ms4 ,g5]ally speak+1 e =m c be conv]t$ into app>5tly diff]5t propositions2 ?us ! f\r? type ,a ,b1 ,b ,,bc may appe> 9 ! =m ,a ,,abc1 99a99 99ab991 or aga9 9 ! =m ( ?ree propositions ,a ,,ab1 ,b ,,bc1 99a99,b 99a99,b99c992 b all ^! sets ( premises yield id5tically ! same s]ies ( comb9ations1 & are !re=e ( equival5t logical mean+4 ,! fif? type1 or ,b>b>a1 c also be ?r[n into ! equival5t =ms ,a ,,abc1 99a99,b 99a99,,bc & ,a ,,ac1 ,b ,a 99a99,,bc4 ,9 o!r cases ,i h obta9$ ! v same logical conditions 9 f\r modes ( /atem5ts4 ,z reg>ds m]e appe>ance & =m ( /atem5t1 ! numb] ( possible premises w\ld be v great1 & difficult to exhibit exhau/ively4 ,! mo/ rem>kable ( all ! types ( logical condition is ! f\rte5?1 namely1 ,a ,,bc 99bc994 ,x is t :i* expresses ! division ( a g5us into two d\bly m>k$ species1 & might be illu/rat$ by ! example--8,compon5t ( ! physical univ]se matt]1 gravitat+1 or n-matt] 7e!r71 n-gravitat+40 ,x is capable ( only two di/9ct logical v>iations1 namely1 ,a ,,bc 99bc99 & ,a ,b99c99 99b99,c4 ,by transposition or negative *ange ( ! lett]s we c inde$ obta9 six diff]5t expressions ( ea* ( ^! propositions2 b :5 _! mean+s are analys$1 by work+ out ! comb9ations1 !y are f\nd to be logically equival5t to "o or o!r ( ! above two4 ,?us ! proposition ,a ,,bc 99bc99 c be writt5 9 any ( ! foll[+ five o!r modes1 99a99 99b99,c ,b99c991 ,b ,,ca 99ca991 99b99 99c99,a ,c99a991 ,c ,,ab 99ab991 99c99 99a99,b ,a99b994 ,i d n ?9k x ne$ful to publi% at pres5t ! complete table ( #aic s]ies ( comb9ations & ! premises correspond+ to ea*4 ,su* a table enables u by m]e inspection to le>n ! laws obey$ by any set ( comb9ations ( ?ree ?+s1 & is to logic :at a table ( factors & prime numb]s is to ! !ory ( numb]s1 or a table ( integrals to ! high] ma!matics4 ,! table already giv5 7p4 #adj7 w\ld enable a p]son ) b little lab\r to discov] ! law ( any comb9ations4 ,if !re be sev5 comb9ations 7"o contradict$7 ! law mu/ be ( ! eigh? type1 & ! prop] v>iety w be app>5t4 ,if !re be six comb9ations 7two contradict$71 ei!r ! second1 elev5?1 or twelf? type applies1 & a c]ta9 numb] ( trials w disclose ! prop] type & v>iety4 ,if !re be b two comb9ations ! law mu/ be ( ! ?ird type1 & s on4 ,! above inve/igations are complete z reg>ds ! possible logical relations ( two or ?ree t]ms4 ,b :5 we attempt to apply ! same k9d ( me?od to ! relations ( f\r or m t]ms1 ! lab\r becomes impracticably great4 ,f\r t]ms give sixte5 comb9ations compatible ) ! laws ( ?\ght1 & ! numb] ( possible selections ( comb9ations is no less ?an #baf or #fe1ecf4 ,! foll[+ table %[s ! extraord9>y mann] 9 :i* ! numb] ( possible logical relations increases ) ! numb] ( t]ms involv$4 ---------------------------------------- --------------------- ,numb] ( ,numb] ( ,numb] ( possible selections ( combi- t]ms4 possible nations correspond+ to consi/5t comb9ations4 or inconsi/5t logical relations4 ---------------------------------------- ---------------------- #b #d #af #c #h #bef #d #af #fe1ecf #e #cb #d1bid1ifg1bif #f #fd #ah1ddf1gdd1jgc1gji1eea1faf ---------------------------------------- --------------------- ,"s ye>s ( cont9u\s lab\r w\ld be requir$ to asc]ta9 ! types ( laws :i* may gov]n ! comb9ations ( only f\r ?+s1 & b a small "p ( su* laws w\ld be exemplifi$ or capable ( practical application 9 sci5ce4 ,! purely logical inv]se problem1 :]eby we pass f comb9ations to _! laws1 is solv$ 9 ! prec$+ pages1 z f> z x is likely to be = a long "t to come2 & x is almo/ impossible t x %\ld ev] be c>ri$ m ?an a s+le /ep fur!r4 ,9 ! fir/ edition1 vol i4 p4 #aeh1 ,i /at$ t ,i _h n be5 able to discov] any mode ( calculat+ ! numb] ( cases 9 :i* inconsi/5cy w\ld be impli$ 9 ! selection ( comb9ations f ! ,logical ,alphabet4 ,! logical complexity ( ! problem appe>$ to be s great t ! ord9>y modes ( calculat+ numb]s ( comb9ations fail$1 9 my op9ion1 to give any aid1 & exhau/ive exam9ation ( ! comb9ations 9 detail seem$ to be ! only me?od applicable4 ,?is op9ion1 h[ev]1 0 mi/ak51 = bo? ,mr4 ,r4 ,b4 ,hayw>d1 ( ,h>r[1 & ,mr4 ,w4 ,h4 ,brew] h calculat$ ! numb]s ( inconsi/5t cases bo? = ?ree & = f\r t]ms1 )\t mu* difficulty4 ,9 ! case ( f\r t]ms !y f9d t !re are #agfa inconsi/5t selections & #fc1ggd consi/5t1 :i* ) "o case :]e no condition exi/s1 make up ! total ( #fe1ecf possible selections4 ,! inconsi/5t cases are di/ribut$ 9 ! mann] %[n 9 ! foll[+ table3-- ---------------------------------------- ------------------------- ,numb] ( ,comb9ations #j #a #b #c #d #e #f #g #h #i #aj1 c4 rema9+4 ---------------------------------------- ------------------------- ,numb] ( ,inconsi/5t #a #af #aab #ceb #ecf #ddh #bbd #fd #h #j #j1 c4 ,cases4 ---------------------------------------- ------------------------- ,:5 m ?an eight comb9ations ( ! ,logical ,alphabet 7p4 #id1 column ,v47 rema9 unexclud$1 !re _c be inconsi/5cy4 ,! :ole numb]s ( ways ( select+ #j1 #a1 #b1 c41 comb9ations out ( #af are giv5 9 ! #ag? l9e ( ! ,ari?metical ,triangle giv5 fur!r on 9 ! ,*apt] on ,comb9ations & ,p]mutations1 ! sum ( ! numb]s 9 t l9e be+ #fe1ecf4 99,pr(essor ,clif=d on ! ,types ( ,comp\nd ,/atem5t involv+ ,f\r ,classes499 ,9 ! fir/ edition 7vol4 i4 p4 #afc71 ,i ass]t$ t "s ye>s ( lab\r w\ld be requir$ to asc]ta9 ev5 ! precise numb] ( types ( law gov]n+ ! comb9ations ( f\r classes ( ?+s4 ,?\gh ,i /ill believe t "s ye>s' lab\r w\ld be requir$ to "w out ! types !mselves1 x is cle>ly a mi/ake to suppose t ! 99numb]s99 ( su* types _c be calculat$ ) a reasonable am\nt ( lab\r1 ,pr(essor ,w4 ,k4 ,clif=d hav+ actually accompli%$ ! task4 ,8 solution ( ! num]ical problem involves ! use ( a complete new sy/em ( nom5clature & is f> too intricate to be fully describ$ "h4 ,i c only give a brief ab/ract ( ! results1 & ref] read]s1 :o wi% to foll[ out ! reason+1 to ! ,proce$+s ( ! ,lit]>y & ,philosophical ,society ( ,man*e/]1 = ! #i? ,janu>y1 #ahgg1 vol4 xvi41 p4 #hh1 :]e ,pr(essor ,clif=d's pap] is pr9t$ 9 full4 ,by a 99simple /atem5t99 ,pr(essor ,clif=d means ! d5ial ( ! exi/5ce ( any s+le comb9ation or 99cross-division991 ( ! classes1 z 9 ,,abcd #j1 or ,a99b99,c99d99 #j4 ,! d5ial ( two or m su* comb9ations is call$ a 99comp\nd /atem5t991 & is fur!r said to be 99tw(old991 99?reefold991 c41 accord+ to ! numb] d5i$4 ,?us ,,abc #j is a tw(old comp\nd /atem5t 9 reg>d to f\r classes1 because x involves bo? ,,abcd #j & ,,abc99d99 #j4 ,:5 two comp\nd /atem5ts c be conv]t$ into "o ano!r by int]*ange ( ! classes1 ,a1 ,b1 ,c1 ,d1 ) ea* o!r or ) _! complem5t>y classes1 99a991 99b991 99c991 99d991 !y are call$ 99simil>991 & all simil> /atem5ts are said to belong to ! same 99type994 ,two /atem5ts are call$ 99complem5t>y99 :5 !y d5y betwe5 !m all ! sixte5 comb9ations )\t bo? d5y+ any "o2 or1 :i* is ! same ?+1 :5 ea* d5ies j ^? comb9ations :i* ! o!r p]mits to exi/4 ,x is obvi\s t :5 two /atem5ts are simil>1 ! complem5t>y /atem5ts w also be simil>1 & consequ5tly = e type ( 99n99-fold /atem5t1 !re is a complem5t>y type ( 7#af--99n997-fold /atem5t4 ,x foll[s t we ne$ only enum]ate ! types z f> z ! eigh? ord]2 = ! types ( m-?an-eight-fold /atem5t w already h be5 giv5 z complem5t>y to types ( l[] ord]s4 ,"o comb9ation1 ,,abcd1 may be conv]t$ into ano!r ,a99b99,c99d99 by int]*ang+ "o or m ( ! classes ) ! complem5t>y classes4 ,! numb] ( su* *anges is call$ ! 99di/ance991 :i* 9 ! above case is #b4 ,9 two simil> comp\nd /atem5ts ! di/ances ( ! comb9ations d5i$ mu/ be ! same2 b x does n foll[ t :5 all ! di/ances are ! same1 ! /atem5ts are simil>4 ,!re is1 h[ev]1 only "o example ( two dissimil> /atem5ts hav+ ! same di/ances4 ,:5 ! di/ance is #d1 ! two comb9ations are said to be 99obv]se99 to "o ano!r1 & ! /atem5ts d5y+ !m are call$ 99obv]se /atem5ts991 z 9 ,,abcd #j & 99abcd99 #j or aga9 ,a99b99,c99d99 #j & 99a99,b99c99,d #j4 ,:5 any "o comb9ation is giv51 call$ ! 99orig9991 all ! o!rs may be gr\p$ 9 respect ( _! relations to x z foll[s3--,f\r are at di/ance 99"o99 f x1 & may be call$ 99proximates992 six are at di/ance 99two991 & may be call$ 99m$iates992 f\r are at di/ance 99?ree991 & may be call$ 99ultimates992 f9ally ! obv]se is at di/ance 99f\r994 ,orig9 & ,six ,obv]se & f\r proximates4 m$iates4 f\r ultimates4 99ab99,,cd 99a99,,bcd ,a99bc99,d ,a99b99,c99d99 ,a99bcd99 _/ _/ _/ ,,abc99d99--,,abcd--,a99b99,,cd 99abc99,d--99abcd99--99a99,b99cd99 _/ _/ _/ ,,ab99c99,d 99a99,b99c99,d 99a99,,bc99d99 99ab99,c99d994 ,,ab99cd99 ,x w be se5 t ! f\r proximates are respectively obv]se to ! f\r ultimates1 & t ! m$iates =m ?ree pairs ( obv]ses4 ,e proximate or ultimate is di/ant #a & #c respectively f su* a pair ( m$iates4 ,aid$ by ?is sy/em ( nom5clature ,pr(essor ,clif=d proce$s to an exhau/ive enum]ation ( types1 9 :i* x is impossible to foll[ him4 ,! results are z foll[s3-- #a-;fold /atem5ts #a type #b #d types #c #f #d #ai #aei #e #bg #f #dg #g #ee #h-;fold /atem5ts #gh ,n[ z ea* sev5-fold or less-?an-sev5-fold /atem5t is complem5t>y to a n9e-fold or m-?an-n9e-fold /atem5t1 x foll[s t ! complete numb] ( types w be #aei #b #gh #cif4 ,x appe>s !n t ! types ( /atem5t conc]n+ f\r classes are only ab\t #bf times z num]\s z ^? conc]n+ ?ree classes1 fifte5 9 numb]1 al?\gh ! numb] ( possible comb9ations is #bef times z great4 ,pr(essor ,clif=d in=ms me t ! k ( ! possible gr\p+s ( subdivisions ( classes :i* he obta9$ by ?is inquiry has be5 ( s]vice to him 9 "s applications ( hyp]-elliptic functions to :i* he has subsequ5tly be5 l$4 ,pr(essor ,cayley has s9ce express$ 8 op9ion t ?is l9e ( inve/igation %\ld be foll[$ out1 ow+ to ! be>+ ( ! !ory ( comp\nd comb9ations ^u ! high] geometry4#hf ,x seems likely t _m unexpect$ po9ts ( connection w 9 "t be disclos$ betwe5 ! sci5ces ( logic & ma!matics4 #hf 99,proce$+s ( ! ,man*e/] ,lit]>y & ,philosophical ,society991 #f? ,febru>y1 #ahgg1 vol4 xvi41 p4 #aac4 99,di/9ction betwe5 ,p]fect & ,imp]fect ,induction499 ,we _c proce$ ) advantage be=e notic+ ! extreme diff]5ce :i* exi/s betwe5 cases ( p]fect & ^? ( imp]fect induction4 ,we call an induction 99p]fect99 :5 all ! objects or ev5ts :i* c possibly come "u ! class treat$ h be5 exam9$4 ,b 9 ! majority ( cases x is impossible to collect toge!r1 or 9 any way to inve/igate1 ! prop]ties ( all portions ( a sub/ance or ( all ! individuals ( a race4 ,! numb] ( objects w\ld (t5 be practically inf9ite1 & ! great] "p ( !m might be beyond our rea*1 9 ! int]ior ( ! e>?1 or 9 ! mo/ di/ant p>ts ( ! ,univ]se4 ,9 all su* cases induction is 99imp]fect991 & is affect$ by m or less unc]ta9ty4 ,z "s writ]s h fall5 into mu* error conc]n+ ! functions & relative importance ( ^! two bran*es ( reason+1 ,i %all h to po9t out t-- #a4 ,p]fect ,induction is a process absolutely requisite1 bo? 9 ! p]=mance ( imp]fect induction & 9 ! treatm5t ( l>ge bodies ( facts ( :i* our k is complete4 #b4 ,imp]fect ,induction is f\nd$ on ,p]fect ,induction1 b involves ano!r process ( inf]5ce ( a widely diff]5t "*4 ,x is c]ta9 t if ,i c draw any inf]5ce at all conc]n+ objects n exam9$1 x mu/ be done on ! data af=d$ by ! objects :i* h be5 exam9$4 ,if ,i judge t a di/ant /> obeys ! law ( gravity1 x mu/ be because all o!r mat]ial objects suffici5tly kn[n to me obey t law4 ,if ,i v5ture to ass]t t all rum9ant animals h clov5 ho(s1 x is because all rum9ant animals :i* h come "u my notice h clov5 ho(s4 ,on ! o!r h&1 ,i _c safely say t all cryptogam\s plants possess a purely cellul> /ructure1 because "s cryptogam\s plants1 :i* h be5 exam9$ by botani/s1 h a p>tially vascul> /ructure4 ,! probability t a new cryptogam w be cellul> only c be e/imat$1 if at all1 on ! gr\nd ( ! comp>ative numb]s ( kn[n cryptogams :i* are & are n cellul>4 ,?us ! fir/ /ep 9 e induction w consi/ 9 accurately summ+ up ! numb] ( in/ances ( a p>ticul> ph5om5on :i* h fall5 "u our obs]vation4 ,adams & ,lev]ri]1 = in/ance1 mu/ h inf]r$ t ! undiscov]$ planet ,neptune w\ld obey ,bode's law1 because 99all ! planets kn[n at t "t obey$ x994 ,on :at pr9ciples ! passage f ! kn[n to ! app>5tly unkn[n is w>rant$1 mu/ be c>efully discuss$ 9 ! next section1 & 9 v>i\s p>ts ( ?is "w4 ,x w\ld be a great mi/ake1 h[ev]1 to suppose t ,p]fect ,induction is 9 itself useless4 ,ev5 :5 ! enum]ation ( objects belong+ to any class is complete1 & admits ( no inf]5ce to unexam9$ objects1 ! /atem5t ( our k 9 a g5]al proposition is a process ( s mu* importance t we may consid] x necess>y4 ,9 _m cases we may r5d] our inve/igations exhau/ive2 all ! tee? or bones ( an animal2 all ! cells 9 a m9ute vegetable organ2 all ! caves 9 a m\nta9 side2 all ! /rata 9 a geological section2 all ! co9s 9 a newly f\nd ho>d1 may be s completely scrut9iz$ t we may make "s g5]al ass]tion conc]n+ !m )\t fe> ( mi/ake4 ,e bone might be prov$ to conta9 phosphate ( lime2 e cell to enclose a nucleus2 e cave to hide rema9s ( ext9ct animals2 e /ratum to exhibit signs ( m>9e orig92 e co9 to be ( ,roman manufacture4 ,^! are cases :]e our inve/igation is limit$ to a def9ite portion ( matt]1 or a def9ite area on ! e>?'s surface4 ,!re is ano!r class ( cases :]e induction is naturally & necess>ily limit$ to a def9ite numb] ( alt]natives4 ,( ! regul> solids we c say )\t ! lea/ d\bt t no "o has m ?an tw5ty faces1 ?irty edges1 & tw5ty corn]s2 = by ! pr9ciples ( geometry we le>n t !re _c exi/ m ?an five regul> solids1 ( ea* ( :i* we easily obs]ve t ! above /atem5ts are true4 ,9 ! !ory ( numb]s1 an endless v>iety ( p]fect inductions might be made2 we c %[ t no numb] less ?an sixty possesses s _m divisors1 & ! l is true ( #cfj2 = x does n require a great am\nt ( lab\r to asc]ta9 & c\nt all ! divisors ( numb]s up to sixty or #cfj4 ,i c ass]t t betwe5 #fj1jda & #fj1jgg no prime numb] occurs1 because ! exhau/ive exam9ation ( ^? :o h con/ruct$ tables ( prime numb]s proves x to be s4 ,9 matt]s ( human appo9tm5t or hi/ory1 we c frequ5tly h a complete limitation ( ! numb] ( in/ances to be includ$ 9 an induction4 ,we might %[ t ! propositions ( ! ?ird book ( ,euclid treat only ( circles2 t no "p ( ! works ( ,gal5 m5tions ! f\r? figure ( ! syllogism2 t none ( ! o!r k+s ( ,engl& reign$ s long z ,george ,,iii42 t ,magna ,*>ta has n be5 repeal$ by any subsequ5t /atute2 t ! price ( corn 9 ,engl& has nev] be5 s high s9ce #ahdg z x 0 9 t ye>2 t ! price ( ! ,engli% funds has nev] be5 l[] ?an x 0 on ! #bcrd ( ,janu>y1 #agih1 :5 x fell to #dg-a_/d4 ,x has be5 urg$ aga9/ ?is process ( ,p]fect ,induction t x gives no new in=mation1 & is m]ely a summ+ up 9 a brief =m ( a multitude ( p>ticul>s4 ,b m]e abbreviation ( m5tal lab\r is "o ( ! mo/ important aids we c enjoy 9 ! acquisition ( k4 ,! p[]s ( ! human m9d are s limit$ t multiplicity ( detail is alone suffici5t to prev5t its progress 9 _m directions4 ,?\ght w\ld be practically impossible if e sep>ate fact _h to be sep>ately ?\ght & treat$4 ,economy ( m5tal p[] may be consid]$ "o ( ! ma9 conditions on :i* our elevat$ intellectual position dep5ds4 ,ma!matical processes are = ! mo/ "p b abbreviations ( ! simpl] acts ( addition & subtraction4 ,! inv5tion ( log>i?ms 0 "o ( ! mo/ /rik+ additions ev] made to human p[]3 yet x 0 a m]e abbreviation ( op]ations :i* c\ld h be5 done be=e _h a suffici5t am\nt ( lab\r be5 available4 ,simil> additions to our p[] w1 x is hop$1 be made f "t to "t2 = ! numb] ( ma!matical problems hi!rto solv$ is b an indef9itely small fraction ( ^? :i* await solution1 because ! lab\r !y h hi!rto dem&$ r5d]s !m impracticable4 ,s x is ?r\gh\t all regions ( ?\ght4 ,! am\nt ( our k dep5ds ^u our p[] ( br++ x )9 practicable compass4 ,unless we arrange & classify facts & cond5se !m into g5]al tru?s1 !y soon surpass our p[]s ( memory1 & s]ve b to confuse4 ,h5ce ,p]fect ,induction1 ev5 z a process ( abbreviation1 is absolutely ess5tial to any high degree ( m5tal a*ievem5t4 99,transition f ,p]fect to ,imp]fect ,induction499 ,x is a "q ( pr(\nd difficulty on :at gr\nds we are w>rant$ 9 inf]r+ ! future f ! pres5t1 or ! nature ( undiscov]$ objects f ^? :i* we h exam9$ ) our s5ses4 ,we pass f ,p]fect to ,imp]fect ,induction :5 once we all[ our conclusion to apply1 at all ev5ts app>5tly1 beyond ! data on :i* x 0 f\nd$4 ,9 mak+ su* a /ep we seem to ga9 a net addition to our k2 = we le>n ! nature ( :at 0 unkn[n4 ,we reap :]e we h nev] s[n4 ,we appe> to possess ! div9e p[] ( creat+ k1 & rea*+ ) our m5tal arms f> beyond ! sph]e ( our own obs]vation4 ,i %all h1 inde$1 to po9t out c]ta9 me?ods ( reason+ 9 :i* we d pass altoge!r beyond ! sph]e ( ! s5ses1 & acquire accurate k :i* obs]vation c\ld nev] h giv52 b x is n imp]fect induction t accompli%es su* a task4 ,( imp]fect induction itself1 ,i v5ture to ass]t t x nev] makes any real addition to our k1 9 ! mean+ ( ! expression sometimes accept$4 ,z 9 o!r cases ( inf]5ce1 x m]ely unfolds ! in=mation conta9$ 9 pa/ obs]vations2 x m]ely r5d]s explicit :at 0 implicit 9 previ\s exp]i5ce4 ,x transmutes1 b c]ta9ly does n create k4 ,!re is no fact :i* ,i %all m con/antly keep be=e ! read]'s m9d 9 ! foll[+ pages ?an t ! results ( imp]fect induction1 h[ev] well au!nticat$ & v]ifi$1 are nev] m ?an probable4 ,we nev] c be sure t ! future w be z ! pres5t4 ,we hang ev] ^u ! w ( ! ,creator3 & x is only s f> z ,he has creat$ two ?+s alike1 or ma9ta9s ! framework ( ! _w un*ang$ f mom5t to mom5t1 t our mo/ c>eful inf]5ces c be fulfill$4 ,all pr$ictions1 all inf]5ces :i* rea* beyond _! data1 are purely hypo!tical1 & proce$ on ! assumption t new ev5ts w con=m to ! conditions detect$ 9 our obs]vation ( pa/ ev5ts4 ,no exp]i5ce ( f9ite duration c give an exhau/ive k ( ! =ces :i* are 9 op]ation4 ,!re is ?us a d\ble unc]ta9ty2 ev5 suppos+ ! ,univ]se z a :ole to proce$ un*ang$1 we d n really "k ! ,univ]se z a :ole4 ,we "k only a po9t 9 its inf9ite ext5t1 & a mom5t 9 its inf9ite duration4 ,we _c be sure1 !n1 t our obs]vations h n escap$ "s fact1 :i* w cause ! future to be app>5tly diff]5t f ! pa/2 nor c we be sure t ! future really w be ! outcome ( ! pa/4 ,we proce$ !n 9 all our inf]5ces to unexam9$ objects & times on ! assumptions-- #a4 ,t our pa/ obs]vation gives u a complete k ( :at exi/s4 #b4 ,t ! conditions ( ?+s :i* did exi/ w cont9ue to be ! conditions :i* w exi/4 ,we %all (t5 ne$ to illu/rate ! "* ( our k ( nature by ! simile ( a ballot-box1 s (t5 employ$ by ma!matical writ]s 9 ! !ory ( probability4 ,nature is to u l an inf9ite ballot-box1 ! cont5ts ( :i* are be+ cont9ually drawn1 ball aft] ball1 & exhibit$ to u4 ,sci5ce is b ! c>eful obs]vation ( ! succession 9 :i* balls ( v>i\s "* pres5t !mselves2 we regi/] ! comb9ations1 notice ^? :i* seem to be exclud$ f occurr5ce1 & f ! proportional frequ5cy ( ^? :i* appe> we inf] ! probable "* ( future draw+s4 ,b "u su* circum/ances c]ta9ty ( pr$iction dep5ds on two conditions3-- #a4 ,t we acquire a p]fect k ( ! comp>ative numb]s ( balls ( ea* k9d )9 ! box4 #b4 ,t ! cont5ts ( ! ballot-box rema9 un*ang$4 ,( ! latt] assumption1 or r t conc]n+ ! con/itution ( ! _w :i* x illu/rates1 ! logician or physici/ c h no?+ to say4 ,z ! ,creation ( ! ,univ]se is necess>ily an act pass+ all exp]i5ce & all conception1 s any *ange 9 t ,univ]se1 or1 x may be1 a t]m9ation ( x1 mu/ likewise be inf9itely beyond ! b\nds ( our m5tal faculties4 ,no sci5ce no reason+ ^u ! subject1 c h any validity2 = )\t exp]i5ce we are )\t ! basis & mat]ials ( k4 ,x is ! fundam5tal po/ulate accord+ly ( all inf]5ce conc]n+ ! future1 t !re %all be no arbitr>y *ange 9 ! subject ( inf]5ce2 ( ! probability or improbability ( su* a *ange ,i conceive t our faculties c give no e/imate4 ,! o!r condition ( inductive inf]5ce--t we acquire an approximately complete k ( ! comb9ations 9 :i* ev5ts d occur1 is 9 "s degree )9 our p[]4 ,!re are bran*es ( sci5ce 9 :i* ph5om5a seem to be gov]n$ by conditions ( a mo/ fix$ & g5]al "*4 ,we h gr\nd 9 su* cases = believ+ t ! future occurr5ce ( su* ph5om5a c be calculat$ & pr$ict$4 ,b ! :ole "q n[ becomes "o ( probability & improbability4 ,we seem to leave ! region ( logic to ent] "o 9 :i* ! numb] ( ev5ts is ! gr\nd ( inf]5ce4 ,we d n really leave ! region ( logic2 we only leave t :]e c]ta9ty1 affirmative or negative1 is ! result1 & ! agreem5t or disagreem5t ( qualities ! means ( inf]5ce4 ,= ! future1 numb] & quantity w commonly ent] into our processes ( reason+2 b !n ,i hold t numb] & quantity are b portions ( ! great logical doma94 ,i v5ture to ass]t t numb] is :olly logical1 bo? 9 its fundam5tal nature & 9 its developm5ts4 ,quantity 9 all its =ms is b a developm5t ( numb]4 ,t :i* is ma!matical is n ! less logical2 if any?+ x is m logical1 9 ! s5se t x pres5ts logical results 9 a high] degree ( complexity & v>iety4 ,be=e proce$+ !n f ,p]fect to ,imp]fect ,induction ,i mu/ devote a portion ( ?is "w to treat+ ! logical conditions ( numb]4 ,i %all !n employ numb] to e/imate ! v>iety ( comb9ations 9 :i* natural ph5om5a may pres5t !mselves1 & ! probability or improbability ( _! occurr5ce "u def9ite circum/ances4 ,x is 9 lat] p>ts ( ! "w t ,i mu/ endeav\r to e/abli% ! notions :i* ,i h set =? ^u ! subject ( ,imp]fect ,induction1 z appli$ 9 ! inve/igation ( ,nature1 :i* notions maybe ?us briefly /at$3-- #a4 ,imp]fect ,induction entirely re/s ^u ,p]fect ,induction = its mat]ials4 #b4 ,! logical process by :i* we seem to pass directly f exam9$ to unexam9$ cases consi/s 9 an inv]se application ( d$uctive inf]5ce1 s t all reason+ may be said to be ei!r directly or inv]sely d$uctive4 #c4 ,! result is always ( a hypo!tical "*1 & is nev] m ?an probable4 #d4 ,no net addition is ev] made to our k by reason+2 :at we "k ( future ev5ts or unexam9$ objects is only ! unfold$ cont5ts ( our previ\s k1 & x becomes less probable z x is m boldly ext5d$ to remote cases4 ,,book ,,ii4 ,,numb]1 ,,v>iety1 ,,& ,,probability4 ,,*apt] ,,viii4 ,,pr9ciples ,,( ,,numb]4 ,n )\t reason did ,py?agoras repres5t ! _w z rul$ by numb]4 ,into almo/ all our acts ( ?\ght numb] ent]s1 & 9 proportion z we c def9e num]ically we enjoy exact & useful k ( ! ,univ]se4 ,! sci5ce ( numb]s1 too1 has hi!rto pres5t$ ! wide/ & mo/ practicable tra9+ 9 logic4 ,s free & en]getic has be5 ! /udy ( ma!matical =ms1 comp>$ ) ! =ms ( logic1 t ma!maticians h pass$ f> 9 advance ( pure logicians4 ,occasionally1 9 rec5t times1 !y h condesc5d$ to apply _! algebraic in/rum5t to a reflex treatm5t ( ! prim>y logical sci5ce4 ,x is ?us t we owe to pr(\nd ma!maticians1 su* z ,john ,h]s*el1 ,:ewell1 ,de ,morgan1 or ,boole1 ! reg5]ation ( logic 9 ! pres5t c5tury4 ,i ent]ta9 no d\bt t x is 9 ma9ta9+ a close alliance ) quantitative reason+ t we mu/ look = fur!r progress 9 our compreh5sion ( qualitative inf]5ce4 ,i _c ass5t1 inde$1 to ! common notion t c]ta9ty beg9s & ends ) num]ical det]m9ation4 ,no?+ is m c]ta9 ?an logical tru?4 ,! laws ( id5tity & diff]5ce are ! te/s ( all t is c]ta9 ?r\gh\t ! range ( ?\ght1 & ma!matical reason+ is cog5t only :5 x con=ms to ^! conditions1 ( :i* logic is ! fir/ developm5t4 ,& if x be errone\s to suppose t all c]ta9ty is ma!matical1 x is equally an error to imag9e t all :i* is ma!matical is c]ta94 ,_m processes ( ma!matical reason+ are ( mo/ d\btful validity4 ,!re are po9ts ( ma!matical doctr9e :i* mu/ long rema9 matt] ( op9ion2 = in/ance1 ! be/ =m ( ! def9ition & axiom conc]n+ p>allel l9es1 or ! true nature ( a limit4 ,9 ! use ( symbolic reason+ que/ions occur on :i* ! be/ ma!maticians may diff]1 z ,b]n\lli & ,leibnitz diff]$ irreconcileably conc]n+ ! exi/5ce ( ! log>i?ms ( negative quantities4#hg ,9 fact we no soon] leave ! simple logical conditions ( numb]1 ?an we f9d ourselves involv$ 9 a mazy & my/]i\s sci5ce ( symbols4 #hg ,montucla4 99,hi/oire des ,ma?matiques991 vol4 iii4 p4 #cgc4 ,ma!matical sci5ce enjoys no monopoly1 & n ev5 a supremacy1 9 c]ta9ty ( results4 ,x is ! b\ndless ext5t & v>iety ( quantitative que/ions t delights ! ma!matical /ud5t4 ,:5 simple logic c give b a b>e answ] ,yes or ,no1 ! algebrai/ raises a score ( subtle que/ions1 & br+s out a cr[d ( curi\s results4 ,! fl[] & ! fruit1 all t is attractive & delightful1 fall to ! %>e ( ! ma!matician1 :o too (t5 despises ! pla9 b necess>y /em f :i* all has aris54 ,9 no region ( ?\ght c a reason] ca/ himself free f ! prior conditions ( logical correctness4 ,! ma!matician is only /rong & true z long z he is logical1 & if numb] rules ! _w1 x is logic :i* rules numb]4 ,ne>ly all writ]s h hi!rto be5 /rangely cont5t to look ^u num]ical reason+ z some?+ ap>t f logical inf]5ce4 ,a long divorce has exi/$ betwe5 quality & quantity1 & x has n be5 uncommon to treat !m z contra/$ 9 nature & re/rict$ to indep5d5t bran*es ( ?\ght4 ,= my own "p1 ,i believe t all ! sci5ces meet some:]e4 ,no "p ( k c /& :olly disconnect$ f o!r p>ts ( ! univ]se ( ?\ght2 x is incr$ible1 above all1 t ! two great bran*es ( ab/ract sci5ce1 int]lac+ & co-op]at+ 9 e disc\rse1 %\ld re/ ^u totally di/9ct f\ndations4 ,i assume t a connection exi/s1 & c>e only to inquire1 ,:at is its nature8 ,does ! sci5ce ( quantity re/ ^u t ( quality2 or1 99vice v]s991 does ! sci5ce ( quality re/ ^u t ( quantity8 ,!re might conceivably be a ?ird view1 t !y bo? re/ ^u "s /ill deep] set ( pr9ciples4 ,x is g5]ally suppos$ t ,boole adopt$ ! second view1 & treat$ logic z an application ( algebra1 a special case ( analytical reason+ :i* admits only two quantities1 unity & z]o4 ,x is n easy to asc]ta9 cle>ly :i* ( ^! views really 0 accept$ by ,boole4 ,9 8 int]e/+ biographical sket* ( ,boole1#hh ! ,rev4 ,r4 ,h>ley prote/s aga9/ ! /atem5t t ,boole's logical calculus import$ ! conditions ( numb] & quantity into logic4 ,he says3 8,logic is nev] id5tifi$ or conf\nd$ ) ma!matics2 ! two sy/ems ( ?\ght are kept p]fectly di/9ct1 ea* be+ subject to its own laws & conditions4 ,! symbols are ! same = bo? sy/ems1 b !y h n ! same int]pretation40 ,! ,rev4 ,j4 ,v5n1 aga91 9 8 review ( ,boole's logical sy/em1#hi holds t ,boole's processes are at bottom logical1 n ma!matical1 ?\gh /at$ 9 a highly g5]aliz$ =m & ) a ma!matical dress4 ,b x is q likely t read]s ( ,boole %\ld be misl$4 ,n only h 8 logical works an entirely ma!matical appe>ance1 b ,i f9d on p4 #ab ( 8 99,laws ( ,?\ght99 ! foll[+ unequivocal /atem5t3 8,t logic1 z a sci5ce1 is susceptible ( v wide applications is admitt$2 b x is equally c]ta9 t its ultimate =ms & processes are ma!matical40 ,a few l9es bel[ he adds1 8,x is n ( ! ess5ce ( ma!matics to be conv]sant ) ! ideas ( numb] & quantity40 #hh 99,briti% ,qu>t]ly ,review991 ,no4 lxxxvii1 ,july #ahff4 #hi 99,m9d991 ,octob] #ahgf1 vol4 i4 p4 #dhd4 ,! solution ( ! difficulty is t ,boole us$ ! t]m ma!matics 9 a wid] s5se ?an t usually attribut$ to x4 ,he probably adopt$ ! ?ird view1 s t 8 ma!matical 99,laws ( ,?\ght99 are ! common basis bo? ( logic & ( quantitative ma!matics4 ,b ,i d n c>e to pursue ! subject because ,i ?9k t1 9 ei!r case ,boole 0 wrong4 ,9 my op9ion logic is ! sup]ior sci5ce1 ! g5]al basis ( ma!matics z well z ( all o!r sci5ces4 ,numb] is b logical discrim9ation1 & algebra a highly develop$ logic4 ,?us x is easy to und]/& ! deep analogy :i* ,boole po9t$ out betwe5 ! =ms ( algebraic & logical d$uction4 ,logic resembles algebra z ! m\ld resembles t :i* is ca/ 9 x4 ,boole mi/ook ! ca/ = ! m\ld4 ,consid]+ t logic imposes its own laws ^u e bran* ( ma!matical sci5ce1 x is no wond] t we con/antly meet ) ! traces ( logical laws 9 ma!matical processes4 99,! ,nature ( ,numb]499 ,numb] is b ano!r "n = 99div]sity994 ,exact id5tity is unity1 & ) diff]5ce arises plurality4 ,an ab/ract notion1 z 0 po9t$ out 7p4 #bh71 possesses a c]ta9 99on5ess994 ,! quality ( 99ju/ice991 = in/ance1 is "o & ! same 9 :atev] j acts x is manife/$4 ,9 ju/ice itself !re are no m>ks ( diff]5ce by :i* to discrim9ate ju/ice f ju/ice4 ,b "o j act c be discrim9at$ f ano!r j act by circum/ances ( "t & place1 & we c c\nt _m acts ?us discrim9at$ ea* f ea*4 ,9 l mann] pure gold is simply pure gold1 & is s f> "o & ! same ?r\gh\t4 ,b besides its intr9sic qualities1 gold occupies space & mu/ h %ape & size4 ,portions ( gold are always mutually exclusive & capable ( discrim9ation1 9 respect t !y mu/ be ea* )\t ! o!r4 ,h5ce !y may be numb]$4 ,plurality arises :5 & only :5 we detect diff]5ce4 ,= in/ance1 9 c\nt+ a numb] ( gold co9s ,i mu/ c\nt ea* co9 once1 & n m ?an once4 ,let ,c d5ote a co91 & ! m>k above x ! ord] ( c\nt+4 ,!n ,i mu/ c\nt ! co9s ,c ,c ,c ,c 4444 ,if ,i 7 to c\nt !m z foll[s ,c ,c ,c ,c ,c 4441 ,i %\ld make ! ?ird co9 into two1 & %\ld imply ! exi/5ce ( diff]5ce :]e !re is no diff]5ce4#ij ,c & ,c are b ! names ( "o co9 nam$ twice ov]4 ,b accord+ to "o ( ! conditions ( logical symbols1 :i* ,i h call$ ! ,law ( ,unity 7p4 #gb71 ! same "n repeat$ has no effect1 & ,a ,a ,a4 #ij 99,pure ,logic991 ,app5dix1 p4 #hb1 #aib4 ,we mu/ apply ! ,law ( ,unity1 & mu/ r$uce all id5tical alt]natives be=e we c c\nt ) c]ta9ty & use ! processes ( num]ical calculation4 ,id5tical alt]natives are h>mless 9 logic1 b are :olly inadmissible 9 numb]4 ,?us logical sci5ce asc]ta9s ! nature ( ! ma!matical unit1 & ! def9ition may be giv5 9 ^! t]ms--99,a unit is any object ( ?\ght :i* c be discrim9at$ f e o!r object treat$ z a unit 9 ! same problem499 ,x has (t5 be5 said t units are units 9 respect ( be+ p]fectly simil> to ea* o!r2 b ?\gh !y may be p]fectly simil> 9 "s respects1 !y mu/ be diff]5t 9 at lea/ "o po9t1 o!rwise !y w\ld be incapable ( plurality4 ,if ?ree co9s 7 s simil> t !y occupi$ ! same space at ! same "t1 !y w\ld n be ?ree co9s1 b "o co94 ,x is a prop]ty ( space t e po9t is discrim9able f e o!r po9t1 & 9 "t e mom5t is necess>ily di/9ct f any o!r mom5t be=e or aft]4 ,h5ce we frequ5tly c\nt 9 space or "t1 & ,locke1 ) "s o!r philosoph]s1 has held t numb] arises f repetition 9 "t4 ,beats ( a p5dulum may be s p]fectly simil> t we c discov] no diff]5ce except t "o beat is be=e & ano!r aft]4 ,"t alone is "h ! gr\nd ( diff]5ce & is a suffici5t f\ndation = ! discrim9ation ( plurality2 b x is by no means ! only f\ndation4 ,?ree co9s are ?ree co9s1 :e!r we c\nt !m successively or reg>d !m all simultane\sly4 ,9 _m cases nei!r "t nor space is ! gr\nd ( diff]5ce1 b pure quality alone ent]s4 ,we c discrim9ate ! weight1 in]tia1 & h>dness ( gold z ?ree qualities1 ?\gh none ( ^! is be=e nor aft] ! o!r1 nei!r 9 space nor "t4 ,e means ( discrim9ation may be a s\rce ( plurality4 ,our logical notation may be us$ to express ! rise ( numb]4 ,! symbol ,a /&s = "o ?+ or "o class1 & 9 itself mu/ be reg>d$ z a unit1 because no diff]5ce is specifi$4 ,b ! comb9ations ,,ab & ,a99b99 are necess>ily 99two991 because !y _c logically coalesce1 & !re is a m>k ,b :i* di/+ui%es "o f ! o!r4 ,a logical def9ition ( ! numb] 99f\r99 is giv5 9 ! comb9ations ,,abc1 ,,ab99c991 ,a99b99,c1 ,a99bc991 :]e !re is a d\ble diff]5ce4 ,z ,puck says-- 8,yet b ?ree8 ,come "o m2 ,two ( bo? k9ds makes up f\r40 ,i conceive t all numb]s might be repres5t$ z aris+ out ( ! comb9ations ( ! ,logical ,alphabet1 m or less ( ea* s]ies be+ /ruck out by v>i\s logical conditions4 ,! numb] ?ree1 = in/ance1 arises f ! condition t ,a mu/ be ei!r ,b or ,c1 s t ! comb9ations are ,,abc1 ,,ab99c991 ,a99b99,c4 99,( ,num]ical ,ab/raction499 ,!re w n[ be little difficulty 9 =m+ a cle> notion ( ! nature ( num]ical ab/raction4 ,x consi/s 9 ab/ract+ ! "* ( ! diff]5ce f :i* plurality arises1 reta9+ m]ely ! fact4 ,:5 ,i speak ( 99?ree m599 ,i ne$ n at once specify ! m>ks by :i* ea* may be kn[n f ea*4 ,^? m>ks mu/ exi/ if !y are really ?ree m5 & n "o & ! same1 & 9 speak+ ( !m z _m ,i imply ! exi/5ce ( ! requisite diff]5ces4 ,ab/ract numb]1 !n1 is 99! empty =m ( diff]5ce992 ! ab/ract numb] 99?ree99 ass]ts ! exi/5ce ( m>ks )\t specify+ _! k9d4 ,num]ical ab/raction is ?us se5 to be a diff]5t process f logical ab/raction 7p4 #bg71 = 9 ! latt] process we drop out ( notice ! v exi/5ce ( diff]5ce & plurality4 ,9 =m+ ! ab/ract notion 99h>dness991 we ignore entirely ! div]se circum/ances 9 :i* ! quality may appe>4 ,x is ! concrete notion 99?ree h>d objects991 :i* ass]ts ! exi/5ce ( h>dness along ) suffici5t o!r undef9$ qualities1 to m>k out 99?ree99 su* objects4 ,num]ical ?\ght is inde$ closely int]wov5 ) logical ?\ght4 ,we _c use a concrete t]m 9 ! plural1 z 99m5991 )\t imply+ t !re are m>ks ( diff]5ce4 ,b :5 we use an ab/ract t]m1 we deal ) unity4 ,! orig9 ( ! great g5]ality ( numb] is n[ app>5t4 ,?ree s\nds diff] f ?ree col\rs1 or ?ree rid]s f ?ree horses2 b !y agree 9 respect ( ! v>iety ( m>ks by :i* !y c be discrim9at$4 ,! symbols #a #a #a are ?us ! empty m>ks ass]t+ ! exi/5ce ( discrim9ation4 ,b 9 dropp+ out ( sight ! "* ( ! diff]5ces we give rise to new agreem5ts on :i* ma!matical reason+ is f\nd$4 ,num]ical ab/raction is s f> f be+ incompatible ) logical ab/raction t x is ! orig9 ( our wide/ acts ( g5]alization4 99,concrete & ,ab/ract ,numb]499 ,! common di/9ction betwe5 concrete & ab/ract numb] c n[ be easily /at$4 ,9 proportion z we specify ! logical *>act]s ( ! ?+s numb]$1 we r5d] !m concrete4 ,9 ! ab/ract numb] ?ree !re is no /atem5t ( ! po9ts 9 :i* ! 99?ree99 objects agree2 b 9 99?ree co9s991 99?ree m5991 or 99?ree horses991 n only are ! objects numb]$ b _! nature is re/rict$4 ,concrete numb] ?us implies ! same consci\sness ( diff]5ce z ab/ract numb]1 b x is m+l$ ) a gr\ndwork ( simil>ity express$ 9 ! logical t]ms4 ,!re is id5tity s f> z logical t]ms ent]2 diff]5ce s f> z ! t]ms are m]ely num]ical4 ,! reason ( ! important ,law ( ,homog5eity w n[ be app>5t4 ,?is law ass]ts t 9 e ari?metical calculation ! logical nature ( ! ?+s numb]$ mu/ rema9 unalt]$4 ,! specifi$ logical agreem5t ( ! ?+s mu/ n be affect$ by ! unspecifi$ num]ical diff]5ces4 ,a calculation w\ld be palpably absurd :i*1 aft] comm5c+ ) l5g?1 gave a result 9 h\rs4 ,x is equally absurd1 9 a purely ari?metical po9t ( view1 to d$uce areas f ! calculation ( l5g?s1 masses f ! comb9ation ( volume & d5sity1 or mom5ta f mass & velocity4 ,x mu/ rema9 = subsequ5t consid]ation to decide 9 :at s5se we may truly say t two l9e> feet multipli$ by two l9e> feet give f\r sup]ficial feet2 ari?metically x is absurd1 because !re is a *ange ( unit4 ,z a g5]al rule we treat 9 ea* calculation only objects ( "o nature4 ,we d n1 & _c prop]ly add1 9 ! same sum y>ds ( clo? & p\nds ( sug>4 ,we _c ev5 conceive ! result ( add+ area to velocity1 or l5g? to d5sity1 or weight to value4 ,! units add$ mu/ h a basis ( homog5eity1 or mu/ be r$ucible to "s common d5om9ator4 ,nev]!less x is possible1 & 9 fact common1 to treat 9 "o complex calculation ! mo/ het]og5e\s quantities1 on ! condition t ea* k9d ( object is kept di/9ct1 & treat$ num]ically only 9 conjunction ) its own k9d4 ,diff]5t units1 s f> z _! logical diff]5ces are specifi$1 mu/ nev] be sub/itut$ "o = ! o!r4 ,*emi/s cont9ually use equations :i* ass]t ! equival5ce ( gr\ps ( atoms4 ,ord9>y f]m5tation is repres5t$ by ! =mula ,c#f ,h#ab ,o#f #b;,c#b ,h#f ,o #b;,,co#b4 ,?ree k9ds ( units1 ! atoms respectively ( c>bon1 hydrog51 & oxyg51 are "h int]m+l$1 b !re is really a sep>ate equation 9 reg>d to ea* k9d4 ,ma!maticians also employ comp\nd equations ( ! same k9d2 = 91 99a99 99b99 - #a 99c99 99d99 - #a1 x is impossible by ord9>y addition to add 99a99 to 99b99 - #a4 ,h5ce we really h ! sep>ate equations 99a99 99b991 & 99c99 - #a 99d99 - #a4 ,simil>ly an equation betwe5 two quat]nions is equival5t to f\r equations betwe5 ord9>y quantities1 :5ce inde$ ! "n 99quat]nion994 99,analogy ( ,logical & ,num]ical ,t]ms499 ,if my ass]tion is correct t numb] arises out ( logical conditions1 we ought to f9d numb] obey+ all ! laws ( logic4 ,x is almo/ sup]flu\s to po9t out t ?is is ! case ) ! fundam5tal laws ( id5tity & diff]5ce1 & x only rema9s to %[ t ma!matical symbols d really obey ! special conditions ( logical symbols :i* 7 =m]ly po9t$ out 7p4 #cb74 ,?us ! ,law ( ,commutativ5ess1 is equally true ( quality & quantity4 ,z 9 logic we h ,,ab ,,ba1 s 9 ma!matics x is famili>ly kn[n t #b #c #c #b1 or 99x99 99y99 99y99 99x994 ,! prop]ties ( space are z indiff]5t 9 multiplication z we f\nd !m 9 pure logical ?\ght4 ,simil>ly1 z 9 logic triangle or squ>e squ>e or triangle1 or g5]ally ,a ,b ,b ,a1 s 9 quantity #b #c #c #b1 or g5]ally 99x99 99y99 99y99 99x994 ,! symbol is n id5tical ) 1 b x is ?us f> analog\s4 ,h[ f>1 n[1 is x true t ma!matical symbols obey ! ,law ( ,simplicity express$ 9 ! =m ,,aa ,a1 or ! example ,r\nd r\nd r\nd8 ,app>5tly !re are b two numb]s :i* obey ?is law2 = x is c]ta9 t 99x99 99x99 99x99 is true only 9 ! two cases :5 99x99 #a1 or 99x99 #j4 ,9 reality all numb]s obey ! law1 = #b #b #b is n really analog\s to ,,aa ,a4 ,accord+ to ! def9ition ( a unit already giv51 ea* unit is discrim9at$ f ea* o!r 9 ! same problem1 s t 9 #b #b1 ! fir/ 99two99 involves a diff]5t discrim9ation f ! second 99two994 ,i get f\r k9ds ( ?+s1 = in/ance1 if ,i fir/ discrim9ate 8heavy & light0 & !n 8cubical & sph]ical10 = we n[ h ! foll[+ classes-- heavy1 cubical4 light1 cubical4 heavy1 sph]ical4 light1 sph]ical4 ,b suppose t my two classes are 9 bo? cases discrim9at$ by ! same diff]5ce ( light & heavy1 !n we h heavy heavy heavy1 heavy light #j1 light heavy #j1 light light light4 ,?us1 7heavy or light7 7heavy or light7 7heavy or light74 ,9 %ort1 99twice two is two99 unless we take c>e t ! second two has a diff]5t mean+ f ! fir/4 ,b "u simil> circum/ances logical t]ms give ! l result1 & x is n true t ,a,a ,a1 :5 ,a is diff]5t 9 mean+ f ,a4 ,9 a simil> mann] x may be %[n t ! ,law ( ,unity ,a ,a ,a4 holds true alike ( logical & ma!matical t]ms4 ,x is absurd inde$ to say t 99x99 99x99 99x99 except 9 ! "o case :5 99x99 absolute z]o4 ,b ?is contradiction 99x99 99x99 99x99 arises f ! fact t we h already def9$ ! units 9 "o x z diff]+ f ^? 9 ! o!r4 ,"u su* circum/ances ! ,law ( ,unity does n apply4 ,= if 9 ,a ,a ,a we mean t ,a is 9 any way diff]5t f ,a ! ass]tion ( id5tity is evid5tly false4 ,! contra/ !n :i* seems to exi/ betwe5 logical & ma!matical symbols is only app>5t4 ,x is because ! ,laws ( ,simplicity & ,unity mu/ always be obs]v$ 9 ! op]ation ( c\nt+ t ^? laws seem no fur!r to apply4 ,?is is ! und]/ood condition "u :i* we use all num]ical symbols4 ,:5ev] ,i write ! symbol #e ,i really mean #a #a #a #a #a1 & x is p]fectly und]/ood t ea* ( ^! units is di/9ct f ea* o!r4 ,if requisite ,i might m>k !m ?us #a #a #a #a #a4 ,7 ?is n ! case & 7 ! units really #a #a #a #a #a1 ! ,law ( ,unity w\ld1 z be=e rem>k$1 apply1 & #a #a #a4 ,ma!matical symbols !n obey all ! laws ( logical symbols1 b two ( ^! laws seem to be inapplicable simply because !y are presuppos$ 9 ! def9ition ( ! ma!matical unit4 ,logic ?us lays d[n ! conditions ( numb]1 & ! sci5ce ( ari?metic develop$ z x is into all ! wondr\s bran*es ( ma!matical calculus is b an outgr[? ( logical discrim9ation4 99,pr9ciple ( ,ma!matical ,inf]5ce499 ,! univ]sal pr9ciple ( all reason+1 z ,i h ass]t$1 is t :i* all[s u to sub/itute l = l4 ,i h n[ to po9t out h[ 9 ! ma!matical sci5ces ?is pr9ciple is involv$ 9 ea* /ep ( reason+4 ,x is 9 ^! sci5ces inde$ t we meet ) ! cle>e/ cases ( sub/itution1 & x is ! simplicity ) :i* ! pr9ciple c be appli$ :i* probably l$ to ! comp>atively e>ly p]fection ( ! sci5ces ( geometry & ari?metic4 ,euclid1 & ! ,greek ma!maticians f ! fir/1 recognis$ 99equality99 z ! fundam5tal relation ( quantitative ?\ght1 b ,ari/otle reject$ ! exactly analog\s1 b f> m g5]al relation ( id5tity1 & ?us crippl$ ! =mal sci5ce ( logic z x has desc5d$ to ! pres5t day4 ,geometrical reason+ />ts f ! axiom t 8?+s equal to ! same ?+ are equal to ea* o!r40 ,two equalities enable u to inf] a ?ird equality2 & ?is is true n only ( l9es & angles1 b ( areas1 volumes1 numb]s1 int]vals ( "t1 =ces1 velocities1 degrees ( int5sity1 or1 9 %ort1 any?+ :i* is capable ( be+ equal or unequal4 ,two />s equally bright ) ! same /> mu/ be equally bright ) ea* o!r1 & two =ces equally int5se ) a ?ird =ce are equally int5se ) ea* o!r4 ,x is rem>kable t ,euclid has n explicitly /at$ two o!r axioms1 ! tru? ( :i* is necess>ily impli$4 ,! second axiom %\ld be t 8,two ?+s ( :i* "o is equal & ! o!r unequal to a ?ird common ?+1 are unequal to ea* o!r40 ,an equality & inequality1 9 %ort1 give an inequality1 & ?is is equally true ) ! fir/ axiom ( all k9ds ( quantity4 ,if ,v5us1 = in/ance1 agrees ) ,m>s 9 d5sity1 b ,m>s diff]s f ,jupit]1 !n ,v5us diff]s f ,jupit]4 ,a ?ird axiom mu/ exi/ to ! effect t 8,?+s unequal to ! same ?+ may or may n be equal to ea* o!r40 99,two inequalities give no gr\nd ( inf]5ce :atev]499 ,if we only "k1 = in/ance1 t ,m]cury & ,jupit] diff] 9 d5sity f ,m>s1 we _c say :e!r or n !y agree betwe5 !mselves4 ,z a fact !y d n agree2 b ,v5us & ,m>s on ! o!r h& bo? diff] f ,jupit] & yet closely agree ) ea* o!r4 ,! =ce ( ! axioms c be mo/ cle>ly illu/rat$ by draw+ equal & unequal l9es4#ia #ia 99,elem5t>y ,lessons 9 ,logic99 7,macmillan71 p4 #abc4 ,x is po9t$ out 9 ! preface to ?is ,second ,edition1 t ! views "h giv5 7 p>tially /at$ by ,leibnitz4 ,! g5]al conclusion !n mu/ be t :]e !re is equality !re may be inf]5ce1 b :]e !re is n equality !re _c be inf]5ce4 ,a pla9 induction w lead u to believe t 99equality is ! condition ( inf]5ce conc]n+ quantity994 ,all ! ?ree axioms may 9 fact be summ$ up 9 "o1 to ! effect1 t 8999 :atev] relation "o quantity /&s to ano!r1 x /&s 9 ! same relation to ! equal ( t o!r9940 ,! active p[] is always ! sub/itution ( equals1 & x is an accid5t t 9 a pair ( equalities we c make ! sub/itution 9 two ways4 ,f 99a99 99b99 99c99 we c inf] 99a99 99c991 ei!r by sub/itut+ 9 99a99 99b99 ! value ( 99b99 z giv5 9 99b99 99c991 or else by sub/itut+ 9 99b99 99c99 ! value ( 99b99 z giv5 9 99a99 99b994 ,9 99a99 99b99 99d99 we c make b ! "o sub/itution ( 99a99 = 99b994 ,9 99e99 99f99 99g99 we c make no sub/itution & get no inf]5ce4 ,9 ma!matics ! relations 9 :i* t]ms may /& to ea* o!r are f> m v>i$ ?an 9 pure logic1 yet our pr9ciple ( sub/itution always holds true4 ,we may say 9 ! mo/ g5]al mann] t 99,9 :atev] relation "o quantity /&s to ano!r1 x /&s 9 ! same relation to ! equal ( t o!r499 ,9 ?is axiom we sum up a numb] ( axioms :i* h be5 /at$ 9 m or less detail by algebrai/s4 ,?us1 8,if equal quantities be add$ to equal quantities1 ! sums w be equal40 ,to expla9 ?is1 let 99a99 99b991 99c99 99d994 ,n[ 99a99 99c991 :atev] x means1 mu/ be id5tical ) itself1 s t 99a99 99c99 99a99 99c994 ,9 "o side ( ?is equation sub/itute = ! quantities _! equival5ts1 & we h ! axiom prov$ 99a99 99c99 99b99 99d994 ,! simil> axiom conc]n+ subtraction is equally evid5t1 = :atev] 99a99 - 99c99 may mean x is equal to 99a99 - 99c991 & !re=e by sub/itution to 99b99 - 99d994 ,aga91 8if equal quantities be multipli$ by ! same or equal quantities1 ! products w be equal10 ,= evid5tly 99ac99 99ac991 & if = 99c99 9 "o side we sub/itute its equal 99d991 we h 99ac99 99ad991 & a second simil> sub/itution gives u 99ac99 99bd994 ,we might prove a l axiom conc]n+ division 9 an exactly simil> mann]4 ,i might ev5 ext5d ! li/ ( axioms & say t 8,equal p[]s ( equal numb]s are equal40 ,= c]ta9ly1 :atev] 99a99 99a99 99a99 may mean1 x is equal to 99a99 99a99 99a992 h5ce by our usual sub/itution x is equal to 99b99 99b99 99b994 ,! same w be true ( roots ( numb]s & c99a99 d99b99 provid$ t ! roots are s tak5 t ! root ( 99a99 %all really be relat$ to 99a99 z ! root ( 99b99 is to 99b994 ,! ambiguity ( mean+ ( an op]ation ?us fails 9 any way to %ake ! univ]sality ( ! pr9ciple4 ,we may g fur!r & ass]t t1 n only ! above common relations1 b all o!r kn[n or conceivable ma!matical relations obey ! same pr9ciple4 ,let ,q99a99 d5ote 9 ! mo/ g5]al mann] t we d some?+ ) ! quantity 99a992 !n if 99a99 99b99 x foll[s t ,q99a99 ,q99b994 ,! read] w also rememb] t "o ( ! mo/ frequ5t op]ations 9 ma!matical reason+ is to sub/itute = a quantity its equal1 z kn[n ei!r by assum$1 natural1 or self-evid5t conditions4 ,:5ev] a quantity appe>s twice ov] 9 a problem1 we may apply :at we le>n ( its relations 9 "o place to its relations 9 ! o!r4 ,all reason+ 9 ma!matics1 z 9 o!r bran*es ( sci5ce1 ?us involves ! pr9ciple ( treat+ equals equally1 or simil>s simil>ly4 ,9 :atev] way we employ quantitative reason+ 9 ! rema9+ p>ts ( ?is "w1 we nev] c des]t ! simple pr9ciple on :i* we fir/ set out4 99,reason+ by ,inequalities499 ,i h /at$ t all ! processes ( ma!matical reason+ may be d$uc$ f ! pr9ciple ( sub/itution4 ,exceptions to ?is ass]tion may seem to exi/ 9 ! use ( inequalities4 ,! great] ( a great] is und\bt$ly a great]1 & :at is less ?an a less is c]ta9ly less4 ,sn[don is high] ?an ! ,wrek91 & ,b5 ,nevis ?an ,sn[don2 !re=e ,b5 ,nevis is high] ?an ! ,wrek94 ,b a little consid]ation discloses suffici5t reason = believ+ t ev5 9 su* cases1 :]e equality does n app>5tly ent]1 ! =ce ( ! reason+ entirely dep5ds ^u und]ly+ & impli$ equalities4 ,9 ! fir/ place1 two /atem5ts ( m]e diff]5ce d n give any gr\nd ( inf]5ce4 ,we le>n no?+ conc]n+ ! comp>ative heights ( ,/4 ,paul's & ,we/m9/] ,abbey f ! ass]tions t !y bo? diff] 9 height f ,/4 ,pet]'s at ,rome4 ,we ne$ some?+ m ?an inequality2 we require "o id5tity 9 addition1 namely ! id5tity 9 direction ( ! two diff]5ces4 ,?us we _c employ inequalities 9 ! simple way 9 :i* we d equalities1 &1 :5 we try to express :at o!r conditions are requisite1 we f9d ourselves laps+ into ! use ( equalities or id5tities4 ,9 ! second place1 e argum5t by inequalities may be repres5t$ 9 ! =m ( equalities4 ,we express t 99a99 is great] ?an 99b99 by ! equation 99a99 99b99 99p991 7#a7 :]e 99p99 is an intr9sically positive quantity1 d5ot+ ! diff]5ce ( 99a99 & 99b994 ,simil>ly we express t 99b99 is great] ?an 99c99 by ! equation 99b99 99c99 99q991 7#b7 & sub/itut+ = 99b99 9 7#a7 its value 9 7#b7 we h 99a99 99c99 99q99 99p994 7#c7 ,n[ z 99p99 & 99q99 are bo? positive1 x foll[s t 99a99 is great] ?an 99c991 & we h ! exact am\nt ( excess specifi$4 ,x w be easily se5 t ! reason+ conc]n+ t :i* is less ?an a less w result 9 an equation ( ! =m 99c99 99a99 - 99r99 - 99s994 ,e argum5t by inequalities may !n be ?r[n into ! =m ( an equality2 b ! conv]se is n true4 ,we _c possibly prove t two quantities are equal by m]ely ass]t+ t !y are bo? great] or bo? less ?an ano!r quantity4 ,f 99e99 99f99 & 99g99 99f991 or 99e99 99f99 & 99g99 99f991 we c inf] no relation betwe5 99e99 & 99g994 ,& if ! read] take ! equations 99x99 99y99 #c & attempt to prove t !re=e 99x99 #c1 by ?r[+ !m into inequalities1 he w f9d x impossible to d s4 ,f ^! consid]ations ,i ga!r t reason+ 9 ari?metic or algebra by s-call$ inequalities1 is only an imp]fectly express$ reason+ by equalities1 & :5 we want to exhibit exactly & cle>ly ! conditions ( reason+1 we are oblig$ to use equalities explicitly4 ,j z 9 pure logic a negative proposition1 z express+ m]e diff]5ce1 _c be ! means ( inf]5ce1 s inequality c nev] really be ! true gr\nd ( inf]5ce4 ,i d n d5y t affirmation & negation1 agreem5t & diff]5ce1 equality & inequality1 are pairs ( equally fundam5tal relations1 b ,i ass]t t inf]5ce is possible only :]e affirmation1 agreem5t1 or equality1 "s species ( id5tity 9 fact1 is pres5t1 explicitly or implicitly4 99,ari?metical ,reason+499 ,x may seem some:at inconsi/5t t ,i ass]t numb] to arise out ( diff]5ce or discrim9ation1 & yet hold t no reason+ c be gr\nd$ on diff]5ce4 ,numb]1 ( c\rse1 op5s a mo/ wide sph]e = inf]5ce1 & a little consid]ation %[s t ?is is due to ! unlimit$ s]ies ( id5tities :i* spr+ up out ( num]ical ab/raction4 ,if six p are sitt+ on six *airs1 !re is no resemblance betwe5 ! *airs & ! p 9 logical "*4 ,b if we ov]look all ! qualities bo? ( a *air & a p]son & m]ely rememb] t !re are m>ks by :i* ea* ( six *airs may be discrim9at$ f ! o!rs1 & simil>ly ) ! p1 !n !re arises a resemblance betwe5 ! *airs & ! p1 & ?is resemblance 9 numb] may be ! gr\nd ( inf]5ce4 ,if on ano!r occasion ! *airs are fill$ by p aga91 we may inf] t ^! p resemble ! o!rs 9 numb] ?\gh !y ne$ n resemble !m 9 any o!r po9ts4 ,gr\ps ( units are :at we really treat 9 ari?metic4 ,! numb] 99five99 is really #a #a #a #a #a1 b = ! sake ( concis5ess we sub/itute ! m compact sign #e1 or ! "n 99five994 ,^! names be+ arbitr>ily impos$ 9 any "o mann]1 an inf9ite v>iety ( relations spr+ up betwe5 !m :i* are n 9 ! lea/ arbitr>y4 ,if we def9e 99f\r99 z #a #a #a #a1 & 99five99 z #a #a #a #a #a1 !n ( c\rse x foll[s t 99five99 99f\r99 #a2 b x w\ld be equally possible to take ?is latt] equality z a def9ition1 9 :i* case "o ( ! =m] equalities w\ld become an inf]5ce4 ,x is h>dly requisite to decide h[ we def9e ! names ( numb]s1 provid$ we rememb] t out ( ! inf9itely num]\s relations ( "o numb] to o!rs1 "s "o relation express$ 9 an equality mu/ be a def9ition ( ! numb] 9 "q & ! o!r relations imm$iately become necess>y inf]5ces4 ,9 ! sci5ce ( numb] ! v>iety ( classes :i* c be =m$ is altoge!r inf9ite1 & /atem5ts ( p]fect g5]ality may be made subject only to difficulty or exception at ! l[] end ( ! scale4 ,e exi/+ numb] = in/ance belongs to ! class 99m99 #g2 t is1 e numb] mu/ be ! sum ( ano!r numb] & sev51 except ( c\rse ! fir/ six or sev5 numb]s1 negative quantities n be+ "h tak5 into acc\nt4 ,e numb] is ! half ( "s o!r1 & s on4 ,! subject ( g5]alization1 z exhibit$ 9 ma!matical tru?s1 is an inf9itely wide "o4 ,9 numb] we are only at ! fir/ /ep ( an ext5sive s]ies ( g5]alizations4 ,z numb] is g5]al comp>$ ) ! p>ticul> ?+s numb]$1 s we h g5]al symbols = numb]s1 & g5]al symbols = relations betwe5 undet]m9$ numb]s4 ,!re is an unlimit$ hi]>*y ( successive g5]alizations4 99,num]ically ,def9ite ,reason+499 ,x 0 fir/ discov]$ by ,de ,morgan t _m argum5ts are valid :i* comb9e logical & num]ical reason+1 al?\gh !y _c be includ$ 9 ! anci5t logical =mulas4 ,he develop$ ! doctr9e ( ! 8,num]ically ,def9ite ,syllogism10 fully expla9$ 9 8 99,=mal ,logic99 7pp4 #ada-agj74 ,boole also devot$ consid]able att5tion to ! det]m9ation ( :at he call$ 8,/ati/ical ,conditions10 mean+ ! num]ical conditions ( logical classes4 ,9 a pap] publi%$ among ! ,memoirs ( ! ,man*e/] ,lit]>y & ,philosophical ,society1 ,?ird ,s]ies1 vol4 ,,iv4 p4 #ccj 7,session #ahfi-gj71 ,i h po9t$ out t we c apply ari?metical calculation to ! ,logical ,alphabet4 ,hav+ giv5 c]ta9 logical conditions & ! numb]s ( objects 9 c]ta9 classes1 we c ei!r det]m9e ! numb]s ( objects 9 o!r classes gov]n$ by ^? conditions1 or c %[ :at fur!r data are requir$ to det]m9e !m4 ,z an example ( ! k9d ( que/ions treat$ 9 num]ical logic1 & ! mode ( treatm5t1 ,i give ! foll[+ problem sugge/$ by ,de ,morgan1 ) my mode ( repres5t+ its solution4 8,= e man 9 ! h\se !re is a p]son :o is ag$2 "s ( ! m5 are n ag$4 ,x foll[s t "s p]sons 9 ! h\se are n m540#ib #ib 99,syllabus ( a ,propos$ ,sy/em ( ,logic991 p4 #bi4 ,n[ let ,a p]son 9 h\se1 ,b male1 ,c ag$4 ,by enclos+ a logical symbol 9 brackets1 let u d5ote ! numb] ( objects belong+ to ! class indicat$ by ! symbol4 ,?us let 7,a7 numb] ( p]sons 9 h\se1 7,,ab7 numb] ( male p]sons 9 h\se1 7,,abc7 numb] ( ag$ male p]sons 9 h\se1 & s on4 ,n[ if we use 99w99 & 99w99 to d5ote unkn[n numb]s1 ! conditions ( ! problem may be ?us /at$ accord+ to my int]pretation ( ! words-- 7,,ab7 7,,ac7 - 99w991 7#a7 t is to say1 ! numb] ( p]sons 9 ! h\se :o are ag$ is at lea/ equal to1 & may exce$1 ! numb] ( male p]sons 9 ! h\se2 7,,ab99c997 99w991 7#b7 t is to say1 ! numb] ( male p]sons 9 ! h\se :o are n ag$ is "s unkn[n positive quantity4 ,if we develop ! t]ms 9 7#a7 by ! ,law ( ,duality 7pp4 #gd1 #ha1 #hi71 we obta9 7,,abc7 7,,ab99c997 7,,abc7 7,a99b99,c7 - 99w994 ,subtract+ ! common t]m 7,,abc7 f ea* side & sub/itut+ = 7,,ab99c997 its value z giv5 9 7#b71 we get at once 7,a99b99,c7 99w99 99w991 & add+ 7,a99bc997 to ea* side1 we h 7,a99b997 7,a99bc997 99w99 99w994 ,! mean+ ( ?is result is t ! numb] ( p]sons 9 ! h\se :o are n m5 is at lea/ equal to 99w99 99w991 & exce$s x by ! numb] ( p]sons 9 ! h\se :o are nei!r m5 nor ag$ 7,a99bc9974 ,x %\ld be und]/ood t ?is solution applies only to ! t]ms ( ! example quot$ above1 & n to ! g5]al problem = :i* ,de ,morgan int5d$ x to s]ve z an illu/ration4 ,z a second in/ance1 let u take ! foll[+ "q3--,! :ole numb] ( vot]s 9 a bor\gh is 99a992 ! numb] aga9/ :om objections h be5 lodg$ by lib]als is 99b992 & ! numb] aga9/ :om objections h be5 lodg$ by cons]vatives is 99c992 requir$ ! numb]1 if any1 :o h be5 object$ to on bo? sides4 ,tak+ ,a vot]1 ,b object$ to by lib]als1 ,c object$ to by cons]vatives1 !n we require ! value ( 7,,abc74 ,n[ ! foll[+ equation is id5tically true-- 7,,abc7 7,,ab7 7,,ac7 7,a99bc997 - 7,a74 7#a7 ,= if we develop all ! t]ms on ! second side we obta9 7,,abc7 7,,abc7 7,,ab99c997 7,,abc7 7,a99b99,c7 7,a99bc997 - 7,,abc7 - 7,,ab99c997 - 7,a99b99,c7 - 7,a99bc9972 & /rik+ out ! correspond+ positive & negative t]ms1 we h left only 7,,abc7 7,,abc74 ,s9ce !n 7#a7 is necess>ily true1 we h only to ins]t ! kn[n values1 & we h 7,,abc7 99b99 99c99 - 99a99 7,a99bc9974 ,h5ce ! numb] :o h receiv$ objections f bo? sides is equal to ! excess1 if any1 ( ! :ole numb] ( objections ov] ! numb] ( vot]s toge!r ) ! numb] ( vot]s :o h receiv$ no objection 7,a99bc9974 ,! foll[+ problem illu/rates ! expression = ! common "p ( any ?ree classes3--,! numb] ( paup]s :o are bl9d males1 is equal to ! excess1 if any1 ( ! sum ( ! :ole numb] ( bl9d p]sons1 add$ to ! :ole numb] ( male p]sons1 add$ to ! numb] ( ^? :o be+ paup]s are nei!r bl9d nor males1 above ! sum ( ! :ole numb] ( paup]s add$ to ! numb] ( ^? :o1 n be+ paup]s1 are bl9d1 & to ! numb] ( ^? :o1 n be+ paup]s1 are male4 ,! read] is reque/$ to prove ! tru? ( ! above /atem5t1 7#a7 by 8 own unaid$ common s5se2 7#b7 by ! ,ari/otelian ,logic2 7#c7 by ! me?od ( num]ical logic j exp\nd$2 & !n to decide :i* me?od is mo/ satisfactory4 99,num]ical mean+ ( ,logical ,conditions499 ,9 _m cases classes ( objects may exi/ "u special logical conditions1 & we mu/ consid] h[ ^! conditions c be int]pret$ num]ically4 ,e logical proposition gives rise to a correspond+ num]ical equation4 ,sam5ess ( qualities occasions sam5ess ( numb]s4 ,h5ce if ,a ,b d5otes ! id5tity ( ! qualities ( ,a & ,b1 we may conclude t 7,a7 7,b74 ,x is evid5t t exactly ^? objects1 & ^? objects only1 :i* are compreh5d$ "u ,a mu/ be compreh5d$ "u ,b4 ,x foll[s t :]ev] we c draw an equation ( qualities1 we c draw a simil> equation ( numb]s4 ,?us1 f ,a ,b ,c we inf] ,a ,c2 & simil>ly f 7,a7 7,b7 7,c71 mean+ t ! numb]s ( ,a's & ,c's are equal to ! numb] ( ,b's1 we c inf] 7,a7 7,c74 ,b1 curi\sly en\gh1 ?is does n apply to negative propositions & inequalities4 ,= if ,a ,b ,d means t ,a is id5tical ) ,b1 :i* diff]s f ,d1 x does n foll[ t 7,a7 7,b7 7,d74 ,two classes ( objects may diff] 9 qualities1 & yet !y may agree 9 numb]4 ,?is po9t /rongly confirms me 9 ! op9ion :i* ,i h already express$1 t all inf]5ce really dep5ds ^u equations1 n diff]5ces4 ,! ,logical ,alphabet ?us enables u to make a complete analysis ( any num]ical problem1 & ?\gh ! symbolical /atem5t may sometimes seem prolix1 ,i conceive t x really repres5ts ! c\rse :i* ! m9d mu/ foll[ 9 solv+ ! "q4 ,al?\gh ?\ght may out/rip ! rapidity ) :i* ! symbols c be writt5 d[n1 yet ! m9d does n really foll[ a diff]5t c\rse f t indicat$ by ! symbols4 ,= a full] explanation ( ?is natural sy/em ( ,num]ically ,def9ite ,reason+1 ) m abundant illu/rations & an analysis ( ,de ,morgan's ,num]ically ,def9ite ,syllogism1 ,i mu/ ref] ! read] to ! pap]#ic 9 ! ,memoirs ( ! ,man*e/] ,lit]>y & ,philosophical ,society1 already m5tion$1 portions ( :i*1 h[ev]1 h be5 embodi$ 9 ! pres5t section4 #ic ,x has be5 po9t$ out to me by ,mr4 ,c4 ,j4 ,monroe1 t section #ad 7p4 #cci7 ( ?is pap] is errone\s1 & ought to be cancell$4 ,! problem conc]n+ ! numb] ( paup]s illu/rates ! answ] :i* %\ld h be5 obta9$4 ,mr4 ,a4 ,j4 ,ellis1 ,f4,r4,s41 _h previ\sly obs]v$ t my solution 9 ! pap] ( ,de ,morgan's problem ab\t 8m5 9 ! h\se0 did n answ] ! conditions int5d$ by ,de ,morgan1 & ,i !re=e give 9 ! text a m satisfactory solution4 ,! read] may be ref]r$1 also1 to ,boole's writ+s ^u ! subject 9 ! 99,laws ( ,?\ght991 *ap4 xix4 p4 #bie1 & 9 a pap] on 8,propositions ,num]ically ,def9ite10 communicat$ by ,de ,morgan1 9 #ahfh1 to ! ,cambridge ,philosophical ,society1 & pr9t$ 9 _! 99,transactions991 vol4 xi4 "p ii4 ,,*apt] ,,ix4 ,,! ,,v>iety ,,( ,,nature1 ,,or ,,! ,,doctr9e ,,( ,,comb9ations ,,& ,,p]mutations4 ,nature may be said to be evolv$ f ! monotony ( non-exi/5ce by ! creation ( div]sity4 ,x is plausibly ass]t$ t we are consci\s only s f> z we exp]i5ce diff]5ce4 ,life is *ange1 & p]fectly uni=m exi/5ce w\ld be no bett] ?an non-exi/5ce4 ,c]ta9 x is t life dem&s incessant novelty1 & t nature1 ?\gh x probably nev] fails to obey ! same fix$ laws1 yet pres5ts to u an app>5tly unlimit$ s]ies ( v>i$ comb9ations ( ev5ts4 ,x is ! "w ( sci5ce to obs]ve & record ! k9ds & comp>ative numb]s ( su* comb9ations ( ph5om5a1 occurr+ spontane\sly or produc$ by our int]f]5ce4 ,pati5t & skilful exam9ation ( ! records may !n disclose ! laws impos$ on matt] at its creation1 & enable u m or less successfully to pr$ict1 or ev5 to regulate1 ! future occurr5ce ( any p>ticul> comb9ation4 ,! ,laws ( ,?\ght are ! fir/ & mo/ important ( all ! laws :i* gov]n ! comb9ations ( ph5om5a1 &1 ?\gh !y be b9d+ on ! m9d1 !y may also be reg>d$ z v]ifi$ 9 ! ext]nal _w4 ,! ,logical ,alphabet develops ! utmo/ v>iety ( ?+s & ev5ts :i* may occur1 & x is evid5t t z ea* new quality is introduc$1 ! numb] ( comb9ations is d\bl$4 ,?us f\r qualities may occur 9 #af comb9ations2 five qualities 9 #cb2 six qualities 9 #fd2 & s on4 ,9 g5]al language1 if n be ! numb] ( qualities1 #bn is ! numb] ( v>ieties ( ?+s :i* may be =m$ f !m1 if !re be no conditions b ^? ( logic4 ,?is numb]1 x ne$ h>dly be said1 increases aft] ! fir/ few t]ms1 9 an extraord9>y mann]1 s t x w\ld require #cjb figures to express ! numb] ( comb9ations 9 :i* #a1jjj qualities might conceivably pres5t !mselves4 ,if all ! comb9ations all[$ by ! ,laws ( ,?\ght occurr$ indiff]5tly 9 nature1 !n sci5ce w\ld beg9 & end ) ^? laws4 ,to obs]ve nature w\ld give u no additional k1 because no two qualities w\ld 9 ! long run be (t5] associat$ ?an any o!r two4 ,we c\ld nev] pr$ict ev5ts ) m c]ta9ty ?an we n[ pr$ict ! ?r[s ( dice1 & exp]i5ce w\ld be )\t use4 ,b ! univ]se1 z actually creat$1 pres5ts a f> diff]5t & mu* m int]e/+ problem4 ,! mo/ sup]ficial obs]vation %[s t "s ?+s are con/antly associat$ ) o!r ?+s4 ,! m mature our exam9ation1 ! m we become conv9c$ t ea* ev5t dep5ds ^u ! prior occurr5ce ( "s o!r s]ies ( ev5ts4 ,action & reaction are gradually discov]$ to und]lie ! :ole sc5e1 & an indep5d5t or casual occurr5ce does n exi/ except 9 appe>ance4 ,ev5 dice z !y fall are surely det]m9$ 9 _! c\rse by prior conditions & fix$ laws4 ,?us ! comb9ations ( ev5ts :i* c really occur are f\nd to be comp>atively re/rict$1 & x is ! "w ( sci5ce to detect ^! re/rict+ conditions4 ,9 ! ,engli% alphabet1 = in/ance1 we h tw5ty-six lett]s4 ,7 ! comb9ations ( su* lett]s p]fectly free1 s t any lett] c\ld be indiff]5tly s\nd$ ) any o!r1 ! numb] ( words :i* c\ld be =m$ )\t any repetition w\ld be #bbf - #a1 or #fg1ajh1hfc1 equal 9 numb] to ! comb9ations ( ! tw5ty-sev5? column ( ! ,logical ,alphabet1 exclud+ "o = ! case 9 :i* all ! lett]s w\ld be abs5t4 ,b ! =mation ( our vocal organs prev5ts u f us+ ! f> great] "p ( ^! conjunctions ( lett]s4 ,at lea/ "o v[el mu/ be pres5t 9 ea* ^w2 m ?an two consonants _c usually be br\ght toge!r2 & to produce words capable ( smoo? utt]ance a numb] ( o!r rules mu/ be obs]v$4 ,to det]m9e exactly h[ _m words might exi/ 9 ! ,engli% language "u ^! circum/ances1 w\ld be an exce$+ly complex problem1 ! solution ( :i* has nev] be5 attempt$4 ,! numb] ( exi/+ ,engli% words may p]haps be said n to exce$ "o hundr$ ?\s&1 & x is only by inve/igat+ ! comb9ations pres5t$ 9 ! diction>y1 t we c le>n ! ,laws ( ,euphony or calculate ! possible numb] ( words4 ,9 ?is example we h an epitome ( ! "w & me?od ( sci5ce4 ,! comb9ations ( natural ph5om5a are limit$ by a great numb] ( conditions :i* are 9 no way br\ght to our k except s f> z !y are disclos$ 9 ! exam9ation ( nature4 ,x is (t5 a v difficult matt] to det]m9e ! numb]s ( p]mutations or comb9ations :i* may exi/ "u v>i\s re/rictions4 ,_m le>n$ m5 puzzl$ !mselves 9 =m] c5turies ov] :at 7 call$ ,protean v]ses1 or v]ses admitt+ _m v>iations 9 accordance ) ! ,laws ( ,metre4 ,! mo/ celebrat$ ( ^! v]ses 0 t inv5t$ by ,b]n>d ,bauhusius1 z foll[s3#id-- 8,tot tibi sunt dotes1 ,virgo1 quot sid]a clo40 #id ,montucla1 99,hi/oire991 c41 vol4 iii4 p4 #chh4 ,"o au?or1 ,ericius ,puteanus1 fill$ =ty-eight pages ( a "w 9 reckon+ up its possible transpositions1 mak+ !m only #ajbb4 ,o!r calculators gave #baif1 #cbgf1 #behj z _! results4 ,wallis assign$ #cjif1 b )\t mu* confid5ce 9 ! accuracy ( 8 result4#ie ,x requir$ ! skill ( ,james ,b]n\lli to decide t ! numb] ( transpositions 0 #ccab1 "u ! condition t ! s5se & metre ( ! v]se %all be p]fectly pres]v$4 #ie ,wallis1 99,( ,comb9ations991 c41 p4 #aai4 ,9 approa*+ ! consid]ation ( ! great ,inductive problem1 x is v necess>y t we %\ld acquire correct notions z to ! comp>ative numb]s ( comb9ations :i* may exi/ "u diff]5t circum/ances4 ,! doctr9e ( comb9ations is t "p ( ma!matical sci5ce :i* applies num]ical calculation to det]m9e ! numb]s ( comb9ations "u v>i\s conditions4 ,x is a "p ( ! sci5ce :i* really lies at ! base n only ( o!r sci5ces1 b ( o!r bran*es ( ma!matics4 ,! =ms ( algebraical expressions are det]m9$ by ! pr9ciples ( comb9ation1 & ,h9d5burg recognis$ ?is fact 9 8 ,comb9atorial ,analysis4 ,! greate/ ma!maticians h1 dur+ ! la/ ?ree c5turies1 giv5 _! be/ p[]s to ! treatm5t ( ?is subject2 x 0 ! fav\rite /udy ( ,pascal2 x e>ly attract$ ! att5tion ( ,leibnitz1 :o wrote 8 curi\s essay1 99,de ,arte ,comb9atoria991 at tw5ty ye>s ( age2 ,james ,b]n\lli1 "o ( ! v pr(\nde/ ma!maticians1 devot$ no small "p ( 8 life to ! inve/igation ( ! subject1 z connect$ ) t ( ,probability2 & 9 8 celebrat$ "w1 99,de ,arte ,conject&i991 he has s f9ely describ$ ! importance ( ! doctr9e ( comb9ations1 t ,i ne$ (f] no excuse = quot+ 8 rem>ks at full l5g?4 8,x is easy to p]ceive t ! prodigi\s v>iety :i* appe>s bo? 9 ! works ( nature & 9 ! actions ( m51 & :i* con/itutes ! greate/ "p ( ! beauty ( ! univ]se1 is ow+ to ! multitude ( diff]5t ways 9 :i* its sev]al p>ts are mix$ )1 or plac$ ne>1 ea* o!r4 ,b1 because ! numb] ( causes t concur 9 produc+ a giv5 ev5t1 or effect1 is (t5times s imm5sely great1 & ! causes !mselves are s diff]5t "o f ano!r1 t x is extremely difficult to reckon up all ! diff]5t ways 9 :i* !y may be arrang$ or comb9$ toge!r1 x (t5 happ5s t m51 ev5 ( ! be/ und]/&+s & greate/ circumspection1 are guilty ( t fault 9 reason+ :i* ! writ]s on logic call 99! insuffici5t or imp]fect enum]ation ( p>ts or cases993 insomu* t ,i w v5ture to ass]t1 t ?is is ! *ief1 & almo/ ! only1 s\rce ( ! va/ numb] ( errone\s op9ions1 & ^? too v (t5 9 matt]s ( great importance1 :i* we are apt to =m on all ! subjects we reflect ^u1 :e!r !y relate to ! k ( nature1 or ! m]its & motives ( human actions4 8,x mu/ !re=e be ackn[l$g$1 t t art :i* af=ds a cure to ?is weakness1 or defect1 ( our und]/&+s1 & tea*es u s to enum]ate all ! possible ways 9 :i* a giv5 numb] ( ?+s may be mix$ & comb9$ toge!r1 t we may be c]ta9 t we h n omitt$ any "o arrangem5t ( !m t c lead to ! object ( our inquiry1 des]ves to be consid]$ z mo/ em95tly useful & wor?y ( our highe/ e/eem & att5tion4 ,& ?is is ! bus9ess ( 99! art or doctr9e ( comb9ations994 ,nor is ?is art or doctr9e to be consid]$ m]ely z a bran* ( ! ma!matical sci5ces4 ,= x has a relation to almo/ e species ( useful k t ! m9d ( man c be employ$ ^u4 ,x proce$s inde$ ^u ma!matical pr9ciples1 9 calculat+ ! numb] ( ! comb9ations ( ! ?+s propos$3 b by ! conclusions t are obta9$ by x1 ! sagacity ( ! natural philosoph]1 ! exactness ( ! hi/orian1 ! skill & judgm5t ( ! physician1 & ! prud5ce & =esight ( ! politician may be assi/$2 because ! bus9ess ( all ^! important pr(essions is b 99to =m reasonable conjectures99 conc]n+ ! sev]al objects :i* engage _! att5tion1 & all wise conjectures are ! results ( a j & c>eful exam9ation ( ! sev]al diff]5t effects t may possibly arise f ! causes t are capable ( produc+ !m40#if #if ,james ,b]n\lli1 99,de ,arte ,conject&i991 translat$ by ,b>on ,mas]es4 ,london1 #agie1 pp4 #ce1 #cf4 99,di/9ction ( ,comb9ations & ,p]mutations499 ,we mu/ fir/ consid] ! deep diff]5ce :i* exi/s betwe5 ,comb9ations & ,p]mutations1 a diff]5ce involv+ important logical pr9ciples1 & influ5c+ ! =m ( ma!matical expressions4 ,9 99p]mutation99 we recognise v>ieties ( ord]1 treat+ ,,ab z a diff]5t gr\p f ,,ba4 ,9 99comb9ation99 we take notice only ( ! pres5ce or abs5ce ( a c]ta9 ?+1 & pay no reg>d to its place 9 ord] ( "t or space4 ,?us ! f\r lett]s 99a991 99e991 99m991 99n99 c =m b "o comb9ation1 b !y occur 9 language 9 sev]al p]mutations1 z 99"n991 99am5991 99mean991 99mane994 ,we h hi!rto be5 deal+ ) purely logical que/ions1 involv+ only comb9ation ( qualities4 ,i h fully po9t$ out 9 m ?an "o place t1 ?\gh our symbols c\ld n b be writt5 9 ord] ( place & read 9 ord] ( "t1 ! relations express$ _h no reg>d to place or "t 7pp4 #cc1 #aad74 ,! ,law ( ,commutativ5ess1 9 fact1 expresses ! condition t 9 logic we deal ) comb9ations1 & ! same law is true ( all ! processes ( algebra4 ,9 "s cases1 ord] may be a matt] ( indiff]5ce2 x makes no diff]5ce1 = in/ance1 :e!r gunp[d] is a mixture ( sulphur1 c>bon1 & nitre1 or c>bon1 nitre1 & sulphur1 or nitre1 sulphur1 & c>bon1 provid$ t ! sub/ances are pres5t 9 prop] proportions & well mix$4 ,b ?is indiff]5ce ( ord] does n usually ext5d to ! ev5ts ( physical sci5ce or ! op]ations ( art4 ,! *ange ( me*anical en]gy into heat is n exactly ! same z ! *ange f heat into me*anical en]gy2 ?und] does n indiff]5tly prec$e & foll[ lightn+2 x is a matt] ( "s importance t we load1 cap1 pres5t1 & fire a rifle 9 ?is precise ord]4 ,"t is ! condition ( all our ?\ghts1 space ( all our actions1 & !re=e bo? 9 art & sci5ce we are to a great ext5t conc]n$ ) p]mutations4 ,language1 = in/ance1 treats diff]5t p]mutations ( lett]s z hav+ diff]5t mean+s4 ,p]mutations ( ?+s are f> m num]\s ?an comb9ations ( ^? ?+s1 = ! obvi\s reason t ea* di/9ct ?+ is reg>d$ diff]5tly accord+ to its place4 ,?us ! lett]s ,a1 ,b1 ,c1 w make diff]5t p]mutations accord+ z ,a /&s fir/1 second1 or ?ird2 hav+ decid$ ! place ( ,a1 !re are two places betwe5 :i* we may *oose = ,b2 & !n !re rema9s b "o place = ,c4 ,accord+ly ! p]mutations ( ^! lett]s w be altoge!r #c #b #a or #f 9 numb]4 ,) f\r ?+s or lett]s1 ,a1 ,b1 ,c1 ,d1 we %all h f\r *oices ( place = ! fir/ lett]1 ?ree = ! second1 two = ! ?ird1 & "o = ! f\r?1 s t !re w be altoge!r1 #d #c #b #a1 or #bd p]mutations4 ,! same simple rule applies 9 all cases2 beg9n+ ) ! :ole numb] ( ?+s we multiply at ea* /ep by a numb] decreas$ by a unit4 ,9 g5]al language1 if 99n99 be ! numb] ( ?+s 9 a comb9ation1 ! numb] ( p]mutations is 99n99 799n99 - #a7799n99 - #b7 4444 #d 4 #c 4 #b 4 #a4 ,if we 7 to re-arrange ! names ( ! days ( ! week1 ! possible arrangem5ts out ( :i* we %\ld h to *oose ! new ord]1 w\ld be no less ?an #g 4 #f 4 #e 4 #d 4 #c 4 #b 4 #a1 or #ejdj1 or1 exclud+ ! exi/+ ord]1 #ejci4 ,! read] w see t ! numb]s :i* we rea* 9 que/ions ( p]mutation1 increase 9 a m extraord9>y mann] ev5 ?an 9 comb9ation4 ,ea* new object or t]m d\bles ! numb] ( comb9ations1 b increases ! p]mutations by a factor cont9ually gr[+4 ,in/ead ( #b #b #b #b 4444 we h #b #c #d #e 4444 & ! products ( ! latt] expression imm5sely exce$ ^? ( ! =m]4 ,^! products ( increas+ factors are frequ5tly employ$1 z we %all see1 9 que/ions bo? ( p]mutation & comb9ation4 ,!y are te*nically call$ 99factorials991 t is to say1 ! product ( all integ] numb]s1 f unity up to any numb] 99n99 is ! 99factorial99 ( 99n991 & is (t5 indicat$ symbolically by 99n9964 ,i give bel[ ! factorials up to t ( twelve3-- #bd #a 4 #b 4 #c 4 #d #abj #a 4 #b 444 #e #gbj #a 4 #b 444 #f #e1jdj #g6 #dj1cbj #h6 #cfb1hhj #i6 #c1fbh1hjj #aj6 #ci1iaf1hjj #aa6 #dgi1jja1fjj #ab6 ,! factorials up to #cf6 are giv5 9 ,rees's #8,cyclopdia1' art4 99,ciph]991 & ! log>i?ms ( factorials up to #bfe6 are to be f\nd at ! end ( ! table ( log>i?ms publi%$ "u ! sup]9t5d5ce ( ! ,society = ! ,diffusion ( ,useful ,k 7p4 #bae74 ,to express ! factorial #bfe6 w\ld require #ebi places ( figures4 ,_m writ]s h f "t to "t rem>k$ ^u ! extraord9>y magnitude ( ! numb]s ) :i* we deal 9 ?is subject4 ,tacquet calculat$#ig t ! tw5ty-f\r sic lett]s ( ! alphabet may be arrang$ 9 m ?an #fbj ?\s& trillions ( ord]s2 & ,s*ott e/imat$#ih t if a ?\s& millions ( m5 7 employ$ = ! same numb] ( ye>s 9 writ+ out ^! arrangem5ts1 & ea* man fill$ ea* day =ty pages ) =ty arrangem5ts 9 ea*1 !y w\ld n h accompli%$ ! task1 z !y w\ld h writt5 only #ehd ?\s& trillions in/ead ( #fbj ?\s& trillions4 #ig 99,ari?metic ,!oria499 ,ed4 ,am/]d4 #agjd4 p4 #eag4 #ih ,rees's 99,cyclopdia991 art4 99,ciph]994 ,9 "s que/ions ! numb] ( p]mutations may be re/rict$ & r$uc$ by v>i\s conditions4 ,"s ?+s 9 a gr\p may be undi/+ui%able f o!rs1 s t *ange ( ord] w produce no diff]5ce4 ,?us if we 7 to p]mutate ! lett]s ( ! "n 99,ann991 accord+ to our previ\s rule1 we %\ld obta9 #c #b #a1 or #f ord]s2 b half ( ^! arrangem5ts w\ld be id5tical ) ! o!r half1 because ! int]*ange ( ! two 99n99's has no effect4 ,! really diff]5t ord]s w !re=e be 7#c 4 #b 4 #a7_/7a 4 #b7 or #c1 namely 99,ann991 99,nan991 99,nna994 ,9 ! ^w 99utility99 !re are two 99i99's & two 99t99's1 9 respect ( bo? ( :i* pairs ! numb]s ( p]mutations mu/ be halv$4 ,?us we obta9 7#g 4 #f 4 #e 4 #d 4 #c 4 #b 4 #a7_/7a 4 #b 4 #a 4 #b7 or #abfj1 z ! numb] ( p]mutations4 ,! simple rule evid5tly is--:5 "s ?+s or lett]s are undi/+ui%$1 proce$ 9 ! fir/ place to calculate all ! possible p]mutations z if all 7 diff]5t1 & !n divide by ! numb]s ( possible p]mutations ( ^? s]ies ( ?+s :i* are n di/+ui%$1 & ( :i* ! p]mutations h !re=e be5 c\nt$ 9 excess4 ,?us s9ce ! ^w 99,utilit>ianism99 conta9s f\rte5 lett]s1 ( :i* f\r are 99i99's1 two 99a99's1 & two 99t99's1 ! numb] ( di/9ct arrangem5ts w be f\nd by divid+ ! factorial ( #ad1 by ! factorials ( #d1 #b1 & #b1 ! result be+ #ijh1ajg1bjj4 ,f ! lett]s ( ! ^w 99,mississippi99 we c get 9 l mann] #aa6_/7d6 #d6 #b67 or #cd1fej p]mutations1 :i* is n ! "o-?\s&? "p ( :at we %\ld obta9 7 all ! lett]s diff]5t4 99,calculation ( ,numb] ( ,comb9ations499 ,al?\gh 9 _m que/ions bo? ( art & sci5ce we ne$ to calculate ! numb] ( p]mutations on acc\nt ( _! own int]e/1 x f> m frequ5tly happ5s 9 sci5tific subjects t !y possess b an indirect int]e/4 ,z ,i h already po9t$ out1 we almo/ always deal 9 ! logical & ma!matical sci5ces ) 99comb9ations991 & v>iety ( ord] ent]s only ?r\gh ! inh]5t imp]fections ( our symbols & modes ( calculation4 ,signs mu/ be us$ 9 "s ord]1 & we mu/ )draw our att5tion f ?is ord] be=e ! signs correctly repres5t ! relations ( ?+s :i* exi/ nei!r be=e nor aft] ea* o!r4 ,n[1 x (t5 happ5s t we _c *oose all ! comb9ations ( ?+s1 )\t fir/ *oos+ !m subject to ! accid5tal v>iety ( ord]1 & we mu/ !n divide by ! numb] ( possible v>iations ( ord]1 t we may get to ! true numb] ( pure comb9ations4 ,suppose t we wi% to det]m9e ! numb] ( ways 9 :i* we c select a gr\p ( ?ree lett]s out ( ! alphabet1 )\t all[+ ! same lett] to be repeat$4 ,at ! fir/ *oice we c take any "o ( #bf lett]s2 at ! next /ep !re rema9 #be lett]s1 any "o ( :i* may be jo9$ ) t already tak52 at ! ?ird /ep !re w be #bd *oices1 s t app>5tly ! :ole numb] ( ways ( *oos+ is #bf #be #bd4 ,b ! fact t "o *oice succe$$ ano!r has caus$ u to obta9 ! same comb9ations ( lett]s 9 diff]5t ord]s2 we %\ld get1 = in/ance1 99a991 99p991 99r99 at "o "t1 & 99p991 99r991 99a99 at ano!r1 & e ?ree di/9ct lett]s w appe> six times ov]1 because ?ree ?+s c be arrang$ 9 six p]mutations4 ,to get ! numb] ( comb9ations1 !n1 we mu/ divide ! :ole numb] ( ways ( *oos+1 by six1 ! numb] ( p]mutations ( ?ree ?+s1 obta9+ 7#bf #be #bd7_/7a #b #c7 or #b1fjj4 ,x is app>5t t we ne$ ! doctr9e ( comb9ations 9 ord] t we may 9 _m que/ions c\nt]act ! exagg]at+ effect ( successive selection4 ,if out ( a s5ate ( #cj p]sons we h to *oose a committee ( #e1 we may *oose any ( #cj fir/1 any ( #bi next1 & s on1 9 fact !re w be #cj #bi #bh #bg #bf selections2 b z ! actual "* ( ! memb]s ( ! committee w n be affect$ by ! accid5tal ord] ( _! selection1 we divide by #a #b #c #d #e1 & ! possible numb] ( diff]5t committees w be #adb1ejf4 ,simil>ly if we want to calculate ! numb] ( ways 9 :i* ! eight major planets may come into conjunction1 x is evid5t t !y may meet ei!r two at a "t or ?ree at a "t1 or f\r or m at a "t1 & z no?+ is said z to ! relative ord] or place 9 ! conjunction1 we require ! numb] ( comb9ations4 ,n[ a selection ( #b out ( #h is possible 9 7#h 4 #g7_/7a 4 #b7 or #bh ways2 ( #c out ( #h 9 7#h 4 #g 4 #f7_/7a 4 #b 4 #c7 or #ef ways2 ( #d out ( #h 9 7#h 4 #g 4 #f 4 #e7_/7a 4 #b 4 #c 4 #d7 or #gj ways2 & x may be simil>ly %[n t = #e1 #f1 #g1 & #h planets1 meet+ at "o "t1 ! numb]s ( ways are #ef1 #bh1 #h1 & #a4 ,?us we h solv$ ! :ole "q ( ! v>iety ( conjunctions ( eight planets2 & add+ all ! numb]s toge!r1 we f9d t #bdg is ! utmo/ possible numb] ( modes ( meet+4 ,9 g5]al algebraic language1 we may say t a gr\p ( 99m99 ?+s may be *os5 out ( a total numb] ( 99n99 ?+s1 9 a numb] ( comb9ations d5ot$ by ! =mula 799n99 4 799n99-#a7799n99-#b7799n99-#c7 4444 799n99 - 99m99 #a77_/7a 4 #b 4 #c 4 #d 4444 99m997 ,! extreme importance & significance ( ?is =mula seems to h be5 fir/ adequately recognis$ by ,pascal1 al?\gh its discov]y is attribut$ by him to a fri5d1 ,m4 de ,ganires4#ii ,we %all f9d x p]petually recurr+ 9 que/ions bo? ( comb9ations & probability1 & ?r\gh\t ! =mul ( ma!matical analysis traces ( its influ5ce may be notic$4 #ii 99uvres ,compltes de ,pascal99 7#ahfe71 vol4 iii4 p4 #cjb4 ,montucla /ates ! "n z ,de ,gruires1 99,hi/oire des ,ma?matiques991 vol4 iii4 p4 #chi4 99,! ,ari?metical ,triangle499 ,! ,ari?metical ,triangle is a "n long s9ce giv5 to a s]ies ( rem>kable numb]s connect$ ) ! subject we are treat+4 ,accord+ to ,montucla#ajj 8?is triangle is 9 ! !ory ( comb9ations & *anges ( ord]1 almo/ :at ! table ( ,py?agoras is 9 ord9>y ari?metic1 t is to say1 x places at once "u ! eyes ! numb]s requir$ 9 a multitude ( cases ( ?is !ory40 ,z e>ly z #aedd ,/ifels _h notic$ ! rem>kable prop]ties ( ^! numb]s & ! mode ( _! evolution4 ,briggs1 ! inv5tor ( ! common sy/em ( log>i?ms1 0 s /ruck ) _! importance t he call$ !m ! ,abacus ,pan*re/us4 ,pascal1 h[ev]1 0 ! fir/ :o wrote a di/9ct treatise on ^! numb]s1 & gave !m ! "n by :i* !y are /ill kn[n4 ,b ,pascal did n by any means exhau/ ! subject1 & x rema9$ = ,james ,b]n\lli to demon/rate fully ! importance ( ! 99figurate numb]s991 z !y are also call$4 ,9 8 treatise 99,de ,arte ,conject&i991 he po9ts out _! application 9 ! !ory ( comb9ations & probabilities1 & rem>ks ( ! ,ari?metical ,triangle1 8,x n only conta9s ! clue to ! my/]i\s doctr9e ( comb9ations1 b x is also ! gr\nd or f\ndation ( mo/ ( ! important & ab/ruse discov]ies t h be5 made 9 ! o!r bran*es ( ! ma!matics40#aja #ajj 99,hi/oire des ,ma?matiques991 vol4 iii4 p4 #cgh4 #aja ,b]n\lli1 99,de ,arte ,conject&i991 translat$ by ,francis ,mas]es4 ,london1 #agie1 p4 #ge4 ,! numb]s ( ! triangle c be calculat$ 9 a v easy mann] by successive additions4 ,we comm5ce ) unity at ! apex2 9 ! next l9e we place a second unit to ! "r ( ?is2 to obta9 ! ?ird l9e ( figures we move ! previ\s l9e "o place to ! "r1 & add !m to ! same figures z !y 7 be=e removal2 we c !n repeat ! same process 99ad inf9itum994 ,! f\r? l9e ( figures1 = in/ance1 conta9s #a1 #c1 #c1 #a2 mov+ !m "o place & add+ z direct$ we obta93-- ,f\r? l9e 444 #a #c #c #a #a #c #c #a -------------- ,fif? l9e 4444 #a #d #f #d #a #a #d #f #d #a ---------------- ,six? l9e 4444 #a #e #aj #aj #e #a ,c>ry+ out ?is simple process ?r\gh t5 m /eps we obta9 ! fir/ sev5te5 l9es ( ! ,ari?metical ,triangle z pr9t$ on ! next page4 ,!oretically speak+ ! ,triangle mu/ be reg>d$ z inf9ite 9 ext5t1 b ! numb]s increase s rapidly t x soon becomes impracticable to cont9ue ! table4 ,! longe/ table ( ! numb]s :i* ,i h f\nd is 9 ,=tia's 8,trait des ,progressions0 7p4 #hj71 :]e !y are giv5 up to ! =tie? l9e & ! n9? column4 ,,! ,,ari?metical ,,triangle4 ,l9e4 ,fir/ ,column4 #a #a ,second ,column4 #b #a #a ,?ird ,column4 #c #a #b #a ,f\r? ,column4 #d #a #c #c #a ,fif? ,column4 #e #a #d #f #d #a ,six? ,column4 #f #a #e #aj #aj #e #a ,sev5? ,column4 #g #a #f #ae #bj #ae #f #a ,eigh? ,column4 #h #a #g #ba #ce #ce #ba #g #a ,n9? ,column4 #i #a #h #bh #ef #gj #ef #bh #h #a ,t5? ,column4 #aj #a #i #cf #hd #abf #abf #hd #cf #i #a ,elev5? ,column4 #aa #a #aj #de #abj #baj #beb #baj #abj #de #aj #a ,twelf? ,column4 #ab #a #aa #ee #afe #ccj #dfb #dfb #ccj #afe #ee #aa #a ,?irte5? ,column4 #ac #a #ab #ff #bbj #die #gib #ibd #gib #die #bbj #ff #ab #a ,f\rte5? ,column4 #ad #a #ac #gh #bhf #gae #abhg #agaf #agaf #abhg #gae #bhf #gh #ac #a ,fifte5? ,column4 #ae #a #ad #ia #cfd #ajja #bjjb #cjjc #cdcb #cjjc #bjjb #ajja #cfd #ia #ad #a ,sixte5? ,column4 #af #a #ae #aje #dee #acfe #cjjc #ejje #fdce #fdce #ejje #cjjc #acfe #dee #aje #ae #a ,sev5te5? ,col4 #ag #a #af #abj #efj #ahbj #dcfh #hjjh #aaddj #abhgj #aaddj #hjjh #dcfh #ahbj #efj #abj #af #a ,exam9+ ^! numb]s1 we f9d t !y are connect$ by an unlimit$ s]ies ( relations1 a few ( ! m simple ( :i* may be notic$4 ,ea* v]tical column ( numb]s exactly corresponds ) an oblique s]ies desc5d+ f left to "r1 s t ! triangle is p]fectly symmetrical 9 its cont5ts4 ,! fir/ column conta9s only 99units992 ! second column conta9s ! 99natural numb]s991 #a1 #b1 #c1 c42 ! ?ird column conta9s a rem>kable s]ies ( numb]s1 #a1 #c1 #f1 #aj1 #ae1 c41 :i* h long be5 call$ 99! triangul> numb]s991 because !y correspond ) ! numb]s ( balls :i* may be arrang$ 9 a triangul> =m1 ?us-- ,illu/ration ,! f\r? column conta9s ! 99pyramidal numb]s991 s call$ because !y correspond to ! numb]s ( equal balls :i* c be pil$ 9 regul> triangul> pyramids4 ,_! diff]5ces are ! triangul> numb]s4 ,! numb]s ( ! fif? column h ! pyramidal numb]s = _! diff]5ces1 b z !re is no regul> figure ( :i* !y express ! cont5ts1 !y h be5 arbitr>ily call$ ! 99trianguli-triangul> numb]s994 ,! succe$+ columns h1 9 a simil> mann]1 be5 said to conta9 ! 99trianguli-pyramidal991 ! 99pyramidi-pyramidal99 numb]s1 & s on4#ajb #ajb ,wallis's 99,algebra991 ,disc\rse ( ,comb9ations1 c41 p4 #aji4 ,f ! mode ( =mation ( ! table1 x foll[s t ! diff]5ces ( ! numb]s 9 ea* column w be f\nd 9 ! prec$+ column to ! left4 ,h5ce ! 99second diff]5ces991 or ! 99diff]5ces ( diff]5ces991 w be 9 ! second column to ! left ( any giv5 column1 ! ?ird diff]5ces 9 ! ?ird column1 & s on4 ,?us we may say t unity :i* appe>s 9 ! fir/ column is ! 99fir/ diff]5ce99 ( ! numb]s 9 ! second column2 ! 99second diff]5ce99 ( ^? 9 ! ?ird column2 ! 99?ird diff]5ce99 ( ^? 9 ! f\r?1 & s on4 ,! triangle is se5 to be a complete classification ( all numb]s accord+ z !y h unity = any ( _! diff]5ces4 ,s9ce ea* l9e is =m$ by add+ ! previ\s l9e to itself1 x is evid5t t ! sum ( ! numb]s 9 ea* horizontal l9e mu/ be d\ble ! sum ( ! numb]s 9 ! l9e next above4 ,h5ce we "k1 )\t mak+ ! additions1 t ! successive sums mu/ be #a1 #b1 #d1 #h1 #af1 #cb1 #fd1 c41 ! same z ! numb]s ( comb9ations 9 ! ,logical ,alphabet4 ,speak+ g5]ally1 ! sum ( ! numb]s 9 ! 99n99? l9e w be #b99n99 - #a4 ,aga91 if ! :ole ( ! numb]s d[n to any l9e be add$ toge!r1 we %all obta9 a numb] less by unity ?an "s p[] ( #b2 ?us1 ! fir/ l9e gives #a or #ba - #a2 ! fir/ two l9es give #c or #bb - #a2 ! fir/ ?ree l9es #g or #bc - #a2 ! fir/ six l9es give #fc or #bf - #a2 or1 speak+ 9 g5]al language1 ! sum ( ! fir/ 99n99 l9es is #b99n99 - #a4 ,x foll[s t ! sum ( ! numb]s 9 any "o l9e is equal to ! sum ( ^? 9 all ! prec$+ l9es increas$ by a unit4 ,= ! sum ( ! 99n99? l9e is1 z already %[n1 #b99n99 - #a1 & ! sum ( ! fir/ 99n99 - #a l9es is #b99n99 - #a - #a1 or less by a unit4 ,?is acc\nt ( ! prop]ties ( ! figurate numb]s does n approa* complet5ess2 a consid]able1 probably an unlimit$1 numb] ( less simple & obvi\s relations might be trac$ out4 ,pascal1 aft] giv+ _m ( ! prop]ties1 exclaims#ajc3 8,mais j'en laisse bi5 plus que je n'en donne2 c'e/ une *ose trange combi5 il e/ f]tile en proprits6 ,*acun peut s'y ex]c]40 ,! ari?metical triangle may be consid]$ a natural classification ( numb]s1 exhibit+1 9 ! mo/ complete mann]1 _! evolution & relations 9 a c]ta9 po9t ( view4 ,x is obvi\s t 9 an unlimit$ ext5sion ( ! triangle1 ea* numb]1 ) ! s+le exception ( ! numb] 99two991 has at lea/ two places4 #ajc 99uvres ,compltes991 vol4 iii4 p4 #bea4 ,?\gh ! prop]ties above expla9$ are highly curi\s1 ! greate/ value ( ! triangle arises f ! fact t x conta9s a complete /atem5t ( ! values ( ! =mula 7p4 #ahb71 = ! numb]s ( comb9ations ( 99m99 ?+s out ( 99n991 = all possible values ( 99m99 & 99n994 ,out ( sev5 ?+s "o may be *os5 9 sev5 ways1 & sev5 occurs 9 ! eigh? l9e ( ! second column4 ,! comb9ations ( two ?+s *os5 out ( sev5 are 7#g #f7_/7a #b7 or #ba1 :i* is ! ?ird numb] 9 ! eigh? l9e4 ,! comb9ations ( ?ree ?+s out ( sev5 are 7#g #f #e7_/7a #b #c7 or #ce1 :i* appe>s f\r? 9 ! eigh? l9e4 ,9 a simil> mann]1 9 ! fif?1 six?1 sev5?1 & eigh? columns ( ! eigh? l9e ,i f9d x /at$ 9 h[ _m ways ,i c select comb9ations ( #d1 #e1 #f1 & #g ?+s out ( #g4 ,proce$+ to ! n9? l9e1 ,i f9d 9 succession ! numb] ( ways 9 :i* ,i c select #a1 #b1 #c1 #d1 #e1 #f1 #g1 & #h ?+s1 out ( #h ?+s4 ,9 g5]al language1 if ,i wi% to "k 9 h[ _m ways 99m99 ?+s c be select$ 9 comb9ations out ( 99n99 ?+s1 ,i mu/ look 9 ! 99n99 #a? l9e1 & take ! 99m99 #a? numb]1 z ! answ]4 ,9 h[ _m ways1 = in/ance1 c a subcommittee ( five be *os5 out ( a committee ( n9e4 ,! answ] is #abf1 & is ! six? numb] 9 ! t5? l9e2 x w be f\nd equal to 7#i 4 #h 4 #g 4 #f 4 #e7_/7a 4 #b 4 #c 4 #d 4 #e71 :i* our =mula 7p4 #ahb7 gives4 ,! full utility ( ! figurate numb]s w be m app>5t :5 we rea* ! subject ( probabilities1 b ,i may give an illu/ration or two 9 ?is place4 ,9 h[ _m ways c we arrange f\r p5nies z reg>ds head & tail8 ,! "q am\nts to ask+ 9 h[ _m ways we c select #j1 #a1 #b1 #c1 or #d heads1 out ( #d heads1 & ! 99fif?99 l9e ( ! triangle gives u ! complete answ]1 ?us-- ,we c select ,no head & #d tails 9 #a way4 #a head & #c tails 9 #d ways4 #b heads & #b tails 9 #f ways4 #c heads & #a tail 9 #d ways4 #d heads & #j tail 9 #a way4 ,! total numb] ( diff]5t cases is #af1 or #bd1 & :5 we come to ! next *apt]1 x w be f\nd t ^! numb]s give u ! respective probabilities ( all ?r[s ) f\r p5nies4 ,i gave 9 p4 #aha a calculation ( ! numb] ( ways 9 :i* eight planets c meet 9 conjunction2 ! read] w f9d all ! numb]s detail$ 9 ! n9? l9e ( ! ari?metical triangle4 ,! sum ( ! :ole l9e is #bh or #bef2 b we mu/ subtract a unit = ! case :]e no planet appe>s1 & #h = ! #h cases 9 :i* only "o planet appe>s2 s t ! total numb] ( conjunctions is #bh -#a - #h or #bdg4 ,if an organ has elev5 /ops we f9d 9 ! twelf? l9e ! numb]s ( ways 9 :i* we c draw !m1 #a1 #b1 #c1 or m at a "t4 ,?us !re are #dfb ways ( draw+ five /ops at once1 & z _m ( draw+ six /ops4 ,! total numb] ( ways ( v>y+ ! s\nd is #bjdh1 includ+ ! s+le case 9 :i* no /op at all is drawn4 ,"o ( ! mo/ important sci5tific uses ( ! ari?metical triangle consi/s 9 ! in=mation :i* x gives conc]n+ ! comp>ative frequ5cy ( div]g5cies f an av]age4 ,suppose1 = ! sake ( argum5t1 t all p]sons 7 naturally ( ! equal /ature ( five feet1 b enjoy$ dur+ y\? sev5 indep5d5t *ances ( gr[+ "o in* 9 addition4 ,( ^! sev5 *ances1 "o1 two1 ?ree1 or m1 may happ5 fav\rably to any individual2 b1 z x does n matt] :at ! *ances are1 s t ! in* is ga9$1 ! "q really turns ^u ! numb] ( comb9ations ( #j1 #a1 #b1 #c1 c41 ?+s out ( sev54 ,h5ce ! eigh? l9e ( ! triangle gives u a complete answ] to ! "q1 z foll[s3-- ,out ( e #abh p-- ,feet ,in*es4 ,"o p]son w\ld h ! /ature ( #e #j #g p]sons #e #a #ba p]sons #e #b #ce p]sons #e #c #ce p]sons #e #d #ba p]sons #e #e #g p]sons #e #f #a p]son #e #g ,by tak+ a prop] l9e ( ! triangle1 an answ] may be _h "u any m natural supposition4 ,?is !ory ( comp>ative frequ5cy ( div]g5ce f an av]age1 0 fir/ adequately notic$ by ,quetelet1 & has lately be5 employ$ 9 a v int]e/+ & bold mann] by ,mr4 ,francis ,galton1#ajd 9 8 rem>kable "w on 8,h]$it>y ,g5ius40 ,we %all aft]w>ds f9d t ! !ory ( error1 to :i* is made ! ultimate appeal 9 cases ( quantitative inve/igation1 is f\nd$ ^u ! comp>ative numb]s ( comb9ations z display$ 9 ! triangle4 #ajd ,see also ,galton's ,lecture at ! ,royal ,in/itution1 #bg? ,febru>y1 #ahgd2 ,catalogue ( ! ,special ,loan ,collection ( ,sci5tific ,in/rum5ts1 ,s\? ,k5s+ton1 ,nos4 #dh1 #di2 & ,galton1 99,philosophical ,magaz9e991 ,janu>y #ahge4 99,connection betwe5 ! ,ari?metical ,triangle & ! ,logical ,alphabet499 ,!re exi/s a close connection betwe5 ! ari?metical triangle describ$ 9 ! la/ section1 & ! s]ies ( comb9ations ( lett]s call$ ! ,logical ,alphabet4 ,! "o is to ma!matical sci5ce :at ! o!r is to logical sci5ce4 ,9 fact ! figurate numb]s1 or ^? exhibit$ 9 ! triangle1 are obta9$ by summ+ up ! logical comb9ations4 ,accord+ly1 j z ! total ( ! numb]s 9 ea* l9e ( ! triangle is twice z great z t = ! prec$+ l9e 7p4 #ahf71 s ea* column ( ! ,alphabet 7p4 #id7 conta9s twice z _m comb9ations z ! prec$+ "o4 ,! l correspond5ce also exi/s betwe5 ! sums ( all ! l9es ( figures d[n to any p>ticul> l9e1 & ( ! comb9ations d[n to any p>ticul> column4 ,by exam9+ any column ( ! ,logical ,alphabet we f9d t ! comb9ations naturally gr\p !mselves accord+ to ! figurate numb]s4 ,take ! comb9ations ( ! lett]s ,a1 ,b1 ,c1 ,d2 !y consi/ ( all ! ways 9 :i* ,i c *oose f\r1 ?ree1 two1 "o1 or none ( ! f\r lett]s1 fill+ up ! vacant spaces ) negative t]ms4 ,!re is "o comb9ation1 ,,abcd1 9 :i* all ! positive lett]s are pres5t2 !re are f\r comb9ations 9 ea* ( :i* ?ree positive lett]s are pres5t2 six 9 :i* two are pres5t2 f\r 9 :i* only "o is pres5t2 &1 f9ally1 !re is ! s+le case1 99abcd991 9 :i* all positive lett]s are abs5t4 ,^! numb]s1 #a1 #d1 #f1 #d1 #a1 are ^? ( ! fif? l9e ( ! ari?metical triangle1 & a l correspond5ce w be f\nd to exi/ 9 ea* column ( ! ,logical ,alphabet4 ,num]ical ab/raction1 x has be5 ass]t$1 consi/s 9 ov]look+ ! k9d ( diff]5ce1 & reta9+ only a consci\sness ( its exi/5ce 7p4 #aeh74 ,:ile 9 logic1 !n1 we h to deal ) ea* comb9ation z a sep>ate k9d ( ?+1 9 ari?metic we di/+ui% only ! classes :i* dep5d ^u m or less positive t]ms be+ pres5t1 & ! numb]s ( ^! classes imm$iately produce ! numb]s ( ! ari?metical triangle4 ,x may "h be po9t$ out t !re are two modes 9 :i* we c calculate ! :ole numb] ( comb9ations ( c]ta9 ?+s4 ,ei!r we may take ! :ole numb] at once z %[n 9 ! ,logical ,alphabet1 9 :i* case ! numb] w be "s p[] ( two1 or else we may calculate successively1 by aid ( p]mutations1 ! numb] ( comb9ations ( none1 "o1 two1 ?ree ?+s1 & s on4 ,h5ce we arrive at a necess>y id5tity betwe5 two s]ies ( numb]s4 ,9 ! case ( f\r ?+s we %all h #b #a #d_/a 7#d 4 #c7_/7a 4 #b7 7#d 4 #c 4 #b7_/7a 4 #b 4 #c7 7#d 4 #c 4 #b 4 #a7_/7a 4 #b 4 #c 4 #d74 ,9 a g5]al =m ( expression we %all h #b #a 99n99_/#a 799n99 4 799n99 - #a77_/7a 4 #b7 799n99 799n99 - #a7799n99 - #b77_/7a 4 #b 4 #c7 c41 ! t]ms be+ cont9u$ until !y cease to h any value4 ,?us we arrive at a pro( ( simple cases ( ! ,b9omial ,!orem1 ( :i* ea* column ( ! ,logical ,alphabet is an exemplification4 ,x may be %[n t all o!r ma!matical expansions likewise arise out ( simple processes ( comb9ation1 b ! m complete consid]ation ( ?is subject mu/ be def]r$ to ano!r "w4 99,possible ,v>iety ( ,nature & ,art499 ,we _c adequately und]/& ! difficulties :i* beset u 9 c]ta9 bran*es ( sci5ce1 unless we h "s cle> idea ( ! va/ numb]s ( comb9ations or p]mutations :i* may be possible "u c]ta9 conditions4 ,?us only c we le>n h[ hopeless x w\ld be to attempt to treat nature 9 detail1 & exhau/ ! :ole numb] ( ev5ts :i* might arise4 ,x is in/ructive to consid]1 9 ! fir/ place1 h[ imm5sely great are ! numb]s ( comb9ations ) :i* we deal 9 _m arts & amusem5ts4 ,9 deal+ a pack ( c>ds1 ! numb] ( h&s1 ( ?irte5 c>ds ea*1 :i* c be produc$ is evid5tly #eb #ea #ej 444 #dj divid$ by #a #b #c 444 #ac4 or #fce1jac1eei1fjj4 ,b 9 :i/ f\r h&s are simultane\sly held1 & ! numb] ( di/9ct deals becomes s va/ t x w\ld require tw5ty-eight figures to express x4 ,if ! :ole population ( ! _w1 say "o ?\s& millions ( p]sons1 7 to deal c>ds day & night1 = a hundr$ million ( ye>s1 !y w\ld n 9 t "t h exhau/$ "o hundr$-?\s&? "p ( ! possible deals4 ,ev5 ) ! same h&s ( c>ds ! play may be almo/ inf9itely v>i$1 s t ! complete v>iety ( games at :i/ :i* may exi/ is almo/ incalculably great4 ,x is 9 ! highe/ degree improbable t any "o game ( :i/ 0 ev] exactly l ano!r1 except x 7 int5tionally s4 ,! end ( novelty 9 art might well be dread$1 did we n f9d t nature at lea/ has plac$ no atta9able limit1 & t ! defici5cy w lie 9 our inv5tive faculties4 ,x w\ld be a *e]less "t inde$ :5 all possible v>ieties ( melody 7 exhau/$1 b x is readily %[n t if a peal ( tw5ty-f\r bells _h be5 rung cont9u\sly f ! s-call$ beg9n+ ( ! _w to ! pres5t day1 no approa* c\ld h be5 made to ! completion ( ! possible *anges4 ,nay1 _h e s+le m9ute be5 prolong$ to #aj1jjj ye>s1 /ill ! task w\ld h be5 unaccompli%$4#aje ,z reg>ds ord9>y melodies1 ! eight notes ( a s+le octave give m ?an #dj1jjj p]mutations1 & two octaves m ?an a million millions4 ,if we 7 to take into acc\nt ! semitones1 x w\ld become app>5t t x is impossible to exhau/ ! v>iety ( music4 ,:5 ! late ,mr4 ,j4 ,s4 ,mill1 9 a depress$ /ate ( m9d1 fe>$ ! approa*+ exhau/ion ( musical melodies1 he _h c]ta9ly n be/[$ suffici5t /udy on ! subject ( p]mutations4 #aje ,wallis1 99,( ,comb9ations991 p4 #aaf1 quot+ ,vossius4 ,simil> consid]ations apply to ! possible numb] ( natural sub/ances1 ?\gh we _c always give precise num]ical results4 ,x 0 recomm5d$ by ,hat*ett#ajf t a sy/ematic exam9ation ( all alloys ( metals %\ld be c>ri$ out1 proce$+ f ! b9>y ones to m complicat$ t]n>y or quat]n>y ones4 ,he c h>dly h be5 aw>e ( ! ext5t ( 8 propos$ inquiry4 ,if we op]ate only ^u ?irty ( ! kn[n metals1 ! numb] ( b9>y alloys w\ld be #dce1 ( t]n>y alloys #djfj1 ( quat]n>y #bg1dje1 )\t pay+ reg>d to ! v>y+ proportions ( ! metals1 & only reg>d+ ! k9d ( metal4 ,if we v>i$ all ! t]n>y alloys by quantities n less ?an "o p] c5t41 ! numb] ( ^! alloys w\ld be #aa1dde1jfj4 ,an exhau/ive inve/igation ( ! subject is !re=e out ( ! "q1 & unless "s laws connect+ ! prop]ties ( ! alloy & its compon5ts c be discov]$1 x is n app>5t h[ our k ( !m c ev] be m ?an fragm5t>y4 #ajf 99,philosophical ,transactions99 7#ahjc71 vol4 xciii4 p4 #aic4 ,! possible v>iety ( def9ite *emical comp\nds1 aga91 is enorm\sly great4 ,*emi/s h already exam9$ _m ?\s&s ( inorganic sub/ances1 & a /ill great] numb] ( organic comp\nds2#ajg !y h nev]!less made no appreciable impression on ! numb] :i* may exi/4 ,tak+ ! numb] ( elem5ts at sixty-"o1 ! numb] ( comp\nds conta9+ diff]5t selections ( f\r elem5ts ea* w\ld be m ?an half a million 7#eba1hee74 ,z ! same elem5ts (t5 comb9e 9 _m diff]5t proportions1 & "s ( !m1 especially c>bon1 h ! p[] ( =m+ an almo/ endless numb] ( comp\nds1 x w\ld h>dly be possible to assign any limit to ! numb] ( *emical comp\nds :i* may be =m$4 ,!re are bran*es ( physical sci5ce1 !re=e1 ( :i* x is unlikely t sci5tific m51 ) all _! indu/ry1 c ev] obta9 a k 9 any appreciable degree approa*+ to complet5ess4 #ajg ,h(mann's 99,introduction to ,*emi/ry991 p4 #cf4 99,high] ,ord]s ( ,v>iety499 ,! consid]ation ( ! facts already giv5 9 ?is *apt] w n produce an adequate notion ( ! possible v>iety ( exi/5ce1 unless we consid] ! comp>ative numb]s ( comb9ations ( diff]5t ord]s4 ,by a comb9ation ( a high] ord]1 ,i mean a comb9ation ( gr\ps1 :i* are !mselves gr\ps4 ,! imm5se numb]s ( comp\nds ( c>bon1 hydrog51 & oxyg51 describ$ 9 organic *emi/ry1 are comb9ations ( a second ord]1 = ! atoms are gr\ps ( gr\ps4 ,! wave ( s\nd produc$ by a musical in/rum5t may be reg>d$ z a comb9ation ( motions2 ! body ( s\nd proce$+ f a l>ge or*e/ra is !re=e a complex aggregate ( s\nds1 ea* 9 itself a complex comb9ation ( movem5ts4 ,all lit]ature may be said to be develop$ out ( ! diff]5ce ( :ite pap] & black ink4 ,f ! unlimit$ numb] ( m>ks :i* might be *os5 we select tw5ty-six conv5tional lett]s4 ,! pron\nceable comb9ations ( lett]s are probably "s trillions 9 numb]4 ,n[1 z a s5t5ce is a selection ( words1 ! possible s5t5ces mu/ be inconceivably m num]\s ?an ! words ( :i* x may be compos$4 ,a book is a comb9ation ( s5t5ces1 & a libr>y is a comb9ation ( books4 ,a libr>y1 !re=e1 may be reg>d$ z a comb9ation ( ! fif? ord]1 & ! p[]s ( num]ical expression w\ld be sev]ely task$ 9 attempt+ to express ! numb] ( di/9ct libr>ies :i* might be con/ruct$4 ,! calculation1 ( c\rse1 w\ld n be possible1 because ! union ( lett]s 9 words1 ( words 9 s5t5ces1 & ( s5t5ces 9 books1 is gov]n$ by conditions s complex z to defy analysis4 ,i wi% only to po9t out t ! inf9ite v>iety ( lit]ature1 exi/+ or possible1 is all develop$ out ( "o fundam5tal diff]5ce4 ,galileo rem>k$ t all tru? is conta9$ 9 ! compass ( ! alphabet4 ,he ought to h said t x is all conta9$ 9 ! diff]5ce ( ink & pap]4 ,"o consequ5ce ( successive comb9ation is t ! simple/ m>ks w suffice to express any in=mation4 ,francis ,bacon propos$ = secret writ+ a bilit]al ciph]1 :i* resolves all lett]s ( ! alphabet into p]mutations ( ! two lett]s 99a99 & 99b994 ,?us ,a 0 99aaaaa991 ,b 99aaaab991 ,x 99babab991 & s on4#ajh ,9 a simil> way1 z ,bacon cle>ly saw1 any "o diff]5ce c be made ! gr\nd ( a code ( signals2 we c express1 z he says1 99omnia p] omnia994 ,! ,morse alphabet uses only a succession ( long & %ort m>ks1 & o!r sy/ems ( telegraphic language employ "r & left /rokes4 ,a s+le lamp obscur$ at v>i\s int]vals1 long or %ort1 may be made to spell out any words1 & ) two lamps1 di/+ui%$ by col\r1 position1 or any o!r circum/ance1 we c\ld at once repres5t ,bacon's bilit]al alphabet4 ,babbage +5i\sly sugge/$ t e ligh?\se 9 ! _w %\ld be made to spell out its own "n or numb] p]petually1 by fla%es or obscurations ( v>i\s duration & succession4 ,a sy/em l t ( ,babbage is n[ be+ appli$ to ligh?\ses 9 ! ,unit$ ,k+dom by ,sir ,w4 ,?omson & ,dr4 ,john ,hopk9son4 #ajh 99,works991 edit$ by ,%aw1 vol4 i4 pp4 #ada-ade1 quot$ 9 ,rees's 99,encyclopdia991 art4 99,ciph]994 ,let u calculate ! numb]s ( comb9ations ( diff]5t ord]s :i* may arise out ( ! pres5ce or abs5ce ( a s+le m>k1 say ,a4 ,9 ^! figures ------ ------ ------ ------ ,a ,a ,a ,a ------ ------ ------ ------ we h f\r di/9ct v>ieties4 ,=m !m into a gr\p ( a high] ord]1 & consid] 9 h[ _m ways we may v>y t gr\p by omitt+ "o or m ( ! compon5t p>ts4 ,n[1 z !re are f\r p>ts1 & any "o may be pres5t or abs5t1 ! possible v>ieties w be #b #b #b #b1 or #af 9 numb]4 ,=m ^! into a new :ole1 & proce$ aga9 to create v>iety by omitt+ any "o or m ( ! sixte54 ,! numb] ( possible *anges w n[ be #b 4 #b 4 #b 4 #b 4 #b 4 #b 4 #b 4 #b 4 #b 4 #b 4 #b 4 #b 4 #b 4 #b 4 #b 4 #b1 or #baf1 & we c repeat ! process aga9 & aga94 ,we are imag9+ ! creation ( objects1 ^: numb]s are repres5t$ by ! successive ord]s ( ! p[]s ( 99two994 ,at ! fir/ /ep we h #b2 at ! next #bb1 or #d2 at ! ?ird 7#bb7b1 or #af1 numb]s ( v mod]ate am\nt4 ,let ! read] calculate ! next t]m1 77#bb7b7b1 & he w be surpris$ to f9d x leap up to #fe1ecf4 ,b at ! next /ep he has to calculate ! value ( #fe1ecf 99two99's multipli$ toge!r1 & x is s great t we c\ld n possibly compute x1 ! m]e expression ( ! result requir+ #ai1gbi places ( figures4 ,b g "o /ep m & we pass ! b\nds ( all reason4 ,! six? ord] ( ! p[]s ( 99two99 becomes s great1 t we c\ld n ev5 express ! numb] ( figures requir$ 9 writ+ x d[n1 )\t us+ ab\t #ai1gbi figures = ! purpose4 ,! successive ord]s ( ! p[]s ( two h !n ! foll[+ values s f> z we c succe$ 9 describ+ !m3-- ,fir/ ord] #b ,second ord] #d ,?ird ord] #af ,f\r? ord] #fe1ecf ,fif? ord]1 numb] express$ by #ai1gbi figures4 ,six? ord]1 numb] express$ by figures1 to express ! numb] ( :i* figures w\ld require ab\t #ai1gbi figures4 ,x may give u "s notion ( inf9ity to rememb] t at ?is six? /ep1 hav+ long surpass$ all b\nds ( intuitive conception1 we make no approa* to a limit4 ,nay1 7 we to make a hundr$ su* /eps1 we %\ld be z f> away z ev] f actual inf9ity4 ,x is well wor? obs]v+ t our p[]s ( expression rapidly ov]come ! possible multitude ( f9ite objects :i* may exi/ 9 any assignable space4 ,ar*im$es %[$ long ago1 9 "o ( ! mo/ rem>kable writ+s ( antiquity1 ! 99,lib] de ,arcn ,num]o991 t ! gra9s ( s& 9 ! _w c\ld be numb]$1 or r1 t if numb]$1 ! result c\ld readily be express$ 9 ari?metical notation4 ,let u ext5d 8 problem1 & asc]ta9 :e!r we c\ld express ! numb] ( atoms :i* c\ld exi/ 9 ! visible univ]se4 ,! mo/ di/ant />s :i* c n[ be se5 by telescopes--^? ( ! sixte5? magnitude--are suppos$ to h a di/ance ( ab\t #cc1ijj1jjj1jjj1jjj1jjj miles4 ,sir ,w4 ,?omson has %[n reasons = suppos+ t !re d n exi/ m ?an f #c #ajbd to #ajbf molecules 9 a cubic c5timetre ( a solid or liquid sub/ance4#aji ,assum+ ^! data to be true1 = ! sake ( argum5t1 a simple calculation enables u to %[ t ! almo/ inconceivably va/ sph]e ( our /ell> sy/em if entirely fill$ ) solid matt]1 w\ld n conta9 m ?an ab\t #fh #ajij atoms1 t is to say1 a numb] requir+ = its expression #ib places ( figures4 ,n[1 ?is numb] w\ld be imm5sely less ?an ! fif? ord] ( ! p[]s ( two4 #aji 99,nature991 vol4 i4 p4 #eec4 ,9 ! v>iety ( logical relations1 :i* may exi/ betwe5 a c]ta9 numb] ( logical t]ms1 we also meet a case ( high] comb9ations4 ,we h se5 7p4 #adb7 t ) only six t]ms ! numb] ( possible selections ( comb9ations is #ah1ddf1gdd1jgc1gji1eea1faf4 ,consid]+ t x is ! mo/ common ?+ 9 ! _w to use an argum5t involv+ six objects or t]ms1 x may excite "s surprise t ! complete inve/igation ( ! relations 9 :i* six su* t]ms may /& to ea* o!r1 %\ld involve an almo/ inconceivable numb] ( cases4 ,yet ^! numb]s ( possible logical relations belong only to ! second ord] ( comb9ations4 ,,*apt] ,x4 ,,! ,,!ory ,,( ,,probability4 ,! subject ^u :i* we n[ ent] mu/ n be reg>d$ z an isolat$ & curi\s bran* ( speculation4 ,x is ! necess>y basis ( ! judgm5ts we make 9 ! prosecution ( sci5ce1 or ! decisions we come to 9 ! conduct ( ord9>y affairs4 ,z ,butl] truly said1 8,probability is ! v guide ( life40 ,_h ! sci5ce ( numb]s be5 /udi$ = no o!r purpose1 x mu/ h be5 develop$ = ! calculation ( probabilities4 ,all our inf]5ces conc]n+ ! future are m]ely probable1 & a due appreciation ( ! degree ( probability dep5ds ^u a compreh5sion ( ! pr9ciples ( ! subject4 ,i am conv9c$ t x is impossible to exp\nd ! me?ods ( induction 9 a s\nd mann]1 )\t re/+ !m ^u ! !ory ( probability4 ,p]fect k alone c give c]ta9ty1 & 9 nature p]fect k w\ld be inf9ite k1 :i* is cle>ly beyond our capacities4 ,we h1 !re=e1 to cont5t ourselves ) p>tial k--k m+l$ ) ignorance1 produc+ d\bt4 ,a great difficulty 9 ?is subject consi/s 9 acquir+ a precise notion ( ! matt] treat$4 ,:at is x t we numb]1 & measure1 & calculate 9 ! !ory ( probabilities8 ,is x belief1 or op9ion1 or d\bt1 or k1 or *ance1 or necessity1 or want ( art8 ,does probability exi/ 9 ! ?+s :i* are probable1 or 9 ! m9d :i* reg>ds !m z su*8 ,! etymology ( ! "n l5ds u no assi/ance3 =1 curi\sly en\gh1 99probable99 is ultimately ! same ^w z 99provable991 a good in/ance ( "o ^w becom+ diff]5tiat$ to two opposite mean+s4 ,*ance _c be ! subject ( ! !ory1 because !re is really no su* ?+ z *ance1 reg>d$ z produc+ & gov]n+ ev5ts4 ,! ^w *ance signifies 99fall+991 & ! notion ( fall+ is cont9ually us$ z a simile to express unc]ta9ty1 because we c seldom pr$ict h[ a die1 a co91 or a leaf w fall1 or :5 a bullet w hit ! m>k4 ,b ev]yone sees1 aft] a little reflection1 t x is 9 our k ! defici5cy lies1 n 9 ! c]ta9ty ( nature's laws4 ,!re is no d\bt 9 lightn+ z to ! po9t x %all /rike2 9 ! greate/ /orm !re is no?+ caprici\s2 n a gra9 ( s& lies ^u ! bea*1 b inf9ite k w\ld acc\nt = its ly+ !re2 & ! c\rse ( e fall+ leaf is guid$ by ! pr9ciples ( me*anics :i* rule ! motions ( ! heav5ly bodies4 ,*ance !n exi/s n 9 nature1 & _c coexi/ ) k2 x is m]ely an expression1 z ,laplace rem>k$1 = our ignorance ( ! causes 9 action1 & our consequ5t inability to pr$ict ! result1 or to br+ x ab\t infallibly4 ,9 nature ! happ5+ ( an ev5t has be5 pre-det]m9$ f ! fir/ fa%ion+ ( ! univ]se4 99,probability belongs :olly to ! m9d499 ,?is is prov$ by ! fact t diff]5t m9ds may reg>d ! v same ev5t at ! same "t ) widely diff]5t degrees ( probability4 ,a /eam-vessel1 = in/ance1 is miss+ & "s p]sons believe t %e has sunk 9 mid-ocean2 o!rs ?9k diff]5tly4 ,9 ! ev5t itself !re c be no su* unc]ta9ty2 ! /eam-vessel ei!r has sunk or has n sunk1 & no subsequ5t discussion ( ! probable nature ( ! ev5t c alt] ! fact4 ,yet ! probability ( ! ev5t w really v>y f day to day1 & f m9d to m9d1 accord+ z ! slighte/ in=mation is ga9$ reg>d+ ! vessels met at sea1 ! wea!r prevail+ !re1 ! signs ( wreck pick$ up1 or ! previ\s condition ( ! vessel4 ,probability ?us belongs to our m5tal condition1 to ! light 9 :i* we reg>d ev5ts1 ! occurr5ce or non-occurr5ce ( :i* is c]ta9 9 !mselves4 ,_m writ]s accord+ly h ass]t$ t probability is conc]n$ ) degree or quantity ( belief4 ,de ,morgan says1#aaj 8,by degree ( probability we really mean or ought to mean degree ( belief40 ,! late ,pr(essor ,donk9 express$ ! mean+ ( probability z 8quantity ( belief20 b ,i h nev] felt satisfi$ ) su* def9itions ( probability4 ,! nature ( 99belief99 is n m cle> to my m9d ?an ! notion :i* x is us$ to def9e4 ,b an all-suffici5t objection is1 t 99! !ory does n measure :at ! belief is1 b :at x ought to be994 ,few m9ds ?9k 9 close accordance ) ! !ory1 & !re are _m cases ( evid5ce 9 :i* ! belief exi/+ is habitually diff]5t f :at x ought to be4 ,ev5 if ! /ate ( belief 9 any m9d c\ld be measur$ & express$ 9 figures1 ! results w\ld be wor?less4 ,! value ( ! !ory consi/s 9 correct+ & guid+ our belief1 & r5d]+ our /ates ( m9d & consequ5t actions h>moni\s ) our k ( ext]ior conditions4 #aaj 99,=mal ,logic991 p4 #agb4 ,?is objection has be5 cle>ly p]ceiv$ by "s ( ^? :o /ill us$ quantity ( belief z a def9ition ( probability4 ,?us ,de ,morgan adds--8,belief is b ano!r "n = imp]fect k40 ,donk9 has well said t ! quantity ( belief is 8always relative to a p>ticul> /ate ( k or ignorance2 b x mu/ be obs]v$ t x is absolute 9 ! s5se ( n be+ relative to any individual m9d2 s9ce1 ! same in=mation be+ presuppos$1 all m9ds 99ought99 to di/ribute _! belief 9 ! same way40#aaa ,boole seem$ to ent]ta9 a l view1 :5 he describ$ ! !ory z engag$ ) 8! equal di/ribution ( ignorance20#aab b we may j z well say t x is engag$ ) ! equal di/ribution ( k4 #aaa 99,philosophical ,magaz9e991 #d? ,s]ies1 vol4 i4 p4 #cee4 #aab 99,transactions ( ! ,royal ,society ( ,ed9burgh991 vol4 xxi4 "p #d4 ,i pref] to disp5se altoge!r ) ?is obscure ^w belief1 & to say t ! !ory ( probability deals ) 99quantity ( k991 an expression ( :i* a precise explanation & measure c pres5tly be giv54 ,an ev5t is only probable :5 our k ( x is dilut$ ) ignorance1 & exact calculation is ne$$ to discrim9ate h[ mu* we d & d n "k4 ,! !ory has be5 describ$ by "s writ]s z pr(ess+ 99to evolve k out ( ignorance992 b z ,donk9 admirably rem>k$1 x is really 8a me?od ( avoid+ ! erection ( belief ^u ignorance40 ,x def9es rational expectation by measur+ ! comp>ative am\nts ( k & ignorance1 & tea*es u to regulate our actions ) reg>d to future ev5ts 9 a way :i* w1 9 ! long run1 lead to ! lea/ disappo9tm5t4 ,x is1 z ,laplace happily said1 99good s5se r$uc$ to calculation994 ,?is !ory appe>s to me ! noble/ creation ( intellect1 & x passes my conception h[ two su* m5 z ,augu/e ,comte & ,j4 ,s4 ,mill c\ld be f\nd depreciat+ x & va9ly que/ion+ its validity4 ,to eulogise ! !ory ought to be z ne$less z to eulogise reason itself4 99,fundam5tal ,pr9ciples ( ! ,!ory499 ,! calculation ( probabilities is really f\nd$1 z ,i conceive1 ^u ! pr9ciple ( reason+ set =? 9 prec$+ *apt]s4 ,we mu/ treat equals equally1 & :at we "k ( "o case may be affirm$ ( e case resembl+ x 9 ! necess>y circum/ances4 ,! !ory consi/s 9 putt+ simil> cases on a p>1 & di/ribut+ equally among !m :atev] k we possess4 ,?r[ a p5ny into ! air1 & consid] :at we "k ) reg>d to its way ( fall+4 ,we "k t x w c]ta9ly fall ^u a side1 s t ei!r head or tail w be upp]mo/2 b z to :e!r x w be head or tail1 our k is equally divid$4 ,:atev] we "k conc]n+ head1 we "k also conc]n+ tail1 s t we h no reason = expect+ "o m ?an ! o!r4 ,! lea/ pr$om9ance ( belief to ei!r side w\ld be irrational2 x w\ld consi/ 9 treat+ unequally ?+s ( :i* our k is equal4 ,! !ory does n require1 z "s writ]s h errone\sly suppos$1 t we %\ld fir/ asc]ta9 by exp]im5t ! equal facility ( ! ev5ts we are consid]+4 ,s f> z we c exam9e & measure ! causes 9 op]ation1 ev5ts are remov$ out ( ! sph]e ( probability4 ,! !ory comes into play :]e ignorance beg9s1 & ! k we possess requires to be di/ribut$ ov] _m cases4 ,nor does ! !ory %[ t ! co9 w fall z (t5 on ! "o side z ! o!r4 ,x is almo/ impossible t ?is %\ld happ51 because "s inequality 9 ! =m ( ! co91 or "s uni=m mann] 9 ?r[+ x up1 is almo/ sure to occasion a slight prepond]ance 9 "o direction4 ,b z we d n previ\sly "k 9 :i* way a prepond]ance w exi/1 we h no reason = expect+ head m ?an tail4 ,our /ate ( k w be *ang$ %\ld we ?r[ up ! co9 _m times & regi/] ! results4 ,e ?r[ gives u "s slight in=mation z to ! probable t5d5cy ( ! co91 & 9 subsequ5t calculations we mu/ take ?is into acc\nt4 ,9 o!r cases exp]i5ce might %[ t we _h be5 entirely mi/ak52 we might expect t a die w\ld fall z (t5 on ea* ( ! six sides z on ea* o!r side 9 ! long run2 trial might %[ t ! die 0 a load$ "o1 & falls mo/ (t5 on a p>ticul> face4 ,! !ory w\ld n h misl$ u3 x treat$ correctly ! in=mation we _h1 :i* is all t any !ory c d4 ,x may be ask$1 z ,mill asks1 ,:y sp5d s mu* tr\ble 9 calculat+ f imp]fect data1 :5 a little tr\ble w\ld enable u to r5d] a conclusion c]ta9 by actual trial8 ,:y calculate ! probability ( a measurem5t be+ correct1 :5 we c try :e!r x is correct8 ,b ,i %all fully po9t out 9 lat] p>ts ( ?is "w t 9 measurem5t we nev] c atta9 p]fect co9cid5ce4 ,two measurem5ts ( ! same base l9e 9 a survey may %[ a diff]5ce ( "s in*es1 & !re may be no means ( kn[+ :i* is ! bett] result4 ,a ?ird measurem5t w\ld probably agree ) nei!r4 ,to select any "o ( ! measurem5ts1 w\ld imply t we knew x to be ! mo/ ne>ly correct "o1 :i* we d n4 ,9 ?is /ate ( ignorance1 ! only guide is ! !ory ( probability1 :i* proves t 9 ! long run ! mean ( div]g5t results w come mo/ ne>ly to ! tru?4 ,9 all o!r sci5tific op]ations :atsoev]1 p]fect k is impossible1 & :5 we h exhau/$ all our in/rum5tal means 9 ! atta9m5t ( tru?1 !re is a m>g9 ( error :i* c only be safely treat$ by ! pr9ciples ( probability4 ,! me?od :i* we employ 9 ! !ory consi/s 9 calculat+ ! numb] ( all ! cases or ev5ts conc]n+ :i* our k is equal4 ,if we h ! slighte/ reason = suspect+ t "o ev5t is m likely to occur ?an ano!r1 we %\ld take ?is k into acc\nt4 ,?is be+ done1 we mu/ det]m9e ! :ole numb] ( ev5ts :i* are1 s f> z we "k1 equally likely4 ,?us1 if we h no reason = suppos+ t a p5ny w fall m (t5 "o way ?an ano!r1 !re are two cases1 head & tail1 equally likely4 ,b if f trial or o!rwise we "k1 or ?9k we "k1 t ( #ajj ?r[s #ee w give tail1 !n ! probability is measur$ by ! ratio ( #ee to #ajj4 ,! ma!matical =mul ( ! !ory are exactly ! same z ^? ( ! !ory ( comb9ations4 ,9 ?is latt] !ory we det]m9e 9 h[ _m ways ev5ts may be jo9$ toge!r1 & we n[ proce$ to use ?is k 9 calculat+ ! numb] ( ways 9 :i* a c]ta9 ev5t may come ab\t4 ,x is ! comp>ative numb]s ( ways 9 :i* ev5ts c happ5 :i* measure _! comp>ative probabilities4 ,if we ?r[ ?ree p5nies into ! air1 :at is ! probability t two ( !m w fall tail upp]mo/8 ,?is am\nts to ask+ 9 h[ _m possible ways c we select two tails out ( ?ree1 comp>$ ) ! :ole numb] ( ways 9 :i* ! co9s c be plac$4 ,n[1 ! f\r? l9e ( ! ,ari?metical ,triangle 7p4 #ahd7 gives u ! answ]4 ,! :ole numb] ( ways 9 :i* we c select or leave ?ree ?+s is eight1 & ! possible comb9ations ( two ?+s at a "t is ?ree2 h5ce ! probability ( two tails is ! ratio ( ?ree to eight4 ,f ! numb]s 9 ! triangle we may simil>ly draw all ! foll[+ probabilities3-- ,"o comb9ation gives #j tail4 ,probability #a_/h4 ,?ree comb9ations gives #a tail4 ,probability #c_/h4 ,?ree comb9ations give #b tails4 ,probability #c_/h4 ,"o comb9ation gives #c tails4 ,probability #a_/h4 ,we c apply ! same consid]ations to ! imag9>y causes ( ! diff]5ce ( /ature1 ! comb9ations ( :i* 7 %[n 9 p4 #ahh4 ,!re are altoge!r #abh ways 9 :i* sev5 causes c be pres5t or abs5t4 ,n[1 tw5ty-"o ( ^! comb9ations give an addition ( two in*es1 s t ! probability ( a p]son "u ! circum/ances be+ five feet two in*es is #ba_/abh4 ,! probability ( five feet ?ree in*es is #ce_/abh2 ( five feet "o in* #g_/abh2 ( five feet #a_/abh1 & s on4 ,?us ! eigh? l9e ( ! ,ari?metical ,triangle gives all ! probabilities aris+ out ( ! comb9ations ( sev5 causes4 99,rules = ! ,calculation ( ,probabilities499 ,i w n[ expla9 z simply z possible ! rules = calculat+ probabilities4 ,! pr9cipal rule is z foll[s3-- ,calculate ! numb] ( ev5ts :i* may happ5 indep5d5tly ( ea* o!r1 & :i*1 z f> z is kn[n1 are equally probable4 ,make ?is numb] ! d5om9ator ( a fraction1 & take = ! num]ator ! numb] ( su* ev5ts z imply or con/itute ! happ5+ ( ! ev5t1 ^: probability is requir$4 ,?us1 if ! lett]s ( ! ^w 99,roma99 be ?r[n d[n casually 9 a r[1 :at is ! probability t !y w =m a significant ,lat9 ^w8 ,! possible arrangem5ts ( f\r lett]s are #d #c #b #a1 or #bd 9 numb] 7p4 #agh71 & if all ! arrangem5ts be exam9$1 sev5 ( ^! w be f\nd to h mean+1 namely 99,roma991 99ramo991 99oram991 99mora991 99m>o991 99armo991 & 99amor994 ,h5ce ! probability ( a significant result is #g_/bd4 ,we mu/ di/+ui% comp>ative f absolute probabilities4 ,9 draw+ a c>d casually f a pack1 !re is no reason to expect any "o c>d m ?an any o!r4 ,n[1 !re are f\r k+s & f\r que5s 9 a pack1 s t !re are j z _m ways ( draw+ "o z ! o!r1 & ! probabilities are equal4 ,b !re are ?irte5 diamonds1 s t ! probability ( a k+ is to t ( a diamond z f\r to ?irte54 ,?us ! probabilities ( ea* are proportional to _! respective numb]s ( ways ( happ5+4 ,aga91 ,i c draw a k+ 9 f\r ways1 & n draw "o 9 =ty-eight1 s t ! probabilities are 9 ?is proportion1 or1 z is commonly said1 ! 99odds99 aga9/ draw+ a k+ are =ty-eight to f\r4 ,! odds are sev5 to sev5te5 9 fav\r1 or sev5te5 to sev5 aga9/ ! lett]s ,r1o1m1a1 accid5tally =m+ a significant ^w4 ,! odds are five to ?ree aga9/ two tails appe>+ 9 ?ree ?r[s ( a p5ny4 ,conv]sely1 :5 ! odds ( an ev5t are giv51 & ! probability is requir$1 99take ! odds 9 fav\r ( ! ev5t = num]ator1 & ! sum ( ! odds = d5om9ator994 ,x is obvi\s t an ev5t is c]ta9 :5 all ! comb9ations ( causes :i* c take place produce t ev5t4 ,if we repres5t ! probability ( su* ev5t accord+ to our rule1 x gives ! ratio ( "s numb] to itself1 or unity4 ,an ev5t is c]ta9 n to happ5 :5 no possible comb9ation ( causes gives ! ev5t1 & ! ratio by ! same rule becomes t ( #j to "s numb]4 ,h5ce x foll[s t 9 ! !ory ( probability c]ta9ty is express$ by #a1 & impossibility by #j2 b no my/ical mean+ %\ld be atta*$ to ^! symbols1 z !y m]ely express ! fact t 99all99 or 99no99 possible comb9ations give ! ev5t4 ,by a 99comp\nd ev5t991 we mean an ev5t :i* may be decompos$ into two or m simpl] ev5ts4 ,?us ! fir+ ( a gun may be decompos$ into pull+ ! trigg]1 ! fall ( ! hamm]1 ! explosion ( ! cap1 c4 ,9 ?is example ! simple ev5ts are n 99indep5d5t991 because if ! trigg] is pull$1 ! o!r ev5ts w "u prop] conditions necess>ily foll[1 & _! probabilities are !re=e ! same z t ( ! fir/ ev5t4 ,ev5ts are 99indep5d5t99 :5 ! happ5+ ( "o does n r5d] ! o!r ei!r m or less probable ?an be=e4 ,?us ! dea? ( a p]son is nei!r m nor less probable because ! planet ,m>s happ5s to be visible4 ,:5 ! compon5t ev5ts are indep5d5t1 a simple rule c be giv5 = calculat+ ! probability ( ! comp\nd ev5t1 ?us--99,multiply toge!r ! fractions express+ ! probabilities ( ! indep5d5t compon5t ev5ts499 ,! probability ( ?r[+ tail twice ) a p5ny is #a_/b #a_/b1 or #a_/d2 ! probability ( ?r[+ x ?ree times runn+ is #a_/b #a_/b #a_/b1 or #a_/h2 a result agree+ ) t obta9$ 9 an app>5tly diff]5t mann] 7p4 #bjb74 ,9 fact1 :5 we multiply toge!r ! d5om9ators1 we get ! :ole numb] ( ways ( happ5+ ( ! comp\nd ev5t1 & :5 we multiply ! num]ators1 we get ! numb] ( ways fav\rable to ! requir$ ev5t4 ,probabilities may be add$ to or subtract$ f ea* o!r "u ! important condition t ! ev5ts 9 "q are exclusive ( ea* o!r1 s t n m ?an "o ( !m c happ54 ,x might be argu$ t1 s9ce ! probability ( ?r[+ head at ! fir/ trial is #a_/b1 & at ! second trial also #a_/b1 ! probability ( ?r[+ x 9 ! fir/ two ?r[s is #a_/b #a_/b1 or c]ta9ty4 ,n only is ?is result evid5tly absurd1 b a repetition ( ! process w\ld lead u to a probability ( #a-a_/b or ( any great] numb]1 results :i* c\ld h no mean+ :atev]4 ,! probability we wi% to calculate is t ( "o head 9 two ?r[s1 b 9 our addition we h includ$ ! case 9 :i* two heads appe>4 ,! true result is #a_/b #a_/b #a_/b or #c_/d1 or ! probability ( head at ! fir/ ?r[1 add$ to ! exclusive probability t if x does n come at ! fir/1 x w come at ! second4 ,! greate/ difficulties ( ! !ory arise f ! confusion ( exclusive & unexclusive alt]natives4 ,i may rem9d ! read] t ! possibility ( unexclusive alt]natives 0 a po9t previ\sly discuss$ 7p4 #fh71 & to ! reasons !n giv5 = consid]+ alt]nation z logically unexclusive1 may be add$ ! exi/5ce ( ^! difficulties 9 ! !ory ( probability4 ,! errone\s result expla9$ above really arose f ov]look+ ! fact t ! expression 8head fir/ ?r[ or head second ?r[0 might include ! case ( head at bo? ?r[s4 99,! ,logical ,alphabet 9 que/ions ( ,probability499 ,:5 ! probabilities ( c]ta9 simple ev5ts are giv51 & x is requir$ to d$uce ! probabilities ( comp\nd ev5ts1 ! ,logical ,alphabet may give assi/ance1 provid$ t !re are no special logical conditions s t all ! comb9ations are possible4 ,?us1 if !re be ?ree ev5ts1 ,a1 ,b1 ,c1 ( :i* ! probabilities are1 1 1 1 !n ! negatives ( ^? ev5ts1 express+ ! abs5ce ( ! ev5ts1 w h ! probabilities #a - 1 #a - 1 #a - 4 ,we h only to ins]t ^! values = ! lett]s ( ! comb9ations & multiply1 & we obta9 ! probability ( ea* comb9ation4 ,?us ! probability ( ,,abc is 2 ( ,a99bc991 7#a - 77#a - 74 ,we c n[ cle>ly di/+ui% betwe5 ! probabilities ( exclusive & unexclusive ev5ts4 ,?us1 if ,a & ,b are ev5ts :i* may happ5 toge!r l ra9 & high tide1 or an e>?quake & a /orm1 ! probability ( ,a or ,b happ5+ is n ! sum ( _! sep>ate probabilities4 ,= by ! ,laws ( ,?\ght we develop ,a ,b into ,,ab ,a99b99 99a99,b1 & sub/itut+ & 1 ! probabilities ( ,a & ,b respectively1 we obta9 4 4 7#a - 7 7#a - 7 4 or - 4 4 ,b if ev5ts are 99incompossible99 or incapable ( happ5+ toge!r1 l a cle> sky & ra91 or a new moon & a full moon1 !n ! ev5ts are n really ,a or ,b1 b ,a n-,b1 or ,b n-,a1 or 9 symbols ,a99b99 99a99,b4 ,n[ if we take probability ( ,a99b99 & probability ( 99a99,b1 !n we may add simply1 & ! probability ( ,a99b99 99a99,b is 4 ,let ! read] c>efully obs]ve t if ! comb9ation ,,ab _c exi/1 ! probability ( ,a99b99 is n ! product ( ! probabilities ( ,a & 99b994 ,:5 c]ta9 comb9ations are logically impossible1 x is no long] all[able to sub/itute ! probability ( ea* t]m = ! t]m1 because ! multiplication ( probabilities presupposes ! indep5d5ce ( ! ev5ts4 ,a l>ge "p ( ,boole's ,laws ( ,?\ght is devot$ to an attempt to ov]come ?is difficulty & to produce a ,g5]al ,me?od 9 ,probabilities by :i* f c]ta9 logical conditions & c]ta9 giv5 probabilities x w\ld be possible to d$uce ! probability ( any o!r comb9ations ( ev5ts "u ^? conditions4 ,boole pursu$ 8 task ) wond]ful +5uity & p[]1 b aft] sp5d+ mu* /udy on 8 "w1 ,i am compell$ to adopt ! conclusion t 8 me?od is fundam5tally errone\s4 ,z po9t$ out by ,mr4 ,wilbraham1#aac ,boole obta9$ 8 results by an arbitr>y assumption1 :i* is only ! mo/ probable1 & n ! only possible assumption4 ,! answ] obta9$ is !re=e n ! real probability1 :i* is usually indet]m9ate1 b only1 z x 71 ! mo/ probable probability4 ,c]ta9 problems solv$ by ,boole are free f logical conditions & !re=e may admit ( valid answ]s4 ,^!1 z ,i h %[n1#aad may be solv$ by ! comb9ations ( ! ,logical ,alphabet1 b ! re/ ( ! problems d n admit ( a det]m9ate answ]1 at lea/ by ,boole's me?od4 #aac 99,philosophical ,magaz9e991 #d? ,s]ies1 vol4 vii4 p4 #dfe2 vol4 viii4 p4 #ia4 #aad 99,memoirs ( ! ,man*e/] ,lit]>y & ,philosophical ,society991 #crd ,s]ies1 vol4 iv4 p4 #cdg4 99,comp>ison ( ! ,!ory ) ,exp]i5ce499 ,! ,laws ( ,probability re/ ^u ! fundam5tal pr9ciples ( reason+1 & _c be really negativ$ by any possible exp]i5ce4 ,x might happ5 t a p]son %\ld always ?r[ a co9 head upp]mo/1 & appe> incapable ( gett+ tail by *ance4 ,! !ory w\ld n be falsifi$1 because x contemplates ! possibility ( ! mo/ extreme runs ( luck4 ,our actual exp]i5ce might be c\nt] to all t is probable2 ! :ole c\rse ( ev5ts might seem to be 9 complete contradiction to :at we %\ld expect1 & yet a casual conjunction ( ev5ts might be ! real explanation4 ,x is j possible t "s regul> co9cid5ces1 :i* we attribute to fix$ laws ( nature1 are due to ! accid5tal conjunction ( ph5om5a 9 ! cases to :i* our att5tion is direct$4 ,all t we c le>n f f9ite exp]i5ce is capable1 accord+ to ! !ory ( probabilities1 ( mislead+ u1 & x is only inf9ite exp]i5ce t c\ld assure u ( any inductive tru?s4 ,at ! same "t1 ! probability t any extreme runs ( luck w occur is s excessively slight1 t x w\ld be absurd s]i\sly to expect _! occurr5ce4 ,x is almo/ impossible1 = in/ance1 t any :i/ play] %\ld h play$ 9 any two games :]e ! di/ribution ( ! c>ds 0 exactly ! same1 by pure accid5t 7p4 #aia74 ,su* a ?+ z a p]son always los+ at a game ( pure *ance1 is :olly unkn[n4 ,co9cid5ces ( ?is k9d are n impossible1 z ,i h said1 b !y are s unlikely t ! lifetime ( any p]son1 or inde$ ! :ole duration ( hi/ory1 does n give any appreciable probability ( _! be+ enc\nt]$4 ,:5ev] we make any ext5sive s]ies ( trials ( *ance results1 z 9 ?r[+ a die or co91 ! probability is great t ! results w agree ne>ly ) ! pr$ictions yield$ by !ory4 ,precise agreem5t mu/ n be expect$1 = t1 z ! !ory %[s1 is highly improbable4 ,sev]al attempts h be5 made to te/1 9 ?is way1 ! accordance ( !ory & exp]i5ce4 ,buffon caus$ ! fir/ trial to be made by a "y *ild :o ?rew a co9 _m times 9 succession1 & he obta9$ #aiib tails to #bjdh heads4 ,a pupil ( ,de ,morgan repeat$ ! trial = 8 own satisfaction1 & obta9$ #bjdd tails to #bjdh heads4 ,9 bo? cases ! co9cid5ce ) !ory is z close z c\ld be expect$1 & ! details may be f\nd 9 ,de ,morgan's 8,=mal ,logic10 p4 #ahe4 ,quetelet also te/$ ! !ory 9 a r m complete mann]1 by plac+ #bj black & #bj :ite balls 9 an urn & draw+ a ball out "t aft] "t 9 an indiff]5t mann]1 ea* ball be+ replac$ be=e a new draw+ 0 made4 ,he f\nd1 z might be expect$1 t ! great] ! numb] ( draw+s made1 ! m ne>ly 7 ! :ite & black balls equal 9 numb]4 ,at ! t]m9ation ( ! exp]im5t he _h regi/]$ #bjff :ite & #bjcj black balls1 ! ratio be+ #ajb4aae #aae 99,lett]s on ! ,!ory ( ,probabilities991 translat$ by ,d[nes1 #ahdi1 pp4 #cf1 #cg4 ,i h made a s]ies ( exp]im5ts 9 a ?ird mann]1 :i* seem$ to me ev5 m int]e/+1 & capable ( m ext5sive trial4 ,tak+ a h&ful ( t5 co9s1 usually %ill+s1 ,i ?rew !m up "t aft] "t1 & regi/]$ ! numb]s ( heads :i* appe>$ ea* "t4 ,n[ ! probability ( obta9+ #aj1 #i1 #h1 #g1 c41 heads is proportional to ! numb] ( comb9ations ( #aj1 #i1 #h1 #g1 c41 ?+s out ( #aj ?+s4 ,consequ5tly ! results ought to approximate to ! numb]s 9 ! elev5? l9e ( ! ,ari?metical ,triangle4 ,i made altoge!r #bjdh ?r[s1 9 two sets ( #ajbd ?r[s ea*1 & ! numb]s obta9$ are giv5 9 ! foll[+ table3-- ---------------------------------------- ----------------------------- ,"* ( ,?r[4,!oretical ,fir/ ,second ,av]age4 ,div]g5ce4 ,numb]s4 ,s]ies4 ,s]ies4 ---------------------------------------- ----------------------------- #aj ,heads #j ,tail #a #c #a #b #a #i #a #aj #ab #bc #ag-a_/b #g-a_/b #h #b #de #eg #gc #fe #bj #g #c #abj #abi #abc #abf #f #f #d #baj #aha #aij #ahe-a_/b - #be #e #e #beb #beg #bcb #bdd-a_/b - #g-a_/b #d #f #baj #bja #aig #aii - #aa #c #g #abj #aaa #aai #aae - #e #b #h #de #eb #ej #ea #f #a #i #aj #ba #ae #ah #h #j #aj #a #j #a #a_/b - #a_/b ---------------------------------------- ----------------------------- ,totals #ajbd #ajbd #ajbd #ajbd - #a ---------------------------------------- ----------------------------- ,! :ole numb] ( s+le ?r[s ( co9s am\nt$ to #aj #bjdh1 or #bj1dhj 9 all1 "o half ( :i* or #aj1bdj %\ld !oretically give head4 ,! total numb] ( heads obta9$ 0 actually #aj1cec1 or #ebbb 9 ! fir/ s]ies1 & #eaca 9 ! second4 ,! co9cid5ce ) !ory is pretty close1 b consid]+ ! l>ge numb] ( ?r[s !re is "s reason to suspect a t5d5cy 9 fav\r ( heads4 ,! special int]e/ ( ?is trial consi/s 9 ! exhibition1 9 a practical =m1 ( ! results ( ,b]n\lli's !orem1 & ! law ( error or div]g5ce f ! mean to be aft]w>ds m fully consid]$4 ,x illu/rates ! connection betwe5 comb9ations & p]mutations1 :i* is exhibit$ 9 ! ,ari?metical ,triangle1 & :i* und]lies _m important !orems ( sci5ce4 99,probable ,d$uctive ,argum5ts994 ,) ! aid ( ! !ory ( probabilities1 we may ext5d ! sph]e ( d$uctive argum5t4 ,hi!rto we h treat$ propositions z c]ta91 & on ! hypo!sis ( c]ta9ty h d$uc$ conclusions equally c]ta94 ,b ! in=mation on :i* we reason 9 ord9>y life is seldom or nev] c]ta91 & almo/ all reason+ is really a "q ( probability4 ,we ought !re=e to be fully aw>e ( ! mode & degree 9 :i* d$uctive reason+ is affect$ by ! !ory ( probability1 & _m p]sons may be surpris$ at ! results :i* mu/ be admitt$4 ,"s controv]sial writ]s appe> to consid]1 z ,de ,morgan rem>k$1#aaf t an inf]5ce f sev]al equally probable premises is itself z probable z any ( !m1 b ! true result is v diff]5t4 ,if an argum5t involves _m propositions1 & ea* ( !m is unc]ta91 ! conclusion w be ( v little =ce4 #aaf 99,encyclopdia ,metropolitana991 art4 99,probabilities991 p4 #cif4 ,! validity ( a conclusion may be reg>d$ z a comp\nd ev5t1 dep5d+ ^u ! premises happ5+ to be true2 ?us1 to obta9 ! probability ( ! conclusion1 we mu/ multiply toge!r ! fractions express+ ! probabilities ( ! premises4 ,if ! probability is #a_/b t ,a is ,b1 & also #a_/b t ,b is ,c1 ! conclusion t ,a is ,c1 on ! gr\nd ( ^! premises1 is #a_/b #a_/b or #a_/d4 ,simil>ly if !re be any numb] ( premises requisite to ! e/abli%m5t ( a conclusion & _! probabilities be 99p991 99q991 99r991 c41 ! probability ( ! conclusion on ! gr\nd ( ^! premises is 99p99 99q99 99r99 444 ,?is product has b a small value1 unless ea* ( ! quantities 99p991 99q991 c41 be ne>ly unity4 ,b x is p>ticul>ly to be notic$ t ! probability ?us calculat$ is n ! :ole probability ( ! conclusion1 b t only :i* x d]ives f ! premises 9 "q4 ,:ately's#aag rem>ks on ?is subject might mislead ! read] into suppos+ t ! calculation is complet$ by multiply+ toge!r ! probabilities ( ! premises4 ,b x has be5 fully expla9$ by ,de ,morgan#aah t we mu/ take into acc\nt ! antec$5t probability ( ! conclusion2 ,a may be ,c = o!r reasons besides its be+ ,b1 & z he rem>ks1 8,x is difficult1 if n impossible1 to produce a *a9 ( argum5t ( :i* ! reason] c re/ ! result on ^? argum5ts only40 ,! failure ( "o argum5t does n1 except "u special circum/ances1 disprove ! tru? ( ! conclusion x is int5d$ to uphold1 o!rwise !re are few tru?s :i* c\ld survive ! ill-consid]$ argum5ts adduc$ 9 _! fav\r4 ,z a rope does n necess>ily break because "o or two /r&s 9 x fail1 s a conclusion may dep5d ^u an endless numb] ( consid]ations besides ^? imm$iately 9 view4 ,ev5 :5 we h no o!r in=mation we mu/ n consid] a /atem5t z devoid ( all probability4 ,! true expression ( complete d\bt is a ratio ( equality betwe5 ! *ances 9 fav\r ( & aga9/ x1 & ?is ratio is express$ 9 ! probability #a_/b4 #aag 99,elem5ts ( ,logic991 ,book ,,iii4 sections #aa & #ah4 #aah 99,encyclopdia ,metropolitana991 art4 99,probabilities991 p4 #djj4 ,n[ if ,a & ,c are :olly unkn[n ?+s1 we h no reason to believe t ,a is ,c r ?an ,a is n ,c4 ,! antec$5t probability is !n #a_/b4 ,if we also h ! probabilities t ,a is ,b1 #a_/b & t ,b is ,c1 #a_/b we h no "r to suppose t ! probability ( ,a be+ ,c is r$uc$ by ! argum5t 9 its fav\r4 ,if ! conclusion is true on its own gr\nds1 ! failure ( ! argum5t does n affect x2 ?us its total probability is its antec$5t probability1 add$ to ! probability t ?is fail+1 ! new argum5t 9 "q e/abli%es x4 ,!re is a probability #a_/b t we %all n require ! special argum5t2 a probability #a_/b t we %all1 & a probability #a_/d t ! argum5t does 9 t case e/abli% x4 ,?us ! complete result is #a_/b #a_/b #a_/d1 or #e_/h4 ,9 g5]al language1 if 99a99 be ! probability f\nd$ on a p>ticul> argum5t1 & 99c99 ! antec$5t probability ( ! ev5t1 ! g5]al result is #a - 7#a - 99a9977#a - 99c9971 or 99a99 99c99 - 99ac994 ,we may put x /ill m g5]ally 9 ?is way3--,let 99a991 99b991 99c991 c4 be ! probabilities ( a conclusion gr\nd$ on v>i\s argum5ts4 ,x is only :5 all ! argum5ts fail t our conclusion proves f9ally untrue2 ! probabilities ( ea* fail+ are respectively1 #a - 99a991 #a - 99b991 #a - 99c991 c42 ! probability t !y w all fail is 7#a - 99a9977#a - 99b9977#a - 99c997 4442 !re=e ! probability t ! conclusion w n fail is #a - 7#a - 99a9977#a - 99b9977#a - 99c997 444 c4 ,x foll[s t e argum5t 9 fav\r ( a conclusion1 h[ev] flimsy & slight1 adds probability to x4 ,:5 x is unkn[n :e!r an ov]due vessel has f\nd]$ or n1 e slight indication ( a lo/ vessel w add "s probability to ! belief ( its loss1 & ! dispro( ( any p>ticul> evid5ce w n disprove ! ev5t4 ,we mu/ apply ^! pr9ciples ( evid5ce ) great c>e1 & obs]ve t 9 a great proportion ( cases ! adduc+ ( a weak argum5t does t5d to ! dispro( ( its conclusion4 ,! ass]tion may h 9 itself great inh]5t improbability z be+ oppos$ to o!r evid5ce or to ! suppos$ law ( nature1 & e reason] may be assum$ to be deal+ pla9ly1 & putt+ =w>d ! :ole =ce ( evid5ce :i* he possesses 9 its fav\r4 ,if he br+s b "o argum5t1 & its probability 99a99 is small1 !n 9 ! =mula #a - 7#a - 99a9977#a - 99c997 bo? 99a99 & 99c99 are small1 & ! :ole expression has b little value4 ,! :ole effect ( an argum5t ?us turns ^u ! "q :e!r o!r argum5ts rema91 s t we c introduce o!r factors 7#a - 99b9971 7#a - 99d9971 c41 into ! above expression4 ,9 a c\rt ( ju/ice1 9 a publication hav+ an express purpose1 & 9 _m o!r cases1 x is d\btless "r to assume t ! :ole evid5ce consid]$ to h any value z reg>ds ! conclusion ass]t$1 is put =w>d4 ,to assign ! antec$5t probability ( any proposition1 may be a matt] ( difficulty or impossibility1 & "o ) :i* logic & ! !ory ( probability h little conc]n4 ,f ! g5]al body ( sci5ce 9 our possession1 we mu/ 9 ea* case make ! be/ judgm5t we c4 ,b 9 ! abs5ce ( all k ! probability %\ld be consid]$ #a_/b1 = if we make x less ?an ?is we incl9e to believe x false r ?an true4 ,?us1 be=e we possess$ any means ( e/imat+ ! magnitudes ( ! fix$ />s1 ! /atem5t t ,sirius 0 great] ?an ! sun _h a probability ( exactly #a_/b2 x 0 z likely t x w\ld be great] z t x w\ld be small]2 & s ( any o!r />4 ,?is 0 ! assumption :i* ,mi*ell made 9 8 admirable speculations4#aai ,x might seem1 inde$1 t z e proposition expresses an agreem5t1 & ! agreem5ts or resemblances betwe5 ph5om5a are inf9itely few] ?an ! diff]5ces 7p4 #dd71 e proposition %\ld 9 ! abs5ce ( o!r in=mation be inf9itely improbable4 ,b 9 our logical sy/em e t]m may be indiff]5tly positive or negative1 s t we express "u ! same =m z _m diff]5ces z agreem5ts4 ,x is impossible !re=e t we %\ld h any reason to disbelieve r ?an to believe a /atem5t ab\t ?+s ( :i* we "k no?+4 ,we c h>dly inde$ inv5t a proposition conc]n+ ! tru? ( :i* we are absolutely ignorant1 except :5 we are entirely ignorant ( ! t]ms us$4 ,if ,i ask ! read] to assign ! odds t a 8,platy?liptic ,coeffici5t is positive0 he w h>dly see 8 way to do+ s1 unless he reg>d !m z ev54 #aai 99,philosophical ,transactions99 7#agfg74 ,abridg4 vol4 xii4 p4 #dce4 ,! assumption t complete d\bt is prop]ly express$ by #a_/b has be5 call$ 9 "q by ,bi%op ,t]rot1#abj :o proposes in/ead ! indef9ite symbol #j_/j2 & he consid]s t 8! 99 priori99 probability d]iv$ f absolute ignorance has no effect ^u ! =ce ( a subsequ5tly admitt$ probability40 ,b if we grant t ! probability may h any value betwe5 #j & #a1 & t e sep>ate value is equally likely1 !n 99n99 & #a - 99n99 are equally likely1 & ! av]age is always #a_/b4 ,or we may take 99p99 4 99dp99 to express ! probability t our e/imate conc]n+ any proposition %\ld lie betwe5 99p99 & 99p99 99dp994 ,! complete probability ( ! proposition is !n ! integral tak5 betwe5 ! limits #a & #j1 or aga9 #a_/b4 #abj 99,transactions ( ! ,ed9burgh ,philosophical ,society991 vol4 xxi4 p4 #cge4 99,difficulties ( ! ,!ory499 ,! !ory ( probability1 ?\gh und\bt$ly true1 requires v c>eful application4 ,n only is x a bran* ( ma!matics 9 :i* ov]sights are frequ5tly committ$1 b x is a matt] ( great difficulty 9 _m cases1 to be sure t ! =mula correctly repres5ts ! data ( ! problem4 ,^! difficulties (t5 arise f ! logical complexity ( ! conditions1 :i* might be1 p]haps1 to "s ext5t cle>$ up by con/antly be>+ 9 m9d ! sy/em ( comb9ations z develop$ 9 ! ,indirect ,logical ,me?od4 ,9 ! /udy ( probabilities1 ma!maticians _h unconsci\sly employ$ logical processes f> 9 advance ( ^? 9 possession ( logicians1 & ! ,indirect ,me?od is b ! full /atem5t ( ^! processes4 ,x is v curi\s h[ (t5 ! mo/ acute & p[]ful intellects h gone a/ray 9 ! calculation ( probabilities4 ,seldom 0 ,pascal mi/ak51 yet he inaugurat$ ! sci5ce ) a mi/ak5 solution4#aba ,leibnitz fell into ! extraord9>y blund] ( ?9k+ t ! numb] twelve 0 z probable a result 9 ! ?r[+ ( two dice z ! numb] elev54#abb ,9 n a few cases ! false solution fir/ obta9$ seems m plausible to ! pres5t day ?an ! correct "o s9ce demon/rat$4 ,james ,b]n\lli c&idly records two false solutions ( a problem :i* he at fir/ ?\ght self-evid5t2 & he adds a w>n+ aga9/ ! risk ( error1 especially :5 we attempt to reason on ?is subject )\t a rigid adh]5ce to me?odical rules & symbols4 ,montmort 0 n free f simil> mi/akes4 ,d',alemb]t con/antly fell into blund]s1 & c\ld n p]ceive1 = in/ance1 t ! probabilities w\ld be ! same :5 co9s are ?r[n successively z :5 ?r[n simultane\sly4 ,"s m5 ( great reputation1 su* z ,ancillon1 ,moses ,m5delssohn1 ,g>ve1 ,augu/e ,comte1#abc ,po9sot1 & ,j4 ,s4 ,mill1#abd h s f> misappreh5d$ ! !ory1 z to "q its value or ev5 to dispute its validity4 ,! errone\s /atem5ts ab\t ! !ory giv5 9 ! e>li] editions ( ,mill's 99,sy/em ( ,logic99 7 p>tially )drawn 9 ! lat] editions4 #aba ,montucla1 99,hi/oire des ,ma?matiques991 vol4 iii4 p4 #chf4 #abb ,leibnitz 99,op]a991 ,dut5s' ,edition1 vol4 vi4 "p i4 p4 #bag4 ,todhunt]'s 99,hi/ory ( ! ,!ory ( ,probability991 p4 #dh4 ,to ! latt] "w ,i am indebt$ = _m ( ! /atem5ts 9 ! text4 #abc 99,positive ,philosophy991 translat$ by ,m>t9eau1 vol4 ii4 p4 #abj4 #abd 99,sy/em ( ,logic991 bk4 iii4 *ap4 #ah1 #e? ,ed4 vol4 ii4 p4 #fa4 ,_m p]sons h a fallaci\s t5d5cy to believe t :5 a *ance ev5t has happ5$ sev]al times toge!r 9 an unusual conjunction1 x is less likely to happ5 aga94 ,d',alemb]t s]i\sly held t if head 0 ?r[n ?ree times runn+ ) a co91 tail w\ld m probably appe> at ! next trial4#abe ,bequel9 adopt$ ! same op9ion1 & yet !re is no reason = x :atev]4 ,if ! ev5t be really casual1 :at has gone be=e _c 9 ! slighte/ degree influ5ce x4 ,z a matt] ( fact1 ! m (t5 a casual ev5t takes place ! m likely x is to happ5 aga92 because !re is "s slight empirical evid5ce ( a t5d5cy4 ,! s\rce ( ! fallacy is to be f\nd entirely 9 ! feel+s ( surprise ) :i* we witness an ev5t happ5+ by *ance1 9 a mann] :i* seems to proce$ f design4 #abe ,montucla1 99,hi/oire991 vol4 iii4 p4 #dje2 ,todhunt]1 p4 #bfc4 ,misappreh5sion may also arise f ov]look+ ! diff]5ce betwe5 p]mutations & comb9ations4 ,to ?r[ t5 heads 9 succession ) a co9 is no m unlikely ?an to ?r[ any o!r p>ticul> succession ( heads & tails1 b x is mu* less likely ?an five heads & five tails )\t reg>d to _! ord]1 because !re are no less ?an #beb diff]5t p>ticul> ?r[s :i* w give ?is result1 :5 we ab/ract ! diff]5ce ( ord]4 ,difficulties arise 9 ! application ( ! !ory f our habitual disreg>d ( slight probabilities4 ,we are oblig$ practically to accept tru?s z c]ta9 :i* are ne>ly s1 because x ceases to be wor? :ile to calculate ! diff]5ce4 ,no puni%m5t c\ld be inflict$ if absolutely c]ta9 evid5ce ( guilt 7 requir$1 & z ,locke rem>ks1 8,he t w n /ir till he infallibly kn[s ! bus9ess he goes ab\t w succe$1 w h b little else to d b to sit /ill & p]i%40#abf ,!re is n a mom5t ( our lives :5 we d n lie "u a slight dang] ( dea?1 or "s mo/ t]rible fate4 ,!re is n a s+le action ( eat+1 dr9k+1 sitt+ d[n1 or /&+ up1 :i* has n prov$ fatal to "s p]son4 ,sev]al philosoph]s h tri$ to assign ! limit ( ! probabilities :i* we reg>d z z]o2 ,buffon nam$ #a_/aj1jjj1 because x is ! probability1 practically disreg>d$1 t a man ( #ef ye>s ( age w die ! next day4 ,pascal rem>k$ t a man w\ld be e/eem$ a fool = hesitat+ to accept dea? :5 ?ree dice gave sixes tw5ty times runn+1 if 8 rew>d 9 case ( a diff]5t result 0 to be a cr[n2 b z ! *ance ( dea? 9 "q is only #a #ffj1 or unity divid$ by a numb] ( #dg places ( figures1 we may be said to incur great] risks e day = less motives4 ,!re is f> great] risk ( dea?1 = in/ance1 9 a game ( cricket or a visit to ! r9k4 #abf 99,essay conc]n+ ,human ,und]/&+991 bk4 iv4 *4 #ad4 #a4 ,no?+ is m requisite ?an to di/+ui% c>efully betwe5 ! tru? ( a !ory & ! tru?ful application ( ! !ory to actual circum/ances4 ,z a g5]al rule1 ev5ts 9 nature & art w pres5t a complexity ( relations exce$+ our p[]s ( treatm5t4 ,! intricate action ( ! m9d (t5 int]v5es & r5d]s complete analysis hopeless4 ,if1 = in/ance1 ! probability t a m>ksman %all hit ! t>get 9 a s+le %ot be #a 9 #aj1 we might seem to h no difficulty 9 calculat+ ! probability ( any succession ( hits2 ?us ! probability ( ?ree successive hits w\ld be "o 9 a ?\s&4 ,b1 9 reality1 ! confid5ce & exp]i5ce d]iv$ f ! fir/ successful %ot w\ld r5d] a second success m probable4 ,! ev5ts are n really indep5d5t1 & !re w\ld g5]ally be a f> great] prepond]ance ( runs ( app>5t luck1 ?an a simple calculation ( probabilities c\ld acc\nt =4 ,9 "s p]sons1 h[ev]1 a rem>kable s]ies ( successes w produce a degree ( excitem5t r5d]+ cont9u$ success almo/ impossible4 ,attempts to apply ! !ory ( probability to ! results ( judicial proce$+s h prov$ ( little value1 simply because ! conditions are f> too intricate4 ,z ,laplace said1 8,tant de passions1 d'intrts div]s et de circon/ances compliqu5t les que/ions relatives ces objets1 qu'elles sont presque t\j\rs insolubles40 ,m5 act+ on a jury1 or giv+ evid5ce be=e a c\rt1 are subject to s _m complex influ5ces t no ma!matical =mulas c be fram$ to express ! real conditions4 ,jurym5 or ev5 judges on ! b5* _c be reg>d$ z act+ indep5d5tly1 ) a def9ite probability 9 fav\r ( ea* deliv]+ a correct judgm5t4 ,ea* man ( ! jury is m or less influ5c$ by ! op9ion ( ! o!rs1 & !re are subtle effects ( "* & mann] & /r5g? ( m9d :i* defy analysis4 ,ev5 9 physical sci5ce we c 9 comp>atively few cases apply ! !ory 9 a def9ite mann]1 because ! data requir$ are too complicat$ & difficult to obta94 ,b su* failures 9 no way dim9i% ! tru? & beauty ( ! !ory itself2 9 reality !re is no bran* ( sci5ce 9 :i* our symbols c cope ) ! complexity ( ,nature4 ,z ,donk9 said1-- 8,i d n see on :at gr\nd x c be d\bt$ t e def9ite /ate ( belief conc]n+ a propos$ hypo!sis1 is 9 itself capable ( be+ repres5t$ by a num]ical expression1 h[ev] difficult or impracticable x may be to asc]ta9 its actual value4 ,x w\ld be v difficult to e/imate 9 numb]s ! 99vis viva99 ( all ! p>ticles ( a human body at any in/ant2 b no "o d\bts t x is capable ( num]ical expression40#abg #abg 99,philosophical ,magaz9e991 #d? ,s]ies1 vol4 i4 p4 #ced4 ,! difficulty1 9 %ort1 is m]ely relative to our k & skill1 & is n absolute or inh]5t 9 ! subject4 ,we mu/ di/+ui% betwe5 :at is !oretically conceivable & :at is practicable ) our pres5t m5tal res\rces4 ,provid$ t our aspirations are po9t$ 9 a "r direction1 we mu/ n all[ !m to be damp$ by ! consid]ation t !y pass beyond :at c n[ be turn$ to imm$iate use4 ,9 spite ( its imm5se difficulties ( application1 & ! asp]sions :i* h be5 mi/ak5ly ca/ ^u x1 ! !ory ( probabilities1 ,i repeat1 is ! noble/1 z x w 9 c\rse ( "t prove1 p]haps ! mo/ fruitful bran* ( ma!matical sci5ce4 ,x is ! v guide ( life1 & h>dly c we take a /ep or make a decision ( any k9d )\t correctly or incorrectly mak+ an e/imation ( probabilities4 ,9 ! next *apt] we proce$ to consid] h[ ! :ole cog5cy ( inductive reason+ re/s ^u probabilities4 ,! tru? or untru? ( a natural law1 :5 c>efully inve/igat$1 resolves itself into a high or l[ degree ( probability1 & ?is is ! case :e!r or n we are capable ( produc+ precise num]ical data4 ,,*apt] ,,xi4 ,,philosophy ,,( ,,inductive ,,inf]5ce4 ,we h inquir$ into ! nature ( p]fect induction1 :]eby we pass backw>ds f c]ta9 obs]v$ comb9ations ( ev5ts1 to ! logical conditions gov]n+ su* comb9ations4 ,we h also inve/igat$ ! gr\nds ( t !ory ( probability1 :i* mu/ be our guide :5 we leave c]ta9ty beh9d1 & dilute k ) ignorance4 ,!re is n[ be=e u ! difficult task ( endeav\r+ to decide h[1 by ! aid ( t !ory1 we c asc5d f ! facts to ! laws ( nature2 & may !n ) m or less success anticipate ! future c\rse ( ev5ts4 ,all our k ( natural objects mu/ be ultimately d]iv$ f obs]vation1 & ! difficult "q arises--,h[ c we ev] "k any?+ :i* we h n directly obs]v$ ?r\gh "o ( our s5ses1 ! ap]tures ( ! m9d8 ,! utility ( reason+ is to assure ourselves t1 at a det]m9ate "t & place1 or "u specifi$ conditions1 a c]ta9 ph5om5on w be obs]v$4 ,:5 we c use our s5ses & p]ceive t ! ph5om5on does occur1 reason+ is sup]flu\s4 ,if ! s5ses _c be us$1 because ! ev5t is 9 ! future1 or out ( rea*1 h[ c reason+ take _! place8 ,app>5tly1 at lea/1 we mu/ inf] ! unkn[n f ! kn[n1 & ! m9d mu/ itself create an addition to ! sum ( k4 ,b ,i hold t x is q impossible to make any real additions to ! cont5ts ( our k1 except ?r\gh new impressions ^u ! s5ses1 or ^u "s seat ( feel+4 ,i %all attempt to %[ t inf]5ce1 :e!r inductive or d$uctive1 is nev] m ?an an unfold+ ( ! cont5ts ( our exp]i5ce1 & t x always proce$s ^u ! assumption t ! future & ! unp]ceiv$ w be gov]n$ by ! same conditions z ! pa/ & ! p]ceiv$1 an assumption :i* w (t5 prove to be mi/ak54 ,9 inductive z 9 d$uctive reason+ ! conclusion nev] passes beyond ! premises4 ,reason+ adds no m to ! implicit cont5ts ( our k1 ?an ! arrangem5t ( ! specim5s 9 a museum adds to ! numb] ( ^? specim5s4 ,arrangem5t adds to our k 9 a c]ta9 s5se3 x all[s u to p]ceive ! simil>ities & peculi>ities ( ! specim5s1 & on ! assumption t ! museum is an adequate repres5tation ( nature1 x enables u to judge ( ! prevail+ =ms ( natural objects4 ,bacon's fir/ aphorism holds p]fectly true1 t man kn[s no?+ b :at he has obs]v$1 provid$ t we include 8 :ole s\rces ( exp]i5ce1 & ! :ole implicit cont5ts ( 8 k4 ,inf]5ce b unfolds ! hidd5 mean+ ( our obs]vations1 & 99! !ory ( probability %[s h[ f> we g beyond our data 9 assum+ t new specim5s w resemble ! old ones991 or t ! future may be reg>d$ z proce$+ uni=mly ) ! pa/4 99,v>i\s ,classes ( ,inductive ,tru?s499 ,x w be desirable1 9 ! fir/ place1 to di/+ui% betwe5 ! sev]al k9ds ( tru?s :i* we endeav\r to e/abli% by induction4 ,al?\gh !re is a c]ta9 common & univ]sal elem5t 9 all our processes ( reason+1 yet div]sity arises 9 _! application4 ,simil>ity ( condition betwe5 ! ev5ts f :i* we argue1 & ^? to :i* we argue1 mu/ always be ! gr\nd ( inf]5ce2 b ?is simil>ity may h reg>d ei!r to "t or place1 or ! simple logical comb9ation ( ev5ts1 or to any conceivable junction ( circum/ances involv+ quality1 "t1 & place4 ,hav+ met ) _m pieces ( sub/ance possess+ ductility & a bright yell[ col\r1 & hav+ discov]$1 by p]fect induction1 t !y all possess a high specific gravity1 & a fre$om f ! corrosive action ( acids1 we are l$ to expect t e piece ( sub/ance1 possess+ l ductility & a simil> yell[ col\r1 w h an equally high specific gravity1 & a l fre$om f corrosion by acids4 ,?is is a case ( ! coexi/5ce ( qualities2 = ! "* ( ! specim5s exam9$ alt]s n ) "t nor place4 ,9 a second class ( cases1 "t w ent] z a pr9cipal gr\nd ( simil>ity4 ,:5 we he> a clock p5dulum beat "t aft] "t1 at equal int]vals1 & ) a uni=m s\nd1 we confid5tly expect t ! /roke w cont9ue to be repeat$ uni=mly4 ,a comet hav+ appe>$ sev]al times at ne>ly equal int]vals1 we inf] t x w probably appe> aga9 at ! end ( ano!r l int]val4 ,a man :o has return$ home ev5+ aft] ev5+ = _m ye>s1 & f\nd 8 h\se /&+1 may1 on l gr\nds1 expect t x w be /&+ ! next ev5+1 & on _m succe$+ ev5+s4 ,ev5 ! cont9u\s exi/5ce ( an object 9 an unalt]$ /ate1 or ! f9d+ aga9 ( t :i* we h hidd51 is b a matt] ( inf]5ce dep5d+ on exp]i5ce4 ,a /ill l>g] & m complex class ( cases involves ! relations ( space1 9 addition to ^? ( "t & quality4 ,hav+ obs]v$ t e triangle drawn ^u ! diamet] ( a circle1 ) its apex ^u ! circumf]5ce1 app>5tly conta9s a "r angle1 we may asc]ta9 t all triangles 9 simil> circum/ances w conta9 "r angles4 ,?is is a case ( pure space reason+1 ap>t f circum/ances ( "t or quality1 & x seems to be gov]n$ by diff]5t pr9ciples ( reason+4 ,i %all endeav\r to %[1 h[ev]1 t geometrical reason+ diff]s b 9 degree f t :i* applies to o!r natural relations4 99,! ,relation ( ,cause & ,effect499 ,9 a v l>ge "p ( ! sci5tific inve/igations :i* mu/ be consid]$1 we deal ) ev5ts :i* foll[ f previ\s ev5ts1 or ) exi/5ces :i* succe$ exi/5ces4 ,sci5ce1 inde$1 might arise ev5 7 mat]ial nature a fix$ & *angeless :ole4 ,end[ m9d ) ! p[] to travel ab\t1 & comp>e "p ) "p1 & x c\ld c]ta9ly draw inf]5ces conc]n+ ! simil>ity ( =ms1 ! coexi/5ce ( qualities1 or ! prepond]ance ( a p>ticul> k9d ( matt] 9 a *angeless _w4 ,a solid univ]se1 9 at lea/ approximate equilibrium1 is n inconceivable1 & !n ! relation ( cause & effect w\ld evid5tly be no m ?an ! relation ( be=e & aft]4 ,z nature exi/s1 h[ev]1 x is a progressive exi/5ce1 ev] mov+ & *ang+ z "t1 ! great indep5d5t v>iable1 proce$s4 ,h5ce x arises t we mu/ cont9ually comp>e :at is happ5+ n[ ) :at happ5$ a mom5t be=e1 & a mom5t be=e t mom5t1 & s on1 until we rea* indef9ite p]iods ( pa/ "t4 ,a comet is se5 mov+ 9 ! sky1 or its con/itu5t p>ticles illum9e ! heav5s ) _! tails ( fire4 ,we _c expla9 ! pres5t movem5ts ( su* a body )\t suppos+ its prior exi/5ce1 ) a def9ite am\nt ( en]gy & a def9ite direction ( motion2 nor c we validly suppose t our task is conclud$ :5 we f9d t x came w&]+ to our sol> sy/em ?r\gh ! unmeasur$ va/ness ( surr\nd+ space4 ,e ev5t mu/ h a cause1 & t cause aga9 a cause1 until we are lo/ 9 ! obscurity ( ! pa/1 & are driv5 to ! belief 9 "o ,fir/ ,cause1 by :om ! c\rse ( nature 0 det]m9$4 99,fallaci\s ,use ( ! ,t]m ,cause499 ,! words ,cause & ,causation h giv5 rise to inf9ite tr\ble & obscurity1 & h 9 no slight degree ret>d$ ! progress ( sci5ce4 ,f ! "t ( ,ari/otle1 ! "w ( philosophy has be5 describ$ z ! discov]y ( ! causes ( ?+s1 & ,francis ,bacon adopt$ ! notion :5 he said 899v]e scire esse p] causas scire9940 ,ev5 n[ x is n uncommonly suppos$ t ! k ( causes is some?+ diff]5t f o!r k1 & consi/s1 z x 71 9 gett+ possession ( ! keys ( nature4 ,a s+le ^w may ?us act z a spell1 & ?r[ ! cle>e/ intellect into confusion1 z ,i h (t5 ?\ght t ,locke 0 ?r[n into confusion :5 endeav\r+ to f9d a mean+ = ! ^w 99p[]994#abh ,9 ,mill's 99,sy/em ( ,logic99 ! t]m 99cause99 seems to h re-ass]t$ its old noxi\s p[]4 ,n only does ,mill treat ! ,laws ( ,causation z almo/ coext5sive ) sci5ce1 b he s uses ! expression z to imply t :5 once we pass )9 ! circle ( causation we deal ) c]ta9ties4 #abh 99,essay conc]n+ ,human ,und]/&+991 bk4 ii4 *ap4 xxi4 ,! philosophical dang] :i* atta*es to ! use ( ?is ^w may be ?us describ$4 ,a cause is def9$ z ! necess>y or inv>iable antec$5t ( an ev5t1 s t :5 ! cause exi/s ! effect w also exi/ or soon foll[4 ,if !n we "k ! cause ( an ev5t1 we "k :at w c]ta9ly happ52 & z x is impli$ t sci5ce1 by a prop] exp]im5tal me?od1 may atta9 to a k ( causes1 x foll[s t exp]i5ce may give u a c]ta9 k ( future ev5ts4 ,b no?+ is m unque/ionable ?an t f9ite exp]i5ce c nev] give u c]ta9 k ( ! future1 s t ei!r a cause is n an inv>iable antec$5t1 or else we c nev] ga9 c]ta9 k ( causes4 ,! fir/ horn ( ?is dilemma is h>dly to be accept$4 ,d\btless !re is 9 nature "s inv>iably act+ me*anism1 su* t f c]ta9 fix$ conditions an inv>iable result always em]ges4 ,b we1 ) our f9ite m9ds & %ort exp]i5ce1 c nev] p5etrate ! my/]y ( ^? exi/5ces :i* embody ! ,w ( ! ,creator1 & evolve x ?r\gh\t "t4 ,we are 9 ! position ( spectators :o witness ! productions ( a complicat$ ma*9e1 b are n all[$ to exam9e its intimate /ructure4 ,we le>n :at does happ5 & :at does appe>1 b if we ask = ! reason1 ! answ] w\ld involve an inf9ite dep? ( my/]y4 ,! simple/ bit ( matt]1 or ! mo/ trivial incid5t1 su* z ! /roke ( two billi>d balls1 (f]s inf9itely m to le>n ?an ev] ! human intellect c fa?om4 ,! ^w cause cov]s j z mu* untold mean+ z any ( ! words 99sub/ance991 99matt]991 99?\ght991 99exi/5ce994 99,confusion ( ,two ,que/ions499 ,! subject is mu* complicat$1 too1 by ! confusion ( two di/9ct que/ions4 ,an ev5t hav+ happ5$1 we may ask-- 7#a7 ,is !re any cause = ! ev5t8 7#b7 ,( :at k9d is t cause8 ,no "o w\ld ass]t t ! m9d possesses any faculty capable ( inf]r+1 prior to exp]i5ce1 t ! occurr5ce ( a sudd5 noise ) flame & smoke indicates ! combu/ion ( a black p[d]1 =m$ by ! mixture ( black1 :ite1 & yell[ p[d]s4 ,! greate/ uphold] ( 99 priori99 doctr9es w all[ t ! p>ticul> aspect1 %ape1 size1 col\r1 texture1 & o!r qualities ( a cause mu/ be ga!r$ ?r\gh ! s5ses4 ,! "q :e!r !re is any cause at all = an ev5t1 is ( a totally diff]5t k9d4 ,if an explosion c\ld happ5 )\t any prior exi/+ conditions1 x mu/ be a new creation--a di/9ct addition to ! univ]se4 ,x may be plausibly held t we c imag9e nei!r ! creation nor annihilation ( any?+4 ,z reg>ds matt]1 ?is has long be5 held true2 z reg>ds =ce1 x is n[ almo/ univ]sally assum$ z an axiom t en]gy c nei!r come into nor g out ( exi/5ce )\t di/9ct acts ( ,creative ,w4 ,t !re exi/s any in/9ctive belief to ?is effect1 inde$1 seems d\btful4 ,we f9d ,lucretius1 a philosoph] ( ! utmo/ intellectual p[] & cultivation1 gravely assum+ t 8 ra9+ atoms c\ld turn aside f _! /raight pa?s 9 a self-det]m9+ mann]1 & by ?is spontane\s orig9ation ( en]gy det]m9e ! =m ( ! univ]se4#abi ,sir ,george ,airy1 too1 s]i\sly discuss$ ! ma!matical conditions "u :i* a p]petual motion1 t is1 a p]petual s\rce ( self-creat$ en]gy1 might exi/4#acj ,! l>g] "p ( ! philosophic _w has long held t 9 m5tal acts !re is free w--9 %ort1 self-causation4 ,x is 9 va9 to attempt to reconcile ?is doctr9e ) t ( an intuitive belief 9 causation1 z ,sir ,w4 ,hamilton c&idly all[$4 #abi 99,de ,r]um ,natura991 bk4 ii4 ll4 #baf-bic4 #acj 99,cambridge ,philosophical ,transactions99 7#ahcj71 vol4 iii4 pp4 #cfi-cgb4 ,x is obvi\s1 moreov]1 t to ass]t ! exi/5ce ( a cause = e ev5t _c d m ?an remove into ! indef9ite pa/ ! inconceivable fact & my/]y ( creation4 ,at any giv5 mom5t matt] & en]gy 7 equal to :at !y are at pres5t1 or !y 7 n2 if equal1 we may make ! same inquiry conc]n+ any o!r mom5t1 h[ev] long prior1 & we are ?us oblig$ to accept "o horn ( ! dilemma--exi/5ce f inf9ity1 or creation at "s mom5t4 ,?is is b "o ( ! _m cases 9 :i* we are compell$ to believe 9 "o or o!r ( two alt]natives1 bo? inconceivable4 ,my pres5t purpose1 h[ev]1 is to po9t out t we mu/ n confuse ?is supremely difficult "q ) t into :i* inductive sci5ce inquires on ! f\ndation ( facts4 ,by induction we ga9 no c]ta9 k2 b by obs]vation1 & ! inv]se use ( d$uctive reason+1 we e/imate ! probability t an ev5t :i* has occurr$ 0 prec$$ by conditions ( specifi$ "*1 or t su* conditions w be foll[$ by ! ev5t4 99,def9ition ( ! ,t]m ,cause499 ,cle> def9itions ( ! ^w cause h be5 giv5 by sev]al philosoph]s4 ,hobbes has said1 8,a cause is ! sum or aggregate ( all su* accid5ts1 bo? 9 ! ag5ts & ! pati5ts1 z concur 9 ! produc+ ( ! effect prop\nd$2 all :i* exi/+ toge!r1 x _c be und]/ood b t ! effect exi/e? ) !m2 or t x c possibly exi/ if any ( !m be abs5t40 ,br[n1 9 8 99,essay on ,causation991 gave a ne>ly correspond+ /atem5t4 8,a cause10 he says1#aca 8may be def9$ to be ! object or ev5t :i* imm$iately prec$es any *ange1 & :i* exi/+ aga9 9 simil> circum/ances w be always imm$iately foll[$ by a simil> *ange40 ,( ! k9dr$ ^w 99p[]991 he likewise says3#acb 8,p[] is no?+ m ?an t inv>iabl5ess ( antec$5ce :i* is impli$ 9 ! belief ( causation40 #aca 99,obs]vations on ! ,nature & ,t5d5cy ( ! ,doctr9e ( ,mr4 ,hume1 conc]n+ ! ,relation ( ,cause & ,effect499 ,second ed4 p4 #dd4 #acb ,ibid4 p4 #ig4 ,^! def9itions may be accept$ ) ! qualification t our k ( causes 9 su* a s5se c be probable only4 ,! "w ( sci5ce consi/s 9 asc]ta9+ ! comb9ations 9 :i* ph5om5a pres5t !mselves4 ,conc]n+ e ev5t we %all h to det]m9e its probable conditions1 or ! gr\p ( antec$5ts f :i* x probably foll[s4 ,an antec$5t is any?+ :i* exi/s prior to an ev5t2 a consequ5t is any?+ :i* exi/s subsequ5tly to an antec$5t4 ,x w n usually happ5 t !re is any probable connection betwe5 an antec$5t & consequ5t4 ,?us nitrog5 is an antec$5t to ! light+ ( a common fire2 b x is s f> f be+ a cause ( ! light+1 t x r5d]s ! combu/ion less active4 ,daylight is an antec$5t to all fires light$ dur+ ! day1 b x probably has no appreciable effect ^u _! burn+4 ,b 9 ! case ( any giv5 ev5t x is usually possible to discov] a c]ta9 numb] ( antec$5ts :i* seem to be always pres5t1 & ) m or less probability we conclude t :5 !y exi/ ! ev5t w foll[4 ,let x be obs]v$ t ! utmo/ latitude is at pres5t enjoy$ 9 ! use ( ! t]m 99cause994 ,n only may a cause be an exi/5t ?+ end[$ ) p[]s1 z oxyg5 is ! cause ( combu/ion1 gunp[d] ! cause ( explosion1 b ! v abs5ce or removal ( a ?+ may also be a cause4 ,x is q correct to speak ( ! dryness ( ! ,egyptian atmosph]e1 or ! abs5ce ( moi/ure1 z be+ ! cause ( ! pres]vation ( mummies1 & o!r rema9s ( antiquity4 ,! cause ( a m\nta9 elevation1 ,+lebor\gh = in/ance1 is ! excavation ( ! surr\nd+ valleys by d5udation4 ,x is n s usual to speak ( ! exi/5ce ( a ?+ at "o mom5t z ! cause ( its exi/5ce at ! next1 b to me x seems ! commone/ case ( causation :i* c occur4 ,! cause ( motion ( a billi>d ball may be ! /roke ( ano!r ball2 & rec5t philosophy leads u to look ^u all motions & *anges1 z b s _m manife/ations ( prior exi/+ en]gy4 ,9 all probability !re is no creation ( en]gy & no de/ruction1 s t z reg>ds bo? me*anical & molecul> *anges1 ! cause is really ! manife/ation ( exi/+ en]gy4 ,9 ! same way ,i see n :y ! prior exi/5ce ( matt] is n also a cause z reg>ds its subsequ5t exi/5ce4 ,all sci5ce t5ds to %[ u t ! exi/5ce ( ! univ]se 9 a p>ticul> /ate at "o mom5t1 is ! condition ( its exi/5ce at ! next mom5t1 9 an app>5tly diff]5t /ate4 ,:5 we analyse ! mean+ :i* we c attribute to ! ^w 99cause991 x am\nts to ! exi/5ce ( suitable portions ( matt] end[$ ) suitable quantities ( en]gy4 ,if we may accept ,horne ,tooke's ass]tion1 99cause99 has etymologically ! mean+ ( 99?+ be=e994 ,?\gh1 inde$1 ! orig9 ( ! ^w is v obscure1 its d]ivatives1 ! ,italian 99cosa991 & ! ,fr5* 99*ose991 mean simply 99?+994 ,9 ! ,g]man equival5t 99ursa*e991 we h pla9ly ! orig9al mean+ ( 99?+ be=e991 ! 99sa*e99 d5ot+ 8int]e/+ or important object10 ! ,engli% 99sake991 & 99ur99 be+ ! equival5t ( ! ,engli% 99ere991 99be=e994 ,we ab&on1 !n1 bo? etymology & philosophy1 :5 we attribute to ! 99laws ( causation99 any mean+ beyond t ( ! 99conditions99 "u :i* an ev5t may be expect$ to happ51 accord+ to our obs]vation ( ! previ\s c\rse ( nature4 ,i h no objection to use ! words cause & causation1 provid$ !y are nev] all[$ to lead u to imag9e t our k ( nature c atta9 to c]ta9ty4 ,i repeat t if a cause is an inv>iable & necess>y condition ( an ev5t1 we c nev] "k c]ta9ly :e!r ! cause exi/s or n4 ,to u1 !n1 a cause is n to be di/+ui%$ f ! gr\p ( positive or negative conditions :i*1 ) m or less probability1 prec$e an ev5t4 ,9 ?is s5se1 !re is no p>ticul> diff]5ce betwe5 k ( causes & our g5]al k ( ! succession ( comb9ations1 9 :i* ! ph5om5a ( nature are pres5t$ to u1 or f\nd to occur 9 exp]im5tal inquiry4 99,di/9ction ( ,inductive & ,d$uctive ,results499 ,we mu/ c>efully avoid confus+ toge!r inductive inve/igations :i* t]m9ate 9 ! e/abli%m5t ( g5]al laws1 & ^? :i* seem to lead directly to ! k ( future p>ticul> ev5ts4 ,t process only c be call$ induction :i* gives g5]al laws1 & x is by ! subsequ5t employm5t ( d$uction t we anticipate p>ticul> ev5ts4 ,if ! obs]vation ( a numb] ( cases %[s t alloys ( metals fuse at l[] temp]atures ?an _! con/itu5t metals1 ,i may ) m or less probability draw a g5]al inf]5ce to t effect1 & may !nce d$uctively asc]ta9 ! probability t ! next alloy exam9$ w fuse at a l[] temp]ature ?an its con/itu5ts4 ,x has be5 ass]t$1 inde$1 by ,mill1#acc & p>tially admitt$ by ,mr4 ,f[l]1#acd t we c argue directly f case to case1 s t :at is true ( "s alloys w be true ( ! next4 ,pr(essor ,ba9 has adopt$ ! same view ( reason+4 ,he ?9ks t ,mill has extricat$ u f ! dead lock ( ! syllogism & effect$ a total revolution 9 logic4 ,he holds t reason+ f p>ticul>s to p>ticul>s is n only ! usual1 ! mo/ obvi\s & ! mo/ ready me?od1 b t x is ! type ( reason+ :i* be/ discloses ! real process4#ace ,d\btless1 ?is is ! usual result ( our reason+1 reg>d be+ _h to degrees ( probability2 b ^! logicians fail entirely to give any explanation ( ! process by :i* we get f case to case4 #acc 99,sy/em ( ,logic991 bk4 ,,ii4 *ap1 iii4 #acd 99,inductive ,logic991 pp4 #ac1 #ad4 #ace ,ba91 99,d$uctive ,logic991 pp4 #bjh1 #bji4 ,x may be all[$ t ! k ( future p>ticul> ev5ts is ! ma9 purpose ( our inve/igations1 & if !re 7 any process ( ?\ght by :i* we c\ld pass directly f ev5t to ev5t )\t asc5d+ into g5]al tru?s1 ?is me?od w\ld be suffici5t1 & c]ta9ly ! briefe/4 ,x is true1 also1 t ! laws ( m5tal association lead ! m9d always to expect ! l aga9 9 app>5tly l circum/ances1 & ev5 animals ( v l[ intellig5ce mu/ h "s trace ( su* p[]s ( association1 s]v+ to guide !m m or less correctly1 9 ! abs5ce ( true reason+ faculties4 ,b x is ! purpose ( logic1 accord+ to ,mill1 to asc]ta9 :e!r inf]5ces h be5 correctly drawn1 r ?an to discov] !m4#acf ,ev5 if we c1 !n1 by habit1 association1 or any rude process ( inf]5ce1 inf] ! future directly f ! pa/1 x is ! "w ( logic to analyse ! conditions on :i* ! correctness ( ?is inf]5ce dep5ds4 ,ev5 ,mill w\ld admit t su* analysis involves ! consid]ation ( g5]al tru?s1#acg & 9 ?is1 z 9 sev]al o!r important po9ts1 we might controv]t ,mill's own views by 8 own /atem5ts4 ,x seems to me undesirable 9 a sy/ematic "w l ?is to ent] into controv]sy at any l5g?1 or to attempt to refute ! views ( o!r logicians4 ,b ,i %all feel b\nd to /ate1 9 a sep>ate publication1 my v delib]ate op9ion t _m ( ,mill's innovations 9 logical sci5ce1 & especially 8 doctr9e ( reason+ f p>ticul>s to p>ticul>s1 are entirely gr\ndless & false4 #acf 99,sy/em ( ,logic499 ,introduction1 #d4 ,fif? ed4 pp4 #h1 #i4 #acg ,ibid4 bk4 ,,ii4 *ap4 iii4 #e1 pp4 #bbe1 c4 99,! ,gr\nds ( ,inductive ,inf]5ce499 ,i hold t 9 all cases ( inductive inf]5ce we mu/ inv5t hypo!ses1 until we fall ^u "s hypo!sis :i* yields d$uctive results 9 accordance ) exp]i5ce4 ,su* accordance r5d]s ! *os5 hypo!sis m or less probable1 & we may !n d$uce1 ) "s degree ( likelihood1 ! nature ( our future exp]i5ce1 on ! assumption t no arbitr>y *ange takes place 9 ! conditions ( nature4 ,we c only argue f ! pa/ to ! future1 on ! g5]al pr9ciple set =? 9 ?is "w1 t :at is true ( a ?+ w be true ( ! l4 ,s f> !n z "o object or ev5t diff]s f ano!r1 all inf]5ce is impossible1 p>ticul>s z p>ticul>s c no m make an inf]5ce ?an gra9s ( s& c make a rope4 ,we mu/ always rise to some?+ :i* is g5]al or same 9 ! cases1 & assum+ t sam5ess to be ext5d$ to new cases we le>n _! nature4 ,he>+ a clock tick five ?\s& times )\t exception or v>iation1 we adopt ! v probable hypo!sis t !re is "s inv>iably act+ ma*9e :i* produces ^? uni=m s\nds1 & :i* w1 9 ! abs5ce ( *ange1 g on produc+ !m4 ,meet+ tw5ty times ) a bright yell[ ductile sub/ance1 & f9d+ x always to be v heavy & incorrodible1 ,i inf] t !re 0 "s natural condition :i* t5d$ 9 ! creation ( ?+s to associate ^! prop]ties toge!r1 & ,i expect to f9d !m associat$ 9 ! next in/ance4 ,b !re always is ! possibility t "s unkn[n *ange may take place betwe5 pa/ & future cases4 ,! clock may run d[n1 or be subject to a hundr$ accid5ts alt]+ its condition4 ,!re is no reason 9 ! nature ( ?+s1 s f> z kn[n to u1 :y yell[ col\r1 ductility1 high specific gravity1 & incorrodibility1 %\ld always be associat$ toge!r1 & 9 o!r cases1 if n 9 ?is1 m5's expectations h be5 deceiv$4 ,our inf]5ces1 !re=e1 always reta9 m or less ( a hypo!tical "*1 & are s f> op5 to d\bt4 ,only 9 proportion z our induction approximates to ! "* ( p]fect induction1 does x approximate to c]ta9ty4 ,! am\nt ( unc]ta9ty corresponds to ! probability t o!r objects ?an ^? exam9$ may exi/ & falsity our inf]5ces2 ! am\nt ( probability corresponds to ! am\nt ( in=mation yield$ by our exam9ation2 & ! !ory ( probability w be ne$$ to prev5t u f ov]-e/imat+ or "u-e/imat+ ! k we possess4 99,illu/rations ( ! ,inductive ,process499 ,to illu/rate ! passage f ! kn[n to ! app>5tly unkn[n1 let u suppose t ! ph5om5a "u inve/igation consi/ ( numb]s1 & t ! foll[+ six numb]s be+ exhibit$ to u1 we are requir$ to inf] ! "* ( ! next 9 ! s]ies3-- #e1 #ae1 #ce1 #de1 #fe1 #ie4 ,! "q fir/ ( all arises1 ,h[ may we describe ?is s]ies ( numb]s8 ,:at is uni=mly true ( !m8 ,! read] _c fail to p]ceive at ! fir/ glance t !y all end 9 five1 & ! problem is1 f ! prop]ties ( ^! six numb]s1 to inf] ! prop]ties ( ! next numb] end+ 9 five4 ,if we te/ _! prop]ties by ! process ( p]fect induction1 we soon p]ceive t !y h ano!r common prop]ty1 namely t ( be+ 99divisible by five )\t rema9d]994 ,may we !n ass]t t ! next numb] end+ 9 five is also divisible by five1 &1 if s1 ^u :at gr\nds8 ,or ext5d+ ! "q1 ,is e numb] end+ 9 five divisible by five8 ,does x foll[ t because six numb]s obey a suppos$ law1 !re=e #cgf1fhe1ige or any o!r numb]1 h[ev] l>ge1 obeys ! law8 ,i answ] 99c]ta9ly n994 ,! law 9 "q is und\bt$ly true2 b its tru? is n prov$ by any f9ite numb] ( examples4 ,all t ^! six numb]s c d is to sugge/ to my m9d ! possible exi/5ce ( su* a law2 & ,i !n asc]ta9 its tru?1 by prov+ d$uctively f ! rules ( decimal num]ation1 t any numb] end+ 9 five mu/ be made up ( multiples ( five1 & mu/ !re=e be itself a multiple4 ,to make ?is m pla91 let ! read] n[ exam9e ! numb]s-- #g1 #ag1 #cg1 #dg1 #fg1 #ig4 ,!y all end 9 #g in/ead ( #e1 & ?\gh n at equal int]vals1 ! int]vals are ! same z 9 ! previ\s case4 ,aft] consid]ation1 ! read] w p]ceive t ^! numb]s all agree 9 be+ 99prime numb]s991 or multiples ( unity only4 ,may we !n inf] t ! next1 or any o!r numb] end+ 9 #g1 is a prime numb]8 ,cle>ly n1 = on trial we f9d t #bg1 #eg1 #aag are n primes4 ,six in/ances1 !n1 treat$ empirically1 lead u to a true & univ]sal law 9 "o case1 & mislead u 9 ano!r case4 ,we ought1 9 fact1 to h no confid5ce 9 any law until we h treat$ x d$uctively1 & h %[n t f ! conditions suppos$ ! results expect$ mu/ ensue4 ,no "o c %[ f ! pr9ciples ( numb]1 t numb]s end+ 9 #g %\ld be primes4 ,f ! hi/ory ( ! !ory ( numb]s "s good examples ( false induction c be adduc$4 ,tak+ ! foll[+ s]ies ( prime numb]s1 #da1 #dc1 #dg1 #ec1 #fa1 #ga1 #hc1 #ig1 #aac1 #aca1 #aea1 c41 x w be f\nd t !y all agree 9 be+ values ( ! g5]al expression 99x99#b 99x99 #da1 putt+ = 99x99 9 succession ! values1 #j1 #a1 #b1 #c1 #d1 c4 ,we seem always to obta9 a prime numb]1 & ! induction is app>5tly /rong1 to ! effect t ?is expression always w give primes4 ,yet a few m trials disprove ?is false conclusion4 ,put 99x99 #dj1 & we obta9 #dj #dj #dj #da1 or #da #da4 ,su* a failure c\ld nev] h happ5$1 _h we %[n any d$uctive reason :y 99x99#b 99x99 #da %\ld give primes4 ,!re c be no d\bt t :at "h happ5s ) =ty in/ances1 might happ5 ) =ty ?\s& or =ty million in/ances4 ,an app>5t law nev] once fail+ up to a c]ta9 po9t may !n sudd5ly break d[n1 s t inductive reason+1 z x has be5 describ$ by "s writ]s1 c give no sure k ( :at is to come4 ,babbage po9t$ out1 9 8 ,n9? ,bridgewat] ,treatise1 t a ma*9e c\ld be con/ruct$ to give a p]fectly regul> s]ies ( numb]s ?r\gh a va/ s]ies ( /eps1 & yet to break ! law ( progression sudd5ly at any requir$ po9t4 ,no numb] ( p>ticul> cases z p>ticul>s enables u to pass by inf]5ce to any new case4 ,x is h>dly ne$ful to inquire "h :at c be inf]r$ f an inf9ite s]ies ( facts1 because !y are nev] practically )9 our p[]2 b we may unhesitat+ly accept ! conclusion1 t no f9ite numb] ( in/ances c ev] prove a g5]al law1 or c give u c]ta9 k ( ev5 "o o!r in/ance4 ,g5]al ma!matical !orems h inde$ be5 discov]$ by ! obs]vation ( p>ticul> cases1 & may aga9 be s discov]$4 ,we h ,newton's own /atem5t1 to ! effect t he 0 ?us l$ to ! all-important ,b9omial ,!orem1 ! basis ( ! :ole /ructure ( ma!matical analysis4 ,speak+ ( a c]ta9 s]ies ( t]ms1 express+ ! area ( a circle or hyp]bola1 he says3 8,i reflect$ t ! d5om9ators 7 9 ari?metical progression2 s t only ! num]ical co-effici5ts ( ! num]ators rema9$ to be inve/igat$4 ,b ^!1 9 ! alt]nate areas1 7 ! figures ( ! p[]s ( ! numb] elev51 namely #aaj1 #aaa1 #aab1 #aac1 #aad2 t is1 9 ! fir/ #a2 9 ! second #a1 #a2 9 ! ?ird #a1 #b1 #a2 9 ! f\r? #a1 #c1 #c1 #a2 9 ! fif? #a1 #d1 #f1 #d1 #a4ach ,i inquir$1 !re=e1 9 :at mann] all ! rema9+ figures c\ld be f\nd f ! fir/ two2 & ,i f\nd t if ! fir/ figure be call$ 99m991 all ! re/ c\ld be f\nd by ! cont9ual multiplication ( ! t]ms ( ! =mula 7799m99 - #j7_/a7 7799m99 - #a7_/b7 7799m99 - #b7_/c7 7799m99 - #c7_/d7 c40#aci #ach ,^! are ! figurate numb]s consid]$ 9 pages #ahc1 #ahg1 c4 #aci 99,comm]cium ,epi/olicum499 99,epi/ola ad ,old5burgum991 ,oct4 #bd1 #afgf4 ,horsley's 99,works ( ,newton991 vol4 iv4 p4 #eda4 ,see ,de ,morgan 9 99,p5ny ,cyclopdia991 art4 8,b9omial ,!orem10 p4 #dab4 ,x is pretty evid5t1 f ?is mo/ int]e/+ /atem5t1 t ,newton1 hav+ simply obs]v$ ! succession ( ! numb]s1 tri$ v>i\s =mul until he f\nd "o :i* agre$ ) !m all4 ,he 0 s little satisfi$ ) ?is process1 h[ev]1 t he v]ifi$ p>ticul> results ( 8 new !orem by comp>ison ) ! results ( common multiplication1 & ! rule = ! extraction ( ! squ>e root4 ,newton1 9 fact1 gave no demon/ration ( 8 !orem2 & ! greate/ ma!maticians ( ! la/ c5tury1 ,james ,b]n\lli1 ,maclaur91 ,l&51 ,eul]1 ,lagrange1 c41 occupi$ !mselves ) discov]+ a conclusive me?od ( d$uctive pro(4 ,!re c be no d\bt t 9 geometry also discov]ies h be5 sugge/$ by direct obs]vation4 ,_m ( ! n[ trivial propositions ( ,euclid's ,elem5ts 7 probably ?us discov]$1 by ! anci5t ,greek geomet]s2 & we h pretty cle> evid5ce ( ?is 9 ! ,comm5t>ies ( ,proclus4#adj ,galileo 0 ! fir/ to exam9e ! rem>kable prop]ties ( ! cycloid1 ! curve describ$ by a po9t 9 ! circumf]5ce ( a :eel roll+ on a plane4 ,by direct obs]vation he asc]ta9$ t ! area ( ! curve is app>5tly ?ree times t ( ! g5]at+ circle or :eel1 b he 0 unable to prove ?is exactly1 or to v]ify x by /rict geometrical reason+4 ,sir ,george ,airy has record$ a curi\s case1 9 :i* he fell accid5tally by trial on a new geometrical prop]ty ( ! sph]e4#ada ,b discov]y 9 su* cases means no?+ m ?an sugge/ion1 & x is always by pure d$uction t ! g5]al law is really e/abli%$4 ,z ,proclus puts x1 99we mu/ pass f s5se to consid]ation994 #adj ,bk4 ii4 *ap4 iv4 #ada 99,philosophical ,transactions99 7#ahff71 vol4 #adf1 p4 #ccd4 ,illu/ration ,giv51 = in/ance1 ! s]ies ( figures 9 ! accompany+ diagram1 measurem5t w %[ t ! curv$ l9es approximate to semicircles1 & ! rectil9e> figures to "r-angl$ triangles4 ,^! figures may seem to sugge/ to ! m9d ! g5]al law t angles inscrib$ 9 semicircles are "r angles2 b no numb] ( in/ances1 & no possible accuracy ( measurem5t w\ld really e/abli% ! tru? ( t g5]al law4 ,avail+ ourselves ( ! sugge/ion furni%$ by ! figures1 we c only inve/igate d$uctively ! consequ5ces :i* fl[ f ! def9ition ( a circle1 until we discov] among !m ! prop]ty ( conta9+ "r angles4 ,p]sons h ?\ght t !y _h discov]$ a me?od ( trisect+ angles by plane geometrical con/ruction1 because a c]ta9 complex arrangem5t ( l9es & circles _h appe>$ to trisect an angle 9 e case tri$ by !m1 & !y inf]r$1 by a suppos$ act ( induction1 t x w\ld succe$ 9 all o!r cases4 ,de ,morgan has record$ a propos$ mode ( trisect+ ! angle :i* c\ld n be discrim9at$ by ! s5ses f a true g5]al solution1 except :5 x 0 appli$ to v obtuse angles4#adb ,9 all su* cases1 x has always turn$ out ei!r t ! angle 0 n trisect$ at all1 or t only c]ta9 p>ticul> angles c\ld be ?us trisect$4 ,! trisectors 7 misl$ by "s app>5t or special co9cid5ce1 & only d$uctive pro( c\ld e/abli% ! tru? & g5]ality ( ! result4 ,9 ?is p>ticul> case1 d$uctive pro( %[s t ! problem attempt$ is impossible1 & t angles g5]ally _c be trisect$ by common geometrical me?ods4 #adb 99,budget ( ,p>adoxes991 p4 #beg4 99,geometrical ,reason+499 ,?is view ( ! matt] is /rongly support$ by ! fur!r consid]ation ( geometrical reason+4 ,no skill & c>e c\ld ev] enable u to v]ify absolutely any "o geometrical proposition4 ,r\sseau1 9 8 99,emile991 tells u t we %\ld tea* a *ild geometry by caus+ him to measure & comp>e figures by sup]position4 ,:ile a *ild 0 yet incapable ( g5]al reason+1 ?is w\ld d\btless be an in/ructive ex]cise2 b x nev] c\ld tea* geometry1 nor prove ! tru? ( any "o proposition4 ,all our figures are rude approximations1 & !y may happ5 to seem unequal :5 !y %\ld be equal1 & equal :5 !y %\ld be unequal4 ,moreov] figures may f *ance be equal 9 case aft] case1 & yet !re may be no g5]al reason :y !y %\ld be s4 ,! results ( d$uctive geometrical reason+ are absolutely c]ta91 & are ei!r exactly true or capable ( be+ c>ri$ to any requir$ degree ( approximation4 ,9 a p]fect triangle1 ! angles mu/ be equal to "o half-revolution precisely2 ev5 an inf9itesimal div]g5ce w\ld be impossible2 & ,i believe ) equal confid5ce1 t h[ev] _m are ! angles ( a figure1 provid$ !re are no re-entrant angles1 ! sum ( ! angles w be precisely & absolutely equal to twice z _m "r-angles z ! figure has sides1 less by f\r "r-angles4 ,9 su* cases1 ! d$uctive pro( is absolute & complete2 empirical v]ification c at ! mo/ gu>d aga9/ accid5tal ov]sights4 ,!re is a second class ( geometrical tru?s :i* c only be prov$ by approximation2 b1 z ! m9d sees no reason :y t approximation %\ld n always g on1 we arrive at complete conviction4 ,we ?us le>n t ! surface ( a sph]e is equal exactly to two-?irds ( ! :ole surface ( ! circumscrib+ cyl9d]1 or to f\r times ! area ( ! g5]at+ circle4 ,! area ( a p>abola is exactly two-?irds ( t ( ! circumscrib+ p>allelogram4 ,! area ( ! cycloid is exactly ?ree times t ( ! g5]at+ circle4 ,^! are tru?s t we c\ld nev] asc]ta91 nor ev5 v]ify by obs]vation2 = any f9ite am\nt ( diff]5ce1 less ?an :at ! s5ses c disc]n1 w\ld falsify !m4 ,!re are geometrical relations aga9 :i* we _c assign exactly1 b c c>ry to any desirable degree ( approximation4 ,! ratio ( ! circumf]5ce to ! diamet] ( a circle is t ( #cadaeibfecehigicbchdf4444 to #a1 & ! approximation may be c>ri$ to any ext5t by ! exp5diture ( suffici5t lab\r4 ,mr4 ,w4 ,%anks has giv5 ! value ( ?is natural con/ant1 kn[n z 1 to ! ext5t ( #gjg places ( decimals4#adc ,"s ye>s s9ce1 ,i amus$ myself by try+ h[ ne> ,i c\ld get to ?is ratio1 by ! c>eful use ( compasses1 & ,i did n come ne>] ?an #a "p 9 #edj4 ,we might imag9e measurem5ts s accurately execut$ z to give u eight or t5 places correctly4 ,b ! p[] ( ! h&s & s5ses mu/ soon /op1 :]eas ! m5tal p[]s ( d$uctive reason+ c proce$ to an unlimit$ degree ( approximation4 ,geometrical tru?s1 !n1 are incapable ( v]ification2 &1 if s1 !y _c ev5 be le>nt by obs]vation4 ,h[ c ,i h le>nt by obs]vation a proposition ( :i* ,i _c ev5 prove ! tru? by obs]vation1 :5 ,i am 9 possession ( x8 ,all t obs]vation or empirical trial c d is to sugge/ propositions1 ( :i* ! tru? may aft]w>ds be prov$ d$uctively4 #adc 99,proce$+s ( ! ,royal ,society99 7#ahgb-c71 vol4 xxi4 p4 #cai4 ,if ,viviani's /ory is to be believ$1 ,galileo endeav\r$ to satisfy himself ab\t ! area ( ! cycloid by cutt+ out sev]al l>ge cycloids 9 pa/ebo>d1 & !n comp>+ ! areas ( ! curve & ! g5]at+ circle by weigh+ !m4 ,9 e trial ! curve seem$ to be r less ?an ?ree times ! circle1 s t ,galileo1 we are told1 began to suspect t ! ratio 0 n precisely #c to #a4 ,x is q cle>1 h[ev]1 t no process ( weigh+ or measur+ c\ld ev] prove tru?s l ^!1 & x rema9$ = ,torricelli to %[ :at 8 ma/] ,galileo _h only guess$ at4#add #add 99,life ( ,galileo991 ,society = ! ,diffusion ( ,useful ,k1 p4 #ajb4 ,mu* has be5 said ab\t ! peculi> c]ta9ty ( ma!matical reason+1 b x is only c]ta9ty ( d$uctive reason+1 & equal c]ta9ty atta*es to all correct logical d$uction4 ,if a triangle be "r-angl$1 ! squ>e on ! hypo!nuse w und\bt$ly equal ! sum ( ! two squ>es on ! o!r sides2 b ,i c nev] be sure t a triangle is "r-angl$3 s ,i c be c]ta9 t nitric acid w n dissolve gold1 provid$ ,i "k t ! sub/ances employ$ really correspond to ^? on :i* ,i tri$ ! exp]im5t previ\sly4 ,"h is l c]ta9ty ( inf]5ce1 & l d\bt z to ! facts4 99,discrim9ation ( ,c]ta9ty & ,probability499 ,we c nev] recur too (t5 to ! tru? t our k ( ! laws & future ev5ts ( ! ext]nal _w is only probable4 ,! m9d itself is q capable ( possess+ c]ta9 k1 & x is well to discrim9ate c>efully betwe5 :at we c & _c "k ) c]ta9ty4 ,9 ! fir/ place1 :atev] feel+ is actually pres5t to ! m9d is c]ta9ly kn[n to t m9d4 ,if ,i see blue sky1 ,i may be q sure t ,i d exp]i5ce ! s5sation ( blu5ess4 ,:atev] ,i d feel1 ,i d feel beyond all d\bt4 ,we are inde$ v likely to confuse :at we really feel ) :at we are incl9$ to associate ) x1 or inf] inductively f x2 b ! :ole ( our consci\sness1 z f> z x is ! result ( pure intuition & free f inf]5ce1 is c]ta9 k beyond all d\bt4 ,9 ! second place1 we may h c]ta9ty ( inf]5ce2 ! fundam5tal laws ( ?\ght1 & ! rule ( sub/itution 7p4 #i71 are c]ta9ly true2 & if my s5ses c\ld in=m me t ,a 0 indi/+ui%able 9 col\r f ,b1 & ,b f ,c1 !n ,i %\ld be equally c]ta9 t ,a 0 indi/+ui%able f ,c4 ,9 %ort1 :atev] tru? !re is 9 ! premises1 ,i c c]ta9ly embody 9 _! correct logical result4 ,b ! c]ta9ty g5]ally assumes a hypo!tical "*4 ,i nev] c be q sure t two col\rs are exactly alike1 t two magnitudes are exactly equal1 or t two bodies :atsoev] are id5tical ev5 9 _! app>5t qualities4 ,almo/ all our judgm5ts involve quantitative relations1 &1 z w be %[n 9 succe$+ *apt]s1 we c nev] atta9 exactness & c]ta9ty :]e cont9u\s quantity ent]s4 ,judgm5ts conc]n+ discont9u\s quantity or numb]s1 h[ev]1 all[ ( c]ta9ty2 ,i may e/abli% beyond d\bt1 = in/ance1 t ! diff]5ce ( ! squ>es ( #ag & #ac is ! product ( #ag #ac & #ag - #ac1 & is !re=e #cj #d1 or #abj4 ,inf]5ces :i* we draw conc]n+ natural objects are nev] c]ta9 except 9 a hypo!tical po9t ( view4 ,x might seem to be c]ta9 t iron is magnetic1 or t gold is incapable ( solution 9 nitric acid2 b1 if we c>efully inve/igate ! mean+s ( ^! /atem5ts1 !y w be f\nd to involve no c]ta9ty b t ( consci\sness & t ( hypo!tical inf]5ce4 ,= :at d ,i mean by iron or gold8 ,if ,i *oose a rem>kable piece ( yell[ sub/ance1 call x gold1 & !n imm]se x 9 a liquid :i* ,i call nitric acid1 & f9d t !re is no *ange call$ solution1 !n consci\sness has c]ta9ly in=m$ me t1 ) my mean+ ( ! t]ms1 8,gold is insoluble 9 nitric acid40 ,i may fur!r be c]ta9 ( some?+ else2 = if ?is gold & nitric acid rema9 :at !y 71 ,i may be sure !re w be no solution on aga9 try+ ! exp]im5t4 ,if ,i take o!r portions ( gold & nitric acid1 & am sure t !y really are id5tical 9 prop]ties ) ! =m] portions1 ,i c be c]ta9 t !re w be no solution4 ,b at ?is po9t my k becomes purely hypo!tical2 = h[ c ,i be sure )\t trial t ! gold & acid are really id5tical 9 nature ) :at ,i =m]ly call$ gold & nitric acid4 ,h[ d ,i "k gold :5 ,i see x8 ,if ,i judge by ! app>5t qualities--col\r1 ductility1 specific gravity1 c41 ,i may be misl$1 because !re may always exi/ a sub/ance :i* to ! col\r1 ductility1 specific gravity1 & o!r specifi$ qualities1 jo9s o!rs :i* we d n expect4 ,simil>ly1 if iron is magnetic1 z %[n by an exp]im5t ) objects answ]+ to ^? names1 !n all iron is magnetic1 mean+ all pieces ( matt] id5tical ) my assum$ piece4 ,b 9 try+ to id5tify iron1 ,i am always op5 to mi/ake4 ,nor is ?is liability to mi/ake a matt] ( speculation only4#ade #ade ,pr(essor ,b[5 has excell5tly /at$ ?is view4 99,treatise on ,logic499 ,cambridge1 ,u4,s4,a41 #ahff1 p4 #ced4 ,! hi/ory ( *emi/ry %[s t ! mo/ confid5t inf]5ces may h be5 falsifi$ by ! confusion ( "o sub/ance ) ano!r4 ,?us /rontia 0 nev] discrim9at$ f b>yta until ,klapro? & ,hay detect$ diff]5ces betwe5 "s ( _! prop]ties4 ,accord+ly *emi/s mu/ (t5 h inf]r$ conc]n+ /rontia :at 0 only true ( b>yta1 & 99vice v]s994 ,!re is n[ no d\bt t ! rec5tly discov]$ sub/ances1 csium & rubidium1 7 long mi/ak5 = potassium4#adf ,o!r elem5ts h (t5 be5 confus$ toge!r--= in/ance1 tantalum & niobium2 sulphur & sel5ium2 c]ium1 lan?anum1 & didymium2 yttrium & erbium4 #adf ,roscoe's 99,spectrum ,analysis991 #a/ edit41 p4 #ih4 ,ev5 ! be/ kn[n laws ( physical sci5ce d n exclude false inf]5ce4 ,no law ( nature has be5 bett] e/abli%$ ?an t ( univ]sal gravitation1 & we believe ) ! utmo/ confid5ce t any body capable ( affect+ ! s5ses w attract o!r bodies1 & fall to ! e>? if n prev5t$4 ,eul] rem>ks t1 al?\gh he _h nev] made trial ( ! /ones :i* compose ! *ur* ( ,magdeburg1 yet he _h n ! lea/ d\bt t all ( !m 7 heavy1 & w\ld fall if unsupport$4 ,b he adds1 t x w\ld be extremely difficult to give any satisfactory explanation ( ?is confid5t belief4#adg ,! fact is1 t ! belief ought n to am\nt to c]ta9ty until ! exp]im5t has be5 tri$1 & 9 ! meantime a slight am\nt ( unc]ta9ty ent]s1 because we _c be sure t ! /ones ( ! ,magdeburg ,*ur* resemble o!r /ones 9 all _! prop]ties4 #adg ,eul]'s 99,lett]s to a ,g]man ,pr9cess991 translat$ by ,hunt]4 #bnd ed41 vol4 ii4 pp4 #ag1 #ah4 ,9 l mann]1 n "o ( ! inductive tru?s :i* m5 h e/abli%$1 or ?9k !y h e/abli%$1 is really safe f exception or rev]sal4 ,lavoisi]1 :5 lay+ ! f\ndations ( *emi/ry1 met ) s _m in/ances t5d+ to %[ ! exi/5ce ( oxyg5 9 all acids1 t he adopt$ a g5]al conclusion to t effect1 & devis$ ! "n oxyg5 accord+ly4 ,he ent]ta9$ no appreciable d\bt t ! acid exi/+ 9 sea salt also conta9$ oxyg52#adh yet subsequ5t exp]i5ce falsifi$ 8 expectations4 ,?is in/ance ref]s to a sci5ce 9 its infancy1 speak+ relatively to ! possible a*ievem5ts ( m54 ,b all sci5ces are & ev] w rema9 9 _! infancy1 relatively to ! ext5t & complexity ( ! univ]se :i* !y und]take to inve/igate4 ,eul] expresses no m ?an ! tru? :5 he says t x w\ld be impossible to fix on any "o ?+ really exi/+1 ( :i* we c\ld h s p]fect a k z to put u beyond ! rea* ( mi/ake4#adi ,we may be q c]ta9 t a comet w g on mov+ 9 a simil> pa? 99if99 all circum/ances rema9 ! same z be=e2 b if we leave out ?is ext5sive qualification1 our pr$ictions w always be subject to ! *ance ( falsification by "s unexpect$ ev5t1 su* z ! division ( ,biela's comet or ! int]f]5ce ( an unkn[n gravitat+ body4 #adh ,lavoisi]'s 99,*emi/ry991 translat$ by ,k]r4 #crd ed41 pp4 #aad1 #aba1 #abc4 #adi ,eul]'s 99,lett]s991 vol4 ii4 p4 #ba4 ,inductive inf]5ce might atta9 to c]ta9ty if our k ( ! ag5ts exi/+ ?r\gh\t ! univ]se 7 complete1 & if we 7 at ! same "t c]ta9 t ! same ,p[] :i* creat$ ! univ]se w\ld all[ x to proce$ )\t arbitr>y *ange4 ,!re is always a possibility ( causes be+ 9 exi/5ce )\t our k1 & ^! may at any mom5t produce an unexpect$ effect4 ,ev5 :5 by ! !ory ( probabilities we succe$ 9 =m+ "s notion ( ! comp>ative confid5ce ) :i* we %\ld receive inductive results1 x yet appe>s to me t we mu/ make an assumption4 ,ev5ts come out l balls f ! va/ ballot-box ( nature1 & close obs]vation w enable u to =m "s notion1 z we %all see 9 ! next *apt]1 ( ! cont5ts ( t ballot-box4 ,b we mu/ /ill assume t1 betwe5 ! "t ( an obs]vation & t to :i* our inf]5ces relate1 no *ange 9 ! ballot-box has be5 made4 ,,*apt] ,,xii4 ,,! ,,inductive ,,or ,,inv]se ,,application ,,( ,,! ,,!ory ,,( ,,probability4 ,we h hi!rto consid]$ ! !ory ( probability only 9 its simple d$uctive employm5t1 9 :i* x enables u to det]m9e f giv5 conditions ! probable "* ( ev5ts happ5+ "u ^? conditions4 ,b z d$uctive reason+ :5 inv]sely appli$ con/itutes ! process ( induction1 s ! calculation ( probabilities may be inv]sely appli$2 f ! kn[n "* ( c]ta9 ev5ts we may argue backw>ds to ! probability ( a c]ta9 law or condition gov]n+ ^? ev5ts4 ,hav+ satisfactorily accompli%$ ?is "w1 we may inde$ calculate =w>ds to ! probable "* ( future ev5ts happ5+ "u ! same conditions2 b ?is "p ( ! process is a direct use ( d$uctive reason+ 7p4 #bbf74 ,n[ x is highly in/ructive to f9d t :e!r ! !ory ( probability be d$uctively or inductively appli$1 ! calculation is always p]=m$ accord+ to ! pr9ciples & rules ( d$uction4 ,! probability t an ev5t has a p>ticul> condition entirely dep5ds ^u ! probability t if ! condition exi/$ ! ev5t w\ld foll[4 ,if we take up a pack ( common play+ c>ds1 & obs]ve t !y are arrang$ 9 p]fect num]ical ord]1 we conclude beyond all reasonable d\bt t !y h be5 ?us int5tionally arrang$ by "s p]son acqua9t$ ) ! usual ord] ( sequ5ce4 ,?is conclusion is q irresi/ible1 & rightly s2 = !re are b two suppositions :i* we c make z to ! reason ( ! c>ds be+ 9 t p>ticul> ord]3-- #a4 ,!y may h be5 int5tionally arrang$ by "s "o :o w\ld probably pref] ! num]ical ord]4 #b4 ,!y may h fall5 into t ord] by *ance1 t is1 by "s s]ies ( conditions :i*1 be+ unkn[n to u1 _c be kn[n to lead by pref]5ce to ! p>ticul> ord] 9 "q4 ,! latt] supposition is by no means absurd1 = any "o ord] is z likely z any o!r :5 !re is no prepond]at+ t5d5cy4 ,b we c readily calculate by ! doctr9e ( p]mutations ! probability t fifty-two objects w\ld fall by *ance into any "o p>ticul> ord]4 ,fifty-two objects c be arrang$ 9 #eb #ea 444 #c #b #a or ab\t #hjff 7#aj7fd possible ord]s1 ! numb] obta9$ requir+ #fh places ( figures = its full expression4 ,h5ce x is excessively unlikely t anyone %\ld ev] meet ) a pack ( c>ds arrang$ 9 p]fect ord] by accid5t4 ,if we d meet ) a pack s arrang$1 we inevitably adopt ! o!r supposition1 t "s p]son1 hav+ reasons = pref]r+ t special ord]1 has ?us put !m toge!r4 ,we "k t ( ! imm5se numb] ( possible ord]s ! num]ical ord] is ! mo/ rem>kable2 x is useful z prov+ ! p]fect con/itution ( ! pack1 & x is ! int5tional result ( c]ta9 games4 ,at any rate1 ! probability t int5tion %\ld produce t ord] is incomp>ably great] ?an ! probability t *ance %\ld produce x2 & z a c]ta9 pack exi/s 9 t ord]1 we rightly pref] ! supposition :i* mo/ probably leads to ! obs]v$ result4 ,by a simil> mode ( reason+ we e day arrive1 & validly arrive1 at conclusions approximat+ to c]ta9ty4 ,:5ev] we obs]ve a p]fect resemblance betwe5 two objects1 z1 = in/ance1 two pr9t$ pages1 two engrav+s1 two co9s1 two foot-pr9ts1 we are w>rant$ 9 ass]t+ t !y proce$ f ! same type1 ! same plate1 ! same pair ( dies1 or ! same boot4 ,& :y8 ,because x is almo/ impossible t ) diff]5t types1 plates1 dies1 or boots "s app>5t di/9ction ( =m %\ld n be produc$4 ,x is impossible = ! h& ( ! mo/ skilful arti/ to make two objects alike1 s t me*anical repetition is ! only probable explanation ( exact simil>ity4 ,we c (t5 e/abli% ) extreme probability t "o docum5t is copi$ f ano!r4 ,suppose t ea* docum5t conta9s #aj1jjj words1 & t ! same ^w is incorrectly spelt 9 ea*4 ,!re is !n a probability ( less ?an #a 9 #aj1jjj t ! same mi/ake %\ld be made 9 ea*4 ,if we meet ) a second error occurr+ 9 ea* docum5t1 ! probability is less ?an #a 9 #aj1jjj #iiii1 t two su* co9cid5ces %\ld occur by *ance1 & ! numb]s gr[ ) extreme rapidity = m num]\s co9cid5ces4 ,we _c make any precise calculations )\t tak+ into acc\nt ! "* ( ! errors committ$1 conc]n+ ! conditions ( :i* we h no accurate means ( e/imat+ probabilities4 ,nev]!less1 abundant evid5ce may ?us be obta9$ z to ! d]ivation ( docum5ts f ea* o!r4 ,9 ! exam9ation ( _m sets ( log>i?mic tables1 six rem>kable errors 7 f\nd to be pres5t 9 all b two1 & x 0 prov$ t tables pr9t$ at ,p>is1 ,b]l91 ,flor5ce1 ,avignon1 & ev5 9 ,*9a1 besides ?irte5 sets pr9t$ 9 ,engl& betwe5 ! ye>s #afcc & #ahbb1 7 d]iv$ directly or indirectly f "s common s\rce4#aej ,) a c]ta9 am\nt ( lab\r1 x is possible to e/abli% beyond reasonable d\bt ! relation%ip or g5ealogy ( any numb] ( copies ( "o docum5t1 proce$+ possibly f p>5t copies n[ lo/4 ,! relations betwe5 ! manuscripts ( ! ,new ,te/am5t h be5 elaborately inve/igat$ 9 ?is mann]1 & ! same "w has be5 p]=m$ = _m classical writ+s1 especially by ,g]man s*ol>s4 #aej ,l>dn]1 99,ed9burgh ,review991 ,july #ahcd1 p4 #bgg4 99,pr9ciple ( ! ,inv]se ,me?od499 ,! inv]se application ( ! rules ( probability entirely dep5ds ^u a proposition :i* may be ?us /at$1 ne>ly 9 ! words ( ,laplace4#aea 99,if an ev5t c be produc$ by any "o ( a c]ta9 numb] ( diff]5t causes1 all equally probable priori1 ! probabilities ( ! exi/5ce ( ^! causes z inf]r$ f ! ev5t1 are proportional to ! probabilities ( ! ev5t z d]iv$ f ^! causes499 ,9 o!r words1 ! mo/ probable cause ( an ev5t :i* has happ5$ is t :i* w\ld mo/ probably lead to ! ev5t suppos+ ! cause to exi/2 b all o!r possible causes are also to be tak5 into acc\nt ) probabilities proportional to ! probability t ! ev5t w\ld happ5 if ! cause exi/$4 ,suppose1 to fix our ideas cle>ly1 t ,e is ! ev5t1 & ,c#a ,c#b ,c#c are ! ?ree only conceivable causes4 ,if ,c#a exi/1 ! probability is 99p99#a t ,e w\ld foll[2 if ,c#b or ,c#c exi/1 ! l probabilities are respectively 99p99#b & 99p99#c4 ,!n z 99p99#a is to 99p99#b1 s is ! probability ( ,c#a be+ ! actual cause to ! probability ( ,c#b be+ x2 &1 simil>ly1 z 99p99#b is to 99p99#c1 s is ! probability ( ,c#b be+ ! actual cause to ! probability ( ,c#c be+ x4 ,by a simple ma!matical process we arrive at ! conclusion t ! actual probability ( ,c#a be+ ! cause is 99p99#a_/799p99#a 99p99#b 99p99#c72 #aea 99,mmoires p> div]s ,savans991 tom4 vi42 quot$ by ,todhunt] 9 8 99,hi/ory ( ! ,!ory ( ,probability991 p4 #deh4 & ! simil> probabilities ( ! exi/5ce ( ,c#b & ,c#c are1 99p99#b_/799p99#a 99p99#b 99p99#c7 & 99p99#c_/799p99#a 99p99#b 99p99#c74 ,! sum ( ^! ?ree fractions am\nts to unity1 :i* correctly expresses ! c]ta9ty t "o cause or o!r mu/ be 9 op]ation4 ,we may ?us /ate ! result 9 g5]al language4 99,if x is c]ta9 t "o or o!r ( ! suppos$ causes exi/s1 ! probability t any "o does exi/ is ! probability t if x exi/s ! ev5t happ5s1 divid$ by ! sum ( all ! simil> probabilities499 ,!re may seem to be an intricacy 9 ?is subject :i* may prove di/a/eful to "s read]s2 b ?is intricacy is ess5tial to ! subject 9 h&4 ,no "o c possibly und]/& ! pr9ciples ( inductive reason+1 unless he w take ! tr\ble to ma/] ! mean+ ( ?is rule1 by :i* we rec$e f an ev5t to ! probability ( ea* ( its possible causes4 ,?is rule or pr9ciple ( ! indirect me?od is t :i* common s5se leads u to adopt almo/ in/9ctively1 be=e we h any compreh5sion ( ! pr9ciple 9 its g5]al =m4 ,x is easy to see1 too1 t x is ! rule :i* w1 out ( a great multitude ( cases1 lead u mo/ (t5 to ! tru?1 s9ce ! mo/ probable cause ( an ev5t really means t cause :i* 9 ! greate/ numb] ( cases produces ! ev5t4 ,donk9 & ,boole h giv5 demon/rations ( ?is pr9ciple1 b ! "o mo/ easy to compreh5d is t ( ,poisson4 ,he imag9es ea* possible cause ( an ev5t to be repres5t$ by a di/9ct ballot-box1 conta9+ black & :ite balls1 9 su* a ratio t ! probability ( a :ite ball be+ drawn is equal to t ( ! ev5t happ5+4 ,he fur!r supposes t ea* box1 z is possible1 conta9s ! same total numb] ( balls1 black & :ite2 !n1 mix+ all ! cont5ts ( ! boxes toge!r1 he %[s t if a :ite ball be drawn f ! aggregate ballot-box ?us =m$1 ! probability t x proce$$ f any p>ticul> ballot-box is repres5t$ by ! numb] ( :ite balls 9 t p>ticul> box1 divid$ by ! total numb] ( :ite balls 9 all ! boxes4 ,?is result corresponds to t giv5 by ! pr9ciple 9 "q4#aeb #aeb ,poisson1 99,re*]*es sur la ,probabilit des ,jugem5ts991 ,p>is1 #ahcg1 pp4 #hb1 #hc4 ,?us1 if !re be ?ree boxes1 ea* conta9+ t5 balls 9 all1 & respectively conta9+ sev51 f\r1 & ?ree :ite balls1 !n on mix+ all ! balls toge!r we h f\rte5 :ite ones2 & if we draw a :ite ball1 t is if ! ev5t happ5s1 ! probability t x came out ( ! fir/ box is #g_/ad2 :i* is exactly equal to 7#g_/aj7_/7g_/aj #d_/aj #c_/aj71 ! fraction giv5 by ! rule ( ! ,inv]se ,me?od4 99,simple ,applications ( ! ,inv]se ,me?od499 ,9 _m cases ( sci5tific induction we may apply ! pr9ciple ( ! inv]se me?od 9 a simple mann]4 ,if only two1 or at ! mo/ a few hypo!ses1 may be made z to ! orig9 ( c]ta9 ph5om5a1 we may sometimes easily calculate ! respective probabilities4 ,x 0 ?us t ,buns5 & ,kir*h(f e/abli%$1 ) a probability little %ort ( c]ta9ty1 t iron exi/s 9 ! sun4 ,on comp>+ ! spectra ( sunlight & ( ! light proce$+ f ! inc&esc5t vap\r ( iron1 x became app>5t t at lea/ sixty bright l9es 9 ! spectrum ( iron co9cid$ ) d>k l9es 9 ! sun's spectrum4 ,su* co9cid5ces c\ld nev] be obs]v$ ) c]ta9ty1 because1 ev5 if ! l9es only closely approa*$1 ! in/rum5tal imp]fections ( ! spectroscope w\ld make !m app>5tly co9cid5t1 & if "o l9e came )9 half a millimetre ( ano!r1 on ! map ( ! spectra1 !y c\ld n be pron\nc$ di/9ct4 ,n[ ! av]age di/ance ( ! sol> l9es on ,kir*h(f's map is #b mm41 & if we ?r[ d[n a l9e1 z x 71 by pure *ance on su* a map1 ! probability is ab\t "o-half t ! new l9e w fall )9 #a_/b mm4 on "o side or ! o!r ( "s "o ( ! sol> l9es4 ,to put x 9 ano!r way1 we may suppose t ea* sol> l9e1 ei!r on acc\nt ( its real bread?1 or ! defects ( ! in/rum5t1 possesses a bread? ( #a_/b mm41 & t ea* l9e 9 ! iron spectrum has a l bread?4 ,! probability !n is j "o-half t ! c5tre ( ea* iron l9e w come by *ance )9 #a mm4 ( ! c5tre ( a sol> l9e1 s z to appe> to co9cide ) x4 ,! probability ( casual co9cid5ce ( ea* iron l9e ) a sol> l9e is 9 l mann] #a_/b4 ,co9cid5ce 9 ! case ( ea* ( ! sixty iron l9es is a v unlikely ev5t if x arises casually1 = x w\ld h a probability ( only 7#a_/b7fj or less ?an #a 9 a trillion4 ,! odds1 9 %ort1 are m ?an a million million millions to unity aga9/ su* casual co9cid5ce4#aec ,b on ! o!r hypo!sis1 t iron exi/s 9 ! sun1 x is highly probable t su* co9cid5ces w\ld be obs]v$2 x is imm5sely m probable t sixty co9cid5ces w\ld be obs]v$ if iron exi/$ 9 ! sun1 ?an t !y %\ld arise f *ance4 ,h5ce by our pr9ciple x is imm5sely probable t iron does exi/ 9 ! sun4 #aec ,kir*h(f's 99,rese>*es on ! ,sol> ,spectrum994 ,fir/ "p1 translat$ by ,roscoe1 pp4 #ah1 #ai4 ,all ! o!r int]e/+ results1 giv5 by ! comp>ison ( spectra1 re/ ^u ! same pr9ciple ( probability4 ,! almo/ complete co9cid5ce betwe5 ! spectra ( sol>1 lun>1 & planet>y light r5d]s x practically c]ta9 t ! light is all ( sol> orig91 & is reflect$ f ! surfaces ( ! moon & planets1 suff]+ only slight alt]ation f ! atmosph]es ( "s ( ! planets4 ,a fre% confirmation ( ! tru? ( ! ,cop]nican !ory is ?us furni%$4 ,h]s*el prov$ 9 ?is way ! connection betwe5 ! direction ( ! oblique faces ( qu>tz cry/als1 & ! direction 9 :i* ! same cry/als rotate ! plane ( pol>isation ( light4 ,= if x is f\nd 9 a second cry/al t ! relation is ! same z 9 ! fir/1 ! probability ( ?is happ5+ by *ance is #a_/b2 ! probability t 9 ano!r cry/al also ! direction w be ! same is #a_/d1 & s on4 ,! probability t 9 99n99 #a cry/als !re w\ld be casual agreem5t ( direction is ! n? p[] ( #a_/b4 ,?us1 if 9 exam9+ f\rte5 cry/als ! same relation ( ! two ph5om5a is discov]$ 9 ea*1 ! odds t x proce$s f uni=m conditions are m ?an #hjjj to #a4aed ,s9ce ! fir/ obs]vations on ?is subject 7 made 9 #ahbj1 no exceptions h be5 obs]v$1 s t ! probability ( inv>iable connection is incalculably great4 #aed 99,ed9burgh ,review991 ,no4 #ahe1 vol4 xcii4 ,july #ahej1 p4 #cb2 ,h]s*el's 99,essays991 p4 #dba2 99,transactions ( ! ,cambridge ,philosophical ,society991 vol4 i4 p4 #dc4 ,x is exce$+ly probable t ! anci5t ,egyptians _h exactly record$ ! eclipses occurr+ dur+ long p]iods ( "t1 = ,diog5es ,la]tius m5tions t #cgc sol> & #hcb lun> eclipses _h be5 obs]v$1 & ! ratio betwe5 ^! numb]s exactly expresses t :i* w\ld hold true ( ! eclipses ( any long p]iod1 ( say #abjj or #acjj ye>s1 z e/imat$ on a/ronomical gr\nds4 ,x is evid5t t an agreem5t betwe5 small numb]s1 or cu/om>y numb]s1 su* z sev51 "o hundr$1 a myriad1 c41 is mu* m likely to happ5 f *ance1 & !re=e gives mu* less presumption ( dep5d5ce4 ,if two anci5t writ]s spoke ( ! sacrifice ( ox51 !y w\ld 9 all probability describe x z a hecatomb1 & !re w\ld be no?+ rem>kable 9 ! co9cid5ce4 ,b x is impossible to po9t out any special reason :y an old writ] %\ld select su* numb]s z #cgc & #hcb1 unless !y _h be5 ! results ( obs]vation4 ,on simil> gr\nds1 we mu/ inevitably believe 9 ! human orig9 ( ! fl9t flakes s copi\sly discov]$ ( late ye>s4 ,= ?\gh ! accid5tal /roke ( "o /one aga9/ ano!r may (t5 produce flakes1 su* z are occasionally f\nd on ! sea-%ore1 yet :5 sev]al flakes are f\nd 9 close company1 & ea* "o be>s evid5ce1 n ( a s+le bl[ only1 b ( sev]al successive bl[s1 all conduc+ to =m a symmetrical knife-l =m1 ! probability ( a natural & accid5tal orig9 becomes incr$ibly small1 & ! contr>y supposition1 t !y are ! "w ( intellig5t be+s1 approximately c]ta94#aee #aee ,evans' 99,anci5t ,/one ,implem5ts ( ,great ,brita9994 ,london1 #ahgb 7,longmans74 99,! ,!ory ( ,probability 9 ,a/ronomy499 ,! sci5ce ( a/ronomy1 occupi$ ) ! simple relations ( di/ance1 magnitude1 & motion ( ! heav5ly bodies1 admits m easily ?an almo/ any o!r sci5ce ( int]e/+ conclusions f\nd$ on ! !ory ( probability4 ,m ?an a c5tury ago1 9 #agfg1 ,mi*ell %[$ ! extreme probability ( bonds connect+ toge!r sy/ems ( />s4 ,he 0 /ruck by ! unexpect$ numb] ( fix$ />s :i* h companions close to !m4 ,su* a conjunction might happ5 casually by "o />1 al?\gh possibly at a great di/ance f ! o!r1 happ5+ to lie on a /raight l9e pass+ ne> ! e>?4 ,b ! probabilities are s greatly aga9/ su* an optical union happ5+ (t5 9 ! expanse ( ! heav5s1 t ,mi*ell ass]t$ ! exi/5ce ( "s connection betwe5 mo/ ( ! d\ble />s4 ,x has s9ce be5 e/imat$ by ,/ruve1 t ! odds are #iegj to #a aga9/ any two />s ( n less ?an ! sev5? magnitude fall+ )9 ! app>5t di/ance ( f\r seconds ( ea* o!r by *ance1 & yet n9ety-"o su* cases 7 kn[n :5 ! e/imation 0 made1 & _m m cases h s9ce be5 discov]$4 ,!re 7 also f\r kn[n triple />s1 & yet ! odds aga9/ ! appe>ance ( any "o su* conjunction are #agc1ebd to #a4aef ,! conclusions ( ,mi*ell h be5 entirely v]ifi$ by ! discov]y t _m d\ble />s are connect$ by gravitation4 #aef ,h]s*el1 99,outl9es ( ,a/ronomy991 #ahdi1 p4 #efe2 b ,todhunt]1 9 8 99,hi/ory ( ! ,!ory ( ,probability991 p4 #cce1 /ates t ! calculations d n agree ) ^? publi%$ by ,/ruve4 ,mi*ell also inve/igat$ ! probability t ! six brighte/ />s 9 ! ,pleiades %\ld h come by accid5ts into su* /rik+ proximity4 ,e/imat+ ! numb] ( />s ( equal or great] brightness at #aejj1 be f\nd ! odds to be ne>ly #ejj1jjj to #a aga9/ casual conjunction4 ,ext5d+ ! same k9d ( argum5t to o!r clu/]s1 su* z t ( ,prsepe1 ! nebula 9 ! hilt ( ,p]seus' sword1 he says3#aeg 8,we may ) ! highe/ probability conclude1 ! odds aga9/ ! contr>y op9ion be+ _m million millions to "o1 t ! />s are really collect$ toge!r 9 clu/]s 9 "s places1 :]e !y =m a k9d ( sy/em1 :ile 9 o!rs !re are ei!r few or none ( !m1 to :atev] cause ?is may be ow+1 :e!r to _! mutual gravitation1 or to "s o!r law or appo9tm5t ( ! ,creator40 #aeg 99,philosophical ,transactions991 #agfg1 vol4 lvii4 p4 #dca4 ,! calculations ( ,mi*ell h be5 call$ 9 "q by ! late ,james ,d4 ,=bes1#aeh & ,mr4 ,todhunt] vaguely c\nt5ances 8 objections1#aei o!rwise ,i %\ld n h ?\ght !m ( mu* weight4 ,c]ta9ly ,laplace accepts ,mi*ell's views1#afj & if ,mi*ell be 9 error x is 9 ! me?ods ( calculation1 n 9 ! g5]al validity ( 8 reason+ & conclusions4 #aeh 99,philosophical ,magaz9e991 #crd ,s]ies1 vol4 xxxvii4 p4 #dja1 ,decemb] #ahej2 also ,augu/ #ahdi4 #aei 99,hi/ory991 c41 p4 #ccd4 #afj 99,essai ,philosophique991 p4 #eg4 ,simil> calculations might no d\bt be appli$ to ! peculi> drift+ motions :i* h be5 detect$ by ,mr4 ,r ,a4 ,proctor 9 "s ( ! con/ellations4#afa ,! odds are v greatly aga9/ any num]\s gr\p ( />s mov+ toge!r 9 any "o direction by *ance4 ,on l gr\nds1 !re c be no d\bt t ! sun has a consid]able prop] motion because on ! av]age ! fix$ />s %[ a t5d5cy to move app>5tly f "o po9t ( ! heav5s t[>ds t diametrically opposite4 ,! sun's motion 9 ! contr>y direction w\ld expla9 ?is t5d5cy1 o!rwise we mu/ believe t ?\s&s ( />s accid5tally agree 9 _! direction ( motion1 or are urg$ by "s common =ce f :i* ! sun is exempt4 ,x may be said t ! rotation ( ! e>? is prov$ 9 l mann]1 because x is imm5sely m probable t "o body w\ld revolve ?an t ! sun1 moon1 planets1 comets1 & ! :ole ( ! />s ( ! heav5s %\ld be :irl$ r\nd ! e>? daily1 ) a uni=m motion sup]add$ to _! own peculi> motions4 ,?is appe>s to be ma9ly ! reason :i* l$ ,gilb]t1 "o ( ! e>lie/ ,engli% ,cop]nicans1 & 9 e way an admirable physici/1 to admit ! rotation ( ! e>?1 :ile ,francis ,bacon d5i$ x4 #afa 99,proce$+s ( ! ,royal ,society992 #bj ,janu>y1 #ahgj2 99,philosophical ,magaz9e991 #d? ,s]ies1 vol4 xxxix4 p4 #cha4 ,9 contemplat+ ! planet>y sy/em1 we are /ruck ) ! simil>ity 9 direction ( ne>ly all its movem5ts4 ,newton rem>k$ ^u ! regul>ity & uni=mity ( ^! motions1 & contra/$ !m ) ! ecc5tricity & irregul>ity ( ! comet>y orbits4#afb ,c\ld we1 9 fact1 look d[n ^u ! sy/em f ! nor!rn side1 we %\ld see all ! planets mov+ r\nd f we/ to ea/1 ! satellites mov+ r\nd _! prim>ies1 & ! sun1 planets1 & satellites rotat+ 9 ! same direction1 ) "s exceptions on ! v]ge ( ! sy/em4 ,9 ! "t ( ,laplace elev5 planets 7 kn[n1 & ! directions ( rotation 7 kn[n = ! sun1 six planets1 ! satellites ( ,jupit]1 ,saturn's r+1 & "o ( 8 satellites4 ,?us !re 7 altoge!r #dc motions all concurr+1 namely3-- ,orbital motions ( elev5 planets #aa ,orbital motions ( eighte5 satellites #ah ,axial rotations #ad -- #dc #afb 99,pr9cipia991 bk4 ii4 ,g5]al s*olium4 ,! probability t #dc motions indep5d5t ( ea* o!r w\ld co9cide by *ance is ! #dbnd p[] ( #a_/b1 s t ! odds are ab\t #d1djj1jjj1jjj1jjj to #a 9 fav\r ( "s common cause = ! uni=mity ( direction4 ,?is probability1 z ,laplace obs]ves1#afc is high] ?an t ( _m hi/orical ev5ts :i* we und\bt+ly believe4 ,9 ! pres5t day1 ! probability is mu* increas$ by ! discov]y ( additional planets1 & ! rotation ( o!r satellites1 & x is only slightly weak5$ by ! fact t "s ( ! outly+ satellites are exceptional 9 direction1 !re be+ consid]able evid5ce ( an accid5tal di/urbance 9 ! m di/ant p>ts ( ! sy/em4 #afc 99,essai ,philosophique991 p4 #ee4 ,laplace appe>s to c\nt ! r+s ( ,saturn z giv+ two indep5d5t movem5ts4 ,h>dly less rem>kable ?an ! uni=m direction ( motion is ! ne> approximation ( ! orbits ( ! planets to a common plane4 ,daniel ,b]n\lli r\ghly e/imat$ ! probability ( su* an agreem5t aris+ f accid5t z #a 7#ab7f ! greate/ incl9ation ( any orbit to ! sun's equator be+ #a-ab? "p ( a quadrant4 ,laplace devot$ to ?is subject "s ( 8 mo/ +5i\s inve/igations4 ,he f\nd ! probability t ! sum ( ! incl9ations ( ! planet>y orbits w\ld n exce$ by accid5t ! actual am\nt 7#iadahg ( a "r angle = ! t5 planets kn[n 9 #ahja7 to be 7#a_/aj76 7#iadahg7aj or ab\t #jjjjjjaabce4 ,?is probability may be comb9$ ) t d]iv$ f ! direction ( motion1 & x !n becomes imm5sely probable t ! con/itution ( ! planet>y sy/em arose out ( uni=m conditions1 or1 z we say1 f "s common cause4#afd #afd ,lubbock1 99,essay on ,probability991 p4 #ad4 ,de ,morgan1 99,encyc4 ,metrop499 art4 99,probability991 p4 #dab4 ,todhunt]'s 99,hi/ory ( ! ,!ory ( ,probability991 p4 #edc4 ,conc]n+ ! objections rais$ to ^! conclusions by ,boole1 see ! 99,philosophical ,magaz9e991 #d? ,s]ies1 vol4 ii4 p4 #ih4 ,boole's 99,laws ( ,?\ght991 pp4 #cfd-cge4 ,if ! same k9d ( calculation be appli$ to ! orbits ( comets1 ! result is v diff]5t4#afe ,( ! orbits :i* h be5 det]m9$ #dhi p] c5t4 only are direct or 9 ! same direction z ! planet>y motions4#aff ,h5ce x becomes app>5t t comets d n prop]ly belong to ! sol> sy/em1 & x is probable t !y are /ray portions ( nebul\s matt] :i* h accid5tally become atta*$ to ! sy/em by ! attractive p[]s ( ! sun or ,jupit]4 #afe ,laplace1 99,essai ,philosophique991 pp4 #ee1 #ef4 #aff ,*amb]s' 99,a/ronomy991 #bnd ed4 pp4 #cdf-di4 99,! ,g5]al ,inv]se ,problem499 ,9 ! in/ances describ$ 9 ! prec$+ sections1 we h be5 occupi$ 9 rec$+ f ! occurr5ce ( c]ta9 simil> ev5ts to ! probability t !re mu/ h be5 a condition or cause = su* ev5ts4 ,we h f\nd t ! !ory ( probability1 al?\gh nev] yield+ a c]ta9 result1 (t5 enables u to e/abli% an hypo!sis beyond ! rea* ( reasonable d\bt4 ,!re is1 h[ev]1 ano!r me?od ( apply+ ! !ory1 :i* possesses = u ev5 great] int]e/1 because x illu/rates1 9 ! mo/ complete mann]1 ! !ory ( inf]5ce adopt$ 9 ?is "w1 :i* !ory inde$ x sugge/$4 ,! problem to be solv$ is z foll[s3-- 99,an ev5t hav+ happ5$ a c]ta9 numb] ( times1 & fail$ a c]ta9 numb] ( times1 requir$ ! probability t x w happ5 any giv5 numb] ( times 9 ! future "u ! same circum/ances499 ,all ! 99l>g]99 planets hi!rto discov]$ move 9 "o direction r\nd ! sun2 :at is ! probability t1 if a new planet ext]ior to ,neptune be discov]$1 x w move 9 ! same direction8 ,all kn[n p]man5t gases1 except *lor9e1 are col\rless2 :at is ! probability t1 if "s new p]man5t gas %\ld be discov]$1 x w be col\rless8 ,9 ! g5]al solution ( ?is problem1 we wi% to inf] ! future happ5+ ( any ev5t f ! numb] ( times t x has already be5 obs]v$ to happ54 ,n[1 x is v in/ructive to f9d t !re is no kn[n process by :i* we c pass directly f ! data to ! conclusion4 ,x is always requisite to rec$e f ! data to ! probability ( "s hypo!sis1 & to make t hypo!sis ! gr\nd ( our inf]5ce conc]n+ future ev5ts4 ,ma!maticians1 9 fact1 make e hypo!sis :i* is applicable to ! "q 9 h&2 !y !n calculate1 by ! inv]se me?od1 ! probability ( e su* hypo!sis accord+ to ! data1 & ! probability t if ea* hypo!sis be true1 ! requir$ future ev5t w happ54 ,! total probability t ! ev5t w happ5 is ! sum ( ! sep>ate probabilities contribut$ by ea* di/9ct hypo!sis4 ,to illu/rate m precisely ! me?od ( solv+ ! problem1 x is desirable to adopt "s concrete mode ( repres5tation1 & ! ballot-box1 s (t5 employ$ by ma!maticians1 w be/ s]ve our purpose4 ,let ! happ5+ ( any ev5t be repres5t$ by ! draw+ ( a :ite ball f a ballot-box1 :ile ! failure ( an ev5t is repres5t$ by ! draw+ ( a black ball4 ,n[1 9 ! inductive problem we are suppos$ to be ignorant ( ! cont5ts ( ! ballot-box1 & are requir$ to gr\nd all our inf]5ces on our exp]i5ce ( ^? cont5ts z %[n 9 successive draw+s4 ,rude common s5se w\ld guide u ne>ly to a true conclusion4 ,?us1 if we _h drawn tw5ty balls "o aft] ano!r1 replac+ ! ball aft] ea* draw+1 & ! ball _h 9 ea* case prov$ to be :ite1 we %\ld believe t !re 0 a consid]able prepond]ance ( :ite balls 9 ! urn1 & a probability 9 fav\r ( draw+ a :ite ball on ! next occasion4 ,?\gh we _h drawn :ite balls = ?\s&s ( times )\t fail1 x w\ld /ill be possible t "s black balls lurk$ 9 ! urn & w\ld at la/ appe>1 s t our inf]5ces c\ld nev] be c]ta94 ,on ! o!r h&1 if black balls came at int]vals1 we %\ld expect t aft] a c]ta9 numb] ( trials ! black balls w\ld appe> aga9 f "t to "t ) some:at ! same frequ5cy4 ,! ma!matical solution ( ! "q consi/s 9 little m ?an a close analysis ( ! mode 9 :i* our common s5se proce$s4 ,if tw5ty :ite balls h be5 drawn & no black ball1 my common s5se tells me t any hypo!sis :i* makes ! black balls 9 ! urn consid]able comp>$ ) ! :ite ones is improbable2 a prepond]ance ( :ite balls is a m probable hypo!sis1 & z a d$uction f ?is m probable hypo!sis1 ,i expect a recurr5ce ( :ite balls4 ,! ma!matician m]ely r$uces ?is process ( ?\ght to exact numb]s4 ,tak+1 = in/ance1 ! hypo!sis t !re are #ii :ite & "o black ball 9 ! urn1 he c calculate ! probability t #bj :ite balls w\ld be drawn 9 succession 9 ^? circum/ances2 he ?us =ms a def9ite e/imate ( ! probability ( ?is hypo!sis1 & kn[+ at ! same "t ! probability ( a :ite ball reappe>+ if su* be ! cont5ts ( ! urn1 he comb9es ^! probabilities1 & obta9s an exact e/imate t a :ite ball w recur 9 consequ5ce ( ?is hypo!sis4 ,b z ?is hypo!sis is only "o out ( _m possible ones1 s9ce ! ratio ( :ite & black balls may be #ih to #b1 or #ig to #c1 or #if to #d1 & s on1 he has to repeat ! e/imate = e su* possible hypo!sis4 ,to make ! me?od ( solv+ ! problem p]fectly evid5t1 ,i w describe 9 ! next section a v simple case ( ! problem1 orig9ally devis$ = ! purpose by ,condorcet1 :i* 0 also adopt$ by ,lacroix1#afg & has pass$ into ! works ( ,de ,morgan1 ,lubbock1 & o!rs4 #afg 99,trait lm5taire du ,calcul des ,probabilits991 #crd ed4 7#ahcc71 p4 #adh4 99,simple ,illu/ration ( ! ,inv]se ,problem499 ,suppose x to be kn[n t a ballot-box conta9s only f\r black or :ite balls1 ! ratio ( black & :ite balls be+ unkn[n4 ,f\r draw+s hav+ be5 made ) replacem5t1 & a :ite ball hav+ appe>$ on ea* occasion b "o1 x is requir$ to det]m9e ! probability t a :ite ball w appe> next "t4 ,n[ ! hypo!ses :i* c be made z to ! cont5ts ( ! urn are v limit$ 9 numb]1 & are at mo/ ! foll[+ five3-- #d :ite & #j black balls #c #a #b #b #a #c #j #d ,! actual occurr5ce ( black & :ite balls 9 ! draw+s puts ! fir/ & la/ hypo!sis out ( ! "q1 s t we h only ?ree left to consid]4 ,if ! box conta9s ?ree :ite & "o black1 ! probability ( draw+ a :ite ea* "t is #c_/d1 & a black #a_/d2 s t ! comp\nd ev5t obs]v$1 namely1 ?ree :ite & "o black1 has ! probability #c_/d #c_/d #c_/d #a_/d1 by ! rule already giv5 7p4 #bjd74 ,b z x is indiff]5t 9 :at ord] ! balls are drawn1 & ! black ball might come fir/1 second1 ?ird1 or f\r?1 we mu/ multiply by f\r1 to obta9 ! probability ( ?ree :ite & "o black 9 any ord]1 ?us gett+ #bg_/fd4 ,tak+ ! next hypo!sis ( two :ite & two black balls 9 ! urn1 we obta9 = ! same probability ! quantity #a_/b #a_/b #a_/b #a_/b #d1 or #af_/fd1 & f ! ?ird hypo!sis ( "o :ite & ?ree black we d$uce likewise #a_/d #a_/d #a_/d #c_/d #d1 or #c_/fd4 ,accord+1 !n1 z we adopt ! fir/1 second1 or ?ird hypo!sis1 ! probability t ! result actually notic$ w\ld foll[ is #bg_/fd1 #af_/fd1 & #c_/fd4 ,n[ x is c]ta9 t "o or o!r ( ^! hypo!ses mu/ be ! true "o1 & _! absolute probabilities are proportional to ! probabilities t ! obs]v$ ev5ts w\ld foll[ f !m 7pp4 #bdb1 #bdc74 ,all we h to d1 !n1 9 ord] to obta9 ! absolute probability ( ea* hypo!sis1 is to alt] ^! fractions 9 a uni=m ratio1 s t _! sum %all be unity1 ! expression ( c]ta9ty4 ,n[1 s9ce #bg #af #c #df1 ?is w be effect$ by divid+ ea* fraction by #df1 & multiply+ by #fd4 ,?us ! probabilities ( ! fir/1 second1 & ?ird hypo!ses are respectively-- #bg_/df1 #af_/df1 #c_/df4 ,! inductive "p ( ! problem is complet$1 s9ce we h f\nd t ! urn mo/ likely conta9s ?ree :ite & "o black ball1 & h assign$ ! exact probability ( ea* possible supposition4 ,b we are n[ 9 a position to resume d$uctive reason+1 & inf] ! probability t ! next draw+ w yield1 say a :ite ball4 ,= if ! box conta9s ?ree :ite & "o black ball1 ! probability ( draw+ a :ite "o is c]ta9ly #c_/d2 & z ! probability ( ! box be+ s con/itut$ is #bg_/df1 ! comp\nd probability t ! box w be s fill$ & w give a :ite ball at ! next trial1 is #bg_/df #c_/d or #ha_/ahd4 ,aga91 ! probability is #af_/df t ! box conta9s two :ite & two black1 & "u ^? conditions ! probability is #a_/b t a :ite ball w appe>2 h5ce ! probability t a :ite ball w appe> 9 consequ5ce ( t condition1 is #af_/df #a_/b or #cb_/ahd4 ,f ! ?ird supposition we get 9 l mann] ! probability #c_/df #a_/d or #c_/ahd4 ,s9ce "o & n m ?an "o hypo!sis c be true1 we may add toge!r ^! sep>ate probabilities1 & we f9d t #ha_/ahd #cb_/ahd #c_/ahd or #aaf_/ahd is ! complete probability t a :ite ball w be next drawn "u ! conditions & data suppos$4 99,g5]al ,solution ( ! ,inv]se ,problem499 ,9 ! in/ance ( ! inv]se me?od describ$ 9 ! la/ section1 ! balls suppos$ to be 9 ! ballot-box 7 few1 = ! purpose ( simplify+ ! calculation4 ,9 ord] t our solution may apply to natural ph5om5a1 we mu/ r5d] our hypo!ses z little arbitr>y z possible4 ,hav+ no 99 priori99 k ( ! conditions ( ! ph5om5a 9 "q1 !re is no limit to ! v>iety ( hypo!ses :i* might be sugge/$4 ,ma!maticians h !re=e _h rec\rse to ! mo/ ext5sive suppositions :i* c be made1 namely1 t ! ballot-box conta9s an inf9ite numb] ( balls2 !y h !n v>i$ ! proportion ( :ite to black balls cont9u\sly1 f ! smalle/ to ! greate/ possible proportion1 & e/imat$ ! aggregate probability :i* results f ?is compreh5sive supposition4 ,to expla9 _! proc$ure1 let u imag9e t1 in/ead ( an inf9ite numb]1 ! ballot-box conta9s a l>ge f9ite numb] ( balls1 say #ajjj4 ,!n ! numb] ( :ite balls might be #a or #b or #c or #d1 & s on1 up to #iii4 ,suppos+ t ?ree :ite & "o black ball h be5 drawn f ! urn z be=e1 !re is a c]ta9 v small probability t ?is w\ld h occurr$ 9 ! case ( a box conta9+ "o :ite & #iii black balls2 !re is also a small probability t f su* a box ! next ball w\ld be :ite4 ,comp\nd ^! probabilities1 & we h ! probability t ! next ball really w be :ite1 9 consequ5ce ( ! exi/5ce ( t proportion ( balls4 ,if !re be two :ite & #iih black balls 9 ! box1 ! probability is great] & w increase until ! balls are suppos$ to be 9 ! proportion ( ^? drawn4 ,n[ #iii diff]5t hypo!ses are possible1 & ! calculation is to be made = ea* ( ^!1 & _! aggregate tak5 z ! f9al result4 ,x is app>5t t z ! numb] ( balls 9 ! box is increas$1 ! absolute probability ( any "o hypo!sis conc]n+ ! exact proportion ( balls is decreas$1 b ! aggregate results ( all ! hypo!ses w assume ! "* ( a wid] av]age4 ,:5 we take ! /ep ( suppos+ ! balls )9 ! urn to be inf9ite 9 numb]1 ! possible proportions ( :ite & black balls also become inf9ite1 & ! probability ( any "o proportion actually exi/+ is inf9itely small4 ,h5ce ! f9al result t ! next ball drawn w be :ite is really ! sum ( an inf9ite numb] ( inf9itely small quantities4 ,x might seem impossible to calculate out a problem hav+ an inf9ite numb] ( hypo!ses1 b ! wond]ful res\rces ( ! integral calculus enable ?is to be done ) f> great] facility ?an if we suppos$ any l>ge f9ite numb] ( balls1 & !n actually comput$ ! results4 ,i w n attempt to describe ! processes by :i* ,laplace f9ally accompli%$ ! complete solution ( ! problem4 ,!y are to be f\nd describ$ 9 sev]al ,engli% works1 especially ,de ,morgan's 99,treatise on ,probabilities991 9 ! 99,encyclopdia ,metropolitana991 & ,mr4 ,todhunt]'s 99,hi/ory ( ! ,!ory ( ,probability994 ,! abbreviat+ p[] ( ma!matical analysis 0 nev] m /rik+ly %[n4 ,b ,i may add t ?\gh ! integral calculus is employ$ z a means ( summ+ inf9itely num]\s results1 we 9 no way ab&on ! pr9ciples ( comb9ations already treat$4 ,we calculate ! values ( inf9itely num]\s factorials1 n1 h[ev]1 obta9+ _! actual products1 :i* w\ld lead to an inf9ite numb] ( figures1 b obta9+ ! f9al answ] to ! problem by devices :i* c only be compreh5d$ aft] /udy ( ! integral calculus4 ,x mu/ be all[$ t ! hypo!sis adopt$ by ,laplace is 9 "s degree arbitr>y1 s t !re 0 "s op5+ = ! d\bt :i* ,boole has ca/ ^u x4#afh ,b x may be repli$1 7#a7 t ! supposition ( an inf9ite numb] ( balls treat$ 9 ! mann] ( ,laplace is less arbitr>y & m compreh5sive ?an any o!r t c be sugge/$4 7#b7 ,! result does n diff] mu* f t :i* w\ld be obta9$ on ! hypo!sis ( any l>ge f9ite numb] ( balls4 7#c7 ,! supposition leads to a s]ies ( simple =mulas :i* c be appli$ ) ease 9 _m cases1 & :i* be> all ! appe>ance ( tru? s f> z x c be indep5d5tly judg$ by a s\nd & practic$ und]/&+4 #afh 99,laws ( ,?\ght991 pp4 #cfh-cge4 99,rules ( ! ,inv]se ,me?od499 ,by ! solution ( ! problem1 z describ$ 9 ! la/ section1 we obta9 ! foll[+ s]ies ( simple rules4 #a4 99,to f9d ! probability t an ev5t :i* has n hi!rto be5 obs]v$ to fail w happ5 once m1 divide ! numb] ( times ! ev5t has be5 obs]v$ increas$ by "o1 by ! same numb] increas$ by two499 ,if !re h be5 99m99 occasions on :i* a c]ta9 ev5t might h be5 obs]v$ to happ51 & x has happ5$ on all ^? occasions1 !n ! probability t x w happ5 on ! next occasion ( ! same k9d 799m99 #a7_/799m99 #b74 ,= in/ance1 we may say t !re are n9e places 9 ! planet>y sy/em :]e planets might exi/ obey+ ,bode's law ( di/ance1 & 9 e place !re is a planet obey+ ! law m or less exactly1 al?\gh no reason is kn[n = ! co9cid5ce4 ,h5ce ! probability t ! next planet beyond ,neptune w con=m to ! law is #aj_/aa4 #b4 99,to f9d !1 probability t an ev5t :i* has n hi!rto fail$ w n fail = a c]ta9 numb] ( new occasions1 divide ! numb] ( times ! ev5t has happ5$ increas$ by "o1 by ! same numb] increas$ by "o & ! numb] ( times x is to happ5499 ,an ev5t hav+ happ5$ 99m99 times )\t fail1 ! probability t x w happ5 99n99 m times is 799m99 #a7_/799m99 99n99 #a74 ,?us ! probability t ?ree new planets w\ld obey ,bode's law is #aj_/ac2 b x mu/ be all[$ t ?is1 z well z ! previ\s result1 w\ld be mu* weak5$ by ! fact t ,neptune c b>ely be said to obey ! law4 99#c4 ,an ev5t hav+ happ5$ & fail$ a c]ta9 numb] ( times1 to f9d ! probability t x w happ5 ! next "t1 divide ! numb] ( times ! ev5t has happ5$ increas$ by "o1 by ! :ole numb] ( times ! ev5t has happ5$ or fail$ increas$ by two499 ,if an ev5t has happ5$ 99m99 times & fail$ 99n99 times1 ! probability t x w happ5 on ! next occasion is 799m99 #a7_/799m99 99n99 #b74 ,?us1 if we assume t ( ! elem5ts discov]$ up to ! ye> #ahgc1 #ej are metallic & #ad non-metallic1 !n ! probability t ! next elem5t discov]$ w be metallic is #ea_/ff4 ,aga91 s9ce ( #cg metals :i* h be5 suffici5tly exam9$ only f\r1 namely1 sodium1 potassium1 lan?anum1 & li?ium1 are ( less d5sity ?an wat]1 ! probability t ! next metal exam9$ or discov]$ w be less d5se ?an wat] is 7#d #a7_/7cg #b7 or #e_/ci4 ,we may /ate ! results ( ! me?od 9 a m g5]al mann] ?us1#afi--;,if "u giv5 circum/ances c]ta9 ev5ts ,a1 ,b1 ,c1 c41 h happ5$ respectively 99m991 99n991 99p991 c41 times1 & "o or o!r ( ^! ev5ts mu/ happ51 !n ! probabilities ( ^! ev5ts are proportional to 99m99 #a1 99n99 #a1 99p99 #a1 c41 s t ! probability ( ,a w be 799m99 #a7_/799m99 #a 99n99 #a 99p99 #a c47 ,b if new ev5ts may happ5 9 addition to ^? :i* h be5 obs]v$1 we mu/ assign unity = ! probability ( su* new ev5t4 ,! odds !n become #a = a new ev5t1 99m99 #a = ,a1 99n99 #a = ,b1 & s on1 & ! absolute probability ( ,a is 799m99 #a7_/7a 99m99 #a 99n99 #a c47 #afi ,de ,morgan's 99,essay on ,probabilities991 ,cab9et ,cyclopdia1 p4 #fg4 ,x is int]e/+ to trace out ! v>iations ( probability accord+ to ^! rules4 ,! fir/ "t a casual ev5t happ5s x is #b to #a t x w happ5 aga92 if x does happ5 x is #c to #a t x w happ5 a ?ird "t2 & on successive occasions ( ! l k9d ! odds become #d1 #e1 #f1 c41 to #a4 ,! odds ( c\rse w be discrim9at$ f ! probabilities :i* are successively #b_/c1 #c_/d1 #d_/e1 c4 ,?us on ! fir/ occasion on :i* a p]son sees a %>k1 & notices t x is accompani$ by a little pilot fi%1 ! odds are #b to #a1 or ! probability #b_/c1 t ! next %>k w be s accompani$4 ,:5 an ev5t has happ5$ a v great numb] ( times1 its happ5+ once aga9 approa*es ne>ly to c]ta9ty4 ,if we suppose ! sun to h ris5 "o ?\s& million times1 ! probability t x w rise aga91 on ! gr\nd ( ?is k m]ely1 is 7#a1jjj1jjj1jjj #a7_/7a1jjj1jjj1jjj #a #a74 ,b !n ! probability t x w cont9ue to rise = z long a p]iod 9 ! future is only 7#a1jjj1jjj1jjj #a7_/7b1jjj1jjj1jjj #a71 or almo/ exactly #a_/b4 ,! probability t x w cont9ue s ris+ a ?\s& times z long is only ab\t #a_/ajja4 ,! lesson :i* we may draw f ^! figures is q t :i* we %\ld adopt on o!r gr\nds1 namely1 t exp]i5ce nev] af=ds c]ta9 k1 & t x is exce$+ly improbable t ev5ts w always happ5 z we obs]ve !m4 ,inf]5ces pu%$ f> beyond _! data soon lose any consid]able probability4 ,de ,morgan has said1#agj 8,no f9ite exp]i5ce :atsoev] c ju/ify u 9 say+ t ! future %all co9cide ) ! pa/ 9 all "t to come1 or t !re is any probability = su* a conclusion40 ,on ! o!r h&1 we ga9 ! assurance t exp]i5ce suffici5tly ext5d$ & prolong$ w give u ! k ( future ev5ts ) an unlimit$ degree ( probability1 provid$ inde$ t ^? ev5ts are n subject to arbitr>y int]f]5ce4 #agj 99,essay on ,probabilities991 p4 #abh4 ,x mu/ be cle>ly und]/ood t ^! probabilities are only su* z arise f ! m]e happ5+ ( ! ev5ts1 irrespective ( any k d]iv$ f o!r s\rces conc]n+ ^? ev5ts or ! g5]al laws ( nature4 ,all our k ( nature is inde$ f\nd$ 9 l mann] ^u obs]vation1 & is !re=e only probable4 ,! law ( gravitation itself is only probably true4 ,b :5 a numb] ( diff]5t facts1 obs]v$ "u ! mo/ div]se circum/ances1 are f\nd to be h>moniz$ "u a suppos$ law ( nature1 ! probability ( ! law approximates closely to c]ta9ty4 ,ea* sci5ce re/s ^u s _m obs]v$ facts1 & d]ives s mu* support f analogies or connections ) o!r sci5ces1 t !re are comp>atively few cases :]e our judgm5t ( ! probability ( an ev5t dep5ds entirely ^u a few antec$5t ev5ts1 disconnect$ f ! g5]al body ( physical sci5ce4 ,ev5ts1 aga91 may (t5 exhibit a regul>ity ( succession or prepond]ance ( "*1 :i* ! simple =mula w n take into acc\nt4 ,= in/ance1 ! majority ( ! elem5ts rec5tly discov]$ are metals1 s t ! probability ( ! next discov]y be+ t ( a metal1 is d\btless great] ?an we calculat$ 7p4 #beh74 ,at ! m di/ant p>ts ( ! planet>y sy/em1 !re are symptoms ( di/urbance :i* w\ld prev5t our plac+ mu* reliance on any inf]5ce f ! prevail+ ord] ( ! kn[n planets to ^? undiscov]$ ones :i* may possibly exi/ at great di/ances4 ,^! & all l complications 9 no way invalidate ! !oretic tru? ( ! =mulas1 b r5d] _! s\nd application mu* m difficult4 ,errone\s objections h be5 rais$ to ! !ory ( probability1 on ! gr\nd t we ought n to tru/ to our 99 priori99 conceptions ( :at is likely to happ51 b %\ld always endeav\r to obta9 precise exp]im5tal data to guide u4#aga ,?is c\rse1 h[ev]1 is p]fectly 9 accordance ) ! !ory1 :i* is our be/ & only guide1 :atev] data we possess4 ,we ought to be always apply+ ! inv]se me?od ( probabilities s z to take into acc\nt all additional in=mation4 ,:5 we ?r[ up a co9 = ! fir/ "t1 we are probably q ignorant :e!r x t5ds m to fall head or tail upw>ds1 & we mu/ !re=e assume ! probability ( ea* ev5t z #a_/b4 ,b if x %[s head 9 ! fir/ ?r[1 we n[ h v slight exp]im5tal evid5ce 9 fav\r ( a t5d5cy to %[ head4 ,! *ance ( two heads is n[ slightly great] ?an #a_/d1 :i* x appe>$ to be at fir/1#agb & z we g on ?r[+ ! co9 "t aft] "t1 ! probability ( head appe>+ next "t con/antly v>ies 9 a slight degree accord+ to ! "* ( our previ\s exp]i5ce4 ,z ,laplace rem>ks1 we ought always to h reg>d to su* consid]ations 9 common life4 ,ev5ts :5 closely scrut9iz$ w h>dly ev] prove to be q indep5d5t1 & ! slighte/ prepond]ance "o way or ! o!r is "s evid5ce ( connection1 & 9 ! abs5ce ( bett] evid5ce %\ld be tak5 into acc\nt4 #aga ,j4 ,s4 ,mill1 99,sy/em ( ,logic991 #e? edition1 bk4 iii4 *ap4 xviii4 #c4 #agb ,todhunt]'s 99,hi/ory991 pp4 #dgb1 #eih4 ,! gr& object ( seek+ to e/imate ! probability ( future ev5ts f pa/ exp]i5ce1 seems to h be5 ent]ta9$ by ,james ,b]n\lli & ,de ,moivre1 at lea/ su* 0 ! op9ion ( ,condorcet2 & ,b]n\lli may be said to h solv$ "o case ( ! problem4#agc ,! ,engli% writ]s ,bayes & ,price are1 h[ev]1 und\bt$ly ! fir/ :o put =w>d any di/9ct rules on ! subject4#agd ,condorcet & sev]al o!r em95t ma!maticians advanc$ ! ma!matical !ory ( ! subject2 b x 0 res]v$ to ! immortal ,laplace to br+ to ! subject ! full p[] ( 8 g5ius1 & c>ry ! solution ( ! problem almo/ to p]fection4 ,x is in/ructive to obs]ve t a !ory :i* arose f petty games ( *ance1 ! rules & ! v names ( :i* are =gott51 gradually advanc$1 until x embrac$ ! mo/ sublime problems ( sci5ce1 & f9ally und]took to measure ! value & c]ta9ty ( all our inductions4 #agc ,todhunt]'s 99,hi/ory991 pp4 #cgh1 #cgi4 #agd 99,philosophical ,transactions991 #agfc1 vol4 liii4 p4 #cgj1 & #agfd1 vol4 liv4 p4 #bif4 ,todhunt]1 pp4 #bid-cjj4 99,=tuit\s ,co9cid5ces499 ,we %\ld h /udi$ ! !ory ( probability to v little purpose1 if we ?\ght t x w\ld furni% u ) an infallible guide4 ,! !ory itself po9ts out ! approximate c]ta9ty1 t we %all sometimes be deceiv$ by extraord9>y =tuit\s co9cid5ces4 ,!re is no run ( luck s extreme t x may n happ51 & x may happ5 to u1 or 9 our "t1 z well z to o!r p]sons or 9 o!r times4 ,we may be =c$ by correct calculation to ref] su* co9cid5ces to a necess>y cause1 & yet we may be deceiv$4 ,all t ! calculus ( probability pret5ds to give1 is 99! result 9 ! long run991 z x is call$1 & ?is really means 9 99an inf9ity ( cases994 ,dur+ any f9ite exp]i5ce1 h[ev] long1 *ances may be aga9/ u4 ,nev]!less ! !ory is ! be/ guide we c h4 ,if we always ?9k & act accord+ to its well-int]pret$ indications1 we %all h ! be/ *ance ( escap+ error2 & if all p]sons1 ?r\gh\t all "t to come1 obey ! !ory 9 l mann]1 !y w und\bt$ly !reby reap ! greate/ advantage4 ,no rule c be giv5 = discrim9at+ betwe5 co9cid5ces :i* are casual & ^? :i* are ! effects ( law4 ,by a =tuit\s or casual co9cid5ce1 we mean an agreem5t betwe5 ev5ts1 :i* nev]!less arise f :olly indep5d5t & diff]5t causes or conditions1 & :i* w n always s agree4 ,x is a =tuit\s co9cid5ce1 if a p5ny ?r[n up repeat$ly 9 v>i\s ways always falls on ! same side2 b x w\ld n be =tuit\s if !re 7 any simil>ity 9 ! motions ( ! h&1 & ! height ( ! ?r[1 s z to cause or t5d to cause a uni=m result4 ,n[ among ! inf9itely num]\s ev5ts1 objects1 or relations 9 ! univ]se1 x is q likely t we %all occasionally notice casual co9cid5ces4 ,!re are sev5 int]vals 9 ! octave1 & !re is no?+ v improbable 9 ! col\rs ( ! spectrum happ5+ to be app>5tly divisible into ! same or simil> s]ies ( sev5 int]vals4 ,x is h>dly yet decid$ :e!r ?is app>5t co9cid5ce1 ) :i* ,newton 0 mu* /ruck1 is well f\nd$ or n1#age b ! "q w probably be decid$ 9 ! negative4 #age ,newton's 99,opticks991 ,bk4 ,i41 ,"p ii4 ,prop4 #c2 99,nature991 vol4 i4 p4 #bhf4 ,x is c]ta9ly a casual co9cid5ce :i* ! anci5ts notic$ betwe5 ! sev5 v[els1 ! sev5 /r+s ( ! lyre1 ! sev5 ,pleiades1 & ! sev5 *iefs at ,!bes4#agf ,! accid5ts connect$ ) ! numb] sev5 h misl$ ! human intellect ?r\gh\t ! hi/orical p]iod4 ,py?agoras imag9$ a connection betwe5 ! sev5 planets & ! sev5 int]vals ( ! mono*ord4 ,! al*emi/s 7 nev] tir$ ( draw+ inf]5ces f ! co9cid5ce 9 numb]s ( ! sev5 planets & ! sev5 metals1 n to speak ( ! sev5 days ( ! week4 #agf ,ari/otle's 99,metaphysics991 xiii4 #f4 #c4 ,a s+ul> circum/ance 0 po9t$ out conc]n+ ! dim5sions ( ! e>?1 sun1 & moon2 ! sun's diamet] 0 almo/ exactly #aaj times z great z ! e>?'s diamet]1 :ile 9 almo/ exactly ! same ratio ! mean di/ance ( ! e>? 0 great] ?an ! sun's diamet]1 & ! mean di/ance ( ! moon f ! e>? 0 great] ?an ! moon's diamet]4 ,! agreem5t 0 s close t x might h prov$ m ?an casual1 b its =tuit\s "* is n[ suffici5tly %[n by ! fact1 t ! co9cid5ce ceases to be rem>kable :5 we adopt ! am5d$ dim5sions ( ! planet>y sy/em4 ,a consid]able numb] ( ! elem5ts h atomic weights1 :i* are app>5tly exact multiples ( t ( hydrog54 ,if ?is be n a law to be ultimately ext5d$ to all ! elem5ts1 z suppos$ by ,pr\t1 x is a mo/ rem>kable co9cid5ce4 ,b1 z ,i h obs]v$1 we h no means ( absolutely discrim9at+ accid5tal co9cid5ces f ^? :i* imply a deep produc+ cause4 ,a co9cid5ce mu/ ei!r be v /rong 9 itself1 or x mu/ be corroborat$ by "s explanation or connection ) o!r laws ( nature4 ,little att5tion 0 ev] giv5 to ! co9cid5ce conc]n+ ! dim5sions ( ! sun1 e>?1 & moon1 because x 0 n v /rong 9 itself1 & _h no app>5t connection ) ! pr9ciples ( physical a/ronomy4 ,pr\t's ,law be>s m probability because x w\ld br+ ! con/itution ( ! elem5ts !mselves 9 close connection ) ! atomic !ory1 repres5t+ !m z built up out ( a simpl] sub/ance4 ,9 hi/orical & social matt]s1 co9cid5ces are frequ5tly po9t$ out :i* are due to *ance1 al?\gh !re is always a /rong popul> t5d5cy to reg>d !m z ! "w ( design1 or z hav+ "s hidd5 mean+4 ,if to #agid1 ! numb] ( ! ye> 9 :i* ,robespi]re fell1 we add ! sum ( its digits1 ! result is #ahae1 ! ye> 9 :i* ,napoleon fell2 ! repetition ( ! process gives #ahcj ! ye> 9 :i* ,*>les ! ,t5? abdicat$4 ,aga91 ! ,fr5* ,*amb] ( ,deputies1 9 #ahcj1 consi/$ ( #djb memb]s1 ( :om #bba =m$ ! p>ty call$ 8,la queue de ,robespi]re10 :ile ! rema9d]1 #aha 9 numb]1 7 nam$ 8,les honntes g5s40 ,if we give to ea* lett] a num]ical value correspond+ to its place 9 ! alphabet1 x w be f\nd t ! sum ( ! values ( ! lett]s 9 ea* "n exactly indicates ! numb] ( ! p>ty4 ,a numb] ( su* co9cid5ces1 (t5 ( a v curi\s "*1 might be adduc$1 & ! probability aga9/ ! occurr5ce ( ea* is enorm\sly great4 ,!y mu/ be attribut$ to *ance1 because !y _c be %[n to h ! slighte/ connection ) ! g5]al laws ( nature2 b p]sons are (t5 f\nd to be greatly influ5c$ by su* co9cid5ces1 reg>d+ !m z evid5ce ( fatality1 t is ( a sy/em ( causation gov]n+ human affairs indep5d5tly ( ! ord9>y laws ( nature4 ,let x be rememb]$ t !re are an inf9ite numb] ( opportunities 9 life = "s /range co9cid5ce to pres5t itself1 s t x is q to be expect$ t rem>kable conjunctions w sometimes happ54 ,9 all matt]s ( judicial evid5ce1 we mu/ be> 9 m9d ! probable occurr5ce f "t to "t ( unacc\ntable co9cid5ces4 ,! ,roman juri/s refus$ = ?is reason to invalidate a te/am5t>y de$1 ! witnesses ( :i* _h seal$ x ) ! same seal4 ,= witnesses indep5d5tly us+ _! own seals might be f\nd to possess id5tical ones by accid5t4#agg ,x is well kn[n t circum/antial evid5ce ( app>5tly ov]:elm+ complet5ess w sometimes lead to a mi/ak5 judgm5t1 & z absolute c]ta9ty is nev] really atta9able1 e c\rt mu/ act ^u probabilities ( a high am\nt1 & 9 a c]ta9 small proportion ( cases !y mu/ almo/ ( necessity condemn ! innoc5t victims ( a rem>kable conjuncture ( circum/ances4#agh ,popul> judgm5ts usually turn ^u probabilities ( f> less am\nt1 z :5 ! palace ( ,nicom$ia1 & ev5 ! b$*amb] ( ,diocletian1 hav+ be5 on fire twice )9 fifte5 days1 ! p entirely refus$ to believe t x c\ld be ! result ( accid5t4 ,! ,romans believ$ t !re 0 fatality connect$ ) ! "n ( ,sextus4 8,semp] sub ,sextis p]dita ,roma fuit40 #agg ,possunt autem omnes te/es et uno annulo sign>e te/am5tum ,quid enim si septem annuli una sculptura fu]9t1 secundum quod ,pomponio visum e/8--99,ju/9ian991 ii4 tit4 x4 #e4 #agh ,see ,wills on 99,circum/antial ,evid5ce991 p4 #adh4 ,! utmo/ precautions w n provide aga9/ all cont+5cies4 ,to avoid errors 9 important calculations1 x is usual to h !m repeat$ by diff]5t comput]s2 b a case is on record 9 :i* ?ree comput]s made exactly ! same calculations ( ! place ( a />1 & yet all did x wrong 9 precisely ! same mann]1 = no app>5t reason4#agi #agi 99,memoirs ( ! ,royal ,a/ronomical ,society991 vol4 iv4 p4 #bij1 quot$ by ,l>dn]1 99,ed9burgh ,review991 ,july #ahcd1 p4 #bgh4 99,summ>y ( ! ,!ory ( ,inductive ,inf]5ce499 ,! !ory ( inductive inf]5ce /at$ 9 ?is & ! previ\s *apt]s1 0 sugge/$ by ! /udy ( ! ,inv]se ,me?od ( ,probability1 b x also be>s mu* resemblance to ! s-call$ ,d$uctive ,me?od describ$ by ,mill1 9 8 celebrat$ 99,sy/em ( ,logic994 ,mill's views conc]n+ ! ,d$uctive ,me?od1 probably =m ! mo/ orig9al & valuable "p ( 8 treatise1 & ,i %\ld h ascrib$ ! doctr9e entirely to him1 _h ,i n f\nd t ! op9ions put =w>d 9 o!r p>ts ( 8 "w are entirely inconsi/5t ) ! !ory "h upheld4 ,z ?is subject is ! mo/ important & difficult "o ) :i* we h to deal1 ,i w try to rem$y ! imp]fect mann] 9 :i* ,i h treat$ x1 by giv+ a recapitulation ( ! views adopt$4 ,all inductive reason+ is b ! inv]se application ( d$uctive reason+4 ,be+ 9 possession ( c]ta9 p>ticul> facts or ev5ts express$ 9 propositions1 we imag9e "s m g5]al proposition express+ ! exi/5ce ( a law or cause2 &1 d$uc+ ! p>ticul> results ( t suppos$ g5]al proposition1 we obs]ve :e!r !y agree ) ! facts 9 "q4 ,hypo!sis is ?us always employ$1 consci\sly or unconsci\sly4 ,! sole conditions to :i* we ne$ con=m 9 fram+ any hypo!sis is1 t we bo? h & ex]cise ! p[] ( inf]r+ d$uctively f ! hypo!sis to ! p>ticul> results1 :i* are to be comp>$ ) ! kn[n facts4 ,?us !re are b ?ree /eps 9 ! process ( induction3-- 7#a7 ,fram+ "s hypo!sis z to ! "* ( ! g5]al law4 7#b7 ,d$uc+ consequ5ces f t law4 7#c7 ,obs]v+ :e!r ! consequ5ces agree ) ! p>ticul> facts "u consid]ation4 ,9 v simple cases ( inv]se reason+1 hypo!sis may seem altoge!r ne$less4 ,to take numb]s aga9 z a conv5i5t illu/ration1 ,i h only to look at ! s]ies1 #a1 #b1 #d1 #h1 #af1 #cb1 c41 to "k at once t ! g5]al law is t ( geometrical progression2 ,i ne$ no successive trial ( v>i\s hypo!ses1 because ,i am famili> ) ! s]ies1 & h long s9ce le>nt f :at g5]al =mula x proce$s4 ,9 ! same way a ma!matician becomes acqua9t$ ) ! integrals ( a numb] ( common =mulas1 s t he ne$ n g ?r\gh any process ( discov]y4 ,b x is none ! less true t :5ev] previ\s reason+ does n furni% ! k1 hypo!ses mu/ be fram$ & tri$ 7p4 #abd74 ,!re naturally arise two cases1 accord+ z ! nature ( ! subject admits ( c]ta9 or only probable d$uctive reason+4 ,c]ta9ty1 inde$1 is b a s+ul> case ( probability1 & ! g5]al pr9ciples ( proc$ure are always ! same4 ,nev]!less1 :5 c]ta9ty ( inf]5ce is possible1 ! process is simplifi$4 ,( sev]al mutually inconsi/5t hypo!ses1 ! results ( :i* c be c]ta9ly comp>$ ) fact1 b "o hypo!sis c ultimately be ent]ta9$4 ,?us 9 ! inv]se logical problem1 two logically di/9ct conditions c\ld n yield ! same s]ies ( possible comb9ations4 ,accord+ly1 9 ! case ( two t]ms we _h to *oose "o ( six diff]5t k9ds ( propositions 7p4 #acf71 & 9 ! case ( ?ree t]ms1 our *oice lay among #aib possible di/9ct hypo!ses 7p4 #adj74 ,natural laws1 h[ev]1 are (t5 quantitative 9 "*1 & ! possible hypo!ses are !n inf9ite 9 v>iety4 ,:5 d$uction is c]ta91 comp>ison ) fact is ne$$ only to assure ourselves t we h rightly select$ ! hypo!tical conditions4 ,! law e/abli%es itself1 & no numb] ( p>ticul> v]ifications c add to its probability4 ,hav+ once d$uc$ f ! pr9ciples ( algebra t ! diff]5ce ( ! squ>es ( two numb]s is equal to ! product ( _! sum & diff]5ce1 no numb] ( p>ticul> trials ( its tru? w r5d] x m c]ta94 ,on ! o!r h&1 no f9ite numb] ( p>ticul> v]ifications ( a suppos$ law w r5d] t law c]ta94 ,9 %ort1 c]ta9ty belongs only to ! d$uctive process1 & to ! tea*+s ( direct intuition2 & z ! conditions ( nature are n giv5 by intuition1 we c only be c]ta9 t we h got a correct hypo!sis :51 out ( a limit$ numb] conceivably possible1 we select t "o :i* alone agrees ) ! facts to be expla9$4 ,9 geometry & k9dr$ bran*es ( ma!matics1 d$uctive reason+ is conspicu\sly c]ta91 & x w\ld (t5 seem z if ! consid]ation ( a s+le diagram yields u c]ta9 k ( a g5]al proposition4 ,b 9 reality all ?is c]ta9ty is ( a purely hypo!tical "*4 ,d\btless if we c\ld asc]ta9 t a suppos$ circle 0 a true & p]fect circle1 we c\ld be c]ta9 conc]n+ a multitude ( its geometrical prop]ties4 ,b geometrical figures are physical objects1 & ! s5ses c nev] assure u z to _! exact =ms4 ,! figures really treat$ 9 ,euclid's 99,elem5ts99 are imag9>y1 & we nev] c v]ify 9 practice ! conclusions :i* we draw ) c]ta9ty 9 inf]5ce2 que/ions ( degree & probability ent]4 ,pass+ n[ to subjects 9 :i* d$uction is only probable1 x ceases to be possible to adopt "o hypo!sis to ! exclusion ( ! o!rs4 ,we mu/ ent]ta9 at ! same "t all conceivable hypo!ses1 & reg>d ea* ) ! degree ( e/eem proportionate to its probability4 ,we g ?r\gh ! same /eps z be=e4 7#a7 ,we frame an hypo!sis4 7#b7 ,we d$uce ! probability ( v>i\s s]ies ( possible consequ5ces4 7#c7 ,we comp>e ! consequ5ces ) ! p>ticul> facts1 & obs]ve ! probability t su* facts w\ld happ5 "u ! hypo!sis4 ,! above processes mu/ be p]=m$ = e conceivable hypo!sis1 & !n ! absolute probability ( ea* w be yield$ by ! pr9ciple ( ! inv]se me?od 7p4 #bdb74 ,z 9 ! case ( c]ta9ty we accept t hypo!sis :i* c]ta9ly gives ! requir$ results1 s n[ we accept z mo/ probable t hypo!sis :i* mo/ probably gives ! results2 b we are oblig$ to ent]ta9 at ! same "t all o!r hypo!ses ) degrees ( probability proportionate to ! probabilities t !y w\ld give ! same results4 ,s f> we h treat$ only ( ! process by :i* we pass f special facts to g5]al laws1 t inv]se application ( d$uction :i* con/itutes induction4 ,b ! direct employm5t ( d$uction is (t5 comb9$ ) ! inv]se4 ,no soon] h we e/abli%$ a g5]al law1 ?an ! m9d rapidly draws p>ticul> consequ5ces f x4 ,9 geometry we may almo/ seem to inf] t 99because99 "o equilat]al triangle is equiangul>1 !re=e ano!r is s4 ,9 reality x is n because "o is t ano!r is1 b because all are4 ,! geometrical conditions are p]fectly g5]al1 & by :at is sometimes call$ 99p>ity ( reason+99 :atev] is true ( "o equilat]al triangle1 s f> z x is equilat]al1 is true ( all equilat]al triangles4 ,simil>ly1 9 all o!r cases ( inductive inf]5ce1 :]e we seem to pass f "s p>ticul> in/ances to a new in/ance1 we g ?r\gh ! same process4 ,we =m an hypo!sis z to ! logical conditions "u :i* ! giv5 in/ances might occur2 we calculate inv]sely ! probability ( t hypo!sis1 & comp\nd+ ?is ) ! probability t a new in/ance w\ld proce$ f ! same conditions1 we ga9 ! absolute probability ( occurr5ce ( ! new in/ance 9 virtue ( ?is hypo!sis4 ,b z sev]al1 or _m1 or ev5 an inf9ite numb] ( mutually inconsi/5t hypo!ses may be possible1 we mu/ repeat ! calculation = ea* su* conceivable hypo!sis1 & !n ! complete probability ( ! future in/ance w be ! sum ( ! sep>ate probabilities4 ,! complication ( ?is process is (t5 v mu* r$uc$ 9 practice1 ow+ to ! fact t "o hypo!sis may be almo/ c]ta9ly true1 & o!r hypo!ses1 ?\gh conceivable1 may be s improbable z to be neglect$ )\t appreciable error4 ,:5 we possess no k :atev] ( ! conditions f :i* ! ev5ts proce$1 we may be unable to =m any probable hypo!ses z to _! mode ( orig94 ,we h n[ to fall back ^u ! g5]al solution ( ! problem effect$ by ,laplace1 :i* consi/s 9 admitt+ on an equal foot+ e conceivable ratio ( fav\rable & unfav\rable *ances = ! production ( ! ev5t1 & !n accept+ ! aggregate result z ! be/ :i* c be obta9$4 ,?is solution is only to be accept$ 9 ! abs5ce ( all bett] means1 b l o!r results ( ! calculus ( probability1 x comes to our aid :]e k is at an end & ignorance beg9s1 & x prev5ts u f ov]-e/imat+ ! k we possess4 ,! g5]al results ( ! solution are 9 accordance ) common s5se1 namely1 t ! m (t5 an ev5t has happ5$ ! m probable1 z a g5]al rule1 is its subsequ5t recurr5ce4 ,) ! ext5sion ( exp]i5ce ?is probability increases1 b at ! same "t ! probability is slight t ev5ts w long cont9ue to happ5 z !y h previ\sly happ5$4 ,we h n[ pursu$ ! !ory ( inductive inf]5ce1 z f> z c be done ) reg>d to simple logical or num]ical relations4 ,! laws ( nature deal ) "t & space1 :i* are inf9itely divisible4 ,z we pass$ f pure logic to num]ical logic1 s we mu/ n[ pass f que/ions ( discont9u\s1 to que/ions ( cont9u\s quantity1 enc\nt]+ fre% consid]ations ( mu* difficulty4 ,be=e1 !re=e1 we consid] h[ ! great inductions & g5]alisations ( physical sci5ce illu/rate ! views ( inductive reason+ j expla9$1 we mu/ break (f = a "t1 & review ! means :i* we possess ( measur+ & comp>+ magnitudes ( "t1 space1 mass1 =ce1 mom5tum1 en]gy1 & ! v>i\s manife/ations ( en]gy 9 motion1 heat1 electricity1 *emical *ange1 & ! o!r ph5om5a ( nature4 ,,book ,,iii4 ,,me?ods ,,( ,,measurem5t4 ,,*apt] ,,xiii4 ,,! ,,exact ,,measurem5t ,,( ,,ph5om5a4 ,z physical sci5ce advances1 x becomes m & m accurately quantitative4 ,que/ions ( simple logical fact aft] a "t resolve !mselves into que/ions ( degree1 "t1 di/ance1 or weight4 ,=ces h>dly suspect$ to exi/ by "o g5]ation1 are cle>ly recognis$ by ! next1 & precisely measur$ by ! ?ird g5]ation4 ,b "o condition ( ?is rapid advance is ! inv5tion ( suitable in/rum5ts ( measurem5t4 ,we ne$ :at ,francis ,bacon call$ 99,in/anti citantes991 or 99evocantes991 me?ods ( r5d]+ m9ute ph5om5a p]ceptible to ! s5ses2 & we also require 99,in/anti radii99 or 99curriculi991 t is measur+ in/rum5ts4 ,accord+ly1 ! introduction ( a new in/rum5t (t5 =ms an epo* 9 ! hi/ory ( sci5ce4 ,z ,davy said1 8,no?+ t5ds s mu* to ! advancem5t ( k z ! application ( a new in/rum5t4 ,! native intellectual p[]s ( m5 9 diff]5t times are n s mu* ! causes ( ! diff]5t success ( _! lab\rs1 z ! peculi> nature ( ! means & artificial res\rces 9 _! possession40 ,9 ! abs5ce inde$ ( advanc$ !ory & analytical p[]1 a v precise in/rum5t w\ld be useless4 ,measur+ app>atus & ma!matical !ory %\ld advance 99p>i passu991 & ) j su* precision z ! !ori/ c anticipate results1 ! exp]im5tali/ %\ld be able to comp>e !m ) exp]i5ce4 ,! scrupul\sly accurate obs]vations ( ,flam/e$ 7 ! prop] complem5t to ! int5se ma!matical p[]s ( ,newton4 ,e bran* ( k comm5ces ) quantitative notions ( a v rude "*4 ,aft] we h f> progress$1 x is (t5 amus+ to look back into ! infancy ( ! sci5ce1 & contra/ pres5t ) pa/ me?ods4 ,at ,gre5wi* ,obs]vatory 9 ! pres5t day1 ! hundr$? "p ( a second is n ?\ght an inconsid]able portion ( "t4 ,! anci5t ,*aldans record$ an eclipse to ! ne>e/ h\r1 & ! e>ly ,alex&rian a/ronom]s ?\ght x sup]flu\s to di/+ui% betwe5 ! edge & c5tre ( ! sun4 ,by ! introduction ( ! a/rolabe1 ,ptolemy & ! lat] ,alex&rian a/ronom]s c\ld det]m9e ! places ( ! heav5ly bodies )9 ab\t t5 m9utes ( arc4 ,little progress !n ensu$ = ?irte5 c5turies1 until ,ty*o ,brahe made ! fir/ great /ep t[>ds accuracy1 n only by employ+ bett] in/rum5ts1 b ev5 m by ceas+ to reg>d an in/rum5t z correct4 ,ty*o1 9 fact1 det]m9$ ! errors ( 8 in/rum5ts1 & correct$ 8 obs]vations4 ,he also took notice ( ! effects ( atmosph]ic refraction1 & succe$$ 9 atta9+ an accuracy (t5 sixty times z great z t ( ,ptolemy4 ,yet ,ty*o & ,hevelius (t5 err$ sev]al m9utes 9 ! det]m9ation ( a />'s place1 & x 0 a great a*ievem5t ( ,rm] & ,flam/e$ to r$uce ?is error to seconds4 ,bradley1 ! mod]n ,hipp>*us1 c>ri$ on ! improvem5t1 8 errors 9 "r asc5sion1 accord+ to ,bessel1 be+ "u "o second ( "t1 & ^? ( decl9ation "u f\r seconds ( arc4 ,9 ! pres5t day ! av]age error ( a s+le obs]vation is probably r$uc$ to ! half or qu>t] ( :at x 0 9 ,bradley's "t2 & fur!r extreme accuracy is atta9$ by ! multiplication ( obs]vations1 & _! skilful comb9ation accord+ to ! !ory ( error4 ,"s ( ! m important con/ants1 = in/ance t ( nutation1 h be5 det]m9$ )9 ! t5? "p ( a second ( space4#ahj #ahj ,baily1 99,briti% ,association ,catalogue ( ,/>s991 pp4 #g1 #bc4 ,x w\ld be a matt] ( great int]e/ to trace out ! dep5d5ce ( ?is progress ^u ! introduction ( new in/rum5ts4 ,! a/rolabe ( ,ptolemy1 ! telescope ( ,galileo1 ! p5dulum ( ,galileo & ,huygh5s1 ! micromet] ( ,horrocks1 & ! telescopic sights & micromet] ( ,gascoygne & ,pic>d1 ,rm]'s transit in/rum5t1 ,newton's & ,hadley's quadrant1 ,dollond's a*romatic l5ses1 ,h>rison's *ronomet]1 & ,ramsd5's divid+ eng9e--su* 7 "s ( ! pr9cipal additions to a/ronomical app>atus4 ,! result is1 t we n[ take note ( quantities1 #cjj1jjj or #djj1jjj times z small z 9 ! "t ( ! ,*aldans4 ,x w\ld be int]e/+ aga9 to comp>e ! scrupul\s accuracy ( a mod]n trigonometrical survey ) ,erato/h5es' rude b +5i\s guess at ! diff]5ce ( latitude betwe5 ,alex&ria & ,sy5e--or ) ,norwood's measurem5t ( a degree ( latitude 9 #afce4 8,sometimes ,i measur$1 sometimes ,i pac$10 said ,norwood2 8& ,i believe ,i am )9 a scantl+ ( ! tru?40 ,su* 0 ! g]m ( ^? elaborate geodesical measurem5ts :i* h made ! dim5sions ( ! globe kn[n to u )9 a few hundr$ y>ds4 ,9 o!r bran*es ( sci5ce1 ! inv5tion ( an in/rum5t has usually m>k$1 if x has n made1 an epo*4 ,! sci5ce ( heat might be said to comm5ce ) ! con/ruction ( ! !rmomet]1 & x has rec5tly be5 advanc$ by ! introduction ( ! !rmo-electric pile4 ,*emi/ry has be5 creat$ *iefly by ! c>eful use ( ! balance1 :i* =ms a unique in/ance ( an in/rum5t rema9+ sub/antially 9 ! =m 9 :i* x 0 fir/ appli$ to sci5tific purposes by ,ar*im$es4 ,! balance nev] has be5 & probably nev] c be improv$1 except 9 details ( con/ruction4 ,! torsion balance1 introduc$ by ,c\lomb t[>ds ! end ( la/ c5tury1 has rapidly become ess5tial 9 _m bran*es ( inve/igation4 ,9 ! h&s ( ,cav5di% & ,baily1 x gave a det]m9ation ( ! e>?'s d5sity2 appli$ 9 ! galvanomet]1 x gave a delicate measure ( electrical =ces1 & is indisp5sable 9 ! !rmo-electric pile4 ,?is balance is made by simply susp5d+ any light rod by a ?9 wire or ?read atta*$ to ! middle po9t4 ,& we owe to x almo/ all ! m delicate inve/igations 9 ! !ories ( heat1 electricity1 & magnetism4 ,?\gh we c n[ take note ( ! million? ( an in* 9 space1 & ! million? ( a second 9 "t1 we mu/ n ov]look ! fact t 9 o!r op]ations ( sci5ce we are yet 9 ! position ( ! ,*aldans4 ,n _m ye>s h elaps$ s9ce ! magnitudes ( ! />s1 mean+ ! am\nts ( light !y s5d to ! obs]v]'s eye1 7 guess$ at 9 ! rude/ mann]1 & ! a/ronom] adjudg$ a /> to ?is or t ord] ( magnitude by a r\gh comp>ison ) o!r />s ( ! same ord]4 ,to ,sir ,john ,h]s*el we owe an attempt to introduce a uni=m me?od ( measurem5t & expression1 be>+ "s relation to ! real photometric magnitudes ( ! />s4#aha ,previ\s to ! rese>*es ( ,buns5 & ,roscoe on ! *emical action ( light1 we 7 devoid ( any mode ( measur+ ! en]gy ( light2 ev5 n[ ! me?ods are t$i\s1 & x is n cle> t !y give ! en]gy ( light s mu* z "o ( its special effects4 ,_m natural ph5om5a h h>dly yet be5 made ! subject ( measurem5t at all1 su* z ! int5sity ( s\nd1 ! ph5om5a ( ta/e & smell1 ! magnitude ( atoms1 ! temp]ature ( ! electric sp>k or ( ! sun's photosph]e4 #aha 99,outl9es ( ,a/ronomy991 #d? ed4 sect4 #gha1 p4 #ebb4 99,results ( ,obs]vations at ! ,cape ( ,good ,hope991 c41 p4 #cg4 ,to suppose1 !n1 t quantitative sci5ce treats only ( exactly measurable quantities1 is a gross if x be a common mi/ake4 ,:5ev] we are treat+ ( an ev5t :i* ei!r happ5s altoge!r or does n happ5 at all1 we are engag$ ) a non-quantitative ph5om5on1 a matt] ( fact1 n ( degree2 b :5ev] a ?+ may be great] or less1 or twice or ?rice z great z ano!r1 :5ev]1 9 %ort1 ratio ent]s ev5 9 ! rude/ mann]1 !re sci5ce w h a quantitative "*4 ,!re c be little d\bt1 inde$1 t e sci5ce z x progresses w become gradually m & m quantitative4 ,num]ical precision is ! s\l ( sci5ce1 z ,h]s*el said1 & z all natural objects exi/ 9 space1 & involve molecul> movem5ts1 measurable 9 velocity & ext5t1 !re is no app>5t limit to ! ultimate ext5sion ( quantitative sci5ce4 ,b ! read] mu/ n = a mom5t suppose t1 because we dep5d m & m ^u ma!matical me?ods1 we leave logical me?ods beh9d u4 ,numb]1 z ,i h endeav\r$ to %[1 is logical 9 its orig91 & quantity is b a developm5t ( numb]1 or analog\s !reto4 99,division ( ! ,subject499 ,! g5]al subject ( quantitative inve/igation w h to be divid$ into sev]al p>ts4 ,we %all fir/ly consid] ! means at our disposal = measur+ ph5om5a1 & ?us r5d]+ !m m or less am5able to ma!matical treatm5t4 ,?is task w involve an analysis ( ! pr9ciples on :i* accurate me?ods ( measurem5t are f\nd$1 =m+ ! subject ( ! rema9d] ( ! pres5t *apt]4 ,z measurem5t1 h[ev]1 only yields ratios1 we h 9 ! next *apt] to consid] ! e/abli%m5t ( unit magnitudes1 9 t]ms ( :i* our results may be express$4 ,z e ph5om5on is usually ! sum ( sev]al di/9ct quantities dep5d+ ^u diff]5t causes1 we h next to inve/igate 9 ,*apt] ,,xv4 ! me?ods by :i* we may dis5tangle complicat$ effects1 & ref] ea* "p ( ! jo9t effect to its sep>ate cause4 ,x yet rema9s = u 9 subsequ5t *apt]s to treat ( quantitative induction1 prop]ly s call$4 ,we mu/ foll[ out ! inv]se logical me?od1 z x pres5ts itself 9 problems ( a f> high] degree ( difficulty ?an ^? :i* treat ( objects relat$ 9 a simple logical mann]1 & incapable ( m]g+ into ea* o!r by addition & subtraction4 99,cont9u\s ,quantity499 ,! ph5om5a ( nature are = ! mo/ "p manife/$ 9 quantities :i* increase or decrease cont9u\sly4 ,:5 we inquire into ! precise mean+ ( cont9u\s quantity1 we f9d t x c only be describ$ z t :i* is divisible )\t limit4 ,we c divide a millimetre into t51 or a hundr$1 or a ?\s&1 or t5 ?\s& p>ts1 & m5tally at any rate we c c>ry on ! division 99ad inf9itum994 ,any f9ite space1 !n1 mu/ be conceiv$ z made up ( an inf9ite numb] ( p>ts ea* inf9itely small4 ,we _c ent]ta9 ! simple/ geometrical notions )\t all[+ ?is4 ,! conception ( a squ>e involves ! conception ( a side & diagonal1 :i*1 z ,euclid beautifully proves 9 ! #aag? proposition ( 8 t5? book1 h no common measure1#ahb mean+ no f9ite common measure4 ,incomm5surable quantities are1 9 fact1 ^? :i* h = _! only common measure an inf9itely small quantity4 ,x is some:at />tl+ to f9d1 too1 t 9 !ory incomm5surable quantities w be inf9itely m frequ5t ?an comm5surable4 ,let any two l9es be drawn haphaz>d2 x is inf9itely unlikely t !y w be comm5surable1 s t ! comm5surable quantities1 :i* we are suppos$ to deal ) 9 practice1 are b s+ul> cases among an inf9itely great] numb] ( incomm5surable cases4 #ahb ,see ,de ,morgan1 99,/udy ( ,ma!matics991 9 ,u4,k4,s4 ,libr>y1 p4 #ha4 ,practically1 h[ev]1 we treat all quantities z made up ( ! lea/ quantities :i* our s5ses1 assi/$ by ! be/ measur+ in/rum5ts1 c p]ceive4 ,s long z microscopes 7 un9v5t$1 x 0 suffici5t to reg>d an in* z made up ( a ?\s& ?\s&?s ( an in*2 n[ we mu/ treat x z compos$ ( a million million?s4 ,we might app>5tly avoid all m5tion ( inf9itely small quantities1 by nev] c>ry+ our approximations beyond quantities :i* ! s5ses c appreciate4 ,9 geometry1 z ?us treat$1 we %\ld nev] ass]t two quantities to be equal1 b only to be 99app>5tly99 equal4 ,leg5dre really adopts ?is mode ( treatm5t 9 ! tw5tie? proposition ( ! fir/ book ( 8 ,geometry2 & x is practically adopt$ ?r\gh\t ! physical sci5ces1 z we %all aft]w>ds see4 ,b ?\gh our f+]s1 & s5ses1 & in/rum5ts mu/ /op some:]e1 !re is no reason :y ! m9d %\ld n g on4 ,we c see t a pro( :i* is only c>ri$ ?r\gh a few /eps 9 fact1 might be c>ri$ on )\t limit1 & x is ?is consci\sness ( no /opp+-place1 :i* r5d]s ,euclid's pro( ( 8 #aag? proposition s impressive4 ,try h[ we w to circumv5t ! matt]1 we _c really avoid ! consid]ation ( ! inf9itely small & ! inf9itely great4 ,! same me?ods ( approximation :i* seem conf9$ to ! f9ite1 m5tally ext5d !mselves to ! inf9ite4 ,"o result ( ^! consid]ations is1 t we _c possibly adju/ two quantities 9 absolute equality4 ,! susp5sion ( ,mahomet's c(f9 betwe5 two precisely equal magnets is !oretically conceivable b practically impossible4 ,! /ory ( ! 99,m]*ant ( ,v5ice99 turns ^u ! inf9ite improbability t an exact quantity ( fle% c\ld be cut4 ,un/able equilibrium _c exi/ 9 nature1 = x is t :i* is de/roy$ by an inf9itely small displacem5t4 ,x might be possible to balance an egg on its end practically1 because no egg has a surface ( p]fect curvature4 ,suppose ! egg %ell to be p]fectly smoo?1 & ! feat w\ld become impossible4 99,! ,fallaci\s ,indications ( ! ,s5ses499 ,i may briefly rem9d ! read] h[ little we c tru/ to our unassi/$ s5ses 9 e/imat+ ! degree or magnitude ( any ph5om5on4 ,! eye _c correctly e/imate ! comp>ative brightness ( two lum9\s bodies :i* diff] mu* 9 brilliancy2 = we "k t ! iris is con/antly adju/+ itself to ! int5sity ( ! light receiv$1 & ?us admits m or less light accord+ to circum/ances4 ,! moon :i* %9es ) almo/ dazzl+ brightness by night1 is pale & ne>ly imp]ceptible :ile ! eye is yet affect$ by ! va/ly m p[]ful light ( day4 ,mu* has be5 record$ conc]n+ ! comp>ative brightness ( ! zodiacal light at diff]5t times1 b x w\ld be difficult to prove t ^! *anges are n due to ! v>y+ d>kness at ! "t1 or ! diff]5t acut5ess ( ! obs]v]'s eye4 ,= a l reason x is exce$+ly difficult to e/abli% ! exi/5ce ( any *ange 9 ! =m or comp>ative brightness ( nebul2 ! appe>ance ( a nebula greatly dep5ds ^u ! ke5ness ( sight ( ! obs]v]1 or ! accid5tal condition ( fre%ness or fatigue ( 8 eye4 ,! same is true ( lun> obs]vations2 & ev5 ! use ( ! be/ telescope fails to remove ?is difficulty4 ,9 judg+ ( col\rs1 aga91 we mu/ rememb] t light ( any giv5 col\r t5ds to dull ! s5sibility ( ! eye = light ( ! same col\r4 ,nor is ! eye :5 unassi/$ by in/rum5ts a mu* bett] judge ( magnitude4 ,our e/imates ( ! size ( m9ute bright po9ts1 su* z ! fix$ />s1 are completely falsifi$ by ! effects ( irradiation4 ,ty*o calculat$ f ! app>5t size ( ! />-discs1 t no "o ( ! pr9cipal fix$ />s c\ld be conta9$ )9 ! area ( ! e>?'s orbit4 ,ap>t1 h[ev]1 f irradiation or o!r di/9ct causes ( error our visual e/imates ( sizes & %apes are (t5 a/oni%+ly incorrect4 ,arti/s almo/ inv>iably draw di/ant m\nta9s 9 ludicr\s disproportion to ne>] objects1 z a comp>ison ( a sket* ) a photograph at once %[s4 ,! extraord9>y app>5t diff]5ce ( size ( ! sun or moon1 accord+ z x is high 9 ! heav5s or ne> ! horizon1 %\ld be suffici5t to make u cauti\s 9 accept+ ! pla9e/ indications ( our s5ses1 unassi/$ by in/rum5tal measurem5t4 ,z to /atem5ts conc]n+ ! height ( ! aurora & ! di/ance ( meteors1 !y are to be utt]ly di/ru/$4 ,:5 ,capta9 ,p>ry says t a ray ( ! aurora %ot sudd5ly d[nw>ds betwe5 him & ! l& :i* 0 only #c1jjj y>ds di/ant1 we mu/ consid] him subject to an illusion ( s5se4#ahc #ahc ,loomis1 99,on ! ,aurora ,borealis994 ,smi?sonian ,transactions1 quot+ ,p>ry's ,?ird ,voyage1 p4 #fa4 ,x is true t errors ( obs]vation are m (t5 errors ( judgm5t ?an ( s5se4 ,t :i* is actually se5 mu/ be s f> truly se52 & if we correctly int]pret ! mean+ ( ! ph5om5on1 !re w\ld be no error at all4 ,b ! weakness ( ! b>e s5ses z measur+ in/rum5ts1 arises f ! fact t !y import v>y+ conditions ( unkn[n am\nt1 & we _c make ! requisite corrections & all[ances z 9 ! case ( a solid & inv>iable in/rum5t4 ,bacon has excell5tly /at$ ! insuffici5cy ( ! s5ses = e/imat+ ! magnitudes ( objects1 or detect+ ! degrees 9 :i* ph5om5a pres5t !mselves4 8,?+s escape ! s5ses10 he says1 8because ! object is n suffici5t 9 quantity to /rike ! s5se3 z all m9ute bodies2 because ! p]cussion ( ! object is too great to be endur$ by ! s5ses3 z ! =m ( ! sun :5 look+ directly at x 9 mid-day2 because ! "t is n proportionate to actuate ! s5se3 z ! motion ( a bullet 9 ! air1 or ! quick circul> motion ( a firebr&1 :i* are too fa/1 or ! h\r-h& ( a common clock1 :i* is too sl[2 f ! di/ance ( ! object z to place3 z ! size ( ! cele/ial bodies1 & ! size & nature ( all di/ant bodies2 f prepossession by ano!r object3 z "o p[]ful smell r5d]s o!r smells 9 ! same room imp]ceptible2 f ! int]ruption ( int]pos+ bodies3 z ! int]nal p>ts ( animals2 & because ! object is unfit to make an impression ^u ! s5se3 z ! air or ! invisible & untangible _s :i* is includ$ 9 e liv+ body40 99,complexity ( ,quantitative ,que/ions499 ,"o rem>k :i* we may well make 9 ent]+ ^u quantitative que/ions1 has reg>d to ! great v>iety & ext5t ( ph5om5a pres5t$ to our notice4 ,s long z we deal only ) a simply logical "q1 t "q is m]ely1 ,does a c]ta9 ev5t happ58 or1 ,does a c]ta9 object exi/8 ,no soon] d we reg>d ! ev5t or object z capable ( m & less1 ?an ! "q bran*es out into _m4 ,we mu/ n[ ask1 ,h[ mu* is x comp>$ ) its cause8 ,does x *ange :5 ! am\nt ( ! cause *anges8 ,if s1 does x *ange 9 ! same or opposite direction8 ,is ! *ange 9 simple proportion to t ( ! cause8 ,if n1 :at m complex law ( connection holds true8 ,?is law det]m9$ satisfactorily 9 "o s]ies ( circum/ances may be v>i$ "u new conditions1 & ! mo/ complex relations ( sev]al quantities may ultimately be e/abli%$4 ,9 e "q ( physical sci5ce !re is ?us a s]ies ( /eps ! fir/ "o or two ( :i* are usually made ) ease :ile ! succe$+ ones dem& m & m c>eful measurem5t4 ,we _c lay d[n any inv>iable s]ies ( que/ions :i* mu/ be ask$ f nature4 ,! exact "* ( ! que/ions w v>y accord+ to ! nature ( ! case1 b !y w usually be ( an evid5t k9d1 & we may readily illu/rate !m by examples4 ,suppose t we are inve/igat+ ! solution ( "s salt 9 wat]4 ,! fir/ is a purely logical "q3 ,is !re solution1 or is !re n8 ,assum+ ! answ] to be 9 ! affirmative1 we next inquire1 ,does ! solubility v>y ) ! temp]ature1 or n8 ,9 all probability "s v>iation w exi/1 & we mu/ h an answ] to ! fur!r "q1 ,does ! quantity dissolv$ increase1 or does x dim9i% ) ! temp]ature8 ,9 by f> ! greate/ numb] ( cases salts & sub/ances ( all k9ds dissolve m freely ! high] ! temp]ature ( ! wat]2 b !re are a few salts1 su* z calcium sulphate1 :i* foll[ ! opposite rule4 ,a consid]able numb] ( salts resemble sodium sulphate 9 becom+ m soluble up to a c]ta9 temp]ature1 & !n v>y+ 9 ! opposite direction4 ,we next require to assign ! am\nt ( v>iation z comp>$ ) t ( ! temp]ature1 assum+ at fir/ t ! increase ( solubility is proportional to ! increase ( temp]ature4 ,common salt is an in/ance ( v slight v>iation1 & potassium nitrate ( v consid]able increase ) temp]ature4 ,accurate obs]vations w probably %[1 h[ev]1 t ! simple law ( proportionate v>iation is only approximately true1 & "s m complicat$ law involv+ ! second1 ?ird1 or high] p[]s ( ! temp]ature may ultimately be e/abli%$4 ,all ^! inve/igations h to be c>ri$ out = ea* salt sep>ately1 s9ce no di/9ct pr9ciples by :i* we may inf] f "o sub/ance to ano!r h yet be5 detect$4 ,!re is /ill an indef9ite field = fur!r rese>* op52 = ! solubility ( salts w probably v>y ) ! pressure "u :i* ! m$ium is plac$2 ! pres5ce ( o!r salts already dissolv$ may h effects yet unkn[n4 ,! rese>*es already effect$ z reg>ds ! solv5t p[] ( wat] mu/ be repeat$ ) alcohol1 e!r1 c>bon bisulphide1 & o!r m$ia1 s t unless g5]al laws c be detect$1 ?is "o ph5om5on ( solution c nev] be exhau/ively treat$4 ,! same k9d ( que/ions recur z reg>ds ! solution or absorption ( gases 9 liquids1 ! pressure z well z ! temp]ature hav+ !n a mo/ decid$ effect1 & ,pr(essor ,roscoe's rese>*es on ! subject pres5t an excell5t example ( ! successive det]m9ation ( v>i\s complicat$ laws4#ahd #ahd ,watts' 99,diction>y ( ,*emi/ry991 vol4 ii4 p4 #gij4 ,!re is h>dly a bran* ( physical sci5ce 9 :i* simil> complications are n ultimately enc\nt]$4 ,9 ! case ( gravity1 inde$1 we arrive at ! f9al law1 t ! =ce is ! same = all k9ds ( matt]1 & v>ies only ) ! di/ance ( action4 ,b 9 o!r subjects ! laws1 if simple 9 _! ultimate nature1 are disguis$ & complicat$ 9 _! app>5t results4 ,?us ! effect ( heat 9 exp&+ solids1 & ! rev]se effect ( =cible ext5sion or compression ^u ! temp]ature ( a body1 w v>y f "o sub/ance to ano!r1 w v>y z ! temp]ature is already high] or l[]1 &1 w probably foll[ a highly complex law1 :i* 9 "s cases gives negative or exceptional results4 ,9 cry/all9e sub/ances ! same rese>*es h to be repeat$ 9 ea* di/9ct axial direction4 ,9 ! sci5ces ( pure obs]vation1 su* z ^? ( a/ronomy1 meteorology1 & t]re/rial magnetism1 we meet ) _m int]e/+ s]ies ( quantitative det]m9ations4 ,! s-call$ fix$ />s1 z ,giordano ,bruno div9$1 are n really fix$1 & may be m truly describ$ z va/ w&]+ orbs1 ea* pursu+ its own pa? ?r\gh space4 ,we mu/ !n det]m9e sep>ately = ea* /> ! foll[+ que/ions3-- #a4 ,does x move8 #b4 ,9 :at direction8 #c4 ,at :at velocity8 #d4 ,is ?is velocity v>iable or uni=m8 #e4 ,if v>iable1 accord+ to :at law8 #f4 ,is ! direction uni=m8 #g4 ,if n1 :at is ! =m ( ! app>5t pa?8 #h4 ,does x approa* or rec$e8 #i4 ,:at is ! =m ( ! real pa?8 ,! successive answ]s to su* que/ions 9 ! case ( c]ta9 b9>y />s1 h af=d$ a pro( t ! motions are due to a c5tral =ce co9cid+ 9 law ) gravity1 & d\btless id5tical ) x4 ,9 o!r cases ! motions are usually s small t x is exce$+ly difficult to di/+ui% !m ) c]ta9ty4 ,& ! "t is yet f> (f :5 any g5]al results z reg>ds /ell> motions c be e/abli%$4 ,! v>iation 9 ! brightness ( />s op5s an unlimit$ field = curi\s obs]vation4 ,!re is n a /> 9 ! heav5s conc]n+ :i* we might n h to det]m9e3-- #a4 ,does x v>y 9 brightness8 #b4 ,is ! brightness increas+ or decreas+8 #c4 ,is ! v>iation uni=m8 #d4 ,if n1 accord+ to :at law does x v>y8 ,9 a majority ( cases ! *ange w probably be f\nd to h a p]iodic "*1 9 :i* case sev]al o!r que/ions w arise1 su* z-- #e4 ,:at is ! l5g? ( ! p]iod8 #f4 ,are !re m9or p]iods8 #g4 ,:at is ! law ( v>iation )9 ! p]iod8 #h4 ,is !re any *ange 9 ! am\nt ( v>iation8 #i4 ,if s1 is x a secul>1 99i4e499 a cont9ually gr[+ *ange1 or does x give evid5ce ( a great] p]iod8 ,already ! p]iodic *anges ( a c]ta9 numb] ( />s h be5 det]m9$ ) accuracy1 & ! l5g?s ( ! p]iods v>y f less ?an ?ree days up to int]vals ( "t at lea/ #bej times z great4 ,p]iods )9 p]iods h also be5 detect$4 ,!re is1 p]haps1 no subject 9 :i* m complicat$ quantitative conditions h to be det]m9$ ?an t]re/rial magnetism4 ,s9ce ! "t :5 ! decl9ation ( ! compass 0 fir/ notic$1 z "s suppose by ,columbus1 we h _h successive discov]ies f "t to "t ( ! progressive *ange ( decl9ation f c5tury to c5tury2 ( ! p]iodic "* ( ?is *ange2 ( ! diff]5ce ( ! decl9ation 9 v>i\s p>ts ( ! e>?'s surface2 ( ! v>y+ laws ( ! *ange ( decl9ation2 ( ! dip or incl9ation ( ! ne$le1 & ! correspond+ laws ( its p]iodic *anges2 ! horizontal & p]p5dicul> int5sities h also be5 ! subject ( exact measurem5t1 & h be5 f\nd to v>y ) place & "t1 l ! directions ( ! ne$le2 daily & ye>ly p]iodic *anges h also be5 detect$1 & all ! elem5ts are f\nd to be subject to occasional /orms or abnormal p]turbations1 9 :i* ! elev5 ye> p]iod1 n[ kn[n to be common to _m planet>y relations1 is app>5t4 ,! complete solution ( ^! motions ( ! compass ne$le involves no?+ less ?an a det]m9ation ( its position & oscillations 9 e "p ( ! _w at any epo*1 ! l det]m9ation = ano!r epo*1 & s on1 "t aft] "t1 until ! p]iods ( all *anges are asc]ta9$4 ,?is "o subject (f]s to m5 ( sci5ce an almo/ inexhau/ible field = int]e/+ quantitative rese>*1 9 :i* we %all d\btless at "s future "t discov] ! op]ation ( causes n[ mo/ my/]i\s & unacc\ntable4 99,! ,me?ods ( ,accurate ,measurem5t499 ,9 /udy+ ! modes by :i* physici/s h accompli%$ v exact measurem5ts1 we f9d t !y are v v>i\s1 b t !y may p]haps be r$uc$ "u ! foll[+ ?ree classes3-- #a4 ,! increase or decrease1 9 "s det]m9ate ratio1 ( ! quantity to be measur$1 s z to br+ x )9 ! scope ( our s5ses1 & to equate x ) ! /&>d unit1 or "s det]m9ate multiple or sub-multiple ( ?is unit4 #b4 ,! discov]y ( "s natural conjunction ( ev5ts :i* w enable u to comp>e directly ! multiples ( ! quantity ) ^? ( ! unit1 or a quantity relat$ 9 a def9ite ratio to t unit4 #c4 ,indirect measurem5t1 :i* gives u n ! quantity itself1 b "s o!r quantity connect$ ) x by kn[n ma!matical relations4 99,conditions ( ,accurate ,measurem5t499 ,sev]al conditions are requisite 9 ord] t a measurem5t may be made ) great accuracy1 & t ! results may be closely accordant :5 sev]al indep5d5t measurem5ts are made4 ,9 ! fir/ place ! magnitude mu/ be exactly def9$ by %>p t]m9ations1 or precise m>ks ( inconsid]able ?ickness4 ,:5 a b\nd>y is vague & graduat$1 l ! p5umbra 9 a lun> eclipse1 x is impossible to say :]e ! end really is1 & diff]5t p w come to diff]5t results4 ,we may sometimes ov]come ?is difficulty to a c]ta9 ext5t1 by obs]vations repeat$ 9 a special mann]1 z we %all aft]w>ds see2 b :5 possible1 we %\ld *oose opportunities = measurem5t :5 precise def9ition is easy4 ,! mom5t ( occultation ( a /> by ! moon c be obs]v$ ) great accuracy1 because ! /> disappe>s ) p]fect sudd5ness2 b !re are o!r a/ronomical conjunctions1 eclipses1 transits1 c41 :i* occupy a c]ta9 l5g? ( "t 9 happ5+1 & ?us op5 ! way to diff]5ces ( op9ion4 ,x w\ld be impossible to obs]ve ) precision ! movem5ts ( a body possess+ no def9ite po9ts ( ref]5ce4 ,! col\rs ( ! complete spectrum %ade into ea* o!r s cont9u\sly t exact det]m9ations ( refractive indices w\ld h be5 impossible1 _h we n ! d>k l9es ( ! sol> spectrum z precise po9ts = measurem5t1 or v>i\s k9ds ( homog5e\s light1 su* z t ( sodium1 possess+ a ne>ly uni=m l5g? ( vibration4 ,9 ! second place1 we _c measure accurately unless we h ! means ( multiply+ or divid+ a quantity )\t consid]able error1 s t we may correctly equate "o magnitude ) ! multiple or submultiple ( ! o!r4 ,9 "s cases we op]ate ^u ! quantity to be measur$1 & br+ x into accurate co9cid5ce ) ! actual /&>d1 z :5 9 photometry we v>y ! di/ance ( our lum9\s body1 until its illum9at+ p[] at a c]ta9 po9t is equal to t ( a /&>d lamp4 ,9 o!r cases we repeat ! unit until x equals ! object1 z 9 survey+ l&1 or det]m9+ a weight by ! balance4 ,! requisites ( accuracy n[ are3--7#a7 ,t we c repeat unit aft] unit ( exactly equal magnitude2 7#b7 ,t ^! c be jo9$ toge!r s t ! aggregate %all really be ! sum ( ! p>ts4 ,! same conditions apply to subdivision1 :i* may be reg>d$ z a multiplication ( subord9ate units4 ,9 ord] to measure to ! ?\s&? ( an in*1 we mu/ be able to add ?\s&? aft] ?\s&? )\t error 9 ! magnitude ( ^! spaces1 or 9 _! conjunction4 99,measur+ ,in/rum5ts499 ,to consid] ! me*anical con/ruction ( sci5tific in/rum5ts1 is no "p ( my purpose 9 ?is book4 ,i wi% to po9t out m]ely ! g5]al purpose ( su* in/rum5ts1 & ! me?ods adopt$ to c>ry out t purpose ) great precision4 ,9 ! fir/ place we mu/ di/+ui% betwe5 ! in/rum5t :i* effects a comp>ison betwe5 two quantities1 & ! /&>d magnitude :i* (t5 =ms "o ( ! quantities comp>$4 ,! a/ronom]'s clock1 = in/ance1 is no /&>d ( ! efflux ( "t2 x s]ves b to subdivide1 ) approximate accuracy1 ! int]val ( successive passages ( a /> across ! m]idian1 :i* x may effect p]haps to ! t5? "p ( a second1 or #a_/hfdjjj "p ( ! :ole4 ,! mov+ globe itself is ! real /&>d clock1 & ! transit in/rum5t ! f+] ( ! clock1 :ile ! />s are ! h\r1 m9ute1 & second m>ks1 none ! less accurate because !y are dispos$ at unequal int]vals4 ,! photomet] is a simple in/rum5t1 by :i* we comp>e ! relative int5sity ( rays ( light fall+ ^u a giv5 spot4 ,! galvanomet] %[s ! comp>ative int5sity ( electric curr5ts pass+ ?r\gh a wire4 ,! calorimet] gauges ! quantity ( heat pass+ f a giv5 object4 ,b no su* in/rum5ts furni% ! /&>d unit 9 t]ms ( :i* our results are to be express$4 ,9 "o peculi> case alone does ! same in/rum5t comb9e ! unit ( measurem5t & ! means ( comp>ison4 ,a !odolite1 mural circle1 sextant1 or o!r in/rum5t = ! measurem5t ( angul> magnitudes has no ne$ ( an additional physical unit2 = ! circle itself1 or complete revolution1 is ! natural unit to :i* all great] or less] am\nts ( angul> magnitude are ref]r$4 ,! result ( e measurem5t is to make kn[n ! purely num]ical ratio exi/+ betwe5 ! magnitude to be measur$1 & a c]ta9 o!r magnitude1 :i* %\ld1 :5 possible1 be a fix$ unit or /&>d magnitude1 or at lea/ an int]m$iate unit ( :i* ! value c be asc]ta9$ 9 t]ms ( ! ultimate /&>d4 ,b ?\gh a ratio is ! requir$ result1 an equation is ! mode 9 :i* ! ratio is det]m9$ & express$4 ,9 e measurem5t we equate "s multiple or submultiple ( "o quantity1 ) "s multiple or submultiple ( ano!r1 & equality is always ! fact :i* we asc]ta9 by ! s5ses4 ,by ! eye1 ! e>1 or ! t\*1 we judge :e!r !re is a discrepancy or n betwe5 two lights1 two s\nds1 two int]vals ( "t1 two b>s ( metal4 ,(t5 inde$ we sub/itute "o s5se = ! o!r1 z :5 ! efflux ( "t is judg$ by ! m>ks ^u a mov+ slip ( pap]1 s t equal int]vals ( "t are repres5t$ by equal l5g?s4 ,!re is a t5d5cy to r$uce all comp>isons to ! comp>ison ( space magnitudes1 b 9 e case "o ( ! s5ses mu/ be ! ultimate judge ( co9cid5ce or non-co9cid5ce4 ,s9ce ! equation to be e/abli%$ may exi/ betwe5 any multiples or submultiples ( ! quantities comp>$1 !re naturally arise sev]al diff]5t modes ( comp>ison adapt$ to diff]5t cases4 ,let 99p99 be ! magnitude to be measur$1 & 99q99 t 9 t]ms ( :i* x is to be express$4 ,!n we wi% to f9d su* numb]s 99x99 & 99y991 t ! equation 99p 7x_/y7q99 may be true4 ,?is equation may be pres5t$ 9 f\r =ms1 namely3-- ,fir/ ,=m4 ,second ,=m4 ,?ird ,=m4 ,f\r? ,=m4 99p 7x_/y7q99 99p7y_/x7 q99 99py qx99 99p_/x q_/y99 ,ea* ( ^! modes ( express+ ! same equation corresponds to "o mode ( effect+ a measurem5t4 ,:5 ! /&>d quantity is great] ?an t to be measur$1 we (t5 adopt ! fir/ mode1 & subdivide ! unit until we get a magnitude equal to t measur$4 ,! angles obs]v$ 9 survey+1 9 a/ronomy1 or 9 goniometry are usually small] ?an a :ole revolution1 & ! measur+ circle is divid$ by ! use ( ! screw & microscope1 until we obta9 an angle undi/+ui%able f t obs]v$4 ,! dim5sions ( m9ute objects are det]m9$ by subdivid+ ! in* or c5timetre1 ! screw micromet] be+ ! mo/ accurate means ( subdivision4 ,ord9>y temp]atures are e/imat$ by division ( ! /&>d int]val betwe5 ! freez+ & boil+ po9ts ( wat]1 z m>k$ on a !rmomet] tube4 ,9 a /ill great] numb] ( cases1 p]haps1 we multiply ! /&>d unit until we get a magnitude equal to t to be measur$4 ,ord9>y measurem5t by a foot rule1 a surveyor's *a91 or ! excessively c>eful measurem5ts ( ! base l9e ( a trigonometrical survey by /&>d b>s1 are suffici5t in/ances ( ?is proc$ure4 ,9 ! second case1 :]e 99p7y_/x7 q991 we multiply or divide a magnitude until we get :at is equal to ! unit1 or to "s magnitude easily comp>able ) x4 ,z a g5]al rule ! quantities :i* we desire to measure 9 physical sci5ce are too small r ?an too great = easy det]m9ation1 & ! problem consi/s 9 multiply+ !m )\t introduc+ error4 ,?us ! expansion ( a metallic b> :5 heat$ f #j;,c to #ajj may be multipli$ by a tra9 ( lev]s or cog :eels4 ,9 ! common !rmomet] ! expansion ( ! m]cury1 ?\gh slight1 is r5d]$ v app>5t1 & easily measurable by ! f95ess ( ! tube1 & _m o!r cases might be quot$4 ,!re are "s ph5om5a1 on ! contr>y1 :i* are too great or rapid to come )9 ! easy range ( our s5ses1 & our task is !n ! opposite "o ( dim9ution4 ,galileo f\nd x difficult to measure ! velocity ( a fall+ body1 ow+ to ! consid]able velocity acquir$ 9 a s+le second4 ,he adopt$ ! elegant device1 !re=e1 ( less5+ ! rapidity by lett+ ! body roll d[n an incl9$ plane1 :i* enables u to r$uce ! accel]at+ =ce 9 any requir$ ratio4 ,! same purpose is effect$ 9 ! well-kn[n exp]im5ts p]=m$ on ,attwood's ma*9e1 & ! measurem5t ( gravity by ! p5dulum really dep5ds on ! same pr9ciple appli$ 9 a f> m advantage\s mann]4 ,:eat/one inv5t$ a beautiful me?od ( galvanometry = /rong curr5ts1 :i* consi/s 9 draw+ (f f ! ma9 curr5t a c]ta9 det]m9ate portion1 :i* is equat$ by ! galvanomet] to a /&>d curr5t4 ,9 %ort1 he measures n ! curr5t itself b a kn[n fraction ( x4 ,9 _m electrical & o!r exp]im5ts1 we wi% to measure ! movem5ts ( a ne$le or o!r body1 :i* are n only v slight 9 !mselves1 b ! manife/ations ( exce$+ly small =ces4 ,we _c ev5 approa* a delicately balanc$ ne$le )\t di/urb+ x4 ,"u ^! circum/ances ! only mode ( proce$+ ) accuracy1 is to atta* a v small mirror to ! mov+ body1 & employ a ray ( light reflect$ f ! mirror z an index ( its movem5ts4 ,! ray may be consid]$ q incapable ( affect+ ! body1 & yet by all[+ ! ray to pass to a suffici5t di/ance1 ! motions ( ! mirror may be increas$ to almo/ any ext5t4 ,a ray ( light is 9 fact a p]fectly weightless f+] or index ( indef9ite l5g?1 ) ! additional advantage t ! angul> deviation is by ! law ( reflection d\ble t ( ! mirror4 ,?is me?od 0 introduc$ by ,gauss1 & is n[ ( great importance2 b 9 ,wolla/on's reflect+ goniomet] a ray ( light _h previ\sly be5 employ$ z an index4 ,lavoisi] & ,laplace _h also us$ a telescope 9 connection ) ! pyromet]4 ,x is a great advantage 9 "s in/rum5ts t !y c be readily made to manife/ a ph5om5on 9 a great] or less degree1 by a v slight *ange 9 ! con/ruction4 ,?us ei!r by enl>g+ ! bulb or contract+ ! tube ( ! !rmomet]1 we c make x give m conspicu\s indications ( *ange ( temp]ature4 ,! ord9>y b>omet]1 on ! o!r h&1 always gives ! v>iations ( pressure on "o scale4 ,! torsion balance is rem>kable = ! extreme delicacy :i* may be atta9$ by increas+ ! l5g? & lightness ( ! rod1 & ! l5g? & ?9ness ( ! support+ ?read4 ,=ces s m9ute z ! attraction ( gravitation betwe5 two balls1 or ! magnetic & diamagnetic attraction ( common liquids & gases1 may ?us be made app>5t1 & ev5 measur$4 ,! common *emical balance1 too1 is capable !oretically ( unlimit$ s5sibility4 ,! ?ird mode ( measurem5t1 :i* may be call$ ! ,me?od ( ,repetition1 is ( su* great importance & int]e/ t we mu/ consid] x 9 a sep>ate section4 ,x consi/s 9 multiply+ bo? magnitudes to be comp>$ until "s multiple ( ! fir/ is f\nd to co9cide v ne>ly ) "s multiple ( ! second4 ,if ! multiplication c be effect$ to an unlimit$ ext5t1 )\t ! introduction ( c\nt]vail+ errors1 ! accuracy ) :i* ! requir$ ratio c be det]m9$ is unlimit$1 & we ?us acc\nt = ! extraord9>y precision ) :i* int]vals ( "t 9 a/ronomy are comp>$ toge!r4 ,! f\r? mode ( measurem5t1 9 :i* we equate submultiples ( two magnitudes1 is comp>atively seldom employ$1 because x does n conduce to accuracy4 ,9 ! photomet]1 p]haps1 we may be said to use x2 we comp>e ! int5sity ( two s\rces ( light1 by plac+ !m bo? at su* di/ances f a giv5 surface1 t ! light fall+ on ! surface is tol]able to ! eye1 & equally int5se f ea* s\rce4 ,s9ce ! int5sity ( light v>ies inv]sely z ! squ>e ( ! di/ance1 ! relative int5sities ( ! lum9\s bodies are proportional to ! squ>es ( _! di/ances4 ,! equal int5sity ( two rays ( simil>ly col\r$ light may be mo/ accurately asc]ta9$ 9 ! mode sugge/$ by ,arago1 namely1 by caus+ ! rays to pass 9 opposite directions ?r\gh two ne>ly flat l5ses press$ toge!r4 ,!re is an exact equation betwe5 ! int5sities ( ! beams :5 ,newton's r+s disappe>1 ! r+ creat$ by "o ray be+ exactly ! complem5t ( t creat$ by ! o!r4 99,! ,me?od ( ,repetition499 ,! ratio ( two quantities c be det]m9$ ) unlimit$ accuracy1 if we c multiply bo? ! object ( measurem5t & ! /&>d unit )\t error1 & !n obs]ve :at multiple ( ! "o co9cides or ne>ly co9cides ) "s multiple ( ! o!r4 ,al?\gh p]fect co9cid5ce c nev] be really atta9$1 ! error ?us aris+ may be indef9itely r$uc$4 ,= if ! equation 99py99 99qx99 be unc]ta9 to ! am\nt 99e991 s t 99py99 99qx99 99e991 !n we h 99p99 99q7x_/y799 99e_/y99 1 & z we are suppos$ to be able to make 99y99 z great z we l )\t increas+ ! error 99e991 x foll[s t we c make 99e99 99y99 z small z we l1 & ?us approximate )9 an inconsid]able quantity to ! requir$ ratio 99x99 99y994 ,?is me?od ( repetition is naturally employ$ :5ev] quantities c be repeat$1 or repeat !mselves )\t error ( juxtaposition1 :i* is especially ! case ) ! motions ( ! e>? & heav5ly bodies4 ,9 det]m9+ ! l5g? ( ! sid]eal day1 we det]m9e ! ratio betwe5 ! e>?'s revolution r\nd ! sun1 & its rotation on its own axis4 ,we might asc]ta9 ! ratio by obs]v+ ! successive passages ( a /> across ! z5i?1 & comp>+ ! int]val by a good clock ) t betwe5 two passages ( ! sun1 ! diff]5ce be+ due to ! angul> movem5t ( ! e>? r\nd ! sun4 ,9 su* obs]vations we %\ld h an error ( a consid]able "p ( a second at ea* obs]vation1 9 addition to ! irregul>ities ( ! clock4 ,b ! revolutions ( ! e>? repeat !mselves day aft] day1 & ye> aft] ye>1 )\t ! slighte/ int]val betwe5 ! end ( "o p]iod & ! beg9n+ ( ano!r4 ,! op]ation ( multiplication is p]fectly p]=m$ = u by nature4 ,if1 !n1 we c f9d an obs]vation ( ! passage ( a /> across ! m]idian a hundr$ ye>s ago1 t is ( ! int]val ( "t betwe5 ! passage ( ! sun & ! />1 ! in/rum5tal errors 9 measur+ ?is int]val by a clock & telescope may be great] ?an 9 ! pres5t day1 b w be divid$ by ab\t #cf1ebd days1 & r5d]$ excessively small4 ,x is ?us t a/ronom]s h be5 able to asc]ta9 ! ratio ( ! mean sol> to ! sid]eal day to ! #h? place ( decimals 7#ajjbgcgia to #a71 or to ! hundr$ million? "p1 probably ! mo/ accurate result ( measurem5t 9 ! :ole range ( sci5ce4 ,! antiquity ( ?is mode ( comp>ison is almo/ z great z t ( a/ronomy itself4 ,hipp>*us made ! fir/ cle> application ( x1 :5 he comp>$ 8 own obs]vations ) ^? ( ,ari/>*us1 made #ade ye>s previ\sly1 & ?us asc]ta9$ ! l5g? ( ! ye>4 ,?is calculation may 9 fact be reg>d$ z ! e>lie/ attempt at an exact det]m9ation ( ! con/ants ( nature4 ,! me?od is ! ma9 res\rce ( a/ronom]s2 ,ty*o1 = in/ance1 detect$ ! sl[ dim9ution ( ! obliquity ( ! e>?'s axis1 by ! comp>ison ( obs]vations at long int]vals4 ,liv+ a/ronom]s use ! me?od z mu* z e>li] ones2 b s sup]ior 9 accuracy are all obs]vations tak5 dur+ ! la/ hundr$ ye>s to all previ\s ones1 t x is (t5 f\nd pref]able to take a %ort] int]val1 r ?an incur ! risk ( great] in/rum5tal errors 9 ! e>li] obs]vations4 ,x is obvi\s t _m ( ! sl[] *anges ( ! heav5ly bodies mu/ require ! lapse ( l>ge int]vals ( "t to r5d] _! am\nt p]ceptible4 ,hipp>*us c\ld n possibly h discov]$ ! small] inequalities ( ! heav5ly motions1 because !re 7 no previ\s obs]vations ( suffici5t age or exactness to exhibit !m4 ,& j z ! obs]vations ( ,hipp>*us =m$ ! />t+-po9t = subsequ5t comp>isons1 s a l>ge "p ( ! lab\r ( pres5t a/ronom]s is direct$ to record+ ! pres5t /ate ( ! heav5s s exactly1 t future g5]ations ( a/ronom]s may detect *anges1 :i* _c possibly become kn[n 9 ! pres5t age4 ,! pr9ciple ( repetition 0 v +5i\sly employ$ 9 an in/rum5t fir/ propos$ by ,may] 9 #agfg1 & c>ri$ into practice 9 ! ,repeat+ ,circle ( ,borda4 ,! exact measurem5t ( angles is indisp5sable1 n only 9 a/ronomy b also 9 trigonometrical surveys1 & ! highe/ skill 9 ! me*anical execution ( ! graduat$ circle & telescope w n prev5t t]m9al errors ( consid]able am\nt4 ,if in/ead ( "o telescope1 ! circle be provid$ ) two simil> telescopes1 ^! may be alt]nately direct$ to two di/ant po9ts1 say ! m>ks 9 a trigonometrical survey1 s t ! circle %all be turn$ ?r\gh any multiple ( ! angle subt5d$ by ^? m>ks1 be=e ! am\nt ( ! angul> revolution is read (f ^u ! graduat$ circle4 ,!oretically speak+1 all error aris+ f imp]fect graduation might ?us be indef9itely r$uc$1 be+ divid$ by ! numb] ( repetitions4 ,9 practice1 ! advantage ( ! inv5tion is n f\nd to be v great1 probably because a c]ta9 error is introduc$ at ea* obs]vation 9 ! *ang+ & fix+ ( ! telescopes4 ,x is moreov] inapplicable to mov+ objects l ! heav5ly bodies1 s t its use is conf9$ to important trigonometrical surveys4 ,! p5dulum is ! mo/ p]fect ( all in/rum5ts1 *iefly because x admits ( almo/ endless repetition4 ,s9ce ! =ce ( gravity nev] ceases1 "o sw+ ( ! p5dulum is no soon] end$ ?an ! o!r is begun1 s t ! juxtaposition ( successive units is absolutely p]fect4 ,provid$ t ! oscillations be equal1 "o ?\s& oscillations w occupy exactly "o ?\s& times z great an int]val ( "t z "o oscillation4 ,n only is ! subdivision ( "t entirely dep5d5t on ?is fact1 b 9 ! accurate measurem5t ( gravity1 & _m o!r important det]m9ations1 x is ( ! greate/ s]vice4 ,9 ! deepe/ m9e1 we c\ld n obs]ve ! rapidity ( fall ( a body = m ?an a qu>t] ( a m9ute1 & ! measurem5t ( its velocity w\ld be difficult1 & subject to unc]ta9 errors f resi/ance ( air1 c4 ,9 ! p5dulum1 we h a body :i* c be kept ris+ & fall+ = _m h\rs1 9 a m$ium entirely "u our comm& or if desirable 9 a vacuum4 ,moreov]1 ! comp>ative =ce ( gravity at diff]5t po9ts1 at ! top & bottom ( a m9e = in/ance1 c be det]m9$ ) wond]ful precision1 by comp>+ ! oscillations ( two exactly simil> p5dulums1 ) ! aid ( electric clock signals4 ,to asc]ta9 ! comp>ative times ( vibration ( two p5dulums1 x is only requisite to sw+ !m "o 9 front ( ! o!r1 to record by a clock ! mom5t :5 !y co9cide 9 sw+1 s t "o hides ! o!r1 & !n c\nt ! numb] ( vibrations until !y aga9 come to co9cid5ce4 ,if "o p5dulum makes 99m99 vibrations & ! o!r 99n991 we at once h our equation 99pn99 99qm992 :i* gives ! l5g? ( vibration ( ei!r p5dulum 9 t]ms ( ! o!r4 ,?is me?od ( co9cid5ce1 embody+ ! pr9ciple ( repetition 9 p]fection1 0 employ$ ) wond]ful skill by ,sir ,george ,airy1 9 8 exp]im5ts on ! ,d5sity ( ! ,e>? at ! ,h>ton ,colli]y1 ! p5dulums above & bel[ be+ comp>$ ) clocks1 :i* aga9 7 comp>$ ) ea* o!r by electric signals4 ,s exce$+ly accurate 0 ?is me?od ( obs]vation1 z c>ri$ out by ,sir ,george ,airy1 t he 0 able to measure a total diff]5ce 9 ! vibrations at ! top & bottom ( ! %aft1 am\nt+ to only #bbd seconds 9 ! tw5ty-f\r h\rs1 ) an error ( less ?an "o hundr$? "p ( a second1 or "o "p 9 #h1fdj1jjj ( ! :ole day4#ahe #ahe 99,philosophical ,transactions991 7#ahef7 vol4 #adf1 ,"p i4 p4 #big4 ,! pr9ciple ( repetition has be5 elegantly appli$ 9 obs]v+ ! motion ( waves 9 wat]4 ,if ! canal 9 :i* ! exp]im5ts are made be %ort1 say tw5ty feet long1 ! waves w pass ?r\gh x s rapidly t an obs]vation ( "o l5g?1 z practis$ by ,walk]1 w be subject to mu* t]m9al error1 ev5 :5 ! obs]v] is v skilful4 ,b x is a result ( ! undulatory !ory t a wave is unalt]$1 & loses no "t by complete reflection1 s t x may be all[$ to travel backw>ds & =w>ds 9 ! same canal1 & its motion1 say ?r\gh sixty l5g?s1 or #abjj feet1 may be obs]v$ ) ! same accuracy z 9 a canal #abjj feet long1 ) ! advantage ( great] uni=mity 9 ! condition ( ! canal & wat]4#ahf ,x is always desirable1 if possible1 to br+ an exp]im5t into a small compass1 s t x may be well "u comm&1 & yet we may (t5 by repetition enjoy at ! same "t ! advantage ( ext5sive trial4 #ahf ,airy1 99,on ,tides & ,waves991 ,encyclopdia ,metropolitana1 p4 #cde4 ,scott ,russell1 99,briti% ,association ,report991 #ahcg1 p4 #dcb4 ,"o reason ( ! great accuracy ( weigh+ ) a good balance is ! fact1 t weights plac$ 9 ! same scale are naturally add$ toge!r )\t ! slighte/ error4 ,!re is no difficulty 9 ! precise juxtaposition ( two grams1 b ! juxtaposition ( two metre measures c only be effect$ ) tol]able accuracy1 by ! use ( microscopes & _m precautions4 ,h5ce1 ! extreme tr\ble & co/ atta*+ to ! exact measurem5t ( a base l9e = a survey1 ! risk ( error ent]+ at e juxtaposition ( ! measur+ b>s1 & indefatigable att5tion to all ! requisite precautions be+ necess>y ?r\gh\t ! op]ation4 99,measurem5ts by ,natural ,co9cid5ce499 ,9 c]ta9 cases a peculi> conjunction ( circum/ances enables u to disp5se m or less ) in/rum5tal aids1 & to obta9 v exact num]ical results 9 ! simple/ mann]4 ,! m]e fact1 = in/ance1 t no human be+ has ev] se5 a diff]5t face ( ! moon f t famili> to u1 conclusively proves t ! p]iod ( rotation ( ! moon on its own axis is equal to t ( its revolution r\nd ! e>?4 ,n only h we ! repetition ( ^! movem5ts dur+ #ajjj or #bjjj ye>s at lea/1 b we h obs]vations made = u at v remote p]iods1 free f in/rum5tal error1 no in/rum5t be+ ne$$4 ,we le>n t ! sev5? satellite ( ,saturn is subject to a simil> law1 because its light und]goes a v>iation 9 ea* revolution1 ow+ to ! exi/5ce ( "s d>k tract ( l&2 n[ ?is failure ( light always occurs :ile x is 9 ! same position relative to ,saturn1 cle>ly prov+ ! equality ( ! axial & revolutional p]iods1 z ,huyg5s p]ceiv$4#ahg ,a l peculi>ity 9 ! motions ( ,jupit]'s f\r? satellite 0 simil>ly detect$ by ,m>aldi 9 #agac4 #ahg 99,hug5ii ,cosmo!oros991 pp4 #aag1 #aah4 ,laplace's 99,sy/me991 translat$1 vol4 i4 p4 #fg4 ,rem>kable conjunctions ( ! planets may sometimes all[ u to comp>e _! p]iods ( revolution1 ?r\gh great int]vals ( "t1 ) mu* accuracy4 ,laplace 9 expla9+ ! long inequality 9 ! motions ( ,jupit] & ,saturn1 0 assi/$ by a conjunction ( ^! planets1 obs]v$ at ,cairo1 t[>ds ! close ( ! elev5? c5tury4 ,laplace calculat$ t su* a conjunction mu/ h happ5$ on ! #ca/ ( ,octob]1 ,a4,d4 #ajhg2 & ! discordance betwe5 ! di/ances ( ! planets z record$1 & z assign$ by !ory1 0 less ?an "o-fif? "p ( ! app>5t diamet] ( ! sun4 ,?is diff]5ce be+ less ?an ! probable error ( ! e>ly record1 ! !ory 0 confirm$ z f> z facts 7 available4#ahh #ahh ,grant's 99,hi/ory ( ,physical ,a/ronomy991 p4 #abi4 ,anci5t a/ronom]s (t5 %[$ ! highe/ +5uity 9 turn+ any opportunities ( measurem5t :i* occurr$ to good acc\nt4 ,erato/h5es1 z e>ly z #bej ,b4,c41 happ5+ to he> t ! sun at ,sy5e1 9 ,upp] ,egypt1 0 visible at ! summ] sol/ice at ! bottom ( a well1 prov+ t x 0 9 ! z5i?1 propos$ to det]m9e ! dim5sions ( ! e>?1 by measur+ ! l5g? ( ! %ad[ ( a rod at ,alex&ria on ! same day ( ! ye>4 ,he ?us le>nt 9 a rude mann] ! diff]5ce ( latitude betwe5 ,alex&ria & ,sy5e & f9d+ x to be ab\t "o fiftie? "p ( ! :ole circumf]5ce1 he asc]ta9$ ! dim5sions ( ! e>? )9 ab\t "o six? "p ( ! tru?4 ,! use ( wells 9 a/ronomical obs]vation appe>s to h be5 occasionally practis$ 9 comp>atively rec5t times z by ,flam/e$ 9 #afgi4ahi ,! ,alex&rian a/ronom]s employ$ ! moon z an in/rum5t ( measurem5t 9 sev]al sagaci\s modes4 ,:5 ! moon is exactly half full1 ! moon1 sun1 & e>?1 are at ! angles ( a "r-angl$ triangle4 ,ari/>*us measur$ at su* a "t ! moon's elongation f ! sun1 :i* gave him ! two o!r angles ( ! triangle1 & enabl$ him to judge ( ! comp>ative di/ances ( ! moon & sun f ! e>?4 ,8 result1 ?\gh v rude1 0 f> m accurate ?an any notions previ\sly ent]ta9$1 & enabl$ him to =m "s e/imate ( ! comp>ative magnitudes ( ! bodies4 ,eclipses ( ! moon 7 v useful to ,hipp>*us 9 asc]ta9+ ! longitude ( ! />s1 :i* are invisible :5 ! sun is above ! horizon4 ,= ! moon :5 eclips$ mu/ be #ahj di/ant f ! sun2 h5ce x is only requisite to measure ! di/ance ( a fix$ /> 9 longitude f ! eclips$ moon to obta9 ) ease its angul> di/ance f ! sun4 #ahi ,baily's 99,acc\nt ( ,flam/e$991 p4 lix4 ,9 lat] times ! eclipses ( ,jupit] h s]v$ to measure an angle2 = at ! middle mom5t ( ! eclipse ! satellite mu/ be 9 ! same /raight l9e ) ! planet & sun1 s t we c le>n f ! kn[n laws ( movem5t ( ! satellite ! longitude ( ,jupit] z se5 f ! sun4 ,if at ! same "t we measure ! elongation or app>5t angul> di/ance ( ,jupit] f ! sun1 z se5 f ! e>?1 we h all ! angles ( ! triangle betwe5 ,jupit]1 ! sun1 & ! e>?1 & c calculate ! comp>ative magnitudes ( ! sides ( ! triangle by trigonometry4 ,! transits ( ,v5us ov] ! sun's face are o!r natural ev5ts :i* give mo/ accurate measurem5ts ( ! sun's p>allax1 or app>5t diff]5ce ( position z se5 f di/ant po9ts ( ! e>?'s surface4 ,! sun =ms a k9d ( backgr\nd on :i* ! place ( ! planet is m>k$1 & s]ves z a measur+ in/rum5t free f all ! errors ( con/ruction :i* affect human in/rum5ts4 ,! rotation ( ! e>?1 too1 by v>i\sly affect+ ! app>5t velocity ( +ress or egress ( ,v5us1 z se5 f diff]5t places1 discloses ! am\nt ( ! p>allax4 ,x has be5 suffici5tly %[n t by rightly *oos+ ! mom5ts ( obs]vation1 ! planet>y bodies may (t5 be made to reveal _! relative di/ance1 to measure _! own position1 to record _! own movem5ts ) a high degree ( accuracy4 ,) ! improvem5t ( a/ronomical in/rum5ts1 su* conjunctions become less necess>y to ! progress ( ! sci5ce1 b x w always rema9 advantage\s to *oose ^? mom5ts = obs]vation :5 in/rum5tal errors ent] ) ! lea/ effect4 ,9 o!r sci5ces1 exact quantitative laws c occasionally be obta9$ )\t in/rum5tal measurem5t1 z :5 we le>n ! exactly equal velocity ( s\nds ( diff]5t pit*1 by obs]v+ t a peal ( bells or a musical p]=mance is he>d h>moni\sly at any di/ance to :i* ! s\nd p5etrates2 ?is c\ld n be ! case1 z ,newton rem>k$1 if "o s\nd ov]took ! o!r4 ,"o ( ! mo/ important pr9ciples ( ! atomic !ory1 0 prov$ by implication be=e ! use ( ! balance 0 introduc$ into *emi/ry4 ,w5zel obs]v$1 be=e #aggg1 t :5 two neutral sub/ances decompose ea* o!r1 ! result+ salts are also neutral4 ,9 mix+ sodium sulphate & b>ium nitrate1 we obta9 insoluble b>ium sulphate & neutral sodium nitrate4 ,?is result c\ld n foll[ unless ! nitric acid1 requisite to saturate "o atom ( sodium1 7 exactly equal to t requir$ by "o atom ( b>ium1 s t an ex*ange c\ld take place )\t leav+ ei!r acid or base 9 excess4 ,an important pr9ciple ( me*anics may also be e/abli%$ by a simple ac\/ical obs]vation4 ,:5 a rod or tongue ( metal fix$ at "o end is set 9 vibration1 ! pit* ( ! s\nd may be obs]v$ to be exactly ! same1 :e!r ! vibrations be small or great2 h5ce ! oscillations are iso*ron\s1 or equally rapid1 indep5d5tly ( _! magnitude4 ,on ! gr\nd ( !ory1 x c be %[n t su* a result only happ5s :5 ! flexure is proportional to ! deflect+ =ce4 ,?us ! simple obs]vation t ! pit* ( ! s\nd ( a h>monium1 = in/ance1 does n *ange ) its l\dness e/abli%es an exact law ( nature4#aij #aij ,jam91 99,c\rs de ,physique991 vol4 i4 p4 #aeb4 ,a closely simil> in/ance is f\nd 9 ! pro( t ! int5sity ( light or heat rays v>ies inv]sely z ! squ>e ( ! di/ance increases4 ,= ! app>5t magnitude c]ta9ly v>ies accord+ to ?is law2 h5ce1 if ! int5sity ( light v>i$ accord+ to any o!r law1 ! brightness ( an object w\ld be diff]5t at diff]5t di/ances1 :i* is n obs]v$ to be ! case4 ,melloni appli$ ! same k9d ( reason+1 9 a some:at diff]5t =m1 to ! radiation ( heat-rays4 99,modes ( ,indirect ,measurem5t499 ,"s ( ! mo/ conspicu\sly beautiful exp]im5ts 9 ! :ole range ( sci5ce1 h be5 devis$ = ! purpose ( indirectly measur+ quantities1 :i* 9 _! extreme greatness or smallness surpass ! p[]s ( s5se4 ,all t we ne$ to d1 is to discov] "s o!r conv5i5tly measurable ph5om5on1 :i* is relat$ 9 a kn[n ratio or accord+ to a kn[n law1 h[ev] complicat$1 ) t to be measur$4 ,hav+ once obta9$ exp]im5tal data1 !re is no fur!r difficulty beyond t ( ari?metic or algebraic calculation4 ,gold is r$uc$ by ! gold-beat] to leaves s ?91 t ! mo/ p[]ful microscope w\ld n detect any measurable ?ickness4 ,if we laid sev]al hundr$ leaves ^u ea* o!r to multiply ! ?ickness1 we %\ld /ill h no m ?an #a_/ajj? ( an in* at ! mo/ to measure1 & ! errors aris+ 9 ! sup]position & measurem5t w\ld be consid]able4 ,b we c readily obta9 an exact result ?r\gh ! connect$ am\nt ( weight4 ,f>aday weigh$ #bjjj leaves ( gold1 ea* #c-c_/h in* squ>e1 & f\nd !m equal to #chd gra9s4 ,f ! kn[n specific gravity ( gold x 0 easy to calculate t ! av]age ?ickness ( ! leaves 0 #a_/bhb1jjj ( an in*4#aia #aia ,f>aday1 99,*emical ,rese>*es991 p4 #cic4 ,we mu/ ascribe to ,newton ! hon\r ( lead+ ! way 9 me?ods ( m9ute measurem5t4 ,he did n call waves ( light by _! "r "n1 & did n und]/& _! nature2 yet he measur$ _! l5g?1 ?\gh x did n exce$ ! #b1jjj1jjj? "p ( a metre or ! "o fifty-?\s&? "p ( an in*4 ,he press$ toge!r two l5ses ( l>ge b kn[n radii4 ,x 0 easy to calculate ! int]val betwe5 ! l5ses at any po9t1 by measur+ ! di/ance f ! c5tral po9t ( contact4 ,n[1 ) homog5e\s rays ! successive r+s ( light & d>kness m>k ! po9ts at :i* ! int]val betwe5 ! l5ses is equal to "o half1 or any multiple ( half a vibration ( ! light1 s t ! l5g? ( ! vibration became kn[n4 ,9 a simil> mann] _m ph5om5a ( int]f]5ce ( rays ( light admit ( ! measurem5t ( ! wave l5g?s4 ,fr+es ( int]f]5ce arise f rays ( light :i* cross ea* o!r at a small angle1 & an excessively m9ute diff]5ce 9 ! l5g?s ( ! waves makes a v p]ceptible diff]5ce 9 ! position ( ! po9t at :i* two rays w int]f]e & produce d>kness4 ,fizeau has rec5tly employ$ ,newton's r+s to measure small am\nts ( motion4 ,by m]ely c\nt+ ! numb] ( r+s ( sodium mono*romatic light pass+ a c]ta9 po9t :]e two glass plates are 9 close proximity1 he is able to asc]ta9 ) ! greate/ accuracy & ease ! *ange ( di/ance betwe5 ^! glasses1 produc$1 = in/ance1 by ! expansion ( a metallic b>1 connect$ ) "o ( ! glass plates4#aib #aib 99,proce$+s ( ! ,royal ,society991 #cj? ,novemb]1 #ahff4 ,no?+ excites m admiration ?an ! mode 9 :i* sci5tific obs]v]s c occasionally measure quantities1 :i* seem beyond ! b\nds ( human obs]vation4 ,we "k ! 99av]age99 dep? ( ! ,pacific ,ocean to be #ad1aij feet1 n by actual s\nd+1 :i* w\ld be impracticable 9 suffici5t detail1 b by notic+ ! rate ( transmission ( e>?quake waves f ! ,s\? ,am]ican to ! opposite coa/s1 ! rate ( movem5t be+ connect$ by !ory ) ! dep? ( ! wat]4#aic ,9 ! same way ! av]age dep? ( ! ,atlantic ,ocean is inf]r$ to be no less ?an #bb1aeg feet1 f ! velocity ( ! ord9>y tidal waves4 ,a tidal wave aga9 gives beautiful evid5ce ( an effect ( ! law ( gravity1 :i* we c\ld nev] 9 any o!r way detect4 ,newton e/imat$ t ! moon's =ce 9 mov+ ! ocean is only "o "p 9 #b1hga1djj ( ! :ole =ce ( gravity1 s t ev5 ! p5dulum1 us$ ) ! utmo/ skill1 w\ld fail to r5d] x app>5t4 ,yet1 ! imm5se ext5t ( ! ocean all[s ! accumulation ( ! effect into a v palpable am\nt2 & f ! comp>ative heights ( ! lun> & sol> tides1 ,newton r\ghly e/imat$ ! comp>ative =ces ( ! moon's & sun's gravity at ! e>?4#aid #aic ,h]s*el1 99,physical ,geography991 #dj4 #aid 99,pr9cipia991 bk4 iii4 ,prop4 #cg1 99,coroll>ies991 #b & #c4 ,motte's translation1 vol4 ii4 p4 #caj4 ,a few ye>s ago x might h seem$ impossible t we %\ld ev] measure ! velocity ) :i* a /> approa*es or rec$es f ! e>?1 s9ce ! app>5t position ( ! /> is !reby unalt]$4 ,b ! spectroscope n[ enables u to detect & ev5 measure su* motions ) consid]able accuracy1 by ! alt]ation :i* x causes 9 ! app>5t rapidity ( vibration1 & consequ5tly 9 ! refrangibility ( rays ( light ( def9ite col\r4 ,& :ile our e/imates ( ! lat]al movem5ts ( />s dep5d ^u our v unc]ta9 k ( _! di/ances1 ! spectroscope gives ! motions ( approa* & recess irrespective ( o!r motions except+ t ( ! e>?4 ,x gives 9 %ort ! motions ( approa* & recess ( ! />s relatively to ! e>?4#aie #aie ,roscoe's 99,spectrum ,analysis991 #a/ ed4 p4 #bif4 ,! rapidity ( vibration = ea* musical tone1 hav+ be5 accurately det]m9$ by comp>ison ) ! ,syr5 7p4 #aj71 we c use s\nds z indirect indications ( rapid vibrations4 ,x is n[ kn[n t ! contraction ( a muscle arises f ! p]iodical contractions ( ea* sep>ate fibre1 & f a fa9t s\nd or susurrus :i* accompanies ! action ( a muscle1 x is inf]r$ t ea* contraction la/s = ab\t "o #cjj? "p ( a second4 ,m9ute quantities ( radiant heat are n[ always measur$ indirectly by ! electricity :i* !y produce :5 fall+ ^u a !rmopile4 ,! extreme delicacy ( ! me?od seems to be due to ! p[] ( multiplication at sev]al po9ts 9 ! app>atus4 ,! numb] ( elem5ts or junctions ( diff]5t metals 9 ! !rmopile c be increas$ s t ! t5sion ( ! electric curr5t d]iv$ f ! same int5sity ( radiation is multipli$2 ! effect ( ! curr5t ^u ! magnetic ne$le c be multipli$ )9 c]ta9 b\nds1 by pass+ ! curr5t _m times r\nd x 9 a coil2 ! excursions ( ! ne$le c be increas$ by r5d]+ x a/atic & increas+ ! delicacy ( its susp5sion2 la/ly1 ! angul> div]g5ce c be obs]v$1 ) any requir$ accuracy1 by ! use ( an atta*$ mirror & di/ant scale view$ ?r\gh a telescope 7p4 #bhg74 ,su* is ! delicacy ( ?is me?od ( measur+ heat1 t ,dr4 ,j\le succe$$ 9 mak+ a !rmopile :i* w\ld indicate a diff]5ce ( #jjjjaad ,c5t4#aif #aif 99,philosophical ,transactions99 7#ahei71 vol4 cxlix4 p4 #id4 ,a /rik+ case ( indirect measurem5t is furni%$ by ! revolv+ mirror ( ,:eat/one & ,f\cault1 :]eby a m9ute int]val ( "t is e/imat$ 9 ! =m ( an angul> deviation4 ,:eat/one view$ an electric sp>k 9 a mirror rotat+ s rapidly1 t if ! duration ( ! sp>k _h be5 m ?an "o #gb1jjj? "p ( a second1 ! po9t ( light w\ld h appe>$ elongat$ to an angul> ext5t ( "o-half degree4 ,9 ! sp>k1 z drawn directly f a ,leyd5 j>1 no elongation 0 app>5t1 s t ! duration ( ! sp>k 0 immeasurably small2 b :5 ! dis*>ge took place ?r\gh a bad conductor1 ! elongation ( ! sp>k d5ot$ a s5sible duration4#aig ,9 ! h&s ( ,f\cault ! rotat+ mirror gave a measure ( ! "t occupi$ by light 9 pass+ ?r\gh a few metres ( space4 #aig ,watts' 99,diction>y ( ,*emi/ry991 vol4 ii4 p4 #cic4 99,comp>ative ,use ( ,measur+ ,in/rum5ts499 ,9 almo/ e case a measur+ in/rum5t s]ves1 & %\ld s]ve only z a means ( comp>ison betwe5 two or m magnitudes4 ,z a g5]al rule1 we %\ld n attempt to make ! divisions ( ! measur+ scale exact multiples or submultiples ( ! unit1 b1 reg>d+ !m z arbitr>y m>ks1 %\ld det]m9e _! values by comp>ison ) ! /&>d itself4 ,! p]p5dicul> wires 9 ! field ( a transit telescope1 are fix$ at ne>ly equal b arbitr>y di/ances1 & ^? di/ances are aft]w>ds det]m9$1 z fir/ sugge/$ by ,malvasia1 by wat*+ ! passage ( /> aft] /> across !m1 & not+ ! int]vals ( "t by ! clock4 ,ow+ to ! p]fectly regul> motion ( ! e>?1 ^! "t int]vals give exact det]m9ations ( ! angul> int]vals4 ,9 ! same way1 ! angul> value ( ea* turn ( ! screw micromet] atta*$ to a telescope1 c be easily & accurately asc]ta9$4 ,:5 a !rmopile is us$ to obs]ve radiant heat1 x w\ld be almo/ impossible to calculate on 99 priori99 gr\nds :at is ! value ( ea* division ( ! galvanomet] circle1 & /ill m difficult to con/ruct a galvanomet]1 s t ea* division %\ld h a giv5 value4 ,b ?is is q unnecess>y1 because by plac+ ! !rmopile be=e a body ( kn[n dim5sions1 at a kn[n di/ance1 ) a kn[n temp]ature & radiat+ p[]1 we measure a kn[n am\nt ( radiant heat1 & inv]sely measure ! value ( ! indications ( ! !rmopile4 ,9 a simil> way ,dr4 ,j\le asc]ta9$ ! actual temp]ature produc$ by ! compression ( b>s ( metal4 ,= hav+ ins]t$ a small !rmopile compos$ ( a s+le junction ( copp] & iron wire1 & not$ ! deflections ( ! galvanomet]1 he _h only to dip ! b>s into wat] ( diff]5t temp]atures1 until he produc$ a l deflection1 9 ord] to asc]ta9 ! temp]ature develop$ by pressure4#aih #aih 99,philosophical ,transactions99 7#ahei71 vol4 cxlix4 p4 #aai1 c4 ,9 "s cases we are oblig$ to accept a v c>efully con/ruct$ in/rum5t z a /&>d1 z 9 ! case ( a /&>d b>omet] or !rmomet]4 ,b x is !n be/ to treat all inf]ior in/rum5ts comp>atively only1 & det]m9e ! values ( _! scales by comp>ison ) ! assum$ /&>d4 99,sy/ematic ,p]=mance ( ,measurem5ts499 ,:5 a l>ge numb] ( accurate measurem5ts h to be effect$1 x is usually desirable to make a c]ta9 numb] ( det]m9ations ) scrupul\s c>e1 & aft]w>ds use !m z po9ts ( ref]5ce = ! rema9+ det]m9ations4 ,9 ! trigonometrical survey ( a c\ntry1 ! pr9cipal triangulation fixes ! relative positions & di/ances ( a few po9ts ) rigid accuracy4 ,a m9or triangulation ref]s e prom95t hill or village to "o ( ! pr9cipal po9ts1 & !n ! details are fill$ 9 by ref]5ce to ! second>y po9ts4 ,! survey ( ! heav5s is effect$ 9 a l mann]4 ,! anci5t a/ronom]s comp>$ ! "r asc5sions ( a few pr9cipal />s ) ! moon1 & ?us asc]ta9$ _! positions ) reg>d to ! sun2 ! m9or />s 7 aft]w>ds ref]r$ to ! pr9cipal />s4 ,ty*o foll[$ ! same me?od1 except t he us$ ! m sl[ly mov+ planet ,v5us in/ead ( ! moon4 ,flam/e$ 0 9 ! habit ( us+ ab\t sev5 />s1 fav\rably situat$ at po9ts all r\nd ! heav5s4 ,9 8 e>ly obs]vations ! di/ances ( ! o!r />s f ^! /&>d po9ts 7 det]m9$ by ! use ( ! quadrant4#aii ,ev5 s9ce ! introduction ( ! transit telescope & ! mural circle1 tables ( /&>d />s are =m$ at ,gre5wi*1 ! positions be+ det]m9$ ) all possible accuracy1 s t !y c be employ$ = purposes ( ref]5ce by a/ronom]s4 #aii ,baily's 99,acc\nt ( ,flam/e$991 pp4 #cgh-chj4 ,9 asc]ta9+ ! specific gravities ( sub/ances1 all gases are ref]r$ to atmosph]ic air at a giv5 temp]ature & pressure2 all liquids & solids are ref]r$ to wat]4 ,we require to comp>e ! d5sities ( wat] & air ) great c>e1 & ! comp>ative d5sities ( any two sub/ances :atev] c !n be asc]ta9$4 ,9 comp>+ a v great ) a v small magnitude1 x is usually desirable to break up ! process into sev]al /eps1 us+ int]m$iate t]ms ( comp>ison4 ,we %\ld nev] ?9k ( measur+ ! di/ance f ,london to ,ed9burgh by lay+ d[n measur+ rods1 ?r\gh\t ! :ole l5g?4 ,a base ( sev]al miles is select$ on level gr\nd1 & comp>$ on ! "o h& ) ! /&>d y>d1 & on ! o!r ) ! di/ance ( ,london & ,ed9burgh1 or any o!r two po9ts1 by trigonometrical survey4 ,aga91 x w\ld be exce$+ly difficult to comp>e ! light ( a /> ) t ( ! sun1 :i* w\ld be ab\t ?irty ?\s& million times great]2 b ,h]s*el#bjj effect$ ! comp>ison by us+ ! full moon z an int]m$iate unit4 ,wolla/on asc]ta9$ t ! sun gave #hja1jgb times z mu* light z ! full moon1 & ,h]s*el det]m9$ t ! light ( ! latt] exce$$ t ( ,c5tauri #bg1djh times1 s t we f9d ! ratio betwe5 ! light ( ! sun & /> to be t ( ab\t #bb1jjj1jjj1jjj to #a4 #bjj ,h]s*el's 99,a/ronomy991 #hag1 #d?4 ed4 p4 #eec4 99,! ,p5dulum499 ,by f> ! mo/ p]fect & beautiful ( all in/rum5ts ( measurem5t is ! p5dulum4 ,consi/+ m]ely ( a heavy body susp5d$ freely at an inv>iable di/ance f a fix$ po9t1 x is mo/ simple 9 con/ruction2 yet all ! highe/ problems ( physical measurem5t dep5d ^u its c>eful use4 ,its excessive value arises f two circum/ances4 7#a7 ,! me?od ( repetition is em95tly applicable to x1 z already describ$ 7p4 #bij74 7#b7 ,unlike o!r in/rum5ts1 x connects toge!r ?ree diff]5t quantities1 ^? ( space1 "t1 & =ce4 ,9 mo/ works on natural philosophy x is %[n1 t :5 ! oscillations ( ! p5dulum are inf9itely small1 ! squ>e ( ! "t occupi$ by an oscillation is directly proportional to ! l5g? ( ! p5dulum1 & indirectly proportional to ! =ce affect+ x1 ( :atev] k9d4 ,! :ole !ory ( ! p5dulum is conta9$ 9 ! =mula1 fir/ giv5 by ,huyg5s 9 8 99,horologium ,oscillatorium994 ,"t ( oscillation #cadaei 7l5g? ( p5dulum_/=ce74 ,! quantity #cadaei is ! con/ant ratio ( ! circumf]5ce & radius ( a circle1 & is ( c\rse kn[n ) accuracy4 ,h5ce1 any two ( ! ?ree quantities conc]n$ be+ giv51 ! ?ird may be f\nd2 or any two be+ ma9ta9$ inv>iable1 ! ?ird w be inv>iable4 ,?us a p5dulum ( inv>iable l5g? susp5d$ at ! same place1 :]e ! =ce ( gravity may be consid]$ con/ant1 furni%es a measure ( "t4 ,! same inv>iable p5dulum be+ made to vibrate at diff]5t po9ts ( ! e>?'s surface1 & ! times ( vibration be+ a/ronomically det]m9$1 ! =ce ( gravity becomes accurately kn[n4 ,f9ally1 ) a kn[n =ce ( gravity1 & "t ( vibration asc]ta9$ by ref]5ce to ! />s1 ! l5g? is det]m9ate4 ,all a/ronomical obs]vations dep5d ^u ! fir/ mann] ( us+ ! p5dulum1 namely1 9 ! a/ronomical clock4 ,9 ! second employm5t x has be5 almo/ equally indisp5sable4 ,! prim>y pr9ciple t gravity is equal 9 all matt] 0 prov$ by ,newton's & ,gauss' p5dulum exp]im5ts4 ,! torsion p5dulum ( ,mi*ell1 ,cav5di%1 & ,baily1 dep5d+ ^u exactly ! same pr9ciples z ! ord9>y p5dulum1 gave ! d5sity ( ! e>?1 "o ( ! =emo/ natural con/ants4 ,kat] & ,sab9e1 by p5dulum obs]vations 9 diff]5t p>ts ( ! e>?1 asc]ta9$ ! v>iation ( gravity1 :5ce comes a det]m9ation ( ! e>?'s ellipticity4 ,! laws ( electric & magnetic attraction h also be5 det]m9$ by ! me?od ( vibrations1 :i* is 9 con/ant use 9 ! measurem5t ( ! horizontal =ce ( t]re/rial magnetism4 ,we mu/ n confuse ) ! ord9>y use ( ! p5dulum its application by ,newton1 to %[ ! abs5ce ( int]nal friction aga9/ space1#bja or to asc]ta9 ! laws ( motion & ela/icity4#bjb ,9 ^! cases ! ext5t ( vibration is ! quantity measur$1 & ! pr9ciples ( ! in/rum5t are diff]5t4 #bja 99,pr9cipia991 bk4 ii4 ,sect4 #f4 ,prop4 #ca4 ,motte's ,translation1 vol4 ii4 p4 #ajg4 #bjb ,ibid4 bk4 i4 ,law iii4 ,coroll>y #f4 ,motte's ,translation1 vol4 i4 p4 #cc4 99,atta9able ,accuracy ( ,measurem5t499 ,x is a matt] ( "s int]e/ to comp>e ! degrees ( accuracy :i* c be atta9$ 9 ! measurem5t ( diff]5t k9ds ( magnitude4 ,few measurem5ts ( any k9d are exact to m ?an six significant figures1#bjc b x is seldom t su* accuracy c be hop$ =4 ,"t is ! magnitude :i* seems to be capable ( ! mo/ exact e/imation1 ow+ to ! prop]ties ( ! p5dulum1 & ! pr9ciple ( repetition describ$ 9 previ\s sections4 ,z reg>ds %ort int]vals ( "t1 x has already be5 /at$ t ,sir ,george ,airy 0 able to e/imate "o "p 9 #h1fdj1jjj1 an exactness1 z he truly rem>ks1 8almo/ beyond conception40#bjd ,! ratio betwe5 ! mean sol> & ! sid]eal day is kn[n to be ab\t "o "p 9 "o hundr$ millions1 or to ! eigh? place ( decimals1 7p4 #bhi74 #bjc ,?omson & ,tait's 99,natural ,philosophy991 vol4 i4 p4 #ccc4 #bjd 99,philosophical ,transactions991 7#ahef71 vol4 cxlvi4 pp4 #ccj1 #cca4 ,det]m9ations ( weight seem to come next 9 exactness1 ow+ to ! fact t repetition )\t error is applicable to !m4 ,an ord9>y good balance %\ld %[ ab\t "o "p 9 #ejj1jjj ( ! load4 ,! f9e/ balance employ$ by ,m4 ,/as1 turn$ ) "o "p 9 #hbe1jjj ( ! load4#bje ,b balances h c]ta9ly be5 con/ruct$ to %[ "o "p 9 a million1#bjf & ,ramsd5 is said to h con/ruct$ a balance = ! ,royal ,society1 to indicate "o "p 9 sev5 millions1 ?\gh ?is is h>dly cr$ible4 ,pr(essor ,cl]k ,maxwell takes x = grant$ t "o "p 9 five millions c be detect$1 b we ought to discrim9ate betwe5 :at a balance c d :5 fir/ con/ruct$1 & :5 9 cont9u\s use4 #bje 99,fir/ ,annual ,report ( ! ,m9t991 p4 #ajf4 #bjf ,jevons1 9 ,watts' 99,diction>y ( ,*emi/ry991 vol4 i4 p4 #dhc4 ,det]m9ations ( l5g?1 unless p]=m$ ) extraord9>y c>e1 are op5 to mu* error 9 ! junction ( ! measur+ b>s4 ,ev5 9 measur+ ! base l9e ( a trigonometrical survey1 ! accuracy g5]ally atta9$ is only t ( ab\t "o "p 9 #fj1jjj1 or an in* 9 ! mile2 b x is said t 9 f\r measurem5ts ( a base l9e c>ri$ out v rec5tly at ,cape ,comor91 ! greate/ error 0 #jjgg in* 9 #afh mile1 or "o "p 9 #a1chb1djj1 an almo/ incr$ible degree ( accuracy4 ,sir ,j4 ,:itwor? has %[n t t\* is ev5 a m delicate mode ( measur+ l5g?s ?an sight1 & by means ( a spl5didly execut$ screw1 & a small cube ( iron plac$ betwe5 two flat-end$ iron b>s1 s z to be susp5d$ :5 t\*+ !m1 he c detect a *ange ( dim5sion 9 a b>1 am\nt+ to no m ?an "o-million? ( an in*4#bjg #bjg ,briti% ,association1 ,glasg[1 #ahef4 99,address ( ! ,presid5t ( ! ,me*anical ,section994 ,,*apt] ,,xiv4 ,,units ,,& ,,/&>ds ,,( ,,measurem5t4 ,z we h se51 in/rum5ts ( measurem5t are only means ( comp>ison betwe5 "o magnitude & ano!r1 & z a g5]al rule we mu/ assume "s "o arbitr>y magnitude1 9 t]ms ( :i* all results ( measurem5t are to be express$4 ,m]e ratios betwe5 any s]ies ( objects w nev] tell u _! absolute magnitudes2 we mu/ h at lea/ "o ratio = ea*1 & we mu/ h "o absolute magnitude4 ,! numb] ( ratios 99n99 are expressible 9 99n99 equations1 :i* w conta9 at lea/ 99n99 #a quantities1 s t if we employ !m to make kn[n 99n99 magnitudes1 we mu/ h "o magnitude kn[n4 ,h5ce1 :e!r we are measur+ "t1 space1 d5sity1 mass1 weight1 en]gy1 or any o!r physical quantity1 we mu/ ref] to "s concrete /&>d1 "s actual object1 :i* if once lo/ & irrecov]able1 all our measures lose _! absolute mean+4 ,?is concrete /&>d is 9 all cases arbitr>y 9 po9t ( !ory1 & its selection a "q ( practical conv5i5ce4 ,!re are two k9ds ( magnitude1 inde$1 :i* d n ne$ to be express$ 9 t]ms ( arbitr>y concrete units1 s9ce !y pre-suppose ! exi/5ce ( natural /&>d units4 ,"o case is t ( ab/ract numb] itself1 :i* ne$s no special unit1 because any object :i* exi/s or is ?\ght ( z sep>ate f o!r objects 7p4 #aeg7 furni%es u ) a unit1 & is ! only /&>d requir$4 ,angul> magnitude is ! second case 9 :i* we h a natural unit ( ref]5ce1 namely ! :ole revolution or 99p]igon991 z x has be5 call$ by ,mr4 ,s&eman4#bjh ,x is a necess>y result ( ! uni=m prop]ties ( space1 t all complete revolutions are equal to ea* o!r1 s t we ne$ n select any "o revolution1 b c always ref] anew to space itself4 ,:e!r we take ! :ole p]igon1 its half1 or its qu>t]1 is really immat]ial2 ,euclid took ! "r angle1 because ! ,greek geomet]s _h nev] g5]alis$ _! notions ( angul> magnitude suffici5tly to treat angles ( all magnitudes1 or ( unlimit$ 99quantity ( revolution994 ,euclid def9es a "r angle z half t made by a l9e ) its own cont9uation1 :i* is ( c\rse equal to half a revolution1 b :i* 0 n treat$ z an angle by him4 ,9 ma!matical analysis a diff]5t fraction ( ! p]igon is tak51 namely1 su* a fraction t ! arc or portion ( ! circumf]5ce includ$ )9 x is equal to ! radius ( ! circle4 ,9 ?is po9t ( view angul> magnitude is an ab/ract ratio1 namely1 ! ratio betwe5 ! l5g? ( arc subt5d$ & ! l5g? ( ! radius4 ,! geometrical unit is !n necess>ily ! angle correspond+ to ! ratio unity4 ,?is angle is equal to ab\t #eg1 #ag1 #ddh1 or decimally #egbieggieac444 4#bji ,x 0 call$ by ,de ,morgan ! 99arcual unit991 b a m conv5i5t "n = common use w\ld be 99radian991 z sugge/$ by ,pr(essor ,ev]ett4 ,?\gh ?is /&>d angle is naturally employ$ 9 ma!matical analysis1 & any o!r unit w\ld introduce great complexity1 we mu/ n look ^u x z a di/9ct unit1 s9ce its am\nt is connect$ ) t ( ! half p]igon1 by ! natural con/ant #cadaei444 usually d5ot$ by ! lett] 4 #bjh 99,pelicotetics1 or ! ,sci5ce ( ,quantity2 an ,elem5t>y ,treatise on ,algebra1 & its gr\ndwork ,ari?metic499 ,by ,ar*ibald ,s&eman1 ,m4 ,a4 ,cambridge 7,deighton1 ,bell1 & ,co471 #ahfh1 p4 #cjd4 #bji ,de ,morgan's 99,trigonometry & ,d\ble ,algebra991 p4 #e4 ,:5 we pass to o!r species ( quantity1 ! *oice ( unit is f\nd to be entirely arbitr>y4 ,!re is absolutely no mode ( def9+ a l5g?1 b by select+ "s physical object exhibit+ t l5g? betwe5 c]ta9 obvi\s po9ts--z1 = in/ance1 ! extremities ( a b>1 or m>ks made ^u its surface4 99,/&>d ,unit ( ,"t499 ,"t is ! great indep5d5t v>iable ( all *ange--t :i* itself fl[s on un9t]rupt$ly1 & br+s ! v>iety :i* we call motion & life4 ,:5 we reflect ^u its intimate nature1 ,"t1 l e o!r elem5t ( exi/5ce1 proves to be an inscrutable my/]y4 ,we c only say ) ,/4 ,augu/91 to "o :o asks u :at is "t1 8,i "k :5 y d n ask me40 ,! m9d ( man w ask :at c nev] be answ]$1 b "o result ( a true & rigor\s logical philosophy mu/ be to conv9ce u t sci5tific explanation c only take place betwe5 ph5om5a :i* h some?+ 9 common1 & t :5 we get d[n to prim>y notions1 l ^? ( "t & space1 ! m9d mu/ meet a po9t ( my/]y beyond :i* x _c p5etrate4 ,a def9ition ( "t mu/ n be look$ =2 if we say ) ,hobbes1#baj t x is 8! phantasm ( be=e & aft] 9 motion10 or ) ,ari/otle t x is 8! numb] ( motion accord+ to =m] & latt]10 we obvi\sly ga9 no?+1 because ! notion ( "t is involv$ 9 ! expressions 99be=e & aft]991 99=m] & latt]994 ,"t is und\bt$ly "o ( ^? prim>y notions :i* c only be def9$ physically1 or by obs]vation ( ph5om5a :i* proce$ 9 "t4 #baj 99,engli% ,works ( ,?os4 ,hobbes991 ,edit4 by ,moleswor?1 vol4 i4 p4 #ie4 ,if we h n advanc$ a /ep beyond ,augu/9's acute reflections on ?is subject1#baa x is curi\s to obs]ve ! wond]ful advances :i* h be5 made 9 ! practical measurem5t ( its efflux4 ,9 e>li] c5turies ! rude sun-dial or ! ris+ ( a conspicu\s /> gave po9ts ( ref]5ce1 :ile ! fl[ ( wat] f ! clepsydra1 ! burn+ ( a c&le1 or1 9 ! mona/ic ages1 ev5 ! cont9u\s *ant+ ( psalms1 7 ! means ( r\ghly subdivid+ p]iods1 & m>k+ ! h\rs ( ! day & night4#bab ,! sun & />s /ill furni% ! /&>d ( "t1 b means ( accurate subdivision h become requisite1 & ?is has be5 furni%$ by ! p5dulum & ! *ronograph4 ,by ! p5dulum we c accurately divide ! day into seconds ( "t4 ,by ! *ronograph we c subdivide ! second into a hundr$1 a ?\s&1 or ev5 a million p>ts4 ,:eat/one measur$ ! duration ( an electric sp>k1 & f\nd x to be no m ?an "o #aae1bjj? "p ( a second1 :ile m rec5tly ,capta9 ,noble has be5 able to appreciate int]vals ( "t n exce$+ ! million? "p ( a second4 #baa 99,confessions991 bk4 xi4 *apt]s #bj-bh4 #bab ,sir ,g4 ,c4 ,lewis gives _m curi\s p>ticul>s conc]n+ ! measurem5t ( "t 9 8 99,a/ronomy ( ! ,anci5ts991 pp4 #bda1 c4 ,:5 we come to inquire precisely :at ph5om5on x is t we ?us s m9utely measure1 we meet insurm\ntable difficulties4 ,newton di/+ui%$ "t accord+ z x 0 99absolute99 or 99app>5t99 "t1 9 ! foll[+ words3--8,absolute1 true1 & ma!matical "t1 ( itself & f its own nature1 fl[s equably )\t reg>d to any?+ ext]nal1 & by ano!r "n is call$ 99duration992 relative1 app>5t & common "t1 is "s s5sible & ext]nal measure ( duration by ! means ( motion40#bac ,?\gh we are p]haps oblig$ to assume ! exi/5ce ( a uni=mly increas+ quantity :i* we call "t1 yet we _c feel or "k ab/ract & absolute "t4 ,duration mu/ be made manife/ to u by ! recurr5ce ( "s ph5om5on4 ,! succession ( our own ?\ghts is no d\bt ! fir/ & simple/ measure ( "t1 b a v rude "o1 because 9 "s p]sons & circum/ances ! ?\ghts evid5tly fl[ ) mu* great] rapidity ?an 9 o!r p]sons & circum/ances4 ,9 ! abs5ce ( all o!r ph5om5a1 ! int]val betwe5 "o ?\ght & ano!r w\ld necess>ily become ! unit ( "t1 b ! mo/ cursory obs]vations %[ t !re are *anges 9 ! outw>d _w mu* bett] fitt$ by _! con/ancy to measure "t ?an ! *ange ( ?\ghts )9 u4 #bac 99,pr9cipia991 bk4 i4 99,s*olium to ,def9itions994 ,translat$ by ,motte1 vol4 i4 p4 #i4 ,see also p4 #aa4 ,! e>?1 z ,i h already said1 is ! real clock ( ! a/ronom]1 & is practically assum$ z inv>iable 9 its movem5ts4 ,b on :at gr\nd is x s assum$8 ,accord+ to ! fir/ law ( motion1 e body p]sev]es 9 its /ate ( re/ or ( uni=m motion 9 a "r l9e1 unless x is compell$ to *ange t /ate by =ces impress$ !reon4 ,rotatory motion is subject to a l condition1 namely1 t x p]sev]es uni=mly unless di/urb$ by extr9sic =ces4 ,n[ uni=m motion means motion ?r\gh equal spaces 9 equal times1 s t if we h a body entirely free f all resi/ance or p]turbation1 & c measure equal spaces ( its pa?1 we h a p]fect measure ( "t4 ,b let x be rememb]$ t ?is law has nev] be5 absolutely prov$ by exp]i5ce2 = we _c po9t to any body1 & say t x is :olly unresi/$ or undi/urb$2 & ev5 if we _h su* a body1 we %\ld ne$ "s indep5d5t /&>d ( "t to asc]ta9 :e!r its motion 0 really uni=m4 ,z x is 9 mov+ bodies t we f9d ! be/ /&>d ( "t1 we _c use !m to prove ! uni=mity ( _! own movem5ts1 :i* w\ld am\nt to a 99petitio pr9cipii994 ,our exp]i5ce comes to ?is1 t :5 we exam9e & comp>e ! movem5ts ( bodies :i* seem to u ne>ly free f di/urbance1 we f9d !m giv+ ne>ly h>moni\s measures ( "t4 ,if any "o body :i* seems to u to move uni=mly is n do+ s1 b is subject to fits & />ts unkn[n to u1 because we h no absolute /&>d ( "t1 !n all o!r bodies mu/ be subject to ! same arbitr>y fits & />ts1 o!rwise !re w\ld be discrepancy disclos+ ! irregul>ities4 ,j z 9 comp>+ toge!r a numb] ( *ronomet]s1 we %\ld soon detect bad ones by _! go+ irregul>ly1 z comp>$ ) ! o!rs1 s 9 nature we detect di/urb$ movem5t by its discrepancy f t ( o!r bodies :i* we believe to be undi/urb$1 & :i* agree ne>ly among !mselves4 ,b inasmu* z ! measure ( motion involves "t1 & ! measure ( "t involves motion1 !re mu/ be ultimately an assumption4 ,we may def9e equal times1 z times dur+ :i* a mov+ body "u ! influ5ce ( no =ce describes equal spaces2#bad b all we c say 9 support ( ?is def9ition is1 t x leads u into no kn[n difficulties1 & t to ! be/ ( our exp]i5ce "o freely mov+ body gives ! same results z any o!r4 #bad ,rank9e1 99,philosophical ,magaz9e991 ,feb4 #ahfg1 vol4 xxxiii4 p4 #ia4 ,:5 we inquire :]e ! freely mov+ body is1 no p]fectly satisfactory answ] c be giv54 ,practically ! rotat+ globe is suffici5tly accurate1 & ,?omson & ,tait say3 8,equal times are times dur+ :i* ! e>? turns ?r\gh equal angles40#bae ,no long "t has pass$ s9ce a/ronom]s ?\ght x impossible to detect any inequality 9 its movem5t4 ,poisson 0 suppos$ to h prov$ t a *ange 9 ! l5g? ( ! sid]eal day am\nt+ to "o t5-million? "p 9 #b1ejj ye>s 0 incompatible ) an anci5t eclipse record$ by ! ,*aldans1 & simil> calculations 7 made by ,laplace4 ,b x is n[ kn[n t ^! calculations 7 some:at 9 error1 & t ! dissipation ( en]gy aris+ out ( ! friction ( tidal waves1 & ! radiation ( ! heat into space1 has slightly decreas$ ! rapidity ( ! e>?'s rotatory motion4 ,! sid]eal day is n[ long] by "o "p 9 #b1gjj1jjj1 ?an x 0 9 #gbj ,b4,c4 ,ev5 be=e ?is discov]y1 x 0 kn[n t inv>iability ( rotation dep5d$ ^u ! p]fect ma9t5ance ( ! e>?'s int]nal heat1 :i* is requisite 9 ord] t ! e>?'s dim5sions %all be unalt]$4 ,n[ ! e>? be+ sup]ior 9 temp]ature to empty space1 mu/ cool m or less rapidly1 s t x _c furni% an absolute measure ( "t4 ,simil> objections c\ld be rais$ to all o!r rotat+ bodies )9 our cognisance4 #bae 99,treatise on ,natural ,philosophy991 vol4 i4 p4 #agi4 ,! moon's motion r\nd ! e>?1 & ! e>?'s motion r\nd ! sun1 =m ! next be/ measure ( "t4 ,!y are subject1 inde$1 to di/urbance f o!r planets1 b x is believ$ t ^! p]turbations mu/ 9 ! c\rse ( "t run ?r\gh _! rhy?mical c\rses1 leav+ ! mean di/ances unaffect$1 & consequ5tly1 by ! ?ird ,law ( ,kepl]1 ! p]iodic times un*ang$4 ,b !re is m reason ?an n to believe t ! e>? enc\nt]s a slight resi/ance 9 pass+ ?r\gh space1 l t :i* is s app>5t 9 ,encke's comet4 ,!re may also be dissipation ( en]gy 9 ! electrical relations ( ! e>? to ! sun1 possibly id5tical ) t :i* is manife/$ 9 ! ret>dation ( comets4#baf ,x is probably an untrue assumption !n1 t ! e>?'s orbit rema9s q inv>iable4 ,x is j possible t "s o!r body may be f\nd 9 ! c\rse ( "t to furni% a bett] /&>d ( "t ?an ! e>? 9 its annual motion4 ,! greatly sup]ior mass ( ,jupit] & its satellites1 & _! great] di/ance f ! sun1 may r5d] ! electrical dissipation ( en]gy less consid]able ?an 9 ! case ( ! e>?4 ,b ! *oice ( ! be/ measure w always be an op5 "o1 & :atev] mov+ body we *oose may ultimately be %[n to be subject to di/urb+ =ces4 #baf 99,proce$+s ( ! ,man*e/] ,philosophical ,society991 #bh? ,nov4 #ahga1 vol4 xi4 p4 #cc4 ,! p5dulum1 al?\gh s admirable an in/rum5t = subdivision ( "t1 fails z a /&>d2 = ?\gh ! same p5dulum affect$ by ! same =ce ( gravity p]=ms equal vibrations 9 equal times1 yet ! slighte/ *ange 9 ! =m or weight ( ! p5dulum1 ! lea/ corrosion ( any "p1 or ! mo/ m9ute displacem5t ( ! po9t ( susp5sion1 falsifies ! results1 & !re ent] _m o!r difficult que/ions ( temp]ature1 friction1 resi/ance1 l5g? ( vibration1 c4 ,?omson & ,tait are ( op9ion#bag t ! ultimate /&>d ( *ronometry mu/ be f\nd$ on ! physical prop]ties ( "s body ( m con/ant "* ?an ! e>?2 = in/ance1 a c>efully arrang$ metallic spr+1 h]metically seal$ 9 an exhau/$ glass vessel4 ,b x is h>d to see h[ we c be sure t ! dim5sions & ela/icity ( a piece ( wr\ght metal w rema9 p]fectly un*ang$ = ! few millions ( ye>s contemplat$ by !m4 ,a ne>ly p]fect gas1 l hydrog51 is p]haps ! only k9d ( sub/ance 9 ! un*ang$ ela/icity ( :i* we c\ld h confid5ce4 ,moreov]1 x is difficult to p]ceive h[ ! undulations ( su* a spr+ c\ld be obs]v$ ) ! requisite accuracy4 ,m rec5tly ,pr(essor ,cl]k ,maxwell has made ! novel sugge/ion1 discuss$ 9 a subsequ5t section1 t undulations ( light 999 vacuo99 w\ld =m ! mo/ univ]sal /&>d ( ref]5ce1 bo? z reg>ds "t & space4 ,accord+ to ?is sy/em ! unit ( "t w\ld be ! "t occupi$ by "o vibration ( ! p>ticul> k9d ( light ^: wave l5g? is tak5 z ! unit ( l5g?4 #bag 99,! ,elem5ts ( ,natural ,philosophy991 "p i4 p4 #aai4 99,! ,unit ( ,space & ! ,b> ,/&>d499 ,next 9 importance aft] ! measurem5t ( "t is t ( space4 ,"t comes fir/ 9 !ory1 because ph5om5a1 our int]nal ?\ghts = in/ance1 may *ange 9 "t )\t reg>d to space4 ,z to ! ph5om5a ( outw>d nature1 !y t5d m & m to resolve !mselves into motions ( molecules1 & motion _c be conceiv$ or measur$ )\t ref]5ce bo? to "t & space4 ,turn+ n[ to space measurem5t1 we f9d x almo/ equally difficult to fix & def9e once & = ev]1 a unit magnitude4 ,!re are ?ree diff]5t modes 9 :i* x has be5 propos$ to attempt ! p]petuation ( a /&>d l5g?4 7#a7 ,by con/ruct+ an actual specim5 ( ! /&>d y>d or metre1 9 ! =m ( a b>4 7#b7 ,by assum+ ! globe itself to be ! ultimate /&>d ( magnitude1 ! practical unit be+ a submultiple ( "s dim5sion ( ! globe4 7#c7 ,by adopt+ ! l5g? ( ! simple seconds p5dulum1 z a /&>d ( ref]5ce4 ,at fir/ sight x might seem t !re 0 no great difficulty 9 ?is matt]1 & t any "o ( ^! me?ods might s]ve well en\gh2 b ! m m9utely we inquire into ! details1 ! m hopeless appe>s to be ! attempt to e/abli% an inv>iable /&>d4 ,we mu/ 9 ! fir/ place po9t out a pr9ciple n ( an obvi\s "*1 namely1 t 99! /&>d l5g? mu/ be def9$ by "o s+le object994#bah ,to make two b>s ( exactly ! same l5g?1 or ev5 two b>s be>+ a p]fectly def9$ ratio to ea* o!r1 is beyond ! p[] ( human art4 ,if two copies ( ! /&>d metre be made & decl>$ equally correct1 future inve/igators w c]ta9ly discov] "s discrepancy betwe5 !m1 prov+ ( c\rse t !y _c bo? be ! /&>d1 & giv+ cause = dispute z to :at magnitude %\ld !n be tak5 z correct4 #bah ,see ,h>ris' 99,essay ^u ,money & ,co9s991 "p4 ii4 #ageh p4 #abg4 ,if "o inv>iable b> c\ld be con/ruct$ & ma9ta9$ z ! absolute /&>d1 no su* inconv5i5ce c\ld arise4 ,ea* successive g5]ation z x acquir$ high] p[]s ( measurem5t1 w\ld detect errors 9 ! copies ( ! /&>d1 b ! /&>d itself w\ld be unimpea*$1 & w\ld1 z x 71 become by degrees m & m accurately kn[n4 ,un=tunately to con/ruct & pres]ve a metre or y>d is also a task :i* is ei!r impossible1 or :at comes ne>ly to ! same ?+1 _c be %[n to be possible4 ,pass+ ov] ! practical difficulty ( def9+ ! ends ( ! /&>d l5g? ) complete accuracy1 :e!r by dots or l9es on ! surface1 or by ! t]m9al po9ts ( ! b>1 we h no means ( prov+ t sub/ances rema9 ( inv>iable dim5sions4 ,j z we _c tell :e!r ! rotation ( ! e>? is uni=m1 except by comp>+ x ) o!r mov+ bodies1 believ$ to be m uni=m 9 motion1 s we _c detect ! *ange ( l5g? 9 a b>1 except by comp>+ x ) "s o!r b> suppos$ to be inv>iable4 ,b h[ are we to "k :i* is ! inv>iable b>8 ,x is c]ta9 t _m rigid & app>5tly inv>iable sub/ances d *ange 9 dim5sions4 ,! bulb ( a !rmomet] c]ta9ly contracts by age1 besides und]go+ rapid *anges ( dim5sions :5 w>m$ or cool$ ?r\gh #ajj ,c5t4 ,c we be sure t ev5 ! mo/ solid metallic b>s d n slightly contract by age1 or und]go v>iations 9 _! /ructure by *ange ( temp]ature4 ,fizeau 0 induc$ to try :e!r a qu>tz cry/al1 subject$ to sev]al hundr$ alt]nations ( temp]ature1 w\ld be modifi$ 9 its physical prop]ties1 & he 0 unable to detect any *ange 9 ! coeffici5t ( expansion4#bai ,x does n foll[1 h[ev]1 t1 because no app>5t *ange 0 discov]$ 9 a qu>tz cry/al1 newly-con/ruct$ b>s ( metal w\ld und]go no *ange4 #bai 99,philosophical ,magaz9e991 7#ahfh71 #d? ,s]ies1 vol4 xxxvi4 p4 #cb4 ,! be/ pr9ciple1 z x seems to me1 ^u :i* ! p]petuation ( a /&>d ( l5g? c be re/$1 is t1 if a v>iation ( l5g? occurs1 x w 9 all probability be ( diff]5t am\nt 9 diff]5t sub/ances4 ,if !n a great numb] ( /&>d metres 7 con/ruct$ ( all k9ds ( diff]5t metals & alloys2 h>d rocks1 su* z granite1 s]p5t9e1 slate1 qu>tz1 lime/one2 artificial sub/ances1 su* z porcela91 glass1 c41 c41 c>eful comp>ison w\ld %[ f "t to "t ! comp>ative v>iations ( l5g? ( ^! diff]5t sub/ances4 ,! mo/ v>iable sub/ances w\ld be ! mo/ div]g5t1 & ! /&>d w\ld be furni%$ by ! mean l5g? ( ^? :i* agre$ mo/ closely ) ea* o!r j z uni=m motion is t ( ^? bodies :i* agree mo/ closely 9 indicat+ ! efflux ( "t4 99,! ,t]re/rial ,/&>d499 ,! second me?od assumes t ! globe itself is a body ( inv>iable dim5sions & ! f\nd]s ( ! metrical sy/em select$ ! t5-million? "p ( ! di/ance f ! equator to ! pole z ! def9ition ( ! metre4 ,! fir/ imp]fection 9 su* a me?od is t ! e>? is c]ta9ly n inv>iable 9 size2 = we "k t x is sup]ior 9 temp]ature to surr\nd+ space1 & mu/ be sl[ly cool+ & contract+4 ,!re is mu* reason to believe t all e>?quakes1 volcanoes1 m\nta9 elevations1 & *anges ( sea level are evid5ces ( ?is contraction z ass]t$ by ,mr4 ,mallet4#bbj ,b su* is ! va/ bulk ( ! e>? & ! duration ( its pa/ exi/5ce1 t ?is contraction is p]haps less rapid 9 proportion ?an t ( any b> or o!r mat]ial /&>d :i* we c con/ruct4 #bbj 99,proce$+s ( ! ,royal ,society991 #bj? ,june1 #ahgb1 vol4 xx4 p4 #dch4 ,! second & *ief difficulty ( ?is me?od arises f ! va/ size ( ! e>?1 :i* prev5ts u f mak+ any comp>ison ) ! ultimate /&>d1 except by a trigonometrical survey ( a mo/ elaborate & co/ly k9d4 ,! ,fr5* physici/s1 :o fir/ propos$ ! me?od1 attempt$ to obviate ?is inconv5i5ce by c>ry+ out ! survey once = all1 & !n con/ruct+ a /&>d metre1 :i* %\ld be exactly ! "o t5 million? "p ( ! di/ance f ! pole to ! equator4 ,b s9ce all measur+ op]ations are m]ely approximate1 x 0 impossible t ?is op]ation c\ld be p]fectly a*iev$4 ,accord+ly1 x 0 %[n 9 #ahch t ! suppos$ ,fr5* metre 0 errone\s to ! consid]able ext5t ( "o "p 9 #eebg4 ,x !n became necess>y ei!r to alt] ! l5g? ( ! assum$ metre1 or to ab&on its suppos$ relation to ! e>?'s dim5sions4 ,! ,fr5* ,gov]nm5t & ! ,int]national ,metrical ,commission h = obvi\s reasons decid$ 9 fav\r ( ! latt] c\rse1 & h ?us rev]t$ to ! fir/ me?od ( def9+ ! metre by a giv5 b>4 ,z f "t to "t ! ratio betwe5 ?is assum$ /&>d metre & ! quadrant ( ! e>? becomes m accurately kn[n1 we h bett] means ( re/or+ t metre by ref]5ce to ! globe if requir$4 ,b until lo/1 de/roy$1 or = "s cle> reason discr$it$1 ! b> metre & n ! globe is ! /&>d4 ,?omson & ,tait rem>k t any ( ! m accurate measurem5ts ( ! ,engli% trigonometrical survey might 9 l mann] be employ$ to re/ore our /&>d y>d1 9 t]ms ( :i* ! results are record$4 99,! ,p5dulum ,/&>d499 ,! ?ird me?od ( def9+ a /&>d l5g?1 by ref]5ce to ! seconds p5dulum1 0 fir/ propos$ by ,huygh5s1 & 0 at "o "t adopt$ by ! ,engli% ,gov]nm5t4 ,f ! pr9ciple ( ! p5dulum 7p4 #cjb7 x cle>ly appe>s t if ! "t ( oscillation & ! =ce actuat+ ! p5dulum be ! same1 ! l5g? ( ! p5dulum mu/ be ! same4 ,we d n get rid ( !oretical difficulties1 = we mu/ assume ! attraction ( gravity at "s po9t ( ! e>?'s surface1 say ,london1 to be un*ang$ f "t to "t1 & ! sid]eal day to be inv>iable1 nei!r assumption be+ absolutely correct s f> z we c judge4 ,! p5dulum1 9 %ort1 is only an indirect means ( mak+ "o physical quantity ( space dep5d ^u two o!r physical quantities ( "t & =ce4 ,! practical difficulties are1 h[ev]1 ( a f> m s]i\s "* ?an ! !oretical ones4 ,! l5g? ( a p5dulum is n ! ord9>y l5g? ( ! in/rum5t1 :i* might be greatly v>i$ )\t affect+ ! duration ( a vibration1 b ! di/ance f ! c5tre ( susp5sion to ! c5tre ( oscillation4 ,!re are no direct means ( det]m9+ ?is latt] c5tre1 :i* dep5ds ^u ! av]age mom5tum ( all ! p>ticles ( ! p5dulum z reg>ds ! c5tre ( susp5sion4 ,huygh5s discov]$ t ! c5tres ( susp5sion & oscillation are int]*angeable1 & ,kat] po9t$ out t if a p5dulum vibrates ) exactly ! same rapidity :5 susp5d$ f two diff]5t po9ts1 ! di/ance betwe5 ^! po9ts is ! true l5g? ( ! equival5t simple p5dulum4#bba ,b ! practical difficulties 9 employ+ ,kat]'s rev]sible p5dulum are consid]able1 & que/ions reg>d+ ! di/urbance ( ! air1 ! =ce ( gravity1 or ev5 ! int]f]5ce ( electrical attractions h to be ent]ta9$4 ,x has be5 %[n t all ! exp]im5ts made "u ! au?ority ( ,gov]nm5t = det]m9+ ! ratio betwe5 ! /&>d y>d & ! seconds p5dulum1 7 vitiat$ by an error 9 ! corrections = ! resi/+1 adh]5t1 or buoyant p[] ( ! air 9 :i* ! p5dulums 7 swung4 ,ev5 if su* corrections 7 r5d]$ unnecess>y by op]at+ 9 a vacuum1 o!r difficult que/ions rema94#bbb ,gauss' mode ( comp>+ ! vibrations ( a wire p5dulum :5 susp5d$ at two diff]5t l5g?s is op5 to equal or great] practical difficulties4 ,?us x is f\nd t ! p5dulum /&>d _c compete 9 accuracy & c]ta9ty ) ! simple b> /&>d1 & ! me?od w\ld only be useful z an accessory mode ( re/or+ ! b> /&>d if at any "t aga9 de/roy$4 #bba ,kat]'s 99,treatise on ,me*anics991 ,cab9et ,cyclopdia1 p4 #aed4 #bbb ,grant's 99,hi/ory ( ,physical ,a/ronomy991 p4 #aef4 99,unit ( ,d5sity499 ,be=e we c measure ! ph5om5a ( nature1 we require a ?ird indep5d5t unit1 :i* %all enable u to def9e ! quantity ( matt] occupy+ any giv5 space4 ,all ! *anges ( nature1 z we %all see1 are probably s _m manife/ations ( en]gy2 b en]gy requires "s sub/ratum or mat]ial ma*9]y ( molecules1 9 & by :i* x may be manife/$4 ,obs]vation %[s t1 z reg>ds =ce1 !re may be two modes ( v>iation ( matt]4 ,z ,newton says 9 ! fir/ def9ition ( ! ,pr9cipia1 8! quantity ( matt] is ! measure ( ! same1 aris+ f its d5sity & bulk conjunctly40 ,?us ! =ce requir$ to set a body 9 motion v>ies bo? accord+ to ! bulk ( ! matt]1 & also accord+ to its quality4 ,two cubic in*es ( iron ( uni=m quality1 w require twice z mu* =ce z "o cubic in* to produce a c]ta9 velocity 9 a giv5 "t2 b "o cubic in* ( gold w require m =ce ?an "o cubic in* ( iron4 ,!re is !n "s new measurable quality 9 matt] ap>t f its bulk1 :i* we may call 99d5sity991 & :i* is1 /rictly speak+1 indicat$ by its capacity to resi/ & absorb ! action ( =ce4 ,= ! unit ( d5sity we may assume t ( any sub/ance :i* is uni=m 9 quality1 & c readily be ref]r$ to f "t to "t4 ,pure wat] at any def9ite temp]ature1 = in/ance t ( sn[ melt+ "u inappreciable pressure1 furni%es an inv>iable /&>d ( d5sity1 & by comp>+ equal bulks ( v>i\s sub/ances ) a l bulk ( ice-cold wat]1 z reg>ds ! velocity produc$ 9 a unit ( "t by ! same =ce1 we %\ld asc]ta9 ! d5sities ( ^? sub/ances z express$ 9 t ( wat]4 ,practically ! =ce ( gravity is us$ to measure d5sity2 = a beautiful exp]im5t ) ! p5dulum1 p]=m$ by ,newton & repeat$ by ,gauss1 %[s t all k9ds ( matt] gravitate equally4 ,two portions ( matt] !n :i* are 9 equilibrium 9 ! balance1 may be assum$ to possess equal in]tia1 & _! d5sities w !re=e be inv]sely z _! cubic dim5sions4 99,unit ( ,mass499 ,multiply+ ! numb] ( units ( d5sity ( a portion ( matt]1 by ! numb] ( units ( space occupi$ by x1 we arrive at ! quantity ( matt]1 or1 z x is usually call$1 ! 99unit ( mass991 z indicat$ by ! in]tia & gravity x possesses4 ,to proce$ 9 ! mo/ simple mann]1 ! unit ( mass ought to be t ( a cubic unit ( matt] ( ! /&>d d5sity2 b ! f\nd]s ( ! metrical sy/em took z _! unit ( mass1 ! cubic c5timetre ( wat]1 at ! temp]ature ( maximum d5sity 7ab\t #d ,c5t474 ,!y call$ ?is unit ( mass ! 99gramme991 & con/ruct$ /&>d specim5s ( ! kilogram1 :i* might be readily ref]r$ to by all :o requir$ to employ accurate weights4 ,un=tunately ! det]m9ation ( ! bulk ( a giv5 weight ( wat] at a c]ta9 temp]ature is an op]ation involv+ _m difficulties1 & x _c be p]=m$ 9 ! pres5t day ) a great] exactness ?an t ( ab\t "o "p 9 #ejjj1 ! results ( c>eful obs]v]s be+ sometimes f\nd to diff] z mu* z "o "p 9 #ajjj4bbc #bbc ,cl]k ,maxwell's 99,!ory ( ,heat991 p4 #gi4 ,weights1 on ! o!r h&1 c be comp>$ ) ea* o!r to at lea/ "o "p 9 a million4 ,h5ce if diff]5t specim5s ( ! kilogram be prep>$ by direct weigh+ aga9/ wat]1 !y w n agree closely ) ea* o!r2 ! two pr9cipal /&>d kilograms agree nei!r ) ea* o!r1 nor ) _! def9ition4 ,accord+ to ,pr(essor ,mill] ! s-call$ ,kilogramme des ,ar*ives weighs #aedcbcdhgd gra9s1 :ile ! kilogram deposit$ at ! ,m9i/ry ( ! ,int]ior 9 ,p>is1 z ! /&>d = comm]cial purposes1 weighs #aedcbcdd gra9s4 ,s9ce a /&>d weight con/ruct$ ( plat9um1 or plat9um & iridium1 c be pres]v$ free f any appreciable alt]ation1 & s9ce x c be v accurately comp>$ ) o!r weights1 we %all ultimately atta9 ! greate/ exactness 9 our measurem5ts ( mass1 by assum+ "s s+le kilogram z a 99provisional /&>d991 leav+ ! det]m9ation ( its actual mass 9 units ( space & d5sity = future inve/igation4 ,?is is :at is practically done at ! pres5t day1 & ?us a unit ( mass takes ! place ( ! unit ( d5sity1 bo? 9 ! ,fr5* & ,engli% sy/ems4 ,! ,engli% p\nd is def9$ by a c]ta9 lump ( plat9um1 pres]v$ at ,we/m9/]1 & is an arbitr>y mass1 *os5 m]ely t x may agree z ne>ly z possible ) old ,engli% p\nds4 ,! gallon1 ! old ,engli% unit ( cubic measurem5t1 is def9$ by ! condition t x %all conta9 exactly t5 p\nds weight ( wat] at #fb ,fahr42 & al?\gh x is /at$ t x has ! capacity ( ab\t #bggbgd cubic in*es1 ?is ratio betwe5 ! cubic & l9e> sy/ems ( measurem5t is n legally enact$1 b left op5 to inve/igation4 ,:ile ! ,fr5* metric sy/em z orig9ally design$ 0 !oretically p]fect1 x does n diff] practically 9 ?is po9t f ! ,engli% sy/em4 99,natural ,sy/em ( ,/&>ds499 ,q rec5tly ,pr(essor ,cl]k ,maxwell has sugge/$ t ! vibrations ( light & ! atoms ( matt] might conceivably be employ$ z ! ultimate /&>ds ( l5g?1 "t1 & mass4 ,we %\ld ?us arrive at a 99natural sy/em ( /&>ds991 :i*1 ?\gh possess+ no pres5t practical importance1 has consid]able !oretical int]e/4 8,9 ! pres5t /ate ( sci5ce10 he says1 8! mo/ univ]sal /&>d ( l5g? :i* we c\ld assume w\ld be ! wave-l5g? 9 vacuum ( a p>ticul> k9d ( light1 emitt$ by "s widely diffus$ sub/ance su* z sodium1 :i* has well-def9$ l9es 9 its spectrum4 ,su* a /&>d w\ld be indep5d5t ( any *anges 9 ! dim5sions ( ! e>?1 & %\ld be adopt$ by ^? :o expect _! writ+s to be m p]man5t ?an t body40#bbd ,9 ! same way we %\ld get a univ]sal /&>d unit ( "t1 indep5d5t ( all que/ions ab\t ! motion ( mat]ial bodies1 by tak+ z ! unit ! p]iodic "t ( vibration ( t p>ticul> k9d ( light ^: wave-l5g? is ! unit ( l5g?4 ,x w\ld foll[ t ) ^! units ( l5g? & "t ! unit ( velocity w\ld co9cide ) ! velocity ( light 9 empty space4 ,z reg>ds ! unit ( mass1 ,pr(essor ,maxwell1 humor\sly z ,i %\ld ?9k1 rem>ks t if we expect soon to be able to det]m9e ! mass ( a s+le molecule ( "s /&>d sub/ance1 we may wait = ?is det]m9ation be=e fix+ a univ]sal /&>d ( mass4 #bbd 99,treatise on ,electricity & ,magnetism991 vol4 i4 p4 #c4 ,9 a !oretical po9t ( view !re c be no reasonable d\bt t vibrations ( light are1 z f> z we c tell1 ! mo/ fix$ 9 magnitude ( all ph5om5a4 ,!re is z usual no c]ta9ty 9 ! matt]1 = ! prop]ties ( ! basis ( light may v>y to "s ext5t 9 diff]5t p>ts ( space4 ,b no diff]5ces c\ld ev] be e/abli%$ 9 ! velocity ( light 9 diff]5t p>ts ( ! sol> sy/em1 & ! spectra ( ! />s %[ t ! times ( vibration !re d n diff] p]ceptibly f ^? 9 ?is "p ( ! univ]se4 ,?us all presumption is 9 fav\r ( ! absolute con/ancy ( ! vibrations ( light--absolute1 t is1 s f> z reg>ds any means ( inve/igation we are likely to possess4 ,ne>ly ! same consid]ations apply to ! atomic weight z ! /&>d ( mass4 ,x is impossible to prove t all atoms ( ! same sub/ance are ( equal mass1 & "s physici/s ?9k t !y diff]1 s t ! fixity ( comb9+ proportions may be due only to ! approximate con/ancy ( ! mean ( c\ntless millions ( discrepant weights4 ,b 9 any case ! detection ( diff]5ce is probably beyond our p[]s4 ,9 a !oretical po9t ( view1 !n1 ! magnitudes sugge/$ by ,pr(essor ,maxwell seem to be ! mo/ fix$ ones ( :i* we h any k1 s t !y necess>ily become ! natural units4 ,9 a practical po9t ( view1 z ,pr(essor ,maxwell w\ld be ! fir/ to po9t out1 !y are ( little or no value1 because 9 ! pres5t /ate ( sci5ce we _c measure a vibration or weigh an atom ) any approa* to ! accuracy :i* is atta9able 9 ! comp>ison ( /&>d metres & kilograms4 ,! velocity ( light is n kn[n probably )9 a ?\s&? "p1 & z we progress 9 ! k ( light1 s we %all progress 9 ! accurate fixation ( o!r /&>ds4 ,all t c be said !n1 is t x is v desirable to det]m9e ! wave-l5g?s & p]iods ( ! pr9cipal l9es ( ! sol> spectrum1 & ! absolute atomic weights ( ! elem5ts1 ) all atta9able accuracy1 9 t]ms ( our exi/+ /&>ds4 ,! numb]s ?us obta9$ w\ld admit ( ! reproduction ( our /&>ds 9 "s future age ( ! _w to a correspond+ degree ( accuracy1 7 !re ne$ ( su* ref]5ce2 b s f> z we c see at pres5t1 !re is no consid]able probability t ?is mode ( reproduction w\ld ev] be ! be/ mode4 99,subsidi>y ,units499 ,hav+ once e/abli%$ ! /&>d units ( "t1 space1 & d5sity or mass1 we might employ !m = ! expression ( all quantities ( su* nature4 ,b x is (t5 conv5i5t 9 p>ticul> bran*es ( sci5ce to use multiples or submultiples ( ! orig9al units1 = ! expression ( quantities 9 a simple mann]4 ,we use ! mile r ?an ! y>d :5 treat+ ( ! magnitude ( ! globe1 & ! mean di/ance ( ! e>? & sun is n too l>ge a unit :5 we h to describe ! di/ances ( ! />s4 ,on ! o!r h&1 :5 we are occupi$ ) microscopic objects1 ! in*1 ! l9e or ! millimetre1 become ! mo/ conv5i5t t]ms ( expression4 ,x is all[able = a sci5tific man to introduce a new unit 9 any bran* ( k1 provid$ t x assi/s precise expression1 & is c>efully br\ght into relation ) ! prim>y units4 ,?us ,pr(essor ,a4 ,w4 ,williamson has propos$ z a conv5i5t unit ( volume 9 *emical sci5ce1 an absolute volume equal to ab\t #aab litres repres5t+ ! bulk ( "o gram ( hydrog5 gas at /&>d temp]ature & pressure1 or ! 99equival5t99 weight ( any o!r gas1 su* z #af grams ( oxyg51 #ad grams ( nitrog51 c42 9 %ort1 ! bulk ( t quantity ( any "o ( ^? gases :i* weighs z _m grams z !re are units 9 ! numb] express+ its atomic weight4#bbe ,h(mann has propos$ a new unit ( weight = *emi/s1 call$ a 99cri?991 to be def9$ by ! weight ( "o litre ( hydrog5 gas at #j ,c4 & #jgf mm41 weigh+ ab\t #jjhif gram4#bbf ,bo? ( ^! units mu/ be reg>d$ z purely subord9ate units1 ultimately def9$ by ref]5ce to ! prim>y units1 & n involv+ any new assumption4 #bbe 99,*emi/ry = ,/ud5ts991 by ,a4 ,w4 ,williamson4 ,cl>5don ,press ,s]ies1 #bnd ed4 ,preface p4 vi4 #bbf 99,introduction to ,*emi/ry991 p4 #aca4 99,d]iv$ ,units499 ,! /&>d units ( "t1 space1 & mass hav+ be5 once fix$1 _m k9ds ( magnitude are naturally measur$ by units d]iv$ f !m4 ,f ! metre1 ! unit ( l9e> magnitude foll[s 9 ! mo/ obvi\s mann] ! c5ti>e or squ>e metre1 ! unit ( sup]ficial magnitude1 & ! litre t is ! cube ( ! t5? "p ( a metre1 ! unit ( capacity or volume4 ,velocity ( motion is express$ by ! ratio ( ! space pass$ ov]1 :5 ! motion is uni=m1 to ! "t occupi$2 h5ce ! unit ( velocity is t ( a body :i* passes ov] a unit ( space 9 a unit ( "t4 ,9 physical sci5ce ! unit ( velocity might be tak5 z "o metre p] second4 ,mom5tum is measur$ by ! mass mov+1 reg>d be+ paid bo? to ! am\nt ( matt] & ! velocity at :i* x is mov+4 ,h5ce ! unit ( mom5tum w be t ( a unit volume ( matt] ( ! unit d5sity mov+ ) ! unit velocity1 or 9 ! ,fr5* sy/em1 a cubic c5timetre ( wat] ( ! maximum d5sity mov+ "o metre p] second4 ,an accel]at+ =ce is measur$ by ! ratio ( ! mom5tum g5]at$ to ! "t occupi$1 ! =ce be+ suppos$ to act uni=mly4 ,! unit ( =ce w !re=e be t :i* g5]ates a unit ( mom5tum 9 a unit ( "t1 or :i* causes1 9 ! ,fr5* sy/em1 "o cubic c5timetre ( wat] at maximum d5sity to acquire 9 "o second a velocity ( "o metre p] second4 ,! =ce ( gravity is ! mo/ famili> k9d ( =ce1 & z1 :5 act+ unimp$$ ^u any sub/ance1 x produces 9 a second a velocity ( #ihjhfh 4 4 metres p] second 9 ,p>is1 x foll[s t ! absolute unit ( =ce is ab\t ! t5? "p ( ! =ce ( gravity4 ,if we employ ,briti% weights & measures1 ! absolute unit ( =ce is repres5t$ by ! gravity ( ab\t half an ounce1 s9ce ! =ce ( gravity ( any portion ( matt] act+ ^u t matt] dur+ "o second1 produces a f9al velocity ( #cbahhi feet p] second or ab\t #cb units ( velocity4 ,al?\gh f its p]petual action & approximate uni=mity we f9d 9 gravity ! mo/ conv5i5t =ce = ref]5ce1 & ?us habitually employ x to e/imate quantities ( matt]1 we mu/ rememb] t x is only "o ( _m in/ances ( =ce4 ,/rictly speak+1 we %\ld express weight 9 t]ms ( =ce1 b practically we express o!r =ces 9 t]ms ( weight4 ,we /ill require ! unit ( en]gy1 a m complex notion4 ,! mom5tum ( a body expresses ! quantity ( motion :i* belongs or w\ld belong to ! aggregate ( ! p>ticles2 b :5 we consid] h[ ?is motion is relat$ to ! action ( a =ce produc+ or remov+ x1 we f9d t ! effect ( a =ce is proportional to ! mass multipli$ by ! squ>e ( ! velocity & x is conv5i5t to take half ?is product z ! expression requir$4 ,b x is %[n 9 books ^u dynamics t x w be exactly ! same ?+ if we def9e en]gy by a =ce act+ ?r\gh a space4 ,! natural unit ( en]gy w !n be t :i* ov]comes a unit ( =ce act+ ?r\gh a unit ( space2 :5 we lift "o kilogram ?r\gh "o metre1 aga9/ gravity1 we !re=e accompli% #ihjhfh 4 4 units ( "w1 t is1 we turn s _m units ( pot5tial en]gy exi/+ 9 ! muscles1 into pot5tial en]gy ( gravitation4 ,9 lift+ "o p\nd ?r\gh "o foot !re is 9 l mann] a conv]sion ( #cbahhi units ( en]gy4 ,accord+ly ! unit ( en]gy w be 9 ! ,engli% sy/em1 t requir$ to lift "o p\nd ?r\gh ab\t ! ?irty-second "p ( a foot2 9 t]ms ( metric units1 x w be t requir$ to lift a kilogram ?r\gh ab\t "o t5? "p ( a metre4 ,e p]son is at lib]ty to measure & record quantities 9 t]ms ( any unit :i* he likes4 ,he may use ! y>d = l9e> measurem5t & ! litre = cubic measurem5t1 only !re w !n be a complicat$ relation betwe5 8 diff]5t results4 ,! sy/em ( d]iv$ units :i* we h be5 briefly consid]+1 is t :i* gives ! mo/ simple & natural relations betwe5 quantitative expressions ( diff]5t k9ds1 & !re=e conduces to ease ( compreh5sion & sav+ ( labori\s calculation4 ,x w\ld evid5tly be a s\rce ( great conv5i5ce if sci5tific m5 c\ld agree ^u "s s+le sy/em ( units1 orig9al & d]iv$1 9 t]ms ( :i* all quantities c\ld be express$4 ,/atem5ts w\ld ?us be r5d]$ easily comp>able1 a l>ge "p ( sci5tific lit]ature w\ld be made intelligible to all1 & ! sav+ ( m5tal lab\r w\ld be imm5se4 ,x seems to be g5]ally all[$1 too1 t ! metric sy/em ( weights & measures pres5ts ! be/ basis = ! ultimate sy/em2 x is ?or\ghly e/abli%$ 9 ,we/]n ,europe2 x is legalis$ 9 ,engl&2 x is already commonly employ$ by sci5tific m52 x is 9 itself ! mo/ simple & sci5tific ( sy/ems4 ,!re is e reason !n :y ! metric sy/em %\ld be accept$ at lea/ 9 its ma9 features4 99,provisional ,units499 ,ultimately1 z we c h>dly d\bt1 all ph5om5a w be recognis$ z s _m manife/ations ( en]gy2 &1 be+ express$ 9 t]ms ( ! unit ( en]gy1 w be ref]able to ! prim>y units ( space1 "t1 & d5sity4 ,to effect ?is r$uction1 h[ev]1 9 any p>ticul> case1 we mu/ n only be able to comp>e diff]5t quantities ( ! ph5om5on1 b to trace ! :ole s]ies ( /eps by :i* x is connect$ ) ! prim>y notions4 ,we c readily obs]ve t ! int5sity ( "o s\rce ( light is great] ?an t ( ano!r2 &1 kn[+ t ! int5sity ( light decreases z ! squ>e ( ! di/ance increases1 we c easily det]m9e _! comp>ative brilliance4 ,h5ce we c express ! int5sity ( light fall+ ^u any surface1 if we h a unit 9 :i* to make ! expression4 ,light is und\bt$ly "o =m ( en]gy1 & ! unit ought !re=e to be ! unit ( en]gy4 ,b at pres5t x is q impossible to say h[ mu* en]gy !re is 9 any p>ticul> am\nt ( light4 ,! "q !n arises1--,are we to def] ! measurem5t ( light until we c assign its relation to o!r =ms ( en]gy8 ,if we answ] ,yes1 x is equival5t to say+ t ! sci5ce ( light mu/ /& /ill p]haps = a g5]ation2 & n only ?is sci5ce b _m o!rs4 ,! true c\rse evid5tly is to select1 z ! provisional unit ( light1 "s light ( conv5i5t int5sity1 :i* c be reproduc$ f "t to "t 9 ! same int5sity1 & :i* is def9$ by physical circum/ances4 ,all ! ph5om5a ( light may be exp]im5tally inve/igat$ relatively to ?is unit1 = in/ance t obta9$ aft] mu* lab\r by ,buns5 & ,roscoe4#bbg ,9 aft] ye>s x w become a matt] ( inquiry :at is ! en]gy ex]t$ 9 su* unit ( light2 b x may be long be=e ! relation is exactly det]m9$4 #bbg 99,philosophical ,transactions99 7#ahei71 vol4 cxlix4 p4 #hhd1 c4 ,a provisional unit1 !n1 means "o :i* is assum$ & physically def9$ 9 a safe & reproducible mann]1 9 ord] t p>ticul> quantities may be comp>$ 99int] se99 m accurately ?an !y c yet be ref]r$ to ! prim>y units4 ,9 reality ! great majority ( our measurem5ts are express$ 9 t]ms ( su* provisionally indep5d5t units1 & ev5 ! unit ( mass1 z we h se51 ought to be consid]$ z provisional4 ,! unit ( heat ought to be simply ! unit ( en]gy1 already describ$4 ,b a weight c be measur$ to ! "o-million? "p1 & temp]ature to less ?an ! ?\s&? "p ( a degree ,fahr5heit1 & to less !re=e ?an ! five-hundr$ ?\s&? "p ( ! absolute temp]ature1 :]eas ! me*anical equival5t ( heat is probably n kn[n to ! ?\s&? "p4 ,h5ce ! ne$ ( a provisional unit ( heat1 :i* is (t5 tak5 z t requisite to raise "o gram ( wat] ?r\gh "o degree ,c5tigrade1 t is f #j to #a4 ,?is quantity ( heat is capable ( approximate expression 9 t]ms ( "t1 space1 & mass2 = by ! natural con/ant1 det]m9$ by ,dr4 ,j\le1 & call$ ! me*anical equival5t ( heat1 we "k t ! assum$ unit ( heat is equal to ! en]gy ( #dbcee gram-metres1 or t en]gy :i* w raise ! mass ( #dbcee grams ?r\gh "o metre aga9/ #ih444 absolute units ( =ce4 ,heat may also be express$ 9 t]ms ( ! quantity ( ice at #j ,c5t41 :i* x is capable ( conv]t+ into wat] "u inappreciable pressure4 99,!ory ( ,dim5sions499 ,9 ord] to und]/& ! relations betwe5 ! quantities dealt ) 9 physical sci5ce1 x is necess>y to pay att5tion to ! ,!ory ( ,dim5sions1 fir/ cle>ly /at$ by ,joseph ,f\ri]1#bbh b 9 lat] ye>s develop$ by sev]al physici/s4 ,?is !ory inve/igates ! mann] 9 :i* ea* d]iv$ unit dep5ds ^u or involves "o or m ( ! fundam5tal units4 ,! numb] ( units 9 a rectangul> area is f\nd by multiply+ toge!r ! numb]s ( units 9 ! sides2 ?us ! unit ( l5g? ent]s twice into ! unit ( area1 :i* is !re=e said to h two dim5sions ) respect to l5g?4 ,d5ot+ l5g? by 99,l991 we may say t ! dim5sions ( area are 99,l99 99,l99 or 99,l99#b4 ,x is obvi\s 9 ! same way t ! dim5sions ( volume or bulk w be 99,l99#c4 #bbh 99,?orie ,analytique de la ,*aleur991 ,p>is2 #ahbb1 #aeg-afb4 ,! numb] ( units ( mass 9 a body is f\nd by multiply+ ! numb] ( units ( volume1 by ^? ( d5sity4 ,h5ce mass is ( ?ree dim5sions z reg>ds l5g?1 & "o z reg>ds d5sity4 ,call+ d5sity 99,d991 ! dim5sions ( mass are 99,l99#c99;,d994 ,z already expla9$1 h[ev]1 x is usual to sub/itute an arbitr>y provisional unit ( mass1 symbolis$ by 99,m992 accord+ to ! view "h tak5 we may say t ! dim5sions ( 99,m99 are 99,l99#c99;,d994 ,introduc+ "t1 d5ot$ by 99,t991 x is easy to see t ! dim5sions ( velocity w be 99,l_/,t99 or 99,,lt99-#a1 because ! numb] ( units 9 ! velocity ( a body is f\nd by 99divid+99 ! units ( l5g? pass$ ov] by ! units ( "t occupi$ 9 pass+4 ,! accel]ation ( a body is measur$ by ! increase ( velocity 9 relation to ! "t1 t is1 we mu/ divide ! units ( velocity ga9$ by ! units ( "t occupi$ 9 ga9+ x2 h5ce its dim5sions w be 99,,lt99-#b4 ,mom5tum is ! product ( mass & velocity1 s t its dim5sions are 99,,mlt99-#a4 ,! effect ( a =ce is measur$ by ! accel]ation produc$ 9 a unit ( mass 9 a unit ( "t2 h5ce ! dim5sions ( =ce are 99,,mlt99-#b4 ,"w done is proportional to ! =ce act+ & to ! space ?r\gh :i* x acts2 s t x has ! dim5sions ( =ce ) t ( l5g? add$1 giv+ 99,,ml99#b99,t99-#b4 ,x %\ld be p>ticul>ly notic$ t angul> magnitude has no dim5sions at all1 be+ measur$ by ! ratio ( ! arc to ! radius 7p4 #cje74 ,?us we h ! dim5sions 99,,ll99-#a or 99,l99#j4 ,?is agrees ) ! /atem5t previ\sly made1 t no arbitr>y unit ( angul> magnitude is ne$$4 ,simil>ly1 all pure numb]s express+ ratios only1 su* z s9es & o!r trigonometrical functions1 log>i?ms1 expon5ts1 c41 are devoid ( dim5sions4 ,!y are absolute numb]s necess>ily express$ 9 t]ms ( unity itself1 & are q unaffect$ by ! selection ( ! arbitr>y physical units4 ,angul> magnitude1 h[ev]1 ent]s into o!r quantities1 su* z angul> velocity1 :i* has ! dim5sions #a_/99,t99 or 99,t99-#a1 ! units ( angle be+ divid$ by ! units ( "t occupi$4 ,! dim5sions ( angul> accel]ation are d5ot$ by 99,t99-#b4 ,! quantities treat$ 9 ! !ories ( heat & electricity are num]\s & complicat$ z reg>ds _! dim5sions4 ,!rmal capacity has ! dim5sions 99,,ml99-#c1 !rmal conductivity1 99,,ml99-#a99,t99-#a4 ,9 ,magnetism ! dim5sions ( ! /r5g? ( pole are 99,m99#a_/b99,l99#c_/b99,t99-#a1 ! dim5sions ( field-int5sity are 99,m99#a_/b99,l99-#a_/b99,t99-#a1 & ! int5sity ( magnetisation has ! same dim5sions4 ,9 ! sci5ce ( electricity physici/s h to deal ) num]\s k9ds ( quantity1 & _! dim5sions are diff]5t too 9 ! electro-/atic & ! electro-magnetic sy/ems4 ,?us electro-motive =ce has ! dim5sions 99,m99#a_/b99,l99#a_/b99,t99-#a1 9 ! =m]1 & 99,m99#a_/b99,l99#c_/b99,t99-#b 9 ! latt] sy/em4 ,capacity simply dep5ds ^u l5g? 9 electro-/atics1 b ^u 99,l99-#a99,t99#b 9 electro-magnetics4 ,x is wor?y ( p>ticul> notice t electrical quantities h simple dim5sions :5 express$ 9 t]ms ( d5sity in/ead ( mass4 ,! in/ances n[ giv5 are suffici5t to %[ ! difficulty ( conceiv+ & foll[+ out ! relations ( ! quantities treat$ 9 physical sci5ce )\t a sy/ematic me?od ( calculat+ & exhibit+ _! dim5sions4 ,x is only 9 q rec5t ye>s t cle> ideas ab\t ^! quantities h be5 atta9$4 ,half a c5tury ago probably no "o b ,f\ri] c\ld h expla9$ :at he meant by temp]ature or capacity = heat4 ,! notion ( measur+ electricity _h h>dly be5 ent]ta9$4 ,besides af=d+ u a cle> view ( ! complex relations ( physical quantities1 ?is !ory is specially useful 9 two ways4 ,fir/ly1 x af=ds a te/ ( ! correctness ( ma!matical reason+4 ,accord+ to ! 99,pr9ciple ( ,homog5eity991 all ! quantities 99add$99 toge!r1 & equat$ 9 any equation1 mu/ h ! same dim5sions4 ,h5ce if1 on e/imat+ ! dim5sions ( ! t]ms 9 any equation1 !y be n homog5e\s1 "s blund] mu/ h be5 committ$4 ,x is impossible to add a =ce to a velocity1 or a mass to a mom5tum4 ,ev5 if ! num]ical values ( ! two memb]s ( a non-homog5e\s equation 7 equal1 ?is w\ld be accid5tal1 & any alt]ation 9 ! physical units w\ld produce inequality & disclose ! falsity ( ! law express$ 9 ! equation4 ,secondly1 ! !ory ( units enables u readily & infallibly to d$uce ! *ange 9 ! num]ical expression ( any physical quantity1 produc$ by a *ange 9 ! fundam5tal units4 ,x is ( c\rse obvi\s t 9 ord] to repres5t ! same absolute quantity1 a numb] mu/ v>y inv]sely z ! magnitude ( ! units :i* are numb]$4 ,! y>d express$ 9 feet is #c2 tak+ ! in* z ! unit in/ead ( ! foot x becomes #cf4 ,e quantity into :i* ! dim5sion l5g? ent]s positively mu/ be alt]$ 9 l mann]4 ,*ang+ ! unit f ! foot to ! in*1 num]ical expressions ( volume mu/ be multipli$ by #ab #ab #ab4 ,:5 a dim5sion ent]s negatively ! opposite rule w hold4 ,if = ! m9ute we sub/itute ! second z unit ( "t1 !n we mu/ divide all numb]s express+ angul> velocities by #fj1 & numb]s express+ angul> accel]ation by #fj #fj4 ,! rule is t a num]ical expression v>ies inv]sely z ! magnitude ( ! unit z reg>ds ea* :ole dim5sion ent]+ positively1 & x v>ies directly z ! magnitude ( ! unit = ea* :ole dim5sion ent]+ negatively4 ,9 ! case ( fractional expon5ts1 ! prop] root ( ! ratio ( *ange has to be tak54 ,! /udy ( ?is subject may be cont9u$ 9 ,pr(essor ,j4 ,d4 ,ev]ett's 8,illu/rations ( ! ,c5timetre-gramme-second ,sy/em ( ,units10 publi%$ by ,taylor & ,francis1 #ahge2 9 ,pr(essor ,maxwell's 8,!ory ( ,heat20 or ,pr(essor ,fleem+ ,j5k9's 8,text ,book ( ,electricity40 99,natural ,con/ants499 ,hav+ acquir$ accurate measur+ in/rum5ts1 & decid$ ^u ! units 9 :i* ! results %all be express$1 !re rema9s ! "q1 ,:at use %all be made ( our p[]s ( measurem5t8 ,our pr9cipal object mu/ be to discov] g5]al quantitative laws ( nature2 b a v l>ge am\nt ( prelim9>y lab\r is employ$ 9 ! accurate det]m9ation ( ! dim5sions ( exi/+ objects1 & ! num]ical relations betwe5 div]se =ces & ph5om5a4 ,/ep by /ep e "p ( ! mat]ial univ]se is survey$ & br\ght into kn[n relations ) o!r p>ts4 ,ea* manife/ation ( en]gy is correlat$ ) ea* o!r k9d ( manife/ation4 ,pr(essor ,tyndall has describ$ ! c>e ) :i* su* op]ations are conduct$4#bbi #bbi ,tyndall's 99,s\nd991 #a/ ed4 p4 #bf4 8,^? :o are unacqua9t$ ) ! details ( sci5tific inve/igation1 h no idea ( ! am\nt ( lab\r exp5d$ on ! det]m9ation ( ^? numb]s on :i* important calculations or inf]5ces dep5d4 ,!y h no idea ( ! pati5ce %[n by a ,b]zelius 9 det]m9+ atomic weights2 by a ,regnault 9 det]m9+ coeffici5ts ( expansion2 or by a ,j\le 9 det]m9+ ! me*anical equival5t ( heat4 ,!re is a morality br\ght to be> ^u su* matt]s :i*1 9 po9t ( sev]ity1 is probably )\t a p>allel 9 any o!r doma9 ( intellectual action40 ,e new natural con/ant :i* is record$ br+s _m fre% inf]5ces )9 our p[]4 ,= if 99n99 be ! numb] ( su* con/ants kn[n1 !n #a_/b 799n99#b--99n997 is ! numb] ( ratios :i* are )9 our p[]s ( calculation1 & ?is increases ) ! squ>e ( 99n994 ,we ?us gradually piece toge!r a map ( nature1 9 :i* ! l9es ( inf]5ce f "o ph5om5on to ano!r rapidly gr[ 9 complexity1 & ! p[]s ( sci5tific pr$iction are correspond+ly augm5t$4 ,babbage#bcj propos$ ! =mation ( a collection ( ! con/ant numb]s ( nature1 a "w :i* has at la/ be5 tak5 9 h& by ! ,smi?sonian ,in/itution4#bca ,x is true t a complete collection ( su* numb]s w\ld be almo/ co-ext5sive ) sci5tific lit]ature1 s9ce almo/ all ! numb]s occurr+ 9 works on *emi/ry1 m9]alogy1 physics1 a/ronomy1 c41 w\ld h to be includ$4 ,/ill a h&y volume giv+ all ! m important numb]s & _! log>i?ms1 ref]r$ :5 requisite to ! diff]5t units 9 common use1 w\ld be v useful4 ,a small collection ( con/ant numb]s w be f\nd at ! end ( ,babbage's1 ,hutton's1 & _m o!r tables ( log>i?ms1 & a some:at l>g] collection is giv5 9 ,templeton's 99,millwright & ,eng9e]'s ,pocket ,companion994 #bcj ,briti% ,association1 ,cambridge1 #ahcc4 ,report1 pp4 #dhd-dij4 #bca 99,smi?sonian ,miscellane\s ,collections991 vol4 xii41 ! ,con/ants ( ,nature1 "p4 i4 ,specific gravities compil$ by ,f4 ,w4 ,cl>ke1 #hvo4 ,wa%+ton1 #ahgc4 ,our pres5t object w be to classify ^! con/ant numb]s r\ghly1 accord+ to _! comp>ative g5]ality & importance1 "u ! foll[+ heads3-- 7#a7 ,ma!matical con/ants4 7#b7 ,physical con/ants4 7#c7 ,a/ronomical con/ants4 7#d7 ,t]re/rial numb]s4 7#e7 ,organic numb]s4 7#f7 ,social numb]s4 99,ma!matical ,con/ants499 ,at ! head ( ! li/ ( natural con/ants mu/ come ^? :i* express ! necess>y relations ( numb]s to ea* o!r4 ,! ord9>y ,multiplication ,table is ! mo/ famili> & ! mo/ important ( su* s]ies ( con/ants1 & is1 !oretically speak+1 inf9ite 9 ext5t4 ,next we mu/ place ! ,ari?metical ,triangle1 ! significance ( :i* has already be5 po9t$ out 7p4 #ahb74 ,tables ( log>i?ms also conta9 va/ s]ies ( natural con/ants1 aris+ out ( ! relations ( pure numb]s4 ,at ! base ( all log>i?mic !ory is ! my/]i\s natural con/ant commonly d5ot$ by 99e991 or 1 be+ equal to ! inf9ite s]ies #a #a_/a #a_/a4b #a_/a4b4c #a_/a4b4c4d 44441 & ?us consi/+ ( ! sum ( ! ratios betwe5 ! numb]s ( p]mutations & comb9ations ( #j1 #a1 #b1 #c1 #d1 c4 ?+s4 ,tables ( prime numb]s & ( ! factors ( composite numb]s mu/ n be =gott54 ,ano!r va/ & 9 fact inf9ite s]ies ( num]ical con/ants conta9s ^? connect$ ) ! measurem5t ( angles1 & embodi$ 9 trigonometrical tables1 :e!r z natural or log>i?mic s9es1 cos9es1 & tang5ts4 ,x %\ld nev] be =gott5 t ?\gh ^! numb]s f9d _! *ief employm5t 9 connection ) trigonometry1 or ! measurem5t ( ! sides ( a "r-angl$ triangle1 yet ! numb]s !mselves arise out ( num]ical relations be>+ no special relation to space4 ,=emo/ among trigonometrical con/ants is ! well kn[n numb] 1 usually employ$ z express+ ! ratio ( ! circumf]5ce & ! diamet] ( a circle2 f foll[s ! value ( ! arcual or natural unit ( angul> value z express$ 9 ord9>y degrees 7p4 #cjf74 ,among o!r ma!matical con/ants n uncommonly us$ may be m5tion$ tables ( factorials 7p4 #agi71 tables ( ,b]n\lli's numb]s1 tables ( ! error function1#bcb :i* latt] are indisp5sable n only 9 ! !ory ( probability b also 9 sev]al o!r bran*es ( sci5ce4 #bcb ,j4 ,w4 ,l4 ,glai%]1 99,philosophical ,magaz9e991 #d? ,s]ies1 vol4 xlii4 p4 #dba4 ,x %\ld be cle>ly und]/ood t ! ma!matical con/ants & tables ( ref]5ce already 9 our possession1 al?\gh v ext5sive1 are only an inf9itely small "p ( :at might be =m$4 ,) ! progress ( sci5ce ! tabulation ( new functions w be cont9ually dem&$1 & x is wor?y ( consid]ation :e!r public money %\ld n be available to rew>d ! sev]e1 long cont9u$1 & g5]ally ?ankless lab\r :i* mu/ be gone ?r\gh 9 calculat+ tables4 ,su* lab\rs are a b5efit to ! :ole human race z long z x %all exi/1 ?\gh !re are few :o c appreciate ! ext5t ( ?is b5efit4 ,a mo/ int]e/+ & excell5t description ( _m ma!matical tables w be f\nd 9 ,de ,morgan's article on 99,tables991 9 ! 99,engli% ,cyclopdia991 ,division ( ,arts & ,sci5ces1 vol4 vii4 p4 #igf4 ,an almo/ exhau/ive critical catalogue ( extant tables is be+ publi%$ by a ,committee ( ! ,briti% ,association1 two portions1 drawn up *iefly by ,mr4 ,j4 ,w4 ,l4 ,glai%] & ,pr(essor ,cayley1 hav+ appe>$ 9 ! ,reports ( ! ,association = #ahgc & #ahge4 99,physical ,con/ants499 ,! second class ( con/ants conta9s ^? :i* ref] to ! actual con/itution ( matt]4 ,= ! mo/ "p !y dep5d ^u ! peculi>ities ( ! *emical sub/ance 9 "q1 b we may beg9 ) ^? :i* are ( ! mo/ g5]al "*4 ,9 a fir/ sub-class we may place ! velocity ( light or heat undulations1 ! numb]s express+ ! relation betwe5 ! l5g?s ( ! undulations1 & ! rapidity ( ! undulations1 ^! numb]s dep5d+ only on ! prop]ties ( ! e!real m$ium1 & be+ probably ! same 9 all p>ts ( ! univ]se4 ,! !ory ( heat gives rise to sev]al numb]s ( ! highe/ importance1 especially ,j\le's me*anical equival5t ( heat1 ! absolute z]o ( temp]ature1 ! mean temp]ature ( empty space1 c4 ,tak+ into acc\nt ! div]se prop]ties ( ! elem5ts we mu/ h tables ( ! atomic weights1 ! specific heats1 ! specific gravities1 ! refractive p[]s1 n only ( ! elem5ts1 b _! almo/ inf9itely num]\s comp\nds4 ,! prop]ties ( h>dness1 ela/icity1 viscosity1 expansion by heat1 conduct+ p[]s = heat & electricity1 mu/ also be det]m9$ 9 imm5se detail4 ,!re are1 h[ev]1 c]ta9 ( ^! numb]s :i* /& out prom95tly because !y s]ve z int]m$iate units or t]ms ( comp>ison4 ,su* are1 = in/ance1 ! absolute coeffici5ts ( expansion ( air1 wat] & m]cury1 ! temp]ature ( ! maximum d5sity ( wat]1 ! lat5t heats ( wat] & /eam1 ! boil+-po9t ( wat] "u /&>d pressure1 ! melt+ & boil+-po9ts ( m]cury1 & s =?4 99,a/ronomical ,con/ants499 ,! ?ird great class consi/s ( numb]s possess+ f> less g5]ality because !y ref] n to ! prop]ties ( matt]1 b to ! special =ms & di/ances 9 :i* matt] has be5 dispos$ 9 ! "p ( ! univ]se op5 to our exam9ation4 ,we h1 fir/ ( all1 to def9e ! magnitude & =m ( ! e>?1 its mean d5sity1 ! con/ant ( ab]ration ( light express+ ! relation betwe5 ! e>?'s mean velocity 9 space & ! velocity ( light4 ,f ! e>?1 z our obs]vatory1 we !n proce$ to lay d[n ! mean di/ances ( ! sun1 & ( ! planets f ! same c5tre2 all ! elem5ts ( ! planet>y orbits1 ! magnitudes1 d5sities1 masses1 p]iods ( axial rotation ( ! sev]al planets are by degrees det]m9$ ) gr[+ accuracy4 ,! same lab\rs mu/ be gone ?r\gh = ! satellites4 ,catalogues ( comets ) ! elem5ts ( _! orbits1 z f> z asc]ta9able1 mu/ n be omitt$4 ,f ! e>?'s orbit z a new base ( obs]vations1 we next proce$ to survey ! heav5s & lay d[n ! app>5t positions1 magnitudes1 motions1 di/ances1 p]iods ( v>iation1 c4 ( ! />s4 ,all catalogues ( />s f ^? ( ,hipp>*us & ,ty*o1 are full ( numb]s express+ rudely ! con=mation ( ! visible univ]se4 ,b !re is obvi\sly no limit to ! lab\rs ( a/ronom]s2 n only are millions ( di/ant />s await+ _! fir/ measurem5ts1 b ^? already regi/]$ require endless scrut9y z reg>ds _! movem5ts 9 ! ?ree dim5sions ( space1 _! p]iods ( revolution1 _! *anges ( brilliance & col\r4 ,x is obvi\s t ?\gh a/ronomical numb]s are conv5tionally call$ 99con/ant991 !y are probably 9 all cases subject to m or less rapid v>iation4 99,t]re/rial ,numb]s499 ,our k ( ! globe we inhabit involves _m num]ical det]m9ations1 :i* h little or no connection ) a/ronomical !ory4 ,! extreme heights ( ! pr9cipal m\nta9s1 ! mean elevations ( cont95ts1 ! mean or extreme dep?s ( ! oceans1 ! specific gravities ( rocks1 ! temp]ature ( m9es1 ! ho/ ( numb]s express+ ! meteorological or magnetic conditions ( e "p ( ! surface1 mu/ fall into ?is class4 ,_m su* numb]s are n to be call$ con/ant1 be+ subject to p]iodic or secul> *anges1 b !y are h>dly m v>iable 9 fact ?an "s :i* 9 a/ronomical sci5ce are set d[n z con/ant4 ,9 _m cases quantities :i* seem mo/ v>iable may g ?r\gh rhy?mical *anges result+ 9 a ne>ly uni=m av]age1 & x is only 9 ! long progress ( physical inve/igation t we c hope to discrim9ate successfully betwe5 ^? elem5tal numb]s :i* are fix$ & ^? :i* v>y4 ,9 ! latt] case ! law ( v>iation becomes ! con/ant relation :i* is ! object ( our se>*4 99,organic ,numb]s499 ,! =ms & prop]ties ( brute nature hav+ be5 suffici5tly def9$ by ! previ\s classes ( numb]s1 ! organic _w1 bo? vegetable & animal1 rema9s out/&+1 & (f]s a high] s]ies ( ph5om5a = our inve/igation4 ,all exact k relat+ to ! =ms & sizes ( liv+ ?+s1 _! numb]s1 ! quantities ( v>i\s comp\nds :i* !y consume1 conta91 or excrete1 _! muscul> or n]v\s en]gy1 c4 mu/ be plac$ ap>t 9 a class by !mselves4 ,all su* numb]s are d\btless m or less subject to v>iation1 & b 9 a m9or degree capable ( exact det]m9ation4 ,man1 s f> z he is an animal1 & z reg>ds 8 physical =m1 mu/ also be treat$ 9 ?is class4 99,social ,numb]s499 ,little allusion ne$ be made 9 ?is "w to ! fact t man 9 8 economic1 sanit>y1 intellectual1 /hetic1 or moral relations may become ! subject ( sci5ces1 ! highe/ & mo/ useful ( all sci5ces4 ,e "o :o is engag$ 9 /ati/ical inquiry mu/ ackn[l$ge ! possibility ( natural laws gov]n+ su* /ati/ical facts4 ,h5ce we mu/ allot a di/9ct place to num]ical in=mation relat+ to ! numb]s1 ages1 physical & sanit>y condition1 mortality1 c41 ( diff]5t peoples1 9 %ort1 to vital /ati/ics4 ,economic /ati/ics1 compreh5d+ ! quantities ( commodities produc$1 exi/+1 ex*ang$ & consum$1 con/itute ano!r ext5sive body ( sci5ce4 ,9 ! progress ( "t exact inve/igation may possibly subdue regions ( ph5om5a :i* at pres5t defy all sci5tific treatm5t4 ,t sci5tific me?od c ev] exhau/ ! ph5om5a ( ! human m9d is incr$ible4 ,,*apt] ,,xv4 ,,analysis ,,( ,,quantitative ,,ph5om5a4 ,9 ! two prec$+ *apt]s we h be5 engag$ 9 consid]+ h[ a ph5om5on may be accurately measur$ & express$4 ,s delicate & complex an op]ation is a measurem5t :i* pret5ds to any consid]able degree ( exactness1 t no small "p ( ! skill & pati5ce ( physici/s is usually sp5t ^u ?is "w4 ,mu* ( ?is difficulty arises f ! fact t x is sc>cely ev] possible to measure a s+le effect at a "t4 ,! ultimate object mu/ be to discov] ! ma!matical equation or law connect+ a quantitative cause ) its quantitative effect2 ?is purpose usually involves1 z we %all see1 ! v>y+ ( "o condition at a "t1 ! o!r conditions be+ ma9ta9$ con/ant4 ,! lab\rs ( ! exp]im5tali/ w\ld be comp>atively light if he c\ld c>ry out ?is rule ( v>y+ "o circum/ance at a "t4 ,he w\ld !n obta9 a s]ies ( correspond+ values ( ! v>iable quantities conc]n$1 f :i* he might by prop] hypo!tical treatm5t obta9 ! requir$ law ( connection4 ,b 9 reality x is seldom possible to c>ry out ?is direction except 9 an approximate mann]4 ,be=e !n we proce$ to ! consid]ation ( ! actual process ( quantitative induction1 x is necess>y to review ! sev]al devices by :i* a complicat$ s]ies ( effects c be dis5tangl$4 ,e ph5om5on measur$ w usually be ! sum1 diff]5ce1 or x may be ! product or quoti5t1 ( two or m diff]5t effects1 & ^! mu/ be 9 "s way analys$ & sep>ately measur$ be=e we possess ! mat]ials = inductive treatm5t4 99,illu/rations ( ! ,complication ( ,effects499 ,x is easy to br+ =w>d a multitude ( in/ances to %[ t a ph5om5on is seldom to be obs]v$ simple & alone4 ,a m or less elaborate process ( analysis is almo/ always necess>y4 ,?us if an exp]im5tali/ wi%es to obs]ve & measure ! expansion ( a liquid by heat1 he places x 9 a !rmomet] tube & regi/]s ! rise ( ! column ( liquid 9 ! n>r[ tube4 ,b he _c heat ! liquid )\t also heat+ ! glass1 s t ! *ange obs]v$ is really ! diff]5ce betwe5 ! expansions ( ! liquid & ! glass4 ,m m9ute inve/igation w %[ ! necessity p]haps ( all[+ = fur!r m9ute effects1 namely ! compression ( ! liquid & ! expansion ( ! bulb due to ! increas$ pressure ( ! column z x becomes l5g!n$4 ,9 a great _m cases an obs]v$ effect w be app>5tly at lea/ ! simple sum ( two sep>ate & indep5d5t effects4 ,! heat evolv$ 9 ! combu/ion ( oil is p>tly due to ! c>bon & p>tly to ! hydrog54 ,a measurem5t ( ! heat yield$ by ! two jo9tly1 _c in=m u h[ mu* proce$s f ! "o & h[ mu* f ! o!r4 ,if by "s sep>ate det]m9ation we c asc]ta9 h[ mu* ! hydrog5 yields1 !n by m]e subtraction we le>n :at is due to ! c>bon2 & 99vice v]s994 ,! heat convey$ by a liquid1 may be p>tly convey$ by true conduction1 p>tly by convection4 ,! light disp]s$ 9 ! int]ior ( a liquid consi/s bo? ( :at is reflect$ by float+ p>ticles & :at is due to true fluoresc5ce2#bcc & we mu/ f9d "s mode ( det]m9+ "o portion be=e we c le>n ! o!r4 ,! app>5t motion ( ! spots on ! sun1 is ! algebraic sum ( ! sun's axial rotation1 & ( ! prop] motion ( ! spots ^u ! sun's surface2 h5ce ! difficulty ( asc]ta9+ by direct obs]vations ! p]iod ( ! sun's rotation4 #bcc ,/okes1 99,philosophical ,transactions99 7#aheb71 vol4 cxlii4 p4 #ebi4 ,we _c obta9 ! weight ( a portion ( liquid 9 a *emical balance )\t weigh+ x ) ! conta9+ vessel4 ,h5ce to h ! real weight ( ! liquid op]at$ ^u 9 an exp]im5t1 we mu/ make a sep>ate weigh+ ( ! vessel1 ) or )\t ! adh]+ film ( liquid accord+ to circum/ances4 ,?is is likewise ! mode 9 :i* a c>t & its load are weigh$ toge!r1 ! 99t>e99 ( ! c>t previ\sly asc]ta9$ be+ d$uct$4 ,! v>iation 9 ! height ( ! b>omet] is a jo9t effect1 p>tly due to ! real v>iation ( ! atmosph]ic pressure1 p>tly to ! expansion ( ! m]curial column by heat4 ,! effects may be discrim9at$1 if1 in/ead ( "o b>omet] tube we h two tubes conta9+ m]cury plac$ closely side by side1 s z to h ! same temp]ature4 ,if "o ( !m be clos$ at ! bottom s z to be unaffect$ by ! atmosph]ic pressure1 x w %[ ! *anges due to temp]ature only1 &1 by subtract+ ^! *anges f ^? %[n 9 ! o!r tube1 employ$ z a b>omet]1 we get ! real oscillations ( atmosph]ic pressure4 ,b ?is correction1 z x is call$1 ( ! b>ometric read+1 is bett] effect$ by calculation f ! read+s ( an ord9>y !rmomet]4 ,9 o!r cases a quantitative effect w be ! diff]5ce ( two causes act+ 9 opposite directions4 ,sir ,john ,h]s*el inv5t$ an in/rum5t l a l>ge !rmomet]1 :i* he call$ ! ,act9omet]1#bcd & ,p\illet con/ruct$ a some:at simil> in/rum5t call$ ! ,pyrheliomet]1 = asc]ta9+ ! heat+ p[] ( ! sun's rays4 ,9 bo? in/rum5ts ! heat ( ! sun 0 absorb$ by a res]voir conta9+ wat]1 & ! rise ( temp]ature ( ! wat] 0 exactly obs]v$1 ei!r by its own expansion1 or by ! read+s ( a delicate !rmomet] imm]s$ 9 x4 ,b 9 expos+ ! act9omet] to ! sun1 we d n obta9 ! full effect ( ! heat absorb$1 because ! receiv+ surface is at ! same "t radiat+ heat into empty space4 ,! obs]v$ increm5t ( temp]ature is 9 %ort ! diff]5ce betwe5 :at is receiv$ f ! sun & lo/ by radiation4 ,! latt] quantity is capable ( ready det]m9ation2 we h only to %ade ! in/rum5t f ! direct rays ( ! sun1 leav+ x expos$ to ! sky1 & we c obs]ve h[ mu* x cools 9 a c]ta9 "t4 ,! total effect ( ! sun's rays w obvi\sly be ! app>5t effect 99plus99 ! cool+ effect 9 an equal "t4 ,by alt]nate exposure 9 sun & %ade dur+ equal int]vals ! desir$ result may be obta9$ ) consid]able accuracy4#bce #bcd 99,admiralty ,manual ( ,sci5tific ,enquiry991 #bnd ed4 p4 #bii4 #bce ,p\illet1 99,taylor's ,sci5tific ,memoirs991 vol4 iv4 p4 #de4 ,two quantitative effects 7 beautifully di/+ui%$ 9 an exp]im5t ( ,john ,canton1 devis$ 9 #agfa = ! purpose ( demon/rat+ ! compressibility ( wat]4 ,he con/ruct$ a !rmomet] ) a l>ge bulb full ( wat] & a %ort capill>y tube1 ! "p ( :i* above ! wat] 0 fre$ f air4 ,"u ^! circum/ances ! wat] 0 reliev$ f ! pressure ( ! atmosph]e1 b ! glass bulb 9 be>+ t pressure 0 some:at contract$4 ,he next plac$ ! in/rum5t "u ! receiv] ( an air-pump1 & on exhau/+ ! air1 ! wat] sank 9 ! tube4 ,hav+ ?us obta9$ a measure ( ! effect ( atmosph]ic pressure on ! bulb1 he op5$ ! top ( ! !rmomet] tube & admitt$ ! air4 ,! level ( ! wat] n[ sank /ill m1 p>tly f ! pressure on ! bulb be+ n[ comp5sat$1 & p>tly f ! compression ( ! wat] by ! atmosph]ic pressure4 ,x is obvi\s t ! am\nt ( ! latt] effect 0 approximately ! diff]5ce ( ! two obs]v$ depressions4 ,n uncommonly ! actual ph5om5on :i* we wi% to measure is consid]ably less ?an v>i\s di/urb+ effects :i* ent] into ! "q4 ,?us ! compressibility ( m]cury is consid]ably less ?an ! expansion ( ! vessels 9 :i* x is measur$ "u pressure1 s t ! att5tion ( ! exp]im5tali/ has *iefly to be conc5trat$ on ! *ange ( magnitude ( ! vessels4 ,_m a/ronomical ph5om5a1 su* z ! p>allax or ! prop] motions ( ! fix$ />s1 are f> less ?an ! errors caus$ by in/rum5tal imp]fections1 or motions aris+ f precession1 nutation1 & ab]ration4 ,we ne$ n be surpris$ t a/ronom]s h f "t to "t mi/ak5 "o ph5om5on = ano!r1 z :5 ,flam/e$ imag9$ t he _h discov]$ ! p>allax ( ! ,pole />4#bcf #bcf ,baily's 99,acc\nt ( ! ,rev4 ,john ,flam/e$991 p4 #eh4 99,me?ods ( ,elim9at+ ,error499 ,9 any p>ticul> exp]im5t x is ! object ( ! exp]im5tali/ to measure a s+le effect only1 & he endeav\rs to obta9 t effect free f int]f]+ effects4 ,if ?is _c be1 z x seldom or nev] c really be1 he makes ! effect z consid]able z possible comp>$ ) ! o!r effects1 :i* he r$uces to a m9imum1 & treats z noxi\s errors4 ,^? quantities1 :i* are call$ 99errors99 9 "o case1 may really be mo/ important & int]e/+ ph5om5a 9 ano!r inve/igation4 ,:5 we speak ( elim9at+ error we really mean dis5tangl+ ! complicat$ ph5om5a ( nature4 ,! physici/ rightly wi%es to treat "o ?+ at a "t1 b z ?is object c seldom be rigor\sly c>ri$ into practice1 he has to seek "s mode ( c\nt]act+ ! irrelevant & int]f]+ causes4 ,! g5]al pr9ciple is t a s+le obs]vation c r5d] kn[n only a s+le quantity4 ,h5ce1 if sev]al diff]5t quantitative effects are kn[n to ent] into any inve/igation1 we mu/ h at lea/ z _m di/9ct obs]vations z !re are quantities to be det]m9$4 ,e complete exp]im5t w !re=e consi/ 9 g5]al ( sev]al op]ations4 ,guid$ if possible by previ\s k ( ! causes 9 action1 we mu/ arrange ! det]m9ations1 s t by a simple ma!matical process we may di/+ui% ! sep>ate quantities4 ,!re appe> to be five pr9cipal me?ods by :i* we may accompli% ?is object2 ^! me?ods are specifi$ bel[ & illu/rat$ 9 ! succe$+ sections4 7#a7 99,! ,me?od ( ,avoidance499 ,! physici/ may seek = "s special mode ( exp]im5t or opportunity ( obs]vation1 9 :i* ! error is non-exi/5t or inappreciable4 7#b7 99,! ,diff]5tial ,me?od499 ,he may f9d opportunities ( obs]vation :5 all int]f]+ ph5om5a rema9 con/ant1 & only ! subject ( obs]vation is at "o "t pres5t & ano!r "t abs5t2 ! diff]5ce betwe5 two obs]vations !n gives its am\nt4 7#c7 99,! ,me?od ( ,correction499 ,he may endeav\r to e/imate ! am\nt ( ! int]f]+ effect by ! be/ available mode1 & !n make a correspond+ correction 9 ! results ( obs]vation4 7#d7 99,! ,me?od ( ,comp5sation499 ,he may inv5t "s mode ( neutralis+ ! int]f]+ cause by balanc+ aga9/ x an exactly equal & opposite cause ( unkn[n am\nt4 7#e7 99,! ,me?od ( ,rev]sal499 ,he may s conduct ! exp]im5t t ! int]f]+ cause may act 9 opposite directions1 9 alt]nate obs]vations1 ! mean result be+ free f int]f]5ce4 ,i4 99,me?od ( ,avoidance ( ,error499 ,a/ronom]s seek opportunities ( obs]vation :5 errors w be z small z possible4 ,9 spite ( elaborate obs]vations & long-cont9u$ !oretical inve/igation1 x is n practicable to assign any satisfactory law to ! refractive p[] ( ! atmosph]e4 ,al?\gh ! app>5t *ange ( place ( a heav5ly body produc$ by refraction may be m or less accurately calculat$ yet ! error dep5ds ^u ! temp]ature & pressure ( ! atmosph]e1 &1 :5 a ray is highly incl9$ to ! p]p5dicul>1 ! unc]ta9ty 9 ! refraction becomes v consid]able4 ,h5ce a/ronom]s always make _! obs]vations1 if possible1 :5 ! object is at ! highe/ po9t ( its daily c\rse1 99i4e499 on ! m]idian4 ,9 "s k9ds ( inve/igation1 z1 = in/ance1 9 ! det]m9ation ( ! latitude ( an obs]vatory1 ! a/ronom] is at lib]ty to select "o or m />s out ( ! c\ntless numb] visible4 ,!re is an evid5t advantage 9 su* a case1 9 select+ a /> :i* passes close to ! z5i?1 s t x may be obs]v$ almo/ entirely free f atmosph]ic refraction1 z 0 done by ,hooke4 ,a/ronom]s endeav\r to r5d] _! clocks z accurate z possible1 by remov+ ! s\rce ( v>iation4 ,! p5dulum is p]fectly iso*ron\s s long z its l5g? rema9s inv>iable1 & ! vibrations are exactly ( equal l5g?4 ,!y r5d] x ne>ly inv>iable 9 l5g?1 t is 9 ! di/ance betwe5 ! c5tres ( susp5sion & oscillation1 by a comp5satory arrangem5t = ! *ange ( temp]ature4 ,b z ?is comp5sation may n be p]fectly accompli%$1 "s a/ronom]s place _! *ief controll+ clock 9 a cell>1 or o!r ap>tm5t1 :]e ! *anges ( temp]ature may be z slight z possible4 ,at ! ,p>is ,obs]vatory a clock has be5 plac$ 9 ! caves b5ea? ! build+1 :]e !re is no appreciable diff]5ce betwe5 ! summ] & w9t] temp]ature4 ,to avoid ! effect ( unequal oscillations ,huygh5s made 8 beautiful inve/igations1 :i* result$ 9 ! discov]y t a p5dulum1 ( :i* ! c5tre ( oscillation mov$ ^u a cycloidal pa?1 w\ld be p]fectly iso*ron\s1 :atev] ! v>iation 9 ! l5g? ( oscillations4 ,b ?\gh a p5dulum may be easily r5d]$ 9 "s degree cycloidal by ! use ( a /eel susp5sion spr+1 x is f\nd t ! me*anical arrangem5ts requisite to produce a truly cycloidal motion introduce m error ?an !y remove4 ,h5ce a/ronom]s seek to r$uce ! error to ! smalle/ am\nt by ma9ta9+ _! clock p5dulums 9 uni=m movem5t2 9 fact1 :ile a clock is 9 good ord] & has ! same weights1 !re ne$ be little *ange 9 ! l5g? ( oscillation4 ,:5 a p5dulum _c be made to sw+ uni=mly1 z 9 exp]im5ts ^u ! =ce ( gravity1 x becomes requisite to resort to ! ?ird me?od1 & a correction is introduc$1 calculat$ on !oretical gr\nds f ! am\nt ( ! obs]v$ *ange 9 ! l5g? ( vibration4 ,x has be5 m5tion$ t ! app>5t expansion ( a liquid by heat1 :5 conta9$ 9 a !rmomet] tube or o!r vessel1 is ! diff]5ce betwe5 ! real expansion ( ! liquid & t ( ! conta9+ vessel4 ,! effects c be accurately di/+ui%$ provid$ t we c le>n ! real expansion by heat ( any "o conv5i5t liquid2 = by obs]v+ ! app>5t expansion ( ! same liquid 9 any requir$ vessel we c by diff]5ce le>n ! am\nt ( expansion ( ! vessel due to any giv5 *ange ( temp]ature4 ,:5 we once "k ! *ange ( dim5sions ( ! vessel1 we c ( c\rse det]m9e ! absolute expansion ( any o!r liquid te/$ 9 x4 ,?us x became an all-important object 9 sci5tific rese>* to measure ) accuracy ! absolute dilatation by heat ( "s "o liquid1 & m]cury ow+ to sev]al circum/ances 0 by f> ! mo/ suitable4 ,dulong & ,petit devis$ a beautiful mode ( effect+ ?is by simply avoid+ altoge!r ! effect ( ! *ange ( size ( ! vessel4 ,two upright tubes full ( m]cury 7 connect$ by a f9e tube at ! bottom1 & 7 ma9ta9$ at two diff]5t temp]atures4 ,z m]cury 0 free to fl[ f "o tube to ! o!r by ! connect+ tube1 ! two columns necess>ily ex]t$ equal pressures by ! pr9ciples ( hydro/atics4 ,h5ce x 0 only necess>y to measure v accurately by a ca!tomet] ! diff]5ce ( level ( ! surfaces ( ! two columns ( m]cury1 to le>n ! diff]5ce ( l5g? ( columns ( equal hydro/atic pressure1 :i* at once gives ! diff]5ce ( d5sity ( ! m]cury1 & ! dilatation by heat4 ,! *anges ( dim5sion 9 ! conta9+ tubes became a matt] ( entire indiff]5ce1 & ! l5g? ( a column ( m]cury at diff]5t temp]atures 0 measur$ z easily z if x _h =m$ a solid b>4 ,! exp]im5t 0 c>ri$ out by ,regnault ) _m improvem5ts ( detail1 & ! absolute dilatation ( m]cury1 at temp]atures betwe5 #j ,c5t4 & #cej1 0 det]m9$ almo/ z accurately z 0 ne$ful4#bcg #bcg ,jam91 99,c\rs de ,physique991 vol4 ii4 pp4 #ae-bh4 ,! pres5ce ( a l>ge & unc]ta9 am\nt ( error may r5d] a me?od ( exp]im5t valueless4 ,f\cault devis$ a beautiful exp]im5t ) ! p5dulum = demon/rat+ popul>ly ! rotation ( ! e>?1 b x c\ld be ( no use = measur+ ! rotation exactly4 ,x is impossible to make ! p5dulum sw+ 9 a p]fect plane1 & ! slighte/ lat]al motion gives x an elliptic pa? ) a progressive motion ( ! axis ( ! ellipse1 :i* disguises & (t5 entirely ov]p[]s t due to ! rotation ( ! e>?4#bch #bch 99,philosophical ,magaz9e991 #ahea1 #d? ,s]ies1 vol4 ii4 99passim994 ,f>aday's labori\s exp]im5ts on ! relation ( gravity & electricity 7 mu* ob/ruct$ by ! fact t x is impossible to move a l>ge weight ( metal )\t g5]at+ curr5ts ( electricity1 ei!r by friction or induction4 ,to di/+ui% ! electricity1 if any1 directly due to ! action ( gravity f ! great] quantities indirectly produc$ 0 a problem ( excessive difficulty4 ,baily 9 8 exp]im5ts on ! d5sity ( ! e>? 0 aw>e ( ! exi/5ce ( inexplicable di/urbances :i* h s9ce be5 ref]r$ ) mu* probability to ! action ( electricity4#bci ,! skill & +5uity ( ! exp]im5tali/ are (t5 exhau/$ 9 try+ to devise a =m ( app>atus 9 :i* su* causes ( error %all be r$uc$ to a m9imum4 #bci ,he>n1 99,philosophical ,transactions991 #ahdg1 vol4 cxxxvii4 pp4 #bag-bba4 ,9 "s rudim5t>y exp]im5ts we wi% m]ely to e/abli% ! exi/5ce ( a quantitative effect )\t precisely measur+ its am\nt2 if !re exi/ causes ( error ( :i* we c nei!r r5d] ! am\nt kn[n or inappreciable1 ! be/ way is to make !m all negative s t ! quantitative effects w be less ?an ! tru? r ?an great]4 ,grove1 = in/ance1 9 prov+ t ! magnetisation or demagnetisation ( a piece ( iron raises its temp]ature1 took c>e to ma9ta9 ! electro-magnet by :i* ! iron 0 magnetis$ at a l[] temp]ature ?an ! iron1 s t x w\ld cool r ?an w>m ! iron by radiation or conduction4#bdj #bdj 99,! ,correlation ( ,physical ,=ces991 #crd ed4 p4 #aei4 ,rum=d's celebrat$ exp]im5t to prove t heat 0 g5]at$ out ( me*anical =ce 9 ! bor+ ( a cannon 0 subject to ! difficulty t heat might be br\ght to ! cannon by conduction f neighb\r+ bodies4 ,x 0 an +5i\s device ( ,davy to produce friction by a piece ( clock-"w re/+ ^u a block ( ice 9 an exhau/$ receiv]2 z ! ma*9e rose 9 temp]ature above #cb1 x 0 c]ta9 t no heat 0 receiv$ by conduction f ! support4#bda ,9 _m o!r exp]im5ts ice may be employ$ to prev5t ! access ( heat by conduction1 & ?is device1 fir/ put 9 practice by ,murray1#bdb is beautifully employ$ 9 ,buns5's calorimet]4 #bda 99,collect$ ,works ( ,sir ,h4 ,davy991 vol4 ii4 pp4 #ab-ad4 99,elem5ts ( ,*emical ,philosophy991 p4 #id4 #bdb 99,ni*olson's ,j\rnal991 vol4 i4 p4 #bda2 quot$ 9 99,treatise on ,heat991 ,useful ,k ,society1 p4 #bd4 ,to obs]ve ! true temp]ature ( ! air1 ?\gh app>5tly s easy1 is really a v difficult matt]1 because ! !rmomet] is sure to be affect$ ei!r by ! sun's rays1 ! radiation f neighb\r+ objects1 or ! escape ( heat into space4 ,^! s\rces ( error are too fluctuat+ to all[ ( correction1 s t ! only accurate mode ( proc$ure is t devis$ by ,dr4 ,j\le1 ( surr\nd+ ! !rmomet] ) a copp] cyl9d] +5i\sly adju/$ to ! temp]ature ( ! air1 z describ$ by him1 s t ! effect ( radiation %all be nullifi$4#bdc #bdc ,cl]k ,maxwell1 99,!ory ( ,heat991 p4 #bbh4 99,proce$+s ( ! ,man*e/] ,philosophical ,society991 ,nov4 #bf1 #ahfg1 vol4 vii4 p4 #ce4 ,:5 ! avoidance ( error is n practicable1 x w yet be desirable to r$uce ! absolute am\nt ( ! int]f]+ error z mu* z possible be=e employ+ ! succe$+ me?ods to correct ! result4 ,z a g5]al rule we c det]m9e a quantity ) less inaccuracy z x is small]1 s t if ! error itself be small ! error 9 det]m9+ t error w be ( a /ill l[] ord] ( magnitude4 ,b 9 "s cases ! absolute am\nt ( an error is ( no consequ5ce1 z 9 ! index error ( a divid$ circle1 or ! diff]5ce betwe5 a *ronomet] & a/ronomical "t4 ,ev5 ! rate at :i* a clock ga9s or loses is a matt] ( little importance provid$ x rema9 con/ant1 s t a sure calculation ( its am\nt c be made4 #b4 99,diff]5tial ,me?od499 ,:5 we _c avoid ! exi/5ce ( error1 we c (t5 resort ) success to ! second mode by measur+ ph5om5a "u su* circum/ances t ! error %all rema9 v ne>ly ! same 9 all ! obs]vations1 & neutralise itself z reg>ds ! purposes 9 view4 ,?is mode is available :5ev] we want a diff]5ce betwe5 quantities & n ! absolute quantity ( ei!r4 ,! det]m9ation ( ! p>allax ( ! fix$ />s is exce$+ly difficult1 because ! am\nt ( p>allax is f> less ?an mo/ ( ! corrections = atmosph]ic refraction1 nutation1 ab]ration1 precession1 in/rum5tal irregul>ities1 c41 & c ) difficulty be detect$ among ^! ph5om5a ( v>i\s magnitude4 ,b1 z ,galileo long ago sugge/$1 all su* difficulties w\ld be avoid$ by ! diff]5tial obs]vation ( />s1 :i*1 ?\gh app>5tly close toge!r1 are really f> sep>at$ on ! l9e ( sight4 ,two su* />s 9 close app>5t proximity w be subject to almo/ exactly equal errors1 s t all we ne$ d is to obs]ve ! app>5t *ange ( place ( ! ne>] /> z ref]r$ to ! m di/ant "o4 ,a good telescope furni%$ ) an accurate micromet] is alone ne$$ = ! application ( ! me?od4 ,huygh5s appe>s to h be5 ! fir/ obs]v] :o actually tri$ to employ ! me?od practically1 b x 0 n until #ahce t ! improvem5t ( telescopes & micromet]s enabl$ ,/ruve to detect 9 ?is way ! p>allax ( ! /> ,lyr4 ,x is "o ( ! _m advantages ( ! obs]vation ( transits ( ,v5us = ! det]m9ation ( ! sol> p>allax t ! refraction ( ! atmosph]e affects 9 an exactly equal degree ! planet & ! portion ( ! sun's face ov] :i* x is pass+4 ,?us ! obs]vations are /rictly ( a diff]5tial nature4 ,by ! process ( sub/itutive weigh+ x is possible to asc]ta9 ! equality or inequality ( two weights ) almo/ p]fect fre$om f error4 ,if two weights ,a & ,b be plac$ 9 ! scales ( ! be/ balance we _c be sure t ! equilibrium ( ! beam indicates exact equality1 because ! arms ( ! beam may be unequal or unbalanc$4 ,b if we take ,b out & put ano!r weight ,c 91 & equilibrium /ill exi/s1 x is app>5t t ! same causes ( errone\s weigh+ exi/ 9 bo? cases1 suppos+ t ! balance has n be5 dis>rang$2 ,b !n mu/ be exactly equal to ,c1 s9ce x has exactly ! same effect "u ! same circum/ances4 ,9 l mann] x is a g5]al rule t1 if by any uni=m me*anical process we get a copy ( an object1 x is unlikely t ?is copy w be precisely ! same z ! orig9al 9 magnitude & =m1 b two copies w equally div]ge f ! orig9al1 & w !re=e almo/ exactly resemble ea* o!r4 ,leslie's ,diff]5tial ,!rmomet]#bdd 0 well adapt$ to ! exp]im5ts = :i* x 0 inv5t$4 ,hav+ two equal bulbs any alt]ation 9 ! temp]ature ( ! air w act equally by conduction on ea* & produce no *ange 9 ! indications ( ! in/rum5t4 ,only t radiant heat :i* is purposely ?r[n ^u "o ( ! bulbs w produce any effect4 ,?is !rmomet] 9 %ort c>ries out ! pr9ciple ( ! diff]5tial me?od 9 a me*anical mann]4 #bdd ,leslie1 99,inquiry into ! ,nature ( ,heat991 p4 #aj4 #c4 99,me?od ( ,correction499 ,:5ev] ! result ( an exp]im5t is affect$ by an int]f]+ cause to a calculable am\nt1 x is suffici5t to add or subtract ?is am\nt4 ,we are said to correct obs]vations :5 we ?us elim9ate :at is due to extrane\s causes1 al?\gh ( c\rse we are only sep>at+ ! correct effects ( sev]al ag5ts4 ,! v>iation 9 ! height ( ! b>omet] is p>tly due to ! *ange ( temp]ature1 b s9ce ! coeffici5t ( absolute dilatation ( m]cury has be5 exactly det]m9$1 z already describ$ 7p4 #cda71 we h only to make calculations ( a simple "*1 or1 :at is bett] /ill1 tabulate a s]ies ( su* calculations = g5]al use1 & ! correction = temp]ature c be made ) all desir$ accuracy4 ,! height ( ! m]cury 9 ! b>omet] is also affect$ by capill>y attraction1 :i* depresses x by a con/ant am\nt dep5d+ ma9ly on ! diamet] ( ! tube4 ,! requisite corrections c be e/imat$ ) accuracy suffici5t = mo/ purposes1 m especially z we c *eck ! correctness ( ! read+ ( a b>omet] by comp>ison ) a /&>d b>omet]1 & introduce if ne$ be an index error includ+ bo? ! error 9 ! affix+ ( ! scale & ! effect due to capill>ity4 ,b 9 con/ruct+ ! /&>d b>omet] itself we mu/ take great] precautions2 ! capill>y depression dep5ds some:at ^u ! quality ( ! glass1 ! abs5ce ( air1 & ! p]fect cleanl9ess ( ! m]cury1 s t we _c assign ! exact am\nt ( ! effect4 ,h5ce a /&>d b>omet] is con/ruct$ ) a wide tube1 sometimes ev5 an in* 9 diamet]1 s t ! capill>y effect may be r5d]$ almo/ z]o4#bde ,gay-,lussac made b>omet]s 9 ! =m ( a uni=m siphon tube1 s t ! capill>y =ces act+ at ! upp] & l[] surfaces %\ld balance & de/roy ea* o!r2 b ! me?od fails 9 practice because ! l[] surface1 be+ op5 to ! air1 becomes sulli$ & subject to a diff]5t =ce ( capill>ity4 #bde ,jevons1 ,watts' 99,diction>y ( ,*emi/ry991 vol4 i4 pp4 #eac-eae4 ,9 me*anical exp]im5ts friction is an int]f]+ condition1 & dra9s away a portion ( ! en]gy int5d$ to be op]at$ ^u 9 a def9ite mann]4 ,we %\ld ( c\rse r$uce ! friction 9 ! fir/ place to ! l[e/ possible am\nt1 b z x _c be altoge!r prev5t$1 & is n calculable ) c]ta9ty f any g5]al laws1 we mu/ det]m9e x sep>ately = ea* app>atus by suitable exp]im5ts4 ,?us ,smeaton1 9 8 admirable b almo/ =gott5 rese>*es conc]n+ wat]-:eels1 elim9at$ friction 9 ! mo/ simple mann] by det]m9+ by trial :at weight1 act+ by a cord & roll] ^u 8 model wat]-:eel1 w\ld make x turn )\t wat] z rapidly z ! wat] made x turn4 ,9 %ort1 he asc]ta9$ :at weight concurr+ ) ! wat] w\ld exactly comp5sate = ! friction4#bdf ,9 ,dr4 ,j\le's exp]im5ts to det]m9e ! me*anical equival5t ( heat by ! cond5sation ( air1 a consid]able am\nt ( heat 0 produc$ by friction ( ! cond5s+ pump1 & a small portion by /irr+ ! wat] employ$ to absorb ! heat4 ,?is heat ( friction 0 measur$ by simply repeat+ ! exp]im5t 9 an exactly simil> mann] except t no cond5sation 0 effect$1 & obs]v+ ! *ange ( temp]ature !n produc$4#bdg #bdf 99,philosophical ,transactions991 vol4 li4 p4 #ajj4 #bdg 99,philosophical ,magaz9e991 #crd ,s]ies1 vol4 xxvi4 p4 #cgb4 ,we may describe z 99te/ exp]im5ts99 any 9 :i* we p]=m op]ations n int5d$ to give ! quantity ( ! pr9cipal ph5om5on1 b "s quantity :i* w\ld o!rwise rema9 z an error 9 ! result4 ,?us 9 a/ronomical obs]vations almo/ e in/rum5tal error may be avoid$ by increas+ ! numb] ( obs]vations & di/ribut+ !m 9 su* a mann] z to produce 9 ! f9al mean z mu* error 9 "o way z 9 ! o!r4 ,b !re is "o s\rce ( error1 fir/ discov]$ by ,maskelyne1 :i* _c be ?us avoid$1 because x affects all obs]vations 9 ! same direction & to ! same av]age am\nt1 namely ! ,p]sonal ,error ( ! obs]v] or ! incl9ation to record ! passage ( a /> across ! wires ( ! telescope a little too soon or a little too late4 ,?is p]sonal error 0 fir/ c>efully describ$ 9 ! 99,ed9burgh ,j\rnal ( ,sci5ce991 vol4 i4 p4 #agh4 ,! diff]5ce betwe5 ! judgm5t ( obs]v]s at ! ,gre5wi* ,obs]vatory usually v>ies f #a_/ajj to #a_/c ( a second1 & rema9s pretty con/ant = ! same obs]v]s4#bdh ,"o practis$ obs]v] 9 ,sir ,george ,airy's p5dulum exp]im5ts record$ all 8 "t obs]vations half a second too e>ly on ! av]age z comp>$ ) ! *ief obs]v]4#bdi ,9 "s obs]v]s x has am\nt$ to sev5 or eight-t5?s ( a second4#bej ,de ,morgan appe>s to h ent]ta9$ ! op9ion t ?is s\rce ( error 0 ess5tially incapable ( elim9ation or correction4#bea ,b x seems cle>1 z ,i sugge/$ )\t kn[+ :at _h be5 done1#beb t ?is p]sonal error might be det]m9$ absolutely ) any desirable degree ( accuracy by te/ exp]im5ts1 consi/+ 9 mak+ an artificial /> move at a consid]able di/ance & record+ by electricity ! exact mom5t ( its passage ov] ! wire4 ,?is me?od has 9 fact be5 successfully employ$ 9 ,leyd51 ,p>is1 & ,neu*atel4#bec ,m rec5tly1 obs]v]s 7 tra9$ = ! ,transit ( ,v5us ,exp$itions by means ( a me*anical model repres5t+ ! motion ( ,v5us ov] ! sun1 ?is model be+ plac$ at a little di/ance & view$ ?r\gh a telescope1 s t diff]5ces 9 ! judgm5ts ( diff]5t obs]v]s w\ld become app>5t4 ,x seems likely t te/s ( ?is nature might be employ$ ) advantage 9 o!r cases4 #bdh 99,gre5wi* ,obs]vations =99 #ahff1 p4 xlix4 #bdi 99,philosophical ,transactions991 #ahef1 p4 #cji4 #bej ,p5ny 99,cyclopdia991 art4 99,transit991 vol4 xxv4 pp4 #abi1 #acj4 #bea ,ibid4 art4 99,obs]vation991 p4 #cij4 #beb 99,nature991 vol4 i4 p4 #he4 #bec 99,nature991 vol4 i4 p #ccg4 ,see ref]5ces to ! ,memoirs describ+ ! me?od4 ,newton employ$ ! p5dulum = mak+ exp]im5ts on ! impact ( balls4 ,two balls 7 hung 9 contact1 & "o ( !m1 be+ drawn aside ?r\gh a measur$ arc1 0 !n all[$ to /rike ! o!r1 ! arcs ( vibration giv+ suffici5t data = calculat+ ! di/ribution ( en]gy at ! mom5t ( impact4 ,! resi/ance ( ! air 0 an int]f]+ cause :i* he e/imat$ v simply by caus+ "o ( ! balls to make sev]al complete vibrations )\t impact & !n m>k+ ! r$uction 9 ! l5g?s ( ! arcs1 a prop] fraction ( :i* r$uction 0 add$ to ea* ( ! o!r arcs ( vibration :5 impact took place4#bed #bed 99,pr9cipia991 ,book ,i4 ,law ,,iii4 ,coroll>y ,,vi4 ,s*olium4 ,motte's translation1 vol4 i4 p4 #cc4 ,! exact def9ition ( ! /&>d ( l5g? is "o ( ! mo/ important1 z x is "o ( ! mo/ difficult que/ions 9 physical sci5ce1 & ! diff]5t practice ( diff]5t nations introduces ne$less confusion4 ,7 all /&>ds con/ruct$ s z to give ! true l5g? at a fix$ uni=m temp]ature1 = in/ance ! freez+-po9t1 !n any two /&>ds c\ld be comp>$ )\t ! int]f]5ce ( temp]ature by br++ !m bo? to exactly ! same fix$ temp]ature4 ,un=tunately ! ,fr5* metre 0 def9$ by a b> ( plat9um at #j;,c1 :ile our y>d 0 def9$ by a bronze b> at #fb;,f4 ,x is q impossible1 !n1 to make a comp>ison ( ! y>d & metre )\t ! introduction ( a correction1 ei!r = ! expansion ( plat9um or bronze1 or bo?4 ,b>s ( metal diff] too s mu* 9 _! rates ( expansion accord+ to _! molecul> condition t x is dang]\s to inf] f "o b> to ano!r4 ,:5 we come to use in/rum5ts ) great accuracy !re are _m m9ute s\rces ( error :i* mu/ be gu>d$ aga9/4 ,if a !rmomet] has be5 graduat$ :5 p]p5dicul>1 x w read some:at diff]5tly :5 laid flat1 z ! pressure ( a column ( m]cury is remov$ f ! bulb4 ,! read+ may also be some:at alt]$ if x has rec5tly be5 rais$ to a high] temp]ature ?an usual1 if x be plac$ "u a vacu\s receiv]1 or if ! tube be unequally heat$ z comp>$ ) ! bulb4 ,= ^! m9ute causes ( error we may h to introduce tr\blesome corrections1 unless we adopt ! simple precaution ( us+ ! !rmomet] 9 circum/ances ( position1 c41 exactly simil> to ^? 9 :i* x 0 graduat$4 ,!re is no end to ! numb] ( m9ute corrections :i* may ultimately be requir$4 ,a l>ge numb] ( exp]im5ts on gases1 /&>d weights & measures1 c41 dep5d ^u ! height ( ! b>omet]2 b :5 exp]im5ts 9 diff]5t p>ts ( ! _w are comp>$ toge!r we ought z a fur!r ref9em5t to take into acc\nt ! v>y+ =ce ( gravity1 :i* ev5 betwe5 ,london & ,p>is makes a diff]5ce ( #jjh in* ( m]cury4 ,! measurem5t ( quantities ( heat is a matt] ( great difficulty1 because !re is no kn[n sub/ance imp]vi\s to heat1 & ! problem is !re=e z difficult z to measure liquids 9 por\s vessels4 ,to det]m9e ! lat5t heat ( /eam we mu/ cond5se a c]ta9 am\nt ( ! /eam 9 a kn[n weight ( wat]1 & !n obs]ve ! rise ( temp]ature ( ! wat]4 ,b :ile we are c>ry+ out ! exp]im5t1 "p ( ! heat w escape by radiation & conduction f ! cond5s+ vessel or calorimet]4 ,we may inde$ r$uce ! loss ( heat by us+ vessels ) d\ble sides & bright surfaces1 surr\nd$ ) swans-d[n wool or o!r non-conduct+ mat]ials2 & we may also avoid rais+ ! temp]ature ( ! wat] mu* above t ( ! surr\nd+ air4 ,yet we _c by any su* means r5d] ! loss ( heat inconsid]able4 ,rum=d +5i\sly propos$ to r$uce ! loss to z]o by comm5c+ ! exp]im5t :5 ! temp]ature ( ! calorimet] is z mu* bel[ t ( ! air z x is at ! end ( ! exp]im5t above x4 ,?us ! vessel w fir/ ga9 & !n lose by radiation & conduction1 & ^! opposite errors w approximately balance ea* o!r4 ,b ,regnault has %[n t ! loss & ga9 d n proce$ by exactly ! same laws1 s t 9 v accurate inve/igations ,rum=d's me?od is n suffici5t4 ,!re rema9s ! me?od ( correction :i* 0 beautifully c>ri$ out by ,regnault 9 8 det]m9ation ( ! lat5t heat ( /eam4 ,he employ$ two calorimet]s1 made 9 exactly ! same way & alt]nately us$ to cond5se a c]ta9 am\nt ( /eam1 s t :ile "o 0 measur+ ! lat5t heat1 ! o!r calorimet] 0 engag$ 9 det]m9+ ! corrections to be appli$1 :e!r on acc\nt ( radiation & conduction f ! vessel or on acc\nt ( heat rea*+ ! vessel by means ( ! connect+ pipes4#bee #bee ,graham's 99,*emical ,reports & ,memoirs991 ,cav5di% ,society1 pp4 #bdg1 #bfh1 c4 #d4 99,me?od ( ,comp5sation499 ,!re are _m cases 9 :i* a cause ( error _c conv5i5tly be r5d]$ null1 & is yet beyond ! rea* ( ! ?ird me?od1 t ( calculat+ ! requisite correction f indep5d5t obs]vations4 ,! magnitude ( an error may be subject to cont9ual v>iations1 on acc\nt ( *ange ( wea!r1 or o!r fickle circum/ances beyond our control4 ,x may ei!r be impracticable to obs]ve ! v>iation ( ^? circum/ances 9 suffici5t detail1 or1 if obs]v$1 ! calculation ( ! am\nt ( error may be subject to d\bt4 ,9 ^! cases1 & only 9 ^! cases1 x w be desirable to inv5t "s artificial mode ( c\nt]pois+ ! v>iable error aga9/ an equal error subject to exactly ! same v>iation4 ,we _c weigh an object ) great accuracy unless we make a correction = ! weight ( ! air displac$ by ! object1 & add ?is to ! app>5t weight4 ,9 v accurate inve/igations relat+ to /&>d weights1 x is usual to note ! b>omet] & !rmomet] at ! "t ( mak+ a weigh+1 &1 f ! measur$ bulks ( ! objects comp>$1 to calculate ! weight ( air displac$2 ! ?ird me?od 9 fact is adopt$4 ,to make ^! calculations 9 ! frequ5t weigh+s requisite 9 *emical analysis w\ld be exce$+ly labori\s1 h5ce ! correction is usually neglect$4 ,b :5 ! *emi/ wi%es to weigh gas conta9$ 9 a l>ge glass globe = ! purpose ( det]m9+ its specific gravity1 ! correction becomes ( mu* importance4 ,h5ce *emi/s avoid at once ! error1 & ! lab\r ( correct+ x1 by atta*+ to ! opposite scale ( ! balance a dummy seal$ glass globe ( equal capacity to t conta9+ ! gas to be weigh$1 not+ only ! diff]5ce ( weight :5 ! op]at+ globe is full & empty4 ,! correction1 be+ ! same = bo? globes1 may be entirely neglect$4#bef #bef ,regnault's 99,c\rs ,elm5taire de ,*imie991 #ahea1 vol i4 p4 #ada4 ,a device ( ne>ly ! same k9d is employ$ 9 ! con/ruction ( galvanomet]s :i* measure ! =ce ( an electric curr5t by ! deflection ( a susp5d$ magnetic ne$le4 ,! resi/ance ( ! ne$le is p>tly due to ! directive influ5ce ( ! e>?'s magnetism1 & p>tly to ! torsion ( ! ?read4 ,b ! =m] =ce may (t5 be inconv5i5tly great z well z tr\blesome to det]m9e = diff]5t incl9ations4 ,h5ce x is cu/om>y to connect toge!r two equally magnetis$ ne$les1 ) _! poles po9t+ 9 opposite directions1 "o ne$le be+ )9 & ano!r )\t ! coil ( wire4 ,z reg>ds ! e>?'s magnetism1 ! ne$les are n[ 99a/atic99 or indiff]5t1 ! t5d5cy ( "o ne$le t[>ds ! pole be+ balanc$ by t ( ! o!r4 ,an elegant in/ance ( ! elim9ation ( a di/urb+ =ce by comp5sation is f\nd 9 ,f>aday's rese>*es ^u ! magnetism ( gases4 ,to obs]ve ! magnetic attraction or repulsion ( a gas seems impossible unless we enclose ! gas 9 an envelope1 probably be/ made ( glass4 ,b any su* envelope is sure to be m or less affect$ by ! magnet1 s t x becomes difficult to di/+ui% betwe5 ?ree =ces :i* ent] into ! problem1 namely1 ! magnetism ( ! gas 9 "q1 t ( ! envelope1 & t ( ! surr\nd+ atmosph]ic air4 ,f>aday avoid$ all difficulties by employ+ two equal & simil> glass tubes connect$ toge!r1 & s susp5d$ f ! arm ( a torsion balance t ! tubes 7 9 simil> p>ts ( ! magnetic field4 ,"o tube be+ fill$ ) nitrog5 & ! o!r ) oxyg51 x 0 f\nd t ! oxyg5 seem$ to be attract$ & ! nitrog5 repell$4 ,! susp5d+ ?read ( ! balance 0 !n turn$ until ! =ce ( torsion re/or$ ! tubes to _! orig9al places1 :]e ! magnetism ( ! tubes z well z t ( ! surr\nd+ air1 be+ ! same & 9 ! opposite directions ^u ! two tubes1 c\ld n produce any int]f]5ce4 ,! =ce requir$ to re/ore ! tubes 0 measur$ by ! am\nt ( torsion ( ! ?read1 & x indicat$ correctly ! diff]5ce betwe5 ! attractive p[]s ( oxyg5 & nitrog54 ,! oxyg5 0 !n )drawn f "o ( ! tubes1 & a second exp]im5t made1 s z to comp>e a vacuum ) nitrog54 ,no =ce 0 n[ requir$ to ma9ta9 ! tubes 9 _! places1 s t nitrog5 0 f\nd to be1 approximately speak+1 indiff]5t to ! magnet1 t is1 nei!r magnetic nor diamagnetic1 :ile oxyg5 0 prov$ to be positively magnetic4#beg ,x requir$ ! highe/ exp]im5tal skill on ! "p ( ,f>aday & ,tyndall1 to di/+ui% betwe5 :at is app>5t & real 9 magnetic attraction & repulsion4 #beg ,tyndall's 99,f>aday991 pp4 #aad1 #aae4 ,exp]i5ce alone c f9ally decide :5 a comp5sat+ arrangem5t is conducive to accuracy4 ,z a g5]al rule me*anical comp5sation is ! la/ res\rce1 & 9 ! m accurate obs]vations x is likely to introduce m unc]ta9ty ?an x removes4 ,a multitude ( in/rum5ts involv+ me*anical comp5sation h be5 devis$1 b !y are usually ( an unsci5tific "*1#beh because ! errors comp5sat$ c be m accurately det]m9$ & all[$ =4 ,b !re are exceptions to ?is rule1 & x seems to be prov$ t 9 ! delicate & tiresome op]ation ( measur+ a base l9e1 inv>iable b>s1 comp5sat$ = expansion by heat1 give ! mo/ accurate results4 ,?is arises f ! fact t x is v difficult to det]m9e accurately ! temp]ature ( ! measur+ b>s "u v>y+ conditions ( wea!r & manipulation4#bei ,aga91 ! la/ ref9em5t 9 ! measurem5t ( "t at ,gre5wi* ,obs]vatory dep5ds ^u me*anical comp5sation4 ,sir ,george ,airy1 obs]v+ t ! /&>d clock increas$ its los+ rate #jcj second = an increase ( "o in* 9 atmosph]ic pressure1 plac$ a magnet mov$ by a b>omet] 9 su* a position bel[ ! p5dulum1 z almo/ entirely to neutralise ?is cause ( irregul>ity4 ,! ?or\gh rem$y1 h[ev]1 w\ld be to remove ! cause ( error altoge!r by plac+ ! clock 9 a vacu\s case4 #beh ,see1 = in/ance1 ! ,comp5sat$ ,sympiesomet]1 99,philosophical ,magaz9e991 #d? ,s]ies1 vol4 xxxix4 p4 #cga4 #bei ,grant1 99,hi/ory ( ,physical ,a/ronomy991 pp4 #adf1 #adg4 ,we ?us see t ! *oice ( "o or o!r mode ( elim9at+ an error dep5ds entirely ^u circum/ances & ! object 9 view2 b we may safely lay d[n ! foll[+ conclusions4 ,fir/ ( all1 seek to avoid ! s\rce ( error altoge!r if x c be conv5i5tly done2 if n1 make ! exp]im5t s t ! error may be z small1 b m especially z con/ant1 z possible4 ,if ! means are at h& = det]m9+ its am\nt by calculation f o!r exp]im5ts & pr9ciples ( sci5ce1 all[ ! error to exi/ & make a correction 9 ! result4 ,if ?is _c be accurately done or involves too mu* lab\r = ! purposes 9 view1 !n ?r[ 9 a c\nt]act+ error :i* %all z ne>ly z possible be ( equal am\nt 9 all circum/ances ) t to be elim9at$4 ,!re yet rema9s1 h[ev]1 "o important me?od1 t ( ,rev]sal1 :i* w =m an appropriate transition to ! succe$+ *apt]s on ! ,me?od ( ,mean ,results & ! ,law ( ,error4 #e4 99,me?od ( ,rev]sal499 ,! fif? me?od ( elim9at+ error is mo/ pot5t & satisfactory :5 x c be appli$1 b x requires t we %all be able to rev]se ! app>atus & mode ( proc$ure1 s z to make ! int]f]+ cause act alt]nately 9 opposite directions4 ,if we c get two exp]im5tal results1 "o ( :i* is z mu* too great z ! o!r is too small1 ! error is equal to half ! diff]5ce1 & ! true result is ! mean ( ! two app>5t results4 ,x is an unavoidable defect ( ! *emical balance1 = in/ance1 t ! po9ts ( susp5sion ( ! pans _c be fix$ at exactly equal di/ances f ! c5tre ( susp5sion ( ! beam4 ,h5ce two weights :i* seem to balance ea* o!r w nev] be q equal 9 reality4 ,! diff]5ce is detect$ by rev]s+ ! weights1 & x may be e/imat$ by add+ small weights to ! defici5t side to re/ore equilibrium1 & !n tak+ z ! true weight ! geometric mean ( ! two app>5t weights ( ! same object4 ,if ! diff]5ce is small1 ! ari?metic mean1 t is half ! sum1 may be sub/itut$ = ! geometric mean1 f :i* x w n appreciably diff]4 ,?is me?od ( rev]sal is mo/ ext5sively employ$ 9 practical a/ronomy4 ,! app>5t elevation ( a heav5ly body is obs]v$ by a telescope mov+ ^u a divid$ circle1 ^u :i* ! incl9ation ( ! telescope is read (f4 ,n[ ?is read+ w be errone\s if ! circle & ! telescope h n accurately ! same c5tre4 ,b if we read (f at ! same "t bo? ends ( ! telescope1 ! "o read+ w be ab\t z mu* too small z ! o!r is too great1 & ! mean w be ne>ly free f error4 ,9 practice ! obs]vation is diff]5tly conduct$1 b ! pr9ciple is ! same2 ! telescope is fix$ to ! circle1 :i* moves ) x1 & ! angle ?r\gh :i* x moves is read (f at ?ree1 six1 or m po9ts1 dispos$ at equal int]vals r\nd ! circle4 ,! old] a/ronom]s1 d[n ev5 to ! "t ( ,flam/e$1 7 accu/om$ to use portions only ( a divid$ circle1 g5]ally quadrants1 & ,rm] made a va/ improvem5t :5 he introduc$ ! complete circle4 ,! transit circle1 employ$ to det]m9e ! m]idian passage ( heav5ly bodies1 is s con/ruct$ t ! telescope & ! axis be>+ x1 9 fact ! :ole mov+ "p ( ! in/rum5t1 c be tak5 out ( ! be>+ sockets & turn$ ov]1 s t :at 0 =m]ly ! we/]n pivot becomes ! ea/]n "o1 & 99vice v]s994 ,x is impossible t ! in/rum5t c\ld h be5 s p]fectly con/ruct$1 m\nt$1 & adju/$ t ! telescope %\ld po9t exactly to ! m]idian1 b ! effect ( ! rev]sal is t x w po9t z mu* to ! we/ 9 "o position z x does to ! ea/ 9 ! o!r1 & ! mean result ( obs]vations 9 ! two positions mu/ be free f su* cause ( error4 ,! accuracy ) :i* ! incl9ation ( ! compass ne$le c be det]m9$ dep5ds almo/ entirely on ! me?od ( rev]sal4 ,! dip ne$le consi/s ( a b> ( magnetis$ /eel1 susp5d$ some:at l ! beam ( a delicate balance on a sl5d] axis pass+ ?r\gh ! c5tre ( gravity ( ! b>1 s t x is at lib]ty to re/ 9 t exact degree ( incl9ation 9 ! magnetic m]idian :i* ! magnetism ( ! e>? induces4 ,! incl9ation is read (f ^u a v]tical divid$ circle1 b to avoid error aris+ f ! c5tr+ ( ! ne$le & circle1 bo? ends are read1 & ! mean ( ! results is tak54 ,! :ole in/rum5t is n[ turn$ c>efully r\nd ?r\gh #ahj1 :i* causes ! ne$le to assume a new position relatively to ! circle & gives two new read+s1 9 :i* any error due to ! wrong position ( ! z]o ( ! division w be rev]s$4 ,z ! axis ( ! ne$le may n be exactly horizontal1 x is n[ rev]s$ 9 ! same mann] z ! transit in/rum5t1 ! end ( ! axis :i* =m]ly po9t$ ea/ be+ made to po9t we/1 & a new set ( f\r read+s is tak54 ,f9ally1 error may arise f ! axis n pass+ accurately ?r\gh ! c5tre ( gravity ( ! b>1 & ?is error c only be detect$ & elim9at$ on *ang+ ! magnetic poles ( ! b> by ! application ( a /rong magnet4 ,! error is ?us made to act 9 opposite directions4 ,to ensure all possible accuracy ea* rev]sal ought to be comb9$ ) ea* o!r rev]sal1 s t ! ne$le w be obs]v$ 9 eight diff]5t positions by sixte5 read+s1 ! mean ( ! :ole ( :i* w give ! requir$ incl9ation free f all elim9able errors4#bfj #bfj ,quetelet1 99,sur la ,physique du ,globe991 p4 #agd4 ,jam91 99,c\rs de ,physique991 vol4 i4 p4 #ejd4 ,!re are c]ta9 cases 9 :i* a di/urb+ cause c ) ease be made to act 9 opposite directions1 9 alt]nate obs]vations1 s t ! mean ( ! results w be free f di/urbance4 ,?us 9 direct exp]im5ts ^u ! velocity ( s\nd 9 pass+ ?r\gh ! air betwe5 /ations two or ?ree miles ap>t1 ! w9d is a cause ( error4 ,x w be well1 9 ! fir/ place1 to *oose a "t = ! exp]im5t :5 ! air is v ne>ly at re/1 & ! di/urbance slight1 b if at ! same mom5t signal s\nds be made at ea* /ation & obs]v$ at ! o!r1 two s\nds w be pass+ 9 opposite directions ?r\gh ! same body ( air & ! w9d w accel]ate "o s\nd almo/ exactly z x ret>ds ! o!r4 ,aga91 9 trigonometrical surveys ! app>5t height ( a po9t w be affect$ by atmosph]ic refraction & ! curvature ( ! e>?4 ,b if 9 ! case ( two po9ts ! app>5t elevation ( ea* z se5 f ! o!r be obs]v$1 ! corrections w be ! same 9 am\nt1 b rev]s$ 9 direction1 & ! mean betwe5 ! two app>5t diff]5ces ( altitude w give ! true diff]5ce ( level4 ,9 ! next two *apt]s we really pursue ! ,me?od ( ,rev]sal into m complicat$ applications4 ,,*apt] ,,xvi4 ,,! ,,me?od ,,( ,,means4 ,all results ( ! measurem5t ( cont9u\s quantity c be only approximately true4 ,7 ?is ass]tion d\bt$1 x c\ld readily be prov$ by direct exp]i5ce4 ,if any p]son1 us+ an in/rum5t ( ! greate/ precision1 makes & regi/]s successive obs]vations 9 an unbiass$ mann]1 x w almo/ inv>iably be f\nd t ! results diff] f ea* o!r4 ,:5 we op]ate ) suffici5t c>e we _c p]=m s simple an exp]im5t z weigh+ an object 9 a good balance )\t gett+ discrepant numb]s4 ,only ! r\gh & c>eless exp]im5t] w ?9k t 8 obs]vations agree1 b 9 reality he w be f\nd to ov]look ! diff]5ces4 ,! mo/ elaborate rese>*es1 su* z ^? und]tak5 9 connection ) /&>d weights & measures1 always r5d] x app>5t t complete co9cid5ce is out ( ! "q1 & t ! m accurate our modes ( obs]vation are r5d]$1 ! m num]\s are ! s\rces ( m9ute error :i* become app>5t4 ,we may look ^u ! exi/5ce ( error 9 all measurem5ts z ! normal /ate ( ?+s4 ,x is absolutely impossible to elim9ate sep>ately ! multitude ( small di/urb+ influ5ces1 except by balanc+ !m (f aga9/ ea* o!r4 ,ev5 9 draw+ a mean x is to be expect$ t we %all come ne> ! tru? r ?an exactly to x4 ,9 ! measurem5t ( cont9u\s quantity1 absolute co9cid5ce1 if x seems to occur1 mu/ be only app>5t1 & is no indication ( precision4 ,x is "o ( ! mo/ emb>rass+ ?+s we c meet :5 exp]im5tal results agree too closely4 ,su* co9cid5ces %\ld raise our suspicion t ! app>atus 9 use is 9 "s way re/rict$ 9 its op]ation1 s z n really to give ! true result at all1 or t ! actual results h n be5 fai?fully record$ by ! assi/ant 9 *>ge ( ! app>atus4 ,if !n we _c get twice ov] exactly ! same result1 ! "q arises1 ,h[ c we ev] atta9 ! tru? or select ! result :i* may be suppos$ to approa* mo/ ne>ly to x8 ,! quantity ( a c]ta9 ph5om5on is express$ 9 sev]al numb]s :i* diff] f ea* o!r2 no m ?an "o ( !m at ! mo/ c be true1 & x is m probable t !y are all false4 ,x may be sugge/$1 p]haps1 t ! obs]v] %\ld select ! "o obs]vation :i* he judg$ to be ! be/ made1 & !re w (t5 d\btless be a feel+ t "o or m results 7 satisfactory1 & ! o!rs less tru/wor?y4 ,?is seems to h be5 ! c\rse adopt$ by ! e>ly a/ronom]s4 ,flam/e$1 :5 he _h made sev]al obs]vations ( a />1 probably *ose 9 an arbitr>y mann] t :i* seem$ to him ne>e/ to ! tru?4#bfa #bfa ,baily's 99,acc\nt ( ,flam/e$991 p4 #cgf4 ,:5 ,horrocks select$ = 8 e/imate ( ! sun's semi-diamet] a mean betwe5 ! results ( ,kepl] & ,ty*o1 he pr(ess$ n to d x f any reg>d to ! idle adage1 8,m$io tutissimus ibis10 b because he ?\ght x f 8 own obs]vations to be correct4#bfb ,b ?is me?od w n apply at all :5 ! obs]v] has made a numb] ( measurem5ts :i* are equally good 9 8 op9ion1 & x is q app>5t t 9 us+ an in/rum5t or app>atus ( consid]able complication ! obs]v] w n necess>ily be able to judge :e!r slight causes h affect$ its op]ation or n4 #bfb 99,! ,transit ( ,v5us across ! ,sun991 by ,horrocks1 ,london1 #ahei1 p4 #adf4 ,9 ?is "q1 z inde$ ?r\gh\t inductive logic1 we deal only ) probabilities4 ,!re is no infallible mode ( arriv+ at ! absolute tru?1 :i* lies beyond ! rea* ( human intellect1 & c only be ! di/ant object ( our long-cont9u$ & pa9ful approximations4 ,nev]!less !re is a mode po9t$ out alike by common s5se & ! highe/ ma!matical reason+1 :i* is m likely ?an any o!r1 z a g5]al rule1 to br+ u ne> ! tru?4 ,! 1 or ! 99aurea m$iocritas991 0 highly e/eem$ 9 ! anci5t philosophy ( ,greece & ,rome2 b x is n probable t any ( ! anci5ts %\ld h be5 able cle>ly to analyse & express ! reasons :y !y advocat$ ! 99mean99 z ! safe/ c\rse4 ,b 9 ! la/ two c5turies ?is app>5tly simple "q ( ! mean has be5 f\nd to af=d a field = ! ex]cise ( ! utmo/ ma!matical skill4 ,rog] ,cotes1 ! editor ( ! 99,pr9cipia991 appe>s to h _h "s insight into ! value ( ! mean2 b pr(\nd ma!maticians su* z ,de ,moivre1 ,daniel ,b]n\lli1 ,laplace1 ,lagrange1 ,gauss1 ,quetelet1 ,de ,morgan1 ,airy1 ,leslie ,ellis1 ,boole1 ,glai%]1 & o!rs1 h h>dly exhau/$ ! subject4 99,sev]al uses ( ! ,mean ,result499 ,! elim9ation ( errors ( unkn[n s\rces1 is almo/ always accompli%$ by ! simple ari?metical process ( tak+ ! 99mean991 or1 z x is (t5 call$1 ! 99av]age99 ( sev]al discrepant numb]s4 ,to take an av]age is to add ! sev]al quantities toge!r1 & divide by ! numb] ( quantities ?us add$1 :i* gives a quoti5t ly+ among1 or 9 ! 99middle99 (1 ! sev]al quantities4 ,be=e h[ev] inquir+ fully into ! gr\nds ( ?is proc$ure1 x is ess5tial to obs]ve t ?is "o ari?metical process is really appli$ 9 at lea/ ?ree diff]5t cases1 = diff]5t purposes1 & ^u diff]5t pr9ciples1 & we mu/ take great c>e n to confuse "o application ( ! process ) ano!r4 ,a 99mean result991 !n1 may h any "o ( ! foll[+ significations4 7#a7 ,x may give a m]ely repres5tative numb]1 express+ ! g5]al magnitude ( a s]ies ( quantities1 & s]v+ z a conv5i5t mode ( comp>+ !m ) o!r s]ies ( quantities4 ,su* a numb] is prop]ly call$ 99,! fictiti\s mean99 or 99,! av]age result994 7#b7 ,x may give a result approximately free f di/urb+ quantities1 :i* are kn[n to affect "s results 9 "o direction1 & o!r results equally 9 ! opposite direction4 ,we may say t 9 ?is case we get a 99,precise mean result994 7#c7 ,x may give a result m or less free f unkn[n & unc]ta9 errors2 ?is we may call ! 99,probable mean result994 ,( ^! ?ree uses ( ! mean ! fir/ is entirely diff]5t 9 nature f ! two la/1 s9ce x does n yield an approximation to any natural quantity1 b furni%es u ) an ari?metic result comp>+ ! aggregate ( c]ta9 quantities ) _! numb]4 ,! ?ird use ( ! mean re/s entirely ^u ! !ory ( probability1 & w be m fully consid]$ 9 a lat] "p ( ?is *apt]4 ,! second use is closely connect$1 or ev5 id5tical )1 ! ,me?od ( ,rev]sal already describ$1 b x w be desirable to ent] some:at fully into all ! ?ree employm5ts ( ! same ari?metical process4 99,! ,mean & ! ,av]age499 ,mu* confusion exi/s 9 ! popul>1 or ev5 ! sci5tific employm5t ( ! t]ms 99mean99 & 99av]age991 & !y are commonly tak5 z synonym\s4 ,x is necess>y to asc]ta9 c>efully :at significations we ought to atta* to !m4 ,! ,engli% ^w 99mean99 is equival5t to 99m$ium991 be+ d]iv$1 p]haps ?r\gh ! ,fr5* 99moy5991 f ! ,lat9 99m$ius991 :i* aga9 is und\bt$ly k9dr$ ) ! ,greek 4 ,etymologi/s believe1 too1 t ?is ,greek ^w is connect$ ) ! preposition 1 ! ,g]man 99mitte991 & ! true ,engli% 99mid99 or 99middle992 s t aft] all ! 99mean99 is a te*nical t]m id5tical 9 its root ) ! m popul> equival5t 99middle994 ,if we inquire :at is ! mean 9 a ma!matical po9t ( view1 ! true answ] is t !re are sev]al or _m k9ds ( means4 ,! old ari?meticians recognis$ t5 k9ds1 :i* are /at$ by ,boe?ius1 & an elev5? 0 add$ by ,jordanus4#bfc #bfc ,de ,morgan1 ,supplem5t to ! 99,p5ny ,cyclopdia991 art4 99,old ,appellations ( ,numb]s994 ,! 99ari?metic mean99 is ! "o by f> ! mo/ commonly d5ot$ by ! t]m1 & t :i* we may und]/& x to signify 9 ! abs5ce ( any qualification4 ,x is ! sum ( a s]ies ( quantities divid$ by _! numb]1 & may be repres5t$ by ! =mula #a_/b799;a99 99b9974 ,b !re is also ! 99geometric mean991 :i* is ! squ>e root ( ! product1 799a99 99b9971 or t quantity ! log>i?m ( :i* is ! ari?metic mean ( ! log>i?ms ( ! quantities4 ,!re is also ! 99h>monic mean991 :i* is ! reciprocal ( ! ari?metic mean ( ! reciprocals ( ! quantities4 ,?us if 99a99 & 99b99 be ! quantities1 z be=e1 _! reciprocals are #a_/99;a99 & #a_/99;b991 ! mean ( :i* is #a_/b 7#a_/99;a99 #a_/99;b9971 & ! reciprocal aga9 is 7#b99;ab997_/799a99 99b9971 :i* is ! h>monic mean4 ,o!r k9ds ( means might no d\bt be inv5t$ = p>ticul> purposes1 & we might apply ! t]m1 z ,de ,morgan po9t$ out1#bfd to any quantity a function ( :i* is equal to a function ( two or m o!r quantities1 & is su* t ! int]*ange ( ^! latt] quantities among !mselves w make no alt]ation 9 ! value ( ! function4 ,symbolically1 if 799y991 99y991 99y99 44447 799x99#a1 99x99#b1 99x99#c 444471 !n 99y99 is a k9d ( mean ( ! quantities1 99x99#a1 99x99#b1 c4 #bfd 99,p5ny ,cyclopdia991 art4 99,mean994 ,! geometric mean is necess>ily adopt$ 9 c]ta9 cases4 ,:5 we e/imate ! "w done aga9/ a =ce :i* v>ies inv]sely z ! squ>e ( ! di/ance f a fix$ po9t1 ! mean =ce is ! geometric mean betwe5 ! =ces at ! beg9n+ & end ( ! pa?4 ,:5 9 an imp]fect balance1 we rev]se ! weights to elim9ate error1 ! true weight w be ! geometric mean ( ! two app>5t weights4 ,9 almo/ all ! calculations ( /ati/ics & comm]ce ! geometric mean ought1 /rictly speak+1 to be us$4 ,if a commodity rises 9 price #ajj p] c5t4 & ano!r rema9s unalt]$1 ! mean rise ( a price is n #ej p] c5t4 because ! ratio #aej 3 #bjj is n ! same z #ajj 3 #aej4 ,! mean ratio is z unity to 7#ajj #bjj7 or #a to #ada4 ,! diff]5ce betwe5 ! ?ree k9ds ( means 9 su* a case#bfe is v consid]able2 :ile ! rise ( price e/imat$ by ! ,ari?metic mean w\ld be #ej p] c5t4 x w\ld be only #da & #cc p] c5t4 respectively accord+ to ! ,geometric & ,h>monic means4 #bfe ,jevons1 99,j\rnal ( ! ,/ati/ical ,society991 ,june #ahfe1 vol4 xxviii1 p4 #bif4 ,9 all calculations conc]n+ ! av]age rate ( progress ( a community1 or any ( its op]ations1 ! geometric mean %\ld be employ$4 ,= if a quantity increases #ajj p] c5t4 9 #ajj ye>s1 x w\ld n on ! av]age increase #aj p] c5t4 9 ea* t5 ye>s1 z ! #aj p] c5t4 w\ld at ! end ( ea* decade be calculat$ ^u l>g] & l>g] quantities1 & give at ! end ( #ajj ye>s mu* m ?an #ajj p] c5t41 9 fact z mu* z #aei p] c5t4 ,! true mean rate 9 ea* decade w\ld be #ajb or ab\t #ajg1 t is1 ! increase w\ld be ab\t #g p] c5t4 9 ea* t5 ye>s4 ,b :5 ! quantities diff] v little1 ! ari?metic & geometric means are approximately ! same4 ,?us ! ari?metic mean ( #ajjj & #ajja is #ajjje1 & ! geometric mean is ab\t #ajjjdiih1 ! diff]5ce be+ ( an ord] inappreciable 9 almo/ all sci5tific & practical matt]s4 ,ev5 9 ! comp>ison ( /&>d weights by ,gauss' me?od ( rev]sal1 ! ari?metic mean may usually be sub/itut$ = ! geometric mean :i* is ! true result4 ,reg>d+ ! mean 9 ! abs5ce ( express qualification to ! contr>y z ! common ari?metic mean1 we mu/ /ill di/+ui% betwe5 its two uses :]e x gives ) m or less accuracy & probability a really exi/+ quantity1 & :]e x acts z a m]e repres5tative ( o!r quantities4 ,if ,i make _m exp]im5ts to det]m9e ! atomic weight ( an elem5t1 !re is a c]ta9 numb] :i* ,i wi% to approximate to1 & ! mean ( my sep>ate results w1 9 ! abs5ce ( any reasons to ! contr>y1 be ! mo/ probable approximate result4 ,:5 we det]m9e ! mean d5sity ( ! e>?1 x is n because any "p ( ! e>? is ( t exact d5sity2 !re may be no "p exactly correspond+ to ! mean d5sity1 & z ! cru/ ( ! e>? has only ab\t half ! mean d5sity1 ! int]nal matt] ( ! globe mu/ ( c\rse be above ! mean4 ,ev5 ! d5sity ( a homog5e\s sub/ance l c>bon or gold mu/ be reg>d$ z a mean betwe5 ! real d5sity ( its atoms1 & ! z]o d5sity ( ! int]v5+ vacu\s space4 ,! v diff]5t signification ( ! ^w 8mean0 9 ^! two uses 0 fully expla9$ by ,quetelet1#bff & ! importance ( ! di/9ction 0 po9t$ out by ,sir ,john ,h]s*el 9 review+ 8 "w4#bfg ,x is mu* to be desir$ t sci5tific m5 w\ld m>k ! diff]5ce by us+ ! ^w 99mean99 only 9 ! =m] s5se :5 x d5otes approximation to a def9ite exi/+ quantity2 & 99av]age991 :5 ! mean is only a fictiti\s quantity1 us$ = conv5i5ce ( ?\ght & expression4 ,! etymology ( ?is ^w 8av]age0 is some:at obscure2 b accord+ to ,de ,morgan#bfh x comes f 99av]ia991 8hav+s or possessions10 especially appli$ to f>m /ock4 ,by ! accid5ts ( language 99av]agium99 came to mean ! lab\r ( f>m horses to :i* ! "l 0 entitl$1 & x probably acquir$ 9 ?is mann] ! notion ( di/ribut+ a :ole into p>ts1 a s5se 9 :i* x 0 e>ly appli$ to m>itime av]ages or contributions ( ! o!r own]s ( c>go to ^? ^: goods h be5 ?r[n ov]bo>d or us$ = ! safety ( ! vessel4 #bff 99,lett]s on ! ,!ory ( ,probabilities991 transl4 by ,d[nes1 ,"p ii4 #bfg ,h]s*el's 99,essays991 c4 pp4 #djd1 #dje4 #bfh 99,on ! ,!ory ( ,errors ( ,obs]vations1 ,cambridge ,philosophical ,transactions991 vol4 x4 ,"p ii4 #daf4 99,on ! ,av]age or ,fictiti\s ,mean499 ,al?\gh ! av]age :5 employ$ 9 its prop] s5se ( a fictiti\s mean1 repres5ts no really exi/+ quantity1 x is yet ( ! highe/ sci5tific importance1 z enabl+ u to conceive 9 a s+le result a multitude ( details4 ,x enables u to make a hypo!tical simplification ( a problem1 & avoid complexity )\t committ+ error4 ,! weight ( a body is ! sum ( ! weights ( inf9itely small p>ticles1 ea* act+ at a diff]5t place1 s t a me*anical problem resolves itself1 /rictly speak+1 into an inf9ite numb] ( di/9ct problems4 ,we owe to ,ar*im$es ! fir/ introduction ( ! beautiful idea t "o po9t may be discov]$ 9 a gravitat+ body su* t ! weight ( all ! p>ticles may be reg>d$ z conc5trat$ 9 t po9t1 & yet ! behavi\r ( ! :ole body w be exactly repres5t$ by ! behavi\r ( ?is heavy po9t4 ,?is ,c5tre ( ,gravity may be )9 ! body1 z 9 ! case ( a sph]e1 or x may be 9 empty space1 z 9 ! case ( a r+4 ,any two bodies1 :e!r connect$ or sep>ate1 may be conceiv$ z hav+ a c5tre ( gravity1 t ( ! sun & e>? ly+ )9 ! sun & only #bfg miles f its c5tre4 ,al?\gh we mo/ commonly use ! notion ( a c5tre or av]age po9t ) reg>d to gravity1 ! same notion is applicable to o!r cases4 ,t]re/rial gravity is a case ( approximately p>allel =ces1 & ! c5tre ( gravity is b a special case ( ! m g5]al ,c5tre ( ,p>allel ,=ces4 ,:]ev] a numb] ( =ces ( :atev] am\nt act 9 p>allel l9es1 x is possible to discov] a po9t at :i* ! algebraic sum ( ! =ces may be imag9$ to act ) exactly ! same effect4 ,wat] 9 a ci/]n presses aga9/ ! side ) a pressure v>y+ accord+ to ! dep?1 b always 9 a direction p]p5dicul> to ! side4 ,we may !n conceive ! :ole pressure z ex]t$ on "o po9t1 :i* w be "o-?ird f ! bottom ( ! ci/]n1 & may be call$ ! ,c5tre ( ,pressure4 ,! ,c5tre ( ,oscillation ( a p5dulum1 discov]$ by ,huygh5s1 is t po9t at :i* ! :ole weight ( ! p5dulum may be consid]$ z conc5trat$1 )\t alt]+ ! "t ( oscillation 7p4 #cae74 ,:5 "o body /rikes ano!r ! ,c5tre ( ,p]cussion is t po9t 9 ! /rik+ body at :i* all its mass might be conc5trat$ )\t alt]+ ! effect ( ! /roke4 ,9 position ! ,c5tre ( ,p]cussion does n diff] f ! ,c5tre ( ,oscillation4 ,ma!maticians h also describ$ ! ,c5tre ( ,gyration1 ! ,c5tre ( ,conv]sion1 ! ,c5tre ( ,friction1 c4 ,we ought c>efully to di/+ui% betwe5 ^? cases 9 :i* an 99inv>iable99 c5tre c be assign$1 & ^? 9 :i* x _c4 ,9 p]fect /rictness1 !re is no su* ?+ z a true inv>iable c5tre ( gravity4 ,z a g5]al rule a body is capable ( possess+ an inv>iable c5tre only = p]fectly p>allel =ces1 & gravity nev] does act 9 absolutely p>allel l9es4 ,?us1 z usual1 we f9d t our conceptions are only hypo!tically correct1 & only approximately applicable to real circum/ances4 ,!re are inde$ c]ta9 geometrical =ms call$ 99,c5trob>ic991#bfi su* t a body ( t %ape w\ld attract ano!r exactly z if ! mass 7 conc5trat$ at ! c5tre ( gravity1 :e!r ! =ces act 9 a p>allel mann] or n4 ,newton %[$ t uni=m sph]es ( matt] h ?is prop]ty1 & ?is tru? prov$ ( ! greate/ importance 9 simplify+ 8 calculations4 ,b x is aft] all a purely hypo!tical tru?1 because we c n[h]e meet )1 nor c we con/ruct1 a p]fectly sph]ical & homog5e\s body4 ,! slighte/ irregul>ity or protrusion f ! surface w de/roy ! rigor\s correctness ( ! assumption4 ,! sph]oid1 on ! o!r h&1 has no inv>iable c5tre at :i* its mass may always be reg>d$ z conc5trat$4 ,! po9t f :i* its resultant attraction acts w move ab\t accord+ to ! di/ance & position ( ! o!r attract+ body1 & x w only co9cide ) ! c5tre z reg>ds an inf9itely di/ant body ^: attractive =ces may be consid]$ z act+ 9 p>allel l9es4 #bfi ,?omson & ,tait1 99,treatise on ,natural ,philosophy991 vol4 i4 p4 #cid4 ,physici/s speak famili>ly ( ! poles ( a magnet1 & ! t]m may be us$ ) conv5i5ce4 ,b1 if we atta* any def9ite mean+ to ! ^w1 ! poles are n ! ends ( ! magnet1 nor any fix$ po9ts )91 b ! v>iable po9ts f :i* ! resultants ( all ! =ces ex]t$ by ! p>ticles 9 ! b> ^u ext]ior magnetic p>ticles may be consid]$ z act+4 ,! poles are1 9 %ort1 ,c5tres ( ,magnetic ,=ces2 b z ^? =ces are nev] really p>allel1 ^! c5tres w v>y 9 position accord+ to ! relative place ( ! object attract$4 ,only :5 we reg>d ! magnet z attract+ a v di/ant1 or1 /rictly speak+1 inf9itely di/ant p>ticle1 d its c5tres become fix$ po9ts1 situat$ 9 %ort magnets approximately at "o-six? ( ! :ole l5g? f ea* end ( ! b>4 ,we h 9 ! above in/ances ( c5tres or poles ( =ce suffici5t examples ( ! mode 9 :i* ! ,fictiti\s ,mean or ,av]age is employ$ 9 physical sci5ce4 99,! ,precise ,mean ,result499 ,we n[ turn to t mode ( employ+ ! mean result :i* is analog\s to ! me?od ( rev]sal1 b :i* is br\ght into practice 9 a mo/ ext5sive mann] ?r\gh\t _m bran*es ( physical sci5ce4 ,we f9d ! simple/ possible case 9 ! det]m9ation ( ! latitude ( a place by obs]vations ( ! ,pole-/>4 ,ty*o ,brahe sugge/$ t if ! elevation ( any circumpol> /> 7 obs]v$ at its high] & l[] passages across ! m]idian1 half ! sum ( ! elevations w\ld be ! latitude ( ! place1 :i* is equal to ! height ( ! pole4 ,su* a /> is z mu* above ! pole at its highe/ passage1 z x is bel[ at its l[e/1 s t ! mean mu/ necess>ily give ! height ( ! pole itself free f d\bt1 except z reg>ds incid5tal errors4 ,! ,pole-/> is usually select$ = ! purpose ( su* obs]vations because x describes ! smalle/ circle1 & is ?us on ! :ole lea/ affect$ by atmosph]ic refraction4 ,:5ev] sev]al causes are 9 action1 ea* ( :i* at "o "t increases & at ano!r "t decreases ! jo9t effect by equal quantities1 we may apply ?is me?od & dis5tangle ! effects4 ,?us ! sol> & lun> tides roll on 9 almo/ complete indep5d5ce ( ea* o!r4 ,:5 ! moon is new or full ! sol> tide co9cides1 or ne>ly s1 ) t caus$ by ! moon1 & ! jo9t effect is ! sum ( ! sep>ate effects4 ,:5 ! moon is 9 quadrature1 or half full1 ! two tides are act+ 9 opposition1 "o rais+ & ! o!r depress+ ! wat]1 s t we obs]ve only ! diff]5ce ( ! effects4 ,we h 9 fact-- ,spr+ tide lun> tide sol> tide2 ,neap tide lun> tide - sol> tide4 ,we h only !n to add toge!r ! heights ( ! maximum spr+ tide & ! m9imum neap tide1 & half ! sum is ! true height ( ! lun> tide4 ,half ! diff]5ce ( ! spr+ & neap tides on ! o!r h& gives ! sol> tide4 ,effects ( v small am\nt may be detect$ ) great approa* to c]ta9ty among mu* great] fluctuations1 provid$ t we h a s]ies ( obs]vations suffici5tly num]\s & long cont9u$ to enable u to balance all ! l>g] effects aga9/ ea* o!r4 ,= ?is purpose ! obs]vations %\ld be cont9u$ ov] at lea/ "o complete cycle1 9 :i* ! effects run ?r\gh all _! v>iations1 & return exactly to ! same relative positions z at ! comm5cem5t4 ,if casual or irregul> di/urb+ causes exi/1 we %\ld probably require _m su* cycles ( results to r5d] _! effect inappreciable4 ,we obta9 ! desir$ result by tak+ ! mean ( all ! obs]vations 9 :i* a cause acts positively1 & ! mean ( all 9 :i* x acts negatively4 ,half ! diff]5ce ( ^! means w give ! effect ( ! cause 9 "q1 provid$ t no o!r effect happ5s to v>y 9 ! same p]iod or ne>ly s4 ,s9ce ! moon causes a movem5t ( ! ocean1 x is evid5t t its attraction mu/ h "s effect ^u ! atmosph]e4 ,! laws ( atmosph]ic tides 7 inve/igat$ by ,laplace1 b z x w\ld be impracticable by !ory to calculate _! am\nts we c only det]m9e !m by obs]vation1 z ,laplace pr$ict$ t !y w\ld "o day be det]m9$4#bgj ,b ! oscillations ( ! b>omet] ?us caus$ are f> small] ?an ! oscillations due to sev]al o!r causes4 ,/orms1 hurricanes1 or *anges ( wea!r produce movem5ts ( ! b>omet] sometimes z mu* z a ?\s& times z great z ! tides 9 "q4 ,!re are also regul> daily1 ye>ly1 or o!r fluctuations1 all great] ?an ! desir$ quantity4 ,to detect & measure ! atmosph]ic tide x 0 desirable t obs]vations %\ld be made 9 a place z free z possible f irregul> di/urbances4 ,on ?is acc\nt sev]al long s]ies ( obs]vations 7 made at ,/4 ,hel5a1 :]e ! b>omet] is f> m regul> 9 its movem5ts ?an 9 a cont95tal climate4 ,! effect ( ! moon's attraction 0 !n detect$ by tak+ ! mean ( all ! read+s :5 ! moon 0 on ! m]idian & ! simil> mean :5 %e 0 on ! horizon4 ,! diff]5ce ( ^! means 0 f\nd to be only #jjcfe1 yet x 0 possible to discov] ev5 ! v>iation ( ?is tide accord+ z ! moon 0 ne>] to or fur!r f ! e>?1 ?\gh ?is diff]5ce 0 only #jjjef in*4#bga ,x is q evid5t t su* m9ute effects c\ld nev] be discov]$ 9 a purely empirical mann]4 ,hav+ no in=mation b ! s]ies ( obs]vations be=e u1 we c\ld h no clue z to ! mode ( gr\p+ !m :i* w\ld give s small a diff]5ce4 ,9 apply+ ?is me?od ( means 9 an ext5sive mann] we mu/ g5]ally !n h 99 priori99 k z to ! p]iods at :i* a cause w act 9 "o direction or ! o!r4 #bgj 99,essai ,philosophique sur les ,probabilits991 pp4 #di1 #ej4 #bga ,grant1 99,hi/ory ( ,physical ,a/ronomy991 p4 #afc4 ,we are sometimes able to elim9ate fluctuations & take a mean result by purely me*anical arrangem5ts4 ,! daily v>iations ( temp]ature1 = in/ance1 become imp]ceptible "o or two feet bel[ ! surface ( ! e>?1 s t a !rmomet] plac$ ) its bulb at t dep? gives v ne>ly ! true daily mean temp]ature4 ,at a dep? ( tw5ty feet ev5 ! ye>ly fluctuations are ne>ly effac$1 & ! !rmomet] /&s a little above ! true mean temp]ature ( ! locality4 ,9 regi/]+ ! rise & fall ( ! tide by a tide-gauge1 x is desirable to avoid ! oscillations aris+ f surface waves1 :i* is v readily accompli%$ by plac+ ! float 9 a ci/]n communicat+ by a small hole ) ! sea4 ,only a g5]al rise or fall ( ! level is !n p]ceptible1 j z 9 ! m>9e b>omet] ! n>r[ tube prev5ts any casual fluctuations & all[s only a cont9u$ *ange ( pressure to manife/ itself4 99,det]m9ation ( ! ,z]o po9t499 ,9 _m important obs]vations ! *ief difficulty consi/s 9 def9+ exactly ! z]o po9t f :i* we are to measure4 ,we c po9t a telescope ) great precision to a /> & c measure to a second ( arc ! angle ?r\gh :i* ! telescope is rais$ or l[]$2 b all ?is precision w be useless unless we "k exactly ! c5tre po9t ( ! heav5s f :i* we measure1 or1 :at comes to ! same ?+1 ! horizontal l9e #ij di/ant f x4 ,s9ce ! true horizon has ref]5ce to ! figure ( ! e>? at ! place ( obs]vation1 we c only det]m9e x by ! direction ( gravity1 z m>k$ ei!r by ! plumb-l9e or ! surface ( a liquid4 ,! "q resolves itself !n into ! mo/ accurate mode ( obs]v+ ! direction ( gravity1 & z ! plumb-l9e has long be5 f\nd hopelessly inaccurate1 a/ronom]s g5]ally employ ! surface ( m]cury 9 repose z ! crit]ion ( horizontality4 ,!y +5i\sly obs]ve ! direction ( ! surface by mak+ a /> ! index4 ,f ! laws ( reflection x foll[s t ! angle betwe5 ! direct ray f a /> & t reflect$ f a surface ( m]cury w be exactly d\ble ! angle betwe5 ! surface & ! direct ray f ! />4 ,h5ce ! horizontal or z]o po9t is ! mean betwe5 ! app>5t place ( any /> or o!r v di/ant object & its reflection 9 m]cury4 ,a plumb-l9e is p]p5dicul>1 or a liquid surface is horizontal only 9 an approximate s5se2 = any irregul>ity ( ! surface ( ! e>?1 a m\nta91 or ev5 a h\se mu/ cause "s deviation by its attract+ p[]4 ,to detect su* deviation might seem v difficult1 because e o!r plumb-l9e or liquid surface w\ld be equally affect$ by gravity4 ,nev]!less x c be detect$2 = if we place "o plumb-l9e to ! nor? ( a m\nta91 & ano!r to ! s\?1 !y w be ab\t equally deflect$ 9 opposite directions1 & if by obs]vations ( ! same /> we c measure ! angle betwe5 ! plumb-l9es1 half ! incl9ation w be ! deviation ( ei!r1 aft] all[ance has be5 made = ! incl9ation due to ! diff]5ce ( latitude ( ! two places ( obs]vation4 ,by ?is mode ( obs]vation appli$ to ! m\nta9 ,s*iehallion ! deviation ( ! plumb-l9e 0 accurately measur$ by ,maskelyne1 & ?us a comp>ison in/itut$ betwe5 ! attractive =ces ( ! m\nta9 & ! :ole globe1 :i* l$ to a probable e/imate ( ! e>?'s d5sity4 ,9 "s cases x is actually bett] to det]m9e ! z]o po9t by ! av]age ( equally div]g+ quantities ?an by direct obs]vation4 ,9 delicate weigh+s by a *emical balance x is requisite to asc]ta9 exactly ! po9t at :i* ! beam comes to re/1 & :5 /&>d weights are be+ comp>$ ! position ( ! beam is asc]ta9$ by a c>efully divid$ scale view$ ?r\gh a microscope4 ,b :5 ! beam is j com+ to re/1 friction1 small imp$im5ts or o!r accid5tal causes may readily ob/ruct x1 because x is ne> ! po9t at :i* ! =ce ( /ability becomes inf9itely small4 ,h5ce x is f\nd bett] to let ! beam vibrate & obs]ve ! t]m9al po9ts ( ! vibrations4 ,! mean betwe5 two extreme po9ts w ne>ly indicate ! position ( re/4 ,friction & ! resi/ance ( air t5d to r$uce ! vibrations1 s t ?is mean w be errone\s by half ! am\nt ( ?is effect dur+ a half vibration4 ,b by tak+ sev]al obs]vations we may det]m9e ?is ret>dation & all[ = x4 ,?us if 99a991 99b991 99c99 be ! read+s ( ! t]m9al po9ts ( ?ree excursions ( ! beam f ! z]o ( ! scale1 !n #a_/b799;a99 99b997 w be ab\t z mu* errone\s 9 "o direction z #a_/b799;b99 99c997 9 ! o!r1 s t ! mean ( ^! two means1 or #a_/d799;a99 #b99;b99 99c9971 w be exce$+ly ne> to ! po9t ( re/4#bgb ,a /ill clos] approximation may be made by tak+ f\r read+s & r$uc+ !m by ! =mula #a_/f799;a99 #b99;b99 #b99;c99 99d9974 #bgb ,gauss1 ,taylor's 99,sci5tific ,memoirs991 vol4 ii4 p4 #dc1 c4 ,! accuracy ( ,baily's exp]im5ts1 direct$ to det]m9e ! d5sity ( ! e>?1 entirely dep5d$ ^u ?is mode ( obs]v+ oscillations4 ,! balls ^: gravitation 0 measur$ 7 s delicately susp5d$ by a torsion balance t !y nev] came to re/4 ,! extreme po9ts ( ! oscillations 7 obs]v$ bo? :5 ! heavy lead5 attract+ ball 0 on "o side & on ! o!r4 ,! diff]5ce ( ! mean po9ts :5 ! lead5 ball 0 on ! "r h& & t :5 x 0 on ! left h& gave d\ble ! am\nt ( ! deflection4 ,a beautiful in/ance ( avoid+ ! use ( a z]o po9t is f\nd 9 ,mr4 ,e4 ,j4 ,/one's obs]vations on ! radiant heat ( ! fix$ />s4 ,! difficulty ( ^! obs]vations arose f ! comp>atively great am\nts ( heat :i* 7 s5t into ! telescope f ! atmosph]e1 & :i* 7 suffici5t to disguise almo/ entirely ! feeble heat rays ( a />4 ,b ,mr4 ,/one fix$ at ! focus ( 8 telescope a d\ble !rmo-electric pile ( :i* ! two p>ts 7 rev]s$ 9 ord]4 ,n[ any di/urbance ( temp]ature :i* act$ uni=mly ^u bo? piles produc$ no effect ^u ! galvanomet] ne$le1 & :5 ! rays ( ! /> 7 made to fall alt]nately ^u "o pile & ! o!r1 ! total am\nt ( ! deflection repres5t$ d\ble ! heat+ p[] ( ! />4 ,?us ,mr4 ,/one 0 able to detect ) mu* c]ta9ty a heat+ effect ( ! /> ,arcturus1 :i* ev5 :5 conc5trat$ by ! telescope am\nt$ only to #jjb ,fahr41 & :i* repres5ts a heat+ effect ( ! direct ray ( only ab\t #jjjjjjacg ,fahr41 equival5t to ! heat :i* w\ld be receiv$ f a ?ree-in* cubic vessel full ( boil+ wat] at ! di/ance ( #djj y>ds4#bgc ,x is probable t ,mr4 ,/one's arrangem5t ( ! pile might be usefully employ$ 9 o!r delicate !rmometric exp]im5ts subject to consid]able di/urb+ influ5ces4 #bgc 99,proce$+s ( ! ,royal ,society991 vol4 xviii4 p4 #aei 7,jan4 #ac1 #ahgj74 99,philosophical ,magaz9e99 7#d? ,s]ies71 vol4 xxxix4 p4 #cgf4 99,det]m9ation ( ,maximum ,po9ts499 ,we employ ! me?od ( means 9 a c]ta9 numb] ( obs]vations direct$ to det]m9e ! mom5t at :i* a ph5om5on rea*es its highe/ po9t 9 quantity4 ,9 not+ ! place ( a fix$ /> at a giv5 "t !re is no difficulty 9 asc]ta9+ ! po9t to be obs]v$1 = a /> 9 a good telescope pres5ts an exce$+ly small disc4 ,9 obs]v+ a nebul\s body :i* f a bright c5tre fades gradually away on all sides1 x w n be possible to select ) c]ta9ty ! middle po9t4 ,9 _m su* cases ! be/ me?od is n to select arbitr>ily ! suppos$ middle po9t1 b po9ts ( equal brightness on ei!r side1 & !n take ! mean ( ! obs]vations ( ^! two po9ts = ! c5tre4 ,z a g5]al rule1 a v>iable quantity 9 rea*+ its maximum increases at a less & less rate1 & aft] pass+ ! highe/ po9t beg9s to decrease by ins5sible degrees4 ,! maximum may inde$ be def9$ z t po9t at :i* ! increase or decrease is null4 ,h5ce x w usually be ! mo/ indef9ite po9t1 & if we c accurately measure ! ph5om5on we %all be/ det]m9e ! place ( ! maximum by det]m9+ po9ts on ei!r side at :i* ! ord9ates are equal4 ,!re is moreov] ?is advantage 9 ! me?od t sev]al po9ts may be det]m9$ ) ! correspond+ ones on ! o!r side1 & ! mean ( ! :ole tak5 z ! true place ( ! maximum4 ,b ?is me?od entirely dep5ds ^u ! exi/5ce ( symmetry 9 ! curve1 s t ( two equal ord9ates "o %all be z f> on "o side ( ! maximum z ! o!r is on ! o!r side4 ,! me?od fails :5 o!r laws ( v>iation prevail4 ,9 tidal obs]vations great difficulty is enc\nt]$ 9 fix+ ! mom5t ( high wat]1 because ! rate at :i* ! wat] is !n ris+ or fall+1 is almo/ imp]ceptible4 ,:ewell propos$1 !re=e1 to note ! "t at :i* ! wat] passes a fix$ po9t some:at bel[ ! maximum bo? 9 ris+ & fall+1 & take ! mean "t z t ( high wat]4 ,b ?is mode ( proce$+ un=tunately does n give a correct result1 because ! tide foll[s diff]5t laws 9 ris+ & 9 fall+4 ,!re is a difficulty aga9 9 select+ ! highe/ spr+ tide1 ano!r object ( mu* importance 9 tidology4 ,laplace discov]$ t ! tide ( ! second day prec$+ ! conjunction ( ! sun & moon is ne>ly equal to t ( ! fif? day foll[+2 &1 believ+ t ! increase & decrease ( ! tides proce$$ 9 a ne>ly symmetrical mann]1 he decid$ t ! highe/ tide w\ld occur ab\t ?irty-six h\rs aft] ! conjunction1 t is half-way betwe5 ! second day be=e & ! fif? day aft]4#bgd #bgd ,airy 99,on ,tides & ,waves991 ,encycl4 ,metrop4 pp4 #cfd99-cff994 ,?is me?od is also employ$ 9 det]m9+ ! "t ( passage ( ! middle or d5se/ po9t ( a /ream ( meteors4 ,! e>? takes two or ?ree days 9 pass+ completely ?r\gh ! ,novemb] /ream2 b a/ronom]s ne$ = _! calculations to h "s def9ite po9t fix$ )9 a few m9utes if possible4 ,:5 ne> to ! middle !y obs]ve ! numb]s ( meteors :i* come )9 ! sph]e ( vision 9 ea* half h\r1 or qu>t] h\r1 & !n1 assum+ t ! law ( v>iation is symmetrical1 !y select a mom5t = ! passage ( ! c5tre equidi/ant betwe5 times ( equal frequ5cy4 ,! eclipses ( ,jupit]'s satellites are n only ( great int]e/ z reg>ds ! motions ( ! satellites !mselves1 b 71 & p]haps /ill are1 ( use 9 det]m9+ longitudes1 because !y are ev5ts occurr+ at fix$ mom5ts ( absolute "t1 & visible 9 all p>ts ( ! planet>y sy/em at ! same "t1 all[ance be+ made = ! int]val occupi$ by ! light 9 travell+4 ,b1 z is expla9$ by ,h]s*el1#bge ! mom5t ( ! ev5t is want+ 9 def9it5ess1 p>tly because ! long cone ( ,jupit]'s %ad[ is surr\nd$ by a p5umbra1 & p>tly because ! satellite has itself a s5sible disc1 & takes "t 9 ent]+ ! %ad[4 ,diff]5t obs]v]s us+ diff]5t telescopes w\ld usually select diff]5t mom5ts = t ( ! eclipse4 ,b ! increase ( light 9 ! em]sion w proce$ accord+ to a law ! rev]se ( t obs]v$ 9 ! imm]sion1 s t if an obs]v] notes ! "t ( bo? ev5ts ) ! same telescope1 he w be z mu* too soon 9 "o obs]vation z he is too late 9 ! o!r1 & ! mean mom5t ( ! two obs]vations w repres5t ) consid]able accuracy ! "t :5 ! satellite is 9 ! middle ( ! %ad[4 ,error ( judgm5t ( ! obs]v] is ?us elim9at$1 provid$ t he takes c>e to act at ! em]sion z he did at ! imm]sion4 #bge 99,outl9es ( ,a/ronomy991 #d? edition1 #ech4 ,,*apt] ,,xvii4 ,,! ,,law ,,( ,,error4 ,to br+ error itself "u law might seem beyond human p[]4 ,he :o errs surely div]ges f law1 & x might be deem$ hopeless out ( error to draw tru?4 ,"o ( ! mo/ rem>kable a*ievem5ts ( ! human intellect is ! e/abli%m5t ( a g5]al !ory :i* n only enables u among discrepant results to approximate to ! tru?1 b to assign ! degree ( probability :i* fairly atta*es to ?is conclusion4 ,x w\ld be a mi/ake inde$ to suppose t ?is law is necess>ily ! be/ guide "u all circum/ances4 ,e measur+ in/rum5t & e =m ( exp]im5t may h its own special law ( error2 !re may 9 "o in/rum5t be a t5d5cy 9 "o direction & 9 ano!r 9 ! opposite direction4 ,e process has its peculi> liabilities to di/urbance1 & we are nev] reliev$ f ! necessity ( provid+ aga9/ special difficulties4 ,! g5]al ,law ( ,error is ! be/ guide only :5 we h exhau/$ all o!r means ( approximation1 & /ill f9d discrepancies1 :i* are due to unkn[n causes4 ,we mu/ treat su* residual diff]5ces 9 "s way or o!r1 s9ce !y w occur 9 all accurate exp]im5ts1 & z _! orig9 is assum$ to be unkn[n1 !re is no reason :y we %\ld treat !m diff]5tly 9 diff]5t cases4 ,accord+ly ! ultimate ,law ( ,error mu/ be a uni=m & g5]al "o4 ,x is p]fectly recognis$ by ma!maticians t 9 ea* case a special ,law ( ,error may exi/1 & %\ld be discov]$ if possible4 8,no?+ c be m unlikely ?an t ! errors committ$ 9 all classes ( obs]vations %\ld foll[ ! same law10#bgf & ! special ,laws ( ,error :i* w apply to c]ta9 in/rum5ts1 z = in/ance ! repeat+ circle1 h be5 inve/igat$ by ,bravais4#bgg ,he concludes t e di/9ct cause ( error gives rise to a curve ( possibility ( errors1 :i* may h any =m1--a curve :i* we may ei!r be able or unable to discov]1 & :i* 9 ! fir/ case may be det]m9$ by 99 priori99 consid]ations on ! peculi> nature ( ?is cause1 or :i* may be det]m9$ 99 po/]iori99 by obs]vation4 ,:5ev] x is practicable & wor? ! lab\r1 we ought to inve/igate ^! special conditions ( error2 nev]!less1 :5 !re are a great numb] ( diff]5t s\rces ( m9ute error1 ! g5]al resultant w always t5d to obey t g5]al law :i* we are ab\t to consid]4 #bgf 99,philosophical ,magaz9e991 #crd ,s]ies1 vol4 xxxvii4 p4 #cbd4 #bgg 99,lett]s on ! ,!ory ( ,probabilities991 by ,quetelet1 translat$ by ,o4 ,g4 ,d[nes1 ,notes to ,lett] ,,xxvi4 pp4 #bhf-bie4 99,e/abli%m5t ( ! ,law ( ,error499 ,ma!maticians agree f> bett] z to ! =m ( ! ,law ( ,error ?an !y d z to ! mann] 9 :i* x c be d$uc$ & prov$4 ,!y agree t among a numb] ( discrepant results ( obs]vation1 t mean quantity is probably ! be/ approximation to ! tru? :i* makes ! sum ( ! squ>es ( ! errors z small z possible4 ,b !re are ?ree pr9cipal ways 9 :i* ?is law has be5 arriv$ at respectively by ,gauss1 by ,laplace & ,quetelet1 & by ,sir ,john ,h]s*el4 ,gauss proce$s mu* ^u assumption2 ,h]s*el re/s ^u geometrical consid]ations2 :ile ,laplace & ,quetelet reg>d ! ,law ( ,error z a developm5t ( ! doctr9e ( comb9ations4 ,a numb] ( o!r ma!maticians1 su* z ,adra9 ( ,new ,brunswick1 ,bessel1 ,ivory1 ,donk91 ,leslie ,ellis1 ,tait1 & ,cr(ton h ei!r attempt$ indep5d5t pro(s or h modifi$ or comm5t$ on ^? "h to be describ$4 ,= full acc\nts ( ! lit]ature ( ! subject ! read] %\ld ref] ei!r to ,mr4 ,todhunt]'s 99,hi/ory ( ! ,!ory ( ,probability99 or to ! able memoir ( ,mr4 ,j4 ,w4 ,l4 ,glai%]4#bgh #bgh 99,on ! ,law ( ,facility ( ,errors ( ,obs]vations1 & on ! ,me?od ( ,lea/ ,squ>es991 ,memoirs ( ! ,royal ,a/ronomical ,society1 vol4 xxxix4 p4 #ge4 ,accord+ to ,gauss ! ,law ( ,error expresses ! comp>ative probability ( errors ( v>i\s magnitude1 & p>tly f exp]i5ce1 p>tly f 99 priori99 consid]ations1 we may readily lay d[n c]ta9 conditions to :i* ! law w c]ta9ly con=m4 ,x may fairly be assum$ z a fir/ pr9ciple to guide u 9 ! selection ( ! law1 t l>ge errors w be f> less frequ5t & probable ?an small ones4 ,we "k t v l>ge errors are almo/ impossible1 s t ! probability mu/ rapidly decrease z ! am\nt ( ! error increases4 ,a second pr9ciple is t positive & negative errors %all be equally probable1 :i* may c]ta9ly be assum$1 because we are suppos$ to be devoid ( any k z to ! causes ( ! residual errors4 ,x foll[s t ! probability ( ! error mu/ be a function ( an ev5 p[] ( ! magnitude1 t is ( ! squ>e1 or ! f\r? p[]1 or ! six? p[]1 o!rwise ! probability ( ! same am\nt ( error w\ld v>y accord+ z ! error 0 positive or negative4 ,! ev5 p[]s 99x99#b1 99x99#d1 99x99#f1 c41 are always intr9sically positive1 :e!r 99x99 be positive or negative4 ,!re is no 99 priori99 reason :y "o r ?an ano!r ( ^! ev5 p[]s %\ld be select$4 ,gauss himself all[s t ! f\r? or six? p[] w\ld fulfil ! conditions z well z ! second2#bgi b 9 ! abs5ce ( any !oretical reasons we %\ld pref] ! second p[]1 because x leads to =mul ( great comp>ative simplicity4 ,did ! ,law ( ,error necessitate ! use ( ! high] p[]s ( ! error1 ! complexity ( ! necess>y calculations w\ld mu* r$uce ! utility ( ! !ory4 #bgi 99,m?ode des ,mo9dres ,c>rs4 ,mmoires sur la ,comb9aison des ,obs]vations1 p> ,*4 ,fr4 ,gauss4 ,traduit en ,franais p> ,j4 ,b]tr&991 ,p>is1 #ahee1 pp4 #f1 #acc1 c4 ,by ma!matical reason+ :i* x w\ld be undesirable to attempt to foll[ 9 ?is book1 x is %[n t "u ^! conditions1 ! facility ( occurr5ce1 or 9 o!r1 words1 ! probability ( error is express$ by a function ( ! g5]al =m -99h99#b 99x99#b1 9 :i* 99x99 repres5ts ! v>iable am\nt ( errors4 ,f ?is law1 to be m fully describ$ 9 ! foll[+ sections1 x at once foll[s t ! mo/ probable result ( any obs]vations is t :i* makes ! sum ( ! squ>es ( ! consequ5t errors ! lea/ possible4 ,let 99a991 99b991 99c991 c41 be ! results ( obs]vation1 & 99x99 ! quantity select$ z ! mo/ probable1 t is ! mo/ free f unkn[n errors3 !n we mu/ det]m9e 99x99 s t 799a99 - 99x997#b 799b99 - 99x997#b 799c99 - 99x997#b 444 %all be ! lea/ possible quantity4 ,?us we arrive at ! celebrat$ 99,me?od ( ,lea/ ,squ>es991 z x is usually call$1 :i* appe>s to h be5 fir/ di/9ctly put 9 practice by ,gauss 9 #agie1 :ile ,leg5dre fir/ publi%$ 9 #ahjf an acc\nt ( ! process 9 8 "w1 entitl$1 99,n\velles ,m?odes p\r la ,dt]m9ation des ,orbites des ,comtes994 ,x is wor?y ( notice1 h[ev]1 t ,rog] ,cotes _h long previ\sly recomm5d$ a me?od ( equival5t nature 9 8 tract1 8,e/imatio ,erroris 9 ,mixta ,ma!si40#bhj #bhj ,de ,morgan1 99,p5ny ,cyclopdia991 art4 99,lea/ ,squ>es994 99,h]s*el's ,geometrical ,pro(499 ,a second way ( arriv+ at ! ,law ( ,error 0 propos$ by ,h]s*el1 & al?\gh only applicable to geometrical cases1 x is rem>kable z %[+ t f :atev] po9t ( view we reg>d ! subject1 ! same pr9ciple w be detect$4 ,aft] assum+ t "s g5]al law mu/ exi/1 & t x is subject to ! pr9ciples ( probability1 he supposes t a ball is dropp$ f a high po9t ) ! int5tion t x %all /rike a giv5 m>k on a horizontal plane4 ,9 ! abs5ce ( any kn[n causes ( deviation x w ei!r /rike t m>k1 or1 z is inf9itely m probable1 div]ge f x by an am\nt :i* we mu/ reg>d z error ( unkn[n orig94 ,n[1 to quote ! words ( ,h]s*el1#bha 8! probability ( t error is ! unkn[n function ( its squ>e1 99i4e499 ( ! sum ( ! squ>es ( its deviations 9 any two rectangul> directions4 ,n[1 ! probability ( any deviation dep5d+ solely on its magnitude1 & n on its direction1 x foll[s t ! probability ( ea* ( ^! rectangul> deviations mu/ be ! same function ( 99its99 squ>e4 ,& s9ce ! obs]v$ oblique deviation is equival5t to ! two rectangul> ones1 suppos$ concurr5t1 & :i* are ess5tially indep5d5t ( "o ano!r1 & is1 !re=e1 a comp\nd ev5t ( :i* !y are ! simple indep5d5t con/itu5ts1 !re=e its probability w be ! product ( _! sep>ate probabilities4 ,?us ! =m ( our unkn[n function comes to be det]m9$ f ?is condition1 viz41 t ! product ( su* functions ( two indep5d5t elem5ts is equal to ! same function ( _! sum4 ,b x is %[n 9 e "w on algebra t ?is prop]ty is ! peculi> *>act]i/ic (1 & belongs only to1 ! expon5tial or antilog>i?mic function4 ,?is1 !n1 is ! function ( ! squ>e ( ! error1 :i* expresses ! probability ( committ+ t error4 ,t probability decreases1 !re=e1 9 geometrical progression1 z ! squ>e ( ! error increases 9 ari?metical40 #bha 99,ed9burgh ,review991 ,july #ahej1 vol4 xcii4 p4 #ag4 ,repr9t$ 99,essays991 p4 #cii4 ,?is me?od ( demon/ration is discuss$ by ,boole1 99,transactions ( ,royal ,society ( ,ed9burgh991 vol4 xxi4 pp4 #fbg-fcj4 99,laplace's & ,quetelet's ,pro( ( ! ,law499 ,h[ev] mu* presumption ! modes ( det]m9+ ! ,law ( ,error1 already describ$1 may give 9 fav\r ( ! law usually adopt$1 x is difficult to feel t ! argum5ts are satisfactory4 ,! law adopt$ is *os5 r on ! gr\nds ( conv5i5ce & plausibility1 ?an because x c be se5 to be ! necess>y law4 ,we c h[ev] approa* ! subject f an entirely diff]5t po9t ( view1 & yet get to ! same result4 ,let u assume t a p>ticul> obs]vation is subject to f\r *ances ( error1 ea* ( :i* w increase ! result "o in* if x occurs4 ,ea* ( ^! errors is to be reg>d$ z an ev5t indep5d5t ( ! re/ & we c !re=e assign1 by ! !ory ( probability1 ! comp>ative probability & frequ5cy ( ea* conjunction ( errors4 ,f ! ,ari?metical ,triangle 7pp4 #ahb-ahh7 we le>n t no error at all c happ5 only 9 "o way2 an error ( "o in* c happ5 9 #d ways2 & ! ways ( happ5+ ( errors ( #b1 #c & #d in*es respectively1 w be #f1 #d & #a 9 numb]4 ,we may inf] t ! error ( two in*es is ! mo/ likely to occur1 & w occur 9 ! long run 9 six cases out ( sixte54 ,errors ( "o & ?ree in*es w be equally likely1 b w occur less frequ5tly2 :ile no error at all1 or "o ( f\r in*es w be a comp>atively r>e occurr5ce4 ,if we n[ suppose ! errors to act z (t5 9 "o direction z ! o!r1 ! effect w be to alt] ! av]age error by ! am\nt ( two in*es1 & we %all h ! foll[+ results3-- ,negative error ( #b in*es #a way4 ,negative error ( #a in* #d ways4 ,no error at all #f ways4 ,positive error ( #a in* #d ways4 ,positive error ( #b in*es #a way4 ,we may n[ imag9e ! numb] ( causes ( error increas$ & ! am\nt ( ea* error decreas$1 & ! ari?metical triangle w give u ! frequ5cy ( ! result+ errors4 ,?us if !re be five positive causes ( error & five negative causes1 ! foll[+ table %[s ! numb]s ( errors ( v>i\s am\nt :i* w be ! result3-- ---------------------------------------- ----------------------- ,direction ( ,error4 ,positive ,error4 ,negative ,error4 ---------------------------------------- ----------------------- ,am\nt ( ,error4 #e1 #d1 #c1 #b1 #a #j #a1 #b1 #c1 #d1 #e ---------------------------------------- ----------------------- ,numb] ( su* ,errors4#a1 #aj1 #de1 #abj1 #bajbebbaj1 #abj1 #de1 #aj1 #a ---------------------------------------- ----------------------- ,x is pla9 t f su* numb]s ,i c asc]ta9 ! probability ( any p>ticul> am\nt ( error "u ! conditions suppos$4 ,! probability ( a positive error ( exactly "o in* is #baj_/ajbd1 9 :i* fraction ! num]ator is ! numb] ( comb9ations giv+ "o in* positive error1 & ! d5om9ator ! :ole numb] ( possible errors ( all magnitudes4 ,i c also1 by add+ toge!r ! appropriate numb]s get ! probability ( an error n exce$+ a c]ta9 am\nt4 ,?us ! probability ( an error ( ?ree in*es or less1 positive or negative1 is a fraction ^: num]ator is ! sum ( #de #abj #baj #beb #baj #abj #de1 & ! d5om9ator1 z be=e1 giv+ ! result #ajjb_/ajbd4 ,we may see at once t1 accord+ to ^! pr9ciples1 ! probability ( small errors is f> great] ?an ( l>ge ones3 ! odds are #ajjb to #bb1 or m ?an #de to #a1 t ! error w n exce$ ?ree in*es2 & ! odds are #ajbb to #b aga9/ ! occurr5ce ( ! greate/ possible error ( five in*es4 ,if any case %\ld arise 9 :i* ! obs]v] kn[s ! numb] & magnitude ( ! *ief errors :i* may occur1 he ought c]ta9ly to calculate f ! ,ari?metical ,triangle ! special ,law ( ,error :i* w\ld apply4 ,b ! g5]al law1 ( :i* we are 9 se>*1 is to be us$ 9 ! d>k1 :5 we h no k :atev] ( ! s\rces ( error4 ,to assume any special numb] ( causes ( error is !n an arbitr>y proce$+1 & ma!maticians h *os5 ! lea/ arbitr>y c\rse ( imag9+ ! exi/5ce ( an inf9ite numb] ( inf9itely small errors1 j z1 9 ! inv]se me?od ( probabilities1 an inf9ite numb] ( inf9itely improbable hypo!ses 7 submitt$ to calculation 7p4 #bee74 ,! reasons 9 fav\r ( ?is *oice are ( sev]al diff]5t k9ds4 #a4 ,x _c be d5i$ t !re may exi/ inf9itely num]\s causes ( error 9 any act ( obs]vation4 #b4 ,! law result+ f ! hypo!sis ( a mod]ate numb] ( causes ( error1 does n appreciably diff] f t giv5 by ! hypo!sis ( an inf9ite numb] ( causes ( error4 #c4 ,we ga9 by ! hypo!sis ( inf9ity a g5]al law capable ( ready calculation1 & applicable by uni=m rules to all problems4 #d4 ,?is law1 :5 te/$ by comp>ison ) ext5sive s]ies ( obs]vations1 is /rik+ly v]ifi$1 z w be %[n 9 a lat] section4 ,:5 we imag9e ! exi/5ce ( any l>ge numb] ( causes ( error1 = in/ance "o hundr$1 ! numb]s ( comb9ations become impracticably l>ge1 z may be se5 to be ! case f a glance at ! ,ari?metical ,triangle1 :i* proce$s only up to ! sev5te5? l9e4 ,quetelet1 by suitable abbreviat+ processes1 calculat$ out a table ( probability ( errors on ! hypo!sis ( "o ?\s& di/9ct causes2#bhb b ma!maticians h g5]ally proce$$ on ! hypo!sis ( inf9ity1 & !n1 by ! devices ( analysis1 h sub/itut$ a g5]al law ( easy treatm5t4 ,9 ma!matical works ^u ! subject1 x is %[n t ! /&>d ,law ( ,error is express$ 9 ! =mula 99y99 99,y99-99cx99#b1 #bhb 99,lett]s on ! ,!ory ( ,probabilities991 ,lett] ,,xv4 & ,app5dix1 note pp4 #bef-bff4 9 :i* 99x99 is ! am\nt ( ! error1 99,y99 ! maximum ord9ate ( ! curve ( error1 & 99c99 a numb] con/ant = ea* s]ies ( obs]vations1 & express+ ! am\nt ( ! t5d5cy to error1 v>y+ betwe5 "o s]ies ( obs]vations & ano!r4 ,! lett] is ! ma!matical con/ant1 ! sum ( ratios betwe5 ! numb]s ( p]mutations & comb9ations1 previ\sly ref]r$ to 7p4 #ccj74 ,illu/ration ,to %[ ! close correspond5ce ( ?is g5]al law ) ! special law :i* might be d]iv$ f ! supposition ( a mod]ate numb] ( causes ( error1 ,i h 9 ! accompany+ figure drawn a curv$ l9e repres5t+ accurately ! v>iation ( 99y99 :5 99x99 9 ! above =mula is tak5 equal #j1 #a_/b1 #a1 #c_/b1 #b1 c41 positive or negative1 ! arbitr>y quantities 99,y99 & 99c99 be+ ea* assum$ equal to unity1 9 ord] to simplify ! calculations4 ,9 ! same figure are ins]t$ elev5 dots1 ^: heights above ! base l9e are proportional to ! numb]s 9 ! elev5? l9e ( ! ,ari?metical ,triangle1 ?us repres5t+ ! comp>ative probabilities ( errors ( v>i\s am\nts aris+ f t5 equal causes ( error4 ,! correspond5ce ( ! g5]al & ! special ,law ( ,error is almo/ z close z c be exhibit$ 9 ! figure1 & ! assumption ( a great] numb] ( equal causes ( error w\ld r5d] ! correspond5ce f> m close4 ,x may be expla9$ t ! ord9ates ,,nm1 99nm991 99nm991 repres5t values ( 99y99 9 ! equation express+ ! ,law ( ,error4 ,! occurr5ce ( any "o def9ite am\nt ( error is inf9itely improbable1 because an inf9ite numb] ( su* ord9ates might be drawn4 ,b ! probability ( an error occurr+ betwe5 c]ta9 limits is f9ite1 & is repres5t$ by a portion ( ! 99area99 ( ! curve4 ,?us ! probability t an error1 positive or negative1 n exce$+ unity w occur1 is repres5t$ by ! area ,m99mnnm991 9 %ort1 by ! area /&+ ^u ! l9e 99nn994 ,s9ce e obs]vation mu/ ei!r h "s def9ite error or none at all1 x foll[s t ! :ole area ( ! curve %\ld be consid]$ z ! unit express+ c]ta9ty1 & ! probability ( an error fall+ betwe5 p>ticul> limits w !n be express$ by ! ratio :i* ! area ( ! curve betwe5 ^? limits be>s to ! :ole area ( ! curve4 ,! m]e fact t ! ,law ( ,error all[s ( ! possible exi/5ce ( errors ( e assignable am\nt %[s t x is only approximately true4 ,we may fairly say t 9 measur+ a mile x w\ld be impossible to commit an error ( a hundr$ miles1 & ! l5g? ( life w\ld nev] all[ ( our committ+ an error ( "o million miles4 ,nev]!less ! g5]al ,law ( ,error w\ld assign a probability = an error ( t am\nt or m1 b s small a probability z to be utt]ly inconsid]able & almo/ inconceivable4 ,all t c1 or 9 fact ne$1 be said 9 def5ce ( ! law is1 t x may be made to repres5t ! errors 9 any special case to a v close approximation1 & t ! probability ( l>ge & practically impossible errors1 z giv5 by ! law1 w be s small z to be entirely inconsid]able4 ,& z we are deal+ ) error itself1 & our results pret5d to no?+ m ?an approximation & probability1 an indef9itely small error 9 our process ( approximation is ( no importance :atev]4 99,logical ,orig9 ( ! ,law ( ,error499 ,x is wor?y ( notice t ?is ,law ( ,error1 ab/ruse ?\gh ! subject may seem1 is really f\nd$ ^u ! simple/ pr9ciples4 ,x arises entirely out ( ! diff]5ce betwe5 p]mutations & comb9ations1 a subject ^u :i* ,i may seem to h dwelt ) unnecess>y prolixity 9 previ\s pages 7pp4 #agj1 #ahi74 ,! ord] 9 :i* we add quantities toge!r does n affect ! am\nt ( ! sum1 s t if !re be ?ree positive & five negative causes ( error 9 op]ation1 x does n matt] 9 :i* ord] !y are consid]$ z act+4 ,!y may be int]mix$ 9 any arrangem5t1 & yet ! result w be ! same4 ,! read] %\ld n fail to notice h[ laws or pr9ciples :i* appe>$ to be absurdly simple & evid5t :5 fir/ notic$1 reappe> 9 ! mo/ complicat$ & my/]i\s processes ( sci5tific me?od4 ,! fundam5tal ,laws ( ,id5tity & ,diff]5ce gave rise to ! ,logical ,alphabet :i*1 aft] ab/ract+ ! "* ( ! diff]5ces1 l$ to ! ,ari?metical ,triangle4 ,! ,law ( ,error is def9$ by an inf9itely high l9e ( t triangle1 & ! law proves t ! mean is ! mo/ probable result1 & t div]g5cies f ! mean become mu* less probable z !y increase 9 am\nt4 ,n[ ! comp>ative greatness ( ! numb]s t[>ds ! middle ( ea* l9e ( ! ,ari?metical ,triangle is entirely due to ! indiff]5ce ( ord] 9 space or "t1 :i* 0 fir/ prom95tly po9t$ out z a condition ( logical relations1 & ! symbols indicat+ !m 7pp4 #cb-ce71 & :i* 0 aft]w>ds %[n to atta* equally to num]ical symbols1 ! d]ivatives ( logical t]ms 7p4 #afj74 99,v]ification ( ! ,law ( ,error499 ,! !ory ( error :i* we h be5 consid]+ re/s entirely ^u an assumption1 namely t :5 kn[n s\rces ( di/urbances are all[$ =1 !re yet rema9 an indef9ite1 possibly an inf9ite numb] ( o!r m9ute s\rces ( error1 :i* w z (t5 produce excess z defici5cy4 ,grant+ ?is assumption1 ! ,law ( ,error mu/ be z x is usually tak5 to be1 & !re is no m ne$ to v]ify x empirically ?an to te/ ! tru? ( "o ( ,euclid's propositions me*anically4 ,nev]!less1 x is an int]e/+ occupation to v]ify ev5 ! propositions ( geometry1 & x is /ill m in/ructive to try :e!r a l>ge numb] ( obs]vations w ju/ify our assumption ( ! ,law ( ,error4 ,encke has giv5 an excell5t in/ance ( ! correspond5ce ( !ory ) exp]i5ce1 9 ! case ( obs]vations ( ! diff]5ces ( ,"r ,asc5sion ( ! sun & two />s1 namely ,aquil & ,canis m9oris4 ,! obs]vations 7 #dgj 9 numb]1 & 7 made by ,bradley & r$uc$ by ,bessel1 :o f\nd ! probable error ( ! f9al result to be only ab\t "o-f\r? "p ( a second 7#jbfcg74 ,he !n comp>$ ! numb]s ( errors ( ea* magnitude f #ja second upw>ds1 z actually giv5 by ! obs]vations1 ) :at %\ld occur accord+ to ! ,law ( ,error4 ,! results 7 z foll[3--#bhc ---------------------------------------- ----------- ,numb] ( errors ( ea* ,magnitude ( ! errors magnitude accord+ to 9 p>ts ( a second4 ------------------------- ,obs]vation4 ,!ory4 ---------------------------------------- ---------- #jj to #ja #id #ie #a #b #hh #hi #b #c #gh #gh #c #d #eh #fd #d #e #ea #ej #e #f #cf #cf #f #g #bf #bd #g #h #ad #ae #h #i #aj #i #i #aj #g #e above #aj #h #e ---------------------------------------- ---------- #bhc ,encke1 99,on ! ,me?od ( ,lea/ ,squ>es991 ,taylor's 99,sci5tific ,memoirs991 vol4 ii4 pp4 #cch1 #cci4 ,! read] w rem>k t ! correspond5ce is v close1 except z reg>ds l>g] errors1 :i* are excessive 9 practice4 ,x is "o objection1 inde$1 to ! !ory ( error1 t1 be+ express$ 9 a cont9u\s ma!matical function1 x contemplates ! exi/5ce ( errors ( e magnitude1 su* z c\ld n practically occur2 yet 9 ?is case ! !ory seems to "u-e/imate ! numb] ( l>ge errors4 ,ano!r comp>ison ( ! law ) obs]vation 0 made by ,quetelet1 :o inve/igat$ ! errors ( #dhg det]m9ations 9 "t ( ! ,"r ,asc5sion ( ! ,pole-,/> made at ,gre5wi* dur+ ! f\r ye>s #ahcf-ci4 ,^! obs]vations1 al?\gh c>efully correct$ = all kn[n causes ( error1 z well z = nutation1 precession1 c41 are yet ( c\rse f\nd to diff]1 & be+ classifi$ z reg>ds int]vals ( "o-half second ( "t1 & !n proportionately increas$ 9 numb]1 s t _! sum may be "o ?\s&1 give ! foll[+ results z comp>$ ) :at ,quetelet's !ory w\ld lead u to expect3--#bhd ---------------------------------------- ------------------------ ,magnitude ( ,numb] ( ,errors ,magnitude ( ,numb] ( ,errors error ------------------- error ------------------- 9 t5?s by by 9 t5?s by by ( a second4,obs]vation4,!ory4( a second4,obs]vation4,!ory4 ---------------------------------------- ---------------------- #jj #afh #afc -- -- -- #je #adh #adg -#je #aej #aeb #aj #abi #aab -#aj #abf #aba #ae #gh #gb -#ae #gd #hb #bj #cc #dj -#bj #dc #df #be #aj #ai -#be #be #bb #cj #b #aj -#cj #ab #aj -- -- -- -#ce #b #d ---------------------------------------- ---------------------- #bhd ,quetelet1 99,lett]s on ! ,!ory ( ,probabilities991 translat$ by ,d[nes1 ,lett] ,,xix4 p4 #hh4 ,see also ,galton's 99,h]$it>y ,g5ius991 p4 #cgi4 ,9 ?is in/ance also ! correspond5ce is satisfactory1 b ! div]g5ce betwe5 !ory & fact is 9 ! opposite direction to t discov]$ 9 ! =m] comp>ison1 ! l>g] errors be+ less frequ5t ?an !ory w\ld indicate4 ,x w be notic$ t ,quetelet's !oretical results are n symmetrical4 99,! ,probable ,mean ,result499 ,"o imm$iate result ( ! ,law ( ,error1 z ?us /at$1 is t ! mean result is ! mo/ probable "o2 & :5 !re is only a s+le v>iable ?is mean is f\nd by ! famili> ari?metical process4 ,an un=tunate error has crept into sev]al works :i* allude to ?is subject4 ,mill1 9 treat+ ( ! 8,elim9ation ( ,*ance10 rem>ks 9 a note#bhe t 8! mean is spok5 ( z if x 7 exactly ! same ?+ z ! av]age4 ,b ! mean1 = purposes ( inductive inquiry1 is n ! av]age1 or ari?metical mean1 ?\gh 9 a famili> illu/ration ( ! !ory ! diff]5ce may be disreg>d$40 ,he goes on to say t1 accord+ to ma!matical pr9ciples1 ! mo/ probable result is t = :i* ! sums ( ! squ>es ( ! deviations is ! lea/ possible4 ,x seems probable t ,mill & o!r writ]s 7 misl$ by ,:ewell1 :o says#bhf t 8,! me?od ( lea/ squ>es is 9 fact a me?od ( means1 b ) "s peculi> *>act]s4444 ,! me?od proce$s ^u ?is supposition3 t all errors are n equally probable1 b t small errors are m probable ?an l>ge ones40 ,he adds t ?is me?od 8removes mu* t is arbitr>y 9 ! me?od ( means40 ,x is /range to f9d a ma!matician l ,:ewell mak+ su* rem>ks1 :5 !re is no d\bt :atev] t ! ,me?od ( ,means is only an application ( ! ,me?od ( ,lea/ ,squ>es4 ,!y are1 9 fact1 ! same me?od1 except t ! latt] me?od may be appli$ to cases :]e two or m quantities h to be det]m9$ at ! same "t4 ,lubbock & ,dr9kwat] say1#bhg 8,if only "o quantity has to be det]m9$1 ?is me?od evid5tly resolves itself into tak+ ! mean ( all ! values giv5 by obs]vation40 ,encke says1#bhh t ! expression = ! probability ( an error 8n only conta9s 9 itself ! pr9ciple ( ! ari?metical mean1 b dep5ds s imm$iately ^u x1 t = all ^? magnitudes = :i* ! ari?metical mean holds good 9 ! simple cases 9 :i* x is pr9cipally appli$1 no o!r law ( probability c be assum$ ?an t :i* is express$ by ?is =mula40 #bhe 99,sy/em ( ,logic991 bk4 iii4 *ap4 #ag1 #c4 #e? ed4 vol4 ii4 p4 #ef4 #bhf 99,philosophy ( ! ,inductive ,sci5ces991 #bnd ed4 vol4 ii4 pp4 #djh1 #dji4 #bhg 99,essay on ,probability991 ,useful ,k ,society1 #ahcc1 p4 #da4 #bhh ,taylor's 99,sci5tific ,memoirs991 vol4 ii4 p4 #ccc4 99,! ,probable ,error ( ,results499 ,:5 we draw a conclusion f ! num]ical results ( obs]vations we ought n to consid] x suffici5t1 9 cases ( importance1 to cont5t ourselves ) f9d+ ! simple mean & treat+ x z true4 ,we ought also to asc]ta9 :at is ! degree ( confid5ce we may place 9 ?is mean1 & our confid5ce %\ld be measur$ by ! degree ( concurr5ce ( ! obs]vations f :i* x is d]iv$4 ,9 "s cases ! mean may be approximately c]ta9 & accurate4 ,9 o!r cases x may really be wor? little or no?+4 ,! ,law ( ,error enables u to give exact expression to ! degree ( confid5ce prop] 9 any case2 = x %[s h[ to calculate ! probability ( a div]g5ce ( any am\nt f ! mean1 & we c !nce asc]ta9 ! probability t ! mean 9 "q is )9 a c]ta9 di/ance f ! true numb]4 ,! 99probable error99 is tak5 by ma!maticians to mean ! limits )9 :i* x is z likely z n t ! tru? w fall4 ,?us if #ede be ! mean ( all ! det]m9ations ( ! d5sity ( ! e>?1 & #bj be approximately ! probable error1 ! mean+ is t ! probability ( ! real d5sity ( ! e>? fall+ betwe5 #ebe & #efe is #a_/b4 ,any o!r limits might h be5 select$ at w4 ,we might calculate ! limits )9 :i* x 0 "o hundr$ or "o ?\s& to "o t ! tru? w\ld fall2 b !re is a conv5tion to take ! ev5 odds "o to "o1 z ! quantity ( probability ( :i* ! limits are to be e/imat$4 ,_m books on probability give rules = mak+ ! calculations1 b z1 9 ! progress ( sci5ce1 p]sons ought to become m famili> ) ^! processes1 ,i propose to repeat ! rules "h & illu/rate _! use4 ,! calculations1 :5 made 9 accordance ) ! directions1 involve none b ari?metic or log>i?mic op]ations4 ,! foll[+ are ! rules = treat+ a mean result1 s z ?or\ghly to asc]ta9 its tru/wor?9ess4 #a4 ,draw ! mean ( all ! obs]v$ results4 #b4 ,f9d ! excess or defect1 t is1 ! error ( ea* result f ! mean4 #c4 ,squ>e ea* ( ^! reput$ errors4 #d4 ,add toge!r all ^! squ>es ( ! errors1 :i* are ( c\rse all positive4 #e4 ,divide by "o less ?an ! numb] ( obs]vations4 ,?is gives ! 99squ>e ( ! mean error994 #f4 ,take ! squ>e root ( ! la/ result2 x is ! 99mean error ( a s+le obs]vation994 #g4 ,divide n[ by ! squ>e root ( ! numb] ( obs]vations1 & we get ! 99mean error ( ! mean result994 #h4 ,la/ly1 multiply by ! natural con/ant #jfgde 7or approximately by #jfgd1 or ev5 by #b_/c71 & we arrive at ! 99probable error ( ! mean result994 ,suppose1 = in/ance1 t five measurem5ts ( ! height ( a hill1 by ! b>omet] or o!rwise1 h giv5 ! numb]s ( feet z #bic1 #cja1 #cjf1 #cjg1 #cac2 we want to "k ! probable error ( ! mean1 namely #cjd4 ,n[ ! diff]5ces betwe5 ?is mean & ! above numb]s1 99pay+ no reg>d to direction991 are #aa1 #c1 #b1 #c1 #i2 _! squ>es are #aba1 #i1 #d1 #i1 #ha1 & ! sum ( ! squ>es ( ! errors consequ5tly #bbd4 ,! numb] ( obs]vations be+ #e1 we divide by #a less1 or #d1 gett+ #ef4 ,?is is ! squ>e ( ! mean error1 & tak+ its squ>e root we h #gdh 7say #g-a_/b71 ! mean error ( a s+le obs]vation4 ,divid+ by #bbcf1 ! squ>e root ( #e1 ! numb] ( obs]vations1 we f9d ! mean error ( ! 99mean99 result to be #cce1 or say #c-a_/c1 & la/ly1 multiply+ by #fgde1 we arrive at ! 99probable error ( ! mean result991 :i* is f\nd to be #bbei1 or say #b-a_/d4 ,! mean+ ( ?is is t ! probability is "o half1 or ! odds are ev5 t ! true height ( ! m\nta9 lies betwe5 #cja-c_/d & #cjf-a_/d feet4 ,we h ?us an exact measure ( ! degree ( cr$ibility ( our mean result1 :i* mean indicates ! mo/ likely po9t = ! tru? to fall ^u4 ,! read] %\ld obs]ve t z ! object 9 ^! calculations is only to ga9 a notion ( ! degree ( confid5ce ) :i* we view ! mean1 !re is no real use 9 c>ry+ ! calculations to any great degree ( precision2 & :5ev] ! neglect ( decimal fractions1 or ev5 ! slight alt]ation ( a numb]1 w mu* abbreviate ! computations1 x may be fe>lessly done1 except 9 cases ( high importance & precision4 ,brodie has %[n h[ ! law ( error may be usefully appli$ 9 *emical inve/igations1 & "s illu/rations ( its employm5t may be f\nd 9 8 pap]4#bhi #bhi 99,philosophical ,transactions991 #ahgc1 p4 #hc4 ,! exp]im5ts ( ,b5z5b]g to detect ! revolution ( ! e>?1 by ! deviation ( a ball f ! p]p5dicul> l9e 9 fall+ d[n a deep pit1 h be5 cit$ by ,encke#bij z an int]e/+ illu/ration ( ! ,law ( ,error4 ,! mean deviation 0 #ejhf l9es1 & its probable error 0 calculat$ by ,encke to be n m ?an #iej l9e1 t is1 ! odds 7 ev5 t ! true result lay betwe5 #dacf & #fjcf4 ,z ! deviation1 accord+ to a/ronomical !ory1 %\ld be #df l9es1 :i* lies well )9 ! limits1 we may consid] t ! exp]im5ts are consi/5t ) ! ,cop]nican sy/em ( ! univ]se4 #bij ,taylor's 99,sci5tific ,memoirs991 vol4 ii4 pp4 #ccj1 #cdg1 c4 ,x w ( c\rse be und]/ood t ! probable error has reg>d only to ^? causes ( errors :i* 9 ! long run act z mu* 9 "o direction z ano!r2 x takes no acc\nt ( con/ant errors4 ,! true result accord+ly w (t5 fall f> beyond ! limits ( probable error1 ow+ to "s consid]able con/ant error or errors1 ( ! exi/5ce ( :i* we are unaw>e4 99,rejection ( ! ,mean ,result499 ,we ought always to be> 9 m9d t ! mean ( any s]ies ( obs]vations is ! be/1 t is1 ! mo/ probable approximation to ! tru?1 only 9 ! abs5ce ( k to ! contr>y4 ,! selection ( ! mean re/s entirely ^u ! probability t unkn[n causes ( error w 9 ! long run fall z (t5 9 "o direction z ! opposite1 s t 9 draw+ ! mean !y w balance ea* o!r4 ,if we h any reason to suppose t !re exi/s a t5d5cy to error 9 "o direction r ?an ! o!r1 !n to *oose ! mean w\ld be to ignore t t5d5cy4 ,we may c]ta9ly approximate to ! l5g? ( ! circumf]5ce ( a circle1 by tak+ ! mean ( ! p]imet]s ( inscrib$ & circumscrib$ polygons ( an equal & l>ge numb] ( sides4 ,! l5g? ( ! circul> l9e und\bt$ly lies betwe5 ! l5g?s ( ! two p]imet]s1 b x does n foll[ t ! mean is ! be/ approximation4 ,x may 9 fact be %[n t ! circumf]5ce ( ! circle is 99v ne>ly99 equal to ! p]imet] ( ! inscrib$ polygon1 toge!r ) "o-?ird "p ( ! diff]5ce betwe5 ! inscrib$ & circumscrib$ polygons ( ! same numb] ( sides4 ,hav+ ?is k1 we ought ( c\rse to act ^u x1 in/ead ( tru/+ to probability4 ,we may (t5 p]ceive t a s]ies ( measurem5ts t5ds t[>ds an extreme limit r ?an t[>ds a mean4 ,9 endeav\r+ to obta9 a correct e/imate ( ! app>5t diamet] ( ! brighte/ fix$ />s1 we f9d a cont9u\s dim9ution 9 e/imates z ! p[]s ( obs]vation increas$4 ,kepl] assign$ to ,sirius an app>5t diamet] ( #bdj seconds2 ,ty*o ,brahe made x #abf2 ,gass5di #aj seconds2 ,galileo1 ,hevelius1 & ,j4 ,cass9i1 #e or #f seconds4 ,halley1 ,mi*ell1 & subsequ5tly ,sir ,w4 ,h]s*el came to ! conclusion t ! brighte/ />s 9 ! heav5s c\ld n h real discs ( a second1 & 7 probably mu* less 9 diamet]4 ,x w\ld ( c\rse be absurd to take ! mean ( quantities :i* diff] m ?an #bdj times2 & z ! t5d5cy has always be5 to small] e/imates1 !re is a consid]able presumption 9 fav\r ( ! smalle/4#bia #bia ,quetelet1 99,lett]s991 c4 p4 #aaf4 ,9 _m exp]im5ts & measurem5ts we "k t !re is a prepond]at+ t5d5cy to error 9 "o direction4 ,! read+s ( a !rmomet] t5d to rise z ! age ( ! in/rum5t increases1 & no draw+ ( means w correct ?is result4 ,b>omet]s1 on ! o!r h&1 are likely to read too l[ in/ead ( too high1 ow+ to ! imp]fection ( ! vacuum & ! action ( capill>y attraction4 ,if ! m]cury be p]fectly pure & no appreciable error be due to ! measur+ app>atus1 ! be/ b>omet] w be t :i* gives ! highe/ result4 ,9 det]m9+ ! specific gravity ( a solid body ! *ief dang] ( error arises f bubbles ( air adh]+ to ! body1 :i* w\ld t5d to make ! specific gravity too small4 ,mu* att5tion mu/ always be giv5 to "o-sid$ errors ( ?is k9d1 s9ce ! multiplication ( exp]im5ts does n remove ! error4 ,9 su* cases "o v c>eful exp]im5t is bett] ?an any numb] ( c>eless ones4 ,:5 we h reasonable gr\nds = suppos+ t c]ta9 exp]im5tal results are liable to grave errors1 we %\ld exclude !m 9 draw+ a mean4 ,if we want to f9d ! mo/ probable approximation to ! velocity ( s\nd 9 air1 x w\ld be absurd to g back to ! old exp]im5ts :i* made ! velocity f #abjj to #adgd feet p] second2 = we "k t ! old obs]v]s did n gu>d aga9/ errors aris+ f w9d & o!r causes4 ,old *emical exp]im5ts are valueless z reg>ds quantitative results4 ,! old *emi/s f\nd ! atmosph]e 9 diff]5t places to diff] 9 composition ne>ly t5 p] c5t41 :]eas mod]n accurate exp]im5t]s f9d v slight v>iations4 ,any me?od ( measurem5t :i* we "k to avoid a s\rce ( error is f> to be pref]r$ to o!rs :i* tru/ to probabilities = ! elim9ation ( ! error4 ,z ,flam/e$ says1#bib 8,"o good in/rum5t is ( z mu* wor? z a hundr$ indiff]5t ones40 ,b an in/rum5t is good or bad only 9 a comp>ative s5se1 & no in/rum5t gives inv>iable & tru?ful results4 ,h5ce we mu/ always ultimately fall back ^u probabilities = ! selection ( ! f9al mean1 :5 o!r precautions are exhau/$4 #bib ,baily1 99,acc\nt ( ,flam/e$991 p4 #ef4 ,leg5dre1 ! discov]] ( ! me?od ( ,lea/ ,squ>es1 recomm5d$ t obs]vations diff]+ v mu* f ! results ( 8 me?od %\ld be reject$4 ,! subject has be5 c>efully inve/igat$ by ,pr(essor ,pi]ce1 :o has propos$ a crit]ion = ! rejection ( d\btful obs]vations bas$ on ! foll[+ pr9ciple3#bic8--obs]vations %\ld be reject$ :5 ! probability ( ! sy/em ( errors obta9$ by reta9+ !m is less ?an t ( ! sy/em ( errors obta9$ by _! rejection multipli$ by ! probability ( mak+ s _m & no m abnormal obs]vations40 ,pr(essor ,pi]ce's inve/igation is giv5 ne>ly 9 8 own words 9 ,pr(essor ,w4 ,*auv5et's 8,manual ( ,sph]ical & ,practical ,a/ronomy10 :i* conta9s a full & excell5t discussion ( ! me?ods ( treat+ num]ical obs]vations4#bid #bic ,g\ld's 99,a/ronomical ,j\rnal991 ,cambridge1 ,mass41 vol4 ii4 p4 #afa4 #bid ,philadelphia 7,london1 ,trbn]7 #ahfc4 ,app5dix1 vol4 ii4 p4 #eeh4 ,v difficult que/ions sometimes arise :5 "o or m results ( a me?od ( exp]im5t div]ge widely f ! mean ( ! re/4 ,are we or are we n to exclude !m 9 adopt+ ! suppos$ true mean result ( ! me?od8 ,! draw+ ( a mean result re/s1 z ,i h frequ5tly expla9$1 ^u ! assumption t e error act+ 9 "o direction w probably be balanc$ by o!r errors act+ 9 an opposite direction4 ,if !n we "k or c possibly discov] any causes ( error n agree+ ) ?is assumption1 we %all be ju/ifi$ 9 exclud+ results :i* seem to be affect$ by ?is cause4 ,9 r$uc+ l>ge s]ies ( a/ronomical obs]vations1 x is n uncommon to meet ) numb]s diff]+ f o!rs by a :ole degree or half a degree1 or "s consid]able integral quantity4 ,^! are errors :i* c\ld h>dly arise 9 ! act ( obs]vation or 9 in/rum5tal irregul>ity2 b !y might readily be acc\nt$ = by misread+ ( figures or mi/ak+ ( division m>ks4 ,x w\ld be absurd to tru/ to *ance t su* mi/akes w\ld balance ea* o!r 9 ! long run1 & x is !re=e bett] to correct arbitr>ily ! suppos$ mi/ake1 or bett] /ill1 if new obs]vations c be made1 to /rike out ! div]g5t numb]s altoge!r4 ,:5 results come sometimes too great or too small 9 a regul> mann]1 we %\ld suspect t "s "p ( ! in/rum5t slips ?r\gh a def9ite space1 or t a def9ite cause ( error ent]s at times1 & n at o!rs4 ,we %\ld !n make x a po9t ( prime importance to discov] ! exact nature & am\nt ( su* an error1 & ei!r prev5t its occurr5ce = ! future or else introduce a correspond+ correction4 ,9 _m rese>*es ! :ole difficulty w consi/ 9 ?is detection & avoidance ( s\rces ( error4 ,pr(essor ,roscoe f\nd t ! pres5ce ( phosphorus caus$ s]i\s & almo/ unavoidable errors 9 ! det]m9ation ( ! atomic weight ( vanadium4#bie ,h]s*el1 9 r$uc+ 8 obs]vations ( d\ble />s at ! ,cape ( ,good ,hope1 0 p]plex$ by an unacc\ntable diff]5ce ( ! angles ( position z measur$ by ! sev5-feet equatorial & ! tw5ty-feet reflector telescopes1 & aft] a c>eful inve/igation 0 oblig$ to be cont5t$ ) introduc+ a correction exp]im5tally det]m9$4#bif #bie ,bak]ian ,lecture1 99,philosophical ,transactions99 7#ahfh71 vol4 clviii4 p4 #f4 #bif 99,results ( ,obs]vations at ! ,cape ( ,good ,hope991 p4 #bhc4 ,:5 obs]vations are suffici5tly num]\s x seems desirable to project ! app>5t errors into a curve1 & !n to obs]ve :e!r ?is curve exhibits ! symmetrical & *>act]i/ic =m ( ! curve ( error4 ,if s1 x may be inf]r$ t ! errors arise f _m m9ute indep5d5t s\rces1 & probably comp5sate ea* o!r 9 ! mean result4 ,any consid]able irregul>ity w indicate ! exi/5ce ( "o-sid$ or l>ge causes ( error1 :i* %\ld be made ! subject ( inve/igation4 ,ev5 ! mo/ pati5t & exhau/ive inve/igations w sometimes fail to disclose any reason :y "s results div]ge f o!rs4 ,! "q aga9 recurs--,are we arbitr>ily to exclude !m8 ,! answ] %\ld be 9 ! negative z a g5]al rule4 ,! m]e fact ( div]g5ce ought n to be tak5 z conclusive aga9/ a result1 & ! ex]tion ( arbitr>y *oice w\ld op5 ! way to ! fatal influ5ce ( bias1 & :at is commonly kn[n z ! 8cook+0 ( figures4 ,x w\ld am\nt to judg+ fact by !ory in/ead ( !ory by fact4 ,! app>5tly div]g5t numb] may prove 9 "t to be ! true "o4 ,x may be an exception ( t valuable k9d :i* upsets our false !ories1 a real exception1 explod+ app>5t co9cid5ces1 & op5+ a way to a new view ( ! subject4 ,to e/abli% ?is position = ! div]g5t fact w require additional rese>*2 b 9 ! meantime we %\ld give x "s weight 9 our mean conclusions1 & %\ld be> 9 m9d ! discrepancy z "o dem&+ att5tion4 ,to neglect a div]g5t result is to neglect ! possible clue to a great discov]y4 99,me?od ( ,lea/ ,squ>es499 ,:5 two or m unkn[n quantities are s involv$ t !y _c be sep>ately det]m9$ by ! ,simple ,me?od ( ,means1 we c yet obta9 _! mo/ probable values by ! ,me?od ( ,lea/ ,squ>es1 )\t m difficulty ?an arises f ! l5g? ( ! ari?metical computations4 ,if ! result ( ea* obs]vation gives an equation betwe5 two unkn[n quantities ( ! =m 99ax99 99by99 99c99 !n1 if ! obs]vations 7 free f error1 we %\ld ne$ only two obs]vations giv+ two equations2 b = ! atta9m5t ( great] accuracy1 we may take _m obs]vations1 & r$uce ! equations s z to give only a pair ) mean coeffici5ts4 ,?is r$uction is effect$ by 7#a471 multiply+ ! coeffici5ts ( ea* equation by ! fir/ coeffici5t1 & add+ toge!r all ! simil> coeffici5ts ?us result+ = ! coeffici5ts ( a new equation2 & 7#b471 by repeat+ ?is process1 & multiply+ ! coeffici5ts ( ea* equation by ! coeffici5t ( ! second t]m4 ,mean+ by 7sum ( 99a99#b7 ! sum ( all quantities ( ! same k9d1 & hav+ ! same place 9 ! equations z 99a99#b1 we may briefly describe ! two result+ mean equations z foll[s3-- 7sum ( 99a99#b7 4 99x99 7sum ( 99ab997 4 99y99 7sum ( 99ac9971 7sum ( 99ab997 4 99x99 7sum ( 99b99#b7 4 99y99 7sum ( 99bc9974 ,:5 !re are ?ree or m unkn[n quantities ! process is exactly ! same 9 nature1 & we get additional mean equations by multiply+ by ! ?ird1 f\r?1 c41 coeffici5ts4 ,z ! numb]s are 9 any case approximate1 x is usually unnecess>y to make ! computations ) accuracy1 & places ( decimals may be freely cut (f to save ari?metical "w4 ,! mean equations hav+ be5 comput$1 _! solution by ! ord9>y me?ods ( algebra gives ! mo/ probable values ( ! unkn[n quantities4 99,works ^u ! ,!ory ( ,probability499 ,reg>d+ ! ,!ory ( ,probability & ! ,law ( ,error z mo/ important subjects ( /udy = any "o :o desires to obta9 a complete compreh5sion ( sci5tific me?od z actually appli$ 9 physical inve/igations1 ,i w briefly indicate ! works 9 "o or o!r ( :i* ! read] w be/ pursue ! /udy4 ,! be/ popul>1 & at ! same "t pr(\nd ,engli% "w on ! subject is ,de ,morgan's 8,essay on ,probabilities & on _! ,application to ,life ,cont+5cies & ,insurance ,(fices10 publi%$ 9 ! 99,cab9et ,cyclopdia991 & to be obta9$ 79 pr9t7 f ,messrs4 ,longman4 ,mr4 ,v5n's "w on 99,! ,logic ( ,*ance99 c n[ be procur$ 9 a greatly enl>g$ second edition2#big x conta9s a mo/ int]e/+ & able discussion ( ! metaphysical basis ( probability & ( relat$ que/ions conc]n+ causation1 belief1 design1 te/imony1 c42 b ,i _c always agree ) ,mr4 ,v5n's op9ions4 ,no ma!matical k beyond t ( common ari?metic is requir$ 9 read+ ^! works4 ,quetelet's 99,lett]s99 =m a good introduction to ! subject1 & ! ma!matical notes are ( value4 ,sir ,george ,airy's brief treatise 99,on ! ,algebraical & ,num]ical ,!ory ( ,errors ( ,obs]vations & ! ,comb9ation ( ,obs]vations991 conta9s a complete explanation ( ! ,law ( ,error & its practical applications4 ,de ,morgan's treatise 8,on ! ,!ory ( ,probabilities0 9 ! 99,encyclopdia ,metropolitana991 pres5ts an ab/ract ( ! m ab/ruse inve/igations ( ,laplace1 toge!r ) a multitude ( pr(\nd & orig9al rem>ks conc]n+ ! !ory g5]ally4 ,9 ,lubbock & ,dr9kwat]'s "w on 99,probability991 9 ! ,libr>y ( ,useful ,k1 we h a concise b good /atem5t ( a numb] ( important problems4 ,! ,rev4 ,w4 ,a4 ,:itwor? has giv51 9 a "w entitl$ 99,*oice & ,*ance991 a numb] ( good illu/rations ( calculations bo? 9 comb9ations & probabilities4 ,9 ,mr4 ,todhunt]'s admirable ,hi/ory we h an exhau/ive critical acc\nt ( almo/ all writ+s ^u ! subject ( probability d[n to ! culm9ation ( ! !ory 9 ,laplace's works4 ,! ,memoir ( ,mr4 ,j4 ,w4 ,l4 ,glai%] has already be5 m5tion$ 7p4 #cge74 ,9 spite ( ! exi/5ce ( ^! & "s o!r good ,engli% works1 !re seems to be a want ( an easy & yet pretty complete ma!matical introduction to ! /udy ( ! !ory4 #big 99,! ,logic ( ,*ance991 an ,essay on ! ,f\ndations & ,prov9ce ( ! ,!ory ( ,probability1 ) especial ref]5ce to its ,logical ,be>+s & its ,application to ,moral & ,social ,sci5ce4 7,macmillan71 #ahgf4 ,among ,fr5* works ! ,trait 99lm5taire du ,calcul des ,probabilits991 by ,s4 ,e4 ,lacroix1 ( :i* sev]al editions h be5 publi%$1 & :i* is n difficult to obta91 =ms probably ! be/ elem5t>y treatise4 ,poisson's 99,re*]*es sur la ,probabilit des ,jugem5ts99 7,p>is #ahcg71 comm5ce ) an admirable inve/igation ( ! gr\nds & me?ods ( ! !ory4 ,:ile ,laplace's great 99,?orie ,analytique des ,probabilits99 is ( c\rse ! 8,pr9cipia0 ( ! subject2 8 99,essai ,philosophique sur les ,probabilits99 is a popul> disc\rse1 & is "o ( ! mo/ pr(\nd & int]e/+ essays ev] publi%$4 ,x %\ld be famili> to e /ud5t ( logical me?od1 & has lo/ little or none ( its importance by lapse ( "t4 99,detection ( ,con/ant ,errors499 ,! ,me?od ( ,means is absolutely incapable ( elim9at+ any error :i* is always ! same1 or :i* always lies 9 "o direction4 ,we sometimes require to be r\s$ f a false feel+ ( security1 & to be urg$ to take suitable precautions aga9/ su* occult errors4 8,x is to ! obs]v]10 says ,gauss1#bih 8t belongs ! task ( c>efully remov+ ! causes ( con/ant errors10 & ?is is q true :5 ! error is absolutely con/ant4 ,:5 we h made a numb] ( det]m9ations ) a c]ta9 app>atus or me?od ( measurem5t1 !re is a great advantage 9 alt]+ ! arrangem5t1 or ev5 devis+ "s entirely diff]5t me?od ( gett+ e/imates ( ! same quantity4 ,! reason obvi\sly consi/s 9 ! improbability t ! same error w affect two or m diff]5t me?ods ( exp]im5t4 ,if a discrepancy is f\nd to exi/1 we %all at lea/ be aw>e ( ! exi/5ce ( error1 & c take measures = f9d+ 9 :i* way x lies4 ,if we c try a consid]able numb] ( me?ods1 ! probability becomes great t errors con/ant 9 "o me?od w be balanc$ or ne>ly s by errors ( an opposite effect 9 ! o!rs4 ,suppose t !re be ?ree diff]5t me?ods ea* affect$ by an error ( equal am\nt4 ,! probability t ?is error w 9 all fall 9 ! same direction is only #a_/d2 & ) f\r me?ods simil>ly #a_/h4 ,if ea* me?od be affect$1 z is always ! case1 by sev]al indep5d5t s\rces ( error1 ! probability becomes mu* great] t 9 ! mean result ( all ! me?ods "s ( ! errors w p>tially comp5sate ! o!rs4 ,9 ?is case z 9 all o!rs1 :5 human vigilance has exhau/$ itself1 we mu/ tru/ ! !ory ( probability4 #bih ,gauss1 translat$ by ,b]tr&1 p4 #be4 ,9 ! det]m9ation ( a z]o po9t1 ( ! magnitude ( ! fundam5tal /&>ds ( "t & space1 9 ! p]sonal equation ( an a/ronomical obs]v]1 we h in/ances ( fix$ errors2 b z a g5]al rule a *ange ( proc$ure is likely to rev]se ! "* ( ! error1 & _m in/ances may be giv5 ( ! value ( ?is precaution4 ,if we measure ov] & ov] aga9 ! same angul> magnitude by ! same divid$ circle1 ma9ta9$ 9 exactly ! same position1 x is evid5t t ! same m>k 9 ! circle w be ! crit]ion 9 ea* case1 & any error 9 ! position ( t m>k w equally affect all our results4 ,b if 9 ea* measurem5t we use a diff]5t "p ( ! circle1 a new m>k w come into use1 & z ! error ( ea* m>k _c be 9 ! same direction1 ! av]age result w be ne>ly free f errors ( division4 ,x w be bett] /ill to use m ?an "o divid$ circle4 ,ev5 :5 we h no p]ception ( ! po9ts at :i* error is likely to ent]1 we may ) advantage v>y ! con/ruction ( our app>atus 9 ! hope t we %all accid5tally detect "s lat5t cause ( error4 ,baily's purpose 9 repeat+ ! exp]im5ts ( ,mi*ell & ,cav5di% on ! d5sity ( ! e>? 0 n m]ely to foll[ ! same c\rse & v]ify ! previ\s numb]s1 b to try :e!r v>iations 9 ! size & sub/ance ( ! attract+ balls1 ! mode ( susp5sion1 ! temp]ature ( ! surr\nd+ air1 c41 w\ld yield diff]5t results4 ,he p]=m$ no less ?an #fb di/9ct s]ies1 compris+ #baec exp]im5ts1 & he c>efully classifi$ & discuss$ ! results s z to disclose ! utmo/ diff]5ces4 ,aga91 9 exp]im5t+ ^u ! resi/ance ( ! air to ! motion ( a p5dulum1 ,baily employ$ no less ?an #hj p5dulums ( v>i\s =ms & mat]ials1 9 ord] to asc]ta9 exactly ^u :at conditions ! resi/ance dep5ds4 ,regnault1 9 8 exact rese>*es ^u ! dilatation ( gases1 made arbitr>y *anges 9 ! magnitude ( p>ts ( 8 app>atus4 ,he ?9ks t if1 9 spite ( su* modification1 ! results are un*ang$1 ! errors are probably ( inconsid]able am\nt2#bii b 9 reality x is always possible1 & usually likely1 t we ov]look s\rces ( error :i* a future g5]ation w detect4 ,?us ! p5dulum exp]im5ts ( ,baily & ,sab9e 7 direct$ to asc]ta9 ! nature & am\nt ( a correction = air resi/ance1 :i* _h be5 entirely misund]/ood 9 ! exp]im5ts by means ( ! seconds p5dulum1 ^u :i* 0 f\nd$ ! def9ition ( ! /&>d y>d1 9 ! ,act ( #e? ,george ,,iv4 c4 #gd4 ,x has already be5 m5tion$ t a consid]able error 0 discov]$ 9 ! det]m9ation ( ! /&>d metre z ! t5-million? "p ( ! di/ance f ! pole to ! equator 7p4 #cad74 #bii ,jam91 99,c\rs de ,physique991 vol4 ii4 p4 #fj4 ,we %all return 9 ,*apt] ,,xxv4 to ! fur!r consid]ation ( ! me?ods by :i* we may z f> z possible secure ourselves aga9/ p]man5t & undetect$ s\rces ( error4 ,9 ! meantime1 hav+ complet$ ! consid]ation ( ! special me?ods requisite = treat+ quantitative ph5om5a1 we mu/ pursue our pr9cipal subject1 & endeav\r to trace out ! c\rse by :i* ! physici/1 f obs]vation & exp]im5t1 collects ! mat]ials ( k1 & !n proce$s by hypo!sis & inv]se calculation to induce f !m ! laws ( nature4 ,book ,,iv4 ,,inductive ,,inve/igation4 ,,*apt] ,,xviii4 ,,obs]vation4 ,,all k proce$s orig9ally f exp]i5ce4 ,us+ ! "n 9 a wide s5se1 we may say t exp]i5ce compreh5ds all t we 99feel991 ext]nally or int]nally--! aggregate ( ! impressions :i* we receive ?r\gh ! v>i\s ap]tures ( p]ception--! aggregate consequ5tly ( :at is 9 ! m9d1 except s f> z "s portions ( k may be ! reason$ equival5ts ( o!r portions4 ,z ! ^w exp]i5ce expresses1 we 99g ?r\gh99 mu* 9 life1 & ! impressions ga!r$ int5tionally or un9t5tionally af=d ! mat]ials f :i* ! active p[]s ( ! m9d evolve sci5ce4 ,no small "p ( ! exp]i5ce actually employ$ 9 sci5ce is acquir$ )\t any di/9ct purpose4 ,we _c use ! eyes )\t ga!r+ "s facts :i* may prove useful4 ,a great sci5ce has 9 _m cases ris5 f an accid5tal obs]vation4 ,erasmus ,b>?ol9us ?us fir/ discov]$ d\ble refraction 9 ,icel& sp>2 ,galvani notic$ ! twit*+ ( a frog's leg2 ,ok5 0 /ruck by ! =m ( a v]tebra2 ,malus accid5tally exam9$ light reflect$ f di/ant w9d[s ) a d\ble refract+ sub/ance2 & ,sir ,john ,h]s*el's att5tion 0 drawn to ! peculi> appe>ance ( a solution ( qu99e sulphate4 ,9 e>li] times !re mu/ h be5 "s "o :o fir/ notic$ ! /range behavi\r ( a load/one1 or ! unacc\ntable motions produc$ by amb]4 ,z a g5]al rule we %all n "k 9 :at direction to look = a great body ( ph5om5a widely diff]5t f ^? famili> to u4 ,*ance !n mu/ give u ! />t+ po9t2 b "o accid5tal obs]vation well us$ may lead u to make ?\s&s ( obs]vations 9 an int5tional & organis$ mann]1 & ?us a sci5ce may be gradually work$ out f ! smalle/ op5+4 99,di/9ction ( ,obs]vation & ,exp]im5t499 ,x is usual to say t ! two s\rces ( exp]i5ce are ,obs]vation & ,exp]im5t4 ,:5 we m]ely note & record ! ph5om5a :i* occur ar\nd u 9 ! ord9>y c\rse ( nature we are said 99to obs]ve994 ,:5 we *ange ! c\rse ( nature by ! int]v5tion ( our muscul> p[]s1 & ?us produce unusual comb9ations & conditions ( ph5om5a1 we are said 99to exp]im5t994 ,h]s*el ju/ly rem>k$#cjj t we might prop]ly call ^! two modes ( exp]i5ce 99passive & active obs]vation994 ,9 bo? cases we mu/ c]ta9ly employ our s5ses to obs]ve1 & an exp]im5t diff]s f a m]e obs]vation 9 ! fact t we m or less influ5ce ! "* ( ! ev5ts :i* we obs]ve4 ,exp]im5t is ?us obs]vation 99plus99 alt]ation ( conditions4 #cjj 99,prelim9>y ,disc\rse on ! ,/udy ( ,natural ,philosophy991 p4 #gg4 ,x may readily be se5 t we pass upw>ds by ins5sible gradations f pure obs]vation to det]m9ate exp]im5t4 ,:5 ! e>lie/ a/ronom]s simply notic$ ! ord9>y motions ( ! sun1 moon1 & planets ^u ! face ( ! />ry heav5s1 !y 7 pure obs]v]s4 ,b a/ronom]s n[ select precise times & places = important obs]vations ( /ell> p>allax1 or ! transits ( planets4 ,!y make ! e>?'s orbit ! basis ( a well arrang$ 99natural exp]im5t991 z x 71 & take well consid]$ advantage ( motions :i* !y _c control4 ,meteorology might seem to be a sci5ce ( pure obs]vation1 because we _c possibly gov]n ! *anges ( wea!r :i* we record4 ,nev]!less we may asc5d m\nta9s or rise 9 balloons1 l ,gay-,lussac & ,glai%]1 & may ?us s v>y ! po9ts ( obs]vation z to r5d] our proc$ure exp]im5tal4 ,we are :olly unable ei!r to produce or prev5t e>?-curr5ts ( electricity1 b :5 we con/ruct long l9es ( telegraph1 we ga!r su* /rong curr5ts dur+ p]iods ( di/urbance z to r5d] !m capable ( easy obs]vation4 ,! be/ arrang$ sy/ems ( obs]vation1 h[ev]1 w\ld fail to give u a l>ge "p ( ! facts :i* we n[ possess4 ,_m processes cont9ually go+ on 9 nature are s sl[ & g5tle z to escape our p[]s ( obs]vation4 ,lavoisi] rem>k$ t ! decomposition ( wat] mu/ h be5 con/antly proce$+ 9 nature1 al?\gh its possibility 0 unkn[n till 8 "t4#cja ,no sub/ance is :olly de/itute ( magnetic or diamagnetic p[]s2 b x requir$ all ! exp]im5tal skill ( ,f>aday to prove t iron & a few o!r metals _h no monopoly ( ^! p[]s4 ,accid5tal obs]vation long ago impress$ ^u m5's m9ds ! ph5om5a ( lightn+1 & ! attractive prop]ties ( amb]4 ,exp]im5t only c\ld h %[n t ph5om5a s div]se 9 magnitude & "* 7 manife/ations ( ! same ag5t4 ,to obs]ve ) accuracy & conv5i5ce we mu/ h ag5ts "u our control1 s z to raise or l[] _! int5sity1 to /op or set !m 9 action at w4 ,j z ,smeaton f\nd x requisite to create an artificial & gov]nable supply ( w9d = 8 inve/igation ( w9dmills1 s we mu/ h gov]nable supplies ( light1 heat1 electricity1 muscul> =ce1 or :atev] o!r ag5ts we are exam9+4 #cja ,lavoisi]'s 99,elem5ts ( ,*emi/ry991 translat$ by ,k]r1 #crd ed4 p4 #adh4 ,x is h>dly ne$ful to po9t out too t on ! e>?'s surface we live "u ne>ly con/ant conditions ( gravity1 temp]ature1 & atmosph]ic pressure1 s t if we are to ext5d our inf]5ces to o!r p>ts ( ! univ]se :]e conditions are widely diff]5t1 we mu/ be prep>$ to imitate ^? conditions on a small scale "h4 ,we mu/ h int5sely high & l[ temp]atures2 we mu/ v>y ! d5sity ( gases f approximate vacuum upw>ds2 we mu/ subject liquids & solids to pressures or /ra9s ( almo/ unlimit$ am\nt4 99,m5tal ,conditions ( ,correct ,obs]vation499 ,e obs]vation mu/ 9 a c]ta9 s5se be true1 = ! obs]v+ & record+ ( an ev5t is 9 itself an ev5t4 ,b be=e we proce$ to deal ) ! suppos$ mean+ ( ! record1 & draw inf]5ces conc]n+ ! c\rse ( nature1 we mu/ take c>e to asc]ta9 t ! "* & feel+s ( ! obs]v] are n to a great ext5t ! ph5om5a record$4 ,! m9d ( man1 z ,francis ,bacon said1 is l an unev5 mirror1 & does n reflect ! ev5ts ( nature )\t di/ortion4 ,we ne$ h>dly take notice ( int5tionally false obs]vations1 nor ( mi/akes aris+ f defective memory1 defici5t light1 & s =?4 ,ev5 :]e ! utmo/ fidelity & c>e are us$ 9 obs]v+ & record+1 t5d5cies to error exi/1 & fallaci\s op9ions arise 9 consequ5ce4 ,x is difficult to f9d p]sons :o c ) p]fect fairness regi/] facts = & aga9/ _! own peculi> views4 ,among uncultivat$ obs]v]s ! t5d5cy to rem>k fav\rable & =get unfav\rable ev5ts is s great1 t no reliance c be plac$ ^u _! suppos$ obs]vations4 ,?us arises ! endur+ fallacy t ! *anges ( ! wea!r co9cide 9 "s way ) ! *anges ( ! moon1 al?\gh exact & imp>tial regi/]s give no c\nt5ance to ! fact4 ,! :ole race ( prophets & quacks live on ! ov]:elm+ effect ( "o success1 comp>$ ) hundr$s ( failures :i* are unm5tion$ & =gott54 ,z ,bacon says1 8,m5 m>k :5 !y hit1 & nev] m>k :5 !y miss40 ,& we %\ld d well to be> 9 m9d ! anci5t /ory1 quot$ by ,bacon1 ( "o :o 9 ,pagan times 0 %[n a temple ) a picture ( all ! p]sons :o _h be5 sav$ f %ipwreck1 aft] pay+ _! v[s4 ,:5 ask$ :e!r he did n n[ ackn[l$ge ! p[] ( ! gods1 8,ay10 he answ]$2 8b :]e are !y pa9t$ t 7 dr[n$ aft] _! v[s80 ,if inde$ we c\ld e/imate ! am\nt ( 99bias99 exi/+ 9 any p>ticul> obs]vations1 x might be treat$ l "o ( ! =ces ( ! problem1 & ! true c\rse ( ext]nal nature might /ill be r5d]$ app>5t4 ,b ! feel+s ( an obs]v] are usually too indet]m9ate1 s t :5 !re is reason to suspect consid]able bias1 rejection is ! only safe c\rse4 ,z reg>ds facts casually regi/]$ 9 pa/ times1 ! capacity & imp>tiality ( ! obs]v] are s little kn[n t we %\ld sp>e no pa9s to replace ^! /atem5ts by a new appeal to nature4 ,an indiscrim9ate m$ley ( tru? & absurdity1 su* z ,francis ,bacon collect$ 9 8 99,natural ,hi/ory991 is :olly unsuit$ to ! purposes ( sci5ce4 ,b ( c\rse :5 records relate to pa/ ev5ts l eclipses1 conjunctions1 meteoric ph5om5a1 e>?quakes1 volcanic eruptions1 *anges ( sea m>g9s1 ! exi/5ce ( n[ ext9ct animals1 ! migrations ( tribes1 rem>kable cu/oms1 c41 we mu/ make use ( /atem5ts h[ev] unsatisfactory1 & mu/ endeav\r to v]ify !m by ! comp>ison ( indep5d5t records or traditions4 ,:5 ext5sive s]ies ( obs]vations h to be made1 z 9 a/ronomical1 meteorological1 or magnetical obs]vatories1 trigonometrical surveys1 & ext5sive *emical or physical rese>*es1 x is an advantage t ! num]ical "w %\ld be execut$ by assi/ants :o are n int]e/$ 91 & are p]haps unaw>e (1 ! expect$ results4 ,! record is ?us r5d]$ p]fectly imp>tial4 ,x may ev5 be desirable t ^? :o p]=m ! purely r\t9e "w ( measurem5t & computation %\ld be unacqua9t$ ) ! pr9ciples ( ! subject4 ,! great table ( log>i?ms ( ! ,fr5* ,revolution>y ,gov]nm5t 0 work$ out by a /aff ( sixty or eighty comput]s1 mo/ ( :om 7 acqua9t$ only ) ! rules ( ari?metic1 & work$ "u ! direction ( skill$ ma!maticians2 yet _! calculations 7 usually f\nd m correct ?an ^? ( p]sons m deeply v]s$ 9 ma!matics4#cjb ,9 ! ,indian ,ordnance ,survey ! actual measur]s 7 select$ s t !y %\ld n h suffici5t skill to falsify _! results )\t detection4 #cjb ,babbage1 99,economy ( ,manufactures991 p4 #aid4 ,bo? passive obs]vation & exp]im5tation mu/1 h[ev]1 be g5]ally conduct$ by p]sons :o "k = :at !y are to look4 ,x is only :5 excit$ & guid$ by ! hope ( v]ify+ a !ory t ! obs]v] w notice _m ( ! mo/ important po9ts2 &1 :]e ! "w is n ( a r\t9e "*1 no assi/ant c sup]s$e ! m9d-direct$ obs]vations ( ! philosoph]4 ,?us ! successful inve/igator mu/ comb9e div]se qualities2 he mu/ h cle> notions ( ! result he expects & confid5ce 9 ! tru? ( 8 !ories1 & yet he mu/ h t c&\r & flexibility ( m9d :i* enable him to accept unfav\rable results & ab&on mi/ak5 views4 99,in/rum5tal & ,s5sual ,conditions ( ,obs]vation499 ,9 e obs]vation "o or m ( ! s5ses mu/ be employ$1 & we %\ld ev] be> 9 m9d t ! ext5t ( our k may be limit$ by ! p[] ( ! s5se conc]n$4 ,:at we le>n ( ! _w only =ms ! l[] limit ( :at is to be le>n$1 &1 = all t we c tell1 ! processes ( nature may inf9itely surpass 9 v>iety & complexity ^? :i* are capable ( com+ )9 our means ( obs]vation4 ,9 "s cases inf]5ce f obs]v$ ph5om5a may make u indirectly aw>e ( :at _c be directly felt1 b we c nev] be sure t we ?us acquire any appreciable fraction ( ! k t might be acquir$4 ,x is a /range reflection t space may be fill$ ) d>k w&]+ />s1 ^: exi/5ce c\ld n h yet become 9 any way kn[n to u4 ,! planets h already cool$ s f> z to be no long] lum9\s1 & x may well be t o!r /ell> bodies ( v>i\s size h fall5 into ! same condition4 ,f ! consid]ation1 inde$1 ( v>iable & ext+ui%$ />s1 ,laplace inf]r$ t !re probably exi/ opaque bodies z great & p]haps z num]\s z ^? we see4#cjc ,"s ( ^! d>k />s might ultimately become kn[n to u1 ei!r by reflect+ light1 or m probably by _! gravitat+ effects ^u lum9\s />s4 ,?us if "o memb] ( a d\ble /> 7 d>k1 we c\ld readily detect its exi/5ce1 & ev5 e/imate its size1 position1 & motions1 by obs]v+ ^? ( its visible companion4 ,x 0 a fav\rite notion ( ,huygh5s t !re may exi/ />s & va/ univ]ses s di/ant t _! light has nev] yet _h "t to rea* our eyes2 & we mu/ also be> 9 m9d t light may possibly suff] sl[ ext9ction 9 space1 s t !re is m ?an "o way 9 :i* an absolute limit to ! p[]s ( telescopic discov]y may exi/4 #cjc 99,sy/em ( ! ,_w991 translat$ by ,h>te1 vol4 ii4 p4 #cce4 ,!re are natural limits aga9 to ! p[] ( our s5ses 9 detect+ undulations ( v>i\s k9ds4 ,x is commonly said t vibrations ( m ?an #ch1jjj /rokes p] second are n audible z s\nd2 & z "s e>s actually d he> s\nds ( mu* high] pit*1 ev5 two octaves high] ?an :at o!r e>s c detect1 x is exce$+ly probable t !re are incessant vibrations :i* we _c call s\nd because !y are nev] he>d4 ,insects may communicate by su* acute s\nds1 con/itut+ a language inaudible to u2 & ! rem>kable agreem5t app>5t among bodies ( ants or bees might ?us p]haps be expla9$4 ,nay1 z ,font5elle long ago sugge/$ 9 8 sci5tific romance1 !re may exi/ unlimit$ numb]s ( s5ses or modes ( p]ception :i* we c nev] feel1 ?\gh ,d>w9's !ory w\ld r5d] x probable t any useful means ( k 9 an ance/or w\ld be develop$ & improv$ 9 ! desc5dants4 ,we might d\btless h be5 end[$ ) a s5se capable ( feel+ electric ph5om5a ) acut5ess1 s t ! positive or negative /ate ( *>ge ( a body c\ld be at once e/imat$4 ,! abs5ce ( su* a s5se is probably due to its comp>ative uselessness4 ,heat undulations are subject to ! same consid]ations4 ,x is n[ app>5t t :at we call light is ! affection ( ! eye by c]ta9 vibrations1 ! less rapid ( :i* are invisible & con/itute ! d>k rays ( radiant heat1 9 detect+ :i* we mu/ sub/itute ! !rmomet] or ! !rmopile = ! eye4 ,at ! o!r end ( ! spectrum1 aga91 ! ultra-violet rays are invisible1 & only indirectly br\ght to our k 9 ! ph5om5a ( fluoresc5ce or photo-*emical action4 ,!re is no reason to believe t at ei!r end ( ! spectrum an absolute limit has yet be5 rea*$4 ,j z our k ( ! /ell> univ]se is limit$ by ! p[] ( ! telescope & o!r conditions1 s our k ( ! m9ute _w has its limit 9 ! p[]s & optical conditions ( ! microscope4 ,!re 0 a "t :5 x w\ld h be5 a reasonable induction t vegetables are motionless1 & animals alone end[$ ) p[] ( locomotion4 ,we are a/oni%$ to discov] by ! microscope t m9ute plants are if any?+ m active ?an m9ute animals4 ,we ev5 f9d t m9]al sub/ances seem to lose _! inactive "* & dance ab\t ) incessant motion :5 r$uc$ to suffici5tly m9ute p>ticles1 at lea/ :5 susp5d$ 9 a non-conduct+ m$ium4#cjd ,microscopi/s w meet a natural limit to obs]vation :5 ! m9ut5ess ( ! objects exam9$ becomes comp>able to ! l5g? ( light undulations1 & ! extreme difficulty already enc\nt]$ 9 det]m9+ ! =ms ( m9ute m>ks on ,diatoms appe>s to be due to ?is cause4 ,accord+ to ,helmholtz ! smalle/ di/ance :i* c be accurately def9$ dep5ds ^u ! int]f]5ce ( light pass+ ?r\gh ! c5tres ( ! bright spaces4 ,) a !oretically p]fect microscope & a dry l5se ! smalle/ visible object w\ld n be less ?an "o #hj1jjj? "p ( an in* 9 r$ light4 #cjd ,?is curi\s ph5om5on1 :i* ,i propose to call 99p$esis991 or ! 99p$etic movem5t991 f 1 to jump1 is c>efully describ$ 9 my pap] publi%$ 9 ! 99,qu>t]ly ,j\rnal ( ,sci5ce99 = ,april1 #ahgh1 vol4 viii4 7,n4,s47 p4 #afg4 ,see also 99,proce$+s ( ! ,lit]>y & ,philosophical ,society ( ,man*e/]991 #be? ,janu>y1 #ahgj1 vol4 ix4 p4 #gh1 99,nature991 #bbnd ,augu/1 #ahgh1 vol4 xviii4 p4 #ddj1 or ! 99,qu>t]ly ,j\rnal ( ,sci5ce991 vol4 viii4 7,n4,s47 p4 #ead4 ,( ! errors likely to arise 9 e/imat+ quantities by ! s5ses ,i h already spok51 b !re are "s cases 9 :i* we actually see ?+s diff]5tly f :at !y are4 ,a jet ( wat] appe>s to be a cont9u\s ?read1 :5 x is really a wond]fully organis$ succession ( small & l>ge drops1 oscillat+ 9 =m4 ,! drops fall s rapidly t _! impressions ^u ! eye run into ea* o!r1 & 9 ord] to see ! sep>ate drops we require "s device = giv+ an in/antane\s view4 ,"o insup]able limit to our p[]s ( obs]vation arises f ! impossibility ( foll[+ & id5tify+ ! ultimate atoms ( matt]4 ,"o atom ( oxyg5 is probably undi/+ui%able f ano!r atom2 only by keep+ a c]ta9 volume ( oxyg5 safely inclos$ 9 a bottle c we assure ourselves ( its id5tity2 all[ x to mix ) o!r oxyg51 & we lose all p[] ( id5tification4 ,accord+ly we seem to h no means ( directly prov+ t e gas is 9 a con/ant /ate ( diffusion ( e "p into e "p4 ,we c only inf] ?is to be ! case f obs]v+ ! behavi\r ( di/9ct gases :i* we c di/+ui% 9 _! c\rse1 & by reason+ on ! gr\nds ( molecul> !ory4#cje #cje ,maxwell1 99,!ory ( ,heat991 p4 #cja4 99,ext]nal ,conditions ( ,correct ,obs]vation499 ,be=e we proce$ to draw inf]5ces f any s]ies ( record$ facts1 we mu/ take c>e to asc]ta9 p]fectly1 if possible1 ! ext]nal conditions "u :i* ! facts are br\ght to our notice4 ,n only may ! obs]v+ m9d be prejudic$ & ! s5ses defective1 b !re may be circum/ances :i* cause "o k9d ( ev5t to come m frequ5tly to our notice ?an ano!r4 ,! comp>ative numb]s ( objects ( diff]5t k9ds exi/+ may 9 any degree diff] f ! numb]s :i* come to our notice4 ,?is diff]5ce mu/ if possible be tak5 into acc\nt be=e we make any inf]5ces4 ,!re long appe>$ to be a /rong presumption t all comets mov$ 9 elliptic orbits1 because no comet _h be5 prov$ to move 9 any o!r k9d ( pa?4 ,! !ory ( gravitation admitt$ ( ! exi/5ce ( comets mov+ 9 hyp]bolic orbits1 & ! "q arose :e!r !y 7 really non-exi/5t or 7 only beyond ! b\nds ( easy obs]vation4 ,f reasonable suppositions ,laplace calculat$ t ! probability 0 at lea/ #fjjj to #a aga9/ a comet :i* comes )9 ! planet>y sy/em suffici5tly to be visible at ! e>?'s surface1 pres5t+ an orbit :i* c\ld be discrim9at$ f a v elongat$ ellipse or p>abola 9 ! "p ( its orbit )9 ! rea* ( our telescopes4#cjf ,9 %ort1 ! *ances are v mu* 9 fav\r ( our see+ elliptic r ?an hyp]bolic comets4 ,laplace's views h be5 confirm$ by ! discov]y ( six hyp]bolic comets1 :i* appe>$ 9 ! ye>s #agbi1 #agga1 #aggd1 #ahah1 #ahdj1 & #ahdc1cjg & z only ab\t #hjj comets altoge!r h be5 record$1 ! proportion ( hyp]bolic ones is q z l>ge z %\ld be expect$4 #cjf ,laplace1 99,essai ,philosophique991 p4 #ei4 ,todhunt]'s 99,hi/ory991 pp4 #dia-did4 #cjg ,*amb]s' 99,a/ronomy991 #a/ ed4 p4 #bjc4 ,:5 we attempt to e/imate ! numb]s ( objects :i* may h exi/$1 we mu/ make l>ge all[ances = ! limit$ sph]e ( our obs]vations4 ,probably n m ?an #djjj or #ejjj comets h be5 se5 9 hi/orical times1 b mak+ all[ance = ! abs5ce ( obs]v]s 9 ! s\!rn hemisph]e1 & = ! small probability t we see any consid]able fraction ( ^? :i* are 9 ! neighb\rhood ( our sy/em1 we mu/ accept ,kepl]'s op9ion1 t !re are m comets 9 ! regions ( space ?an fi%es 9 ! dep?s ( ! ocean4 ,:5 l calculations are made conc]n+ ! numb]s ( meteors visible to u1 x is a/oni%+ to f9d t ! numb] ( meteors ent]+ ! e>?'s atmosph]e 9 e tw5ty-f\r h\rs is probably n less ?an #djj1jjj1jjj1 ( :i* #ac1jjj exi/ 9 e portion ( space equal to t fill$ by ! e>?4 ,s]i\s fallacies may arise f ov]look+ ! inevitable conditions "u :i* ! records ( pa/ ev5ts are br\ght to our notice4 ,?us x is only ! durable objects manufactur$ by =m] races ( m51 su* z fl9t implem5ts1 :i* c h come to our notice z a g5]al rule4 ,! comp>ative abundance ( iron & bronze articles us$ by an anci5t nation mu/ n be suppos$ to be co9cid5t ) _! comp>ative abundance 9 our museums1 because bronze is f> ! m durable4 ,!re is a prevail+ fallacy t our ance/ors built m /rongly ?an we d1 aris+ f ! fact t ! m fragile /ructures h long s9ce crumbl$ away4 ,we h few or no relics ( ! habitations ( ! poor] classes among ! ,greeks or ,romans1 or 9 fact ( any pa/ race2 = ! temples1 tombs1 public build+s1 & mansions ( ! weal?i] classes alone endure4 ,!re is an imm5se expanse ( pa/ ev5ts necess>ily lo/ to u = ev]1 & we mu/ g5]ally look ^u records or relics z exceptional 9 _! "*4 ,! same consid]ations apply to geological relics4 ,we c\ld n g5]ally expect t animals w\ld be pres]v$ unless z reg>ds ! bones1 %ells1 /rong integum5ts1 or o!r h>d & durable p>ts4 ,all ! infusoria & animals devoid ( m9]al framework h probably p]i%$ entirely1 di/ill$ p]haps into oils4 ,x has be5 po9t$ out t ! peculi> "* ( "s ext9ct floras may be due to ! unequal pres]vation ( diff]5t families ( plants4 ,by v>i\s accid5ts1 h[ev]1 we ga9 glimpses ( a _w t is usually lo/ to u--z by insects emb$d$ 9 amb]1 ! great mammo? pres]v$ 9 ice1 mummies1 ca/s 9 solid mat]ial l t ( ! ,roman soldi] at ,pompeii1 & s =?4 ,we %\ld also rememb]1 t j z !re may be conjunctions ( ! heav5ly bodies t c h happ5$ only once or twice 9 ! p]iod ( hi/ory1 s rem>kable t]re/rial conjunctions may take place4 ,great /orms1 e>?quakes1 volcanic eruptions1 l&slips1 floods1 irruptions ( ! sea1 may1 or r mu/1 h occurr$1 ev5ts ( su* unusual magnitude & su* extreme r>ity t we c nei!r expect to witness !m nor readily to compreh5d _! effects4 ,x is a great advantage ( ! /udy ( probabilities1 z ,laplace himself rem>k$1 to make u mi/ru/ ! ext5t ( our k1 & pay prop] reg>d to ! probability t ev5ts w\ld come )9 ! sph]e ( our obs]vations4 99,app>5t ,sequ5ce ( ,ev5ts499 ,de ,morgan has excell5tly po9t$ out#cjh t !re are no less ?an f\r modes 9 :i* "o ev5t may seem to foll[ or be connect$ ) ano!r1 )\t be+ really s4 ,^! involve m5tal1 s5sual1 & ext]nal causes ( error1 & ,i w briefly /ate & illu/rate !m4 #cjh 99,essay on ,probabilities991 ,cab9et ,cyclopdia1 p4 #aba4 ,in/ead ( ,a caus+ ,b1 x may be 99our p]ception ( ,a t causes ,b994 ,?us x is t prophecies1 pres5tim5ts1 & ! devices ( sorc]y & wit*craft (t5 "w _! own ends4 ,a man dies on ! day :i* he has always reg>d$ z 8 la/1 f 8 own fe>s ( ! day4 ,an incantation effects its purpose1 because c>e is tak5 to fright5 ! int5d$ victim1 by lett+ him "k 8 fate4 ,9 all su* cases ! m5tal condition is ! cause ( app>5t co9cid5ce4 ,9 a second class ( cases1 99! ev5t ,a may make our p]ception ( ,b foll[1 :i* w\ld o!rwise happ5 )\t be+ p]ceiv$994 ,?us x 0 believ$ to be ! result ( inve/igation t m comets appe>$ 9 hot ?an cold summ]s4 ,no acc\nt 0 tak5 ( ! fact t hot summ]s w\ld be comp>atively cl\dless1 & af=d bett] opportunities = ! discov]y ( comets4 ,"h ! di/urb+ condition is ( a purely ext]nal "*4 ,c]ta9 anci5t philosoph]s held t ! moon's rays 7 cold-produc+1 mi/ak+ ! cold caus$ by radiation into space = an effect ( ! moon1 :i* is m likely to be visible at a "t :5 ! abs5ce ( cl\ds p]mits radiation to proce$4 ,9 a ?ird class ( cases1 99our p]ception ( ,a may make our p]ception ( ,b foll[994 ,! ev5t ,b may be con/antly happ5+1 b our att5tion may n be drawn to x except by our obs]v+ ,a4 ,?is case seems to be illu/rat$ by ! fallacy ( ! moon's influ5ce on cl\ds4 ,! orig9 ( ?is fallacy is some:at complicat$4 ,9 ! fir/ place1 :5 ! sky is d5sely cl\d$ ! moon w\ld n be visible at all2 x w\ld be necess>y = u to see ! full moon 9 ord] t our att5tion %\ld be /rongly drawn to ! fact1 & ?is w\ld happ5 mo/ (t5 on ^? nights :5 ! sky is cl\dless4 ,mr4 ,w4 ,ellis1#cji moreov]1 has +5i\sly po9t$ out t !re is a g5]al t5d5cy = cl\ds to disp]se at ! comm5cem5t ( night1 :i* is ! "t :5 ! full moon rises4 ,?us ! *ange ( ! sky & ! rise ( ! full moon are likely to attract att5tion mutually1 & ! co9cid5ce 9 "t sugge/s ! relation ( cause & effect4 ,mr4 ,ellis proves f ! results ( obs]vations at ! ,gre5wi* ,obs]vatory t ! moon possesses no appreciable p[] ( ! k9d suppos$1 & yet x is rem>kable t s s\nd an obs]v] z ,sir ,john ,h]s*el 0 conv9c$ ( ! connection4 ,9 8 8,results ( ,obs]vations at ! ,cape ( ,good ,hope10#caj he m5tions _m ev5+s :5 a full moon occurr$ ) a peculi>ly cle> sky4 #cji 99,philosophical ,magaz9e991 #d? ,s]ies 7#ahfg71 vol4 xxxiv4 p4 #fd4 #caj ,see 99,notes to ,measures ( ,d\ble ,/>s991 #abjd1 #accf1 #adgg1 #afhf1 #aghf1 #ahaf1 #ahce1 #aibi1 #bjha1 #bahf1 pp4 #bfe1 c4 ,see also ,h]s*el's 99,famili> ,lectures on ,sci5tific ,subjects991 p4 #adg1 & 99,outl9es ( ,a/ronomy991 #g? ed4 p4 #bhe4 ,!re is yet a f\r? class ( cases1 9 :i* 99,b is really ! antec$5t ev5t1 b our p]ception ( ,a1 :i* is a consequ5ce ( ,b1 may be necess>y to br+ ab\t our p]ception ( ,b994 ,!re c be no d\bt1 = in/ance1 t upw>d & d[nw>d curr5ts are cont9ually circulat+ 9 ! l[e/ /ratum ( ! atmosph]e dur+ ! day-"t2 b ow+ to ! transp>5cy ( ! atmosph]e we h no evid5ce ( _! exi/5ce until we p]ceive cumul\s cl\ds1 :i* are ! consequ5ce ( su* curr5ts4 ,9 l mann] an int]filtration ( bodies ( air 9 ! high] p>ts ( ! atmosph]e is probably 9 ne>ly con/ant progress1 b unless ?reads ( cirr\s cl\d indicate ^! motions we rema9 ignorant ( _! occurr5ce4#caa ,! highe/ /rata ( ! atmosph]e are :olly imp]ceptible to u1 except :5 r5d]$ lum9\s by auroral curr5ts ( electricity1 or by ! passage ( meteoric /ones4 ,mo/ ( ! visible ph5om5a ( comets probably arise f "s sub/ance :i*1 exi/+ previ\sly invisible1 becomes cond5s$ or electrifi$ sudd5ly into a visible =m4 ,sir ,john ,h]s*el attempt$ to expla9 ! production ( comet tails 9 ?is mann] by evaporation & cond5sation4#cab #caa ,jevons1 99,on ! ,cirr\s ,=m ( ,cl\d991 ,philosophical ,magaz9e1 ,july1 #aheg1 #d? ,s]ies1 vol4 xiv4 p4 #bb4 #cab 99,a/ronomy991 #d? ed4 p4 #ceh4 99,negative ,argum5ts f ,non-obs]vation499 ,f :at has be5 sugge/$ 9 prec$+ sections1 x w pla9ly appe> t ! non-obs]vation ( a ph5om5on is n g5]ally to be tak5 z prov+ its non-occurr5ce4 ,z !re are s\nds :i* we _c he>1 rays ( heat :i* we _c feel1 multitudes ( worlds :i* we _c see1 & myriads ( m9ute organisms ( :i* n ! mo/ p[]ful microscope c give u a view1 we mu/ z a g5]al rule int]pret our exp]i5ce 9 an affirmative s5se only4 ,accord+ly :5 inf]5ces h be5 drawn f ! non-occurr5ce ( p>ticul> facts or objects1 m ext5d$ & c>eful exam9ation has (t5 prov$ _! falsity4 ,n _m ye>s s9ce x 0 q a well cr$it$ conclusion 9 geology t no rema9s ( man 7 f\nd 9 connection ) ^? ( ext9ct animals1 or 9 any deposit n actually at pres5t 9 c\rse ( =mation4 ,ev5 ,babbage accept$ ?is conclusion z /rongly confirmatory ( ! ,mosaic acc\nts4#cac ,:ile ! op9ion 0 yet univ]sally held1 fl9t implem5ts _h be5 f\nd disprov+ su* a conclusion1 & ov]:elm+ evid5ce ( man's long-cont9u$ exi/5ce has s9ce be5 =?com+4 ,at ! end ( ! la/ c5tury1 :5 ,h]s*el _h se>*$ ! heav5s ) 8 p[]ful telescopes1 !re seem$ little probability t planets yet rema9$ unse5 )9 ! orbit ( ,jupit]4 ,b on ! fir/ day ( ?is c5tury su* an op9ion 0 ov]turn$ by ! discov]y ( ,c]es1 & m ?an a hundr$ o!r small planets h s9ce be5 add$ to ! li/s ( ! planet>y sy/em4 #cac ,babbage1 99,n9? ,bridgewat] ,treatise991 p4 #fg4 ,! discov]y ( ! ,eozon ,canad5se 9 /rata ( mu* great] age ?an any previ\sly kn[n to conta9 organic rema9s1 has giv5 a %ock to gr\ndless op9ions conc]n+ ! orig9 ( organic =ms2 & ! oceanic dr$g+ exp$itions "u ,dr4 ,c>p5t] & ,sir ,wyville ,?omson h modifi$ "s op9ions ( geologi/s by disclos+ ! cont9u$ exi/5ce ( =ms long suppos$ to be ext9ct4 ,^! & _m o!r cases :i* might be quot$ %[ ! extremely unsafe "* ( negative inductions4 ,b x mu/ n be suppos$ t negative argum5ts are ( no =ce & value4 ,! e>?'s surface has be5 suffici5tly se>*$ to r5d] x highly improbable t any t]re/rial animals ( ! size ( a camel rema9 to be discov]$4 ,x is believ$ t no new l>ge animal has be5 enc\nt]$ 9 ! la/ eighte5 or tw5ty c5turies1#cad & ! probability t if exi/5t !y w\ld h be5 se51 increases ! probability t !y d n exi/4 ,we may ) some:at less confid5ce discr$it ! exi/5ce ( any l>ge unrecognis$ fi%1 or sea animals1 su* z ! alleg$ sea-s]p5t4 ,b1 z we desc5d to =ms ( small] size negative evid5ce loses weight f ! less probability ( our see+ small] objects4 ,ev5 ! /rong induction 9 fav\r ( ! f\r-fold division ( ! animal k+dom into ,v]tebrata1 ,annulosa1 ,mollusca1 & ,cl5t]ata1 may break d[n by ! discov]y ( int]m$iate or anomal\s =ms4 ,z civilisation spreads ov] ! surface ( ! e>?1 & unexplor$ tracts are gradually dim9i%$1 negative conclusions w increase 9 =ce2 b we h mu* to le>n yet conc]n+ ! dep?s ( ! ocean1 almo/ :olly unexam9$ z !y are1 & cov]+ ?ree-f\r?s ( ! e>?'s surface4 #cad ,cuvi]1 99,essay on ! ,!ory ( ! ,e>?991 translation1 p4 #fa1 c4 ,9 geology !re are _m /atem5ts to :i* consid]able probability atta*es on acc\nt ( ! l>ge ext5t ( ! inve/igations already made1 z1 = in/ance1 t true coal is f\nd only 9 rocks ( a p>ticul> geological epo*2 t gold occurs 9 second>y & t]ti>y /rata only 9 exce$+ly small quantities1#cae probably d]iv$ f ! dis9tegration ( e>li] rocks4 ,9 natural hi/ory negative conclusions are exce$+ly trea*]\s & unsatisfactory4 ,! utmo/ pati5ce w n enable a microscopi/ or ! obs]v] ( any liv+ ?+ to wat* ! behavi\r ( ! organism "u all circum/ances cont9u\sly = a great l5g? ( "t4 ,!re is always a *ance !re=e t ! critical act or *ange may take place :5 ! obs]v]'s eyes are )drawn4 ,?is c]ta9ly happ5s 9 "s cases2 = ?\gh ! f]tilisation ( or*ids by ag5cy ( insects is prov$ z well z any fact 9 natural hi/ory1 ,mr4 ,d>w9 has nev] be5 able by ! close/ wat*+ to detect an insect 9 ! p]=mance ( ! op]ation4 ,mr4 ,d>w9 has himself adopt$ "o conclusion on negative evid5ce1 namely1 t ! 99,or*is pyramidalis99 & c]ta9 o!r or*idace\s fl[]s secrete no nect>4 ,b 8 caution & unwe>y+ pati5ce 9 v]ify+ ! conclusion give an impressive lesson to ! obs]v]4 ,= tw5ty-?ree consecutive days1 z he tells u1 he exam9$ fl[]s 9 all /ates ( ! wea!r1 at all h\rs1 9 v>i\s localities4 ,z ! secretion 9 o!r fl[]s sometimes takes place rapidly & might happ5 at e>ly dawn1 t inconv5i5t h\r ( obs]vation 0 specially adopt$4 ,fl[]s ( diff]5t ages 7 subject$ to irritat+ vap\rs1 to moi/ure1 & to e condition likely to br+ on ! secretion2 & only aft] inv>iable failure ( ?is exhau/ive inquiry 0 ! b>r5ness ( ! nect>ies assum$ to be prov$4#caf #cae ,mur*ison's 99,siluria991 #a/ ed4 p4 #dcb4 #caf ,d>w9's 99,f]tilisation ( ,or*ids991 p4 #dh4 ,9 ord] t a negative argum5t f\nd$ on ! non-obs]vation ( an object %all h any consid]able =ce1 x mu/ be %[n to be probable t ! object if exi/5t w\ld h be5 obs]v$1 & x is ?is probability :i* def9es ! value ( ! negative conclusion4 ,! failure ( a/ronom]s to see ! planet ,vulcan1 suppos$ by "s to exi/ )9 ,m]cury's orbit1 is no suffici5t dispro( ( its exi/5ce4 ,simil>ly x w\ld be v difficult1 or ev5 impossible1 to disprove ! exi/5ce ( a second satellite ( small size revolv+ r\nd ! e>?4 ,b if any p]son make a p>ticul> ass]tion1 assign+ place & "t1 !n obs]vation w ei!r prove or disprove ! alleg$ fact4 ,if x is true t :5 a ,fr5* obs]v] pr(ess$ to h se5 a planet on ! sun's face1 an obs]v] 9 ,brazil 0 c>efully scrut9is+ ! sun & fail$ to see x1 we h a negative pro(4 ,false facts 9 sci5ce1 x has be5 well said1 are m mis*iev\s ?an false !ories4 ,a false !ory is op5 to e p]son's criticism1 & is ev] liable to be judg$ by its accordance ) facts4 ,b a false or grossly errone\s ass]tion ( a fact (t5 /&s 9 ! way ( sci5ce = a long "t1 because x may be extremely difficult or ev5 impossible to prove ! falsity ( :at has be5 once record$4 ,9 o!r sci5ces ! =ce ( a negative argum5t w (t5 dep5d ^u ! numb] ( possible alt]natives :i* may exi/4 ,x 0 long believ$ t ! quality ( a musical s\nd z di/+ui%$ f its pit*1 mu/ dep5d ^u ! =m ( ! undulation1 because no o!r cause ( x _h ev] be5 sugge/$ or 0 app>5tly possible4 ,! tru? ( ! conclusion 0 prov$ by ,helmholtz1 :o appli$ a microscope to lum9\s po9ts atta*$ to ! /r+s ( v>i\s in/rum5ts1 & ?us actually obs]v$ ! diff]5t modes ( undulation4 ,9 ma!matics negative inductive argum5ts h seldom mu* =ce1 because ! possible =ms ( expression1 or ! possible comb9ations ( l9es & circles 9 geometry1 are q unlimit$ 9 numb]4 ,an enorm\s numb] ( attempts 7 made to trisect ! angle by ! ord9>y me?ods ( ,euclid's geometry1 b _! inv>iable failure did n e/abli% ! impossibility ( ! task4 ,?is 0 %[n 9 a totally diff]5t mann]1 by prov+ t ! problem involves an irr$ucible cubic equation to :i* !re c\ld be no correspond+ plane geometrical solution4#cag ,?is is a case ( 99r$uctio ad absurdum991 a =m ( argum5t ( a totally diff]5t "*4 ,simil>ly no numb] ( failures to obta9 a g5]al solution ( equations ( ! fif? degree w\ld e/abli% ! impossibility ( ! task1 b 9 an indirect mode1 equival5t to a 99r$uctio ad absurdum991 ! impossibility is consid]$ to be prov$4#cah #cag ,peacock1 99,algebre991 vol4 ii4 p4 #cdd4 #cah ,ibid1 p4 #cei4 ,s]ret1 99,algbre ,suprieure991 #bnd ed4 p4 #cjd4 ,,*apt] ,,xix4 ,,exp]im5t4 ,we may n[ consid] ! great advantages :i* we enjoy 9 exam9+ ! comb9ations ( ph5om5a :5 ?+s are )9 our rea* & capable ( be+ exp]im5t$ on4 ,we are said 99to exp]im5t99 :5 we br+ sub/ances toge!r "u v>i\s conditions ( temp]ature1 pressure1 electric di/urbance1 *emical action1 c41 & !n record ! *anges obs]v$4 ,our object 9 inductive inve/igation is to asc]ta9 exactly ! gr\p ( circum/ances or conditions :i* be+ pres5t1 a c]ta9 o!r gr\p ( ph5om5a w foll[4 ,if we d5ote by ,a ! antec$5t gr\p1 & by ,x subsequ5t ph5om5a1 our object w usually be to discov] a law ( ! =m ,a ,,ax1 ! mean+ ( :i* is t :]e ,a is ,x w happ54 ,! circum/ances :i* might be enum]at$ z pres5t 9 ! simple/ exp]im5t are v num]\s1 9 fact almo/ inf9ite4 ,rub two /icks toge!r & consid] :at w\ld be an exhau/ive /atem5t ( ! conditions4 ,!re are ! =m1 h>dness1 organic /ructure1 & all ! *emical qualities ( ! wood2 ! pressure & velocity ( ! rubb+2 ! temp]ature1 pressure1 & all ! *emical qualities ( ! surr\nd+ air2 ! proximity ( ! e>? ) its attractive & electric p[]s2 ! temp]ature & o!r prop]ties ( ! p]sons produc+ motion2 ! radiation f ! sun1 & to & f ! sky2 ! electric excitem5t possibly exi/+ 9 any ov]hang+ cl\d2 ev5 ! positions ( ! heav5ly bodies mu/ be m5tion$4 ,on 99 priori99 gr\nds x is unsafe to assume t any "o ( ^! circum/ances is )\t effect1 & x is only by exp]i5ce t we c s+le out ^? precise conditions f :i* ! obs]v$ heat ( friction proce$s4 ,! great me?od ( exp]im5t consi/s 9 remov+1 "o at a "t1 ea* ( ^? conditions :i* may be imag9$ to h an influ5ce on ! result4 ,our object 9 ! exp]im5t ( rubb+ /icks is to discov] ! exact circum/ances "u :i* heat appe>s4 ,n[ ! pres5ce ( air may be requisite2 !re=e prep>e a vacuum1 & rub ! /icks 9 e respect z be=e1 except t x is done 999 vacuo994 ,if heat /ill appe>s we may say t air is n1 9 ! pres5ce ( ! o!r circum/ances1 a requisite condition4 ,! conduction ( heat f neighb\r+ bodies may be a condition4 ,prev5t ?is by mak+ all ! surr\nd+ bodies ice cold1 :i* is :at ,davy aim$ at 9 rubb+ two pieces ( ice toge!r4 ,if heat /ill appe>s we h elim9at$ ano!r condition1 & s we may g on until x becomes app>5t t ! exp5diture ( en]gy 9 ! friction ( two bodies is ! sole condition ( ! production ( heat4 ,! great difficulty ( exp]im5t arises f ! fact t we mu/ n assume ! conditions to be indep5d5t4 ,previ\s to exp]im5t we h no "r to say t ! rubb+ ( two /icks w produce heat 9 ! same way :5 air is abs5t z be=e4 ,we may h heat produc$ 9 "o way :5 air is pres5t1 & 9 ano!r :5 air is abs5t4 ,! inquiry bran*es out into two l9es1 & we ought to try 9 bo? cases :e!r cutt+ (f a supply ( heat by conduction prev5ts its evolution 9 friction4 ,! same bran*+ out ( ! inquiry occurs ) reg>d to e circum/ance :i* ent]s into ! exp]im5t4 ,reg>d+ only f\r circum/ances1 say ,a1 ,b1 ,c1 ,d1 we ought to te/ n only ! comb9ations ,,abcd1 ,,abc99d991 ,,ab99c99,d1 ,a99b99,,cd1 99a99,,bcd1 b we ought really to g ?r\gh ! :ole ( ! comb9ations giv5 9 ! fif? column ( ! ,logical ,alphabet4 ,! effect ( ! abs5ce ( ea* condition %\ld be tri$ bo? 9 ! pres5ce & abs5ce ( e o!r condition1 & e selection ( ^? conditions4 ,p]fect & exhau/ive exp]im5tation w\ld1 9 %ort1 consi/ 9 exam9+ natural ph5om5a 9 all _! possible comb9ations & regi/]+ all relations betwe5 conditions & results :i* are f\nd capable ( exi/5ce4 ,x w\ld ?us resemble ! exclusion ( contradictory comb9ations c>ri$ out 9 ! ,indirect ,me?od ( ,inf]5ce1 except t ! exclusion ( comb9ations is gr\nd$ n on prior logical premises1 b on 99 po/]iori99 results ( actual trial4 ,! read] w p]ceive1 h[ev]1 t su* exhau/ive inve/igation is practically impossible1 because ! numb] ( requisite exp]im5ts w\ld be imm5sely great4 ,f\r antec$5ts only w\ld require sixte5 exp]im5ts2 twelve antec$5ts w\ld require #djif1 & ! numb] increases z ! p[]s ( two4 ,! result is t ! exp]im5t] has to fall back ^u 8 own tact & exp]i5ce 9 select+ ^? exp]im5ts :i* are mo/ likely to yield him significant facts4 ,x is at ?is po9t t logical rules & =ms beg9 to fail 9 giv+ aid4 ,! logical rule is--,try all possible comb9ations2 b ?is be+ impracticable1 ! exp]im5tali/ necess>ily ab&ons /rict logical me?od1 & tru/s to 8 own insight4 ,analogy1 z we %all see1 gives "s assi/ance1 & att5tion %\ld be conc5trat$ on ^? k9ds ( conditions :i* h be5 f\nd important 9 l cases4 ,b we are n[ entirely 9 ! region ( probability1 & ! exp]im5t]1 :ile he is confid5tly pursu+ :at he ?9ks ! "r clue1 may be ov]look+ ! "o condition ( importance4 ,x is an impressive lesson1 = in/ance1 t ,newton pursu$ all 8 exquisite rese>*es on ! spectrum unsuspici\s ( ! fact t if he r$uc$ ! hole 9 ! %utt] to a n>r[ slit1 all ! my/]ies ( ! bright & d>k l9es 7 )9 8 grasp1 provid$ ( c\rse t 8 prisms 7 suffici5tly good to def9e ! rays4 ,9 l mann] we "k n :at slight alt]ation 9 ! mo/ famili> exp]im5ts may n op5 ! way to realms ( new discov]y4 ,practical difficulties1 also1 encumb] ! progress ( ! physici/4 ,x is (t5 impossible to alt] "o condition )\t alt]+ o!rs at ! same "t2 & ?us we may n get ! pure effect ( ! condition 9 "q4 ,"s conditions may be absolutely incapable ( alt]ation2 o!rs may be ) great difficulty1 or only 9 a c]ta9 degree1 removable4 ,a v trea*]\s s\rce ( error is ! exi/5ce ( unkn[n conditions1 :i* ( c\rse we _c remove except by accid5t4 ,^! difficulties we w %ortly consid] 9 succession4 ,x is beautiful to obs]ve h[ ! alt]ation ( a s+le circum/ance sometimes conclusively expla9s a ph5om5on4 ,an in/ance is f\nd 9 ,f>aday's inve/igation ( ! behavi\r ( ,lycopodium spores scatt]$ on a vibrat+ plate4 ,x 0 obs]v$ t ^! m9ute spores collect$ toge!r at ! po9ts ( greate/ motion1 :]eas s& & all heavy p>ticles collect$ at ! nodes1 :]e ! motion 0 lea/4 ,x happily occurr$ to ,f>aday to try ! exp]im5t 9 ! exhau/$ receiv] ( an air-pump1 & x 0 !n f\nd t ! light p[d] behav$ exactly l heavy p[d]4 ,a conclusive pro( 0 ?us obta9$ t ! pres5ce ( air 0 ! condition ( importance1 d\btless because x 0 ?r[n into eddies by ! motion ( ! plate1 & c>ri$ ! ,lycopodium to ! po9ts ( greate/ agitation4 ,s& 0 too heavy to be c>ri$ by ! air4 99,exclusion ( ,indiff]5t ,circum/ances499 ,f :at has be5 already said x w be app>5t t ! detection & exclusion ( indiff]5t circum/ances is a "w ( importance1 because x all[s ! conc5tration ( att5tion ^u circum/ances :i* conta9 ! pr9cipal condition4 ,_m beautiful in/ances may be giv5 :]e all ! mo/ obvi\s antec$5ts h be5 %[n to h no "p 9 ! production ( a ph5om5on4 ,a p]son might suppose t ! peculi> col\rs ( "m-(-pe>l 7 due to ! *emical qualities ( ! sub/ance4 ,mu* tr\ble might h be5 sp5t 9 foll[+ out t notion by comp>+ ! *emical qualities ( v>i\s iridesc5t sub/ances4 ,b ,brew/] accid5tally took an impression f a piece ( "m-(-pe>l 9 a cem5t ( res9 & bees'-wax1 & f9d+ ! col\rs repeat$ ^u ! surface ( ! wax1 he proce$$ to take o!r impressions 9 balsam1 fusible metal1 lead1 gum arabic1 is+lass1 c41 & always f\nd ! iridesc5t col\rs ! same4 ,he ?us prov$ t ! *emical nature ( ! sub/ance is a matt] ( indiff]5ce1 & t ! =m ( ! surface is ! real condition ( su* col\rs4#cai ,ne>ly ! same may be said ( ! col\rs exhibit$ by ?9 plates & films4 ,! r+s & l9es ( col\r w be ne>ly ! same 9 "* :atev] may be ! nature ( ! sub/ance2 nay1 a void space1 su* z a crack 9 glass1 w\ld produce !m ev5 ?\gh ! air 7 )drawn by an air-pump4 ,! conditions are simply ! exi/5ce ( two reflect+ surfaces sep>at$ by a v small space1 ?\gh x %\ld be add$ t ! refractive index ( ! int]v5+ sub/ance has "s influ5ce on ! exact nature ( ! col\r produc$4 #cai 99,treatise on ,optics991 by ,brew/]1 ,cab4 ,cyclo4 p4 #aag4 ,:5 a ray ( light passes close to ! edge ( an opaque body1 a portion ( ! light appe>s to be b5t t[>ds x1 & produces col\r$ fr+es )9 ! %ad[ ( ! body4 ,newton attribut$ ?is inflexion ( light to ! attraction ( ! opaque body = ! suppos$ p>ticles ( light1 al?\gh he 0 aw>e t ! nature ( ! surr\nd+ m$ium1 :e!r air or o!r pellucid sub/ance1 ex]cis$ no app>5t influ5ce on ! ph5om5a4 ,graves&e prov$1 h[ev]1 t ! "* ( ! fr+es is exactly ! same1 :e!r ! body be d5se or r>e1 comp\nd or elem5t>y4 ,a wire produces exactly ! same fr+es z a hair ( ! same ?ickness4 ,ev5 ! =m ( ! ob/ruct+ edge 0 subsequ5tly %[n to be a matt] ( indiff]5ce by ,fresnel1 & ! int]f]5ce spectrum1 or ! spectrum se5 :5 light passes ?r\gh a f9e grat+1 is absolutely ! same :atev] be ! =m or *emical nature ( ! b>s mak+ ! grat+4 ,?us x appe>s t ! /oppage ( a portion ( a beam ( light is ! sole necess>y condition = ! diffraction or inflexion ( light1 & ! ph5om5on is %[n to be> no analogy ! refraction ( light1 9 :i* ! =m & nature ( ! sub/ance are all important4 ,x is int]e/+ to obs]ve h[ c>efully ,newton1 9 8 rese>*es on ! spectrum1 asc]ta9$ ! indiff]5ce ( _m circum/ances by actual trial4 ,he says3#cbj 8,n[ ! diff]5t magnitude ( ! hole 9 ! w9d[-%ut1 & diff]5t ?ickness ( ! prism :]e ! rays pass$ ?r\gh x1 & diff]5t incl9ations ( ! prism to ! horizon1 made no s5sible *anges 9 ! l5g? ( ! image4 ,nei!r did ! diff]5t matt] ( ! prisms make any3 = 9 a vessel made ( poli%$ plates ( glass cem5t$ toge!r 9 ! %ape ( a prism1 & fill$ ) wat]1 !re is ! l success ( ! exp]im5t accord+ to ! quantity ( ! refraction40 ,b 9 ! latt] /atem5t1 z ,i %all aft]w>ds rem>k 7p4 #dcb71 ,newton assum$ an indiff]5ce :i* does n exi/1 & fell into an un=tunate mi/ake4 #cbj 99,opticks991 #crd4 ed4 p4 #be4 ,9 ! sci5ce ( s\nd x is %[n t ! pit* ( a s\nd dep5ds solely ^u ! numb] ( impulses 9 a second1 & ! mat]ial excit+ ^? impulses is a matt] ( indiff]5ce4 ,:atev] fluid1 air or wat]1 gas or liquid1 be =c$ into ! ,sir51 ! s\nd produc$ is ! same2 & ! mat]ial ( :i* an organ-pipe is con/ruct$ does n at all affect ! pit* ( its s\nd4 ,9 ! sci5ce ( /atical electricity x is an important pr9ciple t ! nature ( ! int]ior ( a conduct+ body is a matt] ( no importance4 ,! electrical *>ge is conf9$ to ! conduct+ surface1 & ! int]ior rema9s 9 a neutral /ate4 ,a holl[ copp] sph]e takes exactly ! same *>ge z a solid sph]e ( ! same metal4 ,"s ( ,f>aday's mo/ elegant & successful rese>*es 7 devot$ to ! exclusion ( conditions :i* previ\s exp]im5t]s _h ?\ght ess5tial = ! production ( electrical ph5om5a4 ,davy ass]t$ t no kn[n fluids1 except su* z conta9 wat]1 c\ld be made ! m$ium ( connexion betwe5 ! poles ( a batt]y2 & "s *emi/s believ$ t wat] 0 an ess5tial ag5t 9 electro-*emical decomposition4 ,f>aday gave abundant exp]im5ts to %[ t o!r fluids all[$ ( electrolysis1 & he attribut$ ! errone\s op9ion to ! v g5]al use ( wat] z a solv5t1 & its pres5ce 9 mo/ natural bodies4#cba ,x 01 9 fact1 ^u ! weake/ k9d ( negative evid5ce t ! op9ion _h be5 f\nd$4 ,_m exp]im5t]s attribut$ peculi> p[]s to ! poles ( a batt]y1 lik5+ !m to magnets1 :i*1 by _! attractive p[]s1 te> ap>t ! elem5ts ( a sub/ance4 ,by a beautiful s]ies ( exp]im5ts1#cbb ,f>aday prov$ conclusively t1 on ! contr>y1 ! sub/ance ( ! poles is ( no importance1 be+ m]ely ! pa? ?r\gh :i* ! electric =ce rea*es ! liquid act$ ^u4 ,poles ( wat]1 *>coal1 & _m div]se sub/ances1 ev5 air itself1 produc$ simil> results2 if ! *emical nature ( ! pole ent]$ at all into ! "q1 x 0 z a di/urb+ ag5t4 #cba 99,exp]im5tal ,rese>*es 9 ,electricity991 vol4 i4 pp4 #acc1 #acd4 #cbb ,ibid4 vol i4 pp4 #abg1 #afb1 c4 ,x is an ess5tial "p ( ! !ory ( gravitation t ! proximity ( o!r attract+ p>ticles is )\t effect ^u ! attraction exi/+ betwe5 any two molecules4 ,two p\nd weights weigh z mu* toge!r z !y d sep>ately4 ,e pair ( molecules 9 ! _w h1 z x 71 a private communication1 ap>t f _! relations to all o!r molecules4 ,ano!r und\bt$ result ( exp]i5ce po9t$ out by ,newton#cbc is t ! weight ( a body does n 9 ! lea/ dep5d ^u its =m or texture4 ,x may be add$ t ! temp]ature1 electric condition1 pressure1 /ate ( motion1 *emical qualities1 & all o!r circum/ances conc]n+ matt]1 except its mass1 are indiff]5t z reg>ds its gravitat+ p[]4 #cbc 99,pr9cipia991 bk4 iii4 ,prop4 vi4 ,coroll>y i4 ,z natural sci5ce progresses1 physici/s ga9 a k9d ( insight & tact 9 judg+ :at qualities ( a sub/ance are likely to be conc]n$ 9 any class ( ph5om5a4 ,! physical a/ronom] treats matt] 9 "o po9t ( view1 ! *emi/ 9 ano!r1 & ! /ud5ts ( physical optics1 s\nd1 me*anics1 electricity1 c41 make a fair division ( ! qualities among !m4 ,b errors w arise if too mu* confid5ce be plac$ 9 ?is indep5d5ce ( v>i\s k9ds ( ph5om5a1 s t x is desirable f "t to "t1 especially :5 any unexpla9$ discrepancies come into notice1 to "q ! indiff]5ce :i* is assum$ to exi/1 & to te/ its real exi/5ce by appropriate exp]im5ts4 99,simplification ( ,exp]im5ts499 ,"o ( ! mo/ requisite precautions 9 exp]im5tation is to v>y only "o circum/ance at a "t1 & to ma9ta9 all o!r circum/ances rigidly un*ang$4 ,!re are two di/9ct reasons = ?is rule1 ! fir/ & mo/ obvi\s be+ t if we v>y two conditions at a "t1 & f9d "s effect1 we _c tell :e!r ! effect is due to "o or ! o!r condition1 or to bo? jo9tly4 ,a second reason is t if no effect ensues we _c safely conclude t ei!r ( !m is indiff]5t2 = ! "o may h neutralis$ ! effect ( ! o!r4 ,9 our symbolic logic ,,ab ,a99b99 0 %[n to be id5tical ) ,a 7p4 #ig71 s t ,b d5otes a circum/ance :i* is indiff]5tly pres5t or abs5t4 ,b if ,b always goes toge!r ) ano!r antec$5t ,c1 we _c %[ ! same indep5d5ce1 = ,,abc ,a99bc99 is n id5tical ) ,a & none ( our logical processes enables u to r$uce x to ,a4 ,if we want to prove t oxyg5 is necess>y to life1 we mu/ n put a rabbit into a vessel f :i* ! oxyg5 has be5 exhau/$ by a burn+ c&le4 ,we %\ld !n h n only an abs5ce ( oxyg51 b an addition ( c>bonic acid1 :i* may h be5 ! de/ructive ag5t4 ,= a simil> reason ,lavoisi] avoid$ ! use ( atmosph]ic air 9 exp]im5ts on combu/ion1 because air 0 n a simple sub/ance1 & ! pres5ce ( nitrog5 might imp$e or ev5 alt] ! effect ( oxyg54 ,z ,lavoisi] rem>ks1#cbd 8,9 p]=m+ exp]im5ts1 x is a necess>y pr9ciple1 :i* ought nev] to be deviat$ f1 t !y be simplifi$ z mu* z possible1 & t e circum/ance capable ( r5d]+ _! results complicat$ be c>efully remov$40 ,x has also be5 well said by ,cuvi]#cbe t ! me?od ( physical inquiry consi/s 9 isolat+ bodies1 r$uc+ !m to _! utmo/ simplicity1 & br++ ea* ( _! prop]ties sep>ately into action1 ei!r m5tally or by exp]im5t4 #cbd ,lavoisi]'s 99,*emi/ry991 translat$ by ,k]r1 p4 #ajc4 #cbe ,cuvi]'s 99,animal ,k+dom991 introduction1 pp4 #a1 #b4 ,! electro-magnet has be5 ( ! utmo/ s]vice 9 ! inve/igation ( ! magnetic prop]ties ( matt]1 by all[+ ( ! production or removal ( a mo/ p[]ful magnetic =ce )\t di/urb+ any ( ! o!r arrangem5ts ( ! exp]im5t4 ,_m ( ,f>aday's mo/ valuable exp]im5ts w\ld h be5 impossible _h x be5 necess>y to introduce a heavy p]man5t magnet1 :i* c\ld n be sudd5ly mov$ )\t %ak+ ! :ole app>atus1 di/urb+ ! air1 produc+ curr5ts by *anges ( temp]ature1 c4 ,! electro-magnet is p]fectly "u control1 & its influ5ce c be br\ght into action1 rev]s$1 or /opp$ by m]ely t\*+ a button4 ,?us ,f>aday 0 enabl$ to prove ! rotation ( ! plane ( circul>ly pol>is$ light by ! fact t c]ta9 light ceas$ to be visible :5 ! electric curr5t ( ! magnet 0 cut (f1 & re-appe>$ :5 ! curr5t 0 made4 8,^! ph5om5a10 he says1 8c\ld be rev]s$ at pleasure1 & at any in/ant ( "t1 & ^u any occasion1 %[+ a p]fect dep5d5ce ( cause & effect40#cbf #cbf 99,exp]im5tal ,rese>*es 9 ,electricity991 vol4 iii4 p4 #d4 ,x 0 ,newton's omission to obta9 ! sol> spectrum "u ! simple/ conditions :i* prev5t$ him f discov]+ ! d>k l9es4 ,us+ a broad beam ( light :i* _h pass$ ?r\gh a r\nd hole or a triangul> slit1 he obta9$ a brilliant spectrum1 b "o 9 :i* _m diff]5t col\r$ rays ov]lapp$ ea* o!r4 ,9 ! rec5t hi/ory ( ! sci5ce ( ! spectrum1 "o ma9 difficulty has consi/$ 9 ! mixture ( ! l9es ( sev]al diff]5t sub/ances1 :i* are usually to be f\nd 9 ! light ( any flame or sp>k4 ,x is seldom possible to obta9 ! light ( any elem5t 9 a p]fectly simple mann]4 ,ang/rm greatly advanc$ ?is bran* ( sci5ce by exam9+ ! light ( ! electric sp>k :5 =m$ betwe5 poles ( v>i\s metals1 & 9 ! pres5ce ( v>i\s gases4 ,by v>y+ ! pole alone1 or ! gase\s m$ium alone1 he 0 able to discrim9ate correctly betwe5 ! l9es due to ! metal & ^? due to ! surr\nd+ gas4#cbg #cbg 99,philosophical ,magaz9e991 #d? ,s]ies1 vol4 ix4 p4 #cbg4 99,failure 9 ! ,simplification ( ,exp]im5ts499 ,9 "s cases x seems to be impossible to c>ry out ! rule ( v>y+ "o circum/ance at a "t4 ,:5 we attempt to obta9 two in/ances or two =ms ( exp]im5t 9 :i* a s+le circum/ance %all be pres5t 9 "o case & abs5t 9 ano!r1 x may be f\nd t ?is s+le circum/ance entails o!rs4 ,b5jam9 ,frankl9's exp]im5t conc]n+ ! comp>ative absorb+ p[]s ( diff]5t col\rs is well kn[n4 8,i took10 he says1 8a numb] ( little squ>e pieces ( broadclo? f a tailor's patt]n c>d1 ( v>i\s col\rs4 ,!y 7 black1 deep blue1 light] blue1 gre51 purple1 r$1 yell[1 :ite1 & o!r col\rs & %ades ( col\r4 ,i laid !m all out ^u ! sn[ on a bright sun%9y morn+4 ,9 a few h\rs ! black1 be+ mo/ w>m$ by ! sun1 0 sunk s l[ z to be bel[ ! /roke ( ! sun's rays2 ! d>k blue 0 almo/ z l[2 ! light] blue n q s mu* z ! d>k2 ! o!r col\rs less z !y 7 light]4 ,! :ite rema9$ on ! surface ( ! sn[1 n hav+ ent]$ x at all40 ,?is is a v elegant & app>5tly simple exp]im5t2 b :5 ,leslie _h complet$ 8 s]ies ( rese>*es ^u ! nature ( heat1 he came to ! conclusion t ! col\r ( a surface has v little effect ^u ! radiat+ p[]1 ! me*anical nature ( ! surface appe>+ to be m influ5tial4 ,he rem>ks#cbh t 8! "q is incapable ( be+ positively resolv$1 s9ce no sub/ance c be made to assume diff]5t col\rs )\t at ! same "t *ang+ its int]nal /ructure40 ,rec5t inve/igation has %[n t ! subject is "o ( consid]able complication1 because ! absorptive p[] ( a surface may be diff]5t accord+ to ! "* ( ! rays :i* fall ^u x2 b !re c be no d\bt z to ! acut5ess ) :i* ,leslie po9ts out ! difficulty4 ,9 ,well's inve/igations conc]n+ ! nature ( dew1 we h1 aga91 v complicat$ conditions4 ,if we expose plates ( v>i\s mat]ial1 su* z r\gh iron1 glass1 poli%$ metal1 to ! midnight sky1 !y w be dew$ 9 v>i\s degrees2 b s9ce ^! plates diff] bo? 9 ! nature ( ! surface & ! conduct+ p[] ( ! mat]ial1 x w\ld n be pla9 :e!r "o or bo? circum/ances 7 ( importance4 ,we avoid ?is difficulty by expos+ ! same mat]ial poli%$ or v>ni%$1 s z to pres5t diff]5t conditions ( surface2#cbi & aga9 by expos+ diff]5t sub/ances ) ! same k9d ( surface4 #cbh 99,inquiry into ! ,nature ( ,heat991 p4 #ie4 #cbi ,h]s*el1 99,prelim9>y ,disc\rse991 p4 #afa4 ,:5 we are q unable to isolate circum/ances we mu/ resort to ! proc$ure describ$ by ,mill "u ! "n ( ! ,jo9t ,me?od ( ,agreem5t & ,diff]5ce4 ,we mu/ collect z _m in/ances z possible 9 :i* a giv5 circum/ance produces a giv5 result1 & z _m z possible 9 :i* ! abs5ce ( ! circum/ance is foll[$ by ! abs5ce ( ! result4 ,to adduce 8 example1 we _c exp]im5t ^u ! cause ( d\ble refraction 9 ,icel& sp>1 because we _c alt] its cry/all9e condition )\t alt]+ x altoge!r1 nor c we f9d sub/ances exactly l calc sp> 9 e circum/ance except "o4 ,we resort !re=e to ! me?od ( comp>+ toge!r all kn[n sub/ances :i* h ! prop]ty ( d\bly-refract+ light1 & we f9d t !y agree 9 be+ cry/all9e4#ccj ,?is inde$ is no?+ b an ord9>y process ( p]fect or probable induction1 already p>tially describ$1 & to be fur!r discuss$ "u ,classification4 ,x may be add$ t ! subject does admit ( p]fect exp]im5tal treatm5t1 s9ce glass1 :5 compress$ 9 "o direction1 becomes capable ( d\bly-refract+ light1 & z !re is probably no alt]ation 9 ! glass b *ange ( ela/icity1 we le>n t ! p[] ( d\ble refraction is probably due to a diff]5ce ( ela/icity 9 diff]5t directions4 #ccj 99,sy/em ( ,logic991 bk4 iii4 *ap4 viii4 #d1 #e? ed4 vol4 i4 p4 #dcc4 99,removal ( ,usual ,conditions499 ,"o ( ! great objects ( exp]im5t is to enable u to judge ( ! behavi\r ( sub/ances "u conditions widely diff]5t f ^? :i* prevail ^u ! surface ( ! e>?4 ,we live 9 an atmosph]e :i* does n v>y beyond c]ta9 n>r[ limits 9 temp]ature or pressure4 ,_m ( ! p[]s ( nature1 su* z gravity1 :i* con/antly act ^u u1 are ( almo/ fix$ am\nt4 ,n[ x w aft]w>ds be %[n t we _c apply a quantitative law to circum/ances mu* diff]+ f ^? 9 :i* x 0 obs]v$4 ,9 ! o!r planets1 ! sun1 ! />s1 or remote p>ts ( ! ,univ]se1 ! conditions ( exi/5ce mu/ (t5 be widely diff]5t f :at we commonly exp]i5ce "h4 ,h5ce our k ( nature mu/ rema9 re/rict$ & hypo!tical1 unless we c subject sub/ances to unusual conditions by suitable exp]im5ts4 ,! electric arc is an invaluable means ( expos+ metals or o!r conduct+ sub/ances to ! highe/ kn[n temp]ature4 ,by its aid we le>n n only t all ! metals c be vaporis$1 b t !y all give (f di/9ctive rays ( light4 ,at ! o!r extremity ( ! scale1 ! int5sely p[]ful freez+ mixture devis$ by ,f>aday1 consi/+ ( solid c>bonic acid & e!r mix$ 999 vacuo991 enables u to obs]ve ! nature ( sub/ances at temp]atures imm5sely bel[ any we meet ) naturally on ! e>?'s surface4 ,we c h>dly realise n[ ! importance ( ! inv5tion ( ! air-pump1 previ\s to :i* inv5tion x 0 exce$+ly difficult to exp]im5t except "u ! ord9>y pressure ( ! atmosph]e4 ,! ,torricellian vacuum _h be5 employ$ by ! philosoph]s ( ! ,accademia del ,cim5to to %[ ! behavi\r ( wat]1 smoke1 s\nd1 magnets1 electric sub/ances1 c41 999 vacuo991 b _! exp]im5ts 7 (t5 unsuccessful f ! difficulty ( exclud+ air4#cca #cca 99,essayes ( ,natural ,exp]im5ts made 9 ! ,accademia del ,cim5to499 ,engli%$ by ,ri*>d ,wall]1 #afhd1 p4 #dj1 c4 ,among ! mo/ con/ant circum/ances "u :i* we live is ! =ce ( gravity1 :i* does n v>y1 except by a slight fraction ( its am\nt1 9 any "p ( ! e>?'s cru/ or atmosph]e to :i* we c atta94 ,?is =ce is suffici5t to ov]be> & disguise v>i\s actions1 = in/ance1 ! mutual gravitation ( small bodies4 ,x 0 an int]e/+ exp]im5t ( ,plateau to neutralise ! action ( gravity by plac+ sub/ances 9 liquids ( exactly ! same specific gravity4 ,?us a quantity ( oil p\r$ into ! middle ( a suitable mixture ( alcohol & wat] assumes a sph]ical %ape2 on be+ made to rotate x becomes sph]oidal1 & !n successively sep>ates into a r+ & a gr\p ( sph]ules4 ,?us we h an illu/ration ( ! mode 9 :i* ! planet>y sy/em may h be5 produc$1#ccb ?\gh ! extreme diff]5ce ( scale prev5ts our argu+ ) confid5ce f ! exp]im5t to ! conditions ( ! nebul> !ory4 #ccb ,plateau1 99,taylor's ,sci5tific ,memoirs991 vol4 iv4 pp4 #af-dc4 ,x is possible t ! s-call$ elem5ts are elem5t>y only to u1 because we are re/rict$ to temp]atures at :i* !y are fix$4 ,lavoisi] c>efully def9$ an elem5t z a sub/ance :i* _c be decompos$ 99by any kn[n means992 b x seems almo/ c]ta9 t "s s]ies ( elem5ts1 = in/ance ,iod9e1 ,brom9e1 & ,*lor9e1 are really comp\nds ( a simpl] sub/ance4 ,we mu/ look to ! production ( int5sely high temp]atures1 yet q beyond our means1 = ! decomposition ( ^! s-call$ elem5ts4 ,possibly 9 ?is age & "p ( ! univ]se ! dissipation ( en]gy has s f> proce$$ t !re are no s\rces ( heat suffici5tly int5se to effect ! decomposition4 99,int]f]5ce ( ,unsuspect$ ,conditions499 ,x may happ5 t we are n aw>e ( all ! conditions "u :i* our rese>*es are made4 ,"s sub/ance may be pres5t or "s p[] may be 9 action1 :i* escapes ! mo/ vigilant exam9ation4 ,n be+ aw>e ( its exi/5ce1 we are unable to take prop] measures to exclude x1 & ?us det]m9e ! %>e :i* x has 9 ! results ( our exp]im5ts4 ,!re c be no d\bt t ! al*emi/s 7 misl$ & enc\rag$ 9 _! va9 attempts by ! unsuspect$ pres5ce ( traces ( gold & silv] 9 ! sub/ances !y propos$ to transmute4 ,lead1 z drawn f ! smelt+ furnace1 almo/ always conta9s "s silv]1 & gold is associat$ ) _m o!r metals4 ,?us small quantities ( noble metal w\ld (t5 appe> z ! result ( exp]im5t & raise delusive hopes4 ,9 m ?an "o case ! unsuspect$ pres5ce ( common salt 9 ! air has caus$ great tr\ble4 ,9 ! e>ly exp]im5ts on electrolysis x 0 f\nd t :5 wat] 0 decompos$1 an acid & an alkali 7 produc$ at ! poles1 toge!r ) oxyg5 & hydrog54 ,9 ! abs5ce ( any o!r explanation1 "s *emi/s ru%$ to ! conclusion t electricity mu/ h ! p[] ( 99g5]at+99 acids & alkalies1 & "o *emi/ ?\ght he _h discov]$ a new sub/ance call$ 99electric acid994 ,b ,davy proce$$ to a sy/ematic inve/igation ( ! circum/ances1 by v>y+ ! conditions4 ,*ang+ ! glass vessel = "o ( agate or gold1 he f\nd t f> less alkali 0 produc$2 exclud+ impurities by ! use ( c>efully di/ill$ wat]1 he f\nd t ! quantities ( acid & alkali 7 /ill fur!r dim9i%$2 & hav+ ?us obta9$ a clue to ! cause1 he complet$ ! exclusion ( impurities by avoid+ contact ) 8 f+]s1 & by plac+ ! app>atus "u an exhau/$ receiv]1 no acid or alkali be+ !n detect$4 ,x w\ld be difficult to meet ) a m elegant case ( ! detection ( a condition previ\sly unsuspect$4#ccc #ccc 99,philosophical ,transactions99 #ahbf1 vol4 cxvi4 pp4 #chh1 #chi4 ,works ( ,sir ,humphry ,davy1 vol4 v4 pp4 #a-ab4 ,x is rem>kable t ! pres5ce ( common salt 9 ! air1 prov$ to exi/ by ,davy1 nev]!less cont9u$ a /umbl+-block 9 ! sci5ce ( spectrum analysis1 & probably prev5t$ m51 su* z ,brew/]1 ,h]s*el1 & ,talbot1 f anticipat+ by ?irty ye>s ! discov]ies ( ,buns5 & ,kir*h(f4 ,z ,i po9t$ out1#ccd ! utility ( ! spectrum 0 kn[n 9 ! middle ( ! la/ c5tury to ,?omas ,melvill1 a tal5t$ ,scot* physici/1 :o di$ at ! e>ly age ( #bg ye>s4#cce ,b ,melvill 0 /ruck 9 8 exam9ation ( col\r$ flames by ! extraord9>y pr$om9ance ( homog5e\s yell[ light1 :i* 0 due to "s circum/ance escap+ 8 att5tion4 ,wolla/on & ,fraunh(] 7 equally /ruck by ! prom95ce ( ! yell[ l9e 9 ! spectrum ( ne>ly e k9d ( light4 ,talbot expressly recomm5d$ ! use ( ! prism = detect+ ! pres5ce ( sub/ances by :at we n[ call spectrum analysis1 b he f\nd t all sub/ances1 h[ev] diff]5t ! light !y yield$ 9 o!r respects1 7 id5tical z reg>ds ! production ( yell[ light4 ,talbot knew t ! salts ( soda gave ?is col\r$ light1 b 9 spite ( ,davy's previ\s difficulties ) salt 9 electrolysis1 x did n occur to him to ass]t t :]e ! light is1 !re sodium mu/ be4 ,he sugge/$ wat] z ! mo/ likely s\rce ( ! yell[ light1 because ( its frequ5t pres5ce2 b ev5 sub/ances :i* 7 app>5tly devoid ( wat] gave ! same yell[ light4#ccf ,brew/] & ,h]s*el bo? exp]im5t$ ^u flames almo/ at ! same "t z ,talbot1 & ,h]s*el unequivocally en\nc$ ! pr9ciple ( spectrum analysis4#ccg ,nev]!less ,brew/]1 aft] num]\s exp]im5ts att5d$ ) great tr\ble & disappo9tm5t1 f\nd t yell[ light might be obta9$ f ! combu/ion ( almo/ any sub/ance4 ,x 0 n until #ahef t ,swan discov]$ t an almo/ inf9itesimal quantity ( sodium *loride1 say a million? "p ( a gra91 0 suffici5t to t+e a flame ( a bright yell[ col\r4 ,! univ]sal diffusion ( ! salts ( sodium1 jo9$ to ?is unique light-produc+ p[]1 0 ?us %[n to be ! unsuspect$ condition :i* _h de/roy$ ! confid5ce ( all previ\s exp]im5t]s 9 ! use ( ! prism4 ,"s ref]5ces conc]n+ ! hi/ory ( ?is curi\s po9t are giv5 bel[4#cch #ccd 99,national ,review991 ,july1 #ahfa1 p4 #ac4 #cce ,8 publi%$ works are conta9$ 9 99,! ,ed9burgh ,physical & ,lit]>y ,essays991 vol4 ii4 p4 #cd2 99,philosophical ,transactions99 #agec1 vol4 xlviii4 p4 #bfa2 see also ,morgan's ,pap]s 9 99,philosophical ,transactions99 #aghe1 vol4 lxxv4 p4 #aij4 #ccf 99,ed9burgh ,j\rnal ( ,sci5ce991 vol4 v4 p4 #gi4 #ccg 99,encyclopdia ,metropolitana991 art4 99,light991 #ebd2 ,h]s*el's 99,famili> ,lectures991 p4 #bff4 #cch ,talbot1 99,philosophical ,magaz9e991 #crd ,s]ies1 vol4 ix4 p4 #a 7#ahcf72 ,brew/]1 99,transactions ( ! ,royal ,society ( ,ed9burgh99 #ahbc1 vol4 ix4 pp4 #dcc1 #dee2 ,swan1 ibid4 #ahef vol4 xxi4 p4 #daa2 99,philosophical ,magaz9e991 #d? ,s]ies1 vol4 xx4 p4 #agc ,sept4 #ahfj2 ,roscoe1 99,spectrum ,analysis991 ,lecture ,,iii4 ,9 ! sci5ce ( radiant heat1 e>ly inquir]s 7 l$ to ! conclusion t radiation proce$$ only f ! surface ( a solid1 or f a v small dep? bel[ x4 ,b !y happ5$ to exp]im5t ^u surfaces cov]$ by coats ( v>ni%1 :i* is highly a!rman\s or opaque to heat4 ,_h !y prop]ly v>i$ ! "* ( ! surface1 us+ a highly dia!rman\s sub/ance l rock salt1 !y w\ld h obta9$ v diff]5t results4#cci ,"o ( ! mo/ extraord9>y in/ances ( an errone\s op9ion due to ov]look+ int]f]+ ag5ts is t conc]n+ ! increase ( ra9fall ne> to ! e>?'s surface4 ,m ?an a c5tury ago x 0 obs]v$ t ra9-gauges plac$ ^u *ur* /eeples1 h\se tops1 & o!r elevat$ places1 gave consid]ably less ra9 ?an if !y 7 on ! gr\nd1 & x has be5 rec5tly %[n t ! v>iation is mo/ rapid 9 ! close neighb\rhood ( ! gr\nd4#cdj ,all k9ds ( !ories h be5 />t$ to expla9 ?is ph5om5on2 b ,i h %[n#cda t x is simply due to ! int]f]5ce ( w9d1 :i* deflects m or less ra9 f all ! gauges :i* are expos$ to x4 #cci ,balf\r ,/ew>t1 99,elem5t>y ,treatise on ,heat991 p4 #aib4 #cdj ,briti% ,association1 ,liv]pool1 #ahgj4 99,report on ,ra9fall991 p4 #agf4 #cda 99,philosophical ,magaz9e4991 ,dec4 #ahfa4 #d? ,s]ies1 vol4 xxii4 p4 #dba4 ,! great magnetic p[] ( iron r5d]s x a s\rce ( di/urbance 9 magnetic exp]im5ts4 ,9 build+ a magnetic obs]vatory great c>e mu/ !re=e be tak5 t no iron is employ$ 9 ! con/ruction1 & t no masses ( iron are ne> at h&4 ,9 "s cases magnetic obs]vations h be5 s]i\sly di/urb$ by ! exi/5ce ( masses ( iron ore 9 ! neighb\rhood4 ,9 ,f>aday's exp]im5ts ^u feebly magnetic or diamagnetic sub/ances he took ! greate/ precautions aga9/ ! pres5ce ( di/urb+ sub/ances 9 ! copp] wire1 wax1 pap]1 & o!r articles us$ 9 susp5d+ ! te/ objects4 ,x 0 8 cu/om to try ! effect ( ! magnet ^u ! app>atus 9 ! abs5ce ( ! object ( exp]im5t1 & )\t ?is prelim9>y trial no confid5ce c\ld be plac$ 9 ! results4#cdb ,tyndall has also employ$ ! same mode = te/+ ! fre$om ( electro-magnetic coils f iron1 & 0 ?us enabl$ to obta9 !m devoid ( any cause ( di/urbance4#cdc ,x is wor?y ( notice t 9 ! v infancy ( ! sci5ce ( magnetism1 ! acute exp]im5tali/ ,gilb]t correctly acc\nt$ = ! op9ion exi/+ 9 8 day t magnets w\ld attract silv]1 by po9t+ out t ! silv] conta9$ iron4 #cdb 99,exp]im5tal ,rese>*es 9 ,electricity991 vol4 iii4 p4 #hd1 c4 #cdc 99,lectures on ,heat991 p4 #ba4 ,ev5 :5 we are n aw>e by previ\s exp]i5ce ( ! probable pres5ce ( a special di/urb+ ag5t1 we ought n to assume ! abs5ce ( unsuspect$ int]f]5ce4 ,if an exp]im5t is ( really high importance1 s t any consid]able bran* ( sci5ce re/s ^u x1 we ought to try x aga9 & aga91 9 z v>i$ conditions z possible4 ,we %\ld int5tionally di/urb ! app>atus 9 v>i\s ways1 s z if possible to hit by accid5t ^u any weak po9t4 ,especially :5 our results are m regul> ?an we h fair gr\nds = anticipat+1 ought we to suspect "s peculi>ity 9 ! app>atus :i* causes x to measure "s o!r ph5om5on ?an t 9 "q1 j z ,f\cault's p5dulum almo/ always indicates ! movem5t ( ! axes ( its own elliptic pa? in/ead ( ! rotation ( ! globe4 ,x 0 9 ?is cauti\s _s t ,baily act$ 9 8 exp]im5ts on ! d5sity ( ! e>?4 ,! accuracy ( 8 results dep5d$ ^u ! elim9ation ( all di/urb+ influ5ces1 s t ! oscillation ( 8 torsion balance %\ld measure gravity alone4 ,h5ce he v>i$ ! app>atus 9 _m ways1 *ang+ ! small balls subject to attraction1 *ang+ ! connect+ rod1 & ! means ( susp5sion4 ,he obs]v$ ! effect ( di/urbances1 su* z ! pres5ce ( visitors1 ! occurr5ce ( viol5t /orms1 c41 & z no real alt]ation 0 produc$ 9 ! results1 he confid5tly attribut$ !m to gravity4#cdd #cdd ,baily1 99,memoirs ( ! ,royal ,a/ronomical ,society991 vol4 xiv4 pp4 #bi1 #cj4 ,newton w\ld probably h discov]$ ! mode ( con/ruct+ a*romatic l5ses1 b = ! unsuspect$ effect ( "s sug> ( lead :i* he is suppos$ to h dissolv$ 9 ! wat] ( a prism4 ,he tri$1 by means ( a glass prism comb9$ ) a wat] prism1 to produce disp]sion ( light )\t refraction1 & if he _h succe$$ !re w\ld h be5 an obvi\s mode ( produc+ refraction )\t disp]sion4 ,8 failure is attribut$ to 8 add+ lead acetate to ! wat] = ! purpose ( increas+ its refractive p[]1 ! lead hav+ a high disp]sive p[] :i* fru/rat$ 8 purpose4#cde ,judg+ f ,newton's rem>ks1 9 ! 99,philosophical ,transactions991 x w\ld appe> z if he _h n1 )\t _m unsuccessful trials1 despair$ ( ! con/ruction ( a*romatic glasses4#cdf #cde ,grant1 99,hi/ory ( ,physical ,a/ronomy991 p4 #eca4 #cdf 99,philosophical ,transactions991 abridg$ by ,l[?orp1 #d? edition1 vol4 i4 p4 #bjb4 ,! ,academicians ( ,cim5to1 9 _! e>ly & +5i\s exp]im5ts ^u ! vacuum1 7 (t5 misl$ by ! me*anical imp]fections ( _! app>atus4 ,!y conclud$ t ! air _h no?+ to d ) ! production ( s\nds1 evid5tly because _! vacuum 0 n suffici5tly p]fect4 ,otto von ,gu]icke fell into a l mi/ake 9 ! use ( 8 newly-con/ruct$ air-pump1 d\btless f ! unsuspect$ pres5ce ( air suffici5tly d5se to convey ! s\nd ( ! bell4 ,x is h>dly requisite to po9t out t ! doctr9e ( spontane\s g5]ation is due to ! unsuspect$ pres5ce ( g]ms1 ev5 aft] ! mo/ c>eful ef=ts to exclude !m1 & 9 ! case ( _m diseases1 bo? ( animals & plants1 g]ms :i* we h no means z yet ( detect+ are d\btless ! active cause4 ,x has long be5 a subject ( dispute1 aga91 :e!r ! plants :i* spr+ f newly turn$ l& gr[ f se$s long buri$ 9 t l&1 or f se$s br\ght by ! w9d4 ,argum5t is unphilosophical :5 direct trial c readily be appli$2 = by turn+ up "s old gr\nd1 & cov]+ a portion ( x ) a glass case1 ! conveyance ( se$s by ! w9d c be entirely prev5t$1 & if ! same plants appe> )9 & )\t ! case1 x w become cle> t ! se$s are 9 ! e>?4 ,by gross ov]sight "s exp]im5t]s h ?\ght be=e n[ t crops ( rye _h sprung up :]e oats _h be5 s[n4 99,bl9d or ,te/ ,exp]im5ts499 ,e conclusive exp]im5t necess>ily consi/s 9 ! comp>ison ( results betwe5 two diff]5t comb9ations ( circum/ances4 ,to give a fair probability t ,a is ! cause ( ,x1 we mu/ ma9ta9 inv>iable all surr\nd+ objects & conditions1 & we mu/ !n %[ t :]e ,a is ,x is1 & :]e ,a is n ,x is n4 ,?is _c really be accompli%$ 9 a s+le trial4 ,if1 = in/ance1 a *emi/ places a c]ta9 suspect$ sub/ance 9 ,m>%'s te/ app>atus1 & f9ds t x gives a small deposit ( metallic ars5ic1 he _c be sure t ! ars5ic really proce$s f ! suspect$ sub/ance2 ! impurity ( ! z9c or sulphuric acid may h be5 ! cause ( its appe>ance4 ,x is !re=e ! practice ( *emi/s to make :at !y call a 99bl9d exp]im5t991 t is to try :e!r ars5ic appe>s 9 ! abs5ce ( ! suspect$ sub/ance4 ,! same precaution ought to be tak5 9 all important analytical op]ations4 ,inde$1 x is n m]ely a precaution1 x is an ess5tial "p ( any exp]im5t4 ,if ! bl9d trial be n made1 ! *emi/ m]ely assumes t he kn[s :at w\ld happ54 ,:5ev] we ass]t t because ,a & ,x are f\nd toge!r ,a is ! cause ( ,x1 we assume t if ,a 7 abs5t ,x w\ld be abs5t4 ,b :]ev] x is possible1 we ought n to take ?is z a m]e assumption1 or ev5 z a matt] ( inf]5ce4 ,exp]i5ce is ultimately ! basis ( all our inf]5ces1 b if we c br+ imm$iate exp]i5ce to be> ^u ! po9t 9 "q we %\ld n tru/ to any?+ m remote & liable to error4 ,:5 ,f>aday exam9$ ! magnetic prop]ties ( ! be>+ app>atus1 9 ! abs5ce ( ! sub/ance to be exp]im5t$ on1 he really made a bl9d exp]im5t 7p4 #dca74 ,we ought1 also1 to te/ ! accuracy ( a me?od ( exp]im5t :5ev] we c1 by introduc+ kn[n am\nts ( ! sub/ance or =ce to be detect$4 ,a new analytical process = ! quantitative e/imation ( an elem5t %\ld be te/$ by p]=m+ x ^u a mixture comp\nd$ s z to conta9 a kn[n quantity ( t elem5t4 ,! accuracy ( ! gold assay process greatly dep5ds ^u ! precaution ( assay+ alloys ( gold ( exactly kn[n composition4#cdg ,gabriel ,plattes' works give evid5ce ( mu* sci5tific _s1 & :5 discuss+ ! suppos$ m]its ( ! div9+ rod = ! discov]y ( subt]ranean treasure1 he s5sibly sugge/s t ! rod %\ld be tri$ 9 places :]e ve9s ( metal are kn[n to exi/4#cdh #cdg ,jevons 9 ,watts' 99,diction>y ( ,*emi/ry991 vol4 ii4 pp4 #icf1 #icg4 #cdh 99,discov]y ( ,subt]raneal ,treasure499 ,london1 #afci1 p4 #dh4 99,negative ,results ( ,exp]im5t499 ,:5 we pay prop] reg>d to ! imp]fection ( all measur+ in/rum5ts & ! possible m9ut5ess ( effects1 we %all see mu* reason = int]pret+ ) caution ! negative results ( exp]im5ts4 ,we may fail to discov] ! exi/5ce ( an expect$ effect1 n because t effect is really non-exi/5t1 b because x is ( a magnitude inappreciable to our s5ses1 or conf\nd$ ) o!r effects ( mu* great] am\nt4 ,z !re is no limit on 99 priori99 gr\nds to ! smallness ( a ph5om5on1 we c nev]1 by a s+le exp]im5t1 prove ! non-exi/5ce ( a suppos$ effect4 ,we are always at lib]ty to assume t a c]ta9 am\nt ( effect might h be5 detect$ by great] delicacy ( measurem5t4 ,we _c safely affirm t ! moon has no atmosph]e at all4 ,we may d\btless %[ t ! atmosph]e1 if pres5t1 is less d5se ?an ! air 9 ! s-call$ vacuum ( an air-pump1 z did ,du ,sej\r4 ,x is equally impossible to prove t gravity occupies 99no "t99 9 transmission4 ,laplace inde$ asc]ta9$ t ! velocity ( propagation ( ! influ5ce 0 at lea/ fifty million times great] ?an t ( light2#cdi b x does n really foll[ t x is in/antane\s2 & 7 !re any means ( detect+ ! action ( "o /> ^u ano!r exce$+ly di/ant />1 we might possibly f9d an appreciable int]val occupi$ 9 ! transmission ( ! gravitat+ impulse4 ,newton c\ld n demon/rate ! abs5ce ( all resi/ance to matt] mov+ ?r\gh empty space2 b he asc]ta9$ by an exp]im5t ) ! p5dulum 7p4 #ddc71 t if su* resi/ance exi/$1 x 0 9 am\nt less ?an "o five-?\s&? "p ( ! ext]nal resi/ance ( ! air4#cej #cdi ,laplace1 99,sy/em ( ! ,_w991 translat$ by ,h>te1 vol4 ii4 p4 #cbb4 #cej 99,pr9cipia991 bk4 ii4 sect4 #f1 ,prop4 xxxi4 ,motte's translation1 vol4 ii4 p4 #ajh4 ,a curi\s in/ance ( false negative inf]5ce is furni%$ by exp]im5ts on light4 ,eul] reject$ ! corpuscul> !ory on ! gr\nd t p>ticles ( matt] mov+ ) ! imm5se velocity ( light w\ld possess mom5tum1 ( :i* !re 0 no evid5ce4 ,b5net _h attempt$ to detect ! mom5tum ( light by conc5trat+ ! rays ( ! sun ^u a delicately balanc$ body4 ,obs]v+ no result1 x 0 consid]$ to be prov$ t light _h no mom5tum4 ,mr4 ,crookes1 h[ev]1 hav+ susp5d$ ?9 vanes1 black$ on "o side1 9 a ne>ly vacu\s globe1 f\nd t !y move "u ! influ5ce ( light4 ,x is n[ all[$ t ?is effect c be expla9$ 9 accordance ) ! undulatory !ory ( light1 & ! molecul> !ory ( gases4 ,x comes to ?is--t ,b5net fail$ to detect an effect :i* he might h detect$ ) a bett] me?od ( exp]im5t+2 b if he _h f\nd x1 ! ph5om5on w\ld h confirm$1 n ! corpuscul> !ory ( light1 z 0 expect$1 b ! rival undulatory !ory4 ,! conclusion drawn f ,b5net's exp]im5t 0 falsely drawn1 b x 0 nev]!less true 9 matt]4 ,_m incid5ts 9 ! hi/ory ( sci5ce t5d to %[ t ph5om5a1 :i* "o g5]ation has fail$ to discov]1 may become accurately kn[n to a succe$+ g5]ation4 ,! compressibility ( wat] :i* ! ,academicians ( ,flor5ce c\ld n detect1 because at a l[ pressure ! effect 0 too small to p]ceive1 & at a high pressure ! wat] ooz$ ?r\gh _! silv] vessel1#cea has n[ become ! subject ( exact measurem5t & precise calculation4 ,indep5d5tly ( ,newton1 ,hooke ent]ta9$ v rem>kable notions conc]n+ ! nature ( gravitation4 ,9 ?is & o!r subjects he %[$1 inde$1 a g5ius = exp]im5tal inve/igation :i* w\ld h plac$ him 9 ! fir/ rank 9 any o!r age ?an t ( ,newton4 ,he correctly conceiv$ t ! =ce ( gravity w\ld decrease z we rec$e f ! c5tre ( ! e>?1 & he boldly attempt$ to prove x by exp]im5t4 ,hav+ exactly c\nt]pois$ two weights 9 ! scales ( a balance1 or r "o weight aga9/ ano!r weight & a long piece ( f9e cord1 he remov$ 8 balance to ! top ( ! dome ( ,/4 ,paul's1 & tri$ :e!r ! balance rema9$ 9 equilibrium aft] "o weight 0 all[$ to hang d[n to a dep? ( #bdj feet4 ,no diff]5ce c\ld be p]ceiv$ :5 ! weights 7 at ! same & at diff]5t levels1 b ,hooke rightly held t ! failure arose f ! insuffici5t elevation4 ,he says1 8,yet ,i am apt to ?9k "s diff]5ce might be discov]$ 9 great] heights40#ceb ,! radius ( ! e>? be+ ab\t #bj1ibb1jjj feet1 we c n[ readily calculate f ! law ( gravity t a height ( #bdj w\ld n make a great] diff]5ce ?an "o "p 9 #dj1jjj ( ! weight4 ,su* a diff]5ce w\ld d\btless be inappreciable 9 ! balances ( t day1 ?\gh x c\ld readily be detect$ by balances n[ frequ5tly con/ruct$4 ,aga91 ! mutual gravitation ( bodies at ! e>?'s surface is s small t ,newton appe>s to h made no attempt to demon/rate its exi/5ce exp]im5tally1 m]ely rem>k+ t x 0 too small to fall "u ! obs]vation ( our s5ses4#cec ,x has s9ce be5 successfully detect$ & measur$ by ,cav5di%1 ,baily1 & o!rs4 #cea 99,essayes ( ,natural ,exp]im5ts991 c4 p4 #aag4 #ceb ,hooke's 99,po/hum\s ,works991 p4 #ahb4 #cec 99,pr9cipia991 bk4 iii4 ,prop4 vii4 ,coroll>y #a4 ,! smallness ( ! quantities :i* we c sometimes obs]ve is a/oni%+4 ,a balance w weigh to "o million? "p ( ! load4 ,:itwor? c measure to ! million? "p ( an in*4 ,a rise ( temp]ature ( ! #hhjj? "p ( a degree c5tigrade has be5 detect$ by ,dr4 ,j\le4 ,! spectroscope has reveal$ ! pres5ce ( ! #aj1jjj1jjj? "p ( a gram4 ,x is said t ! eye c obs]ve ! col\r produc$ 9 a drop ( wat] by ! #ej1jjj1jjj? "p ( a gram ( fus*9e1 & ab\t ! same quantity ( cyan9e4 ,by ! s5se ( smell we c probably feel /ill small] quantities ( odor\s matt]4#ced ,we mu/ nev]!less rememb] t quantitative effects ( f> less am\nt ?an ^! mu/ exi/1 & we %\ld /ate our negative results ) correspond+ caution4 ,we c only disprove ! exi/5ce ( a quantitative ph5om5on by %[+ d$uctively f ! laws ( nature1 t if pres5t x w\ld am\nt to a p]ceptible quantity4 ,z 9 ! case ( o!r negative argum5ts 7p4 #dad71 we mu/ demon/rate t ! effect w\ld appe>1 :]e x is by exp]im5t f\nd n to appe>4 #ced ,keill's 99,introduction to ,natural ,philosophy991 #crd ed41 ,london1 #agcc1 pp4 #dh-ed4 99,limits ( ,exp]im5t499 ,x w be obvi\s t !re are _m op]ations ( nature :i* we are q incapable ( imitat+ 9 our exp]im5ts4 ,our object is to /udy ! conditions "u :i* a c]ta9 effect is produc$2 b "o ( ^? conditions may involve a great l5g? ( "t4 ,!re are in/ances on record ( exp]im5ts ext5d+ ov] five or t5 ye>s1 & ev5 ov] a l>ge "p ( a lifetime2 b su* int]vals ( "t are almo/ no?+ to ! "t dur+ :i* nature may h be5 at "w4 ,! cont5ts ( a m9]al ve9 9 ,cornwall may h be5 und]go+ gradual *ange = a hundr$ million ye>s4 ,all metamorphic rocks h d\btless endur$ high temp]ature & enorm\s1 pressure = inconceivable p]iods ( "t1 s t *emical geology is g5]ally beyond ! scope ( exp]im5t4 ,argum5ts h be5 br\ght aga9/ ,d>w9's !ory1 f\nd$ ^u ! abs5ce ( any cle> in/ance ( ! production ( a new species4 ,dur+ an hi/orical int]val ( p]haps f\r ?\s& ye>s1 no animal1 x is said1 has be5 s mu* dome/icat$ z to become diff]5t 9 species4 ,x might z well be argu$ t no geological *anges are tak+ place1 because no new m\nta9 has ris5 9 ,great ,brita9 )9 ! memory ( man4 ,our actual exp]i5ce ( geological *anges is l a po9t 9 ! inf9ite progression ( "t4 ,:5 we "k t ra9 wat] fall+ on lime/one w c>ry away a m9ute portion ( ! rock 9 solution1 we d n hesitate to multiply t quantity by millions1 & inf] t 9 c\rse ( "t a m\nta9 may be dissolv$ away4 ,we h actual exp]i5ce conc]n+ ! rise ( l& 9 "s p>ts ( ! globe & its fall 9 o!rs to ! ext5t ( "s feet4 ,d we hesitate to inf] :at may ?us be done 9 c\rse ( geological ages8 ,z ,gabriel ,plattes long ago rem>k$1 8,! sea nev] re/+1 b p]petually w9n+ l& 9 "o place & los+ 9 ano!r1 do? %[ :at may be done 9 l5g? ( "t by a cont9ual op]ation1 n subject unto ceas+ or int]mission40#cee ,! action ( physical circum/ances ^u ! =ms & *>act]s ( animals by natural selection is subject to exactly ! same rem>ks4 ,z reg>ds animals liv+ 9 a /ate ( nature1 ! *ange ( circum/ances :i* c be asc]ta9$ to h occurr$ is s slight1 t we c\ld n expect to obs]ve any *ange 9 ^? animals :atev]4 ,nature has made no exp]im5t at all = u )9 hi/orical times4 ,man1 h[ev]1 by tam+ & dome/icat+ dogs1 horses1 ox51 pigeons1 c41 has made consid]able *ange 9 _! circum/ances1 & we f9d consid]able *ange also 9 _! =ms & *>act]s4 ,suppos+ ! /ate ( dome/ication to cont9ue un*ang$1 ^! new =ms w\ld cont9ue p]man5t s f> z we "k1 & 9 ?is s5se !y are p]man5t4 ,?us ! argum5ts aga9/ ,d>w9's !ory1 f\nd$ on ! non-obs]vation ( natural *anges )9 ! hi/orical p]iod1 are ( ! weake/ "*1 be+ purely negative4 #cee 99,discov]y ( ,subt]raneal ,treasure991 #afci1 p4 #eb4 ,,*apt] ,,xx4 ,,me?od ,,( ,,v>iations4 ,exp]im5ts may be ( two k9ds1 exp]im5ts ( simple fact1 & exp]im5ts ( quantity4 ,9 ! fir/ class ( exp]im5ts we comb9e c]ta9 conditions1 & wi% to asc]ta9 :e!r or n a c]ta9 effect ( any quantity exi/s4 ,hooke wi%$ to asc]ta9 :e!r or n !re 0 any diff]5ce 9 ! =ce ( gravity at ! top & bottom ( ,/4 ,paul's ,ca!dral4 ,! *emi/ cont9ually p]=ms analyses = ! purpose ( asc]ta9+ :e!r or n a giv5 elem5t exi/s 9 a p>ticul> m9]al or mixture2 all su* exp]im5ts & analyses are qualitative r ?an quantitative1 because ?\gh ! result may be m or less1 ! p>ticul> am\nt ( ! result is n ! object ( ! inquiry4 ,s soon1 h[ev]1 z a result is kn[n to be discov]able1 ! sci5tific man ought to proce$ to ! quantitative inquiry1 h[ great a result foll[s f a c]ta9 am\nt ( ! conditions :i* are suppos$ to con/itute ! cause8 ,! possible numb]s ( exp]im5ts are n[ inf9itely great1 = e v>iation 9 a quantitative condition w usually produce a v>iation 9 ! am\nt ( ! effect4 ,! me?od ( v>iation :i* ?us arises is no n>r[ or special me?od1 b x is ! g5]al application ( exp]im5t to ph5om5a capable ( cont9u\s v>iation4 ,z ,mr4 ,f[l] has well rem>k$1#cef ! obs]vation ( v>iations is really an integration ( a suppos$ inf9ite numb] ( applications ( ! s-call$ me?od ( diff]5ce1 t is ( exp]im5t 9 its p]fect =m4 #cef 99,elem5ts ( ,inductive ,logic991 #a/ edit4 p4 #age4 ,9 induction we aim at e/abli%+ a g5]al law1 & if we deal ) quantities t law mu/ really be express$ m or less obvi\sly 9 ! =m ( an equation1 or equations4 ,we treat z be=e ( conditions1 & ( :at happ5s "u ^? conditions4 ,b ! conditions w n[ v>y1 n 9 quality1 b quantity1 & ! effect w also v>y 9 quantity1 s t ! result ( quantitative induction is always to arrive at "s ma!matical expression involv+ ! quantity ( ea* condition1 & express+ ! quantity ( ! result4 ,9 o!r words1 we wi% to "k :at function ! effect is ( its conditions4 ,we %all f9d t x is "o ?+ to obta9 ! num]ical results1 & q ano!r ?+ to detect ! law obey$ by ^? results1 ! latt] be+ an op]ation ( an inv]se & t5tative "*4 99,! ,v>iable & ! ,v>iant499 ,almo/ e s]ies ( quantitative exp]im5ts is direct$ to obta9 ! relation betwe5 ! diff]5t values ( "o quantity :i* is v>i$ at w1 & ano!r quantity :i* is caus$ !reby to v>y4 ,we may conv5i5tly di/+ui% ^! z respectively ! 99v>iable99 & ! 99v>iant994 ,:5 we are exam9+ ! effect ( heat 9 exp&+ bodies1 heat1 or "o ( its dim5sions1 temp]ature1 is ! v>iable1 l5g? ! v>iant4 ,if we compress a body to obs]ve h[ mu* x is !reby heat$1 pressure1 or x may be ! dim5sions ( ! body1 =ms ! v>iable1 heat ! v>iant4 ,9 ! !rmo-electric pile we make heat ! v>iable & measure electricity z ! v>iant4 ,t "o ( ! two measur$ quantities :i* is an antec$5t condition ( ! o!r w be ! v>iable4 ,x is always conv5i5t to h ! v>iable entirely "u our comm&4 ,exp]im5ts may inde$ be made ) accuracy1 provid$ we c exactly measure ! v>iable at ! mom5t :5 ! quantity ( ! effect is det]m9$4 ,b if we h to tru/ to ! action ( "s caprici\s =ce1 !re may be great difficulty 9 mak+ exact measurem5ts1 & ^? results may n be dispos$ ov] ! :ole range ( quantity 9 a conv5i5t mann]4 ,x is "o prime object ( ! exp]im5t]1 !re=e1 to obta9 a regul> & gov]nable supply ( ! =ce :i* he is inve/igat+4 ,to det]m9e correctly ! effici5cy ( w9dmills1 :5 ! natural w9ds 7 con/antly v>y+ 9 =ce1 w\ld be exce$+ly difficult4 ,smeaton1 !re=e1 9 8 exp]im5ts on ! subject1 creat$ a uni=m w9d ( ! requir$ =ce by mov+ 8 models aga9/ ! air on ! extremity ( a revolv+ arm4#ceg ,! velocity ( ! w9d c\ld ?us be r5d]$ great] or less1 x c\ld be ma9ta9$ uni=m = any l5g? ( "t1 & its am\nt c\ld be exactly asc]ta9$4 ,9 det]m9+ ! laws ( ! *emical action ( light x w\ld be out ( ! "q to employ ! rays ( ! sun1 :i* v>y 9 int5sity ) ! cle>ness ( ! atmosph]e1 & ) e pass+ cl\d4 ,"o great difficulty 9 photometry & ! inve/igation ( ! *emical action ( light consi/s 9 obta9+ a uni=m & gov]nable s\rce ( light rays4#ceh #ceg 99,philosophical ,transactions991 vol4 li4 p4 #ach2 abridgm5t1 vol4 xi4 p4 #cee4 #ceh ,see ,buns5 & ,roscoe's rese>*es1 9 99,philosophical ,transactions99 7#ahei71 vol4 cxlix4 p4 #hhj1 c41 :]e !y describe a con/ant flame ( c>bon monoxide gas4 ,fizeau's me?od ( measur+ ! velocity ( light enabl$ him to appreciate ! "t occupi$ by light 9 travell+ ?r\gh a di/ance ( eight or n9e ?\s& metres4 ,b ! revolv+ mirror ( ,:eat/one subsequ5tly enabl$ ,f\cault & ,fizeau to measure ! velocity 9 a space ( f\r metres4 ,9 ?is latt] me?od !re 0 ! advantage t v>i\s m$ia c\ld be sub/itut$ = air1 & ! temp]ature1 d5sity1 & o!r conditions ( ! exp]im5t c\ld be accurately gov]n$ & measur$4 99,measurem5t ( ! ,v>iable499 ,!re is little use 9 obta9+ exact measurem5ts ( an effect unless we c also exactly measure its conditions4 ,x is absurd to measure ! electrical resi/ance ( a piece ( metal1 its ela/icity1 t5acity1 d5sity1 or o!r physical qualities1 if ^! v>y1 n only ) ! m9ute impurities ( ! metal1 b also ) its physical condition4 ,if ! same b> *anges its prop]ties by be+ heat$ & cool$1 & we _c exactly def9e ! /ate 9 :i* x is at any mom5t1 our c>e 9 measur+ w be wa/$1 because x c lead to no law4 ,x is ( little use to det]m9e v exactly ! electric conductibility ( c>bon1 :i* z graphite or gas c>bon conducts l a metal1 z diamond is almo/ a non-conductor1 & 9 sev]al o!r =ms possesses v>iable & int]m$iate p[]s ( conduction4 ,x w be ( use only = imm$iate practical applications4 ,be=e measur+ ^! we ought to h some?+ to measure ( :i* ! conditions are capable ( exact def9ition1 & to :i* at a future "t we c recur4 ,simil>ly ! accuracy ( our measurem5t ne$ n mu* surpass ! accuracy ) :i* we c def9e ! conditions ( ! object treat$4 ,! spe$ ( electricity 9 pass+ ?r\gh a conductor ma9ly dep5ds ^u ! inductive capacity ( ! surr\nd+ sub/ances1 &1 except = te*nical or special purposes1 !re is little use 9 measur+ velocities :i* 9 "s cases are "o hundr$ times z great z 9 o!r cases4 ,b ! maximum spe$ ( electric conduction is probably a con/ant quantity ( great sci5tific importance1 & accord+ to ,pr(4 ,cl]k ,maxwell's det]m9ation 9 #ahfh is #agd1hjj miles p] second1 or little less ?an t ( light4 ,! true boil+ po9t ( wat] is a po9t on :i* practical !rmometry dep5ds1 & x is highly important to det]m9e t po9t 9 relation to ! absolute !rmometric scale4 ,b :5 wat] free f air & impurity is heat$ !re seems to be no def9ite limit to ! temp]ature x may rea*1 a temp]ature ( #ahj ,c5t4 hav+ be5 actually obs]v$4 ,su* temp]atures1 !re=e1 d n require accurate measurem5t4 ,all meteorological measurem5ts dep5d+ on ! accid5tal condition ( ! sky are ( f> less importance ?an physical measurem5ts 9 :i* su* accid5tal conditions d n int]v5e4 ,_m pr(\nd inve/igations dep5d ^u our k ( ! radiant en]gy cont9ually p\r$ ^u ! e>? by ! sun2 b ?is mu/ be measur$ :5 ! sky is p]fectly cle>1 & ! absorption ( ! atmosph]e at its m9imum4 ,! slighte/ int]f]5ce ( cl\d de/roys ! value ( su* a measurem5t1 except = meteorological purposes1 :i* are ( va/ly less g5]ality & importance4 ,x is seldom useful1 aga91 to measure ! height ( a sn[-cov]$ m\nta9 )9 a foot1 :5 ! ?ickness ( ! sn[ alone may cause x to v>y #be feet or m1 :5 9 %ort ! height itself is indef9ite to t ext5t4#cei #cei ,humboldt's 99,cosmos99 7,bohn71 vol4 i4 p4 #g4 99,ma9t5ance ( ,simil> ,conditions499 ,our ultimate object 9 induction mu/ be to obta9 ! complete relation betwe5 ! conditions & ! effect1 b ?is relation w g5]ally be s complex t we c only attack x 9 detail4 ,we mu/1 z f> z possible1 conf9e ! v>iation to "o condition at a "t1 & e/abli% a sep>ate relation betwe5 ea* condition & ! effect4 ,?is is at any rate ! fir/ /ep 9 approximat+ to ! complete law1 & x w be a subsequ5t "q h[ f> ! simultane\s v>iation ( sev]al conditions modifies _! sep>ate actions4 ,9 _m exp]im5ts1 inde$1 x is only "o condition :i* we wi% to /udy1 & ! o!rs are int]f]+ =ces :i* we w\ld avoid if possible4 ,"o ( ! conditions ( ! motion ( a p5dulum is ! resi/ance ( ! air1 or o!r m$ium 9 :i* x sw+s2 b :5 ,newton 0 desir\s ( prov+ ! equal gravitation ( all sub/ances1 he _h no int]e/ 9 ! air4 ,8 object 0 to obs]ve a s+le =ce only1 & s x is 9 a great _m o!r exp]im5ts4 ,accord+ly1 "o ( ! mo/ important precautions 9 inve/igation consi/s 9 ma9ta9+ all conditions con/ant except t :i* is to be /udi$4 ,z t admirable exp]im5tal philosoph]1 ,gilb]t1 express$ x1#cfj 8,!re is always ne$ ( simil> prep>ation1 ( simil> figure1 & ( equal magnitude1 = 9 dissimil> & unequal circum/ances ! exp]im5t is d\btful40 #cfj ,gilb]t1 99,de ,magnete991 p4 #aji4 ,9 ,newton's decisive exp]im5t simil> conditions 7 provid$ =1 ) ! simplicity :i* *>act]ises ! highe/ art4 ,! p5dulums ( :i* ! oscillations 7 comp>$ consi/$ ( equal boxes ( wood1 hang+ by equal ?reads1 & fill$ ) diff]5t sub/ances1 s t ! total weights %\ld be equal & ! c5tres ( oscillation at ! same di/ance f ! po9ts ( susp5sion4 ,h5ce ! resi/ance ( ! air became approximately a matt] ( indiff]5ce2 = ! outw>d size & %ape ( ! p5dulums be+ ! same1 ! absolute =ce ( resi/ance w\ld be ! same1 s long z ! p5dulums vibrat$ ) equal velocity2 & ! weights be+ equal ! resi/ance w\ld dim9i% ! velocity equally4 ,h5ce if any inequality 7 obs]v$ 9 ! vibrations ( ! two p5dulums1 x mu/ arise f ! only circum/ance :i* 0 diff]5t1 namely ! *emical nature ( ! matt] )9 ! boxes4 ,no inequality be+ obs]v$1 ! *emical nature ( sub/ances c h no appreciable influ5ce ^u ! =ce ( gravitation4#cfa #cfa 99,pr9cipia991 bk4 iii4 ,prop4 vi4 ,a beautiful exp]im5t 0 devis$ by ,dr4 ,j\le = ! purpose ( %[+ t ! ga9 or loss ( heat by a gas is connect$1 n ) ! m]e *ange ( its volume & d5sity1 b ) ! en]gy receiv$ or giv5 out by ! gas4 ,two /rong vessels1 connect$ by a tube & /opcock1 7 plac$ 9 wat] aft] ! air _h be5 exhau/$ f "o vessel & cond5s$ 9 ! o!r to ! ext5t ( tw5ty atmosph]es4 ,! :ole app>atus hav+ be5 br\ght to a uni=m temp]ature by agitat+ ! wat]1 & ! temp]ature hav+ be5 exactly obs]v$1 ! /opcock 0 op5$1 s t ! air at once exp&$ & fill$ ! two vessels uni=mly4 ,! temp]ature ( ! wat] be+ aga9 not$ 0 f\nd to be almo/ un*ang$4 ,! exp]im5t 0 !n repeat$ 9 an exactly simil> mann]1 except t ! /rong vessels 7 plac$ 9 sep>ate portions ( ! wat]4 ,n[ cold 0 produc$ 9 ! vessel f :i* ! air ru%$1 & an almo/ exactly equal quantity ( heat appe>$ 9 t to :i* x 0 conduct$4 ,?us ,dr4 ,j\le cle>ly prov$ t r>efaction produces z mu* heat z cold1 & t only :5 !re is disappe>ance ( me*anical en]gy w !re be production ( heat4#cfb ,:at we h to notice1 h[ev]1 is n s mu* ! result ( ! exp]im5t1 z ! simple mann] 9 :i* a s+le *ange 9 ! app>atus1 ! sep>ation ( ! portions ( wat] surr\nd+ ! air vessels1 is made to give indications ( ! utmo/ significance4 #cfb 99,philosophical ,magaz9e991 #crd ,s]ies1 vol4 xxvi4 p4 #cge4 99,collective ,exp]im5ts499 ,!re is an int]e/+ class ( exp]im5ts :i* enable u to obs]ve a numb] ( quantitative results 9 "o act4 ,g5]ally speak+1 ea* exp]im5t yields u b "o numb]1 & be=e we c approa* ! real processes ( reason+ we mu/ labori\sly repeat measurem5t aft] measurem5t1 until we c lay out a curve ( ! v>iation ( "o quantity z dep5d+ on ano!r4 ,we c sometimes abbreviate ?is lab\r1 by mak+ a quantity v>y 9 diff]5t p>ts ( ! same app>atus ?r\gh e requir$ am\nt4 ,9 obs]v+ ! height to :i* wat] rises by ! capill>y attraction ( a glass vessel1 we may take a s]ies ( glass tubes ( diff]5t bore1 & measure ! height ?r\gh :i* x rises 9 ea*4 ,b if we take two glass plates1 & place !m v]tically 9 wat]1 s z to be 9 contact at "o v]tical side1 & slightly sep>at$ at ! o!r side1 ! int]val betwe5 ! plates v>ies ?r\gh e int]m$iate wid?1 & ! wat] rises to a correspond+ height1 produc+ at its upp] surface a hyp]bolic curve4 ,! absorption ( light 9 pass+ ?r\gh a col\r$ liquid may be beautifully %[n by enclos+ ! liquid 9 a w$ge-%ap$ glass1 s t we h at a s+le glance an inf9ite v>iety ( ?icknesses 9 view4 ,z ,newton himself rem>k$1 a r$ liquid view$ 9 ?is mann] is f\nd to h a pale yell[ col\r at ! ?9ne/ "p1 & x passes ?r\gh orange into r$1 :i* gradually becomes ( a deep] & d>k] t9t4#cfc ,! effect may be notic$ 9 a conical w9e-glass4 ,! prismatic analysis ( light f su* a w$ge-%ap$ vessel discloses ! reason1 by exhibit+ ! progressive absorption ( diff]5t rays ( ! spectrum z inve/igat$ by ,dr4 ,j4 ,h4 ,glad/one4#cfd #cfc 99,opticks991 #crd edit4 p4 #aei4 #cfd ,watts1 99,diction>y ( ,*emi/ry991 vol4 iii4 p4 #fcg4 ,a mov+ body may sometimes be made to m>k out its own c\rse1 l a %oot+ /> :i* leaves a tail beh9d x4 ,?us an incl9$ jet ( wat] exhibits 9 ! cle>e/ mann] ! p>abolic pa? ( a projectile4 ,9 ,:eat/one's ,kaleidophone ! curves produc$ by ! comb9ation ( vibrations ( diff]5t ratios are %[n by plac+ bright reflective buttons on ! tops ( wires ( v>i\s =ms4 ,! motions are p]=m$ s quickly t ! eye receives ! impression ( ! pa? z a complete :ole1 j z a burn+ /ick :irl$ r\nd produces a cont9u\s circle4 ,! laws ( electric induction are beautifully %[n :5 iron fil+s are br\ght "u ! influ5ce ( a magnet1 & fall into curves correspond+ to :at ,f>aday call$ ! ,l9es ( ,magnetic ,=ce4 ,:5 ,f>aday tri$ to def9e :at he meant by 8 l9es ( =ce1 he 0 oblig$ to ref] to ! fil+s4 8,by magnetic curves10 he says1#cfe 8,i mean l9es ( magnetic =ces :i* w\ld be depict$ by iron fil+s40 ,robison _h previ\sly produc$ simil> curves by ! action ( frictional electricity1 & f a ma!matical inve/igation ( ! =ms ( su* curves we may inf] t magnetic & electric attractions obey ! g5]al law ( emanation1 t ( ! inv]se squ>e ( ! di/ance4 ,9 ! electric bru% we h a simil> exhibition ( ! laws ( electric attraction4 #cfe 99,f>aday's ,life991 by ,b5ce ,jones1 vol4 ii4 p4 #e4 ,!re are sev]al bran*es ( sci5ce 9 :i* collective exp]im5ts h be5 us$ ) great advantage4 ,li*t5b]g's electric figures1 produc$ by scatt]+ electrifi$ p[d] on an electrifi$ res9 cake1 s z to %[ ! condition ( ! latt]1 sugge/$ to ,*ladni ! notion ( discov]+ ! /ate ( vibration ( plates by /rew+ s& ^u !m4 ,! s& collects at ! po9ts :]e ! motion is lea/1 & we ga9 at a glance a compreh5sion ( ! undulations ( ! plate4 ,to ?is me?od ( exp]im5t we owe ! beautiful obs]vations ( ,sav>t4 ,! exquisite col\r$ figures exhibit$ by plates ( cry/al1 :5 exam9$ by pol>is$ light1 af=d a m complicat$ example ( ! same k9d ( inve/igation4 ,!y l$ ,brew/] & ,fresnel to an explanation ( ! prop]ties ( ! optic axes ( cry/als4 ,! unequal conduction ( heat 9 cry/all9e sub/ances has also be5 %[n 9 a simil> mann]1 by spread+ a ?9 lay] ( wax ov] ! plate ( cry/al1 & apply+ heat to a s+le po9t4 ,! wax !n melts 9 a circul> or elliptic area accord+ z ! rate ( conduction is uni=m or n4 ,nor %\ld we =get t ,newton's r+s 7 an e>ly & mo/ important in/ance ( inve/igations ( ! same k9d1 %[+ ! effects ( int]f]5ce ( light undulations ( all magnitudes at a s+le view4 ,h]s*el gave to all su* opportunities ( obs]v+ directly ! results ( a g5]al law1 ! "n ( 99,collective ,in/ances991#cff & ,i propose to adopt ! "n 99,collective ,exp]im5ts994 #cff 99,prelim9>y ,disc\rse991 c41 p4 #ahe4 ,su* exp]im5ts w 9 _m subjects only give ! fir/ h9t ( ! nature ( ! law 9 "q1 b w n admit ( any exact measurem5ts4 ,! p>abolic =m ( a jet ( wat] may well h sugge/$ to ,galileo 8 views conc]n+ ! pa? ( a projectile2 b x w\ld n s]ve n[ = ! exact inve/igation ( ! laws ( gravity4 ,x is unlikely t capill>y attraction c\ld be exactly measur$ by ! use ( incl9$ plates ( glass1 & tubes w\ld probably be bett] = precise inve/igation4 ,z a g5]al rule1 ^! collective exp]im5ts w\ld be mo/ useful = popul> illu/ration4 ,b :5 ! curves are ( a precise & p]man5t "*1 z 9 ! col\r$ figures produc$ by cry/all9e plates1 !y may admit ( exact measurem5t4 ,newton's r+s & diffraction fr+es all[ ( v accurate measurem5ts4 ,"u collective exp]im5ts we may p]haps place ^? 9 :i* we r5d] visible ! motions ( gas or liquid by diffus+ "s opaque sub/ance 9 x4 ,! behavi\r ( a body ( air may (t5 be /udi$ 9 a beautiful way by ! use ( smoke1 z 9 ! production ( smoke r+s & jets4 ,9 ! case ( liquids lycopodium p[d] is sometimes employ$4 ,to detect ! mixture ( curr5ts or /rata ( liquid1 ,i employ$ v dilute solutions ( common salt & silv] nitrate1 :i* produce a visible cl\d :]ev] !y come into contact4#cfg ,atmosph]ic cl\ds (t5 reveal to u ! movem5ts ( great volumes ( air :i* w\ld o!rwise be q unapp>5t4 #cfg 99,philosophical ,magaz9e991 ,july1 #aheg1 #d? ,s]ies1 vol4 xiv4 p4 #bd4 99,p]iodic ,v>iations499 ,a l>ge class ( inve/igations is conc]n$ ) ,p]iodic ,v>iations4 ,we may def9e a p]iodic ph5om5on z "o :i*1 ) ! uni=m *ange ( ! v>iable1 returns "t aft] "t to ! same value4 ,if we /rike a p5dulum x pres5tly returns to ! po9t f :i* we di/urb$ x1 & :ile "t1 ! v>iable1 progresses uni=mly1 x goes on mak+ excursions & return+1 until /opp$ by ! dissipation ( its en]gy4 ,if "o body 9 space approa*es by gravity t[>ds ano!r1 !y w revolve r\nd ea* o!r 9 elliptic orbits1 & return = an indef9ite numb] ( times to ! same relative positions4 ,on ! o!r h& a s+le body project$ into empty space1 free f ! action ( any extrane\s =ce1 w\ld g on mov+ = ev] 9 a /raight l9e1 accord+ to ! fir/ law ( motion4 ,9 ! latt] case ! v>iation is call$ 99secul>991 because x proce$s dur+ ages 9 a simil> mann]1 & suff]s no or go+ r\nd4 ,x may be d\bt$ :e!r !re really is any motion 9 ! univ]se :i* is n p]iodic4 ,mr4 ,h]b]t ,sp5c] long s9ce adopt$ ! doctr9e t all motion is ultimately rhy?mical1#cfh & abundance ( evid5ce may be adduc$ 9 fav\r ( 8 view4 #cfh 99,fir/ ,pr9ciples991 #crd edit4 *ap4 x4 p4 #bec4 ,! s-call$ secul> accel]ation ( ! moon's motion is c]ta9ly p]iodic1 & z1 s f> z we c tell1 no body is beyond ! attractive p[] ( o!r bodies1 rectil9e> motion becomes purely hypo!tical1 or at lea/ inf9itely improbable4 ,all ! motions ( all ! />s mu/ t5d to become p]iodic4 ,?\gh c]ta9 di/urbances 9 ! planet>y sy/em seem to be uni=mly progressive1 ,laplace is consid]$ to h prov$ t !y really h _! limits1 s t aft] an imm5se "t1 all ! planet>y bodies might return to ! same places1 & ! /ability ( ! sy/em be e/abli%$4 ,su* a !ory ( p]iodic /ability is really hypo!tical1 & does n take into acc\nt ph5om5a result+ 9 ! dissipation ( en]gy1 :i* may be a really secul> process4 ,= our pres5t purposes we ne$ n attempt to =m an op9ion on su* que/ions4 ,any *ange :i* does n pres5t ! appe>ance ( a p]iodic "* w be empirically reg>d$ z a secul> *ange1 s t !re w be pl5ty ( non-p]iodic v>iations4 ,! v>iations :i* we produce exp]im5tally w (t5 be non-p]iodic4 ,:5 we communicate heat to a gas x increases 9 bulk or pressure1 & z f> z we c g ! high] ! temp]ature ! high] ! pressure4 ,our exp]im5ts are ( c\rse re/rict$ 9 temp]ature bo? above & bel[1 b !re is e reason to believe t ! bulk be+ ! same1 ! pressure w\ld nev] return to ! same po9t at any two diff]5t temp]atures4 ,we may ( c\rse repeat$ly raise & l[] ! temp]ature at regul> or irregul> int]vals entirely at our w1 & ! pressure ( ! gas w v>y 9 l mann] & exactly at ! same int]vals1 b su* an arbitr>y s]ies ( *anges w\ld n con/itute ,p]iodic ,v>iation4 ,x w\ld con/itute a succession ( di/9ct exp]im5ts1 :i* w\ld place beyond reasonable d\bt ! connexion ( cause & effect4 ,:5ev] a ph5om5on recurs at equal or ne>ly equal int]vals1 !re is1 accord+ to ! !ory ( probability1 consid]able evid5ce ( connexion1 because if ! recurr5ces 7 entirely casual x is unlikely t !y w\ld happ5 at equal int]vals4 ,! fact t a brilliant comet _h appe>$ 9 ! ye>s #acja1 #acgh1 #adef1 #aeca1 #afjg1 & #afhb gave consid]able presumption 9 fav\r ( ! id5tity ( ! body1 ap>t f simil>ity ( ! orbit4 ,!re is no?+ :i* s fasc9ates ! att5tion ( m5 z ! recurr5ce "t aft] "t ( "s unusual ev5t4 ,?+s & appe>ances :i* rema9 ev] ! same1 l m\nta9s & valleys1 fail to excite ! curiosity ( a primitive p4 ,x has be5 rem>k$ by ,laplace t ev5 9 8 day ! ris+ ( ,v5us 9 its brighte/ phase nev] fail$ to excite surprise & int]e/4 ,s !re is little d\bt t ! fir/ g]m ( sci5ce arose 9 ! att5tion giv5 by ,ea/]n p to ! *anges ( ! moon & ! motions ( ! planets4 ,p]haps ! e>lie/ a/ronomical discov]y consi/$ 9 prov+ ! id5tity ( ! morn+ & ev5+ />s1 on ! gr\nds ( _! simil>ity ( aspect & inv>iable alt]nation4#cfi ,p]iodical *anges ( a some:at complicat$ k9d mu/ h be5 und]/ood by ! ,*aldeans1 because !y 7 aw>e ( ! cycle ( #fehe days or #ai ye>s :i* br+s r\nd ! new & full moon ^u ! same days1 h\rs1 & ev5 m9utes ( ! ye>4 ,! e>lie/ ef=ts ( sci5tific prophecy 7 f\nd$ ^u ?is k1 & if at pres5t we _c help wond]+ at ! precise anticipations ( ! nautical almanack1 we may imag9e ! wond] excit$ by su* pr$ictions 9 e>ly times4 #cfi ,laplace1 99,sy/em ( ! ,_w991 vol4 i4 pp4 #ej1 #ed1 c4 99,comb9$ ,p]iodic ,*anges499 ,we %all seldom f9d a body subject to a s+le p]iodic v>iation1 & free f o!r di/urbances4 ,we may expect ! p]iodic v>iation itself to und]go v>iation1 :i* may possibly be secul>1 b is m likely to prove p]iodic2 nor is !re any limit to ! complication ( p]iods beyond p]iods1 or p]iods )9 p]iods1 :i* may ultimately be disclos$4 ,9 /udy+ a ph5om5on ( rhy?mical "* we h a succession ( que/ions to ask4 ,is ! p]iodic v>iation uni=m8 ,if n1 is ! *ange uni=m8 ,if n1 is ! *ange itself p]iodic8 ,is t new p]iod uni=m1 or subject to any o!r *ange1 or n8 & s on 99ad inf9itum994 ,9 "s cases !re may be _m di/9ct causes ( p]iodic v>iations1 & accord+ to ! pr9ciple ( ! sup]position ( small effects1 to be aft]w>ds consid]$1 ^! p]iodic effects w be simply add$ toge!r1 or at lea/ approximately s1 & ! jo9t result may pres5t a v complicat$ subject ( inve/igation4 ,! tides ( ! ocean consi/ ( a s]ies ( sup]impos$ undulations4 ,n only are !re ! ord9>y semi-diurnal tides caus$ by sun & moon1 b a s]ies ( m9or tides1 su* z ! lun> diurnal1 ! sol> diurnal1 ! lun> mon?ly1 ! lun> =tnightly1 ! sol> annual & sol> semi-annual are gradually be+ dis5tangl$ by ! lab\rs ( ,sir ,w4 ,?omson1 ,pr(essor ,haughton & o!rs4 ,v>iable />s pres5t int]e/+ p]iodic ph5om5a2 :ile "s />s1 ,cephei = in/ance1 are subject to v regul> v>iations1 o!rs1 l ,mira ,ceti1 are less con/ant 9 ! degrees ( brilliancy :i* !y atta9 or ! rapidity ( ! *anges1 possibly on acc\nt ( "s long] p]iodic v>iation4#cgj ,! /> ,lyr pres5ts a d\ble maximum & m9imum 9 ea* ( its p]iods ( ne>ly #ac days1 & s9ce ! discov]y ( ?is v>iation ! p]iod 9 a p]iod has probably be5 on ! increase4 8,at fir/ ! v>iability 0 m rapid1 !n x became gradually sl[]2 & ?is decrease 9 ! l5g? ( "t rea*$ its limit betwe5 ! ye>s #ahdj & #ahdd4 ,dur+ t "t its p]iod 0 ne>ly inv>iable2 at pres5t x is aga9 decid$ly on ! decrease40#cga ,! trac+ out ( su* complicat$ v>iations pres5ts an unlimit$ field = int]e/+ inve/igation4 ,! numb] ( su* v>iable />s already kn[n is consid]able1 & !re is no reason to suppose t any appreciable fraction ( ! :ole numb] has yet be5 detect$4 #cgj ,h]s*el's 99,outl9es ( ,a/ronomy991 #d? edit4 pp4 #eee-eeg4 #cga ,humboldt's 99,cosmos99 7,bohn71 vol4 iii4 p4 #bbi4 99,pr9ciple ( ,=c$ ,vibrations499 ,inve/igations ( ! connection ( p]iodic causes & effects re/ ^u a pr9ciple1 :i* has be5 demon/rat$ by ,sir ,john ,h]s*el = "s special cases1 & cle>ly expla9$ by him 9 sev]al ( 8 works4#cgb ,! pr9ciple may be =mally /at$ 9 ! foll[+ mann]3 8,if "o "p ( any sy/em connect$ toge!r ei!r by mat]ial ties1 or by ! mutual attractions ( its memb]s1 be cont9ually ma9ta9$ by any cause1 :e!r inh]5t 9 ! con/itution ( ! sy/em or ext]nal to x1 9 a /ate ( regul> p]iodic motion1 t motion w be propagat$ ?r\gh\t ! :ole sy/em1 & w give rise1 9 e memb] ( x1 & 9 e "p ( ea* memb]1 to p]iodic movem5ts execut$ 9 equal p]iods1 ) t to :i* !y owe _! orig91 ?\gh n necess>ily syn*ron\s ) !m 9 _! maxima & m9ima40 ,! mean+ ( ! proposition is t ! effect ( a p]iodic cause w be p]iodic1 & w recur at int]vals equal to ^? ( ! cause4 ,accord+ly :5 we f9d two ph5om5a :i* d proce$1 "t aft] "t1 ?r\gh *anges ( ! same p]iod1 !re is mu* probability t !y are connect$4 ,9 ?is mann]1 d\btless1 ,pl9y correctly inf]r$ t ! cause ( ! tides lies 9 ! sun & ! moon1 ! int]vals betwe5 successive high tides be+ equal to ! int]vals betwe5 ! moon's passage across ! m]idian4 ,kepl] & ,desc>tes too admitt$ ! connection previ\s to ,newton's demon/ration ( its precise nature4 ,:5 ,bradley discov]$ ! app>5t motion ( ! />s aris+ f ! ab]ration ( light1 he 0 soon able to attribute x to ! e>?'s annual motion1 because x w5t ?r\gh its phases 9 a ye>4 #cgb 99,encyclopdia ,metropolitana991 art4 99,s\nd991 #cbc2 99,outl9es ( ,a/ronomy991 #d? edit41 #fej4 pp4 #daj1 #dhg-hh2 99,meteorology1 ,encyclopdia ,britannica991 ,repr9t1 p4 #aig4 ,! mo/ beautiful in/ance ( induction conc]n+ p]iodic *anges :i* c be cit$1 is ! discov]y ( an elev5-ye> p]iod 9 v>i\s meteorological ph5om5a4 ,x w\ld be difficult to m5tion any two ?+s app>5tly m disconnect$ ?an ! spots ^u ! sun & auroras4 ,z long ago z #ahbf1 ,s*wabe comm5c$ a regul> s]ies ( obs]vations ( ! spots ^u ! sun1 :i* has be5 cont9u$ to ! pres5t "t1 & he 0 able to %[ t at int]vals ( ab\t elev5 ye>s ! spots increas$ mu* 9 size & numb]4 ,h>dly 0 ?is discov]y made kn[n1 :5 ,lamont po9t$ out a ne>ly equal p]iod ( v>iation 9 ! decl9ation ( ! magnetic ne$le4 ,magnetic /orms or sudd5 di/urbances ( ! ne$le 7 next %[n to take place mo/ frequ5tly at ! times :5 sun-spots 7 preval5t1 & z auroras are g5]ally co9cid5t ) magnetic /orms1 ^! ph5om5a 7 br\ght into ! cycle4 ,x has s9ce be5 %[n by ,pr(essor ,piazzi ,smy? & ,mr4 ,e4 ,j4 ,/one1 t ! temp]ature ( ! e>?'s surface z indicat$ by sunk5 !rmomet]s gives "s evid5ce ( a l p]iod4 ,! exi/5ce ( a p]iodic cause hav+ once be5 e/abli%$1 x is q to be expect$1 accord+ to ! pr9ciple ( =c$ vibrations1 t its influ5ce w be detect$ 9 all meteorological ph5om5a4 99,integrat$ ,v>iations499 ,9 consid]+ ! v>i\s modes 9 :i* "o effect may dep5d ^u ano!r1 we mu/ set 9 a di/9ct class ^? :i* arise f ! accumulat$ effects ( a con/antly act+ cause4 ,:5 wat] runs out ( a ci/]n1 ! velocity ( motion dep5ds1 accord+ to ,torricelli's !orem1 on ! height ( ! surface ( ! wat] above ! v5t2 b ! am\nt ( wat] :i* leaves ! ci/]n 9 a giv5 "t dep5ds ^u ! aggregate result ( t velocity1 & is only to be asc]ta9$ by ! ma!matical process ( integration4 ,:5 "o gravitat+ body falls t[>ds ano!r1 ! =ce ( gravity v>ies accord+ to ! inv]se squ>e ( ! di/ance2 to obta9 ! velocity produc$ we mu/ integrate or sum ! effects ( t law2 & to obta9 ! space pass$ ov] by ! body 9 a giv5 "t1 we mu/ integrate aga94 ,9 p]iodic v>iations ! same di/9ction mu/ be drawn4 ,! heat+ p[] ( ! sun's rays at any place on ! e>? v>ies e day ) ! height atta9$1 & is greate/ ab\t noon2 b ! temp]ature ( ! air w n be greate/ at ! same "t4 ,?is temp]ature is an integrat$ effect ( ! sun's heat+ p[]1 & z long z ! sun is able to give m heat to ! air ?an ! air loses 9 o!r ways1 ! temp]ature cont9ues to rise1 s t ! maximum is def]r$ until ab\t #c ,p4,m4 ,simil>ly ! hotte/ day ( ! ye> falls1 on an av]age1 ab\t "o mon? lat] ?an ! summ] sol/ice1 & all ! seasons lag ab\t a mon? beh9d ! motions ( ! sun4 ,9 ! case ( ! tides1 too1 ! effect ( ! moon's attractive p[] is nev] greate/ :5 ! p[] is greate/2 ! effect always lags m or less beh9d ! cause4 ,yet ! int]vals betwe5 successive tides are equal1 9 ! abs5ce ( di/urbance1 to ! int]vals betwe5 ! passages ( ! moon across ! m]idian4 ,?us ! pr9ciple ( =c$ vibrations holds true4 ,9 p]iodic ph5om5a1 h[ev]1 curi\s results sometimes foll[ f ! integration ( effects4 ,if we /rike a p5dulum1 & !n repeat ! /roke "t aft] "t at ! same "p ( ! vibration1 all ! /rokes concur 9 add+ to ! mom5tum1 & we c ?us increase ! ext5t & viol5ce ( ! vibrations to any degree4 ,we c /op ! p5dulum aga9 by /rokes appli$ :5 x is mov+ 9 ! opposite direction1 & ! effects be+ add$ toge!r w soon br+ x to re/4 ,n[ if we alt] ! int]vals ( ! /rokes s t ea* two successive /rokes act 9 opposite mann]s !y w neutralise ea* o!r1 & ! en]gy exp5d$ w be turn$ into heat or s\nd at ! po9t ( p]cussion4 ,simil> effects occur 9 all cases ( rhy?mical motion4 ,if a musical note is s\nd$ 9 a room conta9+ a piano1 ! /r+ correspond+ to x w be ?r[n into vibration1 because e successive /roke ( ! air-waves ^u ! /r+ f9ds x 9 l position z reg>ds ! vibration1 & ?us adds to its en]gy ( motion4 ,b ! o!r /r+s be+ incapable ( vibrat+ ) ! same rapidity are /ruck at v>i\s po9ts ( _! vibrations1 & "o /roke w soon be oppos$ by "o contr>y 9 effect4 ,all ph5om5a ( 99resonance99 arise f ?is co9cid5ce 9 "t ( undulation4 ,! air 9 a pipe clos$ at "o end1 & ab\t #ab in*es 9 l5g?1 is capable ( vibrat+ #eab times 9 a second4 ,if1 !n1 ! note ,c is s\nd$ 9 front ( ! op5 end ( ! pipe1 e successive vibration ( ! air is treasur$ up z x 7 9 ! motion ( ! air4 ,9 a pipe ( diff]5t l5g? ! pulses ( air w\ld /rike ea* o!r1 & ! me*anical en]gy be+ transmut$ into heat w\ld become no long] p]ceptible z s\nd4 ,accumulat$ vibrations sometimes become s int5se z to lead to unexpect$ results4 ,a glass vessel if t\*$ ) a viol9 b[ at a suitable po9t may be fractur$ ) ! viol5ce ( vibration4 ,a susp5sion bridge may be brok5 d[n if a company ( soldi]s walk across x 9 /eps ! int]vals ( :i* agree ) ! vibrations ( ! bridge itself4 ,b if !y break ! /ep or m>* 9 ei!r quick] or sl[] pace1 !y may h no p]ceptible effect ^u ! bridge4 ,9 fact if ! impulses communicat$ to any vibrat+ body are syn*ron\s ) its vibrations1 ! en]gy ( ^? vibrations w be unlimit$1 & may fracture any body4 ,let u n[ consid] :at w happ5 if ! /rokes be n exactly at ! same int]vals z ! vibrations ( ! body1 b1 say1 a little sl[]4 ,!n a succession ( /rokes w meet ! body 9 ne>ly b n q ! same position1 & _! ef=ts w be accumulat$4 ,aft]w>ds ! /rokes w beg9 to fall :5 ! body is 9 ! opposite phase4 ,imag9e t "o p5dulum mov+ f "o extreme po9t to ano!r 9 a second1 %\ld be /ruck by ano!r p5dulum :i* makes #fa beats 9 a m9ute2 !n1 if ! p5dulums comm5ce toge!r1 !y w at ! end ( #cj-a_/b beats be mov+ 9 opposite directions4 ,h5ce :atev] en]gy 0 communicat$ 9 ! fir/ half m9ute w be neutralis$ by ! opposite effect ( t giv5 9 ! second half4 ,! effect ( ! /rokes ( ! second p5dulum w !re=e be alt]nately to increase & decrease ! vibrations ( ! fir/1 s t a new k9d ( vibration w be produc$ runn+ ?r\gh its phases 9 #fa seconds4 ,an effect ( ?is k9d 0 actually obs]v$ by ,ellicott1 a memb] ( ! ,royal ,society1 9 ! case ( two clocks4#cgc ,he f\nd t ?r\gh ! wood-"w by :i* ! clocks 7 connect$ a slight impulse 0 transmitt$1 & ea* p5dulum alt]nately lo/ & ga9$ mom5tum4 ,ea* clock1 9 fact1 t5d$ to /op ! o!r at regul> int]vals1 & 9 ! int]m$iate times to be /opp$ by ! o!r4 #cgc 99,philosophical ,transactions991 7#agci71 vol4 xli4 p4 #abf4 ,_m di/urbances 9 ! planet>y sy/em dep5d ^u ! same pr9ciple2 = if "o planet happ5s always to pull ano!r 9 ! same direction 9 simil> p>ts ( _! orbits1 ! effects1 h[ev] slight1 w be accumulat$1 & a di/urbance ( l>ge ultimate am\nt & ( long p]iod w be produc$4 ,! long inequality 9 ! motions ( ,jupit] & ,saturn is ?us due to ! fact t five times ! mean motion ( ,saturn is v ne>ly equal to twice ! mean motion ( ,jupit]1 caus+ a co9cid5ce 9 _! relative positions & di/urb+ p[]s4 ,! roll+ ( %ips dep5ds ma9ly ^u ! "q :e!r ! p]iod ( vibration ( ! %ip corresponds or n ) ! int]vals at :i* ! waves /rike h]4 ,mu* :i* seems at fir/ sight unacc\ntable 9 ! behavi\r ( vessels is ?us expla9$1 & ! loss ( ! 99,capta999 is a sad case 9 po9t4 ,,*apt] ,,xxi4 ,,!ory ,,( ,,approximation4 ,9 ord] t we may ga9 a true und]/&+ ( ! k9d1 degree1 & value ( ! k :i* we acquire by exp]im5tal inve/igation1 x is requisite t we %\ld be fully consci\s ( its approximate "*4 ,we mu/ le>n to di/+ui% betwe5 :at we c "k & _c "k--betwe5 ! que/ions :i* admit ( solution1 & ^? :i* only seem to be solv$4 ,_m p]sons may be misl$ by ! expression 99exact sci5ce991 & may ?9k t ! k acquir$ by sci5tific me?ods admits ( our rea*+ absolutely true laws1 exact to ! la/ degree4 ,!re is ev5 a prevail+ impression t :5 once ma!matical =mul h be5 successfully appli$ to a bran* ( sci5ce1 ?is portion ( k assumes a new nature1 & admits ( reason+ ( a high] "* ?an ^? sci5ces :i* are /ill unma!matical4 ,! v satisfactory degree ( accuracy atta9$ 9 ! sci5ce ( a/ronomy gives a c]ta9 plausibility to errone\s notions ( ?is k9d4 ,"s p]sons no d\bt consid] x to be 99prov$99 t planets move 9 ellipses1 9 su* a mann] t all ,kepl]'s laws hold exactly true2 b !re is a d\ble error 9 any su* notions4 ,9 ! fir/ place1 ,kepl]'s laws are 99n prov$991 if by pro( we mean c]ta9 demon/ration ( _! exact tru?4 ,9 ! next place1 ev5 assum+ ,kepl]'s laws to be exactly true 9 a !oretical po9t ( view1 ! planets nev] move accord+ to ^? laws4 ,ev5 if we c\ld obs]ve ! motions ( a planet1 ( a p]fect globul> =m1 free f all p]turb+ or ret>d+ =ces1 we c\ld nev] prove t x mov$ 9 a p]fect ellipse4 ,to prove ! elliptical =m we %\ld h to measure inf9itely small angles1 & inf9itely small fractions ( a second2 we %\ld h to p]=m impossibilities4 ,all we c d is to %[ t ! motion ( an unp]turb$ planet approa*es 99v ne>ly99 to ! =m ( an ellipse1 & m ne>ly ! m accurately our obs]vations are made4 ,b if we g on to ass]t t ! pa? 99is99 an ellipse we pass beyond our data1 & make an assumption :i* _c be v]ifi$ by obs]vation4 ,b1 secondly1 z a matt] ( fact no planet does move 9 a p]fect ellipse1 or manife/ ! tru? ( ,kepl]'s laws exactly4 ,! law ( gravity prev5ts its own results f be+ cle>ly exhibit$1 because ! mutual p]turbations ( ! planets di/ort ! elliptical pa?s4 ,^? laws1 aga91 hold exactly true only ( inf9itely small bodies1 & :5 two great globes1 l ! sun & ,jupit]1 attract ea* o!r1 ! law mu/ be modifi$4 ,! p]iodic "t is !n %ort5$ 9 ! ratio ( ! squ>e root ( ! numb] express+ ! sun's mass1 to t ( ! sum ( ! numb]s express+ ! masses ( ! sun & planet1 z 0 %[n by ,newton4#cgd ,ev5 at ! pres5t day discrepancies exi/ betwe5 ! obs]v$ dim5sions ( ! planet>y orbits & _! !oretical magnitudes1 aft] mak+ all[ance = all di/urb+ causes4#cge ,no?+ is m c]ta9 9 sci5tific me?od ?an t approximate co9cid5ce alone c be expect$4 ,9 ! measurem5t ( cont9u\s quantity p]fect correspond5ce mu/ be accid5tal1 & %\ld give rise to suspicion r ?an to satisfaction4 #cgd 99,pr9cipia991 bk4 iii4 ,prop4 #ae4 #cge ,locky]'s 99,lessons 9 ,elem5t>y ,a/ronomy991 p4 #cja4 ,"o rem>kable result ( ! approximate "* ( our obs]vations is t we c\ld nev] prove ! exi/5ce ( p]fectly circul> or p>abolic movem5t1 ev5 if x exi/$4 ,! circle is a s+ul> case ( ! ellipse1 = :i* ! ecc5tricity is z]o2 x is inf9itely improbable t any planet1 ev5 if undi/urb$ by o!r bodies1 w\ld h a circle = its orbit2 b if ! orbit 7 a circle we c\ld nev] prove ! entire abs5ce ( ecc5tricity4 ,all t we c\ld d w\ld be to decl>e ! div]g5ce f ! circul> =m to be inappreciable4 ,delambre 0 unable to detect ! slighte/ ellipticity 9 ! orbit ( ,jupit]'s fir/ satellite1 b he c\ld only inf] t ! orbit 0 99ne>ly99 circul>4 ,! p>abola is ! s+ul> limit betwe5 ! ellipse & ! hyp]bola4 ,z !re are elliptic & hyp]bolic comets1 s we might conceive ! exi/5ce ( a p>abolic comet4 ,inde$ if an undi/urb$ comet fell t[>ds ! sun f an inf9ite di/ance x w\ld move 9 a p>abola2 b we c\ld nev] prove t x s mov$4 99,sub/itution ( ,simple ,hypo!ses499 ,9 tru? m5 nev] c solve problems fulfill+ ! complex circum/ances ( nature4 ,all laws & explanations are 9 a c]ta9 s5se hypo!tical1 & apply exactly to no?+ :i* we c "k to exi/4 ,9 place ( ! actual objects :i* we see & feel1 ! ma!matician sub/itutes imag9>y objects1 only p>tially resembl+ ^? repres5t$1 b s devis$ t ! discrepancies are n ( an am\nt to alt] s]i\sly ! "* ( ! solution4 ,:5 we probe ! matt] to ! bottom physical a/ronomy is z hypo!tical z ,euclid's elem5ts4 ,!re may exi/ 9 nature p]fect /raight l9es1 triangles1 circles1 & o!r regul> geometrical figures2 to our sci5ce x is a matt] ( indiff]5ce :e!r !y d or d n exi/1 because 9 any case !y mu/ be beyond our p[]s ( p]ception4 ,if we submitt$ a p]fect circle to ! mo/ rigor\s scrut9y1 x is impossible t we %\ld discov] :e!r x 7 p]fect or n4 ,nev]!less 9 geometry we argue conc]n+ p]fect curves1 & rectil9e> figures1 & ! conclusions apply to exi/+ objects s f> z we c assure ourselves t !y agree ) ! hypo!tical conditions ( our reason+4 ,?is is 9 reality all t we c d 9 ! mo/ p]fect ( ! sci5ces4 ,d\btless 9 a/ronomy we meet ) ! ne>e/ approximation to actual conditions4 ,! law ( gravity is n a complex "o 9 itself1 & we believe x ) mu* probability to be exactly true2 b we _c calculate out 9 any real case its accurate results4 ,! law ass]ts t e p>ticle ( matt] 9 ! univ]se attracts e o!r p>ticle1 ) a =ce dep5d+ on ! masses ( ! p>ticles & _! di/ances4 ,we _c "k ! =ce act+ on any p>ticle unless we "k ! masses & di/ances & positions ( all o!r p>ticles 9 ! univ]se4 ,! physical a/ronom] has made a sweep+ assumption1 namely1 t all ! millions ( exi/+ sy/ems ex]t no p]turb+ effects on our planet>y sy/em1 t is to say1 no effects 9 ! lea/ appreciable4 ,! problem at once becomes hypo!tical1 because !re is little d\bt t gravitation betwe5 our sun & planets & o!r sy/ems does exi/4 ,ev5 :5 !y consid] ! relations ( our planet>y bodies 99int] se991 all _! processes are only approximate4 ,9 ! fir/ place !y assume t ea* ( ! planets is a p]fect ellipsoid1 ) a smoo? surface & a homog5e\s int]ior4 ,t ?is assumption is untrue e m\nta9 & valley1 e sea1 e m9e af=ds conclusive evid5ce4 ,if a/ronom]s are to make _! calculations p]fect1 !y mu/ n only take acc\nt ( ! ,himalayas & ! ,&es1 b mu/ calculate sep>ately ! attraction ( e hill1 nay1 ( e ant-hill4 ,s f> are !y f hav+ consid]$ any local inequality ( ! surface1 t !y h n yet decid$ ^u ! g5]al =m ( ! e>?2 x is /ill a matt] ( speculation :e!r or n ! e>? is an ellipsoid ) ?ree unequal axes4 ,if1 z is probable1 ! globe is irregul>ly compress$ 9 "s directions1 ! calculations ( a/ronom]s w h to be repeat$ & ref9$1 9 ord] t !y may approximate to ! attractive p[] ( su* a body4 ,if we _c accurately le>n ! =m ( our own e>?1 h[ c we expect to asc]ta9 t ( ! moon1 ! sun1 & o!r planets1 9 "s ( :i* probably are irregul>ities ( great] proportional am\nt8 ,9 a fur!r way ! sci5ce ( physical a/ronomy is m]ely approximate & hypo!tical4 ,giv5 homog5e\s ellipsoids act+ ^u ea* o!r accord+ to ! law ( gravity1 ! be/ ma!maticians h nev] & p]haps nev] w det]m9e exactly ! result+ movem5ts4 ,ev5 :5 ?ree bodies simultane\sly attract ea* o!r ! complication ( effects is s great t only approximate calculations c be made4 ,a/ronom]s h n ev5 attempt$ ! g5]al problem ( ! simultane\s attractions ( f\r1 five1 six1 or m bodies2 !y resolve ! g5]al problem into s _m diff]5t problems ( ?ree bodies4 ,! pr9ciple ^u :i* ! calculations ( physical a/ronomy proce$1 is to neglect e quantity :i* does n seem likely to lead to an effect appreciable 9 obs]vation1 & ! quantities reject$ are f> m num]\s & complex ?an ! few l>g] t]ms :i* are reta9$4 ,all !n is m]ely approximate4 ,conc]n+ o!r bran*es ( physical sci5ce ! same /atem5ts are ev5 m evid5tly true4 ,we speak & calculate ab\t inflexible b>s1 inext5sible l9es1 heavy po9ts1 homog5e\s sub/ances1 uni=m sph]es1 p]fect fluids & gases1 & we d$uce a great numb] ( beautiful !orems2 b all is hypo!tical4 ,!re is no su* ?+ z an inflexible b>1 an inext5sible l9e1 nor any "o ( ! o!r p]fect objects ( me*anical sci5ce2 !y are to be class$ ) ^? my?ical exi/5ces1 ! /raight l9e1 triangle1 circle1 c41 ab\t :i* ,euclid s freely reason$4 ,take ! simple/ op]ation consid]$ 9 /atics--! use ( a cr[b> 9 rais+ a heavy /one1 & we %all f9d1 z ,?omson & ,tait h po9t$ out1 t we neglect f> m ?an we obs]ve4#cgf ,if we suppose ! b> to be q rigid1 ! fulcrum & /one p]fectly h>d1 & ! po9ts ( contact real po9ts1 we may give ! true relation ( ! =ces4 ,b 9 reality ! b> mu/ b5d1 & ! ext5sion & compression ( diff]5t p>ts involve u 9 difficulties4 ,ev5 if ! b> be homog5e\s 9 all its p>ts1 !re is no ma!matical !ory capable ( det]m9+ ) accuracy all t goes on2 if1 z is inf9itely m probable1 ! b> is n homog5e\s1 ! complete solution w be imm5sely m complicat$1 b h>dly m hopeless4 ,no soon] _h we det]m9$ ! *ange ( =m accord+ to simple me*anical pr9ciples1 ?an we %\ld discov] ! int]f]5ce ( !rmodynamic pr9ciples4 ,compression produces heat & ext5sion cold1 & ?us ! conditions ( ! problem are modifi$ ?r\gh\t4 ,9 attempt+ a f\r? approximation we %\ld h to all[ = ! conduction ( heat f "o "p ( ! b> to ano!r4 ,all ^! effects are utt]ly inappreciable 9 a practical po9t ( view1 if ! b> be a good /\t "o2 b 9 a !oretical po9t ( view !y entirely prev5t our say+ t we h solv$ a natural problem4 ,! faculties ( ! human m9d1 ev5 :5 aid$ by ! wond]ful p[]s ( abbreviation conf]r$ by analytical me?ods1 are utt]ly unable to cope ) ! complications ( any real problem4 ,& _h we exhau/$ all ! kn[n ph5om5a ( a me*anical problem1 h[ c we tell t hidd5 ph5om5a1 z yet undetect$1 d n int]v5e 9 ! commone/ actions8 ,x is pla9 t no ph5om5on comes )9 ! sph]e ( our s5ses unless x possesses a mom5tum capable ( irritat+ ! appropriate n]ves4 ,!re may !n be worlds ( ph5om5a too slight to rise )9 ! scope ( our consci\sness4 #cgf 99,treatise on ,natural ,philosophy991 vol4 i4 pp4 #ccg1 c4 ,all ! in/rum5ts ) :i* we p]=m our measurem5ts are faulty4 ,we assume t a plumb-l9e gives a v]tical l9e2 b ?is is nev] true 9 an absolute s5se1 ow+ to ! attraction ( m\nta9s & o!r inequalities 9 ! surface ( ! e>?4 ,9 an accurate trigonometrical survey1 ! div]g5cies ( ! plumb-l9e mu/ be approximately det]m9$ & all[$ =4 ,we assume a surface ( m]cury to be a p]fect plane1 b ev5 9 ! bread? ( #e in*es !re is a calculable div]g5ce f a true plane ( ab\t "o t5-million? "p ( an in*2 & ?is surface fur!r div]ges f true horizontality z ! plumb-l9e does f true v]ticality4 ,t mo/ p]fect in/rum5t1 ! p5dulum1 is n !oretically p]fect1 except = inf9itely small arcs ( vibration1 & ! delicate exp]im5ts p]=m$ ) ! torsion balance proce$ on ! assumption t ! =ce ( torsion ( a wire is proportional to ! angle ( torsion1 :i* aga9 is only true = inf9itely small angles4 ,su* is ! purely approximate "* ( all our op]ations t x is n uncommon to f9d ! !oretically worse me?od giv+ tru] results ?an ! !oretically p]fect me?od4 ,! common p5dulum :i* is n iso*ron\s is bett] = practical purposes ?an ! cycloidal p5dulum1 :i* is iso*ron\s 9 !ory b subject to me*anical difficulties4 ,! sph]ical =m is n ! correct =m = a speculum or l5se1 b x diff]s s slightly f ! true =m1 & is s mu* m easily produc$ me*anically1 t x is g5]ally be/ to re/ cont5t ) ! sph]ical surface4 ,ev5 9 a six-feet mirror ! diff]5ce betwe5 ! p>abola & ! sph]e is only ab\t "o t5-?\s&? "p ( an in*1 a ?ickness :i* w\ld be tak5 (f 9 a few rubs ( ! poli%]4 ,watts' +5i\s p>allel motion 0 int5d$ to produce rectil9e> movem5t ( ! pi/on-rod4 ,9 reality ! motion 0 always curvil9e>1 b = 8 purposes a c]ta9 "p ( ! curve approximat$ suffici5tly to a /raight l9e4 99,approximation to ,exact ,laws499 ,?\gh we c n prove num]ical laws ) p]fect accuracy1 x w\ld be a great mi/ake to suppose t !re is any inexactness 9 ! laws ( nature4 ,we may ev5 discov] a law :i* we believe to repres5t ! action ( =ces ) p]fect exactness4 ,! m9d may seem to pass 9 advance ( its data1 & *oose out c]ta9 num]ical results z absolutely true4 ,we c nev] really pass beyond our data1 & s f> z assumption ent]s 91 s f> want ( c]ta9ty w atta* to our conclusions2 nev]!less we may sometimes rightly pref] a probable assumption ( a precise law to num]ical results1 :i* are at ! be/ only approximate4 ,we mu/ accord+ly draw a /rong di/9ction betwe5 ! laws ( nature :i* we believe to be accurately /at$ 9 our =mulas1 & ^? to :i* our /atem5ts only make an approximation1 s t at a future "t ! law w be diff]5tly /at$4 ,! law ( gravitation is express$ 9 ! =m ,f ,mm_/,d#b1 mean+ t gravity is proportional directly to ! product ( ! gravitat+ masses1 & indirectly to ! squ>e ( _! di/ance4 ,! lat5t heat ( /eam is express$ by ! equation log ,f 99a99 99b99t 99c99t1 9 :i* are five quantities 99a991 99b991 99c991 1 1 to be det]m9$ by exp]im5t4 ,!re is e reason to believe t 9 ! progress ( sci5ce ! law ( gravity w rema9 entirely unalt]$1 & ! only effect ( fur!r inquiry w be to r5d] x a m & m probable expression ( ! absolute tru?4 ,! law ( ! lat5t heat ( /eam on ! o!r h&1 w be modifi$ by e new s]ies ( exp]im5ts1 & x may n improbably be %[n t ! assum$ law c nev] be made to agree exactly ) ! results ( exp]im5t4 ,philosoph]s h n always suppos$ t ! law ( gravity 0 exactly true4 ,newton1 ?\gh he _h ! highe/ confid5ce 9 its tru?1 admitt$ t !re 7 motions 9 ! planet>y sy/em :i* he c\ld n reconcile ) ! law4 ,eul] & ,clairaut :o 71 ) ,d',alemb]t1 ! fir/ to apply ! full p[]s ( ma!matical analysis to ! !ory ( gravitation z expla9+ ! p]turbations ( ! planets1 did n ?9k ! law suffici5tly e/abli%$ to attribute all discrepancies to ! errors ( calculation & obs]vation4 ,!y did n feel c]ta9 t ! =ce ( gravity exactly obey$ ! well-kn[n rule4 ,! law might involve o!r p[]s ( ! di/ance4 ,x might be express$ 9 ! =m ,f 444 99a99_/,d 99b99_/,d#b 99c99_/,d#c 444 & ! coeffici5ts 99a99 & 99c99 might be s small t ^? t]ms w\ld become app>5t only 9 v accurate comp>isons ) fact4 ,attempts h be5 made to acc\nt = difficulties1 by attribut+ value to su* neglect$ t]ms4 ,gauss at "o "t ?\ght ! ev5 m fundam5tal pr9ciple ( gravity1 t ! =ce is dep5d5t only on mass & di/ance1 might n be exactly true1 & he und]took accurate p5dulum exp]im5ts to te/ ?is op9ion4 ,only z repeat$ d\bts h "t aft] "t be5 resolv$ 9 fav\r ( ! law ( ,newton1 has x be5 assum$ z precisely correct4 ,b ?is belief does n re/ on exp]im5t or obs]vation only4 ,! calculations ( physical a/ronomy1 h[ev] accurate1 c\ld nev] %[ t ! o!r t]ms ( ! above expression 7 absolutely devoid ( value4 ,x c\ld only be %[n t !y _h su* slight value z nev] to become app>5t4 ,!re are1 h[ev]1 o!r reasons :y ! law is probably complete & true z commonly /at$4 ,:atev] influ5ce spreads f a po9t1 & exp&s uni=mly ?r\gh space1 w d\btless v>y inv]sely 9 int5sity z ! squ>e ( ! di/ance1 because ! area ov] :i* x is spread increases z ! squ>e ( ! radius4 ,?is "p ( ! law ( gravity may be consid]$ z due to ! prop]ties ( space1 & !re is a p]fect analogy 9 ?is respect betwe5 gravity & all o!r 99emanat+99 =ces1 z 0 po9t$ out by ,keill4#cgg ,?us ! undulations ( light1 heat1 & s\nd1 & ! attractions ( electricity & magnetism obey ! v same law s f> z we c asc]ta94 ,if ! molecules ( a gas or ! p>ticles ( matt] con/itut+ od\r 7 to />t f a po9t & spread uni=mly1 _! di/ances w\ld increase & _! d5sity decrease accord+ to ! same pr9ciple4 #cgg 99,an ,introduction to ,natural ,philosophy991 #crd edit4 #agcc1 p4 #e4 ,o!r laws ( nature /& 9 a simil> position4 ,dalton's laws ( def9ite comb9+ proportions nev] h be51 & nev] c be1 exactly prov$2 b *emi/s hav+ %[n1 to a consid]able degree ( approximation1 t ! elem5ts comb9e toge!r z if ea* elem5t _h atoms ( an inv>iable mass1 assume t ?is is exactly true4 ,!y g ev5 fur!r4 ,pr\t po9t$ out 9 #ahae t ! equival5t weights ( ! elem5ts appe>$ to be simple numb]s2 & ! rese>*es ( ,dumas1 ,pel\ze1 ,m>ignac1 ,erdmann1 ,/as1 & o!rs h gradually r5d]$ x likely t ! atomic weights ( hydrog51 c>bon1 oxyg51 nitrog51 *lor9e1 & silv]1 are 9 ! ratios ( ! numb]s #a1 #ab1 #af1 #ad1 #cee1 & #ajh4 ,*emi/s !n /ep beyond _! data2 !y ?r[ aside _! actual exp]im5tal numb]s1 & assume t ! true ratios are n ^? exactly indicat$ by any weigh+s1 b ! simple ratios ( ^! numb]s4 ,!y boldly assume t ! discrepancies are due to exp]im5tal errors1 & !y are ju/ifi$ by ! fact t ! m elaborate & skilful ! rese>*es on ! subject1 ! m ne>ly _! assumption is v]ifi$4 ,potassium is ! only elem5t ^: atomic weight has be5 det]m9$ ) great c>e1 b :i* has n %[n an approa* to a simple ratio ) ! o!r elem5ts4 ,?is exception may be due to "s unsuspect$ cause ( error4#cgh ,a simil> assumption is made 9 ! law ( def9ite comb9+ volumes ( gases1 & ,brodie has cle>ly po9t$ out ! l9e ( argum5t by :i* ! *emi/1 obs]v+ t ! discrepancies betwe5 ! law & fact are )9 ! limits ( exp]im5tal error1 assumes t !y are due to error4#cgi #cgh ,watts1 99,diction>y ( ,*emi/ry991 vol4 i4 p4 #dee4 #cgi 99,philosophical ,transactions991 7#ahff7 vol4 clvi4 p4 #hji4 ,f>aday1 9 "o ( 8 rese>*es1 expressly makes an assumption ( ! same k9d4 ,hav+ %[n1 ) "s degree ( exp]im5tal precision1 t !re exi/s a simple proportion betwe5 quantities ( electrical en]gy & ! quantities ( *emical sub/ances :i* x c decompose1 s t = e atom dissolv$ 9 ! batt]y cell an atom ought !oretically1 t is )\t reg>d to dissipation ( "s ( ! en]gy1 to be decompos$ 9 ! electrolytic cell1 he does n /op at 8 num]ical results4 8,i h n hesitat$10 he says1#chj 8to apply ! m /rict results ( *emical analysis to correct ! numb]s obta9$ z electrolytic results4 ,?is1 x is evid5t1 may be done 9 a great numb] ( cases1 )\t us+ too mu* lib]ty t[>ds ! due sev]ity ( sci5tific rese>*40 #chj 99,exp]im5tal ,rese>*es 9 ,electricity991 vol4 i4 p4 #bdf4 ,! law ( ! cons]vation ( en]gy1 "o ( ! wide/ ( all physical g5]alisations1 re/s ^u ! same foot+4 ,! mo/ t we c d by exp]im5t is to %[ t ! en]gy ent]+ into any exp]im5tal comb9ation is almo/ equal to :at comes out ( x1 & m ne>ly s ! m accurately we p]=m ! measurem5ts4 ,absolute equality is always a matt] ( assumption4 ,we _c ev5 prove ! inde/ructibility ( matt]2 = 7 an exce$+ly m9ute fraction ( exi/+ matt] to vani% 9 any exp]im5t1 say "o "p 9 t5 millions1 we c\ld nev] detect ! loss4 99,successive ,approximations to ,natural ,conditions499 ,:5 we exam9e ! hi/ory ( sci5tific problems1 we f9d t "o man or "o g5]ation is usually able to make b a s+le /ep at a "t4 ,a problem is solv$ = ! fir/ "t by mak+ "s bold hypo!tical simplification1 ^u :i* ! next inve/igator makes hypo!tical modifications approa*+ m ne>ly to ! tru?4 ,errors are successively po9t$ out 9 previ\s solutions1 until at la/ !re might seem little m to be desir$4 ,c>eful exam9ation1 h[ev]1 w %[ t a s]ies ( m9or inaccuracies rema9 to be correct$ & expla9$1 7 our p[]s ( reason+ suffici5tly great1 & ! purpose adequate 9 importance4 ,newton's successful solution ( ! problem ( ! planet>y movem5ts entirely dep5d$ at fir/ ^u a great simplification4 ,! law ( gravity only applies directly to two inf9itely small p>ticles1 s t :5 we deal ) va/ globes l ! e>?1 ,jupit]1 & ! sun1 we h an imm5se aggregate ( sep>ate attractions to deal )1 & ! law ( ! aggregate ne$ n co9cide ) ! law ( ! elem5t>y p>ticles4 ,b ,newton1 by a great ef=t ( ma!matical reason+1 0 able to %[ t two homog5e\s sph]es ( matt] act z if ! :ole ( _! masses 7 conc5trat$ at ! c5tres2 9 %ort1 t su* sph]es are c5trob>ic bodies 7p4 #cfd74 ,he 0 !n able ) comp>ative ease to calculate ! motions ( ! planets on ! hypo!sis ( _! be+ sph]es1 & to %[ t ! results r\ghly agre$ ) obs]vation4 ,newton1 inde$1 0 "o ( ! few m5 :o c\ld make two great /eps at once4 ,he did n re/ cont5t$ ) ! sph]ical hypo!sis2 hav+ reason to believe t ! e>? 0 really a sph]oid ) a protub]ance ar\nd ! equator1 he proce$$ to a second approximation1 & prov$ t ! attraction ( ! protub]ant matt] ^u ! moon acc\nt$ = ! precession ( ! equ9oxes1 & l$ to v>i\s complicat$ effects4 ,b1 7p4 #dei71 ev5 ! sph]oidal hypo!sis is f> f ! tru?4 ,x takes no acc\nt ( ! irregul>ities ( surface1 ! great protub]ance ( l& 9 ,c5tral ,asia & ,s\? ,am]ica1 & ! defici5cy 9 ! b$ ( ! ,atlantic4 ,to det]m9e ! law accord+ to :i* a projectile1 su* z a cannon ball1 moves ?r\gh ! atmosph]e is a problem v imp]fectly solv$ at ! pres5t day1 b 9 :i* _m successive advances h be5 made4 ,s little 0 kn[n conc]n+ ! subject ?ree or f\r c5turies ago t a cannon ball 0 suppos$ to move at fir/ 9 a /raight l9e1 & aft] a "t to be deflect$ into a curve4 ,t>taglia v5tur$ to ma9ta9 t ! pa? 0 curv$ ?r\gh\t1 z by ! pr9ciple ( cont9uity x %\ld be2 b ! +5uity ( ,galileo 0 requir$ to prove ?is op9ion1 & to %[ t ! curve 0 approximately a p>abola4 ,x is only1 h[ev]1 "u =c$ hypo!ses t we c ass]t ! pa? ( a projectile to be truly a p>abola3 ! pa? mu/ be ?r\gh a p]fect vacuum1 :]e !re is no resi/+ m$ium ( any k9d2 ! =ce ( gravity mu/ be uni=m & act 9 p>allel l9es2 or else ! mov+ body mu/ be ei!r a m]e po9t1 or a p]fect c5trob>ic body1 t is a body possess+ a def9ite c5tre ( gravity4 ,^! conditions _c be really fulfill$ 9 practice4 ,! next great /ep 9 ! problem 0 made by ,newton & ,huygh5s1 ! latt] ( :om ass]t$ t ! atmosph]e w\ld (f] a resi/ance proportional to ! velocity ( ! mov+ body1 & conclud$ t ! pa? w\ld h 9 consequ5ce a log>i?mic "*4 ,newton inve/igat$ 9 a g5]al mann] ! subject ( resi/+ m$ia1 & came to ! conclusion t ! resi/ance is m ne>ly proportional to ! squ>e ( ! velocity4 ,! subject !n fell into ! h&s ( ,daniel ,b]n\lli1 :o po9t$ out ! enorm\s resi/ance ( ! air 9 cases ( rapid movem5t1 & calculat$ t a cannon ball1 if fir$ v]tically 9 a vacuum1 w\ld rise eight times z high z 9 ! atmosph]e4 ,9 rec5t times an imm5se am\nt bo? ( !oretical & exp]im5tal inve/igation has be5 sp5t ^u ! subject1 s9ce x is "o ( importance 9 ! art ( w>4 ,successive approximations to ! true law h be5 made1 b no?+ l a complete & f9al solution has be5 a*iev$ or ev5 hop$ =4#cha #cha ,hutton's 99,ma!matical ,diction>y991 vol4 ii4 pp4 #bhg-bib4 ,x is q to be expect$ t ! e>lie/ exp]im5t]s 9 any bran* ( sci5ce w ov]look errors :i* aft]w>ds become mo/ app>5t4 ,! ,arabian a/ronom]s det]m9$ ! m]idian by tak+ ! middle po9t betwe5 ! places ( ! sun :5 at equal altitudes on ! same day4 ,!y ov]look$ ! fact t ! sun has its own motion 9 ! "t betwe5 ! obs]vations4 ,newton ?\ght t ! mutual di/urbances ( ! planets might be disreg>d$1 except+ p]haps ! effect ( ! mutual attraction ( ! great] planets1 ,jupit] & ,saturn1 ne> _! conjunction4#chb ,! expansion ( quicksilv] 0 long us$ z ! measure ( temp]ature1 no cle> idea be+ possess$ ( temp]ature ap>t f "s ( its m obvi\s effects4 ,rum=d1 9 ! fir/ exp]im5t lead+ to a det]m9ation ( ! me*anical equival5t ( heat1 disreg>d$ ! heat absorb$ by ! app>atus1 o!rwise he w\ld1 9 ,dr4 ,j\le's op9ion1 h come ne>ly to ! correct result4 #chb 99,pr9cipia991 bk4 iii4 ,prop4 #ac4 ,x is surpris+ to le>n ! numb] ( causes ( error :i* ent] into ! simple/ exp]im5t1 :5 we /rive to atta9 rigid accuracy4 ,we _c accurately p]=m ! simple exp]im5t ( compress+ gas 9 a b5t tube by a column ( m]cury1 9 ord] to te/ ! tru? ( ,boyle's ,law1 )\t pay+ reg>d to--7#a7 ! v>iations ( atmosph]ic pressure1 :i* are communicat$ to ! gas ?r\gh ! m]cury2 7#b7 ! compressibility ( m]cury1 :i* causes ! column ( m]cury to v>y 9 d5sity2 7#c7 ! temp]ature ( ! m]cury ?r\gh\t ! column2 7#d7 ! temp]ature ( ! gas1 :i* is ) difficulty ma9ta9$ inv>iable2 7#e7 ! expansion ( ! glass tube conta9+ ! gas4 ,al?\gh ,regnault took all ^! circum/ances into acc\nt 9 8 exam9ation ( ! law1#chc !re is no reason to suppose t he exhau/$ ! s\rces ( inaccuracy4 #chc ,jam91 99,c\rs de ,physique991 vol4 i4 pp4 #bhb1 #bhc4 ,! e>ly inve/igations conc]n+ ! nature ( waves 9 ela/ic m$ia proce$$ ^u ! assumption t waves ( diff]5t l5g?s w\ld travel ) equal spe$4 ,newton's !ory ( s\nd l$ him to ?is conclusion1 & obs]vation 7p4 #bie7 _h v]ifi$ ! inf]5ce4 ,:5 ! undulatory !ory came to be appli$ at ! comm5cem5t ( ?is c5tury to expla9 ! ph5om5a ( light1 a great difficulty 0 enc\nt]$4 ,! angle at :i* a ray ( light is refract$ 9 ent]+ a d5s] m$ium dep5ds1 accord+ to t !ory1 on ! velocity ) :i* ! wave travels1 s t if all waves ( light 7 to travel ) equal velocity 9 ! same m$ium1 ! disp]sion ( mix$ light by ! prism & ! production ( ! spectrum c\ld n take place4 ,"s mo/ /rik+ ph5om5a 7 ?us 9 direct conflict ) ! !ory4 ,cau*y fir/ po9t$ out ! explanation1 namely1 t all previ\s inve/igators _h made an arbitr>y assumption = ! sake ( simplify+ ! calculations4 ,!y _h assum$ t ! p>ticles ( ! vibrat+ m$ium are s close toge!r t ! int]vals are inconsid]able comp>$ ) ! l5g? ( ! wave4 ,?is hypo!sis happ5$ to be approximately true 9 ! case ( air1 s t no error 0 discov]$ 9 exp]im5ts on s\nd4 ,_h x n be5 s1 ! e>li] analy/s w\ld probably h fail$ to give any solution1 & ! progress ( ! subject might h be5 ret>d$4 ,cau*y 0 able to make a new approximation "u ! m difficult supposition1 t ! p>ticles ( ! vibrat+ m$ium are situat$ at consid]able di/ances1 & act & react ^u ! neighb\r+ p>ticles by attractive & repulsive =ces4 ,to calculate ! rate ( propagation ( di/urbance 9 su* a m$ium is a "w ( excessive difficulty4 ,! complete solution ( ! problem appe>s inde$ to be beyond human p[]1 s t we mu/ be cont5t1 z 9 ! case ( ! planet>y motions1 to look =w>d to successive approximations4 ,all t ,cau*y c\ld d 0 to %[ t c]ta9 quantities1 neglect$ 9 previ\s !ories1 became ( consid]able am\nt "u ! new conditions ( ! problem1 s t !re w exi/ a relation betwe5 ! l5g? ( ! wave1 & ! velocity at :i* x travels4 ,to remove1 !n1 ! difficulties 9 ! way ( ! undulatory !ory ( light1 a new approa* to probable conditions 0 ne$$4#chd #chd ,lloyd's 99,lectures on ! ,wave ,!ory991 pp4 #bb1 #bc4 ,9 a simil> mann] ,f\ri]'s !ory ( ! conduction & radiation ( heat 0 bas$ ^u ! hypo!sis t ! quantity ( heat pass+ along any l9e is simply proportional to ! rate ( *ange ( temp]ature4 ,b x has s9ce be5 %[n by ,=bes t ! conductivity ( a body dim9i%es z its temp]ature increases4 ,all ! details ( ,f\ri]'s solution !re=e require modification1 & ! results are 9 ! meantime to be reg>d$ z only approximately true4#che #che ,tait's 99,!rmodynamics991 p4 #aj4 ,we ought to di/+ui% betwe5 ^? problems :i* are physically & ^? :i* are m]ely ma!matically incomplete4 ,9 ! latt] case ! physical law is correctly seiz$1 b ! ma!matician neglects1 or is m (t5 unable to foll[ out ! law 9 all its results4 ,! law ( gravitation & ! pr9ciples ( h>monic or undulatory movem5t1 ev5 suppos+ ! data to be correct1 c nev] be foll[$ into all _! ultimate results4 ,"y expla9$ ! production ( ,newton's r+s by suppos+ t ! rays reflect$ f ! upp] & l[] surfaces ( a ?9 film ( a c]ta9 ?ickness 7 9 opposite phases1 & ?us neutralis$ ea* o!r4 ,x 0 po9t$ out1 h[ev]1 t z ! light reflect$ f ! ne>] surface mu/ be und\bt$ly a little bright] ?an t f ! fur!r surface1 ! two rays ought n to neutralise ea* o!r s completely z !y are obs]v$ to d4 ,x 0 f9ally %[n by ,poisson t ! discrepancy arose only f incomplete solution ( ! problem2 = ! light :i* has once got into ! film mu/ be to a c]ta9 ext5t reflect$ backw>ds & =w>ds 99ad inf9itum992 & if we foll[ out ?is c\rse ( ! light by p]fect ma!matical analysis1 absolute d>kness may be %[n to result f ! int]f]5ce ( ! rays4#chf ,9 ?is case ! natural laws conc]n$1 ^? ( reflection & refraction1 are accurately kn[n1 & ! only difficulty consi/s 9 develop+ _! full consequ5ces4 #chf ,lloyd's 99,lectures on ! ,wave ,!ory991 pp4 #hb1 #hc4 99,discov]y ( ,hypo!tically ,simple ,laws499 ,9 "s bran*es ( sci5ce we meet ) natural laws ( a simple "* :i* are 9 a c]ta9 po9t ( view exactly true & yet c nev] be manife/$ z exactly true 9 natural ph5om5a4 ,su*1 = in/ance1 are ! laws conc]n+ :at is call$ a 99p]fect gas994 ,! gase\s /ate ( matt] is t 9 :i* ! prop]ties ( matt] are exhibit$ 9 ! simple/ mann]4 ,!re is mu* advantage accord+ly 9 approa*+ ! "q ( molecul> me*anics f ?is side4 ,b :5 we ask ! "q--,:at is a gas8 ! answ] mu/ be a hypo!tical "o4 ,f9d+ t gases 99ne>ly99 obey ! law ( ,boyle & ,m>iotte2 t !y 99ne>ly99 exp& by heat at ! uni=m rate ( "o "p 9 #bgbi ( _! volume at #j = ea* degree c5tigrade2 & t !y 99m ne>ly99 fulfil ^! conditions ! m di/ant ! po9t ( temp]ature at :i* we exam9e !m f ! liquefy+ po9t1 we pass by ! pr9ciple ( cont9uity to ! conception ( a p]fect gas4 ,su* a gas w\ld probably consi/ ( atoms ( matt] at s great a di/ance f ea* o!r z to ex]t no attractive =ces ^u ea* o!r2 b = ?is condition to be fulfill$ ! di/ances mu/ be inf9ite1 s t an absolutely p]fect gas _c exi/4 ,b ! p]fect gas is n m]ely a limit to :i* we may approa*1 x is a limit pass$ by at lea/ "o real gas4 ,x has be5 %[n by ,despretz1 ,p\illet1 ,dulong1 ,arago1 & f9ally ,regnault1 t all gases div]ge f ! ,boylean law1 & 9 ne>ly all cases ! d5sity ( ! gas increases 9 a some:at great] ratio ?an ! pressure1 indicat+ a t5d5cy on ! "p ( ! molecules to approximate ( _! own accord4 ,9 ! m cond5sable gases su* z sulphur\s acid1 ammonia1 & cyanog51 ?is t5d5cy is /rongly app>5t ne> ! liquefy+ po9t4 ,hydrog51 on ! contr>y1 div]ges f ! law ( a p]fect gas 9 ! opposite direction1 t is1 ! d5sity increases less ?an 9 ! ratio ( ! pressure4#chg ,?is is a s+ul> exception1 ! be>+ ( :i* ,i am unable to compreh5d4 #chg ,jam91 99,c\rs de ,physique991 vol4 i4 pp4 #bhc-bhh4 ,all gases div]ge aga9 f ! law ( uni=m expansion by heat1 b ! div]g5ce is less z ! gas 9 "q is less cond5sable1 or exam9$ at a temp]ature m remov$ f its liquefy+ po9t4 ,?us ! p]fect gas mu/ h an inf9itely high temp]ature4 ,accord+ to ,dalton's law ea* gas 9 a mixture reta9s its own prop]ties unaffect$ by ! pres5ce ( any o!r gas4#chh ,?is law is probably true only by approximation1 b x is obvi\s t x w\ld be true ( ! p]fect gas ) inf9itely di/ant p>ticles4#chi #chh ,j\le & ,?omson1 99,philosophical ,transactions991 #ahed1 vol4 cxliv4 p4 #ccg4 #chi ,! prop]ties ( a p]fect gas h be5 describ$ by ,rank9e1 99,transactions ( ! ,royal ,society ( ,ed9burgh991 vol4 xxv4 p4 #efa4 99,ma!matical ,pr9ciples ( ,approximation499 ,! approximate "* ( physical sci5ce w be r5d]$ m pla9 if we consid] x f a ma!matical po9t ( view4 ,?r\gh\t quantitative inve/igations we deal ) ! relation ( "o quantity to o!r quantities1 ( :i* x is a function2 b ! subject is suffici5tly complicat$ if we view "o quantity z a function ( "o o!r4 ,n[1 z a g5]al rule1 a function c be develop$ or express$ z ! sum ( quantities1 ! values ( :i* dep5d ^u ! successive p[]s ( ! v>iable quantity4 ,if 99y99 be a function ( 99x99 !n we may say t 99y99 ,a ,b99x99 ,c99x99#b ,d99x99#c ,e99x99#d 4444 ,9 ?is equation1 ,a1 ,b1 ,c1 ,d1 c41 are fix$ quantities1 ( diff]5t values 9 diff]5t cases4 ,! t]ms may be inf9ite 9 numb] or aft] a "t may cease to h any value4 ,any ( ! coeffici5ts ,a1 ,b1 ,c1 c41 may be z]o or negative2 b :atev] !y be !y are fix$4 ,! quantity 99x99 on ! o!r h& may be made :at we l1 be+ v>iable4 ,suppose1 9 ! fir/ place1 t 99x99 & 99y99 are bo? l5g?s4 ,let u assume t #a_/aj1jjj "p ( an in* is ! lea/ t we c take note (4 ,!n :5 99x99 is "o hundr$? ( an in*1 we h 99x99#b #a_/aj1jjj1 & if ,c be less ?an unity1 ! t]m ,c99x99#b w be inappreciable1 be+ less ?an we c measure4 ,unless any ( ! quantities ,d1 ,e1 c41 %\ld happ5 to be v great1 x is evid5t t all ! succe$+ t]ms w also be inappreciable1 because ! p[]s ( 99x99 become rapidly small] 9 geometrical ratio4 ,?us :5 99x99 is made small en\gh ! quantity 99y99 seems to obey ! equation 99y99 ,a ,b99x994 ,if 99x99 %\ld be /ill less1 if x %\ld become z small1 = in/ance1 z #a_/a1jjj1jjj ( an in*1 & ,b %\ld n be v great1 !n 99y99 w\ld appe> to be ! fix$ quantity ,a1 & w\ld n seem to v>y ) 99x99 at all4 ,on ! o!r h&1 7 x to gr[ great]1 say equal to #a_/aj in*1 & ,c n be v small1 ! t]m ,c99x99#b w\ld become appreciable1 & ! law w\ld n[ be m complicat$4 ,we c inv]t ! mode ( view+ ?is "q1 & suppose t :ile ! quantity 99y99 und]goes v>iations dep5d+ on _m p[]s ( 99x991 our p[] ( detect+ ! *anges ( value is m or less acute4 ,:ile our p[]s ( obs]vation rema9 v rude we may be unable to detect any *ange 9 ! quantity at all1 t is to say1 ,b99x99 may always be too small to come )9 our notice1 j z 9 =m] days ! fix$ />s 7 s call$ because !y rema9$ at app>5tly fix$ di/ances f ea* o!r4 ,) ! use ( telescopes & micromet]s we become able to detect ! exi/5ce ( "s motion1 s t ! di/ance ( "o /> f ano!r may be express$ by ,a ,b99x991 ! t]m includ+ 99x99#b be+ /ill inappreciable4 ,"u ^! circum/ances ! /> w seem to move uni=mly1 or 9 simple proportion to ! "t 99x994 ,) mu* improv$ means ( measurem5t x w probably be f\nd t ?is uni=mity ( motion is only app>5t1 & t !re exi/s "s accel]ation or ret>dation4 ,m c>eful inve/igation w %[ ! law to be m & m complicat$ ?an 0 previ\sly suppos$4 ,!re is yet ano!r way ( expla9+ ! app>5t results ( a complicat$ law4 ,if we take any curve & reg>d a portion ( x free f any k9d ( discont9uity1 we may repres5t ! "* ( su* portion by an equation ( ! =m 99y99 ,a ,b99x99 ,c99x99#b ,d99x99#c 4444 ,re/rict ! att5tion to a v small portion ( ! curve1 & ! eye w be unable to di/+ui% its diff]5ce f a /raight l9e1 :i* am\nts to say+ t 9 ! portion exam9$ ! t]m ,c99x99#b has no value appreciable by ! eye4 ,take a l>g] portion ( ! curve & x w be app>5t t x possesses curvature1 b x w be possible to draw a p>abola or ellipse s t ! curve %all app>5tly co9cide ) a portion ( t p>abola or ellipse4 ,9 ! same way if we take l>g] & l>g] arcs ( ! curve x w assume ! "* successively ( a curve ( ! ?ird1 f\r?1 & p]haps high] degrees2 t is to say1 x corresponds to equations involv+ ! ?ird1 f\r?1 & high] p[]s ( ! v>iable quantity4 ,we h arriv$ !n at ! conclusion t e ph5om5on1 :5 its am\nt c only be rudely measur$1 w ei!r be ( fix$ am\nt1 or w seem to v>y uni=mly l ! di/ance betwe5 two incl9$ /raight l9es4 ,m exact measurem5t may %[ ! error ( ?is fir/ assumption1 & ! v>iation w !n appe> to be l t ( ! di/ance betwe5 a /raight l9e & a p>abola or ellipse4 ,we may aft]w>ds f9d t a curve ( ! ?ird or high] degrees is really requir$ to repres5t ! v>iation4 ,i propose to call ! v>iation ( a quantity 99l9e>991 99elliptic991 99cubic991 99qu>tic991 99qu9tic991 c41 accord+ z x is discov]$ to involve ! fir/1 second1 ?ird1 f\r?1 fif?1 or high] p[]s ( ! v>iable4 ,x is a g5]al rule 9 quantitative inve/igation t we comm5ce by discov]+ l9e>1 & aft]w>ds proce$ to elliptic or m complicat$ laws ( v>iation4 ,! approximate curves :i* we employ are all1 accord+ to ,de ,morgan's use ( ! "n1 p>abolas ( "s ord] or o!r2 & s9ce ! common p>abola ( ! second ord] is approximately ! same z a v elongat$ ellipse1 & is 9 fact an inf9itely elongat$ ellipse1 x is conv5i5t & prop] to call v>iation ( ! second ord] 99elliptic994 ,x might also be call$ 99quadric99 v>iation4 ,z reg>ds _m important ph5om5a we are yet only 9 ! fir/ /age ( approximation4 ,we "k t ! sun & _m s-call$ fix$ />s1 especially #fa ,cygni1 h a prop] motion ?r\gh space1 & ! direction ( ?is motion at ! pres5t "t is kn[n ) "s degree ( accuracy4 ,b x is h>dly consi/5t ) ! !ory ( gravity t ! pa? ( any body %\ld really be a /raight l9e4 ,h5ce1 we mu/ reg>d a rectil9e> pa? z only a provisional description ( ! motion1 & look =w>d to ! "t :5 its curvature w be detect$1 ?\gh c5turies p]haps mu/ fir/ elapse4 ,we are accu/om$ to assume t on ! surface ( ! e>? ! =ce ( gravity is uni=m1 because ! v>iation is ( s slight an am\nt t we are sc>cely able to detect x4 ,b suppos+ we c\ld measure ! v>iation1 we %\ld f9d x simply proportional to ! height4 ,tak+ ! e>?'s radius to be unity1 let 99h99 be ! height at :i* we measure ! =ce ( gravity4 ,!n by ! well-kn[n law ( ! inv]se squ>e1 t =ce w be proportional to 99g99_/7#a 99h997#b1 or to 99g997#a - #b99;h99 #c99;h99#b - #d99;h99#c 44474 ,b at all heights to :i* we c atta9 99h99 w be s small a fraction ( ! e>?'s radius t #c99;h99#b w be inappreciable1 & ! =ce ( gravity w seem to foll[ ! law ( l9e> v>iation1 be+ proportional to #a - #b99;h994 ,:5 ! circum/ances ( an exp]im5t are mu* alt]$1 diff]5t p[]s ( ! v>iable may become prom95t4 ,! resi/ance ( a liquid to a body mov+ ?r\gh x may be approximately express$ z ! sum ( two t]ms respectively involv+ ! fir/ & second p[]s ( ! velocity4 ,at v l[ velocities ! fir/ p[] is ( mo/ importance1 & ! resi/ance1 z ,pr(essor ,/okes has %[n1 is ne>ly 9 simple proportion to ! velocity4 ,:5 ! motion is rapid ! resi/ance increases 9 a /ill great] degree1 & is m ne>ly proportional to ! squ>e ( ! velocity4 99,approximate ,indep5d5ce ( ,small ,effects499 ,"o result ( ! !ory ( approximation possesses su* importance 9 physical sci5ce1 & is s (t5 appli$1 t we may consid] x sep>ately4 ,! inve/igation ( causes & effects is imm5sely simplifi$ :5 we may consid] ea* cause z produc+ its own effect inv>iably1 :e!r o!r causes are act+ or n4 ,?us1 if ! body ,p produces 99x991 & ,q produces 99y991 ! "q is :e!r ,p & ,q act+ toge!r w produce ! sum ( ! sep>ate effects1 99x99 99y994 ,x is "u ?is supposition t we treat$ ! me?ods ( elim9at+ error 7,*ap4 ,,xv471 & errors ( a less am\nt w\ld /ill rema9 if ! supposition 0 a =c$ "o4 ,!re are probably "s p>ts ( sci5ce 9 :i* ! supposition ( indep5d5ce ( effects holds rigidly true4 ,! mutual gravity ( two bodies is entirely unaffect$ by ! pres5ce ( o!r gravitat+ bodies4 ,p d n usually consid] t ?is important pr9ciple is involv$ 9 su* a simple ?+ z putt+ two p\nd weights 9 ! scale ( a balance4 ,h[ d we "k t two p\nds toge!r w weigh twice z mu* z "o8 ,d we "k x to be exactly s8 ,l o!r results f\nd$ on induction we _c prove x absolutely1 b all ! calculations ( physical a/ronomy proce$ ^u ! assumption1 s t we may consid] x prov$ to a v high degree ( approximation4 ,_h n ?is be5 true1 ! calculations ( physical a/ronomy w\ld h be5 inf9itely m complex ?an !y actually are1 & ! progress ( k w\ld h be5 mu* sl[]4 ,x is a g5]al pr9ciple ( sci5tific me?od t if effects be ( small am\nt1 comp>atively to our means ( obs]vation1 all jo9t effects w be ( a high] ord] ( smallness1 & may !re=e be reject$ 9 a fir/ approximation4 ,?is pr9ciple 0 employ$ by ,daniel ,b]n\lli 9 ! !ory ( s\nd1 "u ! title ( 99,! ,pr9ciple ( ! ,coexi/5ce ( ,small ,vibrations994 ,he %[$ t if a /r+ is affect$ by two k9ds ( vibrations1 we may consid] ea* to be go+ on z if ! o!r did n exi/4 ,we _c p]ceive t ! s\nd+ ( "o musical in/rum5t prev5ts or ev5 modifies ! s\nd ( ano!r1 s t all s\nds w\ld seem to travel ?r\gh ! air1 & act ^u ! e> 9 indep5d5ce ( ea* o!r4 ,a simil> assumption is made 9 ! !ory ( tides1 :i* are great waves4 ,"o wave is produc$ by ! attraction ( ! moon1 & ano!r by ! attraction ( ! sun1 & ! "q arises1 :e!r :5 ^! waves co9cide1 z at ! "t ( spr+ tides1 ! jo9t wave w be simply ! sum ( ! sep>ate waves4 ,on ! pr9ciple ( ,b]n\lli ?is w be s1 because ! tides on ! ocean are v small comp>$ ) ! dep? ( ! ocean4 ,! pr9ciple ( ,b]n\lli1 h[ev]1 is only approximately true4 ,a wave nev] is exactly ! same :5 ano!r wave is int]f]+ ) x1 b ! less ! displacem5t ( p>ticles due to ea* wave1 ! less 9 a /ill high] degree is ! effect ( "o wave ^u ! o!r4 ,9 rec5t ye>s ,helmholtz 0 l$ to suspect t "s ( ! ph5om5a ( s\nd might aft] all be due to resultant effects ov]look$ by ! assumption ( previ\s physici/s4 ,he inve/igat$ ! second>y waves :i* w\ld arise f ! int]f]5ce ( consid]able di/urbances1 & 0 able to %[ t c]ta9 summation ( resultant tones ought to be he>d1 & exp]im5ts subsequ5tly devis$ = ! purpose %[$ t !y might be he>d4 ,illu/ration ,?r\gh\t ! me*anical sci5ces ! 99,pr9ciple ( ! ,sup]position ( ,small ,motions99 is ( fundam5tal importance1#cij & x may be ?us expla9$4 ,suppose t two =ces1 act+ f ! po9ts ,b & ,c1 are simultane\sly mov+ a body ,a4 ,let ! =ce act+ f ,b be su* t 9 "o second x w\ld move ,a to 99p991 & simil>ly let ! second =ce1 act+ alone1 move ,a to 99r994 ,! "q arises1 !n1 :e!r _! jo9t action w urge ,a to 99q99 along ! diagonal ( ! p>allelogram4 ,may we say t ,a w move ! di/ance ,a99p99 9 ! direction ,,ab1 & ,a99r99 9 ! direction ,,ac1 or1 :at is ! same ?+1 along ! p>allel l9e 99pq998 ,9 /rictness we _c say s2 = :5 ,a has mov$ t[>ds 99p991 ! =ce f ,c w no long] act along ! l9e ,,ac1 & simil>ly ! motion ( ,a t[>ds 99r99 w modify ! action ( ! =ce f ,b4 ,?is int]f]5ce ( "o =ce ) ! l9e ( action ( ! o!r w evid5tly be great] ! l>g] is ! ext5t ( motion consid]$2 on ! o!r h&1 z we r$uce ! p>allelogram ,a99pqr991 comp>$ ) ! di/ances ,,ab & ,,ac1 ! less w be ! int]f]5ce ( ! =ces4 ,accord+ly ma!maticians avoid all error by consid]+ ! motions z inf9itely small1 s t ! int]f]5ce becomes ( a /ill high] ord] ( inf9ite smallness1 & may be entirely neglect$4 ,by ! res\rces ( ! diff]5tial calculus x is possible to calculate ! motion ( ! p>ticle ,a1 z if x w5t ?r\gh an inf9ite numb] ( inf9itely small diagonals ( p>allelograms4 ,! great discov]ies ( ,newton really arose f apply+ ?is me?od ( calculation to ! movem5ts ( ! moon r\nd ! e>?1 :i*1 :ile con/antly t5d+ to move onw>d 9 a /raight l9e1 is also deflect$ t[>ds ! e>? by gravity1 & moves ?r\gh an elliptic curve1 compos$ z x 7 ( ! inf9itely small diagonals ( inf9itely num]\s p>allelograms4 ,! ma!matician1 9 8 inve/igation ( a curve1 always treats x z made up ( a great numb] ( /raight l9es1 & x may be d\bt$ :e!r he c\ld treat x 9 any o!r mann]4 ,!re is no error 9 ! f9al results1 because hav+ obta9$ ! =mul fl[+ f ?is supposition1 ea* /raight l9e is !n reg>d$ z becom+ inf9itely small1 & ! polygonal l9e becomes undi/+ui%able f a p]fect curve4#cia #cij ,?omson & ,tait's 99,natural ,philosophy991 vol4 i4 p4 #fj4 #cia ,*allis1 99,notes on ! ,pr9ciples ( ,pure & ,appli$ ,calculation991 #ahfi1 p4 #hc4 ,9 ab/ract ma!matical !orems ! approximation to absolute tru? is p]fect1 because we c treat ( inf9itesimals4 ,9 physical sci5ce1 on ! contr>y1 we treat ( ! lea/ quantities :i* are p]ceptible4 ,nev]!less1 :ile c>efully di/+ui%+ betwe5 ^! two diff]5t cases1 we may fe>lessly apply to bo? ! pr9ciple ( ! sup]position ( small effects4 ,9 physical sci5ce we h only to take c>e t ! effects really are s small t any jo9t effect w be unque/ionably imp]ceptible4 ,suppose1 = in/ance1 t !re is "s cause :i* alt]s ! dim5sions ( a body 9 ! ratio ( #a to #a 1 & ano!r cause :i* produces an alt]ation 9 ! ratio ( #a to #a 4 ,if !y bo? act at once ! *ange w be 9 ! ratio ( #a to 7#a 77#a 71 or z #a to #a 4 ,b if & be bo? v small fractions ( ! total dim5sions1 w be yet f> small] & may be disreg>d$2 ! ratio ( *ange is !n approximately t ( #a to #a 1 or ! jo9t effect is ! sum ( ! sep>ate effects4 ,?us if a body 7 subject$ to ?ree /ra9s1 at "r angles to ea* o!r1 ! total *ange 9 ! volume ( ! body w\ld be approximately equal to ! sum ( ! *anges produc$ by ! sep>ate /ra9s1 provid$ t ^! are v small4 ,9 l mann] n only is ! expansion ( e solid & liquid sub/ance by heat approximately proportional to ! *ange ( temp]ature1 :5 ?is *ange is v small 9 am\nt1 b ! cubic expansion may also be consid]$ z be+ ?ree times z great z ! l9e> expansion4 ,= if ! increase ( temp]ature exp&s a b> ( metal 9 ! ratio ( #a to #a 1 & ! expansion be equal 9 all directions1 !n a cube ( ! same metal w\ld exp& z #a to 7#a 7#c1 or z #a to #a #c #cb #c4 ,:5 is a v small quantity ! ?ird t]m #cb w be imp]ceptible1 & /ill m s ! f\r? t]m #c4 ,! coeffici5ts ( expansion ( solids are 9 fact s small1 & s imp]fectly det]m9$1 t physici/s seldom take into acc\nt _! second & high] p[]s4 ,x is a result ( ^! pr9ciples t all small errors may be assum$ to v>y 9 simple proportion to _! causes--a new reason :y1 9 elim9at+ errors1 we %\ld fir/ ( all make !m z small z possible4 ,let u suppose t !re is a "r-angl$ triangle ( :i* ! two sides conta9+ ! "r angle are really ( ! l5g?s #c & #d1 s t ! hypo!nuse is 7#cb #db7 or #e4 ,n[1 if 9 two measurem5ts ( ! fir/ side we commit slight errors1 mak+ x successively #djja & #djjb1 !n calculation w give ! l5g?s ( ! hypo!nuse z almo/ exactly #ejjjh & #ejjaf1 s t ! error 9 ! hypo!nuse w seem to v>y 9 simple proportion to t ( ! side1 al?\gh x does n really d s ) p]fect exactness4 ,! log>i?m ( a numb] does n v>y 9 proportion to t numb]--nev]!less we f9d ! diff]5ce betwe5 ! log>i?ms ( ! numb]s #ajjjjj & #ajjjja to be almo/ exactly equal to t betwe5 ! numb]s #ajjjja & #ajjjjb4 ,x is ?us a g5]al rule t v small diff]5ces betwe5 successive values ( a function are approximately proportional to ! small diff]5ces ( ! v>iable quantity4 ,on ^! pr9ciples x is easy to draw up a s]ies ( rules su* z ^? giv5 by ,kohlraus*#cib = p]=m+ calculations 9 an abbreviat$ =m :5 ! v>iable quantity is v small comp>$ ) unity4 ,?us = #a 7#a 7 we may sub/itute #a - 2 = #a 7#a - 7 we may put #a 2 #a 7#a 7 becomes #a - 7#a_/b71 & s =?4 #cib 99,an ,introduction to ,physical ,measurem5ts991 translat$ by ,wall] & ,proct]1 #ahgc1 p4 #aj4 99,f\r ,mean+s ( ,equality499 ,al?\gh x might seem t !re are few t]ms m free f ambiguity ?an ! t]m 99equal991 yet sci5tific m5 d employ x ) at lea/ f\r mean+s1 :i* x is desirable to di/+ui%4 ,^! mean+s ,i may describe z 7#a7 ,absolute ,equality4 7#b7 ,sub-equality4 7#c7 ,app>5t ,equality4 7#d7 ,probable ,equality4 ,by 99absolute equality99 we signify t :i* is complete & p]fect to ! la/ degree2 b x is obvi\s t we c only "k su* equality 9 a !oretical or hypo!tical mann]4 ,! areas ( two triangles /&+ ^u ! same base & betwe5 ! same p>allels are absolutely equal4 ,hippocrates beautifully prov$ t ! area ( a lunula or figure conta9$ betwe5 two segm5ts ( circles 0 absolutely equal to t ( a c]ta9 "r-angl$ triangle4 ,z a g5]al rule all geometrical & o!r elem5t>y ma!matical !orems involve absolute equality4 ,de ,morgan propos$ to describe z 99sub-equal99 ^? quantities :i* are equal )9 an inf9itely small quantity1 s t 99x99 is sub-equal to 99x99 99dx994 ,! diff]5tial calculus may be said to arise out ( ! neglect ( inf9itely small quantities1 & 9 ma!matical sci5ce o!r subtle di/9ctions may h to be drawn betwe5 k9ds ( equality1 z ,de ,morgan has %[n 9 a rem>kable memoir 8,on ,inf9ity2 & on ! sign ( ,equality40#cic #cic 99,cambridge ,philosophical ,transactions99 7#ahfe71 vol4 xi4 ,"p ,i4 99,app>5t equality99 is t ) :i* physical sci5ce deals4 ,^? magnitudes are app>5tly equal :i* diff] only by an imp]ceptible quantity4 ,to ! c>p5t] any?+ less ?an ! hundr$? "p ( an in* is non-exi/5t2 !re are few arts or arti/s to :i* ! hundr$-?\s&? ( an in* is ( any acc\nt4 ,s9ce all co9cid5ce betwe5 physical magnitudes is judg$ by "o or o!r s5se1 we mu/ be re/rict$ to a k ( app>5t equality4 ,9 reality ev5 app>5t equality is r>ely to be expect$4 ,m commonly exp]im5ts w give only 99probable equality991 t is results w come s ne> to ea* o!r t ! diff]5ce may be ascrib$ to unimportant di/urb+ causes4 ,physici/s (t5 assume quantities to be equal provid$ t !y fall )9 ! limits ( probable error ( ! processes employ$4 ,we _c expect obs]vations to agree ) !ory m closely ?an !y agree ) ea* o!r1 z ,newton rem>k$ ( 8 inve/igations conc]n+ ,halley's ,comet4 99,ari?metic ( ,approximate ,quantities499 ,consid]+ t almo/ all ! quantities :i* we treat 9 physical & social sci5ce are approximate only1 x seems desirable t att5tion %\ld be paid 9 ! tea*+ ( ari?metic to ! correct int]pretation & treatm5t ( approximate num]ical /atem5ts4 ,we seem to ne$ notation = express+ ! approximat5ess or exactness ( decimal numb]s4 ,! fraction #jbe may mean ei!r precisely "o #dj? "p1 or x may mean any?+ betwe5 #jbde & #jbee4 ,i propose t :5 a decimal fraction is completely & exactly giv51 a 99small ciph]99 or circle %\ld be add$ to indicate t !re is no?+ m to come1 z 9 #jbe4 ,:5 ! fir/ figure ( ! decimals reject$ is #e or m1 ! fir/ figure reta9$ %\ld be rais$ by a unit1 accord+ to a rule approv$ by ,de ,morgan1 & n[ g5]ally recognis$4 ,to indicate t ! fraction ?us reta9$ is m ?an ! tru?1 a po9t has be5 plac$ ov] ! la/ figure 9 "s tables ( log>i?ms2 b a simil> po9t is us$ to d5ote ! p]iod ( a repeat+ decimal1 & ,i %\ld !re=e propose to employ a colon 99aft]99 ! figure2 ?us #jbe3 w\ld mean t ! true quantity lies betwe5 #jbde & #jbe inclusive ( ! l[] b n ! high] limit4 ,:5 ! fraction is less ?an ! tru?1 two dots might be plac$ horizontally z 9 #jbe44 :i* w\ld mean any?+ betwe5 #jbe & #jbee n inclusive4 ,:5 approximate numb]s are add$1 subtract$1 multipli$1 or divid$1 x becomes a matt] ( "s complexity to det]m9e ! degree ( accuracy ( ! result4 ,!re are few p]sons :o c\ld ass]t (f-h& t ! sum ( ! approximate numb]s #cdgj1 #ebfic1 #hja1 is #afge 99)9 less ?an99 #jg4 ,mr4 ,s&eman has trac$ out ! rules ( approximate ari?metic 9 a v ?or\gh mann]1 & 8 directions are wor?y ( c>eful att5tion4#cid ,! ?ird "p ( ,sonn5s*e9 & ,nesbitt's excell5t book on ari?metic#cie describes fully all k9ds ( approximate calculations1 & %[s bo? h[ to avoid ne$less lab\r & h[ to take prop] acc\nt ( inaccuracy 9 op]at+ ) approximate decimal fractions4 ,a simple inve/igation ( ! subject is to be f\nd 9 ,sonnet's 99,algbre ,elm5taire99 7,p>is1 #ahdh7 *ap4 xiv41 8,des ,approximations ,absolues et ,relatives40 ,!re is also an ,am]ican "w on ! subject4#cif #cid ,s&eman1 99,pelicotetics991 p4 #bad4 #cie 99,! ,sci5ce & ,art ( ,ari?metic = ! ,use ( ,s*ools499 7,:itak] & ,co47 #cif 99,pr9ciples ( ,approximate ,calculations991 by ,j4 ,j4 ,sk9n]1 ,c4,e4 7,new ,york1 ,h5ry ,holt71 #ahgf4 ,al?\gh ! accuracy ( measurem5t has s mu* advanc$ s9ce ! "t ( ,leslie1 x is n sup]flu\s to repeat 8 prote/ aga9/ ! unfairness ( affect+ by a display ( decimal fractions a great] degree ( accuracy ?an ! nature ( ! case requires & admits4#cig ,i h kn[n a sci5tific man to regi/] ! b>omet] to a second ( "t :5 ! ne>e/ qu>t] ( an h\r w\ld h be5 amply suffici5t4 ,*emi/s (t5 publi% results ( analysis to ! t5-?\s&? or ev5 ! million? "p ( ! :ole1 :5 9 all probability ! processes employ$ _c be dep5d$ on beyond ! hundr$? "p4 ,x is seldom desirable to give m ?an "o place ( figures ( unc]ta9 am\nt2 b x mu/ be all[$ t a nice p]ception ( ! degree ( accuracy possible & desirable is requisite to save misappreh5sion & ne$less computation on ! "o h&1 & to secure all atta9able exactness on ! o!r h&4 #cig ,leslie1 99,inquiry into ! ,nature ( ,heat991 p4 #eje4 ,,*apt] ,,xxii4 ,,quantitative ,,induction4 ,we h n yet =mally consid]$ any processes ( reason+ :i* h = _! object to disclose laws ( nature express$ 9 quantitative equations4 ,we h be5 inquir+ into ! modes by :i* a ph5om5on may be measur$1 &1 if x be a composite ph5om5on1 may be resolv$1 by ! aid ( sev]al measurem5ts1 into its compon5t p>ts4 ,we h also consid]$ ! precautions to be tak5 9 ! p]=mance ( obs]vations & exp]im5ts 9 ord] t we may "k :at ph5om5a we really d measure1 b we mu/ rememb] t1 no numb] ( facts & obs]vations c by !mselves con/itute sci5ce4 ,num]ical facts1 l o!r facts1 are b ! raw mat]ials ( k1 ^u :i* our reason+ faculties mu/ be ex]t$ 9 ord] to draw =? ! pr9ciples ( nature4 ,x is by an inv]se process ( reason+ t we c alone discov] ! ma!matical laws to :i* v>y+ quantities con=m4 ,by well-conduct$ exp]im5ts we ga9 a s]ies ( values ( a v>iable1 & a correspond+ s]ies ( values ( a v>iant1 & we n[ want to "k :at ma!matical function ! v>iant is z reg>ds ! v>iable4 ,9 ! usual progress ( a sci5ce ?ree que/ions w h to be answ]$ z reg>ds e important quantitative ph5om5on3-- 7#a7 ,is !re any con/ant relation betwe5 a v>iable & a v>iant8 7#b7 ,:at is ! empirical =mula express+ ?is relation8 7#c7 ,:at is ! rational =mula express+ ! law ( nature involv$8 99,probable ,connection ( ,v>y+ ,quantities499 ,we f9d x /at$ by ,mill1#cih t 8,:atev] ph5om5on v>ies 9 any mann] :5ev] ano!r ph5om5on v>ies 9 "s p>ticul> mann]1 is ei!r a cause or an effect ( t ph5om5on1 or is connect$ ) x ?r\gh "s fact ( causation40 ,?is ass]tion may be consid]$ true :5 x is int]pret$ ) suffici5t caution2 b x might o!rwise lead u into error4 ,!re is no?+ :atev] 9 ! nature ( ?+s to prev5t ! exi/5ce ( two v>iations :i* %\ld app>5tly foll[ ! same law1 & yet h no connection ) ea* o!r4 ,"o b9>y /> might be go+ ?r\gh a revolution :i*1 s f> z we c\ld tell1 0 ( equal p]iod ) t ( ano!r b9>y />1 & accord+ to ! above rule ! motion ( "o w\ld be ! cause ( ! motion ( ! o!r1 :i* w\ld n be really ! case4 ,two a/ronomical clocks might conceivably be made s ne>ly p]fect t1 = sev]al ye>s1 no diff]5ce c\ld be detect$1 & we might !n inf] t ! motion ( "o clock 0 ! cause or effect ( ! motion ( ! o!r4 ,?is matt] requires c>eful discrim9ation4 ,we mu/ be> 9 m9d t ! cont9u\s quantities ( space1 "t1 =ce1 c41 :i* we measure1 are made up ( an inf9ite numb] ( inf9itely small units4 ,we may !n meet ) two v>iable ph5om5a :i* foll[ laws s ne>ly ! same1 t 9 no "p ( ! v>iations op5 to our obs]vation c any discrepancy be discov]$4 ,i grant t if two clocks c\ld be %[n to h kept 99exactly99 ! same "t dur+ any f9ite int]val1 ! probability w\ld become inf9itely high t !re 0 a connection betwe5 _! motions4 ,b we c nev] absolutely prove su* co9cid5ces to exi/4 ,all[ t we may obs]ve a diff]5ce ( "o-t5? ( a second 9 _! "t1 yet x is possible t !y 7 indep5d5tly regulat$ s z to g toge!r )9 less ?an t quantity ( "t4 ,9 %ort1 x w\ld require ei!r an inf9itely long "t ( obs]vation1 or inf9itely acute p[]s ( measur+ discrepancy1 to decide positively :e!r two clocks 7 or 7 n 9 relation ) ea* o!r4 #cih 99,sy/em ( ,logic991 bk4 iii4 *ap4 viii #f4 ,a simil> "q actually occurs 9 ! case ( ! moon's motion4 ,we h no record t any o!r portion ( ! moon 0 ev] visible to m5 ?an su* z we n[ see4 ,?is fact suffici5tly proves t )9 ! hi/orical p]iod ! rotation ( ! moon on its own axis has co9cid$ ) its revolutions r\nd ! e>?4 ,does ?is co9cid5ce prove a relation ( cause & effect to exi/8 ,! answ] mu/ be 9 ! negative1 because !re might h be5 s slight a discrepancy betwe5 ! motions t !re has n yet be5 "t to produce any appreciable effect4 ,!re may nev]!less be a high probability ( connection4 ,! :ole "q ( ! relation ( quantities ?us resolves itself into "o ( probability4 ,:5 we c only rudely measure a quantitative result1 we c assign b slight importance to any correspond5ce4 ,because ! brightness ( two />s seems to v>y 9 ! same mann]1 !re is no consid]able probability t !y h any relation ) ea* o!r4 ,c\ld x be %[n t _! p]iods ( v>iation 7 ! same to inf9itely small quantities x w\ld be c]ta91 t is inf9itely probable1 t !y 7 connect$1 h[ev] unlikely ?is might be on o!r gr\nds4 ,! g5]al mode ( e/imat+ su* probabilities is id5tical ) t appli$ to o!r inductive problems4 ,t any two p]iods ( v>iation %\ld by *ance become 99absolutely equal99 is inf9itely improbable2 h5ce if1 9 ! case ( ! moon or o!r mov+ bodies1 we c\ld prove absolute co9cid5ce we %\ld h c]ta9ty ( connection4#cii ,) approximate measurem5ts1 :i* alone are )9 our p[]1 we mu/ hope = approximate c]ta9ty at ! mo/4 #cii ,laplace1 99,sy/em ( ! ,_w991 translat$ by ,h>te1 vol4 ii4 p4 #cff4 ,! pr9ciples ( inf]5ce & probability1 accord+ to :i* we treat causes & effects v>y+ 9 am\nt1 are exactly ! same z ^? by :i* we treat$ simple exp]im5ts4 ,cont9u\s quantity1 h[ev]1 af=ds u an inf9itely m ext5sive sph]e ( obs]vation1 because e diff]5t am\nt ( cause1 h[ev] little diff]5t1 ought to be foll[$ by a diff]5t am\nt ( effect4 ,if we c measure temp]ature to ! "o-hundr$? "p ( a degree c5tigrade1 !n betwe5 #j & #ajj we h #aj1jjj possible trials4 ,if ! precision ( our measurem5ts is increas$1 s t ! "o-?\s&? "p ( a degree c be appreciat$1 our trials may be increas$ t5fold4 ,! probability ( connection w be proportional to ! accuracy ( our measurem5ts4 ,:5 we c v>y ! quantity ( a cause at w x is easy to discov] :e!r a c]ta9 effect is due to t cause or n4 ,we c !n make z _m irregul> *anges z we l1 & x is q incr$ible t ! suppos$ effect %\ld by *ance g ?r\gh exactly ! correspond+ s]ies ( *anges except by dep5d5ce4 ,if we h a bell r++ 999 vacuo991 ! s\nd increases z we let 9 ! air1 & x decreases aga9 z we exhau/ ! air4 ,tyndall's s++ flames evid5tly obey$ ! directions ( 8 own voice2 & ,f>aday :5 he discov]$ ! relation ( magnetism & light f\nd t1 by mak+ or break+ or rev]s+ ! curr5t ( ! electro-magnet1 he _h complete comm& ov] a ray ( light1 prov+ beyond all reasonable d\bt ! dep5d5ce ( cause & effect4 ,9 su* cases x is ! p]fect co9cid5ce 9 "t betwe5 ! *ange 9 ! effect & t 9 ! cause :i* raises a high improbability ( casual co9cid5ce4 ,x is by a simple case ( v>iation t we inf] ! exi/5ce ( a mat]ial connection betwe5 two bodies mov+ ) exactly equal velocity1 su* z ! locomotive eng9e & ! tra9 :i* foll[s x4 ,elaborate obs]vations 7 requisite be=e a/ronom]s c\ld all be conv9c$ t ! r$ hydrog5 flames se5 dur+ sol> eclipses belong$ to ! sun1 & n to ! moon's atmosph]e z ,flam/e$ assum$4 ,z e>ly z #agjf1 ,/annyan notic$ a blood-r$ /reak 9 an eclipse :i* he witness$ at ,b]ne1 & he ass]t$ t x belong$ to ! sun2 b 8 op9ion 0 n f9ally e/abli%$ until photographs ( ! eclipse 9 #ahfj1 tak5 by ,mr4 ,de la ,rue1 %[$ t ! moon's d>k body gradually cov]$ ! r$ prom95ces on "o side1 & uncov]$ ^? on ! o!r2 9 %ort1 t ^! prom95ces mov$ precisely z ! sun mov$1 & n z ! moon mov$4 ,ev5 :5 we h no means ( accurately measur+ ! v>iable quantities we may yet be conv9c$ ( _! connection1 if "o always v>ies p]ceptibly at ! same "t z ! o!r4 ,fatigue increases ) ex]tion2 hung] ) ab/95ce f food2 desire & degree ( utility decrease ) ! quantity ( commodity consum$4 ,we "k t ! sun's heat+ p[] dep5ds ^u 8 height ( ! sky2 t ! temp]ature ( ! air falls 9 asc5d+ a m\nta92 t ! e>?'s cru/ is f\nd to be p]ceptibly w>m] z we s9k m9es into x2 we inf] ! direction 9 :i* a s\nd comes f ! *ange ( l\dness z we approa* or rec$e4 ,! facility ) :i* we c "t aft] "t obs]ve ! increase or decrease ( "o quantity ) ano!r suffici5tly %[s ! connection1 al?\gh we may be unable to assign any precise law ( relation4 ,! probability 9 su* cases dep5ds ^u frequ5t co9cid5ce 9 "t4 99,empirical ,ma!matical ,laws499 ,x is important to acquire a cle> compreh5sion ( ! "p :i* is play$ 9 sci5tific inve/igation by empirical =mul & laws4 ,if we h a table conta9+ c]ta9 values ( a v>iable & ! correspond+ values ( ! v>iant1 !re are ma!matical processes by :i* we c infallibly discov] a ma!matical =mula yield+ numb]s 9 m or less exact agreem5t ) ! table4 ,we may g5]ally assume t ! quantities w approximately con=m to a law ( ! =m 99y99 ,a ,b99x99 ,c99x99#b1 9 :i* 99x99 is ! v>iable & 99y99 ! v>iant4 ,we c !n select f ! table ?ree values ( 99y991 & ! correspond+ values ( 99x992 ins]t+ !m 9 ! equation1 we obta9 ?ree equations by ! solution ( :i* we ga9 ! values ( ,a1 ,b1 & ,c4 ,x w be f\nd z a g5]al rule t ! =mula ?us obta9$ yields ! o!r numb]s ( ! table to a consid]able degree ( approximation4 ,9 _m cases ev5 ! second p[] ( ! v>iable w be unnecess>y2 ,regnault f\nd t ! results ( 8 elaborate inquiry into ! lat5t heat ( /eam at diff]5t pressures 7 repres5t$ ) suffici5t accuracy by ! empirical =mula #fjfe #jcje 99t991 9 :i* is ! total heat ( ! /eam1 & 99t99 ! temp]ature4#djj ,9 o!r cases x may be requisite to include ! ?ird p[] ( ! v>iable4 ,?us physici/s assume ! law ( ! dilatation ( liquids to be ( ! =m t 99at99 99bt99#b 99ct99#c1 #djj 99,*emical ,reports & ,memoirs991 ,cav5di% ,society1 p4 #bid4 & !y calculate f results ( obs]vation ! values ( ! ?ree con/ants 99a991 99b991 99c991 :i* are usually small quantities n exce$+ "o-hundr$? "p ( a unit1 b requir+ to be det]m9$ ) great accuracy4#dja ,!oretically speak+1 ?is process ( empirical repres5tation might be appli$ ) any degree ( accuracy2 we might include /ill high] p[]s 9 ! =mula1 & ) suffici5t lab\r obta9 ! values ( ! con/ants1 by us+ an equal numb] ( exp]im5tal results4 ,! me?od ( lea/ squ>es may also be employ$ to obta9 ! mo/ probable values ( ! con/ants4 #dja ,jam91 99,c\rs de ,physique991 vol4 ii4 p4 #ch4 ,9 a simil> mann] all p]iodic v>iations may be repres5t$ ) any requir$ degree ( accuracy by =mul involv+ ! s9es & cos9es ( angles & _! multiples4 ,! =m ( any tidal or o!r wave may ?us be express$1 z ,sir ,g4 ,b4 ,airy has expla9$4#djb ,almo/ all ! ph5om5a regi/]$ by meteorologi/s are p]iodic 9 "*1 & :5 fre$ f di/urb+ causes may be embodi$ 9 empirical =mul4 ,bessel has giv5 a rule by :i* f any regul> s]ies ( obs]vations we may1 on ! pr9ciple ( ! me?od ( lea/ squ>es1 calculate out ) a mod]ate am\nt ( lab\r a =mula express+ ! v>iation ( ! quantity obs]v$1 9 ! mo/ probable mann]4 ,9 meteorology ?ree or f\r t]ms are usually suffici5t = repres5t+ any p]iodic ph5om5on1 b ! calculation might be c>ri$ to any high] degree ( accuracy4 ,z ! details ( ! process h be5 describ$ by ,h]s*el 9 8 treatise on ,meteorology1#djc ,i ne$ n fur!r ent] into !m4 #djb 99,on ,tides & ,waves991 ,encyclopdia ,metropolitana1 p4 #cff994 #djc 99,encyclopdia ,britannica991 art4 99,meteorology994 ,repr9t1 #aeb-aef4 ,! read] might be tempt$ to ?9k t 9 ^! processes ( calculation we h an infallible me?od ( discov]+ inductive laws1 & t my previ\s /atem5ts 7,*ap4 ,,vii47 z to ! purely t5tative & inv]se "* ( ! inductive process are negativ$4 ,7 !re inde$ any g5]al me?od ( inf]r+ laws f facts x w\ld ov]turn my /atem5t1 b x mu/ be c>efully obs]v$ t ^! empirical =mul d n co9cide ) natural laws4 ,!y are only approximations to ! results ( natural laws f\nd$ ^u ! g5]al pr9ciples ( approximation4 ,x has already be5 po9t$ out t h[ev] complicat$ be ! nature ( a curve1 we may exam9e s small a portion ( x1 or we may exam9e x ) su* rude means ( measurem5t1 t its div]g5ce f an elliptic curve w n be app>5t4 ,z a /ill rud] approximation a portion ( a /raight l9e w always s]ve our purpose2 b if we ne$ high] precision a curve ( ! ?ird or f\r? degree w almo/ c]ta9ly be suffici5t4 ,n[ empirical =mul really repres5t ^! approximate curves1 b !y give u no in=mation z to ! precise nature ( ! curve itself to :i* we are approximat+4 ,we d n le>n :at function ! v>iant is ( ! v>iable1 b we obta9 ano!r function :i*1 )9 ! b\nds ( obs]vation1 gives ne>ly ! same values4 99,discov]y ( ,rational ,=mul499 ,let u n[ proce$ to consid] ! modes 9 :i* f num]ical results we c e/abli% ! actual relation betwe5 ! quantity ( ! cause & t ( ! effect4 ,:at we want is a 99rational99 =mula or function1 :i* w exhibit ! 99reason99 or exact nature & orig9 ( ! law 9 "q4 ,!re is no ^w m frequ5tly us$ by ma!maticians ?an ! ^w 99function991 & yet x is difficult to def9e its mean+ ) p]fect accuracy4 ,orig9ally x meant p]=mance or execution1 be+ equival5t to ! ,greek or 4 ,ma!maticians at fir/ us$ x to mean 99any p[] ( a quantity991 b aft]w>ds g5]alis$ x s z to include 8any quantity =m$ 9 any mann] :atsoev] f ano!r quantity40#djd ,any quantity1 !n1 :i* dep5ds ^u & v>ies ) ano!r quantity may be call$ a function ( x1 & ei!r may be consid]$ a function ( ! o!r4 #djd ,lagrange1 99,leons sur le ,calcul des ,fonctions991 #ahjf1 p4 #d4 ,giv5 ! quantities1 we want ! function ( :i* !y are ! values4 ,simple inspection ( ! numb]s _c z a g5]al rule disclose ! function4 ,9 an e>li] *apt] 7p4 #abd7 ,i put be=e ! read] c]ta9 numb]s1 & reque/$ him to po9t out ! law :i* !y obey1 & ! same "q w h to be ask$ 9 e case ( quantitative induction4 ,!re are p]haps ?ree me?ods1 m or less di/9ct1 by :i* we may hope to obta9 an answ]3 7#a7 ,by purely haphaz>d trial4 7#b7 ,by not+ ! g5]al "* ( ! v>iation ( ! quantities1 & try+ by pref]5ce functions :i* give a simil> =m ( v>iation4 7#c7 ,by d$uc+ f previ\s k ! =m ( ! function :i* is mo/ likely to suit4 ,hav+ num]ical results we are always at lib]ty to inv5t any k9d ( ma!matical =mula we l1 & !n try :e!r1 by ! suitable selection ( values = ! unkn[n con/ant quantities1 we c make x give ! requir$ results4 ,if ev] we fall ^u a =mula :i* does s1 to a fair degree ( approximation1 !re is a presumption 9 fav\r ( its be+ ! true function1 al?\gh !re is no c]ta9ty :atev] 9 ! matt]4 ,9 ?is way ,i discov]$ a simple ma!matical law :i* closely agre$ ) ! results ( my exp]im5ts on muscul> ex]tion4 ,?is law 0 aft]w>ds %[n by ,pr(essor ,haughton to be ! true rational law accord+ to 8 !ory ( muscul> action4#dje #dje ,haughton1 99,pr9ciples ( ,animal ,me*anics991 #ahgc1 pp4 #ddd-dej4 ,jevons1 99,nature991 #cj? ( ,june1 #ahgj1 vol4 ii4 p4 #aeh4 ,see also ! exp]im5ts ( ,pr(essor ,niph]1 ( ,wa%+ton ,univ]sity1 ,/4 ,l\is1 9 99,am]ican ,j\rnal ( ,sci5ce991 vol4 ix4 p4 #acj1 vol4 x4 p4 #a2 99,nature991 vol4 xi4 pp4 #bef1 #bgf4 ,b ! *ance ( succe$+ 9 ?is mann] is small4 ,! numb] ( possible functions is inf9ite1 & ev5 ! numb] ( comp>atively simple functions is s l>ge t ! probability ( fall+ ^u ! correct "o by m]e *ance is v slight4 ,ev5 :5 we obta9 ! law x is by a d$uctive process1 n by %[+ t ! numb]s give ! law1 b t ! law gives ! numb]s4 ,9 ! second way1 we may1 by a survey ( ! numb]s1 ga9 a g5]al notion ( ! k9d ( law !y are likely to obey1 & we may be mu* assi/$ 9 ?is process by draw+ !m out 9 ! =m ( a curve4 ,we c 9 ?is way asc]ta9 ) "s probability :e!r ! curve is likely to return into itself1 or :e!r x has inf9ite bran*es2 :e!r su* bran*es are asymptotic1 t is1 approa* inf9itely t[>ds /raight l9es2 :e!r x is log>i?mic 9 "*1 or trigonometric4 ,?is inde$ we c only d if we rememb] ! results ( previ\s inve/igations4 ,! process is /ill inv]sely d$uctive1 & consi/s 9 not+ :at laws give p>ticul> curves1 & !n inf]r+ inv]sely t su* curves belong to su* laws4 ,if we c 9 ?is way discov] ! class ( functions to :i* ! requir$ law belongs1 our *ances ( success are mu* increas$1 because our haphaz>d trials are n[ r$uc$ )9 a n>r[] sph]e4 ,b1 unless we h almo/ ! :ole curve be=e u1 ! id5tification ( its "* mu/ be a matt] ( great unc]ta9ty2 & if1 z 9 mo/ physical inve/igations1 we h a m]e fragm5t ( ! curve1 ! assi/ance giv5 w\ld be q illusory4 ,curves ( almo/ any "* c be made to approximate to ea* o!r = a limit$ ext5t1 s t x is only by a k9d ( 99div9ation99 t we fall ^u ! actual function1 unless we h !oretical k ( ! k9d ( function applicable to ! case4 ,:5 we h once obta9$ :at we believe to be ! correct =m ( function1 ! rema9d] ( ! "w is m]e ma!matical computation to be p]=m$ infallibly accord+ to fix$ rules1#djf :i* include ^? employ$ 9 ! det]m9ation ( empirical =mul 7p4 #dhg74 ,! function w involve two or ?ree or m unkn[n con/ants1 ! values ( :i* we ne$ to det]m9e by our exp]im5tal results4 ,select+ "s ( our results widely ap>t & ne>ly equidi/ant1 we =m by means ( !m z _m equations z !re are con/ant quantities to be det]m9$4 ,! solution ( ^! equations w !n give u ! con/ants requir$1 & hav+ n[ ! actual function we c try :e!r x gives ) suffici5t accuracy ! rema9d] ( our exp]im5tal results4 ,if n1 we mu/ ei!r make a new selection ( results to give a new set ( equations1 & ?us obta9 a new set ( values = ! con/ants1 or we mu/ ackn[l$ge t our =m ( function has be5 wrongly *os54 ,if x appe>s t ! =m ( function has be5 correctly asc]ta9$1 we may reg>d ! con/ants z only approximately accurate & may proce$ by ! ,me?od ( ,lea/ ,squ>es 7p4 #cic7 to det]m9e ! mo/ probable values z giv5 by ! :ole ( ! exp]im5tal results4 #djf ,jam91 99,c\rs de ,physique991 vol4 ii4 p4 #ej4 ,9 mo/ cases we %all f9d ourselves oblig$ to fall back ^u ! ?ird mode1 t is1 anticipation ( ! =m ( ! law to be expect$ on ! gr\nd ( previ\s k4 ,!ory & analogical reason+ mu/ be our guides4 ,! g5]al nature ( ! ph5om5on w (t5 indicate ! k9d ( law to be look$ =4 ,if "o =m ( en]gy or "o k9d ( sub/ance is be+ conv]t$ into ano!r1 we may expect ! law ( direct simple proportion4 ,9 "o di/9ct class ( cases ! effect already produc$ influ5ces ! am\nt ( ! ensu+ effect1 z = in/ance 9 ! cool+ ( a heat$ body1 :5 ! law w be ( an expon5tial =m4 ,:5 ! direction ( a =ce influ5ces its action1 trigonometrical functions ent]4 ,any influ5ce :i* spreads freely ?r\gh tridim5sional space w be subject to ! law ( ! inv]se squ>e ( ! di/ance4 ,f su* consid]ations we may sometimes arrive d$uctively & analogically at ! g5]al nature ( ! ma!matical law requir$4 99,! ,graphical ,me?od499 ,9 endeav\r+ to discov] ! ma!matical law obey$ by exp]im5tal results x is (t5 desirable to call 9 ! aid ( space-repres5tations4 ,e equation involv+ two v>iable quantities corresponds to "s k9d ( plane curve1 & e plane curve may be repres5t$ symbolically 9 an equation conta9+ two unkn[n quantities4 ,n[ 9 an exp]im5tal rese>* we obta9 a numb] ( values ( ! v>iant correspond+ to an equal numb] ( values ( ! v>iable2 b all ! numb]s are affect$ by m or less error1 & ! values ( ! v>iable w (t5 be irregul>ly dispos$4 ,ev5 if ! numb]s 7 absolutely correct & dispos$ at regul> int]vals1 !re is1 z we h se51 no direct mode ( discov]+ ! law1 b ! difficulty ( discov]y is mu* increas$ by ! unc]ta9ty & irregul>ity ( ! results4 ,"u su* circum/ances1 ! be/ mode ( proce$+ is to prep>e a pap] divid$ into equal rectangul> spaces1 a conv5i5t size = ! spaces be+ "o-t5? ( an in* squ>e4 ,! values ( ! v>iable be+ m>k$ (f on ! l[e/ horizontal l9e1 a po9t is m>k$ = ea* correspond+ value ( ! v>iant p]p5dicul>ly above t ( ! v>iable1 & at su* a height z corresponds to ! value ( ! v>iant4 ,! exact scale ( ! draw+ is n ( mu* importance1 b x may require to be adju/$ accord+ to circum/ances1 & diff]5t values mu/ (t5 be attribut$ to ! upright & horizontal divisions1 s z to make ! v>iations conspicu\s b n excessive4 ,if a curv$ l9e be drawn ?r\gh all ! po9ts or ends ( ! ord9ates1 x w probably exhibit irregul> inflections1 ow+ to ! errors :i* affect ! numb]s4 ,b1 :5 ! results are num]\s1 x becomes app>5t :i* results are m div]g5t ?an o!rs1 & guid$ by a s-call$ 99s5se ( cont9uity991 x is possible to trace a l9e among ! po9ts :i* w approximate to ! true law m ne>ly ?an ! po9ts !mselves4 ,! accompany+ figure suffici5tly expla9s itself4 ,illu/ration ,p]k9s employ$ ?is graphical me?od ) mu* c>e 9 exhibit+ ! results ( 8 exp]im5ts on ! compression ( wat]4#djg ,! num]ical results 7 m>k$ ^u a %eet ( pap] v exactly rul$ at int]vals ( "o-t5? ( an in*1 & ! orig9al m>ks 7 left 9 ord] t ! read] might judge ( ! correctness ( ! curve drawn1 or *oose ano!r = himself4 ,regnault c>ri$ ! me?od to p]fection by lay+ (f ! po9ts ) a screw divid+ eng9e2#djh & he !n =m$ a table ( results by draw+ a cont9u\s curve1 & measur+ its height = equidi/ant values ( ! v>iable4 ,n only does a curve drawn 9 ?is mann] enable u to inf] num]ical results m free f accid5tal errors ?an any ( ! numb]s obta9$ directly f exp]im5t1 b ! =m ( ! curve sometimes indicates ! class ( functions to :i* our results belong4 #djg 99,philosophical ,transactions991 #ahbf1 p4 #edd4 #djh ,jam91 99,c\rs de ,physique991 vol4 ii4 p4 #bd1 c4 ,engrav$ %eets ( pap] prep>$ = ! draw+ ( curves may be obta9$ f ,mr4 ,/an=d at ,*>+ ,cross1 ,messrs4 ,w4 & ,a4 ,k4 ,john/on1 ( ,london & ,ed9burgh1 ,wat]l[ & ,sons1 ,letts & ,co41 & probably o!r publi%]s4 ,:5 we d n require great accuracy1 pap] rul$ by ! common ma*9e-rul] into equal squ>es ( ab\t "o-fif? or "o-six? ( an in* squ>e w s]ve well en\gh4 ,i h met ) eng9e]s' & surveyors' memor&um books rul$ ) "o-twelf? in* squ>es4 ,:5 a numb] ( curves h to be drawn1 ,i h f\nd x be/ to rule a good %eet ( draw+ pap] ) l9es c>efully adju/$ at ! mo/ conv5i5t di/ances1 & !n to prick ! po9ts ( ! curve ?r\gh x ^u ano!r %eet fix$ und]nea?4 ,9 ?is way we obta9 an accurate curve ^u a blank %eet1 & ne$ only introduce su* division l9es z are requisite to ! und]/&+ ( ! curve4 ,9 "s cases our num]ical results w correspond1 n to ! height ( s+le ord9ates1 b to ! area ( ! curve betwe5 two ord9ates1 or ! av]age height ( ord9ates betwe5 c]ta9 limits4 ,if we measure1 = in/ance1 ! quantities ( heat absorb$ by wat] :5 rais$ 9 temp]ature f #j to #e1 f #e to #aj1 & s on1 ^! quantities w really be repres5t$ by 99areas99 ( ! curve d5ot+ ! specific heat ( wat]2 & s9ce ! specific heat v>ies cont9u\sly betwe5 e two po9ts ( temp]ature1 we %all n get ! correct curve by simply lay+ (f ! quantities ( heat at ! mean temp]atures1 namely #b-a_/b1 & #g-a_/b1 & s on4 ,"l ,rayleigh has %[n t if we h drawn su* an incorrect curve1 we c ) little tr\ble correct x by a simple geometrical process1 & obta9 to a close approximation ! true ord9ates in/ead ( ^? d5ot+ areas4#dji #dji ,j4 ,w4 ,/rutt1 99,on a correction sometimes requir$ 9 curves pr(ess+ to repres5t ! connexion betwe5 two physical magnitudes994 ,philosophical ,magaz9e1 #d? ,s]ies1 vol4 xlii4 p4 #dda4 99,int]polation & ,extrapolation499 ,:5 we h by exp]im5t obta9$ two or m num]ical results1 & endeav\r1 )\t fur!r exp]im5t1 to calculate int]m$iate results1 we are said to 99int]polate994 ,if we wi% to assign by reason+ results ly+ beyond ! limits ( exp]im5t1 we may be said1 us+ an expression ( ,sir ,george ,airy1 to 99extrapolate994 ,^! two op]ations are ! same 9 pr9ciple1 b diff] 9 practicability4 ,x is a matt] ( great sci5tific importance to appreh5d precisely h[ f> we c practise int]polation or extrapolation1 & on :at gr\nds we proce$4 ,9 ! fir/ place1 if ! int]polation is to be m ?an empirical1 we mu/ h n only ! exp]im5tal results1 b ! laws :i* !y obey--we mu/ 9 fact g ?r\gh ! complete process ( sci5tific inve/igation4 ,hav+ discov]$ ! laws ( nature apply+ to ! case1 & v]ifi$ !m by %[+ t !y agree ) ! exp]im5ts 9 "q1 we are !n 9 a position to anticipate ! results ( simil> exp]im5ts4 ,our k ev5 n[ is n c]ta91 because we _c completely prove ! tru? ( any assum$ law1 & we _c possibly exhau/ all ! circum/ances :i* may affect ! result4 ,at ! be/ !n our int]polations w p>take ( ! want ( c]ta9ty & precision atta*+ to all our k ( nature4 ,yet1 hav+ ! suppos$ laws1 our results w be z sure & accurate z any we c atta9 to4 ,b su* a complete proc$ure is m ?an we commonly mean by int]polation1 :i* usually d5otes "s me?od ( e/imat+ 9 a m]ely approximate mann] ! results :i* might h be5 expect$ indep5d5tly ( a !oretical inve/igation4 ,reg>d$ 9 ?is light1 int]polation is 9 reality an indet]m9ate problem4 ,f giv5 values ( a function x is impossible to det]m9e t function2 = we c inv5t an inf9ite numb] ( functions :i* w give ^? values if we are n re/rict$ by any conditions1 j z ?r\gh a giv5 s]ies ( po9ts we c draw an inf9ite numb] ( curves1 if we may div]ge betwe5 or beyond ! po9ts into b5ds & cusps z we ?9k fit4#daj ,9 int]polation we mu/ 9 fact be guid$ m or less by 99 priori99 consid]ations2 we mu/ "k1 = in/ance1 :e!r or n p]iodical fluctuations are to be expect$4 ,suppos+ t ! ph5om5on is non-p]iodic1 we proce$ to assume t ! function c be express$ 9 a limit$ s]ies ( ! p[]s ( ! v>iable4 ,! numb] ( p[]s :i* c be includ$ dep5ds ^u ! numb] ( exp]im5tal results available1 & mu/ be at lea/ "o less ?an ?is numb]4 ,by processes ( calculation1 :i* h be5 already allud$ to 9 ! section on empirical =mul1 we !n calculate ! coeffici5ts ( ! p[]s1 & obta9 an empirical =mula :i* w give ! requir$ int]m$iate results4 ,9 reality1 !n1 we return to ! me?ods treat$ "u ! head ( approximation & empirical =mul2 & int]polation1 z commonly und]/ood1 consi/s 9 assum+ t a curve ( simple "* is to pass ?r\gh c]ta9 det]m9$ po9ts4 ,if we h1 = in/ance1 two exp]im5tal results1 & only two1 we assume t ! curve is a /raight l9e2 = ! p>abolas :i* c be pass$ ?r\gh two po9ts are inf9itely v>i\s 9 magnitude1 & q indet]m9ate4 ,"o /raight l9e alone c pass ?r\gh two po9ts1 & x w h an equation ( ! =m1 99y99 99mx99 99n991 ! con/ant quantities ( :i* c be det]m9$ f two results4 ,?us1 if ! two values = 99x991 #g & #aa1 give ! values = 99y991 #ce & #ec1 ! solution ( two equations gives 99y99 #de 99x99 #ce z ! equation1 & = any o!r value ( 99x991 = in/ance #aj1 we get a value ( 99y991 t is #dhe4 ,:5 we take a mean value ( 99x991 namely #i1 ?is process yields a simple mean result1 namely #dd4 ,?ree exp]im5tal results be+ giv51 we assume t !y fall ^u a portion ( a p>abola & algebraic calculation gives ! position ( any int]m$iate po9t ^u ! p>abola4 ,conc]n+ ! process ( int]polation z practis$ 9 ! sci5ce ( meteorology ! read] w f9d "s directions 9 ! ,fr5* edition ( ,kamtz's ,meteorology4#daa #daj ,h]s*el3 ,lacroix' 99,diff]5tial ,calculus991 p4 #eea4 #daa 99,c\rs complet de ,mtorologie991 ,note ,a1 p4 #ddi4 ,:5 we h1 ei!r by direct exp]im5t or by ! use ( a curve1 a s]ies ( values ( ! v>iant = equidi/ant values ( ! v>iable1 x is in/ructive to take ! diff]5ces betwe5 ea* value ( ! v>iant & ! next1 & !n ! diff]5ces betwe5 ^? diff]5ces1 & s on4 ,if any s]ies ( diff]5ces approa*es closely to z]o x is an indication t ! numb]s may be correctly repres5t$ by a f9ite empirical =mula2 if ! 99n99? diff]5ces are z]o1 !n ! =mula w conta9 only ! fir/ 99n99 - #a p[]s ( ! v>iable4 ,inde$ we may sometimes obta9 by ! calculus ( diff]5ces a correct empirical =mula2 = if 99p99 be ! fir/ t]m ( ! s]ies ( values1 & 99p991 #b99p991 #c99p991 be ! fir/ numb] 9 ea* column ( diff]5ces1 !n ! 99m99? t]m ( ! s]ies ( values w be 99p99 99m9999p99 99m99799m99 - #a7_/bb99p99 99m99799m99 - #a7_/b799m99 - #b7_/cc99p99 c4 ,a closely equival5t b m practicable =mula = int]polation by diff]5ces1 z devis$ by ,lagrange1 w be f\nd 9 ,?omson & ,tait's 99,elem5ts ( ,natural ,philosophy991 p4 #aae4 ,if no column ( diff]5ces %[s any t5d5cy to become z]o ?r\gh\t1 x is an indication t ! law is ( a m complicat$1 = in/ance ( an expon5tial "*1 s t x requires diff]5t treatm5t4 ,dr4 ,j4 ,hopk9son has sugge/$ a me?od ( ari?metical int]polation1#dab :i* is int5d$ to avoid mu* t is arbitr>y 9 ! graphical me?od4 ,8 process w yield ! same results 9 all h&s4 #dab 99,on ! ,calculation ( ,empirical ,=mul4 ,! ,mess5g] ( ,ma!matics991 ,new ,s]ies1 ,no4 #ag1 #ahgb4 ,s f> z we c inf] ! results likely to be obta9$ by v>iations beyond ! limits ( exp]im5t1 we mu/ proce$ ^u ! same pr9ciples4 ,if possible we mu/ detect ! exact laws 9 action1 & !n tru/ to !m z a guide :5 we h no exp]i5ce4 ,if n1 an empirical =mula ( ! same "* z ^? employ$ 9 int]polation is our only res\rce4 ,b to ext5d our inf]5ce f> beyond ! limits ( exp]i5ce is exce$+ly unsafe4 ,our k is at ! be/ only approximate1 & takes no acc\nt ( small t5d5cies4 ,n[ x usually happ5s t t5d5cies small )9 our limits ( obs]vation become p]ceptible or great "u extreme circum/ances4 ,:5 ! v>iable 9 our empirical =mula is small1 we are ju/ifi$ 9 ov]look+ ! high] p[]s1 & tak+ only two or ?ree l[] p[]s4 ,b z ! v>iable increases1 ! high] p[]s ga9 9 importance1 & 9 "t yield ! pr9cipal "p ( ! value ( ! function4 ,?is is no m]e !oretical inf]5ce4 ,except+ ! few prim>y laws ( nature1 su* z ! law ( gravity1 ( ! cons]vation ( en]gy1 c41 !re is h>dly any natural law :i* we c tru/ 9 circum/ances widely diff]5t f ^? ) :i* we are practically acqua9t$4 ,f ! expansion or contraction1 fusion or vaporisation ( sub/ances by heat at ! surface ( ! e>?1 we c =m a mo/ imp]fect notion ( :at w\ld happ5 ne> ! c5tre ( ! e>?1 :]e ! pressure almo/ inf9itely exce$s any?+ possible 9 our exp]im5ts4 ,! physics ( ! e>? give u a feeble1 & probably a mislead+1 notion ( a body l ! sun1 9 :i* an inconceivably high temp]ature is unit$ ) an inconceivably high pressure4 ,if !re are 9 ! realms ( space nebul consi/+ ( inc&esc5t & unoxidis$ vap\rs ( metals & o!r elem5ts1 s highly heat$ p]haps t *emical composition is out ( ! "q1 we are h>dly able to treat !m z subjects ( sci5tific inf]5ce4 ,h5ce arises ! great importance ( exp]im5ts 9 :i* we inve/igate ! prop]ties ( sub/ances "u extreme circum/ances ( cold or heat1 d5sity or r>ity1 int5se electric excitation1 c4 ,?is insecurity 9 ext5d+ our inf]5ces arises f ! approximate "* ( our measurem5ts4 ,_h we ! p[] ( appreciat+ inf9itely small quantities1 we %\ld by ! pr9ciple ( cont9uity discov] "s trace ( e *ange :i* a sub/ance c\ld und]go "u unatta9able circum/ances4 ,by obs]v+1 = in/ance1 ! t5sion ( aque\s vap\r betwe5 #j & #ajj ,c41 we ought !oretically to be able to inf] its t5sion at e o!r temp]ature2 b ?is is out ( ! "q practically because we _c really asc]ta9 ! law precisely betwe5 ^? temp]atures4 ,_m in/ances might be giv5 to %[ t laws :i* appe> to repres5t correctly ! results ( exp]im5ts )9 c]ta9 limits altoge!r fail beyond ^? limits4 ,! exp]im5ts ( ,roscoe & ,dittm>1 on ! absorption ( gases 9 wat]#dac af=d int]e/+ illu/rations1 especially 9 ! case ( hydro*loric acid1 ! quantity ( :i* dissolv$ 9 wat] "u diff]5t pressures foll[s v closely a l9e> law ( v>iation1 f :i* h[ev] x div]ges widely at l[ pressures4#dad ,h]s*el1 hav+ d$uc$ f obs]vations ( ! d\ble /> ,virg9is an elliptic orbit = ! motion ( "o compon5t r\nd ! c5tre ( gravity ( bo?1 f\nd t = a "t ! motion ( ! /> agre$ v well ) ?is orbit4 ,nev]!less div]g5ce began to appe> & aft] a "t became s great t an entirely new orbit1 ( m ?an d\ble ! dim5sions ( ! old "o1 _h ultimately to be adopt$4#dae #dac ,watts' 99,diction>y ( ,*emi/ry991 vol4 ii4 p4 #gij4 #dad 99,qu>t]ly ,j\rnal ( ! ,*emical ,society991 vol4 viii4 p4 #ae4 #dae 99,results ( ,obs]vations at ! ,cape ( ,good ,hope991 p4 #bic4 99,illu/rations ( ,empirical ,quantitative ,laws499 ,al?\gh our object 9 quantitative inquiry is to discov] ! exact or rational =mul1 express+ ! laws :i* apply to ! subject1 x is in/ructive to obs]ve 9 h[ _m important bran*es ( sci5ce1 no precise laws h yet be5 detect$4 ,! t5sion ( aque\s vap\r at diff]5t temp]atures has be5 det]m9$ by a succession ( em95t exp]im5tali/s--,dalton1 ,kamtz1 ,dulong1 ,arago1 ,magnus1 & ,regnault--& by ! la/ m5tion$ ! measurem5ts 7 conduct$ ) extraord9>y c>e4 ,yet no inconte/able g5]al law has be5 e/abli%$4 ,sev]al functions h be5 propos$ to express ! ela/ic =ce ( ! vap\r z dep5d+ on ! temp]ature4 ,! fir/ =m is t ( ,"y1 namely ,f 799a99 99b t997m1 9 :i* 99a991 99b991 & 99m99 are unkn[n quantities to be det]m9$ by obs]vation4 ,ro*e propos$1 on !oretical gr\nds1 a complicat$ =mula ( an expon5tial =m1 & a ?ird =m ( function is t ( ,biot1#daf z foll[s--log ,f 99a99 99b99t 99c99t4 ,i m5tion ^! =mul1 because !y well illu/rate ! feeble p[]s ( empirical inquiry4 ,none ( ! =mul c be made to correspond closely ) exp]im5tal results1 & ! two la/ =ms correspond almo/ equally well4 ,!re is v little probability t ! real law has be5 rea*$1 & x is unlikely t x w be discov]$ except by d$uction f me*anical !ory4 #daf ,jam91 99,c\rs de ,physique991 vol4 ii4 p4 #ach4 ,mu* +5i\s lab\r has be5 sp5t ^u ! discov]y ( "s g5]al law ( atmosph]ic refraction4 ,ty*o ,brahe & ,kepl] comm5c$ ! inquiry3 ,cass9i fir/ =m$ a table ( refractions1 calculat$ on !oretical gr\nds3 ,newton ent]$ into "s pr(\nd inve/igations ^u ! subject3 ,brooke ,taylor1 ,b\gu]1 ,simpson1 ,bradley1 ,may]1 & ,kramp successively attack$ ! "q1 :i* is ( ! highe/ practical importance z reg>ds ! correction ( a/ronomical obs]vations4 ,laplace next lab\r$ on ! subject )\t exhau/+ x1 & ,br9kley & ,ivory h also treat$ x4 ,! true law is yet undiscov]$4 ,a closely connect$ problem1 t reg>d+ ! relation betwe5 ! pressure & elevation 9 diff]5t /rata ( ! atmosph]e1 has receiv$ ! att5tion ( a long succession ( physici/s & 0 mo/ c>efully inve/igat$ by ,laplace4 ,yet no inv>iable & g5]al law has be5 detect$4 ,! same may be said conc]n+ ! law ( human mortality2 abundant /ati/ics on ?is subject are available1 & _m hypo!ses m or less satisfactory h be5 put =w>d z to ! =m ( ! curve ( mortality1 b x seems to be impossible to discov] m ?an an approximate law4 ,x may p]haps be urg$ t 9 su* subjects no s+le inv>iable law c be expect$4 ,! atmosph]e may be divid$ into sev]al v>iable /rata :i* by _! unconnect$ *anges fru/rate ! exact calculations ( a/ronom]s4 ,human life may be subject at diff]5t ages to a succession ( diff]5t influ5ces incapable ( r$uction "u any "o law4 ,! results obs]v$ may 9 fact be aggregates ( an imm5se numb] ( sep>ate results ea* gov]n$ by its own sep>ate laws1 s t ! subjects may be complicat$ beyond ! possibility ( complete resolution by empirical me?ods4 ,?is is c]ta9ly true ( ! ma!matical functions :i* mu/ "s "t or o!r be introduc$ into ! sci5ce ( political economy4 99,simple ,proportional ,v>iation499 ,:5 we fir/ treat num]ical results 9 any novel k9d ( inve/igation1 our impression w probably be t "o quantity v>ies 9 99simple proportion99 to ano!r1 s z to obey ! law 99y99 99mx99 99n994 ,we mu/ le>n to di/+ui% c>efully betwe5 ! cases :]e ?is proportionality is really1 & :]e x is only app>5tly true4 ,9 consid]+ ! pr9ciples ( approximation we f\nd t a small portion ( any curve w appe> to be a /raight l9e4 ,:5 our modes ( measurem5t are comp>atively rude1 we mu/ expect to be unable to detect ! curvature4 ,kepl] made m]itori\s attempts to discov] ! law ( refraction1 & he approximat$ to x :5 he obs]v$ t ! angles ( incid5ce & refraction 99if small99 be> a con/ant ratio to ea* o!r4 ,angles :5 small are ne>ly z _! s9es1 s t he rea*$ an approximate result ( ! true law4 ,c>dan assum$1 probably z a m]e guess1 t ! =ce requir$ to su/a9 a body on an incl9$ plane 0 simply proportional to ! angle ( elevation ( ! plane4 ,?is is approximately ! case :5 ! angle is small1 b 9 reality ! law is mu* m complicat$1 ! p[] requir$ be+ proportional to ! s9e ( ! angle4 ,! e>ly !rmomet]-mak]s 7 unaw>e :e!r ! expansion ( m]cury 0 proportional or n to ! heat communicat$ to x1 & x is only 9 ! pres5t c5tury t we h le>nt x to be n s4 ,we n[ "k t ev5 gases obey ! law ( uni=m expansion by heat only 9 an approximate mann]4 ,until reason to ! contr>y is %[n1 we %\ld d well to look ^u e law ( simple proportion z only provisionally true4 ,nev]!less _m important laws ( nature are 9 ! =m ( simple proportions4 ,:]ev] a cause acts 9 indep5d5ce ( its previ\s effects1 we may expect ?is relation4 ,an accel]at+ =ce acts equally ^u a mov+ & a motionless body4 ,h5ce ! velocity produc$ is 9 simple proportion to ! =ce1 & to ! duration ( its uni=m action4 ,z gravitat+ bodies nev] int]f]e ) ea* o!r's gravity1 ?is =ce is 9 direct simple proportion to ! mass ( ea* ( ! attract+ bodies1 ! mass be+ measur$ by1 or proportional to in]tia4 ,simil>ly1 9 all cases ( 8direct unimp$$ action10 z ,h]s*el has rem>k$1#dag we may expect simple proportion to manife/ itself4 ,9 su* cases ! equation express+ ! relation may h ! simple =m 99y99 99mx994 #dag 99,prelim9>y ,disc\rse991 c41 p4 #aeb4 ,a simil> relation holds true :5 !re is conv]sion ( "o sub/ance or =m ( en]gy into ano!r4 ,! quantity ( a comp\nd is equal to ! quantity ( ! elem5ts :i* comb9e4 ,! heat produc$ 9 friction is exactly proportional to ! me*anical en]gy absorb$4 ,x 0 exp]im5tally prov$ by ,f>aday t 8! *emical p[] ( ! curr5t ( electricity is 9 direct proportion to ! quantity ( electricity :i* passes40 ,:5 an electric curr5t is produc$1 ! quantity ( electric en]gy is simply proportional to ! weight ( metal dissolv$4 ,if electricity is turn$ into heat1 !re is aga9 simple proportion4 ,:]ev]1 9 fact1 "o ?+ is b ano!r ?+ ) a new aspect1 we may expect to f9d ! law ( simple proportion4 ,b x is only 9 ! mo/ elem5t>y cases t ?is simple relation w hold true4 ,simple conditions d n1 g5]ally speak+1 produce simple results4 ,! planets move 9 approximate circles r\nd ! sun1 b ! app>5t motions1 z se5 f ! e>?1 are v v>i\s4 ,all ^? motions1 aga91 are summ$ up 9 ! law ( gravity1 ( no great complexity2 yet m5 nev] h be51 & nev] w be1 able to exhau/ ! complications ( action & reaction aris+ f t law1 ev5 among a small numb] ( planets4 ,we %\ld be on our gu>d aga9/ a t5d5cy to assume t ! connection ( cause & effect is "o ( direct proportion4 ,bacon rem9ds u ( ! woman 9 sop's fable1 :o expect$ t h] h51 ) a d\ble measure ( b>ley1 w\ld lay two eggs a day in/ead ( "o1 :]eas x grew fat1 & ceas$ to lay any eggs at all4 ,x is a wise maxim t ! half is (t5 bett] ?an ! :ole4 ,,*apt] ,,xxiii4 ,,! ,,use ,,( ,,hypo!sis4 ,if ! views upheld 9 ?is "w be correct1 all inductive inve/igation consi/s 9 ! m>riage ( hypo!sis & exp]im5t4 ,:5 facts are 9 our possession1 we frame an hypo!sis to expla9 _! relations1 & by ! success ( ?is explanation is ! value ( ! hypo!sis to be judg$4 ,9 ! inv5tion & treatm5t ( su* hypo!ses1 we mu/ avail ourselves ( ! :ole body ( sci5ce already accumulat$1 & :5 once we h obta9$ a probable hypo!sis1 we mu/ n re/ until we h v]ifi$ x by comp>ison ) new facts4 ,we mu/ endeav\r by d$uctive reason+ to anticipate su* ph5om5a1 especially ^? ( a s+ul> & exceptional nature1 z w\ld happ5 if ! hypo!sis be true4 ,out ( ! inf9ite numb] ( exp]im5ts :i* are possible1 !ory mu/ lead u to select ^? critical ones :i* are suitable = confirm+ or negativ+ our anticipations4 ,?is "w ( inductive inve/igation _c be guid$ by any sy/em ( precise & infallible rules1 l ^? ( d$uctive reason+4 ,!re is1 9 fact1 no?+ to :i* we c apply rules ( me?od1 because ! laws ( nature mu/ be 9 our possession be=e we c treat !m4 ,if !re 7 any rule ( inductive me?od1 x w\ld direct u to make an exhau/ive arrangem5t ( facts 9 all possible ord]s4 ,giv5 ! specim5s 9 a museum1 we might arrive at ! be/ classification by go+ sy/ematically ?r\gh all possible classifications1 &1 7 we end[$ ) inf9ite "t & pati5ce1 ?is w\ld be an effective me?od4 ,x is ! me?od by :i* ! fir/ simple /eps are tak5 9 an incipi5t bran* ( sci5ce4 ,be=e ! dignifi$ "n ( sci5ce is applicable1 "s co9cid5ces w =ce !mselves ^u ! att5tion4 ,be=e !re 0 a sci5ce ( meteorology obs]vant p]sons le>n$ to associate cle>ness ( ! atmosph]e ) com+ ra91 & a col\rless sunset ) f9e wea!r4 ,k ( ?is k9d is call$ 99empirical991 z seem+ to come directly f exp]i5ce2 & !re is a consid]able portion ( k :i* be>s ?is "*4 ,we may be oblig$ to tru/ to ! casual detection ( co9cid5ces 9 ^? bran*es ( k :]e we are depriv$ ( ! aid ( any guid+ notions2 b a little reflection w %[ ! utt] insuffici5cy ( haphaz>d exp]im5t1 :5 appli$ to inve/igations ( a complicat$ nature4 ,at ! be/1 x w be ! simple id5tity1 or p>tial id5tity1 ( classes1 z illu/rat$ 9 pages #abg or #acd1 :i* c be ?us detect$4 ,x 0 po9t$ out t1 ev5 :5 a law ( nature involves only two circum/ances1 & !re are "o hundr$ di/9ct circum/ances :i* may possibly be connect$1 !re w be no less ?an #d1iej pairs ( circum/ances betwe5 :i* co9cid5ce may exi/4 ,:5 a law involves ?ree or m circum/ances1 ! possible numb] ( relations becomes va/ly great]4 ,:5 consid]+ ! subject ( comb9ations & p]mutations1 x became app>5t t we c\ld nev] cope ) ! possible v>iety ( nature4 ,an exhau/ive exam9ation ( ! possible metallic alloys1 or *emical comp\nds1 0 f\nd to be out ( ! "q 7p4 #aia74 ,x is on su* consid]ations t we c expla9 ! v small additions made to our k by ! al*emi/s4 ,_m ( !m 7 m5 ( ! greate/ acut5ess1 & _! indefatigable lab\rs 7 pursu$ ?r\gh _m c5turies4 ,a few ?+s 7 discov]$ by !m1 b a true insight into nature1 n[ enables *emi/s to discov] m useful facts 9 a ye> ?an 7 yield$ by ! al*emi/s dur+ _m c5turies4 ,!re c be no d\bt t ,newton 0 an al*emi/1 & t he (t5 lab\r$ night & day at al*emical exp]im5ts4 ,b 9 try+ to discov] ! secret by :i* gross metals might be r5d]$ noble1 8 l(ty p[]s ( d$uctive inve/igation 7 :olly useless4 ,depriv$ ( all guid+ clues1 8 exp]im5ts 7 l ^? ( all ! al*emi/s1 purely t5tative & haphaz>d4 ,:ile 8 hypo!tical & d$uctive inve/igations h giv5 u ! true sy/em ( ! ,univ]se1 & op5$ ! way 9 almo/ all ! great bran*es ( natural philosophy1 ! :ole results ( 8 t5tative exp]im5ts are compreh5d$ 9 a few happy guesses1 giv5 9 8 celebrat$ 8,qu]ies40 ,ev5 :5 we are engag$ 9 app>5tly passive obs]vation ( a ph5om5on1 :i* we _c modify exp]im5tally1 x is advantage\s t our att5tion %\ld be guid$ by !oretical anticipations4 ,a ph5om5on :i* seems simple is1 9 all probability1 really complex1 & unless ! m9d is actively engag$ 9 look+ = p>ticul> details1 x is likely t ! critical circum/ances w be pass$ ov]4 ,bessel regrett$ t no di/9ct !ory ( ! con/itution ( comets _h guid$ 8 obs]vations ( ,halley's comet2#dah 9 attempt+ to v]ify or refute a hypo!sis1 n only w\ld !re be a *ance ( e/abli%+ a true !ory1 b if confut$1 ! confutation w\ld involve a /ore ( useful obs]vations4 #dah ,tyndall1 99,on ,comet>y ,!ory991 ,philosophical ,magaz9e1 ,april #ahfi4 #d? ,s]ies1 vol4 xxxvii4 p4 #bdc4 ,x w\ld be an int]e/+ "w1 b "o :i* ,i _c und]take1 to trace out ! gradual reaction :i* has tak5 place 9 rec5t times aga9/ ! purely empirical or ,baconian !ory ( induction4 ,francis ,bacon1 see+ ! futility ( ! s*ola/ic logic1 :i* _h long be5 pr$om9ant1 ass]t$ t ! accumulation ( facts & ! ord]ly ab/raction ( axioms1 or g5]al laws f !m1 con/itut$ ! true me?od ( induction4 ,ev5 ,bacon 0 n :olly unaw>e ( ! value ( hypo!tical anticipation4 ,9 "o or two places he incid5tally ackn[l$ges x1 z :5 he rem>ks t ! subtlety ( nature surpasses t ( reason1 add+ t 8axioms ab/ract$ f p>ticul> facts 9 a c>eful & ord]ly mann]1 readily sugge/ & m>k out new p>ticul>s40 ,nev]!less ,bacon's me?od1 z f> z we c ga!r ! mean+ ( ! ma9 portions ( 8 writ+s1 w\ld correspond to ! process ( empirically collect+ facts & exhau/ively classify+ !m1 to :i* ,i allud$4 ,! value ( ?is me?od may be e/imat$ hi/orically by ! fact t x has n be5 foll[$ by any ( ! great ma/]s ( sci5ce4 ,:e!r we look to ,galileo1 :o prec$$ ,bacon1 to ,gilb]t1 8 contempor>y1 or to ,newton & ,desc>tes1 ,leibnitz & ,huygh5s1 8 successors1 we f9d t discov]y 0 a*iev$ by ! opposite me?od to t advocat$ by ,bacon4 ,?r\gh\t ,newton's works1 z ,i %all %[1 we f9d d$uctive reason+ :olly pr$om9ant1 & exp]im5ts are employ$1 z !y %\ld be1 to confirm or refute hypo!tical anticipations ( nature4 ,9 my 8,elem5t>y ,lessons 9 ,logic0 7p4 #beh71 ,i /at$ my belief t !re 0 no k9d ( ref]5ce to ,bacon 9 ,newton's works4 ,i h s9ce f\nd t ,newton does once or twice employ ! expression 99exp]im5tum crucis99 9 8 8,opticks10 b ?is is ! only expression1 s f> z ,i am aw>e1 :i* c\ld indicate on ! "p ( ,newton direct or indirect acqua9tance ) ,bacon's writ+s4#dai #dai ,see 99,philosophical ,transactions991 abridg$ by ,l[?orp4 #d? edit4 vol4 i4 p4 #acj4 ,i f9d t op9ions simil> to ^? 9 ! text h be5 briefly express$ by ,de ,morgan 9 8 rem>kable preface to 99,f ,matt] to ,_s991 by ,c4,d41 pp4 xxi4 xxii4 ,o!r great physici/s ( ! same age 7 equally prone to ! use ( hypo!ses r ?an ! bl9d accumulation ( facts 9 ! ,baconian mann]4 ,hooke emphatically ass]ts 9 8 po/hum\s "w on ,philosophical ,me?od1 t ! fir/ requisite ( ! ,natural ,philosoph] is read9ess at guess+ ! solution ( ph5om5a & mak+ qu]ies4 8,he ought to be v well skill$ 9 ^? sev]al k9ds ( philosophy already kn[n1 to und]/& _! sev]al hypo!ses1 suppositions1 collections1 obs]vations1 c41 _! v>i\s ways ( ratioc9ations & proce$+s1 ! sev]al fail+s & defects1 bo? 9 _! way ( rais+ & 9 _! way ( manag+ _! sev]al !ories3 = by ?is means ! m9d w be some:at m ready at guess+ at ! solution ( _m ph5om5a almo/ at fir/ sight1 & !reby be mu* m prompt at mak+ qu]ies1 & at trac+ ! subtlety ( ,nature1 & 9 discov]+ & se>*+ into ! true reason ( ?+s40 ,we f9d ,horrocks1 aga91 ?an :om no "o 0 m fill$ ) ! sci5tific _s1 tell+ u h[ he tri$ !ory aft] !ory 9 ord] to discov] "o :i* 0 9 accordance ) ! motions ( ,m>s4#dbj ,huygh5s1 :o possess$ "o ( ! mo/ p]fect philosophical intellects1 foll[$ ! d$uctive process comb9$ ) cont9ual appeal to exp]im5t1 ) a skill closely analog\s to t ( ,newton4 ,z to ,desc>tes & ,leibnitz1 !y fell into excess 9 ! use ( hypo!sis1 s9ce !y sometimes adopt$ hypo!tical reason+ to ! exclusion ( exp]im5tal v]ification4 ,?r\gh\t ! eighte5? c5tury sci5ce 0 suppos$ to be advanc+ by ! pursuance ( ! ,baconian me?od1 b 9 reality hypo!tical inve/igation 0 ! ma9 in/rum5t ( progress4 ,x is only 9 ! pres5t c5tury t physici/s began to recognise ?is tru?4 ,s mu* opprobrium _h be5 atta*$ by ,bacon to ! use ( hypo!ses1 t we f9d ,"y speak+ ( !m 9 an apologetic tone4 8,! practice ( advanc+ g5]al pr9ciples & apply+ !m to p>ticul> in/ances is s f> f be+ fatal to tru? 9 all sci5ces1 t :5 ^? pr9ciples are advanc$ on suffici5t gr\nds1 x con/itutes ! ess5ce ( true philosophy20#dba & he quotes cases 9 :i* ,davy tru/$ to 8 !ories r ?an 8 exp]im5ts4 #dbj ,horrocks1 99,op]a ,po/huma99 7#afgc71 p4 #bgf4 #dba ,"y's 99,works991 vol4 i4 p4 #eic4 ,h]s*el1 :o 0 bo? a practical physici/ & an ab/ract logician1 ent]ta9$ ! deepe/ respect = ,bacon1 & made ! 8,novum ,organum0 z f> z possible ! basis ( 8 own admirable 99,disc\rse on ! ,/udy ( ,natural ,philosophy994 ,yet we f9d him 9 ,*apt] ,,vii4 recognis+ ! "p :i* ! =mation & v]ification ( !ories takes 9 ! high] & m g5]al inve/igations ( physical sci5ce4 ,j4 ,s4 ,mill c>ri$ on ! reaction by describ+ ! ,d$uctive ,me?od 9 :i* ratioc9ation1 t is d$uctive reason+1 is employ$ = ! discov]y ( new opportunities ( te/+ & v]ify+ an hypo!sis4 ,nev]!less ?r\gh\t ! o!r p>ts ( 8 sy/em he inveigh$ aga9/ ! value ( ! d$uctive process1 & ev5 ass]t$ t empirical inf]5ce f p>ticul>s to p>ticul>s is ! true type ( reason+4 ,! irony ( fate w probably decide t ! mo/ orig9al & valuable "p ( ,mill's ,sy/em ( ,logic is irreconcilable ) ^? views ( ! syllogism & ( ! nature ( inf]5ce :i* occupy ! ma9 "p ( ! treatise1 & are said to h effect$ a revolution 9 logical sci5ce4 ,mill w\ld h be5 sav$ f mu* confusion ( ?\ght _h he n fail$ to obs]ve t ! inv]se use ( d$uction con/itutes induction4 ,9 lat] ye>s ,pr(essor ,huxley has /rongly insi/$ ^u ! value ( hypo!sis4 ,:5 he advocates ! use ( 8work+ hypo!ses0 he means no d\bt t any hypo!sis is bett] t none1 & t we _c avoid be+ guid$ 9 our obs]vations by "s hypo!sis or o!r4 ,pr(essor ,tyndall's views z to ! use ( ! ,imag9ation 9 ! pursuit ( ,sci5ce put ! same tru? 9 ano!r light4 ,x ought to be po9t$ out t ,neil 9 8 99,art ( ,reason+991 a popul> b able exposition ( ! pr9ciples ( ,logic1 publi%$ 9 #ahec1 fully recognises 9 ,*apt] ,,xi4 ! value & position ( hypo!sis 9 ! discov]y ( tru?4 ,he endeav\rs to %[1 too 7p4 #aji71 t ,francis ,bacon did n object to ! use ( hypo!sis4 ,! true c\rse ( inductive proc$ure is t :i* has yield$ all ! m l(ty results ( sci5ce4 ,x consi/s 9 99,anticipat+ ,nature991 9 ! s5se ( =m+ hypo!ses z to ! laws :i* are probably 9 op]ation2 & !n obs]v+ :e!r ! comb9ations ( ph5om5a are su* z w\ld foll[ f ! laws suppos$4 ,! inve/igator beg9s ) facts & ends ) !m4 ,he uses facts to sugge/ probable hypo!ses2 d$uc+ o!r facts :i* w\ld happ5 if a p>ticul> hypo!sis is true1 he proce$s to te/ ! tru? ( 8 notion by fre% obs]vations4 ,if any result prove diff]5t f :at he expects1 x leads him to modify or to ab&on 8 hypo!sis2 b e new fact may give "s new sugge/ion z to ! laws 9 action4 ,ev5 if ! result 9 any case agrees ) 8 anticipations1 he does n reg>d x z f9ally confirmatory ( 8 !ory1 b proce$s to te/ ! tru? ( ! !ory by new d$uctions & new trials4 ,9 su* a process ! inve/igator is assi/$ by ! :ole body ( sci5ce previ\sly accumulat$4 ,he may employ analogy1 z ,i %all po9t out1 to guide him 9 ! *oice ( hypo!ses4 ,! manifold connections betwe5 "o sci5ce & ano!r give him clues to ! k9d ( laws to be expect$1 & out ( ! inf9ite numb] ( possible hypo!ses he selects ^? :i* are1 z f> z c be =ese5 at ! mom5t1 mo/ probable4 ,ea* exp]im5t1 !re=e1 :i* he p]=ms is t mo/ likely to ?r[ light ^u 8 subject1 & ev5 if x fru/rate 8 fir/ views1 x t5ds to put him 9 possession ( ! correct clue4 99,requisites ( a good ,hypo!sis499 ,!re is little difficulty 9 po9t+ out to :at condition an hypo!sis mu/ con=m 9 ord] to be accept$ z probable & valid4 ,t condition1 z ,i conceive1 is ! s+le "o ( enabl+ u to inf] ! exi/5ce ( ph5om5a :i* occur 9 our exp]i5ce4 99,agreem5t ) fact is ! sole & suffici5t te/ ( a true hypo!sis499 ,hobbes has nam$ two conditions :i* he consid]s requisite 9 an hypo!sis1 namely 7#a7 ,t x %\ld be conceivable & n absurd2 7#b7 ,t x %\ld all[ ( ph5om5a be+ necess>ily inf]r$4 ,boyle1 9 notic+ ,hobbes' views1 propos$ to add a ?ird condition1 to ! effect t ! hypo!sis %\ld n be inconsi/5t ) any o!r tru? on ph5om5on ( nature4#dbb ,i ?9k t ( ^! ?ree conditions1 ! fir/ _c be accept$1 unless by 99inconceivable99 & 99absurd99 we mean self-contradictory or inconsi/5t ) ! laws ( ?\ght & nature4 ,i %all h to po9t out t "s satisfactory !ories involve suppositions :i* are :olly 99inconceivable99 9 a c]ta9 s5se ( ! ^w1 because ! m9d _c suffici5tly ext5d its ideas to frame a notion ( ! actions suppos$ to take place4 ,t ! =ce ( gravity %\ld act in/antane\sly betwe5 ! mo/ di/ant p>ts ( ! planet>y sy/em1 or t a ray ( violet light %\ld consi/ ( ab\t #gjj billions ( vibrations 9 a second1 are /atem5ts ( an inconceivable & absurd "* 9 "o s5se2 b !y are s f> f be+ oppos$ to fact t we _c on any o!r suppositions acc\nt = ph5om5a obs]v$4 ,b if an hypo!sis involve self-contradiction1 or is inconsi/5t ) kn[n laws ( nature1 x is self-condemn$4 ,we _c ev5 apply d$uctive reason+ to a self-contradictory notion2 & be+ oppos$ to ! mo/ g5]al & c]ta9 laws kn[n to u1 ! prim>y laws ( ?\ght1 x !reby conspicu\sly fails to agree ) facts4 ,s9ce nature1 aga91 is nev] self-contradictory1 we _c at ! same "t accept two !ories :i* lead to contradictory results4 ,if ! "o agrees ) nature1 ! o!r _c4 ,h5ce if !re be a law :i* we believe ) high probability to be v]ifi$ by obs]vation1 we mu/ n frame an hypo!sis 9 conflict ) x1 o!rwise ! hypo!sis w necess>ily be 9 disagreem5t ) obs]vation4 ,s9ce no law or hypo!sis is prov$1 inde$1 ) absolute c]ta9ty1 !re is always a *ance1 h[ev] slight1 t ! new hypo!sis may displace ! old "o2 b ! great] ! probability :i* we assign to t old hypo!sis1 ! great] mu/ be ! evid5ce requir$ 9 fav\r ( ! new & conflict+ "o4 #dbb ,boyle's 99,physical ,exam5991 p4 #hd4 ,i ass]t1 !n1 t !re is b "o te/ ( a good hypo!sis1 namely1 99its con=mity ) obs]v$ facts992 b ?is condition may be said to involve ?ree con/itu5t conditions1 ne>ly equival5t to ^? sugge/$ by ,hobbes & ,boyle1 namely3-- 7#a7 ,t x all[ ( ! application ( d$uctive reason+ & ! inf]5ce ( consequ5ces capable ( comp>ison ) ! results ( obs]vation4 7#b7 ,t x d n conflict ) any laws ( nature1 or ( m9d1 :i* we hold to be true4 7#c7 ,t ! consequ5ces inf]r$ d agree ) facts ( obs]vation4 99,possibility ( ,d$uctive ,reason+499 ,z ! tru? ( an hypo!sis is to be prov$ by its con=mity ) fact1 ! fir/ condition is t we be able to apply me?ods ( d$uctive reason+1 & le>n :at %\ld happ5 accord+ to su* an hypo!sis4 ,ev5 if we c\ld imag9e an object act+ accord+ to laws hi!rto :olly unkn[n x w\ld be useless to d s1 because we c\ld nev] decide :e!r x exi/$ or n4 ,we c only inf] :at w\ld happ5 "u suppos$ conditions by apply+ ! k ( nature we possess to ^? conditions4 ,h5ce1 z ,boscovi* truly said1 we are to und]/& by hypo!ses 8n fictions altoge!r arbitr>y1 b suppositions con=mable to exp]i5ce or analogy40 ,x foll[s t e hypo!sis wor?y ( consid]ation mu/ sugge/ "s lik5ess1 analogy1 or common law1 act+ 9 two or m ?+s4 ,if1 9 ord] to expla9 c]ta9 facts1 99a991 99a991 99a991 c41 we inv5t a cause ,a1 !n we mu/ 9 "s degree appeal to exp]i5ce z to ! mode 9 :i* ,a w act4 ,z ! laws ( nature are n kn[n to ! m9d intuitively1 we mu/ po9t out "s o!r cause1 ,b1 :i* supplies ! requisite notions1 & all we d is to inv5t a f\r? t]m to an analogy4 ,z ,b is to its effects 99b991 99b991 99b991 c41 s is ,a to its effects 99a991 99a991 99a991 c4 ,:5 we attempt to expla9 ! passage ( light & heat radiations ?r\gh space unoccupi$ by matt]1 we imag9e ! exi/5ce ( ! s-call$ 99e!r994 ,b if ?is e!r 7 :olly diff]5t f any?+ else kn[n to u1 we %\ld 9 va9 try to reason ab\t x4 ,we mu/ apply to x at lea/ ! laws ( motion1 t is we mu/ s f> lik5 x to matt]4 ,& z1 :5 apply+ ^? laws to ! ela/ic m$ium air1 we are able to inf] ! ph5om5a ( s\nd1 s by argu+ 9 a simil> mann] conc]n+ e!r we are able to inf] ! exi/5ce ( light ph5om5a correspond+ to :at d occur4 ,all t we d is to take an ela/ic sub/ance1 increase its ela/icity imm5sely1 & d5ude x ( gravity & "s o!r prop]ties ( matt]1 b we mu/ reta9 suffici5t lik5ess to matt] to all[ ( d$uctive calculations4 ,! =ce ( gravity is 9 "s respects an incompreh5sible exi/5ce1 b 9 o!r respects entirely con=mable to exp]i5ce4 ,we obs]ve t ! =ce is proportional to mass1 & t x acts 9 entire indep5d5ce ( o!r matt] :i* may be pres5t or int]v5+4 ,! law ( ! decrease ( int5sity1 z ! squ>e ( ! di/ance increases1 is obs]v$ to hold true ( light1 s\nd1 & o!r influ5ces emanat+ f a po9t1 & spread+ uni=mly ?r\gh space4 ,! law is d\btless connect$ ) ! prop]ties ( space1 & is s f> 9 agreem5t ) our necess>y ideas4 ,x may be said1 h[ev]1 t no hypo!sis c be s mu* z fram$ 9 ! m9d unless x be m or less con=mable to exp]i5ce4 ,z ! mat]ial ( our ideas is d]iv$ f s5sation we _c figure to ourselves any ag5t1 b z end[$ ) "s ( ! prop]ties ( matt]4 ,all t ! m9d c d 9 ! creation ( new exi/5ces is to alt] comb9ations1 or ! int5sity ( s5su\s prop]ties4 ,! ph5om5on ( motion is famili> to sight & t\*1 & diff]5t degrees ( rapidity are also famili>2 we c pass beyond ! limits ( s5se1 & imag9e ! exi/5ce ( rapid motion1 su* z our s5ses c\ld n obs]ve4 ,we "k :at is ela/icity1 & we c !re=e 9 a way figure to ourselves ela/icity a ?\s& or a million times great] ?an any :i* is s5su\sly kn[n to u4 ,! waves ( ! ocean are _m times high] ?an our own bodies2 o!r waves1 are _m times less2 cont9ue ! proportion1 & we ultimately arrive at waves z small z ^? ( light4 ,?us x is t ! p[]s ( m9d enable u f a s5su\s basis to reason conc]n+ ag5ts & ph5om5a diff]5t 9 an unlimit$ degree4 ,if no hypo!sis !n c be absolutely oppos$ to s5se1 accordance ) exp]i5ce mu/ always be a "q ( degree4 ,9 ord] t an hypo!sis may all[ ( satisfactory comp>ison ) exp]i5ce1 x mu/ possess def9it5ess & 9 _m cases ma!matical exactness all[+ ( ! precise calculation ( results4 ,we mu/ be able to asc]ta9 :e!r x does or does n agree ) facts4 ,! !ory ( vortices is an in/ance to ! contr>y1 = x did n pres5t any mode ( calculat+ ! exact relations betwe5 ! di/ances & p]iods ( ! planets & satellites2 x c\ld n1 !re=e1 und]go t rigor\s te/+ to :i* ,newton scrupul\sly submitt$ 8 !ory ( gravity be=e its promulgation4 ,vagu5ess & incapability ( precise pro( or dispro( (t5 enable a false !ory to live2 b ) ^? :o love tru?1 vagu5ess %\ld excite suspicion4 ,! uphold]s ( ! anci5t doctr9e ( ,nature's abhorr5ce ( a vacuum1 _h be5 unable to anticipate ! important fact t wat] w\ld n rise m ?an #cc feet 9 a common suction pump4 ,nor :5 ! fact 0 po9t$ out c\ld !y expla9 x1 except by introduc+ a special alt]ation ( ! !ory to ! effect t ,nature's abhorr5ce ( a vacuum 0 limit$ to #cc feet4 99,consi/5cy ) ! ,laws ( ,nature499 ,9 ! second place an hypo!sis mu/ n be contradictory to :at we believe to be true conc]n+ ,nature4 ,x mu/ n involve self-inconsi/5cy :i* is oppos$ to ! highe/ & simple/ laws1 namely1 ^? ( ,logic4 ,nei!r ought x to be irreconcilable ) ! simple laws ( motion1 ( gravity1 ( ! cons]vation ( en]gy1 nor any p>ts ( physical sci5ce :i* we consid] to be e/abli%$ beyond reasonable d\bt4 ,n t we are absolutely =bidd5 to ent]ta9 su* an hypo!sis1 b if we d s we mu/ be prep>$ to disprove "s ( ! be/ demon/rat$ tru?s 9 ! possession ( mank9d4 ,! fact t conflict exi/s means t ! consequ5ces ( ! !ory are n v]ifi$ if previ\s discov]ies are correct1 & we mu/ !re=e %[ t previ\s discov]ies are incorrect be=e we c v]ify our !ory4 ,an hypo!sis w be exce$+ly improbable1 n to say absurd1 if x supposes a sub/ance to act 9 a mann] unkn[n 9 o!r cases2 = x !n fails to be v]ifi$ 9 our k ( t sub/ance4 ,sev]al physici/s1 especially ,eul] & ,grove1 h suppos$ t we might disp5se ) an e!real basis ( light1 & inf] f ! int]/ell> passage ( rays t !re 0 a k9d ( r>e gas occupy+ space4 ,b if s1 t gas mu/ be excessively r>e1 z we may inf] f ! app>5t abs5ce ( an atmosph]e ar\nd ! moon1 & f o!r facts kn[n to u conc]n+ gases & ! atmosph]e2 yet x mu/ possess an ela/ic =ce at lea/ a billion times z great z atmosph]ic air at ! e>?'s surface1 9 ord] to acc\nt = ! extreme rapidity ( light rays4 ,su* an hypo!sis !n is inconsi/5t ) our k conc]n+ gases4 ,provid$ t !re be no cle> & absolute conflict ) kn[n laws ( nature1 !re is no hypo!sis s improbable or app>5tly inconceivable t x may n be r5d]$ probable1 or ev5 approximately c]ta91 by a suffici5t numb] ( concordances4 ,9 fact ! two be/ f\nd$ & mo/ successful !ories 9 physical sci5ce involve ! mo/ absurd suppositions4 ,gravity is a =ce :i* appe>s to act betwe5 bodies ?r\gh vacu\s space2 x is 9 positive contradiction to ! old dictum t no?+ c act b ?r\gh "s m$ium4 ,x is ev5 m puzzl+ t ! =ce acts 9 p]fect indiff]5ce to int]v5+ ob/acles4 ,light 9 spite ( its extreme velocity %[s mu* respect to matt]1 = x is almo/ in/antane\sly /opp$ by opaque sub/ances1 & to a consid]able ext5t absorb$ & deflect$ by transp>5t ones4 ,b to gravity all m$ia are1 z x 71 absolutely transp>5t1 nay non-exi/5t2 & two p>ticles at opposite po9ts ( ! e>? affect ea* o!r exactly z if ! globe 7 n betwe54 ,! action is1 s f> z we c obs]ve1 in/antane\s1 s t e p>ticle ( ! univ]se is at e mom5t 9 sep>ate cognisance1 z x 71 ( ! relative position ( e o!r p>ticle ?r\gh\t ! univ]se at t same mom5t ( "t4 ,comp>$ ) su* incompreh5sible conditions1 ! !ory ( vortices deals ) commonplace realities4 ,newton's celebrat$ say+ 99hypo!ses non f+o991 be>s ! appe>ance ( irony2 & x 0 n )\t app>5t gr\nds t ,leibnitz & ! cont95tal philosoph]s *>g$ ,newton ) re-introduc+ occult p[]s & qualities4 ,! undulatory !ory ( light pres5ts almo/ equal difficulties ( conception4 ,we are ask$ by physical philosoph]s to give up our prepossessions1 & to believe t int]/ell> space :i* seems empty is n empty at all1 b fill$ ) 99some?+99 imm5sely m solid & ela/ic ?an /eel4 ,z ,"y himself rem>k$1#dbc 8! lum9if]\s e!r1 p]vad+ all space1 & p5etrat+ almo/ all sub/ances1 is n only highly ela/ic1 b absolutely solid6660 ,h]s*el calculat$ ! =ce :i* may be suppos$1 accord+ to ! undulatory !ory ( light1 to be con/antly ex]t$ at ea* po9t 9 space1 & f9ds x to be #a1adh1jjj1jjj1jjj times ! ela/ic =ce ( ord9>y air at ! e>?'s surface1 s t ! pressure ( e!r p] squ>e in* mu/ be ab\t sev5te5 billions ( p\nds4#dbd ,yet we live & move )\t appreciable resi/ance ?r\gh ?is m$ium1 imm5sely h>d] & m ela/ic ?an adamant4 ,all our ord9>y notions mu/ be laid aside 9 contemplat+ su* an hypo!sis2 yet x is no m ?an ! obs]v$ ph5om5a ( light & heat =ce u to accept4 ,we _c d5y ev5 ! /range sugge/ion ( ,"y1 t !re may be indep5d5t worlds1 "s possibly exi/+ 9 diff]5t p>ts ( space1 b o!rs p]haps p]vad+ ea* o!r unse5 & unkn[n 9 ! same space4#dbe ,= if we are b\nd to admit ! conception ( ?is adamant9e firmam5t1 x is equally easy to admit a plurality ( su*4 ,we see1 !n1 t m]e difficulties ( conception mu/ n discr$it a !ory :i* o!rwise agrees ) facts1 & we mu/ only reject hypo!ses :i* are inconceivable 9 ! s5se ( break+ di/9ctly ! prim>y laws ( ?\ght & nature4 #dbc ,"y's 99,works991 vol4 i4 p4 #dae4 #dbd 99,famili> ,lectures on ,sci5tific ,subjects991 p4 #bhb4 #dbe ,"y's 99,works991 vol4 i4 p4 #dag4 99,con=mity ) ,facts499 ,be=e we accept a new hypo!sis x mu/ be %[n to agree n only ) ! previ\sly kn[n laws ( nature1 b also ) ! p>ticul> facts :i* x is fram$ to expla94 ,assum+ t ^! facts are prop]ly e/abli%$1 x mu/ agree ) all ( !m4 ,a s+le absolute conflict betwe5 fact & hypo!sis1 is fatal to ! hypo!sis2 99falsa 9 uno1 falsa 9 omnibus994 ,seldom1 inde$1 %all we h a !ory free f difficulties & app>5t inconsi/5cy ) facts4 ,?\gh "o real inconsi/5cy w\ld ov]turn ! mo/ plausible !ory1 yet !re is usually "s probability t ! fact may be mis9t]pret$1 or t "s suppos$ law ( nature1 on :i* we are rely+1 may n be true4 ,x may be expect$1 moreov]1 t a good hypo!sis1 besides agree+ ) facts already notic$1 w furni% u ) di/9ct cr$5tials by enabl+ u to anticipate d$uctively s]ies ( facts :i* are n already connect$ & acc\nt$ = by any equally probable hypo!sis4 ,we _c lay d[n any precise rule z to ! numb] ( accordances :i* c e/abli% ! tru? ( an hypo!sis1 because ! accordances w v>y mu* 9 value4 ,:ile1 on ! "o h&1 no f9ite numb] ( accordances w give entire c]ta9ty1 ! probability ( ! hypo!sis w increase v rapidly ) ! numb] ( accordances4 ,almo/ e problem 9 sci5ce ?us takes ! =m ( a balance ( probabilities4 ,x is only :5 difficulty aft] difficulty has be5 successfully expla9$ away1 & decisive 99exp]im5ta crucis99 h1 "t aft] "t1 result$ 9 fav\r ( our !ory1 t we c v5ture to ass]t ! falsity ( all objections4 ,! sole real te/ ( an hypo!sis is its accordance ) fact4 ,desc>tes' celebrat$ sy/em ( vortices is explod$1 n because x 0 intr9sically absurd & inconceivable1 b because x c\ld n give results 9 accordance ) ! actual motions ( ! heav5ly bodies4 ,! difficulties ( conception involv$ 9 ! app>atus ( vortices1 are *ild's play comp>$ ) ^? ( gravitation & ! undulatory !ory already describ$4 ,vortices are on ! :ole plausible suppositions2 = planets & satellites be> at fir/ sight mu* resemblance to objects c>ri$ r\nd 9 :irlpools1 an analogy :i* d\btless sugge/$ ! !ory4 ,! failure 0 9 ! fir/ & ?ird requisites2 =1 z already rem>k$1 ! !ory did n all[ ( precise calculation ( planet>y motions1 & 0 ?us incapable ( rigor\s v]ification4 ,b s f> z we c in/itute a comp>ison1 facts are entirely aga9/ ! vortices4 ,newton did n ridicule ! !ory z absurd1 b %[$#dbf t x 0 8press$ ) _m difficulties40 ,he c>efully po9t$ out t ! ,c>tesian !ory 0 inconsi/5t ) ! laws ( ,kepl]1 & w\ld repres5t ! planets z mov+ m rapidly at _! aphelia ?an at _! p]ihelia4#dbg ,! rotatory motion ( ! sun & planets on _! own axes is 9 /rik+ conflict ) ! revolutions ( ! satellites c>ri$ r\nd !m2 & comets1 ! mo/ flimsy ( bodies1 calmly pursue _! c\rses 9 elliptic pa?s1 irrespective ( ! vortices :i* !y pass ?r\gh4 ,we may n[ also po9t to ! int]lac+ orbits ( ! m9or planets z a new & insup]able difficulty 9 ! way ( ! ,c>tesian ideas4 #dbf 99,pr9cipia991 bk4 iii4 ,prop4 #dc4 ,g5]al ,s*olium4 #dbg ,ibid4 bk4 ii4 ,sect4 ix4 ,prop4 #ec4 ,newton1 ?\gh he e/abli%$ ! be/ ( !ories1 0 also capable ( propos+ "o ( ! wor/2 & if we want an in/ance ( a !ory decisively contradict$ by facts1 we h only to turn to 8 views conc]n+ ! orig9 ( natural col\rs4 ,hav+ analys$1 ) incomp>able skill1 ! orig9 ( ! col\rs ( ?9 plates1 he sugge/s t ! col\rs ( all bodies are det]m9$ 9 l mann] by ! size ( _! ultimate p>ticles4 ,a ?9 plate ( a def9ite ?ickness w reflect a def9ite col\r2 h5ce1 if brok5 up into fragm5ts x w =m a p[d] ( ! same col\r4 ,b1 if ?is be a suffici5t explanation ( col\r$ sub/ances1 !n e col\r$ fluid ought to reflect ! complem5t>y col\r ( t :i* x transmits4 ,col\rless transp>5cy arises1 accord+ to ,newton1 f p>ticles be+ too m9ute to reflect light2 b if s1 e black sub/ance %\ld be transp>5t4 ,newton himself s acutely felt ?is la/ difficulty z to sugge/ t true blackness is due to "s int]nal refraction ( ! rays to & fro1 & an ultimate /ifl+ ( !m1 :i* he did n attempt to expla9 fur!r4 ,unless "s o!r process comes into op]ation1 nei!r refraction nor reflection1 h[ev] (t5 repeat$1 w de/roy ! en]gy ( light4 ,! !ory !re=e gives no acc\nt1 z ,brew/] %[s1 ( #bd p>ts out ( #be ( ! light :i* falls ^u a black coal1 & ! rema9+ "p :i* is reflect$ f ! lu/r\s surface is equally inconsi/5t ) ! !ory1 because f9e coal-du/ is almo/ entirely devoid ( reflective p[]4#dbh ,x is n[ g5]ally believ$ t ! col\rs ( natural bodies are due to ! unequal absorption ( rays ( light ( diff]5t refrangibility4 #dbh ,brew/]'s 99,life ( ,newton991 #a/ edit4 *ap4 vii4 99,exp]im5tum ,crucis499 ,z we d$uce m & m conclusions f a !ory1 & f9d !m v]ifi$ by trial1 ! probability ( ! !ory increases 9 a rapid mann]2 b we nev] escape ! risk ( error altoge!r4 ,absolute c]ta9ty is beyond ! p[]s ( inductive inve/igation1 & ! mo/ plausible supposition may ultimately be prov$ false4 ,su* is ! gr\ndwork ( simil>ity 9 nature1 t two v diff]5t conditions may (t5 give closely simil> results4 ,we sometimes f9d ourselves !re=e 9 possession ( two or m hypo!ses :i* bo? agree ) s _m exp]im5tal facts z to h great appe>ance ( tru?4 ,"u su* circum/ances we h ne$ ( "s new exp]im5t1 :i* %all give results agree+ ) "o hypo!sis b n ) ! o!r4 ,any su* exp]im5t :i* decides betwe5 two rival !ories may be call$ an 99,exp]im5tum ,crucis991 an ,exp]im5t ( ! ,f+] ,po/4 ,:5ev] ! m9d /&s1 z x 71 at cross-roads & kn[s n :i* way to select1 x ne$s "s decisive guide1 & ,bacon !re=e assign$ great importance & au?ority to in/ances :i* s]ve 9 ?is capacity4 ,! "n giv5 by ,bacon has become famili>2 x is almo/ ! only "o ( ,bacon's figurative expressions :i* has pass$ into common use4 ,ev5 ,newton1 z ,i h m5tion$ 7p4 #ejg71 us$ ! "n4 ,i d n ?9k1 inde$1 t ! common use ( ! ^w at all agrees ) t int5d$ by ,bacon4 ,h]s*el says t 8we make an exp]im5t ( ! crucial k9d :5 we =m comb9ations1 & put 9 action causes f :i* "s p>ticul> "o %all be delib]ately exclud$1 & "s o!r purposely admitt$40#dbi ,?is1 h[ev]1 seems to be ! description ( any special exp]im5t n made at haphaz>d4 ,pascal's exp]im5t ( caus+ a b>omet] to be c>ri$ to ! top ( ! ,puy-de-,dme has (t5 be5 consid]$ z a p]fect 99exp]im5tum crucis991 if n ! fir/ di/9ct "o on record2#dcj b if s1 we mu/ dignify ! doctr9e ( ,nature's abhorr5ce ( a vacuum ) ! position ( a rival !ory4 ,a crucial exp]im5t mu/ n simply confirm "o !ory1 b mu/ negative ano!r2 x mu/ decide a m9d :i* is 9 equilibrium1 z ,bacon says1#dca betwe5 two equally plausible views4 8,:5 9 se>* ( any nature1 ! und]/&+ comes to an equilibrium1 z x 71 or /&s susp5d$ z to :i* ( two or m natures ! cause ( nature inquir$ aft] %\ld be attribut$ or assign$1 by reason ( ! frequ5t & common occurr5ce ( sev]al natures1 !n ^! ,crucial ,in/ances %[ ! true & inviolable association ( "o ( ^! natures to ! nature s\ght1 & ! unc]ta9 & sep>able alliance ( ! o!r1 :]eby ! "q is decid$1 ! =m] nature admitt$ = ! cause1 & ! o!r reject$4 ,^! in/ances1 !re=e1 af=d great light1 & h a k9d ( ov]rul+ au?ority1 s t ! c\rse ( int]pretation w sometimes t]m9ate 9 !m1 or be f9i%$ by !m40 #dbi 99,disc\rse on ! ,/udy ( ,natural ,philosophy991 p4 #aea4 #dcj ,ibid4 p4 #bbi4 #dca 99,novum ,organum991 bk4 ii4 ,aphorism #cf4 ,! long-cont9u$ /rife betwe5 ! ,corpuscul> & ,undulatory !ories ( light =ms ! be/ possible illu/ration ( an ,exp]im5tum ,crucis4 ,x is rem>kable 9 h[ plausible a mann] bo? ^! !ories agre$ ) ! ord9>y laws ( geometrical optics1 relat+ to reflection & refraction4 ,accord+ to ! fir/ law ( motion a mov+ p>ticle proce$s 9 a p]fectly /raight l9e1 :5 undi/urb$ by extrane\s =ces4 ,if ! p>ticle be+ p]fectly ela/ic1 /rike a p]fectly ela/ic plane1 x w b\nd (f 9 su* a pa? t ! angles ( incid5ce & reflection w be equal4 ,n[ a ray ( light proce$s 9 a /raight l9e1 or appe>s to d s1 until x meets a reflect+ body1 :5 its pa? is alt]$ 9 a mann] exactly simil> to t ( ! ela/ic p>ticle4 ,"h is a rem>kable correspond5ce :i* probably sugge/$ to ,newton's m9d ! hypo!sis t light consi/s ( m9ute ela/ic p>ticles mov+ ) excessive rapidity 9 /raight l9es4 ,! correspond5ce 0 f\nd to ext5d also to ! law ( simple refraction2 = if p>ticles ( light be suppos$ capable ( attract+ matt]1 & be+ attract$ by x at ins5sibly small di/ances1 !n a ray ( light1 fall+ on ! surface ( a transp>5t m$ium1 w suff] an increase 9 its velocity p]p5dicul> to ! surface1 & ! law ( s9es is ! consequ5ce4 ,?is rem>kable explanation ( ! law ( refraction _h d\btless a v /rong effect 9 lead+ ,newton to ent]ta9 ! corpuscul> !ory1 & he appe>s to h ?\ght t ! analogy betwe5 ! propagation ( rays ( light & ! motion ( bodies 0 p]fectly exact1 :atev] might be ! actual nature ( light4#dcb ,x is highly rem>kable1 aga91 t ,newton 0 able to give by 8 corpuscul> !ory1 a plausible explanation ( ! inflection ( light z discov]$ by ,grimaldi4 ,! !ory w\ld inde$ h be5 a v probable "o c\ld ,newton's own law ( gravity h appli$2 b ?is 0 out ( ! "q1 because ! p>ticles ( light1 9 ord] t !y may move 9 /raight l9es1 mu/ be devoid ( any influ5ce ^u ea* o!r4 #dcb 99,pr9cipia991 bk4 i4 ,sect4 xiv4 ,prop4 #if4 ,s*olium4 99,opticks991 ,prop4 vi4 #crd edit4 p4 #gj4 ,! ,huygh5ian or ,undulatory !ory ( light 0 also able to expla9 ! same ph5om5a1 b ) "o rem>kable diff]5ce4 ,if ! undulatory !ory be true1 light mu/ move m sl[ly 9 a d5se refract+ m$ium ?an 9 a r>] "o2 b ! ,newtonian !ory assum$ t ! attraction ( ! d5se m$ium caus$ ! p>ticles ( light to move m rapidly ?an 9 ! r>e m$ium4 ,on ?is po9t1 !n1 !re 0 complete discrepancy betwe5 ! !ories1 & obs]vation 0 requir$ to %[ :i* !ory 0 to be pref]r$4 ,n[ by simply cutt+ a uni=m plate ( glass into two pieces1 & slightly incl9+ "o piece s z to increase ! l5g? ( ! pa? ( a ray pass+ ?r\gh x1 exp]im5t]s 7 able to %[ t light does move m sl[ly 9 glass ?an 9 air4#dcc ,m rec5tly ,fizeau & ,f\cault indep5d5tly measur$ ! velocity ( light 9 air & 9 wat]1 & f\nd t ! velocity is great] 9 air4#dcd #dcc ,airy's 99,ma!matical ,tracts991 #crd edit4 pp4 #bhf-bhh4 #dcd ,jam91 99,c\rs de ,physique991 vol4 iii4 p4 #cgb4 ,!re are a numb] ( o!r po9ts at :i* exp]i5ce decides aga9/ ,newton1 & 9 fav\r ( ,huygh5s & ,"y4 ,laplace po9t$ out t ! attraction suppos$ to exi/ betwe5 matt] & ! corpuscul> p>ticles ( light w\ld cause ! velocity ( light to v>y ) ! size ( ! emitt+ body1 s t if a /> 7 #bej times z great 9 diamet] z our sun1 its attraction w\ld prev5t ! emanation ( light altoge!r4#dce ,b exp]i5ce %[s t ! velocity ( light is uni=m1 & indep5d5t ( ! magnitude ( ! emitt+ body1 z x %\ld be accord+ to ! undulatory !ory4 ,la/ly1 ,newton's explanation ( diffraction or inflection fr+es ( col\rs 0 only 99plausible991 & n true2 = ,fresnel asc]ta9$ t ! dim5sions ( ! fr+es are n :at !y w\ld be accord+ to ,newton's !ory4 #dce ,"y's 99,lectures on ,natural ,philosophy99 7#ahde71 vol4 i4 p4 #cfa4 ,al?\gh ! ,sci5ce ( ,light pres5ts u ) ! mo/ beautiful examples ( crucial exp]im5ts & obs]vations1 in/ances are n want+ 9 o!r bran*es ( sci5ce4 ,cop]nicus ass]t$1 9 opposition to ! anci5t ,ptolemaic !ory1 t ! e>? mov$ r\nd ! sun1 & he pr$ict$ t if ev] ! s5se ( sight c\ld be r5d]$ suffici5tly acute & p[]ful1 we %\ld see phases 9 ,m]cury & ,v5us4 ,galileo ) 8 telescope 0 able1 9 #afaj to v]ify ! pr$iction z reg>ds ,v5us1 & subsequ5t obs]vations ( ,m]cury l$ to a l conclusion4 ,! discov]y ( ! ab]ration ( light add$ a new pro(1 /ill fur!r /r5g!n$ by ! m rec5t det]m9ation ( ! p>allax ( fix$ />s4 ,hooke propos$ to prove ! exi/5ce ( ! e>?'s diurnal motion by obs]v+ ! deviation ( a fall+ body1 an exp]im5t successfully accompli%$ by ,b5z5b]g2 & ,f\cault's p5dulum has s9ce furni%$ an additional indication ( ! same motion1 :i* is inde$ also app>5t 9 ! trade w9ds4 ,all ^! are crucial facts 9 fav\r ( ! ,cop]nican !ory4 99,descriptive ,hypo!ses499 ,!re are hypo!ses :i* we may call 99descriptive hypo!ses991 & :i* s]ve = little else ?an to furni% conv5i5t names4 ,:5 a ph5om5on is ( an unusual k9d1 we _c ev5 speak ( x )\t us+ "s analogy4 ,e ^w implies "s resemblance betwe5 ! ?+ to :i* x is appli$1 & "s o!r ?+1 :i* fixes ! mean+ ( ! ^w4 ,if we are to speak ( :at con/itutes electricity1 we mu/ se>* = ! ne>e/ analogy1 & z electricity is *>act]is$ by ! rapidity & facility ( its movem5ts1 ! notion ( a fluid ( a v subtle "* pres5ts itself z appropriate4 ,!re is ! s+le-fluid & ! d\ble-fluid !ory ( electricity1 & a great deal ( discussion has be5 uselessly sp5t ^u !m4 ,! fact is1 t if ^! !ories be und]/ood z m ?an conv5i5t modes ( describ+ ! ph5om5a1 !y are altoge!r invalid4 ,! analogy ext5ds only to ! rapidity ( motion1 or r ! fact t a ph5om5on occurs successively at diff]5t po9ts ( ! body4 ,! s-call$ electric fluid adds no?+ to ! weight ( ! conductor1 & to suppose t x really consi/s ( p>ticles ( matt] is ev5 m absurd ?an to re9/ate ! corpuscul> !ory ( light4 ,a f> clos] analogy exi/s betwe5 electricity & light undulations1 :i* are ab\t equally rapid 9 propagation4 ,we %all probably cont9ue = a long "t to talk ( ! 99electric fluid991 b !re c be no d\bt t ?is expression repres5ts m]ely a phase ( molecul> motion1 a wave ( di/urbance4 ,! invalidity ( ^! fluid !ories is %[n moreov] 9 ! fact t !y h n l$ to ! inv5tion ( a s+le new exp]im5t4 ,among ^! m]ely descriptive hypo!ses ,i %\ld place ,newton's !ory ( ,fits ( ,easy ,reflection & ,refraction4 ,t !ory did n d m ?an describe :at took place4 ,x involv$ no analogy to o!r ph5om5a ( nature1 = ,newton c\ld n po9t to any o!r sub/ance :i* w5t ?r\gh ^! extraord9>y fits4 ,we n[ "k t ! true analogy w\ld h be5 waves ( s\nd1 ( :i* ,newton _h acquir$ 9 o!r respects s complete a compreh5sion4 ,b ?\gh ! notion ( int]f]5ce ( waves _h di/9ctly occurr$ to ,hooke1 ,newton fail$ to see h[ ! p]iodic ph5om5a ( light c\ld be connect$ ) ! p]iodic "* ( waves4 ,8 hypo!sis fell because x 0 out ( analogy ) ev]y?+ else 9 nature1 & x !re=e did n all[ him1 z 9 o!r cases1 to desc5d by ma!matical d$uction to consequ5ces :i* c\ld be v]ifi$ or refut$4 ,we are at fre$om to imag9e ! exi/5ce ( a new ag5t1 & to give x an appropriate "n1 provid$ !re are ph5om5a incapable ( explanation f kn[n causes4 ,we may speak ( 99vital =ce99 z occasion+ life1 provid$ t we d n take x to be m ?an a "n = an undef9$ some?+ giv+ rise to inexplicable facts1 j z ! ,fr5* *emi/s call$ ,iod9e ! ,sub/ance ,x1 s long z !y 7 unaw>e ( its real "* & place 9 *emi/ry4#dcf ,encke 0 q ju/ifi$ 9 speak+ ( ! 99resi/+ m$ium99 9 space s long z ! ret>dation ( 8 comet c\ld n be o!rwise acc\nt$ =4 ,b su* hypo!ses w d mu* h>m :5ev] !y div]t u f attempts to reconcile ! facts ) kn[n laws1 or :5 !y lead u to mix up discrete ?+s4 ,because we speak ( vital =ce we mu/ n assume t x is a really exi/+ physical =ce l electricity2 we d n "k :at x is4 ,we h no "r to confuse ,encke's suppos$ resi/+ m$ium ) ! basis ( light )\t di/9ct evid5ce ( id5tity4 ,! "n protoplasm1 n[ s famili>ly us$ by physiologi/s1 is d\btless legitimate s long z we d n mix up diff]5t sub/ances "u x1 or imag9e t ! "n gives u any k ( ! obscure orig9 ( life4 ,to "n a sub/ance protoplasm no m expla9s ! inf9ite v>iety ( =ms ( life :i* spr+ out ( ! sub/ance1 ?an does ! 99vital =ce99 :i* may be suppos$ to reside 9 ! protoplasm4 ,bo? expressions are m]e names = an inexplicable s]ies ( causes :i* out ( app>5tly simil> conditions produce ! mo/ div]se results4 #dcf ,p>is1 99,life ( ,davy991 p4 #bgd4 ,h>dly to be di/+ui%$ f descriptive hypo!ses are c]ta9 imag9>y objects :i* we frame = ! ready compreh5sion ( a subject4 ,! ma!matician1 9 treat+ ab/ract que/ions ( probability1 f9ds x conv5i5t to repres5t ! conditions by a concrete hypo!sis 9 ! %ape ( a ballot-box4 ,poisson prov$ ! pr9ciple ( ! inv]se me?od ( probabilities by imag9+ a numb] ( ballot-boxes to h _! cont5ts mix$ 9 "o great ballot-box 7p4 #bdd74 ,_m su* devices are us$ by ma!maticians4 ,! ,ptolemaic !ory ( 99cycles99 & 99epi-cycles99 0 no grotesque & useless "w ( ! imag9ation1 b a p]fectly valid mode ( analys+ ! motions ( ! heav5ly bodies2 9 reality x is us$ by ma!maticians at ! pres5t day4 ,newton employ$ ! p5dulum z a means ( repres5t+ ! nature ( an undulation4 ,c5tres ( gravity1 oscillation1 c41 poles ( ! magnet1 l9es ( =ce1 are o!r imag9>y exi/5ces employ$ to assi/ our ?\ghts 7p4 #cfd74 ,su* devices may be call$ 99,repres5tative ,hypo!ses991 & !y are only p]missible s f> z !y embody analogies4 ,_! fur!r consid]ation belongs ei!r to ! subject ( ,analogy1 or to t ( language & repres5tation1 f\nd$ ^u analogy4 ,,*apt] ,,xxiv4 ,,empirical ,,k1 ,,explanation1 ,,& ,,pr$iction4 ,inductive inve/igation1 z we h se51 consi/s 9 ! union ( hypo!sis & exp]im5t1 d$uctive reason+ be+ ! l9k by :i* exp]im5tal results are made to confirm or confute ! hypo!sis4 ,n[ :5 we consid] ?is relation betwe5 hypo!sis & exp]im5t x is obvi\s t we may classify our k "u f\r heads4 7#a7 ,we may be acqua9t$ ) facts :i* h n yet be5 br\ght into accordance ) any hypo!sis4 ,su* facts con/itute :at is call$ 99,empirical ,k994 7#b7 ,ano!r ext5sive portion ( our k consi/s ( facts :i* hav+ be5 fir/ obs]v$ empirically1 h aft]w>ds be5 br\ght into accordance ) o!r facts by an hypo!sis conc]n+ ! g5]al laws apply+ to !m4 ,?is portion ( our k may be said to be 99expla9$991 99reason$991 or 99g5]alis$994 7#c7 ,9 ! ?ird place comes ! collection ( facts1 m9or 9 numb]1 b mo/ important z reg>ds _! sci5tific int]e/1 :i* h be5 anticipat$ by !ory & aft]w>ds v]ifi$ by exp]im5t4 7#d7 ,la/ly1 !re exi/s k :i* is accept$ solely on ! gr\nd ( !ory1 & is incapable ( exp]im5tal confirmation1 at lea/ ) ! in/rum5tal means 9 our possession4 ,x is a "w ( mu* int]e/ to comp>e & illu/rate ! relative ext5t & value ( ^! f\r gr\ps ( k4 ,we %all obs]ve t z a g5]al rule a great bran* ( sci5ce orig9ates 9 facts obs]v$ accid5tally1 or )\t di/9ct consci\sness ( :at is to be expect$4 ,z a sci5ce progresses1 its p[] ( =esight rapidly increases1 until ! ma!matician 9 8 libr>y acquires ! p[] ( anticipat+ nature1 & pr$ict+ :at w happ5 9 circum/ances :i* ! eye ( man has nev] exam9$4 99,empirical ,k499 ,by empirical k we mean su* z is d]iv$ directly f ! exam9ation ( deta*$ facts1 & re/s entirely on ^? facts1 )\t corroboration f o!r bran*es ( k4 ,x is contra/$ ) g5]alis$ & !oretical k1 :i* embraces _m s]ies ( facts "u a few compreh5sive pr9ciples1 s t ea* s]ies s]ves to ?r[ light ^u ea* o!r s]ies ( facts4 ,j z1 9 ! map ( a half-explor$ c\ntry1 we see deta*$ bits ( riv]s1 isolat$ m\nta9s1 & undef9$ pla9s1 n connect$ into any complete plan1 s a new bran* ( k consi/s ( gr\ps ( facts1 ea* gr\p /&+ ap>t1 s z n to all[ u to reason f "o to ano!r4 ,be=e ! "t ( ,desc>tes1 & ,newton1 & ,huygh5s1 !re 0 mu* empirical k ( ! ph5om5a ( light4 ,! ra9b[ _h always /ruck ! att5tion ( ! mo/ c>eless obs]v]s1 & !re 0 no difficulty 9 p]ceiv+ t its conditions ( occurr5ce consi/$ 9 rays ( ! sun %9+ ^u fall+ drops ( ra94 ,x 0 impossible to ov]look ! resemblance ( ! ord9>y ra9b[ to ! comp>atively r>e lun> ra9b[1 to ! b[ :i* appe>s ^u ! spray ( a wat]fall1 or ev5 ^u beads ( dew susp5d$ on grass & spid]s' webs4 ,9 all ^! cases ! uni=m conditions are rays ( light & r\nd drops ( wat]4 ,rog] ,bacon _h notic$ ^! conditions1 z well z ! analogy ( ! ra9b[ col\rs to ^? produc$ by cry/als4#dcg ,b ! k 0 empirical until ,desc>tes & ,newton %[$ h[ ! ph5om5a 7 connect$ ) facts conc]n+ ! refraction ( light4 #dcg 99,opus ,majus499 ,edit4 #agcc4 ,cap4 x4 p4 #dfj4 ,!re c be no bett] in/ance ( an empirical tru? ?an t detect$ by ,newton conc]n+ ! high refractive p[]s ( combu/ible sub/ances4 ,newton's *emical notions 7 almo/ z vague z ^? preval5t 9 8 day1 b he obs]v$ t c]ta9 8fat1 sulphure\s1 unctu\s bodies10 z he calls !m1 su* z camphor1 oils _s ( turp5t9e1 amb]1 c41 h refractive p[]s two or ?ree times great] ?an might be anticipat$ f _! d5sities4#dch ,! enorm\s refractive index ( diamond1 l$ him ) great sagacity to reg>d ?is sub/ance z ( ! same unctu\s or inflammable nature1 s t he may be reg>d$ z pr$ict+ ! combu/ibility ( ! diamond1 aft]w>ds demon/rat$ by ! ,flor5t9e ,academicians 9 #afid4 ,brew/] hav+ ent]$ into a long inve/igation ( ! refractive p[]s ( diff]5t sub/ances1 confirm$ ,newton's ass]tions1 & f\nd t ! ?ree elem5t>y combu/ible sub/ances1 diamond1 phosphorus1 & sulphur1 h1 9 comp>ison ) _! d5sities1 by f> ! highe/ kn[n refractive indices1#dci & !re are only a few sub/ances1 su* z *romate ( lead or glass ( antimony1 :i* exce$ !m 9 absolute p[] ( refraction4 ,! oils & hydroc>bons g5]ally possess excessive indices4 ,b all ?is k rema9s to ! pres5t day purely empirical1 no connection hav+ be5 po9t$ out betwe5 ?is co9cid5ce ( inflammability & high refractive p[]1 ) o!r laws ( *emi/ry or optics4 ,x is wor? notice1 z po9t$ out by ,brew/]1 t if ,newton _h argu$ conc]n+ two m9]als1 ,gre5ockite & ,octah$rite1 z he did conc]n+ diamond1 8 pr$ictions w\ld h prov$ false1 %[+ suffici5tly t he did n make any sure induction on ! subject4 ,9 ! pres5t day1 ! relation ( ! refractive index to ! d5sity & atomic weight ( a sub/ance is becom+ a matt] ( !ory2 yet !re rema9 specific diff]5ces ( refract+ p[] kn[n only on empirical gr\nds1 & x is curi\s t 9 hydrog5 an abnormally high refractive p[] has be5 f\nd to be jo9$ to inflammability4 #dch ,newton's 99,opticks994 ,?ird edit4 p4 #bdi4 #dci ,brew/]4 99,treatise on ,new ,philosophical ,in/rum5ts991 p4 #bff1 c4 ,! sci5ce ( *emi/ry1 h[ev] mu* its !ory may h progress$1 /ill pres5ts u ) a va/ body ( empirical k4 ,n only is x z yet hopeless to attempt to acc\nt = ! p>ticul> gr\p ( qualities belong+ to ea* elem5t1 b !re are multitudes ( p>ticul> facts ( :i* no fur!r acc\nt c be giv54 ,:y %\ld ! sulphides ( _m metals be int5sely black8 ,:y %\ld a slight am\nt ( phosphoric acid h s great a p[] ( int]f]5ce ) ! cry/allisation ( vanadic acid8#ddj ,:y %\ld ! comp\nd silicates ( alkalies & alkal9e metals be transp>5t8 ,:y %\ld gold be s highly ductile1 & gold & silv] ! only two s5sibly transluc5t metals8 ,:y %\ld sulphur be capable ( s _m peculi> *anges into allotropic modifications8 #ddj ,roscoe1 ,bak]ian ,lecture1 99,philosophical ,transactions99 7#ahfh71 vol4 clviii4 p4 #f4 ,!re are :ole bran*es ( *emical k :i* are m]e collections ( disconnect$ facts4 ,! prop]ties ( alloys are (t5 rem>kable2 b no laws h yet be5 detect$1 & ! laws ( comb9+ proportions seem to h no cle> application4#dda ,n ! slighte/ explanation c be giv5 ( ! wond]ful v>iations ( ! qualities ( iron1 accord+ z x conta9s m or less c>bon & silicon1 nay1 ev5 ! facts ( ! case are (t5 involv$ 9 unc]ta9ty4 ,:y1 aga91 %\ld ! prop]ties ( /eel be rem>kably affect$ by ! pres5ce ( a little tung/5 or manganese8 ,all t 0 det]m9$ by ,mat?iess5 conc]n+ ! conduct+ p[]s ( copp]1 0 ( a purely empirical "*4#ddb ,_m animal sub/ances _c be %[n to obey ! laws ( comb9+ proportions4 ,?us = ! mo/ "p *emi/ry is yet an empirical sci5ce occupi$ ) ! regi/ration ( imm5se numb]s ( disconnect$ facts1 :i* may at "s future "t become ! basis ( a greatly ext5d$ !ory4 #dda 99,life ( ,f>aday991 vol4 ii4 p4 #ajd4 #ddb ,watts1 99,diction>y ( ,*emi/ry991 vol4 ii1 p4 #ci1 c4 ,we mu/ n inde$ suppose t any sci5ce w ev] entirely cease to be empirical4 ,multitudes ( ph5om5a h be5 expla9$ by ! undulatory !ory ( light2 b !re yet rema9 _m facts to be treat$4 ,! natural col\rs ( bodies & ! rays giv5 (f by !m :5 heat$1 are unexpla9$1 & yield few empirical co9cid5ces4 ,! !ory ( electricity is p>tially und]/ood1 b ! conditions ( ! production ( frictional electricity defy explanation1 al?\gh !y h be5 /udi$ = two c5turies4 ,i %all subsequ5tly po9t out t ev5 ! e/abli%m5t ( a wide & true law ( nature is b ! />t+-po9t = ! discov]y ( exceptions & div]g5ces giv+ a new scope to empirical discov]y4 ,!re is probably no sci5ce1 ,i h said1 :i* is entirely free f empirical & unexpla9$ facts4 ,logic approa*es mo/ ne>ly to ?is position1 z x is m]ely a d$uctive developm5t ( ! laws ( ?\ght & ! pr9ciple ( sub/itution4 ,yet "s ( ! facts e/abli%$ 9 ! inve/igation ( ! inv]se logical problem may be consid]$ empirical4 ,t a proposition ( ! =m ,a ,,bc 99b c99 possesses ! lea/ numb] ( di/9ct logical v>iations1 & ! greate/ numb] ( logical equival5ts ( ! same =m among propositions involv+ ?ree classes 7p4 #ada71 is a case 9 po9t4 ,s also is ! fact discov]$ by ,pr(essor ,clif=d t 9 reg>d to /atem5ts involv+ f\r classes1 !re is only "o example ( two dissimil> /atem5ts hav+ ! same di/ances 7p4 #add74 ,ma!matical sci5ce (t5 yields empirical tru?s4 ,:y1 = in/ance1 %\ld ! value ( 1 :5 express$ to a great numb] ( figures1 conta9 ! digit #g mu* less frequ5tly ?an any o!r digit8#ddc ,ev5 geometry may all[ ( empirical tru?s1 :5 ! matt] does n involve quantities ( space1 b num]ical results & ! positive or negative "* ( quantities1 z 9 ,de ,morgan's !orem conc]n+ negative areas4 #ddc ,de ,morgan's 99,budget ( ,p>adoxes991 p4 #bia4 99,accid5tal ,discov]y499 ,!re are n a few cases :]e almo/ pure accid5t has det]m9$ ! mom5t :5 a new bran* ( k 0 to be creat$4 ,! laws ( ! /ructure ( cry/als 7 n discov]$ until ,hay happ5$ to drop a beautiful cry/al ( calc-sp> ^u a /one pavem5t4 ,8 mom5t>y regret at de/roy+ a *oice specim5 0 quickly remov$ :51 9 attempt+ to jo9 ! fragm5ts toge!r1 he obs]v$ regul> geometrical faces1 :i* did n correspond ) ! ext]nal facets ( ! cry/als4 ,a great _m m cry/als 7 soon brok5 int5tionally1 to obs]ve ! planes ( cleavage1 & ! discov]y ( ! int]nal /ructure ( cry/all9e sub/ances 0 ! result4 ,"h we see h[ mu* m 0 due to ! reason+ p[] ( ! philosoph]1 ?an to an accid5t :i* mu/ (t5 h happ5$ to o!r p]sons4 ,9 a simil> mann]1 a =tuit\s occurr5ce l$ ,malus to discov] ! pol>isation ( light by reflection4 ,! ph5om5a ( d\ble refraction _h be5 long kn[n1 & :5 engag$ 9 ,p>is 9 #ahjh1 9 inve/igat+ ! "* ( light ?us pol>is$1 ,malus *anc$ to look ?r\gh a d\ble refract+ prism at ! light ( ! sett+ sun1 reflect$ f ! w9d[s ( ! ,luxemb\rg ,palace4 ,9 turn+ ! prism r\nd1 he 0 surpris$ to f9d t ! ord9>y image disappe>$ at two opposite positions ( ! prism4 ,he rem>k$ t ! reflect$ light behav$ l light :i* _h be5 pol>is$ by pass+ ?r\gh ano!r prism4 ,he 0 induc$ to te/ ! "* ( light reflect$ "u o!r circum/ances1 & x 0 ev5tually prov$ t pol>isation is inv>iably connect$ ) reflection4 ,"s ( ! g5]al laws ( optics1 previ\sly unsuspect$1 7 ?us discov]$ by pure accid5t4 ,9 ! hi/ory ( electricity1 accid5t has _h a l>ge "p4 ,= c5turies "s ( ! m common effects ( magnetism & ( frictional electricity _h pres5t$ !mselves z unacc\ntable deviations f ! ord9>y c\rse ( ,nature4 ,accid5t mu/ h fir/ direct$ att5tion to su* ph5om5a1 b h[ few ( ^? :o witness$ !m _h any conception ( ! all-p]vad+ "* ( ! p[] manife/$4 ,! v exi/5ce ( galvanism1 or electricity ( l[ t5sion1 0 unsuspect$ until ,galvani accid5tally t\*$ ! leg ( a frog ) pieces ( metal4 ,! decomposition ( wat] by voltaic electricity also 0 accid5tally discov]$ by ,ni*olson 9 #ahja1 & ,davy speaks ( ?is discov]y z ! f\ndation ( all t _h s9ce be5 done 9 electro-*emical sci5ce4 ,x is o!rwise ) ! discov]y ( electro-magnetism4 ,o]/$1 9 common ) _m o!rs1 _h suspect$ ! exi/5ce ( "s relation betwe5 ! magnet & electricity1 & he appe>s to h tri$ to detect its exact nature4 ,once1 z we are told by ,han/e51 he _h employ$ a /rong galvanic batt]y dur+ a lecture1 & at ! close x occurr$ to him to try ! effect ( plac+ ! conduct+ wire p>allel to a magnetic ne$le1 in/ead ( at "r angles1 z he _h previ\sly done4 ,! ne$le imm$iately mov$ & took up a position ne>ly at "r angles to ! wire2 he inv]t$ ! direction ( ! curr5t1 & ! ne$le deviat$ 9 a contr>y direction4 ,! great discov]y 0 made1 & if by accid5t1 x 0 su* an accid5t z happ5s1 z ,lagrange rem>k$ ( ,newton1 only to ^? :o des]ve x4#ddd ,!re 01 9 fact1 no?+ accid5tal1 except t1 z 9 all totally new discov]ies1 ,o]/$ did n "k :at to look =4 ,he c\ld n inf] f previ\s k ! nature ( ! relation1 & x 0 only repeat$ trial 9 diff]5t modes :i* c\ld lead him to ! "r comb9ation4 ,high & happy p[]s ( inf]5ce1 & n accid5t1 subsequ5tly l$ ,f>aday to rev]se ! process1 & to %[ t ! motion ( ! magnet w\ld occasion an electric curr5t 9 ! wire4 #ddd 99,life ( ,f>aday991 vol4 ii p4 #cif4 ,suffici5t inve/igation w\ld probably %[ t almo/ e bran* ( art & sci5ce _h an accid5tal beg9n+4 ,9 hi/orical times almo/ e important new in/rum5t z ! telescope1 ! microscope1 or ! compass1 0 probably sugge/$ by "s accid5tal occurr5ce4 ,9 pre-hi/oric times ! g]ms ( ! arts mu/ h aris5 /ill m exclusively 9 ! same way4 ,cultivation ( plants probably arose1 9 ,mr4 ,d>w9's op9ion1 f "s su* accid5t z ! se$s ( a fruit fall+ ^u a heap ( refuse1 & produc+ an unusually f9e v>iety4 ,ev5 ! use ( fire mu/1 "s "t or o!r1 h be5 discov]$ 9 an accid5tal mann]4 ,) ! progress ( a bran* ( sci5ce1 ! elem5t ( *ance becomes mu* r$uc$4 ,n only are laws discov]$ :i* enable results to be pr$ict$1 z we %all see1 b ! sy/ematic exam9ation ( ph5om5a & sub/ances (t5 leads to discov]ies :i* c 9 no s5se be said to be accid5tal4 ,x has be5 ass]t$ t ! an/hetic prop]ties ( *lor(orm 7 disclos$ by a little dog smell+ at a sauc]ful ( ! liquid 9 a *emi/'s %op 9 ,l9li?g[1 ! s+ul> effects ^u ! dog be+ report$ to ,simpson1 :o turn$ ! incid5t to good acc\nt4 ,?is /ory1 h[ev]1 has be5 %[n to be a fabrication1 ! fact be+ t ,simpson _h = _m ye>s be5 endeav\r+ to discov] a bett] an/hetic ?an ^? previ\sly employ$1 & t he te/$ ! prop]ties ( *lor(orm1 among o!r sub/ances1 at ! sugge/ion ( ,waldie1 a ,liv]pool *emi/4 ,! valuable p[]s ( *loral hydrate h s9ce be5 discov]$ 9 a l mann]1 & sy/ematic inquiries are cont9ually be+ made into ! !rapeutic or economic values ( new *emical comp\nds4 ,if we mu/ attempt to draw a conclusion conc]n+ ! "p :i* *ance plays 9 sci5tific discov]y1 x mu/ be all[$ t x m or less affects ! success ( all inductive inve/igation1 b becomes less important ) ! progress ( sci5ce4 ,accid5t may br+ a new & valuable comb9ation to ! notice ( "s p]son :o _h nev] expressly se>*$ = a discov]y ( ! k9d1 & ! probabilities are c]ta9ly 9 fav\r ( a discov]y be+ occasionally made 9 ?is mann]4 ,b ! great] ! tact & indu/ry ) :i* a physici/ applies himself to ! /udy ( nature1 ! great] is ! probability t he w meet ) =tunate accid5ts1 & w turn !m to good acc\nt4 ,?us x comes to pass t1 9 ! ref9$ inve/igations ( ! pres5t day1 g5ius unit$ to ext5sive k1 cultivat$ p[]s1 & indomitable indu/ry1 con/itute ! *>act]i/ics ( ! successful discov]]4 99,empirical ,obs]vations subsequ5tly ,expla9$499 ,! second great portion ( sci5tific k consi/s ( facts :i* h be5 fir/ le>nt 9 a purely empirical mann]1 b h aft]w>ds be5 %[n to foll[ f "s law ( nature1 t is1 f "s highly probable hypo!sis4 ,facts are said to be expla9$ :5 !y are ?us br\ght into h>mony ) o!r facts1 or bodies ( g5]al k4 ,!re are few words m famili>ly us$ 9 sci5tific phraseology ?an ?is ^w 99explanation991 & x is necess>y to decide exactly :at we mean by x1 s9ce ! "q t\*es ! deepe/ po9ts conc]n+ ! nature ( sci5ce4 ,l mo/ t]ms ref]r+ to m5tal actions1 ! v]bs 99to expla9991 or 99to explicate991 involve mat]ial similes4 ,! action is 99ex plicis plana r$d]e991 to take out ! folds1 & r5d] a ?+ pla9 or ev54 ,explanation ?us r5d]s a ?+ cle>ly compreh5sible 9 all its po9ts1 s t !re is no?+ left out/&+ or obscure4 ,e act ( explanation consi/s 9 po9t+ out a resemblance betwe5 facts1 or 9 %[+ t simil>ity exi/s betwe5 app>5tly div]se ph5om5a4 ,?is simil>ity may be ( any ext5t & dep?2 x may be a g5]al law ( nature1 :i* h>monises ! motions ( all ! heav5ly bodies by %[+ t !re is a simil> =ce :i* gov]ns all ^? motions1 or ! explanation may involve no?+ m ?an a s+le id5tity1 z :5 we expla9 ! appe>ance ( %oot+ />s by %[+ t !y are id5tical ) portions ( a comet4 ,:]ev] we detect resemblance1 !re is a m or less explanation4 ,! m9d is disquiet$ :5 x meets a novel ph5om5on1 "o :i* is 99sui g5]is992 x seeks at once = p>allels :i* may be f\nd 9 ! memory ( pa/ s5sations4 ,! s-call$ sulphur\s smell :i* att5ds a /roke ( lightn+ (t5 excit$ att5tion1 & x 0 n expla9$ until ! exact simil>ity ( ! smell to t ( ozone 0 po9t$ out4 ,! m>ks ^u a flag/one are expla9$ :5 !y are %[n to correspond ) ! feet ( an ext9ct animal1 ^: bones are else:]e f\nd4 ,explanation1 9 fact1 g5]ally comm5ces by ! discov]y ( "s simple resemblance2 ! !ory ( ! ra9b[ began z soon z ,antonio de ,dom9is po9t$ out ! resemblance betwe5 its col\rs & ^? pres5t$ by a ray ( sunlight pass+ ?r\gh a glass globe full ( wat]4 ,! nature & limits ( explanation c only be fully consid]$1 aft] we h ent]$ ^u ! subjects ( g5]alisation & analogy4 ,x mu/ suffice to rem>k1 9 ?is place1 t ! mo/ important process ( explanation consi/s 9 %[+ t an obs]v$ fact is "o case ( a g5]al law or t5d5cy4 ,iron is always f\nd comb9$ ) sulphur1 :5 x is 9 contact ) coal1 :]eas 9 o!r p>ts ( ! c>bonif]\s /rata x always occurs z a c>bonate4 ,we expla9 ?is empirical fact z be+ due to ! r$uc+ p[] ( c>bon & hydrog51 :i* prev5ts ! iron f comb9+ ) oxyg51 & leaves x op5 to ! aff9ity ( sulphur4 ,! uni=m /r5g? & direction ( ! trade-w9ds 7 long famili> to m>9]s1 be=e !y 7 expla9$ by ,halley on hydro/atical pr9ciples4 ,! w9ds 7 f\nd to arise f ! action ( gravity1 :i* causes a heavi] body to displace a light] "o1 :ile ! direction f ea/ to we/ 0 expla9$ z a result ( ! e>?'s rotation4 ,:atev] body 9 ! nor!rn hemisph]e *anges its latitude1 :e!r x be a bird1 or a railway tra91 or a body ( air1 mu/ t5d t[>ds ! "r h&4 ,dove's law ( ! w9ds is t ! w9ds t5d to ve] 9 ! nor!rn hemisph]e 9 ! direction ,n4,e4,s4,w41 & 9 ! s\!rn hemisph]e 9 ! direction ,n4,w4,s4,e4 ,?is t5d5cy 0 %[n by him to be ! necess>y effect ( ! same conditions :i* apply to ! trade w9ds4 ,:5ev]1 !n1 any fact is connect$ by resemblance1 law1 !ory1 or hypo!sis1 ) o!r facts1 x is expla9$4 ,al?\gh ! great mass ( record$ facts mu/ be empirical1 & await+ explanation1 su* k is ( m9or value1 because x does n admit ( safe & ext5sive inf]5ce4 ,ea* record$ result in=ms u exactly :at w be exp]i5c$ aga9 9 ! same circum/ances1 b has no be>+ ^u :at w happ5 9 o!r circum/ances4 99,ov]look$ ,results ( ,!ory499 ,we mu/ by no means suppose t1 :5 a sci5tific tru? is 9 our possession1 all its consequ5ces w be =ese54 ,d$uction is c]ta9 & infallible1 9 ! s5se t ea* /ep 9 d$uctive reason+ w lead u to "s result1 z c]ta9 z ! law itself4 ,b x does n foll[ t d$uction w lead ! reason] to e result ( a law or comb9ation ( laws4 ,:atev] road a travell] takes1 he is sure to arrive some:]e1 b unless he proce$s 9 a sy/ematic mann]1 x is unlikely t he w rea* e place to :i* a network ( roads w conduct him4 ,9 l mann] !re are _m ph5om5a :i* 7 virtually )9 ! rea* ( philosoph]s by inf]5ce f _! previ\s k1 b 7 nev] discov]$ until accid5t or sy/ematic empirical obs]vation disclos$ _! exi/5ce4 ,t light travels ) a uni=m high velocity 0 prov$ by ,roem] f obs]vations ( ! eclipses ( ,jupit]'s satellites4 ,corrections 7 !nce=w>d made 9 all a/ronomical obs]vations requir+ x1 = ! diff]5ce ( absolute "t at :i* an ev5t happ5$1 & t at :i* x w\ld be se5 on ! e>?4 ,b no p]son happ5$ to rem>k t ! motion ( light comp\nd$ ) t ( ! e>? 9 its orbit w\ld occasion a small app>5t displacem5t ( ! great] "p ( ! heav5ly bodies4 ,fifty ye>s elaps$ be=e ,bradley empirically discov]$ ?is effect1 call$ by him ab]ration1 :5 r$uc+ 8 obs]vations ( ! fix$ />s4 ,:5 once ! relation betwe5 an electric curr5t & a magnet _h be5 detect$ by ,o]/$ & ,f>aday1 x ought to h be5 possible = !m to =esee ! div]se results :i* mu/ ensue 9 diff]5t circum/ances4 ,if1 = in/ance1 a plate ( copp] 7 plac$ b5ea? an oscillat+ magnetic ne$le1 x %\ld h be5 se5 t ! ne$le w\ld induce curr5ts 9 ! copp]1 b z ?is c\ld n take place )\t a c]ta9 reaction aga9/ ! ne$le1 x ought to h be5 se5 t ! ne$le w\ld come to re/ m rapidly ?an 9 ! abs5ce ( ! copp]4 ,?is peculi> effect 0 accid5tally discov]$ by ,gambey 9 #ahbd4 ,arago acutely inf]r$ f ,gambey's exp]im5t t if ! copp] 7 set 9 rotation :ile ! ne$le 0 /ation>y ! motion w\ld gradually be communicat$ to ! ne$le4 ,! ph5om5on nev]!less puzzl$ ! :ole sci5tific _w1 & x requir$ ! d$uctive g5ius ( ,f>aday to %[ t x 0 a result ( ! pr9ciples ( electro-magnetism4#dde #dde 99,exp]im5tal ,rese>*es 9 ,electricity991 #a/ ,s]ies1 pp4 #bd-dd4 ,_m o!r curi\s facts might be m5tion$ :i* :5 once notic$ 7 expla9$ z ! effects ( well-kn[n laws4 ,x 0 accid5tally discov]$ t ! navigation ( canals ( small dep? c\ld be facilitat$ by increas+ ! spe$ ( ! boats1 ! resi/ance be+ actually r$uc$ by ?is increase ( spe$1 :i* enables ! boat to ride z x 7 ^u its own =c$ wave4 ,n[ ma!matical !ory might h pr$ict$ ?is result _h ! "r application ( ! =mul occurr$ to any "o4#ddf ,giff>d's injector = supply+ /eam boil]s ) wat] by ! =ce ( _! own /eam1 01 ,i believe1 accid5tally discov]$1 b no new pr9ciples ( me*anics are involv$ 9 x1 s t x might h be5 !oretically inv5t$4 ,! same may be said ( ! curi\s exp]im5t 9 :i* a /ream ( air or /eam issu+ f a pipe is made to hold a free disc ^u ! end ( ! pipe & ?us ob/ruct its own outlet4 ,! possession !n ( a true !ory does n by any means imply ! =esee+ ( all ! results4 ,! effects ( ev5 a few simple laws may be manifold1 & "s ( ! mo/ curi\s & useful effects may rema9 undetect$ until accid5tal obs]vation br+s !m to our notice4 #ddf ,airy1 99,on ,tides & ,waves991 ,encyclopdia ,metropolitana1 p4 #cdh994 99,pr$ict$ ,discov]ies499 ,! mo/ int]e/+ ( ! f\r classes ( facts specifi$ 9 p4 #ebe1 is probably ! ?ird1 conta9+ ^? ! occurr5ce ( :i* has be5 fir/ pr$ict$ by !ory & !n v]ifi$ by obs]vation4 ,!re is no m conv9c+ pro( ( ! s\ndness ( k ?an t x conf]s ! gift ( =esight4 ,augu/e ,comte said t 8,prevision is ! te/ ( true !ory20 ,i %\ld say t x is 99"o te/99 ( true !ory1 & t :i* is mo/ likely to /rike ! public att5tion4 ,co9cid5ce ) fact is ! te/ ( true !ory1 b :5 ! result ( !ory is ann\nc$ be=e-h&1 !re c be no d\bt z to ! unprejudic$ _s 9 :i* ! !ori/ int]prets ! results ( 8 own !ory4 ,! e>lie/ in/ance ( sci5tific prophecy is naturally furni%$ by ! sci5ce ( ,a/ronomy1 :i* 0 ! e>lie/ 9 developm5t4 ,h]odotus#ddg n>rates t1 9 ! mid/ ( a battle betwe5 ! ,m$es & ,lydians1 ! day 0 sudd5ly turn$ into night1 & ! ev5t _h be5 =etold by ,?ales1 ! ,fa!r ( ,philosophy4 ,a cessation ( ! combat & peace confirm$ by m>riages 7 ! consequ5ces ( ?is happy sci5tific ef=t4 ,mu* controv]sy has tak5 place conc]n+ ! date ( ?is occurr5ce1 ,baily assign+ ! ye> #faj ,b4,c41 b ,airy has calculat$ t ! exact day 0 ! #bh? ( ,may1 #ehd ,b4,c4 ,!re c be no d\bt t ?is & o!r pr$ictions ( eclipses attribut$ to anci5t philosoph]s 7 due to a k ( ! ,metonic ,cycle1 a p]iod ( #f1ehe days1 or #bbc lun> mon?s1 or ab\t #ai ye>s1 aft] :i* a ne>ly p]fect recurr5ce ( ! phases & eclipses ( ! moon takes place2 b if s1 ,?ales mu/ h _h access to long s]ies ( a/ronomical records ( ! ,egyptians or ! ,*aldeans4 ,!re is a well-kn[n /ory z to ! happy use :i* ,columbus made ( ! p[] ( pr$ict+ eclipses 9 ov]aw+ ! isl&]s ( ,jamaica :o refus$ him necess>y supplies ( food = 8 fleet4 ,he ?reat5$ to deprive !m ( ! moon's light4 8,8 ?reat 0 treat$ at fir/ ) indiff]5ce1 b :5 ! eclipse actually comm5c$1 ! b>b>ians vi$ ) ea* o!r 9 ! production ( ! necess>y supplies = ! ,spani% fleet40 #ddg ,lib4 i4 cap4 #gd4 ,exactly ! same k9d ( awe :i* ! anci5ts exp]i5c$ at ! pr$iction ( eclipses1 has be5 felt 9 mod]n times conc]n+ ! return ( comets4 ,s5eca ass]t$ 9 di/9ct t]ms t comets w\ld be f\nd to revolve 9 p]iodic orbits & return to sight4 ,! anci5t ,*aldeans & ! ,py?agoreans are also said to h ent]ta9$ a l op9ion4 ,b x 0 n until ! age ( ,newton & ,halley t x became possible to calculate ! pa? ( a comet 9 future ye>s4 ,a great comet appe>$ 9 #afhb1 a few ye>s be=e ! fir/ publication ( ! 99,pr9cipia991 & ,halley %[$ t its orbit correspond$ ) t ( rem>kable comets record$ to h appe>$ 9 ! ye>s #aeca & #afjg4 ,! int]vals ( "t 7 n q equal1 b ,halley conceiv$ ! bold idea t ?is diff]5ce might be due to ! di/urb+ p[] ( ,jupit]1 ne> :i* ! comet _h pass$ 9 ! int]val #afjg-afhb4 ,he pr$ict$ t ! comet w\ld return ab\t ! end ( #ageh or ! beg9n+ ( #agei1 & ?\gh ,halley did n live to enjoy ! sight1 x 0 actually detect$ on ! night ( ,*ri/mas-day1 #ageh4 ,a second return ( ! comet 0 witness$ 9 #ahce ne>ly at ! anticipat$ "t4 ,9 rec5t times ! discov]y ( ,neptune has be5 ! mo/ rem>kable in/ance ( prevision 9 a/ronomical sci5ce4 ,a full acc\nt ( ?is discov]y may be f\nd 9 sev]al works1 z = in/ance ,h]s*el's 99,outl9es ( ,a/ronomy991 & 99,grant's ,hi/ory ( ,physical ,a/ronomy991 ,*apt]s ,,xii & ,,xiii4 99,pr$ictions 9 ! ,sci5ce ( ,light499 ,next aft] a/ronomy ! sci5ce ( physical optics has furni%$ ! mo/ beautiful in/ances ( ! prophetic p[] ( correct !ory4 ,^! cases are ! m /rik+ because !y proce$ f ! pr(\nd application ( ma!matical analysis & %[ an insight into ! my/]i\s work+s ( matt] :i* is surpris+ to all1 b especially to ^? :o are unable to compreh5d ! me?ods ( rese>* employ$4 ,by its p[] ( prevision ! tru? ( ! undulatory !ory ( light has be5 conspicu\sly prov$1 & ! contra/ 9 ?is respect betwe5 ! undulatory & ,corpuscul> !ories is rem>kable4 ,ev5 ,newton c\ld get no aid f 8 corpuscul> !ory 9 ! inv5tion ( new exp]im5ts1 & to 8 foll[]s :o embrac$ t !ory we owe little or no?+ 9 ! sci5ce ( light4 ,laplace did n d]ive f ! !ory a s+le discov]y4 ,z ,fresnel rem>ks3#ddh #ddh ,taylor's 99,sci5tific ,memoirs991 vol4 v4 p4 #bda4 8,! assi/ance to be d]iv$ f a good !ory is n to be conf9$ to ! calculation ( ! =ces :5 ! laws ( ! ph5om5a are kn[n4 ,!re are c]ta9 laws s complicat$ & s s+ul>1 t obs]vation alone1 aid$ by analogy1 c\ld nev] lead to _! discov]y4 ,to div9e ^! enigmas we mu/ be guid$ by !oretical ideas f\nd$ on a 99true99 hypo!sis4 ,! !ory ( lum9\s vibrations pres5ts ?is "*1 & ^! preci\s advantages2 = to x we owe ! discov]y ( optical laws ! mo/ complicat$ & mo/ difficult to div9e40 ,physici/s :o embrac$ ! corpuscul> !ory _h no?+ b _! own quickness ( obs]vation to rely ^u4 ,fresnel hav+ once seiz$ ! conditions ( ! true undulatory !ory1 z previ\sly /at$ by ,"y1 0 enabl$ by ! m]e manipulation ( 8 ma!matical symbols to =esee _m ( ! complicat$ ph5om5a ( light4 ,:o c\ld possibly suppose1 t by /opp+ a portion ( ! rays pass+ ?r\gh a circul> ap]ture1 ! illum9ation ( a po9t ^u a scre5 beh9d ! ap]ture might be _m times multipli$4 ,yet ?is p>adoxical effect 0 pr$ict$ by ,fresnel1 & v]ifi$ bo? by himself1 & 9 a c>eful repetition ( ! exp]im5t1 by ,billet4 ,few p]sons are aw>e t 9 ! middle ( ! %ad[ ( an opaque circul> disc is a po9t ( light s5sibly z bright z if no disc _h be5 int]pos$4 ,?is />tl+ fact 0 d$uc$ f ,fresnel's !ory by ,poisson1 & 0 !n v]ifi$ exp]im5tally by ,arago4 ,airy1 aga91 0 l$ by pure !ory to pr$ict t ,newton's r+s w\ld pres5t a modifi$ appe>ance if produc$ betwe5 a l5s ( glass & a plate ( metal4 ,?is effect happ5$ to h be5 obs]v$ fifte5 ye>s be=e by ,arago1 unkn[n to ,airy4 ,ano!r pr$iction ( ,airy1 t !re w\ld be a fur!r modification ( ! r+s :5 made betwe5 two sub/ances ( v diff]5t refractive indices1 0 v]ifi$ by subsequ5t trial ) a diamond4 ,a rev]sal ( ! r+s takes place :5 ! space int]v5+ betwe5 ! plates is fill$ ) a sub/ance ( int]m$iate refractive p[]1 ano!r ph5om5on pr$ict$ by !ory & v]ifi$ by exp]im5t4 ,!re is h>dly a limit to ! numb] ( o!r complicat$ effects ( ! int]f]5ce ( rays ( light "u diff]5t circum/ances :i* might be d$uc$ f ! ma!matical expressions1 if x 7 wor? :ile1 or :i*1 be+ previ\sly obs]v$1 c be expla9$4 ,an int]e/+ case 0 obs]v$ by ,h]s*el & expla9$ by ,airy4#ddi #ddi ,airy's 99,ma!matical ,tracts991 #crd edit4 p4 #cab4 ,by a some:at diff]5t ef=t ( sci5tific =esight1 ,fresnel discov]$ t any solid transp>5t m$ium might be end[$ ) ! p[] ( d\ble refraction by m]e compression4 ,z he attribut$ ! d\ble refract+ p[] ( cry/als to unequal ela/icity 9 diff]5t directions1 he inf]r$ t unequal ela/icity1 if artificially produc$1 w\ld give simil> ph5om5a4 ,) a p[]ful screw & a piece ( glass1 he !n produc$ n only ! col\rs due to d\ble refraction1 b ! actual duplication ( images4 ,?us1 by a great sci5tific g5]alisation1 are ! rem>kable prop]ties ( ,icel& sp> %[n to belong to all transp>5t sub/ances "u c]ta9 conditions4#dej #dej ,"y's 99,works991 vol4 i4 p4 #dab4 ,all o!r pr$ictions 9 optical sci5ce are1 h[ev]1 ?r[n into ! %ade by ! !oretical discov]y ( conical refraction by ! late ,sir ,w4 ,r4 ,hamilton1 ( ,dubl94 ,9 inve/igat+ ! passage ( light ?r\gh c]ta9 cry/als1 ,hamilton f\nd t ,fresnel _h slightly mis9t]pret$ 8 own =mul1 & t1 :5 rightly und]/ood1 !y indicat$ a ph5om5on ( a k9d nev] witness$4 ,a small ray ( light s5t into a cry/al ( arragonite 9 a p>ticul> direction1 becomes spread out into an inf9ite numb] ( rays1 :i* =m a holl[ cone )9 ! cry/al1 & a holl[ cyl9d] :5 em]g+ f ! opposite side4 ,9 ano!r case1 a diff]5t1 b equally /range1 effect is produc$1 a ray ( light be+ spread out into a holl[ cone at ! po9t :]e x quits ! cry/al4 ,^! ph5om5a are peculi>ly int]e/+1 because cones & cyl9d]s ( light are n produc$ 9 any o!r cases4 ,!y are oppos$ to all analogy1 & con/itute s+ul> exceptions1 ( a k9d :i* we %all aft]w>ds consid] m fully4 ,_! /rang5ess r5d]$ !m peculi>ly fitt$ to te/ ! tru? ( ! !ory by :i* !y 7 discov]$2 & :5 ,pr(essor ,lloyd1 at ,hamilton's reque/1 succe$$1 aft] consid]able difficulty1 9 witness+ ! new appe>ances1 no fur!r d\bt c\ld rema9 ( ! validity ( ! wave !ory :i* we owe to ,huygh5s1 ,"y1 & ,fresnel4#dea #dea ,lloyd's 99,wave ,!ory991 ,"p ii4 pp4 #eb-eh4 ,babbage1 99,n9? ,bridgewat] ,treatise991 p4 #ajd1 quot+ ,lloyd1 99,transactions ( ! ,royal ,iri% ,academy991 vol4 xvii4 ,clifton1 99,qu>t]ly ,j\rnal ( ,pure & ,appli$ ,ma!matics991 ,janu>y #ahfj4 99,pr$ictions f ! ,!ory ( ,undulations499 ,x is curi\s t ! undulations ( light1 al?\gh inconceivably rapid & small1 admit ( m accurate measurem5t ?an waves ( any o!r k9d4 ,b s f> z we c c>ry out exact exp]im5ts on o!r k9ds ( waves1 we f9d ! ph5om5a ( int]f]5ce repeat$1 & analogy gives consid]able p[] ( pr$iction4 ,h]s*el 0 p]haps ! fir/ to sugge/ t two s\nds might be made to de/roy ea* o!r by int]f]5ce4#deb ,= if "o-half ( a wave travell+ ?r\gh a tube c\ld be sep>at$1 & conduct$ by a long] passage1 s z1 on rejo9+ ! o!r half1 to be "o-qu>t] ( a vibration beh9d-h&1 ! two portions w\ld exactly neutralise ea* o!r4 ,?is exp]im5t has be5 p]=m$ ) success4 ,! int]f]5ce aris+ betwe5 ! waves f ! two prongs ( a tun+-=k 0 also pr$ict$ by !ory1 & prov$ to exi/ by ,web]2 inde$ x may be obs]v$ by m]ely hold+ a vibrat+ =k close to ! e> & turn+ x r\nd4#dec #deb 99,encyclopdia ,metropolitana991 art4 99,s\nd991 p4 #gec4 #dec ,tyndall's 99,s\nd991 pp4 #bfa1 #bgc4 ,x is a result ( ! !ory ( s\nd t1 if we move rapidly t[>ds a s\nd+ body1 or if x move rapidly t[>ds u1 ! pit* ( ! s\nd w be a little m acute2 &1 99vice v]s991 :5 ! relative motion is 9 ! opposite direction1 ! pit* w be m grave4 ,?is arises f ! less or great] int]vals ( "t elaps+ betwe5 ! successive /rokes ( waves ^u ! auditory n]ve1 accord+ z ! e> moves t[>ds or f ! s\rce ( s\nd relatively speak+4 ,?is effect 0 pr$ict$ by !ory1 & aft]w>ds v]ifi$ by ! exp]im5ts ( ,buys ,ballot1 on ,dut* railways1 & ( ,scott ,russell1 9 ,engl&4 ,:5ev] "o railway tra9 passes ano!r1 on ! locomotive ( :i* ! :i/le is be+ s\nd$1 ! drop 9 ! acut5ess ( ! s\nd may be notic$ at ! mom5t ( pass+4 ,?is *ange gives ! s\nd a peculi> h[l+ "*1 :i* _m p]sons mu/ h notic$4 ,i h calculat$ t ) two tra9s travell+ ?irty miles an h\r1 ! effect w\ld am\nt to r m ?an half a tone1 & ) "s express tra9s x w\ld am\nt to a tone4 ,a correspond+ effect is produc$ 9 ! case ( light undulations1 :5 ! eye & ! lum9\s body approa* or rec$e f ea* o!r4 ,x is %[n by a slight *ange 9 ! refrangibility ( ! rays ( light1 & a consequ5t *ange 9 ! place ( ! l9es ( ! spectrum1 :i* has be5 made to give important & unexpect$ in=mation conc]n+ ! relative approa* or recession ( />s4 ,tides are va/ waves1 & 7 ! e>?'s surface entirely cov]$ by an ocean ( uni=m dep?1 !y w\ld admit ( exact !oretical inve/igation4 ,! irregul> =m ( ! seas introduces unkn[n quantities & complexities ) :i* !ory _c cope4 ,nev]!less1 ,:ewell1 obs]v+ t ! tides ( ! ,g]man ,ocean consi/ ( int]f]+ waves1 :i* arrive p>tly r\nd ! ,nor? ( ,scotl& & p>tly ?r\gh ! ,briti% ,*annel1 0 enabl$ to pr$ict t at a po9t ab\t midway betwe5 ,brill on ! coa/ ( ,holl&1 & ,l[e/(t no tides w\ld be f\nd to exi/4 ,at t po9t ! two waves w\ld be ( ! same am\nt1 b 9 opposite phases1 s z to neutralise ea* o!r4 ,?is pr$iction 0 v]ifi$ by a survey+ vessel ( ! ,briti% navy4#ded #ded ,:ewell's 99,hi/ory ( ! ,inductive ,sci5ces991 vol4 ii4 p4 #dga4 ,h]s*el's 99,physical ,geography991 #gg4 99,pr$iction 9 o!r ,sci5ces499 ,g5]ations1 or ev5 c5turies1 may elapse be=e mank9d are 9 possession ( a ma!matical !ory ( ! con/itution ( matt] z complete z ! !ory ( gravitation4 ,nev]!less1 ma!matical physici/s h 9 rec5t ye>s acquir$ a hold ( "s ( ! relations ( ! physical =ces1 & ! pro( is f\nd 9 anticipations ( curi\s ph5om5a :i* _h nev] be5 obs]v$4 ,pr(essor ,james ,?omson d$uc$ f ,c>not's !ory ( heat t ! application ( pressure w\ld l[] ! melt+-po9t ( ice4 ,he ev5 v5tur$ to assign ! am\nt ( ?is effect1 & 8 /atem5t 0 aft]w>ds v]ifi$ by ,sir ,w4 ,?omson4#dee 8,9 ?is v rem>kable speculation1 an entirely novel physical ph5om5on 0 99pr$ict$991 9 anticipation ( any direct exp]im5ts on ! subject2 & ! actual obs]vation ( ! ph5om5on 0 po9t$ out z a highly int]e/+ object = exp]im5tal rese>*40 ,j z liquids :i* exp& 9 solidify+ w h ! temp]ature ( solidification l[]$ by pressure1 s liquids :i* contract 9 solidify+ w exhibit ! rev]se effect4 ,!y w be assi/$ 9 solidify+1 z x 71 by pressure1 s z to become solid at a high] temp]ature1 z ! pressure is great]4 ,?is latt] result 0 v]ifi$ by ,buns5 & ,hopk9s1 9 ! case ( p>aff91 sp]maceti1 wax1 & /e>94 ,! effect ^u wat] has m rec5tly be5 c>ri$ to su* an ext5t by ,m\sson1 t "u ! va/ pressure ( #acjj atmosph]es1 wat] did n freeze until cool$ d[n to -#ah;,c4 ,ano!r rem>kable pr$iction ( ,pr(essor ,?omson 0 to ! effect t1 if a metallic spr+ be weak5$ by a rise ( temp]ature1 "w done aga9/ ! spr+ 9 b5d+ x w cause a cool+ effect4 ,al?\gh ! effect to be expect$ 9 a c]ta9 app>atus 0 only ab\t f\r-?\s&?s ( a degree ,c5tigrade1 ,dr4 ,j\le#def succe$$ 9 measur+ x to ! ext5t ( ?ree-?\s&?s ( a degree1 su* is ! delicacy ( mod]n heat measurem5ts4 ,i _c refra9 f quot+ ,dr4 ,j\le's reflections ^u ?is fact4 8,?us ev5 9 ! above delicate case10 he says1 8is ! =mula ( ,pr(essor ,?omson completely v]ifi$4 ,! ma!matical inve/igation ( ! !rmo-ela/ic qualities ( metals has enabl$ my illu/ri\s fri5d to pr$ict ) c]ta9ty a :ole class ( highly int]e/+ ph5om5a4 ,to him especially d we owe ! important advance :i* has be5 rec5tly made to a new era 9 ! hi/ory ( sci5ce1 :5 ! fam\s philosophical sy/em ( ,bacon w be to a great ext5t sup]s$$1 & :51 in/ead ( arriv+ at discov]y by induction f exp]im5t1 we %all obta9 our l>ge/ accessions ( new facts by reason+ d$uctively f fundam5tal pr9ciples40 #dee ,maxwell's 99,!ory ( ,heat991 p4 #agd4 99,philosophical ,magaz9e991 ,augu/ #ahej4 ,?ird ,s]ies1 vol4 xxxvii4 p4 #abc4 #def 99,philosophical ,transactions991 #aheh1 vol4 cxlviii4 p4 #abg4 ,! !ory ( electricity is a necess>y "p ( ! g5]al !ory ( matt]1 & is rapidly acquir+ ! p[] ( prevision4 ,z soon z ,:eat/one _h prov$ exp]im5tally t ! conduction ( electricity occupies "t1 ,f>aday rem>k$ 9 #ahch1 ) wond]ful sagacity1 t if ! conduct+ wires 7 connect$ ) ! coat+s ( a l>ge ,leyd5 j>1 ! rapidity ( conduction w\ld be less5$4 ,?is pr$iction rema9$ unv]ifi$ = sixte5 ye>s1 until ! subm>9e cable 0 laid b5ea? ! ,*annel4 ,a consid]able ret>dation ( ! electric sp>k 0 !n detect$1 & ,f>aday at once po9t$ out t ! wire surr\nd$ by wat] resembles a ,leyd5 j> on a l>ge scale1 s t ea* message s5t ?r\gh ! cable v]ifi$ 8 rem>k ( #ahch4deg #deg ,tyndall's 99,f>aday991 pp4 #gc1 #gd2 99,life ( ,f>aday991 vol4 ii4 pp4 #hb1 #hc4 ,! jo9t relations ( heat & electricity to ! metals con/itute a new sci5ce ( !rmo-electricity by :i* ,sir ,w4 ,?omson 0 enabl$ to anticipate ! foll[+ curi\s effect1 namely1 t an electric curr5t pass+ 9 an iron b> f a hot to a cold "p produces a cool+ effect1 b 9 a copp] b> ! effect is exactly opposite 9 "*1 t is1 ! b> becomes heat$4#deh ,! action ( cry/als ) reg>d to heat & electricity 0 p>tly =ese5 on ! gr\nds ( !ory by ,poisson4 #deh ,tait's 99,!rmodynamics991 p4 #gg4 ,*emi/ry1 al?\gh to a great ext5t an empirical sci5ce1 has n be5 )\t prophetic triumphs4 ,! exi/5ce ( ! metals potassium & sodium 0 =ese5 by ,lavoisi]1 & _! elim9ation by ,davy 0 "o ( ! *ief 99exp]im5ta crucis99 :i* e/abli%$ ,lavoisi]'s sy/em4 ,! exi/5ce ( _m o!r metals :i* eye _h nev] se5 0 a natural inf]5ce1 & !ory has n be5 at fault4 ,9 ! above cases ! comp\nds ( ! metal 7 well kn[n1 & x 0 ! result ( decomposition t 0 =etold4 ,! discov]y 9 #ahgf ( ! metal gallium is peculi>ly int]e/+ because ! exi/5ce ( ?is metal1 previ\sly :olly unkn[n1 _h be5 inf]r$ f !oretical consid]ations by ,m4 ,m5delief1 & "s ( its prop]ties _h be5 correctly pr$ict$4 ,no soon]1 too1 _h a !ory ( organic comp\nds be5 conceiv$ by ,pr(essor ,a4 ,w4 ,williamson ?an he =etold ! =mation ( a complex sub/ance consi/+ ( wat] 9 :i* bo? atoms ( hydrog5 are replac$ by atoms ( acetyle4 ,?is sub/ance1 kn[n z ! acetic anhydride1 0 aft]w>ds produc$ by ,g]h>dt4 ,9 ! subsequ5t progress ( organic *emi/ry occurr5ces ( ?is k9d h become common4 ,! !oretical *emi/ by ! classification ( 8 specim5s & ! manipulation ( 8 =mul c plan out :ole s]ies ( unkn[n oils1 acids1 & alcohols1 j z a design] might draw out a multitude ( patt]ns4 ,pr(essor ,cayley has ev5 calculat$ = c]ta9 cases ! possible numb]s ( *emical comp\nds4#dei ,! =mation ( _m su* sub/ances is a matt] ( c\rse2 b !re is an int]e/+ pr$iction giv5 by ,h(mann1 conc]n+ ! possible exi/5ce ( new comp\nds ( sulphur & sel5ium1 & ev5 oxides ( ammonium1 :i* x rema9s = *emi/s to v]ify4#dfj #dei 99,on ! ,analytical ,=ms call$ ,trees1 ) ,application to ! ,!ory ( ,*emical ,comb9ations499 ,report ( ! ,briti% ,association1 #ahge1 p4 #beg4 #dfj ,h(mann's 99,introduction to ,*emi/ry991 pp4 #bbd1 #bbe4 99,pr$iction by ,inv]sion ( ,cause & ,effect499 ,!re is "o process ( exp]im5t :i* has s (t5 l$ to important discov]ies z to des]ve sep>ate illu/ration--,i mean ! inv]sion ( ,cause & ,effect4 ,?us if ,a & ,b 9 "o exp]im5t produce ,c z a consequ5t1 !n antec$5ts ( ! nature ( ,b & ,c may usually be made to produce a consequ5t ( ! nature ( ,a inv]t$ 9 direction4 ,:5 we apply heat to a gas x t5ds to exp&2 h5ce if we all[ ! gas to exp& by its own ela/ic =ce1 cold is ! result2 t is1 ,b 7air7 & ,c 7expansion7 produce ! negative ( ,a 7heat74 ,aga91 ,b 7air7 & compression1 ! negative ( ,c1 produce ,a 7heat74 ,simil> results may be expect$ 9 a multitude ( cases4 ,x is a famili> law t heat exp&s iron4 ,:at may be expect$1 !n1 if in/ead ( increas+ ! l5g? ( an iron b> by heat we use me*anical =ce & /ret* ! b>8 ,hav+ ! b> & ! =m] consequ5t1 expansion1 we %\ld expect ! negative ( ! =m] antec$5t1 namely cold4 ,! tru? ( ?is inf]5ce 0 prov$ by ,dr4 ,j\le1 :o inve/igat$ ! am\nt ( ! effect ) 8 usual skill4#dfa #dfa 99,philosophical ,transactions99 7#ahee71 vol4 cxlv4 pp4 #ajj1 c4 ,?is inv]sion ( cause & effect 9 ! case ( heat may be itself inv]t$ 9 a highly curi\s mann]4 ,x happ5s t !re are a few sub/ances :i* are unexpla9$ exceptions to ! g5]al law ( expansion by heat4 ,india-rubb] especially is rem>kable = 99contract+99 :5 heat$4 ,s9ce1 !n1 iron & india-rubb] are oppositely relat$ to heat1 we may expect t z di/5sion ( ! iron produc$ cold1 di/5sion ( ! india-rubb] w produce heat4 ,?is is actually f\nd to be ! case1 & anyone may detect ! effect by sudd5ly /ret*+ an india-rubb] b& :ile ! middle "p is 9 ! m\?4 ,:5 be+ /ret*$ x gr[s slightly w>m1 & :5 relax$ cold4 ,! read] w see t "s ( ! sci5tific pr$ictions m5tion$ 9 prec$+ sections 7 due to ! pr9ciple ( inv]sion2 = in/ance1 ,?omson's speculations on ! relation betwe5 pressure & ! melt+-po9t4 ,b _m o!r illu/rations c\ld be adduc$4 ,! usual ag5t by :i* we melt a sub/ance is heat2 b if we c melt a sub/ance )\t heat1 !n we may expect ! negative ( heat z an effect4 ,?is is ! f\ndation ( all freez+ mixtures4 ,! aff9ity ( salt = wat] causes x to melt ice1 & we may ?us r$uce ! temp]ature to ,fahr5heit's z]o4 ,calcium *loride has s mu* high] an attraction = wat] t a temp]ature ( -#de ,c4 may be atta9$ by its use4 ,ev5 ! solution ( a c]ta9 alloy ( lead1 t91 & bismu? 9 m]cury1 may be made to r$uce ! temp]ature ?r\gh #bg ,c4 ,all ! o!r modes ( produc+ cold are inv]sions ( m famili> uses ( heat4 ,c>r's freez+ ma*9e is an inv]t$ di/ill+ app>atus1 ! di/illation be+ occasion$ by *emical aff9ity in/ead ( heat4 ,ano!r k9d ( freez+ ma*9e is ! exact inv]se ( ! /eam-eng9e4 ,a v p>adoxical effect is due to ano!r inv]sion4 ,x is h>d to believe t a curr5t ( /eam at #ajj ,c4 c raise a body ( liquid to a high] temp]ature ?an ! /eam itself possesses4 ,b ,mr4 ,sp5ce has po9t$ out t if ! boil+-po9t ( a sal9e solution be above #ajj1 x w cont9ue1 on acc\nt ( its aff9ity = wat]1 to cond5se /eam :5 above #ajj 9 temp]ature4 ,x w cond5se ! /eam until heat$ to ! po9t at :i* ! t5sion ( its vap\r is equal to t ( ! atmosph]e1 t is1 its own boil+-po9t4#dfb ,aga91 s9ce heat melts ice1 we might expect to produce heat by ! inv]se *ange f wat] into ice4 ,?is is accompli%$ 9 ! ph5om5on ( susp5d$ freez+4 ,wat] may be cool$ 9 a clean glass vessel _m degrees bel[ ! freez+-po9t1 & yet reta9$ 9 ! liquid condition4 ,b if di/urb$1 & especially if br\ght into contact ) a small p>ticle ( ice1 x in/antly solidifies & rises 9 temp]ature to #j ,c4 ,! effect is /ill bett] display$ 9 ! lecture-room exp]im5t ( ! susp5d$ cry/allisation ( a solution ( sodium sulphate1 9 :i* a sudd5 rise ( temp]ature ( #ae or #bj ,c4 is (t5 manife/$4 #dfb 99,proce$+s ( ! ,man*e/] ,philosophical ,society991 ,feb4 #ahgj4 ,! sci5ce ( electricity is full ( mo/ int]e/+ cases ( inv]sion4 ,z ,pr(essor ,tyndall has rem>k$1 ,f>aday _h a pr(\nd belief 9 ! reciprocal relations ( ! physical =ces4 ,! great />t+-po9t ( 8 rese>*es1 ! discov]y ( electro-magnetism1 0 cle>ly an inv]sion4 ,o]/$ & ,ampre _h prov$ t ) an electric curr5t & a magnet 9 a p>ticul> position z antec$5ts1 motion is ! consequ5t4 ,if !n a magnet1 a wire & motion be ! antec$5ts1 an 99opposite99 electric curr5t w be ! consequ5t4 ,x w\ld be an endless task to trace out ! results ( ?is f]tile relation%ip4 ,ano!r "p ( ,f>aday's rese>*es 0 occupi$ 9 asc]ta9+ ! direct & inv]se relations ( magnetic & diamagnetic1 amorph\s & cry/all9e sub/ances 9 v>i\s circum/ances4 ,9 all o!r relations ( electricity ! pr9ciple ( inv]sion holds4 ,! voltamet] or ! electro-plat+ cell is ! inv]se ( ! galvanic batt]y4 ,z heat appli$ to a junction ( antimony & bismu? b>s produces electricity1 x foll[s t an electric curr5t pass$ ?r\gh su* a junction w produce cold4 ,b x is n[ suffici5tly app>5t t inv]sion ( cause & effect is a mo/ f]tile means ( discov]y & pr$iction4 99,facts kn[n only by ,!ory499 ,( ! f\r classes ( facts enum]at$ 9 p4 #ebe ! la/ rema9s unconsid]$4 ,x includes ! unv]ifi$ pr$ictions ( sci5ce4 ,sci5tific prophecy arre/s ! att5tion ( ! _w :5 x ref]s to su* /rik+ ev5ts z an eclipse1 ! appe>ance ( a great comet1 or any ph5om5on :i* p c v]ify ) _! own eyes4 ,b x is surely a matt] = great] wond] t a physici/ describes & measures ph5om5a :i* eye _c see1 nor s5se ( any k9d detect4 ,9 mo/ cases ?is arises f ! effect be+ too small 9 am\nt to affect our organs ( s5se1 or come )9 ! p[]s ( our in/rum5ts z at pres5t con/ruct$4 ,b !re is a class ( yet m rem>kable cases1 9 :i* a ph5om5on _c possibly be obs]v$1 & yet we c say :at x w\ld be if x 7 obs]v$4 ,9 a/ronomy1 sy/ematic ab]ration is an effect ( ! sun's prop] motion almo/ c]ta9ly kn[n to exi/1 b :i* we h no hope ( detect+ by obs]vation 9 ! pres5t age ( ! _w4 ,z ! e>?'s motion r\nd ! sun comb9$ ) ! motion ( light causes ! />s to deviate app>5tly f _! true positions to ! ext5t ( ab\t #ah at ! mo/1 s ! motion ( ! :ole planet>y sy/em ?r\gh space mu/ occasion a simil> displacem5t ( at mo/ #e4 ,! ord9>y ab]ration c be readily detect$ ) mod]n a/ronomical in/rum5ts1 because x goes ?r\gh a ye>ly *ange 9 direction or am\nt2 b sy/ematic ab]ration is con/ant s long z ! planet>y sy/em moves uni=mly 9 a s5sibly /raight l9e4 ,only !n 9 ! c\rse ( ages1 :5 ! curvature ( ! sun's pa? becomes app>5t1 c we hope to v]ify ! exi/5ce ( ?is k9d ( ab]ration4 ,a curi\s effect mu/ also be produc$ by ! sun's prop] motion ^u ! app>5t p]iods ( revolution ( ! b9>y />s4 ,to my m9d1 "s ( ! mo/ int]e/+ tru?s 9 ! :ole range ( sci5ce are ^? :i* h n be51 & 9 _m cases probably nev] c be1 v]ifi$ by trial4 ,?us ! *emi/ assigns1 ) a v high degree ( probability1 ! vap\r d5sities ( su* elem5ts z c>bon & silicon1 :i* h nev] be5 obs]v$ sep>ately 9 a /ate ( vap\r4 ,! *emi/ is also famili> ) ! vap\r d5sities ( elem5ts at temp]atures at :i* ! elem5ts 9 "q nev] h be51 & probably nev] c be1 submitt$ to exp]im5t 9 ! =m ( vap\r4 ,j\le & o!rs h calculat$ ! actual velocity ( ! molecules ( a gas1 & ev5 ! numb] ( collisions :i* mu/ take place p] second dur+ _! con/ant circulation4 ,physici/s h n yet giv5 u ! exact magnitudes ( ! p>ticles ( matt]1 b !y h asc]ta9$ by sev]al me?ods ! limits )9 :i* _! magnitudes mu/ lie4 ,su* sci5tific results mu/ be = ev] beyond ! p[] ( v]ification by ! s5ses4 ,i h else:]e _h occasion to rem>k t waves ( light1 ! intimate processes ( electrical *anges1 ! prop]ties ( ! e!r :i* is ! base ( all ph5om5a1 are necess>ily det]m9$ 9 a hypo!tical1 b n !re=e a less c]ta9 mann]4 ,?\gh only two ( ! metals1 gold & silv]1 h ev] be5 obs]v$ to be transp>5t1 we "k on ! gr\nds ( !ory t !y are all m or less s2 we c ev5 e/imate by !ory _! refractive indices1 & prove t !y are exce$+ly high4 ,! ph5om5a ( elliptic pol>isation1 & p]haps also ^? ( int]nal radiation1#dfc dep5d ^u ! refractive index1 & ?us1 ev5 :5 we _c obs]ve any refract$ rays1 we c indirectly le>n h[ !y w\ld be refract$4 #dfc ,balf\r ,/ew>t1 99,elem5t>y ,treatise on ,heat991 #a/ edit4 p4 #aih4 ,9 _m cases l>ge quantities ( electricity mu/ be produc$1 :i* we _c obs]ve because x is in/antly dis*>g$4 ,9 ! common electric ma*9e ! cyl9d] & rubb] are made ( non-conductors1 s t we c sep>ate & accumulate ! electricity4 ,b a little damp1 by s]v+ z a conductor1 prev5ts ?is sep>ation f endur+ any s5sible "t4 ,h5ce !re is no d\bt t :5 we rub two good conductors aga9/ ea* o!r1 = in/ance two pieces ( metals1 mu* electricity is produc$1 b in/antane\sly conv]t$ into "s o!r =m ( en]gy4 ,j\le believes t all ! heat ( friction is transmut$ electricity4 ,z reg>ds ph5om5a ( ins5sible am\nt1 nature is absolutely full ( !m4 ,we mu/ reg>d ^? *anges :i* we c obs]ve z ! comp>atively r>e aggregates ( m9ut] *anges4 ,on a little reflection we mu/ all[ t no object kn[n to u rema9s = two in/ants ( exactly ! same temp]ature4 ,if s1 ! dim5sions ( objects mu/ be 9 a p]petual /ate ( v>iation4 ,! m9or planet>y & lun> p]turbations are inf9itely num]\s1 b usually too small to be detect$ by obs]vation1 al?\gh _! am\nts may be assign$ by !ory4 ,!re is e reason to believe t *emical & electric actions ( small am\nt are con/antly 9 progress4 ,! h>de/ sub/ances1 if r$uc$ to extremely small p>ticles1 & diffus$ 9 pure wat]1 manife/ oscillatory movem5ts :i* mu/ be due to *emical & electric *anges1 s slight t !y g on = ye>s )\t affect+ appreciably ! weight ( ! p>ticles4#dfd ,! e>?'s magnetism mu/ m or less affect e object :i* we h&le4 ,z ,tyndall rem>ks1 8,an upright iron /one influ5c$ by ! e>?'s magnetism becomes a magnet1 ) its bottom a nor? & its top a s\? pole4 ,d\btless1 ?\gh 9 an imm5sely feebl] degree1 e erect m>ble /atue is a true diamagnet1 ) its head a nor? pole & its feet a s\? pole4 ,! same is c]ta9ly true ( man z he /&s ^u ! e>?'s surface1 = all ! tissues ( ! human body are diamagnetic40#dfe ,! sun's light produces a v quick & p]ceptible effect ^u ! photographic plate2 9 all probability x has a less effect ^u a great v>iety ( sub/ances4 ,we may reg>d e ph5om5on z an exagg]at$ & conspicu\s case ( a process :i* is1 9 inf9itely num]\s cases1 beyond ! means ( obs]vation4 #dfd ,jevons1 99,proce$+s ( ! ,man*e/] ,lit]>y & ,philosophical ,society991 #be? ,janu>y1 #ahgj1 vol4 ix4 p4 #gh4 #dfe 99,philosophical ,transactions991 vol4 cxlvi4 p4 #bdi4 ,,*apt] ,,xxv4 ,,accordance ,,( ,,quantitative ,,!ories4 ,9 ! prec$+ *apt] we f\nd t facts may be class$ "u f\r heads z reg>ds _! connection ) !ory1 & our p[]s ( explanation or pr$iction4 ,! facts hi!rto consid]$ 7 g5]ally ( a qualitative r ?an a quantitative nature2 b :5 we look exclusively to ! quantity ( a ph5om5on1 & ! v>i\s modes 9 :i* we may det]m9e its am\nt1 ne>ly ! same sy/em ( classification w hold good4 ,!re w1 h[ev]1 be five possible cases3-- 7#a7 ,we may directly & empirically measure a ph5om5on1 )\t be+ able to expla9 :y x %\ld h any p>ticul> quantity1 or to connect x by !ory ) o!r quantities4 7#b7 ,9 a consid]able numb] ( cases we c !oretically pr$ict ! exi/5ce ( a ph5om5on1 b are unable to assign its am\nt1 except by direct measurem5t1 or to expla9 ! am\nt !oretically :5 ?us asc]ta9$4 7#c7 ,we may measure a quantity1 & aft]w>ds expla9 x z relat$ to o!r quantities1 or z gov]n$ by kn[n quantitative laws4 7#d7 ,we may pr$ict ! quantity ( an effect on !oretical gr\nds1 & aft]w>ds confirm ! pr$iction by direct measurem5t4 7#e7 ,we may indirectly det]m9e ! quantity ( an effect )\t be+ able to v]ity x by exp]im5t4 ,^! classes ( quantitative facts might be illu/rat$ by an imm5se numb] ( int]e/+ po9ts 9 ! hi/ory ( physical sci5ce4 ,only a few in/ances ( ea* class c be giv5 "h4 99,empirical ,measurem5ts499 ,"u ! fir/ head ( purely empirical measurem5ts1 :i* h n be5 br\ght "u any !oretical sy/em1 may be plac$ ! great bulk ( quantitative facts record$ by sci5tific obs]v]s4 ,! tables ( num]ical results :i* ab\nd 9 books on *emi/ry & physics1 ! huge qu>tos conta9+ ! obs]vations ( public obs]vatories1 ! multitud9\s tables ( meteorological obs]vations1 :i* are cont9ually be+ publi%$1 ! m ab/ruse results conc]n+ t]re/rial magnetism--su* results ( measurem5t1 = ! mo/ "p1 rema9 empirical1 ei!r because !ory is defective1 or ! lab\r ( calculation & comp>ison is too =midable4 ,9 ! ,gre5wi* ,obs]vatory1 inde$1 ! salut>y practice has be5 ma9ta9$ by ! pres5t ,a/ronom] ,royal1 ( always r$uc+ ! obs]vations1 & comp>+ !m ) ! !ories ( ! sev]al bodies4 ,! div]g5ces f !ory ?us af=d mat]ial = ! discov]y ( errors or ( new ph5om5a2 9 %ort1 ! obs]vations h be5 turn$ to ! use = :i* !y 7 int5d$4 ,b x is to be fe>$ t o!r e/abli%m5ts are too (t5 engag$ 9 m]ely record+ numb]s ( :i* no real use is made1 because ! lab\r ( r$uction & comp>ison ) !ory is too great = private inquir]s to und]take4 ,9 meteorology1 especially1 great wa/e ( lab\r & money is tak+ place1 only a small fraction ( ! results record$ be+ ev] us$ = ! advancem5t ( ! sci5ce4 ,= "o meteorologi/ l ,quetelet1 ,dove1 or ,bax5dell1 :o devotes himself to ! truly useful lab\r ( r$uc+ o!r p's obs]vations1 !re are hundr$s :o lab\r "u ! delusion t !y are advanc+ sci5ce by load+ our book-%elves ) num]ical tables4 ,x is to be fe>$1 9 l mann]1 t almo/ ! :ole bulk ( /ati/ical numb]s1 :e!r comm]cial1 vital1 or moral1 is ( little sci5tific value4 ,purely empirical measurem5ts may h a direct practical value1 z :5 tables ( ! specific gravity1 or /r5g? ( mat]ials1 assi/ ! eng9e]2 ! specific gravities ( mixtures ( wat] ) acids1 alcohols1 salts1 c41 are useful 9 *emical manufactories1 cu/om-h\se gaug+1 c42 obs]vations ( ra9fall are requisite = que/ions ( wat] supply2 ! refractive index ( v>i\s k9ds ( glass mu/ be kn[n 9 mak+ a*romatic l5ses2 b 9 all su* cases ! use made ( ! measurem5ts is n sci5tific b practical4 ,x may be ass]t$1 t no numb] :i* rema9s isolat$1 & uncomp>$ by !ory ) o!r numb]s1 is ( sci5tific value4 ,hav+ tri$ ! t5sile /r5g? ( a piece ( iron 9 a p>ticul> condition1 we "k :at w be ! /r5g? ( ! same k9d ( iron 9 a simil> condition1 provid$ we c ev] meet ) t exact k9d ( iron aga92 b we _c argue f piece to piece1 nor lay d[n any laws exactly connect+ ! /r5g? ( iron ) ! quantity ( its impurities4 99,quantities indicat$ by ,!ory1 b ,empirically ,measur$499 ,9 _m cases we are able to =esee ! exi/5ce ( a quantitative effect1 on ! gr\nd ( g5]al pr9ciples1 b are unable1 ei!r f ! want ( num]ical data1 or f ! entire abs5ce ( any ma!matical !ory1 to assign ! am\nt ( su* effect4 ,we !n h rec\rse to direct exp]im5t to det]m9e its am\nt4 ,:e!r we argu$ f ! oceanic tides by analogy1 or d$uctively f ! !ory ( gravitation1 !re c\ld be no d\bt t atmosph]ic tides ( "s am\nt mu/ occur 9 ! atmosph]e4 ,!ory1 h[ev]1 ev5 9 ! h&s ( ,laplace1 0 n able to ov]come ! complicat$ me*anical conditions ( ! atmosph]e1 & pr$ict ! am\nts ( su* tides2 &1 on ! o!r h&1 ^! am\nts 7 s small1 & 7 s mask$ by f> l>g] undulations aris+ f ! heat+ p[] ( ! sun1 & f o!r meteorological di/urbances1 t !y w\ld probably h nev] be5 discov]$ by purely empirical obs]vations4 ,!ory hav+1 h[ev]1 indicat$ _! exi/5ce & _! p]iods1 x 0 easy to make s]ies ( b>ometrical obs]vations 9 places select$ s z to be z free z possible f casual fluctuations1 & !n1 by ! suitable application ( ! me?od ( means1 to detect ! small effects 9 "q4 ,! pr9cipal lun> atmosph]ic tide 0 ?us prov$ to am\nt to betwe5 #jjc & #jjd in*4#dff #dff ,grant's 99,hi/ory ( ,physical ,a/ronomy991 p4 #afb4 ,!ory yields ! greate/ possible assi/ance 9 apply+ ! me?od ( means4 ,= if we h a great numb] ( empirical measurem5ts1 ea* repres5t+ ! jo9t effect ( a numb] ( causes1 our object w be to take ! mean ( all ^? 9 :i* ! effect to be measur$ is pres5t1 & comp>e x ) ! mean ( ! rema9d] 9 :i* ! effect is abs5t1 or acts 9 ! opposite direction4 ,! diff]5ce w !n repres5t ! am\nt ( ! effect1 or d\ble ! am\nt respectively4 ,?us1 9 ! case ( ! atmosph]ic tides1 we take ! mean ( all ! obs]vations :5 ! moon 0 on ! m]idian1 & comp>e x ) ! mean ( all obs]vations :5 %e 0 on ! horizon4 ,9 ?is case we tru/ to *ance t all o!r effects w lie ab\t z (t5 9 "o direction z ! o!r1 & w neutralise !mselves 9 ! draw+ ( ea* mean4 ,x is a great advantage1 h[ev]1 to be able to decide by !ory :5 ea* pr9cipal di/urb+ effect is pres5t or abs5t2 = ! means may !n be drawn s z to sep>ate ea* su* effect1 leav+ only m9or & casual div]g5ces to ! law ( error4 ,?us1 if !re be ?ree pr9cipal effects1 & we draw means giv+ respectively ! sum ( all ?ree1 ! sum ( ! fir/ two1 & ! sum ( ! la/ two1 !n we ga9 ?ree simple equations1 by ! solution ( :i* ea* quantity is det]m9$4 99,expla9$ ,results ( ,measurem5t499 ,! second class ( measur$ ph5om5a conta9s ^? :i*1 aft] be+ det]m9$ 9 a direct & purely empirical application ( measur+ in/rum5ts1 are aft]w>ds %[n to agree ) "s hypo!tical explanation4 ,su* results are turn$ to _! prop] use1 & sev]al advantages may arise f ! comp>ison4 ,! correspond5ce ) !ory w seldom or nev] be precise2 &1 ev5 if x be s1 ! co9cid5ce mu/ be reg>d$ z accid5tal4 ,if ! div]g5ces betwe5 !ory & exp]im5t be comp>atively small1 & v>iable 9 am\nt & direction1 !y may (t5 be safely attribut$ to inconsid]able s\rces ( error 9 ! exp]im5tal processes4 ,! /rict me?od ( proc$ure is to calculate ! probable error ( ! mean ( ! obs]v$ results 7p4 #chg71 & !n obs]ve :e!r ! !oretical result falls )9 ! limits ( probable error4 ,if x does1 & if ! exp]im5tal results agree z well ) !ory z !y agree ) ea* o!r1 !n ! probability ( ! !ory is mu* increas$1 & we may employ ! !ory ) m confid5ce 9 ! anticipation ( fur!r results4 ,! probable error1 x %\ld be rememb]$1 gives a measure only ( ! effects ( incid5tal & v>iable s\rces ( error1 b 9 no degree indicates ! am\nt ( fix$ causes ( error4 ,?us1 if ! mean results ( two modes ( det]m9+ a quantity are s f> ap>t t ! limits ( probable error d n ov]lap1 we may inf] ! exi/5ce ( "s ov]look$ s\rce ( fix$ error 9 "o or bo? modes4 ,we w fur!r consid] 9 a subsequ5t section ! discordance ( measurem5ts4 99,quantities det]m9$ by ,!ory & v]ifi$ by ,measurem5t499 ,"o ( ! mo/ satisfactory te/s ( a !ory consi/s 9 its application n only to pr$ict ! nature ( a ph5om5on1 & ! circum/ances 9 :i* x may be obs]v$1 b also to assign ! precise quantity ( ! ph5om5on4 ,if we c subsequ5tly apply accurate in/rum5ts & measure ! am\nt ( ! ph5om5on witness$1 we h an excell5t opportunity ( v]ify+ or negativ+ ! !ory4 ,x 0 9 ?is mann] t ,newton fir/ attempt$ to v]ify 8 !ory ( gravitation4 ,he knew approximately ! velocity produc$ 9 fall+ bodies at ! e>?'s surface1 & if ! law ( ! inv]se squ>e ( ! di/ance held true1 & ! reput$ di/ance ( ! moon 0 correct1 he c\ld inf] t ! moon ought to fall t[>ds ! e>? at ! rate ( fifte5 feet 9 "o m9ute4 ,n[1 ! actual div]g5ce ( ! moon f ! tang5t ( its orbit appe>$ to am\nt only to ?irte5 feet 9 "o m9ute1 & !re 0 a discrepancy ( two feet 9 fifte51 :i* caus$ ,newton to lay 8aside at t "t any fur!r ?\ghts ( ?is matt]40 ,_m ye>s aft]w>ds1 probably fifte5 or sixte5 ye>s1 ,newton obta9$ m precise data f :i* he c\ld calculate ! size ( ! moon's orbit1 & he !n f\nd ! discrepancy to be inconsid]able4 ,8 !ory ( gravitation 0 ?us v]ifi$ z f> z ! moon 0 conc]n$2 b ?is 0 to him only ! beg9n+ ( a long c\rse ( d$uctive calculations1 ea* end+ 9 a v]ification4 ,if ! e>? & moon attract ea* o!r1 & also ! sun & ! e>?1 !re is reason to expect t ! sun & moon %\ld attract ea* o!r4 ,newton foll[$ out ! consequ5ces ( ?is inf]5ce1 & %[$ t ! moon w\ld n move z if attract$ by ! e>? only1 b sometimes fa/] & sometimes sl[]4 ,comp>ison ) ,flam/e$'s obs]vations ( ! moon %[$ t su* 0 ! case4 ,newton argu$ aga91 t z ! wat]s ( ! ocean are n rigidly atta*$ to ! e>?1 !y might attract ! moon1 & be attract$ 9 return1 indep5d5tly ( ! re/ ( ! e>?4 ,c]ta9 daily motions resembl+ ! tides w\ld !n be caus$1 & !re 7 ! tides to v]ify ! reason+4 ,x 0 ! extraord9>y p[] ) :i* ,newton trac$ out geometrically ! consequ5ces ( 8 !ory1 & submitt$ !m to repeat$ comp>ison ) exp]i5ce1 :i* con/itutes 8 pre-em95ce ov] all physici/s4 99,quantities det]m9$ by ,!ory & n v]ifi$499 ,x w cont9ually happ5 t we are able1 f c]ta9 measur$ ph5om5a & a correct !ory1 to det]m9e ! am\nt ( "s o!r ph5om5on :i* we may ei!r be unable to measure at all1 or to measure ) an accuracy correspond+ to t requir$ to v]ify ! pr$iction4 ,?us ,laplace hav+ work$ out a !ory ( ! motions ( ,jupit]'s satellites on ! hypo!sis ( gravitation1 f\nd t ^! motions 7 greatly affect$ by ! sph]oidal =m ( ,jupit]4 ,! motions ( ! satellites c be obs]v$ ) great accuracy ow+ to _! frequ5t eclipses & transits1 & f ^! motions he 0 able to argue inv]sely1 & assign ! ellipticity ( ! planet4 ,! ratio ( ! pol> & equatorial axes ?us det]m9$ 0 v ne>ly t ( #ac to #ad2 & x agrees well ) su* direct micrometrical measurem5ts ( ! planet z h be5 made2 b ,laplace believ$ t ! !ory gave a m accurate result ?an direct obs]vation c\ld yield1 s t ! !ory c\ld h>dly be said to admit ( direct v]ification4 ,! specific heat ( air 0 believ$ on ! gr\nds ( direct exp]im5t to am\nt to #jbffi1 ! specific heat ( wat] be+ tak5 z unity2 b ! me?ods ( exp]im5t 7 op5 to consid]able causes ( error4 ,rank9e %[$ 9 #ahej t x 0 possible to calculate f ! me*anical equival5t ( heat & o!r !rmodynamic data1 :at ?is numb] %\ld be1 & he f\nd x to be #jbcgh4 ,?is det]m9ation 0 at ! "t accept$ z ! mo/ satisfactory result1 al?\gh n v]ifi$2 subsequ5tly 9 #ahec ,regnault obta9$ by direct exp]im5t ! numb] #jbcgg1 prov+ t ! pr$iction _h be5 well gr\nd$4 ,x is readily se5 t 9 quantitative que/ions v]ification is a matt] ( degree & probability4 ,a less accurate me?od ( measurem5t _c v]ify ! results ( a m accurate me?od1 s t if we arrive at a det]m9ation ( ! same physical quantity 9 sev]al di/9ct modes x is (t5 a delicate matt] to decide :i* result is mo/ reliable1 & %\ld be us$ = ! indirect det]m9ation ( o!r quantities4 ,= in/ance1 ,j\le's & ,?omson's +5i\s exp]im5ts ^u ! !rmal ph5om5a ( fluids 9 motion#dfg involv$1 z "o physical con/ant1 ! me*anical equival5t ( heat2 if requisite1 !n1 !y might h be5 us$ to det]m9e t important con/ant4 ,b if m direct me?ods ( exp]im5t give ! me*anical equival5t ( heat ) sup]ior accuracy1 !n ! exp]im5ts on fluids w be turn$ to a bett] use 9 det]m9+ v>i\s quantities relat+ to ! !ory ( fluids4 ,we w fur!r consid] que/ions ( ?is k9d 9 succe$+ sections4 #dfg 99,philosophical ,transactions99 7#ahed71 vol4 cxliv4 p4 #cfd4 ,!re are ( c\rse _m quantities assign$ on !oretical gr\nds :i* we are q unable to v]ify ) correspond+ accuracy4 ,! ?ickness ( a film ( gold leaf1 ! av]age dep?s ( ! oceans1 ! velocity ( a />'s approa* to or regression f ! e>? z inf]r$ f spectroscopic data 7pp4 #bif-ii71 are cases 9 po9t2 b _m o!rs might be quot$ :]e direct v]ification seems impossible4 ,newton & subsequ5t physici/s h measur$ light undulations1 & by sev]al me?ods we le>n ! velocity ) :i* light travels4 ,s9ce an undulation ( ! middle gre5 is ab\t five t5-million?s ( a metre 9 l5g?1 & travels at ! rate ( ne>ly #cjj1jjj1jjj ( metres p] second1 x foll[s t ab\t #fjj1jjj1jjj1jjj1jjj undulations mu/ /rike 9 "o second ! ret9a ( an eye :i* p]ceives su* light4 ,b h[ are we to v]ify su* an a/\nd+ calculation by directly c\nt+ pulses :i* recur six hundr$ billions ( times 9 a second8 99,discordance ( ,!ory & ,exp]im5t499 ,:5 a di/9ct want ( accordance is f\nd to exi/ betwe5 ! results ( !ory & direct measurem5t1 int]e/+ que/ions arise z to ! mode 9 :i* we c acc\nt = ?is discordance4 ,! ultimate explanation ( ! discrepancy may be accompli%$ 9 at lea/ f\r ways z foll[s3-- 7#a7 ,! direct measurem5t may be errone\s ow+ to v>i\s s\rces ( casual error4 7#b7 ,! !ory may be correct z f> z reg>ds ! g5]al =m ( ! suppos$ laws1 b "s ( ! con/ant numb]s or o!r quantitative data employ$ 9 ! !oretical calculations may be inaccurate4 7#c7 ,! !ory may be false1 9 ! s5se t ! =ms ( ! ma!matical equations assum$ to express ! laws ( nature are incorrect4 7#d7 ,! !ory & ! involv$ quantities may be approximately accurate1 b "s regul> unkn[n cause may h int]f]$1 s t ! div]g5ce may be reg>d$ z a 99residual effect99 repres5t+ possibly a new & int]e/+ ph5om5on4 ,no precise rules c be laid d[n z to ! be/ mode ( proce$+ to expla9 ! div]g5ce1 & ! exp]im5tali/ w h to dep5d ^u 8 own insight & k2 b ! foll[+ recomm5dations may be made4 ,if ! exp]im5tal measurem5ts are n num]\s1 repeat !m & take a m ext5sive mean result1 ! probable accuracy ( :i*1 z reg>ds casual errors1 w increase z ! squ>e root ( ! numb] ( exp]im5ts4 ,suppos+ t no consid]able modification ( ! result is ?us effect$1 we may suspect ! exi/5ce ( m deep-seat$ s\rces ( error 9 our me?od ( measurem5t4 ,! next res\rce w be to *ange ! size & =m ( ! app>atus employ$1 & to introduce v>i\s modifications 9 ! mat]ials employ$ or ! c\rse ( proc$ure1 9 ! hope 7p4 #cif7 t "s cause ( con/ant error may ?us be remov$4 ,if ! inconsi/5cy ) !ory /ill rema9s unr$uc$ we may attempt to inv5t "s widely diff]5t mode ( arriv+ at ! same physical quantity1 s t we may be almo/ sure t ! same cause ( error w n affect bo? ! new & old results4 ,9 "s cases x is possible to f9d five or six ess5tially diff]5t modes ( arriv+ at ! same det]m9ation4 ,suppos+ t ! discrepancy /ill exi/s we may beg9 to suspect t our direct measurem5ts are correct1 & t ! data employ$ 9 ! !oretical calculations are inaccurate4 ,we mu/ n[ review ! gr\nds on :i* ^! data dep5d1 consi/+ z !y mu/ ultimately d ( direct measurem5ts4 ,a comp>ison ( ! record$ data w %[ ! degree ( probability atta*+ to ! mean result employ$2 & if !re is any gr\nd = imag9+ ! exi/5ce ( error1 we %\ld repeat ! obs]vations1 & v>y ! =ms ( exp]im5t j z 9 ! case ( ! previ\s direct measurem5ts4 ,! cont9u$ exi/5ce ( ! discrepancy mu/ %[ t we h n atta9$ to a complete acqua9tance ) ! !ory ( ! causes 9 action1 b two diff]5t cases /ill rema94 ,we may h misund]/ood ! action ( ^? causes :i* we "k to exi/1 or we may h ov]look$ ! exi/5ce ( "o or m o!r causes4 ,9 ! fir/ case our hypo!sis appe>s to be wrongly *os5 & inapplicable2 b :e!r we are to reject x w dep5d ^u :e!r we c =m ano!r hypo!sis :i* yields a m accurate accordance4 ,! probability ( an hypo!sis1 x w be rememb]$ 7p4 #bdc71 is to be judg$1 9 ! abs5ce ( 99 priori99 gr\nds ( judgm5t1 by ! probability t if ! suppos$ causes exi/ ! obs]v$ result foll[s2 b z !re is n[ little probability ( reconcil+ ! orig9al hypo!sis ) our direct measurem5ts ! field is op5 = new hypo!ses1 & any "o :i* gives a clos] accordance ) measurem5t w s f> h bett] claims to att5tion4 ,( c\rse we mu/ nev] e/imate ! probability ( an hypo!sis m]ely by its accordance ) a few results only4 ,its g5]al analogy & accordance ) o!r kn[n laws ( nature1 & ! fact t x does n conflict ) o!r probable !ories1 mu/ be tak5 into acc\nt1 z we %all see 9 ! next book4 ,! requisite condition ( a good hypo!sis1 t x mu/ admit ( ! d$uction ( facts v]ifi$ 9 obs]vation1 mu/ be int]pret$ 9 ! wide/ mann]1 z includ+ all ways 9 :i* !re may be accordance or discordance4 ,all our attempts at reconciliation hav+ fail$1 ! only conclusion we c come to is t "s unkn[n cause ( a new "* exi/s4 ,if ! measurem5ts be accurate & ! !ory probable1 !n !re rema9s a 99residual ph5om5on991 :i*1 be+ devoid ( !oretical explanation1 mu/ be set d[n z a new empirical fact wor?y ( fur!r inve/igation4 ,out/&+ residual discrepancies h (t5 be5 f\nd to involve new discov]ies ( ! greate/ importance4 99,accordance ( ,measurem5ts ( ,a/ronomical ,di/ances499 ,"o ( ! mo/ in/ructive in/ances :i* we c meet1 ( ! mann] 9 :i* diff]5t measurem5ts confirm or *eck ea* o!r1 is furni%$ by ! det]m9ation ( ! velocity ( light1 & ! dim5sions ( ! planet>y sy/em4 ,roem] fir/ discov]$ t light requires "t to travel1 by obs]v+ t ! eclipses ( ,jupit]'s satellites1 al?\gh !y occur at fix$ mom5ts ( absolute "t1 are visible at diff]5t mom5ts 9 diff]5t p>ts ( ! e>?'s orbit1 accord+ to ! di/ance betwe5 ! e>? & ,jupit]4 ,! "t occupi$ by light 9 trav]s+ ! mean semi-diamet] ( ! e>?'s orbit is f\nd to be ab\t eight m9utes4 ,! mean di/ance ( ! sun & e>? 0 long assum$ by a/ronom]s z be+ ab\t #ie1bgd1jjj miles1 ?is result be+ d$uc$ by ,bessel f ! obs]vations ( ! transit ( ,v5us1 :i* occurr$ 9 #agfi1 & :i* 7 f\nd to give ! sol> p>allax1 or :i* is ! same ?+1 ! app>5t angul> magnitude ( ! e>? se5 f ! sun1 z equal to #hegh4 ,divid+ ! mean di/ance ( ! sun & e>? by ! numb] ( seconds 9 #hm4 #acs4#c we f9d ! velocity ( light to be ab\t #aib1jjj miles p] second4 ,ne>ly ! same result 0 obta9$ 9 :at seems a diff]5t mann]4 ,! ab]ration ( light is ! app>5t *ange 9 ! direction ( a ray ( light ow+ to ! composition ( its motion ) t ( ! e>?'s motion r\nd ! sun4 ,if we "k ! am\nt ( ab]ration & ! mean velocity ( ! e>?1 we c e/imate t ( light1 :i* is ?us f\nd to be #aia1ajj miles p] second4 ,n[ ?is det]m9ation dep5ds ^u a new physical quantity1 t ( ab]ration1 :i* is asc]ta9$ by direct obs]vation ( ! />s1 s t ! close accordance ( ! e/imates ( ! velocity ( light z ?us arriv$ at by diff]5t me?ods might seem to leave little room = d\bt1 ! diff]5ce be+ less ?an "o p] c5t4 ,nev]!less1 exp]im5tali/s 7 n satisfi$ until !y _h succe$$ 9 measur+ ! velocity ( light by direct exp]im5ts p]=m$ ^u ! e>?'s surface4 ,fizeau1 by a rapidly revolv+ too!d :eel1 e/imat$ ! velocity at #aie1ibj miles p] second4 ,z ?is result diff]$ by ab\t "o "p 9 sixty f e/imates previ\sly accept$1 !re 0 ?\ght to be room = fur!r inve/igation4 ,! revolv+ mirror1 us$ by ,:eat/one 9 measur+ ! velocity ( electricity1 0 n[ appli$ 9 a m ref9$ mann] by ,fizeau & by ,f\cault to det]m9e ! velocity ( light4 ,! latt] physici/ came to ! />tl+ conclusion t ! velocity 0 n really m ?an #ahe1agb miles p] second4 ,no repetition ( ! exp]im5t w\ld %ake ?is result1 & !re 0 accord+ly a discrepancy betwe5 ! a/ronomical & ! exp]im5tal results ( ab\t #g1jjj miles p] second4 ,! late/ exp]im5ts1 ^? ( ,m4 ,cornu1 only slightly raise ! e/imate1 giv+ #ahf1ffj miles p] second4 ,a little consid]ation %[s t bo? ! a/ronomical det]m9ations involve ! magnitude ( ! e>?'s orbit z "o datum1 because our e/imate ( ! e>?'s velocity 9 its orbit dep5ds ^u our e/imate ( ! sun's mean di/ance4 ,accord+ly z reg>ds ?is quantity ! two a/ronomical results c\nt only = "o4 ,?\gh ! transit ( ,v5us _h be5 consid]$ to give ! be/ data = ! calculation ( ! sun's p>allax1 yet a/ronom]s _h n neglect$ less fav\rable opportunities4 ,hans51 calculat+ f c]ta9 inequalities 9 ! moon's motion1 _h e/imat$ x at #hiaf2 ,w9neke1 f obs]vations ( ,m>s1 at #hifd2 ,lev]ri]1 f ! motions ( ,m>s1 ,v5us1 & ! moon1 at #hiej4 ,^! indep5d5t results agree mu* bett] ) ea* o!r ?an ) t ( ,bessel 7#hegh7 previ\sly receiv$1 or t ( ,encke 7#heh7 d$uc$ f ! transits ( ,v5us 9 #agfa & #agfi1 & ?\gh ea* sep>ately might be wor?y ( less cr$it1 yet _! close accordance r5d]s _! mean result 7#hidc7 comp>able 9 probability ) t ( ,bessel4 ,x 0 fur!r f\nd t if ,f\cault's value = ! velocity ( light 7 assum$ to be correct1 & ! sun's di/ance 7 inv]sely calculat$ f t1 ! sun's p>allax w\ld be #hifj1 :i* closely agre$ ) ! above mean result4 ,?is fur!r correspond5ce ( indep5d5t results ?rew ! balance ( probability /rongly aga9/ ! results ( ! transit ( ,v5us1 & r5d]$ x desirable to reconsid] ! obs]vations made on t occasion4 ,mr4 ,e4 ,j4 ,/one1 hav+ re-discuss$ ^? obs]vations1#dfh f\nd t grave ov]sights _h be5 made 9 ! calculations1 :i* be+ correct$ w\ld alt] ! e/imate ( p>allax to #hia1 a quantity 9 su* comp>atively close accordance ) ! o!r results t a/ronom]s did n hesitate at once to r$uce _! e/imate ( ! sun's mean di/ance f #ie1bgd1jjj to #ia1gga1jjj1 miles1 al?\gh ?is alt]ation involv$ a correspond+ correction 9 ! assum$ magnitudes & di/ances ( mo/ ( ! heav5ly bodies4 ,! sol> p>allax is n[ 7#ahge7 believ$ to be ab\t #hhgh1 ! numb] d$uc$ f ,cornu's exp]im5ts on ! velocity ( light4 ,?is result agrees v closely ) #hhgi1 ! e/imate obta9$ f new obs]vations on ! transit ( ,v5us1 by ! ,fr5* obs]v]s1 & ) #hhgc1 ! result ( ,galle's obs]vations ( ! planet ,flora4 ,:5 all ! obs]vations ( ! late transit ( ,v5us are fully discuss$ ! sun's di/ance w probably be kn[n to less ?an "o "p 9 a ?\s&1 if n "o "p 9 t5 ?\s&4#dfi #dfh 99,mon?ly ,notices ( ! ,royal ,a/ronomical ,society991 vol4 xxviii4 p4 #bfd4 #dfi ,x w\ld seem to be absurd to repeat ! pr(use exp5diture ( #ahgd at ! approa*+ transit 9 #ahhb4 ,! aggregate sum sp5t 9 #ahgd by v>i\s gov]nm5ts & individuals c h>dly be less ?an #bjj1jjj1 a sum :i*1 wisely exp5d$ on sci5tific inve/igations1 w\ld give a hundr$ important results4 ,9 ?is "q ! !oretical relations betwe5 ! velocity ( light1 ! con/ant ( ab]ration1 ! sun's p>allax1 & ! sun's mean di/ance1 are ( ! simple/ "*1 & c h>dly be op5 to any d\bt1 s t ! only d\bt 0 z to :i* result ( obs]vation 0 ! mo/ reliable4 ,ev5tually ! *ief discrepancy 0 f\nd to arise f misappreh5sion 9 ! r$uction ( obs]vations1 b we h a satisfactory example ( ! value ( diff]5t me?ods ( e/imation 9 lead+ to ! detection ( a s]i\s error4 ,is x n surpris+ t ,f\cault by measur+ ! velocity ( light :5 pass+ ?r\gh ! space ( a few y>ds1 %\ld lead ! way to a *ange 9 our e/imates ( ! magnitudes ( ! :ole univ]se8 99,selection ( ! be/ ,mode ( ,measurem5t499 ,:5 we once obta9 comm& ov] a "q ( physical sci5ce by compreh5d+ ! !ory ( ! subject1 we (t5 h a wide *oice op5$ to u z reg>ds ! me?ods ( measurem5t1 :i* may !nce=? be made to give ! mo/ accurate results4 ,if we c measure "o fundam5tal quantity v precisely we may be able by !ory to det]m9e accurately _m o!r quantitative results4 ,?us1 if we det]m9e satisfactorily ! atomic weights ( c]ta9 elem5ts1 we d n ne$ to det]m9e ) equal accuracy ! composition & atomic weights ( _! sev]al comp\nds4 ,hav+ le>nt ! relative atomic weights ( oxyg5 & sulphur1 we c calculate ! composition by weight ( ! sev]al oxides ( sulphur4 ,*emi/s accord+ly select ) ! greate/ c>e t comp\nd ( two elem5ts :i* seems to all[ ( ! mo/ accurate analysis1 s z to give ! ratio ( _! atomic weights4 ,x is obvi\s t we only ne$ ! ratio ( ! atomic weight ( ea* elem5t to t ( "s common elem5t1 9 ord] to calculate1 t ( ea* to ea*4 ,moreov] ! atomic weight /&s 9 simple relation to o!r quantitative facts4 ,! weights ( equal volumes ( elem5t>y gases at equal temp]ature & pressure h ! same ratios z ! atomic weights2 n[1 z nitrog5 "u su* circum/ances weighs #adjf times z mu* z hydrog51 we may inf] t ! atomic weight ( nitrog5 is ab\t #adjf1 or m probably #adjj1 t ( hydrog5 be+ unity4 ,!re is mu* evid5ce1 aga91 t ! specific heats ( elem5ts are inv]sely z _! atomic weights1 s t ^! two classes ( quantitative data ?r[ light mutually ^u ea* o!r4 ,9 fact ! atomic weight1 ! atomic volume1 & ! atomic heat ( an elem5t1 are quantities s closely connect$ t ! det]m9ation ( "o w lead to t ( ! o!rs4 ,! *emi/ has to solve a complicat$ problem 9 decid+ 9 ! case ( ea* ( #fj or #gj elem5ts :i* mode ( det]m9ation is mo/ accurate4 ,mod]n *emi/ry pres5ts u ) an almo/ inf9itely ext5sive web ( num]ical ratios develop$ out ( a few fundam5tal ratios4 ,9 hygrometry we h a *oice among at lea/ f\r modes ( measur+ ! quantity ( aque\s vap\r conta9$ 9 a giv5 bulk ( air4 ,we c extract ! vap\r by absorption 9 sulphuric acid1 & directly weigh its am\nt2 we c place ! air 9 a b>omet] tube & obs]ve h[ mu* ! absorption ( ! vap\r alt]s ! ela/ic =ce ( ! air2 we c obs]ve ! dew-po9t ( ! air1 t is ! temp]ature at :i* ! vap\r becomes saturat$2 or1 la/ly1 we c ins]t a dry & wet bulb !rmomet] & obs]ve ! temp]ature ( an evaporat+ surface4 ,! results ( ea* mode c be connect$ by !ory ) ^? ( ! o!r modes1 & we c select = ea* exp]im5t t mode :i* is mo/ accurate or mo/ conv5i5t4 ,! *emical me?od ( direct measurem5t is capable ( ! greate/ accuracy1 b is tr\blesome2 ! dry & wet bulb !rmomet] is suffici5tly exact = meteorological purposes & is mo/ easy to use4 99,agreem5t ( ,di/9ct ,modes ( ,measurem5t499 ,_m illu/rations might be giv5 ( ! accordance :i* has be5 f\nd to exi/ 9 "s cases betwe5 ! results ( entirely diff]5t me?ods ( arriv+ at ! measurem5t ( a physical quantity4 ,:ile su* accordance mu/1 9 ! abs5ce ( in=mation to ! contr>y1 be reg>d$ z ! be/ possible pro( ( ! approximate correctness ( ! mean result1 yet in/ances h occurr$ to %[ t we c nev] take too mu* tr\ble 9 confirm+ results ( great importance4 ,:5 ?ree or ev5 m di/9ct me?ods h giv5 ne>ly co9cid5t numb]s1 a new me?od has sometimes disclos$ a discrepancy :i* x is yet impossible to expla94 ,! ellipticity ( ! e>? is kn[n ) consid]able approa* to c]ta9ty & accuracy1 = x has be5 e/imat$ 9 ?ree indep5d5t ways4 ,! mo/ direct mode is to measure long arcs ext5d+ nor? & s\? ^u ! e>?'s surface1 by means ( trigonometrical surveys1 & !n to comp>e ! l5g?s ( ^! arcs ) _! curvature z det]m9$ by obs]vations ( ! altitude ( c]ta9 />s at ! t]m9al po9ts4 ,! mo/ probable ellipticity ( ! e>? d$uc$ f all measurem5ts ( ?is k9d 0 e/imat$ by ,bessel at #a_/cjj1 ?\gh subsequ5t measurem5ts might lead to a slightly diff]5t e/imate4 ,! div]g5ce f a globul> =m causes a small v>iation 9 ! =ce ( gravity at diff]5t p>ts ( ! e>?'s surface1 s t exact p5dulum obs]vations give ! data = an indep5d5t e/imate ( ! ellipticity1 :i* is ?us f\nd to be #a_/cbj4 ,9 ! ?ird place ! sph]oidal protub]ance ab\t ! e>?'s equator leads to a c]ta9 inequality 9 ! moon's motion1 z %[n by ,laplace2 & f ! am\nt ( t inequality1 z giv5 by obs]vations1 ,laplace 0 enabl$ to calculate back to ! am\nt ( its cause4 ,he ?us inf]r$ t ! ellipticity is #a_/cje1 :i* lies betwe5 ! two numb]s previ\sly giv51 & 0 consid]$ by him ! mo/ satisfactory det]m9ation4 ,9 ?is case ! accordance is undi/urb$ by subsequ5t results1 s t we are oblig$ to accept ,laplace's result z a highly probable "o4 ,! mean d5sity ( ! e>? is a con/ant ( high importance1 because x is necess>y = ! det]m9ation ( ! masses ( all ! o!r heav5ly bodies4 ,a/ronom]s & physici/s accord+ly h be/[$ a great deal ( lab\r ^u ! exact e/imation ( ?is con/ant4 ,! me?od ( proc$ure consi/s 9 comp>+ ! gravitation ( ! globe ) t ( "s body ( matt] ( :i* ! mass is kn[n 9 t]ms ( ! assum$ unit ( mass4 ,?is body ( matt]1 s]v+ z an int]m$iate t]m ( comp>ison1 may be v>i\sly *os52 x may consi/ ( a m\nta91 or a portion ( ! e>?'s cru/1 or a heavy ball ( metal4 ,! me?od ( exp]im5t v>ies s mu* accord+ z we select "o body or ! o!r1 t we may be said to h ?ree indep5d5t modes ( arriv+ at ! desir$ result4 ,! mutual gravitation ( two balls is s exce$+ly small comp>$ ) _! gravitation t[>ds ! imm5se mass ( ! e>?1 t x is usually q imp]ceptible1 & al?\gh ass]t$ by ,newton to exi/1 on ! gr\nd ( !ory1 0 nev] obs]v$ until ! end ( ! #ah? c5tury4 ,mi*ell atta*$ two small balls to ! extremities ( a delicately susp5d$ torsion balance1 & !n br++ heavy balls ( lead alt]nately to ei!r side ( ^! small balls 0 able to detect a slight deflection ( ! torsion balance4 ,he ?us furni%$ a new v]ification ( ! !ory ( gravitation4 ,cav5di% c>ri$ out ! exp]im5t ) m c>e1 & e/imat$ ! gravitation ( ! balls by treat+ ! torsion balance z a p5dulum2 !n tak+ into acc\nt ! respective di/ances ( ! balls f ea* o!r & f ! c5tre ( ! e>?1 he 0 able to assign #edh 7or z re-comput$ by ,baily1 #eddh7 z ! probable mean d5sity ( ! e>?4 ,newton's sagaci\s guess to ! effect t ! d5sity ( ! e>? 0 betwe5 five & six times t ( wat]1 0 ?us rem>kably confirm$4 ,! same k9d ( exp]im5t repeat$ by ,rei* gave #edch4 ,baily hav+ aga9 p]=m$ ! exp]im5t ) e possible ref9em5t obta9$ a slightly high] numb]1 #effj4 ,a diff]5t me?od ( proc$ure consi/$ 9 asc]ta9+ ! effect ( a m\nta9 mass 9 deflect+ ! plumb-l9e2 =1 assum+ t we c det]m9e ! dim5sions & mean d5sity ( ! m\nta91 ! plumb-l9e enables u to comp>e its mass ) t ( ! :ole e>?4 ,! m\nta9 ,s*ehalli5 0 select$ = ! exp]im5t1 & obs]vations & calculations p]=m$ by ,maskelyne1 ,hutton1 & ,playfair1 gave z ! mo/ probable result #dgac4 ,! diff]5ce f ! exp]im5tal results already m5tion$ is consid]able & is important1 because ! in/rum5tal op]ations are ( an entirely diff]5t "* f ^? ( ,cav5di% & ,baily's exp]im5ts4 ,sir ,h5ry ,james' simil> det]m9ation f ! attraction ( ,ar?ur's ,seat gave #ead4 ,a ?ird di/9ct me?od consi/s 9 det]m9+ ! =ce ( gravity at po9ts elevat$ above ! surface ( ! e>? on m\nta9 ranges1 or sunk bel[ x 9 m9es4 ,c>l9i exp]im5t$ ) a p5dulum at ! hospice ( ,mont ,c5is1 #f1cge feet above ! sea1 & by comp>+ ! attractive =ces ( ! e>? & ! ,alps1 f\nd ! d5sity to be /ill small]1 namely1 #dci1 or z correct$ by ,giulio1 #diej4 ,la/ly1 ! ,a/ronom] ,royal has on two occasions adopt$ ! opposite me?od ( obs]v+ a p5dulum at ! bottom ( a deep m9e1 s z to comp>e ! d5sity ( ! /rata p5etrat$ ) ! d5sity ( ! :ole e>?4 ,on ! second occasion he c>ri$ 8 me?od into effect at ! ,h>ton ,colli]y1 #a1bfj feet deep2 all t c\ld be done by skill 9 measurem5t & c>eful consid]ation ( all ! causes ( error1 0 accompli%$ 9 ?is elaborate s]ies ( obs]vations#dgj 7p4 #bia74 ,no d\bt ,sir ,george ,airy 0 mu* p]plex$ :5 he f\nd t 8 new result consid]ably exce$$ t obta9$ by any o!r me?od1 be+ no less ?an #feff1 or #ffbc z f9ally correct$4 ,9 ?is case we le>n an impressive lesson conc]n+ ! value ( repeat$ det]m9ations by di/9ct me?ods 9 disabus+ our m9ds ( ! reliance :i* we are only too apt to place 9 results :i* %[ a c]ta9 degree ( co9cid5ce4 #dgj 99,philosophical ,transactions99 7#ahef71 vol4 cxlvi4 p4 #cdb4 ,9 #ahdd ,h]s*el rem>k$ 9 8 memoir ( ,francis ,baily1#dga 8t ! mean specific gravity ( ?is our planet is1 9 all human probability1 q z well det]m9$ z t ( an ord9>y h&-specim5 9 a m9]alogical cab9et1--a m>vell\s result1 :i* %\ld tea* u to despair ( no?+ :i* lies )9 ! compass ( numb]1 weight & measure40 ,b at ! same "t he po9t$ out t ,baily's f9al result1 ( :i* ! probable error 0 only #jjjcb1 0 ! highe/ ( all det]m9ations !n kn[n1 & ,airy's inve/igation has s9ce giv5 a mu* high] result1 q beyond ! limits ( probable error ( any ( ! previ\s exp]im5ts4 ,if we treat all det]m9ations yet made z ( equal weight1 ! simple mean is ab\t #ede1 ! mean error ne>ly #je1 & ! probable error almo/ #jb1 s t x is z likely z n t ! tru? lies betwe5 #efe & #ebe on ?is view ( ! matt]4 ,b x is rem>kable t ! two mo/ rec5t & c>eful s]ies ( obs]vations by ,baily & ,airy1#dgb lie beyond ^! limits1 & z ) ! increase ( c>e ! e/imate rises1 x seems requisite to reject ! e>li] results1 & look ^u ! "q z /ill requir+ fur!r inve/igation4 ,physici/s (t5 take #e-b_/c or #efg z ! be/ guess at ! tru?1 b x is evid5t t new exp]im5ts are mu* requir$4 ,i _c help ?9k+ t a portion ( ! great sums ( money :i* _m gov]nm5ts & private individuals sp5t ^u ! transit ( ,v5us exp$itions 9 #ahgd1 & :i* !y w probably sp5d aga9 9 #ahhb 7p4 #efb71 w\ld be bett] appropriat$ to new det]m9ations ( ! e>?'s d5sity4 ,x seems desirable to repeat ,baily's exp]im5t 9 a vacu\s case1 & ) ! great] me*anical ref9em5ts :i* ! progress ( ! la/ =ty ye>s places at ! disposal ( ! exp]im5tali/4 ,x w\ld be desirable1 also1 to r5ew ! p5dulum exp]im5ts ( ,airy 9 "s o!r deep m9e4 ,x might ev5 be well to repeat ^u "s suitable m\nta9 ! obs]vations p]=m$ at ,s*ehalli54 ,all ^! op]ations might be c>ri$ out = ! co/ ( "o ( ! sup]flu\s transit exp$itions4 #dga 99,mon?ly ,notices ( ! ,royal ,a/ronomical ,society991 = #h? ,nov4 #ahdd1 ,no4 ,x4 vol4 vi4 p4 #hi4 #dgb 99,philosophical ,magaz9e991 #bnd ,s]ies1 vol4 xxvi4 p4 #fa4 ,s9ce ! e/abli%m5t ( ! dynamical !ory ( heat x has become a matt] ( ! greate/ importance to det]m9e ) accuracy ! me*anical equival5t ( heat1 or ! quantity ( en]gy :i* mu/ be giv51 or receiv$1 9 a def9ite *ange ( temp]ature effect$ 9 a def9ite quantity ( a /&>d sub/ance1 su* z wat]4 ,no less ?an sev5 almo/ entirely di/9ct modes ( det]m9+ ?is con/ant h be5 tri$4 ,dr4 ,j\le fir/ asc]ta9$ by ! friction ( wat] t to raise ! temp]ature ( "o kilogram ( wat] ?r\gh "o degree c5tigrade1 we mu/ employ en]gy suffici5t to raise #dbd kilograms ?r\gh ! height ( "o metre aga9/ ! =ce ( gravity at ! e>?'s surface4 ,j\le1 ,may]1 ,clausius1#dgc ,favre & o!r exp]im5tali/s h made det]m9ations by less direct me?ods4 ,exp]im5ts on ! me*anical prop]ties ( gases give #dbf kilogrammetres z ! con/ant2 ! "w done by a /eam-eng9e gives #dac2 f ! heat evolv$ 9 electrical exp]im5ts sev]al det]m9ations h be5 obta9$2 ?us f induc$ electric curr5ts we get #deb2 f ! electro-magnetic eng9e #ddc2 f ! circuit ( a batt]y #dbj2 &1 f an electric curr5t1 ! l[e/ result ( all1 namely1 #djj4dgd #dgc ,clausius 9 99,philosophical ,magaz9e991 #d? ,s]ies1 vol4 ii4 p4 #aai4 #dgd ,watts' 99,diction>y ( ,*emi/ry991 vol4 iii4 p4 #abi4 ,consid]+ ! div]se & 9 _m cases difficult me?ods ( obs]vation1 ^! results exhibit satisfactory accordance1 & _! mean 7#dbci7 comes v close to ! numb] d]iv$ by ,dr4 ,j\le f ! app>5tly mo/ accurate me?od4 ,! con/ant g5]ally assum$ z ! mo/ probable result is #dbcee kilogrammetres4 99,residual ,ph5om5a499 ,ev5 :5 ! exp]im5tal data employ$ 9 ! v]ification ( a !ory are suffici5tly accurate1 & ! !ory itself is s\nd1 !re may exi/ discrepancies dem&+ fur!r inve/igation4 ,h]s*el po9t$ out ! importance ( su* out/&+ quantities1 & call$ !m 99residual ph5om5a994#dge ,n[ if ! obs]vations & ! !ory be really correct1 su* discrepancies mu/ be due to ! incomplet5ess ( our k ( ! causes 9 action1 & ! ultimate explanation mu/ consi/ 9 %[+ t !re is 9 action1 ei!r #dge 99,prelim9>y ,disc\rse991 #aeh1 #agd4 99,outl9es ( ,a/ronomy991 #d? edit4 #hef4 7#a7 ,"s ag5t ( kn[n nature ^: pres5ce 0 n suspect$2 ,or 7#b7 ,"s new ag5t ( unkn[n nature4 ,9 ! fir/ case we c h>dly be said to make a new discov]y1 = our ultimate success consi/s m]ely 9 reconcil+ ! !ory ) kn[n facts :5 our inve/igation is m compreh5sive4 ,b 9 ! second case we meet ) a totally new fact1 :i* may lead u to realms ( new discov]y4 ,take ! in/ance adduc$ by ,h]s*el4 ,! !ory ( ,newton & ,halley conc]n+ comets 0 t !y 7 gravitat+ bodies revolv+ r\nd ! sun 9 elliptic orbits1 & ! return ( ,halley's ,comet1 9 #ageh1 v]ifi$ ?is !ory4 ,b1 :5 accurate obs]vations ( ,encke's ,comet came to be made1 ! v]ification 0 n f\nd to be exact4 ,encke's ,comet return$ ea* "t a little soon] ?an x ought to d1 ! p]iod regul>ly decreas+ f #ababgi days1 betwe5 #aghf & #aghi1 to #abajdd betwe5 #ahee & #aheh2 & ! hypo!sis has be5 />t$ t !re is a resi/+ m$ium fill+ ! space ?r\gh :i* ! comet passes4 ,?is hypo!sis is a 99deus ex ma*999 = expla9+ ?is solit>y ph5om5on1 & _c possess mu* probability unless x c be %[n t o!r ph5om5a are d$ucible f x4 ,_m p]sons h id5tifi$ ?is m$ium ) t ?r\gh :i* light undulations pass1 b ,i am n aw>e t !re is any?+ 9 ! undulatory !ory ( light to %[ t ! m$ium w\ld (f] resi/ance to a mov+ body4 ,if ,pr(essor ,balf\r ,/ew>t c prove t a rotat+ disc w\ld exp]i5ce resi/ance 9 a vacu\s receiv]1 "h is an exp]im5tal fact :i* di/9ctly supports ! hypo!sis4 ,b 9 ! mean "t x is op5 to "q :e!r o!r kn[n ag5ts1 = in/ance electricity1 may n be br\ght 91 & ,i h tri$ to %[ t if1 z is believ$1 ! tail ( a comet is an electrical ph5om5on1 x is a necess>y result ( ! cons]vation ( en]gy t ! comet %all exhibit a loss ( en]gy manife/$ 9 a dim9ution ( its mean di/ance f ! sun & its p]iod ( revolution4#dgf ,x %\ld be add$ t if ,pr(essor ,tait's !ory be correct1 z seems v probable1 & comets consi/ ( sw>ms ( small meteors1 !re is no difficulty 9 acc\nt+ = ! ret>dation4 ,x has long be5 kn[n t a collection ( small bodies travell+ toge!r 9 an orbit r\nd a c5tral body w t5d to fall t[>ds x4 ,9 ei!r case1 !n1 ?is residual ph5om5on seems likely to be reconcil$ ) kn[n laws ( nature4 #dgf 99,proce$+s ( ! ,man*e/] ,lit]>y & ,philosophical ,society991 #bh? ,novemb]1 #ahga1 vol4 xi4 p4 #cc4 ,s9ce ! above rem>ks 7 writt51 ,pr(essor ,balf\r ,/ew>t has po9t$ out to me 8 pap] 9 ! 99,proce$+s ( ! ,man*e/] ,lit]>y & ,philosophical ,society99 = #ae? ,novemb]1 #ahgj 7vol4 x4 p4 #cb71 9 :i* he %[s t a body mov+ 9 an enclosure ( uni=m temp]ature w\ld probably exp]i5ce resi/ance indep5d5tly ( ! pres5ce ( a pond]able m$ium1 su* z gas1 betwe5 ! mov+ body & ! enclosure4 ,! pro( is f\nd$ on ! !ory ( ! dissipation ( en]gy1 & ?is view is said to be accept$ by ,pr(essors ,?omson & ,tait4 ,! enclosure is us$ 9 ?is case by ,pr(essor ,/ew>t simply z a means ( obta9+ a pro(1 j z x 0 us$ by him on a previ\s occasion to obta9 a pro( ( c]ta9 consequ5ces ( ! ,!ory ( ,ex*anges4 ,he is ( op9ion t 9 bo? ( ^! cases :5 once ! pro( has be5 obta9$1 ! enclosure may be disp5s$ )4 ,we "k1 = in/ance1 t ! relation betwe5 ! inductive & absorptive p[]s ( bodies--al?\gh ?is relation may h be5 prov$ by means ( an enclosure1 does n dep5d ^u its pres5ce1 & ,pr(essor ,/ew>t ?9ks t 9 l mann] two bodies1 or at lea/ two bodies possess+ heat su* z ! sun & ! e>? 9 motion relative to ea* o!r1 w h ! diff]5tial motion ret>d$ until p]haps x is ultimately de/roy$4 ,9 o!r cases residual ph5om5a h involv$ important inf]5ces n recognis$ at ! "t4 ,newton %[$ h[ ! velocity ( s\nd 9 ! atmosph]e c\ld be calculat$ by a !ory ( pulses or undulations f ! obs]v$ t5sion & d5sity ( ! air4 ,he inf]r$ t ! velocity 9 ! ord9>y /ate ( ! atmosph]e at ! e>?'s surface w\ld be #ifh feet p] second1 & rude exp]im5ts made by him 9 ! cloi/]s ( ,tr9ity ,college seem$ to %[ t ?is 0 n f> f ! tru?4 ,subsequ5tly x 0 asc]ta9$ by o!r exp]im5tali/s t ! velocity ( s\nd 0 m ne>ly #a1adb feet1 & ! discrepancy be+ "o-six? "p ( ! :ole 0 f> too mu* to attribute to casual errors 9 ! num]ical data4 ,newton attempt$ to expla9 away ?is discrepancy by hypo!ses z to ! reactions ( ! molecules ( air1 b )\t success4 ,new inve/igations hav+ be5 made f "t to "t conc]n+ ! velocity ( s\nd1 bo? z obs]v$ exp]im5tally & z calculat$ f !ory1 x 0 f\nd t ea* ( ,newton's results 0 inaccurate1 ! !oretical velocity be+ #iaf feet p] second1 & ! real velocity ab\t #a1jij feet4 ,! discrepancy1 nev]!less1 rema9$ z s]i\s z ev]1 & x 0 n until ! ye> #ahaf t ,laplace %[$ x to be due to ! heat develop$ by ! sudd5 compression ( ! air 9 ! passage ( ! wave1 ?is heat hav+ ! effect ( increas+ ! ela/icity ( ! air & accel]at+ ! impulse4 ,x is n[ p]ceiv$ t ?is discrepancy really involves ! doctr9e ( ! equival5ce ( heat & en]gy1 & x 0 appli$ by ,may]1 at lea/ by implication1 to give an e/imate ( ! me*anical equival5t ( heat4 ,! e/imate ?us d]iv$ agrees satisfactorily ) direct det]m9ations by ,dr4 ,j\le & o!r physici/s1 s t ! explanation ( ! residual ph5om5on :i* ex]cis$ ,newton's +5uity is n[ complete1 & =ms an important "p ( ! new sci5ce ( !rmodynamics4 ,z ,h]s*el obs]v$1 almo/ all great a/ronomical discov]ies h be5 disclos$ 9 ! =m ( residual diff]5ces4 ,x is ! practice at well-conduct$ obs]vatories to comp>e ! positions ( ! heav5ly bodies z actually obs]v$ ) :at might h be5 expect$ !oretically4 ,?is practice 0 introduc$ by ,halley :5 ,a/ronom] ,royal1 & 8 r$uction ( ! lun> obs]vations gave a s]ies ( residual errors f #agbb to #agci1 by ! exam9ation ( :i* ! lun> !ory 0 improv$4 ,mo/ ( ! great] a/ronomical v>iations aris+ f nutation1 ab]ration1 planet>y p]turbation 7 discov]$ 9 ! same mann]4 ,! precession ( ! equ9ox 0 p]haps ! e>lie/ residual diff]5ce obs]v$2 ! sy/ematic div]g5ce ( ,uranus f its calculat$ places 0 "o ( ! late/1 & 0 ! clue to ! rem>kable discov]y ( ,neptune4 ,we may also class "u residual ph5om5a all ! s-call$ 99prop] motions99 ( ! />s4 ,a complete /> catalogue1 su* z t ( ! ,briti% ,association1 gives a great] or less am\nt ( prop] motion = almo/ e />1 consi/+ 9 ! app>5t diff]5ce ( position ( ! /> z d]iv$ f ! e>lie/ & late/ good obs]vations4 ,b ^! app>5t motions are (t5 due1 z expla9$ by ,baily1#dgg ! au?or ( ! catalogue1 to errors ( obs]vation & r$uction4 ,9 _m cases ! be/ a/ronomical au?orities h diff]$ z to ! v direction ( ! suppos$ prop] motion ( />s1 & z reg>ds ! am\nt ( ! motion1 = in/ance ( ,pol>is1 ! mo/ diff]5t e/imates h be5 =m$4 ,residual quantities w (t5 be s small t _! v exi/5ce is d\btful4 ,only ! gradual progress ( !ory & ( measurem5t w %[ cle>ly :e!r a discrepancy is to be ref]r$ to casual errors ( obs]vation or to "s new ph5om5on4 ,b no?+ is m requisite = ! progress ( sci5ce ?an ! c>eful record+ & inve/igation ( su* discrepancies4 ,9 no "p ( physical sci5ce c we be free f exceptions & out/&+ facts1 ( :i* our pres5t k c give no acc\nt4 ,x is among su* anomalies t we mu/ look = ! clues to new realms ( facts wor?y ( discov]y4 ,!y are l ! float+ waifs :i* l$ ,columbus to suspect ! exi/5ce ( ! new _w4 #dgg 99,briti% ,association ,catalogue ( ,/>s991 p4 #di4 ,,*apt] ,,xxvi4 ,,"* ,,( ,,! ,,exp]im5tali/4 ,9 ! pres5t age !re seems to be a t5d5cy to believe t ! importance ( individual g5ius is less ?an x 0-- 8,! individual )]s1 & ! _w is m & m40 ,society1 x is suppos$1 has n[ assum$ s highly develop$ a =m1 t :at 0 accompli%$ 9 pa/ times by ! solit>y ex]tions ( a great intellect1 may n[ be work$ out by ! unit$ lab\rs ( an army ( inve/igators4 ,j z ! well-organis$ p[] ( a mod]n army sup]s$es ! s+le-h&$ brav]y ( ! m$ival knights1 s we are to believe t ! comb9ation ( intellectual lab\r has sup]s$$ ! g5ius ( an ,ar*im$es1 a ,newton1 or a ,laplace4 ,s-call$ orig9al rese>* is n[ reg>d$ z a pr(ession1 adopt$ by hundr$s ( m51 & communicat$ by a sy/em ( tra9+4 ,all t we ne$ to secure additions to our k ( nature is ! erection ( great laboratories1 museums1 & obs]vatories1 & ! (f]+ ( pecuni>y rew>ds to ^? :o c inv5t new *emical comp\nds1 detect new species1 or discov] new comets4 ,d\btless ?is is n ! real mean+ ( ! em95t m5 :o are n[ urg+ ^u ,gov]nm5t ! end[m5t ( physical rese>*4 ,!y c only mean t ! great] ! pecuni>y & mat]ial assi/ance giv5 to m5 ( sci5ce1 ! great] ! result :i* ! available g5ius ( ! c\ntry may be expect$ to produce4 ,money & opportunities ( /udy c no m produce g5ius ?an sun%9e & moi/ure c g5]ate liv+ be+s2 ! inexplicable g]m is want+ 9 bo? cases4 ,b z1 :5 ! g]m is pres5t1 ! plant w gr[ m or less vigor\sly accord+ to ! circum/ances 9 :i* x is plac$1 s x may be all[$ t pecuni>y assi/ance may fav\r developm5t ( intellect4 ,public op9ion h[ev] is n discrim9at+1 & is likely to int]pret ! agitation = ! end[m5t ( sci5ce z mean+ t sci5ce c be _h = money4 ,all su* notions are errone\s4 ,9 no bran* ( human affairs1 nei!r 9 politics1 w>1 lit]ature1 indu/ry1 nor sci5ce1 is ! influ5ce ( g5ius less consid]able ?an x 04 ,x is possible t ! ext5sion & organisation ( sci5tific /udy1 assi/$ by ! pr9t+-press & ! accel]at$ means ( communication1 has increas$ ! rapidity ) :i* new discov]ies are made kn[n1 & _! details work$ out by _m heads & h&s4 ,a ,d>w9 n[ no soon] prop\nds orig9al ideas conc]n+ ! evolution ( liv+ creatures1 ?an ^? ideas are discuss$ & illu/rat$1 & appli$ by naturali/s 9 e "p ( ! _w4 ,9 =m] days 8 discov]ies w\ld h be5 hidd5 = decades ( ye>s 9 sc>ce manuscripts1 & g5]ations w\ld h pass$ away be=e 8 !ory _h enjoy$ ! same am\nt ( criticism & corroboration z x has already receiv$4 ,! result is t ! g5ius ( ,d>w9 is m valuable1 n less valuable1 ?an x w\ld =m]ly h be54 ,! advance ( milit>y sci5ce & ! organisation ( enorm\s armies has n decreas$ ! value ( a skilful g5]al2 on ! contr>y1 ! rank & file are /ill m 9 ne$ ?an !y us$ to be ( ! guid+ p[] ( a f>-see+ intellect4 ,! swift de/ruction ( ! ,fr5* milit>y p[] 0 n due alone to ! p]fection ( ! ,g]man army1 nor to ! g5ius ( ,moltke2 x 0 due to ! comb9ation ( a well-discipl9$ multitude ) a lead] ( ! highe/ p[]s4 ,s 9 e bran* ( human affairs ! influ5ce ( ! individual is n )]+1 b is gr[+ ) ! ext5t ( ! mat]ial res\rces :i* are at 8 comm&4 ,turn+ to our own subject1 x is a "w ( undim9i%$ int]e/ to reflect ^u ^? qualities ( m9d :i* lead to great advances 9 natural k4 ,no?+1 inde$1 is less am5able ?an g5ius to sci5tific analysis & explanation4 ,ev5 def9ition is out ( ! "q4 ,buffon said t 8g5ius is pati5ce10 & c]ta9ly pati5ce is "o ( its mo/ requisite compon5ts4 ,b no "o c suppose t pati5t lab\r alone w inv>iably lead to ^? conspicu\s results :i* we attribute to g5ius4 ,9 e bran* ( sci5ce1 lit]ature1 art1 or indu/ry1 !re are ?\s&s ( m5 & wom5 :o "w ) unceas+ pati5ce1 & !reby ensure mod]ate success2 b x w\ld be absurd to suppose t equal am\nts ( intellectual lab\r yield equal results4 ,a ,newton may mode/ly attribute 8 discov]ies to indu/ry & pati5t ?\ght1 & !re is reason to believe t g5ius is unconsci\s & unable to acc\nt = its own peculi> p[]s4 ,z g5ius is ess5tially creative1 & consi/s 9 div]g5ce f ! ord9>y grooves ( ?\ght & action1 x mu/ necess>ily be a ph5om5on beyond ! doma9 ( ! laws ( nature4 ,nev]!less1 x is always an int]e/+ & in/ructive "w to trace out1 z f> z possible1 ! *>act]i/ics ( m9d by :i* great discov]ies h be5 a*iev$1 & we %all f9d 9 ! analysis mu* to illu/rate ! pr9ciples ( sci5tific me?od4 99,error ( ! ,baconian ,me?od499 ,hundr$s ( inve/igators may be con/antly engag$ 9 exp]im5tal inquiry2 !y may compile numb]less note-books full ( sci5tific facts1 & endless tables ( num]ical results2 b1 if ! views ( induction "h ma9ta9$ be true1 !y c nev] by su* "w alone rise to new & great discov]ies4 ,by a sy/em ( rese>* !y may "w out d$uctively ! details ( a previ\s discov]y1 b to arrive at a new pr9ciple ( nature is ano!r matt]4 ,francis ,bacon spread abroad ! notion t to advance sci5ce we mu/ beg9 by accumulat+ facts1 & !n draw f !m1 by a process ( dige/ion1 successive laws ( high] & high] g5]ality4 ,9 prote/+ aga9/ ! false me?od ( ! s*ola/ic logicians1 he exagg]at$ a p>tially true philosophy1 until x became z false z t :i* prec$$ x4 ,8 notion ( sci5tific me?od 0 a k9d ( sci5tific bookkeep+4 ,facts 7 to be indiscrim9ately ga!r$ f e s\rce1 & po/$ 9 a l$g]1 f :i* w\ld em]ge 9 "t a balance ( tru?4 ,x is difficult to imag9e a less likely way ( arriv+ at great discov]ies4 ,! great] ! array ( facts1 ! less is ! probability t !y w by any r\t9e sy/em ( classification disclose ! laws ( nature !y embody4 ,exhau/ive classification 9 all possible ord]s is out ( ! "q1 because ! possible ord]s are practically inf9ite 9 numb]4 ,x is be=e ! glance ( ! philosophic m9d t facts mu/ display _! mean+1 & fall into logical ord]4 ,! natural philosoph] mu/ !re=e h1 9 ! fir/ place1 a m9d ( impressionable "*1 :i* is affect$ by ! slighte/ exceptional ph5om5on4 ,8 associat+ & id5tify+ p[]s mu/ be great1 t is1 a /range fact mu/ sugge/ to 8 m9d :atev] ( l nature has previ\sly come )9 8 exp]i5ce4 ,8 imag9ation mu/ be active1 & br+ be=e 8 m9d multitudes ( relations 9 :i* ! unexpla9$ facts may possibly /& ) reg>d to ea* o!r1 or to m common facts4 ,sure & vigor\s p[]s ( d$uctive reason+ mu/ !n come into play1 & enable him to inf] :at w happ5 "u ea* suppos$ condition4 ,la/ly1 & above all1 !re mu/ be ! love ( c]ta9ty lead+ him dilig5tly & ) p]fect c&\r1 to comp>e 8 speculations ) ! te/ ( fact & exp]im5t4 99,fre$om ( ,!oris+499 ,x w\ld be an error to suppose t ! great discov]] seizes at once ^u ! tru?1 or has any un]r+ me?od ( div9+ x4 ,9 all probability ! errors ( ! great m9d exce$ 9 numb] ^? ( ! less vigor\s "o4 ,f]tility ( imag9ation & abundance ( guesses at tru? are among ! fir/ requisites ( discov]y2 b ! errone\s guesses mu/ be _m times z num]\s z ^? :i* prove well f\nd$4 ,! weake/ analogies1 ! mo/ :imsical notions1 ! mo/ app>5tly absurd !ories1 may pass ?r\gh ! teem+ bra91 & no record rema9 ( m ?an ! hundr$? "p4 ,!re is no?+ really absurd except t :i* proves contr>y to logic & exp]i5ce4 ,! true/ !ories involve suppositions :i* are inconceivable1 & no limit c really be plac$ to ! fre$om ( hypo!sis4 ,kepl] is an extraord9>y in/ance to ?is effect4 ,no m9or laws ( nature are m firmly e/abli%$ ?an ^? :i* he detect$ conc]n+ ! orbits & motions ( planet>y masses1 & on ^! empirical laws ! !ory ( gravitation 0 f\nd$4 ,did we n le>n f 8 own writ+s ! multitude ( errors into :i* he fell1 we might h imag9$ t he _h "s special faculty ( seiz+ on ! tru?4 ,b1 z is well kn[n1 he 0 full ( *im]ical notions2 8 fav\rite & long-/udi$ !ory 0 f\nd$ on a fanciful analogy betwe5 ! planet>y orbits & ! regul> solids4 ,8 celebrat$ laws 7 ! outcome ( a lifetime ( speculation1 = ! mo/ "p va9 & gr\ndless4 ,we "k ?is because he _h a curi\s pleasure 9 dwell+ ^u errone\s & futile tra9s ( reason+1 :i* mo/ p]sons consign to oblivion4 ,b ,kepl]'s "n 0 de/9$ to be immortal1 on acc\nt ( ! pati5ce ) :i* he submitt$ 8 hypo!ses to comp>ison ) obs]vation1 ! c&\r ) :i* he ackn[l$g$ failure aft] failure1 & ! p]sev]ance & +5uity ) :i* he r5ew$ 8 attack ^u ! riddles ( nature4 ,next aft] ,kepl] p]haps ,f>aday is ! physical philosoph] :o has giv5 u ! be/ insight into ! progress ( discov]y1 by record+ errone\s z well z successful speculations4 ,! record$ notions1 inde$1 are probably b a ti! ( ! fancies :i* arose 9 8 active bra94 ,z ,f>aday himself said--8,! _w little kn[s h[ _m ( ! ?\ghts & !ories :i* h pass$ ?r\gh ! m9d ( a sci5tific inve/igator1 h be5 cru%$ 9 sil5ce & secrecy by 8 own sev]e criticism & adv]se exam9ation2 t 9 ! mo/ successful in/ances n a t5? ( ! sugge/ions1 ! hopes1 ! wi%es1 ! prelim9>y conclusions h be5 realis$40 ,nev]!less1 9 ,f>aday's rese>*es1 publi%$ 9 ! 99,philosophical ,transactions991 9 m9or pap]s1 9 manuscript note-books1 or 9 o!r mat]ials1 made kn[n 9 8 int]e/+ life by ,dr4 ,b5ce ,jones1 we f9d invaluable lessons = ! exp]im5tali/4 ,^! writ+s are full ( speculations :i* we mu/ n judge by ! light ( subsequ5t discov]y4 ,x may p]haps be said t ,f>aday committ$ to ! pr9t+ press crude ideas :i* a fri5d w\ld h c\nsell$ him to keep back4 ,!re 0 occasionally ev5 a wildness & vagu5ess 9 8 notions1 :i* 9 a less c>eful exp]im5tali/ w\ld h be5 fatal to ! atta9m5t ( tru?4 ,?is is especially app>5t 9 a curi\s pap] conc]n+ ,ray-vibrations2 b =tunately ,f>aday 0 aw>e ( ! %ad[y "* ( 8 speculations1 & express$ ! feel+ 9 words :i* mu/ be quot$4 8,i ?9k x likely10 he says1#dgh 8t ,i h made _m mi/akes 9 ! prec$+ pages1 = ev5 to myself my ideas on ?is po9t appe> only z ! %ad[ ( a speculation1 or z "o ( ^? impressions ^u ! m9d1 :i* are all[able = a "t z guides to ?\ght & rese>*4 ,he :o lab\rs 9 exp]im5tal inquiries kn[s h[ num]\s ^! are1 & h[ (t5 _! app>5t fitness & beauty vani% be=e ! progress & developm5t ( real natural tru?40 ,if1 !n1 ! exp]im5tali/ has no royal road to ! discov]y ( ! tru?1 x is an int]e/+ matt] to consid] by :at logical proc$ure he atta9s ! tru?4 #dgh 99,exp]im5tal ,rese>*es 9 ,*emi/ry & ,physics991 p4 #cgb4 99,philosophical ,magaz9e991 #crd ,s]ies1 ,may #ahdf1 vol4 xxviii4 p4 #cej4 ,if ,i h tak5 a correct view ( logical me?od1 !re is really no su* ?+ z a di/9ct process ( induction4 ,! probability is inf9itely small t a collection ( complicat$ facts w fall into an arrangem5t capable ( exhibit+ directly ! laws obey$ by !m4 ,! ma!matician might z well expect to integrate 8 functions by a ballot-box1 z ! exp]im5tali/ to draw deep tru?s f haphaz>d trials4 ,all induction is b ! inv]se application ( d$uction1 & x is by ! inexplicable action ( a gift$ m9d t a multitude ( het]og5e\s facts are rang$ 9 lum9\s ord] z ! results ( "s uni=mly act+ law4 ,s diff]5t1 inde$1 are ! qualities ( m9d requir$ 9 diff]5t bran*es ( sci5ce1 t x w\ld be absurd to attempt to give an exhau/ive description ( ! "* ( m9d :i* leads to discov]y4 ,! lab\rs ( ,newton c\ld n h be5 accompli%$ except by a m9d ( ! utmo/ ma!matical g5ius2 ,f>aday1 on ! o!r h&1 has made ! mo/ ext5sive additions to human k )\t pass+ beyond common ari?metic4 ,i d n rememb] meet+ 9 ,f>aday's writ+s ) a s+le algebraic =mula or ma!matical problem ( any complexity4 ,pr(essor ,cl]k ,maxwell1 inde$1 9 ! preface to 8 new 99,treatise on ,electricity991 has /rongly recomm5d$ ! read+ ( ,f>aday's rese>*es by all /ud5ts ( sci5ce1 & has giv5 8 op9ion t ?\gh ,f>aday seldom or nev] employ$ ma!matical =mul1 8 me?ods & conceptions 7 n ! less ma!matical 9 _! nature4#dgi ,i h myself prote/$ aga9/ ! prevail+ confusion betwe5 a ma!matical & an exact sci5ce1#dhj yet ,i c]ta9ly ?9k t ,f>aday's exp]im5ts 7 = ! mo/ "p qualitative1 & t 8 ma!matical ideas 7 ( a rudim5t>y "*4 ,x is true t he c\ld n possibly inve/igate su* a subject z magne-cry/allic action )\t involv+ himself 9 geometrical relations ( "s complexity4 ,nev]!less ,i ?9k t he 0 defici5t 9 ma!matical d$uctive p[]1 t p[] :i* is s highly develop$ by ! mod]n sy/em ( ma!matical tra9+ at ,cambridge4 #dgi ,see also 99,nature991 ,septemb] #ah1 #ahgc2 vol4 viii4 p4 #cih4 #dhj 99,!ory ( ,political ,economy991 pp4 #c-ad4 ,f>aday 0 acqua9t$ ) ! =ms ( 8 celebrat$ l9es ( =ce1 b ,i am n aw>e t he ev] ent]$ into ! algebraic nature ( ^? curves1 & ,i feel sure t he c\ld n h expla9$ _! =ms z dep5d+ on ! resultant attractions ( all ! magnetic p>ticles4 ,!re are ev5 occasional indications t he did n und]/& "s ( ! simpl] ma!matical doctr9es ( mod]n physical sci5ce4 ,al?\gh he s cle>ly =esaw ! correlation ( ! physical =ces1 & lab\r$ s h>d ) 8 own h&s to connect gravity ) o!r =ces1 x is d\btful :e!r he und]/ood ! doctr9e ( ! cons]vation ( en]gy z appli$ to gravitation4 ,f>aday 0 probably equal to ,newton 9 exp]im5tal skill1 & 9 t peculi> k9d ( d$uctive p[] :i* leads to ! inv5tion ( simple qualitative exp]im5ts2 b x mu/ be all[$ t he exhibit$ little ( t ma!matical p[] :i* enabl$ ,newton to foll[ out intuitively ! quantitative results ( a complicat$ problem ) su* wond]ful facility4 ,two in/ances1 ,newton & ,f>aday1 are suffici5t to %[ t m9ds ( widely diff]5t con=mation w meet ) suitable regions ( rese>*4 ,nev]!less1 !re are c]ta9 traits :i* we may discov] 9 all ! highe/ sci5tific m9ds4 99,! ,newtonian ,me?od1 ! ,true ,organum499 ,laplace 0 ( op9ion t ! 99,pr9cipia99 & ! 99,opticks99 ( ,newton furni%$ ! be/ models !n available ( ! delicate art ( exp]im5tal & !oretical inve/igation4 ,9 ^!1 z he says1 we meet ) ! mo/ happy illu/rations ( ! way 9 :i*1 f a s]ies ( inductions1 we may rise to ! causes ( ph5om5a1 & !nce desc5d aga9 to all ! result+ details4 ,! popul> notion conc]n+ ,newton's discov]ies is t 9 e>ly life1 :5 driv5 into ! c\ntry by ! ,great ,plague1 a fall+ apple accid5tally sugge/$ to him ! exi/5ce ( gravitation1 & t1 avail+ himself ( ?is h9t1 he 0 l$ to ! discov]y ( ! law ( gravitation1 ! explanation ( :i* con/itutes ! 99,pr9cipia994 ,x is difficult to imag9e a m ludicr\s & inadequate picture ( ,newton's lab\rs4 ,no orig9ality1 or at lea/ priority1 0 claim$ by ,newton z reg>ds ! discov]y ( ! law ( ! inv]se squ>e1 s closely associat$ ) 8 "n4 ,9 a well-kn[n ,s*olium#dha he ackn[l$ges t ,sir ,*ri/oph] ,wr51 ,hooke1 & ,halley1 _h sev]ally obs]v$ ! accordance ( ,kepl]'s ?ird law ( motion ) ! pr9ciple ( ! inv]se squ>e4 #dha 99,pr9cipia991 bk4 i4 ,prop4 iv4 ,newton's "w 0 really t ( develop+ ! me?ods ( d$uctive reason+ & exp]im5tal v]ification1 by :i* alone great hypo!ses c be br\ght to ! t\*/one ( fact4 ,ar*im$es 0 ! greate/ ( anci5t philosoph]s1 = he %[$ h[ ma!matical !ory c\ld be w$d$ to physical exp]im5ts2 & 8 works are ! fir/ true ,organum4 ,newton is ! mod]n ,ar*im$es1 & ! 99,pr9cipia99 =ms ! true ,novum ,organum ( sci5tific me?od4 ,! laws :i* he e/abli%$ are great1 b 8 example ( ! mann] ( e/abli%+ !m is great] /ill4 ,except+ p]haps *emi/ry & electricity1 !re is h>dly a progressive bran* ( physical & ma!matical sci5ce1 :i* has n be5 develop$ f ! g]ms ( true sci5tific proc$ure :i* he disclos$ 9 ! 99,pr9cipia99 or ! 99,opticks994 ,ov]come by ! success ( 8 !ory ( univ]sal gravitation1 we are apt to =get t 9 8 !ory ( s\nd he orig9at$ ! ma!matical inve/igation ( waves & ! mutual action ( p>ticles2 t 9 8 corpuscul> !ory ( light1 h[ev] mi/ak51 he fir/ v5tur$ to apply ma!matical calculation to molecul> attractions & repulsions2 t 9 8 prismatic exp]im5ts he %[$ h[ f> exp]im5tal v]ification c\ld be pu%$2 t 9 8 exam9ation ( ! col\r$ r+s nam$ aft] him1 he accompli%$ ! mo/ rem>kable in/ance ( m9ute measurem5t yet kn[n1 a m]e practical application ( :i* by ,fizeau 0 rec5tly deem$ wor?y ( a m$al by ! ,royal ,society4 ,we only le>n by degrees h[ complete 0 8 sci5tific insight2 a few words 9 8 ?ird law ( motion display 8 acqua9tance ) ! fundam5tal pr9ciples ( mod]n !rmodynamics & ! cons]vation ( en]gy1 :ile manuscripts long ov]look$ prove t 9 8 inquiries conc]n+ atmosph]ic refraction he _h ov]come ! ma9 difficulties ( apply+ !ory to "o ( ! mo/ complex ( physical problems4 ,aft] all1 x is only by exam9+ ! way 9 :i* he effect$ discov]ies1 t we c rightly appreciate 8 greatness4 ,! 99,pr9cipia99 treats n ( gravity s mu* z ( =ces 9 g5]al1 & ! me?ods ( reason+ ab\t !m4 ,he inve/igates n "o hypo!sis only1 b me*anical hypo!ses 9 g5]al4 ,no?+ s mu* /rikes ! read] ( ! "w z ! exhau/iv5ess ( 8 treatm5t1 & ! unb\nd$ p[] ( 8 insight4 ,if he treats ( c5tral =ces1 x is n "o law ( =ce :i* he discusses1 b _m1 or almo/ all imag9able laws1 ! results ( ea* ( :i* he sket*es out 9 a few pregnant words4 ,if 8 subject is a resi/+ m$ium1 x is n air or wat] alone1 b resi/+ m$ia 9 g5]al4 ,we h a good example ( 8 me?od 9 ! s*olium to ! tw5ty-second proposition ( ! second book1 9 :i* he runs rapidly ov] _m suppositions z to ! laws ( ! compress+ =ces :i* might conceivably act 9 an atmosph]e ( gas1 a consequ5ce be+ drawn f ea* case1 & t "o hypo!sis ultimately select$ :i* yields results agree+ ) exp]im5ts ^u ! pressure & d5sity ( ! t]re/rial atmosph]e4 ,newton said t he did n frame hypo!ses1 b1 9 reality1 ! great] "p ( ! 99,pr9cipia99 is purely hypo!tical1 endless v>ieties ( causes & laws be+ imag9$ :i* h no c\nt]p>t 9 nature4 ,! mo/ grotesque hypo!ses ( ,kepl] or ,desc>tes 7 n m imag9>y4 ,b ,newton's compreh5sion ( logical me?od 0 p]fect2 no hypo!sis 0 ent]ta9$ unless x 0 def9ite 9 conditions1 & admitt$ ( unque/ionable d$uctive reason+2 & ! value ( ea* hypo!sis 0 entirely decid$ by ! comp>ison ( its consequ5ces ) facts4 ,i d n ent]ta9 a d\bt t ! g5]al c\rse ( 8 proc$ure is id5tical ) t view ( ! nature ( induction1 z ! inv]se application ( d$uction1 :i* ,i advocate ?r\gh\t ?is book4 ,francis ,bacon held t sci5ce %\ld be f\nd$ on exp]i5ce1 b he mi/ook ! true mode ( us+ exp]i5ce1 &1 9 attempt+ to apply 8 me?od1 ludicr\sly fail$4 ,newton did n less f\nd 8 me?od on exp]i5ce1 b he seiz$ ! true me?od ( treat+ x1 & appli$ x ) a p[] & success nev] s9ce equall$4 ,x is a great mi/ake to say t mod]n sci5ce is ! result ( ! ,baconian philosophy2 x is ! ,newtonian philosophy & ! ,newtonian me?od :i* h l$ to all ! great triumphs ( physical sci5ce1 & ,i repeat t ! 99,pr9cipia99 =ms ! true 8,novum ,organum40 ,9 br++ 8 !ories to a decisive exp]im5tal v]ification1 ,newton %[$1 z a g5]al rule1 exquisite skill & +5uity4 ,9 8 h&s a few simple pieces ( app>atus 7 made to give results involv+ an unsuspect$ dep? ( mean+4 ,8 mo/ beautiful exp]im5tal inquiry 0 t by :i* he prov$ ! diff]+ refrangibility ( rays ( light4 ,to suppose t he orig9ally discov]$ ! p[] ( a prism to break up a beam ( :ite light w\ld be a mi/ake1 = he speaks ( procur+ a glass prism to try ! 8celebrat$ ph5om5a ( col\rs40 ,b we c]ta9ly owe to him ! !ory t :ite light is a mixture ( rays diff]+ 9 refrangibility1 & t lights :i* diff] 9 col\r1 diff] also 9 refrangibility4 ,o!r p]sons might h conceiv$ ?is !ory2 9 fact1 any p]son reg>d+ refraction z a quantitative effect mu/ see t diff]5t p>ts ( ! spectrum h suff]$ diff]5t am\nts ( refraction4 ,b ! p[] ( ,newton is %[n 9 ! t5acity ) :i* he foll[$ 8 !ory into e consequ5ce1 & te/$ ea* result by a simple b conclusive exp]im5t4 ,he fir/ %[s t diff]5t col\r$ spots are displac$ by diff]5t am\nts :5 view$ ?r\gh a prism1 & t _! images come to a focus at diff]5t di/ances f ! l5se1 z !y %\ld d1 if ! refrangibility diff]$4 ,aft] exclud+ by _m exp]im5ts a v>iety ( indiff]5t circum/ances1 he fixes 8 att5tion ^u ! "q :e!r ! rays are m]ely %att]$1 di/urb$1 & spread out 9 a *ance mann]1 z ,grimaldi suppos$1 or :e!r !re is a con/ant relation betwe5 ! col\r & ! refrangibility4 ,if ,grimaldi 0 "r1 x might be expect$ t a "p ( ! spectrum tak5 sep>ately1 & subject$ to a second refraction1 w\ld suff] a new break+ up1 & produce "s new spectrum4 ,newton inf]r$ f 8 own !ory t a p>ticul> ray ( ! spectrum w\ld h a con/ant refrangibility1 s t a second prism w\ld m]ely b5d x m or less1 b n fur!r disp]se x 9 any consid]able degree4 ,by simply cutt+ (f mo/ ( ! rays ( ! spectrum by a scre51 & all[+ ! rema9+ n>r[ ray to fall on a second prism1 he prov$ ! tru? ( ?is conclusion2 & !n sl[ly turn+ ! fir/ prism1 s z to v>y ! col\r ( ! ray fall+ on ! second "o1 he f\nd t ! spot ( light =m$ by ! twice-refract$ ray travell$ up & d[n1 a palpable pro( t ! am\nt ( refrangibility v>ies ) ! col\r4 ,= 8 fur!r satisfaction1 he sometimes refract$ ! light a ?ird or f\r? "t1 & he f\nd t x might be refract$ upw>ds or d[nw>ds or sideways1 & yet = ea* col\r !re 0 a def9ite am\nt ( refraction ?r\gh ea* prism4 ,he complet$ ! pro( by %[+ t ! sep>at$ rays may aga9 be ga!r$ toge!r into :ite light by an inv]t$ prism1 s t no numb] ( refractions alt]s ! "* ( ! light4 ,! conclusion ?us obta9$ s]ves to expla9 ! confusion aris+ 9 ! use ( a common l5se2 he %[s t ) homog5e\s light !re is "o di/9ct focus1 ) mix$ light an inf9ite numb] ( foci1 :i* prev5t a cle> view f be+ obta9$ at any po9t4 ,:at a/oni%es ! read] ( ! 99,opticks99 is ! p]si/5ce ) :i* ,newton foll[s out ! consequ5ces ( a preconceiv$ !ory1 & te/s ! "o notion by a wond]ful v>iety ( simple comp>isons ) fact4 ,! ease ) :i* he inv5ts new comb9ations1 & =esees ! results1 subsequ5tly v]ifi$1 produces an insup]able conviction 9 ! read] t he has possession ( ! tru?4 ,& x is c]ta9ly ! !ory :i* leads him to ! exp]im5ts1 mo/ ( :i* c\ld h>dly be devis$ by accid5t4 ,newton actually rem>ks t x 0 by ma!matically det]m9+ all k9ds ( ph5om5a ( col\rs :i* c\ld be produc$ by refraction t he _h 8inv5t$0 almo/ all ! exp]im5ts 9 ! book1 & he promises t o!rs :o %all 8argue truly10 & try ! exp]im5ts ) c>e1 w n be disappo9t$ 9 ! results4#dhb #dhb 99,opticks991 bk4 i4 "p ii4 ,prop4 #c4 #crd ed4 p4 #aae4 ,! philosophic me?od ( ,huygh5s 0 ! same z t ( ,newton1 & ,huygh5s' inve/igation ( d\ble refraction furni%es almo/ equally beautiful in/ances ( !ory guid+ exp]im5t4 ,s f> z we "k d\ble refraction 0 fir/ discov]$ by accid5t1 & 0 describ$ by ,erasmus ,b>?ol9us 9 #affi4 ,! ph5om5on !n appe>$ to be entirely exceptional1 & ! laws gov]n+ ! two pa?s ( ! refract$ rays 7 s unapp>5t & complicat$1 t ,newton altoge!r misund]/ood ! ph5om5on1 & x 0 only at ! latt] end ( ! la/ c5tury t sci5tific m5 began to compreh5d its laws4 ,nev]!less1 ,huygh5s _h1 ) r>e g5ius1 arriv$ at ! true !ory z e>ly z #afgh4 ,he reg>d$ light z an undulatory motion ( "s m$ium1 & 9 8 99,trait de la ,lumire99 he po9t$ out t1 9 ord9>y refraction1 ! velocity ( propagation ( ! wave is equal 9 all directions1 s t ! front ( an advanc+ wave is sph]ical1 & rea*es equal di/ances 9 equal times4 ,b 9 cry/als1 z he suppos$1 ! m$ium w\ld be ( unequal ela/icity 9 diff]5t directions1 s t a di/urbance w\ld rea* unequal di/ances 9 equal times1 & ! wave produc$ w\ld h a sph]oidal =m4 ,huygh5s 0 n satisfi$ ) an unv]ifi$ !ory4 ,he calculat$ :at might be expect$ to happ5 :5 a cry/al ( calc-sp> 0 cut 9 v>i\s directions1 & he says3 8,i h exam9$ 9 detail ! prop]ties ( ! extraord9>y refraction ( ?is cry/al1 to see if ea* ph5om5on :i* is d$uc$ f !ory w\ld agree ) :at is really obs]v$4 ,& ?is be+ s1 x is no slight pro( ( ! tru? ( our suppositions & pr9ciples2 b :at ,i am go+ to add "h confirms !m /ill m wond]fully2 t is1 ! diff]5t modes ( cutt+ ?is cry/al1 9 :i* ! surfaces produc$ give rise to refraction exactly su* z !y ought to be1 & z ,i _h =ese5 !m1 accord+ to ! prec$+ !ory40 ,newton's mi/ak5 corpuscul> !ory ( light caus$ ! !ories & exp]im5ts ( ,huygh5s to be disreg>d$ = m ?an a c5tury2 b x is n easy to imag9e a m beautiful or successful application ( ! true me?od ( inductive inve/igation1 !ory guid+ exp]im5t1 & yet :olly rely+ on exp]im5t = confirmation4 99,c&\r & ,c\rage ( ! ,philosophic ,m9d499 ,p]fect read9ess to reject a !ory inconsi/5t ) fact is a prim>y requisite ( ! philosophic m9d4 ,b x w\ld be a mi/ake to suppose t ?is c&\r has any?+ ak9 to fickl5ess2 on ! contr>y1 read9ess to reject a false !ory may be comb9$ ) a peculi> p]t9acity & c\rage 9 ma9ta9+ an hypo!sis z long z its falsity is n actually app>5t4 ,!re mu/1 inde$1 be no prejudice or bias di/ort+ ! m9d1 & caus+ x to pass ov] ! unwelcome results ( exp]im5t4 ,!re mu/ be t scrupul\s hone/y & flexibility ( m9d1 :i* assigns adequate value to all evid5ce2 inde$1 ! m a man loves 8 !ory1 ! m scrupul\s %\ld be 8 att5tion to its faults4 ,x is common 9 life to meet ) "s !ori/1 :o1 by long cogitation ov] a s+le !ory1 has all[$ x to m\ld 8 m9d1 & r5d] him incapable ( receiv+ any?+ b z a contribution to ! tru? ( 8 "o !ory4 ,a n>r[ & int5se c\rse ( ?\ght may sometimes lead to great results1 b ! adoption ( a wrong !ory at ! outset is 9 su* a m9d irretrievable4 ,! man ( "o idea has b a s+le *ance ( tru?4 ,! f]tile discov]]1 on ! contr>y1 *ooses betwe5 _m !ories1 & is nev] w$d$ to any "o1 unless imp>tial & repeat$ comp>ison has conv9c$ him ( its validity4 ,he does n *oose & !n comp>e2 b he comp>es "t aft] "t1 & !n *ooses4 ,hav+ once delib]ately *os51 ! philosoph] may rightly ent]ta9 8 !ory ) ! /ronge/ fidelity4 ,he w neglect no objection2 = he may *ance at any "t to meet a fatal "o2 b he w be> 9 m9d ! inconsid]able p[]s ( ! human m9d comp>$ ) ! tasks x has to und]take4 ,he w see t no !ory c at fir/ be reconcil$ ) all objections1 because !re may be _m int]f]+ causes1 & ! v consequ5ces ( ! !ory may h a complexity :i* prolong$ inve/igation by successive g5]ations ( m5 may n exhau/4 ,if1 !n1 a !ory exhibit a numb] ( /rik+ co9cid5ces ) fact1 x mu/ n be ?r[n aside until at lea/ "o 99conclusive discordance99 is prov$1 reg>d be+ _h to possible error 9 e/abli%+ t discordance4 ,9 sci5ce & philosophy some?+ mu/ be risk$4 ,he :o quails at ! lea/ difficulty w nev] e/abli% a new tru?1 & x 0 n unphilosophic 9 ,leslie to rem>k conc]n+ 8 own inquiries into ! nature ( heat-- 8,9 ! c\rse ( inve/igation1 ,i h f\nd myself compell$ to rel9qui% "s preconceiv$ notions2 b ,i h n ab&on$ !m ha/ily1 nor1 till aft] a w>m & ob/9ate def5ce1 ,i 0 driv5 f e po/40#dhc #dhc 99,exp]im5tal ,inquiry into ! ,nature ( ,heat499 ,preface1 p4 xv4 ,f>aday's life1 aga91 furni%es mo/ int]e/+ illu/rations ( ?is t5acity ( ! philosophic m9d4 ,?\gh s c&id 9 reject+ "s !ories1 !re 7 o!rs to :i* he clung ?r\gh ev]y?+4 ,"o ( 8 fav\rite notions result$ 9 a brilliant discov]y2 ano!r rema9s 9 d\bt to ! pres5t day4 99,! ,philosophic ,"* ( ,f>aday499 ,9 ,f>aday's rese>*es conc]n+ ! connection ( magnetism & light1 we f9d an excell5t in/ance ( ! p]t9acity ) :i* a fav\rite !ory may be pursu$1 s long z ! results ( exp]im5t d n cle>ly negative ! notions ent]ta9$4 ,9 purely quantitative que/ions1 z we h se51 ! abs5ce ( app>5t effect c seldom be reg>d$ z prov+ ! abs5ce ( all effect4 ,n[ ,f>aday 0 conv9c$ t "s mutual relation mu/ exi/ betwe5 magnetism & light4 ,z e>ly z #ahbb1 he attempt$ to produce an effect ^u a ray ( pol>is$ light1 by pass+ x ?r\gh wat] plac$ betwe5 ! poles ( a voltaic batt]y2 b he 0 oblig$ to record t n ! slighte/ effect 0 obs]vable4 ,dur+ _m ye>s ! subject1 we are told1#dhd rose aga9 & aga9 to 8 m9d1 & no failure c\ld make him rel9qui% 8 se>* aft] ?is unkn[n relation4 ,x 0 9 ! ye> #ahde t he ga9$ ! fir/ success2 on ,augu/ #cj? he began to "w ) common electricity1 va9ly try+ glass1 qu>tz1 ,icel& sp>1 c4 ,sev]al days ( lab\r gave no result2 yet he did n desi/4 ,heavy glass1 a transp>5t m$ium ( great refractive p[]s1 compos$ ( borate ( lead1 0 n[ tri$1 be+ plac$ betwe5 ! poles ( a p[]ful electro-magnet :ile a ray ( pol>is$ light 0 transmitt$ ?r\gh x4 ,:5 ! poles ( ! electro-magnet 7 arrang$ 9 c]ta9 positions ) reg>d to ! sub/ance "u trial1 no effects 7 app>5t2 b at la/ ,f>aday happ5$ =tunately to place a piece ( heavy glass s t contr>y magnetic poles 7 on ! same side1 & n[ an effect 0 witness$4 ,! glass 0 f\nd to h ! p[] ( twi/+ ! plane ( pol>isation ( ! ray ( light4 #dhd ,b5ce ,jones1 99,life ( ,f>aday991 vol4 i4 p4 #cfb4 ,all ,f>aday's record$ ?\ghts ^u ?is great exp]im5t are replete ) curi\s int]e/4 ,he attributes 8 success to ! op9ion1 almo/ am\nt+ to a conviction1 t ! v>i\s =ms1 "u :i* ! =ces ( matt] are made manife/1 h "o common orig91 & are s directly relat$ & mutually dep5d5t t !y are conv]tible4 8,?is /rong p]suasion10 he says1#dhe 8ext5d$ to ! p[]s ( light1 & l$ to _m ex]tions hav+ = _! object ! discov]y ( ! direct relation ( light & electricity4 ,^! ineffectual ex]tions c\ld n remove my /rong p]suasion1 & ,i h at la/ succe$$40 ,he describes ! ph5om5on 9 some:at figurative language z 99! magnetisation ( a ray ( light991 & also z 99! illum9ation ( a magnetic curve or l9e ( =ce994 ,he has no soon] got ! effect 9 "o case1 ?an he proce$s1 ) 8 *>act]i/ic compreh5siv5ess ( rese>*1 to te/ ! exi/5ce ( a l ph5om5on 9 all ! sub/ances available4 ,he f9ds t n only heavy glass1 b solids & liquids1 acids & alkalis1 oils1 wat]1 alcohol1 e!r1 all possess ?is p[]2 b he 0 n able to detect its exi/5ce 9 any gase\s sub/ance4 ,8 ?\ghts _c be re/ra9$ f runn+ into curi\s speculations z to ! possible results ( ! p[] 9 c]ta9 cases4 8,:at effect10 he says1 8does ?is =ce h 9 ! e>? :]e ! magnetic curves ( ! e>? trav]se its sub/ance8 ,also :at effect 9 a magnet80 ,& !n he falls ^u ! /range notion t p]haps ?is =ce t5ds to make iron & oxide ( iron transp>5t1 a ph5om5on nev] obs]v$4 ,we c meet ) no?+ m in/ructive z to ! c\rse ( m9d by :i* great discov]ies are made1 ?an ^! records ( ,f>aday's pati5t lab\rs1 & 8 v>i$ success & failure4 ,nor are 8 unsuccessful exp]im5ts ^u ! relation ( gravity & electricity less int]e/+1 or less wor?y ( /udy4 #dhe ,ibid4 vol4 ii4 p4 #aii4 ,?r\gh\t a l>ge "p ( 8 life1 ,f>aday 0 possess$ by ! idea t gravity _c be unconnect$ ) ! o!r =ces ( nature4 ,on ,m>* #ai?1 #ahdi1 he wrote 9 8 laboratory book1--8,gravity4 ,surely ?is =ce mu/ be capable ( an exp]im5tal relation to electricity1 magnetism1 & ! o!r =ces1 s z to b9d x up ) !m 9 reciprocal action & equival5t effect80#dhf ,he fill$ tw5ty p>agraphs or m ) reflections & sugge/ions1 z to ! mode ( treat+ ! subject by exp]im5t4 ,he anticipat$ t ! mutual approa* ( two bodies w\ld develop electricity 9 !m1 or t a body fall+ ?r\gh a conduct+ helix w\ld excite a curr5t *ang+ 9 direction z ! motion 0 rev]s$4 899,all ?is is a dream9910 he rem>ks2 8/ill exam9e x by a few exp]im5ts4 ,no?+ is too wond]ful to be true1 if x be consi/5t ) ! laws ( nature2 & 9 su* ?+s z ^!1 exp]im5t is ! be/ te/ ( su* consi/5cy40 #dhf ,see also 8 m =mal /atem5t 9 ! 99,exp]im5tal ,rese>*es 9 ,electricity991 #bd? ,s]ies1 #bgjb1 vol4 iii4 p4 #afa4 ,he execut$ _m difficult & t$i\s exp]im5ts1 :i* are describ$ 9 ! #bd? ,s]ies ( ,exp]im5tal ,rese>*es4 ,! result 0 99nil991 & yet he concludes3 8,"h end my trials = ! pres5t4 ,! results are negative2 !y d n %ake my /rong feel+ ( ! exi/5ce ( a relation betwe5 gravity & electricity1 ?\gh !y give no pro( t su* a relation exi/s40 ,he return$ to ! "w :5 he 0 t5 ye>s old]1 & 9 #aheh-i record$ _m rem>kable reflections & exp]im5ts4 ,he 0 mu* /ruck by ! fact t electricity is ess5tially a 99dual =ce991 & x _h always be5 a conviction ( ,f>aday t no body c\ld be electrifi$ positively )\t "s o!r body becom+ electrifi$ negatively2 "s ( 8 rese>*es _h be5 simple developm5ts ( ?is relation4 ,b obs]v+ t betwe5 two mutually gravitat+ bodies !re 0 no app>5t circum/ance to det]m9e :i* %\ld be positive & :i* negative1 he does n hesitate to call 9 "q an old op9ion4 8,! evolution ( 99"o99 electricity w\ld be a new & v rem>kable ?+4 ,! idea ?r[s a d\bt on ! :ole2 b /ill try1 = :o kn[s :at is possible 9 deal+ ) gravity80 ,we _c b notice ! c&\r ) :i* he ?us ackn[l$ges 9 8 laboratory book ! d\btfulness ( ! :ole ?+1 & is yet prep>$ z a =lorn hope to frame exp]im5ts 9 opposition to all 8 previ\s exp]i5ce ( ! c\rse ( nature4 ,= a "t 8 ?\ghts fl[ on z if ! /range detection 7 already made1 & he _h only to trace out its consequ5ces ?r\gh\t ! univ]se4 8,let u enc\rage ourselves by a little m imag9ation prior to exp]im5t10 he says2 & !n he reflects ^u ! inf9ity ( actions 9 nature1 9 :i* ! mutual relations ( electricity & gravity w\ld come into play2 he pictures to himself ! planets & ! comets *>g+ !mselves z !y approa* ! sun2 cascades1 ra91 ris+ vap\r1 circulat+ curr5ts ( ! atmosph]e1 ! fumes ( a volcano1 ! smoke 9 a *imney become s _m electrical ma*9es4 ,a multitude ( ev5ts & *anges 9 ! atmosph]e seem to be at once elucidat$ by su* actions2 = a mom5t 8 rev]ies h ! vividness ( fact4 8,i ?9k we h be5 dull & bl9d n to h suspect$ "s su* results10 & he sums up rapidly ! consequ5ces ( 8 great b imag9>y !ory2 an entirely new mode ( excit+ heat or electricity1 an entirely new relation ( ! natural =ces1 an analysis ( gravitation1 & a ju/ification ( ! cons]vation ( =ce4 ,su* 7 ,f>aday's fonde/ dreams ( :at might be1 & to _m a philosoph] !y w\ld h be5 suffici5t basis = ! writ+ ( a great book4 ,b ,f>aday's imag9ation 0 )9 8 full control2 z he himself says1 8,let ! imag9ation g1 gu>d+ x by judgm5t & pr9ciple1 & hold+ x 9 & direct+ x by exp]im5t40 ,8 dreams soon took a v practical =m1 & = _m days he lab\r$ ) ceaseless en]gy1 on ! /aircase ( ! ,royal ,in/itution1 9 ! clock t[] ( ! ,h\ses ( ,p>liam5t1 or at ! top ( ! ,%ot ,t[] 9 ,s\?w>k1 rais+ & l[]+ heavy weights1 & comb9+ electrical helices & wires 9 e conceivable way4 ,8 skill & long exp]i5ce 9 exp]im5t 7 sev]ely tax$ to elim9ate ! effects ( ! e>?'s magnetism1 & "t aft] "t he sav$ himself f accept+ mi/ak5 indications1 :i* to ano!r man might h seem$ conclusive v]ifications ( 8 !ory4 ,:5 all 0 done !re rema9$ absolutely no results4 8,! exp]im5ts10 he says1 87 well made1 b ! results are negative20 & yet1 he adds1 8,i _c accept !m z conclusive40 ,9 ?is position ! "q rema9s to ! pres5t day2 x may be t ! effect 0 too slight to be detect$1 or x may be t ! arrangem5ts adopt$ 7 n suit$ to develop ! p>ticul> relation :i* exi/s1 j z ,o]/$ c\ld n detect electro-magnetism1 s long z 8 wire 0 p]p5dicul> to ! plane ( motion ( 8 ne$le4 ,b ^! are n matt]s :i* conc]n u fur!r "h4 ,we h only to notice ! pr(\nd conviction 9 ! unity ( natural laws1 ! active p[]s ( inf]5ce & imag9ation1 ! unb\nd$ lic5ce ( !oris+1 comb9$ above all ) ! utmo/ dilig5ce 9 exp]im5tal v]ification :i* ?is rem>kable rese>* exhibits4 99,res]vation ( ,judgm5t499 ,!re is yet ano!r *>act]i/ic ne$$ 9 ! philosophic m9d2 x is t ( susp5d+ judgm5t :5 ! data are insuffici5t4 ,_m p w express a confid5t op9ion on almo/ any "q :i* is put be=e !m1 b !y !reby manife/ n /r5g?1 b n>r[ness ( m9d4 ,to see all sides ( a complicat$ subject1 & to weigh all ! diff]5t facts & probabilities correctly1 require no ord9>y p[]s ( compreh5sion4 ,h5ce x is mo/ frequ5tly ! philosophic m9d :i* is 9 d\bt1 & ! ignorant m9d :i* is ready ) a positive decision4 ,f>aday has himself said1 9 a v int]e/+ lecture3#dhg 8,occasionally & frequ5tly ! ex]cise ( ! judgm5t ought to end 9 99absolute res]vation994 ,x may be v di/a/eful1 & great fatigue1 to susp5d a conclusion2 b z we are n infallible1 s we ought to be cauti\s2 we %all ev5tually f9d our advantage1 = ! man :o re/s 9 8 position is n s f> f "r z he :o1 proce$+ 9 a wrong direction1 is ev] increas+ 8 di/ance40 #dhg ,pr9t$ 9 99,mod]n ,culture991 edit$ by ,y\mans1 p4 #bai4 ,arago pres5t$ a conspicu\s example ( ?is high quality ( m9d1 z ,f>aday rem>ks2 = :5 he made kn[n 8 curi\s discov]y ( ! relation ( a magnetic ne$le to a revolv+ copp] plate1 a numb] ( suppos$ m5 ( sci5ce 9 diff]5t c\ntries gave imm$iate & confid5t explanations ( x1 :i* 7 all wrong4 ,b ,arago1 :o _h bo? discov]$ ! ph5om5on & p]sonally inve/igat$ its conditions1 decl9$ to put =w>d publicly any !ory at all4 ,at ! same "t we mu/ n suppose t ! truly philosophic m9d c tol]ate a /ate ( d\bt1 :ile a *ance ( decision rema9s op54 ,9 sci5ce no?+ l compromise is possible1 & tru? mu/ be "o4 ,h5ce1 d\bt is ! confession ( ignorance1 & involves a pa9ful feel+ ( incapacity4 ,b d\bt lies betwe5 error & tru?1 s t if we *oose wrongly we are fur!r away ?an ev] f our goal4 ,summ+ up1 !n1 x w\ld seem z if ! m9d ( ! great discov]] mu/ comb9e contradictory attributes4 ,he mu/ be f]tile 9 !ories & hypo!ses1 & yet full ( facts & precise results ( exp]i5ce4 ,he mu/ ent]ta9 ! feeble/ analogies1 & ! m]e/ guesses at tru?1 & yet he mu/ hold !m z wor?less till !y are v]ifi$ 9 exp]im5t4 ,:5 !re are any gr\nds ( probability he mu/ hold t5aci\sly to an old op9ion1 & yet he mu/ be prep>$ at any mom5t to rel9qui% x :5 a cle>ly contradictory fact is enc\nt]$4 8,! philosoph]10 says ,f>aday1#dhh 8%\ld be a man will+ to li/5 to e sugge/ion1 b det]m9$ to judge = himself4 ,he %\ld n be bias$ by appe>ances2 h no fav\rite hypo!sis2 be ( no s*ool2 & 9 doctr9e h no ma/]4 ,he %\ld n be a respect] ( p]sons1 b ( ?+s4 ,tru? %\ld be 8 prim>y object4 ,if to ^! qualities be add$ indu/ry1 he may inde$ hope to walk )9 ! veil ( ! temple ( nature40 #dhh 99,life ( ,f>aday991 vol4 i4 p4 #bbe4 ,,book ,v4 ,,g5]alisation1 ,,analogy1 ,,& ,,classification4 ,,*apt] ,,xxvii4 ,,g5]alisation4 ,i h endeav\r$ to %[ 9 prec$+ *apt]s t all inductive reason+ is an inv]se application ( d$uctive reason+1 & consi/s 9 demon/rat+ t ! consequ5ces ( c]ta9 assum$ laws agree ) facts ( nature ga!r$ by active or passive obs]vation4 ,! fundam5tal process ( reason+1 z /at$ 9 ! outset1 consi/s 9 inf]r+ ( a ?+ :at we "k ( simil> objects1 & x is on ?is pr9ciple t ! :ole ( d$uctive reason+1 :e!r simply logical or ma!matico-logical1 is f\nd$4 ,all inductive reason+ mu/ be f\nd$ on ! same pr9ciple4 ,x might seem t by a pla9 use ( ?is pr9ciple we c\ld avoid ! complicat$ processes ( induction & d$uction1 & argue directly f "o p>ticul> case to ano!r1 z ,mill propos$4 ,if ! ,e>?1 ,v5us1 ,m>s1 ,jupit]1 & o!r planets move 9 elliptic orbits1 _c we disp5se ) elaborate precautions1 & ass]t t ,neptune1 ,c]es1 & ! la/ discov]$ planet mu/ d s likewise8 ,d we n "k t ,mr4 ,glad/one mu/ die1 because he is l o!r m58 ,may we n argue t because "s m5 die !re=e he mu/8 ,is x requisite to asc5d by induction to ! g5]al proposition 8all m5 mu/ die10 & !n desc5d by d$uction f t g5]al proposition to ! case ( ,mr4 ,glad/one8 ,my answ] und\bt$ly is t we mu/ asc5d to g5]al propositions4 ,! fundam5tal pr9ciple ( ! sub/itution ( simil>s gives u no w>rant 9 affirm+ ( ,mr4 ,glad/one :at we "k ( o!r m51 because we _c be sure t ,mr4 ,glad/one is exactly simil> to o!r m54 ,until 8 dea? we _c be p]fectly sure t he possesses all ! attributes ( o!r m52 x is a "q ( probability1 & ,i h endeav\r$ to expla9 ! mode 9 :i* ! !ory ( probability is appli$ to calculate ! probability t f a s]ies ( simil> ev5ts we may inf] ! recurr5ce ( l ev5ts "u id5tical circum/ances4 ,!re is !n no su* process z t ( inf]r+ f p>ticul>s to p>ticul>s4 ,a c>eful analysis ( ! conditions "u :i* su* an inf]5ce appe>s to be made1 %[s t ! process is really a g5]al "o1 & t :at is inf]r$ ( a p>ticul> case might be inf]r$ ( all simil> cases4 ,all reason+ is ess5tially g5]al1 & all sci5ce implies g5]alisation4 ,9 ! v bir?-"t ( philosophy ?is 0 held to be s3 8,nulla sci5tia e/ de individuis1 s$ de solis univ]salibus10 0 ! doctr9e ( ,plato1 deliv]$ by ,porphyry4 ,& ,ari/otle#dhi held a l op9ion-- ' 444 ' 4 8,no art treats ( p>ticul> cases2 = p>ticul>s are inf9ite & _c be kn[n40 ,no "o :o holds ! doctr9e t reason+ may be f p>ticul>s to p>ticul>s1 c be suppos$ to h ! mo/ rudim5t>y notion ( :at con/itutes reason+ & scence4 #dhi ,ari/otle's 99,rhetoric991 ,lib] ,i4 #b4 #aa4 ,at ! same "t !re c be no d\bt t practically :at we f9d to be true ( _m simil> objects w probably be true ( ! next simil> object4 ,?is is ! result to :i* an analysis ( ! ,inv]se ,me?od ( ,probabilities leads u1 &1 9 ! abs5ce ( precise data f :i* we may calculate probabilities1 we are usually oblig$ to make a r\gh assumption t simil>s 9 "s respects are simil>s 9 o!r respects4 ,?us x comes to pass t a l>ge "p ( ! reason+ processes 9 :i* sci5tific m5 are engag$1 consi/s 9 detect+ simil>ities betwe5 objects1 & !n rudely assum+ t ! l simil>ities w be detect$ 9 o!r cases4 99,di/9ction ( ,g5]alisation & ,analogy499 ,!re is no di/9ction b t ( degree betwe5 :at is kn[n z reason+ by 99g5]alisation99 & reason+ by 99analogy994 ,9 bo? cases f c]ta9 obs]v$ resemblances we inf]1 ) m or less probability1 ! exi/5ce ( o!r resemblances4 ,9 g5]alisation ! resemblances h great ext5sion & usually little int5sion1 :]eas 9 analogy we rely ^u ! great int5sion1 ! ext5sion be+ ( small am\nt 7p4 #bf74 ,if we f9d t ! qualities ,a & ,b are associat$ toge!r 9 a great _m in/ances1 & h nev] be5 f\nd sep>ate1 x is highly probable t on ! next occasion :5 we meet ) ,a1 ,b w also be pres5t1 & 99vice v]s994 ,?us :]ev] we meet ) an object possess+ gravity1 x is f\nd to possess in]tia also1 nor h we met ) any mat]ial objects possess+ in]tia )\t discov]+ t !y also possess gravity4 ,! probability has !re=e become v great1 z indicat$ by ! rules f\nd$ on ! ,inv]se ,me?od ( ,probabilities 7p4 #beg71 t :5ev] 9 ! future we meet an object possess+ ei!r ( ! prop]ties ( gravity & in]tia1 x w be f\nd on exam9ation to possess ! o!r ( ^! prop]ties4 ,?is is a cle> in/ance ( ! employm5t ( g5]alisation4 ,9 analogy1 on ! o!r h&1 we reason f lik5ess 9 _m po9ts to lik5ess 9 o!r po9ts4 ,! qualities or po9ts ( resemblance are n[ num]\s1 n ! objects4 ,at ! poles ( ,m>s are two :ite spots :i* resemble 9 _m respects ! :ite regions ( ice & sn[ at ! poles ( ! e>?4 ,!re probably exi/ no o!r simil> objects ) :i* to comp>e ^!1 yet ! exactness ( ! resemblance enables u to inf]1 ) high probability1 t ! spots on ,m>s consi/ ( ice & sn[4 ,9 %ort1 _m po9ts ( resemblance imply _m m4 ,f ! appe>ance & behavi\r ( ^? :ite spots we inf] t !y h all ! *emical & physical prop]ties ( froz5 wat]4 ,! inf]5ce is ( c\rse only probable1 & bas$ ^u ! improbability t aggregates ( _m qualities %\ld be =m$ 9 a l mann] 9 two or m cases1 )\t be+ due to "s uni=m condition or cause4 ,9 reason+ by analogy1 !n1 we obs]ve t two objects ,,abcde4444 & ,a,b,c,d,e4444 h _m l qualities1 z indicat$ by ! id5tity ( ! lett]s1 & we inf] t1 s9ce ! fir/ has ano!r quality1 ,x1 we %all discov] ?is quality 9 ! second case by suffici5tly close exam9ation4 ,z ,laplace says1--8,analogy is f\nd$ on ! probability t simil> ?+s h causes ( ! same k9d1 & produce ! same effects4 ,! m p]fect ?is simil>ity1 ! great] is ?is probability40#dij ,! nature ( analogical inf]5ce is aptly describ$ 9 ! "w on ,logic attribut$ to ,kant1 :]e ! rule ( ord9>y induction is /at$ 9 ! words1 899,e9es 9 viel51 also 9 all59910 "o quality 9 _m ?+s1 !re=e 9 all2 & ! rule ( analogy is 899,vieles 9 e9em1 also au* das brige 9 demselb59910#dia _m 7qualities7 9 "o1 !re=e also ! rema9d] 9 ! same4 ,x is evid5t t !re may be int]m$iate cases 9 :i*1 f ! id5tity ( a mod]ate numb] ( objects 9 sev]al prop]ties1 we may inf] to o!r objects4 ,probability mu/ re/ ei!r ^u ! numb] ( in/ances or ! dep? ( resemblance1 or ^u ! occurr5ce ( bo? 9 suffici5t degrees4 ,:at !re is want+ 9 ext5sion mu/ be made up by int5sion1 & 99vice v]s994 #dij 99,essai ,philosophique sur les ,probabilits991 p4 #hf4 #dia ,kant's 99,logik991 #hd1 ,knigsb]g1 #ahjj1 p4 #bjg4 99,two ,mean+s ( ,g5]alisation499 ,! t]m g5]alisation1 z commonly us$1 includes two processes :i* are ( diff]5t "*1 b are (t5 closely associat$ toge!r4 ,9 ! fir/ place1 we g5]alise :5 we recognise ev5 9 two objects a common nature4 ,we _c detect ! slighte/ simil>ity )\t op5+ ! way to inf]5ce f "o case to ! o!r4 ,if we comp>e a cubical cry/al ) a regul> octah$ron1 !re is little app>5t simil>ity2 b1 z soon z we p]ceive t ei!r c be produc$ by ! symmetrical modification ( ! o!r1 we discov] a gr\ndwork ( simil>ity 9 ! cry/als1 :i* enables u to inf] _m ?+s ( "o1 because !y are true ( ! o!r4 ,our k ( ozone took its rise f ! "t :5 ! simil>ity ( smell1 att5d+ electric sp>ks1 /rokes ( lightn+1 & ! sl[ combu/ion ( phosphorus1 0 notic$ by ,s*nbe94 ,!re 0 a "t :5 ! ra9b[ 0 an inexplicable ph5om5on--a port5t1 l a comet1 & a cause ( sup]/iti\s hopes & fe>s4 ,b we f9d ! true _s ( sci5ce 9 ,rog] ,bacon1 :o desires u to consid] ! objects :i* pres5t ! same col\rs z ! ra9b[2 he m5tions hexagonal cry/als f ,irel& & ,india1 b he bids u n suppose t ! hexagonal =m is ess5tial1 = simil> col\rs may be detect$ 9 _m transp>5t /ones4 ,drops ( wat] scatt]$ by ! o> 9 ! sun1 ! spray f a wat]-:eel1 ! dewdrops ly+ on ! grass 9 ! summ] morn+1 all display a simil> ph5om5on4 ,no soon] h we gr\p$ toge!r ^! app>5tly div]se in/ances1 ?an we h begun to g5]alise1 & h acquir$ a p[] ( apply+ to "o in/ance :at we c detect ( o!rs4 ,ev5 :5 we d n apply ! k ga9$ to new objects1 our compreh5sion ( ^? already obs]v$ is greatly /r5g!n$ & deep5$ by le>n+ to view !m z p>ticul> cases ( a m g5]al prop]ty4 ,a second process1 to :i* ! "n ( g5]alisation is (t5 giv51 consi/s 9 pass+ f a fact or p>tial law to a multitude ( unexam9$ cases1 :i* we believe to be subject to ! same conditions4 ,in/ead ( m]ely recognis+ simil>ity z x is br\ght be=e u1 we pr$ict its exi/5ce be=e our s5ses c detect x1 s t g5]alisation ( ?is k9d end[s u ) a prophetic p[] ( m or less probability4 ,hav+ obs]v$ t _m sub/ances assume1 l wat] & m]cury1 ! ?ree /ates ( solid1 liquid1 & gas1 & hav+ assur$ ourselves by frequ5t trial t ! great] ! means we possess ( heat+ & cool+1 ! m sub/ances we c vaporise & freeze1 we pass confid5tly 9 advance ( fact1 & assume t all sub/ances are capable ( ^! ?ree =ms4 ,su* a g5]alisation 0 accept$ by ,lavoisi] & ,laplace be=e _m ( ! corroborative facts n[ 9 our possession 7 kn[n4 ,! r$uction ( a s+le comet b5ea? ! sway ( gravity 0 consid]$ suffici5t indication t all comets obey ! same p[]4 ,few p]sons d\bt$ t ! law ( gravity ext5d$ ov] ! :ole heav5s2 c]ta9ly ! fact t a few />s out ( _m millions manife/ ! action ( gravity1 is n[ held to be suffici5t evid5ce ( its g5]al ext5sion ov] ! visible univ]se4 99,value ( ,g5]alisation499 ,x might seem t if we "k p>ticul> facts1 !re c be little use 9 connect+ !m toge!r by a g5]al law4 ,! p>ticul>s mu/ be m full ( useful in=mation ?an an ab/ract g5]al /atem5t4 ,if we "k1 = in/ance1 ! prop]ties ( an ellipse1 a circle1 a p>abola1 & hyp]bola1 :at is ! use ( le>n+ all ^! prop]ties ov] aga9 9 ! g5]al !ory ( curves ( ! second degree8 ,if we und]/& ! ph5om5a ( s\nd & light & wat]-waves sep>ately1 :at is ! ne$ ( erect+ a g5]al !ory ( waves1 :i*1 aft] all1 is inapplicable to practice until resolv$ aga9 into p>ticul> cases8 ,b1 9 reality1 we nev] d obta9 an adequate k ( p>ticul>s until we reg>d !m z cases ( ! g5]al4 ,n only is !re a s+ul> delight 9 discov]+ ! _m 9 ! "o1 & ! "o 9 ! _m1 b !re is a con/ant int]*ange ( light & k4 ,prop]ties :i* are unapp>5t 9 ! hyp]bola may be readily obs]v$ 9 ! ellipse4 ,mo/ ( ! complex relations :i* old geomet]s discov]$ 9 ! circle w be reproduc$ 99mutatis mut&is99 9 ! o!r conic sections4 ,! undulatory !ory ( light might h be5 unkn[n at ! pres5t day1 _h n ! !ory ( s\nd suppli$ h9ts by analogy4 ,! /udy ( light has made kn[n _m ph5om5a ( int]f]5ce & pol>isation1 ! exi/5ce ( :i* _h h>dly be5 suspect$ 9 ! case ( s\nd1 b :i* may n[ be s\ght out1 & p]haps f\nd to possess unexpect$ int]e/4 ,! c>eful /udy ( wat]-waves %[s h[ waves alt] 9 =m & velocity ) v>y+ dep? ( wat]4 ,analog\s *anges may "s "t be detect$ 9 s\nd waves4 ,?us !re is mutual int]*ange ( aid4 8,e /udy ( a g5]alisation or ext5sion10 ,de ,morgan has well said1#dib 8gives additional p[] ov] ! p>ticul> =m by :i* ! g5]alisation is sugge/$4 ,nobody :o has ev] return$ to quadratic equations aft] ! /udy ( equations ( all degrees1 or :o has done ! l1 w d5y my ass]tion t may be pr$icat$ ( any "o :o /udies a bran* or a case1 )\t aft]w>ds mak+ x "p ( a l>g] :ole4 ,accord+ly x is always wor? :ile to g5]alise1 7 x only to give p[] ov] ! 99p>ticul>994 ,?is pr9ciple1 ( daily famili>ity to ! ma!matician1 is almo/ unkn[n to ! logician40 #dib 99,syllabus ( a ,propos$ ,sy/em ( ,logic991 p4 #cd4 99,comp>ative ,g5]ality ( ,prop]ties499 ,mu* ( ! value ( sci5ce dep5ds ^u ! k :i* we gradually acquire ( ! diff]5t degrees ( g5]ality ( prop]ties & ph5om5a ( v>i\s k9ds4 ,! use ( sci5ce consi/s 9 enabl+ u to act ) confid5ce1 because we c =esee ! result4 ,n[ ?is =esight mu/ re/ ^u ! k ( ! p[]s :i* w come into play4 ,t k1 inde$1 c nev] be c]ta91 because x re/s ^u imp]fect induction1 & ! mo/ confid5t beliefs & pr$ictions ( ! physici/ may be falsifi$4 ,nev]!less1 if we always e/imate ! probability ( ea* belief accord+ to ! due tea*+ ( ! data1 & be> 9 m9d t probability :5 =m+ our anticipations1 we %all ensure ! m9imum ( disappo9tm5t4 ,ev5 :5 he _c exactly apply ! !ory ( probabilities1 ! physici/ may acquire ! habit ( mak+ judgm5ts 9 g5]al agreem5t ) its pr9ciples & results4 ,su* is ! con/itution ( nature1 t ! physici/ le>ns to di/+ui% ^? prop]ties :i* h wide & uni=m ext5sion1 f ^? :i* v>y betwe5 case & case4 ,n only are c]ta9 laws di/9ctly laid d[n1 ) _! ext5sion c>efully def9$1 b a sci5tific tra9+ gives a k9d ( tact 9 judg+ h[ f> o!r laws are likely to apply "u any p>ticul> circum/ances4 ,we le>n by degrees t cry/als exhibit ph5om5a dep5d+ ^u ! directions ( ! axes ( ela/icity1 :i* we mu/ n expect 9 uni=m solids4 ,liquids1 comp>$ ev5 ) non-cry/all9e solids1 exhibit laws ( f> less complexity & v>iety2 & gases assume1 9 _m respects1 an aspect ( ne>ly complete uni=mity4 ,to trace out ! bran*es ( sci5ce 9 :i* v>y+ degrees ( g5]ality prevail1 w\ld be an inquiry ( great int]e/ & importance2 b want ( space1 if !re 7 no o!r reason1 w\ld =bid me to attempt x1 except 9 a v slight mann]4 ,gases1 s f> z !y are really gase\s1 n only h exactly ! same prop]ties 9 all directions ( space1 b "o gas exactly resembles o!r gases 9 _m qualities4 ,all gases exp& by heat1 accord+ to ! same law1 & by ne>ly ! same am\nt2 ! specific heats ( equival5t weights are equal1 & ! d5sities are exactly proportional to ! atomic weights4 ,all su* gases obey ! g5]al law1 t ! volume multipli$ by ! pressure1 & divid$ by ! absolute temp]ature1 is con/ant or ne>ly s4 ,! laws ( diffusion & transpiration are ! same 9 all cases1 &1 g5]ally speak+1 all physical laws1 z di/+ui%$ f *emical laws1 apply equally to all gases4 ,ev5 :5 gases diff] 9 *emical or physical prop]ties1 ! diff]5ces are m9or 9 degree4 ,?us ! diff]5ces ( viscosity are f> less m>k$ ?an 9 ! liquid & solid /ates4 ,ne>ly all gases1 aga91 are col\rless1 ! exceptions be+ *lor9e1 ! vap\rs ( iod9e1 brom9e1 & a few o!r sub/ances4 ,only 9 "o s+le po9t1 s f> z ,i am aw>e1 d gases pres5t di/+ui%+ m>ks unkn[n or ne>ly s1 9 ! solid & liquid /ates4 ,i mean z reg>ds ! light giv5 (f :5 inc&esc5t4 ,ea* gas :5 suffici5tly heat$1 yields its own peculi> s]ies ( rays1 aris+ f ! free vibrations ( ! con/itu5t p>ts ( ! molecules4 ,h5ce ! possibility ( di/+ui%+ gases by ! spectroscope4 ,b ! molecules ( solids & liquids appe> to be cont9ually 9 conflict ) ea* o!r1 s t only a confus$ 99noise99 ( atoms is produc$1 in/ead ( a def9ite s]ies ( lum9\s *ords4 ,at ! same temp]ature1 accord+ly1 all solids & liquids give (f ne>ly ! same rays :5 /rongly heat$1 & we h 9 ?is case an exception to ! great] g5]ality ( prop]ties 9 gases4 ,liquids are 9 _m ways int]m$iate 9 "* betwe5 gases & solids4 ,:ile incapable ( possess+ diff]5t ela/icity 9 diff]5t directions1 & ?us d5ud$ ( ! ri* geometrical complexity ( solids1 !y reta9 ! v>iety ( d5sity1 col\r degrees ( transp>5cy1 great div]sity 9 surface t5sion1 viscosity1 coeffici5ts ( expansion1 compressibility1 & _m o!r prop]ties :i* we obs]ve 9 solids1 b n = ! mo/ "p 9 gases4 ,?\gh our k ( ! physical prop]ties ( liquids is mu* want+ 9 g5]ality at pres5t1 !re is gr\nd to hope t by degrees laws connect+ & expla9+ ! v>iations may be trac$ out4 ,solids are 9 e way contra/$ to gases4 ,ea* solid sub/ance has its own peculi> degree ( d5sity1 h>dness1 compressibility1 transp>5cy1 t5acity1 ela/icity1 p[] ( conduct+ heat & electricity1 magnetic prop]ties1 capability ( produc+ frictional electricity1 & s =?4 ,ev5 diff]5t specim5s ( ! same k9d ( sub/ance w diff] widely1 accord+ to ! accid5tal treatm5t receiv$4 ,& n only has ea* sub/ance its own specific prop]ties1 b1 :5 cry/allis$1 its prop]ties v>y 9 ea* direction ) reg>d to ! axes ( cry/allisation4 ,! velocity ( radiation1 ! rate ( conduction ( heat1 ! coeffici5ts ( expansibility & compressibility1 ! !rmo-electric prop]ties1 all v>y 9 diff]5t cry/allographic directions4 ,x is probable t _m app>5t diff]5ces betwe5 liquids1 & ev5 betwe5 solids1 w be expla9$ :5 we le>n to reg>d !m "u exactly correspond+ circum/ances4 ,! extreme g5]ality ( ! prop]ties ( gases is 9 reality only true at an inf9itely high temp]ature1 :5 !y are all equally remote f _! cond5s+ po9ts4 ,n[1 x is f\nd t if we comp>e liquids--= in/ance1 diff]5t k9ds ( alcohols--n at equal temp]atures1 b at po9ts equally di/ant f _! respective boil+ po9ts1 ! laws & coeffici5ts ( expansion are ne>ly equal4 ,! vap\r-t5sions ( liquids also are m ne>ly equal1 :5 comp>$ at correspond+ po9ts1 & ! boil+-po9ts appe> 9 _m cases to be simply relat$ to ! *emical composition4 ,no d\bt ! progress ( inve/igation w enable u to discov] g5]ality1 :]e at pres5t we only see v>iety & puzzl+ complexity4 ,9 "s cases sub/ances exhibit ! same physical prop]ties 9 ! liquid z 9 ! solid /ate4 ,lead has a high refractive p[]1 :e!r 9 solution1 or 9 solid salts1 cry/allis$ or vitre\s4 ,! magnetic p[] ( iron is conspicu\s1 :atev] be its *emical condition2 inde$1 ! magnetic prop]ties ( sub/ances1 ?\gh v>y+ ) temp]ature1 seem n to be greatly affect$ by o!r physical *anges4 ,col\r1 absorptive p[] = heat or light rays1 & a few o!r prop]ties are also (t5 ! same 9 liquids & gases4 ,iod9e & brom9e possess a deep col\r :5ev] !y are *emically uncomb9$4 ,nev]!less1 we c seldom argue safely f ! prop]ties ( a sub/ance 9 "o condition to ^? 9 ano!r condition4 ,ice is an insulator1 wat] a conductor ( electricity1 & ! same contra/ exi/s 9 mo/ o!r sub/ances4 ,! conduct+ p[] ( a liquid = electricity increases ) ! temp]ature1 :ile t ( a solid decreases4 ,by degrees we may le>n to di/+ui% betwe5 ^? prop]ties ( matt] :i* dep5d ^u ! intimate con/ruction ( ! *emical molecule1 & ^? :i* dep5d ^u ! contact1 conflict1 mutual attraction1 or o!r relations ( di/9ct molecules4 ,! prop]ties ( a sub/ance ) respect to light seem g5]ally to dep5d ^u ! molecule2 ?us1 ! p[] ( c]ta9 sub/ances to cause ! plane ( pol>isation ( a ray ( light to rotate1 is exactly ! same :atev] be its degree ( d5sity1 or ! dilut5ess ( ! solution 9 :i* x is conta9$4 ,tak5 z a :ole1 ! physical prop]ties ( sub/ances & _! quantitative laws1 pres5t a problem ( inf9ite complexity1 & c5turies mu/ elapse be=e any mod]ately complete g5]alisations on ! subject become possible4 99,uni=m ,prop]ties ( all ,matt]499 ,"s laws are held to be true ( all matt] 9 ! univ]se absolutely1 )\t exception1 no in/ance to ! contr>y hav+ ev] be5 notic$4 ,?is is ! case ) ! laws ( motion1 z laid d[n by ,galileo & ,newton4 ,x is also conspicu\sly true ( ! law ( univ]sal gravitation4 ,! rise ( mod]n physical sci5ce may p]haps be consid]$ z beg9n+ at ! "t :5 ,galileo %[$1 9 opposition to ! ,ari/otelians1 t matt] is equally affect$ by gravity1 irrespective ( its =m1 magnitude1 or texture4 ,all objects fall ) equal rapidity1 :5 di/urb+ causes1 su* z ! resi/ance ( ! air1 are remov$ or all[$ =4 ,t :i* 0 rudely demon/rat$ by ,galileo f ! lean+ t[] ( ,pisa1 0 prov$ by ,newton to a high degree ( approximation1 9 an exp]im5t :i* has be5 m5tion$ 7p4 #ddc74 ,newton =m$ two p5dulums1 z ne>ly z possible ! same 9 outw>d %ape & size by tak+ two equal r\nd wood5 boxes1 & susp5d+ !m by equal ?reads1 elev5 feet long4 ,! p5dulums 7 !re=e equally subject to ! resi/ance ( ! air4 ,he fill$ "o box ) wood1 & 9 ! c5tre ( oscillation ( ! o!r he plac$ an equal weight ( gold4 ,! p5dulums 7 !n equal 9 weight z well z 9 size2 &1 on sett+ !m simultane\sly 9 motion1 ,newton f\nd t !y vibrat$ = a l5g? ( "t ) equal vibrations4 ,he tri$ ! same exp]im5t ) silv]1 lead1 glass1 s&1 common salt1 wat]1 & :eat1 9 place ( ! gold1 & asc]ta9$ t ! motion ( 8 p5dulum 0 exactly ! same :atev] 0 ! k9d ( matt] inside4#dic ,he consid]$ t a diff]5ce ( a ?\s&? "p w\ld h be5 app>5t4 ,! read] mu/ obs]ve t ! p5dulums 7 made ( equal weight only 9 ord] t !y might suff] equal ret>dation f ! air4 ,! mean+ ( ! exp]im5t is t all sub/ances manife/ exactly equal accel]ation f ! =ce ( gravity1 & t !re=e ! in]tia or resi/ance ( matt] to =ce1 :i* is ! only indep5d5t measure ( mass kn[n to u1 is always proportional to gravity4 #dic 99,pr9cipia991 bk4 iii4 ,prop4 ,,vi4 ,motte's translation1 vol4 ii4 p4 #bbj4 ,^! exp]im5ts ( ,newton 7 consid]$ conclusive up to v rec5t times1 :5 c]ta9 discordances betwe5 ! !ory & obs]vations ( ! movem5ts ( planets l$ ,nicolai1 9 #ahbf1 to sugge/ t ! equal gravitation ( diff]5t k9ds ( matt] might n be absolutely exact4 ,x is p]fectly philosophical ?us to call 9 "q1 f "t to "t1 "s ( ! be/ accept$ laws4 ,on ?is occasion ,bessel c>efully repeat$ ! exp]im5ts ( ,newton ) p5dulums compos$ ( ivory1 glass1 m>ble1 qu>tz1 meteoric /ones1 c41 b 0 unable to detect ! lea/ diff]5ce4 ,?is conclusion is also confirm$ by ! ultimate agreem5t ( all ! calculations ( physical a/ronomy bas$ ^u x4 ,:e!r ! mass ( ,jupit] be calculat$ f ! motion ( its own satellites1 f ! effect ^u ! small planets1 ,ve/a1 ,juno1 c41 or f ! p]turbation ( ,encke's ,comet1 ! results are closely accordant1 %[+ t precisely ! same law ( gravity applies to ! mo/ diff]5t bodies :i* we c obs]ve4 ,! gravity ( a body1 aga91 appe>s to be entirely indep5d5t ( its o!r physical conditions1 be+ totally unaffect$ by any alt]ation 9 ! temp]ature1 d5sity1 electric or magnetic condition1 or o!r physical prop]ties ( ! sub/ance4 ,"o p>adoxical result ( ! law ( equal gravitation is ! !orem ( ,torricelli1 to ! effect t all liquids ( :atev] d5sity fall or fl[ ) equal rapidity4 ,if !re be two equal ci/]ns respectively fill$ ) m]cury & wat]1 ! m]cury1 ?\gh ?irte5 times z heavy1 w\ld fl[ f an ap]ture nei!r m rapidly nor m sl[ly ?an ! wat]1 & ! same w\ld be true ( e!r1 alcohol1 & o!r liquids1 all[ance be+ made1 h[ev]1 = ! resi/ance ( ! air1 & ! diff]+ viscosities ( ! liquids4 ,9 its exact equality & its p]fect indep5d5ce ( all circum/ances1 except mass & di/ance1 ! =ce ( gravity /&s ap>t f all ! o!r =ces & ph5om5a ( nature1 & has n yet be5 br\ght into any relation ) !m except ?r\gh ! g5]al pr9ciple ( ! cons]vation ( en]gy4 ,magnetic attraction1 z rem>k$ by ,newton1 foll[s v diff]5t laws1 dep5d+ ^u ! *emical quality & molecul> /ructure ( ea* p>ticul> sub/ance4 ,we mu/ rememb] t 9 say+ 8all matt] gravitates10 we exclude f ! t]m matt] ! basis ( light-undulations1 :i* is imm5sely m ext5sive 9 am\nt1 & obeys 9 _m respects ! laws ( me*anics4 ,?is adamant9e sub/ance appe>s1 s f> z c be asc]ta9$1 to be p]fectly uni=m 9 its prop]ties :5 exi/+ 9 space unoccupi$ by matt]4 ,light & heat are convey$ by x ) equal velocity 9 all directions1 & 9 all p>ts ( space s f> z obs]vation in=ms u4 ,b ! pres5ce ( gravitat+ matt] modifies ! d5sity & me*anical prop]ties ( ! s-call$ e!r 9 a way :i* is yet q unexpla9$4#did ,leav+ gravity1 x is some:at difficult to discov] o!r laws :i* are equally true ( all matt]4 ,bo]haave 0 consid]$ to h e/abli%$ t all bodies exp& by heat2 b n only is ! expansion v diff]5t 9 diff]5t sub/ances1 b we n[ "k positive exceptions4 ,_m liquids & a few solids contract by heat at c]ta9 temp]atures4 ,!re are inde$ o!r relations ( heat to matt] :i* seem to be univ]sal & uni=m2 all sub/ances beg9 to give (f rays ( light at ! same temp]ature1 accord+ to ! law ( ,drap]2 & gases w n be an exception if suffici5tly cond5s$1 z 9 ! exp]im5ts ( ,frankl&4 ,grove consid]s x to be univ]sally true t all bodies 9 comb9+ produce heat2 ) ! d\btful exception ( sulphur & sel5ium1 all solids 9 becom+ liquids1 & all liquids 9 becom+ gases1 absorb heat2 b ! quantities ( heat absorb$ v>y ) ! *emical qualities ( ! matt]4 ,c>not's ,!rmodynamic ,law is held to be exactly true ( all matt] )\t di/9ction2 x expresses ! fact t ! am\nt ( me*anical en]gy :i* might be !oretically obta9$ f a c]ta9 am\nt ( heat en]gy dep5ds only ^u ! *ange ( ! temp]atures1 s t :e!r an eng9e be work$ by wat]1 air1 alcohol1 ammonia1 or any o!r sub/ance1 ! result w\ld !oretically be ! same1 if ! boil] & cond5s] 7 ma9ta9$ at simil> temp]atures4 #did ,pr(essor ,lov]+ has po9t$ out h[ obscure & unc]ta9 ! ideas ( sci5tific m5 ab\t ?is e!r are1 9 8 int]e/+ ,presid5tial ,address be=e ! ,am]ican ,association at ,h>t=d1 #ahgd4 99,silliman's ,j\rnal991 ,octob] #ahgd1 p4 #big4 99,philosophical ,magaz9e991 vol4 xlviii4 p4 #dic4 99,v>iable ,prop]ties ( ,matt]499 ,i h enum]at$ "s ( ! few prop]ties ( matt]1 :i* are manife/$ 9 exactly ! same mann] by all sub/ances1 :atev] be _! diff]5ces ( *emical or physical con/itution4 ,b by f> ! great] numb] ( qualities v>y 9 degree2 sub/ances are m or less d5se1 m or less transp>5t1 m or less compressible1 m or less magnetic1 & s on4 ,"o common result ( ! progress ( sci5ce is to %[ t qualities suppos$ to be entirely abs5t f _m sub/ances are pres5t only 9 s l[ a degree ( int5sity t ! means ( detection 7 insuffici5t4 ,newton believ$ t mo/ bodies 7 q unaffect$ by ! magnet2 ,f>aday & ,tyndall h r5d]$ x v d\btful :e!r any sub/ance :atev] is :olly devoid ( magnetism1 includ+ "u t t]m diamagnetism4 ,we are rapidly le>n+ to believe t !re are no sub/ances absolutely opaque1 or non-conduct+1 non-electric1 non-ela/ic1 non-visc\s1 non-compressible1 insoluble1 infusible1 or non-volatile4 ,all t5ds to become a matt] ( degree1 or sometimes ( direction4 ,!re may be "s sub/ances oppositely affect$ to o!rs1 z f]ro-magnetic sub/ances are oppositely affect$ to diamagnetics1 or z sub/ances :i* contract by heat are oppos$ to ^? :i* exp&2 b ! t5d5cy is c]ta9ly = e affection ( "o k9d ( matt] to be repres5t$ by some?+ simil> 9 o!r k9ds4 ,on ?is acc\nt "o ( ,newton's rules ( philosophis+ seems to lose all validity2 he said1 8,^? qualities ( bodies :i* are n capable ( be+ height5$1 & remitt$1 & :i* are f\nd 9 all bodies on :i* exp]im5t c be made1 mu/ be consid]$ z univ]sal qualities ( all bodies40 ,z f> z ,i c see1 ! contr>y is m probable1 namely1 t qualities v>iable 9 degree w be f\nd 9 e sub/ance 9 a great] or less degree4 ,x is rem>kable t ,newton ^: me?od ( inve/igation 0 logically p]fect1 seem$ incapable ( g5]alis+ & describ+ 8 own proc$ure4 ,8 celebrat$ 8,rules ( ,reason+ 9 ,philosophy10 describ$ at ! comm5cem5t ( ! ?ird book ( ! 99,pr9cipia991 are ( que/ionable tru?1 & /ill m que/ionable value4 99,extreme ,in/ances ( ,prop]ties499 ,al?\gh sub/ances usually diff] only 9 degree1 great int]e/ may atta* to p>ticul> sub/ances :i* manife/ a prop]ty 9 a conspicu\s & int5se mann]4 ,e bran* ( physical sci5ce has usually be5 develop$ f ! att5tion =cibly drawn to "s s+ul> sub/ance4 ,j z ! load/one disclos$ magnetism & amb] frictional electricity1 s did ,icel& sp> %[ ! exi/5ce ( d\ble refraction1 & sulphate ( qu99e ! ph5om5on ( fluoresc5ce4 ,:5 "o su* />tl+ in/ance has drawn ! att5tion ( ! sci5tific _w1 num]\s less rem>kable cases ( ! ph5om5on w be detect$1 & x w probably prove t ! prop]ty 9 "q is actually univ]sal to all matt]4 ,nev]!less1 ! extreme in/ances reta9 _! int]e/1 p>tly 9 a hi/orical po9t ( view1 p>tly because !y furni% ! mo/ conv5i5t sub/ances = exp]im5t4 ,francis ,bacon 0 fully aw>e ( ! value ( su* examples1 :i* he call$ 99,o/5sive ,in/ances99 or ,light-giv+1 ,free & ,pr$om9ant ,in/ances4 8,!y are ^?10 he says1#die 8:i* %[ ! nature "u inve/igation nak$1 9 an exalt$ condition1 or 9 ! highe/ degree ( p[]2 fre$ f imp$im5ts1 or at lea/ by its /r5g? pr$om9at+ ov] & suppress+ !m40 ,he m5tions quicksilv] z an o/5sive in/ance ( weight or d5sity1 ?9k+ x n mu* less d5se ?an gold1 & m rem>kable ?an gold z jo9+ d5sity to liquidity4 ,! magnet is m5tion$ z an o/5sive in/ance ( attraction4 ,x w\ld n be easy to di/+ui% cle>ly betwe5 ^! o/5sive in/ances & ^? :i* he calls 99,in/antiae ,monodicae991 or 99,irregul>es991 or 99,het]oclitae991 "u :i* he places :atev] is extravagant 9 its prop]ties or magnitude1 or exhibits lea/ simil>ity to o!r ?+s1 su* z ! sun & moon among ! heav5ly bodies1 ! elephant among animals1 ! lett] 99s99 among lett]s1 or ! magnet among /ones4#dif #die 99,novum ,organum991 bk4 ii4 ,aphorisms1 #bd1 #be4 #dif ,ibid4 ,aph4 #bh4 ,9 optical sci5ce great use has be5 made ( ! high disp]sive p[] ( ! transp>5t comp\nds ( lead1 t is1 ! p[] ( giv+ a long spectrum 7p4 #dcb74 ,dollond1 hav+ notic$ ?is peculi> disp]sive p[] 9 l5ses made ( fl9t glass1 employ$ !m to produce an a*romatic arrangem5t4 ,! elem5t /rontium pres5ts a contra/ to lead 9 ?is respect1 be+ *>act]is$ by a rem>kably l[ disp]sive p[]2 b ,i am n aw>e t ?is prop]ty has yet be5 turn$ to acc\nt4 ,comp\nds ( lead h bo? a high disp]sive & a high refractive index1 & 9 ! latt] respect !y prov$ v useful to ,f>aday4 ,hav+ sp5t mu* lab\r 9 prep>+ v>i\s k9ds ( optical glass1 ,f>aday happ5$ to =m a comp\nd ( lead1 silica1 & boracic acid1 n[ kn[n z 99heavy glass991 :i* possess$ an int5sely high refract+ p[]4 ,_m ye>s aft]w>ds 9 attempt+ to discov] ! action ( magnetism ^u light he fail$ to detect any effect1 z has be5 already m5tion$1 7p4 #ehh71 until he happ5$ to te/ a piece ( ! heavy glass4 ,! peculi> refractive p[] ( ?is m$ium caus$ ! magnetic /ra9 to be app>5t1 & ! rotation ( ! plane ( pol>isation 0 discov]$4 ,9 almo/ e "p ( physical sci5ce !re is "s sub/ance ( p[]s pre-em95t = ! special purpose to :i* x is put4 ,rock-salt is invaluable = its extreme dia!rmancy or transp>5cy to ! lea/ refrangible rays ( ! spectrum4 ,qu>tz is equally valuable = its transp>5cy1 z reg>ds ! ultra-violet or mo/ refrangible rays4 ,diamond is ! mo/ highly refract+ sub/ance :i* is at ! same "t transp>5t2 7 x m abundant & easily work$ x w\ld be ( great optical importance4 ,c9nab> is di/+ui%$ by possess+ a p[] ( rotat+ ! plane ( pol>isation ( light1 f #ae to #ag times z mu* z qu>tz4 ,9 electric exp]im5ts copp] is employ$ = its high conduct+ p[]s & exce$+ly l[ magnetic prop]ties2 iron is ( c\rse indisp5sable = its enorm\s magnetic p[]s2 :ile bismu? holds a l place z reg>ds its diamagnetic p[]s1 & 0 ( mu* importance 9 ,tyndall's decisive rese>*es ^u ! pol> "* ( ! diamagnetic =ce4#dig ,9 reg>d to magne-cry/allic action ! m9]al cyanite is highly rem>kable1 be+ s p[]fully affect$ by ! e>?'s magnetism1 t1 :5 delicately susp5d$1 x assumes a con/ant position ) reg>d to ! magnetic m]idian1 & may almo/ be us$ l ! compass ne$le4 ,sodium is di/+ui%$ by its unique light-giv+ p[]s1 :i* are s extraord9>y t probably "o half ( ! :ole numb] ( />s 9 ! heav5s h a yell[ t+e 9 consequ5ce4 #dig 99,philosophical ,transactions99 7#ahef7 vol4 cxlvi4 p4 #bdf4 ,x is rem>kable t wat]1 ?\gh ! mo/ common ( all fluids1 is di/+ui%$ 9 almo/ e respect by extreme qualities4 ,( all kn[n sub/ances wat] has ! highe/ specific heat1 be+ ?us peculi>ly fitt$ = ! purpose ( w>m+ & cool+1 to :i* x is (t5 put4 ,x rises by capill>y attraction to a height m ?an twice t ( any o!r liquid4 ,9 ! /ate ( ice x is ne>ly twice z dilatable by heat z any o!r kn[n solid sub/ance4#dih ,9 proportion to its d5sity x has a f> high] surface t5sion ?an any o!r sub/ance1 be+ surpass$ 9 absolute t5sion only by m]cury2 & x w\ld n be difficult to ext5d consid]ably ! li/ ( its rem>kable & useful prop]ties4 #dih 99,philosophical ,magaz9e991 #d? ,s]ies1 ,janu>y #ahgj1 vol4 xxxix4 p4 #b4 ,"u extreme in/ances we may include cases ( rem>kably l[ p[]s or qualities4 ,su* cases seem to correspond to :at ,bacon calls 99,cl&e/9e ,in/ances991 :i* exhibit a giv5 nature 9 ! lea/ int5sity1 & z x 7 9 a rudim5t>y /ate4#dii ,!y may (t5 be important1 he ?9ks1 z all[+ ! detection ( ! cause ( ! prop]ty by diff]5ce4 ,i may add t 9 "s cases !y may be ( use 9 exp]im5ts4 ,?us hydrog5 is ! lea/ d5se ( all kn[n sub/ances1 & has ! lea/ atomic weight4 ,liquefi$ nitr\s oxide has ! l[e/ refractive index ( all kn[n fluids4#ejj ,! comp\nds ( /rontium h ! l[e/ disp]sive p[]4 ,x is obvi\s t a prop]ty ( v l[ degree may prove z curi\s & valuable a ph5om5on z a prop]ty ( v high degree4 #dii 99,novum ,organum991 bk4 ii4 ,aphorism #be4 #ejj ,f>aday's 99,exp]im5tal ,rese>*es 9 ,*emi/ry & ,physics991 p4 #ic4 99,! ,detection ( ,cont9uity499 ,we %\ld be> 9 m9d t ph5om5a :i* are 9 reality ( a closely simil> or ev5 id5tical nature1 may pres5t to ! s5ses v diff]5t appe>ances4 ,)\t a c>eful analysis ( ! *anges :i* take place1 we may (t5 be 9 dang] ( widely sep>at+ facts & processes1 :i* are actually in/ances ( ! same law4 ,extreme diff]5ce ( degree or magnitude is a frequ5t cause ( error4 ,x is truly difficult at ! fir/ mom5t to recognise any simil>ity betwe5 ! gradual ru/+ ( a piece ( iron1 & ! rapid combu/ion ( a heap ( /raw4 ,yet ,lavoisi]'s *emical !ory 0 f\nd$ ^u ! simil>ity ( ! oxydis+ process 9 "o case & ! o!r4 ,we h only to divide ! iron into excessively small p>ticles to discov] t x is really ! m combu/ible ( ! two1 & t x actually takes fire spontane\sly & burns l t9d]4 ,x is ! excessive sl[ness ( ! process 9 ! case ( a massive piece ( iron :i* disguises its real "*4 ,if ,x5ophon reports truly1 ,socrates 0 misl$ by n mak+ suffici5t all[ance = extreme diff]5ces ( degree & quantity4 ,anaxagoras held t ! sun is a fire1 b ,socrates reject$ ?is op9ion1 on ! gr\nd t we c look at a fire1 b n at ! sun1 & t plants gr[ by sun%9e :ile !y are kill$ by fire4 ,he also po9t$ out t a /one heat$ 9 a fire is n lum9\s1 & soon cools1 :]eas ! sun ev] rema9s equally lum9\s & hot4#eja ,all su* mi/akes evid5tly arise f n p]ceiv+ t diff]5ce ( quantity may be s extreme z to assume ! appe>ance ( diff]5ce ( quality4 ,x is ! lea/ cr$itable ?+ we "k ( ,socrates1 t aft] po9t+ out ^! suppos$ mi/akes ( e>li] philosoph]s1 he advis$ 8 foll[]s n to /udy a/ronomy4 #eja 99,memorabilia991 iv4 #g4 ,masses ( matt] ( v diff]5t size may be expect$ to exhibit app>5t diff]5ces ( conduct1 aris+ f ! v>i\s int5sity ( ! =ces br\ght into play4 ,_m p]sons h ?\ght x requisite to imag9e occult =ces produc+ ! susp5sion ( ! cl\ds1 & !re h ev5 be5 absurd !ories repres5t+ cl\d p>ticles z m9ute wat]-balloons buoy$ up by ! w>m air )9 !m4 ,b we h only to take prop] acc\nt ( ! enorm\s comp>ative resi/ance :i* ! air opposes to ! fall ( m9ute p>ticles1 to see t all cl\d p>ticles are probably con/antly fall+ ?r\gh ! air1 b s sl[ly t !re is no app>5t effect4 ,m9]al matt] aga9 is always reg>d$ z in]t & incapable ( spontane\s movem5t4 ,we are /ruck by a/oni%m5t on obs]v+ 9 a p[]ful microscope1 t e k9d ( solid matt] susp5d$ 9 extremely m9ute p>ticles 9 pure wat]1 acquires an oscillatory movem5t1 (t5 s m>k$ z to resemble danc+ or skipp+4 ,i conceive t ?is movem5t is due to ! comp>atively va/ int5sity ( *emical action :5 ex]t$ ^u m9ute p>ticles1 ! effect be+ #e1jjj or #aj1jjj great] 9 proportion to ! mass ?an 9 fragm5ts ( an in* diamet] 7p4 #djf74 ,mu* t 0 =m]ly obscure 9 ! sci5ce ( electricity arose f ! extreme diff]5ces ( int5sity & quantity 9 :i* ?is =m ( en]gy manife/s itself4 ,betwe5 ! brilliant explosive dis*>ge ( a ?und]-cl\d & ! g5tle cont9u\s curr5t produc$ by two pieces ( metal & "s dilute acid1 !re is no app>5t analogy :atev]4 ,x 0 !re=e a "w ( great importance :5 ,f>aday demon/rat$ ! id5tity ( ! =ces 9 action1 %[+ t common frictional electricity w\ld decompose wat] l t f ! voltaic batt]y4 ,! relation ( ! ph5om5a became pla9 :5 he succe$$ 9 %[+ t x w\ld require #hjj1jjj dis*>ges ( 8 l>ge ,leyd5 batt]y to decompose "o s+le gra9 ( wat]4 ,lightn+ 0 n[ se5 to be electricity ( excessively high t5sion1 b extremely small quantity1 ! diff]5ce be+ some:at analog\s to t betwe5 ! =ce ( "o million gallons ( wat] fall+ ?r\gh "o foot1 & "o gallon ( wat] fall+ ?r\gh "o million feet4 ,f>aday e/imat$ t "o gra9 ( wat] act+ on f\r gra9s ( z9c1 w\ld yield electricity en\gh = a great ?und]/orm4 ,x 0 long believ$ t electrical conductors & insulators belong$ to two oppos$ classes ( sub/ances4 ,betwe5 ! inconceivable rapidity ) :i* ! curr5t passes ?r\gh pure copp] wire1 & ! app>5tly complete mann] 9 :i* x is /opp$ by a ?9 p>tition ( gutta-p]*a or gum-lac1 !re seem$ to be no resemblance4 ,f>aday aga9 lab\r$ successfully to %[ t ^! 7 b ! extreme cases ( a *a9 ( sub/ances v>y+ 9 all degrees 9 _! p[]s ( conduction4 ,ev5 ! be/ conductors1 su* z pure copp] or silv]1 (f] resi/ance to ! electric curr5t4 ,! o!r metals h consid]ably high] p[]s ( resi/ance1 & we pass gradually d[n ?r\gh oxides & sulphides4 ,! be/ insulators1 on ! o!r h&1 all[ ( an atomic induction :i* is ! necess>y antec$5t ( conduction4 ,h5ce ,f>aday inf]r$ t :e!r we c measure ! effect or n1 all sub/ances dis*>ge electricity m or less4#ejb ,"o consequ5ce ( ?is doctr9e mu/ be1 t e dis*>ge ( electricity produces an induc$ curr5t4 ,9 ! case ( ! common galvanic curr5t we c readily detect ! induc$ curr5t 9 any p>allel wire or o!r neighb\r+ conductor1 & c sep>ate ! opposite curr5ts :i* arise at ! mom5ts :5 ! orig9al curr5t beg9s & ends4 ,b a dis*>ge ( high t5sion electricity l lightn+1 ?\gh x c]ta9ly occupies "t & has a beg9n+ & an end1 yet la/s s m9ute a fraction ( a second1 t x w\ld be hopeless to attempt to detect & sep>ate ! two opposite induc$ curr5ts1 :i* are ne>ly simultane\s & exactly neutralise ea* o!r4 ,?us an app>5t failure ( analogy is expla9$ away1 & we are furni%$ ) ano!r in/ance ( a ph5om5on incapable ( obs]vation & yet !oretically kn[n to exi/4#ejc #ejb 99,exp]im5tal ,rese>*es 9 ,electricity991 ,s]ies xii4 vol4 i4 p4 #dbj4 #ejc 99,life ( ,f>aday991 vol4 ii4 p4 #g4 ,p]haps ! mo/ extraord9>y case ( ! detection ( unsuspect$ cont9uity is f\nd 9 ! discov]y ( ,cagni>d de la ,t\r & ,pr(essor ,&rews1 t ! liquid & gase\s conditions ( matt] are only remote po9ts 9 a cont9u\s c\rse ( *ange4 ,no?+ is at fir/ sight m app>5tly di/9ct ?an ! physical condition ( wat] & aque\s vap\r4 ,at ! boil+-po9t !re is an entire brea* ( cont9uity1 & ! gas produc$ is subject to laws incomp>ably m simple ?an ! liquid f :i* x arose4 ,b ,cagni>d de la ,t\r %[$ t if we ma9ta9 a liquid "u suffici5t pressure its boil+ po9t may be indef9itely rais$1 & yet ! liquid w ultimately assume ! gase\s condition ) b a small increase ( volume4 ,pr(essor ,&rews1 rec5tly foll[+ out ?is c\rse ( inquiry1 has %[n t liquid c>bonic acid may1 at a p>ticul> temp]ature 7#cjib ,c471 & "u ! pressure ( #gd atmosph]es1 be at ! same "t 9 a /ate indi/+ui%able f t ( liquid & gas4 ,at high] pressures c>bonic acid may be made to pass f a palpably liquid /ate to a truly gase\s /ate )\t any abrupt *ange :atev]4 ,z ! pressure is great] ! abruptness ( ! *ange f liquid to gas gradually decreases1 & f9ally vani%es4 ,simil> ph5om5a or an approximation to !m h be5 obs]v$ 9 o!r liquids1 & !re is little d\bt t we may make a wide g5]alisation1 & ass]t t1 "u adequate pressure1 e liquid might be made to pass into a gas )\t brea* ( cont9uity4#ejd ,! liquid /ate1 moreov]1 is consid]$ by ,pr(essor ,&rews to be b an int]m$iate /ep betwe5 ! solid & gase\s conditions4 ,!re are v>i\s indications t ! process ( melt+ is n p]fectly abrupt2 & c\ld exp]im5ts be made "u adequate pressures1 x is believ$ t e solid c\ld be made to pass by ins5sible degrees into ! /ate ( liquid1 & subsequ5tly into t ( gas4 #ejd 99,nature991 vol4 ii4 p4 #bgh4 ,^! discov]ies appe> to op5 ! way to mo/ important & fundam5tal g5]alisations1 b x is probable t 9 _m o!r cases ph5om5a n[ reg>d$ z discrete may be %[n to be diff]5t degrees ( ! same process4 ,graham 0 ( op9ion t *emical aff9ity diff]s b 9 degree f ! ord9>y attraction :i* holds diff]5t p>ticles ( a body toge!r4 ,he f\nd t sulphuric acid cont9u$ to evolve heat :5 mix$ ev5 ) ! fiftie? equival5t ( wat]1 s t !re seem$ to be no di/9ct limit to *emical aff9ity4 ,he concludes1 8,!re is reason to believe t *emical aff9ity passes 9 its l[e/ degree into ! attraction ( aggregation40#eje #eje 99,j\rnal ( ! ,*emical ,society991 vol4 viii4 p4 #ea4 ,! atomic !ory is well e/abli%$1 b its limits are n m>k$ out4 ,z ,grove po9ts out1 we may by select+ suffici5tly high multipli]s express any comb9ation or mixture ( elem5ts 9 t]ms ( _! equival5t weights4#ejf ,sir ,w4 ,?omson has sugge/$ t ! p[] :i* vegetable fibre1 oatmeal1 & o!r sub/ances possess ( attract+ & cond5s+ aque\s vap\r is probably cont9u\s1 or1 9 fact1 id5tical ) capill>y attraction1 :i* is capable ( int]f]+ ) ! pressure ( aque\s vap\r & aid+ its cond5sation4#ejg ,!re are _m cases ( s-call$ catalytic or surface action1 su* z ! extraord9>y p[] ( animal *>coal = attract+ organic matt]1 or ( spongy plat9um = cond5s+ hydrog51 :i* c only be consid]$ z exalt$ cases ( a m g5]al p[] ( attraction4 ,! numb] ( sub/ances :i* are decompos$ by light 9 a /rik+ mann] is v limit$2 b _m o!r sub/ances1 su* z vegetable col\rs1 are affect$ by long exposure2 on ! pr9ciple ( cont9uity we might expect to f9d t all k9ds ( matt] are m or less susceptible ( *ange by ! incid5ce ( light rays4#ejh ,x is ! op9ion ( ,grove t :]ev] an electric curr5t passes !re is a t5d5cy to decomposition1 a /ra9 on ! molecules1 :i* :5 suffici5tly int5se leads to disruption4 ,ev5 a metallic conduct+ wire may be reg>d$ z t5d+ to decomposition4 ,davy 0 probably correct 9 describ+ electricity z *emical aff9ity act+ on masses1 or r1 z ,grove sugge/s1 creat+ a di/urbance ?r\gh a *a9 ( p>ticles4#eji ,laplace w5t s f> z to sugge/ t all *emical ph5om5a may be results ( ! ,newtonian law ( attraction1 appli$ to atoms ( v>i\s mass & position2 b ! "t is probably f> di/ant :5 ! progress ( molecul> philosophy & ( ma!matical me?ods w enable su* a g5]alisation to be v]ifi$ or refut$4 #ejf 99,correlation ( ,physical ,=ces991 #crd edit4 p4 #ahd4 #ejg 99,philosophical ,magaz9e991 #d? ,s]ies1 vol4 xlii4 p4 #dea4 #ejh ,grove1 99,correlation ( ,physical ,=ces991 #crd edit4 p4 #aah4 #eji ,ibid4 pp4 #aff1 #aii1 c4 99,! ,law ( ,cont9uity499 ,"u ! title ( ! ,law ( ,cont9uity we may place _m applications ( ! g5]al pr9ciple ( reason+1 t :at is true ( "o case w be true ( simil> cases1 & probably true ( :at are probably simil>4 ,:5ev] we f9d t a law or simil>ity is rigor\sly fulfill$ up to a c]ta9 po9t 9 "t or space1 we expect ) a high degree ( probability t x w cont9ue to be fulfill$ at lea/ a little fur!r4 ,if we see "p only ( a circle1 we naturally expect t ! circul> =m w be cont9u$ 9 ! "p hidd5 f u4 ,if a body has mov$ uni=mly ov] a c]ta9 space1 we expect t x w cont9ue to move uni=mly4 ,! gr\nd ( su* inf]5ces is d\btless id5tical ) t ( o!r inductive inf]5ces4 ,9 cont9u\s motion e inf9itely small space pass$ ov] con/itutes a sep>ate con/itu5t fact1 & _h we p]fect p[]s ( obs]vation ! smalle/ f9ite motion w\ld include an inf9ity ( in=mation1 :i*1 by ! pr9ciples ( ! inv]se me?od ( probabilities1 w\ld enable u to inf] ) c]ta9ty to ! next inf9itely small portion ( ! pa?4 ,b :5 we attempt to inf] f "o f9ite portion ( a pa? to ano!r f9ite portion1 inf]5ce w be only m or less probable1 accord+ to ! comp>ative l5g?s ( ! portions & ! accuracy ( obs]vation2 ! long] our exp]i5ce is1 ! m probable our inf]5ce w be2 ! great] ! l5g? ( "t or space ov] :i* ! inf]5ce ext5ds1 ! less probable4 ,?is pr9ciple ( cont9uity pres5ts itself 9 nature 9 a great v>iety ( =ms & cases4 ,x is famili>ly express$ 9 ! dictum 99,natura non agit p] saltum994 ,z ,graham express$ ! maxim1 !re are 9 nature no abrupt transitions1 & ! di/9ctions ( class are nev] absolute4#eaj ,!re is always "s notice--"s =ew>n+ ( e ph5om5on1 & e *ange beg9s by ins5sible degrees1 c\ld we obs]ve x ) p]fect accuracy4 ,! cannon ball1 inde$1 is =c$ f ! cannon 9 an inappreciable portion ( "t2 ! trigg] is pull$1 ! fuze fir$1 ! p[d] inflam$1 ! ball expell$1 all simultane\sly to our s5ses4 ,b !re is no d\bt t "t is occupi$ by e "p ( ! process1 & t ! ball beg9s to move at fir/ ) inf9ite sl[ness4 ,capta9 ,noble is able to measure by 8 *ronoscope ! progress ( ! %ot 9 a #cjj-p\nd] gun1 & f9ds t ! :ole motion )9 ! b>rel takes place 9 some?+ less ?an "o #bjj? "p ( a second4 ,x is c]ta9 t no f9ite =ce c produce motion1 except 9 a f9ite space ( "t4 ,! am\nt ( mom5tum communicat$ to a body is proportional to ! accel]at+ =ce multipli$ by ! "t dur+ :i* x acts uni=mly4 ,?us a slight =ce produces a great velocity only by long-cont9u$ action4 ,9 a p[]ful %ock1 l t ( a railway collision1 ! /roke ( a hamm] on an anvil1 or ! dis*>ge ( a gun1 ! "t is v %ort1 & !re=e ! accel]at+ =ces br\ght into play are exce$+ly great1 b nev] inf9ite4 ,9 ! case ( a l>ge gun ! p[d] 9 explod+ is said to ex]t = a mom5t a =ce equival5t to at lea/ #b1hjj1jjj horses4 #eaj 99,philosophical ,transactions991 #ahfa4 99,*emical & ,physical ,rese>*es991 p4 #eih4 ,our belief 9 "s ( ! fundam5tal laws ( nature re/s ^u ! pr9ciple ( cont9uity4 ,galileo is held to be ! fir/ philosoph] :o consci\sly employ$ ?is pr9ciple 9 8 argum5ts conc]n+ ! nature ( motion1 & x is c]ta9 t we c nev] by m]e exp]i5ce assure ourselves ( ! tru? ev5 ( ! fir/ law ( motion4 99,a mat]ial p>ticle991 we are told1 99:5 n act$ on by extrane\s =ces w cont9ue 9 ! same /ate ( re/ or motion499 ,?is may be true1 b z we c f9d no body :i* is free f ! action ( extrane\s causes1 h[ are we to prove x8 ,only by obs]v+ t ! less ! am\nt ( ^? =ces ! m ne>ly is ! law f\nd to be true4 ,a ball roll$ along r\gh gr\nd is soon /opp$2 along a smoo? pavem5t x cont9ues long] 9 movem5t4 ,a delicately susp5d$ p5dulum is almo/ free f friction aga9/ its supports1 b x is gradually /opp$ by ! resi/ance ( ! air2 place x 9 ! vacu\s receiv] ( an air-pump & we f9d ! motion mu* prolong$4 ,a l>ge planet l ,jupit] exp]i5ces almo/ inf9itely less friction1 9 comp>ison to its va/ mom5tum1 ?an we c produce exp]im5tally1 & we f9d 9 su* a case t !re is n ! lea/ evid5ce ( ! falsity ( ! law4 ,exp]i5ce1 !n1 in=ms u t we may approximate indef9itely to a uni=m motion by suffici5tly decreas+ ! di/urb+ =ces4 ,x is an act ( inf]5ce :i* enables u to travel on beyond exp]i5ce1 & ass]t t1 9 ! total abs5ce ( any extrane\s =ce1 motion w\ld be absolutely uni=m4 ,! /ate ( re/1 aga91 is a limit+ case 9 :i* motion is inf9itely small or z]o1 to :i* we may atta91 on ! pr9ciple ( cont9uity1 by successively consid]+ cases ( sl[] & sl[] motion4 ,!re are _m classes ( ph5om5a1 9 :i*1 by gradually pass+ f ! app>5t to ! obscure1 we c assure ourselves ( ! nature ( ph5om5a :i* w\ld o!rwise be a matt] ( great d\bt4 ,?us we c suffici5tly prove 9 ! mann] ( ,galileo1 t a musical s\nd consi/s ( rapid uni=m pulses1 by caus+ /rokes to be made at int]vals :i* we gradually dim9i% until ! sep>ate /rokes coalesce into a uni=m hum or note4 ,) great advantage we approa*1 z ,tyndall says1 ! sonor\s ?r\gh ! grossly me*anical4 ,9 li/5+ to a great organ we _c fail to p]ceive t ! longe/ pipes1 or _! p>tial tones1 produce a tremor & flutt]+ ( ! build+4 ,at ! o!r extremity ( ! scale1 !re is no fix$ limit to ! acut5ess ( s\nds :i* we c he>2 "s individuals c he> s\nds too %rill = o!r e>s1 & z !re is no?+ 9 ! nature ( ! atmosph]e to prev5t ! exi/5ce ( undulations f> m rapid ?an any ( :i* we are consci\s1 we may inf]1 by ! pr9ciple ( cont9uity1 t su* undulations probably exi/4 ,!re are _m habitual actions :i* we p]=m we "k n h[4 ,s rapidly are acts ( m9ds accompli%$ t analysis seems impossible4 ,we c only inve/igate !m :5 9 process ( =mation1 obs]v+ t ! be/ =m$ habit is sl[ly & cont9u\sly acquir$1 & x is 9 ! e>ly /ages t we c p]ceive ! rationale ( ! process4 ,let x be obs]v$ t ?is pr9ciple ( cont9uity mu/ be held ( mu* weight only 9 exact physical laws1 ^? :i* d\btless repose ultimately ^u ! simple laws ( motion4 ,if we fe>lessly apply ! pr9ciple to all k9ds ( ph5om5a1 we may (t5 be "r 9 our inf]5ces1 b also (t5 wrong4 ,?us1 be=e ! developm5t ( spectrum analysis1 a/ronom]s _h obs]v$ t ! m !y increas$ ! p[]s ( _! telescopes ! m nebul !y c\ld resolve into di/9ct />s4 ,?is result _h be5 s (t5 f\nd true t !y almo/ irresi/ibly assum$ t all nebul w\ld be ultimately resolv$ by telescopes ( suffici5t p[]2 yet ,hugg9s has 9 rec5t ye>s prov$ by ! spectroscope1 t c]ta9 nebul are actually gase\s1 & 9 a truly nebul\s /ate4 ,! pr9ciple ( cont9uity mu/ h be5 cont9ually employ$ 9 ! inquiries ( ,galileo1 ,newton1 & o!r exp]im5tal philosoph]s1 b x appe>s to h be5 di/9ctly =mulat$ = ! fir/ "t by ,leibnitz4 ,he at lea/ claims to h fir/ spok5 ( 8! law ( cont9uity0 9 a lett] to ,bayle1 pr9t$ 9 ! 99,n\velles de la ,rpublique des ,lettres991 an extract f :i* is giv5 9 ,erdmann's edition ( ,leibnitz's works1 p4 #ajd1 "u ! title 8,sur un ,pr9cipe ,gnral utile l'explication des ,lois de la ,nature40#eaa ,x has inde$ be5 ass]t$ t ! doctr9e ( ! 99lat5s processus99 ( ,francis ,bacon involves ! pr9ciple ( cont9uity1#eab b ,i ?9k t ?is doctr9e1 l t ( ! 99natures99 ( sub/ances1 is m]ely a vague /atem5t ( ! pr9ciple ( causation4 #eaa 99,life ( ,sir ,w4 ,hamilton991 p4 #dci4 #eab ,p[ell's 99,hi/ory ( ,natural ,philosophy991 p4 #bja4 99,novum ,organum991 bk4 ii4 ,aphorisms #e-g4 99,failure ( ! ,law ( ,cont9uity499 ,!re are c]ta9 cautions :i* mu/ be giv5 z to ! application ( ! pr9ciple ( cont9uity4 ,9 ! fir/ place1 :]e ?is pr9ciple really holds true1 x may seem to fail ow+ to our imp]fect means ( obs]vation4 ,?\gh a physical law may n admit ( p]fectly abrupt *ange1 !re is no limit to ! approa* :i* x may make to abruptness4 ,:5 we w>m a piece ( v cold ice1 ! absorption ( heat1 ! temp]ature1 & ! dilatation ( ! ice v>y accord+ to app>5tly simple laws until we come to ! z]o ( ! ,c5tigrade scale4 ,ev]y?+ is !n *ang$2 an enorm\s absorption ( heat takes place )\t any rise ( temp]ature1 & ! volume ( ! ice decreases z x *anges into wat]4 ,unless c>efully inve/igat$1 ?is *ange appe>s to be p]fectly abrupt2 b accurate obs]vation seems to %[ t !re is a c]ta9 =ew>n+2 ! ice does n turn into wat] all at once1 b ?r\gh a small fraction ( a degree ! *ange is gradual4 ,all ! ph5om5a conc]n$1 if measur$ v exactly1 w\ld be repres5t$ n by angul> l9es1 b cont9u\s curves1 und]go+ rapid flexures2 & we may probably ass]t ) safety t betwe5 :atev] po9ts ( temp]ature we exam9e ice1 !re w\ld be f\nd "s indication1 ?\gh almo/ inf9itesimally small1 ( ! app>5tly abrupt *ange :i* 0 to occur at a high] temp]ature4 ,x might also be po9t$ out t ! important & app>5tly simple physical laws1 su* z ^? ( ,boyle & ,m>iotte1 ,dalton & ,gay-,lussac1 c41 are only approximately true1 & ! div]g5ces f ! simple laws are =ew>n+s ( abrupt *anges1 :i* w\ld o!rwise break ! law ( cont9uity4 ,secondly1 x mu/ be rememb]$ t ma!matical laws ( "s complexity w probably pres5t s+ul> cases or negative results1 :i* may be> ! appe>ance ( discont9uity1 z :5 ! law ( retraction sudd5ly yields u ) p]fect abruptness ! ph5om5on ( total int]nal reflection4 ,9 ! undulatory !ory1 h[ev]1 !re is no real *ange ( law betwe5 refraction & reflection4 ,f>aday 9 ! e>li] "p ( 8 c>e] f\nd s _m sub/ances possess+ magnetic p[]1 t he v5tur$ on a great g5]alisation1 & ass]t$ t all bodies %>$ 9 ! magnetic prop]ty ( iron4 ,8 mi/ake1 z he aft]w>ds discov]$1 consi/$ 9 ov]look+ ! fact t ?\gh magnetic 9 a c]ta9 s5se1 "s sub/ances h negative magnetism1 & are repell$ in/ead ( be+ attract$ by ! magnet4 ,?irdly1 :]e we might expect to f9d a uni=m ma!matical law prevail+1 ! law may und]go abrupt *ange at s+ul> po9ts1 & actual discont9uity may arise4 ,we may sometimes be 9 dang] ( treat+ "u "o law ph5om5a :i* really belong to diff]5t laws4 ,= in/ance1 a sph]ical %ell ( uni=m matt] attracts an ext]nal p>ticle ( matt] ) a =ce v>y+ inv]sely z ! squ>e ( ! di/ance f ! c5tre ( ! sph]e4 ,b ?is law only holds true s long z ! p>ticle is ext]nal to ! %ell4 ,)9 ! %ell ! law is :olly diff]5t1 & ! aggregate gravity ( ! sph]e becomes z]o1 ! =ce 9 e direction be+ neutralis$ by an exactly equal opposite =ce4 ,if an inf9itely small p>ticle be 9 ! sup]ficies ( a sph]e1 ! law is aga9 diff]5t1 & ! attractive p[] ( ! %ell is half :at x w\ld be ) reg>d to p>ticles inf9itely close to ! surface ( ! %ell4 ,?us 9 approa*+ ! c5tre ( a %ell f a di/ance1 ! =ce ( gravity %[s d\ble discont9uity 9 pass+ ?r\gh ! %ell4#eac #eac ,?omson & ,tait1 99,treatise on ,natural ,philosophy991 vol4 i4 pp4 #cdf-cea4 ,x may admit ( "q1 too1 :e!r discont9uity is really unkn[n 9 nature4 ,we p]petually d meet ) ev5ts :i* are real breaks ^u ! previ\s law1 ?\gh ! discont9uity may be a sign t "s indep5d5t cause has come into op]ation4 ,if ! ord9>y c\rse ( ! tides is int]rupt$ by an enorm\s irregul> wave1 we attribute x to an e>?quake1 or "s gigantic natural di/urbance4 ,if a meteoric /one falls ^u a p]son & kills him1 x is cle>ly a discont9uity 9 8 life1 ( :i* he c\ld h _h no anticipation4 ,a sudd5 s\nd may pass ?r\gh ! air nei!r prec$$ nor foll[$ by any cont9u\s effect4 ,al?\gh1 !n1 we may reg>d ! ,law ( ,cont9uity z a pr9ciple ( nature hold+ rigor\sly true 9 _m ( ! relations ( natural =ces1 x seems to be a matt] ( difficulty to assign ! limits )9 :i* ! law is v]ifi$4 ,mu* caution is requir$ 9 its application4 99,negative ,argum5ts on ! ,pr9ciple ( ,cont9uity499 ,^u ! pr9ciple ( cont9uity we may sometimes f\nd argum5ts ( great =ce :i* prove an hypo!sis to be impossible1 because x w\ld involve a cont9ual repetition ( a process 99ad inf9itum991 or else a purely arbitr>y brea* at "s po9t4 ,bonnet's fam\s !ory ( reproduction repres5t$ e liv+ creature z conta9+ g]ms :i* 7 p]fect repres5tatives ( ! next g5]ation1 s t on ! same pr9ciple !y necess>ily includ$ g]ms ( ! next g5]ation1 & s on indef9itely4 ,! !ory 0 suffici5tly refut$ :5 once cle>ly /at$1 z 9 ! foll[+ poem call$ ! ,univ]se1#ead by ,h5ry ,bak]3-- 8,ea* se$ includes a plant3 t plant1 aga91 ,has o!r se$s1 :i* o!r plants conta93 ,^? o!r plants h all _! se$s1 & ^? ,m plants aga91 successively inclose4 8,?us1 ev'ry s+le b]ry t we f9d1 ,has1 really1 9 itself :ole =e/s ( its k9d1 ,empire & weal? "o acorn may disp5se1 ,by fleets to sail a ?\s& ages h5ce40 #ead 99,philosophical ,transactions99 7#agdj71 vol4 xli4 p4 #ded4 ,! g5]al pr9ciple ( inf]5ce1 t :at we "k ( "o case mu/ be true ( simil> cases1 s f> z !y are simil>1 prev5ts our ass]t+ any?+ :i* we _c apply "t aft] "t "u ! same circum/ances4 ,on ?is pr9ciple ,/ev9us beautifully demon/rat$ t weights re/+ on two incl9$ planes & balanc+ ea* o!r mu/ be proportional to ! l5g?s ( ! planes betwe5 _! apex & a horizontal plane4 ,he imag9$ a uni=m endless *a9 to be hung ov] ! planes1 & to hang bel[ 9 a symmetrical fe/oon4 ,if ! *a9 7 ev] to move by gravity1 !re w\ld be ! same reason = its mov+ on = ev]1 & ?us produc+ a p]petual motion4 ,z ?is is absurd1 ! portions ( ! *a9 ly+ on ! planes1 & equal 9 l5g? to ! planes1 mu/ balance ea* o!r4 ,on simil> gr\nds we may disprove ! exi/5ce ( any 99self-mov+ ma*9e992 = if x c\ld once alt] its own /ate ( motion or re/1 9 h[ev] small a degree1 !re is no reason :y x %\ld n d ! l "t aft] "t 99ad inf9itum994 ,newton's pro( ( 8 ?ird law ( motion1 9 ! case ( gravity1 is ( ?is "*4 ,= he rem>ks t if two gravitat+ bodies d n ex]t exactly equal =ces 9 opposite directions1 ! "o ex]t+ ! /ronge/ pull w c>ry bo? away1 & ! two bodies w move (f into space toge!r ) velocity increas+ 99ad inf9itum994 ,b ?\gh ! argum5t might seem suffici5tly conv9c+1 ,newton 9 8 *>act]i/ic way made an exp]im5t ) a load/one & iron float$ ^u ! surface ( wat]4#eae ,9 rec5t ye>s ! v f\ndation ( ! pr9ciple ( cons]vation ( en]gy has be5 plac$ on ! assumption t x is impossible by any comb9ation ( natural bodies to produce =ce cont9ually f no?+4#eaf ,! pr9ciple admits ( application 9 v>i\s subtle =ms4 #eae 99,pr9cipia991 bk4 i4 ,law iii4 ,coroll>y #f4 #eaf ,helmholtz1 ,taylor's 99,sci5tific ,memoirs99 7#ahec71 vol4 vi4 p4 #aah4 ,lucretius attempt$ to prove1 by a mo/ +5i\s argum5t ( ?is k9d1 t matt] mu/ be inde/ructible4 ,= if a f9ite quantity1 h[ev] small1 7 to fall out ( exi/5ce 9 any f9ite "t1 an equal quantity might be suppos$ to lapse 9 e equal int]val ( "t1 s t 9 ! inf9ity ( pa/ "t ! univ]se mu/ h ceas$ to exi/4#eag ,b ! argum5t1 h[ev] +5i\s1 seems to fail at sev]al po9ts4 ,if pa/ "t be inf9ite1 :y may n matt] h be5 creat$ inf9ite also8 ,x w\ld be mo/ reasonable1 aga91 to suppose ! matt] de/roy$ 9 any "t to be proportional to ! matt] !n rema9+1 & n to ! orig9al quantity2 "u ?is hypo!sis ev5 a f9ite quantity ( orig9al matt] c\ld nev] :olly disappe> f ! univ]se4 ,= l reasons we _c hold t ! doctr9e ( ! cons]vation ( en]gy is really prov$1 or c ev] be prov$ to be absolutely true1 h[ev] probable x may be reg>d$4 #eag 99,lucretius991 bk4 i4 l9es #bcb-bfd4 99,t5d5cy to ,ha/y ,g5]alisation499 ,9 spite ( all ! p[]s & advantages ( g5]alisation1 m5 require no incitem5t to g5]alise2 !y are too apt to draw ha/y & ill-consid]$ inf]5ces4 ,z ,francis ,bacon said1 our intellects want n w+s1 b r weights ( lead to mod]ate _! c\rse4#eah ,! process is inevitable to ! human m9d2 x beg9s ) *ildhood & la/s ?r\gh ! second *ildhood4 ,! *ild t has once be5 hurt fe>s ! l result on all simil> occasions1 & c ) difficulty be made to di/+ui% betwe5 case & case4 ,x is caution & discrim9ation 9 ! adoption ( conclusions t we h *iefly to le>n1 & ! :ole exp]i5ce ( life is "o cont9u$ lesson to ?is effect4 ,bad5 ,p[ell has excell5tly describ$ ?is /rong natural prop5sity to ha/y inf]5ce1 & ! fondness ( ! human m9d = trac+ resemblances real or fanciful4 8,our fir/ inductions10 he says1#eai 8are always imp]fect & inconclusive2 we advance t[>ds real evid5ce by successive approximations2 & accord+ly we f9d false g5]alisation ! besett+ error ( mo/ fir/ attempts at sci5tific rese>*4 ,! faculty to g5]alise accurately & philosophically requires l>ge caution & long tra9+1 & is n fully atta9$1 especially 9 ref]5ce to m g5]al views1 ev5 by "s :o may prop]ly claim ! title ( v accurate sci5tific obs]v]s 9 a m limit$ field4 ,x is an intellectual habit :i* acquires imm5se & accumulat+ =ce f ! contemplation ( wid] analogies40 #eah 99,novum ,organum991 bk4 #a ,aphorism #ajd4 #eai 99,! ,unity ( ,worlds & ( ,nature991 #bnd edit4 p4 #aaf4 ,ha/y & sup]ficial g5]alisations h always be5 ! bane ( sci5ce1 & !re w\ld be no difficulty 9 f9d+ endless illu/rations4 ,betwe5 ?+s :i* are ! same 9 numb] !re is a c]ta9 resemblance1 namely 9 numb]2 b 9 ! infancy ( sci5ce m5 c\ld n be p]suad$ t !re 0 n a deep] resemblance impli$ 9 t ( numb]4 ,py?agoras 0 n ! inv5tor ( a my/ical sci5ce ( numb]4 ,9 ! anci5t ,ori5tal religions ! sev5 metals 7 connect$ ) ! sev5 planets1 & 9 ! sev5 days ( ! week we /ill h1 & probably always %all h1 a relic ( ! septi=m sy/em ascrib$ by ,dio ,cassius to ! anci5t ,egyptians4 ,! disciples ( ,py?agoras c>ri$ ! doctr9e ( ! numb] sev5 into great detail4 ,sev5 days are m5tion$ 9 ,g5esis2 infants acquire _! tee? at ! end ( sev5 mon?s2 !y *ange !m at ! end ( sev5 ye>s2 sev5 feet 0 ! limit ( man's height2 e sev5? ye> 0 a climact]ic or critical ye>1 at :i* a *ange ( disposition took place4 ,!n aga9 !re 7 ! sev5 sages ( ,greece1 ! sev5 wond]s ( ! _w1 ! sev5 rites ( ! ,grecian games1 ! sev5 gates ( ,!bes1 & ! sev5 g5]als de/9$ to conqu] t city4 ,9 natural sci5ce !re 7 n only ! sev5 planets1 & ! sev5 metals1 b also ! sev5 primitive col\rs1 & ! sev5 tones ( music4 ,s deep a hold did ?is doctr9e take t we /ill h its results 9 _m cu/oms1 n only 9 ! sev5 days ( ! week1 b ! sev5 ye>s' appr5tice%ip1 pub]ty at f\rte5 ye>s1 ! second climact]ic1 & legal majority at tw5ty-"o ye>s1 ! ?ird climact]ic4 ,! idea 0 reproduc$ 9 ! sev5 sacram5ts ( ! ,roman ,ca?olic ,*ur*1 & ! sev5 ye> p]iods ( ,comte's grotesque sy/em ( dome/ic wor%ip4 ,ev5 9 sci5tific matt]s ! l(tie/ intellects h occasionally yield$1 z :5 ,newton 0 misl$ by ! analogy betwe5 ! sev5 tones ( music & ! sev5 col\rs ( 8 spectrum4 ,o!r num]ical analogies1 ?\gh reject$ by ,galileo1 held ,kepl] 9 ?raldom2 no small "p ( ,kepl]'s lab\rs dur+ sev5te5 ye>s 0 sp5t ^u num]ical & geometrical analogies ( ! mo/ baseless "*2 & he gravely held t !re c\ld n be m ?an six planets1 because !re 7 n m ?an five regul> solids4 ,ev5 ! g5ius ( ,huygh5s did n prev5t him f inf]r+ t b "o satellite c\ld belong to ,saturn1 because1 ) ^? ( ,jupit] & ! ,e>?1 x complet$ ! p]fect numb] ( six4 ,a :ole s]ies ( o!r sup]/itions & fallacies atta* to ! numb]s six & n9e4 ,x is by false g5]alisation1 aga91 t ! laws ( nature h be5 suppos$ to possess t p]fection :i* we attribute to simple =ms & relations4 ,! heav5ly bodies1 x 0 held1 mu/ move 9 circles1 = ! circle 0 ! p]fect figure4 ,newton seem$ to adopt ! que/ionable axiom t nature always proce$s 9 ! simple/ way2 9 /at+ 8 fir/ rule ( philosophis+1 he adds3#ebj 8,to ?is purpose ! philosoph]s say1 t nature does no?+ 9 va91 :5 less w s]ve2 = nature is pleas$ ) simplicity1 & affects n ! pomp ( sup]flu\s causes40 ,keill lays d[n#eba z an axiom t 8,! causes ( natural ?+s are su*1 z are ! mo/ simple1 & are suffici5t to expla9 ! ph5om5a3 = nature always proce$s 9 ! simple/ & mo/ exp$iti\s me?od2 because by ?is mann] ( op]at+ ! ,div9e ,wisdom displays itself ! m40 ,if ?is axiom _h any cle> gr\nds ( tru?1 x w\ld n apply to proximate laws2 = ev5 :5 ! ultimate law is simple ! results may be inf9itely div]se1 z 9 ! v>i\s elliptic1 hyp]bolic1 p>abolic1 or circul> orbits ( ! heav5ly bodies4 ,simplicity is naturally agreeable to a m9d ( limit$ p[]s1 b to an inf9ite m9d all ?+s are simple4 #ebj 99,pr9cipia991 bk4 iii1 99ad initium994 #eba ,keill1 99,introduction to ,natural ,philosophy991 p4 #hi4 ,e great advance 9 sci5ce consi/s 9 a great g5]alisation1 po9t+ out deep & subtle resemblances4 ,! ,cop]nican sy/em 0 a g5]alisation1 9 t x class$ ! e>? among ! planets2 x 01 z ,bi%op ,wilk9s express$ x1 8! discov]y ( a new planet10 b x 0 oppos$ by a m %all[ g5]alisation4 ,^? :o argu$ f ! condition ( ?+s ^u ! e>?'s surface1 ?\ght t e object mu/ be atta*$ to & re/ ^u some?+ else4 ,%all ! e>?1 !y said1 alone be free8 ,accu/om$ to c]ta9 special results ( gravity !y c\ld n conceive its action "u widely diff]5t circum/ances4#ebb ,no ha/y ?9k] c\ld seize ! deep analogy po9t$ out by ,horrocks betwe5 a p5dulum & a planet1 true 9 sub/ance ?\gh mi/ak5 9 "s details4 ,all ! advances ( mod]n sci5ce rise f ! conception ( ,galileo1 t 9 ! heav5ly bodies1 h[ev] app>5tly diff]5t _! condition1 we %all ultimately recognise ! same fundam5tal pr9ciples ( me*anical sci5ce :i* are true on e>?4 #ebb ,j]emi ,horroccii 99,op]a ,po/huma99 7#afgc71 pp4 #bf1 #bg4 ,g5]alisation is ! great pr]ogative ( ! intellect1 b x is a p[] only to be ex]cis$ safely ) mu* caution & aft] long tra9+4 ,e m9d mu/ g5]alise1 b !re are ! wide/ diff]5ces 9 ! dep? ( ! resemblances discov]$ & ! c>e ) :i* ! discov]y is v]ifi$4 ,!re seems to be an innate p[] ( insight :i* a few m5 h possess$ pre-em95tly1 & :i* enabl$ !m1 ) no exemption inde$ f lab\r or tempor>y error1 to discov] ! "o 9 ! _m4 ,m9ds ( excessive acut5ess may exi/1 :i* h yet only ! p[]s ( m9ute discrim9ation1 & ( /or+ up1 9 ! treasure-h\se ( memory1 va/ accumulations ( words & incid5ts4 ,b ! p[] ( discov]y belongs to a m re/rict$ class ( m9ds4 ,laplace said t1 ( all inv5tors :o _h contribut$ ! mo/ to ! advancem5t ( human k1 ,newton & ,lagrange appe>$ to possess 9 ! highe/ degree ! happy tact ( di/+ui%+ g5]al pr9ciples among a multitude ( objects envelop+ !m1 & ?is tact he conceiv$ to be ! true *>act]i/ic ( sci5tific g5ius4#ebc #ebc ,"y's 99,works991 vol4 ii4 p4 #efd4 ,,*apt] ,,xxviii4 ,,analogy4 ,z we h se5 9 ! previ\s *apt]1 g5]alisation passes ins5sibly into reason+ by analogy1 & ! diff]5ce is "o ( degree4 ,we are said to g5]alise :5 we view _m objects z agree+ 9 a few prop]ties1 s t ! resemblance is ext5sive r ?an deep4 ,:5 we h only a few objects ( ?\ght1 b are able to discov] _m po9ts ( resemblance1 we argue by analogy t ! correspond5ce w be ev5 deep] ?an appe>s4 ,x may n be true t ! words are always us$ 9 su* di/9ct s5ses1 & !re is great vagu5ess 9 ! employm5t ( ^! & _m logical t]ms2 b if any cle> discrim9ation c be drawn betwe5 g5]alisation & analogy1 x is z indicat$ above4 ,x has be5 said1 inde$1 t analogy d5otes n a resemblance betwe5 ?+s1 b betwe5 ! relations ( ?+s4 ,a pilot is a v diff]5t man f a prime m9i/]1 b he be>s ! same relation to a %ip t ! m9i/] does to ! /ate1 s t we may analogically describe ! prime m9i/] z ! pilot ( ! /ate4 ,a man diff]s /ill m f a horse1 nev]!less f\r m5 be> to ?ree m5 ! same relation z f\r horses be> to ?ree horses4 ,!re is a real analogy betwe5 ! tones ( ! ,mono*ord1 ! ,sages ( ,greece1 & ! ,gates ( ,!bes1 b x does n ext5d beyond ! fact t !y 7 all sev5 9 numb]4 ,betwe5 ! mo/ discrete notions1 z1 = in/ance1 ^? ( "t & space1 analogy may exi/1 aris+ f ! fact t ! ma!matical conditions ( ! lapse ( "t & ( motion along a l9e are simil>4 ,!re is no id5tity ( nature betwe5 a ^w & ! ?+ x signifies2 ! sub/ance 99iron99 is a heavy solid1 ! ^w 99iron99 is ei!r a mom5t>y di/urbance ( ! air1 or a film ( black pigm5t on :ite pap]2 b !re is analogy betwe5 words & _! significates4 ,! sub/ance iron is to ! sub/ance iron-c>bonate1 z ! "n iron is to ! "n iron-c>bonate1 :5 ^! names are us$ accord+ to _! sci5tific def9itions4 ,! :ole /ructure ( language & ! :ole utility ( signs1 m>ks1 symbols1 pictures1 & repres5tations ( v>i\s k9ds1 re/ ^u analogy4 ,i may hope p]haps to ent] m fully ^u ?is important subject at "s future "t1 & to attempt to %[ h[ ! inv5tion ( signs enables u to express1 guide1 & regi/] our ?\ghts4 ,x w be suffici5t to obs]ve "h t ! use ( words con/antly involves analogies ( a subtle k9d2 we %\ld (t5 be at a loss h[ to describe a notion1 7 we n at lib]ty to employ 9 a metaphorical s5se ! "n ( any?+ suffici5tly resembl+ x4 ,!re w\ld be no expression = ! sweetness ( a melody1 or ! brilliancy ( an h>angue1 unless x 7 furni%$ by ! ta/e ( honey & ! brightness ( a tor*4 ,a cursory exam9ation ( ! way 9 :i* we popul>ly use ! ^w analogy1 %[s t x includes all degrees ( resemblance or simil>ity4 ,! analogy may consi/ only 9 simil>ity ( numb] or ratio1 or 9 l relations ( "t & space4 ,x may also consi/ 9 simple resemblance betwe5 physical prop]ties4 ,we %\ld n be us+ ! ^w inconsi/5tly ) cu/om1 if we said t !re 0 an analogy betwe5 iron1 nickel1 & cobalt1 manife/$ 9 ! /r5g? ( _! magnetic p[]s4 ,!re is a /ill m p]fect analogy betwe5 iod9e & *lor9e2 n t e prop]ty ( iod9e is id5tical ) ! correspond+ prop]ty ( *lor9e2 = !n !y w\ld be "o & ! same k9d ( sub/ance1 & n two sub/ances2 b e prop]ty ( iod9e resembles 9 all b degree "s prop]ty ( *lor9e4 ,= almo/ e sub/ance 9 :i* iod9e =ms a compon5t1 a correspond+ sub/ance may be discov]$ conta9+ *lor9e1 s t we may confid5tly inf] f ! comp\nds ( ! "o to ! comp\nds ( ! o!r sub/ance4 ,potassium iodide cry/allises 9 cubes2 !re=e x is to be expect$ t potassium *loride w also cry/allise 9 cubes4 ,! sci5ce ( *emi/ry z n[ develop$ re/s almo/ entirely ^u a c>eful & ext5sive comp>ison ( ! prop]ties ( sub/ances1 br++ deep-ly+ analogies to light4 ,:5 any new sub/ance is enc\nt]$1 ! *emi/ is guid$ 9 8 treatm5t ( x by ! analogies :i* x seems to pres5t ) previ\sly kn[n sub/ances4 ,9 ?is *apt] ,i _c hope to illu/rate ! all-p]vad+ influ5ce ( analogy 9 human ?\ght & sci5ce4 ,all sci5ce1 x has be5 said1 at ! outset1 arises f ! discov]y ( id5tity1 & analogy is b "o "n by :i* we d5ote ! deep]-ly+ cases ( resemblance4 ,i %all only try to po9t out at pres5t h[ analogy betwe5 app>5tly div]se classes ( ph5om5a (t5 s]ves z a guide 9 discov]y4 ,we ?us commonly ga9 ! fir/ insight into ! nature ( an app>5tly unique object1 & ?us1 9 ! progress ( a sci5ce1 we (t5 discov] t we are treat+ ov] aga91 9 a new =m1 ph5om5a :i* 7 well kn[n to u 9 ano!r =m4 99,analogy z a ,guide 9 ,discov]y499 ,!re c be no d\bt t discov]y is mo/ frequ5tly accompli%$ by foll[+ up h9ts receiv$ f analogy1 z ,j]emy ,b5?am rem>k$4#ebd ,:5ev] a ph5om5on is p]ceiv$1 ! fir/ impulse ( ! m9d is to connect x ) ! mo/ ne>ly simil> ph5om5on4 ,if we c\ld ev] meet a ?+ :olly 99sui g5]is991 pres5t+ no analogy to any?+ else1 we %\ld be incapable ( inve/igat+ its nature1 except by purely haphaz>d trial4 ,! probability ( success by su* a process is s slight1 t x is pref]able to foll[ up ! fa9te/ clue4 ,z ,i h po9t$ out already 7p4 #dah71 ! possible exp]im5ts are almo/ inf9ite 9 numb]1 & v num]\s also are ! hypo!ses ^u :i* we may proce$4 ,n[ x is self-evid5t t1 h[ev] slightly sup]ior ! probability ( success by "o c\rse ( proc$ure may be ov] ano!r1 ! mo/ probable "o %\ld always be adopt$ fir/4 #ebd 99,essay on ,logic991 99,works991 vol4 viii4 p4 #bgf4 ,! *emi/ hav+ discov]$ :at he believes to be a new elem5t1 w h be=e him an inf9ite v>iety ( modes ( treat+ & inve/igat+ x4 ,if 9 any ( its qualities ! sub/ance displays a resemblance to an alkal9e metal1 = in/ance1 he w naturally proce$ to try :e!r x possesses o!r prop]ties ( ! alkal9e metals4 ,ev5 ! simple/ ph5om5on pres5ts s _m po9ts = notice t we h a *oice f among _m hypo!ses4 ,x w\ld be difficult to f9d a m in/ructive in/ance ( ! way 9 :i* ! m9d is guid$ by analogy ?an 9 ! description by ,sir ,john ,h]s*el ( ! c\rse ( ?\ght by :i* he 0 l$ to anticipate 9 !ory "o ( ,f>aday's greate/ discov]ies4 ,h]s*el notic$ t a screw-l =m1 te*nically call$ helicoidal dissymmetry1 0 obs]v$ 9 ?ree cases1 namely1 9 electrical helices1 plagih$ral qu>tz cry/als1 & ! rotation ( ! plane ( pol>isation ( light4 ,z he said1#ebe 8,i reason$ ?us3 ,"h are ?ree ph5om5a agree+ 9 a 99v /range peculi>ity994 ,probably1 ?is peculi>ity is a connect+ l9k1 physically speak+1 among !m4 ,n[1 9 ! case ( ! cry/als & ! light1 ?is probability has be5 turn$ into c]ta9ty by my own exp]im5ts4 ,!re=e1 induction l$ me to conclude t a simil> connection exi/s1 & mu/ turn up1 someh[ or o!r1 betwe5 ! electric curr5t & pol>is$ light1 & t ! plane ( pol>isation w\ld be deflect$ by magneto-electricity40 ,by ?is c\rse ( analogical ?\ght ,h]s*el _h actually be5 l$ to anticipate ,f>aday's great discov]y ( ! influ5ce ( magnetic /ra9 ^u pol>is$ light4 ,he _h tri$ 9 #ahbb-be to discov] ! influ5ce ( electricity on light1 by s5d+ a ray ( pol>is$ light ?r\gh a helix1 or ne> a long wire convey+ an electric curr5t4 ,su* a c\rse ( inquiry1 foll[$ up ) ! p]si/5cy ( ,f>aday1 & ) 8 exp]im5tal res\rces1 w\ld d\btless h effect$ ! discov]y4 ,h]s*el also sugge/s t ! plagih$ral =m ( qu>tz cry/als mu/ be due to a screw-l /ra9 dur+ cry/allisation2 b ! notion rema9s unv]ifi$ by exp]im5t4 #ebe 99,life ( ,f>aday991 by ,b5ce ,jones1 vol4 ii4 p4 #bjf4 99,analogy 9 ! ,ma!matical ,sci5ces499 ,:oev] wi%es to acquire a deep acqua9tance ) ,nature mu/ obs]ve t !re are analogies :i* connect :ole bran*es ( sci5ce 9 a p>allel mann]1 & enable u to inf] ( "o class ( ph5om5a :at we "k ( ano!r4 ,x has ?us happ5$ on sev]al occasions t ! discov]y ( an unsuspect$ analogy betwe5 two bran*es ( k has be5 ! />t+-po9t = a rapid c\rse ( discov]y4 ,! tru?s readily obs]v$ 9 ! "o may be ( a diff]5t "* f ^? :i* pres5t !mselves 9 ! o!r4 ,! analogy1 once po9t$ out1 leads u to discov] regions ( "o sci5ce yet undevelop$1 to :i* ! key is furni%$ by ! correspond+ tru?s 9 ! o!r sci5ce4 ,an int]*ange ( aid mo/ wond]ful 9 its results may ?us take place1 & at ! same "t ! m9d rises to a high] g5]alisation1 & a m compreh5sive view ( nature4 ,no two sci5ces might seem at fir/ sight m diff]5t 9 _! subject matt] ?an geometry & algebra4 ,! fir/ deals ) circles1 squ>es1 p>allelograms1 & o!r =ms 9 space2 ! latt] ) m]e symbols ( numb]4 ,prior to ! "t ( ,desc>tes1 ! sci5ces 7 develop$ sl[ly & pa9fully 9 almo/ entire indep5d5ce ( ea* o!r4 ,! ,greek philosoph]s inde$ c\ld n avoid notic+ occasional analogies1 z :5 ,plato 9 ! ,?etetus describes a squ>e numb] z 99equally equal991 & a numb] produc$ by multiply+ two unequal factors z 99oblong994 ,euclid1 9 ! #g? & #h? books ( 8 ,elem5ts1 cont9ually uses expressions display+ a consci\sness ( ! same analogies1 z :5 he calls a numb] ( two factors a 99plane numb]991 1 & di/+ui%es a squ>e numb] ( :i* ! two factors are equal z an equal-sid$ & plane numb]1 4 ,he also calls ! root ( a cubic numb] its side1 4 ,9 ! ,diophant9e algebra _m problems ( a geometrical "* 7 solv$ by algebraic or num]ical processes2 b !re 0 no g5]al sy/em1 s t ! solutions 7 ( an isolat$ "*4 ,9 g5]al ! anci5ts 7 f> m advanc$ 9 geometric ?an symbolic me?ods2 ?us ,euclid 9 8 #d? book gives ! means ( divid+ a circle by purely geometric means into #b1 #c1 #d1 #e1 #f1 #h1 #aj1 #ab1 #ae1 #af1 #bj1 #bd1 #cj p>ts1 b he 0 totally unacqua9t$ ) ! !ory ( ! roots ( unity exactly correspond+ to ?is division ( ! circle4 ,dur+ ! middle ages1 on ! contr>y1 algebra advanc$ beyond geometry1 & modes ( solv+ equations 7 gradually discov]$ by ^? :o _h no notion t at e /ep !y 7 implicitly solv+ geometric problems4 ,x is true t ,regiomontanus1 ,t>taglia1 ,bombelli1 & possibly o!r e>ly algebrai/s1 solv$ isolat$ geometrical problems by ! aid ( algebra1 b p>ticul> numb]s 7 always us$1 & no consci\sness ( a g5]al me?od 0 display$4 ,vieta 9 "s degree anticipat$ ! f9al discov]y1 & occasionally repres5t$ ! roots ( an equation geometrically1 b x 0 res]v$ = ,desc>tes to %[1 9 ! mo/ g5]al mann]1 t e equation may be repres5t$ by a curve or figure 9 space1 & t e b5d1 po9t1 cusp1 or o!r peculi>ity 9 ! curve indicates "s peculi>ity 9 ! equation4 ,x is impossible to describe 9 any adequate mann] ! importance ( ?is discov]y4 ,! advantage 0 two-fold3 algebra aid$ geometry1 & geometry gave reciprocal aid to algebra4 ,curves su* z ! well-kn[n sections ( ! cone 7 f\nd to correspond to quadratic equations2 & x 0 impossible to manipulate ! equations )\t discov]+ prop]ties ( ^? all-important curves4 ,! way 0 ?us op5$ = ! algebraic treatm5t ( motions & =ces1 )\t :i* ,newton's 99,pr9cipia99 c\ld nev] h be5 work$ out4 ,newton inde$ 0 possess$ by a /rong infatuation 9 fav\r ( ! anci5t geometrical me?ods2 b x is well kn[n t he employ$ symbolic me?ods to discov] 8 !orems1 & he n[ & !n1 by "s accid5tal use ( algebraic expression1 confess$ its great] p[] & g5]ality4 ,geometry1 on ! o!r h&1 gave great assi/ance to algebra1 by af=d+ concrete repres5tations ( relations :i* w\ld o!rwise be too ab/ract = easy compreh5sion4 ,a curve ( no great complexity may give ! :ole hi/ory ( ! v>iations ( value ( a tr\blesome ma!matical expression4 ,z soon z we "k1 too1 t e regul> geometrical curve repres5ts "s algebraic equation1 we are pres5t$ by obs]vation ( me*anical movem5ts ) abundant sugge/ions t[>ds ! discov]y ( ma!matical problems4 ,e p>ticle ( a c>riage-:eel :5 mov+ on a level road is con/antly describ+ a cycloidal curve1 ! curi\s prop]ties ( :i* ex]cis$ ! +5uity ( all ! mo/ skilful ma!maticians ( ! sev5te5? c5tury1 & l$ to important advancem5ts 9 algebraic p[]4 ,x may be held t ! discov]y ( ! ,diff]5tial ,calculus 0 ma9ly due to geometrical analogy1 because ma!maticians1 9 attempt+ to treat algebraically ! tang5t ( a curve1 7 oblig$ to ent]ta9 ! notion ( inf9itely small quantities4#ebf ,!re c be no d\bt t ,newton's fluxional1 t is1 geometrical mode ( /at+ ! diff]5tial calculus1 h[ev] mu* x subsequ5tly ret>d$ its progress 9 ,engl&1 facilitat$ its appreh5sion at fir/1 & ,i %\ld ?9k x almo/ c]ta9 t ,newton discov]$ ! pr9ciples ( ! calculus geometrically4 #ebf ,lacroix1 99,trait lm5taire de ,calcul ,diffr5tiel et de ,calcul ,intgral991 #eme dit4 p4 #fii4 ,we may accord+ly look ^u ?is discov]y ( analogy1 ?is happy alliance1 z ,bossut calls x1#ebg betwe5 geometry & algebra1 z ! *ief s\rce ( discov]ies :i* h be5 made = ?ree c5turies pa/ 9 ma!matical me?ods4 ,?is is c]ta9ly ! op9ion ( ,lagrange1 :o says1 8,s long z algebra & geometry h be5 sep>ate1 _! progress 0 sl[1 & _! employm5t limit$2 b s9ce ^! two sci5ces h be5 unit$1 !y h l5t ea* o!r mutual /r5g?1 & h m>*$ toge!r ) a rapid /ep t[>ds p]fection40 #ebg 99,hi/oire des ,ma?matiques991 vol4 i4 p4 #bih4 ,! advancem5t ( me*anical sci5ce has also be5 greatly aid$ by analogy4 ,an ab/ract & intangible exi/5ce l =ce dem&s mu* p[] ( conception1 b x has a p]fect concrete repres5tative 9 a l9e1 ! end ( :i* may d5ote ! po9t ( application1 & ! direction ! l9e ( action ( ! =ce1 :ile ! l5g? c be made arbitr>ily to d5ote ! am\nt ( ! =ce4 ,nor does ! analogy end "h2 = ! mom5t ( ! =ce ab\t any po9t1 or its product into ! p]p5dicul> di/ance ( its l9e ( action f ! po9t1 is f\nd to be repres5t$ by an area1 namely twice ! area ( ! triangle conta9$ betwe5 ! po9t & ! ends ( ! l9e repres5t+ ! =ce4 ,( late ye>s a great g5]alisation has be5 effect$2 ! ,d\ble ,algebra ( ,de ,morgan is true n only ( space relations1 b ( =ces1 s t ! triangle ( =ces is r$uc$ to a case ( pure geometrical addition4 ,nay1 ! triangle ( l9es1 ! triangle ( velocities1 ! triangle ( =ces1 ! triangle ( c\ples1 & p]haps o!r cognate !orems1 are r$uc$ by analogy to "o simple !orem1 :i* am\nts to ?is1 t !re are two ways ( gett+ f "o angul> po9t ( a triangle to ano!r1 :i* ways1 ?\gh diff]5t 9 l5g?1 are id5tical 9 _! f9al results4#ebh ,9 ! sy/em ( quat]nions ( ! late ,sir ,w4 ,r4 ,hamilton1 ^! analogies are embodi$ & c>ri$ out 9 ! mo/ g5]al mann]1 s t :atev] problem involves ! ?reefold dim5sions ( space1 or relations analog\s to ^? ( space1 is treat$ by a symbolic me?od ( ! mo/ compreh5sive simplicity4 #ebh ,see ,goodw91 99,cambridge ,philosophical ,transactions99 7#ahde71 vol4 viii4 p4 #bfi4 ,o',bri51 8,on ,symbolical ,/atics10 99,philosophical ,magaz9e991 #d? ,s]ies1 vol4 i4 pp4 #dia1 c4 ,see also ,pr(essor ,cl]k ,maxwell's delightful 99,manual ( ,elem5t>y ,sci5ce991 call$ 99,matt] & ,motion991 publi%$ by ! ,society = ,promot+ ,*ri/ian ,k4 ,9 ?is admirable little "w "s ( ! mo/ advanc$ results ( me*anical & physical sci5ce are expla9$ accord+ to ! me?od ( quat]nions1 b ) h>dly any use ( algebraic symbols4 ,x ought to be add$ t to ! discov]y ( analogy betwe5 ! =ms ( ma!matical & logical expressions1 we owe ! greate/ advance 9 logical sci5ce4 ,boole bas$ 8 ext5sion ( logical processes ^u ! notion t logic is an algebra ( two quantities #j & #a4 ,8 pr(\nd g5ius = symbolic inve/igation l$ him to p]ceive by analogy t !re mu/ exi/ a g5]al sy/em ( logical d$uction1 ( :i* ! old logicians _h seiz$ only a few fragm5ts4 ,mi/ak5 z he 0 9 plac+ algebra z a high] sci5ce ?an logic1 no "o c d5y t ! developm5t ( ! m complex & dep5d5t sci5ce _h advanc$ f> beyond t ( ! simpl] sci5ce1 & t ,boole1 9 draw+ att5tion to ! connection1 made "o ( ! mo/ important discov]ies 9 ! hi/ory ( sci5ce4 ,z ,desc>tes _h w$d$ algebra & geometry1 s did ,boole accompli% ! m>riage ( logic & algebra4 99,analogy 9 ! ,!ory ( ,undulations499 ,!re is no class ( ph5om5a :i* m ?or\ghly illu/rates alike ! p[] & weakness ( analogy ?an ! waves :i* agitate e k9d ( m$ium4 ,all waves1 :atsoev] be ! matt] ?r\gh :i* !y pass1 obey ! pr9ciples ( rhy?mical or h>monic motion1 & ! subject !re=e pres5ts a f9e field = ma!matical g5]alisation4 ,ea* k9d ( m$ium may all[ ( waves peculi> 9 _! conditions1 s t x is a beautiful ex]cise 9 analogical reason+ to decide h[1 9 mak+ inf]5ces f "o k9d ( m$ium to ano!r1 we mu/ make all[ance = diff]5ce ( circum/ances4 ,! waves ( ! ocean are l>ge & visible1 & !re are ! yet great] tidal waves :i* ext5d ar\nd ! globe4 ,f su* palpable cases ( rhy?mical movem5t we pass to waves ( s\nd1 v>y+ 9 l5g? f ab\t #cb feet to a small fraction ( an in*4 ,we h b to imag9e1 if we c1 ! =tie? octave ( ! middle ,c ( a piano1 & we rea* ! undulations ( yell[ light1 ! ultra-violet be+ ab\t ! =ty-fir/ octave4 ,?us we pass f ! palpable & evid5t to t :i* is obscure1 if n incompreh5sible4 ,yet ! same ph5om5a ( reflection1 int]f]5ce1 & refraction1 :i* we f9d 9 "s k9ds ( waves1 may be expect$ to occur1 99mutatis mut&is991 9 o!r k9ds4 ,f ! great to ! small1 f ! evid5t to ! obscure1 is n only ! natural ord] ( inf]5ce1 b x is ! hi/orical ord] ( discov]y4 ,! physical sci5ce ( ! ,greek philosoph]s mu/ h rema9$ incomplete1 & _! !ories gr\ndless1 because !y did n und]/& ! nature ( undulations4 ,_! sy/ems 7 bas$ ^u ! notion ( movem5t ( translation f place to place4 ,mod]n sci5ce t5ds to ! opposite notion t all motion is alt]nat+ or rhy?mical1 en]gy fl[+ onw>ds b matt] rema9+ comp>atively fix$ 9 position4 ,diog5es ,la]tius inde$ correctly comp>$ ! propagation ( s\nd ) ! spread+ ( waves on ! surface ( wat] :5 di/urb$ by a /one1 & ,vitruvius display$ a m complete compreh5sion ( ! same analogy4 ,x rema9$ = ,newton to create ! !ory ( undulatory motion 9 %[+ by ma!matical d$uctive reason+ t ! p>ticles ( an ela/ic fluid by vibrat+ backw>ds & =w>ds1 might c>ry a pulse or wave mov+ f ! s\rce ( di/urbance1 :ile ! di/urb$ p>ticles return to _! place ( re/4 ,he 0 ev5 able to make a fir/ approximation by !oretical calculation to ! velocity ( s\nd-waves 9 ! atmosph]e4 ,8 !ory ( s\nd =m$ a h>dly less important epo* 9 sci5ce ?an 8 f> m celebrat$ !ory ( gravitation4 ,x op5$ ! way to all ! subsequ5t applications ( me*anical pr9ciples to ! ins5sible motion ( molecules4 ,he seems to h be51 too1 ^u ! br9k ( ano!r application ( ! same pr9ciples :i* w\ld h advanc$ sci5ce by a c5tury ( progress1 & made him ! undisput$ f\nd] ( all ! !ories ( matt]4 ,he express$ op9ions at v>i\s times t light might be due to undulatory movem5ts ( a m$ium occupy+ space1 & 9 "o int5sely int]e/+ s5t5ce rem>ks#ebi t col\rs are probably vibrations ( diff]5t l5g?s1 8mu* aft] ! mann] t1 9 ! s5se ( he>+1 nature makes use ( arial vibrations ( sev]al bignesses to g5]ate s\nds ( div]s tones1 = ! analogy ( nature is to be obs]v$40 ,he correctly =esaw t r$ & yell[ light w\ld consi/ ( ! long] undulations1 & blue & violet ( ! %ort]1 :ile :ite light w\ld be compos$ ( an indiscrim9ate mixture ( waves ( v>i\s l5g?s4 ,newton almo/ ov]came ! /ronge/ app>5t difficulty ( ! undulatory !ory ( light1 namely1 ! propagation ( light 9 /raight l9es4 ,= he obs]v$ t ?\gh waves ( s\nd b5d r\nd an ob/acle to "s ext5t1 !y d n d s 9 ! same degree z wat]-waves4#ecj ,he _h b to ext5d ! analogy proportionally to light-waves1 & n only w\ld ! difficulty h vani%$1 b ! true !ory ( diffraction w\ld h be5 op5 to him4 ,un=tunately he _h a preconceiv$ !ory t rays ( light are b5t f & n t[>ds ! %ad[ ( a body1 a !ory :i* = once he did n suffici5tly comp>e ) obs]vation to detect its falsity4 ,i am n aw>e1 too1 t ,newton has1 9 any ( 8 works1 display$ an und]/&+ ( ! ph5om5a ( int]f]5ce )\t :i* 8 notion ( waves mu/ h be5 imp]fect4 #ebi ,bir*1 99,hi/ory ( ! ,royal ,society991 vol4 iii4 p4 #bfb1 quot$ by ,"y1 99,works991 vol4 i4 p4 #bdf4 #ecj 99,opticks991 ,qu]y #bh1 #crd edit4 p4 #ccg4 ,:ile ! g5]al pr9ciples ( undulatory motion w be ! same 9 :atev] m$ium ! motion takes place1 ! circum/ances may be excessively diff]5t4 ,betwe5 light travell+ #ahf1jjj miles p] second & s\nd travell+ 9 air only ab\t #a1ajj feet 9 ! same "t1 or almo/ #ijj1jjj times z sl[ly1 we _c expect a close outw>d resemblance4 ,!re are great diff]5ces1 too1 9 ! "* ( ! vibrations4 ,gases sc>cely admit ( transv]se vibration1 s t s\nd travell+ 9 air is a longitud9al wave1 ! p>ticles ( air mov+ backw>ds & =w>ds 9 ! same l9e 9 :i* ! wave moves onw>ds4 ,light1 on ! o!r h&1 appe>s to consi/ entirely 9 ! movem5t ( po9ts ( =ce transv]sely to ! direction ( propagation ( ! ray4 ,! light-wave is p>tially analog\s to ! b5d+ ( a rod or ( a /ret*$ cord agitat$ at "o end4 ,n[ ?is b5d+ motion may take place 9 any "o ( an inf9ite numb] ( planes1 & waves ( :i* ! planes are p]p5dicul> to ea* o!r _c int]f]e any m ?an two p]p5dicul> =ces c int]f]e4 ,! complicat$ ph5om5a ( pol>is$ light arise out ( ?is transv]se "* ( ! lum9\s wave1 & we mu/ n expect to meet analog\s ph5om5a 9 atmosph]ic s\nd-waves4 ,x is conceivable t 9 solids we might produce transv]se s\nd undulations1 9 :i* ph5om5a ( pol>isation might be reproduc$4 ,b x w\ld appe> t ev5 betwe5 transv]se s\nd & light-waves ! analogy holds true r ( ! pr9ciples ( h>monic motion ?an ! circum/ances ( ! vibrat+ m$ium2 f exp]im5t & !ory x is inf]r$ t ! plane ( pol>isation 9 plane pol>is$ light is p]p5dicul> to in/ead ( be+ co9cid5t ) ! direction ( vibration1 z x w\ld be 9 ! case ( transv]se s\nd undulations4 ,if s ! laws ( ela/ic =ces are ess5tially diff]5t 9 application to ! lum9if]\s e!r & to ord9>y solid bodies4#eca #eca ,rank9e1 99,philosophical ,transactions99 7#ahef71 vol4 cxlvi4 p4 #bhb4 99,analogy 9 ,a/ronomy499 ,we %all be mu* assi/$ 9 ga9+ a true appreciation ( ! value ( analogy 9 its feebl] degrees1 by consid]+ h[ mu* x has contribut$ to ! progress ( a/ronomical sci5ce4 ,our po9t ( obs]vation is s fix$ ) reg>d to ! univ]se1 & our means ( exam9+ di/ant bodies are s re/rict$1 t we are necess>ily guid$ by limit$ & app>5tly feeble resemblances4 ,9 _m cases ! result has be5 confirm$ by subsequ5t direct evid5ce ( ! mo/ =cible "*4 ,:ile ! sci5tific _w 0 divid$ 9 op9ion betwe5 ! ,cop]nican & ,ptolemaic sy/ems1 x 0 analogy :i* furni%$ ! mo/ satisfactory argum5t4 ,galileo discov]$1 by ! use ( 8 new telescope1 ! f\r small satellites :i* circulate r\nd ,jupit]1 & make a m9iature planet>y _w4 ,^! f\r ,m$icean ,/>s1 z !y 7 call$1 7 pla9ly se5 to revolve r\nd ,jupit] 9 v>i\s p]iods1 b approximately 9 "o plane1 & a/ronom]s irresi/ibly inf]r$ t :at might happ5 on ! small] scale might also be f\nd true ( ! great] planet>y sy/em4 ,?is discov]y gave 8! hold+ turn10 z ,h]s*el express$ x1 to ! op9ions ( mank9d4 ,ev5 ,francis ,bacon1 :o1 little to ! cr$it ( 8 sci5tific sagacity1 _h previ\sly oppos$ ! ,cop]nican views1 n[ became conv9c$1 say+ 8,we affirm ! solisequium ( ,v5us & ,m]cury2 s9ce x has be5 f\nd by ,galileo t ,jupit] also has att5dants40 ,nor did ,huygh5s ?9k x sup]flu\s to adopt ! analogy z a valid argum5t4#ecb ,ev5 9 an advanc$ /age ( physical a/ronomy1 ! ,jovian sy/em has n lo/ its analogical int]e/2 = ! mutual p]turbations ( ! f\r satellites pass ?r\gh all _! phases )9 a few c5turies1 & ?us enable u to v]ify 9 a m9iature case ! pr9ciples ( /ability1 :i* ,laplace e/abli%$ = ! great planet>y sy/em4 ,oscillations or di/urbances :i* 9 ! motions ( ! planets appe> to be secul>1 because _! p]iods ext5d ov] millions ( ye>s1 c be wat*$1 9 ! case ( ,jupit]'s satellites1 ?r\gh complete revolutions )9 ! hi/orical p]iod ( a/ronomy4#ecc #ecb 99,cosmo!oros99 7#afii71 p4 #af4 #ecc ,laplace1 99,sy/em ( ! ,_w991 vol4 ii4 p4 #caf4 ,9 obta9+ a k ( ! /ell> univ]se we mu/ sometimes dep5d ^u prec>i\s analogies4 ,we /ill hold ^u ?is gr\nd ! op9ion1 ent]ta9$ by ,bruno z long ago z #aeia1 t ! />s may be suns att5d$ by planets l our e>?4 ,?is is ! mo/ probable fir/ assumption1 & x is support$ by spectrum obs]vations1 :i* %[ ! simil>ity ( light d]iv$ f _m />s ) t ( ! sun4 ,b at ! same "t we le>n by ! prism t !re are nebul & />s 9 conditions widely diff]5t f any?+ kn[n 9 our sy/em4 ,9 ! c\rse ( "t ! analogy may p]haps be re/or$ to comp>ative complet5ess by ! discov]y ( suns 9 v>i\s /ages ( nebul\s cond5sation4 ,! hi/ory ( ! evolution ( our own _w may be trac$ back 9 bodies less develop$1 or trac$ =w>ds 9 sy/ems m advanc$ t[>ds ! dissipation ( en]gy1 & ! ext9ction ( life4 ,z 9 a great work%op1 we may p]haps see ! mat]ial "w ( ,creation z x has progress$ ?r\gh ?\s&s ( millions ( ye>s4 ,9 speculations conc]n+ ! physical condition ( ! planets & _! satellites1 we dep5d ^u analogies ( a weak "*4 ,we may be said to "k t ! moon has m\nta9s & valleys1 pla9s & ridges1 volcanoes & /reams ( lava1 &1 9 spite ( ! abs5ce ( air & wat]1 ! rocky surface ( ! moon pres5ts s _m famili> appe>ances t we d n hesitate to comp>e !m ) ! features ( our globe4 ,we inf] ) high probability t ,m>s has pol> sn[ & an atmosph]e absorb+ blue rays l our own2 ,jupit] und\bt$ly possesses a cl\dy atmosph]e1 possibly n unlike a magnifi$ copy ( t surr\nd+ ! e>?1 b our t5d5cy to adopt analogies receives a salut>y correction 9 ! rec5tly discov]$ fact t ! atmosph]e ( ,uranus conta9s hydrog54 ,philosoph]s h n /opp$ at ^! comp>atively safe inf]5ces1 b h speculat$ on ! exi/5ce ( liv+ creatures 9 o!r planets4 ,huygh5s rem>k$ t z we inf] by analogy f ! dissect$ body ( a dog to t ( a pig & ox or o!r animal ( ! same g5]al =m1 & z we expect to f9d ! same visc]a1 ! he>t1 /oma*1 lungs1 inte/9es1 c41 9 correspond+ positions1 s :5 we notice ! simil>ity ( ! planets 9 _m respects1 we mu/ expect to f9d !m alike 9 o!r respects4#ecd ,he ev5 ent]s into an inquiry :e!r ! inhabitants ( o!r planets w\ld possess reason & k ( ! same sort z ours1 conclud+ 9 ! affirmative4 ,al?\gh ! p[] ( intellect might be diff]5t1 he consid]s t !y w\ld h ! same geometry if !y _h any at all1 & t :at is true ) u w\ld be true ) !m4#ece ,z reg>ds ! sun1 he wisely obs]ves t e conjecture fails4 ,laplace ent]ta9$ a /rong belief 9 ! exi/5ce ( inhabitants on o!r planets4 ,! b5ign influ5ce ( ! sun gives bir? to animals & plants ^u ! surface ( ! e>?1 & analogy induces u to believe t 8 rays w\ld t5d to h a simil> effect else:]e4 ,x is n probable t matt] :i* is "h s fruitful ( life w\ld be /]ile ^u s great a globe z ,jupit]1 :i*1 l ! e>?1 has its days & nights & ye>s1 & *anges :i* indicate active =ces4 ,man inde$ is =m$ = ! temp]ature & atmosph]e 9 :i* he lives1 &1 s f> z appe>s1 c\ld n live ^u ! o!r planets4 ,b !re might be an inf9ity ( organisations relative to ! div]se con/itutions ( ! bodies ( ! univ]se4 ,! mo/ active imag9ation _c =m any idea ( su* v>i\s creatures1 b _! exi/5ce is n unlikely4#ecf #ecd 99,cosmo!oros99 7#afii71 p4 #ag4 #ece ,ibid4 p4 #cf4 #ecf 99,sy/em ( ! ,_w991 vol4 ii4 p4 #cbf4 99,essai ,philosophique991 p4 #hg4 ,we n[ "k t _m metals & o!r elem5ts nev] f\nd 9 organic /ructures are yet capable ( =m+ comp\nds ) sub/ances ( vegetable or animal orig94 ,x is !re=e j possible t at diff]5t temp]atures creatures =m$ ( diff]5t yet analog\s comp\nds might exi/1 b x w\ld seem indisp5sable t c>bon %\ld =m ! basis ( organic /ructures4 ,we h no analogies to lead u to suppose t 9 ! abs5ce ( t complex elem5t life c exi/4 ,c\ld we f9d globes surr\nd$ by atmosph]es resembl+ our own 9 temp]ature & composition1 we %\ld be almo/ =c$ to believe !m inhabit$1 b ! probability ( any analogical argum5t decreases rapidly z ! condition ( a globe div]ges f t ( our own4 ,! ,c>d9al ,ni*olas de ,cusa held long ago t ! moon 0 inhabit$1 b ! abs5ce ( any appreciable atmosph]e r5d]s ! exi/5ce ( inhabitants highly improbable4 ,speculations re/+ ^u weak analogies h>dly belong to ! scope ( true sci5ce1 & c only be tol]at$ z an antidote to ! f> worse dogmas :i* ass]t t ! ?\s& million ( p]sons on e>?1 or r a small fraction ( !m1 are ! sole objects ( c>e ( ! ,p[] :i* design$ ?is limitless ,univ]se4 99,failures ( ,analogy499 ,s con/ant is ! aid :i* we d]ive f ! use ( analogy 9 all attempts at discov]y or explanation1 t x is mo/ important to obs]ve 9 :at cases x may lead u into difficulties4 ,t :i* we expect by analogy to exi/ 7#a7 ,may be f\nd to exi/2 7#b7 ,may seem n to exi/1 b nev]!less may really exi/2 7#c7 ,may actually be non-exi/5t4 ,9 ! second case ! failure is only app>5t1 & arises f our obtus5ess ( p]ception1 ! smallness ( ! ph5om5on to be notic$1 or ! disguis$ "* 9 :i* x appe>s4 ,i h already po9t$ out t ! analogy ( s\nd & light seems to fail because light does n app>5tly b5d r\nd a corn]1 ! fact be+ t x does s b5d 9 ! ph5om5a ( diffraction1 :i* pres5t ! effect1 h[ev]1 9 su* an unexpect$ & m9ute =m1 t ev5 ,newton 0 misl$1 & turn$ f ! correct hypo!sis ( undulations :i* he _h p>tially ent]ta9$4 ,9 ! ?ird class ( cases analogy fails u altoge!r1 & we expect t to exi/ :i* really does n exi/4 ,?us we fail to discov] ! ph5om5a ( pol>isation 9 s\nd travell+ ?r\gh ! atmosph]e1 s9ce air is n capable ( any appreciable transv]se undulations4 ,^! failures ( analogy are ( peculi> int]e/1 because !y make ! m9d aw>e ( its sup]ior p[]s4 ,!re h be5 _m philosoph]s :o said t we c conceive no?+ 9 ! intellect :i* we h n previ\sly receiv$ ?r\gh ! s5ses4 ,?is is true 9 ! s5se t we _c 99image99 !m to ! m9d 9 ! concrete =m ( a %ape or a col\r2 b we c speak ( !m & reason conc]n+ !m2 9 %ort1 we (t5 "k !m 9 ev]y?+ b a s5su\s mann]4 ,accurate inve/igation %[s t all mat]ial sub/ances ret>d ! motion ( bodies ?r\gh !m by subtract+ en]gy by impact4 ,by ! law ( cont9uity we c frame ! notion ( a vacu\s space 9 :i* !re is no resi/ance :atev]1 nor ne$ we /op !re2 = we h only to proce$ by analogy to ! case :]e a m$ium %\ld accel]ate ! motion ( bodies pass+ ?r\gh x1 some:at 9 ! mode :i* ,ari/otelians attribut$ falsely to ! air4 ,?us we c frame ! notion ( 99negative d5sity991 & ,newton c\ld reason exactly conc]n+ x1 al?\gh no su* ?+ exi/s4#ecg #ecg 99,pr9cipia991 bk4 ii4 ,section ii4 ,prop4 x4 ,9 e direction ( ?\ght we may meet ultimately ) simil> failures ( analogy4 ,a mov+ po9t g5]ates a l9e1 a mov+ l9e g5]ates a surface1 a mov+ surface g5]ates a solid1 b :at does a mov+ solid g5]ate8 ,:5 we comp>e a polyh$ron1 or _m-sid$ solid1 ) a polygon1 or plane figure ( _m sides1 ! volume ( ! fir/ is analog\s to ! area ( ! second2 ! face ( ! solid answ]s to ! side ( ! polygon2 ! edge ( ! solid to ! po9t ( ! figure2 b ! corn]1 or junction ( edges 9 ! polyh$ron1 is left :olly unrepres5t$ 9 ! plane ( ! polygon4 ,ev5 if we attempt$ to draw ! analogies 9 "s o!r mann]1 we %\ld /ill f9d a geometrical notion embodi$ 9 ! solid :i* has no repres5tative 9 ! figure ( two dim5sions4#ech #ech ,de ,morgan1 99,cambridge ,philosophical ,transactions991 vol4 xi4 ,"p ii4 p4 #bdf4 ,f>aday 0 able to frame "s notion ( matt] 9 a f\r? condition1 :i* %\ld be to gas :at gas is to liquid4#eci ,su* sub/ance1 he ?\ght1 w\ld n fall f> %ort ( 99radiant matt]991 by :i* app>5tly he meant ! suppos$ caloric or matt] assum$ to con/itute heat1 accord+ to ! corpuscul> !ory4 ,ev5 if we c\ld frame ! notion1 matt] 9 su* a /ate _c be kn[n to exi/1 & rec5t discov]ies conc]n+ ! cont9uity ( ! solid1 liquid1 & gase\s /ates remove ! basis ( ! speculation4 #eci 99,life ( ,f>aday991 vol4 i4 p4 #baf4 ,f ^! & _m o!r in/ances :i* might be adduc$1 we le>n t analogical reason+ leads u to ! conception ( _m ?+s :i*1 s f> z we c asc]ta91 d n exi/4 ,9 ?is way great p]plexities h aris5 9 ! use ( language & ma!matical symbols4 ,all language dep5ds ^u analogy2 = we jo9 & arrange words s t !y may repres5t ! correspond+ junctions or arrangem5ts ( ?+s & _! equalities4 ,b 9 ! use ( language we are obvi\sly capable ( =m+ _m comb9ations ( words to :i* no correspond+ mean+ app>5tly exi/s4 ,! same difficulty arises 9 ! use ( ma!matical signs1 & ma!maticians h ne$lessly puzzl$ !mselves ab\t ! squ>e root ( a negative quantity1 :i* is1 9 _m applications ( algebraic calculation1 simply a sign )\t any analog\s mean+1 !re be+ a failure ( analogy4 ,,*apt] ,,xxix4 ,,exceptional ,,ph5om5a4 ,if sci5ce consi/s 9 ! detection ( id5tity & ! recognition ( uni=mity exi/+ 9 _m objects1 x foll[s t ! progress ( sci5ce dep5ds ^u ! /udy ( exceptional ph5om5a4 ,su* new ph5om5a are ! raw mat]ial ^u :i* we ex]t our faculties ( obs]vation & reason+1 9 ord] to r$uce ! new facts b5ea? ! sway ( ! laws ( nature1 ei!r ^? laws already well kn[n1 or ^? to be discov]$4 ,n only are /range & inexplicable facts ^? :i* are on ! :ole mo/ likely to lead u to "s novel & important discov]y1 b !y are also be/ fitt$ to ar\se our att5tion4 ,s long z ev5ts happ5 9 accordance ) our anticipations1 & ! r\t9e ( e-day obs]vation is unv>i$1 !re is no?+ to impress ^u ! m9d ! smallness ( its k1 & ! dep? ( my/]y1 :i* may be hidd5 9 ! commone/ sights & objects4 ,9 e>ly times ! myriads ( />s :i* rema9$ 9 app>5tly fix$ relative positions ^u ! heav5ly sph]e1 receiv$ less notice f a/ronom]s ?an ^? few planets ^: w&]+ & inexplicable motions =m$ a riddle4 ,hipp>*us 0 induc$ to prep>e ! fir/ catalogue ( />s1 because a s+le new /> _h be5 add$ to ^? nightly visible2 & 9 ! middle ages two brilliant b tempor>y />s caus$ m popul> int]e/ 9 a/ronomy ?an any o!r ev5ts1 & to "o ( !m we owe all ! obs]vations ( ,ty*o ,brahe1 ! m$ival ,hipp>*us4 ,9 o!r sci5ces1 z well z 9 t ( ! heav5s1 exceptional ev5ts are commonly ! po9ts f :i* we />t to explore new regions ( k4 ,x has be5 beautifully said t ,wond] is ! daught] ( ,ignorance1 b ! "m ( ,inv5tion2 & ?\gh ! mo/ famili> & slight ev5ts1 if fully exam9$1 w af=d endless food = wond] & = wisdom1 yet x is ! few peculi> & unlook$-= ev5ts :i* mo/ (t5 lead to a c\rse ( discov]y4 ,x is true1 inde$1 t x requires mu* philosophy to obs]ve ?+s :i* are too ne> to u4 ,! high sci5tific importance atta*+1 !n1 to exceptions1 r5d]s x desirable t we %\ld c>efully consid] ! v>i\s modes 9 :i* an exception may be dispos$ (2 :ile "s new facts w be f\nd to confirm ! v laws to :i* !y seem at fir/ sight cle>ly oppos$1 o!rs w cause u to limit ! g5]ality ( our previ\s /atem5ts4 ,9 "s cases ! exception may be prov$ to be no exception2 occasionally x w prove fatal to our previ\s mo/ confid5t speculations2 & !re are "s new ph5om5a :i*1 )\t really de/roy+ any ( our =m] !ories1 op5 to u :olly new fields ( sci5tific inve/igation4 ,! /udy ( ?is subject is especially int]e/+ & important1 because1 z ,i h be=e said 7p4 #ehg71 no important !ory c be built up complete & p]fect all at once4 ,:5 unexpla9$ ph5om5a pres5t !mselves z objections to ! !ory1 x w (t5 dem& ! utmo/ judgm5t & sagacity to assign to !m _! prop] place & =ce4 ,! acceptance or rejection ( a !ory w dep5d ^u discrim9at+ ! "o insup]able contradictory fact f _m1 :i*1 h[ev] s+ul> & inexplicable at fir/ sight1 may aft]w>ds be %[n to be results ( diff]5t causes1 or possibly ! mo/ /rik+ results ( ! v law ) :i* !y /& 9 app>5t conflict4 ,i c enum]ate at lea/ eight classes or k9ds ( exceptional ph5om5a1 to "o or o!r ( :i* any suppos$ exception to ! kn[n laws ( nature c usually be ref]r$2 !y may be briefly describ$ z bel[1 & w be suffici5tly illu/rat$ 9 ! succe$+ sections4 7#a7 ,imag9>y1 or false exceptions1 t is1 facts1 objects1 or ev5ts :i* are n really :at !y are suppos$ to be4 7#b7 ,app>5t1 b congru5t exceptions1 :i*1 ?\gh app>5tly 9 conflict ) a law ( nature1 are really 9 agreem5t ) x4 7#c7 ,s+ul> exceptions1 :i* really agree ) a law ( nature1 b exhibit rem>kable & unique results ( x4 7#d7 ,div]g5t exceptions1 :i* really proce$ f ! ord9>y action ( kn[n processes ( nature1 b :i* are excessive 9 am\nt or mon/r\s 9 "*4 7#e7 ,accid5tal exceptions1 aris+ f ! int]f]5ce ( "s entirely di/9ct b kn[n law ( nature4 7#f7 ,novel & unexpla9$ exceptions1 :i* lead to ! discov]y ( a new s]ies ( laws & ph5om5a1 modify+ or disguis+ ! effects ( previ\sly kn[n laws1 )\t be+ inconsi/5t ) !m4 7#g7 ,limit+ exceptions %[+ ! falsity ( a suppos$ law 9 "s cases to :i* x _h be5 ext5d$1 b n affect+ its tru? 9 o!r cases4 7#h7 ,contradictory or real exceptions :i* lead u to ! conclusion t a suppos$ hypo!sis or !ory is 9 opposition to ! ph5om5a ( nature1 & mu/ !re=e be ab&on$4 ,x ought to be cle>ly und]/ood t 9 no case is a law ( nature really ?w>t$ or prev5t$ f be+ fulfill$4 ,! effects ( a law may be disguis$ & hidd5 f our view 9 "s in/ances3 9 o!rs ! law itself may be r5d]$ inapplicable altoge!r2 b if a law is applicable x mu/ be c>ri$ out4 ,e law ( nature mu/ !re=e be /at$ ) ! utmo/ g5]ality ( all ! in/ances really com+ "u x4 ,babbage propos$ to di/+ui% betwe5 99univ]sal pr9ciples991 :i* d n admit ( a s+le exception1 su* z t e numb] end+ 9 #e is divisible by five1 & 99g5]al pr9ciples99 :i* are m frequ5tly obey$ ?an violat$1 z t 8m5 w be gov]n$ by :at !y believe to be _! int]e/40#edj ,b 9 a sci5tific po9t ( view g5]al pr9ciples mu/ be univ]sal z reg>ds "s di/9ct class ( objects1 or !y are n pr9ciples at all4 ,if a law to :i* exceptions exi/ is /at$ )\t allusion to ^? exceptions1 ! /atem5t is errone\s4 ,i h no "r to say t 8,all liquids exp& by heat10 if ,i "k t wat] bel[ #d ,c4 does n2 ,i ought to say1 8,all liquids1 except wat] bel[ #d ,c41 exp& by heat20 & e new exception discov]$ w falsify ! /atem5t until ins]t$ 9 x4 ,to speak ( "s laws z be+ 99g5]ally99 true1 mean+ n univ]sally b 9 ! majority ( cases1 is a hurtful abuse ( ! ^w1 b is q usual4 99,g5]al99 %\ld mean t :i* is true ( a :ole 99g5us99 or class1 & e true /atem5t mu/ be true ( "s assign$ or assignable class4 #edj ,babbage1 99,! ,exposition ( #ahea991 p4 #a4 99,imag9>y or ,false ,exceptions499 ,:5 a suppos$ exception to a law ( nature is br\ght to our notice1 ! fir/ inquiry ought prop]ly to be--,is !re any brea* ( ! law at all8 ,x may be t ! suppos$ exceptional fact is n a fact at all1 b a m]e figm5t ( ! imag9ation4 ,:5 ,k+ ,*>les reque/$ ! ,royal ,society to inve/igate ! curi\s fact t a live fi% put into a bucket ( wat] does n increase ! weight ( ! bucket & its cont5ts1 ! ,royal ,society wisely comm5c$ _! delib]ations by inquir+ :e!r ! fact 0 s or n4 ,e /atem5t1 h[ev] false1 mu/ h "s cause or prior condition1 & ! real "q = ! ,royal ,society to inve/igate 01 h[ ! ,k+ came to ?9k t ! fact 0 s4 ,m5tal conditions1 z we h se51 ent] into all acts ( obs]vation1 & are (t5 a wor?y subject ( inquiry4 ,b !re are _m in/ances 9 ! hi/ory ( sci5ce1 9 :i* tr\ble & error h be5 caus$ by false ass]tions c>elessly made1 & c>elessly accept$ )\t v]ification4 ,! reception ( ! ,cop]nican !ory 0 mu* imp$$ by ! objection1 t if ! e>? 7 mov+1 a /one dropp$ f ! top ( a high t[] %\ld be left beh9d1 & %\ld appe> to move t[>ds ! we/1 j z a /one dropp$ f ! ma/-head ( a mov+ %ip w\ld fall beh9d1 ow+ to ! motion ( ! %ip4 ,! ,cop]nicans attempt$ to meet ?is grave objection 9 e way b ! true "o1 namely1 %[+ by trial t ! ass]t$ facts are n correct4 ,9 ! fir/ place1 if a /one _h be5 dropp$ ) suitable precautions f ! ma/-head ( a mov+ %ip1 x w\ld h fall5 close to ! foot ( ! ma/1 because1 by ! fir/ law ( motion1 x w\ld rema9 9 ! same /ate ( horizontal motion communicat$ to x by ! ma/4 ,z ! anti-,cop]nicans _h assum$ ! contr>y result z c]ta9 to ensue1 _! argum5t w\ld ( c\rse h fall5 ?r\gh4 ,_h ! ,cop]nicans next proce$$ to te/ ) great c>e ! o!r ass]tion involv$1 !y w\ld h become /ill bett] conv9c$ ( ! tru? ( _! own !ory4 ,a /one dropp$ f ! top ( a high t[]1 or into a deep well1 w\ld c]ta9ly n h be5 deflect$ f ! v]tical direction 9 ! consid]able degree requir$ to agree ) ! suppos$ consequ5ces ( ! ,cop]nican views2 b1 ) v accurate obs]vation1 !y might h discov]$1 z ,b5z5b]g subsequ5tly did1 a v small deflection t[>ds ! ea/1 %[+ t ! ea/w>d velocity is great] at ! top ?an ! bottom4 ,_h ! ,cop]nicans !n be5 able to detect & int]pret ! mean+ ( ! small div]g5ce ?us aris+1 !y w\ld h f\nd 9 x corroboration ( _! own views4 ,multitudes ( cases might be cit$ 9 :i* laws ( nature seem to be evid5tly brok51 b 9 :i* ! app>5t brea* arises f a misappreh5sion ( ! case4 ,x is a g5]al law1 absolutely true ( all cry/als yet submitt$ to exam9ation1 t no cry/al has a re-entrant angle1 t is an angle :i* t[>ds ! axis ( ! cry/al is great] ?an two "r angles4 ,:]ev] ! faces ( a cry/al meet !y produce a project+ edge1 & :]ev] edges meet !y produce a corn]4 ,_m cry/als1 h[ev]1 :5 c>elessly exam9$1 pres5t exceptions to ?is law1 b clos] obs]vation always %[s t ! app>5tly re-entrant angle really arises f ! oblique union ( two di/9ct cry/als4 ,o!r cry/als seem to possess faces contradict+ all ! pr9ciples ( cry/allography2 b c>eful exam9ation %[s t ! suppos$ faces are n true faces1 b surfaces produc$ by ! ord]ly junction ( an imm5se numb] ( di/9ct ?9 cry/all9e plates1 ea* plate be+ 9 fact a sep>ate cry/al1 9 :i* ! laws ( cry/allography are /rictly obs]v$4 ,! r\ghness ( ! suppos$ face1 ! /ri detect$ by ! microscope1 or inf]5ce by cont9uity f o!r specim5s :]e ! true faces ( ! plates are cle>ly se51 prove ! mi/ak5 "* ( ! suppos$ exceptions4 ,aga91 f\r ( ! faces ( a regul> octah$ron may become s enl>g$ 9 ! cry/allisation ( iron pyrites & "s o!r sub/ances1 t ! o!r f\r faces become imp]ceptible & a regul> tetrah$ron appe>s to be produc$1 contr>y to ! laws ( cry/allographic symmetry4 ,_m o!r cry/all9e =ms are simil>ly modifi$1 s z to produce a s]ies ( :at are call$ 99hemih$ral99 =ms4 ,9 trac+ out ! isomorphic relations ( ! elem5ts1 great p]plexity has (t5 be5 caus$ by mi/ak+ "o sub/ance = ano!r4 ,x 0 po9t$ out t ?\gh ars5ic 0 suppos$ to be isomorph\s ) phosphorus1 ! ars5iate ( soda cry/allis$ 9 a =m di/9ct f t ( ! correspond+ phosphate4 ,"s *emi/s held ?is to be a fatal objection to ! doctr9e ( isomorphism2 b x 0 aft]w>ds po9t$ out by ,cl>ke1 t ! ars5iate & phosphate 9 "q 7 n correspond+ comp\nds1 z !y diff]$ 9 reg>d to ! wat] ( cry/allisation4#eda ,vanadium aga9 appe>$ to be an exception to ! laws ( isomorphism1 until x 0 prov$ by ,pr(essor ,roscoe1 t :at ,b]zelius suppos$ to be metallic vanadium 0 really an oxide ( vanadium4#edb #eda ,daub5y's 99,atomic ,!ory991 p4 #gf4 #edb 99,bak]ian ,lecture1 ,philosophical ,transactions99 7#ahfh71 vol4 clviii4 p4 #b4 99,app>5t b ,congru5t ,exceptions499 ,n unfrequ5tly a law ( nature w pres5t results 9 c]ta9 circum/ances :i* appe> to be entirely 9 conflict ) ! law itself4 ,n only may ! action ( ! law be mu* complicat$ & disguis$1 b x may 9 v>i\s ways be rev]s$ or inv]t$1 s t c>eless obs]v]s are misl$4 ,anci5t philosoph]s g5]ally believ$ t :ile "s bodies 7 heavy by nature1 o!rs1 su* z flame1 smoke1 bubbles1 cl\ds1 c41 7 ess5tially light1 or possess$ a t5d5cy to move upw>ds4 ,s acute an inquir] z ,ari/otle fail$ to p]ceive ! true nature ( buoyancy1 & ! doctr9e ( intr9sic lightness1 exp\nd$ 9 8 works1 became ! accept$ view = _m c5turies4 ,x is true t ,lucretius 0 aw>e :y flame t5ds to rise1 hold+ t-- 8,! flame has weight1 ?\gh highly r>e1 ,nor m\nts b :5 compell$ by heavi] air40 ,ar*im$es also 0 s p]fectly acqua9t$ ) ! buoyancy ( bodies imm]s$ 9 wat]1 t he c\ld n fail to p]ceive ! exi/5ce ( a p>allel effect 9 air4 ,yet ?r\gh\t ! e>ly middle ages ! light ( true sci5ce c\ld n cont5d ) ! gl>e ( ! ,p]ipatetic doctr9e4 ,! g5ius ( ,galileo & ,newton 0 requir$ to conv9ce p ( ! simple tru? t all matt] is heavy1 b t ! gravity ( "o sub/ance may be ov]borne by t ( ano!r1 z "o scale ( a balance is c>ri$ up by ! prepond]at+ weight 9 ! opposite scale4 ,x is curi\s to f9d ,newton gravely expla9+ ! diff]5ce ( absolute & relative gravity1 z if x 7 a new discov]y proce$+ f 8 !ory4#edc ,m ?an a c5tury elaps$ be=e o!r app>5t exceptions to ! ,newtonian philosophy 7 expla9$ away4 #edc 99,pr9cipia991 bk4 ii4 ,prop4 #bj4 ,coroll>ies1 #e & #f4 ,newton himself all[$ t ! motion ( ! apsides ( ! moon's orbit appe>$ to be irreconcilable ) ! law ( gravity1 & x rema9$ = ,clairaut to remove ! difficulty by m complete ma!matical analysis4 ,!re mu/ always rema91 9 ! motions ( ! heav5ly bodies1 discrepancies ( "s am\nt betwe5 !ory & obs]vation2 b su* discrepancies h s (t5 yield$ 9 pa/ times to prolong$ inve/igation t physici/s n[ reg>d !m z m]ely app>5t exceptions1 :i* w aft]w>ds be f\nd to agree ) ! law ( gravity4 ,! mo/ beautiful in/ance ( an app>5t exception1 is f\nd 9 ! total reflection ( light1 :i* occurs :5 a beam ( light )9 a m$ium falls v obliquely ^u ! b\nd>y sep>at+ x f a r>] m$ium4 ,! g5]al law is t :5 a ray /rikes ! limit betwe5 two m$ia ( diff]5t refractive indices1 "p ( ! light is reflect$ & "p is refract$2 b :5 ! obliquity ( ! ray )9 ! d5s] m$ium passes beyond a c]ta9 po9t1 !re is a sudd5 app>5t brea* ( cont9uity1 & ! :ole ( ! light is reflect$4 ,a cle> reason c be giv5 = ?is exceptional conduct ( ! light4 ,accord+ to ! law ( refraction1 ! s9e ( ! angle ( incid5ce be>s a fix$ ratio to ! s9e ( ! angle ( refraction1 s t ! great] ( ! two angles1 :i* is always t 9 ! less d5se m$ium1 may increase up to a "r angle2 b :5 ! m$ia diff] 9 refractive p[]1 ! less angle _c become a "r angle1 z ?is w\ld require ! s9e ( an angle to be great] ?an ! radius4 ,x might seem t ?is is an exception ( ! k9d describ$ bel[ z a limit+ exception1 by :i* a law is %[n to be inapplicable beyond c]ta9 limits2 b 9 ! explanation ( ! exception accord+ to ! undulatory !ory1 we f9d t !re is really no brea* ( ! g5]al law4 ,:5 an undulation /rikes a po9t 9 a b\nd+ surface1 sph]ical waves are produc$ & spread f ! po9t4 ,! refract$ ray is ! resultant ( an inf9ite numb] ( su* sph]ical waves1 & ! b5d+ ( ! ray at ! common surface ( two m$ia dep5ds ^u ! comp>ative velocities ( propagation ( ! undulations 9 ^? m$ia4 ,b if a ray falls v obliquely ^u ! surface ( a r>] m$ium1 ! waves proce$+ f successive po9ts ( ! surface spread s rapidly z nev] to int]sect1 & no resultant wave w !n be produc$4 ,we ?us p]ceive t f simil> ma!matical conditions arise di/9ct app>5t effects4 ,!re occur f "t to "t failures 9 our be/ gr\nd$ pr$ictions4 ,a comet1 ( :i* ! orbit has be5 well det]m9$1 may fail1 l ,lexell's ,comet1 to appe> at ! appo9t$ "t & place 9 ! heav5s4 ,9 ! pres5t day we %\ld n all[ su* an exception to our successful pr$ictions to weigh aga9/ our belief 9 ! !ory ( gravitation1 b %\ld assume t "s unkn[n body _h ?r\gh ! action ( gravitation deflect$ ! comet4 ,z ,clairaut rem>k$1 9 publi%+ 8 calculations conc]n+ ! expect$ reappe>ance ( ,halley's ,comet1 a body :i* passes into regions s remote1 & :i* is hidd5 f our view dur+ su* long p]iods1 might be expos$ to ! influ5ce ( =ces totally unkn[n to u1 su* z ! attraction ( o!r comets1 or ( planets too f> remov$ f ! sun to be ev] p]ceiv$ by u4 ,9 ! case ( ,lexell's ,comet x 0 aft]w>ds %[n1 curi\sly en\gh1 t its appe>ance 0 n "o ( a regul> s]ies ( p]iodical returns )9 ! sph]e ( our vision1 b a s+le exceptional visit nev] to be repeat$1 & probably due to ! p]turb+ p[]s ( ,jupit]4 ,?is solit>y visit became a /rong confirmation ( ! law ( gravity ) :i* x seem$ to be 9 conflict4 99,s+ul> ,exceptions499 ,among ! mo/ int]e/+ ( app>5t exceptions are ^? :i* ,i call 99s+ul> exceptions991 because !y are m or less analog\s to ! s+ul> cases or solutions :i* occur 9 ma!matical sci5ce4 ,a g5]al ma!matical law embraces an inf9ite multitude ( cases :i* p]fectly agree ) ea* o!r 9 a c]ta9 respect4 ,x may nev]!less happ5 t a s+le case1 :ile really obey+ ! g5]al law1 /&s out z app>5tly diff]5t f all ! re/4 ,! rotation ( ! e>? ^u its axis gives to all ! />s an app>5t motion ( rotation f ea/ to we/2 b :ile c\ntless ?\s&s obey ! rule1 ! ,pole ,/> alone seems to break x4 ,exact obs]vations inde$ %[ t x also revolves 9 a small circle1 b a /> might happ5 = a %ort "t to exi/ s close to ! pole t no appreciable *ange ( place w\ld be caus$ by ! e>?'s rotation4 ,x w\ld !n con/itute a p]fect s+ul> exception2 :ile really obey+ ! law1 x w\ld break ! t]ms 9 :i* x is usually /at$4 ,9 ! same way ! poles ( e revolv+ body are s+ul> po9ts4 ,:5ev] ! laws ( nature are r$uc$ to a ma!matical =m we may expect to meet ) s+ul> cases1 &1 z all ! physical sci5ces w meet 9 ! ma!matical pr9ciples ( me*anics1 !re is no "p ( nature :]e we may n enc\nt] !m4 ,9 me*anical sci5ce ! motion ( rotation may be consid]$ an exception to ! motion ( translation4 ,x is a g5]al law t any numb] ( p>allel =ces1 :e!r act+ 9 ! same or opposite directions1 w h a resultant :i* may be sub/itut$ = !m ) l effect4 ,?is resultant w be equal to ! algebraic sum ( ! =ces1 or ! diff]5ce ( ^? act+ 9 "o direction & ! o!r2 x w pass ?r\gh a po9t :i* is det]m9$ by a simple =mula1 & :i* may be describ$ z ! mean po9t ( all ! po9ts ( application ( ! p>allel =ces 7p4 #cfd74 ,?us we readily det]m9e ! resultant ( p>allel =ces except 9 "o peculi> case1 namely1 :5 two =ces are equal & opposite b n 9 ! same /raight l9e4 ,be+ equal & opposite ! am\nt ( ! resultant is no?+1 yet1 z ! =ces are n 9 ! same /raight l9e1 !y d n balance ea* o!r4 ,exam9+ ! =mula = ! po9t ( application ( ! resultant1 we f9d t x gives an inf9itely great magnitude1 s t ! resultant is no?+ at all1 & acts at an inf9ite di/ance1 :i* is practically ! same z to say t !re is no resultant4 ,two su* =ces con/itute :at is kn[n 9 me*anical sci5ce z a 99c\ple991 :i* occasions rotatory in/ead ( rectil9e> motion1 & c only be neutralis$ by an equal & opposite c\ple ( =ces4 ,! be/ in/ances ( s+ul> exceptions are furni%$ by ! sci5ce ( optics4 ,x is a g5]al law t 9 pass+ ?r\gh transp>5t m$ia ! plane ( vibration ( pol>is$ light rema9s un*ang$4 ,b 9 c]ta9 liquids1 "s peculi> cry/als ( qu>tz1 & transp>5t solid m$ia subject$ to a magnetic /ra91 z 9 ,f>aday's exp]im5t 7pp4 #ehh1 #fcj71 ! plane ( pol>isation is rotat$ 9 a screw-l mann]4 ,?is effect is s entirely 99sui g5]is991 s unlike any o!r ph5om5a 9 nature1 z to appe> truly exceptional2 yet ma!matical analysis %[s x to be only a s+le case ( mu* m g5]al laws4 ,z /at$ by ,?omson & ,tait1#edd x arises f ! composition ( two uni=m circul> motions4 ,if :ile a po9t is mov+ r\nd a circle1 ! c5tre ( t circle move ^u ano!r circle1 a great v>iety ( curi\s curves w be produc$ accord+ z we v>y ! dim5sions ( ! circles1 ! rapidity or ! direction ( ! motions4 ,:5 ! two circles are exactly equal1 ! rapidities ne>ly s1 & ! directions opposite1 ! po9t w be f\nd to move gradually r\nd ! c5tre ( ! /ation>y circle1 & describe a curi\s />-l figure connect$ ) ! molecul> motions out ( :i* ! rotational p[] ( ! m$ia rises4 ,among o!r s+ul> exceptions 9 optics may be plac$ ! conical refraction ( light1 already notic$ 7p4 #edj71 aris+ f ! peculi> =m assum$ by a wave ( light :5 pass+ ?r\gh c]ta9 d\ble-refract+ cry/als4 ,! laws obey$ by ! wave are exactly ! same z 9 o!r cases1 yet ! results are entirely 99sui g5]is994 ,s f> are su* cases f contradict+ ! law ( ord9>y cases1 t !y af=d ! be/ opportunities = v]ification4 #edd 99,treatise on ,natural ,philosophy991 vol4 i4 p4 #ej4 ,9 a/ronomy s+ul> exceptions might occur1 & 9 an approximate mann] !y d occur4 ,we may po9t to ! r+s ( ,saturn z objects :i*1 ?\gh und\bt$ly obey+ ! law ( gravity1 are yet unique1 z f> z our obs]vation ( ! univ]se has gone4 ,!y agree1 inde$1 ) ! o!r bodies ( ! planet>y sy/em 9 ! /ability ( _! movem5ts1 :i* nev] div]ge f> f ! mean position4 ,!re seems to be little d\bt t ^! r+s are compos$ ( sw>ms ( small meteoric /ones2 =m]ly !y 7 ?\ght to be solid cont9u\s r+s1 & ma!maticians prov$ t if s con/itut$ an entirely exceptional ev5t might h happ5$ "u c]ta9 circum/ances4 ,_h ! r+s be5 exactly uni=m all r\nd1 & ) a c5tre ( gravity co9cid+ = a mom5t ) t ( ,saturn1 a s+ul> case ( un/able equilibrium w\ld h aris51 necess>ily result+ 9 ! sudd5 collapse ( ! r+s1 & ! fall ( _! debris ^u ! surface ( ! planet4 ,?us 9 "o s+le case ! !ory ( gravity w\ld give a result :olly unlike any?+ else kn[n 9 ! me*anism ( ! heav5s4 ,x is possible t we might meet ) s+ul> exceptions 9 cry/allography4 ,if a cry/al ( ! second or dimetric sy/em1 9 :i* ! ?ird axis is usually unequal to ei!r ( ! o!r two1 happ5$ to h ! ?ree axes equal1 x might be mi/ak5 = a cry/al ( ! cubic sy/em1 b w\ld exhibit diff]5t faces & dissimil> prop]ties4 ,!re is1 aga91 a possible class ( dicl9ic cry/als 9 :i* two axes are at "r angles & ! ?ird axis incl9$ to ! o!r two4 ,?is class is *iefly rem>kable = its non-exi/5ce1 s9ce no cry/als h yet be5 prov$ to h su* axes4 ,x seems likely t ! class w\ld con/itute only a s+ul> case ( ! m g5]al tricl9ic sy/em1 9 :i* all ?ree axes are incl9$ to ea* o!r at v>i\s angles4 ,n[ if ! dicl9ic =m 7 m]ely accid5tal1 & n produc$ by any g5]al law ( molecul> con/itution1 its actual occurr5ce w\ld be inf9itely improbable1 j z x is inf9itely improbable t any /> %\ld indicate ! ,nor? ,pole ) p]fect exactness4 ,9 ! curves d5ot+ ! relation betwe5 ! temp]ature & pressure ( wat] !re is1 z %[n by ,pr(essor ,j4 ,?omson1 "o v rem>kable po9t entirely unique1 at :i* alone wat] c rema9 9 ! ?ree conditions ( gas1 liquid1 & solid 9 ! same vessel4 ,x is ! triple po9t at :i* ?ree l9es meet1 namely 7#a7 ! /eam l9e1 :i* %[s at :at temp]atures & pressures wat] is j ^u ! po9t ( becom+ gase\s2 7#b7 ! ice l9e1 %[+ :5 ice is j ab\t to melt2 & 7#c7 ! ho>-fro/ l9e1 :i* simil>ly indicates ! pressures & temp]atures at :i* ice is capable ( pass+ directly into ! /ate ( gase\s vap\r4#ede #ede ,maxwell's 99,!ory ( ,heat991 7#ahga71 p4 #age4 99,div]g5t ,exceptions499 ,closely analog\s to s+ul> exceptions are ^? div]g5t exceptions1 9 :i* a ph5om5on manife/s itself 9 unusual magnitude or "*1 )\t becom+ subject to peculi> laws4 ,?us 9 ?r[+ t5 co9s1 x happ5$ 9 f\r cases out ( #b1jdh ?r[s1 t all ! co9s fell ) heads upp]mo/ 7p4 #bjh72 ^! w\ld usually be reg>d$ z v s+ul> ev5ts1 &1 accord+ to ! !ory ( probabilities1 !y w\ld be r>e2 yet !y proce$ only f an unusual conjunction ( accid5tal ev5ts1 & f no really exceptional causes4 ,9 all classes ( natural ph5om5a we may expect to meet ) simil> div]g5cies f ! av]age1 sometimes due m]ely to ! pr9ciples ( probability1 sometimes to deep] reasons4 ,among e l>ge collection ( p]sons1 we %all probably f9d "s p]sons :o are rem>kably l>ge or rem>kably small1 giants or dw>fs1 :e!r 9 bodily or m5tal con=mation4 ,su* cases appe> to be n m]e 99lusus natur991 s9ce !y occur ) a frequ5cy closely accordant ) ! law ( error or div]g5ce f an av]age1 z %[n by ,quetelet & ,mr4 ,galton4#edf ,! rise ( g5ius1 & ! occurr5ce ( extraord9>y musical or ma!matical faculties1 are attribut$ by ,mr4 ,galton to ! same pr9ciple ( div]g5ce4 #edf ,galton1 on ! ,height & ,weight ( ,boys4 99,j\rnal ( ! ,an?ropological ,in/itute991 #ahge1 p4 #agd4 ,:5 sev]al di/9ct =ces happ5 to concur toge!r1 we may h surpris+ or al>m+ results4 ,great /orms1 floods1 dr\ghts1 & o!r extreme deviations f ! av]age condition ( ! atmosph]e ?us arise4 ,!y mu/ be expect$ to happ5 f "t to "t1 & w yet be v infrequ5t comp>$ ) m9or di/urbances4 ,!y are n anomal\s b only extreme ev5ts1 analog\s to extreme runs ( luck4 ,!re seems1 inde$1 to be a fallaci\s impression 9 ! m9ds ( _m p]sons1 t ! !ory ( probabilities necessitates uni=mity 9 ! happ5+ ( ev5ts1 s t 9 ! same space ( "t !re w always be ne>ly ! same numb] ( railway accid5ts & murd]s4 ,buckle has sup]ficially rem>k$ ^u ! con/ancy ( su* ev5ts z asc]ta9$ by ,quetelet1 & "s ( 8 read]s acquire ! false notion t !re is a my/]i\s inexorable law produc+ uni=mity 9 human affairs4 ,b no?+ c be m oppos$ to ! tea*+s ( ! !ory ( probability1 :i* always contemplates ! occurr5ce ( unusual runs ( luck4 ,t !ory %[s ! great improbability t ! numb] ( railway accid5ts p] mon? %\ld be always equal1 or ne>ly s4 ,! public att5tion is /rongly attract$ to any unusual conjunction ( ev5ts1 & !re is a fallaci\s t5d5cy to suppose t su* conjunction mu/ be due to a peculi> new cause com+ into op]ation4 ,unless x c be cle>ly %[n t su* unusual conjunctions occur m frequ5tly ?an !y %\ld d accord+ to ! !ory ( probabilities1 we %\ld reg>d !m z m]ely div]g5t exceptions4 ,eclipses & rem>kable conjunctions ( ! heav5ly bodies may also be reg>d$ z results ( ord9>y laws :i* nev]!less appe> to break ! regul> c\rse ( nature1 & nev] fail to excite surprise4 ,su* ev5ts v>y greatly 9 frequ5cy4 ,"o or o!r ( ! satellites ( ,jupit] is eclips$ almo/ e day1 b ! simultane\s eclipse ( ?ree satellites c only take place1 accord+ to ! calculations ( ,w>g5t91 aft] ! lapse ( #a1cag1ijj ye>s4 ,! relations ( ! f\r satellites are s rem>kable1 t x is actually impossible1 accord+ to ! !ory ( gravity1 t !y %\ld all suff] eclipse simultane\sly4 ,b x may happ5 t :ile "s ( ! satellites are really eclips$ by ent]+ ,jupit]'s %ad[1 ! o!rs are ei!r occult$ or r5d]$ invisible by pass+ ov] 8 disk4 ,?us on f\r occasions1 9 #afha1 #ahjb1 #ahbf1 & #ahdc1 ,jupit] has be5 witness$ 9 ! s+ul> condition ( be+ app>5tly depriv$ ( satellites4 ,a close conjunction ( two planets always excites admiration1 ?\gh su* conjunctions mu/ occur at int]vals 9 ! ord9>y c\rse ( _! motions4 ,we _c wond] t :5 ?ree or f\r planets approa* ea* o!r closely1 ! ev5t is long rememb]$4 ,a mo/ rem>kable conjunction ( ,m>s1 ,jupit]1 ,saturn1 & ,m]cury1 :i* took place 9 ! ye> #bddf ,b4,c41 0 adopt$ by ! ,*9ese ,emp]or1 ,*u5 ,hio1 z a new epo* = ! *ronology ( 8 ,empire1 ?\gh !re is "s d\bt :e!r ! conjunction 0 really obs]v$1 or 0 calculat$ f ! suppos$ laws ( motion ( ! planets4 ,x is c]ta9 t on ! #aa? ,novemb]1 #aebd1 ! planets ,v5us1 ,jupit]1 ,m>s1 & ,saturn 7 se5 v close toge!r1 :ile ,m]cury 0 only di/ant by ab\t #af or ?irty app>5t diamet]s ( ! sun1 ?is conjunction be+ probably ! mo/ rem>kable :i* has occurr$ 9 hi/orical times4 ,among ! p]turbations ( ! planets we f9d div]g5t exceptions aris+ f ! peculi> accumulation ( effects1 z 9 ! case ( ! long inequality ( ,jupit] & ,saturn 7p4 #dee74 ,lev]ri] has %[n t !re is "o place betwe5 ! orbits ( ,m]cury & ,v5us1 & ano!r betwe5 ^? ( ,m>s & ,jupit]1 9 ei!r ( :i*1 if a small planet happ5$ to exi/1 x w\ld suff] comp>atively imm5se di/urbance 9 ! elem5ts ( its orbit4 ,n[ betwe5 ,m>s & ,jupit] !re d occur ! m9or planets1 ! orbits ( :i* are 9 _m cases exceptionally div]g5t4#edg #edg ,grant's 99,hi/ory ( ,physical ,a/ronomy991 p4 #aaf4 ,"u div]g5t exceptions we might place all or ne>ly all ! in/ances ( sub/ances possess+ physical prop]ties 9 a v high or l[ degree1 :i* 7 describ$ 9 ! *apt] on ,g5]alisation 7p4 #fjg74 ,quicksilv] is div]g5t among metals z reg>ds its melt+ po9t1 & potassium & sodium z reg>ds _! specific gravities4 ,mon/r\s productions & v>iations1 :e!r 9 ! animal or vegetable k+doms1 %\ld probably be assign$ to ?is class ( exceptions4 ,x is wor?y ( notice t ev5 9 su* a subject z =mal logic1 div]g5t exceptions seem to occur1 n ( c\rse due to *ance1 b exhibit+ 9 an unusual degree a ph5om5on :i* is m or less manife/$ 9 all o!r cases4 ,i po9t$ out 9 p4 #ada t propositions ( ! g5]al type ,a ,,bc 99bc99 are capable ( expression 9 six equival5t logical =ms1 s t !y manife/ 9 a high] degree ?an any o!r proposition yet discov]$ ! ph5om5on ( logical equival5ce4 99,accid5tal ,exceptions499 ,! ?ird & l>ge/ class ( exceptions conta9s ^? :i* arise f ! casual int]f]5ce ( extrane\s causes4 ,a law may be 9 op]ation1 &1 if s1 mu/ be p]fectly fulfill$2 b1 :ile we conceive t we are exam9+ its results1 we may h be=e u ! effects ( a diff]5t cause1 possess+ no connexion ) ! subject ( our inquiry4 ,! law is n really brok51 b at ! same "t ! suppos$ exception is n illusory4 ,x may be a ph5om5on :i* _c occur b "u ! condition ( ! law 9 "q1 yet !re has be5 su* int]f]5ce t !re is an app>5t failure ( sci5ce4 ,!re is1 = in/ance1 no subject 9 :i* m rigor\s & inv>iable laws h be5 e/abli%$ ?an 9 cry/allography4 ,z a g5]al rule1 ea* *emical sub/ance possesses its own def9ite =m1 by :i* x c be infallibly recognis$2 b ! m9]alogi/ has to be on 8 gu>d aga9/ :at are call$ 99pseudomorphic99 cry/als4 ,9 "s circum/ances a sub/ance1 hav+ assum$ its prop] cry/all9e =m1 may aft]w>ds und]go *emical *ange2 a new +r$i5t may be add$1 a =m] "o remov$1 or "o elem5t may be sub/itut$ = ano!r4 ,9 calcium c>bonate ! c>bonic acid is sometimes replac$ by sulphuric acid1 s t we f9d gypsum 9 ! =m ( calcite2 o!r cases are kn[n :]e ! *ange is inv]t$ & calcite is f\nd 9 ! =m ( gypsum4 ,mica1 talc1 /eatite1 hematite1 are o!r m9]als subject to ^! curi\s transmutations4 ,sometimes a cry/al emb$d$ 9 a matrix is entirely dissolv$ away1 & a new m9]al is subsequ5tly deposit$ 9 ! cavity z 9 a m\ld4 ,qu>tz is ?us f\nd ca/ 9 _m =ms :olly unnatural to x4 ,a /ill m p]plex+ case sometimes occurs4 ,calcium c>bonate is capable ( assum+ two di/9ct =ms ( cry/allisation1 9 :i* x be>s respectively ! names ( calcite & arragonite4 ,n[ arragonite1 :ile reta9+ its outw>d =m un*ang$1 may und]go an int]nal molecul> *ange into calcite1 z indicat$ by ! alt]$ cleavage4 ,?us we may come across cry/als app>5tly ( arragonite1 :i* seem to break all ! laws ( cry/allography1 by possess+ ! cleavage ( a diff]5t sy/em ( cry/allisation4 ,"s ( ! mo/ inv>iable laws ( nature are disguis$ by int]f]5ce ( unlook$-= causes4 ,:ile ! b>omet] 0 yet a new & curi\s subject ( inve/igation1 its !ory1 z /at$ by ,torricelli & ,pascal1 seem$ to be contradict$ by ! fact t 9 a well-con/ruct$ in/rum5t ! m]cury w\ld (t5 /& f> above #ca in*es 9 height4 ,boyle %[$#edh t m]cury c\ld be made to /& z high z #ge in*es 9 a p]fectly cleans$ tube1 or ab\t two & a half times z high z c\ld be due to ! pressure ( ! atmosph]e4 ,_m !ories ab\t ! pressure ( imag9>y fluids 7 9 consequ5ce put =?1#edi & ! subject 0 involv$ 9 mu* confusion until ! adhesive or cohesive =ce betwe5 glass & m]cury1 :5 br\ght into p]fect contact1 0 po9t$ out z ! real int]f]+ cause4 ,x seems to me1 h[ev]1 t ! ph5om5on is n ?or\ghly und]/ood z yet4 #edh 99,disc\rse to ! ,royal ,society991 #bh? ,may1 #afhd4 #edi ,rob]t ,hooke's 99,po/hum\s ,works991 p4 #cfe4 ,gay-,lussac obs]v$ t ! temp]ature ( boil+ wat] 0 v diff]5t 9 "s k9ds ( vessels f :at x 0 9 o!rs4 ,x is only :5 9 contact ) metallic surfaces or %>ply brok5 edges t ! temp]ature is fix$ at #ajj ,c4 ,! susp5d$ freez+ ( liquids is ano!r case :]e ! action ( a law ( nature appe>s to be int]rupt$4 ,sph]oidal ebullition 0 at fir/ sight a mo/ anomal\s ph5om5on2 x 0 almo/ incr$ible t wat] %\ld n boil 9 a r$-hot vessel1 or t ice c\ld actually be produc$ 9 a r$-hot crucible4 ,^! p>adoxical results are n[ fully expla9$ z due to ! int]position ( a non-conduct+ film ( vap\r betwe5 ! globule ( liquid & ! sides ( ! vessel4 ,! feats ( conjurors :o h&le liquid metals are acc\nt$ = 9 ! same mann]4 ,at "o "t ! 99passive /ate99 ( /eel 0 reg>d$ z entirely anomal\s4 ,x may be assum$ z a g5]al law t :5 pieces ( electro-negative & electro-positive metal are plac$ 9 nitric acid1 & made to t\* ea* o!r1 ! electro-negative metal w und]go rapid solution4 ,b :5 iron is ! electro-negative & plat9um ! electro-positive1 ! solution ( ! iron entirely & abruptly ceases4 ,f>aday +5i\sly prov$ t ?is effect is due to a ?9 film ( oxide ( iron1 :i* =ms ^u ! surface ( ! iron & protects x4#eej #eej 99,exp]im5tal ,rese>*es 9 ,electricity991 vol4 ii4 pp4 #bdj-bde4 ,! law ( gravity is s simple1 & disconnect$ f ! o!r laws ( nature1 t x nev] suff]s any di/urbance1 & is 9 no way disguis$1 b by ! complication ( its own effects4 ,x is o!rwise ) ^? second>y laws ( ! planet>y sy/em :i* h only an empirical basis4 ,! fact t all ! long kn[n planets & satellites h a simil> motion f we/ to ea/ is n necessitat$ by any pr9ciples ( me*anics1 b po9ts to "s common condition exi/+ 9 ! nebul\s mass f :i* our sy/em has be5 evolv$4 ,! retrograde motions ( ! satellites ( ,uranus con/itut$ a di/9ct brea* 9 ?is law ( uni=m direction1 :i* became all ! m int]e/+ :5 ! s+le satellite ( ,neptune 0 also f\nd to be retrograde4 ,x n[ became probable1 z ,bad5 ,p[ell well obs]v$1 t ! anomaly w\ld cease to be s+ul>1 & become a case ( ano!r law1 po9t+ to "s g5]al int]f]5ce :i* has tak5 place on ! b\nds ( ! planet>y sy/em4 ,n only h ! satellites suff]$ f ?is p]turbance1 b ,uranus is also anomal\s 9 hav+ an axis ( rotation ly+ ne>ly 9 ! ecliptic2 & ,neptune con/itutes a p>tial exception to ! empirical law ( ,bode conc]n+ ! di/ances ( ! planets1 :i* circum/ance may possibly be due to ! same di/urbance4 ,geology is a sci5ce 9 :i* accid5tal exceptions are likely to occur4 ,only :5 we f9d /rata 9 _! orig9al relative positions c we surely inf] t ! ord] ( succession is ! ord] ( "t4 ,b x n uncommonly happ5s t /rata are inv]t$ by ! b5d+ & d\bl+ action ( extreme pressure4 ,l&slips may c>ry "o body ( rock into proximity ) an unrelat$ s]ies1 & produce results app>5tly inexplicable4#eea ,floods1 /reams1 iceb]gs1 & o!r casual ag5ts1 may lodge rema9s 9 places :]e !y w\ld be :olly unexpect$4 ,?\gh su* int]f]+ causes h be5 sometimes wrongly suppos$ to expla9 important discov]ies1 ! geologi/ mu/ be> ! possibility ( int]f]5ce 9 m9d4 ,sc>cely m ?an a c5tury ago x 0 held t fossils 7 accid5tal productions ( nature1 m]e =ms into :i* m9]als _h be5 %ap$ by no peculi> cause4 ,voltaire appe>s n to h accept$ su* an explanation2 b fe>+ t ! occurr5ce ( fossil fi%es on ! ,alps w\ld support ! ,mosaic acc\nt ( ! deluge1 he did n hesitate to attribute !m to ! rema9s ( fi%es accid5tally br\ght !re by pilgrims4 ,9 ar*ological inve/igations ! greate/ caution is requisite 9 all[+ = second>y burials 9 anci5t tombs & tumuli1 = imitations1 =g]ies1 casual co9cid5ces1 di/urbance by subsequ5t races or by o!r ar*ologi/s4 ,9 common life extraord9>y ev5ts w happ5 f "t to "t1 z :5 a %eph]dess 9 ,france 0 a/oni%$ at an iron *a9 fall+ out ( ! sky close to h]1 ! fact be+ t ,gay-,lussac _h ?r[n x out ( 8 balloon1 :i* 0 pass+ ov] h] head at ! "t4 #eea ,mur*ison's 99,silurian ,sy/em991 vol4 ii4 p4 #gcc1 c4 99,novel & ,unexpla9$ ,exceptions499 ,:5 a law ( nature appe>s to fail because "s o!r law has int]f]$ ) its action1 two cases may pres5t !mselves2--! int]f]+ law may be a kn[n "o1 or x may h be5 previ\sly undetect$4 ,9 ! fir/ case1 :i* we h suffici5tly consid]$ 9 ! prec$+ section1 we h no?+ to d b calculate z exactly z possible ! am\nt ( int]f]5ce1 & make all[ance = x2 ! app>5t failure ( ! law "u exam9ation %\ld !n disappe>4 ,b 9 ! second case ! results may be mu* m important4 ,a ph5om5on :i* _c be expla9$ by any kn[n laws may indicate ! int]f]5ce ( undiscov]$ natural =ces4 ,! anci5ts c\ld n help p]ceiv+ t ! g5]al t5d5cy ( bodies d[nw>ds fail$ 9 ! case ( ! load/one1 nor w\ld ! doctr9e ( ess5tial lightness expla9 ! exception1 s9ce ! sub/ance drawn upw>ds by ! load/one is a heavy metal4 ,we n[ see t !re 0 no brea* 9 ! p]fect g5]ality ( ! law ( gravity1 b t a new =m ( en]gy manife/$ itself 9 ! load/one = ! fir/ "t4 ,o!r sci5ces %[ u t laws ( nature1 rigor\sly true & exact1 may be develop$ by ^? :o are ignorant ( m complex ph5om5a involv$ 9 _! application4 ,newton's compreh5sion ( geometrical optics 0 suffici5t to expla9 all ! ord9>y refractions & reflections ( light4 ,! simple laws ( ! b5d+ ( rays apply to all rays1 :atev] ! "* ( ! undulations compos+ !m4 ,newton suspect$ ! exi/5ce ( o!r classes ( ph5om5a :5 he spoke ( rays z 99hav+ sides992 b x rema9$ = lat] exp]im5tali/s to %[ t light is a transv]se undulation1 l ! b5d+ ( a rod or cord4 ,dalton's atomic !ory is d\btless true ( all *emical comp\nds1 & ! ess5ce ( x is t ! same comp\nd w always be f\nd to conta9 ! same elem5ts 9 ! same def9ite proportions4 ,pure calcium c>bonate conta9s #dh p>ts by weight ( oxyg5 to #dj ( calcium & #ab ( c>bon4 ,b :5 c>eful analyses 7 made ( a great _m m9]als1 ?is law appe>$ to fail4 ,:at 0 unque/ionably ! same m9]al1 judg+ by its cry/all9e =m & physical prop]ties1 w\ld give v>y+ proportions ( its compon5ts1 & w\ld sometimes conta9 unusual elem5ts :i* yet c\ld n be set d[n z m]e impurities4 ,dolomite1 = in/ance1 is a comp\nd ( ! c>bonates ( magnesia & lime1 b specim5s f diff]5t places d n exhibit any fix$ ratio betwe5 ! lime & magnesia4 ,su* facts c\ld be reconcil$ ) ! laws ( ,dalton only by suppos+ ! int]f]5ce ( a new law1 t ( ,isomorphism4 ,x is n[ e/abli%$ t c]ta9 elem5ts are relat$ to ea* o!r1 s t !y c1 z x 71 /ep into ea* o!r's places )\t app>5tly alt]+ ! %apes ( ! cry/als :i* !y con/itute4 ,! c>bonates ( iron1 calcium1 & magnesium1 are ne>ly id5tical 9 _! cry/all9e =ms1 h5ce !y may cry/allise toge!r 9 h>mony1 produc+ mix$ m9]als ( consid]able complexity1 :i* nev]!less p]fectly v]ify ! laws ( equival5t proportions4 ,?is pr9ciple ( isomorphism once e/abli%$1 n only expla9s :at 0 =m]ly a /umbl+-block1 b gives valuable aid to *emi/s 9 decid+ ^u ! con/itution ( new salts1 s9ce comp\nds ( isomorph\s elem5ts :i* h id5tical cry/all9e =ms mu/ possess correspond+ *emical =mul4 ,we may expect t f "t to "t extraord9>y ph5om5a w be discov]$1 & w lead to new views ( nature4 ,! rec5t obs]vation1 = in/ance1 t ! resi/ance ( a b> ( sel5ium to a curr5t ( electricity is affect$ 9 an extraord9>y degree by rays ( light fall+ ^u ! sel5ium1 po9ts to a new relation betwe5 light & electricity4 ,! allotropic *anges :i* sulphur1 sel5ium1 & phosphorus und]go by an alt]ation 9 ! am\nt ( lat5t heat :i* !y conta91 w probably lead at "s future "t to important inf]5ces conc]n+ ! molecul> con/itution ( solids & liquids4 ,! curi\s sub/ance ozone has p]plex$ _m *emi/s1 & ,&rews & ,tait ?\ght t x af=d$ evid5ce ( ! decomposition ( oxyg5 by ! electric dis*>ge4 ,! rese>*es ( ,sir ,b4 ,c4 ,brodie negative ?is notion1 & af=d evid5ce ( ! real con/itution ( ! sub/ance1#eeb :i* /ill1 h[ev]1 rema9s exceptional 9 its prop]ties & relations1 & af=ds a hope ( important discov]ies 9 *emical !ory4 #eeb 99,philosophical ,transactions99 7#ahgb71 vol4 clxii4 ,no4 #bc4 99,limit+ ,exceptions499 ,we pass to cases :]e exceptional ph5om5a are actually irreconcilable ) a law ( nature previ\sly reg>d$ z true4 ,error mu/ n[ be all[$ to h be5 committ$1 b ! error may be m or less ext5sive4 ,x may happ5 t a law hold+ rigor\sly true ( ! facts actually "u notice _h be5 ext5d$ by g5]alisation to o!r s]ies ( facts !n unexam9$4 ,subsequ5t inve/igation may %[ ! falsity ( ?is g5]alisation1 & ! result mu/ be to limit ! law = ! future to ^? objects ( :i* x is really true4 ,! contradiction to our previ\s op9ions is p>tial & n total4 ,newton laid d[n z a result ( exp]im5t t e ray ( homog5e\s light has a def9ite refrangibility1 :i* x pres]ves ?r\gh\t its c\rse until ext+ui%$4 ,?is is "o case ( ! g5]al pr9ciple ( undulatory movem5t1 :i* ,h]s*el /at$ "u ! title 8,pr9ciple ( ,=c$ ,vibrations0 7p4 #dea71 & ass]t$ to be absolutely )\t exception4 ,b ,h]s*el himself describ$ 9 ! 99,philosophical ,transactions99 = #ahde a curi\s appe>ance 9 a solution ( qu99e2 z view$ by transmitt$ light ! solution appe>$ col\rless1 b 9 c]ta9 aspects x exhibit$ a beautiful cele/ial blue t9t4 ,curi\sly en\gh ! col\r is se5 only 9 ! fir/ portion ( liquid :i* ! light ent]s4 ,simil> ph5om5a 9 fluor-sp> _h be5 describ$ by ,brew/] 9 #ahch4 ,pr(essor ,/okes1 hav+ m9utely inve/igat$ ! ph5om5a1 discov]$ t !y 7 m or less pres5t 9 almo/ all vegetable infusions1 & 9 a numb] ( m9]al sub/ances4 ,he came to ! conclusion t ?is ph5om5on1 call$ by him ,fluoresc5ce1 c\ld only be expla9$ by an alt]ation 9 ! refrangibility ( ! rays ( light2 he ass]ts t light-rays ( v %ort l5g? ( vibration 9 fall+ ^u c]ta9 atoms excite undulations ( great] l5g?1 9 opposition to ! pr9ciple ( =c$ vibrations4 ,no complete explanation ( ! mode ( *ange is yet possible1 because x dep5ds ^u ! intimate con/itution ( ! atoms ( ! sub/ances conc]n$2 b ,pr(essor ,/okes believes t ! pr9ciple ( =c$ vibrations is true only s long z ! excursions ( an atom are v small comp>$ ) ! magnitude ( ! complex molecules4#eec #eec 99,philosophical ,transactions99 7#aheb71 vol4 cxlii4 pp4 #dfe1 #edh1 c4 ,x is well kn[n t 9 ,caloresc5ce ! refrangibility ( rays is increas$ & ! wave-l5g? dim9i%$4 ,rays ( obscure heat & l[ refrangibility may be conc5trat$ s z to heat a solid sub/ance1 & make x give out rays belong+ to any "p ( ! spectrum1 & x seems probable t ?is effect arises f ! impact ( di/9ct b conflict+ atoms4 ,nor is x 9 light only t we discov] limit+ exceptions to ! law ( =c$ vibrations2 = if we notice g5tle waves lapp+ ^u ! /ones at ! edge ( a lake we %all see t ea* l>g] wave 9 break+ ^u a /one gives rise to a s]ies ( small] waves4 ,?us !re is con/antly 9 progress a degradation 9 ! magnitude ( wat]-waves4 ,! pr9ciple ( =c$ vibrations seems !n to be too g5]ally /at$ by ,h]s*el1 b x mu/ be a difficult "q ( me*anical !ory to discrim9ate ! circum/ances 9 :i* x does & does n hold true4 ,we sometimes =esee ! possible exi/5ce ( exceptions yet unkn[n by exp]i5ce1 & limit ! /atem5t ( our discov]ies accord+ly4 ,ext5sive inquiries h %[n t all sub/ances yet exam9$ fall into "o ( two classes2 !y are all ei!r f]ro-magnetic1 t is1 magnetic 9 ! same way z iron1 or !y are diamagnetic l bismu?4 ,b x does n foll[ t e sub/ance mu/ be f]ro-magnetic or diamagnetic4 ,! magnetic prop]ties are %[n by ,sir ,w4 ,?omson#eed to dep5d ^u ! specific inductive capacities ( ! sub/ance 9 ?ree rectangul> directions4 ,if ^! inductive capacities are all positive1 we h a f]ro-magnetic sub/ance2 if negative1 a diamagnetic sub/ance2 b if ! specific inductive capacity 7 positive 9 "o direction & negative 9 ! o!rs1 we %\ld h an exception to previ\s exp]i5ce1 & c\ld n place ! sub/ance "u ei!r ( ! pres5t recognis$ classes4 #eed 99,philosophical ,magaz9e991 #d? ,s]ies1 vol4 i4 p4 #ahb4 ,s _m gases h be5 r$uc$ to ! liquid /ate1 & s _m solids fus$1 t sci5tific m5 r ha/ily adopt$ ! g5]alisation t all sub/ances c\ld exi/ 9 all ?ree /ates4 ,a c]ta9 numb] ( gases1 su* z oxyg51 hydrog51 & nitrog51 h resi/$ all ef=ts to liquefy !m1 & x n[ seems probable f ! exp]im5ts ( ,dr4 ,&rews t !y are limit+ exceptions4 ,he f9ds t above #ca ,c4 c>bonic acid _c be liquefi$ by any pressure he c\ld apply1 :]eas bel[ ?is temp]ature liquefaction is always possible4 ,by analogy x becomes probable t ev5 hydrog5 might be liquefi$ if cool$ to a v l[ temp]ature4 ,we mu/ modify our previ\s views1 & ei!r ass]t t 99bel[ a c]ta9 critical temp]ature99 e gas may be liquefi$1 or else we mu/ assume t a highly cond5s$ gas is1 :5 above ! critical temp]ature1 undi/+ui%able f a liquid4 ,at ! same "t we h an explanation ( a rem>kable exception pres5t$ by liquid c>bonic acid to ! g5]al rule t gases exp& m by heat ?an liquids4 ,liquid c>bonic acid 0 f\nd by ,?ilori] 9 #ahce to exp& m ?an f\r times z mu* z air2 b by ! light ( ,&rews' exp]im5ts we le>n to reg>d ! liquid z r a highly cond5s$ gas ?an an ord9>y liquid1 & x is actually possible to r$uce ! gas to ! app>5tly liquid condition )\t any abrupt cond5sation4#eee #eee ,maxwell1 99,!ory ( ,heat991 p4 #abc4 ,limit+ exceptions occur mo/ frequ5tly 9 ! natural sci5ces ( ,botany1 ,zoology1 ,geology1 c41 ! laws ( :i* are empirical4 ,9 innum]able in/ances ! confid5t belief ( "o g5]ation has be5 falsifi$ by ! wid] obs]vation ( a succe$+ "o4 ,ari/otle confid5tly held t all swans are :ite1#eef & ! proposition seem$ true until n a hundr$ ye>s ago black swans 7 discov]$ 9 ,we/]n ,au/ralia4 ,9 zoology & physiology we may expect a fundam5tal id5tity to exi/ 9 ! vital processes1 b cont9ual discov]ies %[ t !re is no limit to ! app>5tly anomal\s exp$i5ts by :i* life is reproduc$4 ,alt]nate g5]ation1 f]tilisation = sev]al successive g5]ations1 h]maphroditism1 are oppos$ to all we %\ld expect f induction f\nd$ ^u ! high] animals4 ,b su* ph5om5a are only limit+ exceptions %[+ t :at is true ( "o class is n true ( ano!r4 ,9 c]ta9 ( ! cephalopoda we meet ! extraord9>y fact t an arm ( ! male is ca/ (f & lives indep5d5tly until x enc\nt]s ! female4 #eef 99,prior ,analytics991 ii4 #b1 #h1 & else:]e4 99,real ,exceptions to ,suppos$ ,laws499 ,! exceptions :i* we h la/ly to consid] are ! mo/ important ( all1 s9ce !y lead to ! entire rejection ( a law or !ory be=e accept$4 ,no law ( nature c fail2 !re are no su* ?+s z real exceptions to real laws4 ,:]e contradiction exi/s x mu/ be 9 ! m9d ( ! exp]im5tali/4 ,ei!r ! law is imag9>y or ! ph5om5a :i* conflict ) x2 if1 !n1 by our s5ses we satisfy ourselves ( ! actual occurr5ce ( ! ph5om5a1 ! law mu/ be reject$ z illusory4 ,! foll[]s ( ,ari/otle held t nature abhors a vacuum1 & ?us acc\nt$ = ! rise ( wat] 9 a pump4 ,:5 ,torricelli po9t$ out ! visible fact t wat] w\ld n rise m ?an #cc feet 9 a pump1 nor m]cury m ?an ab\t #cj in*es 9 a glass tube1 !y attempt$ to repres5t ^! facts z limit+ exceptions1 say+ t nature abhorr$ a vacuum to a c]ta9 ext5t & no fur!r4 ,b ! ,academicians del ,cim5to complet$ _! discomfiture by %[+ t if we remove ! pressure ( ! surr\nd+ air1 & 9 proportion z we remove x1 nature's feel+s ( abhorr5ce decrease & f9ally disappe> altoge!r4 ,ev5 ,ari/otelian doctr9es c\ld n /& su* direct contradiction4 ,lavoisi]'s ideas conc]n+ ! con/itution ( acids receiv$ complete refutation4 ,he nam$ oxyg5 ! 99acid g5]ator991 because he believ$ t all acids 7 comp\nds ( oxyg51 a g5]alisation bas$ on insuffici5t data4 ,b]?ollet1 z e>ly z #aghi1 prov$ by analysis t hydrog5 sulphide & prussic acid1 bo? cle>ly act+ ! "p ( acids1 7 devoid ( oxyg52 ! =m] might p]haps h be5 int]pret$ z a limit+ exception1 b :5 s p[]ful an acid z hydrog5 *loride 7muriatic acid7 0 f\nd to conta9 no oxyg5 ! !ory _h to be rel9qui%$4 ,b]zelius' !ory ( ! dual =mation ( *emical comp\nds met a simil> fate4 ,x is obvi\s t all conclusive 99exp]im5ta crucis99 con/itute real exceptions to ! suppos$ laws ( ! !ory :i* is ov]?r[n4 ,newton's corpuscul> !ory ( light 0 n reject$ on acc\nt ( its absurdity or inconceivability1 = 9 ^! respects x is1 z we h se51 f> sup]ior to ! undulatory !ory4 ,x 0 reject$ because c]ta9 small fr+es ( col\r did n appe> 9 ! exact place & ( ! exact size 9 :i* calculation %[$ t !y ought to appe> accord+ to ! !ory 7pp4 #eaf-eba74 ,"o s+le fact cle>ly irreconcilable ) a !ory involves its rejection4 ,9 ! great] numb] ( cases1 :at appe>s to be a fatal exception may be aft]w>ds expla9$ away z a s+ul> or disguis$ result ( ! laws ) :i* x seems to conflict1 or z due to ! int]f]5ce ( extrane\s causes2 b if we fail ?us to r$uce ! fact to congruity1 x rema9s m p[]ful ?an any !ories or any dogmas4 ,( late ye>s n a few ( ! fav\rite doctr9es ( geologi/s h be5 rudely de/roy$4 ,x 0 ! g5]al belief t human rema9s 7 to be f\nd only 9 ^? deposits :i* are actually 9 progress at ! pres5t day1 s t ! creation ( man appe>$ to h tak5 place 9 ?is geological age4 ,! discov]y ( a s+le work$ fl9t 9 old] /rata & 9 connexion ) ! rema9s ( ext9ct mammals 0 suffici5t to explode su* a doctr9e4 ,simil>ly1 ! op9ions ( geologi/s h be5 alt]$ by ! discov]y ( ! ,eozon 9 ! ,laur5tian rocks ( ,canada2 x 0 previ\sly held t no rema9s ( life occurr$ 9 any old] /rata ?an ^? ( ! ,cambrian sy/em4 ,z ! exam9ation ( ! /rata ( ! globe becomes m complete1 our views ( ! orig9 & succession ( life ^u ! globe mu/ und]go _m *anges4 99,unclass$ ,exceptions499 ,at e p]iod ( sci5tific progress !re w exi/ a multitude ( unexpla9$ ph5om5a :i* we "k n h[ to reg>d4 ,!y are ! out/&+ facts ^u :i* ! lab\rs ( inve/igators mu/ be ex]t$1--! ore f :i* ! gold ( future discov]y is to be extract$4 ,x might be ?\ght t1 z our k ( ! laws ( nature increases1 ! numb] ( su* exceptions %\ld decrease2 b1 on ! contr>y1 ! m we "k ! m !re is yet to expla94 ,?is arises f sev]al reasons2 9 ! fir/ place1 ! pr9cipal laws & =ces 9 nature are num]\s1 s t he :o be>s 9 m9d ! wond]fully l>ge numb]s develop$ 9 ! doctr9e ( comb9ations1 w anticipate ! exi/5ce ( imm5sely num]\s relations ( "o law to ano!r4 ,:5 we are once 9 possession ( a law1 we are pot5tially 9 possession ( all its consequ5ces2 b x does n foll[ t ! m9d ( man1 s limit$ 9 its p[]s & capacities1 c actually "w !m all out 9 detail4 ,j z ! ab]ration ( light 0 discov]$ empirically1 ?\gh x %\ld h be5 =ese51 s !re are multitudes ( unexpla9$ facts1 ! connexion ( :i* ) laws ( nature already kn[n to u1 we %\ld p]ceive1 7 we n h9d]$ by ! imp]fection ( our d$uctive p[]s4 ,b1 9 ! second place1 z w be m fully po9t$ out1 x is n to be suppos$ t we h approximat$ to an exhau/ive k ( nature's p[]s4 ,! mo/ famili> facts may teem ) indications ( =ces1 n[ secrets hidd5 f u1 because we h n m9d-direct$ eyes to discrim9ate !m4 ,! progress ( sci5ce w consi/ 9 ! discov]y f "t to "t ( new exceptional ph5om5a1 & _! assignm5t by degrees to "o or o!r ( ! heads already describ$4 ,:5 a new fact proves to be m]ely a false1 app>5t1 s+ul>1 div]g5t1 or accid5tal exception1 we ga9 a m m9ute & accurate acqua9tance ) ! effects ( laws already kn[n to exi/4 ,we h inde$ no addition to :at 0 implicitly 9 our possession1 b !re is mu* diff]5ce betwe5 kn[+ ! laws ( nature & p]ceiv+ all _! complicat$ effects4 ,%\ld a new fact prove to be a limit+ or real exception1 we h to alt]1 9 "p or 9 :ole1 our views ( nature1 & are sav$ f errors into :i* we _h fall54 ,la/ly1 ! new fact may come "u ! six? class1 & may ev5tually prove to be a novel ph5om5on1 indicat+ ! exi/5ce ( new laws & =ces1 complicat+ b n o!rwise int]f]+ ) ! effects ( laws & =ces previ\sly kn[n4 ,! be/ in/ance :i* ,i c f9d ( an unresolv$ exceptional ph5om5on1 consi/s 9 ! anomal\s vap\r-d5sities ( phosphorus1 ars5ic1 m]cury1 & cadmium4 ,x is "o ( ! mo/ important laws ( *emi/ry1 discov]$ by ,gay-,lussac1 t equal volumes ( gases exactly correspond to equival5t weights ( ! sub/ances4 ,nev]!less phosphorus & ars5ic give vap\rs exactly twice z d5se z !y %\ld d by analogy1 & m]cury & cadmium div]ge 9 ! o!r direction1 giv+ vap\rs half z d5se z we %\ld expect4 ,we _c treat ^! anomalies z limit+ exceptions1 & say t ! law holds true ( sub/ances g5]ally b n ( ^!2 = ! prop]ties ( gases 7p4 #fja71 usually admit ( ! wide/ g5]alisations4 ,besides1 ! precis5ess ( ! ratio ( div]g5ce po9ts to ! real obs]vance ( ! law 9 a modifi$ mann]4 ,we might endeav\r to r$uce ! exceptions by d\bl+ ! atomic weights ( phosphorus & ars5ic1 & halv+ ^? ( m]cury & cadmium4 ,b ?is /ep has be5 maturely consid]$ by *emi/s1 & is f\nd to conflict ) all ! o!r analogies ( ! sub/ances & ) ! pr9ciple ( isomorphism4 ,"o ( ! mo/ probable explanations is1 t phosphorus & ars5ic produce vap\r 9 an allotropic condition1 :i* might p]haps by int5se heat be resolv$ into a simpl] gas ( half ! d5sity2 b facts are want+ to support ?is hypo!sis1 & x _c be appli$ to ! o!r two exceptions )\t suppos+ t gases & vap\rs g5]ally are capable ( resolution into some?+ simpl]4 ,9 %ort1 *emi/s c at pres5t make no?+ ( ^! anomalies4 ,z ,h(mann says1 8,_! philosophical int]pretation belongs to ! future4444 ,!y may turn out to be typical facts1 r\nd :i* _m o!rs ( ! l k9d may come h]eaft] to be gr\p$2 & !y may prove to be alli$ ) special prop]ties1 or dep5d5t on p>ticul> conditions z yet unsuspect$40#eeg #eeg ,h(mann's 99,introduction to ,*emi/ry991 p4 #aih4 ,x w\ld be easy to po9t out a great numb] ( o!r unexpla9$ anomalies4 ,physici/s ass]t1 z an absolutely univ]sal law1 t 9 liquefaction heat is absorb$2#eeh yet sulphur is at lea/ an app>5t exception4 ,! two sub/ances1 sulphur & sel5ium1 are1 9 fact1 v anomal\s 9 _! relations to heat4 ,sulphur may be said to h two melt+ po9ts1 =1 ?\gh liquid l wat] at #abj ,c41 x becomes q ?ick & t5aci\s betwe5 #bba & #bdi1 & melts aga9 at a high] temp]ature4 ,bo? sulphur & sel5ium may be ?r[n into sev]al curi\s /ates1 :i* *emi/s conv5i5tly dispose ( by call+ !m 99allotropic991 a t]m freely us$ :5 !y are puzzl$ to "k :at has happ5$4 ,! *emical & physical hi/ory ( iron1 aga91 is full ( anomalies2 n only does x und]go inexplicable *anges ( h>dness & texture 9 its alloys ) c>bon & o!r elem5ts1 b x is almo/ ! only sub/ance :i* conveys s\nd ) great] velocity at a high] ?an at a l[] temp]ature1 ! velocity increas+ f #bj to #ajj ,c41 & !n decreas+4 ,silv] also is anomal\s 9 reg>d to s\nd4 ,^! are in/ances ( inexplicable exceptions1 ! be>+ ( :i* mu/ be asc]ta9$ 9 ! future progress ( sci5ce4 #eeh ,/ew>t's 99,elem5t>y ,treatise on ,heat991 p4 #hj4 ,:5 ! discov]y ( new & peculi> ph5om5a conflict+ ) our !ories ( ! con/itution ( nature is report$ to u1 x becomes no easy task to /e] a philosophically correct c\rse betwe5 cr$ulity & scepticism4 ,we are n to assume1 on ! "o h&1 t !re is any limit to ! wond]s :i* nature c pres5t to u4 ,no?+ except ! contradictory is really impossible1 & _m ?+s :i* we n[ reg>d z common-place 7 consid]$ z little %ort ( ! miracul\s :5 fir/ p]ceiv$4 ,! electric telegraph 0 a vision>y dream among m$ival physici/s2#eei x has h>dly yet ceas$ to excite our wond]2 to our desc5dants c5turies h5ce x w probably appe> inf]ior 9 +5uity to "s inv5tions :i* !y w possess4 ,n[ e /range ph5om5on may be a secret spr+ :i*1 if rightly t\*$1 w op5 ! door to new *amb]s 9 ! palace ( nature4 ,to refuse to believe 9 ! occurr5ce ( any?+ /range w\ld be to neglect ! mo/ preci\s *ances ( discov]y4 ,we may say ) ,hooke1 t 8! believ+ /range ?+s possible may p]haps be an occasion ( tak+ notice ( su* ?+s z ano!r w\ld pass by )\t reg>d z useless40 ,we are n1 !re=e1 to %ut our e>s ev5 to su* app>5tly absurd /ories z ^? conc]n+ second-sight1 clairvoyance1 animal magnetism1 ode =ce1 table-turn+1 or any ( ! popul> delusions :i* f "t to "t are curr5t4 ,! facts record$ conc]n+ ^! matt]s are facts 9 "s s5se or o!r1 & !y dem& explanation1 ei!r z new natural ph5om5a1 or z ! results ( cr$ulity & impo/ure4 ,mo/ ( ! suppos$ ph5om5a ref]r$ to h be51 or by c>eful inve/igation w\ld d\btless be1 ref]r$ to ! latt] head1 & ! abs5ce ( sci5tific ability 9 _m ( ^? :o describe !m is suffici5t to ca/ a d\bt ^u _! value4 #eei ,jevons1 99,proce$+s ( ! ,man*e/] ,lit]>y & ,philosophical ,society991 #f? ,m>*1 #ahgg1 vol4 xvi4 p4 #afd4 ,see also ,mr4 ,w4 ,e4 ,a4 ,axon's note on ! same subject1 ibid4 p4 #aff4 ,x is to be rememb]$ t accord+ to ! pr9ciple ( ! inv]se me?od ( probability1 ! probability ( any hypo!tical explanation is affect$ by ! probability ( ea* o!r possible explanation4 ,if no o!r reasonable explanation c\ld be sugge/$1 we %\ld be =c$ to look ^u spirituali/ manife/ations z indicat+ my/]i\s causes4 ,b z soon z x is %[n t fraud has be5 committ$ 9 sev]al important cases1 & t 9 o!r cases p]sons 9 a cr$ul\s & excit$ /ate ( m9d h deceiv$ !mselves1 ! probability becomes v consid]able t simil> explanations may apply to mo/ l manife/ations4 ,! p]=mances ( conjurors suffici5tly prove t x requires no v great skill to p]=m tricks ! 99modus op]&i99 ( :i* %all entirely escape ! notice ( spectators4 ,x is on ^! gr\nds ( probability t we %\ld reject ! s-call$ spirituali/ /ories1 & n simply because !y are /range4 ,c]ta9ly 9 ! obscure ph5om5a ( m9d1 ^? relat+ to memory1 dreams1 somnambulism1 & o!r peculi> /ates ( ! n]v\s sy/em1 !re are _m inexplicable & almo/ incr$ible facts1 & x is equally unphilosophical to believe or to disbelieve )\t cle> evid5ce4 ,!re are _m facts1 too1 conc]n+ ! in/9cts ( animals1 & ! mode 9 :i* !y f9d _! way f place to place1 :i* are at pres5t q inexplicable4 ,no d\bt !re are _m /range ?+s n dreamt ( 9 our philosophy1 b ?is is no reason :y we %\ld believe 9 e /range ?+ :i* is report$ to h happ5$4 ,,*apt] ,,xxx4 ,,classification4 ,! ext5sive subject ( ,classification has be5 def]r$ to a late "p ( ?is treatise1 because x involves que/ions ( difficulty1 & did n seem naturally to fall into an e>li] place4 ,b x mu/ n be suppos$ t1 9 n[ =mally tak+ up ! subject1 we are = ! fir/ "t ent]ta9+ ! notion ( classification4 ,all logical inf]5ce involves classification1 :i* is inde$ ! necess>y accompanim5t ( ! action ( judgm5t4 ,x is impossible to detect simil>ity betwe5 objects )\t !reby jo9+ !m toge!r 9 ?\ght1 & =m+ an incipi5t class4 ,nor c we be/[ a common "n ^u objects )\t imply+ ! exi/5ce ( a class4 ,e common "n is ! "n ( a class1 & e "n ( a class is a common "n4 ,x is evid5t also t to speak ( a g5]al notion or concept is b ano!r way ( speak+ ( a class4 ,usage leads u to employ ! ^w classification 9 "s cases & n 9 o!rs4 ,we are said to =m ! 99g5]al notion99 p>allelogram :5 we reg>d an inf9ite numb] ( possible f\r-sid$ rectil9e> figures z resembl+ ea* o!r 9 ! common prop]ty ( possess+ p>allel sides4 ,we %\ld be said to =m a 99class991 ,trilobite1 :5 we place toge!r 9 a museum a numb] ( specim5s resembl+ ea* o!r 9 c]ta9 def9$ *>act]s4 ,b ! logical nature ( ! op]ation is ! same 9 bo? cases4 ,we =m a 99class99 ( figures call$ p>allelograms & we =m a 99g5]al notion99 ( trilobites4 ,sci5ce1 x 0 said at ! outset1 is ! detection ( id5tify1 & classification is ! plac+ toge!r1 ei!r 9 ?\ght or 9 actual proximity ( space1 ^? objects betwe5 :i* id5tity has be5 detect$4 ,accord+ly1 ! value ( classification is co-ext5sive ) ! value ( sci5ce & g5]al reason+4 ,:5ev] we =m a class we r$uce multiplicity to unity1 & detect1 z ,plato said1 ! "o 9 ! _m4 ,! result ( su* classification is to yield g5]alis$ k1 z di/+ui%$ f ! direct & s5su\s k ( p>ticul> facts4 ,( e class1 s f> z x is correctly =m$1 ! pr9ciple ( sub/itution is true1 & :atev] we "k ( "o object 9 a class we "k ( ! o!r objects1 s f> z id5tity has be5 detect$ betwe5 !m4 ,! facilitation & abbreviation ( m5tal lab\r is at ! bottom ( all m5tal progress4 ,! reason+ faculties ( ,newton 7 n diff]5t 9 nature f ^? ( a pl\ghman2 ! diff]5ce lay 9 ! ext5t to :i* !y 7 ex]t$1 & ! numb] ( facts :i* c\ld be treat$4 ,e ?9k+ be+ g5]alises m or less1 b x is ! dep? & ext5t ( 8 g5]alisations :i* di/+ui% ! philosoph]4 ,n[ x is ! ex]tion ( ! classify+ & g5]alis+ p[]s :i* enables ! intellect ( man to cope 9 "s degree ) ! inf9ite numb] ( natural ph5om5a4 ,9 ! *apt]s ^u comb9ations & p]mutations x 0 made evid5t1 t f a few elem5t>y diff]5ces imm5se numb]s ( comb9ations c be produc$4 ,! process ( classification enables u to resolve ^! comb9ations1 & ref] ea* "o to its place accord+ to "o or o!r ( ! elem5t>y circum/ances out ( :i* x 0 produc$4 ,we re/ore nature to ! simple conditions out ( :i* its endless v>iety 0 develop$4 ,z ,pr(essor ,b[5 has said1#efj 8,! fir/ necessity :i* is impos$ ^u u by ! con/itution ( ! m9d itself1 is to break up ! inf9ite weal? ( ,nature into gr\ps & classes ( ?+s1 ) ref]5ce to _! resemblances & aff9ities1 & ?us to enl>ge ! grasp ( our m5tal faculties1 ev5 at ! exp5se ( sacrific+ ! m9ut5ess ( in=mation :i* c be acquir$ only by /udy+ objects 9 detail4 ,! fir/ ef=ts 9 ! pursuit ( k1 !n1 mu/ be direct$ to ! bus9ess ( classification4 ,p]haps x w be f\nd 9 ! sequel1 t classification is n only ! beg9n+1 b ! culm9ation & ! end1 ( human k40 #efj 99,a ,treatise on ,logic1 or1 ! ,laws ( ,pure ,?\ght991 by ,francis ,b[51 ,pr(essor ( ,moral ,philosophy 9 ,h>v>d ,college1 ,cambridge1 ,unit$ ,/ates1 #ahff1 p4 #cae4 99,classification ,involv+ ,induction499 ,! purpose ( classification is ! detection ( ! laws ( nature4 ,h[ev] mu* ! process may 9 "s cases be disguis$1 classification is n really di/9ct f ! process ( p]fect induction1 :]eby we endeav\r to asc]ta9 ! connexions exi/+ betwe5 prop]ties ( ! objects "u treatm5t4 ,!re c be no use 9 plac+ an object 9 a class unless some?+ m ?an ! fact ( be+ 9 ! class is impli$4 ,if we arbitr>ily =m$ a class ( metals & plac$ !re9 a selection f ! li/ ( kn[n metals made by ballot1 we %\ld h no reason to expect t ! metals 9 "q w\ld resemble ea* o!r 9 any po9ts except t !y are metals1 & h be5 select$ by ! ballot4 ,b :5 *emi/s select f ! li/ ! five metals1 potassium1 sodium1 csium1 rubidium1 & li?ium & call !m ! ,alkal9e metals1 a great deal is impli$ 9 ?is classification4 ,on comp>+ ! qualities ( ^! sub/ances !y are all f\nd to comb9e v en]getically ) oxyg51 to decompose wat] at all temp]atures1 & to =m /rongly basic oxides1 :i* are highly soluble 9 wat]1 yield+ p[]fully cau/ic & alkal9e hydrates f :i* wat] _c be expell$ by heat4 ,_! c>bonates are also soluble 9 wat]1 & ea* metal =ms only "o *loride4 ,x may also be expect$ t ea* salt ( "o ( ! metals w correspond to a salt ( ea* o!r metal1 !re be+ a g5]al analogy betwe5 ! comp\nds ( ^! metals & _! prop]ties4 ,n[ 9 =m+ ?is class ( alkal9e metals1 we h done m ?an m]ely select a conv5i5t ord] ( /atem5t4 ,we h arriv$ at a discov]y ( c]ta9 empirical laws ( nature1 ! probability be+ v consid]able t a metal :i* exhibits "s ( ! prop]ties ( alkal9e metals w also possess ! o!rs4 ,if we discov]$ ano!r metal ^: c>bonate 0 soluble 9 wat]1 & :i* en]getically comb9$ ) wat] at all temp]atures1 produc+ a /rongly basic oxide1 we %\ld inf] t x w\ld =m only a s+le *loride1 & t g5]ally speak+1 x w\ld ent] into a s]ies ( comp\nds correspond+ to ! salts ( ! o!r alkal9e metals4 ,! =mation ( ?is class ( alkal9e metals !n1 is no m]e matt] ( conv5i5ce2 x is an important & successful act ( inductive discov]y1 enabl+ u to regi/] _m und\bt$ propositions z results ( p]fect induction1 & to make a great numb] ( inf]5ces dep5d+ ^u ! pr9ciples ( imp]fect induction4 ,an excell5t in/ance z to :at classification c d1 is f\nd 9 ,mr4 ,locky]'s rese>*es on ! sun4#efa ,want+ "s guide z to :at m elem5ts to look = 9 ! sun's photosph]e1 he prep>$ a classification ( ! elem5ts accord+ z !y _h or _h n be5 trac$ 9 ! sun1 toge!r ) a detail$ /atem5t ( ! *ief *emical *>act]s ( ea* elem5t4 ,he 0 !n able to obs]ve t ! elem5ts f\nd 9 ! sun 7 = ! mo/ "p ^? =m+ /able comp\nds ) oxyg54 ,he !n inf]r$ t o!r elem5ts =m+ /able oxides w\ld probably exi/ 9 ! sun1 & he 0 rew>d$ by ! discov]y ( five su* metals4 ,"h we h empirical & t5tative classification lead+ to ! detection ( ! correlation betwe5 exi/5ce 9 ! sun1 & ! p[] ( =m+ /able oxides & !n lead+ by imp]fect induction to ! discov]y ( m co9cid5ces betwe5 ^! prop]ties4 #efa 99,proce$+s ( ! ,royal ,society991 ,novemb]1 #ahgc1 vol4 xxi4 p4 #eab4 ,pr(essor ,huxley has def9$ ! process ( classification 9 ! foll[+ t]ms4#efb 8,by ! classification ( any s]ies ( objects1 is meant ! actual or ideal arrangem5t toge!r ( ^? :i* are l & ! sep>ation ( ^? :i* are unlike2 ! purpose ( ?is arrangem5t be+ to facilitate ! op]ations ( ! m9d 9 cle>ly conceiv+ & reta9+ 9 ! memory ! *>act]s ( ! objects 9 "q40 #efb 99,lectures on ! ,elem5ts ( ,comp>ative ,anatomy991 #ahfd1 p4 #a4 ,?is /atem5t is d\btless correct1 s f> z x goes1 b x does n include all t ,pr(essor ,huxley himself implicitly treats "u classification4 ,he is fully aw>e t deep correlations1 or 9 o!r t]ms deep uni=mities or laws ( nature1 w be disclos$ by any well *os5 & pr(\nd sy/em ( classification4 ,i %\ld !re=e propose to modify ! above /atem5t1 z foll[s3--8,by ! classification ( any s]ies ( objects1 is meant ! actual or ideal arrangem5t toge!r ( ^? :i* are l & ! sep>ation ( ^? :i* are unlike1 ! purpose ( ?is arrangem5t be+1 prim>ily1 to disclose ! correlations or laws ( union ( prop]ties & circum/ances1 &1 second>ily1 to facilitate ! op]ations ( ! m9d 9 cle>ly conceiv+ & reta9+ 9 ! memory ! *>act]s ( ! objects 9 "q40 99,multiplicity ( ,modes ( ,classification499 ,9 approa*+ ! "q h[ any giv5 gr\p ( objects may be be/ classifi$1 let x be rem>k$ t !re mu/ g5]ally be an unlimit$ numb] ( modes ( classify+ a gr\p ( objects4 ,misl$1 z we %all see1 by ! problem ( classification 9 ! natural sci5ces1 philosoph]s seem to ?9k t 9 ea* subject !re mu/ be "o ess5tially natural sy/em ( classification :i* is to be select$1 to ! exclusion ( all o!rs4 ,?is errone\s notion probably arises also 9 "p f ! limit$ p[]s ( ?\ght & ! inconv5i5t me*anical conditions "u :i* we lab\r4 ,if we arrange ! books 9 a libr>y catalogue1 we mu/ arrange !m 9 "s "o ord]2 if we compose a treatise on m9]alogy1 ! m9]als mu/ be successively describ$ 9 "s "o arrangem5t2 if we treat su* simple ?+s z geometrical figures1 !y mu/ be tak5 9 "s fix$ ord]4 ,we %all naturally select t arrangem5t :i* appe>s to be mo/ conv5i5t & in/ructive = our pr9cipal purpose4 ,b x does n foll[ t ?is me?od ( arrangem5t possesses any exclusive excell5ce1 & !re w be usually _m o!r possible arrangem5ts1 ea* valuable 9 its own way4 ,a p]fect intellect w\ld n conf9e itself to "o ord] ( ?\ght1 b w\ld simultane\sly reg>d a gr\p ( objects z classifi$ 9 all ! ways ( :i* !y are capable4 ,?us ! elem5ts may be classifi$ accord+ to _! atomicity into ! gr\ps ( monads1 dyads1 triads1 tetrads1 p5tads1 & hexads1 & ?is is probably ! mo/ in/ructive classification2 b x does n prev5t u f also classify+ !m accord+ z !y are metallic or non-metallic1 solid1 liquid or gase\s at ord9>y temp]atures1 useful or useless1 abundant or sc>ce1 f]ro-magnetic or diamagnetic1 & s on4 ,m9]alogi/s h sp5t a great deal ( lab\r 9 try+ to discov] ! suppos$ natural sy/em ( classification = m9]als4 ,!y h con/antly enc\nt]$ ! difficulty t ! *emical composition does n run toge!r ) ! cry/allographic =m1 & ! v>i\s physical prop]ties ( ! m9]al4 ,sub/ances id5tical 9 ! =ms ( _! cry/als1 especially ^? belong+ to ! fir/ or cubical sy/em ( cry/als1 are (t5 f\nd to h no resemblance 9 *emical composition4 ,! same sub/ance1 aga91 is occasionally f\nd cry/allis$ 9 two ess5tially diff]5t cry/allographic =ms2 calcium c>bonate1 = in/ance1 appe>+ z calc-sp> & arragonite4 ,! simple tru? is t if we are unable to discov] any correspond5ce1 or1 z we may call x1 any 99correlation99 betwe5 ! prop]ties ( m9]als1 we _c make any "o arrangem5t :i* w enable u to treat all ^! prop]ties 9 a s+le sy/em ( classification4 ,we mu/ classify m9]als 9 z _m diff]5t ways z !re are diff]5t gr\ps ( unrelat$ prop]ties ( suffici5t importance4 ,ev5 if1 = ! purpose ( describ+ m9]als successively 9 a treatise1 we select "o *ief sy/em1 t1 = in/ance1 hav+ reg>d to *emical composition1 we ought m5tally to reg>d ! m9]als z classifi$ 9 all o!r useful modes4 ,exactly ! same may be said ( ! classification ( plants4 ,an imm5se numb] ( diff]5t modes ( classify+ plants h be5 propos$ at "o "t or o!r1 an exhau/ive acc\nt ( :i* w be f\nd 9 ! article on classification 9 ,rees's 8,cyclopdia10 or 9 ! introduction to ,l9dley's 8,vegetable ,k+dom40 ,!re h be5 ! ,fructi/s1 su* z ,csalp9us1 ,morison1 ,h]mann1 ,bo]haave or ,ga]tn]1 :o arrang$ plants accord+ to ! =m ( ! fruit4 ,! ,corolli/s1 ,riv9us1 ,ludwig1 & ,t\rne=t1 paid att5tion *iefly to ! numb] & arrangem5t ( ! p>ts ( ! corolla4 ,magnol select$ ! calyx z ! critical "p1 :ile ,sauvage arrang$ plants accord+ to _! leaves2 nor are ^! in/ances m ?an a small selection f ! actual v>iety ( modes ( classification :i* h be5 tri$4 ,( su* attempts x may be said t e sy/em w probably yield "s in=mation conc]n+ ! relations ( plants1 & x is only aft] try+ _m modes t x is possible to approximate to ! be/4 99,natural & ,artificial ,sy/ems ( ,classification499 ,x has be5 usual to di/+ui% sy/ems ( classification z natural & artificial1 ^? be+ call$ natural :i* seem$ to express ! ord] ( exi/+ ?+s z det]m9$ by nature4 ,artificial me?ods ( classification1 on ! o!r h&1 includ$ ^? =m$ = ! m]e conv5i5ce ( m5 9 rememb]+ or treat+ natural objects4 ,! diff]5ce1 z x is commonly reg>d$1 has be5 well describ$ by ,ampre1#efc z foll[s3 8,we c di/+ui% two k9ds ( classifications1 ! natural & ! artificial4 ,9 ! latt] k9d1 "s *>act]s1 arbitr>ily *os51 s]ve to det]m9e ! place ( ea* object2 we ab/ract all o!r *>act]s1 & ! objects are ?us f\nd to be br\ght ne> to or to be sep>at$ f ea* o!r1 (t5 9 ! mo/ biz>re mann]4 ,9 natural sy/ems ( classification1 on ! contr>y1 we employ concurr5tly all ! *>act]s ess5tial to ! objects ) :i* we are occupi$1 discuss+ ! importance ( ea* ( !m2 & ! results ( ?is lab\r are n adopt$ unless ! objects :i* pres5t ! close/ analogy are br\ght mo/ ne> toge!r1 & ! gr\ps ( ! sev]al ord]s :i* are =m$ f !m are also approximat$ 9 proportion z !y (f] m simil> *>act]s4 ,9 ?is way x arises t !re is always a k9d ( connexion1 m or less m>k$1 betwe5 ea* gr\p & ! gr\p :i* foll[s x40 #efc 99,essai sur la ,philosophie des ,sci5ces991 p4 #i4 ,!re is mu*1 h[ev]1 t is vague & logically false 9 ?is & o!r def9itions :i* h be5 propos$ by naturali/s to express _! notion ( a natural sy/em4 ,we are n in=m$ h[ ! 99importance99 ( a resemblance is to be det]m9$1 nor :at is ! measure ( ! 99clos5ess99 ( analogy4 ,until all ! words employ$ 9 a def9ition are made cle> 9 mean+1 ! def9ition itself is worse ?an useless4 ,n[ if ! views conc]n+ classification "h upheld are true1 !re c be no %>p & precise di/9ction betwe5 natural & artificial sy/ems4 ,all arrangem5ts :i* s]ve any purpose at all mu/ be m or less natural1 because1 if closely en\gh scrut9is$1 !y w involve m resemblances ?an ^? :]eby ! class 0 def9$4 ,x is true t 9 ! biological sci5ces !re w\ld be "o arrangem5t ( plants or animals :i* w\ld be conspicu\sly in/ructive1 & 9 a c]ta9 s5se natural1 if x c\ld be atta9$1 & x is t aft] :i* naturali/s h be5 9 reality /riv+ = ne>ly two c5turies1 namely1 t 99arrangem5t :i* w\ld display ! g5ealogical desc5t ( e =m f ! orig9al life g]m994 ,^? morphological resemblances ^u :i* ! classification ( liv+ be+s is almo/ always bas$ are inh]it$ resemblances1 & x is evid5t t desc5dants w usually resemble _! p>5ts & ea* o!r 9 a great _m po9ts4 ,i h said t a natural is di/+ui%$ f an arbitr>y or artificial sy/em only 9 degree4 ,x w be f\nd almo/ impossible to arrange objects accord+ to any circum/ance )\t f9d+ t "s correlation ( o!r circum/ances is ?us made app>5t4 ,no arrangem5t c\ld seem m arbitr>y ?an ! common alphabetical arrangem5t accord+ to ! initial lett] ( ! "n4 ,b we _c scrut9ise a li/ ( names ( p]sons )\t notic+ a pr$om9ance ( ,evans's & ,jones's1 "u ! lett]s ,e & ,j1 & ( names beg9n+ ) ,mac "u ! lett] ,m4 ,! pr$om9ance is s great t we c\ld n attribute x to *ance1 & inquiry w\ld ( c\rse %[ t x arose f important facts conc]n+ ! nationality ( ! p]sons4 ,x w\ld appe> t ! ,evans's & ,jones's 7 ( ,wel% desc5t1 & ^? ^: names be> ! prefix ,mac ( ,keltic desc5t4 ,) ! nationality w\ld be m or less /rictly correlat$ _m peculi>ities ( physical con/itution1 language1 habits1 or m5tal "*4 ,9 o!r cases ,i h be5 int]e/$ 9 notic+ ! empirical inf]5ces :i* are display$ 9 ! mo/ arbitr>y arrangem5ts4 ,if a l>ge regi/] ( ! names ( %ips be exam9$ x w (t5 be f\nd t a numb] ( %ips be>+ ! same "n 7 built ab\t ! same "t1 a correlation due to ! occurr5ce ( "s /rik+ incid5t %ortly previ\s to ! build+ ( ! %ips4 ,! age ( %ips or o!r /ructures is usually correlat$ ) _! g5]al =m1 nature ( mat]ials1 c41 s t %ips ( ! same "n w (t5 resemble ea* o!r 9 _m po9ts4 ,x is impossible to exam9e ! details ( "s ( ! s-call$ artificial sy/ems ( classification ( plants1 )\t f9d+ t _m ( ! classes are natural 9 "*4 ,?us 9 ,t\rne=t's arrangem5t1 dep5d+ almo/ entirely on ! =mation ( ! corolla1 we f9d ! natural ord]s ( ! ,labiat1 ,crucif]1 ,rosace1 ,umbellif]1 ,liliace1 & ,papilionace1 recognis$ 9 8 #d?1 #e?1 #f?1 #g?1 #i?1 & #aj? classes4 ,_m ( ! classes 9 ,l9nu' celebrat$ sexual sy/em also approximate to natural classes4 99,correlation ( ,prop]ties499 ,habits & usages ( language are apt to lead u into ! error ( imag9+ t :5 we employ diff]5t words we always mean diff]5t ?+s4 ,9 introduc+ ! subject ( classification nom9ally ,i 0 c>eful to draw ! read]'s att5tion to ! fact t all reason+ & all op]ations ( sci5tific me?od really involve classification1 ?\gh we are accu/om$ to use ! "n 9 "s cases & n 9 o!rs4 ,! "n 99correlation99 requires to be us$ ) ! same qualification4 ,?+s are correlat$ 799con991 99relata997 :5 !y are s relat$ or b\nd to ea* o!r t 99:]e "o is ! o!r is1 & :]e "o is n ! o!r is n994 ,?r\gh\t ?is "w we h !n be5 deal+ ) correlations4 ,9 geometry ! occurr5ce ( ?ree equal angles 9 a triangle is correlat$ ) ! exi/5ce ( ?ree equal sides2 9 physics gravity is correlat$ ) in]tia2 9 botany exog5\s gr[? is correlat$ ) ! possession ( two cotyl$ons1 or ! production ( fl[]s ) t ( spiral vessels4 ,:]ev] a proposition ( ! =m ,a ,b is true !re correlation exi/s4 ,b x is 9 ! classificatory sci5ces especially t ! ^w correlation has be5 employ$4 ,we f9d x /at$ t 9 ! class ,mammalia ! possession ( two occipital condyles1 ) a well-ossifi$ basi-occipital1 is correlat$ ) ! possession ( m&ibles1 ea* ramus ( :i* is compos$ ( a s+le piece ( bone1 articulat$ ) ! squamosal elem5t ( ! skull1 & also ) ! possession ( mamm & non-nucleat$ r$ blood-corpuscles4 ,pr(essor ,huxley rem>ks#efd t ?is /atem5t ( ! "* ( ! class mammalia is some?+ m ?an an arbitr>y def9ition2 x is a /atem5t ( a law ( correlation or co-exi/5ce ( animal /ructures1 f :i* mo/ important conclusions are d$ucible4 ,x involves a g5]alisation to ! effect t 9 nature ! /ructures m5tion$ are always f\nd associat$ toge!r4 ,?is am\nts to say+ t ! =mation ( ! class mammalia involves an act ( inductive discov]y1 & results 9 ! e/abli%m5t ( c]ta9 empirical laws ( nature4 ,pr(essor ,huxley has excell5tly express$ ! mode 9 :i* discov]ies ( ?is k9d enable naturali/s to make d$uctions or pr$ictions ) consid]able confid5ce1 b he has also po9t$ out t su* inf]5ces are likely f "t to "t to prove mi/ak54 ,i w quote 8 own words3 #efd 99,lectures on ! ,elem5ts ( ,comp>ative ,anatomy1 & on ! ,classification ( ,animals991 #ahfd1 p4 #c4 8,if a fragm5t>y fossil be discov]$1 consi/+ ( no m ?an a ramus ( a m&ible1 & t "p ( ! skull ) :i* x articulat$1 a k ( ?is law may enable ! palontologi/ to affirm1 ) great confid5ce1 t ! animal ( :i* x =m$ a "p suckl$ its "y1 & _h non-nucleat$ r$ blood-corpuscles2 & to pr$ict t %\ld ! back "p ( t skull be discov]$1 x w exhibit two occipital condyles & a well-ossifi$ basi-occipital bone4 8,d$uctions ( ?is k9d1 su* z t made by ,cuvi] 9 ! fam\s case ( ! fossil opossum ( ,montm>tre1 h (t5 be5 v]ifi$1 & are well calculat$ to impress ! vulg> imag9ation2 s t !y h tak5 rank z ! triumphs ( ! anatomi/4 ,b x %\ld c>efully be borne 9 m9d1 t1 l all m]ely empirical laws1 :i* re/ ^u a comp>atively n>r[ obs]vational basis1 ! reason+ f !m may at any "t break d[n4 ,if ,cuvi]1 = example1 _h _h to d ) a fossil ,?ylac9us in/ead ( a fossil ,opossum1 he w\ld n h f\nd ! m>supial bones1 ?\gh ! inflect$ angle ( ! jaw w\ld h be5 obvi\s en\gh4 ,& s1 ?\gh1 practically1 any "o :o met ) a *>act]i/ically mammalian jaw w\ld be ju/ifi$ 9 expect+ to f9d ! *>act]i/ically mammalian occiput associat$ ) x2 yet1 he w\ld be a bold man inde$1 :o %\ld /rictly ass]t ! belief :i* is impli$ 9 ?is expectation1 viz41 t at no p]iod ( ! _w's hi/ory did animals exi/ :i* comb9$ a mammalian occiput ) a reptilian jaw1 or 99vice v]s9940 ,"o ( ! mo/ di/9ct & rem>kable in/ances ( correlation 9 ! animal _w is t :i* occurs 9 rum9at+ animals1 & :i* c\ld n be bett] /at$ ?an 9 ! foll[+ extract f ! classical "w ( ,cuvi]3#efe #efe 99,ossem5s ,fossiles991 #d? edit4 vol4 i4 p4 #afd4 ,quot$ by ,huxley1 99,lectures991 c41 p4 #e4 8,i d\bt if any "o w\ld h div9$1 if untaught by obs]vation1 t all rum9ants h ! foot cleft1 & t !y alone h x4 ,i d\bt if any "o w\ld h div9$ t !re are frontal horns only 9 ?is class3 t ^? among !m :i* h %>p can9es = ! mo/ "p lack horns4 8,h[ev]1 s9ce ^! relations are con/ant1 !y mu/ h "s suffici5t cause2 b s9ce we are ignorant ( x1 we mu/ make good ! defect ( ! !ory by means ( obs]vation3 x enables u to e/abli% empirical laws :i* become almo/ z c]ta9 z rational laws :5 !y re/ on suffici5tly repeat$ obs]vations2 s t n[ :oso sees m]ely ! pr9t ( a cleft foot may conclude t ! animal :i* left ?is impression rum9at$1 & ?is conclusion is z c]ta9 z any o!r 9 physics or morals4 ,?is footpr9t alone !n1 yields1 to him :o obs]ves x1 ! =m ( ! tee?1 ! =m ( ! jaws1 ! =m ( ! v]tebr1 ! =m ( all ! bones ( ! legs1 ( ! ?ighs1 ( ! %\ld]s1 & ( ! pelvis ( ! animal :i* has pass$ by3 x is a sur] m>k ?an all ^? ( ,zadig40 ,we meet ) a good in/ance ( ! purely empirical correlation ( circum/ances :5 we classify ! planets accord+ to _! d5sities & p]iods ( axial rotation4#eff ,if we exam9e a table specify+ ! usual a/ronomical elem5ts ( ! sol> sy/em1 we f9d t f\r planets resemble ea* o!r v closely 9 ! p]iod ( axial rotation1 & ! same f\r planets are all f\nd to h high d5sities1 ?us3-- #eff ,*amb]s1 99,descriptive ,a/ronomy991 #a/ edit4 p4 #bc4 ,"n ( ,p]iod ( ,axial ,planet4 ,rotation4 ,d5sity4 ,m]cury #bd h\rs #e m9utes #gid ,v5us #bc #ba #ecc ,e>? #bc #ef #efg ,m>s #bd #cg #ehd ,a simil> table = ! o!r l>g] planets1 is z foll[s3-- ,jupit] #i h\rs #ee m9utes #acf ,saturn #aj #bi #gd ,uranus #i #cj #ig ,neptune -- -- #ajb ,x w be obs]v$ t 9 nei!r gr\p is ! equality ( ! rotational p]iod or ! d5sity m ?an rudely approximate2 nev]!less ! diff]5ce ( ! numb]s 9 ! fir/ & second gr\p is s v well m>k$1 ! p]iods ( ! fir/ be+ at lea/ d\ble & ! d5sities f\r or five times ^? ( ! second1 t ! co9cid5ce _c be attribut$ to accid5t4 ,! read] w also notice t ! fir/ gr\p consi/s ( ! planets ne>e/ to ! sun2 t ) ! exception ( ! e>? none ( !m possess satellites2 & t !y are all comp>atively small4 ,! second gr\p are fur!/ f ! sun1 & all ( !m possess sev]al satellites1 & are comp>atively great4 ,!re=e1 ) b slight exceptions1 ! foll[+ correlations hold true3-- ,int]ior planets4 ,long p]iod4 ,small size4 ,high ,d5sity4 ,no satellites4 ,ext]ior ,%ort ,great ,l[ ,_m ,^! co9cid5ces po9t ) mu* probability to a diff]5ce 9 ! orig9 ( ! two gr\ps1 b no fur!r explanation ( ! matt] is yet possible4 ,! classification ( comets accord+ to _! p]iods by ,mr4 ,h9d & ,mr4 ,a4 ,s4 ,davies1 t5ds to e/abli% ! conclusion t di/9ct gr\ps ( comets h be5 br\ght into ! sol> sy/em by ! attractive p[]s ( ,jupit]1 ,uranus1 or o!r planets4#efg ,! classification ( nebul z comm5c$ by ! two ,h]s*els1 & cont9u$ by ,"l ,rosse1 ,mr4 ,hugg9s1 & o!rs1 w probably lead at "s future "t to ! discov]y ( important empirical laws conc]n+ ! con/itution ( ! univ]se4 ,! m9ute exam9ation & classification ( meteorites1 z c>ri$ on by ,mr4 ,sorby & o!rs1 seems likely to af=d u an insight into ! =mation ( ! heav5ly bodies4 #efg 99,philosophical ,magaz9e991 #d? ,s]ies1 vol4 xxxix4 p4 #cif2 vol4 xl4 p4 #ahc2 vol4 xli4 p4 #dd4 ,see also ,proctor1 99,popul> ,sci5ce ,review991 ,octob] #ahgd1 p4 #cej4 ,we %\ld nev] fail to rememb] ! slighte/ & mo/ inexplicable correlations1 = !y may prove ( importance 9 ! future4 ,discov]ies beg9 :5 we are lea/ expect+ !m4 ,x is a significant fact1 = in/ance1 t ! great] numb] ( v>iable />s are ( a r$di% col\r4 ,n all v>iable />s are r$1 nor all r$ />s v>iable2 b consid]+ t only a small fraction ( ! obs]v$ />s are kn[n to be v>iable1 & only a small fraction are r$1 ! numb] :i* fall into bo? classes is too great to be accid5tal4#efh ,x is also rem>kable t ! great] numb] ( />s possess+ great prop] motion are d\ble />s1 ! /> #fa ,cygni be+ especially noticeable 9 ?is respect4#efi ,! correlation 9 ^! cases is n )\t exception1 b ! prepond]ance is s great z to po9t to "s natural connexion1 ! exact nature ( :i* mu/ be a matt] = future inve/igation4 ,h]s*el rem>k$ t ! two d\ble />s #fa ,cygni & ,c5tauri ( :i* ! orbits 7 well asc]ta9$1 evid5tly belong$ to ! same family or g5us4#egj #efh ,humboldt1 99,cosmos99 7,bohn71 vol4 iii4 p4 #bbd4 #efi ,baily1 ,briti% 99,association ,catalogue991 p4 #dh4 #egj 99,outl9es ( ,a/ronomy991 #hej1 #d? edit4 p4 #egh4 99,classification 9 ,cry/allography499 ,p]haps ! mo/ p]fect & in/ructive in/ance ( classification :i* we c f9d is furni%$ by ! sci5ce ( cry/allography 7p4 #acc74 ,! sy/em ( arrangem5t n[ g5]ally adopt$ is conspicu\sly natural1 & is ev5 ma!matically p]fect4 ,a cry/al consi/s 9 e "p ( simil> molecules simil>ly relat$ to ! adjo9+ molecules1 & connect$ ) !m by =ces ! nature ( :i* we c only le>n by _! app>5t effects4 ,b ^! =ces are ex]t$ 9 space ( ?ree dim5sions1 s t !re is a limit$ numb] ( suppositions :i* c be ent]ta9$ z to ! relations ( ^! =ces4 ,9 "o case ea* molecule w be simil>ly relat$ to all ^? :i* are next to x2 9 a second case1 x w be simil>ly relat$ to ^? 9 a c]ta9 plane1 b diff]5tly relat$ to ^? n 9 t plane4 ,9 ! simpl] cases ! arrangem5t ( molecules is rectangul>2 9 ! rema9+ cases oblique ei!r 9 "o or two planes4 ,9 ord] to simplify ! explanation & conception ( ! complicat$ ph5om5a :i* cry/als exhibit1 an hypo!sis has be5 inv5t$ :i* is an excell5t in/ance ( ! ,descriptive ,hypo!ses be=e m5tion$ 7p4 #ebb74 ,cry/allograph]s imag9e t !re are )9 ea* cry/al c]ta9 axes1 or l9es ( direction1 by ! comp>ative l5g? & ! mutual incl9ation ( :i* ! nature ( ! cry/al is det]m9$4 ,9 "o class ( cry/als !re are ?ree su* axes ly+ 9 "o plane1 & a f\r? p]p5dicul> to t plane2 b 9 all ! o!r classes !re are imag9$ to be only ?ree axes4 ,n[ ^! axes c be v>i$ 9 ?ree ways z reg>ds l5g?3 !y may be 7#a7 all equal1 or 7#b7 two equal & "o unequal1 or 7#c7 all unequal4 ,!y may also be v>i$ 9 f\r ways z reg>ds direction3 7#a7 !y may be all at "r angles to ea* o!r2 7#b7 two axes may be oblique to ea* o!r & at "r angles to ! ?ird2 7#c7 two axes may be at "r angles to ea* o!r & ! ?ird oblique to bo?2 7#d7 ! ?ree axes may be all oblique4 ,n[1 if all ! v>iations z reg>ds l5g? 7 comb9$ ) ^? reg>d+ direction1 x w\ld seem to be possible to h twelve classes ( cry/als 9 all1 ! enum]ation be+ !n logically & geometrically complete4 ,b z a matt] ( empirical obs]vation1 _m ( ^! classes are n f\nd to occur1 oblique axes be+ seldom or nev] equal4 ,!re rema9 sev5 recognis$ classes ( cry/als1 b ev5 ( ^! "o class is n positively kn[n to be repres5t$ 9 nature4 ,! fir/ class ( cry/als is def9$ by possess+ ?ree equal rectangul> axes1 & equal ela/icity 9 all directions4 ,! prim>y or simple =m ( ! cry/als is ! cube1 b by ! removal ( ! corn]s ( ! cube by planes v>i\sly incl9$ to ! axes1 we h ! regul> octoh$ron1 ! dodecah$ron1 & v>i\s comb9ations ( ^! =ms4 ,n[ x is a law ( ?is class ( cry/als t z ea* axis is exactly l ea* o!r axis1 e modification ( any corn] ( a cry/al mu/ be repeat$ symmetrically ) reg>d to ! o!r axes2 ?us ! =ms produc$ are symmetrical or regul>1 & ! class is call$ ! 99,regul> ,sy/em99 ( cry/als4 ,x includes a great v>iety ( sub/ances1 "s ( !m be+ elem5ts1 su* z c>bon 9 ! =m ( diamond1 o!rs m or less complex comp\nds1 su* z rock-salt1 potassium iodide & bromide1 ! sev]al k9ds ( alum1 fluor-sp>1 iron bisulphide1 g>net1 sp9elle1 c4 ,no correlation !n is app>5t betwe5 ! =m ( cry/allisation & ! *emical composition4 ,b :at we h to notice is t ! physical prop]ties ( ! cry/allis$ sub/ances ) reg>d to light1 heat1 electricity1 c41 are closely simil>4 ,light & heat undulations1 :]ev] !y ent] a cry/al ( ! regul> sy/em1 spread ) equal rapidity 9 all directions1 j z !y w\ld 9 a uni=m fluid4 ,cry/als ( ! regul> sy/em accord+ly d n 9 any case exhibit ! ph5om5a ( d\ble refraction1 unless by me*anical compression we alt] ! conditions ( ela/icity4 ,^! cry/als1 aga91 exp& equally 9 all directions :5 heat$1 & if we c\ld cut a suffici5tly l>ge plate f a cubical cry/al1 & exam9e ! s\nd vibrations ( :i* x is capable1 we %\ld f9d t !y indicat$ an equal ela/icity 9 e direction4 ,?us we see t a great numb] ( important prop]ties are correlat$ ) t ( cry/allisation 9 ! regul> sy/em1 & z soon z we "k t ! prim>y =m ( a sub/ance is ! cube1 we are able to inf] ) approximate c]ta9ty t x possesses all ^! prop]ties4 ,! class ( regul> cry/als is !n an em95tly natural class1 "o disclos+ _m g5]al laws connect+ toge!r ! physical & me*anical prop]ties ( ! sub/ances classifi$4 ,9 ! second class ( cry/als1 call$ ! dimetric1 squ>e prismatic1 or pyramidal sy/em1 !re are also ?ree axes at "r angles to ea* o!r2 two ( ! axes are equal1 b ! ?ird or pr9cipal axis is unequal1 be+ ei!r great] or less ?an ei!r ( ! o!r two4 ,9 su* cry/als accord+ly ! ela/icity & o!r prop]ties are alike 9 all directions p]p5dicul> to ! pr9cipal axis1 b v>y 9 all o!r directions4 ,if a po9t )9 a cry/al ( ?is sy/em be heat$1 ! heat spreads ) equal rapidity 9 planes p]p5dicul> to ! pr9cipal axis1 b m or less rapidly 9 ! direction ( ?is axis1 s t ! iso!rmal surface is an ellipsoid ( revolution r\nd t axis4 ,ne>ly ! same /atem5t may be made conc]n+ ! ?ird or hexagonal or rhomboh$ral sy/em ( cry/als1 9 :i* !re are ?ree axes ly+ 9 "o plane & meet+ at angles ( #fj1 :ile ! f\r? axis is p]p5dicul> to ! o!r ?ree4 ,! hexagonal prism & rhomboh$ron are ! commone/ =ms assum$ by cry/als ( ?is sy/em1 & 9 ice1 qu>tz1 & calc-sp>1 we h abundance ( beautiful specim5s ( ! v>i\s %apes produc$ by ! modification ( ! primitive =m4 ,calc-sp> alone is said to cry/allise 9 at lea/ #gjj v>ieties ( =m4 ,n[ ( all ! cry/als belong+ bo? to ?is & ! dimetric class1 we "k t a ray ( light pass+ 9 ! direction ( ! pr9cipal axis w be refract$ s+ly z 9 a cry/al ( ! regul> sy/em2 b 9 e o!r direction ! light w suff] d\ble refraction be+ sep>at$ into two rays1 "o ( :i* obeys ! ord9>y law ( refraction1 b ! o!r a mu* m complicat$ law4 ,! o!r physical prop]ties v>y 9 an analog\s mann]4 ,?us calc-sp> exp&s by heat 9 ! direction ( ! pr9cipal axis1 b contracts a little 9 directions p]p5dicul> to x4 ,s closely are ! physical prop]ties correlat$ t ,mits*]li*1 hav+ obs]v$ ! law ( expansion 9 calc-sp>1 0 enabl$ to pr$ict t ! d\ble refract+ p[] ( ! sub/ance w\ld be decreas$ by a rise ( temp]ature1 z 0 prov$ by exp]im5t to be ! case4 ,9 ! f\r? sy/em1 call$ ! trimetric1 rhombic1 or "r prismatic sy/em1 !re are ?ree axes1 at "r angles1 b all unequal 9 l5g?4 ,x may be ass]t$ 9 g5]al t]ms t ! me*anical prop]ties v>y 9 su* cry/als 9 e direction1 & heat spreads s t ! iso!rmal surface is an ellipsoid ) ?ree unequal axes4 ,9 ! rema9+ ?ree classes1 call$ ! monocl9ic1 dicl9ic1 & tricl9ic1 ! axes are m or less oblique1 & at ! same "t unequal4 ,! complication ( ph5om5a is !re=e greatly increas$1 & x ne$ only be /at$ t !re are always two directions 9 :i* a ray is s+ly refract$1 b t 9 all o!r directions d\ble refraction takes place4 ,! conduction ( heat is unequal 9 all directions1 ! iso!rmal surface be+ an ellipsoid ( ?ree unequal axes4 ,! relations ( su* cry/als to o!r ph5om5a are (t5 v complicat$1 & h>dly yet r$uc$ to law4 ,"s cry/als1 call$ pyro-electric1 manife/ vitre\s electricity at "s po9ts ( _! surface1 & res9\s electricity at o!r po9ts :5 ris+ 9 temp]ature1 ! "* ( ! electricity be+ *ang$ :5 ! temp]ature s9ks aga94 ,?is production ( electricity is believ$ to be connect$ ) ! hemih$ral "* ( ! cry/als exhibit+ x4 ,! cry/all9e /ructure ( a sub/ance aga9 influ5ces its magnetic behavi\r1 ! g5]al law be+ t ! direction 9 :i* ! molecules ( a cry/al are mo/ approximat$ t5ds to place itself axially or equatorially betwe5 ! poles ( a magnet1 respectively z ! body is magnetic or diamagnetic4 ,fur!r que/ions arise if we apply pressure to cry/als4 ,?us d\bly refract+ cry/als ) "o pr9cipal axis acquire two axes :5 ! pressure is p]p5dicul> 9 direction to ! pr9cipal axis4 ,all ! ph5om5a peculi> to cry/all9e bodies are ?us closely correlat$ ) ! =mation ( ! cry/al1 or w almo/ c]ta9ly be f\nd to be s z inve/igation proce$s4 ,x is ^u empirical obs]vation inde$ t ! laws ( connexion are 9 ! fir/ place f\nd$1 b ! simple hypo!sis t ! ela/icity & approximation ( ! p>ticles v>y 9 ! directions ( ! cry/all9e axes all[s ( ! application ( d$uctive reason+4 ,! :ole ( ! ph5om5a are gradually be+ prov$ to be consi/5t ) ?is hypo!sis1 s t we h 9 ?is subject ( cry/allography a beautiful in/ance ( successful classification1 connect$ ) a ne>ly p]fect physical hypo!sis4 ,moreov] ?is hypo!sis 0 v]ifi$ exp]im5tally z reg>ds ! me*anical vibrations ( s\nd by ,sav>t1 :o f\nd t ! vibrations 9 a plate ( biaxial cry/al indicat$ ! exi/5ce ( v>y+ ela/icity 9 v>y+ directions4 99,classification an ,inv]se & ,t5tative ,op]ation499 ,if attempts at s-call$ natural classification are really attempts at p]fect induction1 x foll[s t !y are subject to ! rem>ks :i* 7 made ^u ! inv]se "* ( ! inductive process1 & ^u ! difficulty ( e inv]se op]ation 7pp4 #aa1 #ab1 #abb1 c474 ,!re w be no royal road to ! discov]y ( ! be/ sy/em1 & x w ev5 be impossible to lay d[n rules ( proc$ure to assi/ ^? :o are 9 se>* ( a good arrangem5t4 ,! only logical rule w\ld be z foll[s3--,hav+ giv5 c]ta9 objects1 gr\p !m 9 e way 9 :i* !y c be gr\p$1 & !n obs]ve 9 :i* me?od ( gr\p+ ! correlation ( prop]ties is mo/ conspicu\sly manife/$4 ,b ?is me?od ( exhau/ive classification w 9 almo/ e case be impracticable1 ow+ to ! imm5sely great numb] ( modes 9 :i* a comp>atively small numb] ( objects may be gr\p$ toge!r4 ,ab\t sixty-?ree elem5ts h be5 classifi$ by *emi/s 9 six pr9cipal gr\ps z monad1 dyad1 triad1 c41 elem5ts1 ! numb]s 9 ! classes v>y+ f ?ree to tw5ty elem5ts4 ,n[ if we 7 to calculate ! :ole numb] ( ways 9 :i* sixty-?ree objects c be arrang$ 9 six gr\ps1 we %\ld f9d ! numb] to be s great t ! life ( ! longe/ liv$ man w\ld be :olly inadequate to enable him to g ?r\gh ^! possible gr\p+s4 ,! rule ( exhau/ive arrangem5t1 !n1 is absolutely impracticable4 ,x foll[s t m]e haphaz>d trial _c z a g5]al rule give any useful result4 ,if we 7 to write ! names ( ! elem5ts 9 succession ^u sixty-?ree c>ds1 ?r[ !m into a ballot-box1 & draw !m out haphaz>d 9 six h&fuls "t aft] "t1 ! probability is excessively small t we %\ld take !m out 9 a specifi$ ord]1 t = in/ance at pres5t adopt$ by *emi/s4 ,! usual mode 9 :i* an inve/igator proce$s to =m a classification ( a new gr\p ( objects seems to consi/ 9 t5tatively arrang+ !m accord+ to _! mo/ obvi\s simil>ities4 ,any two objects :i* pres5t a close resemblance to ea* o!r w be jo9$ & =m$ into ! rudim5t ( a class1 ! def9ition ( :i* w at fir/ include all ! app>5t po9ts ( resemblance4 ,o!r objects z !y come to our notice w be gradually assign$ to ^? gr\ps ) :i* !y pres5t ! greate/ numb] ( po9ts ( resemblance1 & ! def9ition ( a class w (t5 h to be alt]$ 9 ord] to admit !m4 ,! e>ly *emi/s c\ld h>dly avoid class+ toge!r ! common metals1 gold1 silv]1 copp]1 lead1 & iron1 :i* pres5t su* conspicu\s po9ts ( simil>ity z reg>ds d5sity1 metallic lu/re1 malleability1 c4 ,) ! progress ( discov]y1 h[ev]1 difficulties began to pres5t !mselves 9 su* a gr\p+4 ,antimony1 bismu?1 & ars5ic are di/9ctly metallic z reg>ds lu/re1 d5sity1 & "s *emical prop]ties1 b are want+ 9 malleability4 ,! rec5tly discov]$ tellurium pres5ts great] difficulties1 = x has _m ( ! physical prop]ties ( metal1 & yet all its *emical prop]ties are analog\s to ^? ( sulphur & sel5ium1 :i* h nev] be5 reg>d$ z metals4 ,great *emical diff]5ces aga9 are discov]$ by degrees betwe5 ! five metals m5tion$2 & ! class1 if x is to h any *emical validity1 mu/ be made to include o!r elem5ts1 hav+ none ( ! orig9al prop]ties on :i* ! class 0 f\nd$4 ,hydrog5 is a transp>5t col\rless gas1 & ! lea/ d5se ( all sub/ances2 yet 9 its *emical analogies x is a metal1 z sugge/$ by ,f>aday#ega 9 #ahch1 & almo/ prov$ by ,graham2#egb x mu/ be plac$ 9 ! same class z silv]4 ,9 ?is way x comes to pass t almo/ e classification :i* is propos$ 9 ! e>ly /ages ( a sci5ce w be f\nd to break d[n z ! deep] simil>ities ( ! objects come to be detect$4 ,! mo/ obvi\s po9ts ( diff]5ce w h to be neglect$4 ,*lor9e is a gas1 brom9e a liquid1 & iod9e a solid1 & at fir/ sight ^! might h seem$ =midable circum/ances to ov]look2 b 9 *emical analogy ! sub/ances are closely unit$4 ,! progress ( organic *emi/ry1 aga91 has yield$ :olly new ideas ( ! simil>ities ( comp\nds4 ,:o1 = in/ance1 w\ld recognise )\t ext5sive rese>* a close simil>ity betwe5 glyc]9e & alcohol1 or betwe5 fatty sub/ances & e!r8 ,! class ( p>aff9s conta9s ?ree sub/ances gase\s at ord9>y temp]atures1 sev]al liquids1 & "s cry/all9e solids4 ,x requir$ mu* insight to detect ! analogy :i* exi/s betwe5 su* app>5tly diff]5t sub/ances4 #ega 99,life ( ,f>aday991 vol4 ii4 p4 #hg4 #egb 99,proce$+s ( ! ,royal ,society991 vol4 xvii4 p4 #bab4 99,*emical & ,physical ,rese>*es991 repr9t1 by ,"y & ,angus ,smi?1 p4 #bij4 ,! sci5ce ( *emi/ry n[ dep5ds to a great ext5t on a correct classification ( ! elem5ts1 z w be le>nt by consult+ ! able article on ,classification by ,pr(essor ,g4 ,c4 ,fo/] 9 ,watts' 99,diction>y ( ,*emi/ry994 ,b ! pres5t sy/em ( *emical classification 0 n rea*$ until at lea/ ?ree previ\s false sy/ems _h be5 long ent]ta9$4 ,& ?\gh !re is mu* reason to believe t ! pres5t mode ( classification accord+ to atomicity is sub/antially correct1 errors may yet be discov]$ 9 ! details ( ! gr\p+4 99,symbolic ,/atem5t ( ! ,!ory ( ,classification499 ,! !ory ( classification c be expla9$ 9 ! mo/ complete & g5]al mann]1 by rev]t+ = a "t to ! use ( ! ,logical ,alphabet1 :i* 0 f\nd to be ( supreme importance 9 ,=mal ,logic4 ,t =m expresses ! necess>y classification ( all objects & ideas z dep5d+ on ! laws ( ?\ght1 & !re is no po9t conc]n+ ! purpose & me?ods ( classification :i* may n be /at$ precisely by ! use ( lett] comb9ations1 ! only inconv5i5ce be+ ! ab/ract =m 9 :i* ! subject is ?us repres5t$4 ,if we pay reg>d only to ?ree qualities 9 :i* ?+s may resemble ea* o!r1 namely1 ! qualities ,a1 ,b1 ,c1 !re are accord+ to ! laws ( ?\ght eight possible classes ( objects1 %[n 9 ! f\r? column ( ! ,logical ,alphabet 7p4 #id74 ,if !re exi/ objects belong+ to all ^! eight classes1 x foll[s t ! qualities ,a1 ,b1 ,c1 are subject to no conditions except ! prim>y laws ( ?\ght & ?+s 7p4 #e74 ,!re is !n no special law ( nature to discov]1 &1 if we arrange ! objects 9 any "o ord] r ?an ano!r1 x mu/ be = ! purpose ( %[+ t ! comb9ations are logically complete4 ,suppose1 h[ev]1 t !re are b f\r k9ds ( objects possess+ ! qualities ,a1 ,b1 ,c1 & t ^! k9ds are repres5t$ by ! comb9ations ,,abc1 ,a99b99,c1 99a99,b99c991 99abc994 ,! ord] ( arrangem5t w n[ be ( importance2 = if we place !m 9 ! ord] ,,abc ,a99b99,c 99a99,b99c99 99abc99 plac+ ! ,b's fir/ & ^? :i* are 99b99's la/1 we %all p]haps ov]look ! law ( correlation ( prop]ties involv$4 ,b if we arrange ! comb9ations z foll[s ,,abc 99a99,b99c99 ,a99b99,c 99abc99 x becomes app>5t at once t :]e ,a is1 & only :]e ,a is1 ! prop]ty ,c is to be f\nd1 ,b be+ indiff]5tly pres5t & abs5t4 ,! second arrangem5t !n w\ld be call$ a natural "o1 z r5d]+ manife/ ! conditions "u :i* ! comb9ations exi/4 ,z a fur!r in/ance1 let u suppose t eight objects are pres5t$ to u = classification1 :i* exhibit comb9ations ( ! five prop]ties1 ,a1 ,b1 ,c1 ,d1 ,e1 9 ! foll[+ mann]3-- ,,abc99d99,e 99a99,,bc99d99,e ,,ab99cde99 99a99,b99cde99 ,a99b99,,cde 99ab99,,cde ,a99bc99,d99e99 99abc99,d99e99 ,!y are n[ classifi$1 s t ^? conta9+ ,a /& fir/1 & ^? devoid ( ,a second1 b no o!r prop]ty seems to be correlat$ ) ,a4 ,let u alt] ?is arrangem5t & gr\p ! comb9ations ?us3-- ,,abc99d99,e ,a99b99,,cde ,,ab99cde99 ,a99bc99,d99e99 99a99,,bc99d99,e 99ab99,,cde 99a99,b99cde99 99abc99,d99e99 ,x requires little exam9ation to discov] t 9 ! fir/ gr\p ,b is always pres5t & ,d abs5t1 :]eas 9 ! second gr\p1 ,b is always abs5t & ,d pres5t4 ,?is is ! result :i* foll[s f a law ( ! =m ,b d 7p4 #acf71 s t 9 ?is mode ( arrangem5t we readily discov] correlation betwe5 two lett]s4 ,alt]+ ! gr\ps aga9 z foll[s3-- ,,abc99d99,e ,,ab99cde99 99a99,,bc99d99,e 99a99,b99cde99 ,a99b99,,cde ,a99bc99,d99e99 99ab99,,cde 99abc99,d99e991 we discov] ano!r evid5t correlation betwe5 ,c & ,e4 ,betwe5 ,a & ! o!r lett]s1 or betwe5 ! two pairs ( lett]s ,b1 ,d & ,c1 ,e1 !re is no logical connexion4 ,?is example may seem t$i\s1 b x w be f\nd in/ructive 9 ?is way4 ,we are classify+ only eight objects or comb9ations1 9 ea* ( :i* only five qualities are consid]$4 ,!re are only two laws ( correlation betwe5 f\r ( ^? five qualities1 & ^? laws are ( ! simple/ logical "*4 ,yet ! read] w\ld h>dly discov] :at ^? laws are1 & confid5tly assign !m by rapid contemplation ( ! comb9ations1 z giv5 9 ! fir/ gr\p4 ,sev]al t5tative classifications mu/ probably be made be=e we c resolve ! "q4 ,let u n[ suppose t in/ead ( eight objects & five qualities1 we h1 say1 five hundr$ objects & fifty qualities4 ,if we 7 to attempt ! same me?od ( exhau/ive gr\p+ :i* we be=e employ$1 we %\ld h to arrange ! five hundr$ objects 9 fifty diff]5t ways1 be=e we c\ld be sure t we _h discov]$ ev5 ! simpl] laws ( correlation4 ,b ev5 ! successive gr\p+ ( all ^? possess+ ea* ( ! fifty prop]ties w\ld n necess>ily give u all ! laws4 ,!re might exi/ complicat$ relations betwe5 sev]al prop]ties simultane\sly1 = ! detection ( :i* no rule ( proc$ure :atev] c be giv54 99,bifurcate ,classification499 ,e sy/em ( classification ought to be =m$ on ! pr9ciples ( ! ,logical ,alphabet4 ,ea* sup]ior class %\ld be divid$ into two inf]ior classes1 di/+ui%$ by ! possession & non-possession ( a s+le specifi$ diff]5ce4 ,ea* ( ^! m9or classes1 aga91 is divisible by any o!r quality :atev] :i* c be sugge/$1 & ?us e classification logically consi/s ( an inf9itely ext5d$ s]ies ( subalt]n g5]a & species4 ,! classifications :i* we =m are 9 reality v small fragm5ts ( ^? :i* w\ld correctly & fully repres5t ! relations ( exi/+ ?+s4 ,b if we take m ?an f\r or five qualities into acc\nt1 ! numb] ( subdivisions gr[s impracticably l>ge4 ,our f9ite m9ds are unable to treat any complex gr\p exhau/ively1 & we are oblig$ to simplify & g5]alise sci5tific problems1 (t5 at ! risk ( ov]look+ p>ticul> conditions & exceptions4 ,e sy/em ( classes display$ 9 ! mann] ( ! ,logical ,alphabet may be call$ 99bifurcate991 because e class bran*es out at ea* /ep into two m9or classes1 exi/5t or imag9>y4 ,x w\ld be a great mi/ake to reg>d ?is arrangem5t z 9 any way a peculi> or special me?od2 x is n only a natural & important "o1 b x is ! inevitable & only sy/em :i* is logically p]fect1 accord+ to ! fundam5tal laws ( ?\ght4 ,all o!r arrangem5ts ( classes correspond to ! bifurcate arrangem5t1 ) ! implication t "s ( ! m9or classes are n repres5t$ among exi/+ ?+s4 ,if we take ! g5us ,a & divide x into ! species ,,ab & ,,ac1 we imply two propositions1 namely t 9 ! class ,a1 ! prop]ties ( ,b & ,c nev] occur toge!r1 & t !y are nev] bo? abs5t2 ^! propositions are logically equival5t to "o1 namely ,,ab ,a99c994 ,our classification is !n id5tical ) ! foll[+ bifurcate "o3-- ,a -------------------- ,,ab ,a99b99 ------------ ------------ ,,abc #j ,,ab99c99 ,a99b99,c ,a99bc99 #j ,if1 aga91 we divide ! g5us ,a into ?ree species1 ,,ab1 ,,ac1 ,,ad1 we are ei!r logically 9 error1 or else we mu/ be und]/ood to imply t1 z reg>ds ! o!r lett]s1 !re exi/ only ?ree comb9ations conta9+ ,a1 namely ,,ab99cd991 ,a99b99,c99d991 & ,a99bc99,d4 ,! logical necessity ( bifurcate classification has be5 cle>ly & correctly /at$ 9 ! 99,outl9e ( a ,new ,sy/em ( ,logic99 by ,george ,b5?am1 ! em95t botani/1 a "w ( :i* ! logical value has be5 q ov]look$ until lately4 ,mr4 ,b5?am po9ts out1 9 p4 #aac1 t e classification mu/ be ess5tially bifurcate1 & takes1 z an example1 ! division ( v]tebrate animals into f\r sub-classes1 z foll[s3-- ,mammif]a--end[$ ) mamm & lungs4 ,birds )\t mamm b ) lungs & w+s4 ,fi% depriv$ ( lungs4 ,reptiles depriv$ ( mamm & w+s b ) lungs4 ,we h1 !n1 z ,mr4 ,b5?am says1 ?ree bifid divisions1 ?us repres5t$3-- ,v]tebrata ---------------------- ,end[$ ) lungs depriv$ ( lungs ,fi%4 ------------------------ ,end[$ ) depriv$ ( mamm mamm ,mammif]a4 ------------ ) w+s )\t w+s ,birds4 ,reptiles4 ,x is q evid5t t accord+ to ! laws ( ?\ght ev5 ?is arrangem5t is incomplete4 ,! sub-class mammif]a mu/ ei!r h w+s or be depriv$ ( !m2 we mu/ ei!r subdivide ?is class1 or assume t none ( ! mammif]a h w+s1 :i* is1 z a matt] ( fact1 ! case1 ! w+s ( bats n be+ true w+s 9 ! mean+ ( ! t]m z appli$ to birds4 ,fi%1 aga91 ought to be consid]$ ) reg>d to ! possession ( mamm & w+s2 & 9 leav+ !m undivid$ we really imply t !y nev] h mamm nor w+s1 ! w+s ( ! fly+-fi%1 aga91 be+ no exception4 ,if we resort to ! use ( our lett]s & def9e !m z foll[s-- ,a v]tebrata1 ,b hav+ lungs1 ,c hav+ mamm1 ,d hav+ w+s1 !n !re are f\r exi/5t classes ( v]tebrata :i* appe> to be ?us describ$-- ,,abc ,,ab99c99,d ,,ab99cd99 ,a99b994 ,b 9 reality ! comb9ations are impli$ to be ,,abc99d99 ,mammif]a1 ,,ab99c99,d ,birds1 ,,ab99cd99 ,reptiles1 ,a99bcd99 ,fi%1 & we imply at ! same "t t ! o!r f\r conceivable comb9ations conta9+ ,b1 ,c1 or ,d1 namely ,,abcd1 ,a99b99,,cd1 ,a99b99,c99d991 & ,a99bc99,d1 d n exi/ 9 nature4 ,mr4 ,b5?am po9ts out#egc t x is really ?is me?od ( classification :i* 0 employ$ by ,lam>ck & ,de ,c&olle 9 _! s-call$ analytical arrangem5t ( ! ,fr5* ,flora4 ,he gives z an example a table ( ! pr9cipal classes ( ,de ,c&olle's sy/em1 z also a bifurcate arrangem5t ( animals aft] ! me?od propos$ by ,dumril 9 8 99,zoologie ,analytique991 ?is naturali/ be+ di/+ui%$ by 8 cle> p]ception ( ! logical importance ( ! me?od4 ,a bifurcate classification ( ! animal k+dom may also be f\nd 9 ,pr(essor ,reay ,gre5e's 99,manual ( ! ,cl5t]ata991 p4 #ah4 #egc 99,essai sur la ,nom5clature et la ,classification991 ,p>is1 #ahbc1 pp4 #ajg1 #ajh4 ,! bifurcate =m ( classification seems to be ne$less :5 ! quality accord+ to :i* we classify any gr\p ( ?+s admits ( num]ical discrim9ation4 ,x w\ld seem absurd to arrange ?+s accord+ z !y h "o degree ( ! quality or n "o degree1 two degrees or n two degrees1 & s on4 ,! elem5ts are classifi$ accord+ z ! atom ( ea* saturates "o1 two1 ?ree1 or m atoms ( a monad elem5t1 su* z *lor9e1 & !y are call$ accord+ly monad1 dyad1 triad1 tetrad elem5ts1 & s on4 ,x w\ld be useless to apply ! bifid arrangem5t1 ?us3-- ,elem5t ------------ ,monad n-,monad ------------------ ,dyad n-,dyad ------------------ ,triad n-,triad ----------------- ,tetrad n-,tetrad4 ,! reason ( ?is is t1 by ! nature ( numb] 7p4 #aeg7 e numb] is logically discrim9at$ f e o!r numb]4 ,!re c ?us be no logical confusion 9 a num]ical arrangem5t1 & ! s]ies ( numb]s indef9itely ext5d$ is also exhau/ive4 ,e ?+ admitt+ ( a quality expressible 9 numb]s mu/ f9d its place some:]e 9 ! s]ies ( numb]s4 ,! *ords 9 music correspond to ! simpl] num]ical ratios & mu/ admit ( complete exhau/ive classification 9 respect to ! complexity ( ! ratios =m+ !m4 ,plane rectil9e> figures may be classifi$ accord+ to ! numb]s ( _! sides1 z triangles1 quadrilat]al figures1 p5tagons1 hexagons1 heptagons1 c4 ,! bifurcate arrangem5t is n false :5 appli$ to su* s]ies ( objects2 x is ev5 necess>ily involv$ 9 ! arrangem5t :i* we d apply1 s t its =mal /atem5t is ne$less & t$i\s4 ,! same may be said ( ! division ( portions ( space4 ,reid & ,kames endeav\r$ to ca/ ridicule on ! bifurcate arrangem5t#egd by propos+ to classify ! p>ts ( ,engl& into ,middlesex & :at is n ,middlesex1 divid+ ! latt] aga9 into ,k5t & :at is n ,k5t1 ,sussex & :at is n ,sussex2 & s on4 ,?is is s f>1 h[ev]1 f be+ an absurd proce$+ t x is requisite to assure u t we h made an exhau/ive enum]ation ( ! p>ts ( ,engl&4 #egd ,george ,b5?am1 99,outl9e ( a ,new ,sy/em ( ,logic991 p4 #aae4 99,! ,five ,pr$icables499 ,z a rule x is highly desirable to consign to oblivion ! anci5t logical names & expressions1 :i* h infe/$ ! sci5ce = _m c5turies pa/4 ,if logic is ev] to be a useful & progressive sci5ce1 logicians mu/ di/+ui% betwe5 logic & ! hi/ory ( logic4 ,z 9 ! case ( any o!r sci5ce x may be desirable to exam9e ! c\rse ( ?\ght by :i* logic has1 be=e or s9ce ! "t ( ,ari/otle1 be5 br\ght to its pres5t /ate2 ! hi/ory ( a sci5ce is always in/ructive z giv+ in/ances ( ! mode 9 :i* discov]ies take place4 ,b at ! same "t we ought c>efully to dis5cumb] ! /atem5t ( ! sci5ce itself ( all names & o!r ve/iges ( antiquity :i* are n actually useful at ! pres5t day4 ,among ! anci5t expressions :i* may well be except$ f su* consid]ations & reta9$ 9 use1 are ! 8,five ,words0 or 8,five ,pr$icables0 :i* 7 describ$ by ,porphyry 9 8 introduction to ,ari/otle's ,organum4 ,two ( !m1 99,g5us99 & 99,species991 are ! mo/ v5]able names 9 philosophy1 hav+ probably be5 fir/ employ$ 9 _! pres5t logical mean+s by ,socrates4 ,9 ! pres5t day x requires "s m5tal ef=t1 z rem>k$ by ,grote1 to see any?+ important 9 ! inv5tion ( notions n[ s famili> z ^? ( ,g5us & ,species4 ,b 9 reality ! introduction ( su* t]ms %[$ ! rise ( ! fir/ g]ms ( logic & sci5tific me?od2 x %[$ t m5 7 beg9n+ to analyse _! processes ( ?\ght4 ,! ,five ,pr$icables are ,g5us1 ,species1 ,diff]5ce1 ,prop]ty1 & ,accid5t1 or 9 ! orig9al ,greek1 1 1 1 1 4 ,( ^!1 ,g5us may be tak5 to mean any class ( objects :i* is reg>d$ z brok5 up into two m9or classes1 :i* =m ,species ( x4 ,! g5us is def9$ by a c]ta9 numb] ( qualities or circum/ances :i* belong to all objects includ$ 9 ! class1 & :i* are suffici5t to m>k out ^! objects f all o!rs :i* we d n int5d to include4 ,int]pret$ z reg>ds int5sion1 !n1 ! g5us is a gr\p ( qualities2 int]pret$ z reg>ds ext5sion1 x is a gr\p ( objects possess+ ^? qualities4 ,if ano!r quality be tak5 into acc\nt :i* is possess$ by "s ( ! objects & n by ! o!rs1 ?is quality becomes a diff]5ce :i* divides ! g5us into two species4 ,we may int]pret ! species ei!r 9 int5sion or ext5sion2 9 ! =m] respect x is m ?an ! g5us z conta9+ "o m quality1 ! diff]5ce3 9 ! latt] respect x is less ?an ! g5us z conta9+ only a portion ( ! gr\p con/itut+ ! g5us4 ,we may say1 !n1 ) ,ari/otle1 t 9 "o s5se ! g5us is 9 ! species1 namely 9 int5sion1 & 9 ano!r s5se ! species is 9 ! g5us1 namely 9 ext5sion4 ,! diff]5ce1 x is evid5t1 c be int]pret$ 9 int5sion only4 ,a ,prop]ty is a quality :i* belongs to ! :ole ( a class1 b does n ent] into ! def9ition ( t class4 ,a g5]ic prop]ty belongs to e individual object conta9$ 9 ! g5us4 ,x is a prop]ty ( ! g5us p>allelogram t ! opposite angles are equal4 ,if we reg>d a rectangle z a species ( p>allelogram1 ! diff]5ce be+ t 99"o99 angle is a "r angle1 x foll[s z a specific prop]ty t all ! angles are "r angles4 ,?\gh a prop]ty 9 ! /rict logical s5se mu/ belong to ea* ( ! objects includ$ 9 ! class ( :i* x is a prop]ty1 x may or may n belong to o!r objects4 ,! prop]ty ( hav+ ! opposite angles equal may belong to _m figures besides p>allelograms1 = in/ance1 regul> hexagons4 ,x is a prop]ty ( ! circle t all triangles con/ruct$ ^u ! diamet] ) ! apex ^u ! circumf]5ce are "r-angl$ triangles1 & 99vice v]s991 all curves ( :i* ?is is true mu/ be circles4 ,a prop]ty :i* ?us belongs to ! :ole ( a class & only to t class1 corresponds to ! ( ,ari/otle & ,porphyry2 we might conv5i5tly call x 99a peculi> prop]ty994 ,e su* prop]ty enables u to make a /atem5t 9 ! =m ( a simple id5tity 7p4 #cg74 ,?us we "k x to be a peculi> prop]ty ( ! circle t = a giv5 l5g? ( p]imet] x encloses a great] area ?an any o!r possible curve2 h5ce we may say-- ,curve ( equal curvature curve ( greate/ area4 ,x is a peculi> prop]ty ( equilat]al triangles t !y are equiangul>1 & 99vice v]s991 x is a peculi> prop]ty ( equiangul> triangles t !y are equilat]al4 ,x is a prop]ty ( cry/als ( ! regul> sy/em t !y are devoid ( ! p[] ( d\ble refraction1 b ?is is n a prop]ty peculi> to !m1 because liquids & gases are devoid ( ! same prop]ty4 ,an ,accid5t1 ! fif? & la/ ( ! ,pr$icables1 is any quality :i* may or may n belong to c]ta9 objects1 & :i* has no connexion ) ! classification adopt$4 ,! p>ticul> size ( a cry/al does n 9 ! slighte/ degree affect ! =m ( ! cry/al1 nor does ! mann] 9 :i* x is gr\p$ ) o!r cry/als2 ^!1 !n1 are accid5ts z reg>ds a cry/allographic classification4 ,) respect to ! *emical composition ( a sub/ance1 aga91 x is an accid5t :e!r ! sub/ance be cry/allis$ or n1 or :e!r x be organis$ or n4 ,z reg>ds botanical classification ! absolute size ( a plant is an accid5t4 ,?us we see t a logical accid5t is any quality or circum/ance :i* is n kn[n to be correlat$ ) ^? qualities or circum/ances =m+ ! def9ition ( ! species4 ,! mean+s ( ! ,pr$icables c be cle>ly expla9$ by our symbols4 ,let ,a be any def9ite gr\p ( qualities & ,b ano!r quality or gr\p ( qualities2 !n ,a w con/itute a g5us1 & ,,ab1 ,a99b99 w be species ( x1 ,b be+ ! diff]5ce4 ,let ,c1 ,d & ,e be o!r qualities or gr\ps ( qualities1 & on exam9+ ! comb9ations 9 :i* ,a1 ,b1 ,c1 ,d1 ,e occur let !m be z foll[s3-- ,,abcde ,a99b99,c99d99,e ,,abcd99e99 ,a99b99,c99de994 ,"h we see t :]ev] ,a is we also f9d ,c1 s t ,c is a g5]ic prop]ty2 ,d occurs always ) ,b1 s t x con/itutes a specific prop]ty1 :ile ,e is indiff]5tly pres5t & abs5t1 s z n to be relat$ to any o!r lett]2 x repres5ts1 !re=e1 an accid5t4 ,x w n[ be se5 t ! ,logical ,alphabet repres5ts an int]m9able s]ies ( subord9ate g5]a & species2 x is b a concise symbolic /atem5t ( :at 0 involv$ 9 ! anci5t doctr9e ( ! ,pr$icables4 99,summum ,g5us & ,infima ,species499 ,z a g5us means any class :atev] :i* is reg>d$ z compos$ ( m9or classes or species1 x foll[s t ! same class w be a g5us 9 "o po9t ( view & a species 9 ano!r4 ,metal is a g5us z reg>ds alkal9e metal1 a species z reg>ds elem5t1 & any ext5sive sy/em ( classes consi/s ( a s]ies ( subord9ate1 or z !y are te*nically call$1 99subalt]n99 g5]a & species4 ,! "q1 h[ev]1 arises1 :e!r su* a *a9 ( classes has a def9ite t]m9ation at ei!r end4 ,! doctr9e ( ! old logicians 0 to ! effect t x t]m9at$ upw>ds 9 a 99g5us g5]alissimum99 or 99summum g5us991 :i* 0 n a species ( any wid] class4 ,"s v g5]al notion1 su* z sub/ance1 object1 or ?+1 0 suppos$ to be s compreh5sive z to include all ?9kable objects1 & = all practical purposes ?is might be s4 ,b z ,i h already expla9$ 7p4 #gd71 we _c really ?9k ( any object or class )\t !reby sep>at+ x f :at is n t object or class4 ,all ?9k+ is relative1 & implies discrim9ation1 s t e class & e logical notion mu/ h its negative4 ,if s1 !re is no su* ?+ z a 99summum g5us992 = we _c frame ! requisite notion ( a class =m+ x )\t imply+ ! exi/5ce ( ano!r class discrim9at$ f x2 add ?is new negative class to ! suppos$ 99summum g5us991 & we =m a /ill high] g5us1 :i* is absurd4 ,al?\gh !re is no absolute summum g5us1 nev]!less relatively to any bran* ( k or any p>ticul> argum5t1 !re is always "s class or notion :i* b\nds our horizon z x 74 ,! *emi/ re/ricts 8 view to mat]ial sub/ances & ! =ces manife/$ 9 !m2 ! ma!matician ext5ds 8 view s z to compreh5d all notions capable ( num]ical discrim9ation4 ,! biologi/1 on ! o!r h&1 has a n>r[] sph]e conta9+ only organis$ bodies1 & ( ^! ! botani/ & ! zoologi/ take p>ts4 ,9 o!r subjects !re may be a /ill n>r[] summum g5us1 z :5 ! lawy] reg>ds only reason+ be+s ( 8 own c\ntry toge!r ) _! prop]ty4 ,9 ! description ( ! ,logical ,alphabet x 0 po9t$ out 7p4 #ic7 t e s]ies ( comb9ations is really ! developm5t ( a s+le class1 d5ot$ by ,x1 :i* lett] 0 accord+ly plac$ 9 ! fir/ column ( ! table on p4 #id4 ,?is is ! =mal ackn[l$gm5t ( ! pr9ciple cle>ly /at$ by ,de ,morgan1 t all reason+ proce$s )9 an assum$ summum g5us4 ,b at ! same "t ! fact t ,x z a logical t]m mu/ h its negative 99x991 %[s t x _c be an absolute summum g5us4 ,!re arises1 aga91 ! "q :e!r !re be any su* ?+ z an 99infima species991 :i* _c be divid$ into m9or species4 ,! anci5t logicians 7 ( op9ion t !re always 0 "s assignable class :i* c\ld only be divid$ into individuals1 b ?is doctr9e appe>s to be !oretically incorrect1 z ,mr4 ,george ,b5?am long ago /at$4#ege ,we may put an arbitr>y limit to ! subdivision ( our classes at any po9t conv5i5t to our purpose4 ,! cry/allograph] w\ld n g5]ally treat z diff]5t species cry/all9e =ms :i* diff] only 9 ! degree ( developm5t ( ! faces4 ,! naturali/ ov]looks innum]able slight diff]5ces betwe5 animals :i* he ref]s to ! same species4 ,b 9 a /rictly logical po9t ( view classification might be c>ri$ on z long z !re is a diff]5ce1 h[ev] m9ute1 betwe5 two objects1 & we might ?us g on until we arrive at individual objects :i* are num]ically di/9ct 9 ! logical s5se attribut$ to t expression 9 ! *apt] ^u ,numb]4 ,ei!r1 !n1 we mu/ call ! individual ! 99infima species99 or all[ t !re is no su* ?+ at all4 #ege 99,outl9e ( a ,new ,sy/em ( ,logic991 #ahbg1 p4 #aag4 99,! ,tree ( ,porphyry499 ,bo? ,ari/otle & ,plato 7 acqua9t$ ) ! value ( bifurcate classification1 :i* !y occasionally employ$ 9 an explicit mann]4 ,x is impossible too t ,ari/otle %\ld /ate ! laws ( ?\ght1 & employ ! pr$icables )\t implicitly recognis+ ! logical necessity ( t me?od4 ,x is1 h[ev]1 9 ,porphyry's rem>kable & 9 _m respects excell5t 99,introduction to ! ,categories ( ,ari/otle99 t we f9d ! mo/ di/9ct acc\nt ( x4 ,porphyry n only fully & accurately describes ! ,pr$icables1 b incid5tally introduces an example = illu/rat+ ^? pr$icables1 :i* con/itutes a good specim5 ( bifurcate classification4 ,translat+ 8 words#egf freely we may say t he takes ,sub/ance z ! g5us to be divid$1 "u :i* are successively plac$ z ,species--,body1 ,animat$ ,body1 ,animal1 ,rational ,animal1 & ,man4 ,"u ,man1 aga91 come ,socrates1 ,plato1 & o!r p>ticul> m54 ,n[ ( ^! notions ,sub/ance is ! g5us g5]alissimum1 & is a g5us only1 n a species4 ,man1 on ! o!r h&1 is ! species specialissima 7infima species71 & is a species only1 n a g5us4 ,body is a species ( sub/ance1 b a g5us ( animat$ body1 :i*1 aga91 is a species ( body b a g5us ( animal4 ,animal is a species ( animat$ body1 b a g5us ( rational animal1 :i*1 aga91 is a species ( animal1 b a g5us ( man4 ,f9ally1 man is a species ( rational animal1 b is a species m]ely & n a g5us1 be+ divisible only into p>ticul> m54 #egf 99,porphyrii ,isagoge991 ,caput ii4 #bd4 ,porphyry proce$s at "s l5g? to employ 8 example 9 fur!r illu/ration ( ! pr$icables4 ,we d n f9d 9 ,porphyry's own "w any s*eme or diagram exhibit+ ?is curi\s specim5 ( classification1 b "s ( ! e>li] comm5tators & epitome writ]s drew :at has long be5 call$ ! ,tree ( ,porphyry4 ,?is diagram1 :i* may be f\nd 9 mo/ elem5t>y works on ,logic1#egg is also call$ ! ,ramean ,tree1 because ,ramus insi/$ mu* ^u ! value ( ,di*otomy4 ,) ! exception ( ,j]emy ,b5?am#egh & ,george ,b5?am1 h>dly any mod]n logicians h %[n an appreciation ( ! value ( bifurcate classification4 ,! latt] au?or has treat$ ! subject1 bo? 9 8 99,outl9e ( a ,new ,sy/em ( ,logic99 7pp4 #aje-aah71 & 9 8 e>li] "w entitl$ 99,essai sur la ,nom5clature et la ,classification des ,pr9cipales ,bran*es d',art-et-,sci5ce99 7,p>is1 #ahbc71 :i* consi/s ( a free translation or improv$ v]sion ( 8 uncle's ,essay on ,classification 9 ! 99,*re/oma?ia994 ,"s int]e/ atta*es to ! hi/ory ( ! ,tree ( ,porphyry & ,ramus1 because x is ! prototype ( ! ,logical ,alphabet :i* lies at ! basis ( logical me?od4 ,j]emy ,b5?am speaks truly ( 8! mat*less beauty ( ! ,ramean ,tree40 ,aft] fully %[+ its logical value z an exhau/ive me?od ( classification1 & refut+ ! objections ( ,reid & ,kames1 on a wrong gr\nd1 z ,i ?9k1 he proce$s to inquire to :at l5g? x may be c>ri$4 ,he correctly po9ts out two objections to ! ext5sive use ( bifid arrangem5ts1 7#a7 t !y soon become impracticably ext5sive & unwieldy1 & 7#b7 t !y are uneconomical4 ,9 8 day ! record$ numb] ( diff]5t species ( plants 0 #dj1jjj1 & he leaves ! read] to e/imate ! imm5se numb] ( bran*es & ! enorm\s area ( a bifurcate table :i* %\ld exhibit all ^! species 9 "o s*eme4 ,he also po9ts out ! app>5t loss ( lab\r 9 mak+ any l>ge bifurcate classification2 b ?is he consid]s to be fully recomp5s$ by ! logical value ( ! result1 & ! logical tra9+ acquir$ 9 its execution4 ,j]emy ,b5?am1 !n1 fully recognises ! value ( ! ,logical ,alphabet "u ano!r "n1 ?\gh he appreh5ds also ! limit to its use plac$ by ! f9it5ess ( our m5tal & manual p[]s4 #egg ,jevons1 99,elem5t>y ,lessons 9 ,logic991 p4 #ajd4 #egh 99,*re/oma?ia2 be+ a ,collection ( ,pap]s1 c499 ,london1 #ahaf1 ,app5dix ,v4 99,does ,ab/raction imply ,g5]alisation899 ,be=e we c acquire a s\nd compreh5sion ( ! subject ( classification we mu/ answ] ! v difficult "q :e!r logical ab/raction does or does n imply g5]alisation4 ,x comes to exactly ! same ?+ if we ask :e!r a species may be coext5sive ) its g5us1 or :e!r1 on ! o!r h&1 ! g5us mu/ conta9 m ?an ! species4 ,to ab/ract logically is 7p4 #bg71 to ov]look or )draw our notice f "s po9t ( diff]5ce4 ,:5ev] we =m a class we ab/ract1 = ! "t be+1 ! diff]5ces ( ! objects s unit$ 9 respect ( "s common quality4 ,if we class toge!r a great numb] ( objects z dwell+-h\ses1 we ov]look ! fact t "s dwell+-h\ses are con/ruct$ ( /one1 o!rs ( brick1 wood1 iron1 c4 ,(t5 at lea/ ! ab/raction ( a circum/ance increases ! numb] ( objects includ$ "u a class accord+ to ! law ( ! inv]se relation ( ! quantities ( ext5sion & int5sion 7p4 #bf74 ,dwell+-h\se is a wid] t]m ?an brick-dwell+-h\se4 ,h\se is m g5]al ?an dwell+-h\se4 ,b ! "q be=e u is1 :e!r ab/raction 99always99 increases ! numb] ( objects includ$ 9 a class1 :i* am\nts to ask+ :e!r ! law ( ! inv]se relation ( logical quantities is 99always99 true4 ,! int]e/ ( ! "q p>tly arises f ! fact1 t s high a philosophical au?ority z ,mr4 ,h]b]t ,sp5c] has d5i$ t g5]alisation is impli$ 9 ab/raction1#egi mak+ ?is doctr9e ! gr\nd = reject+ previ\s me?ods ( classify+ ! sci5ces1 & = =m+ an +5i\s b peculi> me?od ( 8 own4 ,! "q is also a fundam5tal "o ( ! highe/ logical importance1 & involves subtle difficulties :i* h made me long hesitate 9 =m+ a decisive op9ion4 #egi 99,! ,classification ( ! ,sci5ces991 c41 #crd edit4 p4 #g4 99,essays3 ,sci5tific1 ,political1 & ,speculative991 vol4 iii4 p4 #ac4 ,let u attempt to answ] ! "q by exam9ation ( a few examples4 ,comp>e ! two classes 99gun99 & 99iron gun994 ,x is c]ta9 t !re are _m guns :i* are n made ( iron1 s t ab/raction ( ! circum/ance 8made ( iron0 increases ! ext5t ( ! notion4 ,next comp>e 99gun99 & 99metallic gun994 ,all guns made at ! pres5t day consi/ ( metal1 s t ! two notions seem to be coext5sive2 b guns 7 at fir/ made ( pieces ( wood b\nd toge!r l a tub1 & z ! logical t]m gun takes no acc\nt ( "t1 x mu/ include all guns t h ev] exi/$4 ,"h aga9 ext5sion increases z int5sion decreases4 ,comp>e once m 8/eam-locomotive eng9e0 & 8locomotive eng9e40 ,9 ! pres5t day1 z f> z ,i am aw>e1 all locomotives are work$ by /eam1 s t ! omission ( t qualification might seem n to wid5 ! t]m2 b x is q possible t 9 "s future age a diff]5t motive p[] may be us$ 9 locomotives2 & z !re is no limitation ( "t 9 ! use ( logical t]ms1 we mu/ c]ta9ly assume t !re is a class ( locomotives n work$ by /eam1 z well z a class t is work$ by /eam4 ,:5 ! natural class ( ,euphorbiace 0 orig9ally =m$1 all ! plants kn[n to belong to x 7 devoid ( corollas2 x w\ld h seem$ !re=e t ! two classes 8,euphorbiace10 & 8,euphorbiace devoid ( ,corollas10 7 ( equal ext5t4 ,subsequ5tly a numb] ( plants pla9ly belong+ to ! same class 7 f\nd 9 tropical c\ntries1 & !y possess$ bright col\r$ corollas4 ,naturali/s believe ) ! utmo/ confid5ce t 8,rum9ants0 & 8,rum9ants ) cleft feet0 are id5tical t]ms1 because no rum9ant has yet be5 discov]$ )\t cleft feet4 ,b we c see no impossibility 9 ! conjunction ( rum9ation ) uncleft feet1 & x w\ld be too great an assumption to say t we are c]ta9 t an example ( x w nev] be met )4 ,in/ances c be quot$1 )\t end1 ( objects be+ ultimately discov]$ comb9+ prop]ties :i* _h nev] be=e be5 se5 toge!r4 ,9 ! animal k+dom ! ,black ,swan1 ! ,orni?orhyn*us ,p>adoxus1 & m rec5tly ! s+ul> fi% call$ ,c]atodus ,=/]i1 all discov]$ 9 ,au/ralia1 h unit$ *>act]s nev] previ\sly kn[n to coexi/4 ,at ! pres5t "t deep-sea dr$g+ is br++ to light _m animals ( an unprec$5t$ nature4 ,s+ul> exceptional discov]ies may c]ta9ly occur 9 o!r bran*es ( sci5ce4 ,:5 ,davy fir/ discov]$ metallic potassium1 x 0 a well e/abli%$ empirical law t all metallic sub/ances possess$ a high specific gravity1 ! lea/ d5se ( ! metals !n kn[n be+ z9c1 ( :i* ! specific gravity is #ga4 ,yet to ! surprise ( *emi/s1 potassium 0 f\nd to be an und\bt$ metal ( less d5sity ?an wat]1 its specific gravity be+ #jhfe4 ,x is h>dly requisite to prove by fur!r examples t our k ( nature is incomplete1 s t we _c safely assume ! non-exi/5ce ( new comb9ations4 ,logically speak+1 we ought to leave a place op5 = animals :i* rum9ate b are )\t cleft feet1 & = e possible int]m$iate =m ( animal1 plant1 or m9]al4 ,a purely logical classification mu/ take acc\nt n only ( :at c]ta9ly does exi/1 b ( :at may 9 aft] ages be f\nd to exi/4 ,i w g a /ep fur!r1 & say t we mu/ h places 9 our sci5tific classifications = purely imag9>y exi/5ces4 ,a l>ge proportion ( ! ma!matical functions :i* are conceivable h no application to ! circum/ances ( ?is _w4 ,physici/s c]ta9ly d inve/igate ! nature & consequ5ces ( =ces :i* n[h]e exi/4 ,newton's 99,pr9cipia99 is full ( su* inve/igations4 ,9 "o *apt] ( 8 99,mcanique ,cle/e99 ,laplace indulges 9 a rem>kable speculation z to :at ! laws ( motion w\ld h be5 if mom5tum1 in/ead ( v>y+ simply z ! velocity1 _h be5 a m complicat$ function ( x4 ,i h already m5tion$ 7p4 #bbc7 t ,airy contemplat$ ! exi/5ce ( a _w 9 :i* ! laws ( =ce %\ld be su* t a p]petual motion w\ld be possible1 & ! ,law ( ,cons]vation ( ,en]gy w\ld n hold true4 ,?\ght is n b\nd d[n to ! limits ( :at is mat]ially exi/5t1 b is circumscrib$ only by ^? ,fundam5tal ,laws ( ,id5tity1 ,contradiction & ,duality1 :i* 7 laid d[n at ! outset4 ,?is is ! po9t at :i* ,i %\ld diff] f ,mr4 ,sp5c]4 ,he appe>s to suppose t a classification is complete if x has a place = e exi/+ object1 & ?is may p]haps seem to be practically suffici5t2 b x is subject to two pr(\nd objections4 ,fir/ly1 we d n "k all t exi/s1 & !re=e 9 limit+ our classes we are errone\sly omitt+ multitudes ( objects ( unkn[n =m & nature :i* may exi/ ei!r on ?is e>? or 9 o!r p>ts ( space4 ,secondly1 z ,i h expla9$1 ! p[]s ( ?\ght are n limit$ by mat]ial exi/5ces1 & we may1 or1 = "s purposes1 mu/ imag9e objects :i* probably d n exi/1 & if we imag9e !m we ought to f9d places = !m 9 ! classifications ( sci5ce4 ,! *ief difficulty ( ?is subject1 h[ev]1 consi/s 9 ! fact t ma!matical or o!r c]ta9 laws may entirely =bid ! exi/5ce ( "s comb9ations4 ,! circle may be def9$ z a plane curve ( equal curvature1 & x is a prop]ty ( ! circle t x conta9s ! greate/ area )9 ! lea/ possible p]imet]4 ,may we !n contemplate m5tally a circle n a figure ( greate/ possible area8 ,or1 to take a /ill simpl] example1 a p>allelogram possesses ! prop]ty ( hav+ ! opposite angles equal4 ,may we !n m5tally divide p>allelograms into two classes accord+ z !y d or d n h _! opposite angles equal8 ,x might seem absurd to d s1 because we "k t "o ( ! two species ( p>allelogram w\ld be non-exi/5t4 ,b1 !n1 unless ! /ud5t _h previ\sly contemplat$ ! exi/5ce ( bo? species z possible1 :at is ! mean+ ( ! ?irty-f\r? proposition ( ,euclid's fir/ book8 ,we _c d5y or disprove ! exi/5ce ( a c]ta9 comb9ation )\t !reby 9 a c]ta9 way recognis+ t comb9ation z an object ( ?\ght4 ,! conclusion at :i* ,i arrive is 9 opposition to t ( ,mr4 ,sp5c]4 ,i ?9k t :5ev] we ab/ract a quality or circum/ance we d g5]alise or wid5 ! notion f :i* we ab/ract4 ,:atev] ! t]ms ,a1 ,b1 & ,c may be1 ,i hold t 9 /rict logic ,,ab is m5tally a wid] t]m ?an ,,abc1 because ,,ab includes ! two species ,,abc & ,,ab99c994 ,! t]m ,a is wid] /ill1 = x includes ! f\r species ,,abc1 ,,ab99c991 ,a99b99,c1 ,a99bc994 ,! ,logical ,alphabet1 9 %ort1 is ! only limit ( ! classes ( objects :i* we mu/ contemplate 9 a purely logical po9t ( view4 ,:atev] notions be br\ght be=e u1 we mu/ m5tally comb9e !m 9 all ! ways sanction$ by ! laws ( ?\ght & exhibit$ 9 ! ,logical ,alphabet1 & x is a matt] = aft] consid]ation to det]m9e h[ _m ( ^! comb9ations exi/ 9 outw>d nature1 or h[ _m are actually =bidd5 by ! conditions ( space4 ,a classification is ess5tially a m5tal1 n a mat]ial ?+4 99,discov]y ( ,m>ks or ,*>act]i/ics499 ,al?\gh ! *ief purpose ( classification is to disclose ! deepe/ & mo/ g5]al resemblances ( ! objects classifi$1 yet ! practical value ( a sy/em w dep5d p>tly ^u ! ease ) :i* we c ref] an object to its prop] class1 & ?us inf] conc]n+ x all t is kn[n g5]ally ( t class4 ,?is op]ation ( discov]+ to :i* class ( a sy/em a c]ta9 specim5 or case belongs1 is g5]ally call$ 99,diagnosis991 a te*nical t]m famili>ly us$ by physicians1 :o con/antly require to diagnose or det]m9e ! nature ( ! disease f :i* a pati5t is suff]+4 ,n[ e class is def9$ by c]ta9 specifi$ qualities or circum/ances1 ! :ole ( :i* are pres5t 9 e object conta9$ 9 ! class1 & 99n all pres5t99 9 any object exclud$ f x4 ,^! def9+ circum/ances ought to consi/ ( ! deepe/ & mo/ important circum/ances1 by :i* we vaguely mean ^? probably =m+ ! conditions ) :i* ! m9or circum/ances are correlat$4 ,b x w (t5 happ5 t ! s-call$ important po9ts ( an object are n ^? :i* c mo/ readily be obs]v$4 ,?us ! two great classes ( phan]ogam\s plants are def9$ respectively by ! possession ( two cotyl$ons or se$-leaves1 & "o cotyl$on4 ,b :5 a plant comes to our notice & we want to ref] x to ! "r class1 x w (t5 happ5 t we h no se$ at all to exam9e1 9 ord] to discov] :e!r !re be "o se$-leaf or two 9 ! g]m4 ,ev5 if we h a se$ x w (t5 be small1 & a c>eful dissection "u ! microscope w be requisite to asc]ta9 ! numb] ( cotyl$ons4 ,occasionally ! exam9ation ( ! g]m w\ld mislead u1 = ! cotyl$ons may be obsolete1 z 9 ,cuscuta1 or unit$ toge!r1 z 9 ,cl9tonia4 ,botani/s !re=e seldom actually ref] to ! se$ = su* in=mation4 ,c]ta9 o!r *>act]s ( a plant are correlat$ ) ! numb] ( se$-leaves2 ?us monocotyl$on\s plants almo/ always possess leaves ) p>allel ve9s l ^? ( grass1 :ile dicotyl$on\s plants h leaves ) reticulat$ ve9s l ^? ( an oak leaf4 ,9 monocotyl$on\s plants1 too1 ! p>ts ( ! fl[] are mo/ (t5 ?ree or "s multiple ( ?ree 9 numb]1 :ile 9 dicotyl$on\s plants ! numb]s f\r & five & _! multiples prevail4 ,botani/s1 !re=e1 by a glance at ! leaves & fl[]s c almo/ c]ta9ly ref] a plant to its "r class1 & c inf] n only ! numb] ( cotyl$ons :i* w\ld be f\nd 9 ! se$ or "y plant1 b also ! /ructure ( ! /em & o!r g5]al *>act]s4 ,any conspicu\s & easily discrim9at$ prop]ty :i* we ?us select = ! purpose ( decid+ to :i* class an object belongs1 may be call$ a 99*>act]i/ic994 ,! logical conditions ( a good *>act]i/ic m>k are v simple1 namely1 t x %\ld be possess$ by all objects ent]+ into a c]ta9 class1 & by none o!rs4 ,e *>act]i/ic %\ld enable u to ass]t a simple id5tity2 if ,a is a *>act]i/ic1 & ,b1 view$ int5sively1 ! class ( objects ( :i* x is ! m>k1 !n ,a ,b ought to be true4 ,! *>act]i/ic may consi/ ei!r ( a s+le quality or circum/ance1 or ( a gr\p ( su*1 provid$ t !y all be con/ant & easily detect$4 ,?us 9 ! classification ( mammals ! tee? are ( ! greate/ assi/ance1 n because a slight v>iation 9 ! numb] & =m ( ! tee? is ( importance 9 ! g5]al economy ( ! animal1 b because su* v>iations are prov$ by empirical obs]vation to co9cide ) mo/ important diff]5ces 9 ! g5]al aff9ities4 ,x is f\nd t ! m9or classes & g5]a ( mammals c be discrim9at$ accurately by _! tee?1 especially by ! =emo/ mol>s & ! h9dmo/ pre-mol>s4 ,"s tee?1 inde$1 are occasionally miss+1 s t zoologi/s pref] to tru/ to ^? *>act]i/ic tee? :i* are mo/ con/ant1#ehj & to inf] f !m n only ! arrangem5t ( ! o!r tee?1 b ! :ole con=mation ( ! animal4 #ehj ,ow51 99,essay on ! ,classification & ,geographical ,di/ribution ( ! ,mammalia991 p4 #bj4 ,x is a v difficult matt] to m>k out a b\nd>y-l9e betwe5 ! animal & vegetable k+doms1 & x may ev5 be d\bt$ :e!r a rigor\s b\nd>y c be e/abli%$4 ,! mo/ fundam5tal & important diff]5ce ( a vegetable z comp>$ ) an animal sub/ance probably consi/s 9 ! abs5ce ( nitrog5 f ! con/itu5t membranes4 ,suppos+ ?is to be ! case1 ! difficulty arises t 9 exam9+ m9ute organisms we _c asc]ta9 directly :e!r !y conta9 nitrog5 or n4 ,"s m9or b easily detect$ circum/ance is !re=e ne$$ to discrim9ate betwe5 animals & vegetables1 & ?is is furni%$ to "s ext5t by ! fact t ! production ( />* granules is re/rict$ to ! vegetable k+dom4 ,?us ! ,desmidiace may be safely assign$ to ! vegetable k+dom1 because !y conta9 />*4 ,b we mu/ n employ ?is *>act]i/ic negatively2 ! ,diatomace are probably vegetables1 ?\gh !y d n produce />*4 99,diagno/ic ,sy/ems ( ,classification499 ,we h se5 t diagnosis is ! process ( discov]+ ! place 9 any sy/em ( classes1 to :i* an object has be5 ref]r$ by "s previ\s inve/igation1 ! object be+ to avail ourselves ( ! in=mation relat+ to su* an object :i* has be5 accumulat$ & record$4 ,x is obvi\s t ?is is a matt] ( great importance1 =1 unless we c recognise1 f "t to "t1 objects or sub/ances :i* h be5 inve/igat$1 record$ discov]ies w\ld lose _! value4 ,ev5 a s+le inve/igator mu/ h means ( record+ & sy/ematis+ 8 obs]vations ( any l>ge gr\ps ( objects l ! vegetable & animal k+doms4 ,n[ :5ev] a class has be5 prop]ly =m$1 a def9ition mu/ h be5 laid d[n1 /at+ ! qualities & circum/ances possess$ by all ! objects :i* are int5d$ to be includ$ 9 ! class1 & n possess$ 99completely99 by any o!r objects4 ,diagnosis1 !re=e1 consi/s 9 comp>+ ! qualities ( a c]ta9 object ) ! def9itions ( a s]ies ( classes2 ! abs5ce 9 ! object ( any "o quality /at$ 9 ! def9ition excludes x f ! class ?us def9$2 :]eas1 if we f9d e po9t ( a def9ition exactly fulfill$ 9 ! specim51 we may at once assign x to ! class 9 "q4 ,x is ( c\rse by no means c]ta9 t ev]y?+ :i* has be5 affirm$ ( a class is true ( all objects aft]w>ds ref]r$ to ! class2 = ?is w\ld be a case ( imp]fect inf]5ce1 :i* is nev] m ?an matt] ( probability4 ,a def9ition c only make kn[n a f9ite numb] ( ! qualities ( an object1 & x always rema9s possible t objects agree+ 9 ^? assign$ qualities w diff] 9 o!rs4 99,an individual _c be def9$991 & c only be made kn[n by ! exhibition ( ! individual itself1 or by a mat]ial specim5 exactly repres5t+ x4 ,b ?is & o!r que/ions relat+ to def9ition mu/ be treat$ :5 ,i am able to take up ! subject ( language 9 ano!r "w4 ,diagno/ic sy/ems ( classification %\ld1 z a g5]al rule1 be arrang$ on ! bifurcate me?od explicitly4 ,any quality may be *os5 :i* divides ! :ole gr\p ( objects into two di/9ct p>ts1 & ea* "p may be sub-divid$ successively by any prom95t & well-m>k$ circum/ance :i* is pres5t 9 a l>ge "p ( ! g5us & n 9 ! o!r4 ,to ref] an object to its prop] place 9 su* an arrangem5t we h only to note :e!r x does or does n possess ! successive critical diff]5ti4 ,dana devis$ a classification ( ?is k9d#eha by :i* to ref] a cry/al to its place 9 ! s]ies ( six or sev5 classes already describ$4 ,if a cry/al has all its edges modifi$ alike or ! angles replac$ by ?ree or six simil> planes1 x belongs to ! monometric sy/em2 if n1 we obs]ve :e!r ! numb] ( simil> planes at ! extremity ( ! cry/al is ?ree or "s multiple ( ?ree1 9 :i* case x is a cry/al ( ! hexagonal sy/em2 & s we proce$ ) fur!r successive discrim9ations4 ,to asc]ta9 ! "n ( a m9]al by exam9ation ) ! bl[-pipe1 an arrangem5t m or less evid5tly on ! bifurcate plan1 has be5 laid d[n by ,von ,kobell4#ehb ,m9]als are divid$ accord+ z !y possess or d n possess metallic lu/re2 z !y are fusible or n fusible1 accord+ z !y d or d n on *>coal give a metallic bead1 & s on4 #eha ,dana's 99,m9]alogy991 vol4 i4 p4 #abc2 quot$ 9 ,watts' 99,diction>y ( ,*emi/ry991 vol4 ii4 p4 #aff4 #ehb 99,in/ructions = ! ,discrim9ation ( ,m9]als by ,simple ,*emical ,exp]im5ts991 by ,franz von ,kobell1 translat$ f ! ,g]man by ,r4 ,c4 ,campbell4 ,glasg[1 #ahda4 ,p]haps ! be/ example to be f\nd ( an arrangem5t devis$ simply = ! purpose ( diagnosis1 is ,mr4 ,george ,b5?am's 99,analytical ,key to ! ,natural ,ord]s & ,anomal\s ,g5]a ( ! ,briti% ,flora991 giv5 9 8 99,h&book ( ! ,briti% ,flora994#ehc ,9 ?is s*eme1 ! great composite family ( plants1 toge!r ) ! closely approximate g5us ,jasione1 are fir/ sep>at$ f all o!r fl[]+ plants by ! comp\nd "* ( _! fl[]s4 ,! rema9+ plants are sub-divid$ accord+ z ! p]ian? is d\ble or s+le4 ,s9ce no plants are yet kn[n 9 :i* ! p]ian? c be said to h ?ree or m di/9ct r+s1 ?is division becomes practically ! same z "o into d\ble & n-d\ble4 ,fl[]s ) a d\ble p]ian? are next discrim9at$ accord+ z ! corolla does or does n consi/ ( "o piece2 accord+ z ! ov>y is free or n free2 z x is simple or n simple2 z ! corolla is regul> or irregul>2 & s on4 ,on look+ ov] ?is arrangem5t1 x w be f\nd t num]ical discrim9ations (t5 occur1 ! numb]s ( petals1 /am5s1 capsules1 or o!r p>ts be+ ! crit]ia1 9 :i* cases1 z already expla9$ 7p4 #fig71 ! actual exhibition ( ! bifid division w\ld be t$i\s4 #ehc ,edition ( #ahff1 p4 lxiii4 ,l9nu appe>s to h be5 p]fectly acqua9t$ ) ! nature & uses ( diagno/ic classification1 :i* he describes "u ! "n ( ,synopsis1 say+3#ehd--8,synopsis tradit ,divisiones arbitr>ias1 longiores aut breviores1 plures aut pauciores3 a ,botanicis 9 g5]e non agnosc5da4 ,synopsis e/ di*otomia arbitr>ia1 qu in/> vi ad ,botanicem ducit4 ,limites autem non det]m9at40 #ehd 99,philosophia ,botanica99 7#aggj71 #aed1 p4 #ih4 ,! rules & tables drawn out by *emi/s to facilitate ! discov]y ( ! nature ( a sub/ance 9 qualitative analysis are usually arrang$ on ! bifurcate me?od1 & =m excell5t examples ( diagno/ic classification1 ! qualities ( ! sub/ances produc$ 9 te/+ be+ 9 mo/ cases m]ely *>act]i/ic prop]ties ( little importance 9 o!r respects4 ,! *emi/ does n detect potassium by r$uc+ x to ! /ate ( metallic potassium1 & !n obs]v+ :e!r x has all ! pr9cipal qualities belong+ to potassium4 ,he selects f among ! :ole numb] ( comp\nds ( potassium t salt1 namely ! comp\nd ( plat9um tetra-*loride1 & potassium *loride1 :i* has ! mo/ di/9ctive appe>ance1 z x is comp>atively insoluble & produces a peculi> yell[ & highly cry/all9e precipitate4 ,accord+ly1 potassium is pres5t :5ev] ?is precipitate c be produc$ by add+ plat9um *loride to a solution4 ,! f9e purple or violet col\r :i* potassium salts communicate to ! bl[pipe flame1 _h long be5 us$ z a *>act]i/ic m>k4 ,"s o!r elem5ts 7 readily detect$ by ! col\r+ ( ! bl[pipe flame1 b>ium giv+ a pale yell[i% gre51 & salts ( /rontium a bright r$4 ,by ! use ( ! spectroscope ! col\r$ light giv5 (f by an inc&esc5t vap\r is made to give p]fectly *>act]i/ic m>ks ( ! elem5ts conta9$ 9 ! vap\r4 ,diagnosis seems to be id5tical ) ! process t]m$ by ! anci5t logicians 99abscissio inf9iti991 ! cutt+ (f ( ! inf9ite or negative "p ( a g5us :5 we discov] by obs]vation t an object possesses a p>ticul> diff]5ce4 ,at e /ep 9 a bifurcate division1 "s objects possess+ ! diff]5ce w fall into ! affirmative "p or species2 all ! rema9+ objects 9 ! _w fall into ! negative "p1 :i* w be inf9ite 9 ext5t4 ,diagnosis consi/s 9 ! successive rejection f fur!r notice ( ^? inf9ite classes ) :i* ! specim5 9 "q does n agree4 99,index ,classifications499 ,"u classification we may include all arrangem5ts ( objects or names1 :i* we make = sav+ lab\r 9 ! discov]y ( an object4 ,ev5 alphabetical indices are real classifications4 ,no su* arrangem5t c be ( use unless x involves "s correlation ( circum/ances1 s t kn[+ "o ?+ we le>n ano!r4 ,if we m]ely arrange lett]s 9 ! pigeon-holes ( a secretaire we e/abli% a correlation1 = all lett]s 9 ! fir/ hole w be writt5 by p]sons1 = in/ance1 ^: names beg9 ) ,a1 & s on4 ,kn[+ !n ! initial lett] ( ! writ]'s "n1 we "k also ! place ( ! lett]1 & ! lab\r ( se>* is ?us r$uc$ to "o tw5ty-six? "p ( :at x w\ld be )\t arrangem5t4 ,n[ ! purpose ( a catalogue is to discov] ! place 9 :i* an object is to be f\nd2 b ! art ( catalogu+ involves logical consid]ations ( "s importance4 ,we want to e/abli% a correlation betwe5 ! place ( an object & "s circum/ance ab\t ! object :i* %all enable u readily to ref] to x2 ?is circum/ance !re=e %\ld be t :i* w mo/ readily dwell 9 ! memory ( ! se>*]4 ,a piece ( poetry w be be/ rememb]$ by ! fir/ l9e ( ! piece1 & ! "n ( ! au?or w be ! next mo/ def9ite circum/ance2 a catalogue ( poetry %\ld !re=e be arrang$ alphabetically accord+ to ! fir/ ^w ( ! piece1 or ! "n ( ! au?or1 or1 /ill bett]1 9 bo? ways4 ,x w\ld be impossible to arrange poems accord+ to _! subjects1 s vague & mix$ are ^! f\nd to be :5 ! attempt is made4 ,x is a matt] ( consid]able lit]>y importance to decide ^u ! be/ mode ( catalogu+ books1 s t any requir$ book 9 a libr>y %all be mo/ readily f\nd4 ,books may be classifi$ 9 a great numb] ( ways1 accord+ to subject1 language1 date1 or place ( publication1 size1 ! initial words ( ! text or title-page1 or colophon1 ! au?or's "n1 ! publi%]'s "n1 ! pr9t]'s "n1 ! "* ( ! type1 & s on4 ,e "o ( ^! modes ( arrangem5t may be useful1 = we may happ5 to rememb] "o circum/ance ab\t a book :5 we h =gott5 all o!rs2 b z we _c usually g to ! exp5se ( =m+ m ?an two or ?ree indices1 we mu/ select ^? circum/ances :i* w lead to ! discov]y ( a book mo/ frequ5tly4 ,_m ( ! crit]ia m5tion$ are evid5tly inapplicable4 ,! language 9 :i* a book is writt5 is def9ite en\gh1 provid$ t ! :ole book is writt5 9 ! same language2 b x is obvi\s t language gives no means = ! subdivision & arrangem5t ( ! lit]ature ( any "o p4 ,classification by subjects w\ld be an exce$+ly useful me?od if x 7 practicable1 b exp]i5ce %[s x to be a logical absurdity4 ,x is a v difficult matt] to classify ! sci5ces1 s complicat$ are ! relations betwe5 !m4 ,b ) books ! complication is va/ly great]1 s9ce ! same book may treat ( diff]5t sci5ces1 or x may discuss a problem involv+ _m bran*es ( k4 ,a good acc\nt ( ! /eam-eng9e w be antiqu>ian1 s f> z x traces out ! e>lie/ ef=ts at discov]y2 purely sci5tific1 z reg>ds ! pr9ciples ( !rmodynamics involv$2 te*nical1 z reg>ds ! me*anical means ( apply+ ^? pr9ciples2 economical1 z reg>ds ! indu/rial results ( ! inv5tion2 biographical1 z reg>ds ! lives ( ! inv5tors4 ,a hi/ory ( ,we/m9/] ,abbey might belong ei!r to ! hi/ory ( ar*itecture1 ! hi/ory ( ! ,*ur*1 or ! hi/ory ( ,engl&4 ,if we ab&on ! attempt to c>ry out an arrangem5t accord+ to ! natural classification ( ! sci5ces1 & =m compreh5sive practical gr\ps1 we %all be cont9ually p]plex$ by ! occurr5ce ( int]m$iate cases1 & op9ions w diff] 99ad inf9itum99 z to ! details4 ,if1 to avoid ! difficulty ab\t ,we/m9/] ,abbey1 we =m a class ( books devot$ to ! ,hi/ory ( ,build+s1 ! "q w !n arise :e!r ,/oneh5ge is a build+1 & if s1 :e!r cromle*s1 m\nds1 & monoli?s are s4 ,we %all be unc]ta9 :e!r to include ligh?\ses1 monum5ts1 bridges1 c4 ,9 reg>d to lit]>y works1 rigor\s classification is /ill less possible4 ,! same "w may p>take ( ! nature ( poetry1 biography1 hi/ory1 philosophy1 or if we =m a compreh5sive class ( ,belles-lettres1 nobody c say exactly :at does or does n come "u ! t]m4 ,my own exp]i5ce entirely be>s out ! op9ion ( ,de ,morgan1 t classification accord+ to ! "n ( ! au?or is ! only "o practicable 9 a l>ge libr>y1 & ?is me?od has be5 admirably c>ri$ out 9 ! great catalogue ( ! ,briti% ,museum4 ,! "n ( ! au?or is ! mo/ precise circum/ance conc]n+ a book1 :i* usually dwells 9 ! memory4 ,x is a bett] *>act]i/ic ( ! book ?an any?+ else4 ,9 an alphabetical arrangem5t we h an exhau/ive classification1 includ+ a place = e "n4 ,! foll[+ rem>ks#ehe ( ,de ,morgan seem !re=e to be entirely correct4 8,f mu*1 almo/ daily use1 ( catalogues = _m ye>s1 ,i am p]fectly satisfi$ t a class$ catalogue is m difficult to use ?an to make4 ,x is "o man's !ory ( ! subdivision ( k1 & ! *ances are aga9/ its suit+ any o!r man4 ,ev5 if all d\btful works 7 ent]$ "u sev]al diff]5t heads1 ! fronti] ( ! dubi\s region w\ld itself be a m]e matt] ( d\bt4 ,i nev] turn f a class$ catalogue to an alphabetical "o )\t a feel+ ( relief & security4 ,) ! latt] ,i c always1 by tak+ prop] pa9s1 make a libr>y yield its utmo/2 ) ! =m] ,i c nev] be satisfi$ t ,i h tak5 prop] pa9s1 until ,i h made x1 9 fact1 z _m diff]5t catalogues z !re are diff]5t head+s1 ) sep>ate tr\ble = ea*4 ,^? to :om bibliographical rese>* is famili>1 "k t !y h mu* m frequ5tly to hunt an au?or ?an a subject3 !y "k also t 9 se>*+ = a subject1 x is nev] safe to take ano!r p]son's view1 h[ev] good1 ( ! limits ( t subject ) ref]5ce to _! own p>ticul> purposes40 #ehe 99,philosophical ,magaz9e991 #crd ,s]ies 7#ahde71 vol4 xxvi4 p4 #ebb4 ,see also ,de ,morgan's evid5ce be=e ! ,royal ,commission on ! ,briti% ,museum 9 #ahdi1 ,report 7#ahej71 ,que/ions1 #egjd99-ehae991 #fdha-feac4 ,?is evid5ce %\ld be /udi$ by e p]son :o wi%es to und]/& ! elem5ts ( ,bibliography4 ,x is (t5 desirable1 h[ev]1 t a "n catalogue %\ld be accompani$ by a subord9ate subject catalogue1 b 9 ?is case no attempt %\ld be made to devise a !oretically complete classification4 ,e pr9cipal subject treat$ 9 a book %\ld be ent]$ sep>ately 9 an alphabetical li/1 "u ! "n mo/ likely to occur to ! se>*]1 or "u sev]al names4 ,?is me?od 0 p>tially c>ri$ out 9 ,watts' 99,biblio!ca ,britannica991 b x 0 excell5tly appli$ 9 ! admirable subject index to ! 99,briti% ,catalogue ( ,books991 & equally well 9 ! 99,catalogue ( ! ,man*e/] ,free ,libr>y99 at ,campfield1 drawn up "u ! direction ( ,mr4 ,cre/adoro1 ?is latt] be+ ! mo/ p]fect model ( a pr9t$ catalogue ) :i* ,i am acqua9t$4 ,! ,catalogue ( ! ,london ,libr>y is also 9 ! "r =m1 & has a useful index ( subjects1 ?\gh x is too mu* cond5s$ & abbreviat$4 ,! public catalogue ( ! ,briti% ,museum is arrang$ z f> z possible accord+ to ! alphabetical ord] ( ! au?ors' names1 b 9 writ+ ! titles = ?is catalogue sev]al copies are simultane\sly produc$ by a manifold writ]1 s t a catalogue accord+ to ! ord] ( ! books on ! %elves1 & ano!r accord+ to ! fir/ words ( ! title-page1 are creat$ by a m]e re>rangem5t ( ! sp>e copies4 ,9 ! 99,engli% ,cyclopdia99 x is sugge/$ t tw5ty copies ( ! book titles might readily h be5 utilis$ 9 =m+ additional catalogues1 arrang$ accord+ to ! place ( publication1 ! language ( ! book1 ! g5]al nature ( ! subject1 & s =?4#ehf ,an excell5t sugge/ion has also be5 made to ! effect t ea* book :5 publi%$ %\ld h a fly-leaf conta9+ half a doz5 pr9t$ copies ( ! title1 drawn up 9 a =m suitable = ins]tion 9 catalogues4 ,e own] ( a libr>y c\ld !n easily make accurate pr9t$ catalogues to suit 8 own purposes1 by m]ely cutt+ out ^! titles & pa/+ !m 9 books 9 any desirable ord]4 #ehf 99,engli% ,cyclopdia1 ,arts & ,sci5ces991 vol4 v4 p4 #bcc4 ,x w h>dly be a digression to po9t out ! enorm\s sav+ ( lab\r1 or1 :at comes to ! same ?+1 ! enorm\s increase 9 our available k1 bo? lit]>y & sci5tific1 :i* arises f ! =mation ( ext5sive indices4 ,! 8,/ate ,pap]s10 conta9+ ! :ole hi/ory ( ! nation1 7 practically seal$ to lit]>y inquir]s until ! ,gov]nm5t und]took ! task ( cal5d>+ & index+ !m4 ,! ,briti% ,museum ,catalogue is ano!r national "w1 ( :i* ! importance 9 advanc+ k _c be ov]rat$4 ,! ,royal ,society is do+ great s]vice 9 publi%+ a complete catalogue ( memoirs ^u physical sci5ce4 ,! "t w p]haps come :5 our views ^u ?is subject w be ext5d$1 & ei!r ,gov]nm5t or "s public society w und]take ! sy/ematic catalogu+ & index+ ( masses ( hi/orical & sci5tific in=mation :i* are n[ almo/ clos$ aga9/ inquiry4 99,classification 9 ! ,biological ,sci5ces499 ,! great g5]alisations e/abli%$ 9 ! works ( ,h]b]t ,sp5c] & ,*>les ,d>w9 h ?r[n mu* light ^u o!r sci5ces1 & h remov$ sev]al difficulties out ( ! way ( ! logician4 ,! subject ( classification has long be5 /udi$ 9 almo/ exclusive ref]5ce to ! arrangem5t ( animals & plants4 ,sy/ematic botany & zoology h be5 commonly kn[n z ! ,classificatory ,sci5ces1 & sci5tific m5 seem$ to suppose t ! me?ods ( arrangem5t1 :i* 7 suitable = liv+ creatures1 mu/ be ! be/ = all o!r classes ( objects4 ,sev]al m9]alogi/s1 especially ,mohs1 h attempt$ to arrange m9]als 9 g5]a & species1 j z if !y _h be5 animals capable ( reproduc+ _! k9d ) v>iations4 ,?is confusion ( ideas betwe5 ! relation%ip ( liv+ =ms & ! logical relation%ip ( ?+s 9 g5]al prevail$ f ! e>lie/ times1 z manife/$ 9 ! etymology ( words4 ,we famili>ly speak ( a 99k9d99 ( ?+s mean+ a class ( ?+s1 & ! k9d consi/s ( ^? ?+s :i* are 99ak9991 or come ( ! same race4 ,:5 ,socrates & 8 foll[]s want$ a "n = a class reg>d$ 9 a philosophical light1 !y adopt$ ! analogy 9 "q1 & call$ x a 1 or race1 ! root - be+ connect$ ) ! notion ( g5]ation4 ,s long z species ( plants & animals 7 believ$ to proce$ f di/9ct acts ( ,creation1 !re 0 no app>5t reason :y me?ods ( classification suitable to !m %\ld n be treat$ z a guide to ! classification ( o!r objects g5]ally4 ,b :5 once we reg>d ^! resemblances z h]$it>y 9 _! orig91 we see t ! sci5ces ( sy/ematic botany & zoology h a special "* ( _! own4 ,!re is no reason to suppose t ! same k9d ( natural classification :i* is be/ 9 biology w apply also 9 m9]alogy1 9 *emi/ry1 or 9 a/ronomy4 ,! logical pr9ciples :i* und]lie all classification are ( c\rse ! same 9 natural hi/ory z 9 ! sci5ces ( lifeless matt]1 b ! special resemblances :i* arise f ! relation ( p>5t & (fspr+ w n be f\nd to prevail betwe5 diff]5t k9ds ( cry/als or m9]al bodies4 ,! g5ealogical view ( ! relations ( animals & plants leads u to disc>d all notions ( a regul> progression ( liv+ =ms1 or any !ory z to _! symmetrical relations4 ,x 0 at "o "t a "q :e!r ! ultimate s*eme ( natural classification w\ld lead to arrangem5t 9 a simple l9e1 or a circle1 or a comb9ation ( circles4 ,macleay's once celebrat$ sy/em 0 a circul> "o1 & ea* class-circle 0 compos$ ( five ord]-circles1 ea* ( :i* 0 compos$ aga9 ( five tribe-circles1 & s on1 ! subdivision be+ at ea* /ep into five m9or circles4 ,macleay held t 9 ! animal k+dom !re are five sub-k+doms--! ,v]tebrata1 ,annulosa1 ,radiata1 ,acrita1 & ,mollusca4 ,ea* ( ^! 0 aga9 divid$ into five--! ,v]tebrata1 consi/+ ( ,mammalia1 ,reptilia1 ,pisces1 ,amphibia1 & ,aves4#ehg ,x is evid5t t 9 su* a symmetrical sy/em ! animals 7 made to suit !mselves to ! classes in/ead ( ! classes be+ suit$ to ! animals4 #ehg ,swa9son1 8,treatise on ! ,geography & ,classification ( ,animals10 99,cab9et ,cyclopdia991 p4 #bja4 ,we n[ p]ceive t ! ultimate sy/em w h ! =m ( an imm5sely ext5d$ g5ealogical tree1 :i* w be capable ( repres5tation by l9es on a plane surface ( suffici5t ext5t4 ,/rictly speak+1 ?is g5ealogical tree ought to repres5t ! desc5t ( ea* individual liv+ =m n[ exi/+ or :i* has exi/$4 ,x %\ld be z p]sonal & m9ute 9 its detail ( relations1 z ! ,/emma ( ! ,k+s ( ,engl&4 ,we mu/ n assume t any two =ms are exactly alike1 & 9 any case !y are num]ically di/9ct4 ,e p>5t !n mu/ be repres5t$ at ! apex ( a s]ies ( div]g5t l9es1 repres5t+ ! g5]ation ( s _m *ildr54 ,any complete sy/em ( classification mu/ reg>d individuals z ! infim species4 ,b z 9 ! l[] races ( animals & plants ! diff]5ces betwe5 individuals are slight & app>5tly unimportant1 :ile ! numb]s ( su* individuals are imm5sely great1 beyond all possibility ( sep>ate treatm5t1 sci5tific m5 h always /opp$ at "s conv5i5t b arbitr>y po9t1 & h assum$ t =ms s closely resembl+ ea* o!r z to pres5t no con/ant diff]5ce 7 all ( "o k9d4 ,!y h1 9 %ort1 fix$ _! att5tion entirely ^u ! ma9 features ( family diff]5ce4 ,9 ! g5ealogical tree :i* !y h be5 unconsci\sly aim+ to con/ruct1 div]g+ l9es meant races div]g+ 9 "*1 & ! purpose ( all ef=ts at s-call$ natural classification 0 to trace out ! desc5ts betwe5 exi/+ gr\ps ( plants or animals4 ,n[ x is evid5t t h]$it>y desc5t may h 9 diff]5t cases produc$ v diff]5t results z reg>ds ! problem ( classification4 ,9 "s cases ! diff]5tiation ( *>act]s may h be5 v frequ5t1 & specim5s ( all ! *>act]s produc$ may h be5 transmitt$ to ! pres5t "t4 ,a liv+ =m w !n h1 z x 71 an almo/ inf9ite numb] ( c\s9s ( v>i\s degrees1 & !re w be an imm5se numb] ( =ms f9ely graduat$ 9 _! resemblances4 ,exact & di/9ct classification w !n be almo/ impossible1 & ! wise/ c\rse w be n to attempt arbitr>ily to di/+ui% =ms closely relat$ 9 nature1 b to all[ t !re exi/ transitional =ms ( e degree1 to m>k out if possible ! extreme limits ( ! family relation%ip1 & p]haps to select ! mo/ g5]alis$ =m1 or t :i* pres5ts ! greate/ numb] ( close resemblances to o!rs ( ! family1 z ! 99type99 ( ! :ole4 ,mr4 ,d>w91 9 8 mo/ int]e/+ "w ^u ,or*ids1 po9ts out t ! tribe ( ,malaxe are di/+ui%$ f ,epid5dre by ! abs5ce ( a caudicle to ! poll9ia2 b z "s ( ! ,malaxe h a m9ute caudicle1 ! division really breaks d[n 9 ! mo/ ess5tial po9t4 8,?is is a mis=tune10 he rem>ks1#ehh 8:i* e naturali/ enc\nt]s 9 attempt+ to classify a l>gely develop$ or s-call$ natural gr\p1 9 :i*1 relatively to o!r gr\ps1 !re has be5 little ext9ction4 ,9 ord] t ! naturali/ may be enabl$ to give precise & cle> def9itions ( 8 divisions1 :ole ranks ( int]m$iate or gradational =ms mu/ h be5 utt]ly swept away3 if "h & !re a memb] ( ! int]m$iate ranks has escap$ annihilation1 x puts an effectual b> to any absolutely di/9ct def9ition40 #ehh ,d>w91 99,f]tilisation ( ,or*ids991 p4 #aei4 ,9 o!r cases a p>ticul> plant or animal may p]haps h transmitt$ its =m f g5]ation to g5]ation almo/ un*ang$1 or1 :at comes to ! same result1 ^? =ms :i* div]g$ 9 "* f ! p>5t /ock may h prov$ unsuitable to _! circum/ances1 & p]i%$4 ,we %all !n f9d a p>ticul> =m /&+ ap>t f all o!rs1 & m>k$ by _m di/9ct *>act]s4 ,occasionally we may meet ) specim5s ( a race :i* 0 =m]ly f> m common b is n[ und]go+ ext9ction1 & is ne>ly ! la/ ( its k9d4 ,?us we expla9 ! occurr5ce ( exceptional =ms su* z are f\nd 9 ! ,amphioxus4 ,! ,equisetace p]plex botani/s by _! want ( aff9ity to o!r ord]s ( ,acrog5\s plants4 ,?is d\btless indicates t _! g5ealogical connection ) o!r plants mu/ be s\ght = 9 ! mo/ di/ant ages ( geological developm5t4 ,con/ancy ( "*1 z ,mr4 ,d>w9 has said1#ehi is :at is *iefly valu$ & s\ght aft] by naturali/s2 t is to say1 naturali/s wi% to f9d "s di/9ct family m>k1 or gr\p ( *>act]s1 by :i* !y may cle>ly recognise ! relation%ip ( desc5t betwe5 a l>ge gr\p ( liv+ =ms4 ,x is accord+ly a great relief to ! m9d ( ! naturali/ :5 he comes ^u a def9itely m>k$ gr\p1 su* z ! ,diatomace1 :i* are cle>ly sep>at$ f _! ne>e/ neighb\rs ! ,desmidiace by _! silice\s framework & ! abs5ce ( *lorophyll4 ,b we mu/ no long] ?9k t because we fail 9 detect+ con/ancy ( "* ! fault is 9 our classificatory sci5ces4 ,:]e gradation ( "* really exi/s1 we mu/ devote ourselves to def9+ & regi/]+ ! degrees & limits ( t gradation4 ,! ultimate natural arrangem5t w (t5 be devoid ( /rong l9es ( dem>cation4 #ehi 99,desc5t ( ,man991 vol4 i4 p4 #bad4 ,let naturali/s1 too1 =m _! sy/ems ( natural classification ) all c>e !y c1 yet x w c]ta9ly happ5 f "t to "t t new & exceptional =ms ( animals or vegetables w be discov]$ & w require ! modification ( ! sy/em4 ,a natural sy/em is direct$1 z we h se51 to ! discov]y ( empirical laws ( correlation1 b ^! laws be+ purely empirical w frequ5tly be falsifi$ by m ext5sive inve/igation4 ,f "t to "t ! notions ( naturali/s h be5 greatly wid5$1 especially 9 ! case ( ,au/ralian animals & plants1 by ! discov]y ( unexpect$ comb9ations ( organs1 & su* ev5ts mu/ (t5 happ5 9 ! future4 ,if inde$ ! "t %all come :5 all ! =ms ( plants are discov]$ & accurately describ$1 ! sci5ce ( ,sy/ematic ,botany w !n be plac$ 9 a new & m fav\rable position1 z rem>k$ by ,alphonse ,dec&olle4#eij #eij 99,laws ( ,botanical ,nom5clature991 p4 #af4 ,x ought to be rememb]$ t ?\gh ! g5ealogical classification ( plants or animals is d\btless ! mo/ in/ructive ( all1 x is n necess>ily ! be/ = all purposes4 ,!re may be correlations ( prop]ties important = m$ic9al1 or o!r practical purposes1 :i* d n correspond to ! correlations ( desc5t4 ,we mu/ reg>d ! bamboo z a tree r ?an a grass1 al?\gh x is botanically a grass4 ,= legal purposes we may cont9ue ) advantage to treat ! :ale1 seal1 & o!r cetace1 z fi%4 ,we mu/ also class plants accord+ z !y belong to arctic1 alp9e1 temp]ate1 sub-tropical or tropical regions4 ,!re are causes ( lik5ess ap>t f h]$it>y relation%ip1 & 99we mu/ n attribute exclusive excell5ce to any "o me?od ( classification994 99,classification by ,types499 ,p]plex$ by ! difficulties aris+ 9 natural hi/ory f ! discov]y ( int]m$iate =ms1 naturali/s h resort$ to :at !y call classification by types4 ,in/ead ( =m+ "o di/9ct class def9$ by ! inv>iable possession ( c]ta9 assign$ prop]ties1 & rigidly includ+ or exclud+ objects accord+ z !y d or d n possess all ^! prop]ties1 naturali/s select a typical specim51 & !y gr\p ar\nd x all o!r specim5s :i* resemble ?is type m ?an any o!r select$ type4 8,! type ( ea* g5us10 we are told1#eia 8%\ld be t species 9 :i* ! *>act]s ( its gr\p are be/ exhibit$ & mo/ ev5ly balanc$40 ,x w\ld usually consi/ ( ^? desc5dants ( a =m :i* _h und]gone little alt]ation1 :ile o!r desc5dants _h suff]$ slight diff]5tiation 9 v>i\s directions4 #eia ,wat]h\se1 quot$ by ,woodw>d 9 8 99,rudim5t>y ,treatise ( ,rec5t & ,fossil ,%ells991 p4 #fa4 ,x w\ld be a great mi/ake to suppose t ?is classification by types is a logically di/9ct me?od4 ,x is ei!r n a real me?od ( classification at all1 or x is m]ely an abbreviat$ mode ( repres5t+ a complicat$ sy/em ( arrangem5t4 ,a class mu/ be def9$ by ! inv>iable pres5ce ( c]ta9 common prop]ties4 ,if1 !n1 we include an individual 9 :i* "o ( ^! prop]ties does n appe>1 we ei!r fall into logical contradiction1 or else we =m a new class ) a new def9ition4 ,ev5 a s+le exception con/itutes a new class by itself1 & by call+ x an exception we m]ely imply t ?is new class closely resembles t f :i* x div]ges 9 "o or two po9ts only4 ,?us 9 ! def9ition ( ! natural ord] ( ,rosace1 we f9d t ! se$s are "o or two 9 ea* c>pel1 b t 9 ! g5us ,spira !re are ?ree or f\r2 ?is mu/ mean ei!r t ! numb] ( se$s is n a "p ( ! fix$ def9ition ( ! class1 or else t ,spira does n belong to t class1 ?\gh x may closely approximate to x4 ,naturali/s cont9ually f9d !mselves betwe5 two horns ( a dilemma2 if !y re/rict ! numb] ( m>ks specifi$ 9 a def9ition s t e =m int5d$ to come )9 ! class %all possess all ^? m>ks1 x w !n be usually f\nd to include too _m =ms2 if ! def9ition be made m p>ticul>1 ! result is to produce s-call$ anomal\s g5]a1 :i*1 :ile !y are held to belong to ! class1 d n 9 all respects con=m to its def9ition4 ,! practice has h5ce aris5 ( all[+ consid]able latitude 9 ! def9ition ( natural ord]s4 ,! family ( ,crucif]1 = in/ance1 =ms an exce$+ly well-m>k$ natural ord]1 & among its *>act]s we f9d x specifi$ t ! fruit is a pod1 divid$ into two cells by a ?9 p>tition1 f :i* ! valves g5]ally sep>ate at maturity2 b we are also in=m$ t1 9 a few g5]a1 ! pod is "o-cell$1 or indehisc5t1 or sep>ates transv]sely into sev]al jo9ts4#eib ,n[ ?is mu/ ei!r mean t ! =mation ( ! pod is n an ess5tial po9t 9 ! def9ition ( ! family1 or t !re are sev]al closely associat$ families4 #eib ,b5?am's 99,h&book ( ! ,briti% ,flora99 7#ahff71 p4 #be4 ,! same holds true ( typical classification4 ,! type itself is an individual1 n a class1 & no o!r object c be exactly l ! type4 ,b z soon z we ab/ract ! individual peculi>ities ( ! type & ?us specify a f9ite numb] ( qualities 9 :i* o!r objects may resemble ! type1 we imm$iately con/itute a class4 ,if "s objects resemble ! type 9 "s po9ts1 & o!rs 9 o!r po9ts1 !n ea* def9ite collection ( po9ts ( resemblance con/itutes int5sively a sep>ate class4 ,! v notion ( classification by types is 9 fact errone\s 9 a logical po9t ( view4 ,! naturali/ is con/antly occupi$ 9 endeav\r+ to m>k out def9ite gr\ps ( liv+ =ms1 :]e ! =ms !mselves d n 9 _m cases admit ( su* rigor\s l9es ( dem>cation4 ,a c]ta9 laxity ( logical me?od is ?us apt to creep 91 ! only rem$y = :i* w be ! frank recognition ( ! fact1 t1 accord+ to ! !ory ( h]$it>y desc5t1 gradation ( *>act]s is probably ! rule1 & precise dem>cation betwe5 gr\ps ! exception4 99,natural ,g5]a & ,species499 ,"o important result ( ! e/abli%m5t ( ! !ory ( evolution is to explode all notions ab\t natural gr\ps con/itut+ sep>ate creations4 ,naturali/s long held t e plant belongs to "s species1 m>k$ out by inv>iable *>act]s1 :i* d n *ange by diff]5ce ( soil1 climate1 cross-bre$+1 or o!r circum/ances4 ,!y 7 unable to d5y ! exi/5ce ( su* ?+s z sub-species1 v>ieties1 & hybrids1 s t a species ( plants 0 (t5 subdivid$ & classifi$ )9 itself4 ,b !n ! diff]5ces ^u :i* ?is sub-classification dep5d$ 7 suppos$ to be v>iable1 & ?us di/+ui%$ f ! inv>iable *>act]s impos$ ^u ! :ole species at its creation4 ,simil>ly a natural g5us 0 a gr\p ( species1 & 0 m>k$ out f o!r g5]a by et]nal diff]5ces ( /ill great] importance4 ,we n[1 h[ev]1 p]ceive t ! exi/5ce ( any su* gr\ps z g5]a & species is an arbitr>y creation ( ! naturali/'s m9d4 ,all resemblances ( plants are natural s f> z !y express h]$it>y aff9ities2 b ?is applies z well to ! v>iations )9 ! species z to ! species itself1 or to ! l>g] gr\ps4 ,all is a matt] ( degree4 ,! deep] diff]5ces betwe5 plants h be5 produc$ by ! diff]5tiat+ action ( circum/ances dur+ millions ( ye>s1 s t x w\ld naturally require millions ( ye>s to undo ?is result1 & prove exp]im5tally t ! =ms c be approximat$ aga94 ,sub-species may sometimes h aris5 )9 hi/orical times1 & v>ieties approa*+ to sub-species may (t5 be produc$ by ! horticulturi/ 9 a few ye>s4 ,su* v>ieties c easily be br\ght back to _! orig9al =ms1 or1 if plac$ 9 ! orig9al circum/ances1 w !mselves rev]t to ^? =ms2 b accord+ to ,d>w9's views all =ms are capable ( unlimit$ *ange1 & x might possibly be1 unlimit$ rev]sion if suitable circum/ances & suffici5t "t be grant$4 ,_m fruitless attempts h be5 made to e/abli% a rigor\s crit]ion ( specific & g5]ic diff]5ce1 s t ^! classes might h a def9ite value & rank 9 all bran*es ( biology4 ,l9nu adopt$ ! view t ! species 0 to be def9$ z a di/9ct creation1 say+1#eic 8,species tot num]amus1 quot div]s =m 9 pr9cipio sunt creat20 or aga91 8,species tot sunt1 quot div]sas =mas ab initio produxit ,inf9itum ,ens2 qu =m1 secundum g5]ationis inditas leges1 produx]e plures1 at sibi semp] similes40 ,( g5]a he also says1#eid 8,g5us omne e/ naturale1 9 primordio tale creatum40 ,x 0 a common doctr9e add$ to & ess5tial to t ( di/9ct creation t ^! species c\ld n produce int]m$iate & v>iable =ms1 s t we f9d ,l9nu oblig$ by ! asc]ta9$ exi/5ce ( hybrids to take a diff]5t view 9 ano!r "w2 he says1#eie 8,novas species immo et g5]a ex copula div]s>um speci]um 9 regno vegetabilium oriri primo intuitu p>adoxum videtur2 int]im obs]vationes sic fi]i non ita dissuad5t40 ,ev5 suppos+ 9 ! pres5t day t we c\ld ass5t to ! notion ( a c]ta9 numb] ( di/9ct creational acts1 ?is notion w\ld n help u 9 ! !ory ( classification4 ,naturali/s h nev] po9t$ out any me?od ( decid+ :at are ! results ( di/9ct creations1 & :at are n4 ,z ,d>w9 says1#eif 8! def9ition mu/ n include an elem5t :i* _c possibly be asc]ta9$1 su* z an act ( creation40 ,x is1 9 fact1 by inve/igation ( =ms & classification t we %\ld asc]ta9 :at 7 di/9ct creations & :at 7 n2 ?is in=mation w\ld be a result & n a means ( classification4 #eic 99,philosophia ,botanica99 7#aggj71 #aeg1 p4 #ii4 #eid 99,ibid499 #aei1 p4 #ajj4 #eie 99,amnitates ,academic99 7#agdd71 vol4 i4 p4 #gj4 ,quot$ 9 99,ed9burgh ,review991 ,octob] #ahfh1 vol4 cxxviii4 pp4 #daf1 #dag4 #eif 99,desc5t ( ,man991 vol4 i4 p4 #bbh4 ,agassiz seem$ to consid] t he _h discov]$ an important pr9ciple1 to ! effect t g5]al plan or /ructure is ! true gr\nd = ! discrim9ation ( ! great classes ( animals1 :i* may be call$ bran*es ( ! animal k+dom4#eig ,he also ?\ght t g5]a are def9ite & natural gr\ps4 8,g5]a10 he says1#eih 8are mo/ closely alli$ gr\ps ( animals1 diff]+ nei!r 9 =m1 nor 9 complication ( /ructure1 b simply 9 ! ultimate /ructural peculi>ities ( "s ( _! p>ts2 & ?is is1 ,i believe1 ! be/ def9ition :i* c be giv5 ( g5]a40 ,b x is surely app>5t t !re are endless degrees bo? ( /ructural peculi>ity & ( complication ( /ructure4 ,x is impossible to def9e ! am\nt ( /ructural peculi>ity :i* con/itutes ! g5us z di/+ui%$ f ! species4 #eig ,agassiz1 99,essay on ,classification991 p4 #bai4 #eih 99,ibid499 p4 #bdi4 ,! =m :i* any classification ( plants or animals t5ds to take is t ( an unlimit$ s]ies ( subalt]n classes4 ,orig9ally botani/s conf9$ !mselves = ! mo/ "p to a small numb] ( su* classes4 ,l9nu adopt$ ,class1 ,ord]1 ,g5us1 ,species1 & ,v>iety1 & ev5 seem$ to ?9k t !re 0 some?+ ess5tially natural 9 a five-fold arrangem5t ( gr\ps4#eii #eii 99,philosophia ,botanica991 #aee1 p4 #ih4 ,) ! progress ( botany int]m$iate & additional gr\ps h gradually be5 introduc$4 ,accord+ to ! ,laws ( ,botanical ,nom5clature adopt$ by ! ,int]national ,botanical ,congress1 held at ,p>is#fjj 9 ,augu/ #ahfg1 no less ?an tw5ty-"o names ( classes are recognis$--namely1 ,k+dom1 ,division1 ,sub-division1 ,class1 ,sub-class1 ,cohort1 ,sub-cohort1 ,ord]1 ,sub-ord]1 ,tribe1 ,sub-tribe1 ,g5us1 ,sub-g5us1 ,section1 ,sub-section1 ,species1 ,sub-species1 ,v>iety1 ,sub-v>iety1 ,v>iation1 ,sub-v>iation4 ,x is all[$ by ! au?ors ( ?is s*eme1 t ! rank or degree ( importance to be attribut$ to any ( ^! divisions may v>y 9 a c]ta9 degree accord+ to individual op9ion4 ,! only po9t on :i* botani/s are n all[$ discretion is z to ! ord] ( ! successive sub-divisions2 any inv]sion ( ! arrangem5t1 su* z division ( a g5us into tribes1 or ( a tribe into ord]s1 is q inadmissible4 ,!re is no reason to suppose t ev5 ! above li/ is complete & inext5sible4 ,! ,botanical ,congress itself recognis$ ! di/9ction betwe5 v>iations accord+ z !y are ,se$l+s1 ,half-bre$s1 or 99,lusus ,natur994 ,! complication ( ! inf]ior classes is increas$ aga9 by ! exi/5ce ( 99hybrids991 aris+ f ! f]tilisation ( "o species by ano!r deem$ a di/9ct species1 nor c we place any limit to ! m9ut5ess ( discrim9ation ( degrees ( bre$+ %ort ( an actual p$igree ( individuals4 #fjj 99,laws ( ,botanical ,nom5clature991 by ,alphonse ,dec&olle1 translat$ f ! ,fr5*1 #ahfh1 p4 #ai4 ,x w be evid5t to ! read] t 9 ! rem>ks ^u classification z appli$ to ! ,natural ,sci5ces1 giv5 9 ?is & ! prec$+ sections1 ,i h n 9 ! lea/ attempt$ to treat ! subject 9 a mann] adequate to its ext5t & importance4 ,a volume w\ld be insuffici5t = trac+ out ! pr9ciples ( sci5tific me?od specially applicable to ^! bran*es ( sci5ce4 ,:at m ,i may be able to say ^u ! subject w be bett] said1 if ev]1 :5 ,i am able to take up ! closely-connect$ subjects ( ,sci5tific ,nom5clature1 ,t]m9ology1 & ,descriptive ,repres5tation4 ,9 ! meantime1 ,i h wi%$ to %[1 9 a negative po9t ( view1 t natural classification 9 ! animal & vegetable k+doms is a special problem1 & t ! p>ticul> me?ods & difficulties to :i* x gives rise are n ^? common to all cases ( classification1 z s _m physici/s h suppos$4 ,g5ealogical resemblances are only a special case ( resemblances 9 g5]al4 99,unique or ,exceptional ,objects499 ,9 fram+ a sy/em ( classification 9 almo/ any bran* ( sci5ce1 we mu/ expect to meet ) unique or peculi> objects1 :i* /& alone1 hav+ comp>atively few analogies ) o!r objects4 ,!y may also be said to be 99sui g5]is991 ea* unique object =m+1 z x 71 a g5us by itself2 or !y are call$ 99nondescript991 because f ?us /&+ ap>t x is difficult to f9d t]ms 9 :i* to describe _! prop]ties4 ,! r+s ( ,saturn1 = in/ance1 =m a unique object among ! cele/ial bodies4 ,we h inde$ consid]$ ?is & _m o!r in/ances ( unique objects 9 ! prec$+ *apt] on ,exceptional ,ph5om5a4 ,app>5t1 ,s+ul>1 & ,div]g5t ,exceptions especially1 are analog\s to unique objects4 ,9 ! classification ( ! elem5ts1 ,c>bon /&s ap>t z a sub/ance entirely unique 9 its p[]s ( produc+ comp\nds4 ,x is consid]$ to be a quadrival5t elem5t1 & x obeys all ! ord9>y laws ( *emical comb9ation4 ,yet x manife/s p[]s ( aff9ity 9 su* an exalt$ degree t ! sub/ances 9 :i* x appe>s are m num]\s ?an all ! o!r comp\nds kn[n to *emi/s4 ,almo/ ! :ole ( ! sub/ances :i* h be5 call$ organic conta9 c>bon1 & are probably held toge!r by ! c>bon atoms1 s t _m *emi/s are n[ incl9$ to ab&on ! "n ,organic ,*emi/ry1 & sub/itute ! "n ,*emi/ry ( ! ,c>bon ,comp\nds4 ,x us$ to be believ$ t ! production ( organic comp\nds c\ld be effect$ only by ! action ( vital =ce1 or ( "s inexplicable cause involv$ 9 ! ph5om5a ( life2 b x is n[ f\nd t *emi/s are able to comm5ce ) ! elem5t>y mat]ials1 pure c>bon1 hydrog51 & oxyg51 & by /rictly *emical op]ations to comb9e ^! s z to =m complicat$ organic comp\nds4 ,s _m sub/ances h already be5 =m$ t we might be incl9$ to g5]alise & inf] t all organic comp\nds might ultimately be produc$ )\t ! ag5cy ( liv+ be+s4 ,?us ! di/9ction betwe5 ! organic & ! inorganic k+doms seems to be break+ d[n1 b our wond] at ! peculi> p[]s ( c>bon mu/ increase at ! same "t4 ,9 consid]+ g5]alisation1 ! law ( cont9uity 0 appli$ *iefly to physical prop]ties capable ( ma!matical treatm5t4 ,b 9 ! classificatory sci5ces1 also1 ! same important pr9ciple is (t5 beautifully exemplifi$4 ,_m objects or ev5ts seem to be entirely exceptional & abnormal1 & 9 reg>d to degree or magnitude !y may be s t]m$2 b x is (t5 easy to %[ t !y are connect$ by int]m$iate l9ks ) ord9>y cases4 ,9 ! organic k+doms !re is a common gr\ndwork ( simil>ity runn+ ?r\gh all classes1 b p>ticul> actions & processes pres5t !mselves conspicu\sly 9 p>ticul> families & classes4 ,t5acity ( life is mo/ m>k$ 9 ! ,rotif]a1 & "s o!r k9ds ( microscopic organisms1 :i* c be dri$ & boil$ )\t loss ( life4 ,reptiles are di/+ui%$ by torpidity1 & ! l5g? ( "t !y c live )\t food4 ,birds1 on ! contr>y1 exhibit ceaseless activity & high muscul> p[]4 ,! ant is z conspicu\s = intellig5ce & size ( bra9 among insects z ! quadrumana & man among v]tebrata4 ,among plants ! ,legum9os are di/+ui%$ by a t5d5cy to sleep1 fold+ _! leaves at ! approa* ( night4 ,9 ! g5us ,mimosa1 especially ! ,mimosa pudica1 commonly call$ ! s5sitive plant1 ! same t5d5cy is magnifi$ into an extreme irritability1 almo/ resembl+ volunt>y motion4 ,m or less ( ! same irritability probably belongs to vegetable =ms ( e k9d1 b x is ( c\rse to be inve/igat$ ) special ease 9 su* an extreme case4 ,9 ! ,gymnotus & ,torp$o1 we f9d t organic /ructures c act l galvanic batt]ies4 ,are we to suppose t su* animals are entirely anomal\s exceptions2 or may we n ju/ly expect to f9d less int5se manife/ations ( electric action 9 all animals8 ,"s extraord9>y diff]5ces betwe5 ! modes ( reproduction ( animals h be5 %[n to be f> less ?an 0 at fir/ sight app>5t4 ,! l[] animals seem to diff] entirely f ! high] ones 9 ! p[] ( reproduc+ lo/ limbs4 ,a k9d ( crab has ! habit ( ca/+ portions ( its claws :5 mu* fright5$1 b !y soon gr[ aga94 ,!re are multitudes ( small] animals :i*1 l ! ,hydra1 may be cut 9 two & yet live & develop into new complete individuals4 ,no mammalian animal c reproduce a limb1 & 9 appe>ance !re is no analogy4 ,b x 0 sugge/$ by ,blum5ba* t ! heal+ ( a w\nd 9 ! high] animals really repres5ts 9 a l[] degree ! p[] ( reproduc+ a limb4 ,t ?is is true may be %[n by adduc+ a multitude ( int]m$iate cases1 ea* adjo9+ pair ( :i* are cle>ly analog\s1 s t we pass gradually f "o extreme to ! o!r4 ,d>w9 holds1 moreov]1 t any su* re/oration ( p>ts is closely connect$ ) t p]petual replacem5t ( ! p>ticles :i* causes e organis$ body to be aft] a "t entirely new z reg>ds its con/itu5t sub/ance4 ,9 %ort1 we approa* to a great g5]alisation "u :i* all ! ph5om5a ( gr[?1 re/oration1 & ma9t5ance ( organs are effects ( "o & ! same p[]4#fja ,x is p]haps /ill m surpris+ to f9d t ! complicat$ process ( reproduction 9 ! high] animals may be gradually trac$ d[n to a simpl] & simpl] =m1 :i* at la/ becomes undi/+ui%able f ! budd+ out ( "o plant f ! /em ( ano!r4 ,by a great g5]alisation we may reg>d all ! modes ( reproduction ( organic life z alike 9 _! nature1 & v>y+ only 9 complexity ( developm5t4#fjb #fja ,d>w91 99,! ,v>iation ( ,animals & ,plants991 vol4 ii4 pp4 #bic1 #cei1 c42 quot+ ,paget1 99,lectures on ,pa?ology991 #ahec1 pp4 #aeb1 #afd4 #fjb 99,ibid499 vol4 ii4 p4 #cgb4 99,limits ( ,classification499 ,sci5ce c ext5d only s f> z ! p[] ( accurate classification ext5ds4 ,if we _c detect resemblances1 & assign _! exact "* & am\nt1 we _c h t g5]alis$ k :i* con/itutes sci5ce2 we _c inf] f case to case4 ,classification is ! opposite process to discrim9ation4 ,if we feel t two ta/es diff]1 ! ta/es ( two k9ds ( w9e = in/ance1 ! m]e fact ( diff]5ce exi/+ prev5ts inf]5ce4 ,! detection ( ! diff]5ce saves u1 inde$1 f false inf]5ce1 because s f> z diff]5ce exi/s1 inf]5ce is impossible4 ,b classification consi/s 9 detect+ resemblances ( all degrees ( g5]ality1 & asc]ta9+ exactly h[ f> su* resemblances ext5d1 :ile assign+ precisely ! po9ts at :i* diff]5ce beg9s4 ,x enables u1 !n1 to g5]alise1 & make inf]5ces :]e x is possible1 & x saves u at ! same "t f go+ too f>4 ,a full classification con/itutes a complete record ( all our k ( ! objects or ev5ts classifi$1 & ! limits ( exact k are id5tical ) ! limits ( classification4 ,x mu/ by no means be suppos$ t e gr\p ( natural objects w be f\nd capable ( rigor\s classification4 ,!re may be sub/ances :i* v>y by ins5sible degrees1 consi/+1 = in/ance1 9 v>y+ mixtures ( simpl] sub/ances4 ,granite is a mixture ( qu>tz1 felsp>1 & mica1 b !re are h>dly two specim5s 9 :i* ! proportions ( ^! ?ree con/itu5ts are alike1 & x w\ld be impossible to lay d[n def9itions ( di/9ct species ( granite )\t f9d+ an inf9ite v>iety ( int]m$iate species4 ,! only true classification ( granites1 !n1 w\ld be f\nd$ on ! proportions ( ! con/itu5ts pres5t1 & a *emical or microscopic analysis w\ld be requisite1 9 ord] t we might assign a specim5 to its true position 9 ! s]ies4 ,granites v>y1 aga91 by ins5sible degrees1 z reg>ds ! magnitude ( ! cry/als ( felsp> & mica4 ,precisely simil> rem>ks might be made conc]n+ ! classification ( o!r plutonic rocks1 su* z sy5ite1 basalt1 pumice-/one1 lava4 ,! nature ( a ray ( homog5e\s light is /rictly def9$1 ei!r by its place 9 ! spectrum or by ! correspond+ wave-l5g?1 b a ray ( mix$ light admits ( no simple classification2 any ( ! inf9itely num]\s rays ( ! cont9u\s spectrum may be pres5t or abs5t1 or pres5t 9 v>i\s int5sities1 s t we c only class & def9e a mix$ col\r by def9+ ! int5sity & wave-l5g? ( ea* ray ( homog5e\s light :i* is pres5t 9 x4 ,complete spectroscopic analysis & ! det]m9ation ( ! int5sity ( e "p ( ! spectrum yield$ by a mix$ ray is requisite = its accurate classification4 ,ne>ly ! same may be said ( complex s\nds4 ,a simple s\nd undulation1 if we c\ld meet ) su* a s\nd1 w\ld admit ( precise & exhau/ive classification z reg>ds pit*1 ! l5g? ( wave1 or ! numb] ( waves rea*+ ! e> p] second be+ a suffici5t crit]ion4 ,b almo/ all ord9>y s\nds1 ev5 ^? ( musical in/rum5ts1 consi/ ( complex aggregates ( undulations ( diff]5t pit*es1 & 9 ord] to classify ! s\nd we %\ld h to measure ! int5sities ( ea* ( ! con/itu5t s\nds1 a "w :i* has be5 p>tially accompli%$ by ,helmholtz1 z reg>ds ! v[el s\nds4 ,! diff]5t tones ( voice di/9ctive ( diff]5t individuals mu/ also be due to ! int]mixture ( m9ute waves ( v>i\s pit*1 :i* are yet q beyond ! range ( exp]im5tal inve/igation4 ,we _c1 !n1 at pres5t attempt to classify ! diff]5t k9ds or 99timbres99 ( s\nd4 ,! difficulties ( classification are /ill great] :5 a v>y+ ph5om5on _c be %[n to be a mixture ( simpl] ph5om5a4 ,if we attempt to classify ta/es1 we may rudely gr\p !m accord+ z !y are sweet1 bitt]1 sal9e1 alkal9e1 acid1 a/r+5t or fi]y2 b x is evid5t t ^! gr\ps are b\nd$ by no %>p l9es ( def9ition4 ,ta/es ( mix$ or int]m$iate "* may exi/ almo/ 99ad inf9itum991 & :at is /ill m tr\blesome1 ! ta/es cle>ly unit$ )9 "o class may diff] m or less f ea* o!r1 )\t our be+ able to arrange !m 9 subord9ate g5]a & species4 ,! same rem>ks may be made conc]n+ ! classification ( od\rs1 :i* may be r\ghly gr\p$ accord+ to ! arrangem5t ( ,l9nu z1 aromatic1 fragrant1 ambrosiac1 alliace\s1 fetid1 virul5t1 nause\s4 ,)9 ea* ( ^! vague classes1 h[ev]1 !re w\ld be inf9ite %ades ( v>iety1 & ea* class w\ld graduate into o!r classes4 ,! od\rs :i* c be discrim9at$ by an acute nose are inf9ite2 e rock1 /one1 plant1 or animal has "s slight smell1 & x is well kn[n t dogs1 or ev5 bl9d m51 c discrim9ate p]sons by a slight di/9ctive od\r :i* usually passes unnotic$4 ,simil> rem>ks may be made conc]n+ ! feel+s ( ! human m9d1 call$ emotions4 ,we "k :at is ang]1 grief1 fe>1 hatr$1 love2 & _m sy/ems = classify+ ^! feel+s h be5 propos$4 ,!y may be r\ghly di/+ui%$ accord+ z !y are pleasurable or pa9ful1 prospective or retrospective1 selfi% or sympa!tic1 active or passive1 & possibly 9 _m o!r ways2 b ea* mode ( arrangem5t w be indef9ite & unsatisfactory :5 foll[$ into details4 ,z a g5]al rule1 ! emotional /ate ( ! m9d at any mom5t w be nei!r pure ang] nor pure fe>1 nor any "o pure feel+1 b an indef9ite & complex aggregate ( feel+s4 ,x may be t ! /ate ( m9d is really a sum ( sev]al di/9ct modes ( agitation1 j z a mix$ col\r is ! sum ( ! sev]al rays ( ! spectrum4 ,9 ?is case !re may be m hope ( "s me?od ( analysis be+ successfully appli$ at a future "t4 ,b x may be f\nd t /ates ( m9d really graduate into ea* o!r s t rigor\s classification w\ld be hopeless4 ,a little reflection w %[ t !re are :ole worlds ( exi/5ces :i* 9 l mann] are incapable ( logical analysis & classification4 ,"o fri5d may be able to s+le out & id5tify ano!r fri5d by 8 c\nt5ance among a million o!r c\nt5ances4 ,faces are capable ( inf9ite discrim9ation1 b :o %all classify & def9e !m1 or say by :at p>ticul> %ades ( feature he does judge8 ,!re are ( c\rse c]ta9 di/9ct types ( face1 b ea* type is connect$ ) ea* o!r type by inf9ite int]m$iate specim5s4 ,we may classify melodies accord+ to ! major or m9or key1 ! "* ( ! "t1 & "s o!r di/9ct po9ts2 b e melody has1 indep5d5tly ( su* circum/ances1 its own di/9ctive "* & effect ^u ! m9d4 ,we c detect diff]5ces betwe5 ! /yles ( lit]>y1 musical1 or arti/ic compositions4 ,we c ev5 9 "s cases assign a picture to its pa9t]1 or a symphony to its compos]1 by a subtle feel+ ( resemblances or diff]5ces :i* may be felt1 b _c be describ$4 ,f9ally1 x is app>5t t 9 human "* !re is unfa?omable & inexhau/ible div]sity4 ,e m9d is m or less l e o!r m9d2 !re is always a basis ( simil>ity1 b !re is a sup]/ructure ( feel+s1 impulses1 & motives :i* is di/9ctive = ea* p]son4 ,we c sometimes pr$ict ! g5]al "* ( ! feel+s & actions :i* w be produc$ by a giv5 ext]nal ev5t 9 an individual well kn[n to u2 b we also "k t we are (t5 inexplicably at fault 9 our inf]5ces4 ,no "o c safely g5]alise ^u ! subtle v>iations ( temp] & emotion :i* may arise ev5 9 a p]son ( ord9>y "*4 ,z human k & civilisation progress1 ^! *>act]i/ic diff]5ces t5d to develop & multiply !mselves1 r ?an decrease4 ,"* gr[s m _m-sid$4 ,two well educat$ ,engli%m5 are f> bett] di/+ui%$ f ea* o!r ?an two common lab\r]s1 & ^! are bett] di/+ui%$ ?an two ,au/ralian aborig9es4 ,! complexities ( exi/+ ph5om5a probably develop !mselves m rapidly ?an sci5tific me?od c ov]take !m4 ,9 spite ( all ! boa/$ p[]s ( sci5ce1 we _c really apply sci5tific me?od to our own m9ds & *>act]s1 :i* are m important to u ?an all ! />s & nebul4 ,,book ,,vi4 ,,*apt] ,,xxxi4 ,,reflections ,,on ,,! ,,results ,,& ,,limits ,,( ,,sci5tific ,,me?od4 ,be=e conclud+ a "w on ! ,pr9ciples ( ,sci5ce1 x w n be inappropriate to add "s rem>ks ^u ! limits & ultimate be>+s ( ! k :i* we may acquire by ! employm5t ( sci5tific me?od4 ,all sci5ce consi/s1 x has sev]al times be5 /at$1 9 ! detection ( id5tities 9 ! action ( natural ag5ts4 ,! purpose ( inductive inquiry is to asc]ta9 ! app>5t exi/5ce ( necess>y connection betwe5 causes & effects1 express$ 9 ! =m ( natural laws4 ,n[ s f> z we ?us le>n ! inv>iable c\rse ( nature1 ! future becomes ! necess>y sequel ( ! pres5t1 & we are br\ght b5ea? ! sway ( p[]s ) :i* no?+ c int]f]e4 ,by degrees x is f\nd1 too1 t ! *emi/ry ( organis$ sub/ances is n entirely sep>at$ f1 b is cont9u\s )1 t ( e>? & /ones4 ,life seems to be no?+ b a special =m ( en]gy :i* is manife/$ 9 heat & electricity & me*anical =ce4 ,! "t may come1 x almo/ seems1 :5 ! t5d] me*anism ( ! bra9 w be trac$ out1 & e ?\ght r$uc$ to ! exp5diture ( a det]m9ate weight ( nitrog5 & phosphorus4 ,no app>5t limit exi/s to ! success ( sci5tific me?od 9 weigh+ & measur+1 & r$uc+ b5ea? ! sway ( law1 ! ph5om5a bo? ( matt] & ( m9d4 ,& if m5tal ph5om5a be ?us capable ( treatm5t by ! balance & ! micromet]1 c we any long] hold t m9d is di/9ct f matt]8 ,mu/ n ! same inexorable reign ( law :i* is app>5t 9 ! motions ( brute matt] be ext5d$ to ! subtle feel+s ( ! human he>t8 ,are n plants & animals1 & ultimately man himself1 m]ely cry/als1 z x 71 ( a complicat$ =m8 ,if s1 our boa/$ free w becomes a delusion1 moral responsibility a fiction1 _s a m]e "n = ! m curi\s manife/ations ( mat]ial en]gy4 ,all t happ5s1 :e!r "r or wrong1 pleasurable or pa9ful1 is b ! outcome ( ! necess>y relations ( "t & space & =ce4 ,mat]ialism seems1 !n1 to be ! com+ religion1 & resignation to ! non5tity ( human w ! only duty4 ,su* may n g5]ally be ! reflections ( m5 ( sci5ce1 b ,i believe t we may ?us describe ! secret feel+s ( fe> :i* ! con/ant advance ( sci5tific inve/igation excites 9 ! m9ds ( _m4 ,is sci5ce1 !n1 ess5tially a!i/ic & mat]iali/ic 9 its t5d5cy8 ,does ! uni=m action ( mat]ial causes1 :i* we le>n ) an ev]-increas+ approximation to c]ta9ty1 preclude ! hypo!sis ( a b5evol5t ,creator1 :o has n only design$ ! exi/+ univ]se1 b :o /ill reta9s ! p[] to alt] its c\rse f "t to "t8 ,to ent] ^u actual !ological discussions w\ld be evid5tly beyond ! scope ( ?is "w4 ,x is ) ! sci5tific me?od common to all ! sci5ces1 & n ) any ( ! sep>ate sci5ces1 t we are conc]n$4 ,!ology !re=e w\ld be at lea/ z mu* beyond my scope z *emi/ry or geology4 ,b ,i believe t grave misappreh5sions exi/ z reg>ds ! v nature ( sci5tific me?od4 ,!re are sci5tific m5 :o ass]t t ! int]position ( ,provid5ce is impossible1 & pray] an absurdity1 because ! laws ( nature are inductively prov$ to be inv>iable4 ,inf]5ces are drawn n s mu* f p>ticul> sci5ces z f ! logical nature ( sci5ce itself1 to negative ! impulses & hopes ( m54 ,n[ ,i may /ate t my own /udies 9 logic lead me to call 9 "q su* negative inf]5ces4 ,laws ( nature are uni=mities obs]v$ to exi/ 9 ! action ( c]ta9 mat]ial ag5ts1 b x is logically impossible to %[ t all o!r ag5ts mu/ behave z ^! d4 ,! too exclusive /udy ( p>ticul> bran*es ( physical sci5ce seems to g5]ate an ov]-confid5t & dogmatic _s4 ,rejoic+ 9 ! success ) :i* a few gr\ps ( facts are br\ght b5ea? ! app>5t sway ( laws1 ! inve/igator ha/ily assumes t he is close ^u ! ultimate spr+s ( be+4 ,a p>ticle ( gelat9\s matt] is f\nd to obey ! ord9>y laws ( *emi/ry2 yet x moves & lives4 ,! _w is !re=e ask$ to believe t *emi/ry c resolve ! my/]ies ( exi/5ce4 99,! ,mean+ ( ,natural ,law499 ,p9d> speaks ( ,law z ! ,rul] ( ! ,mortals & ! ,immortals1 & x seems to be commonly suppos$ t ! s-call$ ,laws ( ,nature1 9 l mann]1 rule man & 8 ,creator4 ,! c\rse ( nature is reg>d$ z be+ det]m9$ by inv>iable pr9ciples ( me*anics :i* h act$ s9ce ! _w began1 & w act = ev]more4 ,ev5 if ! orig9 ( all ?+s is attribut$ to an intellig5t creative m9d1 t ,be+ is reg>d$ z hav+ yield$ up arbitr>y p[]1 & z be+ subject l a human legislator to ! laws :i* he has himself enact$4 ,su* notions ,i %\ld describe z sup]ficial & errone\s1 be+ d]iv$1 z ,i ?9k1 f false views ( ! nature ( sci5tific inf]5ce1 & ! degree ( c]ta9ty ( ! k :i* we acquire by inductive inve/igation4 ,a law ( nature1 z ,i reg>d ! mean+ ( ! expression1 is n a uni=mity :i* mu/ be obey$ by all objects1 b m]ely a uni=mity :i* is z a matt] ( fact obey$ by ^? objects :i* h come b5ea? our obs]vation4 ,!re is no?+ :atev] incompatible ) logic 9 ! discov]y ( objects :i* %\ld prove exceptions to any law ( nature4 ,p]haps ! be/ e/abli%$ law is t :i* ass]ts an inv>iable correlation to exi/ betwe5 gravity & in]tia1 s t all gravitat+ bodies are f\nd to possess in]tia1 & all bodies possess+ in]tia are f\nd to gravitate4 ,b x w\ld be no reproa* to our sci5tific me?od1 if some?+ 7 ultimately discov]$ to possess gravity )\t in]tia4 ,/rictly def9$ & correctly int]pret$1 ! law itself w\ld ackn[l$ge ! possibility2 = ) ! /atem5t ( e law we ought prop]ly to jo9 an e/imate ( ! numb] ( in/ances 9 :i* x has be5 obs]v$ to hold true1 & ! probability !nce calculat$1 t x w hold true 9 ! next case4 ,n[1 z we f\nd 7p4 #bei71 no f9ite numb] ( in/ances c w>rant u 9 expect+ ) c]ta9ty t ! next in/ance w be ( l nature2 9 ! =mulas yield$ by ! inv]se me?od ( probabilities a unit always appe>s to repres5t ! probability t our inf]5ce w be mi/ak54 ,i demur to ! assumption t !re is any necess>y tru? ev5 9 su* fundam5tal laws ( nature z ! ,inde/ructibility ( ,matt]1 ! ,cons]vation ( ,en]gy1 or ! ,laws ( ,motion4 ,c]ta9 x is t m5 ( sci5ce h recognis$ ! conceivability ( o!r laws1 & ev5 inve/igat$ _! ma!matical consequ5ces4 ,airy inve/igat$ ! ma!matical conditions ( a p]petual motion 7p4 #bbc71 & ,laplace & ,newton discuss$ imag9>y laws ( =ces inconsi/5t ) ^? obs]v$ to op]ate 9 ! univ]se 7pp4 #fdb1 #gjf74 ,! laws ( nature1 z ,i v5ture to reg>d !m1 are simply g5]al propositions conc]n+ ! correlation ( prop]ties :i* h be5 obs]v$ to hold true ( bodies hi!rto obs]v$4 ,on ! assumption t our exp]i5ce is ( adequate ext5t1 & t no arbitr>y int]f]5ce takes place1 we are !n able to assign ! probability1 always less ?an c]ta9ty1 t ! next object ( ! same app>5t nature w con=m to ! same laws4 99,inf9it5ess ( ! ,univ]se499 ,we may safely accept z a satisfactory sci5tific hypo!sis ! doctr9e s gr&ly put =? by ,laplace1 :o ass]t$ t a p]fect k ( ! univ]se1 z x exi/$ at any giv5 mom5t1 w\ld give a p]fect k ( :at 0 to happ5 !nce=? & = ev] aft]4 ,sci5tific inf]5ce is impossible1 unless we may reg>d ! pres5t z ! outcome ( :at is pa/1 & ! cause ( :at is to come4 ,to ! view ( p]fect intellig5ce no?+ is unc]ta94 ,! a/ronom] c calculate ! positions ( ! heav5ly bodies :5 ?\s&s ( g5]ations ( m5 %all h pass$ away1 & 9 ?is fact we h "s illu/ration1 z ,laplace rem>ks1 ( ! p[] :i* sci5tific presci5ce may atta94 ,d\btless1 too1 all ef=ts 9 ! inve/igation ( nature t5d to br+ u ne>] to ! possession ( t ideally p]fect p[] ( intellig5ce4 ,nev]!less1 z ,laplace ) pr(\nd wisdom adds1#fjc we mu/ ev] rema9 at an inf9ite di/ance f ! goal ( our aspirations4 #fjc 99,?orie ,analytique des ,probabilits991 quot$ by ,babbage1 99,n9? ,bridgewat] ,treatise991 p4 #agc4 ,let u assume1 = a "t at lea/1 z a highly probable hypo!sis1 t :atev] is to happ5 mu/ be ! outcome ( :at is2 !re !n arises ! "q1 ,:at is8 ,n[ our k ( :at exi/s mu/ ev] rema9 imp]fect & fallible 9 two respects4 ,fir/ly1 we d n "k all ! matt] t has be5 creat$1 nor ! exact mann] 9 :i* x has be5 di/ribut$ ?r\gh space4 ,secondly1 assum+ t we _h t k1 we %\ld /ill be want+ 9 a p]fect k ( ! way 9 :i* ! p>ticles ( matt] w act ^u ea* o!r4 ,! p[] ( sci5tific pr$iction ext5ds at ! mo/ to ! limits ( ! data employ$4 ,e conclusion is purely hypo!tical & conditional ^u ! non-int]f]5ce ( ag5cies previ\sly undetect$4 ,! law ( gravity ass]ts t e body t5ds to approa* t[>ds e o!r body1 ) a c]ta9 det]m9ate =ce2 b1 ev5 suppos+ ! law to hold true1 x does n ass]t t ! body 99w99 approa*4 ,no s+le law ( nature c w>rant u 9 mak+ an absolute pr$iction4 ,we mu/ "k all ! laws ( nature & all ! exi/+ ag5ts act+ accord+ to ^? laws be=e we c say :at w happ54 ,to assume1 !n1 t sci5tific me?od c take ev]y?+ )9 its cold embrace ( uni=mity1 is to imply t ! ,creator _c out/rip ! intellig5ce ( 8 creatures1 & t ! exi/+ ,univ]se is n inf9ite 9 ext5t & complexity1 an assumption = :i* ,i see no logical basis :atev]4 99,! ,indet]m9ate ,problem ( ,creation499 ,a second & v s]i\s misappreh5sion conc]n+ ! import ( a law ( nature may n[ be po9t$ out4 ,x is n uncommonly suppos$ t a law det]m9es ! "* ( ! results :i* %all take place1 z1 = in/ance1 t ! law ( gravity det]m9es :at =ce ( gravity %all act ^u a giv5 p>ticle4 ,surely a little reflection mu/ r5d] x pla9 t a law by itself det]m9es no?+4 ,x is 99law plus ag5ts obey+ law :i* has results991 & x is no function ( law to gov]n or def9e ! numb] & place ( its own ag5ts4 ,:e!r a p>ticle ( matt] %all gravitate1 dep5ds n only ^u ! law ( ,newton1 b also ^u ! di/ribution ( surr\nd+ p>ticles4 ,! !ory ( gravitation may p]haps be true ?r\gh\t all "t & 9 all p>ts ( space1 & ! ,creator may nev] f9d occasion to create ^? possible exceptions to x :i* ,i h ass]t$ to be conceivable4 ,let ?is be z x may2 our sci5ce _c c]ta9ly det]m9e ! "q4 ,c]ta9 x is1 t ! law ( gravity does n alone det]m9e ! =ces :i* may be br\ght to be> at any po9t ( space4 ,! =ce ( gravitation act+ ^u any p>ticle dep5ds ^u ! mass1 di/ance1 & relative position ( all ! o!r p>ticles ( matt] )9 ! b\nds ( space at ! in/ant 9 "q4 ,ev5 assum+ t all matt] :5 once di/ribut$ ?r\gh space at ! ,creation 0 !nce=? to act 9 an inv>iable mann] )\t subsequ5t int]f]5ce1 yet ! actual configuration ( matt] at any mom5t1 & ! consequ5t results ( ! law ( gravitation1 mu/ h be5 entirely a matt] ( free *oice4 ,*alm]s has mo/ di/9ctly po9t$ out t ! exi/+ 99collocations99 ( ! mat]ial _w are z important z ! laws :i* ! objects obey4 ,he rem>ks t a c]ta9 class ( writ]s entirely ov]look ! di/9ction1 & =get t m]e laws )\t collocations w\ld h af=d$ no security aga9/ a turbid & disord]ly *aos4#fjd ,mill has recognis$#fje ! tru? ( ,*alm]s' /atem5t1 )\t draw+ ! prop] inf]5ces f x4 ,he says#fjf ( ! di/ribution ( matt] ?r\gh space1 8,we c discov] no?+ regul> 9 ! di/ribution itself2 we c r$uce x to no uni=mity1 to no law40 ,m lately ! ,duke ( ,argyll 9 8 well-kn[n "w on ! 99,reign ( ,law99 has drawn att5tion to ! pr(\nd di/9ction betwe5 laws & collocations ( causes4 #fjd 99,fir/ ,bridgewat] ,treatise99 7#ahcd71 pp4 #af-bd4 #fje 99,sy/em ( ,logic991 #e? edit4 bk4 ,,iii4 *ap4 ,v4 #g2 *ap4 ,,xvi4 #c4 #fjf 99,sy/em ( ,logic991 vol4 i4 p4 #chd4 ,! orig9al con=mation ( ! mat]ial univ]se1 z f> z we c tell1 0 free f all re/riction4 ,!re 0 unlimit$ space 9 :i* to frame x1 & an unlimit$ numb] ( mat]ial p>ticles1 ea* ( :i* c\ld be plac$ 9 any "o ( an inf9ite numb] ( diff]5t positions4 ,x %\ld be add$1 t ea* p>ticle might be end[$ ) any "o ( an inf9ite numb] ( quantities ( 99vis viva99 act+ 9 any "o ( an inf9ite numb] ( diff]5t directions4 ,! problem ( ,creation 01 !n1 :at a ma!matician w\ld call 99an indet]m9ate problem991 & x 0 indet]m9ate 9 a great numb] ( ways4 ,inf9itely num]\s & v>i\s univ]ses might !n h be5 fa%ion$ by ! v>i\s di/ribution ( ! orig9al nebul\s matt]1 al?\gh all ! p>ticles ( matt] %\ld obey ! law ( gravity4 ,lucretius tells u h[ 9 ! orig9al ra9 ( atoms "s ( ^! little bodies div]g$ f ! rectil9e> direction1 & com+ into contact ) o!r atoms gave rise to ! v>i\s comb9ations ( sub/ances :i* exi/4 ,he omitt$ to tell u :5ce ! atoms came1 or by :at =ce "s ( !m 7 caus$ to div]ge2 b surely ^! omissions involve ! :ole "q4 ,i accept ! ,lucretian conception ( creation :5 prop]ly supplem5t$4 ,e atom :i* exi/$ 9 any po9t ( space mu/ h exi/$ !re previ\sly1 or mu/ h be5 creat$ !re by a previ\sly exi/+ ,p[]4 ,:5 plac$ !re x mu/ h _h a def9ite mass & a def9ite en]gy4 ,n[1 z be=e rem>k$1 an unlimit$ numb] ( atoms c be plac$ 9 unlimit$ space 9 an unlimit$ numb] ( modes ( di/ribution4 ,out ( inf9itely inf9ite *oices :i* 7 op5 to ! ,creator1 t "o *oice mu/ h be5 made :i* has yield$ ! ,univ]se z x n[ exi/s4 ,x w\ld be a mi/ake1 inde$1 to suppose t ! law ( gravity1 :5 x holds true1 is no re/riction on ! di/ribution ( =ce4 ,t law is a geometrical law1 & x w\ld 9 _m cases be ma!matically impossible1 z f> z we c see1 t ! =ce ( gravity act+ on "o p>ticle %\ld be small :ile t on a neighb\r+ p>ticle is great4 ,we _c conceive t ev5 ,omnipot5t ,p[] %\ld make ! angles ( a triangle great] ?an two "r angles4 ,! prim>y laws ( ?\ght & ! fundam5tal notions ( ! ma!matical sci5ces d n seem to admit ( error or alt]ation4 ,into ! metaphysical orig9 & mean+ ( ! app>5t necessity atta*+ to su* laws ,i h n attempt$ to inquire 9 ?is "w1 & x is n requisite = my pres5t purpose4 ,if ! law ( gravity 7 ! only law ( nature & ! ,creator _h *os5 to r5d] all matt] ob$i5t to t law1 !re w\ld d\btless be re/rictions ^u ! effects d]ivable f any "o di/ribution ( matt]4 99,hi]>*y ( ,natural ,laws499 ,a fur!r consid]ation pres5ts itself4 ,a natural law l t ( gravity expresses a c]ta9 uni=mity 9 ! action ( ag5ts submitt$ to x1 & ?is produces1 z we h se51 c]ta9 geometrical re/rictions ^u ! effects :i* ^? ag5ts may produce4 ,b !re are o!r =ces & laws besides gravity4 ,"o =ce may ov]ride ano!r1 & two laws may ea* be obey$ & may ea* disguise ! action ( ! o!r4 ,9 ! intimate con/itution ( matt] !re may be hidd5 spr+s :i*1 :ile act+ 9 accordance ) _! own fix$ laws1 may lead to sudd5 & unexpect$ *anges4 ,s at lea/ x has be5 f\nd f "t to "t 9 ! pa/1 & s !re is e reason to believe x w be f\nd 9 ! future4 ,to ! anci5ts x seem$ incr$ible t "o lifeless /one c\ld make ano!r leap t[>ds x4 ,a piece ( iron :ile x obeys ! magnetic =ce ( ! load/one does n ! less obey ! law ( gravity4 ,a plant gravitates d[nw>ds z reg>ds e con/itu5t cell or fibre1 & yet x p]si/s 9 gr[+ upw>ds4 ,life is altoge!r an exception to ! simpl] ph5om5a ( m9]al sub/ances1 n 9 ! s5se ( disprov+ ^? laws1 b 9 sup]add+ =ces ( new & inexplicable "*4 ,d\btless no law ( *emi/ry is brok5 by ! action ( ! n]v\s cells1 & no law ( physics by ! pulses ( ! n]v\s fibres1 b some?+ requires to be add$ to our sci5ces 9 ord] t we may expla9 ^! subtle ph5om5a4 ,n[ !re is absolutely no?+ 9 sci5ce or 9 sci5tific me?od to w>rant u 9 assign+ a limit to ?is hi]>*y ( laws4 ,:5 9 _m und\bt$ cases we f9d law ov]rid+ law1 & at c]ta9 po9ts 9 our exp]i5ce produc+ unexpect$ results1 we _c v5ture to affirm t we h exhau/$ ! /range ph5om5a :i* may h be5 provid$ = 9 ! orig9al con/itution ( matt]4 ,! ,univ]se might h be5 s design$ t x %\ld g = long int]vals ?r\gh ! same r\nd ( unv>i$ exi/5ce1 & yet t ev5ts ( exceptional "* %\ld be produc$ f "t to "t4 ,babbage %[$ 9 t mo/ pr(\nd & eloqu5t "w1 99,! ,n9? ,bridgewat] ,treatise991 t x 0 !oretically possible = human arti/s to design a ma*9e1 consi/+ ( metallic :eels & lev]s1 :i* %\ld "w inv>iably accord+ to a simple law ( action dur+ any f9ite numb] ( /eps1 & yet at a fix$ mom5t1 h[ev] di/ant1 %\ld manife/ a s+le brea* ( law4 ,su* an eng9e might g on c\nt+1 = in/ance1 ! natural numb]s until !y w\ld rea* a numb] requir+ = its expression a hundr$ million digits4 8,if e lett] 9 ! volume n[ be=e ! read]'s eyes10 says ,babbage1#fjg 87 *ang$ into a figure1 & if all ! figures conta9$ 9 a ?\s& su* volumes 7 arrang$ 9 ord]1 ! :ole toge!r w\ld yet fall f> %ort ( ! va/ induction ! obs]v] w\ld h _h 9 fav\r ( ! tru? ( ! law ( natural numb]s4444 ,yet %all ! eng9e1 true to ! pr$iction ( its director1 aft] ! lapse ( myriads ( ages1 fulfil its task1 & give t "o1 ! fir/ & only exception to t "t-sanction$ law4 ,:at w\ld h be5 ! *ances aga9/ ! appe>ance ( ! except$ case1 imm$iately prior to its occurr5ce80 #fjg 99,n9? ,bridgewat] ,treatise991 p4 #adj4 ,z ,babbage fur!r %[$1#fjh a calculat+ eng9e1 aft] proce$+ ?r\gh any requir$ numb] ( motions accord+ to a fir/ law1 may be made sudd5ly to suff] a *ange1 s t x %all !n comm5ce to calculate accord+ to a :olly new law4 ,aft] giv+ ! natural numb]s = a f9ite "t1 x might sudd5ly beg9 to give triangul>1 or squ>e1 or cube numb]s1 & ^! *anges might be conceiv$ !oretically z occurr+ "t aft] "t4 ,n[ if su* occurr5ces c be design$ & =ese5 by a human arti/1 x is surely )9 ! capacity ( ! ,div9e ,arti/ to provide = analog\s *anges ( law 9 ! me*anism ( ! atom1 or ! con/ruction ( ! heav5s4 #fjh 99,ibid499 pp4 #cd-dc4 ,physical sci5ce1 s f> z its highe/ speculations c be tru/$1 gives "s indication ( a *ange ( law 9 ! pa/ hi/ory ( ! ,univ]se4 ,accord+ to ,sir ,w4 ,?omson's d$uctions f ,f\ri]'s 99,!ory ( ,heat991 we c trace d[n ! dissipation ( heat by conduction & radiation to an inf9itely di/ant "t :5 all ?+s w be uni=mly cold4 ,b we _c simil>ly trace ! heat-hi/ory ( ! ,univ]se to an inf9ite di/ance 9 ! pa/4 ,= a c]ta9 negative value ( ! "t ! =mul give impossible values1 indicat+ t !re 0 "s initial di/ribution ( heat :i* c\ld n h result$1 accord+ to kn[n laws ( nature1#fji f any previ\s di/ribution4#faj ,!re are o!r cases 9 :i* a consid]ation ( ! dissipation ( en]gy leads to ! conception ( a limit to ! antiquity ( ! pres5t ord] ( ?+s4#faa ,human sci5ce1 ( c\rse1 is fallible1 & "s ov]sight or errone\s simplification 9 ^! !oretical calculations may aft]w>ds be discov]$2 b z ! pres5t /ate ( sci5tific k is ! only gr\nd on :i* errone\s inf]5ces f ! uni=mity ( nature & ! suppos$ reign ( law are f\nd$1 ,i am "r 9 appeal+ to ! pres5t /ate ( sci5ce 9 opposition to ^! inf]5ces4 ,n[ ! !ory ( heat places u 9 ! dilemma ei!r ( believ+ 9 ,creation at an assignable date 9 ! pa/1 or else ( suppos+ t "s inexplicable *ange 9 ! work+ ( natural laws !n took place4 ,physical sci5ce gives no c\nt5ance to ! notion ( inf9ite duration ( matt] 9 "o cont9u\s c\rse ( exi/5ce4 ,& if 9 "t pa/ !re has be5 a discont9uity ( law1 :y may !re n be a simil> ev5t await+ ! _w 9 ! future8 ,inf9ite +5uity c\ld h implant$ "s ag5cy 9 matt] s t x might nev] yet h made its trem5d\s p[]s manife/4 ,we h a v good !ory ( ! cons]vation ( en]gy1 b ! =emo/ physici/s d n d5y t !re may possibly be =ms ( en]gy1 nei!r k9etic nor pot5tial1 & !re=e ( unkn[n nature4#fab #fji ,pr(essor ,clif=d1 9 8 mo/ int]e/+ lecture on 8,! ,fir/ & ,la/ ,cata/rophe0 799,=tnightly ,review991 ,april #ahge1 p4 #dhj1 repr9t by ! ,sunday ,lecture ,society1 p4 #bd71 objects t ,i h errone\sly sub/itut$ 8kn[n laws ( nature0 = 8kn[n laws ( conduction ( heat40 ,i q admit ! error1 )\t admitt+ all ! conclusions :i* ,pr(essor ,clif=d proce$s to draw2 b ,i ma9ta9 ! p>agraph un*ang$1 9 ord] t x may be discuss$ 9 ! ,preface4 #faj ,tait's 99,!rmodynamics991 p4 #ch4 99,cambridge ,ma!matical ,j\rnal991 vol4 iii4 p4 #agd4 #faa ,cl]k ,maxwell's 99,!ory ( ,heat991 p4 #bde4 #fab ,maxwell's 99,!ory ( ,heat991 p4 #ib4 ,we c imag9e reason+ creatures dwell+ 9 a _w :]e ! atmosph]e 0 a mixture ( oxyg5 & inflammable gas l ! fire-damp ( coal-m9es4 ,if devoid ( fire1 !y might h liv$ ?r\gh long ages unconsci\s ( ! trem5d\s =ces :i* a s+le sp>k w\ld call into play4 ,9 ! tw9kl+ ( an eye new laws might come into action1 & ! poor reason+ creatures1 s confid5t ab\t _! k ( ! reign ( law 9 _! _w1 w\ld h no "t to speculate ^u ! ov]?r[ ( all _! !ories4 ,c we ) our f9ite k be sure t su* an ov]?r[ ( our !ories is impossible8 99,! ,ambigu\s ,expression1 8,uni=mity ( ,nature4099 ,i h ass]t$ t s]i\s misconception arises f an errone\s int]pretation ( ! expression ,uni=mity ( ,nature4 ,e law ( nature is ! /atem5t ( a c]ta9 uni=mity obs]v$ to exi/ among ph5om5a1 & s9ce ! laws ( nature are inv>iably obey$1 x seems to foll[ t ! c\rse ( nature itself is uni=m1 s t we c safely judge ( ! future by ! pres5t4 ,?is inf]5ce is support$ by "s ( ! results ( physical a/ronomy4 ,laplace prov$ t ! planet>y sy/em is /able1 s t no p]turbation :i* planet produces ^u planet c become s great z to cause disruption & p]man5t alt]ation ( ! planet>y orbits4 ,a full compreh5sion ( ! law ( gravity %[s t all su* di/urbances are ess5tially p]iodic1 s t aft] ! lapse ( millions ( ye>s ! planets w return to ! same relative positions1 & a new cycle ( di/urbances w !n comm5ce4 ,z o!r bran*es ( sci5ce progress1 we seem to ga9 assurance t no great alt]ation ( ! _w's condition is to be expect$4 ,conflict ) a comet has long be5 ! cause ( fe>1 b n[ x is cr$ibly ass]t$ t we h pass$ ?r\gh a comet's tail )\t ! fact be+ kn[n at ! "t1 or manife/$ by any m s]i\s a ph5om5on ?an a slight lum9osity ( ! sky4 ,m rec5tly /ill ! e>? is said to h t\*$ ! comet ,biela1 & ! only result 0 a beautiful & p]fectly h>mless display ( meteors4 ,a decrease 9 ! heat+ p[] ( ! sun seems to be ! next mo/ probable circum/ance f :i* we might fe> ! ext9ction ( life on ! e>?4 ,b calculations f\nd$ on reasonable physical data %[ t no appreciable *ange c be go+ on1 & exp]im5tal data to indicate a *ange are :olly want+4 ,geological inve/igations %[ inde$ t !re h be5 ext5sive v>iations ( climate 9 pa/ times2 va/ glaci]s & iceb]gs h swept ov] ! temp]ate regions at "o "t1 & tropical vegetation has fl\ri%$ ne> ! poles at ano!r "t4 ,b "h aga9 ! vicissitudes ( climate assume a p]iodic "*1 s t ! /ability ( ! e>?'s condition does n seem to be ?reat5$4 ,all ^! /atem5ts may be reasonable1 b !y d n e/abli% ! ,uni=mity ( ,nature 9 ! s5se t ext5sive alt]ations or sudd5 cata/rophes are impossible4 ,9 ! fir/ place1 ,laplace's !ory ( ! /ability ( ! planet>y sy/em is ( an ab/ract "*1 z pay+ reg>d to no?+ b ! mutual gravitation ( ! planet>y bodies & ! sun4 ,x ov]looks sev]al physical causes ( *ange & decay 9 ! sy/em :i* 7 n s well kn[n 9 8 day z at pres5t1 & x also presupposes ! abs5ce ( any int]ruption ( ! c\rse ( ?+s by conflict ) =eign a/ronomical bodies4 ,x is n[ ackn[l$g$ by a/ronom]s t !re are at lea/ two ways 9 :i* ! 99vis viva99 ( ! planets & satellites may suff] loss4 ,! friction ( ! tides ^u ! e>? produces a small quantity ( heat :i* is radiat$ into space1 & ?is loss ( en]gy mu/ result 9 a decrease ( ! rotational velocity1 s t ultimately ! t]re/rial day w become id5tical ) ! ye>1 j z ! p]iods ( revolution ( ! moon ^u its axis & ar\nd ! e>? h already become equal4 ,secondly1 !re c be little d\bt t c]ta9 manife/ations ( electricity ^u ! e>?'s surface dep5d ^u ! relative motions ( ! planets & ! sun1 :i* give rise to p]iods ( increas$ int5sity4 ,su* electrical ph5om5a mu/ result 9 ! production & dissipation ( heat1 ! en]gy ( :i* mu/ be drawn1 p>tially at lea/1 f ! mov+ bodies4 ,?is effect is probably id5tical 7p4 #egj7 ) ! loss ( en]gy ( comets attribut$ to ! s-call$ resi/+ m$ium4 ,b :atev] be ! !oretical explanation ( ^! ph5om5a1 x is almo/ c]ta9 t !re exi/s a t5d5cy to ! dissipation ( ! en]gy ( ! planet>y sy/em1 :i* w1 9 ! indef9ite c\rse ( "t1 result 9 ! fall ( ! planets into ! sun4 ,x is h>dly probable1 h[ev]1 t ! planet>y sy/em w be left undi/urb$ ?r\gh\t ! enorm\s int]val ( "t requir$ = ! dissipation ( its en]gy 9 ?is way4 ,conflict ) o!r bodies is s f> f be+ improbable1 t x becomes approximately c]ta9 :5 we take v long int]vals ( "t into acc\nt4 ,z reg>ds comet>y conflicts1 ,i am by no means satisfi$ ) ! negative conclusions drawn f ! rem>kable display on ! ev5+ ( ! #bg? ( ,novemb]1 #ahgb4 ,we may (t5 h pass$ ?r\gh ! tail ( a comet1 ! light ( :i* is probably an electrical manife/ation no m sub/antial ?an ! aurora borealis4 ,e rem>kable %[] ( %oot+ />s may also be consid]$ z proce$+ f a comet>y body1 s t we may be said to h pass$ ?r\gh ! ?9n] p>ts ( innum]able comets4 ,b ! e>? has probably nev] pass$1 9 times ( :i* we h any record1 ?r\gh ! nucleus ( a comet1 :i* consi/s p]haps ( a d5se sw>m ( small meteorites4 ,we c only speculate ^u ! effects :i* might be produc$ by su* a conflict1 b x w\ld probably be a mu* m s]i\s ev5t ?an any yet regi/]$ 9 hi/ory4 ,! probability ( its occurr5ce1 too1 _c be assign$2 = ?\gh ! probability ( conflict ) any "o comet>y nucleus is almo/ inf9itesimal1 yet ! numb] ( comets is imm5sely great 7p4 #djh74 ,x is f> f impossible1 aga91 t ! planet>y sy/em may be invad$ by bodies ( great] mass ?an comets4 ,! sun seems to be plac$ 9 s ext5sive a portion ( empty space t its own prop] motion w\ld n br+ x to ! ne>e/ kn[n /> 7 ,c5tauri7 9 less ?an #aci1bjj ye>s4 ,b 9 ord] to be sure t ?is int]val ( undi/urb$ life is grant$ to our globe1 we mu/ prove t !re are no />s mov+ s z to meet u1 & no d>k bodies ( consid]able size fly+ ?r\gh int]v5+ space unkn[n to u4 ,! intrusion ( comets into our sy/em1 & ! fact t _m ( !m h hyp]bolic pa?s1 is suffici5t to %[ t ! surr\nd+ p>ts ( space are occupi$ by multitudes ( d>k bodies ( "s size4 ,x is q probable t small suns may h cool$ suffici5tly to become non-lum9\s2 = ev5 if we discr$it ! !ory t ! v>iation ( brightness ( p]iodic />s is due to ! revolution ( d>k companion />s1 yet !re is 9 our own globe an unque/ionable example ( a small] body :i* has cool$ bel[ ! lum9\s po9t4 ,altoge!r1 !n1 x is a m]e assumption t ! uni=mity ( nature involves ! unalt]$ exi/5ce ( our own globe4 ,!re is no k9d ( cata/rophe :i* is too great or too sudd5 to be !oretically consi/5t ) ! reign ( law4 ,= all t our sci5ce c tell1 human hi/ory may be clos$ 9 ! next in/ant ( "t4 ,! _w may be da%$ to pieces aga9/ a w&]+ />2 x may be involv$ 9 a nebul\s atmosph]e ( hydrog5 to be explod$ a second aft]w>ds2 x may be scor*$ up or dissipat$ into vap\r by "s great explosion 9 ! sun2 !re might ev5 be )9 ! globe itself "s secret cause ( disruption1 :i* only ne$s "t = its manife/ation4 ,!re are "s indications1 z already notic$ 7p4 #ffj71 t viol5t di/urbances h actually occurr$ 9 ! hi/ory ( ! sol> sy/em4 ,olb]s s\ght = ! m9or planets on ! supposition t !y 7 fragm5ts ( an explod$ planet1 & he 0 rew>d$ ) ! discov]y ( "s ( !m4 ,! retrograde motion ( ! satellites ( ! m di/ant planets1 ! abnormal position ( ! poles ( ,uranus & ! excessive di/ance ( ,neptune1 are o!r indications ( "s viol5t ev5t1 ( :i* we h no o!r evid5ce4 ,i adduce all ^! facts & argum5ts1 n to %[ t !re is any consid]able probability1 z f> z we c judge1 ( int]ruption )9 ! scope ( human hi/ory1 b to prove t ! ,uni=mity ( ,nature is !oretically consi/5t ) ! mo/ unexpect$ ev5ts ( :i* we c =m a conception4 99,possible ,/ates ( ! ,univ]se499 ,:5 we give ! re9 to sci5tific imag9ation1 x becomes app>5t t conflict ( body ) body mu/ n be reg>d$ z ! r>e exception1 b z ! g5]al rule & ! inevitable fate ( ea* /> sy/em4 ,s f> z we c trace out ! results ( ! law ( gravitation1 & ( ! dissipation ( en]gy1 ! univ]se mu/ be reg>d$ z und]go+ gradual cond5sation into a s+le cold solid body ( gigantic dim5sions4 ,^? :o s frequ5tly use ! expression ,uni=mity ( ,nature seem to =get t ! ,univ]se might exi/ consi/5tly ) ! laws ( nature 9 ! mo/ div]se conditions4 ,x might consi/1 on ! "o h&1 ( a gl[+ nebul\s mass ( gase\s sub/ances4 ,! heat might be s int5se t all elem5ts1 ev5 c>bon & silicon1 w\ld be 9 ! /ate ( gas1 & all atoms1 ( :atev] nature1 w\ld be fly+ ab\t 9 *emical indep5d5ce1 diffus+ !mselves almo/ uni=mly 9 ! neighb\r+ p>ts ( space4 ,!re w\ld !n be no life1 unless we c apply t "n to ! passage ?r\gh ea* "p ( space ( simil> av]age tra9s ( atoms1 ! p>ticul> succession ( atoms be+ gov]n$ only by ! !ory ( probability1 & ! law ( div]g5ce f a mean exhibit$ 9 ! ,ari?metical ,triangle4 ,su* a univ]se w\ld correspond p>tially to ! ,lucretian ra9 ( atoms1 & to t nebul> hypo!sis out ( :i* ,laplace propos$ philosophically to expla9 ! evolution ( ! planet>y sy/em4 ,accord+ to ano!r extreme supposition1 ! int5se heat-en]gy ( ?is nebul\s mass might be radiat$ away into ! unkn[n regions ( out] space4 ,! attraction ( gravity w\ld ex]t itself betwe5 ea* two p>ticles1 & ! en]gy ( motion !nce aris+ w\ld1 by incessant conflicts1 be resolv$ into heat & dissipat$4 ,inconceivable ages might be requir$ = ! completion ( ?is process1 b ! dissipation ( en]gy ?us proce$+ c\ld end only 9 ! production ( a cold & motionless univ]se4 ,! relation ( cause & effect1 z we see x manife/$ 9 life & gr[?1 w\ld deg5]ate into ! con/ant exi/5ce ( e p>ticle 9 a fix$ position relative to e o!r p>ticle4 ,logical & geometrical resemblances w\ld /ill exi/ betwe5 atoms1 & betwe5 gr\ps ( atoms cry/allis$ 9 _! appropriate =ms = ev]more4 ,b "t1 ! great v>iable1 w\ld br+ no v>iation1 & z to human hopes & tr\bles1 !y w\ld h gone to et]nal re/4 ,sci5ce is n really adequate to prov+ t su* is ! inevitable fate ( ! univ]se1 = we c seldom tru/ our be/-e/abli%$ !ories f> f _! data4 ,nev]!less1 ! mo/ probable speculations :i* we c =m z to ! hi/ory1 especially ( our own planet>y sy/em1 is t x orig9at$ 9 a heat$ revolv+ nebul\s mass ( gas1 & is 9 a /ate ( excessively sl[ progress t[>ds ! cold & /ony condition4 ,o!r speculative hypo!ses might d\btless be ent]ta9$4 ,e hypo!sis is press$ by difficulties4 ,if ! :ole univ]se be cool+1 :i!r does ! heat g8 ,if we are to get rid ( x entirely1 out] space mu/ be inf9ite 9 ext5t1 s t x %all nev] be /opp$ & reflect$ back4 ,b n to speak ( metaphysical difficulties1 if ! m$ium ( heat undulations be inf9ite 9 ext5t1 :y %\ld n ! mat]ial bodies plac$ 9 x be inf9ite also 9 numb] & aggregate mass8 ,x is app>5t t we are v5tur+ into speculations :i* surpass our p[]s ( sci5tific inf]5ce4 ,b !n ,i am argu+ negatively2 ,i wi% to %[ t ^? :o speak ( ! uni=mity ( nature1 & ! reign ( law1 mis9t]pret ! mean+ involv$ 9 ^? expressions4 ,law is n inconsi/5t ) extreme div]sity1 &1 s f> z we c read ! hi/ory ( ?is planet>y sy/em1 x did probably orig9ate 9 heat$ nebul\s matt]1 & man's hi/ory =ms b a brief span 9 its progress t[>ds ! cold & /ony condition4 ,x is by d\btful & speculative hypo!ses alone t we c avoid su* a conclusion1 & ,i dep>t lea/ f und\bt$ facts & well-e/abli%$ laws :5 ,i ass]t t1 :atev] uni=mities may und]lie ! ph5om5a ( nature1 con/ant v>iety & ev]-progress+ *ange is ! real outcome4 99,speculations on ! ,reconc5tration ( ,en]gy499 ,!re are unequivocal indications1 z ,i h said1 t ! mat]ial univ]se1 z we at pres5t see x1 is progress+ f "s act ( creation1 or "s discont9uity ( exi/5ce ( :i* ! date may be approximately fix$ by sci5tific inf]5ce4 ,x is progress+ t[>ds a /ate 9 :i* ! available en]gy ( matt] w be dissipat$ ?r\gh inf9ite surr\nd+ space1 & all matt] w become cold & lifeless4 ,?is con/itutes1 z x 71 ! hi/orical p]iod ( physical sci5ce1 t ov] :i* our sci5tific =esight may m or less ext5d4 ,b 9 ?is1 z 9 o!r cases1 we h no "r to int]pret our exp]i5ce negatively1 s z to inf] t because ! pres5t /ate ( ?+s began at a p>ticul> "t1 !re 0 no previ\s exi/5ce4 ,x may be t ! pres5t p]iod ( mat]ial exi/5ce is b "o ( an indef9ite s]ies ( l p]iods4 ,all t we c see1 & feel1 & inf]1 & reason ab\t may be1 z x 71 b a "p ( "o s+le pulsation 9 ! exi/5ce ( ! univ]se4 ,aft] ,sir ,w4 ,?omson _h po9t$ out ! prepond]at+ t5d5cy :i* n[ seems to exi/ t[>ds ! conv]sion ( all en]gy into heat-en]gy1 & its equal diffusion by radiation ?r\gh\t space1 ! late ,pr(essor ,rank9e put =? a rem>kable speculation4#fac ,he sugge/$ t ! e!real1 or1 z ,i h call$ x1 ! 99adamant9e99 m$ium 9 :i* all ! />s exi/1 & all radiation takes place1 may h b\nds1 beyond :i* only empty space exi/s4 ,all heat undulations rea*+ ?is b\nd>y w be totally reflect$1 accord+ to ! !ory ( undulations1 & w be reconc5trat$ into foci situat$ 9 v>i\s p>ts ( ! m$ium4 ,:5ev] a cold & ext9ct /> happ5s to pass ?r\gh "o ( ^! foci1 x w be in/antly ignit$ & resolv$ by int5se heat into its con/itu5t elem5ts4 ,discont9uity w occur 9 ! hi/ory ( t portion ( matt]1 & ! /> w beg9 its hi/ory afre% ) a r5ew$ /ore ( en]gy4 #fac 99,report ( ! ,briti% ,association99 7#aheb71 ,report ( ,sections1 p4 #ab4 ,?is is d\btless a m]e speculation1 practically incapable ( v]ification by obs]vation1 & almo/ free f re/rictions af=d$ by pres5t k4 ,we might attribute v>i\s %apes to ! adamant9e m$ium1 & ! consequ5ces w\ld be v>i\s4 ,b !re is ?is value 9 su* speculations1 t !y draw att5tion to ! f9it5ess ( our k4 ,we _c d5y ! possible tru? ( su* an hypo!sis1 nor c we place a limit to ! sci5tific imag9ation 9 ! fram+ ( o!r l hypo!ses4 ,x is impossible1 inde$1 to foll[ out our sci5tific inf]5ces )\t fall+ into speculation4 ,if heat be radiat$ into outw>d space1 x mu/ ei!r proce$ 99ad inf9itum991 or x mu/ be /opp$ some:]e4 ,9 ! latt] case we fall ^u ,rank9e's hypo!sis4 ,b if ! mat]ial univ]se consi/ ( a f9ite collection ( heat$ matt] situat$ 9 a f9ite portion ( an inf9ite adamant9e m$ium1 !n ei!r ?is univ]se mu/ h exi/$ = a f9ite "t1 or else x mu/ h cool$ d[n dur+ ! inf9ity ( pa/ "t indef9itely ne> to ! absolute z]o ( temp]ature4 ,i object$ to ,lucretius' argum5t aga9/ ! de/ructibility ( matt]1 t we h no k :atev] ( ! laws accord+ to :i* x w\ld und]go de/ruction4 ,b we d "k ! laws accord+ to :i* ! dissipation ( heat appe>s to proce$1 & ! conclusion inevitably is t a f9ite heat$ mat]ial body plac$ 9 a p]fectly cold inf9itely ext5d$ m$ium w\ld 9 an inf9ite "t s9k to z]o ( temp]ature4 ,n[ our own _w is n yet cool$ d[n ne> to z]o1 s t physical sci5ce seems to place u 9 ! dilemma ( admitt+ ei!r ! f9it5ess ( pa/ duration ( ! _w1 or else ! f9it5ess ( ! portion ( m$ium 9 :i* we exi/4 ,9 ei!r case we become involv$ 9 metaphysical & me*anical difficulties surpass+ our m5tal p[]s4 99,! ,div]g5t ,scope = ,new ,discov]y499 ,9 ! writ+s ( "s rec5t philosoph]s1 especially ( ,augu/e ,comte1 & 9 "s degree ,john ,/u>t ,mill1 !re is an errone\s & hurtful t5d5cy to repres5t our k z assum+ an approximately complete "*4 ,at lea/ ^! & _m o!r writ]s fail to impress ^u _! read]s a tru? :i* _c be too con/antly borne 9 m9d1 namely1 t ! utmo/ successes :i* our sci5tific me?od c accompli% w n enable u to compreh5d m ?an an inf9itesimal fraction ( :at !re d\btless is to compreh5d4#fad ,pr(essor ,tyndall seems to me op5 to ! same *>ge 9 a less degree4 ,he rem>ks#fae t we c probably nev] br+ natural ph5om5a completely "u ma!matical laws1 because ! approa* ( our sci5ces t[>ds complet5ess may be asymptotic1 s t h[ev] f> we may g1 !re may /ill rema9 "s facts n subject to sci5tific explanation4 ,he ?us lik5s ! supply ( novel ph5om5a to a conv]g5t s]ies1 ! e>li] & l>g] t]ms ( :i* h be5 successfully dispos$ (1 s t comp>atively m9or gr\ps ( ph5om5a alone rema9 = future inve/igators to occupy !mselves ^u4 #fad ,mr4 ,c4 ,j4 ,monroe objects t 9 ?is /atem5t ,i d inju/ice to ,comte1 :o1 he ?9ks1 did impress ^u 8 read]s ! inadequacy ( our m5tal p[]s comp>$ ) ! va/ness ( ! subject matt] ( sci5ce4 ,! error ( ,comte1 he holds1 0 9 ma9ta9+ t sci5ce _h be5 c>ri$ ab\t z f> z x is wor? :ile to c>ry x1 :i* is a diff]5t matt]4 ,9 ei!r case1 ,comte's position is s unt5able t ,i am cont5t to leave ! "q undecid$4 #fae 99,fragm5ts ( ,sci5ce991 p4 #cfb4 ,on ! contr>y1 z x appe>s to me1 ! supply ( new & unexpla9$ facts is div]g5t 9 ext5t1 s t ! m we h expla9$1 ! m !re is to expla94 ,! fur!r we advance 9 any g5]alisation1 ! m num]\s & intricate are ! exceptional cases /ill dem&+ fur!r treatm5t4 ,! exp]im5ts ( ,boyle1 ,m>iotte1 ,dalton1 ,gay-,lussac1 & o!rs1 ^u ! physical prop]ties ( gases1 might seem to h exhau/$ t subject by %[+ t all gases obey ! same laws z reg>ds temp]ature1 pressure1 & volume4 ,b 9 reality ^! laws are only approximately true1 & ! div]g5ces af=d a wide & q unexhau/$ field = fur!r g5]alisation4 ,! rec5t discov]ies ( ,pr(essor ,&rews h summ$ up "s ( ^! exceptional facts "u a wid] g5]alisation1 b 9 reality !y h op5$ to u va/ new regions ( int]e/+ inquiry1 & !y leave :olly unt\*$ ! "q :y "o gas behaves diff]5tly f ano!r4 ,! sci5ce ( cry/allography is t p]haps 9 :i* ! mo/ precise & g5]al laws h be5 detect$1 b x w\ld be untrue to ass]t t x has less5$ ! area ( future discov]y4 ,we c %[ t ea* "o ( ! sev5 or eight hundr$ =ms ( calcite is d]ivable by geometrical modifications f an hexagonal prism2 b :o has attempt$ to expla9 ! molecul> =ces produc+ ^! modifications1 or ! *emical conditions 9 :i* !y arise8 ,! law ( isomorphism is an important g5]alisation1 = x e/abli%es a g5]al resemblance betwe5 ! =ms ( cry/allisation ( natural classes ( elem5ts4 ,b if we exam9e a little m closely we f9d t ^! =ms are only approximately alike1 & ! div]g5ce peculi> to ea* sub/ance is an unexpla9$ exception4 ,by _m simil> illu/rations x might readily be %[n t 9 :atev] direction we ext5d our inve/igations & successfully h>monise a few facts1 ! result is only to raise up a ho/ ( o!r unexpla9$ facts4 ,c any sci5tific man v5ture to /ate t !re is less op5+ n[ = new discov]ies ?an !re 0 ?ree c5turies ago8 ,is x n r true t we h b to op5 a sci5tific book & read a page or two1 & we %all come to "s record$ ph5om5on ( :i* no explanation c yet be giv58 ,9 e su* fact !re is a possible op5+ = new discov]ies1 & x c only be ! fault ( ! inve/igator's m9d if he c look ar\nd him & f9d no scope = ! ex]cise ( 8 faculties4 99,inf9ite ,incomplet5ess ( ! ,ma!matical ,sci5ces499 ,!re is "o privilege :i* a c]ta9 am\nt ( k %\ld conf]2 x is t ( becom+ aw>e ( ! weakness ( our p[]s comp>$ ) ! tasks :i* !y might und]take if /rong]4 ,to ! poor savage :o _c c\nt tw5ty ! ari?metical accompli%m5ts ( ! s*oolboy are miracul\sly great4 ,! s*oolboy _c compreh5d ! va/ly great] p[]s ( ! /ud5t1 :o has acquir$ facility 9 algebraic processes4 ,! /ud5t c b look ) feel+s ( surprise & rev]5ce at ! p[]s ( a ,newton or a ,laplace4 ,b ! "q at once sugge/s itself1 ,d ! p[]s ( ! highe/ human intellect be> a f9ite ratio to ! ?+s :i* are to be und]/ood & calculat$8 ,h[ _m fur!r /eps mu/ we take 9 ! rise ( m5tal ability & ! ext5sion ( ma!matical me?ods be=e we beg9 to exhau/ ! kn[able8 ,i am incl9$ to f9d fault ) ma!matical writ]s because !y (t5 exult 9 :at !y c accompli%1 & omit to po9t out t :at !y d is b an inf9itely small "p ( :at might be done4 ,!y exhibit a g5]al incl9ation1 ) few exceptions1 n to d s mu* z m5tion ! exi/5ce ( problems ( an impracticable "*4 ,?is may be excusable z f> z ! imm$iate practical result ( _! rese>*es is 9 "q1 b ! cu/om has ! effect ( mislead+ ! g5]al public into ! fallaci\s notion t ma!matics is a 99p]fect99 sci5ce1 :i* accompli%es :at x und]takes 9 a complete mann]4 ,on ! contr>y1 x may be said t if a ma!matical problem 7 select$ by *ance out ( ! :ole numb] :i* might be propos$1 ! probability is inf9itely slight t a human ma!matician c\ld solve x4 ,j z ! numb]s we c c\nt are no?+ comp>$ ) ! numb]s :i* might exi/1 s ! accompli%m5ts ( a ,laplace or a ,lagrange are1 z x 71 ! little corn] ( ! multiplication-table1 :i* has really an inf9ite ext5t4 ,i h po9t$ out t ! rude "* ( our obs]vations prev5ts u f be+ aw>e ( ! great] numb] ( effects & actions 9 nature4 ,x mu/ be add$ t1 if we p]ceive !m1 we %\ld usually be incapable ( includ+ !m 9 our !ories f want ( ma!matical p[]4 ,"s p]sons may be surpris$ t ?\gh ne>ly two c5turies h elaps$ s9ce ! "t ( ,newton's discov]ies1 we h yet no g5]al !ory ( molecul> action4 ,"s approximations h be5 made t[>ds su* a !ory4 ,j\le & ,clausius h measur$ ! velocity ( gase\s atoms1 or ev5 det]m9$ ! av]age di/ance betwe5 ! collisions ( atom & atom4 ,?omson has approximat$ to ! numb] ( atoms 9 a giv5 bulk ( sub/ance4 ,rank9e has =m$ "s reasonable hypo!ses z to ! actual con/itution ( atoms4 ,x w\ld be a mi/ake to suppose t ^! +5i\s results ( !ory & exp]im5t =m any appreciable approa* to a complete solution ( molecul> motions4 ,!re is e reason to believe1 judg+ f ! spectra ( ! elem5ts1 _! atomic weights & o!r data1 t *emical atoms are v complicat$ /ructures4 ,an atom ( pure iron is probably a f> m complicat$ sy/em ?an t ( ! planets & _! satellites4 ,a comp\nd atom may p]haps be comp>$ ) a /ell> sy/em1 ea* /> a m9or sy/em 9 itself4 ,! smalle/ p>ticle ( solid sub/ance w consi/ ( a great numb] ( su* /ell> sy/ems unit$ 9 regul> ord]1 ea* b\nd$ by ! o!r1 communicat+ ) x 9 "s mann] yet :olly incompreh5sible4 ,:at are our ma!matical p[]s 9 comp>ison ) ?is problem8 ,aft] two c5turies ( cont9u\s lab\r1 ! mo/ gift$ m5 h succe$$ 9 calculat+ ! mutual effects ( ?ree bodies ea* ^u ! o!r1 "u ! simple hypo!sis ( ! law ( gravity4 ,conc]n+ ^! calculations we mu/ fur!r rememb] t !y are purely approximate1 & t ! me?ods w\ld n apply :]e f\r or m bodies are act+1 & all produce consid]able effects ^u ea* o!r4 ,!re is reason to believe t ea* con/itu5t ( a *emical atom goes ?r\gh an orbit 9 ! million? "p ( ! tw9kl+ ( an eye4 ,9 ea* revolution x is successively or simultane\sly "u ! influ5ce ( _m o!r con/itu5ts1 or possibly comes into collision ) !m4 ,x is no exagg]ation to say t ma!maticians h ! lea/ notion ( ! way 9 :i* !y c\ld successfully attack s difficult a problem ( =ces & motions4 ,z ,h]s*el has rem>k$1#faf ea* ( ^! p>ticles is = ev] solv+ diff]5tial equations1 :i*1 if writt5 out 9 full1 might belt ! e>?4 #faf 99,famili> ,lectures on ,sci5tific ,subjects991 p4 #deh4 ,"s ( ! mo/ ext5sive calculations ev] made 7 ^? requir$ = ! r$uction ( ! measurem5ts execut$ 9 ! c\rse ( ! ,trigonometrical ,survey ( ,great ,brita94 ,! calculations aris+ out ( ! pr9cipal triangulation occupi$ tw5ty calculators dur+ ?ree or f\r ye>s1 9 ! c\rse ( :i* ! comput]s _h to solve simultane\s equations involv+ sev5ty-sev5 unkn[n quantities4 ,! r$uction ( ! levell+s requir$ ! solution ( a sy/em ( n9ety-"o equations4 ,b ^! va/ calculations pres5t no approa* :atev] to :at w\ld be requisite = ! complete treatm5t ( any "o physical problem4 ,! motion ( glaci]s is suppos$ to be mod]ately well und]/ood 9 ! pres5t day4 ,a glaci] is a viscid1 sl[ly yield+ mass1 nei!r absolutely solid nor absolutely rigid1 b x is expressly rem>k$ by ,=bes1#fag t n ev5 an approximate solution ( ! ma!matical conditions ( su* a mov+ mass c yet be possible4 8,e "o kn[s10 he says1 8t su* problems are beyond ! compass ( exact ma!matics20 b ?\gh ma!maticians may "k ?is1 !y d n (t5 en\gh impress t k on o!r p4 #fag 99,philosophical ,magaz9e991 #crd ,s]ies1 vol4 xxvi4 p4 #djf4 ,! problems :i* are solv$ 9 our ma!matical books consi/ ( a small selection ( ^? :i* happ5 f peculi> conditions to be solvable4 ,b ! v simple/ problem 9 appe>ance w (t5 give rise to impracticable calculations4 ,mr4 ,todhunt]#fah seems to blame ,condorcet1 because 9 "o ( 8 memoirs he m5tions a problem to solve :i* w\ld require a great & impracticable numb] ( successive integrations4 ,n[1 if our ma!matical sci5ces are to cope ) ! problems :i* await solution1 we mu/ be prep>$ to effect an unlimit$ numb] ( successive integrations2 yet at pres5t1 & almo/ beyond d\bt = ev]1 ! probability t an integration tak5 haphaz>d w come )9 our p[]s is exce$+ly small4 #fah 99,hi/ory ( ! ,!ory ( ,probability991 p4 #cih4 ,9 "s passages ( t rem>kable "w1 ! 99,n9? ,bridgewat] ,treatise99 7pp4 #aac-aae71 ,babbage has po9t$ out t if we _h p[] to foll[ & detect ! m9ute/ effects ( any di/urbance1 ea* p>ticle ( exi/+ matt] w\ld furni% a regi/] ( all t has happ5$4 8,! track ( e canoe--( e vessel t has yet di/urb$ ! surface ( ! ocean1 :e!r impell$ by manual =ce or elem5tal p[]1 rema9s = ev] regi/]$ 9 ! future movem5t ( all succe$+ p>ticles :i* may occupy its place4 ,! furr[ :i* x left is1 inde$1 in/antly fill$ up by ! clos+ wat]s2 b !y draw aft] !m o!r & l>g] portions ( ! surr\nd+ elem5t1 & ^! aga91 once mov$1 communicate motion to o!rs 9 endless succession40 ,we may ev5 say t 8,! air itself is "o va/ libr>y1 on ^: pages are = ev] writt5 all t man has ev] said or ev5 :isp]$4 ,!re1 9 _! mutable b un]r+ *>act]s1 mix$ ) ! e>lie/ z well z ! late/ sighs ( mortality1 /& = ev] record$1 v[s unr$eem$1 promises unfulfill$1 p]petuat+ 9 ! unit$ movem5ts ( ea* p>ticle ! te/imony ( man's *angeful w40 ,:5 we read reflections su* z ^!1 we may congratulate ourselves t we h be5 end[$ ) m9ds :i*1 rightly employ$1 c =m "s e/imate ( _! incapacity to trace out & acc\nt = all t proce$s 9 ! simpl] actions ( mat]ial nature4 ,x ought to be add$ t1 wond]ful z is ! ext5t ( physical ph5om5a op5 to our inve/igation1 intellectual ph5om5a are yet va/ly m ext5sive4 ,( ?is ,i might pres5t "o satisfactory pro( 7 space available by po9t+ out t ! ma!matical functions employ$ 9 ! calculations ( physical sci5ce =m an inf9itely small fraction ( ! functions :i* might be inv5t$4 ,common trigonometry consi/s ( a great s]ies ( useful =mul1 all ( :i* arise out ( ! relation ( ! s9e & cos9e express$ 9 "o equation1 s9 #b99x99 cos #b99x99 #a4 ,b ?is is n ! only trigonometry :i* may exi/2 ma!maticians also recognise hyp]bolic trigonometry1 ( :i* ! fundam5tal equation is cos #b99x99 - s9 #b99x99 #a4 ,de ,morgan has po9t$ out t ! symbols ( ord9>y algebra =m b ?ree ( an int]m9able s]ies ( conceivable sy/ems4#fai ,z ! log>i?mic op]ation is to addition or addition to multiplication1 s is ! latt] to a high] op]ation1 & s on )\t limit4 #fai 99,trigonometry & ,d\ble ,algebra991 *ap4 ix4 ,we may rely ^u x t imm5se1 & to u inconceivable1 advances w be made by ! human intellect1 9 ! abs5ce ( any cata/rophe to ! species or ! globe4 ,)9 hi/orical p]iods we c trace ! rise ( ma!matical sci5ce f its simple/ g]ms4 ,we c prove our desc5t f ance/ors :o c\nt$ only on _! f+]s4 ,h[ inf9itely is a ,newton or a ,laplace above ^? simple savages4 ,py?agoras is said to h sacrific$ a hecatomb :5 he discov]$ ! =ty-sev5? proposition ( ,euclid1 & ! occasion 0 wor?y ( ! sacrifice4 ,ar*im$es 0 beside himself :5 he fir/ p]ceiv$ 8 beautiful mode ( det]m9+ specific gravities4 ,yet ^! great discov]ies are ! commonplaces ( our s*ool books4 ,/ep by /ep we c trace upw>ds ! acquirem5t ( new m5tal p[]s4 ,:at c\ld be m wond]ful ?an ,napi]'s discov]y ( log>i?ms1 a new mode ( calculation :i* has multipli$ p]haps a hundr$fold ! work+ p[]s ( e comput]1 & has r5d]$ easy calculations :i* 7 be=e impracticable8 ,s9ce ! "t ( ,newton & ,leibnitz worlds ( problems h be5 solv$ :i* be=e 7 h>dly conceiv$ z matt]s ( inquiry4 ,9 our own day ext5d$ me?ods ( ma!matical reason+1 su* z ! sy/em ( quat]nions1 h be5 br\ght into exi/5ce4 ,:at intellig5t man w d\bt t ! recondite speculations ( a ,cayley1 a ,sylve/]1 or a ,clif=d may lead to "s new developm5t ( new ma!matical p[]1 at ! simplicity ( :i* a future age w wond]1 & yet wond] m t to u !y 7 s d>k & difficult4 ,may we n repeat ! words ( ,s5eca3 8,v5iet tempus1 quo i/a qu nunc lat5t1 9 lucem dies extrahat1 et longioris vi dilig5tia3 ad inquisitionem tantorum tas una non sufficit4 ,v5iet tempus1 quo po/]i no/ri tam ap]ta nos nescisse mir5tur40 99,! ,reign ( ,law 9 ,m5tal & ,social ,ph5om5a499 ,aft] we pass f ! s-call$ physical sci5ces to ^? :i* attempt to inve/igate m5tal & social ph5om5a1 ! same g5]al conclusions w hold true4 ,no "o w be f\nd to d5y t !re are c]ta9 uni=mities ( ?9k+ & act+ :i* c be detect$ 9 reason+ be+s1 & s f> z we detect su* laws we successfully apply sci5tific me?od4 ,b ^? :o attempt to e/abli% social or moral sci5ces soon become aw>e t !y are deal+ ) subjects ( enorm\s p]plexity4 ,take z an in/ance ! sci5ce ( political economy4 ,if a sci5ce at all1 x mu/ be a ma!matical sci5ce1 because x deals ) quantities ( commodities4 ,b z soon z we attempt to draw out ! equations express+ ! laws ( dem& & supply1 we discov] t !y h a complexity entirely surpass+ our p[]s ( ma!matical treatm5t4 ,we may lay d[n ! g5]al =m ( ! equations1 express+ ! dem& & supply = two or ?ree commodities among two or ?ree trad+ bodies1 b all ! functions involv$ are s complicat$ 9 "* t !re is n mu* fe> ( sci5tific me?od mak+ rapid progress 9 ?is direction4 ,if su* be ! prospects ( a comp>atively =mal sci5ce1 l political economy1 :at %all we say ( moral sci5ce8 ,any complete !ory ( morals mu/ deal ) quantities ( pleasure & pa91 z ,b5?am po9t$ out1 & mu/ sum up ! g5]al t5d5cy ( ea* k9d ( action ^u ! good ( ! community4 ,if we are to apply sci5tific me?od to morals1 we mu/ h a calculus ( moral effects1 a k9d ( physical a/ronomy inve/igat+ ! mutual p]turbations ( individuals4 ,b z a/ronom]s h n yet fully solv$ ! problem ( ?ree gravitat+ bodies1 :5 %all we h a solution ( ! problem ( ?ree moral bodies8 ,! sci5ces ( political economy & morality are comp>atively ab/ract & g5]al1 treat+ mank9d f simple po9ts ( view1 & attempt+ to detect g5]al pr9ciples ( action4 ,!y are to social ph5om5a :at ! ab/ract sci5ces ( *emi/ry1 heat1 & electricity are to ! concrete sci5ce ( meteorology4 ,be=e we c inve/igate ! actions ( any aggregate ( m51 we mu/ h fairly ma/]$ all ! m ab/ract sci5ces apply+ to !m1 some:at 9 ! way t we h acquir$ a fair compreh5sion ( ! simpl] tru?s ( *emi/ry & physics4 ,b all our physical sci5ces d n enable u to pr$ict ! wea!r two days h5ce ) any great probability1 & ! g5]al problem ( meteorology is almo/ unattempt$ z yet4 ,:at %all we say !n ( ! g5]al problem ( social sci5ce1 :i* %all enable u to pr$ict ! c\rse ( ev5ts 9 a nation8 ,sev]al writ]s h propos$ to lay ! f\ndations ( ! sci5ce ( hi/ory4 ,buckle und]took to write ! 99,hi/ory ( ,civilisation 9 ,engl&991 & to %[ h[ ! "* ( a nation c\ld be expla9$ by ! nature ( ! climate & ! f]tility ( ! soil4 ,he omitt$ to expla9 ! contra/ betwe5 ! anci5t ,greek nation & ! pres5t "o2 !re mu/ h be5 an extraord9>y revolution 9 ! climate or ! soil4 ,augu/e ,comte detect$ ! simple laws ( ! c\rse ( developm5t ?r\gh :i* nations pass4 ,!re are always ?ree phases ( intellectual condition1--! !ological1 ! metaphysical1 & ! positive2 apply+ ?is g5]al law ( progress to concrete cases1 ,comte 0 enabl$ to pr$ict t 9 ! hi]>*y ( ,european nations1 ,spa9 w\ld necess>ily hold ! highe/ place4 ,su* are ! p>odies ( sci5ce (f]$ to u by ! 99positive99 philosoph]s4 ,a sci5ce ( hi/ory 9 ! true s5se ( ! t]m is an absurd notion4 ,a nation is n a m]e sum ( individuals :om we c treat by ! me?od ( av]ages2 x is an organic :ole1 held toge!r by ties ( inf9ite complexity4 ,ea* individual acts & re-acts ^u 8 small] or great] circle ( fri5ds1 & ^? :o acquire a public position ex]t an influ5ce on mu* l>g] sections ( ! nation4 ,!re w always be a few great lead]s ( exceptional g5ius or opportunities1 ! unacc\ntable phases ( ^: op9ions & incl9ations sway ! :ole body4 ,f "t to "t arise critical situations1 battles1 delicate negotiations1 int]nal di/urbances1 9 :i* ! slighte/ incid5ts may *ange ! c\rse ( hi/ory4 ,a ra9y day may h9d] a =c$ m>*1 & *ange ! c\rse ( a campaign2 a few injudici\s words 9 a despat* may irritate ! national pride2 ! accid5tal dis*>ge ( a gun may precipitate a collision ! effects ( :i* w la/ = c5turies4 ,x is said t ! hi/ory ( ,europe dep5d$ at "o mom5t ^u ! "q :e!r ! look-out man ^u ,nelson's vessel w\ld or w\ld n descry a %ip ( ,napoleon's exp$ition to ,egypt :i* 0 pass+ n f> (f4 ,9 human affairs1 !n1 ! smalle/ causes may produce ! greate/ effects1 & ! real application ( sci5tific me?od is out ( ! "q4 99,! ,!ory ( ,evolution499 ,pr(\nd philosoph]s h lately g5]alis$ conc]n+ ! production ( liv+ =ms & ! m5tal & moral ph5om5a reg>d$ z _! highe/ developm5t4 ,h]b]t ,sp5c]'s !ory ( evolution purports to expla9 ! orig9 ( all specific diff]5ces1 s t n ev5 ! rise ( a ,hom] or a ,bee?ov5 w\ld escape f 8 broad !ories4 ,! homog5e\s is un/able & mu/ diff]5tiate itself1 says ,sp5c]1 & h5ce comes ! v>iety ( human in/itutions & *>act]s4 ,9 ord] t a liv+ =m %all cont9ue to exi/ & propagate its k9d1 says ,d>w91 x mu/ be suitable to its circum/ances1 & ! mo/ suitable =ms w prevail ov] & extirpate ^? :i* are less suitable4 ,f ^! fruitful ideas are develop$ !ories ( evolution & natural selection :i* g f> t[>ds acc\nt+ = ! exi/5ce ( imm5se numb]s ( liv+ creatures--plants1 & animals4 ,app>5t adaptations ( organs to useful purposes1 :i* ,paley reg>d$ z di/9ct products ( creative intellig5ce1 are n[ se5 to foll[ z natural effects ( a con/antly act+ t5d5cy4 ,ev5 man1 accord+ to ^! !ories1 is no di/9ct creation1 b r an extreme case ( bra9 developm5t4 ,8 ne>e/ c\s9s are ! apes1 & 8 p$igree ext5ds backw>ds until x jo9s t ( ! l[lie/ zoophytes4 ,! !ories ( ,d>w9 & ,sp5c] are d\btless n demon/rat$2 !y are to "s ext5t hypo!tical1 j z all ! !ories ( physical sci5ce are to "s ext5t hypo!tical1 & op5 to d\bt4 ,judg+ f ! imm5se numb]s ( div]se facts :i* !y h>monise & expla91 ,i v5ture to look ^u ! !ories ( evolution & natural selection 9 _! ma9 features z two ( ! mo/ probable hypo!ses ev] propos$4 ,i "q :e!r any sci5tific works :i* h appe>$ s9ce ! 99,pr9cipia99 ( ,newton are comp>able 9 importance ) ^? ( ,d>w9 & ,sp5c]1 revolutionis+ z !y d all our views ( ! orig9 ( bodily1 m5tal1 moral1 & social ph5om5a4 ,grant+ all ?is1 ,i _c = a mom5t admit t ! !ory ( evolution w de/roy !ology4 ,t !ory embraces sev]al laws or uni=mities :i* are obs]v$ to be true 9 ! production ( liv+ =ms2 b ^! laws d n det]m9e ! size & figure ( liv+ creatures1 any m ?an ! law ( gravitation det]m9es ! magnitudes & di/ances ( ! planets4 ,suppose t ,d>w9 is correct 9 say+ t man is desc5d$ f ! ,ascidians3 yet ! precise =m ( ! human body mu/ h be5 influ5c$ by an inf9ite tra9 ( circum/ances affect+ ! reproduction1 gr[?1 & heal? ( ! :ole *a9 ( int]m$iate be+s4 ,no d\bt1 ! circum/ances be+ :at !y 71 man c\ld n be o!rwise ?an he is1 & if 9 any o!r "p ( ! univ]se an exactly simil> e>?1 furni%$ ) exactly simil> g]ms ( life1 exi/$1 a race mu/ h gr[n up !re exactly simil> to ! human race4 ,by a diff]5t di/ribution ( atoms 9 ! primeval _w a diff]5t s]ies ( liv+ =ms on ?is e>? w\ld h be5 produc$4 ,f ! same causes act+ accord+ to ! same laws1 ! same results w foll[2 b f diff]5t causes act+ accord+ to ! same laws1 diff]5t results w foll[4 ,s f> z we c see1 !n1 inf9itely div]se liv+ creatures might h be5 creat$ consi/5tly ) ! !ory ( evolution1 & ! precise reason :y we h a backbone1 two h&s ) opposable ?umbs1 an erect /ature1 a complex bra91 ab\t #bbc bones1 & _m o!r peculi>ities1 is only to be f\nd 9 ! orig9al act ( creation4 ,i d n1 any less ?an ,paley1 believe t ! eye ( man manife/s design4 ,i believe t ! eye 0 gradually develop$1 & we c 9 fact trace its gradual developm5t f ! fir/ g]m ( a n]ve affect$ by light-rays 9 "s simple zoophyte4 ,9 proportion z ! eye became a m accurate in/rum5t ( vision1 x enabl$ its possessor ! bett] to escape de/ruction1 b ! ultimate result mu/ h be5 conta9$ 9 ! aggregate ( ! causes1 & ^! causes1 z f> z we c see1 7 subject to ! arbitr>y *oice ( ! ,creator4 ,al?\gh ,agassiz 0 cle>ly wrong 9 hold+ t e species ( liv+ creature appe>$ on e>? by ! imm$iate int]v5tion ( ! ,creator1 :i* w\ld am\nt to say+ t no laws ( connection betwe5 =ms are discov]able1 yet he seems to be "r 9 ass]t+ t liv+ =ms are di/9ct f ^? produc$ by purely physical causes4 8,! products ( :at are commonly call$ physical ag5ts10 he says1#fbj 8are ev]y:]e ! same 799i4e499 ^u ! :ole surface ( ! e>?71 & h always be5 ! same 799i4e499 dur+ all geological p]iods72 :ile organis$ be+s are ev]y:]e diff]5t & h diff]$ 9 all ages4 ,betwe5 two su* s]ies ( ph5om5a !re c be no causal or g5etic connection40 ,liv+ =ms z we n[ reg>d !m are ess5tially v>iable1 b f con/ant me*anical causes con/ant effects w\ld ensue4 ,if vegetable cells are =m$ on geometrical pr9ciples be+ fir/ sph]ical1 & !n by mutual compression dodecah$ral1 !n all cells %\ld h simil> =ms4 ,9 ! ,=am9if]a & "s o!r l[ly organisms1 we seem to obs]ve ! production ( complex =ms on geometrical pr9ciples4 ,b f simil> causes act+ accord+ to simil> laws only simil> results c\ld be produc$4 ,if ! orig9al life g]m ( ea* creature is a simple p>ticle ( protoplasm1 un5d[$ ) any di/9ctive =ces1 !n ! :ole ( ! complex ph5om5a ( animal & vegetable life are effects )\t causes4 ,protoplasm may be *emically ! same sub/ance1 & ! g]m-cell ( a man & ( a fi% may be app>5tly ! same1 s f> z ! microscope c decide2 b if c]ta9 cells produce m51 & o!rs z uni=mly produce a species ( fi%1 !re mu/ be a hidd5 con/itution det]m9+ ! extremely diff]5t results4 ,if ?is 7 n s1 ! g5]ation ( e liv+ creature f ! uni=m g]m w\ld h to be reg>d$ z a di/9ct act ( creation4 #fbj ,agassiz1 99,essay on ,classification991 p4 #ge4 ,!ologians h dread$ ! e/abli%m5t ( ! !ories ( ,d>w9 & ,huxley & ,sp5c]1 z if !y ?\ght t ^? !ories c\ld expla9 ev]y?+ ^u ! pure/ me*anical & mat]ial pr9ciples1 & exclude all notions ( design4 ,!y d n see t ^? !ories h op5$ up m que/ions ?an !y h clos$4 ,! doctr9e ( evolution gives a complete explanation ( no s+le liv+ =m4 ,:ile %[+ ! g5]al pr9ciples :i* prevail 9 ! v>iation ( liv+ creatures1 x only po9ts out ! inf9ite complexity ( ! causes & circum/ances :i* h l$ to ! pres5t /ate ( ?+s4 ,any "o ( ,mr4 ,d>w9's books1 admirable ?\gh !y all are1 consi/s b 9 ! sett+ =? ( a multitude ( indet]m9ate problems4 ,he proves 9 ! mo/ beautiful mann] t ea* fl[] ( an or*id is adapt$ to "s insect :i* frequ5ts & f]tilises x1 & ^! adaptations are b a few cases ( ^? imm5sely num]\s ones :i* h occurr$ 9 ! lives ( plants & animals4 ,b :y or*ids %\ld h be5 =m$ s diff]5tly f o!r plants1 :y any?+1 inde$1 %\ld be z x is1 r ?an 9 "s ( ! o!r inf9itely num]\s possible modes ( exi/5ce1 he c nev] %[4 ,! orig9 ( ev]y?+ t exi/s is wrapp$ up 9 ! pa/ hi/ory ( ! univ]se4 ,at "s "o or m po9ts 9 pa/ "t !re mu/ h be5 arbitr>y det]m9ations :i* l$ to ! production ( ?+s z !y are4 99,possibility ( ,div9e ,int]f]5ce499 ,i w n[ draw ! read]'s att5tion to pages #adi to #aeb4 ,i !re po9t$ out t all inductive inf]5ce involves ! assumption t our k ( :at exi/s is complete1 & t ! conditions ( ?+s rema9 unalt]$ betwe5 ! "t ( our exp]i5ce & ! "t to :i* our inf]5ces ref]4 ,recurr+ to ! illu/ration ( a ballot-box1 employ$ 9 ! *apt] on ! inv]se me?od ( probabilities1 we assume :5 pr$ict+ ! probable nature ( ! next draw+1 fir/ly1 t our previ\s draw+s h be5 suffici5tly num]\s to give u k ( ! cont5ts ( ! box2 &1 secondly1 t no int]f]5ce ) ! ballot-box takes place betwe5 ! previ\s & ! next draw+s4 ,! results yield$ by ! !ory ( probability are q pla94 ,no f9ite numb] ( casual draw+s c give u sure k ( ! cont5ts ( ! box1 s t1 ev5 9 ! abs5ce ( all di/urbance1 our inf]5ces are m]ely ! be/ :i* c be made1 & d n approa* to infallibility4 ,if1 h[ev]1 int]f]5ce be possible1 ev5 ! !ory ( probability ceases to be applicable1 =1 ! am\nt & nature ( t int]f]5ce be+ arbitr>y & unkn[n1 !re ceases to be any connection betwe5 premises & conclusion4 ,_m ye>s ( reflection h n enabl$ me to see ! way ( avoid+ ?is hiatus 9 sci5tific c]ta9ty4 ,! conclusions ( sci5tific inf]5ce appe> to be always ( a hypo!tical & provisional nature4 ,giv5 c]ta9 exp]i5ce1 ! !ory ( probability yields u ! true int]pretation ( t exp]i5ce & is ! sure/ guide op5 to u4 ,b ! be/ calculat$ results :i* x c give are nev] absolute probabilities2 !y are purely relative to ! ext5t ( our in=mation4 ,x seems to be impossible = u to judge h[ f> our exp]i5ce gives u adequate in=mation ( ! univ]se z a :ole1 & ( all ! =ces & ph5om5a :i* c h place !re94 ,i feel t ,i _c 9 ! space rema9+ at my comm& 9 ! pres5t volume1 suffici5tly foll[ out ! l9es ( ?\ght sugge/$1 or def9e ) precision my own conclusions4 ,?is *apt] conta9s m]ely 99,reflections99 ^u subjects ( s weighty a "* t ,i %\ld myself wi% = _m ye>s--nay = m ?an a lifetime ( fur!r reflection4 ,my purpose1 z ,i h repeat$ly said1 is ! purely negative "o ( %[+ t a!ism & mat]ialism are no necess>y results ( sci5tific me?od4 ,f ! prec$+ reviews ( ! value ( our sci5tific k1 ,i draw "o di/9ct conclusion1 t we _c disprove ! possibility ( ,div9e int]f]5ce 9 ! c\rse ( nature4 ,su* int]f]5ce might arise1 s f> z our k ext5ds1 9 two ways4 ,x might consi/ 9 ! disclosure ( ! exi/5ce ( "s ag5t or spr+ ( en]gy previ\sly unkn[n1 b :i* effects a giv5 purpose at a giv5 mom5t4 ,l ! pre-arrang$ *ange ( law 9 ,babbage's imag9>y calculat+ ma*9e1 !re may exi/ pre-arrang$ surprises 9 ! ord] ( nature1 z x pres5ts itself to u4 ,secondly1 ! same ,p[]1 :i* creat$ mat]ial nature1 might1 s f> z ,i c see1 create additions to x1 or annihilate portions :i* d exi/4 ,su* ev5ts are 9 a c]ta9 s5se inconceivable to u2 yet !y are no m inconceivable ?an ! exi/5ce ( ! _w z x is4 ,! inde/ructibility ( matt]1 & ! cons]vation ( en]gy1 are v probable sci5tific hypo!ses1 :i* accord satisfactorily ) exp]im5ts ( sci5tific m5 dur+ a few ye>s pa/1 b x w\ld be gross misconception ( sci5tific inf]5ce to suppose t !y are c]ta9 9 ! s5se t a proposition 9 geometry is c]ta94 ,philosoph]s no d\bt hold t 99de nihilo nihil fit991 t is to say1 _! s5ses give !m no means ( imag9+ to ! m9d h[ creation c take place4 ,b we are on ! horns ( a trilemma2 we mu/ ei!r d5y t any?+ exi/s1 or we mu/ all[ t x 0 creat$ out ( no?+ at "s mom5t ( pa/ "t1 or t x exi/$ f et]nity4 ,! fir/ alt]native is absurd2 ! o!r two seem to me equally conceivable4 99,conclusion499 ,x may seem t !re is "o po9t :]e our speculations mu/ end1 namely :]e contradiction beg9s4 ,! laws ( ,id5tity & ,diff]5ce & ,duality 7 ! f\ndations f :i* we />t$1 & !y are1 s f> z ,i c see1 ! f\ndations :i* we c nev] quit )\t tott]+4 ,sci5tific ,me?od mu/ beg9 & end ) ! laws ( ?\ght1 b x does n foll[ t x w save u f enc\nt]+ inexplicable1 & at lea/ app>5tly contradictory results4 ,! nature ( cont9u\s quantity leads u into extreme difficulties4 ,any f9ite space is compos$ ( an inf9ite numb] ( inf9itely small spaces1 ea* ( :i*1 aga91 is compos$ ( an inf9ite numb] ( spaces ( a second ord] ( smallness2 ^! spaces ( ! second ord] are compos$1 aga91 ( inf9itely small spaces ( ! ?ird ord]4 ,ev5 ^! spaces ( ! ?ird ord] are n absolute geometrical po9ts answ]+ to ,euclid's def9ition ( a po9t1 z position )\t magnitude4 ,g on z f> z we w1 9 ! subdivision ( cont9u\s quantity1 yet we nev] get d[n to ! absolute po9t4 ,?us sci5tific me?od leads u to ! inevitable conception ( an inf9ite s]ies ( successive ord]s ( inf9itely small quantities4 ,if s1 !re is no?+ impossible 9 ! exi/5ce ( a myriad univ]ses )9 ! compass ( a ne$le's po9t1 ea* ) its /ell> sy/ems1 & its suns & planets1 9 numb] & v>iety unlimit$4 ,sci5ce does no?+ to r$uce ! numb] ( /range ?+s t we may believe4 ,:5 fairly pursu$ x makes absurd drafts ^u our p[]s ( compreh5sion & belief4 ,"s ( ! mo/ precise & beautiful !orems 9 ma!matical sci5ce seem to me to involve app>5t contradiction4 ,c we imag9e t a po9t mov+ along a p]fectly /raight l9e t[>ds ! we/ w\ld ev] get r\nd to ! ea/ & come back aga91 hav+ p]=m$1 z x 71 a circuit ?r\gh inf9ite space1 yet )\t ev] div]g+ f a p]fectly /raight direction8 ,yet ?is is :at happ5s to ! int]sect+ po9t ( two /raight l9es 9 ! same plane1 :5 "o l9e revolves4 ,! same p>adox is exhibit$ 9 ! hyp]bola reg>d$ z an inf9ite ellipse1 "o extremity ( :i* has pass$ to an inf9ite di/ance & come back 9 ! opposite direction4 ,a v>y+ quantity may *ange its sign by pass+ ei!r ?r\gh z]o or ?r\gh inf9ity4 ,9 ! latt] case !re mu/ be "o int]m$iate value ( ! v>iable = :i* ! v>iant is indiff]5tly negative inf9ity & positive inf9ity4 ,pr(essor ,clif=d tells me t he has f\nd a ma!matical function :i* approa*es inf9ity z ! v>iable approa*es a c]ta9 limit2 yet at ! limit ! function is f9ite6 ,ma!maticians may %irk difficulties1 b !y _c make su* results ( ma!matical pr9ciples appe> o!rwise ?an contradictory to our common notions ( space4 ,! hypo!sis t !re is a ,creator at once all-p[]ful & all-b5evol5t is press$1 z x mu/ seem to e c&id inve/igator1 ) difficulties v]g+ closely ^u logical contradiction4 ,! exi/5ce ( ! smalle/ am\nt ( pa9 & evil w\ld seem to %[ t ,he is ei!r n p]fectly b5evol5t1 or n all-p[]ful4 ,no "o c h liv$ long )\t exp]i5c+ sorr[ful ev5ts ( :i* ! significance is inexplicable4 ,b if we _c succe$ 9 avoid+ contradiction 9 our notions ( elem5t>y geometry1 c we expect t ! ultimate purposes ( exi/5ce %all pres5t !mselves to u ) p]fect cle>ness8 ,i c see no?+ to =bid ! notion t 9 a high] /ate ( intellig5ce mu* t is n[ obscure may become cle>4 ,we p]petually f9d ourselves 9 ! position ( f9ite m9ds attempt+ inf9ite problems1 & c we be sure t :]e we see contradiction1 an inf9ite intellig5ce might n discov] p]fect logical h>mony8 ,f sci5ce1 mode/ly pursu$1 ) a due consci\sness ( ! extreme f9itude ( our intellectual p[]s1 !re c arise only nobl] & wid] notions ( ! purpose ( ,creation4 ,our philosophy w be an affirmative "o1 n ! false & negative dogmas ( ,augu/e ,comte1 :i* h usurp$ ! "n1 & misrepres5t$ ! t5d5cies ( a true 99positive philosophy994 ,true sci5ce w n d5y ! exi/5ce ( ?+s because !y _c be weigh$ & measur$4 ,x w r lead u to believe t ! wond]s & subtleties ( possible exi/5ce surpass all t our m5tal p[]s all[ u cle>ly to p]ceive4 ,! /udy ( logical & ma!matical =ms has conv9c$ me t ev5 space itself is no requisite condition ( conceivable exi/5ce4 ,ev]y?+1 we are told by mat]iali/s1 mu/ be "h or !re1 ne>] or fur!r1 be=e or aft]4 ,i d5y ?is1 & po9t to logical relations z my pro(4 ,!re =m]ly seem$ to me to be some?+ my/]i\s 9 ! d5om9ators ( ! b9omial expansion 7p4 #aij71 :i* are reproduc$ 9 ! natural con/ant 1 or #a #a_/a #a_/7a 4 #b7 #a_/7a 4 #b 4 #c7 444 & 9 _m results ( ma!matical analysis4 ,i n[ p]ceive1 z already expla9$ 7pp4 #cc1 #afj1 #chc71 t !y arise out ( ! fact t ! relations ( space d n apply to ! logical conditions gov]n+ ! numb]s ( comb9ations z contra/$ to ^? ( p]mutations4 ,s f> am ,i f accept+ ,kant's doctr9e t space is a necess>y =m ( ?\ght1 t ,i reg>d x z an accid5t1 & an imp$im5t to pure logical reason+4 ,mat]ial exi/5ces mu/ exi/ 9 space1 no d\bt1 b intellectual exi/5ces may be nei!r 9 space nor out ( space2 !y may h no relation to space at all1 j z space itself has no relation to "t4 ,= all t ,i c see1 !n1 !re may be intellectual exi/5ces to :i* bo? "t & space are nullities4 ,n[ among ! mo/ unque/ionable rules ( sci5tific me?od is t fir/ law t 99:atev] ph5om5on is1 is994 ,we mu/ ignore no exi/5ce :atev]2 we may v>i\sly int]pret or expla9 its mean+ & orig91 b1 if a ph5om5on does exi/1 x dem&s "s k9d ( explanation4 ,if !n !re is to be competition = sci5tific recognition1 ! _w )\t u mu/ yield to ! und\bt$ exi/5ce ( ! _s )94 ,our own hopes & wi%es & det]m9ations are ! mo/ und\bt$ ph5om5a )9 ! sph]e ( consci\sness4 ,if m5 d act1 feel1 & live z if !y 7 n m]ely ! brief products ( a casual conjunction ( atoms1 b ! in/rum5ts ( a f>-rea*+ purpose1 are we to record all o!r ph5om5a & pass ov] ^!8 ,we inve/igate ! in/9cts ( ! ant & ! bee & ! beav]1 & discov] t !y are l$ by an inscrutable ag5cy to "w t[>ds a di/ant purpose4 ,let u be fai?ful to our sci5tific me?od1 & inve/igate also ^? in/9cts ( ! human m9d by :i* man is l$ to "w z if ! approval ( a ,high] ,be+ 7 ! aim ( life4 ,,index4 ,abacus1 logical1 #ajd2 ari?metical1 #ajg2 ,pan*re/us1 #ahb4 ,ab]ration ( light1 #efa2 sy/ematic1 #edg4 ,abscissio inf9iti1 #gi1 #gac4 ,ab/ract t]ms1 #bg2 numb]1 #aei4 ,ab/raction1 #gjd2 logical1 #be2 num]ical1 #aeh2 ( indiff]5t circum/ances1 #ig4 ,accademia del ,cim5to1 #dbg1 #dcb1 #dcf1 #ebg4 ,accid5t1 logical1 #gjj4 ,accid5tal discov]y1 #ebi4 ,a*romatic l5ses1 #dcb4 ,act9omet]1 #ccg4 ,adamant9e m$ium1 #fje1 #gea4 ,adjectives1 #ad1 #cj1 #ca1 #ce2 indet]m9ate1 #da4 ,adra91 ( ,new ,brunswick1 #cge4 ,affirmation1 #dd4 ,agassiz1 on g5]a1 #gbf2 on creation ( species1 #gfc4 ,agreem5t1 #dd4 ,airy1 ,sir ,george ,biddell1 on p]petual motion1 #bbc2 new prop]ty ( sph]e1 #bcb2 p5dulum exp]im5ts1 #bia1 #cjd1 #cdh1 #efg2 /&>d clock1 #cec2 book on 99,errors ( ,obs]vation991 #cie2 tides1 #dhh2 extra-polation1 #die2 ,?ales' eclipse1 #ecg2 int]f]5ce ( light1 #eci2 d5sity ( e>?1 #bia4 ,al*emi/s1 #eje2 h[ misl$1 #dbh4 ,algebra1 #abc1 #aee1 #afd2 ,diophant9e1 #fca4 ,algebraic1 equations1 #abc2 geometry1 #fcc4 ,allotropic /ate1 #ffc1 #fgj4 ,alloys1 possible numb]1 #aia2 prop]ties1 #ebh4 ,alphabet1 ! ,logical1 #ic1 #ajd1 #abe2 ,morse1 #aic4 ,alphabet1 p]mutations ( lett]s ( !1 #agd1 #agi4 ,alphabetic indexes1 #gad4 ,alt]native relations1 #fg2 exclusive & unexclusive1 #bje4 ,ampre1 electricity1 #edg2 classification1 #fgi4 ,anagrams1 #abh4 ,analogy1 #fbg2 ( logical & num]ical t]ms1 #afj2 & g5]alisation1 #eif2 9 ma!matical sci5ces1 #fca2 9 !ory ( undulations1 #fce2 9 a/ronomy1 #fch2 failure (1 #fda4 ,analysis1 logical1 #abb4 ,&rews1 ,pr(4 ,?omas1 exp]im5ts on gase\s /ate1 #ga1 #fac1 #ffe1 #gec4 ,ang/rm1 on spectrum1 #dbd4 ,angul> magnitude1 #cje1 #cjf1 #cbf4 ,antec$5t def9$1 #bbe4 ,anticipation ( ,nature1 #eji4 ,anticipations1 ( ,pr9ciple ( ,sub/itution1 #ba2 ( electric telegraph1 #fga4 ,app>5t1 equality1 #bge2 sequ5ce ( ev5ts1 #dji4 ,approximation1 !ory (1 #def2 to exact laws1 #dfb2 ma!matical pr9ciples (1 #dga2 ari?metic (1 #dha4 ,aque\s vap\r1 #ejj4 ,aqu9as1 on disjunctive propositions1 #fi4 ,arago1 photomet]1 #bhh2 rotat+ disc1 #ece2 8 philosophic "*1 #eib4 ,ar*im$es1 99,de ,ar5 ,num]o991 #aie2 c5tre ( gravity1 #cfc4 ,arcual unit1 #cjf1 #ccj4 ,argyll1 ,duke (1 #gda4 ,ari/>*us on sun's & moon's di/ances1 #bid4 ,ari/otelian doctr9es1 #fff4 ,ari/otle1 dictum1 #ba2 s+ul> t]ms1 #ci2 ov]look$ simple id5tities1 #dj2 ord] ( premises1 #aad2 logical error1 #aag2 def9ition ( "t1 #cjg2 on sci5ce1 #eie2 on :ite swans1 #fff4 ,ari?metic1 reason+ 91 #afg2 ( approximate quantities1 #dha4 ,ari?metical triangle1 #ic1 #adc1 #ahb1 #bjb1 #cgh1 #chc2 diagram (1 #ahd2 connection ) ,logical ,alphabet1 #ahi2 9 probability1 #bjh4 ,a/]oids1 discov]y (1 #dab1 #gdh4 ,a/ronomy1 physical1 #dei4 ,atmosph]ic tides1 #eec4 ,atomic !ory1 #ffb4 ,atomic weights1 #efc4 ,atoms1 size (1 #aie2 impossibility ( obs]v+1 #djf4 ,augu/9 on "t1 #cjg4 ,av]age1 #cei1 #cfj2 div]g5ce f1 #ahh2 etymology (1 #cfc4 ,axes ( cry/als1 #fhf4 ,axioms ( algebra1 #afd4 ,babbage1 ,*>les1 calculat+ ma*9e1 #ajg1 #bca1 #gdc2 ligh?\se signals1 #aid2 natural con/ants1 #cbi2 ,mosaic hi/ory1 #dab2 univ]sal & g5]al tru?s1 #fdf2 *ange ( law1 #bcj2 p]si/5ce ( effects1 #geg4 ,bacon1 ,francis ,"l1 99,novum ,organum991 #ajg2 on induction1 #aba2 bilit]al ciph]1 #aic2 ,fir/ ,aphorism1 #bai2 on causes1 #bba2 ,cop]nican sy/em1 #bdi1 #fch2 defici5t p[]s ( s5ses1 #bgh2 obs]vation1 #djb2 ,natural ,hi/ory1 #djc2 use ( hypo!sis1 #ejf2 8 me?od1 #ejg2 99exp]im5tum crucis991 #eai2 error ( 8 me?od1 #egf2 o/5sive1 cl&e/9e in/ances1 c41 #fjh1 #faj2 99lat5s precessus991 #fai4 ,bacon1 ,rog]1 on ! ra9b[1 #ebf1 #eih4 ,baily1 ,francis1 #bgb2 d5sity ( e>?1 #cdb1 #eff2 exp]im5ts ) torsion balance1 #cgj1 #cig1 #dcb1 #efg-h2 motions ( />s1 #egb4 ,ba91 ,alex&]1 on p[]s ( m9d1 #d2 ,mill's re=m ( logic1 #bbg4 ,bak]'s poem1 99,! ,univ]se991 #fba4 ,balance1 use ( ! *emical1 #bib1 #cea1 #ced1 #cfi2 delicacy (1 #cjd2 vibrations (1 #cfi4 ,ballot1 ,buys1 exp]im5t on s\nd1 #eda4 ,ballot-box1 simile (1 #aej1 #bea-f1 #gfe4 ,b>b>a1 #ee1 #eg1 #hh1 #aje1 #ada4 ,b>oko1 #he4 ,b>omet]1 #fei2 ,gay ,lussac's /&>d1 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