( ,ma!matics at ! ,univ]sity ( ,glasg[47 ---------------------------------------- ---------------------------- ,,transcrib]',s ,,notes3 ,ma!matical expressions :i* are 9 italics 9 ! orig9al text are display$ 9 non-italic *>act]s to increase ! readability ( ! book4 ,= sup] & subscripts unicode *>act]s h be5 us$ except a few cases :]e c>at symbol & und]l9e h be5 us$4 ,ma!matical notation 9 ! body ( text is duly cons]v$ b p>an!ses h be5 add$ to expressions to avoid any k9d ( mis5t]pretation4 ---------------------------------------- ---------------------------- ,,engli% ,,m5 ,,( ,,sci5ce ,,edit$ ,,by ,j4 ,,reynolds ,,gre51 ,sc4,d4 ,,"l ,,kelv9 ,,engli% ,,m5 ,,( ,,sci5ce ,,edit$ ,,by ,,dr4 ,j4 ,,reynolds ,,gre54 ,) ,photogravure ,frontispiece4 ,small ,cr4 #hvo1 #bs4 #f;d4 net p] vol4 ,,sp5c]4 ,by ,j4 ,,ar?ur ,,?ompson4 ,,prie/ley4 ,by ,dr4 ,,?orpe1 ,c4,b41 ,f4,r4,s4 ,,fl[]4 ,by ,pr(4 ,r4 ,,lydekk]1 ,f4,r4,s4 ,,huxley4 ,by ,pr(4 ,,a9swor? ,,davis4 ,,b5?am4 ,by ,b4 ,,daydon ,,jackson1 ,f4,l4,s4 ,,dalton4 ,by ,j4 ,p4 ,,mill+ton1 ,m4,a4 ,j4 ,m4 ,,d5t ,,co4 ,all ,rights ,res]v$ ,illu/ration3 ,"l ,kelv9 ,,"l ,,kelv9 ,,an ,,acc\nt ,,( ,,8 ,,sci5tific ,,life ,,& ,,"w ,,by ,,&rew ,,gray ,,ll4,d41 ,f4,r4,s41 ,v4-,p4,r4,s4,e4 ,,pr(essor ,,( ,,natural ,,philosophy ,,9 ,,! ,,univ]sity ,,( ,,glasg[ ,,publi%$ ,,9 ,,london ,,by ,j4 ,m4 ,,d5t ,,co41 ,,& ,,9 ,,new ,,york ,,by ,e4 ,p4 ,,dutton ,,co4 #aijh ,,ri*>d ,,clay ,,sons1 ,,limit$1 ,,bread ,,/reet ,,hill1 ,e4,c41 ,,& ,,bungay1 ,,suffolk4 ,,preface ,?is book makes no claim to be a biography ( ,"l ,kelv9 9 ! usual s5se4 ,x is an ext5sion ( an article :i* appe>$ 9 ! ,glasg[ ,h]ald = ,decemb] #ai1 #aijg1 & has be5 writt5 at ! sugge/ion ( v>i\s fri5ds ( ,"l ,kelv91 9 ! ,univ]sity ( ,glasg[ & else:]e1 :o _h read t article4 ,! aim ( ! volume is to give an acc\nt ( ,"l ,kelv9's life ( sci5tific activity1 & to expla9 to ! /ud5t1 & to ! g5]al read] :o takes an int]e/ 9 physical sci5ce & its applications1 ! nature ( 8 discov]ies4 ,only su* a /atem5t ( biographical facts z seems 9 h>mony ) ?is purpose is attempt$4 ,b ,i h v5tur$1 z an old pupil & assi/ant ( ,"l ,kelv91 to sket* "h & !re ! sc5e 9 8 class-room & laboratory1 & to record "s ( ! incid5ts ( 8 tea*+ & "w4 ,i am "u obligations to ! proprietors ( ! ,glasg[ ,h]ald = _! freely accord$ p]mission to make use ( _! article1 & to ,messrs4 ,annan1 photograph]s1 ,glasg[1 & ,messrs4 ,james ,mac,lehose ,sons1 ,glasg[1 = ! illu/rations :i* are giv51 & :i* ,i hope may add to ! int]e/ ( ! book4 ,a4 ,,gray4 ,! ,univ]sity1 ,glasg[1 ,may #bj1 #aijh4 ,,cont5ts ,,*ap4 ,,page ,i4 ,,p>5tage ,,& ,,e>ly ,,education #a ,,ii4 ,,classes ,,at ,,! ,,univ]sity ,,( ,,glasg[4 ,,fir/ ,,sci5tific ,,pap]s #ac ,,iii4 ,,univ]sity ,,( ,,cambridge4 ,,sci5tific ,,"w ,,z ,,und]graduate #bc ,,iv4 ,,! ,,ma!matical ,,!ory ,,( ,,electricity ,,9 ,,equilibrium4 ,,electric ,,images4 ,,electric ,,inv]sion #cc ,v4 ,,! ,,*air ,,( ,,natural ,,philosophy ,,at ,,glasg[4 ,,e/abli%m5t ,,( ,,! ,,fir/ ,,physical ,,laboratory #fa ,,vi4 ,,fri5d%ip ,,) ,,/okes ,,& ,,j\le4 ,,e>ly ,,"w ,,at ,,glasg[ #gi ,,vii4 ,,! ',,acc\nt ,,( ,,c>not',s ,,!ory ,,( ,,! ,,motive ,,p[] ,,( ,,heat'--,,transition ,,to ,,! ,,dynamical ,,!ory ,,( ,,heat #ii ,,viii4 ,,!rmodynamics ,,& ,,absolute ,,!rmometry #aad ,,ix4 ,,hydrodynamics--,,dynamical ,,!orem ,,( ,,m9imum ,,en]gy--,,vortex ,,motion #aec ,x4 ,,! ,,en]gy ,,!ory ,,( ,,electrolysis--,,electrical ,,units--,,electrical ,,oscillations #agf ,,xi4 ,,?omson ,,& ,,tait',s ',,natural ,,philosophy'--,,gyro/atic ,,action--',,electro/atics ,,& ,,magnetism' #aid ,,xii4 ,,! ,,age ,,( ,,! ,,e>? #bbi ,,xiii4 ,,briti% ,,association ,,committee ,,on ,,electrical ,,/&>ds #bdd ,,xiv4 ,,! ,,baltimore ,,lectures #bed ,,xv4 ,,spe$ ,,( ,,telegraph ,,signall+--,,lay+ ,,( ,,subm>9e ,,cables--,,telegraph ,,in/rum5ts--,,navigational ,,in/rum5ts1 ,,compass ,,& ,,s\nd+ ,,ma*9e #bfd ,,xvi4 ,,"l ,,kelv9 ,,9 ,,8 ,,class-,,room ,,& ,,laboratory #bgi ,,xvii4 ,,practical ,,activities--,,hon\rs ,,& ,,di/9ctions--,,la/ ,,illness ,,& ,,dea? #bii ,,conclusion #cje ,,index #cag ,,corrig5dum ,page #aje1 l9e #i f foot1 = e ,o read e o ,,li/ ,,( ,,illu/rations ,to face page ,,"l ,,kelv9 7photogravure7 ,frontispiece ,,"l ,,kelv9 ,,9 #ahdf #fd ,,view ,,( ,,old ,,college #gj ,,"l ,,kelv9 ,,*apt] ,i ,,p>5tage ,,& ,,e>ly ,,education ,"l ,kelv9 came ( a /ock :i* has help$ to give to ! nor? ( ,irel& its comm]cial & indu/rial supremacy ov] ! re/ ( t di/ressful c\ntry4 ,8 ance/ors 7 c\nty ,d[n agriculturi/s ( ,scotti% extraction4 ,8 fa!r 0 ,james ,?omson1 ! well-kn[n ,glasg[ ,pr(essor ( ,ma!matics1 & au?or ( ma!matical text-books :i* at "o "t 7 mu* valu$1 & are ev5 n[ wor? consult+4 ,james ,?omson 0 born on ,novemb] #ac1 #aghf1 ne> ,ballynah9*1 c\nty ,d[n4 ,be+ ! son ( a small f>m] he 0 probably unable to ent] on univ]sity /udies at ! usual age1 = he did n matriculate 9 ,scotl& until #ahaj4 ,! class-li/s ( ! "t %[ t he di/+ui%$ himself highly 9 ma!matics1 natural philosophy1 & classics4 ,an int]e/+ incid5t ( ^! /ud5t days ( 8 fa!r 0 relat$ by ,"l ,kelv9 9 8 in/allation address z ,*ancellor ( ! ,univ]sity 9 #aijd1 & is notewor?y z indicat+ h[ comp>atively rec5t are _m ( ! *>act]i/ics ( our pres5t-day life & comm]ce4 ,james ,?omson & "s companions1 walk+ f ,gre5ock to ,glasg[1 on _! way to jo9 ! college classes at ! comm5cem5t ( ! session1 saw a prodigy--a black *imney mov+ rapidly beyond a field on ! left-h& side ( _! road4 ,!y jump$ ! f5ce1 ran across ! field1 & saw1 to _! a/oni%m5t1 ,h5ry ,bell's ',comet' 7!n n a ye> old7 travell+ on ! ,clyde betwe5 ,glasg[ & ,gre5ock4#a ,sometimes !n ! passage f ,belfa/ to ,gre5ock took a long "t4 ,once ,james ,?omson1 cross+ 9 an old lime-c>ry+ smack1 0 ?ree or f\r days on ! way1 9 ! c\rse ( :i* ! vessel1 becalm$1 0 c>ri$ ?ree times by ! tide r\nd ,ailsa ,craig4 ,mr4 ,?omson 0 elect$ 9 #ahae to ! ,pr(essor%ip ( ,ma!matics 9 ! ,royal ,academical ,in/itution ( ,belfa/1 & held ! po/ = sev5te5 ye>s1 build+ up = himself an excell5t reputation z a tea*]1 & z a cle> & accurate writ]4 ,j !n analytical me?ods 7 beg9n+ to sup]s$e ! processes ( geometrical demon/ration :i* ! =m adopt$ by ,newton = ! ,pr9cipia _h t5d$ to p]petuate 9 ?is c\ntry4 ,laplace 0 at ! height ( 8 fame 9 ,france1 & 0 writ+ ! great analytical ,pr9cipia1 8 ,mcanique ,cle/e1 apply+ ! :ole =ce ( 8 g5ius1 & all ! res\rces ( ! diff]5tial & integral calculus inv5t$ by ,newton & improv$ by ! ma!maticians ( ! int]v5+ c5tury1 to ! elucidation & ext5sion ( ! sy/em ( ! _w1 :i* _h be5 s boldly sket*$ by ! f\nd] ( mod]n physical sci5ce4 ,9 t p]iod ,f\ri] wrote 8 memoirs on ! conduction ( heat1 & gave to ! _w 8 immortal book to be an inspiration to ! physical philosoph]s ( succe$+ g5]ations4 ,leg5dre _h writt5 memoirs :i* 7 to lead1 9 ! h&s ( ,jacobi & 8 successors1 to a new prov9ce ( ma!matics1 :ile1 9 ,g]many1 ,gauss _h begun 8 /ately m>* ( discov]y4 ,! me?ods & results ( ?is p]iod ( ma!matical activity 7 at fir/ h>dly kn[n 9 ?is c\ntry3 ! slavi% devotion ( ,cambridge to ! geometrical processes & ! fluxional notation ( ,newton1 an exclusive p>tiality :i* ,newton himself w\ld h be5 ! fir/ to condemn1 l$ analytical me?ods1 equally ,newtonian1 to be /igmatis$ z innovations1 because clo!d 9 ! unfamili> g>b ( ! cont95tal notation4 ,a revolt aga9/ ?is 0 l$ by ,sir ,john ,h]s*el1 ,woodh\se1 ,peacock1 & "s o!rs at ,cambridge1 :o wrote books :i* _h a great effect 9 br++ ab\t a *ange ( me?ods4 ,sir ,john ?us describ$ ! effect ( ! new movem5ts3--,/ud5ts at our univ]sities1 fett]$ by no prejudices1 entangl$ by no habits1 & excit$ by ! ard\r & emulation ( y\?1 _h he>d ( ! exi/5ce ( masses ( k f :i* !y 7 deb>r$ by ! m]e accid5t ( position4 ,!y requir$ no m4 ,! pre/ige :i* magnifies :at is unkn[n1 & ! attractions inh]5t 9 :at is =bidd51 co9cid$ 9 _! impulse4 ,! books 7 procur$ & read1 & produc$ _! natural effects4 ,! br[s ( _m a ,cambridge exam9] 7 elevat$1 half 9 ire1 half 9 admiration1 at ! unusual answ]s :i* began to appe> 9 exam9ation pap]s4 ,ev5 mod]ators are n made ( imp5etrable /uff1 ?\gh f5c$ ) sev5fold ,jacqui]1 & t\gh bull-hide ( ,v9ce & ,wood4 ,! memoirs & treatises ( ! cont95tal analy/s 7 eag]ly procur$ & /udi$ by ,james ,?omson1 & z he 0 b\nd by no exam9ation traditions1 he freely adopt$ _! me?ods1 s f> z ^! came )9 ! scope ( 8 tea*+1 & made !m kn[n to ! ,engli% read+ public 9 8 text-books4 ,h5ce :5 ! *air ( ,ma!matics at ,glasg[ became vacant 9 #ahcb by ! dea? ( ,mr4 ,james ,mill>1 ,mr4 ,?omson 0 at once *os5 by ! ,faculty1 :i* at t "t 0 ! elect+ body4 ,! ,faculty consi/$ ( ! ,pr9cipal & ! ,pr(essors ( ,div9ity1 ,*ur* ,hi/ory1 ,ori5tal ,languages1 ,natural ,philosophy1 ,moral ,philosophy1 ,ma!matics1 ,logic1 ,greek1 ,humanity1 ,civil ,law1 ,practice ( ,m$ic9e1 ,anatomy1 & ,practical ,a/ronomy4 ,x adm9i/]$ ! :ole rev5ues & prop]ty ( ! ,college1 & possess$ ! patronage ( ! above-nam$ *airs ) ! exception ( ,*ur* ,hi/ory1 ,civil ,law1 ,m$ic9e1 ,anatomy1 & ,a/ronomy1 s t ,mr4 ,?omson became n only ,pr(essor ( ,ma!matics1 b also1 9 virtue ( 8 (fice1 a memb] ( :at 0 really ! supreme gov]n+ body ( ! ,univ]sity4 ,! memb]s ( ! ,faculty1 ) ! exception ( ! ,pr(essor ( ,a/ronomy1 :o resid$ at ! obs]vatory1 7 provid$ ) (ficial resid5ces 9 ! ,college4 ,?is arrangem5t is /ill adh]$ to2 ?\gh n[ ! gov]nm5t is 9 ! h&s ( a ,univ]sity ,c\rt1 ) ! ,s5ate 7:i* =m]ly only met to conf] degrees or to manage ! libr>y & "s o!r matt]s7 to regulate & sup]9t5d tea*+ & discipl9e4 ,pr(essor ,?omson 0 by no means ! fir/ or ! only pr(essor ( ! "n 9 ! ,univ]sity ( ,glasg[1 z ! foll[+ passage quot$ f a lett] ( ,john ,ni*ol1 son ( ,dr4 ,j4 ,p4 ,ni*ol1 & fir/ ,pr(essor ( ,engli% at ,glasg[1 amus+ly te/ifies3-- ,niebuhr1 aft] exam9+ a portion ( ! ,fa/i ,consul>es1 arriv$ at ! conclusion t ! s5atus populusque ,romanus _h made a compact to elect e ye> a memb] ( ! ,fabian h\se to "o ( ! highe/ (fices ( /ate1 s ?ickly are ! records /udd$ ) ! "n ( ! ,fabii4 ,"s future ,niebuhr ( ! ,new ,zeal& ,macaulay imag9es1 turn+ 8 att5tion to ! annals ( ,glasg[ ,college1 w und\bt$ly arrive at ! conclusion t ! lead]s ( t illu/ri\s corporation _h1 dur+ ! p]iod ( :i* ,i am writ+1 become b\nd 9 a simil> mann] to ! "n ( ,?omson4 ,memb]s ( t great g5s fill$ "o-half ( ! *airs 9 ! ,univ]sity4 ,i w n v5ture to say h[ _m ,i h kn[n4 ,!re 0 ,tommy ,?omson ! *emi/2 ,william ,?omson ( ,mat]ia ,m$ica2 ,all5 ,?omson ( ,anatomy1 bro!r ( ! la/2 ,dr4 ,james ,?omson ( ,ma!matics2 ,william1 8 son1 etc41 etc4 ,old ,dr4 ,james 0 "o ( ! be/ ( ,iri%m51 a good ma!matician1 an en?usia/ic & successful tea*]1 ! au?or ( sev]al valuable s*ool-books1 a fri5d ( my fa!r's1 & himself ! fa!r ( a l>ge family1 ! memb]s ( :i* h be5 prosp]\s 9 ! _w4 ,!y liv$ ne> u 9 ! c\rt1 & we made a pretty close acqua9tance%ip ) !m all4 ,a =m] ,pr(essor ( ,natural ,philosophy1 ,dr4 ,&]son1#b :o appe>s to h liv$ ! clos+ ye>s ( 8 life 9 almo/ con/ant w>f>e ) 8 colleagues ( ! ,faculty1 & :o e/abli%$ sci5ce classes = workm5 9 ,glasg[1 bequea!d a sum ( money to set up a college 9 ,glasg[ 9 :i* su* classes might be c>ri$ on4 ,! result 0 ! f\ndation ( :at us$ to be call$ ! ,&]sonian ,univ]sity 9 ,george ,/reet1 ! precursor ( ! magnific5t ,te*nical ,college ( ! pres5t day4 ,?is "n1 & ! l>ge numb] ( ,?omsons :o _h be5 & 7 /ill connect$ ) ! ,univ]sity ( ,glasg[1 caus$ ! m anci5t in/itution to be n infrequ5tly ref]r$ to z ! ,?omsonian ,univ]sity6 ,! ,?omas ,?omson 7no relative ( ! ,belfa/ ,?omsons7 affectionately1 if a little irrev]5tly1 m5tion$ 9 ! above quotation1 0 !n ! ,pr(essor ( ,*emi/ry4 ,he 0 ! fir/ to e/abli% a *emical laboratory = /ud5ts 9 ?is c\ntry2 inde$1 8 laboratory prec$$ t ( ,liebig at ,giess5 by "s ye>s1 & x is probable t z reg>ds exp]im5tal *emi/ry ,glasg[ 0 !n 9 advance ( ! re/ ( ! _w4 ,8 pupil & life-long admir] 0 de/9$ to e/abli% ! fir/ physical laboratory = su* /ud5ts z 7 will+ to sp5d "s "t 9 ! exp]im5tal inve/igation & v]ification ( physical pr9ciples1 or to help ! pr(essor 9 8 rese>*es4 ,! sy/ematic in/ruction ( /ud5ts 9 me?ods ( exp]im5t+ by practical ex]cises ) app>atus 0 a mu* lat] idea1 & ?is fact mu/ be tak5 acc\nt ( :5 ! laboratories ( ! pres5t "t are contra/$ ) ! mu* m meagre provision ( ^? e>ly days4 ,! laboratory is n[1 z mu* z ! lecture-room1 ! place :]e classes are held & in/ruction giv5 9 exp]im5tal sci5ce to cr[ds ( /ud5ts1 & x is a *ange = ! bett]4 ,! arrival ( ,james ,?omson & 8 family at ,glasg[ ,college1 9 #ahcb1 0 rem>k$ at ! "t z an ev5t :i* br\ght a l>ge re9=cem5t to ! g5s already insep>ably associat$ ) ! place3 h[ great 7 to be its consequ5ces n m]ely to ! ,univ]sity b to ! _w at l>ge nobody c !n h imag9$4 ,8 family consi/$ ( f\r sons & two daught]s3 8 wife1 ,m>g>et ,g>dn]1 daught] ( ,william ,g>dn]1 a m]*ant 9 ,glasg[1 _h di$ %ortly be=e1 & ! c>e ( ! family 0 und]tak5 by h] si/]1 ,mrs4 ,gall4 ,! elde/ son1 ,james ,?omson1 long aft] to be ,rank9e's successor 9 ! ,*air ( ,eng9e]+1 0 t5 ye>s ( age & ev5 !n an invet]ate inv5tor2 ,william1 ! future ,"l ,kelv9 7born ,june #bf1 #ahbd71 0 a *ild ( eight4 ,two y\ng] sons 7 ,john 7born 9 #ahbf7--:o a*iev$ di/9ction 9 ,m$ic9e1 became ,resid5t ,assi/ant 9 ! ,glasg[ ,royal ,infirm>y1 & di$ !re ( a fev] caught 9 ! dis*>ge ( 8 duty--& ,rob]t1 :o 0 born 9 #ahbi1 & di$ 9 ,au/ralia 9 #aije4 ,besides ^! f\r sons !re 7 9 all ?ree daught]s3--,elizabe?1 aft]w>ds wife ( ! ,rev4 ,david ,k+1 ,d4,d42 ,anna1 :o 0 m>ri$ to ,mr4 ,william ,bottomley ( ,belfa/ 7^! two 7 ! elde/ ( ! family71 & ,m>g>et1 ! y\nge/1 :o di$ 9 *ildhood4 ,?us began ,william ,?omson's resid5ce 9 & connection ) ! ,univ]sity ( ,glasg[1 a connection only t]m9at$ by ! fun]al c]emony 9 ,we/m9/] ,abbey on ,decemb] #bc1 #aijg4 ,pr(essor ,?omson himself c>efully sup]9t5d$ ! education ( 8 sons1 :i* 0 c>ri$ out at home4 ,!y 7 well gr\nd$ 9 ! old classical languages1 & moreov] receiv$ s\nd in/ruction 9 :at ev5 n[ are call$1 b 9 a some:at disp>ag+ s5se1 mod]n subjects4 ,z ,john ,ni*ol has said 9 8 lett]s1 ,he 0 a /]n discipl9>ian1 & did n relax 8 discipl9e :5 he appli$ x to 8 *ildr51 & yet ! aim ( 8 life 0 _! advancem5t4 ,x w\ld appe> f ,john ,ni*ol's recollections t ev5 9 *ildhood & y\?1 "y ,james ,?omson 0 an en?usia/ic exp]im5tali/ & inv5tor1 eag] to describe 8 ideas & %[ 8 models to a sympa!tic li/5]4#c ,& bo? !n & 9 lat] ye>s 8 *>m+ simplicity1 8 dev\r+ passion = accuracy ( v]bal expression 9 all 8 sci5tific writ+ & tea*+1 & 8 unaffect$ & unconsci\s g5ius = ! inv5tion ( me*anical appliances1 all bas$ on true & intuitively p]ceiv$ physical pr9ciples1 %[$ t if he _h _h ! unrel5t+ p[] ( ignor+ accessories & unimportant details :i* 0 possess$ by 8 y\ng] bro!r1 he might h accompli%$ f> m ?an he did1 consid]able z t 04 ,b ,william _h m rapid decision1 & ?\gh c>eful & exact 9 express+ 8 mean+1 0 less influ5c$ by consid]ations ( ! errors t might arise f ! v>i\s connotations ( su* sci5tific t]ms z are also words 9 common use2 & he quickly complet$ "w :i* 8 bro!r w\ld h pond]$ ov] = a long "t1 & p]haps nev] f9i%$4 ,x is difficult = a /rang] to ,glasg[1 or ev5 = a resid5t 9 ,glasg[ 9 ^! days ( quick & frequ5t communication ) ,engl&1 & = t matt] ) all p>ts ( ! _w1 to =m a true idea ( life & "w at ! ,univ]sity ( ,glasg[ sev5ty ye>s ago4 ,! ,univ]sity _h !n its home 9 ! old t\nis coll$ge 9 ! ,high ,/reet1 :]e _m c\ld h wi%$ x to rema91 &1 ext5d+ its build+s on ,college ,gre51 reta9 ! old & include ! new4 ,its f9e old gateway1 & "p ( "o ( ! c\rts1 7 /ill a qua9t adornm5t ( ! some:at squalid /reet 9 #ahga1 aft] ! ,univ]sity _h mov$ to its pres5t situation on ! w9dy top ( ,gilmorehill4 ,des]t$ z x 01 its old walls told some?+ ( ! hi/ory ( ! pa/1 & rem9d$ ! pass]-by t le>n+ _h fl\ri%$ amid ! %ops & boo?s ( ! t[nspeople1 & t /ud5ts & pr(essors _h !re liv$ & work$ )9 s\nd ( ! %uttle & ! =ge4 ,! old associations ( a t[n or a /reet or a build+1 l9k$ z !y (t5 are ) ! hi/ory ( a nation1 are a valuable possession1 n always plac$ 9 ! acc\nt :5 ! advantages or disadvantages ( propos$ *anges are discuss$2 b a ,univ]sity :i* = f\r hundr$ ye>s has se5 ! tide ( human life fl[ r\nd x 9 a great city1 is in/9ct ) memories :i* ev5 ! demolition ( its walls c only p>tially de/roy4 ,poets & /atesm51 m5 ( ?\ght & m5 ( action1 lords & common]s1 ri* m5's sons & ! *ildr5 ( f>m]s1 craftsm5 & lab\r]s1 _h m+l$ 9 its classes & sat toge!r on its b5*es2 & s _h be5 br\ght ab\t a community ( ?\ght & feel+ :i* ! practice ( our mod]n & weal?y cosmopolites1 :o affect to despise nationality1 c]ta9ly does no?+ to enc\rage4 ,9 ! eighte5? c5tury ! ,provo/s & ! ,bailies ( ! "t /ill dwelt among m5 & wom5 9 ! ,high ,/reet1 & its cont9uation ! ,saltm>ket1 or n f> (f 9 ,virg9ia ,/reet1 ! home ( ! tobacco lords & ! ,we/ ,india m]*ants4 ,_! homely hospitality1 _! cauti\s & at ! same "t spl5did g5]osity1 _! prud5t c\rage1 & _! fai?ful & c&id fri5d%ips are depict$ 9 ! pages ( ,scott2 & ?\gh a *ange 9 m5 & mann]s1 n altoge!r = ! bett]1 has be5 gradually br\ght ab\t by sport & fa%ion1 ^? peculi>ly ,scotti% virtues are /ill to be f\nd 9 ! civic /atesm5 & m]*ant pr9ces ( ! ,glasg[ ( to-day4 ,sev5ty ye>s ago ! great migration ( ! well-to-d t[>ds ! we/ _h comm5c$1 b x _h b little int]f]$ ) ! life ( ! ,high ,/reet or ( ! ,college4 ,n[ _m old slums besides ! ,v5nel & ! ,havannah h disappe>$1 mu* to ! cr$it ( ! ,corporation ( ,glasg[2 &1 alas1 s has e ve/ige ( ! ,old ,college1 mu* to ! regret ( all :o rememb] its qua9t old c\rts4 ,a railway company1 x is to be suppos$1 d>e n possess an arti/ic s\l to be sav$2 & !re=e1 p]haps1 x is t x builds huge & ugly c>avans]ais ( :i* no "o1 except p]haps ! %>ehold]s1 w\ld ke5ly regret ! disappe>ance4 ,b bo? arti/s & antiqu>ies w\ld h bless$ ! directors--& su* a bless+ w\ld h done !m no h>m--if !y _h be5 +5i\s & pi\s en\gh to leave "s relic ( ! old build+s z a memorial ( ! old days & ! old life ( ! ,high ,/reet4 ,a picture ( ! ,college 9 ! ,high ,/reet has rec5tly be5 drawn by "o :o liv$ & work$ 9 x1 ?\gh "s ?irty ye>s aft] ,james ,?omson br\ght 8 family to live 9 its c\rts4 ,pr(essor ,g4 ,g4 ,ramsay has ?us portray$ "s features ( ! place1 :i* may int]e/ ^? :o w\ld l to imag9e ! environm5t 9 :i* ,"l ,kelv9 grew up f *ildhood1 until1 a y\? ( sev5te51 he left ,glasg[ = ,cambridge4#d ,!re 0 some?+ 9 ! v disam5ities ( ! old place t creat$ a bond ( fell[%ip among ^? :o liv$ & work$ !re1 & t makes all old /ud5ts1 to ?is day1 look back to x ) a sort ( family pride & rev]5ce4 ,! grimy1 d+y1 l[-ro($ rooms2 ! n>r[1 picturesque c\rts1 buzz+ ) /ud5t-life2 ! dismal1 foggy morn+s & ! p]petual gas2 ! sudd5 passage f ! brawl+1 huck/]+ ,high ,/reet into ! academic quietude1 or ! /ill m academic hubbub1 ( ^? qua9t cloi/]s1 into :i* ! policeman1 s busy outside1 0 nev] p]mitt$ to p5etrate2 ! t9kl+ ( ! 'angry bell' t made ! /ud5ts hurry along to ! door :i* 0 clos$ ! mom5t t x /opp$2 ! ro> & ! fl>e ( ! ,saturday nights1 ) ! cries ( c>\se or incipi5t murd] :i* w\ld rise into our quiet rooms f ! ,v5nel or ! ,havannah2 ! exhau/$ lassitude ( ,sunday morn+s1 :5 poor slip%od creatures might be se51 z soon z ! /reet 0 cle> ( *ur*go]s1 sneak+ ov] to ! *emi/'s = a dose ( laudanum to ease (f ! debau* ( ye/]day2 ! conv]sations "o w\ld h aft] breakfa/ ) ! old ladies on ! o!r side ( ! ,v5nel1 n tw5ty feet f "o's breakfa/-table1 :o divid$ ! day betwe5 smok+ %ort cutty pipes & dr9k+ poison\s black tea--^! %>p contra/s b\nd toge!r ! ,college folk & ! ,college /ud5ts1 mak+ !m feel at once "p ( ! v]itable populace ( ! city1 & also h$g$ (f f x by sep>ate pursuits & int]e/s4 ,! univ]sity remov$ 9 #ahga to l>g] & m airily situat$ build+s 9 ! we/]n "p ( ! city4 ,r\nd ^! h gr[n up1 9 ! int]v5+ ?irty-eight ye>s1 new build+s = mo/ ( ! great dep>tm5ts ( sci5ce1 includ+ a sep>ate ,in/itute ( ,natural ,philosophy1 :i* 0 op5$ 9 ,april #aijg1 by ! ,pr9ce & ,pr9cess ( ,wales4 ,,*apt] ,,ii ,,classes ,,at ,,! ,,univ]sity ,,( ,,glasg[4 ,,fir/ ,,sci5tific ,,pap]s ,9 #ahcd1 t is at ! age ( t51 ,william ,?omson ent]$ ! ,univ]sity classes4 ,?\gh small 9 /ature1 & y\?ful ev5 = a "t :5 m]e boys 7 ,univ]sity /ud5ts1 he soon made himself conspicu\s by 8 read9ess 9 answ]+ que/ions1 & by 8 g5]al pr(ici5cy1 especially 9 ma!matical & physical /udies4 ,! classes met at t "t twice a day--9 ma!matics once = lecture & once = oral exam9ation & ! work+ ( unse5 examples by /ud5ts ( ! class4 ,x is /ill matt] ( tradition h[1 9 8 fa!r's class1 ,william 0 conspicu\s = ! brilliancy ( ! "w he did 9 ?is second h\r4 ,8 eld] bro!r ,james & he seem to h gone ?r\gh _! ,univ]sity c\rse toge!r4 ,9 #ahcd-e !y 7 bracket$ ?ird 9 ,lat9 ,prose ,composition4 ,9 #ahce-f ,william receiv$ a prize = a vacation ex]cise--a translation ( ,lucian's ,dialogues ( ! ,gods ) full p>s+ ( ! fir/ ?ree ,dialogues4 ,9 #ahcf-g & #ahcg-h ! bro!rs 7 9 ! ,junior & ,s5ior ,ma!matical ,classes1 & 9 ea* ye> ! fir/ & ! second place 9 ! prize-li/ fell to ,william & ,james respectively4 ,9 ! second ( ^! ye>s1 ,william appe>s z second prizeman 9 ! ,logic ,class1 :ile ,james 0 ?ird1 & ,john ,caird 7aft]w>ds ,pr9cipal ( ! ,univ]sity7 0 fif?4 ,william & ,james ,?omson took ! fir/ & second prizes 9 ! ,natural ,philosophy ,class at ! close ( session #ahch-i2 & 9 t ye> ,william ga9$ ! ,class ,prize 9 ,a/ronomy1 & a ,univ]sity ,m$al = an ,essay on ! ,figure ( ! ,e>?4 ,9 #ahdj-a he appe>s once m1 ?is "t z fif? prizeman 9 ! ,s5ior ,humanity ,class4 ,9 8 inaugural address z ,*ancellor ( ! ,univ]sity1 already quot$ above1 ,"l ,kelv9 ref]s to 8 tea*]s 9 ,glasg[ ,college 9 ! foll[+ words3 ,to ?is day ,i look back to ,william ,ramsay's lectures on ,roman ,antiquities1 & read+s ( ,juv5al & ,plautus1 z m int]e/+ ?an _m a good /age play t ,i h se5 9 ! !atre4444 ,greek "u ,sir ,daniel ,s&=d & ,lu%+ton1 ,logic "u ,rob]t ,bu*anan1 ,moral ,philosophy "u ,william ,flem+1 ,natural ,philosophy & ,a/ronomy "u ,john ,pr+le ,ni*ol1 ,*emi/ry "u ,?omas ,?omson1 a v advanc$ tea*] & inve/igator1 ,natural ,hi/ory "u ,william ,c[p]1 71 z ,i c te/ify by my exp]i5ce1 all made int]e/+ & valuable to ! /ud5ts ( ,glasg[ ,univ]sity 9 ! ?irties & =ties ( ! n9ete5? c5tury4444 ,my pr$ecessor 9 ! ,natural ,philosophy *air1 ,dr4 ,meikleham1 taught 8 /ud5ts rev]5ce = ! great ,fr5* ma!maticians ,leg5dre1 ,lagrange1 & ,laplace4 ,8 imm$iate successor 9 ! tea*+ ( ! ,natural ,philosophy ,class1#e ,dr4 ,ni*ol1 add$ ,fresnel & ,f\ri] to ?is li/ ( sci5tific nobles3 & by 8 own inspir+ en?usiasm = ! great ,fr5* s*ool ( ma!matical physics1 cont9ually manife/$ 9 8 exp]im5tal & !oretical tea*+ ( ! wave !ory ( light & ( practical a/ronomy1 he l>gely promot$ sci5tific /udy & ?or\gh appreciation ( sci5ce 9 ! ,univ]sity ( ,glasg[4444 ,z f> back z #ahah to #ahcj ,?omas ,?omson1 ! fir/ ,pr(essor ( ,*emi/ry 9 ! ,univ]sity ( ,glasg[1 began ! sy/ematic tea*+ ( practical *emi/ry to /ud5ts1 &1 aid$ by ! ,faculty ( ,glasg[ ,college1 :i* gave ! site & ! money = ! build+1 realis$ a well-equipp$ laboratory1 :i* prec$$1 ,i believe1 by "s ye>s ,liebig's fam\s laboratory ( ,giess51 & 01 ,i believe1 ! fir/ e/abli%$ ( all ! laboratories 9 ! _w = *emical rese>* & ! practical in/ruction ( ,univ]sity /ud5ts 9 *emi/ry4 ,t 0 at a "t :5 an imp]fectly in=m$ public us$ to reg>d ! ,univ]sity ( ,glasg[ z a /agnant survival ( m$ivalism1 & us$ to call its pr(essors ! ',monks ( ! ,mol5d9>'6 ,! ,univ]sity ( ,adam ,smi?1 ,james ,watt1 & ,?omas ,reid 0 nev] /agnant4 ,= two c5turies & a half x has be5 v progressive4 ,ne>ly two c5turies ago x _h a laboratory ( human anatomy4 ,sev5ty-five ye>s ago x _h ! fir/ *emical /ud5ts' laboratory4 ,sixty-five ye>s ago x _h ! fir/ ,pr(essor%ip ( ,eng9e]+ ( ! ,briti% ,empire4 ,fifty ye>s ago x _h ! fir/ physical /ud5ts' laboratory--a des]t$ w9e-cell> ( an old pr(essorial h\se1 enl>g$ a few ye>s lat] by ! annexation ( a des]t$ exam9ation-room4 ,?irty-f\r ye>s ago1 :5 x migrat$ f its f\r-hundr$-ye>s-old site (f ! ,high ,/reet ( ,glasg[ to ?is bright] & airi] hill-top1 x acquir$ laboratories ( physiology & zoology2 b too small & too meagrely equipp$4 ,9 ! summ] ( #ahdj ,pr(essor ,james ,?omson & 8 two sons w5t = a t\r 9 ,g]many4 ,x 0 /ipulat$ t ,g]man %\ld be ! *ief1 if n ! only1 subject ( /udy dur+ ! holidays4 ,b ,william _h j begun to /udy ,f\ri]'s fam\s book1 ,la ,?orie ,analytique de la ,*aleur1 & took x ) him4 ,he read t great "w1 full z x 0 ( new !orems & processes ( ma!matics1 ) ! greate/ delight1 & f9i%$ x 9 a =tnight4 ,! result 0 8 fir/ orig9al pap] ,on ,f\ri]'s ,expansions ( ,functions 9 ,trigonometrical ,s]ies1 :i* is dat$ ,frank=t1 ,july #ahdj1 & ,glasg[1 ,april #ahda1 & 0 publi%$ 9 ! ,cambridge ,ma!matical ,j\rnal 7vol4 ii1 ,may #ahda74 ,! object ( ! pap] is to %[ 9 :at cases a function f7x71 :i* is to h c]ta9 arbitr>y values betwe5 c]ta9 values ( x1 c be exp&$ 9 a s]ies ( s9es & :5 9 a s]ies ( cos9es4 ,! conclusion come to is t1 = assign$ limits ( x1 betwe5 #j & a1 say1 & = ! assign$ values ( ! function1 f7x7 c be express$ ei!r z a s]ies ( s9es or z a s]ies ( cos9es4 ,if1 h[ev]1 ! function is to be calculat$ = any value ( x1 :i* lies outside ! limits ( t v>iable betwe5 :i* ! values ( ! function are assign$1 ! values ( f7x7 !re are to be f\nd f ! expansion adopt$1 by rules :i* are laid d[n 9 ! pap]4 ,f\ri] us$ s9e-expansions or cos9e-expansions z x suit$ him = ! function betwe5 ! limits1 & 8 results _h be5 pron\nc$ to be ne>ly all errone\s4 ,f ?is *>ge ( error1 :i* 0 br\ght by a di/+ui%$ & exp]i5c$ ma!matician1 ! "y analy/ ( sixte5 successfully v9dicat$ ,f\ri]'s "w4 ,f\ri] 0 inconte/ably "r 9 hold+1 ?\gh he n[h]e directly prov$1 t a function giv5 = any value ( x betwe5 c]ta9 limits1 c\ld be express$ ei!r by a s9e-s]ies or by a cos9e-s]ies4 ,! div]g5ce ( ! values ( ! two expressions takes place outside ^! limits1 z has be5 /at$ above4 ,! next pap] is ( ! same f9al date1 b appe>$ 9 ! ,cambridge ,ma!matical ,j\rnal ( ! foll[+ ,novemb]4 ,9 8 treatm5t ( ! problem ( ! cool+ ( a sph]e1 giv5 ) an arbitr>y initial di/ribution ( temp]ature symmetrical ab\t ! c5tre1 ,f\ri] assumes t ! arbitr>y function ,f7x71 :i* expresses ! temp]ature at di/ance x f ! c5tre1 c be exp&$ 9 an inf9ite s]ies ( ! =m a s9 nx a s9 nx 444 :]e a1 a1 444 are multipli]s to be det]m9$ & n1 n1 444 are ! roots1 inf9ite 9 numb]1 ( ! transc5d5tal equation 7tan n,x7n,x #a h,x4 ,?is equation expresses1 accord+ to a p>ticul> solution ( ! diff]5tial equation ( ! fl[ ( heat 9 ! sph]e1 ! condition fulfill$ at ! surface1 t ! heat rea*+ ! surface by conduction f ! int]ior 9 any "t is radiat$ 9 t "t to ! surr\nd+s4 ,?omson dealt 9 ?is second pap] ) ! possibility ( ! expansion4 ,he %[$ t1 inasmu* z ! fir/ ( ! roots ( ! transc5d5tal equation lies betwe5 #j & #ab1 ! second betwe5 #a & #cb1 ! ?ird betwe5 #b & #eb1 & s on1 ) v close approa* to ! upp] limit z ! roots become ( high ord]1 ! s]ies assum$ z possible has betwe5 ! giv5 limits ( x ! same value z ! s]ies ,a s9 7#ab7x ,a s9 7#cb7x 444 :]e ,a1 ,a1 444 are kn[n 9 t]ms ( a1 a1 444 ,conv]sely1 any s]ies ( ?is =m is capable ( be+ replac$ by a s]ies ( ! =m assum$4 ,fur!r1 a s]ies ( ! =m j writt5 c be made to repres5t any arbitr>y sy/em ( values betwe5 ! giv5 limits1 & s ! possibility ( ! expansion is demon/rat$4 ,! next t5 pap]s1 ) two exceptions1 are all on ! motion ( heat1 & appe>$ 9 ! ,cambridge ,ma!matical ,j\rnal betwe5 #ahda & #ahdc1 & deal ) important topics sugge/$ by ,f\ri]'s treatise4 ,( ! ideas conta9$ 9 "o or two ( !m "s acc\nt w be giv5 pres5tly4 ,f\ri]'s book 0 call$ by ,cl]k ,maxwell1 himself a man ( mu* spirituality ( feel+1 & no mean poet1 a great ma!matical poem4 ,?omson (t5 ref]r$ to x 9 simil> t]ms4 ,! idea ( ! ma!matician z poet may seem /range to "s2 b ! g5ius ( ! greate/ ma!maticians is ak9 to t ( ! true creative arti/1 :o is v]itably inspir$4 ,= su* a book 0 a "w ( ! imag9ation z well z ( ! reason4 ,x conta9$ a new me?od ( analysis appli$ ) sublime success to ! solution ( ! equations ( heat conduction1 an analysis :i* has s9ce be5 transf]r$ to o!r bran*es ( physical ma!matics1 & has illum9at$ !m ) j ^? rays :i* c\ld reveal ! texture & /ructure ( ! physical ph5om5a4 ,t me?od & its applications came f ,f\ri]'s m9d 9 full developm5t2 he trod un]r+ly 9 its use along an almo/ unkn[n pa?1 ) pitfalls on e side2 & he rea*$ results :i* h s9ce be5 v]ifi$ by a criticism se>*+ & ke51 & la/+ f ,f\ri]'s day to ours4 ,! criticism has be5 m9ute & logical3 x has n1 x is ne$less to say1 be5 poetical4 ,two o!r great works ( 8 fa!r's collection ( ma!matical books1 ,laplace's ,mcanique ,cle/e & ,lagrange's ,mcanique ,analytique1 seem also to h be5 read ab\t ?is "t1 & to h made a deep impression on ! m9d ( ! y\?ful philosoph]4 ,! effect ( ^! books c be easily trac$ 9 ,?omson & ,tail's ,natural ,philosophy4 ,! /udy ( ,f\ri] _h a pr(\nd influ5ce on ,?omson's future "w1 an influ5ce :i* has ext5d$ to 8 late/ writ+s on ! !ory ( c]ta9 k9ds ( waves4 ,8 treatm5t is f\nd$ on a /rik+ly orig9al use ( a peculi> =m ( solution 7giv5 by ,f\ri]7 ( a c]ta9 fundam5tal diff]5tial equation 9 ! !ory ( ! fl[ ( heat4 ,x is probable t ,william ,?omson's e>lie/ pr$ilections z reg>ds /udy 7 9 ! direction ( ma!matics r ?an ( physics4 ,b ! /udies ( ! "y ma!matician1 = su* 9 a v real & high s5se he _h become1 7 wid5$ & deep5$ by ! int]e/ 9 physical ?+s & _! explanation ar\s$ by ! lectures ( ,meikleham1 !n ,pr(essor ( ,natural ,philosophy1 & especially 7z ,"l ,kelv9 te/ifi$ 9 8 inaugural address z ,*ancellor7 by ! tea*+ ( ,j4 ,p4 ,ni*ol1 ! ,pr(essor ( ,a/ronomy1 a man ( poetical imag9ation & ( great gifts ( vivid & cle> exposition4 ,! ,cyclopdia ( ,physical ,sci5ce :i* ,dr4 ,ni*ol publi%$ is little kn[n n[2 b ! fir/ edition1 publi%$ 9 #aheg1 to :i* ,?omson contribut$ sev]al articles1 includ+ a sket* ( !rmodynamics1 conta9$ mu* t 0 new & /imulat+ to ! /ud5t ( natural philosophy1 & "s idea ( ! accompli%m5ts ( its compil] & au?or c be ga!r$ f its p]usal4 ,de ,morgan's ,diff]5tial & ,integral ,calculus 0 a fav\rite book 9 ,?omson's /ud5t days1 & lat] :5 he 0 at ,cambridge1 & he delight$ to pore ov] its pages be=e ! fire :5 ! "w ( ! day 0 ov]4 ,long aft]1 he paid a grateful tribute to ,de ,morgan & 8 great "w1 9 ! ,presid5tial ,address to ! ,briti% ,association at its ,ed9burgh ,meet+ 9 #ahgj4 ,! next pap] :i* ,?omson publi%$1 aft] ! two ( :i* a sket* has be5 giv5 above1 0 entitl$ ,! ,uni=m ,motion ( ,heat 9 ,homog5e\s ,solid ,bodies1 & its ,connection ) ! ,ma!matical ,!ory ( ,electricity4 ,x is dat$ ,lamla%1 ,augu/ #ahda1 s t x foll[$ ! fir/ two at an int]val ( only f\r mon?s4 ,x appe>$ 9 ! ,cambridge ,ma!matical ,j\rnal 9 ,febru>y #ahdb1 & is republi%$ 9 ! ,repr9t ( ,pap]s on ,electro/atics & ,magnetism4 ,x w always be a notewor?y pap] 9 ! hi/ory ( physical ma!matics4 ,= al?\gh1 = ! mo/ "p1 only kn[n !orems reg>d+ ! conduction ( heat 7 discuss$1 an analogy 0 po9t$ out betwe5 ! di/ribution ( l9es ( fl[ & surfaces ( equal temp]ature 9 a solid & unequally heat$ body1 ) s\rces ( heat 9 its int]ior1 & ! arrangem5t ( l9es ( =ces & equipot5tial surfaces 9 an insulat+ m$ium surr\nd+ electrifi$ bodies1 :i* correspond to ! s\rces ( heat 9 ! !rmal case4 ,! di/ribution ( l9es ( =ce 9 a space fill$ ) insulat+ m$ia ( diff]5t inductive qualities 0 %[n to be precisely analog\s to t ( l9es ( fl[ ( heat 9 a correspond+ arrangem5t ( m$ia ( diff]5t heat-conduct+ p[]s4 ,s ! :ole analysis & sy/em ( solutions 9 ! !rmal case c\ld be at once transf]r$ to ! electrical "o4 ,! idea ( ! conduction ( l9es ( =ce1 z ,f>aday fir/ & ,?omson aft]w>ds call$ x1 0 fur!r develop$ 9 subsequ5t pap]s1 & ?rew light on ! :ole subject ( electro/atic =ce 9 ! field surr\nd+ an electric di/ribution4 ,moreov]1 x made ! subject def9ite & quantitative1 & n only gave a guide to ! int]pretation ( unexpla9$ facts1 b op5$ a way to new !orems & to fur!r inve/igation4 ,?is pap] conta9s ! extremely important !orem ( ! equival5ce1 s f> z ext]nal field is conc]n$1 ( any di/ribution ( electricity & a c]ta9 def9ite di/ribution1 ov] any equipot5tial surface1 ( a quantity equal to t conta9$ )9 ! surface4 ,b ?is g5]al !orem & o!rs conta9$ 9 ! pap] _h be5 anticipat$ 9 ,gre5's ,essay on ! ,application ( ,ma!matical ,analysis to ! ,!ories ( ,electricity & ,magnetism1 9 memoirs by ,*asles 9 ,li\ville's ,j\rnal 7vols4 iii & v71 & 9 ! celebrat$ memoir by ,gauss ,on ,g5]al ,!orems relat+ to ,attractive & ,repulsive ,=ces v>y+ inv]sely z ! ,squ>e ( ! ,di/ance1 publi%$ 9 ,g]man 9 ,leipzig 9 #ahdj1 & 9 ,engli% 9 ,taylor's ,sci5tific ,memoirs 9 #ahdb4 ,^! anticipations are aga9 ref]r$ to bel[4 ,,*apt] ,,iii ,,univ]sity ,,( ,,cambridge4 ,,sci5tific ,,"w ,,z ,,und]graduate ,?omson ent]$ at ,/4 ,pet]'s ,college1 ,cambridge1 9 ,octob] #ahda1 & began ! c\rse ( /udy !n 9 vogue = ma!matical hon\rs4 ,at t "t1 z always d[n almo/ to ! pres5t day1 ev]y?+ dep5d$ on ! *oice ( a private tutor or coa*1 & ! devotion ( ! pupil to 8 directions1 & on adh]5ce to ! subjects ( ! programme4 ,8 private tutor 0 ,william ,hopk9s1 be/ ( all private tutors1 "o ( ! mo/ em95t ( 8 pupils call$ him1 a man ( great atta9m5t & ( di/9ction z an orig9al inve/igator 9 a subject :i* _h always deeply int]e/$ ,?omson--! int]nal rigidity ( ! e>?4 ,b ! curriculum = ! tripos did n exhau/ ,?omson's en]gy1 nor 0 x possible to keep him entirely to ! groove ( ma/]+ & writ+ out book-"w1 & to ! solution ( problems ( ! k9d de> to ! he>t ( ! ma!matical exam9]4 ,he wrote orig9al articles = ! ,cambridge ,ma!matical ,j\rnal1 on po9ts 9 pure & 9 appli$ ma!matics1 & read ma!matical books altoge!r outside ! scope ( ! tripos4 ,nor did he neglect a?letic ex]cises & amusem5ts2 he won ! ,colquh\n ,sculls z an o>sman1 & 0 an active memb]1 & lat]1 dur+ 8 resid5ce at ,cambridge1 presid5t ( ! ,c4,u4,m4,s41 ! ,cambridge ,univ]sity ,musical ,society4#f ,! musical in/rum5ts he fav\r$ 7 ! cornet & especially ! ,fr5* horn--he 0 second horn 9 ! orig9al ,pet]h\se b&--b no?+ seems to be on record z to ! difficulties or incid5ts ( 8 practice6 ,long aft]w>ds1 9 a few extremely int]e/+ lectures :i* he gave annually on s\nd1 he disc\rs$ on ! vibrations ( columns ( air 9 w9d in/rum5ts1 & sometimes illu/rat$ 8 rem>ks by %[+ h[ notes 7 v>i$ 9 pit* on ! old-fa%ion$ ,fr5* horn1 play$ ) ! h& 9 ! bell1 a p]=mance :i* always int5sely delight$ ! ,natural ,philosophy ,class4 ,at ! ,jubilee commemoration ( ! society1 #ahic1 ,"l ,kelv9 recall$ t ,m5delssohn1 ,web] & ,bee?ov5 7 ! gods ( ! infant association4 ,^? ( 8 pupils :o came m intimately 9 contact ) him w rememb] 8 ke5 admiration = ^! & o!r great compos]s1 especially ,ba*1 ,moz>t1 & ,bee?ov51 & 8 delight 9 he>+ _! works4 ,! ,wald/e9 sonata 0 a special fav\rite4 ,x has be5 rem>k$ be=e n[1 & x seems to be true1 t ! music ( ,ba* & ,bee?ov5 has _h special attractions = _m great ma!maticians4 ,at ,cambridge ,?omson made ! acqua9tance ( ,george ,gabriel ,/okes1 :o graduat$ z ,s5ior ,wrangl] & ,fir/ ,smi?'s ,prizeman 9 #ahda1 & eight ye>s lat] became ,lucasian ,pr(essor ( ,ma!matics 9 ! ,univ]sity ( ,cambridge4 ,_! acqua9tance soon rip5$ into a close fri5d%ip1 :i* la/$ until ! dea? ( ,/okes 9 #aijc4 ,! ,s5ior ,wrangl] & ! ,pet]h\se ,und]graduate und]took ! composition ( a s]ies ( notes & pap]s on po9ts 9 pure & physical ma!matics :i* requir$ cle>+ up1 or putt+ 9 a new po9t ( view2 & s began a life-long int]c\rse & correspond5ce :i* 0 ( great value to sci5ce4 ,?omson's pap]s ( ?is p]iod are on a consid]able v>iety ( subjects1 includ+ 8 fav\rite subject ( ! flux ( heat4 ,!re are sixte5 9 all t seem to h be5 writt5 & publi%$ dur+ 8 und]graduate resid5ce at ,cambridge4 ,mo/ ( !m appe>$ 9 ! ,cambridge ,ma!matical ,j\rnal betwe5 #ahdb & #ahde2 b ?ree appe>$ 9 #ahde 9 ,li\ville's ,j\rnal de ,ma?matiques4 ,f\r are on subjects ( pure ma!matics1 su* z ,dup9's !orem reg>d+ l9es ( curvature ( or?ogonally int]sect+ surfaces1 ! r$uction ( ! g5]al equation ( surfaces ( ! second ord] 7n[ call$ second degree71 six are on v>i\s subjects ( ! !ory ( heat1 "o is on attractions1 five are on electrical !ory1 & "o is on ! law ( gravity at ! surface ( a revolv+ homog5e\s fluid4 ,x is impossible to give an acc\nt ( all ^! pap]s "h4 ,"s ( !m are new pres5tations or new pro(s ( kn[n !orems1 "o or two are fre% & cle> /atem5ts ( fundam5tal pr9ciples to be us$ lat] z ! f\ndation ( m complete /atem5ts ( ma!matical !ory2 b all are m>k$ by cle>ness & vig\r ( treatm5t4 ,ano!r pap]1 publi%$ 9 ! =m ( a lett]1 ( date ,octob] #h1 #ahde1 to ,m4 ,li\ville1 & publi%$ 9 ! ,j\rnal de ,ma?matiques 9 ! same ye>1 indicates t ei!r be=e or %ortly aft] tak+ 8 degree1 ,?omson _h inv5t$ 8 celebrat$ me?od ( ,electric ,images = ! solution ( problems ( electric di/ribution4 ,( ?is me?od1 :i* is "o ( ! mo/ elegant 9 ! :ole range ( physical ma!matics1 & solves at a /roke "s problems1 o!rwise almo/ intractable1 we %all give "s acc\nt 9 ! foll[+ *apt]4 ,?is record ( "w is prodigi\s = a /ud5t read+ = ! ma!matical tripos2 & x is some:at ( an irony ( fate t su* sci5tific activity is1 on ! :ole1 r a h9drance ?an a help 9 ! prep>ation = t elaborate ordeal ( exam9ation4 ,great expectations _h be5 =m$ reg>d+ ,?omson's p]=mance2 h>dly ev] be=e _h a c&idate appe>$ :o _h done s mu* & s brilliant orig9al "w1 & !re 0 little d\bt t he w\ld be easily fir/ 9 any conte/ involv+ real ma!matical p[]1 t is1 ability to deal ) new problems & to express new relations ( facts 9 ma!matical language4 ,b ! tripos 0 n a te/ ( p[] m]ely2 x 0 a te/ also ( acquisition1 &1 to c&idates fairly equal 9 ?is respect1 also ( memory & ( quickness ( reproduction on pap] ( acquir$ k4 ,! mod]ators on ! occasion 7 ,rob]t ,leslie ,ellis & ,h>vey ,goodw91 bo? di/+ui%$ m54 ,ellis _h be5 ,s5ior ,wrangl] & fir/ ,smi?'s ,prizeman a few ye>s be=e1 & 0 a ma!matician ( orig9al p[] & promise1 :o _h already writt5 memoirs ( great m]it4 ,goodw9 _h be5 ,second ,wrangl] :5 ,ellis 0 ,s5ior1 & became kn[n to a lat] g5]ation z ,bi%op ( ,c>lisle4 ,9 a life ( ,ellis prefix$ to a volume ( 8 collect$ pap]s1 ,goodw9 says3--,x 0 9 ?is ye> t ,pr(essor ,w4 ,?omson took 8 degree2 great expectations _h be5 excit$ conc]n+ him1 & ,i rememb] ,ellis rem>k+ to me1 ) a smile1 ',y & ,i are j ab\t fit to m5d 8 p5s4' ,surely nev] 0 high] tribute paid to c&idate by exam9]6 ,ano!r /ory1 :i*1 h[ev]1 does n seem capable ( su* complete au!ntication1 is told ( ! same exam9ation1 or x may be ( ! ,smi?'s ,prize ,exam9ation :i* foll[$4 ,a c]ta9 problem 0 solv$1 s x is said1 9 practically id5tical t]ms by bo? ! ,fir/ & ,second ,wrangl]s4 ,! exam9]s rem>k$ ! co9cid5ce1 & 7 curi\s z to its orig94 ,on be+ ask$ reg>d+ x1 ! ,s5ior ,wrangl] repli$ t he _h se5 ! solution he gave 9 a pap] :i* _h appe>$ 9 a rec5t numb] ( ! ,cambridge ,ma!matical ,j\rnal2 ,?omson's answ] 0 t he 0 ! au?or ( ! pap] 9 "q6 ,?omson 0 ,second ,wrangl]1 & ,p>k9son1 ( ,/4 ,john's ,college1 aft]w>ds4 ,dr4 ,p>k9son1 tutor ( ,/4 ,john's & au?or ( v>i\s ma!matical text-books1 0 ,s5ior4 ,^! positions 7 rev]s$ 9 ! exam9ation = ,smi?'s ,prizes1 :i* 0 v g5]ally reg>d$ z a bett] te/ ( orig9al ability ?an ! tripos1 s t ! tempor>y disappo9tm5t ( ,?omson's fri5ds 0 quickly =gott5 9 ?is high] success4 ,! ,tripos ,exam9ation 0 held 9 ! e>ly "p ( ,janu>y4 ,on ! #be? ( t mon? ,?omson met 8 private tutor ,hopk9s 9 ! ,s5ior ,wrangl]s' ,walk at ,cambridge1 & 9 ! c\rse ( conv]sation ref]r$ to 8 desire to obta9 a copy ( ,gre5's ',essay' 7supra1 p4 #ba74 ,hopk9s at once took him to ! rooms :]e he _h att5d$ almo/ daily = a consid]able "t z a pupil1 & produc$ no less ?an ?ree copies ( ! ,essay1 & gave him "o ( !m4 ,a ha/y p]usal %[$ ,?omson t all ! g5]al !orems ( attractions conta9$ 9 8 pap] ,on ! ,uni=m ,motion ( ,heat1 etc41 z well z ^? ( ,gauss & ,*asles1 _h be5 set =? by ,gre5 & 7 d]ivable f a g5]al !orem ( analysis :]eby a c]ta9 integral tak5 ?r\gh\t a space b\nd$ by surfaces fulfill+ a c]ta9 condition is express$ z two integrals1 "o tak5 ?r\gh\t ! space1 ! o!r tak5 ov] ! b\nd+ surface or surfaces4 ,x has be5 /at$ 9 ! la/ *apt] t ,?omson _h e/abli%$1 z a d$uction f ! fl[ ( heat 9 a uni=m solid f s\rces di/ribut$ )9 x1 ! rem>kable !orem ( ! replacem5t1 )\t alt]ation ( ! ext]nal fl[1 ( ^! s\rces by a c]ta9 di/ribution ov] any surface ( uni=m temp]ature1 & _h po9t$ out ! analogue ( ?is !orem 9 electricity4 ,?is me?od ( pro( 0 p]fectly orig9al & _h n be5 anticipat$1 ?\gh ! !orem1 z has be5 /at$1 _h already be5 giv5 by ,gre5 & by ,gauss4 ,9 ! pap] entitl$ ,propositions 9 ! ,!ory ( ,attraction1 publi%$ 9 ! ,cambridge ,ma!matical ,j\rnal 9 ,novemb] #ahdb1 ,?omson gave an analytical pro( ( ?is great !orem1 b aft]w>ds f\nd t ?is _h be5 done almo/ contemporane\sly by ,/urm 9 ,li\ville's ,j\rnal4 ,soon aft] ! ,tripos & ,smi?'s ,prize ,exam9ations 7 ov]1 ,?omson w5t to ,london1 & visit$ ,f>aday 9 8 laboratory 9 ! ,royal ,in/itution4 ,!n he w5t on to ,p>is ) 8 fri5d ,hugh ,blackburn1 & sp5t ! summ] work+ 9 ,regnault's fam\s laboratory1 mak+ ! acqua9tance ( ,li\ville1 ,/urm1 ,*asles1 & o!r ,fr5* ma!maticians ( ! "t1 & att5d+ meet+s ( ! ,acadmie des ,sci5ces4 ,he made kn[n to ! ma!maticians ( ,p>is ,gre5's ',essay1' & ! treasures x conta9$1 & frequ5tly told 9 aft] ye>s ) :at a/oni%m5t its results 7 receiv$4 ,he us$ to relate t "o day1 :ile he & ,blackburn sat 9 _! rooms1 !y he>d "s "o come pant+ up ! /air4 ,/urm bur/ 9 ^u !m 9 great excitem5t1 & exclaim$1 ,v\s avez un ,mmoire de ,gre56 ,m4 ,li\ville me l'a dit4 ,he sat d[n & turn$ ov] ! pages ( ! ',essay1' look+ at "o result aft] ano!r1 until he came to a complete anticipation ( 8 pro( ( ! replacem5t !orem4 ,he jump$ up1 po9t$ to ! page1 & cri$ out1 ,voila mon affaire6 ,to ?is visit to ,p>is ,?omson (t5 ref]r$ 9 lat] life ) grateful recognition ( ,regnault's k9dness1 & admiration ( 8 wond]ful exp]im5tal skill4 ,! great exp]im5tali/ 0 !n engag$ 9 8 rese>*es on ! !rmal con/ants ( bodies1 ) ! elaborate app>atus :i* he design$ = himself1 & ) :i* he 0 suppli$ by ! wise lib]ality ( ! ,fr5* ,gov]nm5t4 ,?is initiation into laboratory "w bore fruit n long aft] 9 ! e/abli%m5t ( ! ,glasg[ ,physical ,laboratory1 ! fir/ physical laboratory = /ud5ts 9 ?is c\ntry4 ,x is a /rik+ te/imony to ,?omson's g5ius t1 at ! age ( only sev5te51 he _h arriv$ at su* a fundam5tal & g5]al !orem ( attractions1 & _h po9t$ out its applications to electrical !ory4 ,& x is also v rem>kable t ! !orem %\ld h be5 prov$ )9 an int]val ( two or ?ree ye>s by ?ree diff]5t au?ors1 two ( !m--,/urm & ,gauss--already fam\s z ma!maticians4 ,gre5's treatm5t ( ! subject 01 h[ev]1 ! mo/ g5]al & f>-rea*+1 =1 z has be5 /at$1 ! !orem ( ,gauss1 ,/urm1 & ,?omson 0 m]ely a p>ticul> case ( a g5]al !orem ( analysis conta9$ 9 ,gre5's ',essay4' ,x has be5 said 9 je/1 b n )\t tru?1 t physical ma!matics is made up ( cont9u$ applications ( ,gre5's !orem4 ,( ?is enorm\sly p[]ful relation1 a m lately discov]$ result1 :i* is v fundam5tal 9 ! !ory ( functions ( a complex v>iable1 & :i* is g5]ally quot$ z ,riemann's !orem1 is only a p>ticul> case4 ,?omson _h ! greate/ rev]5ce = ! g5ius ( ,gre51 & f\nd 9 8 memoirs1 & 9 ^? ( ,cau*y on wave propagation1 ! inspiration = mu* ( 8 own lat] "w4#g ,9 #ahej he obta9$ ! republication ( ,gre5's ',essay' 9 ,crelle's ,j\rnal2 9 lat] ye>s he frequ5tly express$ regret t x _h n be5 publi%$ 9 ,engl&4 ,9 ! comm5cem5t ( #ahde ,?omson told ,li\ville ( ! me?od ( ,electric ,images :i* he _h discov]$ = ! solution ( problems ( electric di/ribution4 ,on ,octob] #h1 #ahde1 aft] 8 return to ,cambridge1 he wrote to ,li\ville a %ort acc\nt ( ! results ( ! me?od 9 a numb] ( diff]5t cases1 & 9 two lett]s writt5 on ,june #bf & ,septemb] #af ( ! foll[+ ye>1 he /at$ "s fur!r results1 includ+ ! solution ( ! problem ( ! di/ribution ^u a sph]ical b[l 7a segm5t ( a sph]ical conduct+ %ell made by a plane section7 insulat$ & electrifi$4 ,?is la/ v rem>kable result 0 giv5 )\t pro(1 & rema9$ unprov$ until ,?omson publi%$ 8 demon/ration tw5ty-?ree ye>s lat] 9 ! ,philosophical ,magaz9e4#h ,?is _h be5 prec$$ by a s]ies ( pap]s 9 ,m>*1 ,may1 & ,novemb] #ahdh1 ,novemb] #ahdi1 & ,febru>y #ahej1 9 ! ,cambridge & ,dubl9 ,ma!matical ,j\rnal1 on v>i\s p>ts ( ! ma!matical !ory ( electricity 9 equilibrium1#i 9 :i* ! !ory ( images is dealt )4 ,! lett]s to ,li\ville promptly appe>$ 9 ! ,j\rnal1 & ! vet]an analy/ wrote a long ,note on _! subject1 :i* concludes z foll[s3 ,mon b s]a rempli1 je le rpte1 s'ils ces dveloppem5ts peuv5t aid] bi5 faire compr5dre la haute importance du travail de ce jeune gomtre1 et si ,m4 ,?omson lui-mme veut bi5 y voir une preuve n\velle de l'amiti que je lui porte et de l'e/ime qui j'ai p\r son tal5t4 ,! me?od ( images may be reg>d$ z a developm5t 9 a p>ticul> direction ( ! pap] ,on ! ,uni=m ,motion ( ,heat already ref]r$ to1 &1 tak5 along ) ?is latt] pap]1 =ms ! mo/ /rik+ indication af=d$ by ! :ole range ( ,?omson's e>li] "w ( ! /r5g? & orig9ality ( 8 ma!matical g5ius4 ,accord+ly a *apt] is "h devot$ to a m complete explanation ( ! fir/ pap] & ! developm5ts :i* fl[$ f x4 ,! g5]al read] may pass ov] ! *apt]1 & return to x f "t to "t z he f9ds opportunity1 until x is completely und]/ood4 ,,*apt] ,,iv ,,! ,,ma!matical ,,!ory ,,( ,,electricity ,,9 ,,equilibrium4 ,,electric ,,images4 ,,electric ,,inv]sion ,9 describ+ ,?omson's e>ly electrical rese>*es we %all n ent] into detail$ calculations1 b m]ely expla9 ! me?ods employ$4 ,! mean+ ( c]ta9 te*nical t]ms may be recall$ 9 ! fir/ place4 ,! :ole space 9 :i* a di/ribution ( electricity produces any action on electrifi$ bodies is call$ ! electrical field ( ! di/ribution4 ,! =ce ex]t$ on a v small insulat$ trial conductor1 on :i* is an electric *>ge ( am\nt equal to t tak5 z ! unit quantity ( electricity1 measures ! field-int5sity at any po9t at :i* ! conductor is plac$4 ,! direction ( ! field-int5sity at ! po9t is t 9 :i* ! small conductor is !re urg$4 ,if ! *>ge on ! small conductor 7 a negative unit1 in/ead ( a positive1 ! direction ( ! =ce w\ld be rev]s$2 ! magnitude ( ! =ce w\ld rema9 ! same4 ,to make ! field-int5sity q def9ite1 a positive unit is *os5 = its specification4 ,= a *>ge on ! trial-conductor consi/+ ( any numb] ( units1 ! =ce is t numb] ( times ! field-int5sity4 ,! field-int5sity is (t5 specifi$ by its compon5ts1 ,x1 ,y1 ,z 9 ?ree *os5 directions at "r angles to "o ano!r4 ,n[ 9 all cases 9 :i* ! action1 :e!r attraction or repulsion1 betwe5 two unit quantities ( matt] conc5trat$ at po9ts is inv]sely z ! squ>e ( ! di/ance betwe5 ! *>ges1 ! field-int5sity1 or its compon5ts1 c be f\nd f a c]ta9 function ,v ( ! *>ges =m+ ! act+ di/ribution :i* is always capable ( be+ reg>d$ = ma!matical purposes z a sy/em ( small *>ges exi/+ at po9ts ( space1 po9t-*>ges we %all call !m1 _! positions1 & ! position ( ! po9t at :i* ! field-int5sity is to be f\nd4 ,if q1 q1 444 be ! po9t-*>ges1 & be positive :5 ! *>ges are positive & negative :5 ! *>ges are negative1 & r1 r1 444 be _! di/ances f ! po9t ,p1 ,v is qr qr 444 ,! field-int5sity is ! rate ( dim9ution ( ! value ( ,v at ,p1 tak5 along ! specifi$ direction4 ,! ?ree gradi5ts p>allel to ! ?ree *os5 coord9ate directions are ,x1 ,y1 ,z2 b = _! calculation x is necess>y to ins]t ! values ( r1 r1 444 9 t]ms ( ! coord9ates :i* specify ! positions ( ! po9t-*>ges1 & ! coord9ates x1 y1 z :i* specify ! position ( ,p4 ,once ?is is done1 ,x1 ,y1 ,z are obta9$ by a simple sy/ematic process ( calculation1 namely1 diff]5tiation ( ! function ,v ) respect to x1 y1 z4 ,?is function ,v seems to h be5 fir/ us$ by ,laplace = gravitational matt] 9 ! ,mcanique ,cle/e2 its importance = electricity & magnetism 0 recognis$ by ,gre51 :o nam$ x ! pot5tial4 ,x has an important physical signification4 ,x repres5ts ! "w :i* w\ld h to be done to br+ a unit ( positive electricity1 aga9/ ! electrical repulsion ( ! di/ribution1 up to ! po9t ,p f a po9t at an inf9ite di/ance f e "p ( ! di/ribution2 or1 9 o!r words1 :at we n[ call ! pot5tial en]gy ( a *>ge q situat$ at ,p is q,v4 ,! excess ( ! pot5tial at ,p1 ov] ! pot5tial at any o!r po9t ,q 9 ! field1 is ! "w :i* mu/ be sp5t 9 c>ry+ a positive unit f ,q to ,p aga9/ electrical repulsion4 ,( c\rse1 if ! =ce to be ov]come f ,q to ,p is on ! :ole an attraction1 "w has n be5 sp5t 9 effect+ ! transf]5ce1 b ga9$ by all[+ x to take place4 ,! diff]5ce ( pot5tial is !n negative1 t is1 ! pot5tial ( ,q is high] ?an t ( ,p4 ,! diff]5ce ( pot5tial dep5ds only on ! po9ts ,p & ,q1 & n at all on ! pa? pursu$ betwe5 !m4 ,?us1 if a unit ( electricity be c>ri$ f ,p to ,q by any pa?1 & back by any o!r1 no "w is done on ! :ole by ! ag5t c>ry+ ! unit4 ,?is simple fact precludes ! possibility ( obta9+ a s-call$ p]petual motion 7a self-act+ ma*9e do+ useful "w7 by means ( electrical action4 ,! same ?+ is true mutatis mut&is ( gravitational action4 ,9 ! !rmal analogy expla9$ by ,?omson 9 8 fir/ pap]1 ! positive po9t-*>ges are po9t-s\rces ( heat1 :i* is !re p\r$ at con/ant rate into ! m$ium 7suppos$ ( uni=m quality7 to be drawn (f 9 "p f ! m$ium at con/ant rate :]e !re are s9ks 7or negative s\rces71--! negative po9t-*>ges 9 ! electrical case1--:ile ! rema9d] is conduct$ away to m & m di/ant p>ts ( ! conduct+ m$ium suppos$ inf9itely ext5d$4 ,:5ev] a po9t-s\rce1 or a po9t-s9k1 exi/s at a di/ance f o!r s\rces or s9ks1 ! fl[ 9 ! vic9ity is 9 /raight l9es f or to ! po9t1 & ^! /raight l9es w\ld be indef9itely ext5d$ if ei!r s\rce or s9k exi/$ by itself4 ,z x is1 ! direction & am\nt ( fl[ ev]y:]e dep5ds on ! fl[ result+ f ! :ole arrangem5t ( s\rces & s9ks4 ,l9es c be drawn 9 ! m$ium :i* %[ ! direction ( ! resultant fl[ f po9t to po9t1 & ^! l9es ( fl[ c be s spac$ z to indicate1 by _! clos5ess toge!r or _! di/ance ap>t1 :]e ! rate ( fl[ is great] or small]2 & su* l9es />t f s\rces1 & ei!r end 9 s9ks or cont9ue _! c\rse to inf9ity4 ,9 ! electrical case ^! l9es are ! analogues ( ! l9es ( electric =ce 7or field-int5sity7 9 ! insulat+ m$ium1 :i* />t f positive *>ges & end 9 negative1 or are prolong$ to inf9ity4 ,across su* l9es ( fl[ c be drawn a family ( surfaces1 to ea* ( :i* ! l9es met by ! surface are p]p5dicul>4 ,^! surfaces are ! equitemp]ature surfaces1 or1 z !y are usually call$1 ! iso!rmal surfaces4 ,!y c be drawn m closely cr[d$ toge!r1 or m widely sep>at$1 s z to indicate :]e ! rate ( fall+ (f ( temp]ature 7! temp]ature slope7 is great] or less1 j z ! cont\r l9es 9 a map %[ ! slopes on a hill-side4 ,in/ead ( ! !rmal analogy might h be5 us$ equally well t ( /eady fl[ 9 an indef9itely ext5d$ mass ( homog5e\s frictionless & incompressible fluid1 into :i* fluid is be+ p\r$ at a con/ant rate by s\rces & )drawn by s9ks4 ,! iso!rmal surfaces are replac$ by surfaces ( equal pressure1 :ile l9es ( fl[ 9 "o are also l9es ( fl[ 9 ! o!r4 ,n[ let heat be p\r$ into ! m$ium at con/ant rate by a s+le po9t-s\rce ,p 7,fig4 #a71 & drawn (f at a small] rate by a s+le po9t-s9k ,p'1 :ile ! rema9d] fl[s to m & m remote p>ts ( ! m$ium1 suppos$ inf9ite 9 ext5t 9 e direction4 ,aft] a suffici5t "t f ! beg9n+ ( ! fl[ a def9ite sy/em ( l9es ( fl[ & iso!rmal surfaces c be trac$ = ?is case 9 ! mann] describ$ above4 ,"o ( ! iso!rmal surfaces w be a sph]e ,s surr\nd+ ! s9k1 :i*1 h[ev]1 w n be at ! c5tre ( ! sph]e1 b s situat$ t ! s\rce1 s9k1 & c5tre are 9 l9e1 & t ! radius ( ! sph]e is a mean proportional betwe5 ! di/ances ( ! s\rce & s9k f ! c5tre4 ,if a be ! radius ( ! sph]e & f ! di/ance ( ! s\rce f ! c5tre ( ! sph]e1 ! heat c>ri$ (f by ! s9k is ! fraction af ( t giv5 out by ! s\rce4 ,illu/ration3 ,,fig4 #a4 ,9 ! electrical analogue1 ! s\rce & s9k are respectively a po9t-*>ge & :at is call$ ! electric image ( t *>ge ) respect to ! sph]e1 :i* is 9 ?is case an equipot5tial surface4 ,& j z ! l9es ( fl[ ( heat meet ! sph]ical iso!rmal surface at "r angles1 s ! l9es ( =ce 9 ! electrical case meet ! equipot5tial surface also at "r angles4 ,n[ obvi\sly 9 ! !rmal case a sph]ical s9k c\ld be arrang$ co9cid+ ) ! sph]ical surface s z to receive ! fl[ !re arriv+ & c>ry (f ! heat f ! m$ium1 )\t 9 ! lea/ di/urb+ ! fl[ outside ! sph]e4 ,! :ole am\nt ( heat arriv+ w\ld be ! same3 ! am\nt receiv$ p] unit area at any po9t on ! sph]e w\ld evid5tly be proportional to ! gradi5t ( temp]ature !re t[>ds ! surface4 ,( c\rse ! same ?+ c\ld be done at any iso!rmal surface1 & ! same proportionality w\ld hold 9 t case4 ,simil>ly ! s\rce c\ld be replac$ by a surface-di/ribution ( s\rces ov] any surr\nd+ iso!rmal surface2 & ! condition to be fulfill$ 9 t case w\ld be t ! am\nt ( heat giv5 out p] unit area any:]e %\ld be exactly t :i* fl[s out along ! l9es ( fl[ !re 9 ! actual case4 ,outside ! surface ! field ( fl[ w\ld n be affect$ by ?is replacem5t4 ,x is obvi\s t 9 ?is case ! outfl[ p] unit area mu/ be proportional to ! temp]ature slope outw>d f ! surface4 ,! same /atem5ts hold = any complex sy/em ( s\rces & s9ks4 ,!re mu/ be ! same outfl[ f ! iso!rmal surface or infl[ t[>ds x1 z !re is 9 ! actual case1 & ! proportionality to temp]ature slope mu/ hold4 ,?is is exactly analog\s to ! replacem5t by a di/ribution on an equipot5tial surface ( ! electrical *>ge or *>ges )9 ! surface1 by a di/ribution ov] ! surface1 ) fulfilm5t ( ,c\lomb's !orem 7p4 #dc bel[7 at ! surface4 ,?omson's pap] on ! ,uni=m ,motion ( ,heat gave an intuitive pro( ( ?is great !orem ( electro/atics1 :i* ! /atem5ts above may help to make cle> to ^? :o h1 or are will+ to acquire1 "s elem5t>y k ( electricity4 ,return+ to ! di/ribution on any iso!rmal surface surr\nd+ ! s9k 7or s9ks7 we see t x repres5ts a surface-s9k 9 equilibrium ) ! fl[ 9 ! field4 ,! di/ribution on a metal %ell1 co9cid+ ) ! surface1 :i* keeps ! surface at a pot5tial :i* is ! analogue ( ! temp]ature at ! iso!rmal surface1 :ile ! %ell is "u ! influ5ce ( a po9t-*>ge ( electricity--! analogue ( ! !rmal s\rce--is ! di/ribution z affect$ by ! induction ( ! po9t-*>ge4 ,if ! %ell co9cide ) ! sph]ical equipot5tial surface ref]r$ to above1 & ! di/ribution giv5 by ! !orem ( replacem5t be made ^u x1 ! %ell w be at z]o pot5tial1 & ! *>ge w be t :i* w\ld exi/ if ! %ell 7 un9sulat$1 t is1 ! induc$ *>ge4 ,! consid]ation ( ! foll[+ simple problem w s]ve to make cle> ! mean+ ( an electric image1 & =m a suitable introduction to a description ( ! application ( ! me?od to ! electrification ( sph]ical surfaces4 ,imag9e a v l>ge plane %eet ( t9foil connect$ by a conduct+ wire ) ! e>?4 ,if !re are no electrifi$ bodies ne>1 ! %eet w be unelectrifi$4 ,b let a v small metallic ball ) a *>ge ( positive electricity ^u x be br\ght mod]ately close to "o face ( ! t9foil4 ,! t9foil w be electrifi$ negatively by induction1 & ! di/ribution ( ! negative *>ge w dep5d on ! position ( ! ball4 ,n[1 x c be %[n t ! field ( electric =ce1 on ! same side ( ! t9foil z ! ball1 is precisely ! same z w\ld be produc$ if ! foil 7& ev]y?+ beh9d x7 7 remov$1 & an equal negative *>ge ( electricity plac$ beh9d ! t9foil on ! prolong$ p]p5dicul> f ! ball to ! foil1 & z f> f ! foil beh9d z ! ball is f x 9 front4 ,su* a negative *>ge beh9d ! t9foil %eet is call$ an electric image ( ! positive *>ge 9 front4 ,x is situat$1 z w be se5 at :at w\ld be1 if ! t9foil 7 a mirror1 ! optical image ( ! ball 9 ! mirror4 ,illu/ration3 ,,fig4 #b4 ,n[1 suppose a second v l>ge %eet ( t9foil to be plac$ p>allel to ! fir/ %eet1 s t ! small electrifi$ sph]e is betwe5 ! two %eets1 & t ?is second %eet is also connect$ to ! e>?4 ,! *>ge on ! ball induces negative electricity on bo? %eets1 b besides ?is ea* %eet by its *>ge influ5ces ! o!r4 ,! problem ( di/ribution is mu* m complicat$ ?an 9 ! case ( a s+le %eet1 b its solution is capable ( v simple /atem5t4 ,let u call ! two %eets ,a & ,b 7,fig4 #b71 & reg>d !m = ! mom5t z mirrors4 ,a fir/ image ( an object ,p betwe5 ! two mirrors is produc$ directly by ea*1 b ! image ,i 9 ,a is virtually an object 9 front ( ,b1 & ! image ,j 9 ,b an object 9 front ( ,a1 s t a second image m remote f ! mirror ?an ! fir/ is produc$ 9 ea* case4 ,^! second images ,i & ,j 9 ! same way produce ?ird images /ill m remote1 & s on4 ,! positions are det]m9$ j z = an object & a s+le mirror4 ,!re is ?us an inf9ite trail ( images beh9d ea* mirror1 ! places ( :i* any "o c assign4 ,illu/ration3 ,,fig4 #c4 ,e "o may see ! realisation ( ?is arrangem5t 9 a %op w9d[1 ! two sides ( :i* are cov]$ by p>allel %eets ( mirror-glass4 ,an inf9ite succession ( ! objects 9 ! w9d[ is app>5tly se5 on bo? sides4 ,:5 ! objects display$ are glitt]+ new bicycles 9 a r[ ! effect is v /rik+2 b :at we are conc]n$ ) "h is a s+le small object l ! little ball1 & its two trails ( images4 ,! electric =ce at any po9t betwe5 ! two %eets ( t9foil is exactly ! same z if ! %eets 7 remov$ & *>ges alt]nately negative & positive 7 plac$ at ! image-po9ts1 negative at ! fir/ images1 positive at ! second images1 & s on1 ea* *>ge be+ ! same 9 am\nt z t on ! ball4 ,we h an electric kaleidoscope ) p>allel mirrors4 ,:5 ! angle betwe5 ! conduct+ planes is an aliquot "p ( #cfj1 let u say #fj1 ! electrifi$ po9t & ! images are situat$1 j z are ! object & its image 9 ,brew/]'s kaleidoscope1 namely at ! angul> po9ts ( a hexagon1 ! sides ( :i* are alt]nately 7z %[n 9 ,fig4 #c7 ( l5g?s twice ! di/ance ( ! electrifi$ po9t f ,a & f ,b4 ,illu/ration3 ,,fig4 #d4 ,n[ consid] ! sph]ical surface ref]r$ to at p4 #cg1 :i* is kept at uni=m pot5tial by a *>ge at ! ext]nal po9t ,p1 & a *>ge q' at ! inv]se po9t ,p' )9 ! sph]e4 ,if ,e 7,fig4 #d7 be any po9t :atev] on ! surface1 & r1 r' be its di/ances f ,p & ,p'1 x is easy to prove by geometry t ! two triangles ,,cpe & ,,cep' are simil>1 & !re=e r' raf4 ,"h af is us$ to mean a divid$ by f4 ,! m>k is adopt$ in/ead ( ! usual b> ( ! fraction1 = conv5i5ce ( pr9t+4 ,n[1 by ! explanation giv5 above1 ! pot5tial produc$ at any po9t by a *>ge q at ano!r po9t1 is equal to ! ratio ( ! *>ge q to ! di/ance betwe5 ! po9ts4 ,?us ! pot5tial at ,e due to ! *>ge q at ,p is qr1 & t at ,e due to a *>ge q' at ,p' is q'r'4 ,?us if q' qaf1 q' at ,p' w produce a pot5tial at ,e qafr' qr1 by ! value ( r4 ,h5ce q at ,p & -qaf at ,p' coexi/+ w give pot5tial qr qr or z]o1 at ,e4 ,?us ! *>ge qaf1 at ! int]nal po9t ,p' w 9 pres5ce ( q at ,p keep all po9ts ( ! sph]ical surface at z]o pot5tial4 ,^! two *>ges repres5t ! s\rce & s9k 9 ! !rmal analogue ( p4 #cg above4 ,n[ replace ,s by a sph]ical %ell ( metal connect$ to ! e>? by a long f9e wire1 & imag9e all o!r conductors to be at a great di/ance f x4 ,if ?is be "u ! influ5ce ( ! *>ge q at ,p alone1 a *>ge is induc$ ^u x :i*1 9 pres5ce ( ,p1 ma9ta9s x at z]o pot5tial4 ,! int]nal *>ge qaf1 & ! induc$ di/ribution on ! %ell are ?us equival5t z reg>ds ! pot5tial produc$ by ei!r at ! sph]ical surface2 = ea* c\nt]acts !n ! pot5tial produc$ by q at ,p4 ,b x c be prov$ t if a di/ribution ov] an equipot5tial surface c be made to produce ! same pot5tial ov] t surface z a giv5 int]nal di/ribution does1 !y produce ! same pot5tials at all ext]nal po9ts1 or1 z x is usually put1 ! ext]nal fields are ! same4 ,?is is "p ( ! /atem5t ( :at has be5 call$ ! !orem ( replacem5t discov]$ by ,gre51 ,gauss1 ,?omson1 & ,*asles z describ$ above4 ,ano!r "p ( ! /atem5t ( ! !orem may n[ be =mulat$4 ,c\lomb %[$ long ago t ! surface-d5sity ( electricity at any po9t on a conductor is proportional to ! resultant field-int5sity j outside ! surface at t po9t4 ,s9ce ! surface is ?r\gh\t at "o pot5tial ?is int5sity is normal to ! surface4 ,let x be d5ot$ by ,n1 & s be ! surface-d5sity3 !n accord+ to ! sy/em ( units usually adopt$ #ds ,n4 ,let n[ ! rate ( dim9ution ( pot5tial p] unit ( di/ance outw>ds 7or d[nw>d gradi5t ( pot5tial7 f ! equipot5tial surface be det]m9$ = e po9t ( ! surface1 & let electricity be di/ribut$ ov] ! surface1 s t ! am\nt p] unit area at ea* po9t 7! surface-d5sity7 is made num]ically equal to ! gradi5t !re divid$ by #d4 ,?is1 by ,c\lomb's law1 /at$ above1 gives t field-int5sity j outside ! surface :i* exi/s = ! actual di/ribution1 & !re=e1 z c be prov$1 gives ! same field ev]y:]e else outside ! surface4 ,! ext]nal fields w !re=e be equival5t1 & fur!r1 ! am\nt ( electricity on ! surface w be ! same z t situat$ )9 x 9 ! actual di/ribution4 ,?us x is only necess>y to f9d = qaf at ,p' & q at ,p1 ! fall+ (f gradi5t ,n ( pot5tial outside ! sph]ical surface at any po9t ,e1 & to take ,n#d1 to obta9 s ! surface-d5sity at ,e4 ,calculation ( ?is gradi5t = ! sph]e gives #ds q7f a7ar4 ,! surface-d5sity is ?us inv]sely z ! cube ( ! di/ance ,,pe4 ,if ! influ5c+ po9t ,p be situat$ )9 ! sph]ical %ell1 & ! %ell be connect$ to e>? z be=e1 ! induc$ di/ribution w be on its int]ior surface4 ,! correspond+ po9t ,p w n[ be outside1 b giv5 by ! same relation4 ,& a w n[ be great] ?an f1 & ! d5sity w be giv5 by #ds q7a f7ar1 :]e1 f & r h ! same mean+s ) reg>d to ,e & ,p z be=e4 ,p' is 9 ea* case call$ ! image ( ,p 9 ! sph]e ,s1 & ! *>ge qaf !re suppos$ situat$ is ! electric image ( ! *>ge q at ,p4 ,x w be se5 t an electric image is a *>ge1 or sy/em ( *>ges1 on "o side ( an electrifi$ surface :i* produces on ! o!r side ( t surface ! same electrical field z is produc$ by ! actual electrification ( ! surface4 ,:ile by ! !orem ( replacem5t !re is only "o di/ribution ov] a surface :i* produces at all po9ts on "o side ( a surface ! same field z does a di/ribution ,d on ! o!r side ( ! surface1 ?is surface di/ribution may be equival5t to sev]al diff]5t arrangem5ts ( ,d4 ,?us ! po9t-*>ge at ,p' is only "o ( v>i\s image-di/ributions equival5t to ! surface-di/ribution 9 ! s5se expla9$4 ,= example1 a uni=m di/ribution ov] any sph]ical surface ) c5tre at ,p' 7,fig4 #d7 w\ld d z well1 provid$ ?is sph]ical surface 7 n l>ge en\gh to ext5d beyond ! surface ,s4 ,9 ord] to f9d ! pot5tial ( ! sph]e 7,fig4 #d7 :5 insulat$ ) a *>ge ,q ^u x1 9 pres5ce ( ! influ5c+ *>ge q at ! ext]nal po9t ,p1 x is only necess>y to imag9e uni=mly di/ribut$ ov] ! sph]e1 already electrifi$ 9 ! mann] j expla9$1 ! *>ge ,q aqf4 ,!n ! :ole *>ge w be ,q1 & ! uni=mity ( di/ribution w be di/urb$1 z requir$ by ! action ( ! influ5c+ po9t-*>ge4 ,! pot5tial w be ,qa qf4 ,= a giv5 pot5tial ,v ( ! sph]e1 ! total *>ge is a,v aqf1 t is ! *>ge is a,v ov] & above ! induc$ *>ge4 ,if in/ead ( a s+le influ5c+ po9t-*>ge at ,p !re be a sy/em ( influ5c+ po9t-*>ges at diff]5t ext]nal po9ts1 ea* ( ^! has an image-*>ge to be f\nd 9 am\nt & situation by ! me?od j describ$1 & ! induc$ di/ribution is t obta9$ by sup]impos+ all ! surface di/ributions f\nd = ! diff]5t influ5c+ po9ts4 ,! =ce ( repulsion betwe5 ! po9t-*>ge q & ! sph]e 7) total *>ge ,q7 c be f\nd at once by calculat+ ! sum ( ! =ces betwe5 q at ,p & ! *>ges ,q aqf at ,c & aqf at ,p'4 ,?is c be f\nd also by calculat+ ! en]gy ( ! sy/em1 :i* w be f\nd to consi/ ( ?ree t]ms1 "o repres5t+ ! en]gy ( ! sph]e ) *>ge ,q un9flu5c$ by an ext]nal *>ge1 "o repres5t+ ! en]gy on a small conductor 7n a po9t7 at ,p exi/+ alone1 & a ?ird repres5t+ ! mutual en]gy ( ! electrification on ! sph]e & ! *>ge q at ,p exi/+ 9 pres5ce ( "o ano!r4 ,by a kn[n !orem ! en]gy ( a sy/em ( conductors is "o half ( ! sum obta9$ by multiply+ ! pot5tial ( ea* conductor by its *>ge & add+ ! products toge!r4 ,x is only necess>y !n to f9d ! v>iation ( ! la/ t]m caus$ by increas+ f by a small am\nt df4 ,?is w be ! product ,f4df ( ! =ce ,f requir$ & ! displacem5t4 ,ei!r me?od may be appli$ to f9d ! =ces ( attraction & repulsion = ! sy/ems ( electrifi$ sph]es describ$ bel[4 ,! problem ( two mutually influ5c+ non-int]sect+ sph]es1 ,s1 ,s 7,fig4 #e71 insulat$ ) giv5 *>ges1 q1 q1 may n[ be dealt ) 9 ! foll[+ mann]4 ,let ea* be suppos$ at fir/ *>g$ uni=mly4 ,by ! kn[n !orem ref]r$ to above1 ! ext]nal field ( ea* is ! same z if its :ole *>ge 7 situat$ at ! c5tre4 ,n[ if ! di/ribution on ,s1 say1 be kept unalt]$1 :ile t on ,s is all[$ to *ange1 ! action ( ,s on ,s is ! same z if ! *>ge q 7 at ! c5tre ,c ( ,s4 ,?us if f be ! di/ance betwe5 ! c5tres ,c1 ,c1 & a be ! radius ( ,s1 ! di/ribution w be t correspond+ to q aqf uni=mly di/ribut$ on ,s toge!r ) ! induc$ *>ge aqf1 :i* corresponds to ! image-*>ge at ! po9t ,i 7)9 ,s71 ! inv]se ( ,c ) respect to ,s4 ,n[ let ! *>ge on ,s be fix$ 9 ! /ate j suppos$ :ile t on ,s is fre$4 ,! *>ge on ,s w re>range itself "u ! influ5ce ( q aqf 7 q'7 & aqf1 consid]$ z at ,c & ,i respectively4 ,! =m] ( ^! w give a di/ribution equival5t to q aq'f uni=mly di/ribut$ ov] ,s1 & an induc$ di/ribution ( am\nt aq'f at ,j1 ! inv]se po9t ( ,c ) reg>d to ,s4 ,! image-*>ge aqf at ,i 9 ,s w react on ,s & give an induc$ di/ribution a7aqf7f'1 7,i,c f'7 correspond+ to an image-*>ge aaqff' at ! inv]se po9t ,j ( ,p ) respect to ,c,s4 ,?us ! di/ribution on ,s is equival5t to q aq'f aaqff' di/ribut$ uni=mly ov] x1 toge!r ) ! two induc$ di/ributions j describ$4 ,illu/ration3 ,,fig4 #e4 ,9 ! same way ^! two induc$ di/ributions on ,s may n[ be reg>d$ z react+ on ! di/ribution on ,s z w\ld po9t-*>ges aqf & aaqff'1 situat$ at ,j & ,j respectively1 & w\ld give two induc$ di/ributions on ,s correspond+ to _! images 9 ,s4 ,?us by p>tial influ5ces 9 un5d+ succession ! equilibrium /ate ( ! two sph]es c\ld be approximat$ to z ne>ly z may be desir$4 ,an inf9ite trail ( electric images )9 ea* ( ! two sph]es is ?us obta9$1 & ! f9al /ate ( ea* conductor c be calculat$ by summation ( ! effects ( ea* set ( images4 ,if ! f9al pot5tials1 ,v1 ,v1 say1 ( ! sph]es are giv5 ! process is some:at simpl]4 ,let fir/ ! *>ges be suppos$ to exi/ uni=mly di/ribut$ ov] ea* sph]e1 & to be ( am\nt a,v1 a,v 9 ! two cases4 ,! uni=m di/ribution on ,s w raise ! pot5tial ( ,s above ,v1 & to br+ ! pot5tial d[n to ,v 9 pres5ce ( ?is di/ribution we mu/ place an induc$ di/ribution ov] ,s1 repres5t$ z reg>ds ! ext]nal field by ! image-*>ge aa,vf 7at ! image ( ,c 9 ,s7 :]e f is ! di/ance betwe5 ! c5tres4 ,! *>ge a,v on ,s w simil>ly h an action on ,s to be comp5sat$ 9 ! same way by an image-*>ge aa,vf at ! image ( ,c 9 ,s4 ,n[ ^! two image-*>ges w react on ! sph]es ,s & ,s respectively1 & w h to be balanc$ by induc$ di/ributions repres5t$ by second image-*>ges1 to be f\nd 9 ! mann] j exemplifi$4 ,^! w aga9 react on ! sph]es & w h to be comp5sat$ z be=e1 & s on indef9itely4 ,! *>ges dim9i% 9 am\nt1 & _! positions approximate m & m1 accord+ to def9ite laws1 & ! f9al /ate is to be f\nd by summation z be=e4 ,! =ce ( repulsion is to be f\nd by summ+ ! =ces betwe5 all ! diff]5t pairs ( *>ges :i* c be =m$ by tak+ "o *>ge ( ea* sy/em at its prop] po9t3 or x c be obta9$ by calculat+ ! en]gy ( ! sy/em4 ,! me?od ( successive influ5ces 0 giv5 orig9ally by ,murphy1 b ! mode ( repres5t+ ! effects ( ! successive induc$ *>ges by image-*>ges is due to ,?omson4 ,q ano!r solution ( ?is problem is1 h[ev]1 possible by ,?omson's me?od ( electrical inv]sion4 ,a simil> process to t j expla9$ = two *>g$ & mutually influ5c+ sph]es w give ! di/ribution on two conc5tric conduct+ sph]es1 "u ! influ5ce ( a po9t-*>ge q at ,p betwe5 ! inn] surface ( ! out] & ! out] surface ( ! inn]1 z %[n 9 ,fig4 #g4 ,!re ! influ5ce ( q at ,p1 & ( ! induc$ di/ributions on "o ano!r1 is repres5t$ by two s]ies ( images1 "o )9 ! inn] sph]e & "o outside ! out]4 ,^! *>ges & positions c be calculat$ f ! result = a s+le sph]e & po9t-*>ge4 ,?omson's me?od ( electrical inv]sion1 ref]r$ to above1 enabl$ ! solutions ( unsolv$ problems to be inf]r$ f kn[n solutions ( simpl] cases ( di/ribution4 ,we give "h a brief acc\nt ( ! me?od1 & "s ( its results4 ,fir/ we h to recall ! mean+ ( geometrical inv]sion4 ,9 ,fig4 #f ! di/ances ,,op1 ,,op1 ,,oq1 ,,oq' fulfil ! relation ,,op4,,op' ,,oq4,,oq' a4 ,?us ,p' is 7see p4 #cg7 ! inv]se ( ! po9t ,p ) respect to a sph]e ( radius a & c5tre ,o 7indicat$ by ! dott$ l9e 9 ,fig4 #f71 & simil>ly ,q' is ! inv]se ( ,q ) respect to ! same sph]e & c5tre4 ,o is call$ ! c5tre ( inv]sion1 & ! sph]e ( radius a is call$ ! sph]e ( inv]sion4 ,?us ! sph]e ( ,figs4 #a & #d is ! sph]e ( inv]sion = ! po9ts ,p & ,p'1 :i* are inv]se po9ts ( "o ano!r4 ,= any sy/em ( po9ts ,p1 ,q1 4441 ano!r sy/em ,p'1 ,q'1 444 ( inv]se po9ts c be f\nd1 & if ! fir/ sy/em =m a def9ite locus1 ! second w =m a d]iv$ locus1 :i* is call$ ! inv]se ( ! =m]4 ,also if ,p'1 ,q'1 444 be reg>d$ z ! direct sy/em1 ,p1 ,q1 444 w be ! correspond+ inv]se sy/em ) reg>d to ! same sph]e & c5tre4 ,p' is ! image ( ,p1 & ,p is ! image ( ,p'1 & s on1 ) reg>d to ! same sph]e & c5tre ( inv]sion4 ,illu/ration3 ,,fig4 #f4 ,! inv]se ( a circle is ano!r circle1 & !re=e ! inv]se ( a sph]e is ano!r sph]e1 & ! inv]se ( a /raight l9e is a circle pass+ ?r\gh ! c5tre ( inv]sion1 & ( an inf9ite plane a sph]e pass+ ?r\gh ! c5tre ( inv]sion4 ,obvi\sly ! inv]se ( a sph]e conc5tric ) ! sph]e ( inv]sion is a conc5tric sph]e4 ,! l9e ,p',q' is ( c\rse n ! inv]se ( ! l9e ,,pq1 :i* has = its inv]se ! circle pass+ ?r\gh ! ?ree po9ts ,o1 ,p'1 ,q'1 z indicat$ 9 ,fig4 #f4 ,! foll[+ results are easily prov$4 ,a locus & its inv]se cut any l9e ,,op at ! same angle4 ,to a sy/em ( po9t-*>ges q1 q1 444 at po9ts ,p1 ,p1 444 on "o side ( ! surface ( ! sph]e ( inv]sion !re is a sy/em ( *>ges aqf1 aqf1 444 on ! o!r side ( ! sph]ical surface ,,op f1 ,,op f4 ,?is inv]se sy/em1 z we %all call x1 produces ! same pot5tial at any po9t ( ! sph]e ( inv]sion1 z does ! direct sy/em f :i* x is d]iv$4 ,if ,v1 ,v' be ! pot5tials produc$ by ! :ole direct sy/em at ,q1 & by ! :ole inv]se sy/em at ,q'1 ,v',v ra ar'1 :]e ,,oq r1 ,,oq' r'4 ,?us if ,v is con/ant ov] any surface ,s'1 ,v' is n a con/ant ov] ! inv]se surface ,s'1 unless r is a con/ant1 t is1 unless ! surface ,s' is a sph]e conc5tric ) ! sph]e ( inv]sion1 9 :i* case ! inv]se surface is conc5tric ) x & is an equipot5tial surface ( ! inv]se di/ribution4 ,fur!r1 if q be di/ribut$ ov] an elem5t d,s ( a surface1 ! inv]se *>ge aqf w be di/ribut$ ov] ! correspond+ elem5t d,s' ( ! inv]se surface4 ,b d,s'd,s af f'a :]e f1 f' are ! di/ances ( ,o f d,s & d,s'4 ,?us if s be ! d5sity on d,s & s' ! inv]se d5sity on d,s' we h s's af' fa4 ,:5 ,v is con/ant ov] ! direct surface1 :ile r has diff]5t values = diff]5t directions ( ,,oq1 ! diff]5t po9ts ( ! inv]se surface may be br\ght to z]o pot5tial by plac+ at ,o a *>ge a,v4 ,= ?is w produce at ,q' a pot5tial a,vr' :i* ) ,v' w give at ,q' a pot5tial z]o4 ,?is %[s t ,v' is ! pot5tial ( ! induc$ di/ribution on ,s' due to a *>ge a,v at ,o1 or t ,v' is ! pot5tial due to ! induc$ *>ge on ,s' produc$ by ! *>ge a,v at ,o4 ,?us we h ! conclusion t by ! process ( inv]sion we get f a di/ribution 9 equilibrium1 on a conductor ( any =m1 an induc$ di/ribution on ! inv]se surface suppos$ insulat$ & conduct+2 & conv]sely we obta9 f a giv5 induc$ di/ribution on an insulat$ conduct+ surface1 a natural equilibrium di/ribution on ! inv]se surface4 ,9 ea* case ! induc+ *>ge is situat$ at ! c5tre ( inv]sion4 ,! *>ges on ! conductor 7or conductors7 aft] inv]sion are always obta9able at once f ! fact t !y are ! inv]ses ( ! *>ges on ! conductor 7or conductors7 9 ! direct case1 & ! surface-d5sities or volume-d5sities c be f\nd f ! relations /at$ above4 ,illu/ration3 ,,fig4 #g4 ,n[ take ! case ( two conc5tric sph]es insulat$ & influ5c$ by a po9t-*>ge q plac$ at a po9t ,p betwe5 !m z %[n 9 ,fig4 #g4 ,we h se5 at p4 #di h[ ! induc$ di/ribution1 & ! am\nt ( ! *>ge1 on ea* sph]e is obta9$ f ! two conv]g5t s]ies ( images1 "o outside ! out] sph]e1 ! o!r inside ! inn] sph]e4 ,we d n "h calculate ! d5sity ( di/ribution at any po9t1 z our object is only to expla9 ! me?od2 b ! quantities on ! sph]es ,s & ,s1 are respectively q4,,oa4,,pb7,,op4,,ab71 q4,,ob4,,ap7,,op4,,ab74 ,x may be notic$ t ! sum ( ! induc$ *>ges is q1 & t z ! radii ( ! sph]es are bo? made indef9itely great1 :ile ! di/ance ,,ab is kept f9ite1 ! ratios ,,oa,,op1 ,,ob,,op approximate to unity1 & ! *>ges to q4,,pb,,ab1 q4,,ap,,ab1 t is1 ! *>ges are inv]sely z ! di/ances ( ,p f ! ne>e/ po9ts ( ! two surfaces4 ,b :5 ! radii are made indef9itely great we h ! case ( two inf9ite plane conduct+ surfaces ) a po9t-*>ge betwe5 !m1 :i* we h describ$ above4 ,n[ let ?is induc$ di/ribution1 on ! two conc5tric sph]es1 be inv]t$ f ,p z c5tre ( inv]sion4 ,we obta9 two non-int]sect+ sph]es1 z 9 ,fig4 #e1 = ! inv]se geometrical sy/em1 & = ! inv]se electrical sy/em an equilibrium di/ribution on ^! two sph]es 9 pres5ce ( "o ano!r1 & *>g$ ) ! *>ges :i* are ! inv]ses ( ! induc$ *>ges4 ,^! ma9ta9 ! sy/em ( two sph]es at "o pot5tial4 ,f ?is inv]sion x is possible to proce$ z %[n by ,maxwell 9 8 ,electricity & ,magnetism1 vol4 i1 #agc1 to ! di/ribution on two sph]es at two diff]5t pot5tials2 b we h %[n above h[ ! problem may be dealt ) directly by ! me?od ( images4 ,illu/ration3 ,,fig4 #h4 ,aga9 take ! case ( two p>allel inf9ite planes "u ! influ5ce ( a po9t-*>ge betwe5 !m4 ,?is sy/em inv]t$ f ,p z c5tre gives ! equilibrium di/ribution on two *>g$ insulat$ sph]es 9 contact 7,fig4 #h72 = ?is sy/em is ! inv]se ( ! planes & ! *>ges ^u !m4 ,ano!r int]e/+ case is t ( ! electric kaleidoscope ref]r$ to above4 ,"h ! two inf9ite conduct+ planes are incl9$ at an angle #cfjn1 :]e n is a :ole numb]1 & are !re=e b\nd$ 9 "o direction by ! /raight l9e :i* is _! int]section4 ,! image po9ts ,i1 ,j1 4441 ( ,p plac$ 9 ! angle betwe5 ! planes are situat$ z %[n 9 ,fig4 #c1 & are n #a 9 numb]4 ,?is sy/em inv]t$ f ,p z c5tre gives two sph]ical surfaces :i* cut "o ano!r at ! same angle z d ! planes4 ,?is sy/em is "o ( electrical equilibrium 9 free space1 & !re=e ! problem ( ! di/ribution on two int]sect+ sph]es is solv$1 = ! case at lea/ 9 :i* ! angle ( int]section is an aliquot "p ( #cfj4 ,:5 ! planes are at "r angles ! result is t = two p]p5dicul>ly int]sect+ planes1 = :i* ,fig4 #i gives a diagram4 ,illu/ration3 ,,fig4 #i4 ,b ! greate/ a*ievem5t ( ! me?od 0 ! det]m9ation ( ! di/ribution on a segm5t ( a ?9 sph]ical %ell ) edge 9 "o plane4 ,! solution ( ?is problem 0 communicat$ to ,m4 ,li\ville 9 ! lett] ( date ,septemb] #af1 #ahdf1 ref]r$ to above1 b )\t pro(1 :i* ,?omson /at$ he _h n "t to write out ow+ to prep>ation = ! comm5cem5t ( 8 duties z ,pr(essor ( ,natural ,philosophy at ,glasg[ on ,novemb] #a1 #ahdf4 ,x 0 n suppli$ until ,decemb] #ahfh & ,janu>y #ahfi2 & 9 ! meantime ! problem _h n be5 solv$ by any o!r ma!matician4 ,z a />t+ po9t = ?is inve/igation ! di/ribution on a ?9 plane circul> disk ( radius a is requir$4 ,?is c be obta9$ by consid]+ ! disk z a limit+ case ( an oblate ellipsoid ( revolution1 *>g$ to pot5tial ,v1 say4 ,if ,fig4 #aj repres5t ! disk & ,p ! po9t at :i* ! d5sity is s\ght1 s t ,,cp r1 & ,,ca a1 ! d5sity is ,v#b7;a r74 ,! ratio q,v1 ( *>ge to pot5tial1 :i* is call$ ! electro/atic capacity ( ! conductor1 is ?us #b;a1 t is a#a4ega4 ,x is1 z ,?omson notes 9 8 pap]1 v rem>kable t ! ,hon4 ,h5ry ,cav5di% %\ld h f\nd long ago by exp]im5t ) ! rude/ app>atus ! electro/atic capacity ( a disk to be #aa4eg ( t ( a sph]e ( ! same radius4 ,illu/ration3 ,,fig4 #aj4 ,illu/ration3 ,,fig4 #aa4 ,n[ inv]t ?is disk di/ribution ) any po9t ,q z c5tre ( inv]sion1 & ) radius ( inv]sion a4 ,! geometrical inv]se is a segm5t ( a sph]ical surface :i* passes ?r\gh ,q4 ,! inv]se di/ribution is ! induc$ di/ribution on a conduct+ %ell un9sulat$ & co9cid5t ) ! segm5t1 & "u ! influ5ce ( a *>ge a,v situat$ at ,q 7,fig4 #aa74 ,call ?is conduct+ %ell ! b[l4 ,if ! surface-d5sities at correspond+ po9ts on ! disk & on ! inv]se1 say po9ts ,p & ,p'1 be s & s'1 !n1 z on page #ea1 s' sa,,qp'4 ,if we put 9 ! value ( s giv5 above1 t ( s' c be put 9 a =m giv5 by ,?omson1 :i* x is important to rem>k is indep5d5t ( ! radius ( ! sph]ical surface4 ,?is expression is applicable to ! o!r side ( ! b[l1 inasmu* z ! d5sities at ne> po9ts on opposite sides ( ! plane disk are equal4 ,if v1 v' be ! pot5tials at any po9t ,r ( space1 due to ! disk & to its image respectively1 v' av,,qr4 ,if !n ,r be co9cid5t ) a po9t ,p' on ! sph]ical segm5t we h 7s9ce !n v ,v7 ,v' a,v,,qp'1 :i* is ! pot5tial due to ! induc$ di/ribution caus$ by ! *>ge a,v at ,q z already /at$4 ,! fact t ! value ( s' does n involve ! radius makes x possible to suppose ! radius inf9ite1 9 :i* case we h ! solution = a circul> disk un9sulat$ & "u ! influ5ce ( a *>ge ( electricity at a po9t ,q 9 ! same plane b outside ! b\nd+ circle4 ,n[ consid] ! two p>ts ( ! sph]ical surface1 ! b[l ,b1 & ! rema9d] ,s ( ! sph]ical surface4 ,q ) ! *>ge a,v may be reg>d$ z situat$ on ! latt] "p ( ! surface4 ,any o!r influ5c+ *>ges situat$ on ,s w give di/ributions on ! b[l to be f\nd z describ$ above1 & ! result+ induc$ electrification c be f\nd f ^! by summation4 ,if ,s be uni=mly electrifi$ to d5sity s1 & held s electrifi$1 ! induc+ di/ribution w be "o giv5 by integration ov] ! :ole ( ,s1 & ! b[l ,b w be at z]o pot5tial "u ! influ5ce ( ?is electrification ( ,s1 j z if ,b 7 replac$ by a %ell ( metal connect$ to ! e>? by a long f9e wire4 ,! d5sities are equal at inf9itely ne> po9ts on ! two sides ( ,b4 ,let ! b[l be a ?9 metal %ell connect$ ) ! e>? by a long ?9 wire & be surr\nd$ by a conc5tric & complete %ell ( diamet] f great] ?an t ( ! sph]ical surface1 & let ?is %ell be rigidly electrifi$ ) surface d5sity s4 ,!re w be no =ce )9 ?is %ell due to its own electrification1 & h5ce x w produce no *ange ( ! di/ribution 9 ! int]ior4 ,b ! pot5tial )9 w be #b;fs1 = ! *>ge is fs1 & ! capacity ( ! %ell is f4 ,! pot5tial ( ! b[l w n[ be z]o1 & its electrification w j neutralise ! pot5tial -#b;fs1 t is1 w be exactly ! free electrification requir$ to produce pot5tial #b;fs4 ,to f9d ?is electrification let ! value ( f be only inf9itesimally great] ?an ! diamet] ( ! sph]ical surface ( :i* ,b is a "p2 !n ! b[l is "u ! influ5ce 7#a7 ( a uni=m electrification ( d5sity s inf9itely close to its out] surface1 & 7#b7 ( a uni=m electrification ( ! same d5sity1 :i* may be reg>d$ z ^u ! surface :i* has be5 call$ ,s above4 ,x is obvi\s t by 7#a7 a d5sity s is produc$ on ! out] surface ( ! b[l1 & no o!r effect2 by 7#b7 an equal d5sity at inf9itely ne> po9ts on ! opposite sides ( ! b[l is produc$ :i* we h se5 h[ to calculate4 ,?us ! di/ribution on ! b[l freely electrifi$ is completely det]m9$ & ! d5sity c easily be calculat$4 ,! value w be f\nd 9 ,?omson's pap]4 ,int]e/+ results are obta9$ by dim9i%+ ,s m & m until ! %ell is a complete sph]e ) a circul> hole 9 x4 ,tabulat$ results = diff]5t relative dim5sions ( ,s w be f\nd 9 ,?omson's pap]1 ,repr9t ( ,pap]s1 ,articles ,v1 ,,xiv1 ,,xv4 ,also ! read] w !re f9d full p>ticul>s ( ! ma!matical calculations indicat$ 9 ?is *apt]1 & an ext5sion ( ! me?od to ! case ( an influ5c+ po9t n on ! sph]ical surface ( :i* ! %ell =ms "p4 ,fur!r developm5ts ( ! problem h be5 work$ out by o!r writ]s1 & fur!r in=mation ) ref]5ces w be f\nd 9 ,maxwell's ,electricity & ,magnetism1 loc4 cit4 ,x is n q cle> :e!r ,?omson discov]$ geometrical inv]sion indep5d5tly or n3 v likely he did4 ,8 lett] to ,li\ville ( date ,octob] #h1 #ahde1 c]ta9ly reads z if he claim$ ! geometrical trans=mation z well z ! application to electricity4 ,li\ville1 h[ev]1 9 8 ,note 9 :i* he dwells on ! analytical !ory ( ! trans=mation says1 ,la trans=mation dont il s'agit e/ bi5 connue1 du re/e1 et des plus simples2 c'e/ celle que ,m4 ,?omson lui-mme a jadis employe s\s le nom de pr9cipe des images4 ,9 ,?omson & ,tail's ,natural ,philosophy1 #eac1 ! ref]5ce to ! me?od is z foll[s3 ,irrespectively ( ! special electric application1 ! me?od ( images gives a rem>kable k9d ( trans=mation :i* is (t5 useful4 ,x sugge/s = m]e geometry :at has be5 call$ ! trans=mation by reciprocal radius-rectors1 t is to say4444 ,!n ,maxwell1 9 8 review ( ! ,repr9t ( ,pap]s 7,nature1 vol4 vii71 aft] ref]r+ to ! fact t ! solution ( ! problem ( ! sph]ical b[l rema9$ undemon/rat$ f #ahdf to #ahfi1 says t ! geometrical idea ( inv]sion _h probably be5 discov]$ & r$iscov]$ repeat$ly1 b t 9 8 op9ion mo/ ( ^! discov]ies 7 lat] ?an #ahde1 ! date ( ,?omson's fir/ pap]4#aj ,a v g5]al me?od ( f9d+ ! pot5tial at any po9t ( a region ( space enclos$ by a giv5 b\nd>y 0 /at$ by ,gre5 9 8 ',essay' = ! case 9 :i* ! pot5tial is kn[n = e po9t ( ! b\nd>y4 ,! success ( ! me?od dep5ds on f9d+ a c]ta9 function1 n[ call$ ,gre5's function4 ,:5 ?is is kn[n ! pot5tial at any po9t is at once obta9$ by an integration ov] ! surface4 ,?omson's me?od ( images am\nts to f9d+ = ! case ( a region b\nd$ by "o sph]ical surface or m ! prop] value ( ,gre5's function4 ,gre5's me?od has be5 successfully employ$ 9 m complicat$ cases1 & is n[ a p[]ful me?od ( attack = a l>ge range ( problems 9 o!r dep>tm5ts ( physical ma!matics4 ,?omson only obta9$ a copy ( ,gre5's pap] 9 ,janu>y #ahde1 & probably work$ out 8 solutions q indep5d5tly ( any ideas d]iv$ f ,gre5's g5]al !ory4 ,,*apt] ,v ,,! ,,*air ,,( ,,natural ,,philosophy ,,at ,,glasg[4 ,,e/abli%m5t ,,( ,,! ,,fir/ ,,physical ,,laboratory ,! incumb5t ( ! ,*air ( ,natural ,philosophy 9 ! ,univ]sity ( ,glasg[1 ,pr(essor ,meikleham1 _h be5 9 fail+ heal? = sev]al ye>s1 & f #ahdb to #ahde 8 duties _h be5 dis*>g$ by ano!r memb] ( ! ,?omson g5s1 ,mr4 ,david ,?omson1 ,b4,a41 ( ,tr9ity ,college1 ,cambridge1 aft]w>ds ,pr(essor ( ,natural ,philosophy at ,ab]de54 ,dr4 ,meikleham di$ 9 ,may #ahdf1 & ! ,faculty !reaft] proce$$ on ! invitation ( ,dr4 ,j4 ,p4 ,ni*ol1 ! ,pr(essor ( ,a/ronomy1 to consid] :e!r 9 consequ5ce ( ! great advances ( physical sci5ce dur+ ! prec$+ qu>t] ( a c5tury x 0 n urg5tly necess>y to remodel ! arrangem5ts = ! tea*+ ( natural philosophy 9 ! ,univ]sity4 ,! advance ( sci5ce _h inde$ be5 v great4 ,o]/$ & ,ampre1 ,h5ry & ,f>aday & ,regnault1 ,gauss & ,web]1 _h made discov]ies & introduc$ quantitative ideas1 :i* _h *ang$ ! :ole aspect ( exp]im5tal & ma!matical physics4 ,! electrical discov]ies ( ! "t react$ on ! o!r bran*es ( natural philosophy1 & 9 no small degree on ma!matics itself4 ,z a result ! progress ( t p]iod has cont9u$ & has increas$ 9 rapidity1 until n[ ! accumulat$ results1 = ! mo/ "p already unit$ 9 ! grasp ( rational !ory1 h gone f> beyond ! p[] ( any s+le man to foll[1 mu* less to ma/]4 ,x is int]e/+ to look into a c\rse ( lectures su* z 7 usually deliv]$ 9 ! univ]sities a hundr$ ye>s ago by ! ,pr(essor ( ,natural ,philosophy4 ,we f9d a little discussion ( me*anics1 hydro/atics & pneumatics1 a little heat1 & a v little optics4 ,electricity & magnetism1 :i* 9 our day h a lit]ature f> exce$+ t ( ! :ole ( physics only sixty ye>s ago1 c\ld h>dly be said to exi/4 ,! pr(essor ( ! beg9n+ ( ! n9ete5? c5tury1 :5 ,"l ,kelv9's pr$ecessor 0 appo9t$1 app>5tly f\nd himself q free to devote a consid]able "p ( ea* lecture to reflections on ! beauties ( nature1 & to rhetorical flights fitt] = ! pulpit ?an = ! physics lecture-table4 ,9 ! int]v5+ "t ! =m & fa%ion ( sci5tific lectures has entirely *ang$1 & ! *ange is a te/imony to ! progress ( sci5ce4 ,x is visible ev5 9 ! design ( ! app>atus4 ,microscopes1 = example1 h a p]fection & a p[] undream$ ( by our great-gr&fa!rs1 & !y are support$ on /&s :i* lack ! ornam5tation ( t bygone "t1 b possess /ability & conv5i5ce4 ,ev]y?+ & ev]ybody--ev5 ! pr(essor1 if t be possible--mu/ be bus9ess-l2 & ea* mom5t ( "t mu/ be utilis$ 9 exp]im5ts = demon/ration1 n = applause1 & 9 brief & cog5t /atem5ts ( !ory & fact4 ,to wa/e "t 9 talk t is n to ! po9t is crim9al4 ,b )al !re is ne$ ( grace ( expression & vividness ( description1 ( cle>ness ( exposition1 ( imag9ation1 ev5 ( poetical intuition3 b ! /]n beauty ( mod]n sci5ce is only disfigur$ by ! old artificial adornm5ts & irrelevancies4 ,?is is ! tone & temp] ( sci5ce at ! pres5t day3 ! task is imm5se1 ! "t is %ort4 ,& sixty ye>s s9ce "s t+e ( ! same ca/ ( ?\ght 0 visible 9 sci5tific work]s & tea*]s4 ,! ,faculty agre$ ) ,dr4 ,ni*ol t !re 0 ne$ to br+ physical tea*+ & equipm5t into l9e ) ! /ate ( sci5ce at ! "t2 b !y wisely decid$ to d no?+ until !y _h appo9t$ a ,pr(essor ( ,natural ,philosophy :o w\ld be able to advise !m fully & 9 detail4 ,!y det]m9$1 h[ev]1 to make ! appo9tm5t subject to su* alt]ations 9 ! arrangem5ts ( ! dep>tm5t z !y might aft]w>ds f9d desirable4 ,on ,septemb] #aa1 #ahdf1 ! ,faculty met1 & hav+ consid]$ ! resolutions :i* _h be5 propos$ by ,dr4 ,ni*ol1 resolv$ to ! effect t ! appo9tm5t ab\t to be made %\ld n prejudice ! "r ( ! ,faculty to orig9ate or support1 dur+ ! incumb5cy ( ! new pr(essor1 su* *anges 9 ! arrangem5ts = conduct+ in/ruction 9 physical sci5ce z x might be exp$i5t to adopt1 & t ?is resolution %\ld be communicat$ to ! c&idate elect$4 ,! m9ute !n runs3 ,! ,faculty hav+ delib]at$ on ! respective qualifications ( ! g5tlem5 :o h ann\nc$ !mselves c&idates = ?is *air1 & ! vote hav+ be5 tak51 x c>ri$ unanim\sly 9 fav\r ( ,mr4 ,william ,?omson1 ,b4,a41 ,fell[ ( ,/4 ,pet]'s ,college1 ,cambridge1 & =m]ly a /ud5t ( ?is ,univ]sity1 :o is accord+ly decl>$ to be duly elect$3 & ,mr4 ,?omson be+ )9 call appe>$ 9 ,faculty1 & ! :ole ( ?is m9ute hav+ be5 read to him he agre$ to ! resolution ( ,faculty above record$ & accept$ ! (fice4 ,x 0 also resolv$ z foll[s3 ,! ,faculty h]eby prescribe ,mr4 ,?omson an essay on ! subject1 ,de caloris di/ributione p] t]r corpus1 & resolve t 8 admission be on ,tuesday ! #ac? ,octob]1 provid$ t he %all be f\nd qualifi$ by ! ,meet+ & %all h tak5 ! oa? & made ! subscriptions :i* are requir$ by law4 ,at t "t1 & d[n to )9 ! la/ fifte5 ye>s1 e pr(essor1 be=e 8 induction to 8 *air1 _h to submit a ,lat9 essay on "s prescrib$ subject4 ,?is 0 almo/ ! la/ relic ( ! cu/oms ( ! days :5 univ]sity lectures 7 deliv]$ 9 ,lat91 a practice :i* appe>s to h be5 fir/ brok5 ?r\gh by ,adam ,smi? :5 ,pr(essor ( ,moral ,philosophy4 ,:atev] x may h be5 9 ! eighte5? c5tury1 ! ,lat9 essay at ! end ( ! n9ete5? 0 p]haps h>dly an infallible crit]ion ( ! pr(essor-elect's ,lat9ity1 & x 0 j z well to disc>d x4 ,b fifty ye>s be=e1 & = long aft]1 classical languages bulk$ l>gely 9 ! curriculum ( e /ud5t ( ! ,scotti% ,univ]sities1 & x is und\bt$ly ! case t mo/ ( ^? :o aft]w>ds came to em95ce 9 o!r dep>tm5ts ( le>n+ _h 9 _! "t acquitt$ !mselves well 9 ! old ,litt] ,humaniores4 ,?is 0 true1 z we h se51 ( ,?omson1 & x is unlikely t ! =m ( 8 inaugural diss]tation co/ him mu* m ef=t ?an its matt]4 ,illu/ration3 ,,pr(essor ,,william ,,?omson1 #ahdf ,! subject *os5 _h ref]5ce no d\bt to ! pap]s on ! !ory ( heat :i* ,mr4 ,?omson _h already publi%$4 ,! !sis 0 pres5t$ to ! ,faculty on ! day appo9t$1 & approv$1 & ,mr4 ,?omson hav+ produc$ a c]tificate ( 8 hav+ tak5 ! oa?s to gov]nm5t1 & promis$ to subscribe ! =mula ( ! ,*ur* ( ,scotl& z requir$ by law1 on ! fir/ conv5i5t opportunity1 ! foll[+ oa? 0 !n adm9i/]$ to him1 :i* he took & subscrib$3 ,ego1 ,gulielmus ,?omson1 ,b4,a41 physicus pr(essor 9 hac ,academia designatus1 promitto sancteque polliceor me 9 mun]e mihi dem&ato /udiose fidelit]que v]saturum4 ,pr(essor ,?omson 0 !n solemnly admitt$ & receiv$ by all ! ,memb]s pres5t1 & took 8 seat z a ,memb] ( ,faculty4 ,no translation ( ?is essay 0 ev] publi%$1 b its sub/ance 0 conta9$ 9 v>i\s pap]s :i* appe>$ lat]4 ,! foll[+ ref]5ce to x is made 9 an introduction atta*$ to ,article ,,xi ( 8 ,ma!matical & ,physical ,pap]s 7vol4 i1 #ahhb74 ,an application to ,t]re/rial ,temp]ature1 ( ! pr9ciple set =? 9 ! fir/ "p ( ?is pap] relat+ to ! age ( !rmal di/ributions1 0 made ! subject ( ! au?or's ,inaugural ,diss]tation on ! occasion ( 8 induction to ! pr(essor%ip ( ,natural ,philosophy 9 ! ,univ]sity ( ,glasg[1 9 ,octob] #ahdf1 ',de ,motu ,caloris p] ,t]r ,corpus'#aa3 :i*1 m fully develop$ aft]w>ds1 gave a v decisive limitation to ! possible age ( ! e>? z a habitation = liv+ creatures2 & prov$ ! unt5ability ( ! enorm\s claims = ,,"t :i*1 uncurb$ by physical sci5ce1 geologi/s & biologi/s _h begun to make & to reg>d z un*all5geable4 ,see ',secul> ,cool+ ( ! ,e>?1 ,geological ,"t1' & sev]al o!r ,articles bel[4 ,"s /atem5t ( ! argum5t = ?is limitation w be giv5 lat]4 ,see ,*ap4 ,,xiv4 ,?omson ?us ent]$ at ! age ( tw5ty-five on :at 0 to be 8 life "w z a tea*]1 inve/igator1 & inv5tor4 ,= he cont9u$ 9 (fice fifty-?ree ye>s1 s t ! unit$ t5ures ( 8 pr$ecessor & himself am\nt$ to only f\r ye>s less ?an a c5tury6 ,he took up 8 duties at ! op5+ ( ! college session 9 ,novemb]1 & promptly call$ ! att5tion ( ! ,faculty to ! defici5cies ( ! equipm5t ( app>atus1 :i* _h be5 all[$ to fall beh9d ! times1 & requir$ to h add$ to x _m new in/rum5ts4 ,a committee 0 appo9t$ to consid] ! "q & report1 & z a result ( ! repres5tations ( ?is committee a sum ( #ajj 0 plac$ at ,pr(essor ,?omson's disposal to supply 8 mo/ press+ ne$s4 ,9 ! foll[+ ye>s repeat$ applications = fur!r grants 7 made & v>i\s sums 7 vot$--n am\nt+ to m ?an #ejj or #fjj 9 all--:i* 7 app>5tly reg>d$ z 7& no d\bt 71 consid]+ ! times & ! funds at ! disposal ( ! ,faculty7 a lib]al provision = ! tea*+ ( physical sci5ce4 ,a m9ute ( ! ,faculty1 ( date ,nov4 #bf1 #ahdg1 is int]e/+4 ,aft] emphatically deprecat+ all idea t su* l>ge annual exp5diture = any "o dep>tm5t 0 to be regul>ly contemplat$1 ! committee ref] 9 _! report to ! inadequate condition ( ! dep>tm5t 9 "q1 & express _! satisfaction ) ! reasonable mann] 9 :i* ! ,pr(essor ( ,natural ,philosophy has on all occasions readily modifi$ 8 dem&s 9 accordance ) ! economical sugge/ions ( ! committee4 ,!y conclude by say+ t !y view 8 ard\r & anxiety 9 ! prosecution ( 8 pr(ession ) ! greate/ pleasure1 & he>tily concur 9 ^? anticipations ( 8 future celebrity :i* ,monsr4 ,s]ville1#ab ! ,fr5* ma!matician1 has rec5tly ?\ght fit to publi% to ! sci5tific _w4 ,aga91 9 ,april #aheb1 ! ,faculty agree to pay a sum ( #acg #fs4 #a;d4 z ! price ( pur*ases ( philosophical app>atus already made1 & approve ( a sugge/ion ( ! committee t ! exp5diture on ?is behalf dur+ ! next ye> %\ld n exce$ #ej1 & !y desire t ! pur*ases %all be made s f> z is possible ) ! previ\sly obta9$ concurr5ce ( ! committee4 ,x is easy to imag9e t ! ard5t "y ,pr(essor ( ,natural ,philosophy f\nd ! leisurely me?ods ( 8 old] colleagues mu* too sl[1 & 9 8 en?usiasm anticipat$ cons5t to 8 dem&s by ord]+ 8 new in/rum5ts )\t wait+ = committees & meet+s & reports4 ,9 an address at ! op5+ ( ! ,physical & ,*emical ,laboratories ( ! ,univ]sity ,college ( ,nor? ,wales1 on ,febru>y #b1 #ahhe1 ,sir ,william ,?omson 7z he 0 !n7 ref]r$ to 8 e>ly equipm5t & "w z foll[s3 ,:5 ,i ent]$ ^u ! pr(essor%ip ( ,natural ,philosophy at ,glasg[1 ,i f\nd app>atus ( a v old-fa%ion$ k9d4 ,mu* ( x 0 m ?an a hundr$ ye>s old1 little ( x less ?an fifty ye>s old1 & mo/ ( x 0 worm-eat54 ,/ill1 ) su* appliances1 ye> aft] ye>1 /ud5ts ( natural philosophy _h be5 br\ght toge!r & taught z well z possible4 ,! pr9ciples ( dynamics & electricity _h be5 well illu/rat$ & well taught1 z well taught z lectures & s imp]fect app>atus--b app>atus m]ely ( ! lecture-illu/ration k9d--c\ld tea*4 ,b !re 0 absolutely no provision ( any k9d = exp]im5tal inve/igation1 /ill less idea1 ev51 = any?+ l /ud5ts' practical "w4 ,/ud5ts' laboratories = physical sci5ce 7 n !n ?\ght (4#ac ,x appe>s t ! class ( ,natural ,philosophy 7!re 0 !n z a rule only "o class 9 any subject1 ?\gh supplem5t>y "w 0 done 9 v>i\s ways7 met = sy/ematic lectures at #i a4m41 :i* is ! h\r /ill adh]$ to1 & = :at 0 call$ ,exp]im5tal ,physics at #h p4m46 ,! ,univ]sity ,cal5d> = #ahfc-d /ates t ! ,natural ,philosophy ,class meets two h\rs daily1 #i a4m4 & #aa a4m4 ,! fir/ h\r is *iefly sp5t 9 /atem5ts ( ,pr9ciples1 description ( ,results ( ,obs]vation1 & ,exp]im5tal ,illu/rations4 ,! second h\r is devot$ to ,ma!matical ,demon/rations & ,ex]cises1 & ,exam9ations on all p>ts ( ! ,c\rse4 ,! ,text ,books to be us$ are3 ',elem5ts ( ,dynamics' 7fir/ "p n[ ready71 ,pr9t$ by ,george ,ri*>dson1 ,univ]sity ,pr9t]4 ',elem5ts ( ,natural ,philosophy1' by ,pr(essors ,w4 ,?omson & ,p4 ,g4 ,tait 7,two ,treatises to be publi%$ be=e ,novemb]4 ,macmillan4#ad7 ,! %ort] ( ! la/ m5tion$ ,treatises w be us$ = ! "w requir$ ( all /ud5ts ( ,natural ,philosophy 9 ! regul> curriculum4 ,! :ole or specifi$ p>ts ( ! l>g] ,treatise w be prescrib$ 9 connection ) volunt>y exam9ations & ex]cises 9 ! ,class1 & = c&idates = ! degree ( ,m4,a4 ) hon\rs4 ,/ud5ts :o desire to und]take ^! high] p>ts ( ! bus9ess ( ! class1 ought to be well prep>$ on all ! subjects ( ! ,s5ior ,ma!matical ,class4 ,! ,laboratory 9 connection ) ! class is op5 daily f #i a4m4 to #d p4m4 = ,exp]im5tal ,ex]cises & ,inve/igations1 "u ! direction ( ! ,pr(essor & 8 (ficial assi/ant4 ,9 #ahdg ! meet+s = exp]im5tal physics 7 *ang$ to #aa a4m4 ,! h\r #i a4m4 is /ill 7#aijh7 reta9$ = ! regul> meet+s ( ! ord9>y class1 & #aa a4m4 = meet+s held twice a week = ex]cises & tutorial "w1 att5dance at :i* is optional4 ,a second graduat+ class has n[ be5 in/itut$ & is v l>gely att5d$4 ,ea* /ud5t att5ds ?ree lectures & sp5ds f\r h\rs 9 ! laboratory ea* week4 ,a high] class1 9 two divisions1 is also held4 ,at an e>ly date 9 8 c>e] z a pr(essor ,?omson call$ 9 ! aid ( 8 /ud5ts = exp]im5tal rese>*4 ,9 _m directions ! prop]ties ( matt] /ill lay unexplor$1 & x 0 necess>y to obta9 exact data = ! p]fect+ ( ! !ories ( ela/icity1 electricity & heat1 :i* _h be5 bas$ on ! rese>*es ( ! fir/ half ( ! n9ete5? c5tury4 ,to ! au?ors ( ^! !ories--,gauss1 ,gre51 ,cau*y & o!rs--he 0 a fit successor4 ,n kn[+ all t _h be5 done by ^! m5 ( g5ius1 he re9v5t$1 z we h se51 "s ( _! great !orems1 & 9 some:at lat] "w1 notably 9 electricity & magnetism1 set ! !ories on a new basis cle>$ ( all extrane\s & unnecess>y matt]1 & r$uc$ ! hypo!ses & assumptions to ! smalle/ possible numb]1 /at$ ) ! mo/ c>eful precautions aga9/ misund]/&+4 ,z ?is "w 0 gradually accompli%$ ! ne$ = fur!r exp]im5t became m & m cle>ly app>5t4 ,accord+ly he e/abli%$ at ! old ,college 9 ! ,high ,/reet1 :at he has ju/ly claim$ 0 ! fir/ physical laboratory = /ud5ts4#ae ,an old w9e-cell> 9 ! basem5t adjo9+ ! ,natural ,philosophy ,class-room 0 fir/ annex$1 & 0 ! sc5e ( e>ly rese>*es1 :i* 7 to lead to mu* ( ! be/ "w ( ! pres5t "t4 ,to ?is 0 add$ a little lat] ! ,black/one ,exam9ation-room1 :i*1 disus$ & left unprotect$1 0 add$ to ! w9e-cell>1 & gave space = ! increas+ corps ( en?usia/ic work]s :o came "u ! influ5ce ( ! new tea*]1 & 7 eag] to be associat$ ) 8 "w4 ,a good _m ( ! rese>*es :i* 7 c>ri$ out 9 ?is meagre accommodation 9 ! old ,college w be m5tion$ 9 :at foll[s4 ,illu/ration3 ,,inn] ,,c\rt ,,( ,,! ,,old ,,college ,%[+ ,natural ,philosophy ,rooms ,9 ! view ( ! inn] c\rt ( ! ,old ,college giv5 opposite1 ! w9d[s on ! gr\nd-floor to ! "r ( ! turret 9 front1 are ^? ( ! ,black/one ,exam9ation-room1 :i* =m$ a l>ge "p ( ! new ,physical ,laboratory4 ,! w9d[s above ^!1 on ! second floor1 are ^? ( ! ,app>atus-room ( ! ,natural ,philosophy ,dep>tm5t4 ,betwe5 ! turret on ! "r ( ! picture & ! angle ( ! c\rt are ! w9d[s ( ! ,natural ,philosophy ,class-room4 ,! attic above ! ,app>atus-room 0 at a lat] "t occupi$ by ! ,eng9e]+ ,dep>tm5t1 "u ,pr(essor ,macquorn ,rank9e4 ,"h aga9 we may quote f ! ,bangor address3 ,soon aft] ,i ent]$ my pres5t *air 9 ! ,univ]sity ( ,glasg[ 9 #ahdf ,i _h occasion to und]take "s inve/igations ( electrodynamic qualities ( matt]1 to answ] que/ions sugge/$ by ! results ( ma!matical !ory1 que/ions :i* c\ld only be answ]$ by direct exp]im5t4 ,! lab\r ( obs]v+ prov$ too heavy1 mu* ( x c\ld sc>cely be c>ri$ on )\t two or m p]sons1 work+ toge!r4 ,i !re=e invit$ /ud5ts to aid 9 ! "w4 ,!y will+ly accept$ ! invitation1 & l5t me mo/ *e]ful & able help4 ,soon aft]1 o!r /ud5ts1 he>+ t _! class-fell[s _h got exp]im5tal "w to d1 came to me & volunte]$ to assi/ 9 ! inve/igation4 ,i c\ld n give !m all "w 9 ! p>ticul> inve/igation ) :i* ,i _h comm5c$--'! electric convection ( heat'--= want ( means & "t & possibilities ( arrangem5t1 b ,i did all 9 my p[] to f9d "w = !m on alli$ subjects 7,electrodynamic ,prop]ties ( ,metals1 ,moduluses ( ,ela/icity ( ,metals1 ,ela/ic ,fatigue1 ,atmosph]ic ,electricity1 etc474 ,i !n _h an ord9>y class ( a hundr$ /ud5ts1 ( :om "s att5d$ lectures 9 natural philosophy two h\rs a day1 & _h no?+ m to d f morn+ till night4 ,^! 7 ! balmy days ( natural philosophy 9 ! ,univ]sity ( ,glasg[--! pre-,commissional days4 ,b ! majority ( ! class really _h v h>d "w1 & _m ( !m work$ aft] class-h\rs = self-support4 ,"s 7 engag$ 9 tea*+1 "s 7 city-mission>ies1 int5d+ to g into ! ,e/abli%$ ,*ur* ( ,scotl& or "s o!r religi\s d5om9ation ( ,scotl&1 or "s ( ! d5om9ations ( ,wales1 = ,i always _h _m ,wel% /ud5ts4 ,9 ^? days1 z n[1 9 ! ,scotti% ,univ]sities all int5d+ !ological /ud5ts took a 'philosophical curriculum'--'zu]/ collegium logicum1' !n moral philosophy1 & 7g5]ally la/7 natural philosophy4 ,?ree-f\r?s ( my volunte] exp]im5tali/s us$ to be /ud5ts :o ent]$ ! !ological classes imm$iately aft] ! completion ( ! philosophical curriculum4 ,i well rememb] ! surprise ( a great ,g]man pr(essor :5 he he>d ( ?is rule & usage3 ',:at6 d ! !ologians le>n physics8' ,i said1 ',yes1 !y all d2 & _m ( !m h made capital exp]im5ts4 ,i believe !y d n f9d t _! !ology suff]s at all f 7_!7 hav+ le>n$ some?+ ( ma!matics & dynamics & exp]im5tal physics be=e !y ent] ^u x4' ,?is /atem5t1 besides ?r[+ an int]e/+ light on ! conditions ( univ]sity "w sixty ye>s ago1 gives an illu/ration ( ! wide int]pretation 9 ,scotl& ( ! t]m ,arts4 ,"h x has meant1 s9ce ! ,*air ( ,natural ,philosophy 0 f\nd$ 9 #aegg1 & held by "o ( ! ,reg5ts ( ! ,univ]sity1 ,artes ,lib]ales 9 ! wide/ s5se1 t is1 ! /udy ( ,litt] ,humaniores 7includ+ m5tal & moral philosophy7 & physical & ma!matical sci5ce4 ,^! 7 all deem$ necess>y = a lib]al education at t "t3 9 ! sci5tific age 9 :i* we live x is m imp]ative ?an ev] t nei!r %\ld be exclud$ f ! ,arts curriculum ( our ,univ]sities4 ,! common di/9ction betwe5 ,arts & ,sci5ce is a false "o1 & ! product ( a n>r[ idea :i* is ali5 to ! traditions ( our nor!rn ,univ]sities4 ,x is to be not$1 h[ev]1 t ! laboratory ?us f\nd$ 0 ess5tially a rese>* laboratory2 x 0 n design$ = ! sy/ematic in/ruction ( /ud5ts 9 me?ods ( exp]im5t+4 ,laboratories = ?is purpose came lat]1 & z a natural consequ5ce4 ,b = ! be/ /ud5ts1 ill prep>$ z1 no d\bt1 "s ( !m 7 = ! "w ( rese>*1 ! exp]i5ce ga9$ 9 su* a laboratory 0 v valuable4 ,!y le>n$--&1 inde$1 _h to le>n--9 an incid5tal mann] h[ to det]m9e physical con/ants1 su* z specific gravities1 !rmal capacities1 electric resi/ances1 & s =?4 ,=1 ap>t f ! ,relations des ,expri5ces ( ,regnault1 & ! magnetic & electric "w ( ,gauss & ,web]1 !re 0 no sy/ematis$ body ( in=mation available = ! guidance ( /ud5ts4 ,good /ud5ts c\ld bran* out f ! ma9 l9e ( inquiry1 s z to acquire skill 9 subsidi>y det]m9ations ( ?is k9d2 to ! m easily daunt$ /ud5t su* difficulties prov$ =midable1 & (t5 absolutely det]r5t4 ,x is n easy = a physici/ ( ! pres5t day to realise ! /ate ( k ( ! "t1 & s he (t5 fails to recognise ! full importance ( ,?omson's "w4 ,! want ( precise k ( physical con/ants 0 to a consid]able ext5t a consequ5ce ( ! want ( exact def9itions ( quantities to be det]m9$1 & 9 a mu* great] degree ( ! lack ( any sy/em ( units ( measurem5t4 ,! /udy ( ph5om5a 0 9 ! ma9 m]ely qualitative2 :]e an attempt _h be5 made to obta9 quantitative det]m9ations1 ! units employ$ 7 arbitr>y & dep5d5t on app>atus 9 ! possession ( ! exp]im5t]1 & !re=e unavailable to o!rs4 ,9 ! dep>tm5t ( heat1 z has be5 said1 a great beg9n+ _h be5 made by ,regnault1 9 ^: h&s ! exact det]m9ation ( physical con/ants _h become a f9e art4 ,9 electricity & magnetism !re 7 already ! rudim5ts ( quantitative measurem5t4 ,b x 0 only long aft]1 :5 ! actions ( magnets & ( electric curr5ts _h be5 mu* fur!r /udi$1 t ! ,briti% ,association ent]$ on its great "w ( sett+ up a sy/em ( absolute units = ! measurem5t ( su* actions4 ,up till !n ! resi/ance1 = example1 ( a piece ( wire1 to ! passage ( an electric curr5t along x1 0 express$ by "s su* specification z t x 0 equal to ! resi/ance ( a c]ta9 piece ( copp] wire 9 ! exp]im5t]'s possession4 ,x 0 !re=e practically impossible = exp]im5t]s else:]e to pr(it by ! in=mation4 ,& s 9 o!r cases4 ,an example f ,?omson's pap]s on ! ,dynamical ,!ory ( ,heat may be cit$ "h1 ?\gh x ref]s to a "t 7#ahea7 :5 "s progress t[>ds obta9+ a sy/em ( absolute units _h be5 made4 ,9 #aah 7,art4 ,,xlviii7 he /ates t ! electromotive =ce ( a !rmoelectric c\ple ( copp] & bismu?1 at temp]atures #j ,c4 & #ajj ,c4 ( its functions1 might be e/imat$ f a comp>ison made by ,p\illet ( ! /r5g? ( ! curr5t s5t by ?is electromotive =ce ?r\gh a copp] wire #bj metres long & #a millimetre 9 diamet]1 ) ! /r5g? ( a curr5t decompos+ wat] at a c]ta9 rate1 7 x n t ! specific resi/ances ( diff]5t specim5s ( copp] are f\nd to diff] consid]ably f "o ano!r4 ,h5ce1 ?\gh an e/imate is made1 x is /at$ t1 )\t exp]im5ts on ! actual wire us$ by ,p\illet1 x 0 impossible to arrive at an accurate result4 ,n[ if x _h be5 9 ,p\illet's p[] to det]m9e accurately ! resi/ance ( 8 circuit 9 absolute units1 !re w\ld h be5 no difficulty 9 ! matt]1 & 8 result w\ld h be5 imm$iately available = ! e/imate requir$4 ,:5 subm>9e cables came to be manufactur$ & laid all ?is _h to be *ang$4 ,= !y 7 exp5sive2 an ,atlantic cable1 = example1 co/ half a million /]l+4 ,! /ate ( ! cable _h to be asc]ta9$ at %ort int]vals dur+ manufacture2 a simil> wat* _h to be kept ^u x dur+ ! process ( lay+1 & aft]w>ds dur+ its life ( telegraphic use4 ,! obs]vations made by "o obs]v] _h !re=e to be made available to all1 s t1 ) o!r in/rum5ts & at ano!r place1 equival5t obs]vations c\ld be made & _! results quantitatively comp>$ ) ^? ( ! =m]4 ,to set up a sy/em ( measurem5t = su* purposes z ^! involv$ mu* !oretical discussion & an enorm\s am\nt ( exp]im5tal inve/igation4 ,?is 0 und]tak5 by a special committee ( ! ,association1 & a pr9cipal "p 9 furni%+ discussions ( !ory & 9 devis+ exp]im5tal me?ods 0 tak5 by ,?omson4 ,! committee's inve/igations took place at a date some:at lat] 9 ,?omson's c>e] ?an t ) :i* we are "h deal+1 & "s acc\nt ( !m w be giv5 9 a lat] *apt]2 b mu* "w1 prep>atory = & lead+ up to ! det]m9ation ( electrical /&>ds1 0 done by ! volunte] laboratory corps 9 ! trans=m$ w9e-cell> ( ! old ,college4 ,! selection & realisation ( electrical /&>ds 0 a "w ( extraord9>y importance to ! _w f e po9t ( view--political1 comm]cial1 & social4 ,x n only r5d]$ applications ( electricity possible 9 ! arts & indu/ries1 b by reliev+ exp]im5tal results f ! vagu5ess ( ! specifications =m]ly 9 use1 made ! fur!r progress ( pure electrical sci5ce a matt] 9 :i* e /ep =w>d1 tak5 by an individual work]1 facilitat$ ! advance ( all4 ,b l o!r toilsome s]vices1 ! nature ( :i* is n cle> to ! g5]al public1 x has nev] receiv$ prop] ackn[l$gm5t f ^? :o h pr(it$ by x4 ,if ,?omson _h done no?+ m ?an ! "w he did 9 ?is connection1 fir/ ) 8 /ud5ts & lat] ) ! ,briti% ,association ,committee1 he w\ld h des]v$ well ( 8 fell[-c\ntrym54 ,:5 ,pr(essor ,?omson 0 ent]+ on ! duties ( 8 *air1 & call+ 8 /ud5ts to 8 aid1 ! discov]ies ( ,f>aday on ! induction ( curr5ts by ! motion ( magnets 9 ! neighb\rhood ( clos$ circuits ( wire1 or1 :at comes to ! same ?+1 ! motion ( su* circuits 9 ! fields ( magnets1 _h n be5 long giv5 to ! _w1 & 7 be+ pond]$ deeply by natural philosoph]s4 ,! "t 0 ripe = a quantitative inve/igation ( curr5t induction1 l t furni%$ by ! g5ius ( ,ampre aft] ! discov]y by ,o]/$ ( ! deflection ( a magnet by an electric curr5t4 ,su* an inve/igation 0 imm5sely facilitat$ by ,f>aday's conception ( l9es ( magnetic =ce1 ! cutt+ ( :i* by ! wire ( ! circuit gave rise to ! induc$ curr5t4 ,inde$1 ! ma!matical ideas involv$ 7 indicat$1 & n obscurely1 by ,f>aday himself4 ,b to r5d] ! ma!matical !ory explicit1 & to inve/igate & te/ its consequ5ces1 requir$ ! highe/ g5ius4 ,?is "w 0 accompli%$ 9 great measure by ,?omson1 ^: pres5tation ( electrodynamic !ory help$ ,maxwell to ! view t light 0 an affair ( ! propagation ( electric & magnetic vibrations 9 an insulat+ m$ium1 ! light-c>ry+ e!r4 ,ano!r inve/igation on :i* he _h already ent]$ 9 #ahdg 0 ( great importance1 n only = pure sci5ce b = ! developm5t & prop] economy ( all indu/rial op]ations4 ,! f\ndations on :i* a dynamical !ory ( heat 0 to be rais$ _h be5 p>tly laid by ,c>not & 7 be+ complet$ on ! exp]im5tal side by ,james ,prescott ,j\le1 :om ,?omson met 9 #ahdg at ! meet+ ( ! ,briti% ,association at ,ox=d4 ,! meet+ at ,ox=d 9 #ahfj is memorable to ! public at l>ge1 ma9ly on acc\nt ( ! discussion :i* took place on ! ,d>w9ian !ory1 & ! fam\s dialectic enc\nt] betwe5 ,bi%op ,wilb]=ce & ,pr(essor ,huxley2 ! ,ox=d meet+ ( #ahid w always be associat$ ) ! ann\ncem5t ( ! discov]y ( argon by ,"l ,rayleigh & ,sir ,william ,ramsay3 ! meet+ ( #ahdg might q z wor?ily be rememb]$ z t at :i* ,j\le laid d[n1 ) num]ical exactitude1 ! fir/ law ( !rmodynamics4 ,j\le br\ght 8 exp]im5tal results be=e ! ,ma!matical & ,physical ,section at t meet+2 & x appe>s probable t !y w\ld h receiv$ scant att5tion _h n _! importance be5 =cibly po9t$ out by ,?omson4 ,communications !reaft] pass$ frequ5tly betwe5 ! two "y physici/s1 & !re soon began a collaboration ( great value to sci5ce1 & a fri5d%ip :i* la/$ till ! dea? ( ,j\le 9 #ahhd4 ,see p4 #hh bel[4 ,we %all devote ! next few *apt]s to an acc\nt1 z free f te*nicalities z possible1 ( ^! great divisions ( ,?omson's e>li] orig9al "w z pr(essor at ,glasg[4 ,,*apt] ,,vi ,,fri5d%ip ,,) ,,/okes ,,& ,,j\le4 ,,e>ly ,,"w ,,at ,,glasg[ ,dur+ 8 resid5ce at ,cambridge ,?omson ga9$ ! fri5d%ip ( ,george ,gabriel ,/okes1 :o _h graduat$ z ,s5ior ,wrangl] & ,fir/ ,smi?'s ,prizeman 9 #ahda4 ,!y discuss$ ma!matical que/ions toge!r & contribut$ articles on v>i\s topics to ! ,cambridge ,ma!matical ,j\rnal4 ,9 #ahdf ,cambridge & ,dubl9 0 sub/itut$ = ,cambridge 9 ! title ( ! ,j\rnal1 & a new s]ies 0 begun "u ! editor%ip ( ,?omson4 ,a feature ( ! e>li] volumes ( ! new issue 0 a s]ies ( ,notes on ,hydrodynamics writt5 by agreem5t betwe5 ,?omson & ,/okes1 & pr9t$ 9 vols4 ii1 iii1 & v4 ,! fir/1 second1 & fif? ( ! s]ies 7 writt5 by ,?omson1 ! o!rs by ,/okes4 ,! matt] ( ^! ,notes 0 n altoge!r novel2 b _m po9ts 7 put 9 a new & m truly physical light1 & ! s]ies 0 no d\bt ( mu* s]vice to /ud5ts1 = ^: use ! articles 7 int5d$4 ,"s acc\nt ( ^! ,notes w be giv5 9 a lat] *apt] on ,?omson's hydrodynamical pap]s4 ,= ! ma!matical p[] & sure physical in/9ct ( ,/okes ,?omson _h always ! greate/ admiration4 ,:5 ask$ on "o occasion :o 0 ! mo/ out/&+ work] 9 physical sci5ce on ! cont95t1 he repli$1 ,i d n "k1 b :oev] he is1 ,i am c]ta9 t ,/okes is a mat* = him4 ,9 a report ( an address :i* he deliv]$ 9 ,june #ahig1 at ! celebration ( ! ,jubilee ( ,sir ,george ,/okes z ,lucasian ,pr(essor ( ,ma!matics1 ,"l ,kelv9 ref]r$ to _! e>ly int]c\rse at ,cambridge 9 t]ms :i* 7 report$ z foll[s3 ,:5 he reflect$ on 8 own e>ly progress1 he 0 l$ to recall ! great k9dness %[n to himself1 & ! great value :i* 8 int]c\rse ) ,sir ,george ,/okes _h be5 to him ?r\gh life4 ,:5ev] a ma!matical difficulty occurr$ he us$ to say to himself1 ',ask ,/okes :at he ?9ks ( x4' ,he got an answ] if answ] 0 possible2 he 0 told1 at all ev5ts1 if x 0 unansw]able4 ,he felt t 9 8 und]graduate days1 & he felt x m n[4 ,aft] ! dea? ( ,/okes 9 ,febru>y #aijb1 ,"l ,kelv9 aga9 ref]r$1 9 an en?usia/ic tribute 9 ,nature = ,febru>y #ab1 to ^! e>ly discussions4 ,/okes's sci5tific "w & sci5tific ?\ght is b p>tially repres5t$ by 8 publi%$ writ+s4 ,he gave g5]\sly & freely ( 8 treasures to all :o 7 =tunate en\gh to h an opportunity ( receiv+ f him4 ,8 tea*+ me ! pr9ciples ( sol> & /ell> *emi/ry :5 we 7 walk+ ab\t among ! colleges sometime prior to #aheb 7:5 ,i vacat$ my ,pet]h\se ,fell[%ip to be no m 9 ,cambridge = _m ye>s7 is b "o example4 ,! int]*ange ( ideas betwe5 ,/okes & ,?omson :i* began 9 ^? e>ly days w5t on con/antly & seems to h be5 /imulat+ to bo?4 ,! two m5 7 9 a s5se complem5t>y 9 nature & temp]am5t4 ,bo? _h great p[] & great insight1 b :ile ,/okes 0 uni=mly calm1 reflective1 & judicial1 ,?omson's en?usiasm 0 m outspok5ly f]vid1 & he 0 apt to be at times vehem5t & impetu\s 9 8 eag]ness to pu% on an inve/igation2 & ?\gh1 z became 8 nationality1 he 0 cauti\s 9 committ+ himself to conclusions1 he ex]cis$ p]haps less res]ve 9 plac+ 8 results be=e ! public ( sci5ce4 ,a *>act]i/ic in/ance ( ,?omson's vehem5t pursuit ( exp]im5tal results may be giv5 "h1 al?\gh ! incid5ts occurr$ at a mu* lat] date 9 8 c>e] ?an t ) :i* we are at pres5t conc]n$4 ,9 #ahhj ! inv5tion ( ! ,faure ,second>y ,batt]y attract$ 8 att5tion4 ,m4 ,faure br\ght f ,p>is "s cells made up & ready *>g$1 & %[$ 9 ! ,physical ,laboratory at ,glasg[ ! v p[]ful curr5ts :i*1 9 consequ5ce ( _! v l[ int]nal resi/ance1 !y 7 capable ( produc+ 9 a ?ick piece ( copp] wire4 ,! cells 7 ( ! orig9al =m1 con/ruct$ by coat+ /rips ( %eet lead on bo? sides ) a pa/e ( m9ium moi/5$ ) dilute sulphuric acid1 swa?+ !m 9 wooll5 clo? sew$ r\nd !m1 & !n roll+ two toge!r to =m ! pair ( plates = "o cell4 ,a supply ( %eet lead1 m9ium1 & wooll5 clo? 0 at once obta9$1 & ! :ole laboratory corps ( /ud5ts & /aff 0 set to "w to manufacture second>y batt]ies4 ,a small ,siem5s-,halske dynamo 0 telegraph$ = to *>ge ! cells1 & ! v5tilat+ /eam-eng9e ( ! ,univ]sity 0 requisition$ to drive ! dynamo dur+ ! night4 ,?us ! ,univ]sity /ok]s & eng9e] 7 put on d\ble %ifts2 ! cells 7 *>g$ dur+ ! night & ! *>g+ curr5t & batt]y-pot5tial measur$ at int]vals4 ,!n ! cells 7 run d[n dur+ ! day1 & _! output measur$ 9 ! same way4 ,j z ?is began1 ,?omson 0 laid up ) an ailm5t :i* conf9$ him to b$ = a c\ple ( weeks or s2 b ?is l$ to no cessation ( ! laboratory activity4 ,on ! contr>y1 ! laboratory corps 0 divid$ into two squads1 "o = ! night1 ! o!r = ! day1 & ! "w ( *>g+ & dis*>g+1 & ( measurem5t ( exp5diture & return ( en]gy w5t on )\t int]mission4 ,! results obta9$ dur+ ! day 7 tak5 to ,?omson's b$side 9 ! ev5+1 & e>ly 9 ! morn+ he 0 ready to review ^? :i* _h be5 obta9$ dur+ ! night1 & to sugge/ fur!r que/ions to be answ]$ )\t delay4 ,?is mode ( work+ c\ld n g on indef9itely1 b x cont9u$ until 8 assi/ants 7"s ( :om _h to take bo? %ifts671 to say no?+ ( ! /ok]s & /ud5ts1 7 fairly well exhau/$4 ,on o!r occasions1 :5 he 0 f home1 he f\nd ! po/ too sl[ to convey 8 directions to 8 laboratory work]s1 & telegraph$ f day to day que/ions & in/ructions reg>d+ ! "w on h&4 ,?us "o important result 7anticipat$1 h[ev]1 by ,vill>i7 ( ! s]ies ( rese>*es on ! effects ( /ress on magnetisation :i* =ms ,"p ,,vii ( 8 ,electrodynamic ,qualities ( ,metals--! fact t up to a c]ta9 magnetis+ =ce ! effect ( pull1 appli$ to a wire ( s(t iron1 is to increase ! magnetisation produc$1 & = high] magnetis+ =ces to dim9i% x--0 telegraph$ to him on ! night on :i* ! pap] 0 read to ! ,royal ,society4 ,x w ?us be se5 t ,?omson1 :e!r conf9$ to 8 room or on holiday1 kept 8 m9d fix$ ^u 8 sci5tific or practical "w1 & 0 almo/ impati5t = its progress4 ,/okes work$ ma9ly by himself2 b ev5 if he _h _h a corps ( work]s & assi/ants1 x is improbable t su* di/urbances ( h\rs ( att5dance & laboratory & work%op r\t9e w\ld h occurr$1 z 7 n infrequ5t at ,glasg[ :5 ,?omson's "w 01 9 ! 'sixties & 'sev5ties1 at its int5se/4 ,/okes & ,?omson 7 9 succession presid5ts ( ! ,royal ,society1 ,/okes f #ahhe to #ahij1 & ,?omson 7f #ahib z ,"l ,kelv97 f #ahij to #ahie4 ,?is is ! highe/ di/9ction :i* any sci5tific man 9 ?is c\ntry c a*ieve1 & x is v rem>kable t !re %\ld h be5 9 rec5t times two presid5ts 9 succession ^: modes ( ?\ght & ma!matical p[] are s directly comp>able ) ^? ( ! great f\nd] ( mod]n natural philosophy4 ,/okes _h ! additional di/9ction ( be+ ! l9eal successor ( ,newton z ,lucasian ,pr(essor ( ,ma!matics at ,cambridge4 ,b x 0 res]v$ = ,?omson to d mu* by ! publication ( ,?omson & ,tait's ,natural ,philosophy to br+ back ! curr5t ( tea*+ & ?\ght 9 dynamical sci5ce to ! ideas ( ! ,pr9cipia1 & to %[ h[ completely ! fundam5tal laws1 z laid d[n 9 t great classic1 avail = ! inclusion ( ! mod]n !ory ( en]gy1 9 all its trans=mations1 )9 ! category ( dynamical action betwe5 mat]ial sy/ems4 ,an exce$+ly em95t politician1 n[ deceas$1 said "s ye>s ago t ! pres5t age 0 s+ul>ly defici5t 9 m9ds ( ! fir/ quality4 ,s f> z sci5tific g5ius is conc]n$1 ! dictum 0 s+ul>ly false3 we h "h a /rik+ pro( ( ! contr>y4 ,b !n few politicians "k any?+ ( sci5ce2 inde$ "s ( ^? :o guide1 or aspire to guide1 ! de/9ies ( ! mo/ sci5tific & indu/rial empire ! _w has ev] se5 are almo/ boa/ful ( _! ignorance4 ,!re are1 ( c\rse1 hon\rable exceptions4 ,x is conv5i5t to ref] "h to ! %>e :i* ,/okes & ,?omson took 9 ! physical explanation ( ! d>k l9es ( ! sol> spectrum1 & to _! pr$iction ( ! possibility ( det]m9+ ! con/itution ( ! />s & ( t]re/rial sub/ances by :at is n[ kn[n z spectrum analysis4 ,?omson us$ to give ! physical !ory ( ^! l9es 9 8 lectures1 & say t he obta9$ ! idea f ,/okes 9 a conv]sation :i* !y _h 9 ! g>d5 ( ,pembroke at ,cambridge1 "s "t prior to #aheb 7see ! quotation f 8 ,nature article quot$ above1 p4 #hj1 & ! ,baltimore ,lectures1 p4 #aja74 ,?is is confirm$ by a /ud5t's note-book1 ( date #ahed1 :i* is n[ 9 ! ,natural ,philosophy ,dep>tm5t4 ,! /atem5ts !re9 record$ are p]fectly def9ite & cle>1 & %[ t at t e>ly date ! :ole affair ( spectrum analysis 0 9 8 h&s1 & only requir$ confirmation by exp]im5ts on ! rev]sal ( ! l9es ( t]re/rial sub/ances by an atmosph]e ( ! sub/ance :i* produc$ ! l9es1 & a comp>ison ( ! positions ( ! bright l9es ( t]re/rial sub/ances ) ^? ( ! d>k l9es ( ! sol> spectrum4 ,:y ,?omson did n c>ry out all ^! exp]im5ts x w\ld be difficult to say4 ,"s ( !m he did make1 = ,pr(essor ,john ,f]guson1 :o 0 a /ud5t ( ,natural ,philosophy 9 #ahei-fj1 has rec5tly told h[ he witness$ ,?omson make ! exp]im5t ( rev]s+ ! l9es ( sodium by pass+ ! light f ! salt$ flame ( a _s lamp ?r\gh vap\r ( sodium produc$ by heat+ ! metal 9 an iron spoon4 ,a few days lat]1 says ,pr(essor ,f]guson1 ,?omson read a lett] to 8 class ann\nc+ ,buns5 & ,kir*h(f's discov]y4 ,a lett] ( ,/okes to ,sir ,john ,lubbock1 pr9t$ 9 ! ,sci5tific ,correspond5ce ( ,sir ,george ,gabriel ,/okes1 /ates 8 recollection ( ! matt]1 & gives ,?omson ! cr$it ( hav+ inf]r$ ! me?od ( spectrum analysis1 a me?od to :i* ,/okes himself makes no claim4 ,he says1 ,i "k1 ,i ?9k1 :at ,sir ,william ,?omson 0 allud+ to4 ,i knew well1 :at 0 g5]ally kn[n1 & is m5tion$ by ,h]s*el 9 8 treatise on ,light1 t ! bright ,d se5 9 flames is specially produc$ :5 a salt ( soda is introduc$4 ,i connect$ x 9 my own m9d ) ! pres5ce ( sodium1 & ,i suppose o!rs did s too4 ,! co9cid5ce 9 position ( ! bright & d>k ,d is too /rik+ to all[ u to reg>d x z =tuit\s4 ,9 conv]sation ) ,?omson ,i expla9$ ! connection ( ! d>k & bright l9e by ! analogy ( a set ( piano /r+s tun$ to ! same note1 :i*1 if /ruck1 w\ld give out t note1 & also w\ld be ready to s\nd x1 to take x up1 9 fact1 if x 7 s\nd$ 9 air4 ,?is w\ld imply absorption ( ! arial vibrations1 z o!rwise !re w\ld be a creation ( en]gy4 ,accord+ly ,i acc\nt$ = ! pres5ce ( ! d>k ,d 9 ! sol> spectrum by suppos+ t !re 0 sodium 9 ! atmosph]e1 capable ( absorb+ light ( t p>ticul> refrangibility4 ,he ask$ me if !re 7 any o!r in/ances ( su* co9cid5ces ( bright & d>k l9es1 & ,i said ,i ?\ght !re 0 "o m5tion$ by ,brew/]4 ,he 0 mu* /ruck ) ?is1 & jump$ to ! conclusion t to f9d out :at sub/ances 7 9 ! />s we mu/ comp>e ! positions ( ! d>k l9es se5 9 _! spectra ) ! spectra ( metals1 etc4444 ,i %\ld h said t ,i ?\ght ,?omson 0 go+ too fa/ ahead1 = my notion at ! "t 0 t1 ?\gh a few ( ! d>k l9es might be trac$ to elem5t>y sub/ances1 sodium = "o1 probably potassium = ano!r1 yet ! great bulk ( !m 7 probably due to comp\nd vap\rs1 :i*1 l p]oxide ( nitrog5 & "s o!r kn[n comp\nd gases1 h ! "* ( selective absorption4 ,x w be rememb]$ t ! exp]im5tal e/abli%m5t ( ! me?od ( spectrum analysis 0 publi%$ t[>ds ! end ( #ahei by ,buns5 & ,kir*h(f1 to :om1 !re=e1 ! full cr$it ( discov]]s mu/ be giv54 ,"l ,kelv9 9 ! lat] ye>s ( 8 life us$ to tell ! /ory ( 8 fir/ meet+ ) ,j\le at ,ox=d1 & ( _! second meet+ a =tnight lat] 9 ,switz]l&4 ,he did s also 9 8 address deliv]$ on ! occasion ( ! unveil+ ( a /atue ( ,j\le1 9 ,man*e/] ,t[n ,hall1 on ,decemb] #g1 #ahic1 & we quote ! n>rative on acc\nt ( its sci5tific & p]sonal int]e/4 ,i c nev] =get ! ,briti% ,association at ,ox=d 9 #ahdg1 :5 9 "o ( ! sections ,i he>d a pap] read by a v unassum+ "y man1 :o betray$ no consci\sness 9 8 mann] t he _h a great idea to unfold4 ,i 0 trem5d\sly /ruck ) ! pap]4 ,i at fir/ ?\ght x c\ld n be true1 because x 0 diff]5t f ,c>not's !ory1 & imm$iately aft] ! read+ ( ! pap] ,i _h a few words ) ! au?or1 ,james ,j\le1 :i* 0 ! beg9n+ ( our =ty ye>s' acqua9tance & fri5d%ip4 ,on ! ev5+ ( ! same day1 t v valuable in/itution ( ! ,briti% ,association1 its conv]sazione1 gave u opportunity = a good h\r's talk & discussion ov] all t ei!r ( u knew ( !rmodynamics4 ,i ga9$ ideas :i* _h nev] ent]$ my m9d be=e1 & ,i ?\ght ,i1 too1 sugge/$ some?+ wor?y ( ,j\le's consid]ation :5 ,i told him ( ,c>not's !ory4 ,!n & !re 9 ! ,radcliffe ,libr>y1 ,ox=d1 we p>t$1 bo? ( u1 ,i am sure1 feel+ t we _h mu* m to say to "o ano!r & mu* matt] = reflection 9 :at we _h talk$ ov] t ev5+4 ,b 444 a =tnight lat]1 :5 walk+ d[n ! valley ( ,*am\nix1 ,i saw 9 ! di/ance a "y man walk+ up ! road t[>ds me1 & c>ry+ 9 8 h& some?+ :i* look$ l a /ick1 b :i* he 0 us+ nei!r z an alp5/ock nor z a walk+-/ick4 ,x 0 ,j\le ) a long !rmomet] 9 8 h&1 :i* he w\ld n tru/ by itself 9 ! *>--banc1 com+ sl[ly up ! hill beh9d him1 le/ x %\ld get brok54 ,b !re1 com=tably & safely seat$ 9 ! *>--banc1 0 8 bride--! sympa!tic companion & %>] 9 8 "w ( aft] ye>s4 ,he _h n told me 9 ,section ,a1 or 9 ! ,radcliffe ,libr>y1 t he 0 go+ to be m>ri$ 9 ?ree days1 b n[ 9 ! valley ( ,*am\nix he introduc$ me to 8 "y wife4 ,we appo9t$ to meet aga9 a =tnight lat] at ,m>tigny to make exp]im5ts on ! heat ( a wat]fall 7,sallan*es7 ) t !rmomet]3 & aft]w>ds we met aga9 & aga91 & f t "t1 inde$1 rema9$ close fri5ds till ! end ( ,j\le's life4 ,i _h ! great pleasure & satisfaction = _m ye>s1 beg9n+ j =ty ye>s ago1 ( mak+ exp]im5ts along ) ,j\le :i* l$ to "s important results 9 respect to ! !ory ( !rmodynamics4 ,?is is "o ( ! mo/ valuable recollections ( my life1 & is inde$ z valuable a recollection z ,i c conceive 9 ! possession ( any man int]e/$ 9 sci5ce4 ,at ! beg9n+ ( 8 c\rse ( lectures ea* session1 ,pr(essor ,?omson read1 or r attempt$ to read1 an introductory address on ! scope & me?ods ( physical sci5ce1 :i* he _h prep>$ = 8 fir/ session 9 #ahdf4 ,x set =? ! fact t 9 sci5ce !re 7 two /ages ( progress--a natural hi/ory /age & a natural philosophy /age4 ,9 ! fir/ ! discov]] or tea*] is occupi$ ) ! collection ( facts1 & _! arrangem5t 9 classes accord+ to _! nature2 9 ! second he is conc]n$ ) ! relations ( facts already discov]$ & classifi$1 & endeav\rs to br+ !m )9 ! scope ( g5]al pr9ciples or causes4 ,once ! philosophical /age is rea*$1 its me?ods & results are connect$ & enl>g$ by cont9u$ rese>* aft] facts1 controll$ & direct$ by ! conclusions ( g5]al !ory4 ,?us ! me?od is at fir/ purely inductive1 b becomes 9 ! second /age bo? inductive & d$uctive2 ! g5]al !ory pr$icts by its d$uctions1 & ! v]ification ( ^! by exp]im5t & obs]vation give a validity to ! !ory :i* no m]e induction c\ld af=d4 ,^! /ages ( sci5tific inve/igation are well illu/rat$ by ! laws ( ,kepl] arriv$ at by m]e comp>ison ( ! motions ( ! planets1 & ! d$uction ( ^! laws1 ) ! rem>kable correction ( ! ?ird law1 giv5 by ! !ory ( univ]sal gravitation4 ,! pr$iction ( ! exi/5ce & place ( ! planet ,neptune f ! p]turbations ( ,uranus is an excell5t example ( ! pr$ictive quality ( a true philosophical !ory4 ,! lecture !n proce$$ to /ate ! prov9ce ( dynamics1 to def9e its diff]5t p>ts1 & to insi/ on ! importance ( k9ematics1 :i* 0 describ$ z a purely geometrical subject1 ! geometry ( motion1 consid]ations f :i* ent]$ into e dynamical problem4 ,?is di/9ction betwe5 dynamical & k9ematical consid]ations--betwe5 ^? 9 :i* =ce is conc]n$ & ^? into :i* ent] only ! idea ( displacem5t 9 space & 9 "t--is emphasis$ 9 ,?omson & ,tait's ,natural ,philosophy1 :i* comm5ces ) a long *apt] devot$ entirely to k9ematics4 ,:e!r ,pr(essor ,?omson read ! :ole ( ! ,introductory ,lecture on ! fir/ occasion is unc]ta9--,cl]k ,maxwell is said to h ass]t$ t x 0 closely adh]$ to1 = t "o "t only1 & f9i%$ 9 mu* less ?an ! h\r allott$ to x4 ,9 lat] ye>s he _h nev] read m ?an a c\ple ( pages :5 "s new illu/ration1 or new fact ( sci5ce1 :i* bore on 8 subject1 l$ him to digress f ! manuscript1 :i* 0 h>dly ev] return$ to1 & aft] a few m9utes 0 me*anically laid aside & =gott54 ,once on beg9n+ ! session he humor\sly in=m$ ! assembl$ class t he did n ?9k he _h ev] succe$$ 9 read+ ! lecture ?r\gh be=e1 & add$ t he _h det]m9$ t !y %\ld he> ! :ole ( x6 ,b aga9 occurr$ ! inevitable digression1 9 ! pr(essor's absorption 9 ! new topic ! promise 0 =gott51 & ! writt5 lecture f>$ z be=e6 ,^! digressions 7 exce$+ly int]e/+ to ! be/ /ud5ts3 :e!r !y comp5sat$ = ! want ( a c>efully prep>$ pres5tation ( ! elem5ts ( ! subject1 suit$ to ! wants ( ! mass ( ! memb]s ( ! class1 is a matt] :i* ne$ n "h be discuss$4 ,all ?r\gh 8 elem5t>y lectures--introductory or n--new ideas & new problems cont9ually pres5t$ !mselves4 ,an em95t physici/ once rem>k$ t ,?omson 0 p]haps ! only liv+ man :o made discov]ies :ile lectur+4 ,t 0 h>dly true2 9 ! gl[ ( action & /ress ( expression ! m9d ( e int5se ?9k] (t5 sees new relations1 & f9ds new po9ts ( view1 :i* am\nt to discov]ies4 ,b fecundity ( m9d has1 ( c\rse1 its disadvantages3 ! unexpect$ _c happ5 )\t caus+ di/ractions to all conc]n$4 ,a m9d :i* c see a !ory ( ! physical univ]se 9 a smoke-r+ is likely1 unless kept "u extraord9>y & hamp]+ re/ra9t1 to be tempt$ to digress f :at is /rictly ! subject 9 h&1 to ! _w ( matt]s :i* t subject sugge/s4 ,pr(essor ,?omson 01 x mu/ be admitt$1 too discursive = ! ord9>y /ud5t1 & p]haps did n /udy ! art ( boil+ d[n physical !ories to ! =m mo/ easily dige/ible4 ,8 eag]ness ( m9d & wid? ( m5tal outlook gave 8 lectures a special value to ! advanc$ /ud5t1 s t !re 0 a comp5sat+ advantage4 ,! tea*] ( natural philosophy is really plac$ 9 a position ( extraord9>y difficulty4 ,! fabric ( nature is wov5 )\t seam1 & to take x to pieces is 9 a mann] to de/roy x4 ,x mu/1 aft] exam9ation 9 detail1 be recon/ruct$ & consid]$ z a :ole1 or its mean+ escapes u4 ,& "h lies ! difficulty3 e bit ( matt] /&s 9 relation to ev]y?+ else1 & bo? sides ( e relation mu/ be consid]$4 ,9 o!r words1 9 ! explanation ( any "o ph5om5on ! explanation ( all o!rs is m or less involv$4 ,?is does n mean t inve/igation or exposition is impossible1 or t we _c proce$ /ep by /ep2 b x %[s ! fooli%ness ( t criticism ( sci5ce & sci5tific me?od :i* asks = complete or ultimate k1 & ( ! popul> dem& = a simple =m ( words to express :at is 9 reality inf9itely complex4 ,9 ! e>li] ye>s ( 8 pr(essor%ip ,pr(essor ,?omson taught 8 class entirely himself1 & ga!r$ r\nd him1 z he has told u 9 ! ,bangor address1 an en?usia/ic b& ( work]s :o aid$ him 9 ! rese>*es :i* he began on ! electrodynamic qualities ( metals1 ! ela/ic prop]ties ( sub/ances1 ! !rmal & electrical conductivities ( metals1 & at a lat] date 9 ! electric & magnetic "w :i* he und]took z a memb] ( ! ,briti% ,association ,committee on ,electrical ,/&>ds4 ,! class met1 z has be5 /at$1 twice a day1 fir/ = lectures1 !n = ex]cises & oral exam9ation4 ,! *anges :i* took place lat] 9 ! curriculum1 & especially ! introduction ( hon\rs classes 9 ! diff]5t subjects1 r5d]$ x difficult1 if n impossible1 = two h\rs' att5dance to be giv5 daily on all subjects1 & /ud5ts 7 at fir/ excus$ att5dance at ! second h\r1 & f9ally su* att5dance became practically optional4 ,b s long z ! old traditional curriculum 9 ,arts--( ,humanity1 ,greek1 ,logic1 ,ma!matics1 ,moral ,philosophy & ,natural ,philosophy--endur$1 a l>ge numb] ( /ud5ts f\nd x pr(itable to att5d at bo? h\rs1 & x 0 possible to give a l>ge am\nt ( excell5t tutorial in/ruction by ! work+ ( examples & oral exam9ation4 ,?omson always held t 8 commission includ$ ! subject ( physical a/ronomy1 & ?\gh 8 lectures on t subject 71 z a rule1 conf9$ to a /atem5t ( ,kepl]'s laws & ,newton's d$uctions f !m1 he took c>e t ! writt5 & oral exam9ations includ$ a/ronomical que/ions1 = :i* ! /ud5ts 7 enjo9$ to prep>e by read+ ,h]s*el's ,outl9es1 or "s simil> text-book4 ,?is injunction n infrequ5tly 0 disreg>d$1 & discomfiture ( ! /ud5t foll[$ z a matt] ( c\rse1 if he 0 call$ on to answ]4 ,nor 7 ! que/ions always easy to prep>e = by read+4 ,a man might h a fair k ( elem5t>y a/ronomy1 & be unable to answ] (fh& su* a "q z1 ,:y is ! ecliptic call$ ! ecliptic8 or to say1 :5 ! lectures on ,kepl] _h be5 omitt$1 %ort & t]sely j :at 0 ,newton's d$uction f ! ?ird law ( ! planet>y motions4 ,home ex]cises 7 n prescrib$ z "p ( ! regul> "w except f "t to "t 9 ! ,high] ,ma!matical ,class :i* = ?irty ye>s or m ( ,?omson's t5ure ( (fice 0 held 9 ! dep>tm5t4 ,b ! :ole ord9>y class met e ,monday morn+ & sp5t ! usual lecture h\r 9 answ]+ a pap] ( dynamical & physical que/ions4 ,z _m z t51 & sometimes elev51 que/ions 7 set 9 ^! pap]s1 "s ( !m fairly difficult & involv+ novel ideas1 & by ?is weekly pap] ( problems ! be/ /ud5ts1 a doz5 or m p]haps1 7 help$ to acquire a faculty ( prompt & brief expression4 ,x 0 n uncommon = a good man to score #hj or #ij or ev5 #ajj p] c5t4 9 ! pap]1 no small feat to accompli% 9 a s+le h\r4 ,b to a consid]able majority ( ! class1 x is d\btful :e!r ! weekly exam9ation 0 ( mu* advantage3 !y attempt$ "o or two ( ! m descriptive que/ions p]haps1 b a good _m did next to no?+4 ,! exam9ations came e week1 & s ! prep>ation = "o aft] ano!r 0 neglect$1 & z mu* procra/9ation ( "w ensu$ z !re w\ld h be5 if only f\r or five pap]s a session _h be5 prescrib$4 ,!n ! "w ( look+ ov] s _m pap]s 0 a heavy task to ! pr(essor's assi/ant1 a task :i* became impossible :51 = a few ye>s 9 ! e>ly 'eighties1 ! /ud5ts 9 ! ord9>y class numb]$ ab\t #bej4 ,! subject ( natural philosophy _h become s ext5sive 9 #ahdf t ,pr(essor ,j4 ,p4 ,ni*ol call$ att5tion to ! necessity = special arrangem5ts = its adequate tea*+4 ,:at w\ld he say if he c\ld survey its dim5sions at ! pres5t "t6 ,to give ev5 a brief outl9e ( ! pr9cipal topics 9 dynamics1 heat1 ac\/ics1 light1 magnetism1 & electricity is m ?an c be accompli%$ 9 any c\rse ( univ]sity lectures2 & ! only way to tea* well & economically ! l>ge numb]s ( /ud5ts#af :o n[ ?rong ! physics classes is to give ea* week1 say1 ?ree lectures z well consid]$ & arrang$ z possible1 )\t any int]ruption f oral exam9ation1 & assemble ! /ud5ts 9 small] classes two or ?ree times a week = ex]cises & oral exam9ation4 ,?omson /at$ 8 views z to exam9ations & lectures 9 ! ,bangor address4 ,! object ( a univ]sity is tea*+1 n te/+1 444 9 respect to ! tea*+ ( a univ]sity ! object ( exam9ation is to promote ! tea*+4 ,! exam9ation %\ld be1 9 ! fir/ place1 daily4 ,no pr(essor %\ld meet 8 class )\t talk+ to !m4 ,he %\ld talk to !m & !y to him4 ,! ,fr5* call a lecture a confr5ce1 & ,i admire t idea4 ,e lecture %\ld be a conf]5ce ( tea*]s & /ud5ts4 ,x is ! true ideal ( a pr(essorial lecture4 ,i h f\nd t _m /ud5ts are afflict$ :5 !y come up to college ) ! disease call$ 'aphasia4' ,!y w n answ] :5 que/ion$1 ev5 :5 ! v words ( ! answ] are put 9 _! m\?s1 or :5 ! answ] is simply 'yes' or 'no4' ,t disease we>s (f 9 a few weeks1 b ! great cure = x is 9 repeat$ & c>eful & v free int]*ange ( "q & answ] betwe5 tea*] & /ud5t4444 ,writt5 exam9ations are v important1 z tra9+ ! /ud5t to express ) cle>ness & accuracy ! k he has ga9$1 b !y %\ld be once a week to be b5eficial4 ,! great difficulty n[1 :5 bo? classes & subject h gr[n enorm\sly1 is to h free conv]sation betwe5 pr(essor & /ud5t1 & yet give an adequate acc\nt ( ! subject4 ,to exam9e orally 9 a ?or\gh way two /ud5ts 9 ea* class-h\r is ab\t z mu* z c be done if !re is to be any sy/ematic exposition by lecture at all2 & ?us ! conf]5ce betwe5 tea*] & individual /ud5t c occur only twice a ye> at mo/4 ,nev]!less ,"l ,kelv9 0 und\bt$ly "r3 oral exam9ation & ! tra9+ ( individual /ud5ts 9 ! art ( cle> & ready expression are v desirable4 ,! real difficulties ( ! subject are ^? :i* occur to ! be/ /ud5ts1 & a discussion ( !m 9 ! pres5ce ( o!rs is good = all4 ,?is is difficult n[adays1 = l>ge classes _c af=d to wait :ile two or ?ree backw>d /ud5ts grope aft] answ]s to que/ions--:i* 9 _m cases mu/ be on po9ts :i* are suffici5tly pla9 to ! majority--to say no?+ ( ! temptation to disord] :i* ! display ( p]sonal peculi>ities or oddities ( expression g5]ally af=ds to an assembly ( /ud5ts4 ,b "t w be economis$ & _m advantages add$1 if l>ge classes are split up into sections = tutorial "w1 to supplem5t ! c>eful pres5tation ( ! subject made 9 ! sy/ematic lectures deliv]$ to ! :ole class 9 ea* case4 ,! introduction ( a tutorial sy/em w1 h[ev]1 d f> m h>m ?an good1 unless ! me?od ( in/ruction is su* z to fo/] ! self-reliance ( ! /ud5t1 :o mu/ n be1 s to speak1 spoon-f$3 su* a me?od1 & ! advantages ( ! weekly exam9ation on pap] may be secur$1 by sett+ ! tutorial class to "w out on ! spot ex]cises prescrib$ by ! lectur]4 ,b ! dang]1 :i* is a v real "o1 c only be fully avoid$ by ! precautions ( a skilful tea*]1 :o 9 ^? small classes w draw out & direct ! ideas ( 8 /ud5ts1 r ?an imp>t k directly4 ,aft] a few ye>s ,?omson f\nd x necess>y to appo9t an assi/ant1 & ,mr4 ,donald ,mc,farlane1 :o _h di/+ui%$ himself 9 ! ,ma!matics & ,natural ,philosophy classes1 0 *os54 ,mr4 ,mc,farlane 0 orig9ally a block-pr9t]1 & seems to h be5 an appr5tice at ,alex&ria 9 ! ,vale ( ,lev51 at ! "t ( ! pass+ ( ! fir/ ,re=m ,bill4 ,aft] "s "t sp5t 9 ! cotton indu/ry ( ! di/rict1 he became a tea*] 9 a village s*ool 9 ! ,vale ( ,lev51 & aft]w>ds ent]$ ! ,univ]sity z a /ud5t4 ,he dis*>g$ 8 duties 9 ! mo/ fai?ful & self-abnegat+ mann] until 8 retirem5t 9 #ahhj1 :5 he _h become advanc$ 9 ye>s4 ,he _h *>ge ( ! in/rum5ts ( ! dep>tm5t1 got ready ! lecture illu/rations & att5d$ dur+ lecture to assi/ 9 ! exp]im5ts & supply num]ical data :5 requir$1 prep>$ ! weekly class exam9ation pap] & read ! answ]s h&$ 91 & assi/$ 9 ! orig9al inve/igations :i* ! pr(essor 0 always en?usia/ically pursu+4 ,a k9d ( univ]sal physical g5ius 0 ,mc,farlane2 an exp]t calculator & an exact & c>eful exp]im5tali/4 ,_m a long & involv$ ari?metical rese>* he c>ri$ out1 mu* app>atus he made 9 a homely way1 & mu* he repair$ & adju/$4 ,!n1 always :5 ! pr(essor 0 out ( ! way & calm _h desc5d$ on ! app>atus-room1 if n on ! laboratory1 ,mc,farlane sat d[n to r$uce 8 pile ( exam9ation pap]s1 le/ ,monday %\ld arrive ) a new deluge ( crude answ]s & que] mi/akes1 ere ! =m] _h disappe>$4 ,on ,friday aft]noons at #c o'clock he gave solutions ( ! previ\s ,monday's que/ions to any memb]s ( ! class :o c>$ to att5d2 & 8 cle> & delib]ate explanations 7 mu* appreciat$4 ,an unfail+ tribute 0 r5d]$ to him e ye> by ! /ud5ts1 & (t5 took ! =m ( a valuable gift = :i* "o & all _h subscrib$4 ,a recluse he 0 9 8 way1 h>dly anybody knew :]e he liv$--! pr(essor c]ta9ly did n--& a man ( ! highe/ ability & ( ! mo/ absolute unselfi%ness4 ,an h\r 9 ! ev5+ ) "o or two special fri5ds1 & ! /udy ( ,g]man1 7 ! only recreations ( ,mc,farlane's solit>y life4 ,he 0 full ( hum\r1 & told ) ke5 enjoym5t /ories ( ! ,univ]sity wor?ies ( a bygone age4 ,= ?irty ye>s he work$ on = a meagre sal>y1 = dur+ ! e>li] "p ( t "t no provision = assi/ants 0 made 9 ! ,gov]nm5t grant to ! ,scotti% ,univ]sities4 ,by an ord9ance issu$ 9 #ahfa by ! ,univ]sity ,commission]s1 appo9t$ "u ! ,act ( #aheh1 a grant ( #ajj a ye> 0 made f ! ,consolidat$ ,fund = an assi/ant 9 ea* ( ! dep>tm5ts ( ,humanity1 ,greek1 ,ma!matics1 & ,natural ,philosophy1 & = two 9 ! dep>tm5t ( ,*emi/ry2 & ,mc,farlane's position 0 some:at improv$4 ,8 v5]ation = ,?omson 0 su* z few /ud5ts or assi/ants h _h = a ma/]3 8 devotion resembl$ t ( ! old famulus r ?an ! mu* m measur$ respect paid by mod]n assi/ants to _! *iefs4 ,aft] 8 retirem5t ,mc,farlane liv$ on 9 ,glasg[1 & amus$ himself read+ out-(-!-way ,lat9 lit]ature & ) ! calculation ( eclipses6 ,he f9ally return$ to ,alex&ria1 :]e he di$ 9 ,febru>y #ahig4 ,old ,mc,farlane w be held 9 affectionate remembrance s long z /ud5ts ( ! ,natural ,philosophy ,class 9 ! 'fifties & 'sixties & 'sev5ties1 n[1 alas6 a fa/ vani%+ b&1 survive4 ,soon aft] tak+ 8 degree ( ,b4,a4 at ,cambridge 9 #ahde1 ,?omson _h be5 elect$ a ,fell[ ( ,/4 ,pet]'s ,college4 ,9 #aheb he vacat$ 8 ,fell[%ip on 8 m>riage to ,miss ,m>g>et ,crum1 daught] ( ,mr4 ,walt] ,crum ( ,?ornliebank1 ne> ,glasg[1 b 0 re-elect$ 9 #ahga1 & rema9$ !reaft] a ,fell[ ( ,pet]h\se ?r\gh\t 8 life4 ,,*apt] ,,vii ,,! ,,acc\nt ,,( ,,c>not',s ,,!ory ,,( ,,! ,,motive ,,p[] ,,( ,,heat--,,transition ,,to ,,! ,,dynamical ,,!ory ,,( ,,heat ,! meet+ ( ,?omson & ,j\le at ,ox=d 9 #ahdg 0 fraught ) important results to ! !ory ( heat4 ,?omson _h previ\sly become acqua9t$ ) ,c>not's essay1 mo/ probably ?r\gh ,clapeyron's acc\nt ( x 9 ! ,j\rnal de l'cole ,polyte*nique1 #ahcd1 & _h adopt$ ,c>not's view t :5 "w 0 done by a heat eng9e heat 0 m]ely let d[n f a body at "o temp]ature to a body at a l[] temp]ature4 ,j\le app>5tly knew no?+ ( ,c>not's !ory1 & _h !re=e come to ! consid]ation ( ! subject )\t any preconceiv$ op9ions4 ,he _h ?us be5 l$ to =m a cle> notion ( heat z some?+ :i* c\ld be trans=m$ into "w1 & vice v]sa4 ,?is 0 ! root idea ( 8 attempt to f9d ! dynamical equival5t ( heat4 ,x 0 obvi\s t a heat eng9e took heat f a s\rce & gave heat to a refrig]ator1 & ,j\le naturally conclud$ t ! appe>ance ( ! "w done by ! eng9e mu/ be accompani$ by ! disappe>ance ( a quantity ( heat ( :i* ! "w done 0 ! equival5t4 ,he c>ri$ ?is idea consi/5tly ?r\gh all 8 "w ^u en]gy-*anges1 n m]ely 9 heat eng9es b 9 :at might be call$ electric eng9es4 ,= he po9t$ out t ! heat produc$ 9 ! circuit ( a voltaic batt]y 0 ! equival5t ( ! en]gy-*anges )9 ! batt]y1 & t1 moreov]1 :5 an electromagnetic eng9e 0 driv5 by ! curr5t1 or :5 electro*emical decomposition 0 effect$ 9 a voltamet] 9 ! circuit1 ! heat evolv$ 9 ! circuit = a giv5 exp5diture ( ! mat]ials ( ! batt]y 0 less ?an x w\ld o!rwise h be51 by ! equival5t ( ! "w done by ! eng9e1 or ( ! *emical *anges effect$ 9 ! voltamet]4 ,?us ,j\le 0 9 possession at an e>li] date ?an ,?omson ( ! fundam5tal notion ^u :i* ! true dynamical !ory ( heat eng9es is f\nd$4 ,?omson1 on ! o!r h&1 z soon z he _h receiv$ ?is idea1 0 able to add to x ! conception1 d]iv$ f ,c>not1 ( a rev]sible eng9e z ! eng9e ( greate/ effici5cy1 & to d$uce 9 a highly orig9al mann] all ! consequ5ces ( ^! doctr9es :i* g to make up ! ord9>y !rmodynamics ev5 ( ! pres5t "t4 ,?\gh ,clausius 0 ! fir/1 z we %all see1 to d$uce v>i\s important !orems1 yet ,?omson's discussion ( ! "q _h a quality peculi>ly its own4 ,x 0 m>k$ by t fre$om f un/at$ assumptions1 f extrane\s consid]ations1 f vagu5ess ( /atem5t & ( ?\ght1 :i* *>act]ises all 8 applications ( ma!matics to physics4 ,! physical ideas are always set =? cle>ly & 9 su* a mann] t _! quantitative repres5tation is imm$iate3 we %all h an example ( ?is 9 ! doctr9e ( absolute temp]ature4 ,9 mo/ ( ! !rmodynamical discussions :i* take ! great memoir ( ,clausius z _! />t+ po9t1 temp]ature is suppos$ to be giv5 by a hypo!tical some?+ :i* is call$ a p]fect gas1 & x is v difficult1 if n impossible1 to ga!r a precise notion ( ! prop]ties ( su* a gas & ( ! temp]ature scale !reon f\nd$4 ,?omson's scale enables a p]fect gas to be def9$1 & ! deviations ( ! prop]ties ( ord9>y gases f ^? ( su* a gas to be obs]v$ & measur$4 ,! idea1 !n1 :i* ,j\le _h communicat$ to ,section ,a1 :5 ,?omson int]pos$ to call att5tion to its importance1 0 t "w sp5t 9 ov]com+ friction _h its equival5t 9 ! heat produc$1 t1 9 fact1 ! am\nt ( heat g5]at$ 9 su* a case 0 proportional to ! "w sp5t1 q irrespective ( ! mat]ials us$ 9 ! process1 provid$ no *ange ( ! int]nal en]gy ( any ( !m took place s z to affect ! result+ quantity ( heat4 ,?is =c$ ^u physici/s ! view po9t$ to by ! doctr9e ( ! immat]iality ( heat1 e/abli%$ by ! exp]im5ts ( ,rum=d & ,davy1 t heat itself 0 a =m ( en]gy2 & ?us ! pr9ciple ( cons]vation ( en]gy 0 fre$ f its "o defect1 its app>5t failure :5 "w 0 done aga9/ friction4 ,rum=d _h not$ ! v great evolution ( heat :5 gun-metal 0 rubb$ by a blunt bor]1 & _h come to ! reasonable conclusion t :at 0 evolv$ 9 app>5tly unlimit$ quantity by ! abrasion or cutt+ d[n ( a negligible quantity ( mat]ials c\ld n be a mat]ial sub/ance4 ,he _h also made a r\gh e/imate ( ! relation betwe5 ! "w sp5t 9 driv+ ! bor] by horse-p[] & ! heat g5]at$4 ,j\le's me?od ( det]m9+ ! "w-equival5t ( heat 0 a ref9em5t ( ,rum=d's1 b diff]$ 9 ! all-important respect t accurate means 7 employ$ = measur+ ! exp5diture ( "w & ! ga9 ( heat4 ,he /irr$ a liquid1 su* z wat] or m]cury1 9 a k9d ( *urn driv5 by a fall+ weight4 ,! range ( desc5t ( ! weight enabl$ ! "w consum$ to be exactly e/imat$1 & a s5sitive !rmomet] 9 ! liquid measur$ ! rise ( temp]ature2 ?us ! heat produc$ 0 accurately det]m9$4 ,! rise ( temp]ature 0 v slight1 & ! *ange ( /ate ( ! liquid1 & !re=e any possible *ange 9 its int]nal en]gy1 0 inf9itesimal4 ,! exp]im5ts 7 c>ri$ out ) great c>e1 & includ$ v exact measurem5ts ( ! v>i\s corrections--= example1 ! am\nt ( "w sp5t at pulleys & pivots )\t affect+ ! liquid1 & ! loss ( heat by radiation4 ,! exp]im5ts prov$ t ! "w sp5t on ! liquid & ! heat produc$ 7 9 direct proportion to "o ano!r4 ,he f\nd1 f9ally1 9 #ahej1 t #ggb foot-p\nds ( "w at ,man*e/] g5]at$ "o ,briti% !rmal unit1 t is1 z mu* heat z suffic$ to raise a p\nd ( wat] f #fj ,f4 to #fa ,f4 ,an approximation to ?is conclusion 0 conta9$ 9 ! pap] :i* he communicat$ to ! ,briti% ,association at ,ox=d 9 #ahdg4 ,! results ( a lat] det]m9ation made ) an improv$ app>atus1 & complet$ 9 #ahgh1 gave a v slightly high] result4 ,:5 correct$ to ! correspond+ ,fahr5heit degree on ! air !rmomet] x mu/ be increas$ by some:at less ?an "o p] c5t4 ,! exact relation has be5 ! subject dur+ ! la/ tw5ty ye>s ( mu* ref9$ exp]im5tal "w1 b )\t any s]i\s alt]ation ( ! numb] indicat$ above4 ,x is probable t 9 consequ5ce ( ! conf]5ce :i* he _h ) ,j\le at ,ox=d ,?omson _h 8 ?\ghts turn$ = "s "t almo/ exclusively to ! dynamical !ory ( heat eng9es4 ,he work$ at ! subject almo/ cont9u\sly = a long "t1 s5d+ pap] aft] pap] to ! ,ed9burgh ,royal ,society4 ,z we h se51 he _h giv5 ,j\le a description ( ,c>not's essay on ! ,motive ,p[] ( ,heat & ! conclusions1 or "s ( !m1 !re9 conta9$4 ,j\le's result1 & ! !rmodynamic law :i* x e/abli%$1 gave ! key to ! correction ( ,c>not's !ory necess>y to br+ x into l9e ) a complete doctr9e ( en]gy1 :i* %\ld take acc\nt ( "w done aga9/ frictional resi/ances4 ,may] ( ,heilbronn _h endeav\r$ to det]m9e ! dynamical equival5t ( heat 9 #ahdb1 by calculat+ f ! k available at ! "t ( ! two specific heats ( air--! specific heat at con/ant pressure & ! specific heat at con/ant volume--! heat value ( ! "w sp5t 9 compress+ air f a giv5 volume to a small] "o4 ,! pr9ciple ( ?is det]m9ation is easily und]/ood1 b x involves an assumption t is n always cle>ly p]ceiv$4 ,let ! air be imag9$ conf9$ 9 a cyl9d] clos$ by a frictionless pi/on1 :i* is kept f mov+ out "u ! air pressure by =ce appli$ f )\t4 ,let heat be giv5 to ! air s z to raise its temp]ature1 :ile ! pi/on moves out s z to keep ! pressure con/ant4 ,if ! pressure be p & ! increase ( volume be dv1 ! "w done aga9/ ! ext]nal =ce is pdv4 ,let ! rise ( temp]ature be "o degree ( ! ,c5tigrade scale1 & ! mass ( air be "o gramme1 ! heat giv5 to ! gas is ! specific heat ,cp ( ! gas at con/ant pressure1 = !re is only slight v>iation ( specific heat ) temp]ature4 ,b if ! pi/on _h be5 fix$ ! heat requir$ = ! same rise ( temp]ature w\ld h be5 ,cv1 ! specific heat at con/ant volume4 ,n[ ,may] assum$ t ! excess ( ! specific heat ,cp above ,cv 0 ! !rmal equival5t ( ! "w pdv done 9 ! =m] case4 ,?us he obta9$ ! equation ,j7,cp ,cv7 pdv1 :]e ,j d5otes ! dynamical equival5t ( heat & ,cp1 ,cv are tak5 9 !rmal units4 ,b if a be ! coeffici5t ( expansion ( ! air "u con/ant pressure 7t is #abgc71 & v be ! volume ( ! air at #j ,c41 we h dv av1 s t ,j7,cp ,cv7 apv4 ,n[ if p be "o atmosph]e1 say #a4jad #ajf dynes p] squ>e c5timetre1 & ! temp]ature be ! freez+ po9t ( wat]1 ! volume ( a gramme ( air is #a4jjabic 9 cubic c5timetres4 ,h5ce ,j7,cp ,cv7 7#a4jad #ajf77bgc 4#jjabic7 f :i*1 if ,cp ,cv is kn[n1 ! value ( ,j c be f\nd4 ,9 ,may]'s "t ! diff]5ce ( ! specific heats ( air 0 imp]fectly kn[n1 & s ,j c\ld n be f\nd ) any?+ l accuracy4 ,f ,regnault's exp]im5ts on ! specific heat at con/ant pressure1 & f ! kn[n ratio ( ! specific heats z d$uc$ f ! velocity ( s\nd comb9$ ) ,regnault's result1 ! value ( ,cp ,cv may be tak5 z 4#jfhf4 ,?us ,j works out to #db4b #ajf1 9 ergs p] calorie1 :i* is n f> f ! true value4 ,may] obta9$ a result equival5t to #cf4e #ajf ergs p] calorie4 ,! assumption on :i* ?is calculation is f\nd$ is t !re is no alt]ation ( ! int]nal en]gy ( ! gas 9 consequ5ce ( expansion4 ,if ! air :5 rais$ 9 temp]ature1 & at ! same "t increas$ 9 volume1 conta9$ less int]nal en]gy ?an :5 simply heat$ )\t alt]ation ( volume1 ! en]gy evolv$ w\ld be available to aid ! p]=mance ( ! "w done aga9/ ext]nal =ces1 & less heat w\ld be requir$1 or1 9 ! contr>y case1 m heat w\ld be requir$1 ?an w\ld be necess>y if ! int]nal en]gy rema9$ unalt]$4 ,?us putt+ d,w = pdv1 ! "w done1 e = ! int]nal en]gy be=e expansion1 & d,h = ! heat giv5 to ! gas1 we h obvi\sly ! equation ,jd,h de d,w :]e de is ! *ange ( int]nal en]gy due to ! alt]ation ( volume1 toge!r ) ! alt]ation ( temp]ature4 ,if n[ ! temp]ature be alt]$ )\t expansion1 no ext]nal "w is done & d,w = t case is z]o4 ,let e & ,h be ! en]gy *ange & ! heat suppli$1 !n 9 ?is case ,j,h e ,o ,?us ,j7d,h ,h7 de e d,w & ! assumption is t de e1 s t d,w ,j7d,h ,h72 t is1 d,w ,j7,cp ,cv71 :5 ! rise ( temp]ature is #a ,c4 & ! mass ( air is "o gramme4 ,?is assumption requires ju/ification1 & by an exp]im5t ( ,j\le's1 :i* 0 repeat$ 9 a m s5sitive =m devis$ by ,?omson1 x 0 %[n to be a v close approximation to ! tru?4 ,j\le's exp]im5t is well kn[n3 ! explanation giv5 above may s]ve to make cle> ! nature ( ! rese>* und]tak5 lat] by ,?omson & ,j\le conjo9tly4 ,! inv]se process1 ! conv]sion ( heat into "w1 requir$ inve/igation1 & x is ?is t con/itutes ! sci5ce ( !rmodynamics4 ,x 0 ! subject ( ! celebrat$ ,rflexions sur la ,puissance ,motrice du ,feu1 et sur les ,ma*9es ,propres ,dvelopp] cette ,puissance1 publi%$ 9 #ahbd by ,sadi ,c>not1 an uncle ( ! late ,presid5t ( ! ,fr5* ,republic4 ,only a few copies ( ?is essay 7 issu$1 & its text 0 kn[n to v few p]sons tw5ty-f\r ye>s lat]1 :5 x 0 repr9t$ by ! ,academy ( ,sci5ces4 ,its me?ods & conclusions 7 set =? by ,?omson 9 #ahdi 9 a memoir :i* he entitl$1 ,an ,acc\nt ( ,c>not's ,!ory ( ! ,motive ,p[] ( ,heat4 ,num]ical results d$uc$ f ,regnault's exp]im5ts on /eam 7 includ$2 & ! memoir z a :ole l$ naturally 9 ,?omson's h&s to a correct$ !ory ( heat eng9es1 :i* he publi%$ 9 #aheb4 ,c>not's view ( ! work+ ( a heat eng9e 0 f\nd$ on ! analogy ( ! p]=mance ( "w by a /ream ( wat] desc5d+ f a high] level to a l[]4 ,! same quantity ( wat] fl[s away 9 a giv5 "t f a wat] :eel 9 ! tail-race z is receiv$ 9 t "t by ! :eel f ! supply /ream4 ,n[ a heat eng9e receives heat f a supply+ body1 or s\rce1 at "o temp]ature & p>ts ) heat to ano!r body 7= example1 ! cond5s] ( a /eam eng9e7 at a l[] temp]ature4 ,?is body is usually call$ ! refrig]ator4 ,accord+ to ,c>not ^! temp]atures correspond$ to ! two levels 9 ! case ( ! wat] :eel2 ! heat 0 :at fl[$ ?r\gh ! eng9e4 ,?us 9 8 !ory z mu* heat 0 giv5 up by a heat eng9e to ! body at ! l[] temp]ature z 0 receiv$ by x f ! s\rce4 ,! heat 0 simply transf]r$ f ! body at ! high] temp]ature to ! body at ! l[]2 & ?is transf]5ce 0 suppos$ to be ! s\rce ( ! "w4#ag ,! fir/ law ( !rmodynamics bas$ on ,j\le's proportionality ( heat produc$ to "w exp5d$1 & ! conv]se assum$ & v]ifi$ a po/]iori1 %[$ t ?is view is errone\s1 & t ! heat deliv]$ to ! refrig]ator mu/ be less 9 am\nt ?an t receiv$ f ! s\rce1 by exactly ! am\nt :i* is conv]t$ into "w1 toge!r ) ! heat :i*1 9 an imp]fect eng9e1 is lo/ by conduction1 etc41 f ! cyl9d] or o!r work+ *amb]4 ,?is *ange 0 made by ,?omson 9 8 second pap]3 b he f\nd ! ideas ( ,c>not ( direct & fruitful application 9 ! new !ory4 ,^! 7 ! cycle ( op]ations & ! ideal rev]sible eng9e4 ,9 ! ,c>not cycle ! work+ sub/ance--:i* might be a gas or a vap\r1 or a liquid1 or a vap\r & its liquid 9 contact3 x did n matt] :at = ! result--0 suppos$ to be put ?r\gh a succession ( *anges 9 :i* ! f9al /ate co9cid$ ) ! initial4 ,?us ! sub/ance hav+ be5 br\ght back to ! same physical condition z x _h :5 ! cycle began1 has ! same int]nal en]gy z x _h at ! beg9n+1 & 9 ! reckon+ ( ! "w done by or aga9/ ext]nal =ces1 no?+ requires to be set to ! acc\nt ( ! work+ sub/ance4 ,?is is ! fir/ great advantage ( ! me?od ( reason+ :i* ,c>not introduc$4 ,! ideal eng9e 0 a v simple affair3 b ! notion ( rev]sibility is difficult to express 9 a =m suffici5tly def9ite & precise4 ,c>not does n attempt ?is2 he m]ely cont5ts himself ) describ+ c]ta9 cycles ( op]ations :i* obvi\sly c be c>ri$ ?r\gh 9 ! rev]se ord]4 ,nor does ,?omson g fur!r 9 8 ,acc\nt ( ,c>not's ,!ory1 ?\gh he /ates ! crit]ion ( a p]fect eng9e 9 ! words1 ,a p]fect !rmodynamic eng9e is su* t1 :atev] am\nt ( me*anical effect x c d]ive f a c]ta9 !rmal ag5cy1 if an equal am\nt be sp5t 9 work+ x backw>ds1 an equal rev]se !rmal effect w be produc$4 ,?is proposition 0 prov$ by ,c>not3 & ! foll[+ =mal /atem5t 9 ! essay is made3 ,la puissance motrice de la *aleur e/ indep5dante des ag5ts mis en uvre p\r la ralis]3 sa quantit e/ fixe uniquem5t p> les temp]atures des corps entre lesquels se fait1 en d]ni] rsultat1 le transport du calorique4 ,! result involv$ 9 ea*1 t ! "w done 9 a cycle by an ideal eng9e dep5ds on ! temp]atures betwe5 :i* x works & n at all on ! work+ sub/ance1 is1 z we %all see1 ( ! greate/ importance4 ,! pro( ( ! proposition1 by suppos+ a m effici5t eng9e ?an ! ideal "o to exi/1 & to be c\pl$ ) ! latt]1 s t ! m effici5t w\ld p]=m ! cycle =w>ds & ! ideal eng9e ! same cycle backw>ds1 is well kn[n4 ,9 ,c>not's view ! =m] w\ld d m "w by lett+ d[n a giv5 quantity ( heat f ! high] to ! l[] temp]ature ?an 0 sp5t on ! latt] 9 transf]r+ ! same quantity ( heat f ! l[] to ! high] temp]ature1 s t no heat w\ld be tak5 f or giv5 to s\rce or refrig]ator1 :ile !re w\ld be a ga9 ( "w on ! :ole4 ,?is w\ld be equival5t to admitt+ t useful "w c\ld be cont9ually p]=m$ )\t any result+ !rmal or o!r *ange 9 ! ag5ts p]=m+ ! "w4 ,ev5 at t "t ?is c\ld n be admitt$ z possible1 & h5ce ! supposition t a m effici5t eng9e ?an ! rev]sible "o c\ld exi/ 0 unt5able4 ,c>not %[$ t ! "w done by an ideal eng9e1 9 transf]r+ heat f "o temp]ature to ano!r1 0 to be f\nd by means ( a c]ta9 function ( ! temp]ature1 h5ce call$ ,c>not's function4 ,! correspond+ function 9 ! true dynamical !ory is always call$ ,c>not's4 ,a c]ta9 assignm5t ( value to x gave1 z we %all see1 ,?omson's fam\s absolute !rmodynamic scale ( temp]ature4 ,9 ! light ( ! facts & !ories :i* n[ exi/1 & are almo/ ! commonplaces ( physical text books1 x is v int]e/+ to review ! ideas & difficulties :i* occurr$ to ! f\nd]s ( ! sci5ce ( heat sixty ye>s ago4 ,= example1 ,?omson asks1 9 8 ,acc\nt ( ,c>not's ,!ory1 :at becomes ( ! me*anical effect :i* might be produc$ by heat :i* is transf]r$ f "o body to ano!r by conduction4 ,! heat leaves "o body & ent]s ano!r & no me*anical effect results3 if x pass$ f "o to ! o!r ?r\gh a heat eng9e1 me*anical effect w\ld be produc$3 :at is produc$ 9 place ( ! me*anical effect :i* is lo/8 ,?is he calls a v p]plex+ "q1 & hopes t x w1 be=e long1 be cle>$ up4 ,he /ates1 fur!r1 t ! difficulty w\ld be entirely avoid$ by ab&on+ ,c>not's pr9ciple t me*anical effect is obta9$ by ! transf]5ce ( heat f "o body to ano!r at a l[] temp]ate4 ,j\le urges precisely ?is solution ( ! difficulty 9 8 pap]1 ,on ! ,*anges ( ,temp]ature produc$ by ! ,r>efaction & ,cond5sation ( ,air 7,phil4 ,mag41 ,may #ahde74 ,?omson notes ?is1 b adds1 ,if we d s1 h[ev]1 we meet ) innum]able o!r difficulties--insup]able )\t fur!r exp]im5tal inve/igation1 & an entire recon/ruction ( ! !ory ( heat f its f\ndation4 ,x is 9 reality to exp]im5t t we mu/ look1 ei!r = a v]ification ( ,c>not's axiom1 & an explanation ( ! difficulty we h be5 consid]+1 or = an entirely new basis ( ! ,!ory ( ,heat4 ,! exp]im5ts "h ask$ = _h already1 z 0 soon aft] p]ceiv$ by ,?omson1 be5 made by ,j\le1 n m]ely 9 8 det]m9ations ( ! dynamical equival5t ( heat1 b 9 8 exce$+ly important inve/igation ( ! en]gy *anges 9 ! circuit ( a voltaic cell1 or ( a magneto-electric ma*9e4 ,moreov]1 ! answ] to ?is v p]plex+ "q 0 aft]w>ds to be giv5 by ,?omson himself 9 8 pap]1 ,on a ,univ]sal ,t5d5cy 9 ,nature to ! ,dissipation ( ,me*anical ,en]gy1 publi%$ 9 ! ,ed9burgh ,proce$+s 9 #aheb4 ,aga91 we f9d1 a page or two e>li] 9 ! ,acc\nt ( ,c>not's ,!ory1 ! "q ask$ ) respect to ! heat evolv$ 9 ! circuit ( a magneto-electric ma*9e1 ,is ! heat :i* is evolv$ 9 "o "p ( ! clos$ conductor m]ely transf]r$ f ^? p>ts :i* are subject to ! induc+ influ5ce8 & ! /atem5t made t ,j\le _h exam9$ ?is "q1 & decid$ t x mu/ be answ]$ 9 ! negative4 ,b ,?omson goes on to say1 ,be=e we c f9ally conclude t heat is absolutely g5]at$ 9 su* op]ations1 x w\ld be necess>y to prove t ! induc+ magnet does n become l[] 9 temp]ature & ?us comp5sate = ! heat evolv$ 9 ! conductor4 ,"h1 app>5tly1 ! idea ( "w done 9 mov+ ! magnet1 or ! conductor 9 ! magnetic field1 is n pres5t to ,?omson's m9d2 = if x _h be51 ! idea t ! "w ?us sp5t might h its equival5t1 9 "p1 at lea/1 9 heat g5]at$ 9 ! circuit1 w\ld no d\bt h occurr$ to him & be5 /at$4 ,?is idea _h be5 us$ j a ye> be=e by ,helmholtz1 9 8 essay ,die ,erhaltung d] ,kraft1 to acc\nt = ! heat produc$ 9 ! circuit by ! induc$ curr5t1 t is1 to answ] ! fir/ "q put above 9 ! s5se 9 :i* ,j\le answ]$ x4 ,! subject1 h[ev]1 0 fully work$ out by ,?omson 9 a pap] publi%$ 9 ! ,philosophical ,magaz9e = ,decemb] #ahea1 to :i* we %all ref] lat]4 ,tables ( ! "w p]=m$ by v>i\s /eam eng9es work+ betwe5 diff]5t /at$ temp]atures 7 giv5 at ! close ( ! ,acc\nt1 & comp>$ ) ! !oretical duty z calculat$ = ,c>not's ideal p]fect eng9e4 ,( c\rse ! !oretical duty 0 calculat$ f ! temp]atures ( ! boil] & cond5s]2 ! mu* great] fall ( temp]ature f ! furnace to ! boil] 0 neglect$ z inevitable1 s t ! loss involv$ 9 t fall is n tak5 acc\nt (4 ,c>not's !ory gave = ! !oretical duty ( "o heat unit 7equival5t to #acij foot-p\nds ( "w7 #ddj foot-p\nds = boil] at #adj ,c4 & cond5s] at #cj ,c42 & ! be/ p]=mance record$ 0 #bec foot-p\nds1 giv+ a p]c5tage ( #eg4e p] c5t4 ,! wor/ 0 t ( common eng9es consum+ #ab lb4 ( coal p] horse-p[] p] h\r1 & gave #ch4a foot-p\nds1 or a p]c5tage ( #h4f p] c5t4 ,^! p]c5tages become on ! dynamical !ory #fh & #aj4c1 s9ce ! true !oretical duty = ! heat unit is only #cga foot-p\nds4 ,x is wor?y ( notice t ! indicator-diagram me?od ( graphically repres5t+ ! *anges 9 a cycle ( op]ations is adopt$ 9 ,?omson's ,acc\nt1 b does n occur 9 ,c>not's essay4 ,! cycles consi/ ( two iso!rmal *anges & two adiabatic *anges2 t is1 two *anges at ! temp]atures ( ! s\rce & refrig]ator respectively1 & two *anges--f ! high] to ! l[] temp]ature1 & f ! l[] to ! high]4 ,^! *anges are made subject to ! condition 9 ea* case t ! sub/ance nei!r ga9s nor loses en]gy 9 ! =m ( heat1 b is cool$ 9 ! "o case by expansion & heat$ 9 ! o!r by compression4 ,! indicator diagram 0 due n to ,?omson b to ,clapeyron 7see p4 #ii above71 :o us$ x to illu/rate an acc\nt ( ,c>not's !ory4 ,!re appe>$ 9 ! issue ( ! ,ed9burgh ,philosophical ,transactions = ,janu>y #b1 #ahdi1 along ) ! ,acc\nt ( ,c>not's ,!ory1 a pap] by ,james ,?omson1 entitl$1 ,!oretical ,consid]ations on ! ,effect ( ,pressure 9 ,l[]+ ! ,freez+ ,po9t ( ,wat]4 ,! au?or pr$ict$ t1 unless ! pr9ciple ( cons]vation ( en]gy 0 at fault1 ! effect ( increase ( pressure on wat] 9 ! act ( freez+ w\ld be to l[] ! freez+ po9t2 & he calculat$ f ,c>not's !ory ! am\nt ( l[]+ :i* w\ld be produc$ by a giv5 increm5t ( pressure4 ,! pr$iction ?us made 0 te/$ by exp]im5ts c>ri$ out 9 ! ,physical ,laboratory by ,?omson1 & ! results obta9$ completely confirm$ ! conclusions arriv$ at by !ory4 ,?is pr$iction & its v]ification h be5 ju/ly reg>d$ z ( great importance 9 ! hi/ory ( ! dynamical !ory ( heat2 & !y af=d an excell5t example ( ! pr$ictive "* ( a true sci5tific !ory4 ,! !ory ( ! matt] w be ref]r$ to 9 ! next *apt]4 ,,*apt] ,,viii ,,!rmodynamics ,,& ,,absolute ,,!rmometry ,! fir/ /atem5t ( ! true dynamical !ory ( heat1 bas$ on ! fundam5tal idea t ! "w done 9 a ,c>not cycle is to be acc\nt$ = by an excess ( ! heat receiv$ f ! s\rce ov] ! heat deliv]$ to ! refrig]ator1 0 giv5 by ,clausius 9 a pap] :i* appe>$ 9 ,pogg5dorff's ,annal5 9 ,m>* & ,april #ahej1 & 9 ! ,philosophical ,magaz9e = ,july #ahej1 "u a title :i* is a ,g]man translation ( t ( ,c>not's essay4 ,9 t pap] ! ,fir/ ,law ( ,!rmodynamics is explicitly /at$ z foll[s3 ,9 all cases 9 :i* "w is produc$ by ! ag5cy ( heat1 a quantity ( heat proportional to ! am\nt ( "w produc$ is exp5d$1 &1 inv]sely1 by ! exp5diture ( t am\nt ( "w exactly ! same am\nt ( heat is g5]at$4 ,mod]n !rmodynamics is bas$ on ?is pr9ciple & on ! s-call$ ,second ,law ( ,!rmodynamics2 :i* is1 h[ev]1 v>i\sly /at$ by diff]5t au?ors4 ,accord+ to ,clausius1 :o us$ 9 8 pap] an argum5t l t ( ,c>not bas$ on ! transf]5ce ( heat f ! s\rce to ! refrig]ator1 ! f\ndation ( ! second law 0 ! fact t heat t5ds to pass f hott] to cold] bodies4 ,9 #ahed 7,pogg4 ,ann41 ,dec4 #ahed7 he /at$ 8 fundam5tal pr9ciple explicitly 9 ! =m3 ,heat c nev] pass f a cold] to a hott] body1 unless "s o!r *ange1 connect$ !re)1 take place at ! same "t1 & gives 9 a note ! %ort] /atem5t1 :i* he reg>ds z equival5t3 ,heat _c ( itself pass f a cold] to a hott] body4 ,we %all n "h discuss ! mann] 9 :i* ,clausius appli$ ?is pr9ciple3 b he arriv$ at & describ$ 9 8 pap] _m important results1 ( :i* he mu/ !re=e be reg>d$ z ! prim>y discov]]4 ,8 !ory z orig9ally set =? 0 lack+ 9 cle>ness & simplicity1 & 0 mu* improv$ by additions made to x on its republication1 9 #ahfd1 ) o!r memoirs on ! ,!ory ( ,heat4 ,9 ! ,transactions ,r4,s4,e41 = ,m>* #ahea1 ,?omson publi%$ 8 great pap]1 ,on ! ,dynamical ,!ory ( ,heat4 ,! object ( ! pap] 0 /at$ to be ?reefold3 7#a7 ,to %[ :at modifications ( ,c>not's conclusions are requir$1 :5 ! dynamical !ory is adopt$3 7#b7 ,to indicate ! significance 9 ?is !ory ( ! num]ical results d$uc$ f ,regnault's obs]vations on /eam3 7#c7 ,to po9t out c]ta9 rem>kable relations connect+ ! physical prop]ties ( all sub/ances e/abli%$ by reason+ analog\s to t ( ,c>not1 b f\nd$ on ! dynamical !ory4 ,?is pap]1 ?\gh subsequ5t to t ( ,clausius1 is v diff]5t 9 "*4 ,_m ( ! results are id5tical ) ^? previ\sly obta9$ by ,clausius1 b !y are rea*$ by a process :i* is prec$$ by a cle> /atem5t ( fundam5tal pr9ciples4 ,^! pr9ciples h s9ce be5 ! subject ( discussion1 & are n free f difficulty ev5 n[2 b a great /ep 9 advance 0 made by _! c>eful =mulation 9 ,?omson's pap]1 z a prelim9>y to ! erection ( ! !ory & ! d$uction ( its consequ5ces4 ,two propositions are /at$ :i* may be tak5 z ! ,fir/ & ,second ,laws ( ,!rmodynamics4 ,"o is equival5t to ! ,fir/ ,law z /at$ 9 p4 #aaf1 ! o!r enunciates ! pr9ciple ( ,rev]sibility z a crit]ion ( p]fection ( a heat eng9e4 ,we quote ^! propositions4 ,prop4 ,i 7,j\le74--,:5 equal quantities ( me*anical effect are produc$ by any means :atev] f purely !rmal s\rces1 or lo/ 9 purely !rmal effects1 equal quantities ( heat are put out ( exi/5ce or are g5]at$4 ,prop4 ,,ii 7,c>not & ,clausius74--,if an eng9e be su* t :5 work$ backw>ds1 ! physical & me*anical ag5cies 9 e "p ( its motions are all rev]s$1 x produces z mu* me*anical effect z c be produc$ by any !rmodynamic eng9e1 ) ! same temp]atures ( s\rce & refrig]ator1 f a giv5 quantity ( heat4 ,prop4 ,i 0 prov$ by assum+ t heat is a =m ( en]gy & consid]+ always ! "w effect$ by caus+ a work+ sub/ance to pass ?r\gh a clos$ cycle ( *anges1 s t !re 0 no *ange ( int]nal en]gy to be reckon$ )4 ,prop4 ,,ii 0 prov$ by ! foll[+ axiom3 ,x is impossible1 by means ( inanimate mat]ial ag5cy1 to d]ive me*anical effect f any portion ( matt] by cool+ x bel[ ! temp]ature ( ! colde/ ( ! surr\nd+ objects4 ,?is is r a po/ulate ?an an axiom2 = x c h>dly be cont5d$ t x comm&s ass5t z soon z x is /at$1 ev5 f a m9d :i* is conv]sant ) !rmal ph5om5a4 ,x sets =? cle>ly1 h[ev]1 & ) suffici5t gu>d$ness ( /atem5t1 a pr9ciple :i*1 :5 ! process by :i* "w is done is always a cyclical "o1 is n f\nd contradict$ by exp]i5ce1 & "o1 moreov]1 :i* c be at once explicitly appli$ to demon/rate t no eng9e c be m effici5t ?an a rev]sible "o1 & t !re=e ! effici5cy ( a rev]sible eng9e is indep5d5t ( ! nature ( ! work+ sub/ance4 ,x has be5 sugge/$ by ,cl]k ,maxwell t ?is axiom is contradict$ by ! behavi\r ( a gas4 ,accord+ to ! k9etic !ory ( gases an elevation ( temp]ature consi/s 9 an increase ( ! k9etic en]gy ( ! translatory motion ( ! gase\s p>ticles2 & no d\bt !re actually is1 f "t to "t1 a passage ( "s m quickly mov+ p>ticles f a portion ( a gas 9 :i* ! av]age k9etic en]gy is l[1 to a region 9 :i* ! av]age k9etic en]gy is high1 & ?us a transf]5ce ( heat f a region ( l[ temp]ature to "o ( high] temp]ature4 ,maxwell imag9$ a space fill$ ) gas to be divid$ into two comp>tm5ts ,a & ,b by a p>tition 9 :i* 7 small massless trapdoors1 to op5 & %ut :i* requir$ no exp5diture ( en]gy4 ,at ea* ( ^! doors 0 /ation$ a sort+ demon1 ^: duty x 0 to all[ e p>ticle hav+ a velocity great] ?an ! av]age to pass ?r\gh f ,a to ,b1 & to /op all ^? ( small] velocity ?an ! av]age4 ,simil>ly1 ! demons 7 to prev5t all quickly mov+ p>ticles f go+ across f ,b to ,a1 & to pass all sl[ly mov+ p>ticles4 ,9 ?is way1 )\t ! exp5diture ( "w1 all ! quickly mov+ p>ticles c\ld be assembl$ 9 "o comp>tm5t1 & all ! sl[ly mov+ p>ticles 9 ! o!r2 & ?us a diff]5ce ( temp]atures betwe5 ! two comp>tm5ts c\ld be br\ght ab\t1 or a previ\sly exi/+ "o increas$ by transf]5ce ( heat f a cold] to a hott] mass ( gas4 ,contr>y to a n uncommon belief1 ?is process does n invalidate ,?omson's axiom z he int5d$ x to be und]/ood4 ,= ! gas ref]r$ to "h is :at he w\ld h reg>d$ z ! work+ sub/ance ( ! eng9e1 by ! cycles ( :i* all ! me*anical effect 0 d]iv$2 & x is n1 at ! end ( ! process1 9 ! /ate z reg>ds av]age k9etic en]gy ( ! p>ticles 9 :i* x 0 at fir/4 ,t ?is 0 8 answ] to ! impli$ criticism ( 8 axiom conta9$ 9 ,maxwell's illu/ration1 ^? :o h he>d him ref] to ! matt] 9 8 lectures are well aw>e4 ,b ( c\rse x is to be und]/ood t ! sub/ance returns to ! same /ate only 9 a /ati/ical s5se4 ,?omson's demon/ration t a rev]sible eng9e is ! mo/ effici5t is well kn[n1 & ne$ n "h be repeat$ 9 detail4 ,! rev]sible eng9e may be work$ backw>ds1 & ! work+ sub/ance w take 9 heat :]e 9 ! direct action x gave x out1 & vice v]sa3 ! sub/ance w d "w aga9/ ext]nal =ces :]e 9 ! direct action x _h "w done ^u x1 & vice v]sa3 9 %ort1 all ! physical & me*anical *anges w be ( ! same am\nt1 b m]ely rev]s$1 at e /age ( ! backw>d process4 ,?us if an eng9e ,a be m effici5t ?an a rev]sible "o ,b1 x w conv]t a l>g] p]c5tage ( an am\nt ( heat ,h tak5 9 at ! s\rce into "w ?an w\ld ! rev]sible "o work+ betwe5 ! same temp]atures4 ,?us if h be ! heat giv5 to ! refrig]ator by ,a1 & h' t giv5 by ,b :5 bo? "w directly & take 9 ,h2 h mu/ be less ?an h'4 ,!n c\ple ! eng9es toge!r s t ,b works backw>ds :ile ,a works directly4 ,a w take 9 ,h & deliv] h1 & d "w equival5t to ,h h4 ,b w take h' f ! refrig]ator & deliv] ,h to ! s\rce1 & h "w equival5t to ,h h' sp5t ^u x4 ,!re w be no heat on ! :ole giv5 to or tak5 f ! s\rce2 b heat h' h w be tak5 f ! refrig]ator1 & "w equival5t to ?is w be done4 ,?us by a cyclical process1 :i* leaves ! work+ sub/ance z x 01 "w is done at ! exp5se ( heat tak5 f ! refrig]ator1 :i* ,?omson's po/ulate affirms to be impossible4 ,!re=e ! assumption t an eng9e m effici5t ?an ! rev]sible eng9e exi/s mu/ be ab&on$2 & we h ! conclusion t all rev]sible eng9es are equally effici5t4 ,?omson ackn[l$g$ 9 8 pap] ! priority ( ,clausius 9 8 pro( ( ?is proposition1 b /at$ t ?is demon/ration _h occurr$ to him be=e he 0 aw>e t ,clausius _h dealt ) ! matt]4 ,he n[ cit$1 z examples ( ! ,fir/ ,law ( ,!rmodynamics1 ! results ( ,j\le's exp]im5ts reg>d+ ! heat produc$ 9 ! circuits ( magneto-electric ma*9es1 & ! fact t :5 an electric curr5t produc$ by a !rmal ag5cy or by a batt]y drives a motor1 ! heat evolv$ 9 ! circuit by ! passage ( ! curr5t is less5$ by ! equival5t ( ! "w done on ! motor4 ,illu/ration3 ,,fig4 #ab4 ,9 ! ,c>not cycle1 ! fir/ op]ation is an iso!rmal expansion 7,,ab 9 ,fig4 #ab71 9 :i* ! sub/ance increases 9 volume by dv1 & takes 9 f ! s\rce heat ( am\nt ,mdv4 ,! second op]ation is an adiabatic expansion1 ,,bc1 9 :i* ! volume is fur!r increas$ & ! temp]ature s9ks by dt to ! temp]ature ( ! refrig]ator4 ,! ?ird op]ation is an iso!rmal compression1 ,,cd1 until ! volume & pressure are su* t an adiabatic compression ,,da w j br+ ! sub/ance back to ! orig9al /ate4 ,if pt be ! rate ( increase ( pressure ) temp]ature :5 ! volume is con/ant1 ! /ep ( pressure f "o iso!rmal to ! o!r is pt4dt2 & ?us ! area ( ! clos$ cycle 9 ! diagram :i* measures ! ext]nal "w done 9 ! succession ( *anges is pt4dtdv4 ,n[1 by ! second law1 ! "w done mu/ be a c]ta9 fraction ( ! "w-equival5t ( ! heat1 ,mdv1 tak5 9 f ! s\rce4 ,?is fraction is indep5d5t ( ! nature ( ! work+ sub/ance1 b v>ies ) ! temp]ature1 & is !re=e a function ( ! temp]ature4 ,its ratio to ! diff]5ce ( temp]ature dt betwe5 s\rce & refrig]ator 0 call$ ,c>not's function1 & ! det]m9ation ( ?is function by exp]im5t 0 at fir/ p]haps ! mo/ important problem ( !rmodynamics4 ,d5ot+ x by 1 we h ! equation pt ,m 444 7,a7 :i* may be tak5 z express+ 9 ma!matical language ! second law ( !rmodynamics4 ,m is "h s *os5 t ,mdv is ! heat express$ 9 units ( "w1 s t does n involve ,j\le's equival5t ( heat4 ,?is equation 0 giv5 by ,c>not3 x is "h obta9$ by ! dynamical !ory :i* reg>ds ! "w done z acc\nt$ = by disappe>ance1 n transf]5ce m]ely1 ( heat4 ,! "w done 9 ! cycle becomes n[ ,mdtdv1 or if ,h d5ote ,mdv1 x is ,hdt4 ,! fraction ( ! heat utilis$ is ?us dt4 ,?is is call$ ! effici5cy ( ! eng9e = ! cycle4 ,f ! fir/ law ,?omson obta9$ ano!r fundam5tal equation4 ,= e sub/ance !re is a relation connect+ ! pressure p 7or m g5]ally ! /ress ( "s type71 ! volume v 7or ! configuration accord+ to ! specifi$ /ress71 & ! temp]ature4 ,we may !re=e take arbitr>y *anges ( any two ( ^! quantities3 ! relation ref]r$ to w give ! correspond+ *ange ( ! ?ird4 ,?omson *ose v & t z ! quantities to be v>i$1 & suppos$ !m to su/a9 arbitr>y small *anges dv & dt 9 consequ5ce ( ! passage ( heat to ! sub/ance f )\t4 ,! am\nt ( heat tak5 9 is ,mdv ,ndt1 :]e ,mdv & ,ndt are heats requir$ = ! *anges tak5 sep>ately4 ,b ! sub/ance exp&+ ?r\gh dv does ext]nal "w pdv4 ,?us ! net am\nt ( en]gy giv5 to ! sub/ance f )\t is ,mdv ,ndt pdv or 7,m p7dv ,ndt2 & if ! sub/ance is made to pass ?r\gh a cycle ( *anges s t x returns to ! physical /ate f :i* x />t$1 ! :ole en]gy receiv$ 9 ! cycle mu/ be z]o4 ,f ?is x foll[s t ! rate ( v>iation ( ,m p :5 ! temp]ature b n ! volume v>ies1 is equal to ! rate ( v>iation ( ,n :5 ! volume b n ! temp]ature v>ies4 ,to see t ?is relation holds1 ! read] unacqua9t$ ) ! prop]ties ( p]fect diff]5tials may proce$ ?us4 ,let ! sub/ance be subject$ to ! inf9itesimal clos$ cycle ( *anges def9$ by 7#a7 a v>iation consi/+ ( ! simultane\s *anges dv1 dt ( volume & temp]ature1 7#b7 a v>iation dv ( volume only1 7#c7 a v>iation dt ( temp]ature only4 ,m p & ,n v>y s z to h def9ite values = ! beg9n+ & end ( ea* /ep1 & ! prop] mean values c be writt5 d[n = ea* /ep at once1 & !re=e ! value ( 7,m p7dv ,ndt obta9$4 ,add+ toge!r ^! values = ! ?ree /eps we get ! integral = ! cycle4 ,! condition t ?is %\ld vani% is at once se5 to be ! relation /at$ above4 ,?is result comb9$ ) ! equation ,a d]iv$ f ! second law1 gives an important expression = ,c>not's function4 ,we %all n pursue ?is discussion fur!r3 s mu* is giv5 to make cle> h[ c]ta9 results z to ! physical prop]ties ( sub/ances 7 obta9$1 & to expla9 ,?omson's scale ( absolute !rmodynamic temp]ature1 :i* is by f> ! mo/ important discov]y )9 ! range ( !oretical !rmodynamics4 ,!re are sev]al scales ( temp]ature3 9 po9t ( fact ! scale ( a m]cury-9-glass !rmomet] is def9$ by ! process ( graduation1 & !re=e !re are z _m su* scales z !re are !rmomet]s1 s9ce no two specim5s ( glass exp& 9 precisely ! same way4 ,equal diff]5ces ( temp]ature d n correspond to equal increm5ts ( volume ( ! m]cury3 = ! glass envelope exp&s also & 9 its own way4 ,on ! scale ( a con/ant pressure gas !rmomet] *anges ( temp]ature are measur$ by v>iations ( volume ( ! gas1 :ile ! pressure is ma9ta9$ con/ant2 on a con/ant volume gas !rmomet] *anges ( temp]ature are measur$ by alt]ations ( pressure :ile ! volume ( ! gas is kept con/ant4 ,ea* scale has its own indep5d5t def9ition1 ?us if ! pressure ( ! gas be kept con/ant1 & ! volume at temp]ature #j ,c4 be v & t at any o!r temp]ature be v we def9e ! num]ical value t1 ?is latt] temp]ature1 by ! equation v v7#a ,et71 :]e ,e is #aajj ( ! increase ( volume su/a9$ by ! gas 9 be+ rais$ f #j ,c4 to #ajj ,c4 ,^! are ! temp]atures ( ref]5ce on an ord9>y c5tigrade !rmomet]1 t is1 ! temp]ature ( melt+ ice & ( saturat$ /eam "u /&>d atmosph]ic pressure1 respectively4 ,?us t has ! value 7vv #a7;,e1 & is ! temp]ature 7on ! con/ant pressure scale ( ! gas !rmomet]7 correspond+ to ! volume v4 ,equal diff]5ces ( temp]ature are su* z correspond to equal increm5ts ( ! volume at #j ,c4 ,simil>ly1 on ! con/ant volume scale we obta9 a def9ition ( temp]ature f ! pressure p1 by ! equation t 7pp #a7;,e'1 :]e p is ! pressure at #j ,c41 & ,e' is #aajj ( ! *ange ( pressure produc$ by rais+ ! temp]ature f #j ,c4 to #ajj ,c4 ,= air ,e is approximately #abgc1 & ?us t #bgc7v v7v4 ,if we take ! case ( v #j1 we get t #bgc4 ,n[1 al?\gh ?is temp]ature may be inaccessible1 we may take x z z]o1 & ! temp]ature d5ot$ by t is1 :5 reckon$ f ?is z]o1 #bgc t4 ,?is z]o is call$ ! absolute z]o on ! con/ant pressure air !rmomet]4 ,! value ( ,e' is v ne>ly ! same z t ( ,e2 & we get 9 a simil> mann] an absolute z]o = ! con/ant volume scale4 ,if ! gas obey$ ,boyle's law exactly at all temp]atures1 ,e w\ld n diff] f ,e'4 ,x 0 sugge/$ to ,?omson by ,j\le1 9 a lett] dat$ ,decemb] #i1 #ahdh1 t ! value ( might be giv5 by ! equation ,,je7#a ,et74 ,"h we take heat 9 dynamical units1 & !re=e ! factor ,j is n requir$4 ,) ^! units ,j\le's sugge/ion is t ,e7#a ,et71 or ) ,e #abgc #a7bgc t71 t is1 #a,t :]e ,t is ! temp]ature reckon$ 9 c5tigrade degrees f ! absolute z]o ( ! con/ant pressure air !rmomet]4 ,! possibility ( adopt+ ?is value ( 0 %[n by ,?omson to dep5d on :e!r or n ! heat absorb$ by a giv5 mass ( gas 9 exp&+ )\t alt]ation ( temp]ature is ! equival5t ( ! "w done by ! exp&+ gas aga9/ ext]nal pressure4 ,! heat ,h absorb$ by ! air 9 exp&+ f volume ,v to ano!r volume ,v' at con/ant temp]ature is ! integral ( ,mdv tak5 f ! =m] volume to ! latt]4 ,b by ! value ( ,m giv5 on p4 #aba1 if ,w be ! integral ( pdv1 t is ! "w done by ! air 9 ! expansion1 ,wt ,h4 ,! equation fulfill$ by ! gas at con/ant pressure 7! def9+ equation = t71 v v7#a ,et71 gives = ! integral ( pdv1 t is ,w1 ! equation ,w pv7#a ,et7log7,v',v71 s t ,wt ,,ew7#a ,et74 ,?us ,h ,,ew7#a ,et74 ,h5ce x foll[s t if ,e7#a ,et71 ! value ( ,h w be simply ,w4 ,?us ,j\le's sugge/$ value ( is only admissible if ! "w done by ! gas 9 exp&+ f a giv5 volume to any o!r is ! equival5t ( ! heat absorb$2 or1 :i* is ! same ?+1 if ! ext]nal "w done 9 compress+ ! gas f "o volume to ano!r is ! equival5t ( ! heat develop$4 ,?is result naturally sugge/s ! =mation ( a new scale ( !rmometry by ! adoption ( ! def9+ relation ,t #a1 :]e ,t d5otes temp]ature4 ,a scale ( temp]ature ?us def9$ is propos$ 9 ! pap] by ,j\le & ,?omson1 ,on ! ,!rmal ,effects ( ,fluids 9 ,motion1 ,"p ,,ii1 :i* 0 publi%$ 9 ! ,philosophical ,transactions = ,june #ahed1 & is :at is n[ univ]sally kn[n z ,?omson's scale ( absolute !rmodynamic temp]ature4 ,x c1 ( c\rse1 be made to give #ajj z ! num]ical value ( ! temp]ature diff]5ce betwe5 #j ,c4 & #ajj ,c4 by prop]ly fix+ ! unit ( ,t4 ,?is scale 0 ! natural successor1 9 ! dynamical !ory1 ( "o :i* ,?omson _h sugge/$ 9 #ahdh1 & :i* 0 f\nd$1 accord+ to ,c>not's idea1 on ! condition t a unit ( heat %\ld d ! same am\nt ( "w 9 desc5d+ ?r\gh ea* degree4 ,?is1 z he po9t$ out1 might ju/ly be call$ an absolute scale1 s9ce x w\ld be indep5d5t ( ! physical prop]ties ( any sub/ance4 ,9 ! same s5se ! scale def9$ by ,t #a is truly an absolute scale4 ,! new scale gives a simple expression = ! effici5cy ( a p]fect eng9e work+ betwe5 two physically giv5 temp]atures1 & assigns ! num]ical values ( ^! temp]atures2 = ! heat ,h tak5 9 f ! s\rce 9 ! iso!rmal expansion :i* =ms ! fir/ op]ation ( ! cycle 7p4 #abj7 is ,mdv1 &1 z we h se51 ! "w done 9 ! cycle is pt4dtdv1 or ,hdt4 ,if we adopt ! expression #a,t = 1 we may put d,t = dt2 & we obta9 = ! "w done ! expression ,hd,t,t4 ,! "w done is ?us ! fraction d,t,t ( ! heat tak5 91 & ?is is :at is prop]ly call$ ! effici5cy ( ! eng9e = ! cycle4 ,if we suppose ! diff]5ce ( temp]atures betwe5 s\rce & refrig]ator to be f9ite1 ,t ,t'1 say1 !n s9ce ,t is ! temp]ature ( ! s\rce1 we h = ! effici5cy 7,t ,t'7,t4 ,if ! heat tak5 9 be ,h1 ! heat reject$ is ,,ht',t1 s t ! heat receiv$ by ! eng9e is to ! heat reject$ by x 9 ! ratio ( ,t' to ,t4 ,?us1 z 0 done by ,?omson1 we may def9e ! temp]atures ( ! s\rce & refrig]ator z proportional to ! heat tak5 9 f ! s\rce & ! heat reject$ to ! refrig]ator by a p]fect eng9e1 work+ betwe5 ^? temp]atures4 ,! scale may be made to h #ajj degrees betwe5 ! temp]ature ( melt+ ice & ! boil+ po9t1 z already expla9$4 ,we %all return to ! comp>ison ( ?is scale ) t ( ! air !rmomet]4 ,at pres5t we consid] "s ( ! !rmodynamic relations ( ! prop]ties ( bodies arriv$ at by ,?omson4 ,fir/ we take ! work+ sub/ance ( ! eng9e z consi/+ ( matt] 9 two /ates or phases2 = example1 ice & wat]1 or wat] & saturat$ /eam4 ,let u apply equation 7,a7 to ?is case4 ,if v1 v be ! volume ( unit ( mass 9 ! fir/ & second /ates respectively1 ! iso!rmal expansion ( ! fir/ "p ( ! cycle w take place 9 consequ5ce ( ! conv]sion ( a mass dm f ! fir/ /ate to ! second4 ,?us dv1 ! *ange ( volume1 is dm7v v74 ,also if ,l be ! lat5t heat ( ! sub/ance 9 ! second /ate1 e4g4 ! lat5t heat ( wat]1 ,mdv ,ldm2 s t ,m7v v7 ,l4 ,if dp be ! /ep ( pressure correspond+ to ! /ep d,t ( temp]ature1 equation 7,a7 becomes d,t,t dp7v v7,l 444 7,b7 ,9 ! case ( coexi/5ce ( ! liquid & solid phases1 ?is gives u ! v rem>kable result t a *ange ( pressure dp w raise or l[] ! temp]ature ( coexi/5ce ( ! two phases1 t is1 ! melt+ po9t ( ! solid1 by ! diff]5ce ( temp]ature1 d,t1 accord+ z v is great] or less ?an v ,?us a sub/ance l wat]1 :i* exp&s 9 freez+1 s t v v is negative1 has its freez+ po9t l[]$ by increase ( pressure & rais$ by dim9ution ( pressure4 ,?is is ! result pr$ict$ by ,pr(essor ,james ,?omson & v]ifi$ exp]im5tally by 8 bro!r 7p4 #aac above74 ,on ! o!r h&1 a sub/ance l p>aff9 wax1 :i* contracts 9 solidify+1 w\ld h its melt+ po9t rais$ by increase ( pressure & l[]$ by a dim9ution ( pressure4 ,! same conclusions w\ld be applicable :5 ! phases are liquid & vap\r ( ! same sub/ance1 if !re 7 any case 9 :i* v v is negative4 ,z x is we see1 :at is well kn[n to be ! case1 t ! temp]ature ( equilibrium ( a liquid ) its vap\r is rais$ by increase ( pressure4 ,ano!r important result ( equation 7,b71 z appli$ to ! liquid & vap\r phases ( a sub/ance1 is ! in=mation :i* x gives z to ! d5sity ( ! saturat$ vap\r4 ,:5 ! two phases coexi/ ! pressure is a function ( ! temp]ature only4 ,h5ce if ! relation ( pressure to temp]ature is kn[n1 dpd,t c be calculat$1 or obta9$ graphically f a curve2 & ! volume v p] unit mass ( ! vap\r w be giv5 9 t]ms ( dpd,t1 ! temp]ature ,t1 & ! volume v p] unit mass ( ! liquid4 ,! d5sity ( saturat$ /eam at diff]5t temp]atures is v difficult to measure exp]im5tally ) any approa* ( accuracy3 b s f> z exp]im5t goes equation 7,b7 is confirm$4 ,! !ory "h giv5 is fully confirm$ by o!r results1 & equation 7,b7 is available = ! calculation ( v = any sub/ance = :i* ! relation betwe5 p & ,t is kn[n4 ,x is ?us t ! d5sity ( saturat$ /eam c be/ be f\nd4 ,we c obta9 ano!r important result = ! case ( ! work+ sub/ance 9 two phases f equation 7,b74 ,! relation is ,l,t c h ,l,t 444 7,c7 :]e c & h are ! specific heats ( ! sub/ance 9 ! two phases respectively1 & ,l is ! lat5t heat ( ! second phase at absolute temp]ature ,t4 ,we %all obta9 ! relation 9 ano!r way1 :i* w illu/rate ano!r mode ( deal+ ) a cycle ( op]ations :i* ,?omson employ$4 ,any small /ep ( *ange ( a sub/ance may be reg>d$ z made up ( a /ep ( volume1 say1 foll[$ by a /ep ( temp]ature1 t is1 by an iso!rmal /ep foll[$ by an adiabatic /ep4 ,9 ?is way any cycle ( op]ations :atev] may be reg>d$ z made up ( a s]ies ( ,c>not cycles4 ,b )\t reg>d+ any cycle ( a m g5]al k9d ?an ,c>not's z ?us comp\nd$1 we c draw conclusions f x by ! dynamical !ory provid$ only x is rev]sible4 ,suppose a gramme1 say1 ( ! sub/ance to be tak5 at a specifi$ temp]ature ,t 9 ! l[] phase1 & to be *ang$ to ! o!r phase at t temp]ature4 ,! heat tak5 9 w be ,l & ! expansion w be v v4 ,next1 keep+ ! sub/ance 9 ! second phase1 & 9 equilibrium ) ! fir/ phase 7t is1 = example1 if ! second phase is saturat$ vap\r1 ! saturation is to cont9ue 9 ! fur!r *ange71 let ! sub/ance be l[]$ 9 temp]ature by d,t4 ,! heat giv5 out by ! sub/ance w be hd,t1 :]e h is ! specific heat ( ! sub/ance 9 ! second phase4 ,n[ at ! new temp]ature ,t d,t let ! sub/ance be :olly br\ght back to ! second phase2 ! heat giv5 out w be ,l ,l,t4d,t4 ,f9ally1 let ! sub/ance1 n[ aga9 all 9 ! fir/ phase1 be br\ght to ! orig9al temp]ature3 ! heat tak5 9 w be cdt1 :]e c is ! specific heat 9 ! fir/ phase4 ,?us ! net excess ( heat tak5 9 ov] heat giv5 out 9 ! cycle is 7,l,t c h7d,t4 ,?is mu/1 9 ! indicator diagram = ! *anges specifi$1 be ! area ( ! cycle or 7v v7p,t4d,t4 ,b by equation 7,b7 ,l,t7v v7 p,t1 & ! area ( ! cycle is 7,l,t7d,t4 ,equat+ ! two expressions ?us f\nd = ! area we get equation 7,c74 ,?is relation 0 arriv$ at by ,clausius 9 8 pap] ref]r$ to above1 & ! priority ( publication is 83 x is "h giv5 9 ! =m :i* x takes :5 ,?omson's scale ( absolute temp]ature is us$4 ,regnault's exp]im5tal results = ! heat requir$ to raise unit mass ( wat] f ! temp]ature ( melt+ ice to any high] temp]ature & evaporate x at t temp]ature enable ! values ( ,l,t & ,l,t to be calculat$1 & !re=e t ( h to be f\nd4 ,x appe>s t h is negative = all ! temp]atures to :i* ,regnault's exp]im5tal results c be held to apply4 ,?is1 z 0 po9t$ out by ,?omson1 means t if a mass ( saturat$ vap\r is made to exp& s z at ! same "t to fall 9 temp]ature1 x mu/ h heat giv5 to x1 o!rwise x w be p>tly cond5s$ into liquid2 &1 on ! o!r h&1 if ! vap\r be compress$ & made to rise 9 temp]ature :ile at ! same "t x is kept saturat$1 heat mu/ be tak5 f x1 o!rwise ! vap\r w become sup]heat$ & s cease to be saturat$4 ,x is conv5i5t to notice "h ! article on ,heat :i* ,?omson wrote = ! n9? edition ( ! ,encyclopdia ,britannica4 ,9 t article he gave a valuable discussion ( ord9>y !rmometry1 ( !rmometry by means ( ! pressures ( saturat$ vap\r ( diff]5t sub/ances--/eam-pressure !rmomet]s1 he call$ !m--( absolute !rmodynamic !rmometry1 all enri*$ ) new exp]im5tal & !oretical inve/igations1 & app5d$ to ! :ole a valuable synopsis1 ) additions ( 8 own1 ( ! ,f\ri] ma!matics ( heat conduction4 ,fir/ deal+ ) temp]ature z measur$ by ! expansion ( a liquid 9 a less expansible vessel1 he %[$ h[ x is 9 reality num]ically reckon$4 ,?is am\nt$ to a discussion ( ! scale ( an ord9>y m]cury-9-glass !rmomet]1 a subject conc]n+ :i* errone\s /atem5ts are n infrequ5tly made 9 text-books4 ,a sket* ( ,?omson's treatm5t ( x is giv5 "h4 ,consid]+ ?is !rmomet] z a vessel consi/+ ( a glass bulb & a long glass /em ( f9e & uni=m bore1 h]metically seal$ & conta9+ only m]cury & m]cury vap\r1 he expla9$ ! num]ical relation betwe5 ! temp]ature z %[n by ! in/rum5t & ! volumes ( ! m]cury & vessel4 ,! scale is really def9$ by ! me?od ( graduation adopt$4 ,two po9ts ( ref]5ce are m>k$ on ! /em at :i* ! top ( ! m]cury /&s :5 ! vessel is imm]s$ 7#a7 9 melt+ ice1 7#b7 9 saturat$ /eam "u /&>d atmosph]ic pressure4 ,! /em is divid$ into p>ts ( equal volume ( bore betwe5 ^! two po9ts & beyond ea* ( !m4 ,= a c5tigrade !rmomet] ! bore-space betwe5 ! two po9ts is divid$ into #ajj equal p>ts1 & ! l[] po9t ( ref]5ce is m>k$ #j & ! upp] #ajj1 & ! o!r divid+ m>ks are numb]$ 9 accordance ) ?is along ! /em4 ,ea* ( ^! p>ts ( ! bore may be call$ a degree-space4 ,n[ let ! in/rum5t conta9 9 its bulb & /em1 up to ! m>k #j1 ,n degree-spaces1 & let v be ! volume ( a degree-space at t temp]ature4 ,! volume up to ! m>k #j w be ,nv1 at t temp]ature2 & if ! sub/ance ( ! vessel be q uni=m 9 quality & free f /ress1 ,n w be ! same = all temp]atures4 ,if v be ! volume ( a degree-space at ! temp]ature ( melt+ ice ! volume ( ! m]cury at t temp]ature w be ,nv4 ,if ,g be ! expansion ( ! glass :5 ! volume ( a degree-space is increas$ f v to v by ! rise ( temp]ature1 !n v v7#a ,g74 ,! volume ( ! m]cury has be5 increas$ !re=e to 7,n n7v7#a ,g7 by ! same rise ( temp]ature1 if ! top ( ! column is !reby made to rise f ! m>k #j s z to occupy n degree-spaces m ?an be=e4 ,b if ,e be ! expansion ( ! m]cury betwe5 ! temp]ature ( melt+ ice & t :i* has n[ be5 atta9$1 ! volume ( ! m]cury is also ,nv7#a ,e74 ,h5ce ,n7#a ,e7 7,n n77#a ,g74 ,?is gives n ,n7,e ,g77#a ,g74 ,if we take1 z is usual1 n z measur+ ! temp]ature1 & sub/itute = x ! symbol t1 we h1 s9ce ,n #ajj7a ,g77,e ,g71 t #ajj 7#a ,g77#a ,g7 7,e ,g77,e ,g7 444 7,d7 ,9 ?is reckon+ ! def9ition ( any temp]ature1 let u say #cg ,c41 is ! temp]ature ( ! vessel & its cont5ts :5 ! top ( ! m]cury column /&s at ! m>k #cg above #j1 on ! scale def9$ by ! graduation ( ! in/rum5t2 b ! num]ical signification ) relation to ! volumes is giv5 by equation 7,d74 ,?is %[s t ! num]ical measure ( any temp]ature involves bo? ! expansion ( ! vessel & t ( ! glass vessel betwe5 ! temp]ature ( melt+ ice & ! temp]ature 9 "q4 ,?is result may be contra/$ ) ! errone\s /atem5t frequ5tly made t equal increm5ts ( temp]ature correspond to equal increm5ts ( ! volume ( ! !rmometric sub/ance4 ,x also %[s t diff]5t m]cury-9-glass !rmomet]s1 h[ev] accurately made & graduat$1 ne$ n agree :5 plac$ 9 a ba? at any o!r temp]ature ?an #j ,c4 or #ajj ,c4 ,?is fact1 & ! results ( ! comp>ison ( !rmomet]s made ) diff]5t k9ds ( glass ) ! normal air !rmomet]1 :i* 0 c>ri$ out by ,regnault1 7 always insi/$ on by ,?omson 9 8 tea*+ :5 he dealt ) ! subject ( heat4 ,! scale ( a m]cury-9-glass !rmomet] is too (t5 9 text-books1 & ev5 9 ,acts ( ,p>liam5t reg>d$ z a p]fectly def9ite ?+1 & ! expansion ( a gas is n infrequ5tly def9$ by ?is indef9ite scale1 in/ead ( be+ us$ z x ought to be1 z ! basis ( def9ition ( ! scale ( ! gas !rmomet]4 ,! :ole treatm5t ( ! s-call$ gase\s laws is too (t51 f a logical po9t ( view1 a mass ( confusion4 ,9 8 article on ,heat ,?omson gave two def9itions ( ! scale ( absolute temp]ature4 ,"o is t /at$ on p4 #abf above1 namely1 t ! temp]ature ( ! s\rce & refrig]ator are 9 ! ratio ( ! heat tak5 9 f ! s\rce to ! heat giv5 to ! refrig]ator1 :5 ! eng9e describes a ,c>not cycle consi/+ ( two iso!rmal & two adiabatic *anges4 ,! o!r def9ition is bett] adapt$ = g5]al use1 z x applies to any cycle :atev] :i* is rev]sible4 ,let ! work+ sub/ance exp& "u con/ant pressure by an am\nt dv 7,,ab' 9 ,fig4 #ab71 & let heat ,h be giv5 to ! sub/ance at ! same "t4 ,! ext]nal "w done is pdv4 ,?omson call$ pdv,h ! "w ratio4 ,n[ let ! temp]ature be rais$ by d,t )\t giv+ heat to ! sub/ance or tak+ heat f x1 & let ! correspond+ pressure rise be dp2 & call dpp ! pressure ratio4 ,! temp]ature ratio d,t,t is equal to ! product ( ! "w ratio & ! pressure ratio1 t is1 d,t,t dvdp,h ,?is is cle>ly true2 = dvdp is ! area ( a cycle l ,,ab',c',d1 repres5t$ 9 ,fig4 #ab1 = :i* an am\nt ( heat ,h is tak5 91 ?\gh n 9 ?is case /rictly at "o temp]ature4 ,& cle>ly1 s9ce 9 ,fig4 #ab ! *ange f ,b' to ,b is adiabatic1 ,h is ! heat :i* w\ld h to be tak5 9 = ! iso!rmal *ange ,,ab 9 ! ,c>not cycle ,,abcd1 :i* has ! same area z ,,ab',c',d4 ,?us ! effici5cy ( ! cycle is dvdp,h1 & ?is by ! =m] def9ition is d,t,t4 ,or we may reg>d ! matt] ?us3--,! am\nt ( heat ,h :i* corresponds to an inf9itesimal expansion dv may be us$ 9 equation 7,a7 :e!r ! expansion is iso!rmal or n1 if we take ,t z ! av]age temp]ature ( ! expansion4 ,h5ce we h dpd,t ,h7dv4,t71 t is1 d,t,t dpdv,h4 ,! !orem on p4 #abh is obta9$ by :at is virtually ?is process4 ,,comp>ison ,,( ,,absolute ,,scale ,,) ,,scale ,,( ,,air ,,!rmomet] ,! comp>ison :i* ,j\le & ,?omson c>ri$ out ( ! absolute !rmodynamic scale ) ! scale ( ! con/ant pressure gas !rmomet] has already be5 ref]r$ to1 & x has be5 %[n t ! two scales w\ld exactly agree1 t is1 absolute temp]ature w\ld be simply proportional to ! volume ( ! gas 9 a gas !rmomet] kept at ! temp]ature to be measur$1 if ! int]nal en]gy ( ! gas 7 n alt]$ by an alt]ation ( volume )\t alt]ation ( temp]ature1 t is1 if ! de e ( p4 #ajg above 7 z]o4 ,j\le te/$ :e!r ?is 0 ! case by imm]s+ two vessels1 connect$ by a tube :i* c\ld be op5$ or clos$ by a /opcock1 9 ! wat] ( a calorimet]1 asc]ta9+ ! temp]ature ) a v s5sitive !rmomet]1 & !n all[+ air :i* _h already be5 compress$ into "o ( ! vessels to fl[ into ! o!r1 :i* 0 initially empty4 ,x 0 f\nd t no alt]ation ( temp]ature ( ! wat] ( ! calorimet] t c\ld be obs]v$ 0 produc$4 ,b ! volume ( ! air _h be5 d\bl$ by ! process1 & if any s5sible alt]ation ( int]nal en]gy _h tak5 place x w\ld h %[n itself by an elevation or a l[]+ ( ! temp]ature ( ! wat]1 accord+ z ! en]gy _h be5 dim9i%$ or increas$4 ,?omson sugge/$ t ! gas to be exam9$ %\ld be =c$ ?r\gh a pipe end+ 9 a f9e nozzle1 or1 pref]ably1 ?r\gh a plug ( por\s mat]ial plac$ 9 a pipe along :i* ! gas 0 =c$ by a pump1 & obs]vations made ( ! temp]ature 9 ! /eady /ream on bo? sides ( ! plug4 ,! exp]im5ts 7 c>ri$ out ) a plug ( compress$ cotton-wool held betwe5 two metal disks pi]c$ ) holes1 9 a tube ( boxwood surr\nd$ also by cotton-wool1 & plac$ 9 a ba? ( wat] closely surr\nd+ ! supply pipe4 ,?is 0 ( metal1 & =m$ ! end ( a long spiral all imm]s$ 9 ! ba?4 ,?us ! temp]ature ( ! gas approa*+ ! plug 0 kept at a uni=m temp]ature det]m9$ by a delicate !rmomet]2 ano!r !rmomet] gave ! temp]ature 9 ! /eady /ream beyond ! plug4 ,9 ! case ( hydrog5 ! exp]im5ts %[$ a slight heat+ effect ( passage ?r\gh ! plug2 air1 oxyg51 nitrog5 & c>bonic acid 7 cool$ by ! passage4 ,! !ory ( ! matt] is set =? 9 ! orig9al pap]s1 & 9 a v elegant mann] 9 ! article on ,heat4 ,! result ( ! analysis %[s t if w be ! positive or negative "w-value ( ! heat :i* w conv]t "o gramme ( ! gas aft] passage to its orig9al temp]ature2 & ,t be absolute temp]ature1 & v volume ( a gramme ( ! gas at pressure p1 & ! diff]5ce ( pressure on ! two sides ( ! plug be dp1 ! equation :i* holds is 7#a,t7 7,tv7 #av 7wdp7 444 7,e7#ah ,x 0 f\nd by ,j\le & ,?omson t w 0 proportional to dp = values ( dp up to five or six atmosph]es4 ,at diff]5t temp]atures1 h[ev]1 9 ! case ( hydrog5 ! heat+ effect 0 f\nd to dim9i% ) rise ( temp]ature1 be+ 4#ajj ( a degree c5tigrade at #d or #e c5tigrade1 & 4#aee at temp]atures ( f #hi to #ic c5tigrade = a diff]5ce ( pressure due to #ajj in*es ( m]cury4 ,if !re is nei!r heat+ nor cool+ w #j1 & we obta9 by integration ,t ,cv1 :]e ,c is a con/ant4 ,elaborate discussions ( ! !ory ( ?is exp]im5t w be f\nd 9 mod]n treatises on !rmodynamics1 & 9 v>i\s rec5t memoirs1 & ! diff]5tial equation has be5 modifi$ 9 v>i\s ways1 & integrat$ on v>i\s suppositions1 :i* x w\ld be out ( place to discuss "h4 ,! cool+ effect ( pass+ a gas su* z air or oxyg5 ?r\gh a n>r[ orifice has be5 us$ to liquefy ! gas4 ,! /ream ( gas is pump$ along a pipe t[>ds ! op5+1 & t :i* has pass$ ! orifice & be5 slightly cool$ is l$ on its way back to ! pump along ! outside ( ! pipe by :i* m gas is approa*+ ! orifice1 & s cools slightly ! advanc+ curr5t4 ,! gas :i* em]ges lat] is ?us cool] ?an t :i* em]g$ be=e1 & ! process goes on until ! issu+ gas is liquefi$ & falls d[n into ! l[] "p ( ! pipe surr\nd+ ! orifice1 :5ce x c be drawn (f into vessels con/ruct$ to receive & pres]ve x4 ,x is possible ?us to liquefy hydrog51 :i* %[s t at ! l[ temp]ature at :i* ! process is usually />t$ 7an initial cool+ is appli$7 ! passage ?r\gh ! orifice has a cool+ effect z 9 ! o!r cases4 ,ano!r idea1 t ( !rmodynamic motivity1 on :i* ,?omson sugge/$ might be f\nd$ a fruitful pres5tation ( ! subject ( !rmodynamics1 may be m5tion$ "h4 ,x 0 set =? 9 a lett] writt5 to ,pr(essor ,tait 9 ,may #ahgi4 ,if a sy/em ( bodies be giv51 all at diff]5t temp]atures1 x is possible to r$uce !m to a common temp]ature1 & by do+ s to extract a c]ta9 am\nt ( me*anical en]gy f !m4 ,! temp]atures mu/ = ?is purpose be equalis$ by p]fect !rmodynamic eng9es work+ betwe5 ! f9al temp]ature ,t1 say1 & ! temp]atures ( ! diff]5t p>ts ( ! sy/em4 ,?is process is "o ( ! levell+ up & ! levell+ d[n ( temp]ature2 & ! temp]ature ,t is su* t exactly ! heat giv5 out at ,t by c]ta9 eng9es1 receiv+ heat f bodies ( high] temp]ature ?an ,t1 is suppli$ to ! eng9es :i* "w betwe5 ,t & bodies at l[] temp]atures4 ,! :ole useful "w obta9$ 9 ?is way 0 call$ by ,?omson ! motivity ( ! sy/em4 ,( c\rse equalisation ( temp]ature may be obta9$ by conduction1 & 9 ?is case ! en]gy :i* might be utilis$ is lo/4 ,) two equal & simil> bodies at absolute temp]atures ,t1 ,t' ! temp]ature to :i* !y are r$uc$ :5 _! motivity is extract$ is 7,,tt'74 ,if ! temp]atures are equalis$ by conduction ! result+ temp]ature is high]1 be+ 7,t ,t'74 ,?us1 if only ! two bodies are available = eng9es to "w betwe51 ! motivity is ! measure ( ! en]gy lo/ :5 conduction br+s ab\t equalisation ( temp]ature4 ,a v sugge/ive pap] on ! subject 0 publi%$ by ,"l ,kelv9 9 ! ,trans4 ,r4,s4,e41 vol4 #bh1 #ahgg-h4 ,,dissipation ,,( ,,en]gy ,9 connection ) ! !ory ( heat mu/ be m5tion$ ,?omson's great g5]alisation1 ! !ory ( ! dissipation ( en]gy4#ai ,mo/ p h "s notion ( ! mean+ ( ! physical doctr9e ( cons]vation ( en]gy1 ?\gh 9 popul> disc\rses x is usually mis/at$4 ,:at is meant is t 9 a f9ite mat]ial sy/em1 :i* is isolat$ 9 ! s5se t x is n act$ on by =ce f )\t1 ! total am\nt ( en]gy--t is1 en]gy ( motion & en]gy ( relative position 7includ+ en]gy ( *emical aff9ity7 ( ! p>ts--rema9s con/ant4 ,! usual mis/atem5t is t ! en]gy ( ! univ]se is con/ant4 ,?is may be true if ! univ]se is f9ite2 if ! univ]se is inf9ite 9 ext5t ! /atem5t has no mean+4 ,9 any case1 we "k no?+ ab\t ! univ]se z a :ole1 & !re=e make no /atem5ts reg>d+ x4 ,b :ile !re is ?us cons]vation or con/ancy ( am\nt ( en]gy 9 an isolat$ & f9ite mat]ial sy/em1 ?is en]gy may to resid5ts on ! sy/em become unavailable4 ,= useful "w )9 su* a sy/em is done by conv]sion ( en]gy f "o =m to ano!r & ! total am\nt rema9s un*ang$4 ,b if ?is conv]sion is prev5t$ all processes :i* involve su* conv]sion mu/ cease1 & among ^! are vital processes4 ,! unavailable =m :i* ! en]gy ( ! sy/em ) :i* we are directly & at pres5t conc]n$1 :atev] may become ( u ultimately1 is tak+1 accord+ to ,?omson's !ory1 is univ]sally diffus$ heat4 ,h[ ?is comes ab\t may be se5 z foll[s4 ,ev5 a p]fect eng9e1 if ! refrig]ator be at ! l[e/ available temp]ature1 rejects a quantity ( heat :i* _c be utilis$ = ! p]=mance ( ! "w4 ,?is heat is diffus$ by conduction & radiation to surr\nd+ bodies1 & s to bodies m remote1 & ! g5]al temp]ature ( ! sy/em is rais$4 ,moreov]1 z heat eng9es are imp]fect !re is heat reject$ to ! surr\nd+s by conduction1 & produc$ by "w done aga9/ friction1 s t ! heat ?r[n on ! unavailable or wa/e heap is /ill fur!r increas$4 ,conduction ( heat is ! great ag5cy by :i* en]gy is m & m disp]s$ 9 ?is unavailable =m ?r\gh\t ! totality ( mat]ial bodies4 ,z has be5 se51 available motivity is cont9ually wa/$ ?r\gh its ag5cy2 & 9 ! fl[ ( heat 9 ! e>? & 9 ! sun & o!r unequally heat$ bodies ( our sy/em ! wa/e ( en]gy is prodigi\s4 ,aid$ by convection curr5ts 9 ! air & 9 ! ocean x cont9ually equalises temp]atures1 b does s at an imm5se co/ ( useful en]gy4 ,!n 9 our insanely wa/eful me?ods ( heat+ our h\ses by op5 fires1 ( half burn+ ! coal us$ 9 boil] furnaces1 & all[+ unconsum$ c>bon to escape into ! atmosph]e 9 enorm\s quantities1 :ile a v l>ge portion ( ! heat actually g5]at$ is all[$ to escape up *imneys ) heat$ gases1 ! /ore ( unavailable heat is be+ add$ to at a rate :i* w entail great di/ress1 if n ru91 on humanity at no indef9itely di/ant future4 ,x w be ! height ( imprud5ce to tru/ to ! prospect1 n infrequ5tly ref]r$ to at ! pres5t "t1 ( draw+ on ! en]gy lock$ up 9 ! atomic /ructure ( matt]4 ,he w\ld be a fooli% man :o w\ld wa/efully squ&] ! weal? he possesses1 9 ! belief t he c rec\p himself f m9es :i* all exp]i5ce s f> %[s require an exp5diture to "w !m f> beyond any return t has z yet be5 obta9$4 ,x is n ap>t f our pres5t !me to urge t x is high "t ! "q ( ! national economy ( fuel1 & ! desirability ( utilis+ by af=e/ation ! sol> en]gy cont9ually go+ to wa/e on ! surface ( ! e>?1 7 dealt ) by /atesm54 ,if /atesm5 w\ld b make !mselves acqua9t$ ) ! results ( physical sci5ce 9 ?is magnific5t region ( cosmic economics !re w\ld be "s hope1 b1 alas6 z a rule _! education is "o :i* inevitably leads to neglect1 if n to disda9 ( physical tea*+4 ,f ! causes :i* h be5 ref]r$ to1 en]gy is cont9ually be+ dissipat$1 n de/roy$1 b lock$ up 9 great] & great] quantity 9 ! g5]al heat ( bodies4 ,!re is always friction1 always heat conduction & convection1 s t z our /ores ( motional or positional en]gy1 :e!r ( *emical sub/ances uncomb9$1 ! e>?'s motion1 or :at n1 are drawn ^u1 ! inevitable fraction1 too (t5 a l>ge proportion1 is %$ (f & ! g5]al temp]ature rais$4 ,aft] a l>ge "p ( ! :ole exi/5t en]gy has gone ?us to raise ! dead level ( ?+s1 no diff]5ce ( temp]ature adequate = heat eng9es to "w betwe5 w be possible1 & ! inevitable dea? ( all ?+s w approa* ) headlong rapidity4 ,,!rmoela/icity ,,& ,,!rmoelectricity ,9 ! second def9ition ( ! scale ( absolute temp]ature j discuss$1 /ress ( any type may be sub/itut$ = pressure1 & ! correspond+ displacem5t s = ! *ange ( volume4 ,?us = a piece ( ela/ic mat]ial put ?r\gh a cycle ( *anges we may sub/itute d,s = dp & ,ads = dv2 :]e ,a is su* a factor t ,ad,sds is ! "w done 9 ! displacem5t ds by ! /ress d,s4 ,z an example consid] a wire subject$ to simple longitud9al /ress ,s4 ,longitud9al ext5sion is produc$1 b ?is is n ! only *ange2 !re is at ! same "t lat]al contraction4 ,h[ev]1 s )9 c]ta9 limits is proportional to ,s4 ,let heat d,h 9 dynamical measure be giv5 to ! wire :ile ! /ress ,s is ma9ta9$ con/ant1 & let ! ext5sion increase f s to s ds4 ,! /ress ,s w d "w ,a,sds on ! wire1 & ! "w ratio w be -,a,sdsd,h4 ,n[ let ! /ress be increas$ to ,s d,s :ile ! ext5sion is kept con/ant1 & ! absolute temp]ature rais$ f ,t to ,t d,t4 ,! /ress ratio 7z we may call x7 is d,s,s & ! temp]ature ratio d,t,t4 ,?us we obta9 7p4 #acd above7 7d,sd,t7 7#a,,ta7 7d,hds7 ,9 8 ,heat article ,?omson us$ ! alt]ation e ( /ra9 "u con/ant /ress 7t is dsl1 :]e l is ! l5g? ( ! wire7 correspond+ to an am\nt ( heat suffici5t to raise ! temp]ature "u con/ant /ress by #a4 ,h5ce if ,k be ! specific heat "u con/ant /ress1 & le be put = ds 9 ! s5se j /at$1 we h d,t 7,ted,s,k7 444 7,f7 :]e is ! d5sity1 s9ce d,h ,kl,a4 ,! ratio ( d,h to ! increase ds ( ! ext5sion is positive or negative1 t is1 ! sub/ance absorbs or evolves heat1 :5 /ra9$ "u ! condition ( con/ant /ress1 accord+ z d,sd,t is negative or positive4 ,or we may put ! same ?+ 9 ano!r way :i* is frequ5tly useful4 ,if a wire subject$ to con/ant /ress has heat giv5 to x1 ds is negative or positive1 9 o!r words ! wire %ort5s or l5g!ns1 accord+ z d,sd,t is positive or negative1 t is1 accord+ z ! /ress = a giv5 /ra9 is increas$ or dim9i%$ by increase ( temp]ature4 ,x is kn[n f exp]im5t t a metal wire exp&s "u con/ant /ress :5 heat is giv5 to x1 & ?us we le>n f ! equation 7,f7 t ! /ress requir$ = a giv5 /ra9 is dim9i%$ :5 ! temp]ature ( ! wire is rais$4 ,aga91 a /rip ( india-rubb] /ret*$ by a weight is %ort5$ if its temp]ature is rais$1 consequ5tly ! /ress requir$ = a giv5 /ra9 is increas$ by rise ( temp]ature4 ,^! results1 f a qualitative po9t ( view1 are self-evid5t4 ,b f :at has be5 set =? x w be obvi\s t an equation exactly simil> to 7,f7 holds :e!r ! *ange ds ( s is tak5 z be=e "u con/ant /ress1 or at uni=m temp]ature1 or :e!r ! *ange d,s ( ,s is effect$ adiabatically or at con/ant /ra94 ,9 all ^! cases ! same equation d,t ,t 7ed,s,k7 444 7,g7 applies1 ) ! *ange ( mean+ ( d,t involv$4 ,?is equation diff]s f t ( ,?omson z giv5 9 v>i\s places 7e4g4 9 ! ,encyclopdia ,britannica article on ,ela/icity :i* he also wrote7 9 ! negative sign on ! "r-h& side1 b ! diff]5ce is only app>5t4 ,accord+ to 8 specification a pressure w\ld be a positive /ress1 & an expansion a positive displacem5t1 & 9 apply+ ! equation to num]ical examples ?is mu/ be borne 9 m9d s t ! prop] signs may be giv5 to ea* num]ical magnitude4 ,z an example ( adiabatic *ange1 a sudd5 ext5sion ( ! wire already ref]r$ to by an increase ( /ress d,s may be consid]$4 ,if !re is n "t = ! passage ( heat f or to ! surr\nd+s ( ! wire1 ! *ange ( temp]ature w be giv5 by equation 7,g74 ,?is equation 0 appli$ by ,?omson 7article ,ela/icity7 to f9d ! relation betwe5 :at he call$ ! k9etic modulus ( ela/icity & ! /atic modulus1 t is1 betwe5 ! modulus = adiabatic /ra9 & ! modulus = iso!rmal /ra94 ,! augm5tation ( ! /ra9 produc$ by rais+ ! temp]ature #a is e1 & !re=e ed,t1 t is1 ,ted,s,k1 is ! increase ( /ra9 due to ! sudd5 rise ( temp]ature d,t4 ,?is add$ to ! iso!rmal /ra9 produc$ by d,s w give ! :ole adiabatic /ra94 ,?us if ,m be ! /atic or iso!rmal modulus1 ! adiabatic /ra9 is d,s,m ,ted,s,k4 ,if ,m' d5ote ! k9etic or adiabatic modulus its value is d,s divid$ by ! :ole adiabatic /ra91 t is1 ,m' ,m7#a ,m,te,k7 & ! ratio ,m',m #a7a ,m,te,k74 ,x is well kn[n & easy to prove1 )\t ! use ( any !orem :i* c be prop]ly call$ !rmodynamic1 t ?is ratio ( moduli is equal to ! ratio ( ! specific heat ,k ( ! sub/ance1 "u ! condition ( con/ant /ress1 to ! specific heat ,n "u ! condition ( con/ant /ra9 ( ! correspond+ type4 ,?is1 inde$1 is self-evid5t if two *anges ( /ress1 "o iso!rmal ! o!r adiabatic1 :i* produce ! same /eps ( displacem5t ds1 be consid]$1 & x be rememb]$ t ! /ep ,t ( temp]ature :i* accompanies ! adiabatic *ange may be reg>d$ z made up ( a /ep d,t ( temp]ature1 accompany+ a displacem5t ds effect$ at con/ant /ress1 & !n two successive /eps d,t & ,t effect$1 at con/ant /ra91 along ) ! /eps ( /ress d,s4 ,! ratio ,m',m is easily se5 to h ! value 7,t d,t7dt1 & s9ce ,kd,t ,n7,t d,t7 #j1 by ! adiabatic condition1 ! !orem is prov$4 ,laplace's celebrat$ result = air1 accord+ to :i* ! adiabatic bulk-modulus is equal to ! /atic bulk-modulus multipli$ by ! ratio ( ! specific heat ( air pressure con/ant to ! specific heat ( air volume con/ant1 is a p>ticul> example ( ?is !ory4 ,?omson %[$ 9 ! ,ela/icity article h[1 by ! value ( ,m',m1 d]iv$ z above f !rmodynamic !ory1 ! value ( ,k,n c\ld be obta9$ = diff]5t sub/ances & = diff]5t types ( /ress1 & gave v int]e/+ tables ( results = solids1 liquids1 & gases subject$ to pressure-/ress 7bulk-modulus7 & = solids subject$ to longitud9al /ress 7,"y's modulus74 ,! discussion z to ! relation ( ! adiabatic & iso!rmal moduli ( ela/icity is "p ( a v important pap] on ,!rmoela/ic1 ,!rmomagnetic1 & ,!rmoelectric ,prop]ties ( ,matt]1 :i* he publi%$ 9 ! ,philosophical ,magaz9e = ,janu>y #ahgh4 ,?is 0 9 ! ma9 a repr9t ( an article entitl$1 ,on ! ,!rmoela/ic & ,!rmomagnetic ,prop]ties ( ,matt]1 ,"p ,i1 :i* appe>$ 9 ,april #ahee 9 ! fir/ numb] ( ! ,qu>t]ly ,j\rnal ( ,ma!matics4 ,only !rmoela/icity 0 consid]$ 9 ?is article2 ! !rmomagnetic results _h1 h[ev]1 be5 indicat$ 9 an article on ,!rmomagnetism 9 ! second edition ( ! ,cyclopdia ( ,physical ,sci5ce1 edit$ & 9 great "p writt5 by ,pr(essor ,j4 ,p4 ,ni*ol1 & publi%$ 9 #ahfj4 ,= ! same ,cyclopdia ,?omson also wrote an article entitl$1 ,!rmo-electric1 ,division ,i4--,pyro-,electricity1 or ,!rmo-,electricity ( ,non-conduct+ ,cry/als1 & ! enl>g$ ,phil4 ,mag4 article also conta9$ ! application ( !rmodynamics to ?is k9d ( !rmoelectric action4 ,?is great pap] _c be describ$ )\t a good deal ( ma!matical analysis2 b ! /ud5t :o has read ! e>li] !rmodynamical pap]s ( ,?omson w h little difficulty 9 ma/]+ x4 ,x mu/ suffice to say "h t x may be reg>d$ z giv+ ! keynote ( mu* ( ! g5]al !rmodynamic treatm5t ( physical ph5om5a1 :i* =ms s l>ge a "p ( ! physical ma!matics ( ! pres5t day1 & :i* we owe to ,will>d ,gibbs ,duhem1 & o!r contempor>y writ]s4 ,?omson _h1 h[ev]1 previ\s to ! publication ( ?is pap]1 appli$ !rmodynamic !ory to !rmoelectric ph5om5a4 ,a long s]ies ( pap]s conta9+ exp]im5tal inve/igations1 & entitl$1 ,electrodynamic ,qualities ( ,metals1 are plac$ 9 ! second volume ( 8 ,ma!matical & ,physical ,pap]s4 ,?is s]ies beg9s ) ! ,bak]ian ,lecture 7publi%$ 9 ! ,transactions ( ! ,royal ,society = #ahef7 :i* includes an acc\nt ( ! rem>kable exp]im5tal "w accompli%$ dur+ ! prec$+ f\r or five ye>s by ! volunte] laboratory corps 9 ! newly-e/abli%$ physical laboratory 9 ! old ,college4 ,! subjects dealt ) are ! ,electric ,convection ( ,heat1 ,!rmoelectric ,inv]sions1 ! ,effects ( ,me*anical ,/ra9 & ( ,magnetisation on ! ,!rmoelectric ,qualities ( ,metals1 & ! ,effects ( ,t5sion & ,magnetisation on ! ,electric ,conductivity ( ,metals4 ,x is only possible to give "h a v %ort indication ( ! !rmodynamic treatm5t1 & ( ! nature ( ,?omson's rem>kable discov]y ( ! electric convection ( heat4 ,x 0 f\nd by ,seebeck 9 #ahbb t :5 a circuit is =m$ ( two diff]5t metals 7)\t any cell or batt]y7 a curr5t fl[s r\nd ! circuit if ! two junctions are n at ! same temp]ature4 ,= example1 if ! two metals be rods ( antimony & bismu?1 jo9$ at _! extremities s z to =m a complete circuit1 & "o junction be w>m$ :ile ! o!r is kept at ! ord9>y temp]ature1 a curr5t fl[s across ! hot junction 9 ! direction f bismu? to antimony4 ,simil>ly1 if a circuit be made ( a copp] wire & an iron wire1 a curr5t passes across ! w>m] junction f copp] to iron4 ,! curr5t /r5g?--o!r ?+s be+ ! same--dep5ds on ! metals us$2 = example1 bismu? & antimony are m effective ?an o!r metals4 ,x 0 f\nd by ,pelti] t :5 a curr5t1 say f a batt]y1 is s5t r\nd su* a circuit1 t junction is cool$ & t junction is heat$ by ! passage ( ! curr5t1 :i*1 be+ respectively heat$ & cool$1 w\ld )\t ! cell h caus$ a curr5t to fl[ 9 ! same direction4 ,?us ! curr5t produc$ by ! diff]5ce ( temp]ature ( ! junctions causes an absorption ( heat f ! w>m] junction1 & an evolution ( heat at ! cold] junction4 ,?is naturally sugge/$ to ,?omson ! consid]ation ( a circuit ( two metals1 ) ! junctions at diff]5t temp]atures1 z a heat eng9e1 ( :i* ! hot junction 0 ! s\rce & ! cold junction ! refrig]ator1 :ile ! heat g5]at$ 9 ! circuit by ! curr5t & o!r "w p]=m$1 if !re 0 any1 0 ! equival5t ( ! diff]5ce betwe5 ! heat absorb$ & ! heat evolv$4 ,( c\rse 9 su* an arrangem5t !re is always irrev]sible loss ( heat by conduction2 b :5 su* losses are prop]ly all[$ = ! circuit is capable ( be+ correctly reg>d$ z a rev]sible eng9e4 ,%ortly aft] ,seebeck's discov]y x 0 f\nd by ,cumm+ t :5 ! hot junction 0 increas$ 9 temp]ature ! electromotive =ce increas$ m & m sl[ly1 at a c]ta9 temp]ature ( ! hot junction took its maximum value1 & !n z ! temp]ature ( ! hot junction 0 fur!r increas$ began to dim9i%1 & ultimately1 at a suffici5tly high temp]ature1 9 mo/ in/ances *ang$ sign4 ,! temp]ature ( maximum electromotive =ce 0 f\nd to be indep5d5t ( ! temp]ature ( ! cold] junction4 ,x is call$ ! temp]ature ( ! neutral po9t1 f ! fact t if ! two junctions ( a !rmoelectric circuit be kept at a con/ant small diff]5ce ( temp]ature1 & be bo? rais$ 9 temp]ature until "o is at a high] temp]ature ?an ! neutral po9t1 & ! o!r is at a l[]1 ! electromotive =ce w fall (f1 until f9ally1 :5 ?is po9t is rea*$1 x has become z]o4 ,?us x 0 f\nd t = e pair ( metals !re 0 at lea/ "o su* temp]ature ( ! hot junction1 & x 0 assum$1 ) consequ5ces 9 agreem5t ) exp]im5tal results1 t :5 ! temp]ature 0 ! neutral temp]ature !re 0 nei!r absorption nor evolution ( heat at ! junction4 ,b !n ! s\rce provid$ by ! !rmodynamic view j /at$ _h ceas$ to exi/4 ,! curr5t /ill fl[$1 !re 0 evolution ( heat at ! cold junction1 & likewise ,j\lean evolution ( heat 9 ! wires ( ! circuit 9 consequ5ce ( _! resi/ance4 ,h5ce x 0 cle> t en]gy mu/ be obta9$ else:]e ?an at ! junctions4 ,?omson solv$ ! problem by %[+ t 7besides ! ,j\lean evolution ( heat7 !re is absorption 7or evolution7 ( heat :5 a curr5t fl[s 9 a conductor along :i* !re is a gradi5t ( temp]ature4 ,= example1 :5 an electric curr5t fl[s along an unequally heat$ copp] wire1 heat is evolv$ :]e ! curr5t fl[s f ! hot p>ts to ! cold1 & heat is absorb$ :]e ! fl[ is f cold to hot4 ,:5 ! hot junction is at ! temp]ature ( z]o absorption or evolution ( heat--! s-call$ neutral temp]ature--! heat absorb$ 9 ! fl[ ( ! circuit along ! unequally heat$ conductors is great] ?an t evolv$ on ! :ole1 by an am\nt :i* is ! equival5t ( ! en]gy electrically exp5d$ 9 ! circuit 9 ! same "t4 ,x 0 f\nd1 moreov]1 t ! am\nt ( heat absorb$ by a giv5 curr5t 9 asc5d+ or desc5d+ ?r\gh a giv5 diff]5ce ( temp]ature is diff]5t 9 diff]5t metals4 ,:5 ! curr5t 0 unit curr5t & ! temp]ature diff]5ce also unity1 ,?omson call$ ! heat absorb$ or evolv$ 9 a metal ! specific heat ( electricity 9 ! metal1 a "n :i* is conv5i5t 9 "s ways1 b mislead+ 9 o!rs4 ,! t]m r conveys ! notion t electricity has a mat]ial exi/5ce4 ,a sub/ance su* z copp]1 lead1 wat]1 or m]cury has a specific heat 9 a p]fectly und]/ood s5se2 electricity is n a sub/ance1 h5ce !re _c be 9 ! same prop] s5se a specific heat ( electricity4 ,h[ev]1 ?is absorption & evolution ( heat 0 inve/igat$ exp]im5tally & ma!matically by ,?omson1 & is g5]ally n[ ref]r$ to 9 !rmoelectric discussions z ! ,?omson effect4 ,"p ,,vi 7,trans4 ,r4,s41 #ahge7 ( ! inve/igations ( ! electrodynamic qualities ( metals dealt ) ! effects ( /ret*+ & compress+ =ce1 & ( torsion1 on ! magnetisation ( iron & /eel & ( nickel & cobalt4 ,"o ( ! pr9cipal results 0 ! discov]y t ! effect ( longitud9al pull is to increase ! inductive magnetisation ( s(t iron1 & ( transv]se ?ru/ to dim9i% x1 s long z ! magnetis+ field does n exce$ a c]ta9 value4 ,:5 ?is value1 :i* dep5ds on ! specim51 is exce$$1 ! effect ( /ress is rev]s$4 ,! field-int5sity at :i* ! effect is rev]s$ is call$ ! ,vill>i critical int5sity1 f ! fact1 aft]w>ds asc]ta9$1 t ! result _h previ\sly be5 e/abli%$ by ,vill>i 9 ,italy4 ,no su* critical value ( ! field 0 f\nd to exi/ = /eel1 or nickel1 or cobalt4 ,9 "s ( ! exp]im5ts ! specim5 0 put ?r\gh a cycle ( magnetic *anges1 & ! results record$ by curves4 ,^! prov$ t 9 go+ f "o /ate to ano!r & return+ ! mat]ial lagg$ 9 its return pa? beh9d ! correspond+ /ates 9 ! outw>d pa?4 ,?is is ! ph5om5on call$ lat] hy/]esis1 & /udi$ 9 m9ute detail by ,ew+ & o!rs4 ,?omson's magnetic "w 0 ?us ! />t+ po9t ( _m m rec5t rese>*es4 ,,*apt] ,,ix ,,hydrodynamics--,,dynamical ,,!orem ,,( ,,m9imum ,,en]gy--,,vortex ,,motion ,?omson devot$ great att5tion f "t to "t to ! sci5ce ( hydrodynamics4 ,?is is p]haps ! mo/ ab/ruse subject 9 ! doma9 ( appli$ ma!matics1 & :5 viscosity 7! frictional resi/ance to ! relative motion ( p>ticles ( ! fluid7 is tak5 into acc\nt1 passes beyond ! res\rces ( ma!matical sci5ce 9 its pres5t /ate ( developm5t4 ,b leav+ viscosity entirely aside1 & deal+ only ) s-call$ p]fect fluids1 ! difficulties are (t5 ov]:elm+4 ,= a long "t ! only k9d ( fluid motion consid]$ 01 ) ! exception ( a few simple cases1 t :i* is call$ irrotational motion4 ,?is motion is *>act]is$ by ! analytical peculi>ity1 t ! velocity ( an elem5t ( ! fluid 9 any direction is ! rate ( v>iation p] unit di/ance 9 t direction ( a function ( ! coord9ates 7! di/ances :i* specify ! position7 ( ! p>ticle4 ,?is condition v mu* simplifies ! analysis2 b :5 x does n hold we h mu* m s]i\s difficulties to ov]come4 ,!n ! elem5ts ( ! fluid h :at is g5]ally1 b q improp]ly1 call$ molecul> rotation4 ,= we "k little ( ! molecules ( a fluid2 ev5 :5 we deal ) inf9itesimal elem5ts1 9 ! analysis ( fluid motion1 we are consid]+ ! fluid 9 mass4 ,b :at is meant is elem5tal rotation1 a rotation ( ! inf9itesimal elem5ts z !y move4 ,we h an example ( su* motion 9 ! air :5 a r+ ( smoke escapes f ! funnel ( a locomotive or ! lips ( a tobacco-smok]1 9 ! motion ( "p ( ! liquid :5 a cup ( tea is /irr$ by draw+ ! spoon f "o side to ! o!r1 or :5 ! blade ( an o> is mov+ ?r\gh ! wat]4 ,9 ^! la/ two cases ! depressions se5 9 ! surface are ! ends ( a vortex :i* ext5ds betwe5 !m & t]m9ates on ! surface4 ,9 all ^! examples :at h be5 call$ vortices are =m$1 & h5ce ! "n vortex motion has be5 giv5 to all ^? cases 9 :i* ! condition ( irrotationality is n satisfi$4 ,! fir/ great pap] on vortex motion 0 publi%$ by von ,helmholtz 9 #aheh1 & t5 ye>s lat] a memoir on ! same subject by ,?omson 0 publi%$ 9 ! ,transactions ( ! ,royal ,society ( ,ed9burgh4 ,9 t memoir are giv5 v mu* simpl] pro(s ( von ,helmholtz's ma9 !orems1 &1 moreov]1 "s new !orems ( wide application to ! motion ( fluids4 ,"o ( ^! is s compreh5sive t x may be said ) tru? to conta9 ! :ole ( ! dynamics ( a p]fect fluid4 ,we g on to indicate ! cont5ts ( ! pr9cipal pap]s1 z f> z t c be done )\t ! introduction ( analysis ( a difficult description4 ,9 ,*apt] ,,vi ref]5ce has be5 made to ! ,notes on ,hydrodynamics publi%$ by ,?omson 9 ! ,cambridge & ,dubl9 ,ma!matical ,j\rnal = #ahdh & #ahdi4 ,^! ,notes 7 n int5d$ to be entirely orig9al1 b 7 compos$ = ! use ( /ud5ts1 l ,airy's ,tracts ( fifte5 ye>s be=e4 ,! fir/ ,note dealt ) ! equation ( cont9uity1 t is to say1 ! ma!matical expression ( ! obvi\s fact t if any region ( space 9 a mov+ fluid be consid]$1 ! excess ( rate ( fl[ into ! space across ! b\nd+ surface1 above ! rate ( fl[ out1 is equal to ! rate ( gr[? ( ! quantity ( fluid )9 ! space4 ,! pro( giv5 is t n[ usually repeat$ 9 text-books ( hydrodynamics4 ,! second ,note discuss$ ! condition fulfill$ at ! b\nd+ surface ( a mov+ fluid4 ,! *ief ma!matical result is ! equation :i* expresses ! fact1 also obvi\s )\t analysis1 t !re is no fl[ ( ! fluid across ! surface4 ,9 o!r words1 ! compon5t ( ! motion ( a fluid p>ticle 9 ! imm$iate neighb\rhood ( ! surface at any in/ant1 tak5 9 ! direction p]p5dicul> to ! surface1 mu/ be equal to ! motion ( ! surface 9 t direction at ! same in/ant4 ,! ?ird ,note1 publi%$ a ye> lat] 7,febru>y #ahdi71 is ( consid]able sci5tific importance4 ,x is entitl$1 ,on ! ,vis ,viva ( a ,liquid 9 ,motion4 ,:at us$ to be call$ ! vis viva ( a body is d\ble :at is n[ call$ ! en]gy ( motion1 or k9etic en]gy1 ( ! body4 ,! t]m liquid is m]ely a brief expression = a fluid1 ! mass ( :i* p] unit volume is ! same ?r\gh\t1 & suff]s no v>iation4 ,! fluid1 moreov]1 is suppos$ devoid ( friction1 t is1 ! relative motions ( its p>ts are unresi/$ by tang5tial =ce betwe5 !m4 ,! *ief !orem prov$ & discuss$ may be describ$ z foll[s4 ,! liquid is suppos$ to fill ! space )9 a clos$ envelope1 :i* fulfils ! condition ( be+ simply cont9u\s4 ,! condition w be und]/ood by imag9+ any two po9ts ,a1 ,b1 )9 ! space1 to be jo9$ by two l9es ,,acb1 ,,adb bo? ly+ )9 ! space4 ,^! two l9es w =m a circuit ,,acbda4 ,if n[ ?is circuit1 h[ev] x may be drawn1 c be contract$ d[n to a po9t1 )\t any "p ( ! circuit pass+ out ( ! space1 ! condition is fulfill$4 ,cle>ly ! space )9 ! surface ( an an*or-r+1 or a curta9-r+1 w\ld n fulfil ?is condition1 = "o "p ( ! circuit might pass f ,a to ,b r\nd ! r+ "o way1 & ! o!r f ,a to ,b ! o!r way4 ,! circuit c\ld n !n be contract$ t[>ds a po9t )\t pass+ out ( ! r+4 ,n[ let ! liquid giv5 at re/ 9 su* a space be set 9 motion by any arbitr>ily specifi$ v>iation ( position ( ! envelope4 ,! liquid )9 w be set 9 motion 9 a mann] dep5d+ entirely on ! motion ( ! envelope4 ,x is possible to conceive ( o!r motions ( ! liquid ?an t tak51 :i* all agree 9 hav+ ! specifi$ motion ( ! surface4 ,?omson's !orem ass]ts t ! motion actually tak5 has less k9etic en]gy ?an t ( any ( ! o!r motions :i* h ! same motion ( ! b\nd+ surface4 ,! motion produc$ has ! prop]ty describ$ by ! ^w irrotational1 t is1 ! elem5ts ( ! fluid h no sp9n+ motion--!y move )\t rotation4 ,a small portion ( a fluid may describe any pa?--may g r\nd 9 a circle1 = example--& yet h no rotation4 ,! read] may imag9e a ball c>ri$ r\nd 9 a circle1 b 9 su* a way t no l9e 9 ! body ev] *anges its direction4 ,! body has translation1 b no sp94 ,irrotationality ( a fluid is secur$1 z /at$ above1 :5 ! velocity ( ea* elem5t 9 any direction is ! rate ( v>iation p] unit di/ance 9 t direction ( a c]ta9 function ( ! coord9ates1 ! di/ances1 tak5 p>allel to ?ree l9es p]p5dicul> to "o ano!r & drawn f a po9t1 :i* specify ! position ( ! p>ticle4 ,9 fact1 :at is call$ a velocity-pot5tial exi/s1 simil> to ! pot5tial describ$ 9 ,*apt] ,,iv above1 = an electric field4 ,?is condition1 toge!r ) ! specifi$ motion ( ! surface1 suffices to det]m9e ! motion ( ! fluid4 ,two important p>ticul> consequ5ces 7 po9t$ out by ,?omson3 7#a7 t ! motion ( ! fluid at any in/ant dep5ds solely on ! =m & motion ( ! b\nd+ surface1 & is !re=e indep5d5t ( ! previ\s motion2 & 7#b7 t if ! b\nd+ surface be in/antane\sly br\ght to re/1 ! liquid ?r\gh\t ! vessel w also be in/antly br\ght to re/4 ,?is !orem 0 aft]w>ds g5]alis$ by ,?omson 7,proc4 ,r4,s4,e41 #ahfc71 & appli$ to any mat]ial sy/em ( connect$ p>ticles set into motion by specifi$ velocities simultane\sly & sudd5ly impos$ at select$ po9ts ( ! sy/em4 ,x 0 already kn[n t ! k9etic en]gy ( a sy/em ( bodies connect$ 9 any mann]1 & set 9 motion by impulses appli$ at specifi$ po9ts1 0 ei!r a maximum or a m9imum1 z comp>$ ) t = any o!r motion compatible ) ^! impulses1 & ) ! connections ( ! sy/em4 ,?is 0 prov$ by ,lagrange 9 ! ,mcanique ,analytique z a g5]alisation ( a !orem giv5 by ,eul] = a rigid body set into rotation by an impulse4 ,b]tr& prov$ 9 #ahdb t :5 ! impulses appli$ are giv5 9 am\nt1 & are appli$ at specifi$ po9ts1 ! sy/em />ts (f ) k9etic en]gy great] ?an t ( any o!r motion :i* is consi/5t ) ! giv5 impulses & ! connections ( ! sy/em4 ,?is o!r motion mu/ be su* z c\ld be produc$ 9 ! sy/em by ! giv5 impulses1 toge!r ) any o!r set ( impulses capable ( do+ no "w on ! :ole4 ,?omson's !orem is curi\sly complem5t>y to ,b]tr&'s4 ,let ! sy/em be act$ on by impulses appli$ at c]ta9 specifi$ po9ts1 & by no o!r impulses ( any k9d2 & let ! impulses be su* z to />t ^? select$ po9ts ) any prescrib$ velocities4 ,! sy/em w />t (f ) k9etic en]gy :i* is less ?an t ( any o!r motion :i* ! sy/em c\ld h consi/5tly ) ! prescrib$ velocities1 & :i* x c\ld be con/ra9$ to take by impulses :i* d no "w on ! :ole4 ,9 ea* case ! diff]5ce ( en]gies is ! en]gy ( ! motion :i* mu/ be comp\nd$ ) "o motion to give ! o!r :i* is comp>$ ) x4 ,a simple example1 su* z might be tak5 ( ! p>ticul> case consid]$ by ,eul]1 may help to make ^! !orems cle>4 ,imag9e a /raight uni=m rod to lie on a horizontal table1 betwe5 :i* & ! rod !re is no friction4 ,let ! rod be /ruck a bl[ at "o end 9 a horizontal direction at "r angles to ! l5g? ( ! rod4 ,if no o!r impulse acts1 ! end ( ! rod w move (f ) a c]ta9 def9ite velocity1 & ! o!r p>ts ( ! rod 7:i* is suppos$ p]fectly unb5d+7 w be />t$ by ! connections ( ! sy/em4 ,x is obvi\s t any numb] ( o!r motions ( ! rod c be imag9$1 all ( :i* give ! same motion ( ! extremity /ruck4 ,b ! actual motion tak5 is "o ( turn+ ab\t t po9t ( ! rod :i* is two-?irds ( ! l5g? f ! end /ruck4 ,if ! read] w consid] ! k9etic en]gy = any o!r horizontal turn+ motion consi/5t ) ! same motion ( ! end1 he w f9d t ! k9etic en]gy is great] ?an t ( ! motion j specifi$4 ,?is motion c\ld be produc$ by apply+ at ! po9t ab\t :i* ! rod turns ! impulse requir$ to keep t po9t at re/4 ,! impulse s appli$ w\ld d no "w4 ,! actual value is #ahmv1 :]e m d5otes ! mass ( ! rod & v ! velocity ( ! end4 ,if ! motion tak5 7 "o ( rotation ab\t a po9t ( ! rod at di/ance x f ! end /ruck1 ! k9etic en]gy w\ld be m7#dl #flx #cx7v#fx1 :]e #bl is ! l5g? ( ! rod1 & ?is has its lea/ value #ahmv = x #dl#c4 ,= example1 x #bl gives #afmv1 :i* is great] ?an ! value j f\nd4 ,b]tr&'s !orem appli$ to ?is case ( motion is n q s easy1 p]haps1 to und]/&4 ,! motion :i* is said to h maximum en]gy is "o giv5 by a specifi$ impulse at ! end /ruck1 & ?is1 9 ! abs5ce ( any o!r impulses1 w\ld be a motion ( m9imum en]gy4 ,b let ! alt]native motion1 :i* is to be comp>$ ) t actually tak51 be "o con/ra9$ by additional impulses su* z c toge!r effect no "w1 & ! exi/5ce ( ! maximum is acc\nt$ =4 ,! k9etic en]gy produc$ is "o-half ! product ( ! impulse into ! velocity ( ! po9t /ruck1 t is ,iv1 & x has j be5 se5 t ?is is ! product ( 7#af7mv by ! factor 7#dl #flx #cx7x4 ,?is factor is #c;,imv1 & is a m9imum :5 x #dl#c4 ,?us = a giv5 ,i1 v w h its maximum value :5 ! factor ref]r$ to is lea/1 & ,iv w !n be a maximum4 ,! b> c be con/ra9$ to turn ab\t ano!r po9t by a fix$ pivot !re situat$4 ,an impulse w be appli$ to ! rod by ! pivot1 simultane\sly ) ! bl[2 & x is obvi\s t ?is impulse does no "w1 s9ce !re is no displacem5t ( ! po9t to :i* x is appli$4 ,! two !orems are consequ5ces ( "o pr9ciple4 ,! con/ra9t 9 ea* case increases :at may be call$ ! effective in]tia1 :i* may be tak5 z ,iv4 ,?us :5 v is giv51 ,i is increas$ by any con/ra9t compell+ ! rod to rotate ab\t a p>ticul> axis1 & s ,iv1 or ! k9etic en]gy1 is increas$4 ,on ! o!r h&1 :5 ,i is giv5 ! same con/ra9t dim9i%es v1 & s ,iv is dim9i%$4 ,a %ort pap] publi%$ 9 ! ,b4 ,a4 ,report = #aheb po9ts out t ! l9es ( =ce ne> a small magnet1 plac$ ) its axis along ! l9es ( =ce 9 a uni=m magnetic field1 z x w\ld re/ "u ! action ( ! field1 are at correspond+ po9ts simil> to ^? ( ! field ( an insulat$ sph]ical conductor1 "u ! inductive influ5ce ( a di/ant electric *ange4 ,fur!r1 ! fact is not$ t1 if ! magnet be oppositely direct$ to ! field1 ! l9es ( =ce are curv$ outw>ds1 j z ! l9es ( fl[ ( a uni=m /ream w\ld be by a sph]ical ob/acle1 at ! surface ( :i* no eddies 7 caus$4 ,?is is "o ( ^? in/ructive analogies betwe5 ! !ory ( fluid motion & o!r !ories involv+ p]fectly analog\s fundam5tal ideas1 :i* ,?omson 0 fond ( po9t+ out1 & :i* help$ him 9 8 repeat$ attempts to imag9e me*anical repres5tations ( physical ph5om5a ( diff]5t k9ds4 ,) ^! may be plac$ ano!r1 :i* 9 lectures he frequ5tly dwelt on--a simple d\blet1 z x is call$1 consi/+ ( a po9t-s\rce ( fluid & an equal & closely adjac5t po9t-s9k4 ,a %ort tube 9 an inf9ite mass ( liquid1 :i* is cont9ually fl[+ 9 at "o end & out at ! o!r1 may s]ve z a realisation ( ?is arrangem5t4 ,! l9es ( fl[ outside ! tube are exactly analog\s to ! l9es ( =ce ( a small magnet2 & if at ! same "t !re exi/ a uni=m fl[ ( ! liquid 9 ! direction ( ! l5g? ( ! tube1 ! field ( fl[ w be an exact picture ( ! field ( =ce ( ! small magnet1 :5 x is plac$ ) its l5g? along ! l9es ( a previ\sly exi/+ uni=m field4 ,! fl[ 9 ! d\blet w be ) or aga9/ ! g5]al fl[ accord+ z ! magnet is direct$ ) or aga9/ ! field4 ,! pap] on vortex-motion has be5 ref]r$ to above1 & an indication giv5 ( ! nature ( ! fluid-motion describ$ by ?is title4 ,!re are1 h[ev]1 two cases ( fluid-motion :i* are ref]r$ to z vortices1 ?\gh ! fundam5tal crit]ion ( vortex-motion--! non-exi/5ce ( a velocity-pot5tial--is satisfi$ 9 only "o ( !m4 ,! exhibition ( "o ( ^! 0 a fav\rite exp]im5t 9 ,?omson's ord9>y lectures1 z 8 old /ud5ts w rememb]4 ,if wat] 9 a l>ge b[l is /irr$ rapidly ) a teaspoon c>ri$ r\nd & r\nd 9 a circle ab\t ! axis ( ! b[l1 ! surface w become concave1 & ! =m ( ! c5tral "p w be a p>aboloid ( revolution ab\t ! v]tical ?r\gh ! l[e/ po9t1 t is to say1 any section ( t "p ( ! surface made by a v]tical plane conta9+ ! axis w be a p>abola symmetrical ab\t ! axis4 ,! motion c be bett] produc$ by m\nt+ ! vessel on a :irl+-table1 & rotat+ x ab\t ! v]tical axis co9cid+ ) its axis ( figure2 b ! ph5om5on c be q well se5 )\t ?is ma*9]y4 ,9 ?is case ! velocity ( ea* p>ticle ( ! wat] is proportional to its di/ance f ! axis1 & ! :ole mass1 :5 relative equilibrium is set up1 turns1 z if x 7 rigid1 ab\t ! axis ( ! vessel4 ,ea* elem5t ( ! fluid 9 ?is =c$ vortex1 z x is call$1 is 9 rotation1 &1 l ! moon1 makes "o turn 9 "o revolution ab\t ! c5tre ( its pa?4 ,?is is1 !re=e1 a true1 ?\gh v simple1 case ( vortex-motion4 ,on ! o!r h&1 :at may be call$ a free vortex may exi/1 & is approximat$ to sometimes :5 wat] 9 a vessel is all[$ to run (f ?r\gh an escape pipe at ! bottom4 ,! velocity ( an elem5t 9 ?is vortex is inv]sely proportional to its di/ance f ! c5tre1 & ! =m ( ! free surface is q diff]5t f t 9 ! o!r case4 ,! "n free vortex is (t5 giv5 to ?is case ( motion1 b !re is no vortex-motion ab\t x :atev]4 ,?omson's great pap] on vortex-motion 0 read be=e ! ,royal ,society ( ,ed9burgh 9 #ahfg1 & 0 reca/ & augm5t$ 9 ! foll[+ ye>4 ,x w be possible to give "h only a sket* ( its scope & ma9 results4 ,! fluid is suppos$ conta9$ 9 a clos$ fix$ vessel :i* is ei!r simply or multiply cont9u\s 7see p4 #aef71 & may conta9 imm]s$ 9 x simply or multiply cont9u\s solids4 ,:5 ^! solids exi/ _! surfaces are "p ( ! b\nd>y ( ! liquid2 !y are surr\nd$ by ! liquid unless !y are any:]e 9 contact ) ! conta9+ vessel1 & _! d5sity is suppos$ to be ! same z t ( ! liquid4 ,!y may be act$ on by =ces f )\t1 & !y act on ! liquid ) pressure-=ces1 & ei!r directly or ?r\gh ! liquid on "o ano!r4 ,! fir/ result obta9$ is fairly obvi\s4 ,! c5tre ( mass ( ! :ole sy/em mu/ rema9 at re/ :atev] ext]nal =ces act on ! solids1 s9ce ! d5sity is ! same ev]y:]e )9 ! vessel1 & ! vessel is fix$2 t is to say1 !re is no mom5tum ( ! cont5ts ( ! vessel 9 any direction4 ,= :atev] motion ( ! solids is set up by ! ext]nal =ces1 mu/ be accompani$ by a motion ( ! liquid1 equal & opposite 9 ! s5se "h indicat$4 ,aft] a discussion ( :at he calls ! impulse ( ! motion1 :i* is ! sy/em ( impulsive =ces on ! movable solids :i* w\ld g5]ate ! motion f re/1 ,?omson proce$s to prove ! important proposition t ! rotational motion ( e portion ( ! liquid mass1 if x is z]o at any "o in/ant = e portion ( ! mass1 rema9s always z]o4 ,?is is done by consid]+ ! angul> mom5tum ( any small sph]ical portion ( ! liquid relatively to an axis ?r\gh ! c5tre ( ! sph]e1 & prov+ t 9 ord] t x may vani%1 = e axis1 ! compon5t velocities ( ! fluid at ! c5tre mu/ be d]ivable f a velocity-pot5tial4 ,! angul> mom5tum ( a p>ticle ab\t an axis is ! product ( ! compon5t ( ! p>ticle's mom5tum1 at "r angles to ! plane ?r\gh ! p>ticle & ! axis1 by ! di/ance ( ! p>ticle f ! axis4 ,! sum ( all su* products = ! p>ticles mak+ up ! body 7:5 prop] acc\nt is tak5 ( ! signs accord+ to ! direction ( turn+ r\nd ! axis7 is ! angul> mom5tum4 ,! pro( ( ?is result adopt$ is due to ,/okes4 ,! angul> velocities ( an elem5t ( fluid at a po9t x1 y1 z1 ab\t ! axes ( x1 y1 z are %[n to be 7wy vz71 etc4 ,! condition 0 !re=e %[n to be necess>y2 x rema9$ to prove t x 0 suffici5t4 ,?is is obvi\s at once f ! def9ition ( ! velocity-pot5tial1 :i* mu/ n[ be suppos$ to exi/ 9 ord] t its suffici5cy may be prov$4 ,if any diamet] ( ! sph]ical portion be tak5 z ! axis1 & any plane ?r\gh t axis be consid]$1 ! velocity ( a p>ticle at "r angles to t plane c be at once express$ z ! rate at :i* ! velocity-pot5tial v>ies p] unit di/ance along ! circle1 symmetrical ab\t ! axis1 on :i* ! p>ticle lies4 ,! integral ( ! velocity-pot5tial r\nd ?is circle vani%es1 & s ! angul> mom5tum = any ?9 uni=m r+ ( p>ticles ab\t ! axis also vani%es1 & z ! sph]e is made up ( su* r+s1 ! :ole angul> mom5tum is z]o4 ,?us ! condition is suffici5t4 ,?omson !n proves t if ! angul> mom5tum ?us consid]$ be z]o = e portion ( ! liquid at any "o in/ant1 x rema9s z]o at e subsequ5t in/ant2 t is1 no physical action :atsoev] c\ld set up angul> mom5tum )9 ! fluid1 :i*1 x is to be rememb]$1 is suppos$ to be frictionless4 ,! pro( "h giv5 _c be sket*$ because x dep5ds on ! diff]5tial equation ( cont9uity satisfi$ by ! velocity-pot5tial ?r\gh\t ! fluid 7! same diff]5tial equation1 9 fact1 t is satisfi$ by ! di/ribution ( temp]ature 9 a uni=m conduct+ m$ium 9 ! /ation>y /ate71 & ! consequ5t expression ( ?is function = any sph]ical space 9 ! fluid z a s]ies ( sph]ical h>monic functions4 ,to a read] to :om ! prop]ties ( ^! functions are kn[n ! process c pres5t no difficulty4 ,an entirely diff]5t pro( ( ?is proposition is giv5 subsequ5tly 9 ! pap]1 & dep5ds on a new & v g5]al !orem1 :i* has be5 describ$ z conta9+ almo/ ! :ole !ory ( ! motion ( a fluid4 ,?is dep5ds on :at ,?omson call$ ! fl[ along any pa? jo9+ any two po9ts ,p1 ,q 9 ! fluid4 ,let q be ! velocity ( ! fluid at any elem5t ( l5g? ds ( su* a pa?1 & be ! angle betwe5 ! direction ( ds 7tak5 positive 9 ! s5se f ,p to ,q7 & ! direction ( q3 q cos 4ds is ! fl[ along ds4 ,if u1 v1 w be ! compon5ts ( q at ds1 p>allel to ! axes1 & dx1 dy1 dz be ! projections ( ds on ! axes1 udx vdy wdz is ! same ?+ z q cos 4ds4 ,! sum ( ! values ( ei!r ( ^! expressions = all ! elem5ts ( ! pa? betwe5 ,p & ,q is ! fl[ along ! pa?4 ,! /atem5t t u1 v1 w are ! space-rates ( v>iation ( a function 7( x1 y1 z7 p>allel to ! axes1 or t q cos is ! space-rate ( v>iation ( along ds1 m]ely means t ?is sum is ! same = :atev] pa? may be drawn f ,p to ,q4 ,?is1 h[ev]1 is only ! case :5 ! pa?s are s tak5 t 9 ea* case ! value ( returns aft] v>iation along a clos$ pa? to ! value :i* x _h at ! />t+ po9t1 t is1 ! clos$ pa? mu/ be capable ( be+ contract$ to a po9t )\t pass+ out ( space occupi$ by irrotationally mov+ fluid4 ,s9ce ! fl[ f ,p to ,q is ! same = any two pa?s :i* fulfil ?is condition1 ! fl[ f ,p to ,q by any "o pa? & f ,q to ,p by any o!r mu/ be z]o4 ,! fl[ r\nd su* a clos$ pa? is n z]o if ! condition is n fulfill$1 & its value 0 call$ by ,?omson ! circulation r\nd ! pa?4 ,! g5]al !orem :i* he e/abli%$ may n[ be /at$4 ,consid] any pa? jo9+ ,,pq1 & mov+ ) ! fluid1 s t ! l9e conta9s always ! same fluid p>ticles4 ,let u1 v1 be ! "t-rates ( *ange ( u1 v1 w at an elem5t ds ( ! pa?1 at any in/ant1 & du1 dv1 dw ! excesses ( ! values ( u1 v1 w at ! t]m9al extremity ( ds above ! values at ! o!r extremity2 !n ! "t-rate ( v>iation ( udx vdy wdz is udx vdy dz udu vdv wdw or udx vdy dz qdq1 :]e q has ! mean+ specifi$ above4 ,?us if ,s be ! fl[ = ! :ole pa? ,,pq1 & its "t-rate ( v>iation1 ,s' d5ote ! sum ( udx vdy dz along ! pa? f ,p to ,q1 & q1 q ! resultant fluid velocities at ,q & ,p1 we get ,s' 7q q74 ,?is is ,?omson's !orem4 ,if ! curve be clos$1 t is1 if ,p & ,q be co9cid5t1 q q & ,s'4 ,b 9 c]ta9 circum/ances ,s' is z]o1 & s !re=e is also 4 ,?us 9 ! circum/ances ref]r$ to1 z ! clos$ pa? moves ) ! fluid is cont9ually z]o1 & x foll[s t if is z]o at any in/ant x rema9s z]o ev] aft]4 ,b is only z]o if u1 v1 w are d]ivable f a pot5tial1 s+le valu$ 9 ! space 9 :i* ! clos$ pa? is drawn1 s t ! pa? c\ld be %runk d[n to a po9t )\t ev] pass+ out ( su* space4 ,9 a p]fect fluid if ?is condition is once fulfill$ = a clos$ curve mov+ ) ! fluid1 x is fulfill$ = ?is curve ev] aft]4 ,! circum/ances 9 :i* ,s' is z]o are ^!3--! ext]nal =ce1 p] unit mass1 act+ on ! fluid at any po9t is to be d]ivable f a pot5tial-function1 & ! d5sity ( ! fluid is to be a function ( ! pressure 7also a function ( ! coord9ates72 & ^! functions mu/ be su* z to r5d] ,s' always z]o = ! clos$ pa?4 ,?is condition is manife/ly fulfill$ 9 _m important cases2 = example1 ! =ces are d]ivable f a pot5tial due to actions1 su* z gravity1 ! orig9 ( :i* is ext]nal to ! fluid2 & ! d5sity is a function ( ! pressure 79 ! pres5t case x is a con/ant71 su* t ! "p ( ,s' :i* dep5ds on pressure & d5sity vani%es = ! circuit4 ,x is to be cle>ly und]/ood t ! motion ( a fluid may be irrotational al?\gh ! value ( ,s does n vani% = e clos$ pa? t c be drawn 9 x4 ,! fluid may occupy multiply cont9u\s space1 & ! pa? may or may n be drawn s t ,s %all be z]o2 b :at is necess>y = irrotational motion )9 any space is t ,s %\ld vani% = all pa?s :i* are capable ( be+ %runk d[n to z]o )\t pass+ out ( t space4 ,s ne$ n vani% = a pa? :i* _c be s %runk d[n1 b x mu/1 if ! condition j /at$ is fulfill$1 h ! same value = any two pa?s1 "o ( :i* c be made to pass into ! o!r by *ange ( position )\t ev] pass+ 9 :ole or 9 "p out ( ! space4 ,! pot5tial is always s+le valu$ 9 fluid fill+ a s+ly cont9u\s space su* z t )9 a sph]ical %ell1 or betwe5 two conc5tric %ells2 )9 a holl[ an*or-r+ ! pot5tial1 ?\gh x exi/1 & ! motion be irrotational1 is n s+le valu$4 ,9 ! latt] case ! motion is said to be cyclic1 9 ! =m] acyclic4 ,a numb] ( consequ5ces are d$uc$ f ?is !orem2 & f ^! ! prop]ties ( vortices1 :i* _h previ\sly be5 discov]$ by von ,helmholtz1 imm$iately foll[4 ,fir/ take any surface :atev] :i* has = b\nd+ edge a clos$ curve drawn 9 ! fluid1 & draw f any elem5t ( ?is surface1 ( area d,s1 a l9e p]p5dicul> to ! surface t[>ds ! side *os5 z ! positive side1 & calculate ! angul> velocity 1 say1 ( ! fluid ab\t t normal f ! compon5ts ( angul> velocity det]m9$ 9 ! mann] expla9$ at p4 #afd4 ,?is ,?omson call$ ! rotation ( ! elem5t4 ,n[ take ! product d,s = ! surface elem5t4 ,x is easy to see t ?is is equal to half ! circulation r\nd ! b\nd+ edge ( ! elem5t4 ,z ! fluid compos+ ! elem5t moves ! area d,s may *ange1 b ! circulation r\nd its edge by ,?omson's !orem rema9s unalt]$4 ,?us alt]s 9 ! inv]se ratio ( d,s1 & ! l9e drawn at "r angles to ! surface at d,s1 if kept ( l5g? proportional to 1 w l5g!n or %ort5 z d,s contracts or exp&s4 ,n[ sum ! values ( d,s = ! f9ite surface enclos$ by ! b\nd+ curve4 ,x foll[s f ! fact t d,s is equal to half ! circulation r\nd ! edge ( d,s1 t ?is sum1 :i* is usually d5ot$ by d,s1 is equal to half ! circulation r\nd ! clos$ curve :i* =ms ! edge ( ! surface4 ,also z ! fluid moves ! circulation r\nd ! edge rema9s unalt]$1 & !re=e s does also d,s = ! elem5ts enclos$ by x4 ,x is important to notice t ?is sum be+ det]m9$ by ! circulation 9 ! b\nd+ curve is ! same = all surfaces :i* h ! same b\nd>y4 ,! equality ( #b;d,s = ! surface to ! circulation r\nd its edge 0 express$ by ,?omson z an analytical !orem ( integration1 :i* 0 fir/ giv5 by ,/okes 9 a ,smi?'s ,prize pap] set 9 #ahed4 ,x is "h /at$1 app>5tly by an ov]sight1 t x 0 fir/ giv5 9 ,?omson & ,tait's ,natural ,philosophy1 #aij4 ,9 ! second edition ( ! ,natural ,philosophy ! !orem is attribut$ to ,/okes4 ,x is n[ well kn[n z ,/okes's !orem connect+ a c]ta9 surface integral ) a l9e integral1 & has _m applications bo? 9 physics & 9 geometry4 ,n[ consid] ! resultant angul> velocity at any po9t ( ! fluid1 & draw a %ort l9e ?r\gh t po9t 9 ! direction ( ! axis ( rotation4 ,t l9e may be cont9u$ f po9t to po9t1 & w co9cide at e "o ( its po9ts ) ! direction ( ! axis ( rotation !re4 ,su* an axial curve1 z x may be call$1 x is cle> moves ) ! fluid4 ,= take any inf9itesimal area conta9+ an elem5t ( ! l9e2 ! circulation r\nd ! edge ( ?is area is z]o1 s9ce !re is no rotation ab\t a l9e p]p5dicul> to ! area4 ,h5ce ! circulation along ! axial curve is z]o1 & ! axial curves move ) ! fluid4 ,take n[ any small plane area d,s mov+ ) ! fluid1 & draw axial l9es ?r\gh e po9t ( its b\nd>y4 ,^! w =m an axial tube enclos+ d,s4 ,if be ! angle betwe5 ! direction ( resultant rotation & a p]p5dicul> to d,s1 ! cross-section ( ! tube at "r angles to ! normal1 & to ! axial l9es :i* b\nd x1 is d,s4cos4 ,let ^! axial l9es be cont9u$ 9 bo? directions f ! elem5t d,s4 ,!y w enclose a tube ( v>y+ normal cross-section2 b ! product ( rotation & area ( normal cross-section has ev]y:]e ! same value4 ,a vortex-tube ) ! fluid )9 x is call$ a vortex-filam5t4 ,x w be se5 t ?is vortex-tube mu/ be endless1 t is1 x mu/ ei!r return into itself1 or be inf9itely long 9 "o or bo? directions4 ,= if x 7 t]m9at$ any:]e )9 ! fluid1 x w\ld be possible to =m a surface1 />t+ f a clos$ circuit r\nd ! tube1 cont9u$ along ! surface ( ! tube to ! t]m9ation1 & !n clos$ by a cap situat$ beyond ! t]m9ation4 ,at no "p ( ?is surface w\ld !re be any rotation1 & d,s1 :i* is equal to ! circulation1 w\ld be z]o = x2 & ( c\rse ?is _c be ! case4 ,?us ! tube _c t]m9ate )9 ! fluid4 ,x c1 h[ev]1 h bo? ( its ends on ! surface1 or "o on ! b\nd+ surface & ! o!r at inf9ity1 if ! fluid is inf9itely ext5d$ 9 "o direction1 b 9 t case ! t]m9ation is only app>5t4 ,! section is wid5$ out at ! surface2 "s ( ! b\nd+ l9es pass across to ! o!r app>5t t]m9ation1 :5 x also lies on ! surface1 :ile ! o!r l9es pass (f to inf9ity along ! surface1 & correspond to o!r l9es com+ 9 f inf9ity to ! o!r t]m9ation4 ,:e!r ! surface is inf9ite or n1 ! vortex is spread out into :at is call$ a vortex-%eet1 t is1 9 a surface on ! two sides ( :i* ! fluid moves ) diff]5t tang5tial velocities4 ,?r\gh a vortex-r+ or tube1 ! fluid circulates 9 clos$ l9es ( fl[1 ea* "o ( :i* is lac$ ?r\gh ! tube4 ,! circulation along e l9e ( fl[ :i* encloses ! same sy/em ( vortex-tubes has ! same value4 ,if any surface be drawn cutt+ a vortex-tube1 x is cle> f ! def9ition ( ! tube t ! value ( d,s = e su* surface mu/ be ! same4 ,?is ,?omson calls ! rotation ( ! tube4 ,z 0 po9t$ out fir/ by von ,helmholtz1 vortex-filam5ts correspond to circuits c>ry+ curr5ts & ! velocity 9 ! surr\nd+ fluid to magnetic field-int5sity4 ,! rotation ( ! tube corresponds to ! /r5g? ( ! curr5t1 & s\rces & s9ks to positive & negative magnetic poles4 ,?omson made great use ( ?is analogy 9 8 pap]s on electromagnetism4 ,examples ( vortex-tubes are indicat$ on p4 #aed2 & ! read] may exp]im5t ) vortices 9 liquids ) wat] 9 a tea-cup1 or 9 a riv] or pond1 at pleasure4 ,air vortices may be exp]im5tally /udi$ by means ( a simple app>atus devis$ by ,pr(essor ,tait1 :i* may be con/ruct$ by anyone4 ,9 "o end ( a pack+-box1 ab\t #b;ft4 long by #ah;94 wide & #ah;94 deep1 a circul> hole is cut1 & ! edges ( ! hole are ?9n$ d[n to a blunt edge4 ,?is c be clos$ at pleasure by a piece ( bo>d4 ,! opposite end is remov$1 & a %eet ( canvas /ret*$ tightly 9 its place1 & tack$ to ! ends ( ! sides4 ,?r\gh two holes bor$ 9 "o ( ! sides ! m\?s ( two flasks ) b5t necks protrude into ! box4 ,"o ( ^! flasks conta9s ammonia1 ! o!r hydro*loric acid4 ,:5 ! hole at "o end is clos$ up by a slip ( t9plate1 & ! liquids are heat$ ) a _s-lamp1 ! vap\rs =m a cl\d ( sal-ammoniac )9 ! box1 :i* is reta9$ dur+ its =mation4 ,! hole is !n op5$1 & ! canvas /ruck sm>tly ) ! palm ( ! op5 h&4 ,imm$iately a beautiful r+ ( smoke em]ges1 cle>-cut & def9ite z a solid1 & moves across ! room4 7,see ,fig4 #ac47 ,( c\rse1 x is a r+ ( air1 made visible by ! smoke c>ri$ ) x4 ,by v>y+ ! %ape ( ! ap]ture--= example1 by us+ in/ead ( ! hole cut 9 ! wood1 a slide ( t9plate ) an elliptic hole cut 9 x--! vortex-r+s c be set 9 vibration z !y are creat$1 & ! vibrations /udi$ z ! vortex moves4 ,illu/ration3 ,,fig4 #ac4 ,/ill m beautiful vortices c be =m$ 9 wat] by us+ a long tank ( cle> wat] to replace ! air 9 :i* ! vortex moves1 & a comp>tm5t at "o end fill$ ) wat] col\r$ ) anil9e1 in/ead ( ! smoke-box4 ,a hole 9 ! divid+ p>tition enables ! vortex to be =m$1 & a pi/on arrangem5t fitt$ to ! opposite side enables ! impulse to ! wat] to be giv5 f )\t4 ,f ! acc\nt ( ! nature ( vortex-motion giv5 above1 x w be cle> t vortices 9 a p]fect fluid once exi/5t mu/ be ev] exi/5t4 ,to create a vortex )9 a mass ( irrotationally mov+ p]fect fluid is physically impossible4 ,x occurr$ to ,?omson1 !re=e1 t ord9>y matt] might be portions ( a p]fect fluid1 fill+ all space1 diff]5tiat$ f ! surr\nd+ fluid by ! rotation :i* !y possess4 ,su* matt] w\ld fulfil ! law ( cons]vation1 z x c\ld nei!r be creat$ nor de/roy$ by any physical act4 ,! results ( su* exp]im5ts l$ ,?omson to frame 8 fam\s vortex-atom !ory ( matt]1 a !ory1 h[ev]1 :i* he felt ultimately 0 beset ) s _m difficulties z to be unworkable4 ,! pap] on vortex-motion also deals ) ! modification ( ,gre5's celebrat$ !orem ( analysis1 :i*1 x 0 po9t$ out by ,helmholtz1 0 necess>y to adapt x to a space :i* is multiply cont9u\s4 ,! !orem connects a c]ta9 volume-integral tak5 ?r\gh\t a clos$ space ) an integral tak5 ov] ! b\nd+ surface ( ! space4 ,?is arises f ! fact notic$ above t 9 multiply cont9u\s space 7= example1 ! space )9 an endless tube7 ! functions :i* are ! subject ( integration may n be s+le valu$4 ,su* a function w\ld be ! velocity-pot5tial = fluid circulat+ r\nd ! tube--cyclic motion1 z x 0 call$ by ,?omson4 ,if a clos$ pa? ( any =m be drawn 9 su* a tube1 />t+ f a po9t ,p1 & d\bl+ back s z to return to ,p )\t mak+ ! circuit ( ! tube1 ! velocity-pot5tial w v>y along ! tube1 b w f9ally return to its orig9al value :5 ! />t+ po9t is rea*$4 ,& ! circulation r\nd ?is circuit w be z]o4 ,b if ! clos$ pa? make ! circuit ( ! tube1 ! velocity-pot5tial w cont9u\sly v>y along ! pa?1 until f9ally1 :5 ,p is rea*$ aga91 ! value ( ! function is great] 7or less7 ?an ! value assum$ = ! />t+ po9t1 by a c]ta9 def9ite am\nt :i* is ! same = e circuit ( ! space4 ,if ! pa? be c>ri$ twice r\nd 9 ! same direction1 ! *ange ( ! function w be twice ?is am\nt1 & s on4 ,! space )9 a s+le endless tube su* z an an*or-r+ is d\bly cont9u\s2 b mu* m complicat$ cases c be imag9$4 ,= example1 an an*or-r+ ) a cross-connect+ tube f "o side to ! o!r w\ld be triply cont9u\s4 ,?omson %[$ t ! prop] modification ( ! !orem is obta9$ by imag9+ diaphragms plac$ across ! space1 :i* are n to be cross$ by any clos$ pa? drawn )9 ! space1 & ! two surfaces ( ea* ( :i* are to be reckon$ z "p ( ! b\nd+ surface ( ! space4 ,"o su* diaphragm is suffici5t to conv]t a holl[ an*or-r+ into a s+ly cont9u\s space1 two w\ld be requir$ = ! holl[ an*or-r+ ) cross-connection1 & s on4 ,! numb] ( diaphragms requir$ is always "o less ?an ! degree ( multiplicity ( ! cont9uity4 ,! pap] also deals ) ! motion ( solids 9 ! fluid & ! analog\s motions ( vortex-r+s & _! attraction by ord9>y matt]4 ,^! c be /udi$ ) vortex-r+s 9 air produc$ by ! app>atus describ$ above4 ,su* a r+ made to pass ! re-entrant corn] ( a wall--! edge ( a w9d[ recess1 = example--w appe> to be attract$4 ,a l>ge sph]e su* z a l>ge t]re/rial globe s]ves also v well z an attract+ body4 ,two vortex-r+s project$ "o aft] ! o!r also act on "o ano!r 9 a v curi\s mann]4 ,_! planes are p]p5dicul> to ! direction ( motion1 & ! fluid is mov+ r\nd ! circul> core ( ! r+4 ,!re is irrotational cyclic motion ( ! fluid ?r\gh ! r+ 9 "o direction & back outside1 z %[n 9 ,fig4 #ac1 :i* c be detect$ by plac+ a c&le flame 9 ! pa? ( ! c5tre4 ,! fir/ r+1 9 consequ5ce ( ! exi/5ce ( t :i* foll[s x1 moves m sl[ly1 & op5s out m widely1 ! foll[+ r+ ha/5s its motion & dim9i%es 9 diamet]1 until f9ally x ov]takes ! =m] & p5etrates x4 ,z soon z x has pass$ ?r\gh x moves ahead m & m sl[ly1 until ! "o :i* has be5 left beh9d beg9s to cat* x up1 & ! *anges :i* took place be=e are repeat$4 ,! "o p5etrat+ becomes 9 its turn ! p5etrat$1 & s on 9 alt]nation4 ,great c>e & skill are1 h[ev]1 necess>y to make ?is int]e/+ exp]im5t succe$4 ,we h n space to deal "h ) o!r hydrodynamical inve/igations1 su* z ! contributions :i* ,?omson made to ! discussion ( ! _m difficult problems ( ! motion ( solids ?r\gh a liquid1 or to 8 v num]\s & important contributions to ! !ory ( waves4 ,! numb] & importance ( 8 hydrodynamical pap]s may be judg$ f ! fact t !re are no less ?an fifty-two ref]5ces to 8 pap]s1 & ?irty-five to ,?omson & ,tait's ,natural ,philosophy 9 ! late/ edition ( ,lamb's ,hydrodynamics1 & t _m ( ^! are conc]n$ ) g5]al !orems & results ( great value4 ,,*apt] ,x ,,! ,,en]gy ,,!ory ,,( ,,electrolysis--,,electrical ,,units--,,electrical ,,oscillations ,,electrolysis ,,& ,,electrical ,,units ,9 ,decemb] #ahea ,?omson communicat$ an important pap] to ! ,philosophical ,magaz9e on ,! ,me*anical ,!ory ( ,electrolysis1 & ,applications ( ,me*anical ,effect to ! ,measurem5t ( ,electromotive ,=ces1 & ( ,galvanic ,resi/ances1 9 ,absolute ,units4 ,9 ! fir/ ( ^! he suppos$ a ma*9e ( ! k9d imag9$ by ,f>aday1 consi/+ ( a metal disk1 rotat+ uni=mly ) its plane at "r angles to ! l9es ( =ce ( a uni=m magnetic field1 & t\*$ at its c5tre & its circumf]5ce by fix$ wires1 to s5d a curr5t ?r\gh an electro*emical app>atus1 to :i* ! wires are connect$4 ,a c]ta9 am\nt ( "w ,w 0 suppos$ to be sp5t 9 a giv5 "t1 dur+ :i* a quantity ( heat ,h 0 evolv$ 9 ! circuit1 & a c]ta9 am\nt ( "w ,m sp5t 9 ! *emical app>atus 9 effect+ *emical *ange4 ,if ,h be tak5 9 dynamical units1 ,w ,h ,m4 ,! "w done 9 driv+ ! disk1 if ! int5sity ( ! field is ,i1 ! curr5t produc$ c1 ! radius ( ! disc r1 & ! angul> velocity ( turn+ w1 is ,ircw4 ,?omson assum$ t ! "w done 9 ! electro*emical app>atus 0 equal to ! heat ( *emical comb9ation ( ! sub/ance or sub/ances :i* und]w5t ! *emical action1 tak5 ) ! prop] sign accord+ to ! *ange1 if m comp\nd sub/ances ?an "o 7 act$ on4 ,h5ce ,m repres5t$ ?is resultant heat ( comb9ation4 ,! electro*emical app>atus 0 a voltamet] conta9+ a def9ite comp\nd to be electrolys$1 or a voltaic cell or batt]y4 ,& by ,f>aday's exp]im5ts on electrolysis x 0 kn[n t ! am\nt ( *emical action 0 proportional to ! :ole quantity ( electricity pass$ ?r\gh ! cell 9 a giv5 "t1 s t ! rate at :i* en]gy 0 be+ sp5t 9 ! cell 0 at any in/ant proportional to ! curr5t at t in/ant4 ,! *emical *ange c\ld be measur$ by consid]+ only "o ( ! elem5ts set free1 or made to comb9e1 by ! passage ( ! curr5t1 & consid]+ ! quantity ( heat 1 say1 = ! :ole *emical *ange 9 ! cell correspond+ to ! action on unit mass ( t elem5t4 ,?us if ,e d5ote ! :ole quantity ( t elem5t op]at$ on ! heat ( comb9ation 9 ! vessel 0 ,e4 ,if ,e be tak5 = unit ( "t1 & d5ote ! quantity set free by ! passage ( unit quantity ( electricity1 !n ,e c1 s9ce a curr5t conveys c units ( electricity 9 "o second4 ,! numb] is a def9ite quantity ( ! elem5t1 & is call$ its electro*emical equival5t4 ,aga91 f ,j\le's exp]im5ts1 ,h ,rc1 if ,r d5ote ! resi/ance ( ! curr5t1 & s ,ircw ,rc c & c 7,irw 7,r ,! quantity ,irw is ! electromotive =ce due to ! disk4 ,?us c 0 positive or negative accord+ z ,irw 0 great] or less ?an 1 & 0 z]o :5 ,irw 4 ,?us ! electromotive =ce ( ! disk 0 oppos$ by a back electromotive =ce due to ! *emical action 9 ! voltamet] or batt]y1 to :i* ! wires f ! disk 7 connect$4 ,! conclusion arriv$ at !re=e 0 t ! electromotive =ce 7or1 z x 0 !n t]m$1 ! int5sity7 ( ! electro*emical action 0 equal to ! dynamical value ( ! :ole *emical *ange effect$ by a curr5t ( unit /r5g? 9 unit ( "t4 ,f ?is result ,?omson proce$$ to calculate ! electromotive =ces requir$ to effect *emical *anges ( diff]5t k9ds1 & ^? ( v>i\s types ( voltaic cell4 ,suppos+ a unit ( electricity to be c>ri$ by ! curr5t ?r\gh ! cell1 he consid]$ ! *emical *anges :i* accompani$ its passage1 & f ! kn[n values ( heats ( comb9ation calculat$ _! en]gy values4 ,9 "s p>ts ! *ange 0 "o ( *emical comb9ation1 9 o!rs "o ( decomposition ( ! mat]ials1 & reg>d _h to be paid to ! sign ( ! heat-equival5t4 ,by prop]ly summ+ up ! :ole heat-equival5ts a net total 0 obta9$ :i*1 accord+ to ,?omson1 0 ! en]gy consum$ 9 ! passage ( unit curr5t1 & 0 !re=e ! electromotive =ce4 ,! !ory 0 incomplete1 & requir$ to be supplem5t$ by !rmodynamic !ory1 :i* %[s t besides ! electromotive =ce !re mu/ be includ$ 9 ! quantity set aga9/ ! sum ( heats a t]m repres5t$ by ! product ( ! absolute temp]ature multipli$ by ! rate ( v>iation ( electromotive =ce ) alt]ation ( temp]ature4 ,?us ! !ory is only applicable :5 ! electromotive =ce is n affect$ by v>iation ( temp]ature4 ,! necess>y addition "h indicat$ 0 made by ,helmholtz4 ,9 ! next pap]1 :i* appe>$ 9 ! same numb] 7,decemb] #ahea7 ( ! ,philosophical ,magaz9e1 ! pr9ciple ( "w is appli$ to ! measurem5t ( electromotive =ces & resi/ances 9 absolute units4 ,! advantages ( su* units are obvi\s4 ,ne>ly ! :ole ( ! quantitative "w ( ! old] exp]im5t]s 0 useless except = ^? :o _h actually made ! obs]vations3 x 0 h>dly possible = "o man to advance 8 rese>*es by employ+ data obta9$ by o!rs4 ,= ! results 7 express$ by ref]5ce to app>atus & mat]ials 9 ! possession ( ! obs]v]s1 & to ^! o!rs c\ld obta9 access only ) great difficulty & at great exp5se--to say no?+ ( ! unc]ta9ty ( comp>isons made to enable ! results ( "o man to be l9k$ on to ^? made else:]e1 & ) o!r app>atus1 by ano!r4 ,x 0 imp]ative1 !re=e1 to obta9 absolute units--units indep5d5t ( accid5ts ( place & app>atus--= ! expression ( curr5ts1 electromotive =ces1 & resi/ances1 s z to enable ! results ( ! "w ( exp]im5ts all ov] ! _w to be made available to e "o :o read ! publi%$ record4 7,see ,*ap4 ,,xiii47 ,! magneto-electric ma*9e imag9$ 9 ! =m] pap] gave a means ( e/imat+ ! electromotive =ce ( a cell or batt]y 9 absolute units4 ,! same k9d ( ma*9e is us$ "h1 9 ! simpl] =m ( a slid+ conductor connect+ a pair ( insulat$ rails laid ) _! plane p]p5dicul> to ! l9es ( =ce ( a uni=m magnetic field4 ,if ! rails be connect$ by a wire1 & ! slid] be mov$ s z to cut across ! l9es ( =ce1 a curr5t w be produc$ 9 ! circuit4 ,! curr5t c be measur$ 9 t]ms ( ! already kn[n unit ( curr5t1 t curr5t :i* fl[+ 9 a circle ( radius unity produces a magnetic field at ! c5tre ( #b units4 ,?is curr5t1 c1 say1 9 /r5g?1 fl[+ 9 ! circuit1 r5d]s a dynamical =ce c,il necess>y to move ! slid] ( l5g? l across ! l9es ( =ce ( ! field ( int5sity ,i1 & if ! spe$ ( ! slid] requir$ = ! curr5t c be v1 ! rate at :i* "w is done 9 mov+ ! slid] is c,ilv4 ,?is mu/ be ! rate at :i* "w is done 9 ! circuit by ! curr5t1 & if ! only "w done be 9 ! heat+ ( ! conductor1 we h c,ilv ,rc1 or ,ilv ,rc1 s t ,ilv is ! electromotive =ce4 ,any electromotive =ce o!rwise produc$1 :i* gave rise to ! same curr5t1 mu/ obvi\sly be equal to ,ilv1 s t ! unit ( electromotive =ce c ?us be prop]ly def9$4 ,?omson us$ a foot-gra9-second sy/em ( units2 b f ?is arrangem5t are n[ obta9$ ! ,c4,g4,s4 units ( electromotive =ce & resi/ance4 ,if ,i is "o ,c4,g4,s4 unit1 l "o c5timetre1 & v "o c5timetre p] second1 we h unit electromotive =ce 9 ! ,c4,g4,s4 sy/em4 ,also 9 "o ,c4,g4,s4 unit ( resi/ance if c be unity z well z ,ilv4 ,! idea ( ! det]m9ation ( a resi/ance 9 absolute units on correct pr9ciples 0 due to ,w4 ,web]1 :o also gave me?ods ( c>ry+ out ! measurem5t2 & ! fir/ det]m9ation 0 made by ,kir*h(f 9 #ahdi4 ,?omson appe>s1 h[ev]1 to h be5 ! fir/ to discuss ! subject ( units f ! po9t ( view ( en]gy4 ,?is mode ( reg>d+ ! matt] is important1 z ! absolute units are s *os5 z to enable "w done by electric & magnetic =ces to be reckon$ 9 ! ord9>y dynamical units4 ,a va/ am\nt ( exp]im5tal res\rce & skill has be5 sp5t s9ce t "t on ! det]m9ation ( resi/ance1 ?\gh n m ?an ! importance ( ! subject w>rant$4 ,we %all h to return to ! subject 9 deal+ ) ! "w ( ! ,briti% ,association on ,electrical ,/&>ds1 ( :i* ,?omson 0 = long an active memb]4 ,,electrical ,,oscillations ,9 8 fam\s tract on ! cons]vation ( en]gy1 publi%$ 9 #ahdg1 von ,helmholtz discuss$ "s puzzl+ results obta9$ by ,riess 9 ! magnetisation ( iron wires by ! curr5t ( a ,leyd5 j> dis*>ge fl[+ 9 a coil surr\nd+ !m1 & by ! fact1 obs]v$ by ,wolla/on1 t :5 wat] 0 decompos$ by ,leyd5 j> dis*>ges a mixture ( oxyg5 & hydrog5 appe>$ at ea* electrode1 & sugge/$ t possibly ! dis*>ge 0 oscillatory 9 "*4 ,9 #ahec ! subject 0 discuss$ ma!matically by ,?omson1 9 a pap] :i* 0 to prove fruitful 9 our own "t 9 a mann] !n little anticipat$4 ,! j> is giv51 let u say1 ) ! int]ior coat+ *>g$ positively1 & ! ext]ior coat+ *>g$ negatively4 ,a coil or helix ( wire has its ends connect$ to ! two coat+s1 & a curr5t imm$iately beg9s 9 ! wire1 & gradually 7n sl[ly7 increases 9 /r5g?4 ,accompany+ ! creation ( ! curr5t is ! production ( a magnetic field1 t is1 ! surr\nd+ space is made ! seat ( magnetic action4 ,! magnetic field1 z we %all see f ano!r inve/igation ( ,?omson's1 almo/ c]ta9ly involves motion 9 or ( a m$ium--! e!r--fill+ ! space :]e ! magnetic action is f\nd to exi/4 ,! *>ge ( ! j> consi/s ( a /ate ( int5se & peculi> /ra9 9 ! glass plate betwe5 ! coat+s4 ,:5 ! plates are connect$ by ! coil1 ?is /ate ( /ra9 breaks d[n & motion 9 ! m$ium ensues1 n m]ely betwe5 ! plates1 b also 9 ! surr\nd+ space--9 fact1 9 ! :ole field4 ,?is motion--:i* is n to be confus$ ) bodily displacem5t ( f9ite p>ts ( ! m$ium--is oppos$ by some?+ ak9 to in]tia ( ! m$ium 7! prop]ty t conf]s en]gy on matt] :5 9 motion71 s t :5 ! motion is />t$ x p]si/s1 until x is f9ally wip$ out by resi/ance ( ! nature ( friction4 ,! in]tia "h ref]r$ to dep5ds on ! mode 9 :i* ! coil is w\nd1 or :e!r x conta9s or n an iron core4 ,if ! "w done 9 *>g+ a ,leyd5 j> or electric cond5s]1 by br++ ! *>ge to ! cond5s] 9 successive small portions1 is consid]$1 x is at once cle> t x mu/ be proportional to ! squ>e ( ! :ole quantity ( electricity br\ght up4 ,= :atev] ! *>ge may be1 let x be br\ght up f a great di/ance 9 a l>ge numb] ,n ( equal in/alm5ts4 ,! l>g] ! :ole am\nt ! l>g] mu/ ea* in/alm5t be1 & !re=e ! great] ! am\nt accumulat$ on ! cond5s] :5 any giv5 numb] ( in/alm5ts h be5 deposit$4 ,b ! great] any *>ge t is be+ br\ght up1 & also ! great] ! *>ge t has already arriv$1 ! great] is ! repulsion t mu/ be ov]come 9 br++ up t in/alm5t1 9 simple proportion 9 ea* case1 & !re=e ! great] ! "w done4 ,?us ! :ole "w done 9 br++ up ! *>ge mu/ be proportional to ,q4 ,we suppose x to be ,q,c1 :]e ,c is a con/ant dep5d+ on ! cond5s] & call$ its capacity4 ,! idea ( ! *>ge z a quantity ( "s k9d ( matt]1 br\ght up & plac$ on ! insulat$ plate ( ! cond5s]1 has only a correspond5ce to ! fact1 :i* is t ! m$ium betwe5 ! plates is ! seat1 :5 ! cond5s] is *>g$1 ( a /ore ( en]gy1 :i* c only be made available by connect+ ! plates ( ! cond5s] by a wire or o!r conductor4 ,! *>ge is only a surface aspect ( ! /ate ( ! m$ium1 app>5tly a /ate ( /ra91 to :i* ! en]gy belongs4 ,:5 a wire is us$ to connect ! plates ! /ate ( /ra9 disappe>s2 ! en]gy comes out f ! m$ium betwe5 ! plates by motion sideways ( ! tubes ( /ra9 7s t ! insulat+ m$ium is "u longitud9al t5sion & lat]al pressure7 :i*1 accord+ to ,f>aday's conception ( l9es ( electric =ce connect+ ! *>ge on a body ) ! opposite *>ges on o!r bodies1 run f plate to plate1 :5 ! cond5s] is 9 equilibrium 9 ! *ang$ /ate4 ,^! tubes move out ) _! ends on ! wire1 c>ry+ ! en]gy ) !m1 & ! ends run t[>ds "o ano!r along ! wire2 ! tube %ort5s 9 ! process1 & en]gy is lo/ 9 ! wire4 ,! ends ( a tube ?us mov+ repres5t portions ( ! *>ges :i* 7 on ! plates1 & ! oppositely-direct$ motions ( ! opposite *>ges repres5t a curr5t along ! wire f "o conductor to ! o!r4 ,! motion ( ! tubes is accompani$ by ! developm5t ( a magnetic field1 ! l9es ( =ce ( :i* are endless1 & ! direction ( :i* at e po9t is p]p5dicul> at once to ! l5g? ( ! tube & to ! direction 9 :i* x is !re mov+4 ,9 c]ta9 circum/ances ! tube1 by ! "t its ends h met1 w h :olly disappe>$ 9 ! wire1 & ! :ole en]gy w h gone to heat ! wire3 9 o!r circum/ances ! ends w meet be=e ! tube has disappe>$1 ! ends w cross1 & ! tube w be c>ri$ back to ! cond5s] & re9s]t$ 9 ! opposite direction4 ,at a c]ta9 "t ?is w h happ5$ to all ! tubes1 ?\gh !y w h lo/ "s ( _! en]gy 9 ! process2 & ! cond5s] w aga9 be *>g$1 ?\gh 9 ! opposite way to t 9 :i* x 0 at fir/4 ,!n ! tubes w move out aga91 & ! same process w be repeat$3 once m ! cond5s] w be *>g$1 b 9 ! same direction z at fir/1 & once m ) a c]ta9 loss ( en]gy4 ,aga9 ! process ( dis*>ge & *>ge w take place1 & s on1 aga9 & aga91 until ! :ole en]gy has disappe>$4 ,?is process repres5ts1 accord+ to ! mod]n !ory ( ! fl[ ( en]gy 9 ! electromagnetic field1 ) m or less accuracy1 :at takes place 9 ! oscillatory dis*>ge ( a cond5s]4 ,! motion ( ! tubes ) _! ends on ! wire repres5ts a c]ta9 am\nt ( en]gy1 commonly reg>d$ z k9etic1 & /yl$ electrok9etic en]gy4 ,if c d5ote ! curr5t1 t is1 ! rate1 -d,qdt1 at :i* ! *>ge ( ! cond5s] is be+ *ang$1 & ,l a quantity call$ self-inductance1 dep5d+ ma9ly on ! arrangem5t ( ! connect+ wire--:e!r x is w\nd 9 a coil or helix1 ) or )\t an iron core1 or n--! electrok9etic en]gy w be ,lc4 ,?is is analog\s to ! k9etic en]gy mv ( a body 7say a p5dulum bob7 ( mass m & velocity v1 s t ,l repres5ts a quantity = ! conduct+ arrangem5t analog\s to in]tia1 & c is ! analogue ( ! velocity ( ! body4 ,! :ole en]gy at any in/ant is ?us ,q,c ,lc1 or ,q,c ,l7d,qdt74 ,! loss ( en]gy due to heat+ ( ! conduct+ connection is n completely und]/ood1 ?\gh its quantitative laws h be5 q fully asc]ta9$ & express$ 9 t]ms ( magnitudes t are capable ( measurem5t4 ,x 0 f\nd by ,j\le to be proportional to ! second p[]1 or squ>e1 ( ! curr5t1 & to a quantity ,r dep5d+ on ! conductor1 & call$ its resi/ance4 ,! g5]ation ( heat 9 ! conductor seems to be due to "s k9d ( frictional action ( p>ticles ( ! conductor set up by ! p5etration ( ! ,f>aday tubes into x4 ,a conductor is unable to be> any tang5tial action ex]t$ ^u x by ,f>aday tubes1 :i*1 h[ev]1 :5 !y exi/1 beg9 & end at mat]ial p>ticles1 except :5 !y are endless1 z !y may be 9 ! radiation ( en]gy4 ,:5 ! ,f>aday tubes are mov+ ) any ord9>y spe$ !y are n at _! ends p]p5dicul> to ! conduct+ surface f :i* !y />t or at :i* !y t]m9ate1 b are !re m or less incl9$ to ! surface1 & consequ5tly !re is tang5tial action :i* appe>s to displace ! p>ticles 7n m]ely at ! surface1 unless ! alt]nation is v rapid7 relatively to "o ano!r & s cause frictional g5]ation ( heat4 ,! "t rate ( g5]ation ( heat is ?us ,rc1 or ,r7d,qdt71 :5 ! units 9 :i* ,r & c are express$ are su* z to make ?is quantity a rate ( do+ "w 9 ! true dynamical s5se4 ,?is is ! rate at :i* ! sum ( en]gy already f\nd is be+ dim9i%$1 & s ! equation d_/dt7,q,c7 ,l7d,qdt7 ,r7d,qdt7 holds1 or leav+ out ! common factor d,qdt1 ! equation ,l7d,qdt7 ,r7d,qdt7 ,q,c #j ,?is la/ equation 0 e/abli%$ by ,?omson1 & is precisely t :i* w\ld be obta9$ = a p5dulum bob ( mass ,l1 pull$ back t[>ds ! position ( equilibrium ) a =ce ,q,c1 :]e ,q is ! displacem5t f ! middle position1 & hav+ its motion damp$ out by resi/+ =ce ( am\nt ,r p] unit ( ! velocity4 ,x is m in/ructive p]haps to take ! oscillatory motion ( a spiral spr+ hung v]tically ) a weight on its l[] end1 z t :i* has a diff]5tial equation equival5t to ! equation j f\nd4 ,:5 ! /ret* is ( a c]ta9 am\nt1 !re is equilibrium--! action ( ! spr+ j balances ! weight1--& if ! spr+ be /ret*$ fur!r !re w be a balance ( pull develop$ t5d+ to br+ ! sy/em back t[>ds ! equilibrium position4 ,if left to itself ! sy/em gets into motion1 :i*1 if ! resi/ance is n too great1 is add$ to until ! equilibrium position is rea*$2 & ! motion1 :i* is cont9u$ by ! in]tia ( ! mass1 only beg9s to fall (f z t position is pass$1 & ! pull ( ! spr+ becomes insuffici5t to balance ! weight4 ,?us ! mass oscillates ab\t ! position ( equilibrium1 & ! oscillations are successively small] & small] 9 ext5t1 & die out z _! en]gy is exp5d$ f9ally 9 do+ "w aga9/ friction4 ,if ! resi/+ =ce = f9ite motion is v great1 z = example :5 ! vibrat+ mass ( ! p5dulum or spr+ is imm]s$ 9 a v visc\s fluid1 l treacle1 oscillation w n take place at all4 ,aft] displacem5t ! mass w move at fir/ fairly quickly1 !n m & m sl[ly back to ! position ( equilibrium1 :i* x w1 /rictly speak+1 only exactly rea* aft] an inf9ite "t4 ,! resi/+ =ce is "h indef9itely small = an indef9itely small spe$1 b x becomes s great :5 any motion ensues1 t z ! re/or+ =ce falls (f ) ! displacem5t1 no "w is f9ally done by x1 except to move ! body ?r\gh ! resi/+ m$ium4 ,! diff]5tial equation is applicable to ! spr+ if ,q is aga9 tak5 z displacem5t f ! equilibrium position1 ,l z ! in]tia ( ! vibrat+ body1 #a;,c z ! pull ex]t$ by ! spr+ p] unit ( its ext5sion 7t is1 ! /iffness ( ! spr+71 & ,r has ! same mean+ z be=e4 ,9 ?is case ( motion1 z well z 9 t ( ! p5dulum1 en]gy is c>ri$ (f by ! production ( waves 9 ! m$ium 9 :i* ! vibrator is imm]s$4 ,^! are propagat$ out f ! vibrator z _! s\rce1 b no acc\nt ( !m is tak5 9 ! diff]5tial equation1 :i* 9 t respect is imp]fect4 ,!re is no difficulty1 only ! addition ( a little complication1 9 supply+ ! omission4 ,! =mation ( su* waves by ! spiral spr+ vibrator c be well %[n by imm]s+ ! vibrat+ body 9 a tr\gh ( wat]1 & ! mu* great] rate ( damp+ out ( ! motion 9 t case c !n be comp>$ ) ! rate ( damp+ 9 air4 ,x has be5 indicat$ t ! diff]5tial equation does n repres5t oscillatory motion if ! value ( ,r is too great4 ,! exact condition dep5ds on ! roots ( ! quadratic equation ,lx ,rx #a;,c #j1 obta9$ by writ+ #a = ,q1 & x = ddt1 & !n treat+ x z a quantity4 ,^! roots are ,r#b,l 7,r#d,l #a;,,cl71 & are !re=e real or imag9>y accord+ z #d,l,c is less or great] ?an ,r4 ,if ! roots are real1 t is1 if ,r be great] ?an #d,l,c1 ! dis*>ge w n be oscillatory2 ! ,f>aday tubes ref]r$ to above w be absorb$ 9 ! wire )\t any return to ! cond5s]4 ,! correspond+ result happ5s ) ! vibrator :5 ,r is suffici5tly great1 or ,l,c suffici5tly small 7a weak spr+ & a small mass1 or bo?71 to enable ! condition to be fulfill$4 ,if1 h[ev]1 ! roots ( ! quadratic are imag9>y1 t is1 if #d,l,c be great] ?an ,r 7a condition :i* w be fulfill$ 9 ! spr+ analogue1 by mak+ ! spr+ suffici5tly /iff & ! mass l>ge en\gh to prev5t ! friction f controll+ ! motion7 ! motion is "o 9 :i* ,q disappe>s by oscillations ab\t z]o1 ( cont9ually dim9i%+ amplitude4 ,a complete discussion gives = ! p]iod ( oscillation #d,l7#d,l,c ,r71 or if ,r be comp>atively small1 #b7,,lc74 ,! *>ge ,q falls (f by ! fraction e,,rt#b,l 7:]e e is ! numb] #b4gahbh4447 9 ea* p]iod ,t1 & s gradually disappe>s4 ,?us electric oscillations are produc$1 t is to say1 ! *>g$ /ate ( ! cond5s] subsides by oscillations1 9 :i* ! *>g$ /ate und]goes successive rev]sals1 ) dissipation ( en]gy 9 ! wire2 & bo? ! p]iod & ! rate ( dissipation c be calculat$ if ,l1 ,c1 & ,r are kn[n1 or c be f\nd1 = ! sy/em4 ,^! quantities c be calculat$ & adju/$ 9 c]ta9 def9ite cases1 & z ! electric oscillations c be exp]im5tally obs]v$1 ! !ory c be v]ifi$4 ,?is has be5 done by v>i\s exp]im5t]s4 ,return+ to ! p5dulum illu/ration1 x w be se5 t ! p5dulum held deflect$ is analog\s to ! *>g$ j>1 lett+ ! p5dulum g corresponds to connect+ ! dis*>g+ coil to ! coat+s1 ! motion ( ! p5dulum is ! analogue ( t motion ( ! m$ium 9 :i* consi/s ! magnetic field1 ! friction ( ! air answ]s to ! resi/ance ( ! wire :i* f9ally damps out ! curr5t4 ,! in]tia or mass ( ! bob is ! analogue ( :at ,?omson call$ ! electromagnetic in]tia ( ! coil & connections2 :at is n[ g5]ally call$ ! self-inductance ( ! conduct+ sy/em4 ,! compon5t ( gravity along ! pa? t[>ds ! l[e/ po9t1 answ]s to ! reciprocal1 #a;,c1 ( ! capacity ( ! cond5s]4 ,x appe>s f ! analogy t j z ! oscillations ( a p5dulum c be prev5t$ by imm]s+ ! bob 9 a m resi/+ m$ium1 su* z treacle or oil1 s t :5 releas$ ! p5dulum slips d[n to ! v]tical )\t pass+ x1 s by prop]ly proportion+ ! resi/ance 9 ! circuit to ! electromagnetic in]tia ( ! coil1 oscillatory dis*>ge ( ! ,leyd5 j> may also be r5d]$ impossible4 ,all ?is 0 work$ out 9 an exce$+ly in/ructive mann] 9 ,?omson's pap]2 ! acc\nt ( ! matt] by ! motion ( ,f>aday tubes is m rec5t1 & is valuable z sugge/+ h[ ! in]tia effect ( ! coil arises4 ,! analogy ( ! p5dulum is a true "o1 & enables ! facts to be describ$2 b x is to be rememb]$ t x becomes evid5t only z a consequ5ce ( ! ma!matical treatm5t ( ! electrical problem4 ,! pap] 0 ( great importance = ! inve/igation ( ! electric waves us$ 9 wireless telegraphy 9 our own "t4 ,x enabl$ ! p]iod ( oscillation ( diff]5t sy/ems to be calculat$1 & s ! rates ( excit]s & receiv]s ( electric waves to be f\nd4 ,= su* vibrators are really ,leyd5 j>s1 or cond5s]s1 caus$ to dis*>ge 9 an oscillatory mann]4 ,?is application 0 n =ese5 by ,?omson1 &1 inde$1 c\ld h>dly be1 z ! idea ( electric waves 9 an insulat+ m$ium came a good deal lat] 9 ! "w ( ,maxwell4 ,yet ! analogy ( ! p5dulum1 if x _h !n be5 exam9$1 might h sugge/$ su* waves4 ,z ! bob oscillates backw>ds & =w>ds ! air 9 :i* x is imm]s$ is p]iodically di/urb$1 & waves radiate outw>ds f x ?r\gh ! surr\nd+ atmosph]e4 ,! en]gy ( ^! waves is exce$+ly small1 o!rwise1 z po9t$ out above1 a t]m w\ld h to be includ$ 9 ! !ory ( ! resi/$ motion ( ! p5dulum to acc\nt = ?is en]gy ( radiation4 ,s likewise :5 ! electric vibrations proce$1 & ! insulat+ m$ium is ! seat ( a p]iodically v>y+ magnetic field1 electromagnetic waves are propagat$ outw>ds ?r\gh ! surr\nd+ m$ium--! e!r--& ! en]gy c>ri$ away by ! waves is d]iv$ f ! initial en]gy ( ! *>g$ cond5s]4 ,9 /rictness also ,?omson's !ory ( electric oscillations requires an addition to acc\nt = ! en]gy lo/ by radiation4 ,?is is want+1 & ! :ole decay ( ! am\nt ( en]gy pres5t at ! oscillator is put d[n to ! action ( resi/ance--t is1 to some?+ ( ! nature ( frictional ret>dation4 ,not)/&+ ?is defect ( ! !ory1 :i* is aft] all n s s]i\s z c]ta9 difficulties ( exact calculation ( ! self-inductance ( ! dis*>g+ conductor1 ! p]iods ( vibrators c be v accurately f\nd4 ,:5 ^! are kn[n x is only necess>y to measure ! l5g? ( an electrical wave to f9d its velocity ( propagation4 ,:5 electromagnetic waves 7 discov]$ exp]im5tally 9 #ahhh by ,he9ri* ,h]tz1 x 0 ?us t he 0 able to demon/rate t !y travell$ ) ! velocity ( light4 ,?omson sugge/$ t d\ble1 triple & quadruple fla%es ( lightn+ might be successive fla%es ( an oscillatory dis*>ge4 ,he also po9t$ out t if a sp>k-gap 7 includ$ 9 a prop]ly arrang$ cond5s] & dis*>g+ wire1 x might be possible1 by means ( ,:eat/one's revolv+ mirror1 to see ! sp>ks produc$ 9 ! successive oscillations1 z po9ts or %ort l9es ( light sep>at$ by d>k int]vals1 in/ead ( a s+le po9t ( light1 or ( an unbrok5 l9e ( light1 z x w\ld be if ! dis*>ge 7 in/antane\s1 or 7 cont9u\s1 or ( appreciable duration4 ,?is anticipation 0 v]ifi$ by exp]im5ts made by ,f$d]s51 & publi%$ 9 #ahei 7,pogg4 ,ann41 #ajh1 #ahei74 ,! subject 0 also inve/igat$ 9 ,helmholtz's laboratory at ,b]l91 by ,n4 ,s*ill]1 :o1 det]m9+ ! p]iod = cond5s]s ) diff]5t sub/ances betwe5 ! plates1 0 able to d$uce ! inductive capacities ( ^! sub/ances 7,pogg4 ,ann41 #aeb1 #ahgd74 ,! specific inductive capacity ( an insulator is ! ratio ( ! capacity ( a cond5s] ) ! sub/ance betwe5 ! plates to ! capacity ( an exactly simil> cond5s] ) air betwe5 ! plates4 ,! p>ticul> case ( non-oscillatory dis*>ge obta9$ by suppos+ ,c & ,q bo? inf9itely great & to h a f9ite ratio ,v 7:i* w be ! pot5tial1 p4 #cd1 ( ! *>g$ plate71 is consid]$ 9 ! pap]4 ,! dis*>g+ conductor is ?us subject$ to a diff]5ce ( pot5tial sudd5ly appli$ & ma9ta9$ at "o end1 :ile ! o!r end is kept at pot5tial z]o4 ,! solution ( ! diff]5tial equation = ?is case w %[ h[ ! curr5t rises f z]o 9 ! wire to its f9al /eady value4 ,if c be put z be=e = ! curr5t d,qdt1 & ! con/ant value ,v = ,q,c1 ! equation is ,l7dcdt7 ,rc ,v :i* gives1 s9ce c #j :5 t #j1 c 7,v,r7#a e7,r,l7t4 ,?us1 :5 an inf9ite "t has elaps$ ! curr5t has become ,v,r1 ! /eady value4 ,?omson concludes by %[+ h[1 by measur+ ! non-oscillatory dis*>ge ( a cond5s] 7! capacity ( :i* c be calculat$7 by means ( an electrodynamomet] & an ord9>y galvanomet] arrang$ 9 s]ies1 :at ,w4 ,web] call$ ! duration ( ! dis*>g+ curr5t may be det]m9$4 ,f ?is ,?omson d$uc$ a value = ! ratio ( ! electromagnetic unit ( electricity to ! electro/atic unit1 & indicat$ me?ods ( det]m9+ ?is ratio exp]im5tally4 ,?is ratio is ( fundam5tal importance 9 electromagnetic !ory1 & is ess5tially ( ! nature ( a spe$4 ,accord+ to ,maxwell x is ! spe$ ( propagation ( electromagnetic waves 9 an insulat+ m$ium = :i* ! units are def9$4 ,x 0 fir/ det]m9$ 9 ! ,glasg[ laboratory by ,mr4 ,dugald ,mc,kichan1 & has be5 det]m9$ _m times s9ce4 ,x is practically id5tical ) ! spe$ ( light z asc]ta9$ by ! be/ exp]im5ts4 ,,*apt] ,,xi ,,?omson ,,& ,,tait',s ',,natural ,,philosophy'--,,gyro/atic ,,action--',,electro/atics ,,& ,,magnetism' ,,! ',,natural ,,philosophy' ,pr(essor ,tait 0 appo9t$ to ! ,*air ( ,natural ,philosophy 9 ! ,univ]sity ( ,ed9burgh 9 #ahfj1 & came almo/ imm$iately into frequ5t contact ) ,?omson4 ,bo? 7 ,pet]h\se m51 tra9$ by ! same private tutor--,william ,hopk9s--bo? 7 en?usia/ic inve/igators 9 ma!matical z well z 9 exp]im5tal physics1 !y taught 9 ! si/] univ]sities ( ,ed9burgh & ,glasg[1 & _h mu* ! same k9d ( classes to deal ) & ! same educational problems to solve4 ,tait 0 an ,ed9burgh man--an old s*ool-fell[ ( ,cl]k ,maxwell at ! ,ed9burgh ,academy--& _h !re=e be5 expos$ to t contact1 9 play & 9 "w1 ) compe]s ( l age & capabilities1 :i* is "o ( ! be/ prep>ations = ! l>g] s*ool & m s]i\s /ruggles ( life4 ,?omson's e>ly education1 "u 8 fa!r's anxi\s c>e1 _h no d\bt c]ta9 advantages1 & 8 e>ly entrance into college classes gave him to a great ext5t t int]c\rse ) o!rs = :i* su* advantages are nev] complete comp5sation4 ,! two m5 _h mu* community ( ?\ght & exp]i5ce1 & ! lit]>y p>tn]%ip into :i* !y ent]$ 0 hail$ z "o likely to d mu* = ! progress ( sci5ce4 ,9 "s ways1 h[ev]1 ,?omson & ,tait 7 v diff]5t p]sonalities4 ,?omson tr\bl$ himself little ) metaphysical subtleties1 8 conceptions 7 l ^? ( ,newton1 absolutely cle> s f> z !y w5t2 he nev]1 9 8 tea*+ at lea/1 %[$ any disposition to discuss ! f\ndations ( dynamics1 or ! conception ( motion 9 a /raight l9e4 ,^! 7 tak5 = grant$ l ! fundam5tal ideas 9 a book on geometry2 & ! /ud5t 0 left to d :at e true dynamical /ud5t mu/ d = himself soon] or lat]--to comp>e ! ab/ractions ( dynamics ) ! products ( 8 exp]i5ce 9 ! _w ( matt] & =ce4 ,p]haps a little guidance n[ & !n 9 ! difficulties ab\t conceptions1 :i* beset e beg9n]1 might n h be5 amiss3 b ,?omson 0 s int5t on ! concrete example 9 h&--p5dulum or gyro/at1 or :at n--t he left ea* man to =m or correct 8 own ideas by ! lessons :i* su* examples af=d to e "o :o c>efully exam9es !m4 ,tait1 on ! o!r h&1 ?\gh he cont9ually d5\nc$ metaphysical discussion1 0 9 reality mu* m metaphysical ?an ,?omson1 & seem$ to take pleasure 9 ! some:at transc5d5tal argum5ts ) reg>d to matt]s ( analysis :i* 7 put =w>d1 especially 9 ! ,elem5ts ( ,quat]nions1 by ,sir ,william ,r[an ,hamilton1 ( ,dubl91 a ma/] :om he mu* rev]$4 ,b !re is metaphysics & metaphysics6 & ! pron\ncem5ts ( pr(ess$ metaphysicians 7 (t5 *>act]is$ z non-sci5tific & fruitless1 :i* no d\bt !y 7 f ! physical po9t ( view4 ,!n ,tait 0 /rongly conv9c$ ( ! importance = physics ( ! quat]nion analysis3 ,?omson 0 n1 to say ! lea/2 & ?is 0 probably ! ma9 reason :y ! vectorial treatm5t ( displacem5t1 velocities1 & o!r direct$ quantities1 has no place 9 ! jo9t writ+s ( ! two ,scotti% pr(essors4 ,9 controv]sy ,tait 0 a =midable antagoni/3 :5 w> 0 decl>$ he gave no qu>t] & ask$ = none1 ?\gh he nev] f\ght an un*ivalric battle4 ,he admir$ =eign inve/igators--& especially von ,helmholtz--b he 0 always ready to put on 8 arm\r & place lance 9 re/ = ! cause ( ,briti% sci5ce4 ,?omson 0 mu* less ( a combatant1 ?\gh he also c\ld bravely spl9t] a spe> ) an oppon5t on occasion1 z 9 ! memorable discussion ) ,huxley on ! ,age ( ! ,e>?4 ,tait's pr(essorial lectures 7 always models ( cle> & logical arrangem5t4 ,e /atem5t bore on ! bus9ess 9 h&2 ! exp]im5tal illu/rations1 always c>efully prep>$ be=eh&1 7 call$ = at ! prop] "t & 7 inv>iably successful4 ,) ,?omson x 0 o!rwise3 8 digressions1 ?\gh sometimes inspir$ & inspir+1 7 fatal to ! success ( ! utmo/ ef=ts ( 8 assi/ants to make 8 lectures successful sy/ematic expositions ( ! facts & pr9ciples ( elem5t>y physics4 ,z has be5 /at$ 9 ,*apt] ,,iv1 two books 7 ann\nc$ 9 #ahfc z 9 c\rse ( prep>ation = ! ensu+ session ( ,college4 ,^! 7 n publi%$ until #ahfg & #ahgc2 ! fir/ issu$ 0 ! fam\s ,treatise on ,natural ,philosophy1 ! second 0 entitl$ ,elem5ts ( ,natural ,philosophy1 & consi/$ 9 ! ma9 ( "p ( ! non-ma!matical or l>ge type portions ( ! ,treatise4 ,! s*eme ( ! latt] 0 t ( an articulat$ skeleton ( /atem5ts ( pr9ciples & results1 pr9t$ 9 ord9>y type1 ) ! ma!matical d$uctions & pro(s 9 small] type4 ,z 0 to be expect$1 ! ,elem5ts1 to a /ud5t ^: ma!matical read+ 0 wide en\gh to tackle ! ,treatise1 0 ! m difficult book ( ! two to completely ma/]4 ,b ! cont9u$ l>ge pr9t n>rative1 z x may be call$1 is extremely valuable4 ,x is a memorial ( a habit ( m9d :i* 0 *>act]i/ic ( bo? au?ors4 ,!y kept be=e !m always ! idea or ?+ r ?an its symbol2 & ?us ! edifice :i* !y built up seem$ nev] obscur$ by ! scaffold+ & ma*9]y us$ 9 its erection4 ,& z f> z possible 9 processes ( d$uction ! ideas are emphasis$ ?r\gh\t2 !re is no m]e putt+ 9 at "o end & tak+ out at ! o!r2 ! result is exam9$ & describ$ at e /age4 ,z 9 all else ( ,?omson's "w1 physical int]pretation is kept 9 view at e /ep1 & made available = correction & avoidance ( errors1 & ! sugge/ion ( new inquiries4 ,! book z x /&s consi/s ( ,division ,i1 ,prelim9>y & "p ( ,division ,,ii1 ,ab/ract ,dynamics4 ,division ,i includes ! *apt] on ,k9ematics already ref]r$ to1 a *apt] on ,dynamical ,laws & ,pr9ciples1 *apt]s on ,exp]i5ce & ,measures & ,in/rum5ts4 ,division ,,ii is repres5t$ only by ,*apt] ,v1 ,introductory2 ,*apt] ,,vi1 ,/atics ( a ,p>ticle & ,attractions2 & ,*apt] ,,vii1 ,/atics ( ,solids & ,fluids4 ,?us ,ab/ract ,dynamics is )\t ! m complete treatm5t ( ,k9etics to :i*1 z well z to ,/atics1 ! discussion ( ,dynamical ,laws & ,pr9ciples 0 int5d$ to be an introduction4 ,b to a consid]able ext5t1 z we %all see1 ,k9etics is treat$ 9 ?is introductory *apt]3 inde$1 ! discussion ( ! g5]al !orems ( dynamics & _! applications to k9etics is rem>kably complete4 ,9 ,volume ,,ii x 0 int5d$ to include *apt]s on ! k9etics ( a p>ticle & ( solid & fluid bodies1 on ! vibrations ( solid bodies1 & on wave-motion 9 g5]al4 ,x 0 expect$ also to conta9 a *apt] mu* ref]r$ to 9 ,volume ,i1 on ,prop]ties ( ,matt]4 ,t ! "w 0 n complet$ is a matt] ( ke5 regret to all physici/s1 regret1 h[ev]1 n[ temp]$ by ! fact t _m ( ! subjects ( ! unfulfill$ programme are repres5t$ by su* works z ,"l ,rayleigh's ,!ory ( ,s\nd1 ,lamb's ,hydrodynamics1 & ,r\?'s ,dynamics ( a ,sy/em ( ,rigid ,bodies4 ,b all deeply lam5t ! loss ( ! ,prop]ties ( ,matt]4 ,no "o c ev] write x z ,?omson w\ld h writt5 x4 ,8 /ud5ts obta9$ 9 8 lectures glimpses ( ! ?+s x might h conta9$1 & x 0 mo/ eag]ly look$ =4 ,if t *apt] only _h be5 giv51 ! loss caus$ by ! discont9uance ( ! book w\ld n h be5 s irrep>able4 ,! fir/ edition ( ! book 0 publi%$ by ! ,cl>5don ,press1 ,ox=d4 ,x 0 pr9t$ by ,messrs4 ,con/able1 ( ,ed9burgh1 & is a beautiful specim5 ( ma!matical typography4 ,9 "s ways ! fir/ edition is exce$+ly int]e/+1 = x is n too mu* to say t its issue _h an influ5ce on dynamical sci5ce1 & its exposition 9 ?is c\ntry1 only second to t due to ,newton's ,pr9cipia4 ,?ree o!r works1 p]haps1 h _h ! same degree & k9d ( influ5ce on ma!matical ?\ght--,laplace's ,mcanique ,cle/e1 ,lagrange's ,mcanique ,analytique1 & ,f\ri]'s ,?orie ,analytique de la ,*aleur4 ,! second edition 0 issu$ by ! ,cambridge ,univ]sity ,press z ,p>ts ,i & ,,ii 9 #ahgh & #ahhc4 ,v>i\s y\ng] ma!maticians n[ ( em95ce--,pr(essor ,*ry/al1 ( ,ed9burgh1 & ,pr(essor ,burnside1 ( ,gre5wi*1 may be m5tion$--read ! pro(s1 & x is on ! :ole rem>kably free f typographical & o!r errors4 ,) ! issue ( ,"p ,,ii1 ! cont9uation 0 def9itely ab&on$4 ,9 ! second edition _m topics are m fully discuss$1 & ! cont5ts include a v valuable acc\nt ( cycloidal motion 7or oscillatory motion1 z x is m usually call$71 & ( a revis$ v]sion ( ! *apt] on ,/atics :i* =ms ! conclud+ portion ( ! book1 & :i* discusses "s ( ! great problems ( t]re/rial & cosmical physics4 ,v>i\s speculations h be5 indulg$ 91 f "t to "t1 z to ! respective p>ts contribut$ to ! "w by ! two au?ors1 b ^! are g5]ally v wide ( ! m>k4 ,! mode ( composition ( ! sections on cycloidal 7oscillatory7 motion gives "s idea ( ,?omson's me?od ( work+4 ,8 pro(s 7( ,t & ,t-da% z ! au?ors call$ ! book7 7 c>ri$ ) him by rail & /eam]1 & he work$ incessantly 7)\t1 h[ev]1 altoge!r )draw+ 8 att5tion f :at 0 go+ on ar\nd him67 at corrections & additions4 ,he correct$ heavily on ! pro(s1 & !n ov]fl[$ into additional manuscript4 ,?us1 :5 he came to ! %ort orig9al #cdc1 he greatly ext5d$ t 9 ! fir/ in/ance1 & proce$$ f section to section until additions numb]$ f #cdc;a to #cdcp1 am\nt+ 9 all to "s t5 pages ( small pr9t1 _h be5 int]polat$4 ,simil>ly #cde 0 ext5d$ by ! addition ( #cde 7i7 to #cde 7xxviii71 ma9ly on gyro/atic dom9ation4 ,! me?od _h ! disadvantage ( int]rupt+ ! pr9t]s & keep+ type long /&+1 b ! matt] 0 (t5 all ! m inspir+ ?r\gh hav+ be5 produc$ "u pressure f ! pr9t+ (fice4 ,inde$1 mu* 0 no d\bt writt5 9 ?is way :i*1 to ! great loss ( dynamical sci5ce1 w\ld o!rwise nev] h be5 writt5 at all4 ,! k9ematical discussion beg9s ) ! consid]ation ( motion along a cont9u\s l9e1 curv$ or /raight4 ,?is naturally sugge/s ! ideas ( curvature & tortuosity1 :i* are fully dealt ) ma!matically1 be=e ! notion ( velocity is introduc$4 ,:5 t is done1 ! directional quality ( velocity is n s mu* insi/$ on z is n[ ! case3 = example1 a po9t is spok5 ( z mov+ 9 a curve ) a uni=m velocity2 & ( c\rse 9 ! language ( ! pres5t "t1 :i* has be5 r5d]$ m precise by vector ideas1 if n by vector-analysis1 ! velocity ( a po9t :i* is cont9ually *ang+ ! direction ( its motion1 _c be uni=m4 ,! same rem>k may be made reg>d+ ! treatm5t ( accel]ation3 9 bo? cases ! ref]5ce ( ! quantity to ?ree ,c>tesian axes is imm$iate1 & ! *anges ( ! compon5ts1 ?us fix$ 9 direction1 are alone consid]$4 ,!re c be no d\bt t great] cle>ness is obta9$ by ! process aft]w>ds insi/$ on by ,tait1 ( consid]+ by a hodographic diagram ! *anges ( velocity 9 successive int]vals ( "t1 & f ^! discov]+ ! direction & magnitude ( ! rate ( *ange at ea* in/ant4 ,?is me?od is inde$ indicat$ at #cg1 b no diagram is giv51 & ! prop]ties ( ! hodograph are inve/igat$ by means ( ,c>tesians4 ,! subject is1 h[ev]1 treat$ 9 ! ,elem5ts by ! me?od "h indicat$4 ,rem>kable features ( ?is *apt] are ! v complete discussion ( simple h>monic or vibratory motion1 ! sections on rotation1 & ! geometry ( roll+ & precessional motion1 & on ! curvature ( surfaces z inve/igat$ by k9ematical me?ods4 ,a rem>k made 9 #if %\ld be borne 9 m9d by all :o essay to solve gyro/atic problems4 ,x is t j z accel]ation1 :i* is always at "r angles to ! motion ( a po9t1 produces a *ange 9 ! direction ( ! motion b none 9 ! spe$ ( ! po9t 7x does influ5ce ! velocity71 s an action1 t5d+ always to produce rotation ab\t an axis at "r angles to t ab\t :i* a rigid body is already rotat+1 w *ange ! direction ( ! axis ab\t :i* ! body revolves1 b w produce no *ange 9 ! rate ( turn+4#bj ,a v full & cle> acc\nt ( ! analysis ( /ra9s is giv5 9 ?is *apt]1 9 prep>ation = ! treatm5t ( ela/icity :i* comes lat] 9 ! book2 & a long app5dix is add$ on ,sph]ical ,h>monics1 :i* are def9$ z homog5e\s functions ( ! coord9ates :i* satisfy ! diff]5tial equation ( ! di/ribution ( temp]ature 9 a m$ium 9 :i* !re is /eady fl[ ( heat1 or ( di/ribution ( pot5tial 9 an electrical field4 ,?is app5dix is )9 its scope "o ( ! mo/ ma/]ly discussions ( ?is subject ev] writt51 ?\gh1 f ! po9t ( view ( rigidity ( pro(1 requir$ by mod]n function-!ory1 x may be op5 to objection4 ,9 ! next *apt]1 :i* is entitl$ ,dynamical ,laws & ,pr9ciples1 ! au?ors at ! outset decl>e _! int5tion ( foll[+ ! ,pr9cipia closely 9 ! discussion ( ! g5]al f\ndations ( ! subject4 ,accord+ly1 aft] "s def9itions ! laws ( motion are /at$1 & ! opportunity is tak5 to adopt & en=ce ! ,gaussian sy/em ( absolute units = dynamical quantities4 ,z has be5 indicat$ above1 ! v>i\s difficulties m or less metaphysical :i* mu/ occur to e ?\ghtful /ud5t 9 consid]+ ,newton's laws ( motion are n discuss$1 & probably su* a discussion 0 beyond ! s*eme :i* ! au?ors _h 9 view4 ,b metaphysics is n altoge!r exclud$4 ,x is /at$ t matt] has an innate p[] ( resi/+ ext]nal influ5ces1 s t e body1 z f> z x c1 rema9s at re/1 or moves uni=mly 9 a /raight l9e1 & x is /at$ t ?is prop]ty--in]tia--is proportional to ! quantity ( matt] 9 ! body4 ,?is /atem5t is criticis$ by ,maxwell 9 8 review ( ! ,natural ,philosophy 9 ,nature 9 #ahgi 7"o ( ! la/ pap]s t ,maxwell wrote74 ,he asks1 ,is x a fact t 'matt] has any p[]1 ei!r innate or acquir$1 ( resi/+ ext]nal influ5ces'8 ,does n e =ce :i* acts on a body always produce t *ange 9 ! motion ( ! body by :i* its value1 z a =ce1 is reckon$8 ,is a cup ( tea to be accus$ ( resi/+ ! sweet5+ influ5ce ( sug>1 because x p]si/5tly refuses to turn sweet unless ! sug> is put into x8 ,?is innate p[] ( resi/+ is m]ely ! mat]i vis insita ( ,newton's ,def9itio ,,iii1 giv5 9 ! ,pr9cipia1 & ! /atem5t to :i* ,maxwell objects is only a free translation ( t def9ition4 ,moreov]1 :5 a body is drawn or pu%$ by o!r bodies1 x reacts on ^? bodies ) an equal =ce1 & ?is reaction is j z real z ! action3 its exi/5ce is due to ! in]tia ( ! body4 ,! def9ition1 f "o po9t ( view1 is only a /atem5t ( ! fact t ! accel]ation produc$ 9 a body 9 c]ta9 circum/ances dep5ds ^u ! body itself1 z well z on ! o!r bodies conc]n$1 b f ano!r x may be reg>d$ z acc\nt+ = ! reaction4 ,! mass or in]tia ( ! body is only su* a numb] t1 = diff]5t bodies 9 ! same circum/ances z to ! action ( o!r bodies 9 giv+ !m accel]ation1 ! product ( ! mass & ! accel]ation is ! same = all4 ,x is1 h[ev]1 a v important prop]ty ( ! body1 = x is "o factor ( ! quantum ( k9etic en]gy :i* ! body contributes to ! en]gy ( ! sy/em1 9 consequ5ce ( its motion relatively to ! *os5 axes ( ref]5ce1 :i* are tak5 z at re/4 ,! relativity ( motion is n emphasis$ s greatly 9 ! ,natural ,philosophy z 9 "s m mod]n treatises1 b x is n ov]look$2 & :atev] may be ! view tak5 z to ! importance ( dwell+ on su* consid]ations 9 a treatise on dynamics1 !re c be no d\bt t ! return to ,newton 0 on ! :ole a salut>y *ange ( ! mann] ( tea*+ ! subject4 ,! treatm5t ( =ce 9 ! fir/ & second laws ( motion is frankly causal4 ,=ce is !re ! cause ( rate ( *ange ( mom5tum2 & ?is view ,pr(essor ,tait 9 8 own writ+s has always combat$1 x mu/ be admitt$1 9 a v cog5t mann]4 ,accord+ to him1 =ce is m]ely rate ( *ange ( mom5tum4 ,h5ce ! =ces 9 equations ( motion are only expressions1 ! values ( :i* z rates ( *ange ( mom5tum1 are to be made explicit by ! solution ( su* equations 9 t]ms ( kn[n quantities4 ,& !re does n seem to be any logical escape f ?is conclusion1 ?\gh1 except z a way ( speak+1 ! ref]5ce to cause disappe>s4 ,! discussion ( ! ?ird law ( motion is p>ticul>ly valuable1 =1 z is well kn[n1 att5tion 0 !re9 call$ to ! fact t 9 ! la/ s5t5ces ( ! ,s*olium :i* ,newton app5d$ to 8 rem>ks on ! ?ird law1 ! rates ( work+ ( ! act+ & react+ =ces betwe5 ! bodies are equal & opposite4 ,?us ! :ole "w done 9 any "t by ! p>ts ( a sy/em on "o ano!r is z]o1 & ! doctr9e ( cons]vation ( en]gy is virtually conta9$ 9 ,newton's /atem5t4 ,! only po9t 9 :i* ! !ory 0 n complete s f> z ord9>y dynamical actions are conc]n$1 0 9 reg>d to "w done aga9/ friction1 = :i*1 :5 heat 0 left out ( acc\nt1 !re 0 no visible equival5t4 ,newton's /atem5t ( ! equality ( :at ,?omson & ,tait call$ activity & c\nt]-activity is1 h[ev]1 p]fectly absolute4 ,9 ! completion ( ! !ory ( en]gy on ! side ( ! conv]sion ( heat into "w1 ,?omson1 z we h se51 took a v prom95t "p4 ,aft] ! introduction ( ! dynamical laws ! mo/ int]e/+ "p ( ?is *apt] is ! elaborate discussion :i* x conta9s ( ! ,lagrangian equations ( motion1 ( ! pr9ciple ( ,lea/ ,action1 ) ! l>ge numb] ( extremely important applications ( ^! !ories4 ,! orig9ality & sugge/iv5ess ( ?is "p ( ! book1 tak5 alone1 w\ld entitle x to rank ) ! great classics--! ,mcanique ,cle/e1 ! ,mcanique ,analytique1 & ! memoirs ( ,jacobi & ,hamilton--all ( :i* 7 an outcome ( ! ,pr9cipia1 & f :i*1 ) ! ,pr9cipia1 ! au?ors ( ! ,natural ,philosophy drew _! inspiration4 ,x is p]haps ! case1 z ,pr(essor ,tait himself sugge/$1 t no "o has yet aris5 :o c b5d to ! fulle/ ext5t ! b[ :i* ,hamilton fa%ion$2 b :5 ?is ,ulysses appe>s x w be f\nd t 8 /r5g? & skill h be5 nurtur$ by ! /udy ( ! ,natural ,philosophy4 ,lagrange's equations are n[1 ?anks to ! physical reality :i* ! expositions & examples ( ,?omson & ,tait h giv5 to g5]alis$ =ces1 coord9ates1 & velocities1 appli$ to all k9ds ( sy/ems :i* =m]ly seem$ to be outside ! range ( dynamical treatm5t4 ,z ,maxwell put x1 ,! cr$it ( break+ up ! monopoly ( ! great ma/]s ( ! spell1 & mak+ all _! *>ms famili> 9 our e>s z h\sehold words1 belongs 9 great measure to ,?omson & ,tait4 ,! two nor!rn wiz>ds 7 ! fir/ :o1 )\t compunction or dread1 utt]$ 9 _! "m tongue ! true & prop] names ( ^? dynamical concepts1 :i* ! magicians ( old 7 wont to invoke only by ! aid ( mutt]$ symbols & in>ticulate equations4 ,& n[ ! feeble/ among u c repeat ! words ( p[]1 & take "p 9 dynamical discussions :i* a few ye>s ago we %\ld h left to our bett]s4 ,a v rem>kable feature 9 ?is discussion is ! use made ( ! idea ( ignoration ( coord9ates4 ,! v>iables made use ( 9 ! ,lagrangian equations mu/ be su* z to enable ! positions ( ! p>ts ( ! sy/em :i* det]m9e ! motion to be express$ = any in/ant ( "t4 ,^! p>ts1 by _! displacem5ts1 control ^? ( ! o!r p>ts1 ?r\gh ! connections ( ! sy/em4 ,!y are call$ ! indep5d5t coord9ates1 & sometimes ! degrees ( fre$om1 ( ! sy/em4 ,into ! expressions ( ! k9etic & pot5tial en]gies1 f :i* by a =mal process ! equations ( motion1 z _m 9 numb] z !re are degrees ( fre$om1 are d]iv$1 ! value ( ^! v>iables & ( ! correspond+ velocities ent] 9 ! g5]al case4 ,b 9 c]ta9 cases "s ( ! v>iables are repres5t$ by ! correspond+ velocities only1 & ! v>iables !mselves d n appe> 9 ! equations ( motion4 ,= example1 :5 fly-:eels =m "p ( ! sy/em1 & are connect$ ) ! re/ ( ! sy/em only by _! be>+s1 ! angle ?r\gh :i* ! :eel has turn$ f any epo* ( "t is ( no consequ5ce1 ! only ?+ :i* affects ! en]gy ( ! sy/em is ! angul> velocity or angul> mom5tum ( ! :eel4 ,! sy/em is said by ,?omson & ,tait 9 su* a case to be "u gyro/atic dom9ation4 7,see ,gyro/atic ,action1 p4 #bad bel[47 ,moreov]1 s9ce ! =ce :i* is ! rate ( gr[? ( ! mom5tum correspond+ to any coord9ate is num]ically ! rate ( v>iation ) t coord9ate ( ! diff]5ce ( ! k9etic & pot5tial en]gies1 e =ce is z]o = :i* ! coord9ate does n appe>2 & !re=e ! correspond+ mom5tum is con/ant4 ,b t mom5tum is express$ by means ( ! values ( o!r coord9ates :i* d appe> & _! velocities1 ) ! velocities = ! abs5t coord9ates2 & z _m equations are furni%$ by ! con/ant values ( su* mom5ta z !re are coord9ates abs5t4 ,! correspond+ velocities c be det]m9$ f ^! equations 9 t]ms ( ! con/ant mom5ta & ! coord9ates :i* appe> & _! velocities4 ,! values s f\nd1 sub/itut$ 9 ! expressions = ! k9etic & pot5tial en]gies1 remove f ^! expressions e ref]5ce to ! abs5t coord9ates4 ,!n f ! new expression = ! k9etic en]gy 79 :i* a function ( ! con/ant mom5ta n[ appe>s1 & is tak5 z an addition to ! pot5tial en]gy7 ! equations ( motion are =m$ = ! coord9ates actually pres5t1 & ^! are suffici5t to det]m9e ! motion4 ,! o!r coord9ates are ?us 9 a c]ta9 s5se ignor$1 & ! me?od is call$ t ( ignoration ( coord9ates4 ,!orems ( action ( great importance = a g5]al !ory ( optics conclude ?is *apt]2 b ( ^! x is impossible to give "h any acc\nt1 )\t a discussion ( te*nicalities beyond ! read+ ( ord9>y /ud5ts ( dynamics4 ,9 an ,app5dix to ,"p ,i an acc\nt is giv5 ( ,cont9u\s ,calculat+ ,ma*9es4 ,ord9>y calculat+ ma*9es1 su* z ! ari?momet] ( ,?omas ( ,colm>1 c>ry out calculations & exhibit ! result z a r[ ( figures4 ,b ! ma*9es "h describ$ are ( a diff]5t "*3 !y exhibit _! results by values ( a cont9u\sly v>y+ quantity4 ,! fir/ is "o = pr$ict+ ! height ( ! tides = future "t1 at any port = :i* data h be5 already obta9$ reg>d+ tidal heights1 by means ( a self-regi/]+ tide-gauge4 ,two ( ^! 7 made accord+ to ! ideas set =? 9 ?is ,app5dix2 "o is 9 ! ,s\? ,k5s+ton ,museum1 ! o!r is at ! ,national ,physical ,laboratory at ,bu%y ,h\se1 :]e x is us$ ma9ly = draw+ on pap] curves ( future tidal heights1 = ports 9 ! ,indian ,ocean4 ,f ^! curves tide-tables are compil$1 & issu$ = ! use ( m>9]s & o!rs4 ,ano!r ma*9e describ$ 9 ?is ,app5dix 0 design$ = ! me*anical solution ( simultane\s l9e> equations4 ,x is impossible to expla9 "h ! int]e/+ arrangem5t ( six frames1 c>ry+ z _m pulleys1 adju/able along slides 7= ! solution ( equations involv+ six unkn[n quantities71 :i* ,?omson con/ruct$1 & :i* is n[ 9 ! ,natural ,philosophy ,dep>tm5t at ,glasg[4 ,! idea ( arrang+ ! fir/ practical ma*9e = ?is numb] ( v>iables1 0 t x might be us$ = ! calculation ( ! corrections on values already f\nd = ! six elem5ts ( a comet or a/]oid4 ,! ma*9e 0 made1 b "s me*anical difficulties arose 9 apply+ x1 & ! exp]im5ts ) x 7 n at ! "t p]sev]$ )4 ,v possibly1 h[ev]1 x may yet be br\ght into use4 ,illu/ration3 ,,fig4 #ad4 ,b ! mo/ wond]ful ( ^! me*anical arrangem5ts is ! ma*9e = analys+ ! curves drawn by a self-regi/]+ tide gauge1 s z to exhibit ! con/ants ( ! h>monic curves1 & ?us enable ! pr$iction ( tidal heights to be c>ri$ out ei!r by ! tide-pr$ict+ ma*9e1 or by calculation4 ,"o day 9 #ahgf1 ,?omson rem>k$ to 8 bro!r1 ,james ,?omson1 !n ,pr(essor ( ,eng9e]+ at ,glasg[1 t all he requir$ = ! con/ruction ( a tidal analys] 0 a =m ( integrat+ ma*9e m satisfactory = 8 purpose ?an ! usual type ( integrator employ$ by surveyors & naval ar*itects4 ,james ,?omson at once repli$ t he _h inv5t$1 a long "t be=e1 :at he call$ a disk-globe-cyl9d]-integrator4 ,?is consi/$ ( a brass disk1 ) its plane incl9$ to ! horizontal1 :i* c\ld be turn$ ab\t its axis by a :eel ge>+ 9 tee? on ! edge ( ! disk1 & driv5 by ! op]ator 9 a mann] :i* w pres5tly appe>4 ,p>allel & close to ! disk1 b n t\*+ x1 0 plac$ a horizontal cyl9d] ( brass1 ab\t #b in*es 9 diamet] 7call$ ! regi/]+ cyl9d]71 & betwe5 ! disk & ?is cyl9d] 0 laid a metal ball ab\t #b in*es 9 diamet]4 ,:5 ! disk 0 kept at re/1 & ! ball 0 roll$ along betwe5 ! cyl9d] & disk1 ! trace ( its roll+ on ! latt] 0 a /raight horizontal l9e pass+ ?r\gh ! c5tre4 ,suppos+ !n t ! po9t ( contact ( ! ball ) ! disk 0 on "o side1 at a di/ance f ! c5tre1 & t ! disk 0 !n turn$1 ! ball 0 by ! friction betwe5 x & ! disk made to roll1 & s to turn ! cyl9d]4 ,! angul> velocity ( roll+1 & !re=e ! angul> velocity ( ! cyl9d]1 0 proportional to ! spe$ ( ! "p ( ! disk 9 contact ) x1 t is1 to y4 ,x 0 also proportional to ! spe$ ( turn+ ( ! disk4 ,! mode by :i* ?is ma*9e effects an integration w n[ be evid5t4 ,imag9e ! area to be f\nd to lie betwe5 a curve & a /raight datum l9e1 drawn on a b& ( pap]4 ,?is is /ret*$ on a l>ge cyl9d]1 ) ! datum l9e r\nd ! cyl9d]4 ,we call ?is ! pap]-cyl9d]4 ,! di/ances ( ! diff]5t po9ts ( ! curve f ! datum l9e are values ( y4 ,a horizontal b> p>allel to ! cyl9d] c>ries a =k at "o end & a project+ /yle at ! o!r4 ,! globe j fits betwe5 ! prongs ( ! =k1 & :5 ! b> is mov$ 9 ! direction ( its l5g? c>ries ! ball along ! disk & cyl9d]4 ,:5 ! /yle at ! o!r end is on ! datum l9e1 ! c5tre ( ! ball is at ! c5tre ( ! disk1 & ! turn+ ( ! disk does n turn ! cyl9d]4 ,:5 ! b> is displac$ 9 ! l9e ( its own l5g? to br+ ! /yle f ! datum l9e to a po9t on ! curve1 ! ball is displac$ a di/ance y1 & !re is a correspond+ turn+ ( ! cyl9d] by ! action ( ! ball4 ,9 ! use ( ! in/rum5t ! pap]-cyl9d] is turn$ by ! op]ator :ile ! /yle is kept on ! curve1 & ! disk is turn$ by ! ge>+ already ref]r$ to1 :i* is driv5 by a %aft ge>$ ) t ( ! pap]-cyl9d]4 ,?us ! displacem5t ( ! ball is always y1 ! ord9ate ( ! curve1 & = any displacem5t dx along ! datum l9e1 ! regi/]+ cyl9d] is turn$ ?r\gh an angle proportional to ydx4 ,?us any f9ite angle turn$ ?r\gh is proportional to ! integral ( ydx = ! correspond+ "p ( ! curve3 a scale r\nd "o end ( ! regi/]+ cyl9d] gives t angle4 ,?omson imm$iately p]ceiv$ t ?is extremely +5i\s integrat+ ma*9e 0 j :at he requir$ = 8 purpose4 ,! curve ( tidal heights drawn 7on a r$uc$ scale1 ( c\rse7 by a tide-gauge1 is really ! resultant ( a l>ge numb] ( simple curves1 repres5t$ by a s]ies ( h>monic t]ms1 ! coeffici5ts ( :i* are c]ta9 integrals4 ,! problem is ! evaluation ( ^! integrals2 & ! me?od usually employ$ is to obta9 !m by measurem5t ( ord9ates ( ! curve & an elaborate process ( calculation4 ,b "o ( !m is simply ! integral area betwe5 ! curve & ! datum l9e correspond+ to ! mean wat] level1 & ! o!rs are ! integrals ( quantities ( ! type y s9 nx4dx1 :]e y is ! ord9ate ( ! curve1 & n a numb] inv]sely proportional to ! p]iod ( ! tidal con/itu5t repres5t$ by ! t]m4 ,all t 0 necess>y1 9 ord] to give ! integral ( a t]m y s9 nx4dx1 0 to make ! disk oscillate ab\t its axis z ! pap]-cyl9d] 0 turn$ ?r\gh an angle proportional to x4 ,?us "o disk1 globe1 & cyl9d] 0 arrang$ exactly z has be5 describ$ = ! integral ( ydx1 & ) ?is z _m o!rs z !re 7 h>monic t]ms to be evaluat$ f ! curve 7 comb9$ z foll[s4 ,! disks 7 plac$ all 9 "o plane ) _! c5tres all on "o horizontal l9e1 & ! cyl9d]s ) _! axes also 9 l9e1 & a s+le slid+ b>1 ) a =k = ea* globe1 gave 9 ea* case ! displacem5t y f ! c5tre ( ! disk4 ,! requisite diff]5t spe$s ( oscillation 7 giv5 to ! disks by %afts ge>$ ) ! pap]-cyl9d]1 by tra9s ( :eels cut ) ! prop] numb] ( tee? = ! spe$ requir$4 ,?us ! angles turn$ ?r\gh by ! regi/]+ cyl9d]s :5 a curve on ! pap]-cyl9d] 0 pass$ "u ! /yle 7 proportional to ! integrals requir$1 & x 0 only necess>y to calibrate ! graduation ( ! scales ( ^! cyl9d]s by means ( kn[n curves to obta9 ! integrals 9 prop] units4 ,"o ( ^! ma*9es1 :i* analyses f\r h>monic con/itu5ts1 is 9 ! ,natural ,philosophy ,dep>tm5t at ,glasg[2 a mu* l>g] ma*9e1 to analyse a tidal curve conta9+ five pairs ( h>monic t]ms1 or elev5 con/itu5ts 9 all1 0 made = ! ,briti% ,association ,committee on ,tidal ,obs]vations1 & is probably n[ 9 ! ,s\? ,k5s+ton ,museum4 ,b /ill m rem>kable applications :i* ,?omson made ( 8 bro!r's integrat+ ma*9e 7 to ! me*anical integration ( l9e> diff]5tial equations1 ) v>iable coeffici5ts1 to ! integration ( ! g5]al l9e> diff]5tial equation ( any ord]1 &1 f9ally1 to ! integration ( any diff]5tial equation ( any ord]4 ,^! applications 7 all made 9 a few days1 almo/ 9 a few h\rs1 aft] ,james ,?omson fir/ describ$ ! elem5t>y ma*9e1 & pap]s conta9+ descriptions ( ! comb9ations requir$ 7 at once dictat$ by ,?omson to 8 secret>y1 & despat*$ = publication4 ,v possibly he _h ?\ght out ! applications to "s ext5t be=e2 b x is unlikely t he _h done s 9 detail4 ,b1 ev5 if x 7 s1 ! connection ( a s]ies ( ma*9es by ! s+le controll+ b>1 & ! production ( ! oscillations ( ! disks1 all controll$1 z !y 71 by ! motion ( a simple po9t along ! curve1 s z to give ! requir$ ,f\ri] coeffici5ts1 7 almo/ in/antane\s1 & af=d an example ( inv5tion am\nt+ to inspiration4 ,!re %\ld be notic$ "h also ! geometrical slide = use 9 safety-valves1 ca!tomet]s & o!r in/rum5ts1 & ! hole-slot-&-plane mode ( s support+ an in/rum5t n[ us$ 9 all laboratories4 ,^! 7 ,?omson's inv5tions1 & _! importance is insi/$ on 9 ! ,natural ,philosophy4 ,9 ,"p ,,ii1 ! pr9cipal subjects treat$ are attractions1 ela/icity1 su* great hydro/atical examples z ! equilibrium !ory ( ! tides & ! equilibrium ( rotat+ liquid sph]oids1 & su* problems ( a/ronomical & t]re/rial dynamics z ! di/ribution ( matt] 9 ! e>?1 ) ! be>+ on ?is subject ( ! precession ( ! equ9oxes1 tidal friction1 ! e>?'s rigidity1 ! effects ( ela/ic tides1 ! secul> cool+ ( ! e>?1 ! age ( ! e>?1 & ! age ( ! sun's heat4 ,( ^!1 ) ! exception ( ! age ( ! e>?1 we %all n attempt to give any acc\nt4 ,! importance ( ! orig9al contributions to ela/icity conta9$ 9 ! book is indicat$ by ! l>ge space devot$ to ! ,natural ,philosophy 9 ,pr(essor ,k>l ,pe>son's cont9uation ( ,todhunt]'s ,hi/ory ( ,ela/icity4 ,! heavy task ( edit+ ,"p ,,ii 0 p]=m$ ma9ly by ,sir ,george ,d>w91 :o made _m notable additions f 8 own rese>*es to ! matt] conta9$ 9 ! fir/ edition4 ,9 ! next *apt] an attempt w be made to pres5t ,?omson's views on ! subject ( ! age ( ! e>?4 ,^!1 :5 !y 7 publi%$1 attract$ mu* att5tion1 & receiv$ a good deal ( ho/ile criticism f geologi/s & biologi/s1 ^: processes !y 7 deem$ to re/rict to an entirely inadequate p]iod ( "t4 ,,gyro/atic ,,action ,?omson 9 8 lectures & o!rwise gave a great deal ( att5tion to ! motion ( gyro/ats1 & to ! effect ( ! inclusion ( gyro/ats 9 a sy/em on its prop]ties4 ,ref]5ce has be5 made to ! treatm5t ( gyro/atic dom9ation 9 ,?omson & ,tait4 ,a gyro/at consi/s ( a disk or :eel ) a massive rim1 :i* revolves )9 a case or framework1 by :i* ! :ole arrangem5t c be mov$ ab\t1 or support$1 )\t int]f]+ ) ! :eel4 ,! ord9>y toy consi/+ ( :eel ) a massive rim1 & a light frame1 is an example4 ,b mu* l>g] & m c>efully made in/rum5ts1 9 :i* ! :eel is entirely enclos$1 give ! mo/ int]e/+ exp]im5ts4 ,! body seems to h its prop]ties entirely alt]$ by ! rotation ( ! :eel1 & ( c\rse ! case prev5ts any outw>d *ange f be+ visible4 ,illu/ration3 ,,fig4 #ae4 ,figure #ae %[s "o =m ( gyro/at m\nt$ on a horizontal frame1 held 9 ! h&s ( an exp]im5t]4 ,! axis ( ! fly-:eel is v]tical )9 ! tubul> "p ( ! case2 ! fly-:eel is )9 ! "p on :i* is engrav$ an arr[-head to %[ ! direction ( rotation4 ,r\nd ! case 9 ! plane ( ! :eel is a project+ rim %>p5$ to an edge1 on :i* ! gyro/at c be support$ 9 o!r exp]im5ts4 ,to ! rim are screw$ two project+ pivots1 :i* c turn 9 be>+s on ! two sides ( ! frame z %[n4 ,! c5tre ( mass ( ! :eel is on ! level ( ^! pivots1 s t ! in/rum5t w rema9 ) ei!r end ( ! axis up4 ,if ! fly-:eel be n 9 rotation1 ! exp]im5t] c c>ry ! arrangem5t ab\t1 & ! fly-:eel & case move ) x z if ! gyro/at 7 m]ely an ord9>y rigid body4 ,b n[ remove ! gyro/at f ! frame1 & set ! :eel 9 rotation4 ,?is is done by an endless cord wrapp$ r\nd a small pulley fa/ on ! axle 7to :i* access is obta9$ by a hole j opposite 9 ! case7 & pass$ also r\nd a l>g] pulley on ! %aft ( a motor4 ,:5 ! motor is />t$ ! cord mu/ be tight5$ only v g5tly at fir/1 s t x slips on ! pulley1 o!rwise ! motor w\ld be ret>d$1 & possibly burn$ by ! curr5t4 ,! fly-:eel gradually gets up spe$1 & !n ! cord c be br\ght q tight s t no slipp+ occurs4 ,:5 ! spe$ is great en\gh ! cord is cut ) a /roke f a %>p knife & runs out4 ,! gyro/at is n[ replac$ on its pivots 9 ! frame1 ) its axis v]tical1 & mov$ ab\t z x 0 be=e4 ,if ! exp]im5t]1 hold+ ! frame z %[n1 turns r\nd 9 ! direction ( ! arr[1 :i* is t ( rotation1 no?+ happ5s4 ,if1 h[ev]1 he turns r\nd ! o!r way1 ! gyro/at imm$iately turns on its pivots s z to po9t ! o!r end ( ! axis up4 ,if ! exp]im5t] cont9ues 8 turn+ motion1 ! gyro/at is n[ quiesc5t3 = x is be+ c>ri$ r\nd n[ 9 ! direction ( rotation4 ,?us1 ) no gravitational /ability at all 7s9ce ! c5tre is on a level ) ! pivots7 ! gyro/at is 9 /able equilibrium :5 c>ri$ r\nd 9 ! direction ( rotation1 b is 9 un/able equilibrium :5 c>ri$ r\nd ! opposite way4 ,?us1 if ! obs]v] knew no?+ ( ! rotation ( ! fly-:eel1 & c\ld see & feel only ! outside ( ! case1 ! behavi\r ( ! in/rum5t might well appe> v a/oni%+4 ,?is is a case ( :at ,?omson & ,tait call gyro/atic dom9ation1 :i* is treat$ v fully 9 _! ,sections #cde 7vi7 to #cde 7xxviii7 ( ,"p ,i4 ,x may be rem>k$ "h t ?is case ( motion may be easily treat$ ma!matically 9 an exce$+ly elem5t>y mann]1 & ! in/ability ( ! "o case1 & ! /ability ( ! o!r1 made cle> to ! beg9n] :o has only a notion ( ! composition ( angul> mom5ta ab\t diff]5t axes4 ,a ye> or two ago x 0 sugge/$ by ,pr(essor ,pick]+1 ( ,h>v>d1 t ! fact t ! out]mo/ satellite ( ,saturn revolves 9 ! direction opposite to ! planet's rotation1 may be due to ! fact t orig9ally ,saturn rotat$ 9 ! direction ( ! motion ( ?is moon1 b inasmu* z 8 motion r\nd ! sun 0 opposite 9 direction to 8 rotation1 he 0 turn$1 s to speak1 upside d[n1 l ! gyro/at6 ,! o!r satellites1 x is sugge/$1 7 ?r[n (f lat]1 z _! revolution is direct4 ,pr(essor ,pick]+ ref]s to an exp]im5t 7simil> to t describ$ above7 :i* he gives z new4 ,?omson _h %[n ?is exp]im5t = _m ye>s1 z an example ( ! g5]al discussion 9 ,?omson & ,tait1 & its !ory _h already be5 explicitly publi%$4#ba ,_m o!r exp]im5ts ) gyro/ats us$ to be %[n by ,?omson to visitors4 ,_m ( ^! are indicat$ 9 ,?omson & ,tait4 ,! e>?'s precessional motion is a gyro/atic effect due to ! diff]5tial attraction ( ! sun1 :i* t5ds to br+ ! plane ( ! equator into co9cid5ce ) ! ecliptic1 & s alt]s ! direction ( ! axis ( rotation4 ,old /ud5ts w rememb] ! balanc$ globe--) incl9$ mat]ial axis roll+ r\nd a horizontal r+--by :i* ! k9ematics ( ! motion c\ld be /udi$1 & ! displacem5t ( ! equ9oxes on ! ecliptic trac$4 ,illu/ration3 ,,fig4 #af4 ,ano!r example ( ! gyro/atic dom9ation discuss$ 9 ,?omson & ,tait is giv5 9 ! v rem>kable address entitl$ ,a ,k9etic ,!ory ( ,matt]1 :i* ,sir ,william ,?omson deliv]$ to ,section ,a ( ! ,briti% ,association at ,montreal1 9 #ahhd4 ,figure #af %[s an ord9>y d\ble coa* spr+1 ! upp] & l[] memb]s ( :i* c>ry two hook$ rods z %[n4 ,if ! upp] hook is atta*$ to a fix$ support1 & a weight is hung on ! l[]1 ! spr+ w be drawn out1 & ! arrangem5t w be 9 equilibrium "u a c]ta9 elongation4 ,if ! weight be pull$ d[n fur!r & !n left to itself1 x w vibrate up & d[n 9 a p]iod dep5d+ ^u ! equilibrium elongation produc$ by ! weight4 ,! same ?+ w happ5 if a spiral spr+ be sub/itut$ = ! coa* spr+4 ,a sph]ical case1 ?r\gh :i* ! hook$ rods pass freely1 hides ! int]nal p>ts f view4 ,illu/ration3 ,,fig4 #ag4 ,figure #ag %[s two hook$ rods1 z 9 ! =m] case1 atta*$ by swivels to two opposite corn]s ( a frame =m$ ( f\r rods jo9t$ toge!r at _! ends4 ,ea* ( ^! is divid$ 9 ! middle = ! ins]tion ( a gyro/at1 ! axis ( :i* is pivot$ on ! adjac5t ends ( ! two halves ( ! rod4 ,a sph]ical case1 indicat$ by ! circle1 aga9 hides ! int]nal arrangem5t f inspection1 b p]mits ! hook$ rods to move freely up & d[n4 ,! swivels all[ ! frame1 gyro/ats & all1 to be turn$ ab\t ! l9e ( ! hooks4 ,if n[ ! gyro/ats be n 9 rotation1 ! frame w be p]fectly limp1 & w n 9 ! lea/ resi/ pull appli$ by a weight4 ,b if ! gyro/ats be rotat$ 9 ! directions %[n by ! circles1 ) arr[-heads drawn r\nd ! rods1 !re w be angul> mom5tum ( ! :ole sy/em ab\t ! l9e jo9+ ! hooks1 & if a weight or a =ce be appli$ to pull out ! frame along t l9e1 ! pull w be resi/$ j z x 0 9 ! o!r case by ! spr+4 ,moreov]1 equilibrium w be obta9$ ) an elongation proportional to ! weight hung on1 & small oscillations w be p]=m$ j z if !re 7 a spr+ 9 ! int]ior in/ead ( ! gyro/ats4 ,accord+ z ! frame is pull$ out1 or %ort5$1 ! angul> mom5tum ( ! gyro/ats ab\t ! l9e jo9+ ! hooks is increas$ or dim9i%$1 & ! frame1 c>ry+ ! gyro/ats ) x1 turns ab\t ! swivels 9 "o direction or ! o!r1 at ! rate necess>y to ma9ta9 ! angul> mom5tum at a con/ant value4 ,b ?is w n be p]ceiv$ f )\t4 ,! rotation ( ! fly-:eels ?us gives to ! o!rwise limp frame ! ela/icity :i* ! spr+ possesses2 )\t dissection ( ! model ! diff]5ce _c be p]ceiv$4 ,?is illu/rates ,?omson's idea t ! ela/icity ( matt] may be due to motion ( molecules or gr\ps ( molecules ( ! body1 imb$d$ 9 a connect+ framework1 de=m$ by appli$ =ces z 9 ?is model1 & produc+ displacem5ts :i* are resi/$ 9 consequ5ce ( ! motion4 ,& "h may be m5tion$ also ,?omson's explanation ( ! ph5om5on1 discov]$ by ,f>aday1 ( ! rotation ( ! plane ( a beam ( pol>is$ light :i* is pass$ along ! l9es ( =ce ( a magnetic field4 ,?is rotation is di/9ct altoge!r f t :i* is produc$ :5 pol>is$ light is pass$ along a tube fill$ ) a solution ( sug> or t>t>ic acid4 ,if ! ray be reflect$ aft] passage1 & made to retrav]se ! m$ium1 ! rotation is annull$ 9 ! latt] case1 x is d\bl$ 9 ! =m]4 ,?is l$ ,?omson to ! view t 9 sug>1 t>t>ic acid1 qu>tz1 etc41 ! turn+ is due to ! /ructure ( ! sub/ance1 & 9 ! magnetic field to rotation already exi/+ 9 ! m$ium4 ,he us$ to say t a v l>ge numb] ( m9ute spiral cavities all 9 ! same direction1 & all "r-h&$ or all left-h&$1 9 ! sug> or qu>tz1 w\ld give ! effect2 on ! o!r h&1 ! magnetic ph5om5on c\ld only be produc$ by "s arrangem5t analog\s to a v l>ge numb] ( tops1 or gyro/ats1 imb$d$ 9 ! m$ium ) _! axes all 9 "o direction 7or prepond]at+ly s7 & all turn+ ! same way4 ,! rotation ( ^! tops or gyro/ats ,?omson suppos$ to be caus$ by ! magnetic field1 & to be ess5tially t :i* con/itutes ! magnetisation ( ! m$ium4 ,let ! frame ( ! gyro/atic spr+-balance describ$ above1 turn r\nd ! l9e jo9+ ! hooks s z to exactly comp5sate1 by turn+ 9 ! opposite direction1 ! angul> mom5tum ab\t t l9e giv5 by ! fly-:eels2 !n ! arrangem5t w h no angul> mom5tum on ! :ole2 & a l>ge numb] ( su* balances1 all v m9ute & hook$ toge!r1 w =m a sub/ance )\t angul> mom5tum 9 any "p4 ,b n[ by ! equival5t ( a magnetic =ce along ! l9es ( ! hooks1 let a diff]5t angul> turn+ ( ! frames be produc$2 ! m$ium w possess a specific angul> mom5tum 9 e "p4 ,if a wave ( transv]se vibrations :i* are p>allel to "o direction 7t is1 if ! wave be plane-pol>is$7 ent] ! m$ium 9 ! direction ( ! axes ( ! frames1 ! direction ( vibration w be turn$ z ! wave proce$s1 t is1 ! plane ( pol>isation w be turn$ r\nd4 ,m rec5t rese>* has %[n an effect ( a magnetic field on ! spectrum ( light produc$ 9 ! field1 & view$ ) a spectroscope 9 a direction at "r angles to ! field--! ,zeeman effect1 z x is call$--& ! explanation ( ?is effect by equations ( mov+ electric *>ges1 :i* are ess5tially gyro/atic equations1 is sugge/ive ( an analogy or correspond5ce betwe5 ! sy/ems ( mov+ electrons :i* con/itute ^! *>ges1 & "s su* gyro/atic molecules z ,?omson imag9$4 ,x has be5 po9t$ out t ! ,zeeman effect1 9 its simple =ms at lea/1 c be exactly imitat$ by ! motion ( an ord9>y p5dulum hav+ a gyro/at 9 its bob1 ) its axis direct$ along ! susp5sion rod4#bb ,,electro/atics ,,& ,,magnetism ,9 ! t5 ye>s f #ahfc to #ahgc ,?omson 0 extremely busy ) lit]>y "w4 ,9 #ahgb1 five ye>s aft] ! publication ( ! treatise on ,natural ,philosophy1 & j be=e ! appe>ance ( ! ,elem5ts1 ,messrs4 ,macmillan ,co4 publi%$ = him a collection ( memoirs entitl$ ,repr9t ( ,pap]s on ,electro/atics & ,magnetism4 ,! volume conta9s #eif pages1 & ! subjects dealt ) range f ! ,uni=m ,motion ( ,heat & its ,connection ) ! ,ma!matical ,!ory ( ,electricity 7! pap] already describ$ 9 ,*apt] ,,ii above7 & ! discussion ( ,electromet]s & ,electro/atic ,measur+ ,in/rum5ts1 to a complete ma!matical !ory ( magnetism4 ,! subject ( electro/atics l$ naturally to ! consid]ation ( electrical measur+ in/rum5ts z !y exi/$ =ty ye>s ago 7ab\t #ahfg71 & _! replacem5t by o!rs1 ! indications ( :i* f day to day %\ld be directly comp>able1 & capable ( be+ int]pret$ 9 absolute units4 ,d[n to t "t p _h be5 oblig$ to cont5t !mselves ) gold-leaf electroscopes1 & inde$ x 0 impossible = accurate measur+ in/rum5ts to be inv5t$ until a sy/em ( absolute units _h be5 completely work$ out4 ,! task ( fix+ ^u def9itions ( units & ( realis+ !m 9 suitable /&>ds _h be5 begun by ! ,briti% ,association1 & x 0 z "p ( ! ,report ( t ,committee to ! ,dundee ,meet+ 9 #ahfg t ,?omson's pap] on ,electromet]s fir/ appe>$4 ,x 0 !re po9t$ out t an electromet] is ess5tially an in/rum5t = measur+ diff]5ces ( electric pot5tial betwe5 conductors1 by means ( effects ( electro/atic =ce4 ,su* a diff]5ce is :at a gold-leaf electroscope indicates = its gold leaves & ! walls surr\nd+ ! air-space 9 :i* !y are susp5d$4 ,z electroscopes us$ to be con/ruct$1 ^! walls 7 made ( glass imp]fectly cov]$1 if at all1 by conduct+ mat]ial1 & ! electroscope 0 q indef9ite & unc]ta9 9 its action4 ,! in/rum5t 0 also1 z made1 q ins5sitive4 ,rec5tly1 h[ev]1 x has be5 rehabilitat$ 9 reputation1 & br\ght into use z a v s5sitive indicator ( effects ( radio-activity4 ,?omson describ$ 9 ?is pap] six species ( electromet]s ( 8 own devis+4 ,! be/ kn[n ( ^! are 8 quadrant electromet] & 8 attract$-disk electromet]s4 ,! =m] is to be f\nd 9 "s =m or o!r 9 e laboratory n[adays1 & ne$ n be describ$ 9 detail4 ,! action is ( two conductors--! two pairs ( opposite quadrants ( a %all[1 horizontal1 cyl9drical box1 made by divid+ ! box into f\r by two slits at "r angles--^u an electrifi$ slip ( alum9ium susp5d$ by a two-?read susp5sion )9 ! box1 ) its l5g? along "o ( ! slits4 ,! two pairs ( opposite quadrants are at ! pot5tial diff]5ce to be measur$1 & ! slip ( alum9ium1 or ne$le1 has ea* end urg$ r\nd f a quadrant at high] pot5tial t[>ds "o at a l[]1 & ^! actions conspire to turn ! slip aga9/ its t5d5cy to return to ! position 9 :i* ! two ?reads are 9 "o plane4 ,?us ! deflection 7measur$ by ! displacem5t ( a reflect$ ray ( light us$ z index7 gives an indication ( ! am\nt ( ! pot5tial diff]5ce4 ,! electrification ( ! ne$le 0 kept up by enclos+ ! quadrantal box )9 an electrifi$ ,leyd5 j>1 to ! int]ior coat+ ( :i* contact is made by a plat9um wire1 dep5d+ f ! ne$le to sulphuric acid conta9$ 9 ! j>4 ,! :ole app>atus 0 enclos$ 9 a conduct+ case connect$ to e>?4 ,?is made its action p]fectly def9ite4 ,v>iations ( ?is electrification ( ! j> 7 %[n by an atta*$ attract$-disk electromet]1 ! pr9ciple ( :i* we %all m]ely indicate4 ,! quadrant electromet] has n[ be5 va/ly increas$ 9 s5sibility by ! use ( a s+le qu>tz fibre z susp5sion4 ,by ! inv5tion ( ?is fibre1 :i* is exce$+ly /rong & is1 moreov]1 s def9ite 9 its ela/ic prop]ties t x comes back at once exactly to its =m] z]o /ate aft] twi/1 ,mr4 ,c4 ,v4 ,boys has increas$ ! delicacy ( all k9ds ( susp5d$ indicators _m fold4 ,b x ought to be rememb]$ t a ,dolezalek electromet]1 ) "s hundr$ or m times ! s5sibility ( ! bifil> in/rum5t1 0 only made possible by its pr$ecessor4 ,attract$-disk-electromet]s simply measure1 ei!r by weigh+ or by ! deflection ( a spr+1 ! attractive =ce betwe5 two p>allel disks at diff]5t pot5tials4 ,f ! det]m9ation ( ?is =ce1 & ! measurem5t ( ! di/ance betwe5 ! disks 7or bett]1 ( an alt]ation ( ! di/ance7 a diff]5ce ( pot5tials c be det]m9$1 & a unit = x obta9$1 :i* is 9 direct & kn[n relation to ord9>y dynamical units4 ,?omson's ,absolute ,electromet] 0 design$ specially = accurate det]m9ations ( ?is k9d4 ,ano!r =m1 call$ ! ,long ,range ,electromet]1 0 devis$ = ! measurem5t ( ! pot5tials ( ! *>g$ conductors 9 electric ma*9es & ,leyd5 j>s4 ,accurate det]m9ations ( ! sp>k+ resi/ance betwe5 p>allel plates *>g$ to diff]5t pot5tials 9 air 7 made by means ( attract$-disk-electromet]s 9 ! c\rse ( "s important exp]im5ts describ$ 9 ! ,electro/atics & ,magnetism4 ,^! results h be5 mu* ref]r$ to 9 lat] rese>*es4 ,a small attract$-disk-electromet] 0 us$ z indicat$ above to keep a wat* on ! electrification ( ! ,leyd5 j> ( ! quadrant in/rum5t1 & a small induction ma*9e 0 add$1 by turn+ :i* ! op]ator c\ld make good any loss ( *>ge ( ! j>4 ,?is electrical ma*9e 0 an example ( an app>atus on precisely ! same pr9ciple z ! ,voss or ,wim%ur/ ma*9es ( ! pres5t day4 ,9 x by a set ( mov+ c>ri]s1 influ5c$ by conductors1 ! *>ges ( ! latt] 7 increas$ accord+ to a comp\nd int]e/ pr9ciple only int]f]$ ) by leakage to ! air or by ! supports4 ,sev]al =ms ( ?is ma*9e1 on ! same pr9ciple1 7 con/ruct$ by ,?omson1 & describ$ 9 #ahfh2 b he aft]w>ds f\nd t he _h be5 anticipat$ by ,c4 ,f4 ,v>ley 9 #ahfj4 ,/ill lat] x 0 discov]$ t a simil> in/rum5t _h be5 made a c5tury be=e by ,ni*olson1 & call$ by him ! ,revolv+ ,d\bl]4 ,! exp]im5ts :i* ,?omson made on atmosph]ic electricity at ! old ,college t[]1 & by means ( portable electromet]s 9 ,arran & else:]e1 c only be m5tion$4 ,!y l$ no d\bt to "s improvem5ts on electromet]s :i* he made1 ! me?od ( br++ ! nozzle ( a wat]-dropp]1 or a po9t on a portable electromet] to ! pot5tial ( ! air1 by ! inductive action on a /ream ( wat]-drops 9 ! "o case1 or ! p>ticles ( smoke f a burn+ mat* 9 ! o!r4 ,he inv5t$ a self-act+ ma*9e1 work$ by a /ream ( wat]-drops1 = accumulat+ electric *>ges1 on ! pr9ciple ( ! revolv+ d\bl]4 ,x 0 ?is app>5tly t l$ to ! ma*9es ) revolv+ c>ri]s1 to :i* ref]5ce has be5 made above4 ,! ma!matical !ory ( magnetism :i* ,?omson gave 9 #ahdi1 9 ! ,phil4 ,trans4 ,r4,s41 01 :5 complet$ by v>i\s lat] pap]s1 a sy/ematic discussion ( ! :ole subject1 includ+ electromagnetism & diamagnetism4 ,to a l>ge ext5t ! gr\nd cov]$ by ! #ahdi pap] _h be5 trav]s$ be=e by ,poisson1 & p>tially by ,murphy & ,gre52 b ,?omson /at$ t "o *ief object ( 8 memoir 0 to =mally con/ruct ! !ory )\t ref]5ce to ! two magnetic fluids1 by means ( :i* ! facts ( exp]im5t & conclusions ( !ory _h s f> be5 express$4 ,he f\nd x1 h[ev]1 conv5i5t to introduce ! idea ( positive & negative magnetic matt] 7attract+ & repell+ z d *>ges ( positive & negative electricity71 :i* are to be reg>d$ z always pres5t 9 equal am\nts1 n only 9 a magnet z a :ole1 b 9 e portion ( a magnet2 & at fir/ sight ?is might appe> l a return to ! magnetic fluids4 ,b x am\nts on ! :ole r to a conception ( a magnet z a conglom]ation ( d\blets ( magnetic matt] 7t is1 v close1 equal & insep>able *>ges ( ! two k9ds ( matt]71 ! arrangem5t ( :i* c be *ang$ by ! action ( magnetic =ce4 ,?is idea is set =? n[ 9 all ! books on magnetism & electricity4 ,!re c be no d\bt t ! sy/ematic pres5tm5t ( ! subject by ,?omson1 & ! !orems & ideas ( magnetic =ce & magnetic p]meability by :i* he r5d]$ ! cle>1 & !re=e ma!matical1 notions ( ,f>aday explicitly quantitative1 _h mu* influ5ce 9 fur!r+ ! progress ( electrical sci5ce1 & s lead+ on ! "o h& to ! electromagnetic !ories ( ,maxwell1 & on ! o!r to mod]n rese>* on ! magnetic prop]ties ( iron1 & to ! correct ideas :i* n[ prevail z to con/ruction ( dynamo-electric ma*9es & motors4 ,,*apt] ,,xii ,,! ,,age ,,( ,,! ,,e>? ,f 8 /ud5t days ?r\gh\t 8 life1 ,"l ,kelv9 took a ke5 int]e/ 9 geological que/ions4 ,he 0 always an active memb] ( ! ,geological ,society ( ,glasg[1 & 0 its presid5t = tw5ty-"o ye>s 7#ahgb-ahic74 ,! di/ribution ( heat 9 ! sub/ance ( ! e>? 0 ! subject ( 8 inaugural diss]tation z ,pr(essor ( ,natural ,philosophy2 & previ\sly1 z a /ud5t1 he _h writt5 an essay on ,! ,figure ( ! ,e>?1 = :i* he _h be5 aw>d$ a ,univ]sity ,gold ,m$al4 ,he nev] ceas$ to pond] ov] ! problems ( t]re/rial physics1 & he wrote mu* on ! subject4 ,8 pap]s are to be f\nd z ,app5dices to ,?omson & ,tait's ,natural ,philosophy1 & 9 vol4 ii ( 8 ,popul> ,lectures & ,addresses1 :i* is devot$ to geology & g5]al physics4 ,8 conclusions reg>d+ ! age ( ! e>? h be5 ref]r$ to 9 ! la/ *apt]4 ,! fir/ allusion to ! subject 0 conta9$ 7see p4 #fe above7 9 8 inaugural diss]tation ,de ,caloris di/ributione 9 ,t]r ,corpus2 b he return$ to x aga9 9 a communication made to ! ,royal ,society ( ,ed9burgh 9 ,decemb]1 #ahfe1 & entitl$ ,! ,doctr9e ( ,uni=mity 9 ,geology briefly refut$4 ,on ,febru>y #bg1 #ahfh1 he deliv]$ to ! ,geological ,society ( ,glasg[ an address entitl$ ,on ,geological ,"t1 9 :i* ! necessity = limit+ geological & o!r *anges to an almo/ inf9itesimal fraction ( ! va/ p]iods at t "t dem&$ 0 insi/$ on1 & :i* gave rise to mu* discussion4 ,! address began ) a prote/ aga9/ ! old uni=mit>ian view ( geological *anges z express$ by ,playfair 9 8 ,illu/rations ( ! ,huttonian ,!ory4 ,! fir/ objection tak5 to ! idea t 9 ! cont9uation ( ! diff]5t species ( animals & vegetables t inhabit ! e>?1 we disc]n nei!r a beg9n+ nor an end2 9 ! planet>y motions :]e geometry has c>ri$ ! eye s f>1 bo? into ! future & ! pa/1 we discov] no m>k ei!r ( ! comm5cem5t or ! t]m9ation ( ! pres5t ord] is1 t ! /ability ( ! motions ( ! heav5ly bodies1 to :i* ref]5ce is made 9 ?is /atem5t1 is f\nd$ ^u :at is ess5tially an approximate calculation1 :i* leaves out1 by int5tion1 ! consid]ation ( frictional resi/ance4 ,he po9ts out1 = example1 t ! friction :i* accompanies ! relative motion ( ! wat]s ( ! e>? & ! l& is att5d$ by ! production ( heat1 & t1 by ! doctr9e ( ! cons]vation ( en]gy1 heat _c be produc$ )\t a disappe>ance ( an equival5t quantity ( en]gy1 ei!r ( motion or ( position4 ,! *ief s\rce ( ?is en]gy is ! e>?'s rotation4 ,s9ce ! e>? turns "u ! moon & ! tidal sph]oid--t is1 ! e>?'s %ape z di/ort$ by ! heap+ up ( ! wat]s 9 ! tides--rema9s on ! :ole /ation>y ) respect to ! moon1 ! solid matt] ( ! e>? turns "u ! di/ribution ( ! wat]1 held m or less fix$ by ! moon1 z does a fly-:eel "u a /ation>y friction b& r\nd its rim4 ,!n j z ! b& held fix$ ret>ds ! fly-:eel1 s ! e>? mu/ be ret>d$ 9 its rotation by ?is wat]-brake4 ,9 ! e>?'s rotation !re is a /ore ( k9etic en]gy :i*1 r\ghly e/imat$1 w\ld n be exhau/$ 9 less ?an t5 million million ye>s1 al?\gh drawn ^u cont9u\sly by friction1 or o!r actions1 at ! rate ( "o million horse-p[]2 s t1 no imm$iate cata/rophe1 su* z t we %\ld be involv$ 9 by ! /oppage or consid]able ret>dation ( ! sp9n+ motion ( ! e>?1 is possible4 ,b x 0 po9t$ out by ,?omson t ! be/ results ( a/ronomical obs]vation %[ t ! e>? w\ld 9 "o hundr$ ye>s fall beh9d a p]fect "t-keep]1 ) :i* its rotation kept pace at ! beg9n+ ( ! "t1 by ab\t tw5ty seconds4 ,! t5d5cy is to make ! e>? turn sl[]1 & ! moon to increase its di/ance & move m sl[ly 9 its orbit1 b ) a resultant effect t[>ds co9cid5ce ( ! p]iod ( ! e>?'s rotation ) t ( revolution ( ! moon r\nd ! e>?4 ,aft] ?is co9cid5ce has be5 atta9$1 h[ev]1 ! sol> tides w t5d to make ! moon fall 9 t[>ds ! e>?4 ,if !n ! e>? be rotat+ m & m sl[ly1 z "t goes on1 at pres5t1 x mu/ h be5 rotat+ m rapidly 9 pa/ "t4 ,a ?\s& million ye>s ago1 at ! pres5t rate ( ret>dation1 ! e>? mu/ h be5 rotat+ "o sev5? "p ( its spe$ fa/] ?an x is rotat+ at pres5t1 & ?is w\ld give = c5trifugal =ce at ! surface "o ?\s& million ye>s ago1 great] ?an ! c5trifugal =ce at pres5t1 9 ! ratio ( #fd to #di4 ,app>5tly !re=e ! e>? mu/ h solidifi$ at a mu* lat] date ?an t epo*1 a date :5 x 0 rotat+ mu* m ne>ly ) ! angul> spe$ :i* x has n[2 o!rwise ! figure ( ! e>? w\ld h deviat$ mu* m f ! sph]ical =m ?an x actually does4 ,on ! o!r h&1 "o hundr$ million ye>s ago c5trifugal =ce w\ld be only ?ree p] c5t4 great] ?an x is at pres5t1 & consolidation ( ! e>? at t less remote p]iod w\ld give a %ape to ! e>? n v diff]5t f t :i* x n[ possesses4 ,! argum5t !re=e f tidal ret>dation w\ld cut d[n ! "t available = geological & biological *anges to some?+ n mu* m ?an "o hundr$ million ye>s1 p]haps to less4 ,a second argum5t = limitation ( ! "t available = su* processes is d]iv$ f ! sun's heat4 ,! sun _c be reg>d$ z a miracul\s body produc+ its light & heat f no?+4 ,*anges ( ! con/itution ( ! sun mu/ be cont9ually proce$+1 to acc\nt = its enorm\s radiation ( en]gy into space1 a radiation ( :i* only an inf9itesimal "p is receiv$ by ! bodies ( ! sol> sy/em1 & a /ill m m9ute portion by ! e>?4 ,! effects ( ! sun's light & heat on ! e>? %[ h[ enorm\s mu/ be ! quantity ( en]gy lo/ f ! sun 9 a ye>4 ,h[ is ?is loss ( en]gy to be acc\nt$ =8 ,:at is ! physical *ange :i* gives rise to x8 ,9 #ahed ,?omson put =w>d ! !ory t ! sun's heat is kept up by ! fall+ 9 ( meteors on ! sun's surface1 b he aft]w>ds saw reason to ab&on t view4 ,helmholtz _h advocat$ ! !ory t ! sun 0 a body heat$ by ! com+ toge!r ( ! matt] compos+ x by its mutual attraction1 a process :i*1 al?\gh ! sun is n[ a cont9u\s mass1 is to be reg>d$ z /ill go+ on4 ,x is easy to calculate ! exhau/ion ( pot5tial en]gy caus$ by ! com+ toge!r ( ! matt] ( ! sun f univ]sal disp]sion ?r\gh inf9ite space to a sph]e ( uni=m d5sity ( ! pres5t size ( ! sun4 ,! result is ab\t z mu* en]gy z w\ld be g5]at$ by burn+ sev5 million million million million million tons ( coal4 ,! am\nt radiat$ 9 ea* h\r is ab\t z mu* z w\ld be g5]at$ by burn+ some?+ l n9e tons ( coal e h\r on e squ>e y>d ( ! sun's surface4 ,x is c]ta9 t ! sun mu/ be /ill contract+1 & if x contracts suffici5tly to j make good ?is exp5diture by ! fur!r exhau/ion ( pot5tial en]gy involv$ 9 ! clos] aggregation ( ! matt]1 x mu/ dim9i% 9 radius 9 ea* ye> by z mu* z #acj feet4 ,! am\nt ( en]gy g5]at$ by ! fall+ toge!r ( ! matt] ( ! sun f univ]sal diffusion to ! dim5sions :i* ! sun has at pres5t1 is only ab\t #ac1jjj1jjj times ! am\nt n[ radiat$ p] annum4 ,9 ,?omson's pap] ,p\illet's e/imate ( ! en]gy radiat$ p] second is us$1 & ?is numb] is rais$ to #bj1jjj1jjj4 ,tak+ ! latt] e/imate1 ! :ole pot5tial en]gy exhau/$ by ! cond5sation ( ! sun's mass to uni=m d5sity w\ld suffice = only #bj1jjj1jjj ye>s' supply4 ,b ! sun is und\bt$ly ( mu* great] d5sity 9 ! c5tral p>ts ?an ne> ! surface1 & s ! en]gy exhau/$ mu/ be mu* great] ?an t /at$ above4 ,?is w raise ! numb] ( ye>s provid$ =4 ,on ! o!r h&1 a consid]able am\nt ( en]gy w\ld be dissipat$ dur+ ! process ( cond5sation1 & ?is w\ld r$uce ! p]iod ( radiation e/imat$4 ,?omson sugge/s t #ej1jjj1jjj1 or #ajj1jjj1jjj1 ye>s is a possible e/imate4 ,x is n unlikely t ! rate ( radiation 9 pa/ "t1 :5 ! sun _h n ne>ly cond5s$ to its pres5t size1 0 s mu* less ?an x is at pres5t t ! p]iod sugge/$ above may h to be consid]ably augm5t$4 ,ano!r s\rce ( radiation1 :i* seems to be reg>d$ by "s au?orities z a probable1 if n a c]ta91 "o1 has be5 sugge/$ 9 rec5t ye>s--! pres5ce ( radio-active sub/ances 9 ! sun4 ,s f> z we "k1 ,"l ,kelv9 did n admit t ?is s\rce ( radiation 0 wor?y ( consid]ation2 b ( c\rse1 grant$ its exi/5ce to an ext5t comp>able ) ! en]gy d]ivable f cond5sation ( ! sun's mass1 ! age ( ! sun's heat w\ld h to be v greatly ext5d$4 ,^! are matt]s1 h[ev]1 on :i* fur!r light may be ?r[n z rese>* 9 radio-activity progresses4 ,"l ,kelv9 0 engag$ :5 seiz$ ) 8 la/ illness 9 discuss+ ! *anges ( en]gy 9 a gase\s1 or p>tially gase\s1 globe1 sl[ly cool+ & %r9k+ 9 do+ s2 & a po/hum\s pap] on ! subject w %ortly be publi%$ :i* may possibly conta9 fur!r in=mation on ?is "q ( sol> physics4 ,b ,?omson put =w>d a ?ird argum5t 9 ! pap] on ,geological ,"t1 :i* has always be5 reg>d$ z ! mo/ important4 ,x is d]iv$ f ! fact1 e/abli%$ by abundant obs]vations1 t ! temp]ature 9 ! e>?'s cru/ increases f ! surface inw>ds2 & t !re=e ! e>? mu/ be cont9ually los+ heat by conduction f )94 ,if ! e>? be suppos$ to h be5 ( uni=m temp]ature at "s p]iod ( pa/ "t & 9 a molt5 /ate1 & c]ta9 assumptions z to ! conductive p[] & melt+ po9t ( its mat]ial be made1 ! "t ( cool+ until ! gradi5t ( temp]ature at ! surface acquir$ its pres5t value c be calculat$4 ,?is 0 done by ,?omson 9 a pap] publi%$ 9 ! ,transactions1 ,r4,s4,e41 9 #ahfb4 ,we propose to give "h a %ort sket* ( 8 argum5t1 :i* has excit$ mu* int]e/1 & be5 ! cause ( "s controv]sy4 ,9 ord] to und]/& ?is argum5t1 ! read] mu/ be> 9 m9d "s fundam5tal facts ( ! fl[ ( heat 9 a solid4 ,let him imag9e a slab ( any uni=m mat]ial1 say s&/one or m>ble1 ! two p>allel faces ( :i* are cont9ually ma9ta9$ at two diff]5t temp]atures1 uni=m ov] ea* face4 ,= example1 /eam may be cont9ually bl[n aga9/ "o face1 :ile ice-cold wat] is made to fl[ ov] ! o!r4 ,heat w fl[ across ! slab f ! hott] face to ! cold]4 ,x w be f\nd t ! rate ( fl[ ( heat p] unit area ( face1 t is p] squ>e c5timetre1 or p] squ>e in*1 is proportional to ! diff]5ce ( ! temp]atures 9 ! slab at ! two faces1 & inv]sely proportional to ! ?ickness ( ! slab4 ,9 o!r words1 x is proportional to ! fall ( temp]ature f "o face to ! o!r tak5 p] unit ( ! ?ickness1 t is1 to ! gradi5t ( temp]ature f "o face to ! o!r4 ,moreov]1 comp>+ ! fl[ 9 "o sub/ance ) ! fl[ 9 ano!r1 we f9d x diff]5t 9 diff]5t sub/ances = ! same gradi5t ( temp]ature4 ,?us we get f9ally a fl[ ( heat across unit area ( ! slab :i* is equal to ! gradi5t ( temp]ature multipli$ by a numb] :i* dep5ds on ! mat]ial3 t numb] is call$ ! conductivity ( ! sub/ance4 ,n[1 bor+s made 9 ! e>? %[ t ! temp]ature increases inw>ds1 & ! same ?+ is %[n by ! high] temp]atures f\nd 9 deep] coal m9es4 ,by means ( !rmomet]s sunk to diff]5t dep?s1 ! rate ( increase ( temp]ature ) dep? has be5 det]m9$4 ,simil> obs]vations %[ t ! daily & annual v>iations ( temp]ature caus$ by ! succession ( day & night1 & summ] & w9t]1 p5etrate to only a comp>atively small dep? bel[ ! surface--?ree or f\r feet 9 ! =m] case1 sixty or sev5ty 9 ! latt]4 ,leav+ ^! v>iations out ( acc\nt1 s9ce ! av]age ( _! effects ov] a consid]able int]val ( "t mu/ be no?+1 we h 9 ! e>? a body at e po9t ( ! cru/ ( :i* !re is a gradi5t ( increas+ temp]ature inw>ds4 ,! am\nt ( ?is may be tak5 z "o degree ( ,fahr5heit's scale = e #ej feet ( desc5t4 ,?is gradi5t is n uni=m1 b dim9i%es at great] dep?s4 ,suppos+ ! mat]ial ( uni=m quality z reg>ds heat-conduct+ p[]1 ! ma!matical !ory ( a cool+ globe ( solid mat]ial 7or ( a /raight b> :i* does n lose heat f its sides7 gives on c]ta9 suppositions ! gradi5ts at diff]5t dep?s4 ,! surface gradi5t ( #a ,f4 9 #ej feet may be tak5 z hold+ = #ejjj feet or #fjjj feet or m4 ,?is gradi5t ( dim9ution ( temp]ature outw>ds leads inevitably to ! conclusion t heat mu/ be con/antly fl[+ f ! int]ior ( ! e>? t[>ds ! surface4 ,?is is z c]ta9 z t heat fl[s along a pok]1 "o end ( :i* is 9 ! fire1 f ! heat$ end to ! o!r4 ,! heat :i* arrives at ! surface ( ! e>? is radiat$ to ! atmosph]e or c>ri$ (f by convection curr5ts2 !re is no d\bt t x is lo/ f ! e>?4 ,?us ! e>? mu/ be cool+ at a rate :i* c be calculat$ on c]ta9 assumptions1 & x is possible on ^! assumptions to calculate backw>ds1 & det]m9e ! int]val ( "t :i* mu/ h elaps$ s9ce ! e>? 0 j beg9n+ to cool f a molt5 condition1 :5 ( c\rse life _c h exi/$ on its surface1 & ^? geological *anges :i* h effect$ s mu* c h>dly h began4 ,consid]+ a globe ( uni=m mat]ial1 & ( great radius1 :i* 0 initially at "o temp]ature1 & at a c]ta9 in/ant _h its surface sudd5ly br\ght to1 let u say1 ! temp]ature ( melt+ ice1 at :i* ! surface 0 kept ev] aft]1 we c f9d1 by ,f\ri]'s ma!matical !ory ( ! fl[ ( heat1 ! gradi5t ( temp]ature at any subsequ5t "t = a po9t on ! surface1 or at any specifi$ di/ance )9 x4 ,= a po9t on ! surface ?is gradi5t is simply proportional to ! initial uni=m temp]ature1 & inv]sely proportional to ! squ>e root ( ! product ( ! diffusivity ( ! mat]ial 7! ratio ( ! conductivity to ! specific heat7 by ! int]val ( "t :i* has elaps$ s9ce ! cool+ 0 />t$4 ,tak+ a foot z ! unit ( l5g?1 & a ye> z ! unit ( "t1 we f9d ! diffusivity ( ! surface /rata to be #djj4 ,if we take ! initial temp]ature z #gjjj degrees ,f4--:i* is high en\gh = melt+ rock--& take ! int]val ( "t :i* has elaps$ z #ajj1jjj1jjj ye>s1 we obta9 at ! surface a gradi5t approximately equal to t :i* n[ exi/s4 ,a great] int]val ( "t w\ld give a l[] gradi5t1 a small] int]val w\ld give a high] gradi5t ?an t :i* exi/s at pres5t4 ,a l[] initial temp]ature w\ld require a small] int]val ( "t1 a high] initial temp]ature a long] int]val = ! pres5t gradi5t4 ,) ! initial temp]ature ( #g1jjj degrees ,f41 an int]val ( #d1jjj1jjj ye>s w\ld give a surface gradi5t ( #a ,f4 9 #aj ft4 ,?us1 on ! assumption made1 ! surface gradi5t ( temp]ature has dim9i%$ f #aaj to #aej 9 ab\t #if1jjj1jjj ye>s4 ,aft] #aj1jjj ye>s f ! beg9n+ ( ! cool+ ! gradi5t ( temp]ature w\ld be #b ,f4 p] foot4 ,b1 z ,?omson %[$1 su* a l>ge gradi5t w\ld n lead to any s5sible augm5tation ( ! surface temp]ature1 = ! radiation f e>? & atmosph]e into space w\ld almo/ c]ta9ly be s rapid z to prev5t ?is4 ,h5ce he inf]r$ t conduct$ heat1 ev5 at t e>ly p]iod1 c\ld n s5sibly affect ! g5]al climate4 ,two objections 7ap>t f ! assumptions already indicat$7 w readily occur to any "o consid]+ ?is !ory1 & ^! ,?omson answ]$ by anticipation4 ,! fir/ is1 t no natural action c\ld possibly br+ ! surface ( a uni=mly heat$ globe in/antane\sly to a temp]ature #gjjj l[]1 & keep x s ev] aft]4 ,9 reply to ?is ,?omson urg$ t a l>ge mass ( melt$ rock1 expos$ freely to our e>? & sky1 w1 aft] x once becomes cru/$ ov]1 pres5t 9 a few h\rs1 or a few days1 or at mo/ a few weeks1 a surface s cool t x c be walk$ ov] ) impunity4 ,h5ce1 aft] #aj1jjj ye>s1 or inde$1 ,i may say1 aft] a s+le ye>1 its condition w be s5sibly ! same z if ! actual l[]+ ( temp]ature exp]i5c$ by ! surface _h be5 produc$ 9 an in/ant1 & ma9ta9$ con/ant ev] aft]4 ,! o!r objection 01 t ! e>? 0 probably nev] a uni=mly heat$ solid #gjjj ,f4 above ! pres5t surface temp]ature z assum$ = ! purpose ( calculation4 ,?is ,?omson answ]s by giv+ reasons = believ+ t ! e>?1 al?\gh once all melt$1 or melt$ all r\nd its surface1 did1 9 all probability1 really become a solid at its melt+ temp]ature all ?r\gh1 or all ?r\gh ! out] lay] :i* has be5 melt$2 & n until ! solidification 0 ?us complete1 or ne>ly s1 did ! surface beg9 to cool4 ,?omson 0 incl9$ to believe t a temp]ature ( #gjjj ,f4 0 probably too high1 & results ( exp]im5ts on ! melt+ ( basalt & o!r rocks l$ him to pref] a mu* r$uc$ temp]ature4 ,?is1 z has already be5 po9t$ out1 w\ld give a small] value = ! age ( ! e>?4 ,9 a lett] on ! subject publi%$ 9 ,nature 7vol4 #ea1 #ahie7 he /ates t he is n l$ to diff] mu* f an e/imate ( #bd1jjj1jjj ye>s f\nd$ by ,mr4 ,cl>5ce ,k+ 7,am]ican ,j\rnal ( ,sci5ce1 ,janu>y #ahic7 on exp]im5ts on ! physical prop]ties ( rocks at high temp]atures4 ,x is to be obs]v$ t ! assumptions made above t ! physical con/ants ( ! mat]ial are con/ant ?r\gh\t ! e>?1 & at all temp]atures1 are confess$ly f> f ! tru?4 ,nev]!less ,?omson /rongly held t ! unc]ta9ty ( ! data c at mo/ ext5d ! e>?'s age to "s value betwe5 #bj1jjj1jjj & #bjj1jjj1jjj ( ye>s1 & t ! enorm\sly long p]iods :i* 7 wont to be ask$ = by geologi/s & biologi/s = ! *anges ( ! e>?'s surface & ! developm5t ( its flora & fauna1 _c possibly be conc$$4 ,9 ,nature = ,janu>y #c1 #ahie1 ,pr(essor ,john ,p]ry sugge/$ t v possibly ! conductivity ( ! mat]ial compos+ ! int]ior ( ! e>? 0 consid]ably high] ?an t ( ! surface /rata4 ,if ?is 7 s1 !n1 z c be %[n )\t difficulty1 ! atta9m5t ( ! pres5t gradi5t w\ld be v greatly ret>d$1 & !re=e ! age ( ! e>? correspond+ly increas$4 ,! "q !n arose1 & 0 discuss$1 z to :e!r ! rocks & o!r mat]ials at high temp]atures 7 m or less conduct+ ?an at l[ temp]atures1 & exp]im5ts on ! subject 7 in/itut$ & c>ri$ out4 ,on ! :ole1 ! evid5ce seem$ to %[ t ! conductivity ( mo/ sub/ances is dim9i%$1 n increas$1 by ! rise ( temp]ature1 & s f> z x w5t1 !re=e1 ! evid5ce 0 aga9/ ,pr(essor ,p]ry's sugge/ion4 ,on ! o!r h&1 he cont5d$ t ! inside ( ! e>? may be a mass ( great rigidity1 p>tly solid & p>tly fluid1 possess+ a quasi-conductivity :i* might greatly increase ! p]iod ( cool+4 ,! subject is a difficult "o bo? f a ma!matical & f ! physical po9t ( view1 & fur!r inve/igation is necess>y1 especially ( ! behavi\r ( mat]ials "u ! enorm\s /resses :i* !y und\bt$ly su/a9 9 ! int]ior ( ! e>?4 ,aft] ! publication ( ! pap] on ,geological ,"t a reply to x 0 made by ,pr(essor ,huxley1 9 an address to ! ,geological ,society ( ,london1 deliv]$ on ,febru>y #ai1 #ahfi4 ,he adopt$ ! rle ( an advocate reta9$ = ! def5ce ( geology aga9/ :at seems to h be5 reg>d$ z an unw>rant$ attack1 made by "o :o _h no "r to (f] an op9ion on a geological "q4 ,=1 aft] a long & eloqu5t plead+1 he concludes 8 address ) ! words3 ,my functions1 z y\r advocate1 are at an end4 ,i speak ) m ?an ! s9c]ity ( a m]e advocate :5 ,i express ! belief t ! case aga9/ u has entirely brok5 d[n4 ,! cry = re=m :i* has be5 rais$ f )\t is sup]flu\s1 inasmu* z we h long be5 re=m+ f )9 ) all ne$ful spe$2 & ! critical exam9ation ( ! gr\nds ^u :i* ! v grave *>ge ( opposition to ! pr9ciples ( ,natural ,philosophy has be5 br\ght aga9/ u1 r %[s t we h ex]cis$ a wise discrim9ation 9 decl9+ to m$dle ) our f\ndations at ! bidd+ ( ! fir/ pass]-by :o fancies our h\se is n s well built z x might be4 ,to ?is ,?omson rejo9$ 9 an address entitl$ ,( ,geological ,dynamics1 also deliv]$ to ! ,geological ,society ( ,glasg[ on ,april #e1 #ahfi2 & to ?is1 ) ,pr(essor ,huxley's address1 ! read] mu/ be ref]r$ = ! objection1 br\ght aga9/ ,?omson's argum5ts1 & ! replies :i* 7 imm$iately =?com+4 ,?is is n ! place to discuss ! "q1 b ref]5ce may be made to an int]e/+ pap] on ! subject 9 ! ,glasg[ ,h]ald = ,febru>y #bb1 #aijh1 by ,pr(essor ,j4 ,w4 ,gregory1 9 :i* ! sugge/ion ( ,pr(essor ,p]ry1 ( a ne>] approa* to uni=mity ( temp]ature 9 ! int]ior ( ! e>? ?an ,?omson _h ?\ght possible1 is welcom$ z possibly ext5d+ ! int]val ( "t available to a p]iod suffici5t = all purposes4 ,9 ,pr(essor ,gregory's op9ion1 ,"l ,kelv9 9 "o respect %[$ a ke5] insight ?an ,huxley1 :o1 ref]r+ to possible *anges 9 ! rate ( rotation ( ! e>?1 or 9 ! heat giv5 =? f ! sun or 9 ! cool+ ( ! e>?1 decl>$ t geologi/s are ,gallios1 ':o c>e = none ( ^! ?+s4' ,an ev]-increas+ s*ool ( geologi/s n[ c>es greatly = ^! que/ions1 & rev]es ,"l ,kelv9 z "o ( ! f\nd]s ( ! geology ( ! inn] e>?4 ,aft] all1 ! problem is n "o to be dealt ) by ! geologi/ or biologi/ alone1 b to be solv$1 s f> z x c be solv$ at all1 by a consid]ation ( all relevant evid5ce1 f :atsoev] qu>t] x may come4 ,x w n d 9 ^! days = sci5tific m5 to %ut !mselves up )9 _! special dep>tm5ts & to say1 ) reg>d to bran*es ( sci5ce :i* deal ) o!r aspects ( nature & o!r problems ( ! pa/1 pres5t & future ( t same e>? on :i* all dwell & "w1 t !y c>e = none ( ^! ?+s4 ,?is is an e*o ( an old _s1 n yet dead1 t has done mu* h>m to ! progress ( sci5ce4 ,! division ( sci5ce into dep>tm5ts is unavoidable1 = specialisation is imp]ative2 b x is all ! m necess>y to rememb] t ! divisions set up are m or less arbitr>y1 & t !re are absolutely no fronti]s to be gu>d$ & en=c$4 ,*emi/ry1 physiology1 & physics _c be wall$ (f f "o ano!r )\t loss to all2 & geology has suff]$ imm5sely ?r\gh its hav+ be5 reg>d$ z ess5tially a bran* ( natural hi/ory1 ! devotees ( :i* h no conc]n ) consid]ations ( natural philosophy4 ,"l ,kelv9's dignifi$ que/ions 7 unansw]able4 ,:o are ! occupants ( 'our h\se1' & :o is ! 'pass]-by'8 ,is geology n a bran* ( physical sci5ce8 ,are inve/igations1 exp]im5tal & ma!matical1 ( und]gr\nd temp]ature n to be reg>d$ z an integral "p ( geology8444 ,= myself1 ,i am anxi\s to be reg>d$ by geologi/s n z a m]e pass]-by1 b z "o con/antly int]e/$ 9 _! gr& subject1 & anxi\s 9 any way1 h[ev] slight1 to assi/ !m 9 _! se>* = tru?4 ,,*apt] ,,xiii ,,briti% ,,association ,,committee ,,on ,,electrical ,,/&>ds ,:5 ,pr(essor ,?omson began 8 "w z a tea*] 9 ! ,univ]sity ( ,glasg[1 !re 01 z has already be5 notic$1 great vagu5ess ( specification ( physical quantities4 ,few ( ! =mal def9itions ( units ( measurem5t1 n[ to be f\nd 9 ! pages ( e elem5t>y text book1 _h be5 fram$1 & !re 0 mu* confusion ( quantities ess5tially di/9ct1 a confusion :i* is n[1 to "s ext5t at lea/1 gu>d$ aga9/ by ! adoption ( a def9ite unit1 ) a di/9ctive "n = ea* magnitude to be measur$4 ,?us rate ( work+1 or activity1 0 confus$ ) "w done2 ! condition = maximum activity 9 ! circuit ( a batt]y or dynamo 0 (t5 quot$ z ! condition ( greate/ effici5cy1 t is ( greate/ economy ( en]gy1 al?\gh x 0 exactly t 9 :i* half ! available en]gy 0 wa/$4 ,p>tly z a consequ5ce ( ?is vagu5ess ( specification1 !re 0 a great want ( k ( ! values ( physical con/ants2 = )\t exact def9itions ( quantities to be det]m9$1 su* def9itions z w\ld indicate units = _! measurem5t1 relat$ to ord9>y dynamical units accord+ to a consi/5t s*eme1 x 0 impossible to devise satisfactory exp]im5tal me?ods to d = electricity & magnetism :at _h be5 done by ,regnault & o!rs = heat4 ,! fir/ /eps t[>ds ! con/ruction ( a complete sy/em ( units = ! quantitative measurem5t ( magnetic & electric quantities 7 tak5 by ,gauss1 9 8 celebrat$ pap] entitl$ ,int5sitas vis magnetic t]re/ris ad m5suram absolutam revocata1 publi%$ 9 #ahcb4 ,9 ?is he %[$ h[ magnetic =ces c\ld be express$ 9 absolute units1 & ?us be connect$ ) ! absolute dynamical units :i* ,gauss1 9 ! same pap]1 bas$ on *os5 fundam5tal units ( l5g?1 mass1 & "t4 ,?us ! mod]n sy/em ( absolute units ( dynamical quantities1 & its ext5sion to magnetism1 are due to ! practical insight ( a great ma!matician1 n to ! exp]im5tali/s or practicians ( ! "t4 ,me?ods ( measur+ electric quantities 9 absolute units 7 describ$ by ,w4 ,web]1 9 ,p>ts ,,ii & ,,iii ( 8 ,elecktrodynamis*e ,maassbe/immung51 publi%$ 9 #aheb4 ,^! 7 great /eps 9 advance1 & r5d]$ fur!r progress 9 ! sci5ce ( absolute measurem5t comp>atively easy4 ,b !y rema9$ ! only /eps tak5 until ! ,briti% ,association ,committee began _! "w4 ,we h already 7pp4 #gd-gf7 ref]r$ to ! great importance ( t "w1 n only = practical applications b also = ! advancem5t ( sci5ce4 ,b x 0 n a task :i* /ruck ! imag9ation or excit$ ! wond] ( ! multitude4 ,= ! realisation ( /&>ds ( resi/ance1 = example1 involv$ long & t$i\s inve/igations ( ! effects ( impurities on ! resi/ance ( metals1 & ! v>iation ( resi/ance caus$ by *ange ( temp]ature & lapse ( "t4 ,!n alloys _h to be s\ght :i* w\ld h a temp]ature effect ( small am\nt1 & :i* 7 /able & durable 9 all _! prop]ties4 ,! discov]ies ( ! exp]im5tali/ :o f9ds a new elem5t ( hi!rto undream$-( prop]ties attract _w-wide att5tion1 & ! glory ( ! a*ievem5t is des]v$ly great4 ,b ! pati5t1 plodd+ "w :i* gives a univ]sal sy/em ( units & relat$ /&>ds1 & :i* enables a great physical subject l electricity & magnetism to rise f a m]e enum]ation ( qualitative results to a sci5ce ( ! mo/ delicate & exact measurem5t1 & to f9d its practical applications 9 all ! affairs ( daily life & comm]ce1 is equally des]v+ ( ! admiration & gratitude ( mank9d4 ,yet x receives little or no recognition4 ,! con/ruction ( a /&>d ( resi/ance 0 ! fir/ task und]tak5 by ! committee2 b o!r units1 = example ( quantity ( electricity1 int5sity ( electric field & diff]5ce ( pot5tial1 _h also to be def9$1 & me?ods ( employ+ !m 9 exp]im5tal "w devis$4 ,x w\ld be out ( place to endeav\r to discuss ^! units "h1 b "s idea ( ! mann] 9 :i* _! def9itions are f\nd$ on dynamical conceptions may be obta9$ f "o or two examples4 ,!re=e we %all describe two simple exp]im5ts1 :i* w illu/rate ?is dynamical f\ndation4 ,an acc\nt has be5 giv5 9 ,*apt] ,,xi ( ! s]ies ( electromet]s :i* ,?omson inv5t$ = ! measurem5t ( diff]5ces ( electric pot5tial4 ,^! all act by ! evaluation 9 t]ms ( ord9>y dynamical units ( ! =ce urg+ an electrifi$ body f a place ( high] t[>ds a place ( l[] pot5tial4 ,"s indication ( ! mean+ ( electrical quantities has be5 giv5 9 ,*apt] ,,iv4 ,diff]5ce ( electric pot5tial betwe5 two po9ts 9 an electric field 0 !re def9$ z ! dynamical "w done 9 c>ry+ a unit ( positive electricity aga9/ ! =ces ( ! field f ! po9t ( l[] to ! po9t ( high] pot5tial4 ,n[ by ! def9ition ( unit quantity ( electricity giv5 9 electrical !ory--t quantity :i*1 conc5trat$ at a po9t at unit di/ance f an equal quantity also conc5trat$ at a po9t1 is repell$ ) unit =ce--we c f9d1 by ! simple exp]im5t ( hang+ two pi? balls 7or1 bett]1 two holl[1 gild$ beads ( equal size7 by two f9e fibres ( qu>tz1 a metre long1 say1 electrify+ ! two balls z !y hang 9 contact1 & obs]v+ ! di/ance at :i* !y !n hang1 ! num]ical magnitude 9 absolute units ( a *>ge ( electricity1 & apply t to f9d+ ! *>ge on a l>ge sph]ical conductor & ! pot5tial at po9ts 9 its field also 9 absolute units4 ,if m be ! mass ( a ball1 g gravity 9 cm4 sec4 units1 d ! di/ance 9 cms4 ( ! c5tres ( ! balls ap>t1 & l ! l5g? 9 cms4 ( a ?read1 ! *>ge q1 say1 on ea* ball is easily f\nd to be mgd#d7l d74 ,?us ! *>ge is got 9 absolute c5timetre-gramme-second units 9 t]ms ( ! mass m obta9$ by ord9>y weigh+1 & l & d obta9$ by easy & exact measurem5ts4 ,if "o ( ! balls be n[ tak5 away )\t dis*>g+ ! o!r1 & ! latt] be plac$ 9 ! field ( a l>ge electrifi$ sph]ical conductor1 ! fibre w be deflect$ f ! v]tical by ! =ce on ! ball4 ,let ! two c5tres be n[ on ! same level4 ,t =ce is got at once f ! angle ( deflection 7:i* is easily obs]v$71 ! *>ge on ! ball1 & ! value ( m4 ,! electric field-int5sity is obta9$ by divid+ ! value ( ! =ce by q4 ,! field int5sity multipli$ by ,d1 ! di/ance ap>t 9 cms4 ( ! c5tres ( ! ball & ! conductor1 gives ! pot5tial at ! c5tre ( ! ball 9 ,c4,g4,s4 units4 ,multiplication aga9 by ,d gives ! *>ge on ! conductor4 ,:5 x made its fir/ ,report 9 #ahfb 7to ! meet+ at ,cambridge7 ! committee consi/$ ( ,pr(essors ,a4 ,williamson1 ,c4 ,:eat/one1 ,w4 ,?omson1 ,w4 ,h4 ,mill]1 ,dr4 ,a4 ,mat?iess51 & ,mr4 ,f4 ,j5k94 ,at ! next meet+1 at ,newca/le1 x _h be5 augm5t$ by ! addition ( ,messrs4 ,balf\r ,/ew>t1 ,c4 ,w4 ,siem5s1 ,pr(essor ,cl]k ,maxwell1 ,dr4 ,j\le1 ,dr4 ,esselba*1 & ,sir ,*>les ,bright4 ,! duty ) :i* ! committee _h be5 *>g$ 0 t ( con/ruct+ a suitable /&>d ( resi/ance4 ,a ref]5ce to ! acc\nt giv5 9 ,*apt] ,x above1 ( ! d]ivation ( :at came to be call$ ! electromagnetic unit ( diff]5ce ( pot5tial1 or electromotive =ce1 by means ( a simple magneto-electric ma*9e--a disk turn+ on a uni=m magnetic field1 or ! simple rails & slid] & magnetic field arrangem5t !re describ$--w %[ h[ f ?is unit & ! electromagnetic unit ( curr5t 7!re also def9$7 ! unit ( resi/ance is def9$4 ,x is ! resi/ance ( ! circuit ( slid]1 rails1 & connect+ wire1 :5 ) ?is electromagnetic unit ( electromotive =ce ! unit ( curr5t is made to fl[4 ,?is 0 "o cle> & def9ite way ( def9+ ! unit ( curr5t1 & ( atta9+ ! important object ( connect+ ! units 9 su* a way t ! rate ( work+ 9 a circuit1 or ! en]gy exp5d$ 9 any "t1 %\ld be express$ at once 9 ord9>y dynamical units ( activity or en]gy4 ,a consid]able numb] ( proposals 7 discuss$ by ! committee2 b x 0 f9ally det]m9$ to take ! basis "h indicat$1 & to realise a /&>d ( resi/ance 9 mat]ial ( con/ant & durable prop]ties1 :i* %\ld h "s simple multiple ( ! unit ( resi/ance1 9 ! sy/em ( dynamical units bas$ on ! c5timetre z unit ( l5g?1 ! gramme z unit ( mass1 & ! second z unit ( "t--! s-call$ ,c4,g4,s4 sy/em4 ,! comp>ison ( ! diff]5t metals & alloys available 0 a mo/ important b exce$+ly labori\s s]ies ( inve/igations1 c>ri$ out ma9ly by ,dr4 ,mat?iess5 & ,pr(essor ,williamson4 ,pr(essor ,?omson sugge/$ to ! committee ! celebrat$ me?od ( det]m9+ ! resi/ance ( a circuit by revolv+ a coil1 :i* =m$ ! ma9 "p ( ! circuit ab\t a v]tical axis 9 ! e>?'s magnetic field4 ,an acc\nt ( ! exp]im5ts made ) ?is me?od is conta9$ 9 ! ,report ( #ahfc4 ,!y 7 c>ri$ out at ,k+'s ,college1 ,london1 :]e ,maxwell 0 !n ,pr(essor ( ,exp]im5tal ,physics1 by ,maxwell1 ,balf\r ,/ew>t1 & ,fleem+ ,j5k94 ,! !oretical discussion & ! description ( ! exp]im5ts 0 writt5 by ,maxwell1 ! details ( ! app>atus 7 describ$ by ,j5k94 ,! pr9ciple ( ! me?od is ess5tially ! same z t ( ! simple magneto-electric ma*9e1 to :i* ref]5ce has j be5 made4 ,two p>allel coils ( wire 7 w\nd 9 *annels cut r\nd r+s ( brass1 :i*1 h[ev]1 7 cut across by slots fill$ ) vulcanite1 to prev5t induc$ curr5ts f circulat+ 9 ! brass4 ,^! coils 7 m\nt$ 9 a v]tical position & c\ld be driv5 z a rigid sy/em1 at a con/ant measur$ spe$1 ab\t a v]tical axis pass+ ?r\gh ! c5tre ( ! sy/em4 ,betwe5 ! coils at ?is c5tre 0 hung1 f a /eady support1 a small magnetic ne$le by a s+le fibre ( silk2 & a surr\nd+ scre5 prev5t$ ! ne$le & susp5sion f be+ affect$ by curr5ts ( air4 ,! ends ( ! coil 7 connect$ toge!r s t ! :ole revolv$ z a clos$ circuit ab\t ! v]tical axis4 ,:5 ! coil sy/em 0 at "r angles to ! magnetic m]idian !re 0 a magnetic induction ?r\gh x ( am\nt ,,ah1 :]e ,a d5otes ! effective area ( ! coils1 & ,h ! horizontal compon5t ( ! e>?'s magnetic field4 ,by "o half-turn ! coil 0 rev]s$ ) ref]5ce to ?is magnetic induction1 & z ! coil turn$ an induc$ curr5t 0 g5]at$1 :i* dep5d$ at any in/ant on ! rate at :i* ! magnetic induction 0 v>y+ at ! in/ant1 on ! inductive electromotive =ce due to ! v>y+ ( ! curr5t 9 ! coil itself1 & on ! resi/ance ( ! circuit4 ,a p]iodic curr5t ?us fl[$ 9 "o direction relatively to ! coil 9 "o half-turn f a position p]p5dicul> to ! magnetic m]idian1 & 9 ! opposite direction 9 ! next half-turn4 ,b z ! position ( ! coil 0 rev]s$ 9 e half-turn z well z ! curr5t 9 x1 ! curr5t fl[$ on ! :ole 9 ! same av]age direction relatively to ! ne$le1 & b = self-induction w\ld h _h its maximum value always :5 ! plane ( ! coil 0 9 ! magnetic m]idian4 ,! ne$le 0 deflect$ z x w\ld h be5 by a c]ta9 av]age curr5t1 & ! deflection 0 oppos$ by ! action ( ! e>?'s horizontal magnetic field ,h4 ,b ?is 0 ! field cut by ! coil z x turn$1 & !re=e 7except = a small t]m dep5d+ on ! turn+ ( ! coil 9 ! field ( ! ne$le7 ! value ( ,h did n appe> 9 ! result1 & did n require to be kn[n4 ,full details ( ! !ory ( ?is me?od & ( ! exp]im5ts c>ri$ out to te/ x w be f\nd 9 v>i\s memoirs & treatises#bc2 b x mu/ suffice "h to /ate t ! resi/ance ( ! coil 0 det]m9$ 9 ?is way1 by a l>ge s]ies ( exp]im5ts1 be=e & aft] e "o ( :i* ! resi/ance 0 comp>$ ) t ( a ,g]man-silv] /&>d4 ,! resi/ance ( ?is /&>d !re=e became kn[n 9 absolute units1 & copies ( x1 or multiples or sub-multiples ( x1 c\ld be made4 ,a unit call$ ! ,b4,a4 unit1 :i* 0 int5d$ to conta9 #aji ,c4,g4,s4 electromagnetic units ( resi/ance1 0 con/ruct$ f ^! exp]im5ts1 & copies ( x 7 soon aft] to be f\nd 9 ne>ly all ! physical laboratories ( ! _w4 ,resi/ance boxes 7 con/ruct$ by v>i\s mak]s1 9 :i* ! coils 7 v>i\s multiples ( ! ,b4,a4 unit1 s t any resi/ance )9 a c]ta9 range c\ld be obta9$ by connect+ ^! coils 9 s]ies 7:i* 0 easily done by remov+ %ort circuit+ plugs71 & ?us ! absolute units ( curr5t electromotive =ce & resi/ance came into g5]al use4 ,9 #ahha ,"l ,rayleigh & ,pr(essor ,s*u/] c>ri$ out a v c>eful repetition ( ! ,briti% ,association exp]im5ts ) ! same app>atus at ! ,cav5di% ,laboratory1 & obta9$ a some:at diff]5t result4 ,!y f\nd t ! =m] result 0 ab\t #a4ag p] c5t4 too small4 ,"l ,rayleigh next c>ri$ out an indep5d5t set ( exp]im5ts by ! same me?od ) improv$ app>atus1 & f\nd t ?is p]c5tage error mu/ be increas$ to ab\t #a4ce4 ,x may be notic$ "h t ! simple disk ma*9e1 ( ,?omson's illu/ration ( ! absolute unit ( electromotive =ce1 has be5 us$ by ,lor5z to give a me?od ( det]m9+ resi/ance :i* is n[ recognis$ z ! be/ ( all4 ,x is sket*$ "h t ! read] may obta9 "s idea ( lat] "w on ?is v important subject2 "w :i* is a cont9uation ( t ( ! orig9al ,briti% ,association ,committee by _! successors4 ,a circuit is made up ( a /&>d coil ( wire1 ! ends ( :i* are made to t\* at ! circumf]5ce & ne> ! c5tre ( ! disk1 :i* is plac$ symmetrically ) respect to a cyl9drical coil1 & )9 x4 ,a curr5t is s5t r\nd ?is coil f a batt]y1 & produces a magnetic field )9 ! coil1 ! l9es ( magnetic =ce ( :i* pass across ! plane ( ! disk4 ,?is curr5t1 or a measur$ fraction ( x1 is also made to fl[ ?r\gh ! /&>d coil4 ,! disk is n[ turn$ at a measur$ spe$ ab\t its axis1 s t ! electromotive =ce due to ! cutt+ ( ! field t5ds to produce a curr5t 9 ! /&>d coil ( wire4 ,! electromotive =ce ( ! disk is made to oppose ! pot5tial diff]5ce betwe5 ! ends ( ?is coil due to ! curr5t1 s t no curr5t fl[s along ! disk or ! wires connect+ x ) ! /&>d coil4 ,! magnetic field )9 ! coil c be calculat$ f ! =m & dim5sions ( ! coil & ! curr5t 9 x 7suppos$ = ! mom5t to be kn[n71 & ! electromotive =ce ( ! disk is obta9$ 9 t]ms ( its dim5sions & its spe$ & ! field int5sity4 ,b ?is electromotive =ce1 :i* is proportional to ! curr5t 9 ! coil1 is equal to ! product ( ! resi/ance ( ! wire & ! same curr5t1 or a kn[n fraction ( x4 ,?us ! curr5t appe>s on bo? sides ( ! equation & goes out1 & ! value ( ! resi/ance is f\nd 9 absolute units4 ,"l ,rayleigh obta9$1 by ?is me?od1 a result :i* %[$ t ! ,b4,a4 unit 0 #a4cbc p] c5t4 too small2 & exact exp]im5ts h be5 made by o!rs ) concordant results4 ,values ( ! units h be5 agre$ on by ,int]national ,congresses z exact en\gh = g5]al "w1 & ) ^! units all electrical rese>*es1 :]ev] made1 are available = use by o!r exp]im5t]s4 ,a va/ am\nt ( "w has be5 done on ?is subject dur+ ! la/ =ty ye>s1 & ?\gh ! value ( ! practical unit ( resi/ance--#aji ,c4,g4,s4 units1 n[ call$ ! ohm--is tak5 z settl$1 & copies c n[ be _h 9 resi/ance boxes1 or sep>ately1 adju/$ ) all ne$ful accuracy1 at ! ,national ,physical ,laboratory & at ! ,bureau ( ,/&>ds at ,wa%+ton1 & else:]e1 exp]im5ts are be+ made on ! exact measurem5t ( curr5ts2 :ile a c>eful wat* is kept on ! /&>ds laid up at ^! places to see :e!r any p]ceptible v>iation ( _! resi/ance takes place ) lapse ( "t4 ,! ,briti% ,association ,committee also work$ out a complete sy/em ( units = all electrical & magnetic quantities1 & gave ! fir/ sy/ematic /atem5t ( _! relations1 t is1 ( ! s-call$ dim5sional equations ( ! quantities4 ,?is w be f\nd 9 ! works to :i* ref]5ce has already be5 made 7p4 #bea74 ,,*apt] ,,xiv ,,! ,,baltimore ,,lectures ,! ,baltimore ,lectures 7 deliv]$ 9 #ahhd at ,johns ,hopk9s ,univ]sity1 soon aft] ! ,montreal meet+ ( ! ,briti% ,association4 ,! subject *os5 0 ! ,wave ,!ory ( ,light2 & ! idea und]ly+ ! c\rse 0 to discuss ! difficulties ( ?is !ory to ,pr(essorial fell[-/ud5ts 9 physical sci5ce4 ,a /5ographic report ( ! c\rse 0 tak5 by ,mr4 ,a4 ,s4 ,ha?away1 & 0 publi%$ soon aft]4 ,! lectures 7 revis$ by ,"l ,kelv91 & ! book n[ kn[n z ,! ,baltimore ,lectures 0 publi%$ j tw5ty ye>s lat] 79 #aijd7 at ! ,cambridge ,univ]sity ,press4 ,x is absolutely impossible 9 su* a memoir z ! pres5t to give any acc\nt ( ! discussions conta9$ 9 ! lectures z n[ publi%$4 ,! difficulties dealt ) c = ! mo/ "p only be und]/ood by ^? :o are acqua9t$ ) ! wave !ory ( light 9 its details1 & su* read]s w naturally g direct to ! book itself4 ,"s ( ! difficulties1 h[ev]1 7 frequ5tly allud$ to 9 ,"l ,kelv9's ord9>y lectures1 & all 8 old /ud5ts w rememb] ! animation ) :i* he discuss$ ! app>5t anomaly ( a m$ium l ! lum9if]\s e!r1 :i* is ( su* enorm\s rigidity t 7on ! ela/ic solid !ory7 a wave ( transv]se oscillation is propagat$ ?r\gh x ) a spe$ ( #c #ajaj c5timetres 7#ahf1jjj miles7 p] second1 & yet appe>s to (f] no imp$im5t to ! sl[ motion ( ! heav5ly bodies4 ,= ,"l ,kelv9 adopt$ ! ela/ic solid !ory ( propagation ( light z ! only t5able f\ndation = ! wave !ory ( light 9 ! pres5t /ate ( our k1 & dismiss$ ! electromagnetic !ory 78 words 7 spok5 9 #ahhd1 x is to be rememb]$7 ) ! /atem5t ( 8 /rong view t an electric displacem5t p]p5dicul> to ! l9e ( propagation1 accompani$ by a magnetic di/urbance at "r angles to bo?1 is inadmissible4 ,& he goes on to say t :5 we h an electromagnetic !ory ( light1 electric displacem5t w be se5 z 9 ! direction ( propagation1 ) ,fresnelian vibrations p]p5dicul> to t direction4 ,9 ! preface1 ( date ,janu>y #aijd1 ! insuffici5cy ( ! ela/ic solid !ory is admitt$1 & ! "q ( ! electromagnetic !ory aga9 ref]r$ to4 ,he says !re t ! object ( ! ,baltimore ,lectures 0 to asc]ta9 h[ f> ! ph5om5a ( light c\ld be expla9$ )9 ! limits ( ! ela/ic solid !ory4 ,& ! answ] is ev]y?+ non-magnetic2 no?+ magnetic4 ,b he adds1 ,! s-call$ electromagnetic !ory ( light has n help$ u hi!rto1 & t ! problem is n[ fully be=e physici/s ( con/ruct+ a compreh5sive dynamics ( e!r1 electricity1 & pond]able matt] :i* %all include electro/atic =ce1 magneto/atic =ce1 electromagnetism1 electro*emi/ry1 & ! wave !ory ( light4 ,all ?is is exce$+ly int]e/+1 = x seems to make cle> ,"l ,kelv9's attitude ) respect to ! electromagnetic !ory ( ,maxwell1 :i* is n[ reg>d$ by mo/ physici/s z af=d+ on ! :ole a satisfactory acc\nt1 if n a dynamical !ory 9 ! s5se und]/ood by ,"l ,kelv91 ( light-propagation4 ,t !re is an electric displacem5t p]p5dicul> to ! direction ( propagation & a magnetic displacem5t 7or motion7 p]p5dicul> to bo? seems prov$ by ! exp]im5ts ( ,h]tz1 & ! velocity ( propagation ( ^! di/urbances has be5 f\nd to be t ( light4 ,( c\rse x rema9s to be f\nd out 9 :at ! electric & magnetic *anges consi/1 & :e!r ! e!r has or has n an atomic /ructure4 ,t[>ds ! answ] to ?is "q on electromagnetic presuppositions "s progress has already be5 made1 pr9cipally by ,l>mor4 ,&1 aft] all1 :ile we may imag9e t we "k some?+ m def9ite ( dynamical actions on pond]able matt]1 x is n q c]ta9 t we d3 we are m famili> ) !m1 t is almo/ all4 ,we "k1 = example1 t at e po9t 9 ! gravitational field ( ! e>? we may set up a gravitation vector1 or field-int5sity2 = a p>ticle ( matt] !re is subject$ to accel]ation along t direction4 ,b ( ! rationale ( ! action we "k no?+1 or next to no?+4 ,s we set up electric & magnetic vectors 9 an insulat+ m$ium1 correspond+ to electric & magnetic effects :i* we c obs]ve2 & x is n too mu* to say t we "k h>dly less 9 ?is case ?an we d 9 ! o!r1 ( ! inn] me*anism ( ! action ( :i* we see ! effects4 ,return+ to ! difficulty ( ! ela/ic solid !ory1 t :ile its rigidity is enorm\s1 x (f]s no ob/acle to ! planets & o!r heav5ly bodies :i* move ?r\gh x1 x may be int]e/+ to recall h[ ,"l ,kelv9 us$ to deal ) x 9 8 elem5t>y lectures4 ,! same discussion 0 giv5 9 ! ,introductory ,lecture at ,baltimore4 ,! difficulty is n got ov] by an explanation ( :at takes place3 x is turn$ by %[+ t a simil> difficulty exi/s 9 reconcil+ ph5om5a :i* c be obs]v$ e day ) su* ord9>y mat]ials z pit* or %oemak]s' wax4 ,a piece ( su* wax c be m\ld$ into a tun+-=k or a bell1 & w !n1 if /ruck1 s\nd a musical note ( def9ite pit*4 ,?is indicates1 = rapidly alt]nat+ de=mations />t$ by a =ce ( %ort duration1 ! exi/5ce ( int]nal =ces ( ! k9d call$ ela/ic1 t is1 dep5d+ on ! am\nt ( de=mation caus$1 n on ! rate at :i* ! de=mation is increas+ or dim9i%+1 z is ! case = ! s-call$ visc\s =ces :i* are usually display$ by su* mat]ial4 ,b ! tun+-=k or bell1 if left ly+ on ! table1 w gradually flatt5 d[n into a ?9 %eet "u only its own weight4 ,"h ! de=mation is oppos$ only by visc\s =ces1 :i*1 z ! *ange is v sl[1 are exce$+ly small4 ,b let a l>ge slab ( x1 ?ree or f\r in*es ?ick1 be plac$ 9 a glass j> t5 or twelve in*es 9 diamet]1 already p>tly fill$ ) wat]1 & let "s ord9>y corks be imprison$ b5ea?1 :ile "s lead bullets are laid on ! upp] surface4 ,aft] a mon? or two x w be f\nd t ! corks h disappe>$ f ! wat] into ! wax1 & t ! orifices :i* !y made 9 ent]+ x h heal$ up completely2 simil>ly ! bullets h sunk d[n into ! slab1 leav+ no trace beh9d4 ,aft] two or ?ree mon?s m1 ! corks w be se5 to be bur/+ _! way out ?r\gh ! upp] surface ( ! slab1 & ! bullets w be f\nd 9 ! wat] bel[4 ,! v ?+ has tak5 place t w\ld h happ5$ if wat] _h be5 us$ in/ead ( pit*1 only x has tak5 a v mu* long] "t to br+ x ab\t4 ,! corks h float$ up ?r\gh ! wax 9 consequ5ce ( hydro/atic upw>d =ce ex]t$ by ! wax act+ z a fluid2 & ! bullets h sunk d[n 9 consequ5ce ( ! excess ( _! weights above ! upw>d hydro/atic =ce ex]t$ on !m z on ! corks4 ,! motion 9 bo? cases has be5 oppos$ by ! visc\s =ces call$ into play4 ,! application ( ?is to ! lum9if]\s e!r is imm$iate4 ,let ! e!r be reg>d$ z a sub/ance :i* c p]=m vibrations only :5 times & =ces are suitable1 t is1 :5 ! =ces produc+ di/ortion act = only an inf9itesimal "t 7z 9 ! />t+ ( ! tun+-=k by a small bl[71 & are n too great4 ,vibrations may be set up locally1 & ! m$ium may h a true rigidity by :i* !y are propagat$ to m remote p>ts2 t is to say1 waves travel out f ! c5tre ( di/urbance4 ,on ! o!r h&1 if ! =ces are long cont9u$1 ev5 if !y be small1 !y produce cont9u\sly increas+ *ange ( %ape4 ,?us ! planets move seem+ly )\t resi/ance4 ,! conclusion is t ! app>5tly contradictory prop]ties ( ! e!r are no m my/]i\s ?an ! prop]ties ( pit* or %oemak]s' wax4 ,&1 aft] all1 matt] is /ill a pr(\nd my/]y4 ,dynamical illu/rations1 :i* old ,glasg[ /ud5ts w recognise1 appe> cont9ually 9 ! lectures4 ,!y w rememb]1 almo/ ) affection1 ! sy/em ( ?ree p>ticles 7#g lb4 or #ad lb4 weights67 jo9$ toge!r 9 a v]tical r[ by /\t spiral spr+s ( /eel1 :i* 7 always to be tak5 z massless1 & w recall ,"l ,kelv9's exp]im5ts ) !m1 demon/rat+ ! ?ree modes ( vibration ( a sy/em ( ?ree masses1 ea* ( :i* influ5c$ ^? next x on ! two sides4 ,"h !y w f9d ! problem solv$ = any numb] ( p>ticles & int]v5+ spr+s1 & ! solution appli$ to an ext5sion ( ! massive molecule :i* von ,helmholtz imb$d$ 9 ! ela/ic e!r1 & us$ to expla9 anomal\s disp]sion4 ,a highly complex molecule is sugge/$1 consi/+ ( an out] %ell emb$d$ 9 ! e!r z 9 ! simpl] case1 a second %ell )9 t connect$ to ! out] by a suffici5t numb] ( equal radial spr+s1 a ?ird )9 & simil>ly connect$ to ! second by radial spr+s1 & s on4 ,?is molecule w h z _m modes ( vibration z !re are sets ( spr+s1 & c !re=e imp>t1 if x is set into motion1 a complex di/urbance to ! e!r 9 :i* x is imb$d$4 ,! modification ( ?is arrangem5t by :i* ,"l ,kelv9 expla9$ ! phosphoresc5ce ( su* sub/ances z lum9\s pa9t is also describ$1 & w be recognis$ by "s z an old fri5d4 ,a numb]1 two doz5 or s1 ( /raight rods ( wood eighte5 in*es long are atta*$ to a /eel wire f\r or five in*es ap>t1 l /eps on a ladd] made ) a s+le rope along ! c5tres ( ! /eps4 ,! wire is s atta*$ to ea* rod t ! rod mu/ turn ) ! wire if ! latt] is twi/$ r\nd4 ,ea* rod is load$ ) a piece ( lead at ea* end to give x m mom5t ( in]tia ab\t ! wire4 ,! wire1 ) ?is ladd] atta*$ to x1 is rigidly atta*$ to ! c5tre ( a cross-b> at ! top1 :i* c be made to sw+ ab\t ! wire z an axis & s imp>t twi/+ vibrations to ! wire 9 a p]iod dep5d+ on ?is driv]4 ,slid+ weights atta*$ to ! b> enable its mom5t ( in]tia to be *ang$ at pleasure4 ,! l[] end ( ! wire c>ries a cross-b> ) two vanes1 imm]s$ 9 treacle 9 a vessel bel[4 ,:5 ! p]iod ( ! excit] 0 v long ! waves ( torsion did n travel d[n ! ladd]1 b :5 ! p]iod 0 made suffici5tly %ort ! waves travell$ d[n & 7 absorb$ 9 ! treacle bel[4 ,9 ! =m] case ! vibrations p]si/$2 ! case 0 analog\s to t ( phosphoresc5ce4 ,illu/ration3 ,,fig4 #ah4 ,incid5tally a full & v attractive acc\nt ( ! ela/ic solid !ory is giv5 9 ^! lectures1 accompani$ z x is by *>act]i/ic digressions on po9ts ( int]e/ :i* sugge/ !mselves1 & on topics on :i* ! lectur] held /rong op9ions1 su*1 = example1 z ! absurd ,briti% sy/em ( weights & measures4 ,! book reads 9 _m places l a report ( "s ( ! high] ma!matical lectures :i* 7 giv5 e session at ,glasg[2 & on t acc\nt1 if on no o!r1 x w be read by ! old /ud5ts ( ! high] class ) affectionate int]e/4 ,b ! discussions ( ! great fundam5tal difficulty pres5t$ at once by disp]sion--! fact1 t is1 t light ( diff]5t wave l5g?s has diff]5t velocities 9 ord9>y transp>5t matt]--! discussions ( ! v>i\s !ories ( disp]sion t h be5 put =w>d1 ! con/ruction ( ! molecules1 gyro/atic & non-gyro/atic1 ) all _! rem>kable prop]ties1 :i* ,"l ,kelv9 inv5ts 9 ord] to frame a dynamical me*anism :i* w imitate ! action ( matt] z display$ 9 ! complex manife/ations ( ! optical ph5om5a1 n only ( isotropic matt]1 b ( cry/als1 w ev] af=d in/ruction to e ma!matician :o has ! c\rage to attack ?is subject1 & rema9 z a monum5t to ! extraord9>y g5ius ( _! au?or4 ,a subject is t\*$ on 9 ^! lectures :i* has n be5 dealt ) 9 ! pres5t review ( ,"l ,kelv9's "w4 ,by f\r l9es ( argum5t--by ! heat ( comb9ation ( copp] & z9c1 toge!r ) ! diff]5ce ( electric pot5tial develop$ :5 ^! metals are put 9 contact1 f ! ?ickness ( a capill>y film ( soap & wat] 7measur$ by ,rck] & ,re9old7 j be=e x gives way1 & ! "w sp5t 9 /ret*+ x1 f ! k9etic !ory ( gases & ! e/imat$ l5g? ( free pa? ( a p>ticle 7giv5 also by ,los*midt & by ,john/one ,/oney71 & f ! undulatory !ory ( light--,"l ,kelv9 e/imat$ sup]ior & inf]ior limits to ! size ( ! atoms ( bodies1 or1 m prop]ly speak+1 ( ! molecul> /ructure ( ! matt]4 ,we _c discuss ^! argum5ts--& !y c be read at leisure by any "o :o w consult ,volume ,i 7,con/itution ( ,matt]7 ( ,"l ,kelv9's ,popul> ,lectures & ,addresses1 = 8 ,royal ,in/itution ,lecture on ! subject1 !re giv5 9 full--b we may /ate 8 conclusion4 ,let a drop ( wat]1 a ra9 drop1 = example1 be magnifi$ to ! size ( ! e>?1 t is1 f a sph]e a qu>t] ( an in*1 or less1 9 diamet] to a sph]e #hjjj miles 9 diamet]1 & let ! dim5sions ( ! molecul> /ructure be magnifi$ 9 ! same proportion4 ,! magnifi$ /ructure w\ld be m co>se-gra9$ ?an a heap ( small %ot1 b probably less co>se-gra9$ ?an a heap ( cricket-balls4 ,( c\rse1 x is n int5d$ "h to convey ! idea t ! molecules are sph]es l %ot or cricket-balls2 !y und\bt$ly h a /ructure ( _! own4 ,& no pron\ncem5t is made z to ! divisibility or non-divisibility ( ! molecules4 ,all t is alleg$ is t if ! division be c>ri$ to a m9ut5ess ne> to or beyond t ( ! dim5sions ( ! /ructure1 portions ( ! sub/ance w be obta9$ :i* h n ! physical prop]ties ( ! sub/ance 9 bulk4 ,! rec5t int]e/+ rese>*es ( *emi/s & physici/s into ph5om5a :i* seem to demon/rate ! dis9tegration1 n m]ely ( molecules1 b ev5 ( ! atomic /ructure ( matt]1 attract$ ,"l ,kelv9's att5tion 9 8 la/ ye>s1 & suo m he endeav\r$ to frame dynamical explanations ( electronic 7or1 z he pref]r$ to call x1 electrionic7 action4 ,b ?\gh ke5ly int]e/$ 9 all k9ds ( rese>*1 he turn$ aga9 & aga9 to ! old] !ories ( light1 & 8 dynamical repres5tations ( ! e!r & ( cry/als1 ) r5ew$ vig\r & en?usiasm4 ,,*apt] ,,xv ,,spe$ ,,( ,,telegraph ,,signall+--,,lay+ ,,( ,,subm>9e ,,cables--,,telegraph ,,in/rum5ts--,,navigational ,,in/rum5ts1 ,,compass ,,& ,,s\nd+ ,,ma*9e ,,!ory ,,( ,,signall+ ,:5 ! "q ( lay+ an ,atlantic cable began to be debat$ 9 ! middle ( ! n9ete5? c5tury1 ,pr(essor ,?omson und]took ! discussion ( ! !ory ( signall+ ?r\gh su* a cable4 ,x 0 n g5]ally und]/ood by practical telegraphi/s t ! conditions ( work+ w\ld be v diff]5t f ^? to :i* !y 7 accu/om$ on l& l9es1 & t ! in/rum5ts employ$ on su* l9es w\ld be useless = a cable4 ,su* a cable consi/s ( a copp] conductor sep>at$ f ! sea-wat] by a coat+ ( gutta-p]*a2 x =ms an elongat$ ,leyd5 j> ( v great capacity1 :i*1 :5 a batt]y is connect$ to "o end ( ! conduct+ core1 is gradually *>g$ up1 fir/ at t end1 & lat] & lat] at great] di/ances f x1 & !n is gradually dis*>g$ aga9 :5 ! batt]y is )drawn & ! end ( ! conductor connect$ to e>?4 ,"h1 aga91 an application ( ,f\ri]'s analysis solv$ ! problem1 :i*1 ) c]ta9 modifications1 & on ! supposition t ! work+ is sl[1 is ess5tially ! same problem z ! diffusion ( heat along a conduct+ b>1 or ! diffusion ( a salt solution along a column ( wat]4 ,! signals are ret>d$ 7& ?is 0 "o ( ! results ( ! inve/igation7 9 su* a mann] t ! "t requir$ to rea* a /at$ fraction ( ! maximum /r5g? ( curr5t at ! remote end1 :5 a giv5 pot5tial diff]5ce is appli$ at ! o!r1 or home end1 is proportional to ! product ( ! capacity & resi/ance ( ! cable1 ea* tak5 p] unit ( ! l5g?1 & also proportional to ! squ>e ( ! l5g? ( cable4 ,9 o!r words1 ! ret>dation is proportional to ! product ( ! resi/ance ( ! copp] conductor & ! total capacity ( ! cable4 ,?is gave a practical rule ( great importance = guidance 9 ! manufacture ( subm>9e cables4 ,! conductor %\ld h ! highe/ conductivity obta9able1 & %\ld !re=e be ( pure copp]2 ! insulat+ cov]+ %\ld1 :ile =m+ a ne>ly absolutely non-conduct+ %ea?1 h z l[ a specific inductive capacity z possible4 ,! fir/ ( ^! conditions ran c\nt] to "s views t _h be5 put =w>d1 to ! effect t x 0 only necess>y to h ! int]nal conductor highly conduct+ on its surface2 & "s controv]sy on ! subject ensu$4 ,! inv]se squ>e law1 z x 0 call$1 0 vehem5tly call$ 9 "q1 f a mi/ak5 int]pretation ( "s exp]im5ts t 7 made to te/ x4 ,= if ! pot5tial at ! home end be regul>ly alt]$1 accord+ to ! simple h>monic law1 s t ! numb] ( p]iods ( oscillation 9 a second is n1 ! *anges ( pot5tial are propagat$ ) velocity #b7ncr71 :]e c & r are ! capacity & resi/ance ( ! cable1 ea* tak5 p] unit l5g?4 ,9 ?is case1 = a long cable1 !re is a velocity ( propagation indep5d5t ( ! l5g?2 & ?is fact seems to h misl$ ! exp]im5t]s4 ,?omson's view prevail$1 & ! result 0 ! e/abli%m5t1 fir/ by ,?omas ,bolton ,sons1 ,/oke-on-,tr5t1 ( mills = ! manufacture ( high conductivity copp]1 :i* is n[ a great indu/ry4 ,! ,f\ri] ma!matics ( ! conduction ( heat along a b> suffices to solve ! problem1 s long z ! signall+ is s sl[ z n to br+ into play electromagnetic induction to any s]i\s ext5t4 ,= rapid signall+ 9 :i* v quick *anges ( curr5t are conc]n$ ! electromotive =ces due to ! gr[? or dy+ out ( ! curr5t w\ld be s]i\s1 & ! !ory ( diffusion w\ld n apply4 ,b ord9>y cable work+ is q sl[ en\gh to enable su* electromotive =ces to be disreg>d$4 ,,lay+ ,,( ,,fir/ ,,am]ican ,,cables ,! fir/ cable ( #aheh 0 laid by ! ,u4,s4 frigate ,niag>a & ,h4,m4,s4 ,agamemnon1 aft] hav+ be5 manufactur$ ) all ! precautions sugge/$ by ,pr(essor ,?omson's rese>*es4 ,x is h>d to realise h[ difficult su* an ent]prise 0 at ! "t4 ,! manufacture ( a huge cable1 ! /[age ( x 9 cable tanks on bo>d ! vessels1 ! inv5tion ( lay+ & controll+ & pick+-up ma*9]y _h to be fac$ ) b little exp]i5ce to guide ! eng9e]s4 ,"h aga9 ,?omson1 by 8 k ( dynamics & true eng9e]+ in/9ct1 0 ( great assi/ance4 ,9 #ahfe he read a v valuable pap] on ! =ces conc]n$ 9 ! lay+ & lift+ ( deep-sea cables1 %[+ h[ ! /ra9s c\ld be m9imis$ 9 v>i\s practical cases ( importance--= example1 9 ! lift+ ( a cable = repairs4 ,a fir/ ,atlantic cable _h be5 p>tly laid 9 #aheg by ! ,niag>a1 :5 x broke 9 #bjjj fa?oms ( wat]1 ab\t #ccj miles f ,val5tia1 :]e ! lay+ _h begun4 ,an additional l5g? ( #ijj miles 0 made1 & ! ent]prise 0 resum$4 ,?is "t x 0 decid$ t ! two vessels1 ea* ) half ( ! cable on bo>d1 %\ld meet & splice ! cable 9 mid-ocean1 & !n /eam 9 opposite directions1 ! ,agamemnon t[>ds ,val5tia1 ! ,niag>a t[>ds ,newf\ndl&4 ,pr(essor ,?omson 0 eng9e] 9 *>ge ( ! electrical te/+ on bo>d ( ! ,agamemnon4 ,aft] v>i\s mi%aps ! cable 0 at la/ safely laid on ,augu/ #f1 #aheh1 & congratulations 7 %ortly aft] ex*ang$ betwe5 ,great ,brita9 & ! ,unit$ ,/ates4 ,on ,septemb] #f x 0 ann\nc$ t signals _h ceas$ to pass1 & an inve/igation ( ! cause ( ! /oppage 0 und]tak5 by ,pr(essor ,?omson & ! o!r eng9e]s4 ,! report /at$ t ! cable _h be5 too ha/ily made1 t1 9 fact1 x 0 n good en\gh1 & t ! /ra9s 9 lay+ x _h be5 too great & unequal4 ,x 0 f\nd impossible to repair x1 s t !re 0 no option b to ab&on x4 ,?is cable probably suff]$ s]i\sly f ! viol5t means :i* seem to h be5 employ$ to =ce signals ?r\gh x4 ,n[ only a v mod]ate diff]5ce ( pot5tial is appli$ to a cable at ! s5d+ end1 & spe$ ( signall+ is obta9$ by ! use ( in/rum5ts1 ! mov+ p>ts ( :i* h little in]tia1 & readily respond to only an exce$+ly feeble curr5t4 ,a second cable 0 made & laid 9 #ahfe by ! ,great ,ea/]n1 :i* c\ld take on bo>d ! :ole at once & /eam f %ore to %ore4 ,x 0 also well adapt$ = cable "w ?r\gh hav+ bo? screw & paddles4 ,z ,?omson po9ts out1 /e]age way c\ld be got on ! vessel by driv+ ! screw ahead1 s z to s5d a /ream ( wat] a/]n t[>ds ! rudd]1 :ile ! paddles 7 driv5 a/]n to prev5t ! %ip f go+ ahead4 ,?is 0 ( great advantage 9 manuvr+ on _m occasions4 ,?is cable also broke1 b a ?ird 0 laid successfully 9 #ahff by ! same vessel1 & ! second 0 recov]$ & repair$1 s t two good cables 7 secur$ = comm]cial work+4 ,on bo? exp$itions ,pr(essor ,?omson act$ z electrical eng9e]1 & receiv$ ! hon\r ( knigh?ood & ! ?anks ( ! ,anglo-,am]ican ,telegraph ,company on 8 return home1 :5 he 0 also pres5t$ ) ! fre$om ( ! city ( ,glasg[4 ,he aft]w>ds act$ z eng9e] = ! ,fr5* ,atlantic ,cable1 = ! ,brazilian & ,riv] ,plate ,company1 & = ! ,comm]cial ,company1 ^: two new ,atlantic cables 7 laid 9 #ahhb-d4 ,,mirror ,,galvanomet] ,,& ,,siphon ,,record] ,s9ce :atev] ! pot5tial appli$ at ! s5d+ end ( ! cable might be 7&1 ( c\rse1 z has be5 /at$1 ?is pot5tial _h to be kept to z l[ a value z possible7 ! curr5t at ! receiv+ end only rose gradually1 x 0 necess>y to h z delicate a receiv+ in/rum5t z possible1 s t x w\ld quickly respond to ! gr[+ & /ill feeble curr5t4 ,= unless ! cable c\ld be work$ at a rate :i* w\ld p]mit ( *>ges p] ^w transmitt$ :i* 7 )9 ! rea* ( comm]cial p1 x 0 obvi\s t ! ent]prise w\ld fail ( its object4 ,& z a cable c\ld n co/ less ?an half a million /]l+1 ! rev5ue to be aim$ at 0 v consid]able4 ,?is problem ,?omson also solv$ by ! inv5tion ( 8 mirror galvanomet]4 ,! susp5d$ magnet 0 made ( small pieces ( wat*-spr+ cem5t$ to a small mirror1 s t ! :ole mov+ "p weigh$ only a gra9 or two4 ,its in]tia1 or resi/ance to be+ set into motion1 0 ?us v small1 & x 0 hung by a s+le fibre ( silk )9 a clos$ *amb] at ! c5tre ( ! galvanomet] coil4 ,a ray ( light f a lamp 0 reflect$ to a :ite pap] scale 9 front ( ! mirror1 :i* z x turn$ caus$ a spot ( illum9ation to move along ! pap]4 ,a motion ( ?is long massless index to ! left 0 reg>d$ z a dot1 a motion to ! "r z a da%1 & ! ,morse alphabet c\ld !re=e be employ$4 ,?is in/rum5t 0 us$ 9 ! #aheh cable exp$ition1 & a special =m ( susp5sion 0 inv5t$ = x by ,?omson1 to enable x to be us$ on bo>d %ip4 ,! susp5sion ?read1 in/ead ( be+ held at "o end only1 0 /ret*$ f top to bottom ( ! *amb] 9 :i* ! ne$le hung1 & kept tight by be+ secur$ at bo? ends4 ,?us ! m9imum ( di/urbance 0 caus$ to ! mirror by ! roll+ or pit*+ ( ! %ip4 ,! galvanomet] 0 also enclos$ 9 a ?ick iron case to gu>d x aga9/ ! magnetic field due to ! iron ( ! %ip4 ,! iron-clad galvanomet] fir/ us$ 9 subm>9e telegraphy 7on ! #aheh exp$ition 9 ! ,u4,s4 frigate ,niag>a7 is 9 ! collection ( hi/orical app>atus 9 ! ,natural ,philosophy ,dep>tm5t ( ! ,univ]sity ( ,glasg[4 ,! mirror galvanomet] !n inv5t$ has become "o ( ! mo/ useful in/rum5ts ( ! laboratory4 ,mirror deflection is n[ us$ also = ! indicators ( _m k9ds ( in/rum5ts4 ,! galvanomet] 0 replac$ lat] by ano!r inv5tion ( ,pr(essor ,?omson--! siphon record]4 ,"h a small & delicate p5 0 =m$ by a piece ( v f9e glass tube 7vacc9ation tub+1 9 fact7 9 ! =m ( a siphon1 ( :i* ! %ort] end dipp$ into an ink-bottle1 :ile ! o!r end wrote ! message 9 little zig-zag not*es on a ribbon ( pap] drawn pa/ x by ma*9]y4 ,! siphon 0 mov$ to & fro by ! signall+ curr5ts1 :i* fl[$ 9 a small coil hung betwe5 ! poles ( an electromagnet1 excit$ by a local batt]y1 & ! ink 0 spirt$ 9 a succession ( f9e drops f ! p5 to ! pap]4 ,?is 0 accompli%$ by electrify+ ! ink-bottle & ink by a local electrical ma*9e1 & keep+ ! pap] 9 contact ) an un9sulat$ metal roll]4 ,electric attraction betwe5 ! electrifi$ ink & ! unelectrifi$ pap] ?us drew ! ink-drops out1 & ! p51 :i* nev] t\*$ ! pap]1 0 q unret>d$ by friction4 ,bo? ^! in/rum5ts _h ! ine/imable advantage t ! to & fro motions ( ! spot ( light or ! p5 took place indep5d5tly ( ord9>y e>?-curr5ts ?r\gh ! cable4 ,! arrangem5t ( magnet & susp5d$ coil 9 ?is in/rum5t has become widely kn[n z t ( ! d',arsonval galvanomet]4 ,?is application 0 anticipat$ by ,?omson1 & is di/9ctly m5tion$ 9 8 record] pat5t1 long be=e su* galvanomet]s 7 ev] us$4 ,x 0 lat] propos$ by sev]al exp]im5t]s be=e ,m4 d',arsonval4 ,x is n too mu* to say t1 by 8 discussion ( ! spe$ ( signall+1 8 s]vices z an electrical eng9e]1 & especially by 8 inv5tion ( in/rum5ts capable ( respond+ to v feeble curr5ts1 ,?omson made subm>9e telegraphy comm]cially possible4 ,lat] he ent]$ into p>tn]%ip ) ,mr4 ,c4 ,f4 ,v>ley & ,pr(essor ,fleem+ ,j5k94 ,a comb9ation ( inv5tions 0 made by ! firm3 ,v>ley _h pat5t$ a me?od ( signall+ by cond5s]s1 & ,j5k9 lat] sugge/$ & pat5t$ an automatic key = curb-s5d+ on a cable--t is1 signall+ by plac+ "o pole ( ! batt]y = an int]val a little %ort] ?an ! usual "o to ! l9e1 & !n rev]s+ ! batt]y = ! rema9d]4 ,?is gave %>p] signals1 z ! rev]sal help$ to dis*>ge ! cable m rapidly ?an x w\ld h be5 by ! m]e connection to e>? betwe5 two signals4 ,! firm ( ,?omson1 ,v>ley ,j5k9 took a prom95t "p 9 cable "w2 & ,?omson & ,j5k9 act$ z eng9e]s = _m l>ge und]tak+s4 ,!y employ$ a /aff ( "y electricians at ! cable-works at ,millwall & else:]e1 keep+ wat* ov] ! cable dur+ manufacture1 & s5t !m to sea z repres5tatives & assi/ants to p]=m simil> duties dur+ ! process ( cable-lay+4 ,on _! /aff 7 _m m5 :o h come to em95ce 9 electrical & eng9e]+ pursuits 9 lat] life4 ,,m>9]s' ,,compass ,,& ,,s\nd+ ,,ma*9e ,aft] ! e>li] ,atlantic exp$itions ,sir ,william ,?omson turn$ 8 att5tion to ! con/ruction ( navigational in/rum5ts1 & inv5t$ ! m>9]'s compass & wire-s\nd+ app>atus :i* are n[ s well kn[n4 ,he _h come to ! conclusion t ! compasses 9 use _h mu* too l>ge ne$les 7"s ( !m b>-magnets sev5 or eight in*es long67 to respond quickly & c]ta9ly to *anges ( c\rse1 &1 :at 0 /ill m s]i\s1 to admit ( ! application ( correct+ magnets1 & ( masses ( s(t-iron to annul ! action ( ! magnetism ( ! %ip4 ,! compass c>d consi/s ( a pap] r+1 on :i* ! po9ts & degrees are engrav$ 9 ! ord9>y way1 & is kept circul> by a light r+ ( alum9ium4 ,?reads ( silk ext5d radially f ! rim to a c5tral boss ( alum9ium 9 :i* is a cap ( alum9ium4 ,9 ! top ( ! cap is a sapphire be>+1 :i* re/s on an iridium po9t project+ upw>d f ! compass b[l4 ,eight magnets ( glass-h>d /eel1 f #c in*es to #b in*es long1 & ab\t ! ?ickness ( a knitt+-ne$le1 :i* =m ! compass ne$le1 are /rung l ! /eps ( a rope ladd]1 on two silk ?reads atta*$ to f\r ( ! radial ?reads4 ,! weight ( ! c>d is extremely small--only #agj gra9s2 t is less ?an ( an ounce4 ,b ! matt] is n m]ely made small 9 am\nt2 x is di/ribut$ on ! :ole at a great di/ance f ! axis2 consequ5tly ! p]iod ( free vibration is long1 & ! c>d is v /eady4 ,! great lightness ( ! c>d also causes ! error due to friction on ! po9t ( support to be v small4 ,! errors ( ! compass 9 an iron %ip are ma9ly ! semicircul> error & ! quadrantal error4 ,we c only briefly indicate h[ ^! arise & h[ !y are correct$4 ,! %ip's magnetism may be consid]$ z p>tly p]man5t1 & p>tly inductive4 ,! =m] *anges only v sl[ly1 ! latt] alt]s z ! %ip *anges c\rse & position4 ,= ! %ip is a comb9ation ( longitud9al1 transv]se1 & v]tical gird]s & beams4 ,z a :ole x is a great iron or /eel gird]1 b its /ructure gives x longitud9al1 transv]se1 & v]tical magnetisation4 ,?is di/urbs ! compass1 :i* is also affect$ by ! magnetisation ( ! iron or /eel ma/s & sp>s1 or ( iron or /eel c>ri$ z c>go4 ,! semicircul> error is due to a great ext5t to p]man5t magnetism1 b also 9 "p to induc$ magnetism4 ,x is s call$ because :5 ! %ip's head is turn$ ?r\gh #cfj1 ! error atta9s a maximum on two c\rses #ahj ap>t4 ,x may am\nt to ov] #bj 9 an ord9>y iron vessel1 & to #cj or #dj 9 an arm\r-clad4 ,x is correct$ by two sets ( /eel magnets plac$ ) _! c5tres "u ! ne$le 9 ! b9nacle4 ,"o set h _! l5g?s =e & aft1 ! o!rs 9 ! ?w>t-%ip direction4 ,^! magnets annul ! error on ! nor? & s\? & on ! ea/ & we/ c\rses1 due to ! two horizontal compon5ts ( magnetic =ce produc$ ma9ly by ! p]man5t magnetism ( ! %ip4 ,a regul> r\t9e ( sw++ ! %ip :5 m>ks on ! %ore 7! true be>+s ( :i* f ! %ip are kn[n7 are available1 is foll[$ = ! adju/m5t4 ,! quadrantal error is s call$ because its maxima are f\nd on f\r compass c\rses successively a quadrant1 or #ij1 f "o ano!r4 ,x am\nts 9 g5]al to f #e to #aj at mo/4 ,x is due to induc$ magnetism1 & is correct$ by a pair ( s(t-iron sph]es1 plac$ on ! two sides ( ! compass ) _! c5tres 9 a l9e transv]se to ! %ip1 ?r\gh ! c5tre ( ! compass ne$le4 ,!re are1 h[ev]1 exceptional cases 9 :i* !y are plac$ 9 ! =e & aft l9e "o a=e1 ! o!r abaft1 ! ne$le4 ,:5 ! quadrantal error has once be5 annull$ x is always z]o1 = z ! induc$ magnetism *anges1 s does t ( ! sph]es1 & ! adju/m5t rema9s good4 ,9 a new %ip ! p]man5t magnetism sl[ly alt]s1 & s ! semicircul> correction has to be improv$ f "t to "t by *ang+ ! magnets4 ,^! adju/m5ts are n q all t h to be made2 b en\gh has be5 /at$ to %[ h[ ! process ( comp5sation c be c>ri$ out ) ! ,?omson compass4 ,! imm5sely-too-l>ge magnets us$ =m]ly z compass ne$les1 ?r\gh a mi/ak5 notion1 app>5tly1 t m directive =ce w\ld be got by _! means1 r5d]$ ! quadrantal adju/m5t an impossibility4 ,! c>d sw++ r\nd br\ght ! l>ge ne$les into diff]5t positions relatively to ! iron balls1 :5 ^! 7 us$1 & ex]t$ an inductive action on !m :i* react$ on ! ne$les1 produc+ m error1 p]haps1 ?an 0 correct$4 ,?omson inv5t$ also an in/rum5t call$ a deflector1 by :i* x is possible to adju/ a compass :5 sights ( sun or />s1 or be>+s ( t]re/rial objects1 _c be obta9$4 ,by means ( x ! directive =ces on ! ne$les on diff]5t c\rses c be comp>$4 ,!n ! adju/m5t is made by plac+ ! correctors s t ! directive =ce is z ne>ly z may be ! same on all c\rses4 ,! compass is !n q correct4 ,! !ory ( deviations ( ! compass1 x is "r to say1 0 discuss$ fir/ p>tially by ,poisson1 b aft]w>ds v completely & elegantly by ! late ,mr4 ,ar*ibald ,smi? ( ,jordanhill1 ^: memoirs1 n[ incorporat$ 9 ! ,admiralty ,manual ( ,deviations ( ! ,compass1 l$ to ,"l ,kelv9's inv5tions4 ,"l ,kelv9's compass is n[ almo/ univ]sally 9 use 9 ! m]*ant s]vice ( ?is c\ntry1 & 9 mo/ ( ! navies ( ! _w4 ,x has add$ greatly to ! c]ta9ty & safety ( navigation4 ,! s\nd+ ma*9e is also well kn[n4 ,at fir/ pian(orte wire 0 us$ = deep-sea s\nd+ by ,commodore ,belknap ( ! ,u4,s4 ,navy1 & by o!rs1 on ,sir ,william ,?omson's recomm5dation4 ,f9ally1 a =m ( ma*9e 0 made by :i* a s9k] c\ld be l[]$ to ! bottom ( ! sea & br\ght up aga9 9 a few m9utes2 s t x 0 possible to take a s\nd+ )\t ! long delay involv$ 9 ! old me?od ) a reel ( hemp-rope1 :i* (t5 tempt$ %ipma/]s to run risks ( go+ a%ore r ?an /op ! %ip = ! purpose4 ,! wire (f]$ little resi/ance to motion ?r\gh ! wat]1 & by a prop] w9d+ ma*9e1 ) brake to prev5t ! wire f runn+ out too fa/ & k9k+1 :5 x 0 almo/ c]ta9 to break1 "o man c\ld quickly s\nd & heave up aga91 :ile ano!r att5d$ to ! wire & s9k]4 ,a gauge consi/+ ( a long quill-tube clos$ at ! upp] end1 & coat$ inside ) *romate ( silv]1 %[$ by ! action ( ! sea-wat] on ! coat+ h[ f> ! wat] _h pass$ up ! tube1 compress+ ! air above x2 & f ?is1 by plac+ ! tube along a wood5 rule prop]ly graduat$1 ! dep? 0 read (f at once4 ,) ! improv$ ma*9e a %ip approa*+ ! %ore 9 ?ick wea!r c\ld take s\nd+s at %ort int]vals )\t /opp+1 & discov] at once any beg9n+ ( %all[+ ( ! wat]1 & s avoid dang]4 ,! s+le wire is n n[ us$1 z a ?9 /r&$ wire is f\nd saf] & q z effective4 ,! gauge also has be5 improv$4 ,! app>atus c be se5 9 any well-f\nd sea-go+ vessel2 ?\gh !re are /ill1 or 7 until n v long ago1 /eam vessels )\t ?is app>atus1 ?\gh cross+ ! ,engli% ,*annel ) pass5g]s4 ,^! dep5d$ = s\nd+s on ! obsolete hemp-rope1 wrapp$ r\nd an iron sp9dle held v]tically on ! deck by memb]s ( ! %ip's company1 :ile ! cord 0 unw\nd by ! desc5t ( ! s9k]4#bd ,sir ,william ,?omson's electrical & o!r inv5tions are too num]\s to specify "h1 & !y are 9 con/ant use :]ev] precision ( measurem5t is aim$ at or requir$4 ,long ago he inv5t$ electromet]s = absolute measurem5ts ( electrical pot5tial 7electric pressure72 m rec5tly 8 curr5t-balances h giv5 ! same precision to electrodynamic measurem5t ( curr5ts4 ,all 8 e>ly in/rum5ts 7 made by ,mr4 ,james ,:ite1 ,glasg[4 ,! bus9ess f\nd$ by ,mr4 ,:ite1 & latt]ly c>ri$ on at ,cambridge ,/reet1 has develop$ imm5sely1 & is n[ own$ by a limit$ liability company--,messrs4 ,kelv9 & ,james ,:ite 7,limit$74 ,= _m ye>s ,sir ,william ,?omson 0 a ke5 ya*tsman1 & 8 s*oon] ya*t1 ! ,lalla ,rookh1 0 well kn[n on ! ,clyde & 9 ! ,sol5t4 ,an exp]t navigator1 he delight$ to take deep-sea voyages 9 8 ya*t1 & w5t m ?an once z f> z ,madeira4 ,_m navigational & hydrodynamical problems 7 work$ out on ^! exp$itions4 ,= a good _m ye>s1 h[ev]1 he _h giv5 up sea-f>+ dur+ 8 times ( relaxation1 & liv$ 9 ,glasg[ & ,london & 9 ,l>gs1 ,ayr%ire1 :]e he built1 9 #ahge1 a l>ge & com=table h\se1 look+ out t[>ds ! ,fir? & ! ,argyle%ire lo*s he knew & lov$ s well4 ,9 ! c\rse ( 8 deep-sea exp$itions 9 8 ya*t he became impress$ ) ! utility ( ,sumn]'s me?od ( det]m9+ ! position ( a %ip4 ,let u suppose t at a giv5 in/ant ! altitude ( ! sun is det]m9$ f ! %ip4 ,! ,gre5wi* meantime1 & !re=e ! longitude at :i* ! sun is v]tical1 is kn[n by *ronomet]1 & ! decl9ation ( ! sun is kn[n f ! ,nautical ,almanac4 ,! po9t on ! e>? v]tically "u ! sun c be m>k$ on ! *>t1 & a circle 7or r1 :at w\ld be a circle on a t]re/rial globe7 drawn r\nd x f e po9t ( :i* ! sun w\ld h ! obs]v$ altitude4 ,! %ip is at a po9t on ?is circle4 ,"s "t aft] ! altitude ( ! sun is obs]v$ aga91 & a new circle is drawn4 ,if ! fir/ circle be bodily %ift$ on ! *>t along ! di/ance run 9 ! int]val1 x w int]sect ! second 9 two po9ts1 "o ( :i* w be ! position ( ! %ip1 & x is g5]ally possible to tell :i*1 )\t dang] ( mi/ake4 ,sir ,william ,?omson pr9t$ tables = facilitat+ ! calculations 9 ! use ( ,sumn]'s me?od1 & cont9ually us$ !m 9 8 own voyages4 ,he 0 well v]s$ 9 seaman%ip ( all k9ds1 & us$ 8 exp]i5ce habitually to ?r[ light on ab/ruse problems ( dynamics4 ,"s ( ^! w be f\nd 9 ,?omson & ,tait2 = in/ance1 9 ,"p ,i1 #cbe1 :]e a numb] ( nautical ph5om5a are cit$ 9 illu/ration ( an important pr9ciple ( hydrodynamics4 ,! fif? example /at$ is z foll[s3 ,9 a smoo? sea1 ) mod]ate w9d bl[+ p>allel to ! %ore1 a sail+ %ip head+ t[>ds ! %ore1 ) n en\gh ( sail set1 c only be sav$ f creep+ a%ore by sett+ m sail1 & sail+ rapidly t[>ds ! %ore1 or ! dang] t is to be avoid$1 s z to all[ h] to be /e]$ away f x4 ,! risk ( go+ a%ore 9 fulfilm5t ( ,lagrange's equations is a frequ5t incid5t ( 'gett+ "u way' :ile lift+ an*or or ev5 aft] slipp+ f moor+s4 ,8 seaman%ip 0 well kn[n to %ipma/]s1 ) :om he _h mu* int]c\rse1 & ^: intellig5ce & practical skill he held 9 v high reg>d4 ,,*apt] ,,xvi ,,"l ,,kelv9 ,,9 ,,8 ,,class-,,room ,,& ,,laboratory ,x is impossible to convey to ^? :o nev] /udi$ at ,glasg[ any cle> conception ( ,?omson z he appe>$ to /ud5ts :om he met daily dur+ ! session4 ,8 appe>ance at meet+s ( ! ,briti% ,association1 & 8 vivaci\s que/ion+s ( ! v>i\s au?ors ( pap]s1 8 absorption 9 8 subject & oblivion to ! flight ( "t :5 he read a pap] himself1 w long be rememb]$ by sci5tific m53 b ?\gh !y suffice to sugge/ :at he 0 l 9 8 own lecture-room1 ! picture lacks ! sett+ ( furniture1 app>atus1 assi/ants1 & /ud5ts1 :i* all contribut$ to ! unique impression made by 8 p]sonality on 8 pupils4 ,! lecture-table--) long /raight front & ends refract$ inw>d1 flank$ by high] small r\nd tables support$ on cyl9drical pill>s--lad5 ) in/rum5ts2 ! pa9t$ diagrams ( ! sol> spectrum & ( ! pa?s ( col\r$ rays ?r\gh a prism1 hung r\nd ! walls2 ! long wire ) ! cyl9drical vibrator atta*$1 = exp]im5ts on torsion1 & ! triple spiral spr+ vibrator1 :i* hung at ! two ends ( ! long blackbo>d2 ! p5dulum ?irty feet long1 consi/+ ( a /eel wire & a twelve-p\nd cannon-ball z bob1 susp5d$ f ! apex ( ! dome-ro( above ! lecture-table2 ! l>ge iron :eel 9 ! beautiful oriel w9d[ on ! "r ( ! lectur]1 & ! collection ( optical in/rum5ts on ! table 9 front ( ! c5tral w9d[ spaces1 f :i* ! small iron-fram$ panes--de> to ! he>t ( ! ar*itect--_h be5 remov$2 ! clock on ei!r side ( ! room1 "o motionless1 ! o!r indicat+ ! "t1 & hav+ atta*$ to x ! al>m :i* %[$ :5 ! angry bell outside _h ceas$ to toll2 ! t5 b5*es ( eag] & m]ry /ud5ts1 :i* fill$ ! auditorium2 all ^! comb9$ to =m a sc5e :i* e /ud5t fondly recalls1 & :i* _c be adequately describ$4 ,a simil> sc5e1 ) "s diff]5ces ( arrangem5t & hav+ its own p>ticul> associations1 w occur to e /ud5t :o att5d$ 9 ! ,old ,college4 ,! writ] w nev] =get ! lecture-room :5 he fir/ beheld x1 f 8 place on ,b5* ,,viii1 a few days aft] ! beg9n+ ( session #ahgd-e4 ,sir ,william ,?omson1 ) activity emphasis$ r ?an o!rwise by 8 lam5ess1 came 9 ) ! /ud5ts1 pass$ beh9d ! table1 &1 putt+ up 8 eye-glass1 survey$ ! app>atus set out4 ,!n1 z ! /ud5ts p\r$ 91 an increas+ /ream1 ! al>m weight 0 releas$ by ! bell-r+]1 & fell sl[ly "s f\r or five feet1 f ! top ( ! clock to a plat=m bel[4 ,by ! "t ! weight _h desc5d$ ! /ud5ts 7 9 _! places1 & !n1 z ,?omson advanc$ to ! table1 all rose to _! feet1 & he recit$ ! ?ird ,collect f ! ,morn+ ,s]vice ( ! ,*ur* ( ,engl&4 ,x 0 ! cu/om !n1 & x is /ill "o bett] hon\r$ 9 ! obs]vance ?an 9 ! brea* 7:i* has become r common7 to op5 all ! fir/ & second classes ( ! day ) pray]2 & ! selection ( ! pray]s 0 left to ! discretion ( ! pr(essors4 ,next came ! roll-call by ! assi/ant2 ea* "n 0 call$ 9 its ,engli%1 or ,scotti% 7= ! clans 7 always well repres5t$7 =m1 & ! answ] adsum 0 return$4 ,!n ! ,pr(essor began 8 lecture1 g5]ally ) ! exam9ation ( "o ( ! /ud5ts1 :o rose 9 8 place :5 8 "n 0 call$4 ,?omson1 z ! quotation 9 ,*apt] ,,vi f ! ,bangor ,address %[s1 0 fond ( oral exam9ation1 & aft] ! second h\r _h begun to decl9e z "o ( regul> att5dance1 habitually devot$ t5 or fifte5 m9utes to ask+ que/ions & criticis+ ! answ]s4 ,! names ( ! /ud5ts to be que/ion$ 7 select$ at r&om f ! class regi/]1 or by a k9d ( lott]y1 c>ri$ out by plac+ a small c>d = ea* /ud5t 9 a box on ! table1 & draw+ a "n :5ev] a memb] ( ! class 0 to be exam9$4 ,! int]e/ 9 ! draw+ ea* day 0 int5se1 = !re 0 a glori\s unc]ta9ty z to :at might be ! l9e ( exam9ation adopt$4 ,sometimes1 9 ! mid/ ( a criticism ( an answ]1 an idea w\ld sudd5ly occur to ! ,pr(essor1 & he w\ld enl>ge ^u x1 until ! =gott5 exam9ee slipp$ quietly back into 8 seat1 to be no m di/urb$ at lea/ = t day6 ,& h[ great ! relief if ! ordeal 0 well pass$ & ! c>d 0 plac$ 9 t receptacle ( ! bless$1 ! comp>tm5t res]v$ = ^? :o _h be5 call$ & duly pass$ ! assize6 ,b !re 0 a ?ird comp>tm5t res]v$ = ! c>ds ( ^? un=tunates :o fail$ to satisfy ! judge6 ,! read] may h anticipat$ ! fact t ! ?ree divisions ( ?is fateful box 7 commonly kn[n to /ud5ts by ! names ( ! ?ree great habitations ( spirits describ$ 9 ! ,div9a ,comm$ia ( ,dante4 ,z has be5 /at$1 ! oral exam9ation ) :i* ! lectures op5$ 0 ! cause ( a good deal ( excitem5t1 :i* 0 add$ to by ! elem5t ( *ance introduc$ by draw+ ! names f ! purgatorial comp>tm5t ( ! box4 ,! ordeal 0 dread$ by backw>d /ud5ts1 :om ,?omson f\nd1 z he said1 aphasic1 :5 call$ on to answ] 9 exam9ation1 b :o c]ta9ly 7 any?+ b aphasic 9 m cong5ial circum/ances4 ,occasionally !y ab/a9$ f respond+ to _! names1 mode/ly seek+ ! seclusion ( ! cr[d1 & "s little "t w\ld be sp5t 9 asc]ta9+ :e!r ! exam9ee-designate 0 pres5t4 ,:5 at la/ he 0 discov]$1 he g5]ally rose ) a f]v5t appeal to 8 fell[s on ei!r side to help him 9 8 ne$4 ,mc,farlane us$ to tell ( an incid5t :i* illu/rat$ ! +5uity ) :i* x 0 sometimes attempt$ to evade ! ordeal ( ! viva voce exam9ation4 ,"o aft]noon1 :5 he 0 busily prep>+ ! lecture-illu/rations = next day1 a /ud5t came into ! class-room1 & engag+ him 9 conv]sation on "s po9t ( dynamics1 reg>d+ :i* he pr(ess$ to h a difficulty1 hov]$ r\nd ! box :i* conta9$ ! ?ree comp>tm5ts popul>ly kn[n z ,purgatory1 ,heav51 & ,hell6 ,always :5 ,mc,farlane left ! room to br+ some?+ f ! adjo9+ cab9et ( app>atus1 he f\nd1 :5 he return$1 8 inquir+ fri5d hurri$ly quitt+ ! imm$iate vic9ity ( ! box4 ,at la/ ! /ud5t took leave1 ) _m apologies = giv+ s mu* tr\ble4 ,z ,mc,farlane suspect$ w\ld be ! case1 ! ticket be>+ ! "n ( t /ud5t 0 no long] to be f\nd6 ,he us$ to conclude ! /ory z foll[s3 ,i j made a new ticket = him1 & plac$ x on ! top ( ! o!r tickets1 & next day ,sir ,william call$ him1 ! v fir/ "t4 ,:at 7 8 feel+s1 :o _h fondly ?\ght himself safe = ! session1 & n[ f\nd himself subject$ to a heckl+ :i* he probably expect$ w\ld be repeat$ indef9itely1 may be imag9$4 ,! subject ( ! fir/ lecture :i* ! writ] att5d$ 0 simple h>monic motion1 & 0 illu/rat$ by means ( p5dulums1 spiral spr+s ) weights1 a long v]tical rod ( /eel tipp$ ) an ivory ball & fa/5$ to a heavy base1 tun+-=ks1 etc4 ,! motion 0 def9$ z t ( a p>ticle mov+ along ! diamet] ( a circle--! auxili>y circle1 ,?omson call$ x--s z always to keep pace1 z reg>ds displacem5t 9 ! direction along t diamet]1 ) a p>ticle mov+ ) uni=m spe$ 9 ! circle4 ,!n ! velocity & accel]ation 7 f\nd1 & x 0 %[n t ! p>ticle 0 cont9ually accel]at$ t[>ds ! c5tre 9 proportion to ! di/ance ( ! p>ticle f t po9t4 ,! con/ant ratio ( accel]ation to displacem5t 0 prov$ to be equal to ! squ>e ( ! angul> velocity 9 ! auxili>y circle1 & f ?is fact1 & ! p>ticul> value ( ! accel]ation :5 ! p>ticle 0 at ei!r end ( its range ( motion1 an expression = ! p]iod 9 t]ms ( ! spe$ & radius ( ! auxili>y circle 0 d$uc$4 ,!n ! ord9>y simple p5dulum =mula 0 obta9$4 ,?is mode ( treatm5t ( an elem5t>y matt]1 s entirely diff]5t f any?+ 9 ! ord9>y text-books1 arre/$ ! att5tion at once1 & convey$1 to "s at lea/ ( ^? pres5t1 an idea ( simple h>monic motion :i* 0 directly applicable to all k9ds ( cases1 su* z ! motion ( ! air 9 a s\nd wave1 or ( ! m$ium :i* conveys ! waves ( light4 ,! subject ( ,kepl]'s laws 0 dealt ) 9 ! e>ly lectures ( e c\rse1 & ,newton's d$uctions 7 insi/$ on z conta9+ ! philosophy ( ! :ole "q1 lead+1 z !y did1 to ! s+le pr9ciple f :i* ! laws c\ld be d$uc$1 & ! ?ird law correct$ :5 ! mass ( ! planet 0 comp>able ) t ( ! sun4 ,sometimes ,?omson w\ld read ! rem>kable passage 9 ,hegel's ,logik1 9 :i* he ref]s to ! ,newtonian !ory ( gravitation & says1 ,! planets are n pull$ ?is way & t1 !y move along 9 _! orbits l ! bless$ gods1 & rem>k ^u x4 ,on "o occasion 8 rem>k 01 ,well1 g5tlem51 if ^! be 8 physics1 :at mu/ 8 metaphysics be8 ,& c]ta9ly t a philosoph] %\ld d5y1 z ,hegel seem$ to d1 all m]it to ! philosophical sett+ 9 :i* ,newton plac$ ! empirical results ( ,kepl]1 is a v rem>kable ph5om5on4 ,! vivacity & en?usiasm ( ! ,pr(essor at t "t 7 v great4 ,! animation ( 8 c\nt5ance z he look$ at a gyro/at sp9n+1 /&+ on a knife-edge on ! glass plate 9 front ( him1 & lean+ ov] s t its c5tre ( gravity 0 on "o side ( ! po9t ( support2 ! delight ) :i* he %[$ t hurry+ ( ! precessional motion caus$ ! gyro/at to rise1 & ret>d+ ! precessional motion caus$ ! gyro/at to fall1 s t ! fre$om to precess 0 ! secret ( its n fall+2 ! imm$iate application ( ! /udy ( ! gyro/at to ! explanation ( ! precession ( ! equ9oxes1 & illu/ration by a model ( a t]re/rial globe1 arrang$ s t ! c5tre %\ld be a fix$ po9t1 :ile its axis--a mat]ial spike ( brass--roll$ r\nd a horizontal circle1 ! c5tre ( :i* repres5t$ ! pole ( ! ecliptic1 & ! diamet] ( :i* subt5d$ an angle at ! c5tre ( ! globe ( twice ! obliquity ( ! ecliptic2 ! pleasure ) :i* he po9t$ to ! motion ( ! equ9octial po9ts along a circle surr\nd+ ! globe on a level ) its c5tre1 & repres5t+ ! plane ( ! ecliptic1 & ! smile ) :i* he ann\nc$1 :5 ! axis _h roll$ once r\nd ! circle1 t #bf1jjj ye>s _h elaps$--all ^! delight$ 8 he>]s1 & made ! lecture memorable4 ,!n ! gyro/at1 m\nt$ ) its axis v]tical on trunnions on a level ) ! fly-:eel1 & re/+ on a wood5 frame c>ri$ ab\t by ! pr(essor6 ,! delight ( ! /ud5ts ) ! quiesc5ce ( ! gyro/at :5 ! frame1 gyro/at & all1 0 c>ri$ r\nd 9 ! direction ( ! sp9 ( ! fly-:eel1 & its sudd5 turn+ upside d[n :5 ! frame 0 c>ri$ r\nd ! o!r way1 0 extreme1 & :5 he sugge/$ t a gyro/at might be conceal$ on a tray ( glasses c>ri$ by a wait]1 _! appreciation ( :at w\ld happ5 0 %[n by laught] & a tumult ( applause4 ,"s w\ld h lik$ to foll[ ! motions ( sp9n+ bodies a little m closely1 & to h made out cle>ly :y !y behav$ z !y did4 ,app>5tly ,?omson imag9$ ! :ole affair 0 self-evid5t1 = he nev] gave m ?an ! simple p>allelogram diagram %[+ ! composition1 ) ! already exi/+ angul> mom5tum ab\t ! axis ( ! top1 ( t g5]at$ ab\t ano!r axis1 9 any %ort "t1 by ! action ( gravity4 ,z a matt] ( fact1 ! /ability & in/ability ( ! gyro/at on ! tray give ! be/ possible illu/ration ( ! two diff]5t =ms ( solution ( ! diff]5tial equation1 3 #j1 accord+ z is positive or negative2 ?\gh x is also possible to expla9 ! inv]sion v simply f fir/ pr9ciples4 ,all ?is 0 no d\bt reg>d$ by ,?omson z obvi\s2 b x 0 f> f be+ self-evid5t to ev5 good /ud5ts ( ! ord9>y class1 :o1 )\t exception1 7 beg9n+ ! /udy ( dynamics4 ,?omson's absorption 9 ! "w ( ! mom5t 0 (t5 v great1 & on ^! occasions he mu* dislik$ to be br\ght d[n to sublun>y ?+s by any slight mis*ance or inconv5i5ce4 ,examples w occur to e old pupil ( ! great emphasis ) :i* he comm&$ t precautions %\ld be tak5 to prev5t ! l f happ5+ aga94 ,copies ( ,?omson & ,tait's ,natural ,philosophy--,t & ,t' 0 its famili> title--& ( o!r books1 includ+ ,b>l['s ,tables & o!r collections ( num]ical data1 7 always kept on ! lecture-table4 ,b occasionally a laboratory /ud5t w\ld /ray 9 aft] ev]y?+ _h be5 prep>$ = ! morn+ lecture1 & c>ry (f ,b>l[ to make "s calculation1 & ( c\rse =get to return x4 ,next morn+ "s numb] w\ld be want$ f ,b>l[ 9 a hurry1 & ! book w\ld be miss+4 ,!n ,?omson w\ld ord] t ,b>l[ %\ld be *a9$ to ! lecture-table1 & enjo9 8 assi/ant to see t t 0 done )\t an h\r's delay6 ,on "o occasion1 aft] work+ out "p ( a calculation on ! long fix$ blackbo>d on ! wall beh9d ! table1 8 *alk gave out1 & he dropp$ 8 h& d[n to ! long l$ge :i* project$ f ! bottom ( ! bo>d to f9d ano!r piece4 ,none 0 j !re2 & he _h to walk a /ep or two to obta9 "o4 ,s he enjo9$ ,mc,farlane1 8 assi/ant1 :o 0 always 9 att5dance1 to h a suffici5t numb] ( pieces on ! l$ge 9 future1 to enable him to f9d "o h&y :]ev] he might ne$ x4 ,mc,farlane =got ! injunction1 or c\ld n obta9 m *alk at ! "t1 & ! same ?+ happ5$ next day4 ,s ! comm& 0 issu$1 ,mc,farlane1 ,i told y to get pl5ty ( *alk1 & y hav5't done x4 ,n[ h a hundr$ pieces ( *alk on ?is l$ge to-morr[2 rememb]1 a hundr$ pieces2 ,i w c\nt !m6 ,mc,farlane1 afraid to be caught napp+ aga91 s5t t aft]noon = sev]al boxes ( *alk1 & c>efully laid ! new %9+ :ite /icks on ! %elf1 all neatly p>allel at an angle to ! edge4 ,! %elf 0 ab\t sixte5 feet long1 s t !re 0 "o piece ( *alk = e two in*es1 & ! effect 0 v f9e4 ,! class next morn+ 0 delight$1 & v appreciative ( ,mc,farlane's dilig5ce4 ,?omson came 91 put up 8 eye-glass1 look$ at ! display1 smil$ sweetly1 &1 turn+ to ! applaud+ /ud5ts1 began 8 lecture4 ,f "t to "t !re 7 special exp]im5ts1 :i* excit$ ! int]e/ ( ! class to an extraord9>y degree4 ,"o 0 ! det]m9ation ( ! velocity ( a bullet fir$ f a rifle into a ,rob9s balli/ic p5dulum4 ,! p5dulum1 consi/+ ( a massive bob ( lead atta*$ to a rigid frame ( iron b>s turn+ ab\t knife-edges1 0 set up beh9d ! lecture-table1 & ! bullet 0 fir$ by ,?omson f a ,jacob rifle into ! bob ( ! p5dulum4 ,! velocity 0 d$uc$ f ! deflection ( ! p5dulum1 its kn[n mom5t ( in]tia ab\t ! l9e ( ! knife-edges1 ! di/ance ( ! l9e ( fire f t l9e1 & ! mass ( ! bullet4 ,9 "s ( ! notices ( ,"l ,kelv9 t h appe>$ 9 ! newspap]s1 ! imag9ation ( ! writ]s has conv]t$ ! ,jacob rifle into "o :i* ,pr(essor ,?omson c>ri$ 9 ! e>ly ye>s ( ! volunte] movem5t1 z a memb] ( a ,glasg[ corps4 ,x is /ill us$ 9 ! ,natural ,philosophy ,dep>tm5t = ! same exp]im5t1 & is a muzzle-load+ rifle ( l>ge calibre1 :i* ?r[s an ounce bullet4 ,x 0 inv5t$ by ! well-kn[n ,indian sportsman1 ,colonel ,jacob1 = big-game %oot+ 9 ,india4 ,?omson held a commission z capta9 9 ! ,k 7or ,univ]sity7 ,company ( rifle volunte]s1 & s did n %\ld] a rifle1 except :5 he may h indulg$ 9 t>get practice4 ,! front b5* /ud5ts 7 always 9 a /ate ( excitem5t1 m+l$ 9 "s cases p]haps ) a little trepidation4 ,= ! t>get 0 v ne> !m1 & ?\gh dang] 0 av]t$ by plac+ a l>ge wood5 scre5 9 front ( ! bob1 to prev5t spl9t]s ( ! bullet f fly+ ab\t 9 ! ev5t ( its miss+ ! t>get & /rik+ ! iron cas+ ( ! bob1 !re 0 a slight am\nt ( n]v\sness z to :at might happ54 ,! rifle1 load$ by ,mc,farlane1 :o _h weigh$ out ! *>ge ( p[d] 7s _m drams7 f a prescription kept 9 a cavity ( ! /ock1 0 plac$ on ! table1 & two re/s1 provid$ ) not*es to receive ! rifle1 7 plac$ 9 ! prop] position to enable a bull's eye to be obta9$4 ,?omson g5]ally produc$ a small box ( cotton wool1 & ins]t$ a little 9 ea* ( 8 e>s to prev5t injury to ! tympanum f ! report1 & advis$ ! spectators to d ! same4 ,!n1 adju/+ 8 eye-glass1 he b5t d[n1 plac$ ! rifle 9 position1 & fir$1 & ! solemn /illness ) :i* ! aim+ & adju/m5ts _h be5 witness$ 0 succe$$ by vocif]\s applause4 ,! l5g? ( tape drawn out "u a light spr+ 0 read (f by ,mc,farlane1 :o _h already plac$ on ! blackbo>d ! =mula = calculation ( ! velocity1 ) ! factor by :i* ! l5g? ( tape _h to be multipli$ to give ! velocity 9 feet p] second4 ,!n1 ) ! intimation t a "q involv+ num]ical calculation w\ld be set on ! subject1 9 ! ensu+ ,monday morn+ exam9ation pap]1 ! lecture g5]ally clos$1 or 0 r\nd$ (f ) "s fur!r obs]vations on angul> 7or1 z ,?omson always pref]r$ to call x1 mom5t (7 mom5tum4 ,long aft] 9 ! c\rse ( a debate 9 ! ,h\se ( ,lords on a proposal to make ! use ( ! metric sy/em ( weights & measures compulsory1 ,"l ,kelv9 told _! lord%ips h[ he _h weigh$ out ! p[d] to *>ge ?is rifle1 &1 mi/ak+ ! weights1 _h load$ ! rifle ) an am\nt ( p[d] :i* w\ld h be5 almo/ c]ta9 to bur/ ! piece1 b _h happily paus$ be=e fir+ x (f4 ,he (t5 int]rupt$ ! c\rse ( a lecture ) a d5unciation ( ! ,briti% no-sy/em ( weights & measures--insane1 bra9-wa/+1 dang]\s1 7 among ! milde/ epi!ts he appli$ to x1 & he w\ld deeply sympa?ise ) ! /ud5t ^: recollection ( avoirdupois weight1 troy weight1 apo!c>ies' weight1 etc41 0 some:at hazy4 ,! dang] ( ! sy/em consi/$ ma9ly 9 ! fact t ! apo!c>ies' dram is #fj gra9s1 :ile ! avoirdupois dram is #bg gra9s4 ,?us s _m drams ( p[d] requir$ to *>ge a rifle is a v mu* l>g] quantity :5 reckon$ 9 apo!c>ies' drams ?an :5 reckon$ 9 avoirdupois4 ,z a rule he left ! load+ ( ! rifle1 l all ! o!r lecture-room exp]im5ts1 to 8 assi/ants4 ,ano!r exp]im5t :i* caus$ a great s5sation 0 t kn[n z ! dewdrop6 ,a funnel ( brass1 compos$ ( a tube ab\t #cj in*es long & an in* wide1 & a conical m\? ab\t t5 in*es wide1 _h a piece ( /\t %eet ,india-rubb] /ret*$1 z tightly z x c\ld be by h&1 across its m\?1 & made wat]-tight by a s]v+ ( tw9e & cem5t r\nd ! edge4 ,a wire sold]$ r\nd ! outside ( ! lip gave a good hold = ?is s]v+ & made all p]fectly secure4 ,on ! plane surface ( ! %eet geometrical figures 7 drawn 9 ink1 s t _! di/ortion c\ld be aft]w>ds /udi$4 ,! funnel 0 !n hung by a /rong support 9 an inv]t$ position beh9d ! table1 & wat] p\r$ g5tly into x f a rubb] supply pipe connect$ ) ! wat]-ma94 ,z ! wat] 0 all[$ to accumulate--v sl[ly at fir/--! %eet ( rubb] gradually /ret*$ & bulg$ out1 at fir/ to a flat l5s-%ape1 & gradually m & m1 till an imm5se wat]-drop _h be5 =m$1 #ae or #ah in*es 9 horizontal diamet]1 & ( /ill great] v]tical dim5sions4 ,! rubb] film 0 n[1 at ! place ( greate/ t5sion1 q ?9 & transp>5t1 & its giv+ way 0 anticipat$ by ! /ud5ts ) ke5 enjoym5t4 ,a l>ge tub _h be5 plac$ bel[ to receive ! wat]1 b ! deluge always ext5d$ ov] ! :ole floor space beh9d ! table1 & 0 greet$ ) raptur\s applause4 ,be=e ! drop bur/1 & :ile x 0 =m+1 ,?omson disc\rs$ on surface t5sion1 emphasis+ ! ess5tial diff]5ce betwe5 ! t5sion 9 ! rubb]-film & ! surface-film ( a dewdrop1 & po9t+ out h[ ! geometrical figures _h *ang$ 9 %ape4 ,!n he w\ld poke x ) ! po9t] he held 9 8 h&1 &1 turn+ to ! class1 z ! mass quiv]$1 rem>k1 ,! trembl+ ( ! dewdrop1 g5tlem56 ,vibrations ( ela/ic solids 7 illu/rat$ 9 v>i\s ways1 frequ5tly by means ( a symmetrical %ape ( calves'-foot jelly1 at ! top ( :i* a col\r$ m>ble _h be5 imb$d$ z a molecule1 ! motions ( :i* c\ld be foll[$4 ,& !n he w\ld disc\rse on ! ,poisson-,navi] !ory ( isotropic solids1 & ! impossibility ( ! fix$ relation :i* t !ory impos$ betwe5 ! modulus ( rigidity & ! modulus ( compression2 & ref] ) approval to ! s]ies ( examples ( p]fectly uni=m1 homog5e\s1 isotropic solids1 :i* ,/okes _h %[n c\ld be obta9$ by mak+ jellies ( diff]5t degrees ( /iffness4 ,ano!r example1 frequ5tly adduc$ z indicat+ ! falsity ( ! !ory1 0 ! entirely diff]5t behavi\r ( blocks ( ,india-rubb] & cork1 "u compression appli$ by a ,bramah press4 ,! cork dim9i%$ 9 ?ickness )\t spread+ out lat]ally2 ! rubb]1 be+ v little compressible1 bulg$ out all r\nd z its ?ickness 0 dim9i%$4 ,! lectures on ac\/ics1 :i* came late 9 ! c\rse1 7 also exce$+ly popul>4 ,two ,fr5* horns1 ) all _! crooks & accessories1 7 display$1 & sometimes1 to ! great delight ( ! class1 ,?omson w\ld essay to %[ h[ ! pit* ( a note c\ld be modifi$ by means ( ! keys1 or by ! h& ins]t$ 9 ! bell4 ,! det]m9ation by ! sir5 ( ! pit* ( ! notes ( tun+-=ks excit$ by a 'cello b[1 & ! tun+ ( a major ?ird by s\nd+ at ! same "t ! p]fect fif? ( ! l[] note1 7 (t5 exhibit$1 & comm5t$ on ) acute rem>ks1 ( :i* x is a pity no /atem5t 0 ev] publi%$4#be ,! clos+ lecture ( ! ord9>y c\rse 0 usually on light1 & ! subject :i* 0 g5]ally ! la/ to be tak5 up--= z ! days l5g!n$ 9 spr+1 x 0 possible sometimes to obta9 sunlight = ! exp]im5ts--0 (t5 relegat$ to ! la/ day or two ( ! session4 ,s aft] an h\r's lecture ,?omson w\ld say1 ,z ?is is ! la/ day ( ! session1 ,i w g on = a little long]1 aft] ^? :o h to leave h gone to _! classes4 ,!n he w\ld resume aft] t5 o'clock1 & g on to elev51 :5 ano!r opportunity w\ld be giv5 = /ud5ts to leave1 & ! lecture w\ld be aga9 resum$4 ,mess5g]s w\ld be s5t f 8 h\se1 :]e he 0 want$ = bus9ess ( diff]5t sorts1 to f9d out :at _h become ( him1 & ! answ] br\ght w\ld be1 h\r aft] h\r1 ,he is /ill lectur+4 ,at la/ he w\ld conclude ab\t "o o'clock1 & g5tly ?ank ! small & devot$ b& :o _h rema9$ to ! end1 = _! k9d & prolong$ att5tion4 ,9 ! c\rse ( 8 lectures ,?omson cont9ually call$ on 8 assi/ants = data ( all k9ds4 ,9 ! busie/ "t ( 8 life--! fifte5 ye>s f #ahgj to #ahhe--;he tru/$ to 8 assi/ants = ! prep>ation ( 8 class illu/rations1 & x 0 sometimes a little difficult to anticipate 8 wi%es1 = )\t c>eful rehe>sal x is almo/ impossible to make sure t 9 an exp]im5tal lecture ev]y?+ w g )\t a hit*4 ,! digressions1 g5]ally mo/ int]e/+ & in/ructive1 9 :i* he frequ5tly indulg$1 almo/ always r5d]$ x necess>y to br+ "s exp]im5t be=e ! class :i* _h n be5 anticipat$1 & all k9ds ( ?+s 7 kept 9 read9ess1 le/ !y %\ld be want$ sudd5ly4 ,x has (t5 be5 ass]t$ t ,?omson appeal$ to 8 assi/ant = in=mation conta9$ 9 ! multiplication-table1 & c\ld n p]=m ! ord9>y op]ations ( ari?metic4 ,8 active m9d1 work+ on ahead ( ! /atem5ts he 0 mak+ at ! mom5t1 (t5 c\ld n be br\ght back to ! consid]ation ( ! value ( #i times #f1 & ! l2 b x 0 q untrue t he 0 incapable ( mak+ calculations4 ,8 memory 0 good1 & ?\gh he nev] c\ld be1 = example1 sure :e!r ! aque\s hum\r 0 be=e or beh9d ! cry/all9e 9 ! eye1 he 0 g5]ally able at once to tell :5 a mis/atem5t _h be5 made z to any num]ical "q reg>d+ ! subject "u discussion4 ,9 ! high] ma!matical class1 to :i* he lectur$ on ,w$nesdays1 at noon1 ,?omson 0 exce$+ly int]e/+4 ,!re he seem$ to "w at ! subject z he lectur$2 new po9ts to be inve/igat$ cont9ually pres5t$ !mselves1 & ! /ud5ts 7 enc\rag$ to "w !m out 9 ! week-long int]vals betwe5 8 lectures4 ,always ! physical int]pretation ( results 0 aim$ at1 ev5 int]m$iate /eps 7 discuss$4 ,?us ! mean+ ( ! ma!matical processes 0 ev] kept 9 view1 & ! m5 :o c\ld foll[ 7 made to ?9k :ile !y work$1 & to reg>d ! ma!matical analysis z m]ely an aid1 n an end 9 itself4 ,a little exp5diture ( *alk is a sav+ ( bra9s2 ! art ( read+ ma!matical books is judici\s skipp+1 7 rem>ks he sometimes made1 & illu/rate 8 view ( ! relative importance ( ma!matical "w :5 he reg>d$ x z ! h&maid ( ! physical ?9k]4 ,yet he valu$ ma!matics = its own sake1 & 0 ke5ly alive to elegance ( =m & me?od1 z read]s ( su* great ma!matical discussions z ! ,app5dix on ,sph]ical ,h>monics1 9 ,?omson & ,tait1 w obs]ve4 ,he spoke ) unqualifi$ admiration ( ! "w ( ,gre5 & ,/okes1 ( ,cau*y's great memoir on ,waves1 & ( ,hamilton's pap]s on ,dynamics4 ,b no =m ( vector-analysis1 nei!r ! ,quat]nions ( ,hamilton nor ! ,vectors ( ,will>d ,gibbs & ,heaviside1 appeal$ to him1 & ! example ( 8 fri5d & co-work]1 ,tait1 _h no effect 9 modify+ 8 adv]se v]dict reg>d+ ?is dep>tm5t ( ma!matics1 a v]dict :i* 9 lat] ye>s became only m emphatic4 ,"o session he began ! fir/ lecture ( ! high] class by writ+ dxdt 9 ! middle ( ! blackbo>d1 & dem&+ ( ea* ( ! t5 or a doz5 /ud5ts pres5t1 "s ( !m di/+ui%$ graduates1 :at x meant6 ,"o /ud5t describ$ x z ! limit+ value ( ! ratio ( ! increm5t ( ! dep5d5t v>iable x to ! increm5t ( ! indep5d5t v>iable t1 :5 ! latt] increm5t is made indef9itely small4 ,he retort$1 ,t's :at ,todhunt] w\ld say6 ,! o!rs gave v>i\s slightly diff]5t v]sions ( ! same def9ition4 ,at la/ he impati5tly rem>k$1 ,does nobody "k t dxdt means velocity8 ,"h ! physical idea z a :ole 0 be=e 8 m9d2 & he did n reflect t if t d5ot$ "t & x di/ance 9 any direction1 ! explanation giv5 by ! /ud5t did describe velocity ) fair accuracy4 ,an emb>rass+ peculi>ity ( 8 ma!matical discussions 0 8 t5d5cy1 :5 a difficulty ( symbolisation occurr$1 to completely *ange ! notation4 ,also he 0 n uni=mly accurate 9 analytical "w2 b he m ?an made up = ?is by ! faculty he _h ( devis+ a te/ ( ! accuracy ( ! result & ( div9+ ! error :i* _h crept 91 if ! te/ 0 n satisfi$4 ,! subjects he treat$ 7 always su* great bran*es ( ma!matics z ! !ory ( ! tides--he discuss$ ! tidal ph5om5a ( ! ,engli% ,*annel 9 "o c\rse--! g5]al !ory ( vibrations1 ,f\ri] analysis1 ! !ory ( waves 9 wat]1 etc41 etc4 ,a v good idea ( ! mann] & matt] ( 8 ma!matical prelections c be obta9$ f a p]usal ( ! ,baltimore ,lectures4 ,9 ! physical laboratory he 0 bo? inspir+ & di/ract+4 ,he cont9ually ?\ght ( new ?+s to be tri$1 & int]rupt$ ! c\rse ( ! "w ) int]polat$ exp]im5ts :i* (t5 robb$ ! prec$+ sequ5ce ( op]ations ( _! f9al result4 ,8 ideas 7 on ! :ole bett] work$ out by a really good corps ( /ud5ts :5 he 0 f home1 & c\ld only communicate by lett] 8 views on ! "w set =? 9 ! daily reports :i* 7 =w>d$ to him4 ,he insi/$ ) emphasis t a /ud5t :o f\nd t a quadrant electromet] w\ld n "w well %\ld take x to pieces to asc]ta9 :at 0 ! matt]4 ,?is ( c\rse g5]ally result$ 9 ! return ( ! in/rum5t to ,:ite's %op to be put toge!r aga9 & adju/$4 ,b1 z he said1 !re 0 a cause = e tr\ble ( t k9d1 & ! great ?+ 0 to f9d out at once :at x 04 ,?omson's conc5tration on ! "w 9 h&1 & 8 p[] ( simply tak+ possession ( m51 ev5 m]e spectators1 & conv]t+ !m into assi/ants1 0 (t5 %[n 9 ! laboratory4 ,sev]al m5 :o h s9ce become em95t 7 among ! assi/ants enroll$ f ! laboratory /ud5ts4 ,pr(essor ,w4 ,e4 ,ayrton &1 lat]1 ,pr(essor ,john ,p]ry1 7 /ud5ts at ,glasg[ = a "t1 & r5d]$ ! mo/ able & will+ help 9 ! rese>*es :i* 7 !n proce$+4 ,?is p[] 01 no d\bt1 ! secret ( 8 success 9 ga!r+ r\nd him an en?usia/ic corps ( laboratory work]s 9 ! e>ly ye>s ( 8 pr(essor%ip1 & x 0 %[n also by ! ease ) :i* he annex$ ! ,black/one exam9ation-room &1 lat]1 v>i\s spaces 9 ! new ,univ]sity build+s4 ,!re1 aft] a "t1 ! ,natural ,philosophy rooms 7 f\nd by ! s5atus to include n only ! orig9al class-room1 laboratory1 etc41 b also all ! sp>e attics & corridors 9 ! neighb\rhood1 & ev5 ! ,univ]sity t[] itself6 ,"o ( 8 colleagues1 :o v5]at$ him highly1 rem>k$ rec5tly1 ,he _h a great faculty = annexation6 ,! incid5t ref]r$ to occurr$ :ile he 0 prep>+ ! article on ,heat = ! n9? edition ( ! ,encyclopdia ,britannica4 ,x seem$ at fir/ a pity t ,?omson %\ld und]take to write su* articles2 b 9 ! c\rse ( _! prep>ation he came ^u s _m po9ts on :i* exp]im5tal in=mation 0 want+1 & in/itut$ s _m rese>*es to answ] 8 que/ions1 t ! essays took v mu* ! "* ( orig9al pap]s4 ,9 ! article on ,heat 7he also wrote ,ela/icity71 w be f\nd a long acc\nt ( ,/eam ,!rmometry1 t is1 ( !rmomet]s 9 :i* ! indicat+ sub/ance 0 to be ! saturat$ vap\rs ( diff]5t sub/ances1 wat]1 sulphur\s acid1 etc41 etc41 = he did n limit ! t]m /eam to wat]-vap\r4 ,= "s "t e "o 9 ! laboratory 0 employ$ 9 mak+ sulphur\s acid1 by heat+ copp] 9 sulphuric acid 9 ! usual way1 & cond5s+ ! gas 9 tubes imm]s$ 9 freez+ mixtures2 & ! atmosph]e ( ! room 0 ( a sort :i*1 h[ev] noxi\s to g]ms ( diff]5t k9ds1 x 0 a little difficult to brea!4 ,"o morn+1 :5 all 7 ?us occupi$1 an em95t *emi/1 :o _h j come home f ! s\? = a vacation1 call$ to pay 8 respects4 ,aft] a ^w or two ( inquiry z to h[ 8 "y fri5d 0 prosp]+ 9 8 new po/1 ,?omson said1 ,we are all v busy brew+ liquid sulphur\s acid1 = use 9 sulphur\s acid /eam !rmomet]s2 we want a l>ge quantity ( ! liquid2 w\ld y m9d help+ u8 ,s1 desir+ an assi/ant to f9d a flask & mat]ials1 he enroll$ ?is new & excell5t recruit on ! spot2 & :at 0 int5d$ to be a m]e call1 0 prolong$ into a long day ( ungrudg+ "w at an elem5t>y *emical ex]cise6 ,,*apt] ,,xvii ,,practical ,,activities--,,hon\rs ,,& ,,di/9ctions--,,la/ ,,illness ,,& ,,dea? ,x rema9s to say some?+ ( ,"l ,kelv9's public & practical activities4 ,all ov] ! _w he came ultimately to be recognis$ z ! greate/ liv+ sci5tific au?ority 9 almo/ all bran*es ( physics4 ,e exi/+ le>n$ society s\ght to make him a ,fell[1 honor>y degrees 7 %[]$ on him f all qu>t]s4 ,a li/ ( "s ( ! mo/ important ( ^! di/9ctions is giv5 9 ! ,royal ,society ,ye>-,book = #aijg2 x is d\btful if a complete li/ c\ld be compil$4 ,he 0 aw>d$ ! ,kei? ,m$al & ! ,victoria ,jubilee ,m$al by ! ,royal ,society ( ,ed9burgh1 & receiv$ 9 succession ! ,copley & ,royal ,m$als ( ! ,royal ,society ( ,london1 ( :i* he 0 elect$ a ,fell[ 9 #ahea1 & 0 ,presid5t f #ahij to #ahie4 ,= sev]al p]iods ( ye>s he 0 ,presid5t ( ! ,royal ,society ( ,ed9burgh1 to :i* he communicat$ 8 pap]s on heat1 dissipation ( en]gy1 vortex motion1 & _m o!r memoirs4 ,he 0 ,presid5t ( ! ,briti% ,association at ! ,ed9burgh meet+ 9 #ahga1 :5 he deliv]$ a presid5tial address1 notewor?y 9 _m respects1 b *iefly rem>kable 9 ! popul> m9d on acc\nt ( 8 sugge/ion t life 0 convey$ to ! e>? by a se$1 a g]m enclos$ 9 a crevice ( a meteorite4 ,?is 0 und]/ood at ! "t by _m p z an attempt to expla9 ! orig9 ( life itself1 in/ead ( :at x 0 int5d$ to be1 an explanation ( ! beg9n+ ( ! exi/5ce ( liv+ ?+s on a planet :i* 0 orig9ally1 on ! completion ( its =mation by ! cond5sation ( nebul> matt]1 r$ hot ev5 at its surface4 ,on sev]al occasions he 0 presid5t ( ,section ,a1 & he 0 con/ant 9 att5dance at ! ,association meet+s1 & an eag] li/5] & p>ticipator 9 ! discussions & debates4 ,8 sci5tific curiosity 0 nev] at re/1 & he de>ly lik$ to meet & conv]se ) sci5tific work]s4 ,lady ,?omson1 :o _h be5 long an invalid1 di$ 9 #ahgj1 & 9 #ahgd ,sir ,william ,?omson 0 m>ri$ to ,miss ,frances ,anna ,bl&y 7daught] ( ,mr4 ,*>les ,r4 ,bl&y ( ,madeira7 :o survives him z ,lady ,kelv94 ,to h] t5d] solicitude he ow$ mu* ( 8 con/ant & long-cont9u$ activity 9 all k9ds ( "w4 ,%e accompani$ him on all public occasions1 & he reli$ greatly on h] helpfulness & ev] wat*ful c>e4 ,9 #ahib ,sir ,william ,?omson1 :ile ,presid5t ( ! ,royal ,society1 0 rais$ to ! ,pe]age1 ) ! title ( ,b>on ,kelv9 ( ,ne!rhall1 ,l>gs2 & m lately he 0 creat$ a memb] ( ! ,ord] ( ,m]it & a ,g4,c4,v4,o4 ,8 =eign di/9ctions 7 v num]\s4 ,he 0 a ,knight ( ! ,ord] ,p\r le ,mrite ( ,prussia1 a ,=eign ,associate ( ! ,in/itute ( ,france1 & a ,gr& ,(fic] ( ! ,legion ( ,hon\r4 ,b no public hon\r or m>k ( royal fav\r c\ld raise him 9 ! e/imation ( all :o "k any?+ ( sci5ce or ( ! lab\rs ( ! sci5tific m5 to :om we owe ! necessities & luxuries ( our pres5t civilisation4 ,9 #ahif ! ,city & ,univ]sity ( ,glasg[ celebrat$ ! jubilee ( 8 ,pr(essor%ip ( ,natural ,philosophy4 ,! rejoic+s on t occasion w nev] be =gott5 by ^? ^: privilege x 0 to take "p 9 !m4 ,delegates came f e c\ntry 9 ! _w1 & k+s & pr9ces1 univ]sities & le>n$ societies1 colleges & s*ola/ic in/itutions ( e k9d1 vi$ ) ea* o!r 9 do+ hon\r to ! vet]an :o _h f\ght = tru? & light = s _m ye>s1 & won s _m victories4 ,a memorial volume ( ! proce$+s 0 publi%$1 includ+ a review ( ,"l ,kelv9's "w by ! late ,pr(essor ,fitz,gerald1 & a full report appe>$ 9 ,nature & o!r j\rnals at ! "t1 s t x is unnecess>y to give p>ticul>s "h4 ,& inde$ x is impossible by any v]bal description to convey an idea ( ! en?usiasm ) :i* ! sci5tific _w acclaim$ its lead]1 & ( ! dignity & /ate ( ! c]emonies4 ,9 #ahii1 at ! age ( sev5ty-five1 ,"l ,kelv9 resign$ ! ,*air ( ,natural ,philosophy1 & retir$1 n to re/1 b to inve/igate m vigor\sly ?an ev] ! prop]ties ( matt]4 ,"o rem>kable fruit ( 8 leisure we h 9 8 great book1 ! ,baltimore ,lectures1 9 :i* !ories ( light are discuss$ ) a p[] :i* excites ! rev]5ce ( all engag$ 9 ! new rese>*es & :i* rec5t discov]ies h call$ into exi/5ce4 ,& x is n too mu* to say t ! means ( discuss+ & ext5d+ ^! discov]ies are 9 great measure due to ,"l ,kelv94 ,dur+ ! ye> #aijg ,"l ,kelv9 p]=m$ _m ,univ]sity duties & seem$ to be 9 unusually good heal?4 ,he presid$ z ,*ancellor at ! in/allation ( ,mr4 ,asqui? z ,"l ,rector on ,janu>y #aa1 & 9 ! same capacity att5d$ a few days lat] ! fun]al ( ,pr9cipal ,/ory1 ! ,vice-,*ancellor1 :o di$ on ,janu>y #ac4 ,on ,april #bc he presid$ at ! long & ardu\s c]emonies ( honor>y graduation1 & ! public op5+ ( ! new ,natural ,philosophy ,in/itute & ! new ,m$ical ,build+s1 by ! ,pr9ce ( ,wales4 ,z ,*ancellor he conf]r$ ! degree ( ,doctor ( ,laws on ! ,pr9ce & ,pr9cess1 & took ! *air at ! lun*eon :i* foll[$ ! proce$+s1 :5 he propos$ 9 a %ort & graceful spee* ! heal? ( ! ,pr9cess4 ,he 0 able to take "p also 9 v>i\s political & social meet+s1 & to give att5tion to ! "w 9 progress at ! factories ( 8 firm 9 ,cambridge ,/reet4 ,lady ,kelv9 & he left ,ne!rhall1 ,l>gs1 = ,aix les ,ba9s1 at ! end ( ,july1 b visit$ ! ,briti% ,association at ,leice/] 9 pass+4 ,!re he he>d ! presid5tial address ( 8 old fri5d1 ,sir ,david ,gill1 to :om he mov$ a vote ( ?anks 9 8 usual vivaci\s mann]4 ,"l ,kelv9 _h be5 accu/om$ = a good _m ye>s to sp5d a mon? or six weeks 9 summ] or e>ly autumn at ! fam\s ,fr5* wat]+-place1 f :i* he seem$ always to receive mu* b5efit4 ,= a long "t he _h suff]$ f an int]mitt5t & pa9ful =m ( facial neuralgia1 :i*1 except dur+ its attacks1 :i* came & pass$ sudd5ly1 did n incapacitate him f "w4 ,) ! exception ( a r s]i\s illness 9 #aijf1 ?is 0 ! only ailm5t f :i* he _h suff]$ = _m ye>s1 & 8 g5]al heal? 0 o!rwise uni=mly good4 ,"l & ,lady ,kelv9 return$ to ,ne!rhall on ,septemb] #ad1 ) ! int5tion ( go+ 9 a day or two to ,belfa/1 to op5 ! new sci5tific build+s ( ,que5's ,college4 ,b1 un=tunately1 on ! day ( _! arrival ,lady ,kelv9 became v s]i\sly ill1 & ! visit to ,irel& _h to be ab&on$4 ,8 address 01 h[ev]1 read by 8 nephew1 ,james ,?omson1 son ( 8 eld] bro!r1 & 0 a tribute to ! city ( 8 bir?1 & ! memory ( 8 fa!r4 ,! illness ( ,lady ,kelv9 caus$ mu* anxiety = _m weeks1 & ?is1 & p]haps "s incauti\s exposure1 l$ to ! impairm5t ( ,"l ,kelv9's heal?4 ,a *ill caught on ,novemb] #bc caus$ him to be conf9$ to b$2 & ?\gh he manag$ = a week or two /ill to d "s "w on a pap] ) :i* he _h be5 occupi$ = a consid]able "t1 he became worse1 & gradually sank1 until 8 dea? at a qu>t]-pa/ t5 o'clock on ! ev5+ ( ,decemb] #ah4 ,! ke5 sorr[ :i* 0 univ]sally felt = ,"l ,kelv9's dea? 0 manife/$ by all classes ( ! community4 ,9 ,glasg[ e "o m\rn$ z = ! greate/ ( ! l&1 & ! te/imony to ! affection 9 :i* he 0 held1 & ! rev]5ce = 8 "* & sci5tific a*ievem5ts1 0 extraord9>y4 ,& ?is feel+ 0 univ]sal2 f all p>ts ( ! _w p\r$ 9 telegrams ( respectful sympa?y ) ,lady ,kelv9 & ) ! ,univ]sity ( ,glasg[ 9 _! b]eavem5t4 ,! view 0 imm$iately & /rongly express$1 bo? privately & by ! press1 t ! mo/ illu/ri\s natural philosoph] s9ce ,newton %\ld re/ beside ! great f\nd] ( physical sci5ce 9 ,we/m9/] ,abbey1 & a requisition 0 imm$iately prep>$ & =w>d$ by ! ,royal ,society ( ,london to ! ,dean ( ,we/m9/]4 ,! wi% ( ! :ole sci5tific _w 0 at once acc$$ to1 & on ,decemb] #bc1 at noon1 ! int]m5t took place1 ) a /ate & yet a simplicity :i* w nev] be =gott5 by ^? :o 7 pres5t4 ,ne>ly all ! sci5tific notabilities ( ! c\ntry 7 pres5t1 & ! c(f91 prec$$ by ! *ori/]s & ! cl]gy1 :ile ! hymn1 ,brief life is "h our portion1 0 sung1 0 foll[$ r\nd ! cloi/]$ aisles f ,/4 ,fai?'s *apel to ! *oir1 by ! relatives1 repres5tatives ( ,8 ,maje/y ! ,k+ & ! ,pr9ce ( ,wales1 by ! ,royal ,society1 by delegates f ! ,in/itute ( ,france1 repres5tatives ( ! ,univ]sities ( ,cambridge1 ,ox=d1 ,glasg[1 & o!r univ]sities1 ( ! ,royal ,society ( ,ed9burgh 7( :i* ,"l ,kelv9 0 presid5t :5 he di$71 & ( mo/ ( ! le>n$ societies ( ! k+dom4 ,!n1 aft] a %ort s]vice1 ! body 0 foll[$ to ! grave 9 ! cloi/]s by ! same company ( m\rn]s1 & to ! solemn words ( ! ,burial ,s]vice 0 laid close by :]e re/s all t 0 mortal ( ,isaac ,newton4 ,!re he sleeps well :o toil$ dur+ a long life = ! cause ( natural k1 & s]v$ nobly1 z a h]o ( peace1 8 c\ntry & ! _w4 ,,conclusion ,! imp]fect sket* ( ,"l ,kelv9's sci5tific life & "w :i* ?is book conta9s c only give a fa9t notion ( ! great a*ievem5ts ( ! long life t has n[ end$4 ,beyond ! rese>*es :i* he c>ri$ out & ! discov]ies he made1 !re is ! inspiration :i* 8 "w & example gave to o!rs4 ,inspir$ himself by ,lagrange1 ,laplace1 ,ampre1 & ,f\ri]1 & l$ to exp]im5tal rese>* by ! necessity = answ]s to ! que/ions :i* 8 ma!matical expression ( ! discov]ies ( ! tw5ty-five ye>s :i* prec$$ ! e/abli%m5t ( 8 laboratory _h sugge/$--! !ories ( electricity & magnetism1 ( heat1 ( ela/icity1 8 discov]ies 9 g5]al dynamics & 9 fluid motion1 ! publication ( ,?omson & ,tait1 all made him ! inspir] ( o!rs2 & !re 0 no "o1 h[ev] em95t1 :o 0 n pr\d to ackn[l$ge 8 obligations to 8 g5ius4 ,cl]k ,maxwell1 be=e he wrote ! mo/ orig9al treatise on electricity t has ev] appe>$1 gave himself to ! /udy ( ,f>aday's ,exp]im5tal ,rese>*es & to ! pap]s ( ,?omson4 ,& if "s1 l ,fitz,gerald & o!rs1 h regrett$ t ! electromagnetic !ory ( light to :i* ,maxwell 0 l$ by ,f>aday1 &1 inde$1 by ,?omson himself1 did n meet ) a m sympa!tic reception at 8 h&s1 !y h n be5 unm9dful ( ! s\rce f :i* mu* ( _! illum9ation has come4 ,he has f\nd$ a s*ool ( ?\ght 9 ma!matical physics1 ( m5 9 ^: m9ds ! symbol is always ! s]vant ( ! ideas1 ^: motto is int]pretation by dynamical processes & models z f> z t is possible1 :o %irk no ma!matical difficulties :5 !y h to be enc\nt]$1 b are nev] l$ away f ! /raight road to ! goal :i* !y seek to rea*--! sy/ematic & cle> =mulation ( ! c\rse ( physical action4 ,& 9 ,"l ,kelv9's m9d !re 0 bl5d$ ) a cle> physical in/9ct :i* put aside all t 0 extrane\s & uness5tial to ! ma9 issue an extraord9>y p[] ( conc5tration on ! problem 9 h&1 & a det]m9ation t 0 nev] daunt$ by failure1 :i* cons5t$ to po/ponem5t b nev] to rel9qui%m5t1 & :i* l$ (t5 aft] long int]vals ( "t to success 9 ! end4 ,he believ$ t light w\ld come at la/ on ! mo/ baffl+ ( problems1 if only x 7 look$ at f e po9t ( view & its conditions 7 completely =mulat$2 b he c\ld put :at 0 = ! "t impossible aside1 & devote himself to ! imm$iately possible & realisable4 ,& z (t5 happ5s ) e ?9k]1 8 m9d1 releas$ f ! task1 return$ to x ( itself1 & :at be=e appe>$ %r\d$ 9 imp5etrable mi/ /ood out sudd5ly %>p & di/9ct l a m\nta9-top be=e a climb] :o has at la/ ris5 above ! cl\ds4 ,) ! great ma!matical p[] & sure in/9ct :i* l$ him to success 9 physical rese>* 0 comb9$ a ke5 p]ception ( ! importance ( practical applications4 ,sometimes ! practical "q sugge/$ ! !oretical & exp]im5tal rese>*1 z :5 ! ne$s ( subm>9e telegraphy l$ to ! discussion ( ! spe$ ( signall+ & ! evolution ( ! reflect+ galvanomet] & ! siphon record]4 ,on ! o!r h&1 ! ma!matical !ory ( electricity & magnetism _h l$ to quantitative measurem5t & absolute units at an e>li] "t1 :5 ! ne$ = ^! 0 beg9n+ to be felt cle>ly by sci5tific work]s & dimly by ^? f>-sight$ practical m5 :o dream$--= a dream x 0 ?\ght at ! "t--( l9k+ ! ,old ,_w ) ! ,new by a subm>9e cable4 ,b ! quantitative /udy ( electricity 9 ! laboratory ?rew light on economic conditions1 & ! mass ( data already obta9$1 ma9ly z a m]e matt] ( exp]im5tal inve/igation ( ! prop]ties ( matt]1 became at once a valuable asset ( ! race ( subm>9e cable eng9e]s :i* sudd5ly sprang into exi/5ce4 ,& s x has be5 ) ! m rec5t applications ( electricity4 ,! induction ( curr5ts discov]$ by ,f>aday c\ld n become ( practical importance until its laws _h be5 quantitatively discuss$1 a mu* long] process ?an t ( discov]y2 & we h se5 h[ ! ,briti% ,association ,committee1 l$ by ,?omson & ,maxwell1 br\ght ! ideas & quantities ( ?is new bran* ( sci5ce into num]ical relation ) ! units ( already exi/+ practical ent]prise4 ,! electrical measur+ in/rum5ts--fir/ ! electromet]s1 & m rec5tly ! electric curr5t balances & o!r beautiful in/rum5ts = ! dynamo-room & ! work%op--:i* ,"l ,kelv9 inv5t$ h br\ght ! precision ( ! laboratory into ! ev]yday duties ( ! second>y batt]y att5dant & ! wireman4 ,& z to me?ods ( measurem5t1 ^? :o rememb] ! haz9ess ( ev5 telegraph eng9e]s z to ! measurem5t ( ! effici5cy ( electrical curr5ts & electromotive =ces 9 ! circuits ( lamps & dynamos1 9 ! e>ly days ( electric light+1 "k h[ mu* ! _w is indebt$ to ,?omson4#bf ,he x 0 :o %[$ at fir/ h[ cables 7 to be te/$1 z well z h[ !y 7 to be work$2 x 0 8 task1 aga91 to %[ h[ in/rum5ts 7 to be calibrat$ = practical measurem5t ( curr5t & en]gy suppli$ by ! e>ly contractors to consum]s4 ,he _h 9 ! quiet ( 8 laboratory long be=e elaborat$ me?ods ( comp>+ resi/ances1 & giv5 ! ,:eat/one balance its second>y conductors = ! comp>ison ( l[ resi/ances2 he n[ %[$ h[ ! same pr9ciples c\ld be appli$ to measure ! effici5cies ( dynamos & to make up ! acc\nt ( *>ge & dis*>ge = a second>y batt]y4 ,& if ! siphon-record] & ! m>9]s' compass & ! s\nd+ ma*9e prov$ pecuni>ily pr(itable1 ! rew>d 0 t ( ! inv5tor1 :o has an indefeasible "r to ! fruit ( 8 bra9 & 8 h&4 ,b ,"l ,kelv9's activity 0 n conf9$ m]ely to ^? practical ?+s :i* h1 to use ! ord9>y phrase1 money 9 !m2 he gave 8 "t & en]gies freely to ! p]fect+ ( ! h>monic analysis ( ! tides1 und]took aga91 = a ,committee ( ! ,briti% ,association1 ! inve/igation ( ! tides = diff]5t p>ts ( ! _w1 sup]9t5d$ ! analysis ( tidal records1 & inv5t$ tide-pr$ict+ ma*9es & improv$ tide-gauges4 ,"l ,kelv9's "w 9 ! !ory ( heat & 9 ! sci5ce ( en]gy g5]ally w\ld h giv5 him a title to immortality ev5 if x _h /ood alone2 & !re c be no d\bt1 ev5 9 ! m9d ( ! mo/ det]m9$ practical contemn] ( ! ,c>not cycle1 ( ! enorm\s importance ( ^! a*ievem5ts4 ,"h he 0 a pione]1 & yet 8 pap]s1 !oretical & yet practical1 writt5 "o aft] ano!r 9 p5cil & despat*$1 r\gh z !y 71 to be pr9t$ by ! ,royal ,society ( ,ed9burgh1 =m1 z !y are collect$ 9 volume i ( 8 ,ma!matical & ,physical ,pap]s1 9 "s respects ! be/ treatise on !rmodynamics at ! pres5t "t6 ,!re are treatises writt5 f a m g5]al /&po9t1 :i* deal ) complex problems ( *emical & physical *ange ( means ( !rmodynamic pot5tials1 & processes :i* are n to be f\nd set =? 9 ?is volume ( pap]s2 b ev5 ^! are to a great ext5t an outcome ( 8 ,!rmoela/ic1 ,!rmomagnetic & ,!rmoelectric ,prop]ties ( ,matt]4 ,9 hydrodynamics also ,"l ,kelv9 nev] lo/ sight ( practical applications1 ev5 :ile pursu+ ! mo/ int5sely !oretical rese>*es into ! action ( vortices or ! propagation ( waves4 ,9 8 lat] ye>s he work$ out ! !ory ( %ip-waves ) a p[] :i* has made m ?an "o skilful & successful cultivator ( ?is bran* ( sci5ce say t he 0 no m]e ma!matician1 b a man :o1 l ! prophets ( old1 c\ld div9e :at is hid f ! eyes ( ord9>y mortals4 ,( ! ultimate importance ( ^! = practical que/ions ( ! con/ruction ( %ips1 & ! economy ( fuel 9 _! propulsion1 !re c be little d\bt4 ,unhappily1 ! applications w h n[ to be made by o!rs4 ,x is int]e/+ to note t ! inve/igation ( waves 9 canals ) :i* ,"l ,kelv9 rec5tly enri*$ ! ,proce$+s ( ! ,royal ,society ( ,ed9burgh h be5 c>ri$ out by a /rik+ly +5i\s adaptation ( ! ,f\ri] solution ( ! diff]5tial equation ( ! diffusion ( heat along a b>1 or ( electricity along a sl[ly work$ cable4 ,?us1 beg9n+ ) ,f\ri] ma!matics 9 8 e>lie/ rese>*es1 he has 9 "s ( 8 la/ "w appli$ ! special expon5tial =m ( ,f\ri] solution ( ! diffusion equation to a case1 t ( wave propagation1 ess5tially diff]5t 9 physical nature1 & di/9ct 9 ma!matical signification1 f t = :i* x 0 orig9ally giv54 ,"l ,kelv9's writt5 "w consi/s ( ! ,electro/atics & ,magnetism1 ?ree volumes ( ,collect$ ,ma!matical & ,physical ,pap]s1 ?ree ( ,popul> ,lectures & ,addresses1 ! ,baltimore ,lectures1 a v consid]able numb] ( pap]s z yet uncollect$1 & ! ,natural ,philosophy4 ,b ?is1 great z x 01 repres5t$ only a relatively small "p ( 8 activities4 ,he advis$ public companies on special eng9e]+ & electrical que/ions1 s]v$ on ,royal ,commissions1 act$ z consult+ eng9e] to cable companies & o!r corporations1 0 employ$ z arbit] 9 disputes :5 sci5tific que/ions 7 involv$1 advocat$ di/9ctive signall+ = ligh?\ses & devis$ app>atus = ?is purpose1 & he 01 above all1 a great inv5tor4 ,8 pat5ts are _m & important4 ,"o ( !m 0 = a wat]-tap w>rant$ n to drip1 ano!r1 = electrical g5]at+ ma*9es1 met]s1 etc41 0 p]haps ! pat5t ( l>ge/ ext5t ev] grant$4 ,to ,"l ,kelv9's class tea*+ ref]5ce has be5 made 9 an e>li] *apt]4 ,he 0 c]ta9ly inspir+ to ! be/ /ud5ts4 ,at meet+s ( ! ,briti% ,association 8 lum9\s rem>ks 9 discussion help$ & enc\rag$ y\ng] work]s1 & 8 en?usiasm 0 infecti\s4 ,b ) ! ord9>y /ud5t :o _c receive or reta9 8 m5tal nutrim5t except by a c>efully /udi$ mode ( pres5tation1 he 0 n s successful4 ,he saw too mu* :ile he spoke2 new ideas or novel modes ( view+ old ones pres5t$ !mselves unexpect$ly1 associations cr[d$ ^u 8 m9d1 & he 0 apt to be discursive1 to ! p]plexity ( all except ^? ^: m9ds 7 endu$ also ) some?+ ( ! same k9d ( physical in/9ct or p]ception4 ,!n he 0 s busy ) _m ?+s t he did n f9d "t to pond] ov] & arrange ! matt] ( 8 elem5t>y lectures1 f ! po9t ( view ( ! pres5tm5t mo/ suitable to ! capacity ( 8 he>]s4 ,to ! sugge/ion :i* has lately be5 made1 t he %\ld n h be5 oblig$ to lecture to elem5t>y /ud5ts1 he w\ld h be5 ! fir/ to object4 ,z a matt] ( fact1 9 8 lat] ye>s he lectur$ to ! ord9>y class only twice a week1 & to ! high] class once4 ,! rema9d] ( ! lectures 7 giv5 by 8 nephew1 ,dr4 ,j4 ,t4 ,bottomley1 :o = ne>ly ?irty ye>s act$ z 8 deputy z reg>ds a great "p ( ! r\t9e "w ( ! *air4 ,x is h>dly wor? :ile to refute ! /atem5t (t5 made t ,"l ,kelv9 c\ld n p]=m ! op]ations ( simple ari?metic4 ,! tru? is1 t 9 ! class-room he 0 too eag] 9 ! anticipation ( ! results ( a calculation1 or too busy ) ?\ghts ( :at lay beyond1 to be tr\bl$ ) ! multiplication table1 & s he (t5 appeal$ to 8 assi/ants = elem5t>y in=mation :i* at ! mom5t 8 rapidly work+ m9d c\ld n be made to supply = itself4 ,to sum up1 ,"l ,kelv9's sci5tific activity _h la/$ = ne>ly sev5ty ye>s4 ,he 0 born f\r ye>s aft] ,o]/$ made 8 fam\s discov]y ( ! action ( an electric curr5t on a magnet1 & two ye>s be=e ,ampre1 f\nd+ on ?is exp]im5t1 br\ght =? ! fir/ great memoir on electromagnetism4 ,?us 8 life _h se5 ! gr[? ( mod]n electrical sci5ce f its real infancy to its n[ vigor\s y\?4 ,! discov]ies ( ,f>aday 9 electrical induction 7 giv5 to ! _w :5 ,"l ,kelv9 0 a boy1 & "o ( ! great tasks :i* he accompli%$ 0 to weave ^! discov]ies toge!r 9 a uni=m web ( ma!matical !ory4 ,?is !ory sugge/$1 z we h se51 new problems to be solv$ by exp]im5t1 :i* he attack$ ) ! aid ( 8 /ud5ts 9 ! small & meagrely equipp$ laboratory e/abli%$ sixty ye>s ago 9 ! ,old ,college 9 ! ,high ,/reet4 ,x 0 8 lot to live to see 8 pres5tations ( !ory lead to new developm5ts 9 8 own h&s & ! h&s ( o!r m5 ( g5ius--,helmholtz & ,cl]k ,maxwell1 = example--& to survive until ^! developm5ts _h l$ to practical applications ?r\gh\t our indu/ries1 & 9 all ! affairs ( pres5t-day life & "w4 ,8 true monum5t w be 8 "w & its results1 & to only a few m5 9 ! _w's hi/ory has su* a massive & maje/ic memorial be5 re>$4 ,he 0 a tireless work]4 ,9 e day ( 8 life he 0 occupi$ ) _m ?+s1 b he 0 nev] cumb]$4 ,! problems ( nature 7 ev] 9 8 m9d1 b he c\ld put !m aside 9 ! press ( affairs1 & take !m up aga9 imm$iately to pu% !m =w>d ano!r /age t[>ds solution4 ,8 gre5 book 0 at h& on 8 table or 9 8 pocket2 & :5ev] a mom5t's leisure occurr$ he _h p5cil 9 h&1 & 0 deep 9 triple integrals & applications ( ,gre5's ,!orem1 t unfail+ res\rce ( physical ma!maticians4 ,saepe /ilum v]tas quae digna legi s9t ,scripturus1 ! motto :i* ,horace recomm5ds1 0 81 & he w\ld playfully quote x1 po9t+ to ! eras]-pad 9 ! top ( 8 gold p5cil-case4 ,he eras$1 correct$1 am5d$1 & rewrote ) unceas+ dilig5ce1 to ! dismay ( 8 %or?&-writ+ secret>y4 ,! !ories & facts ( electricity & magnetism1 ! production & propagation ( waves 9 wat] or 9 ! lum9if]\s e!r1 ! /ructure & d5sity ( ! e!r itself1 ! relations ( heat & "w1 ! motions ( ! heav5ly bodies1 ! con/itution ( cry/als1 ! !ory ( music1 ! practical problems ( navigation1 ( telegraph+ "u ! sea1 & ( ! electric light+ ( cities--all ^! & m came be=e 8 m9d 9 turn1 & sometimes mo/ ( !m 9 ! c\rse ( a s+le day4 ,he c\ld turn f "o ?+ to ano!r1 & f9d m5tal re/ 9 div]sity ( m5tal occupation4 ,he w\ld lecture f n9e to t5 o'clock 9 ! morn+ to 8 ord9>y class1 ?\gh g5]ally ?is 0 by no means ! fir/ sci5tific "w ( ! day4 ,at t5 o'clock he pass$ ?r\gh 8 laboratory & spoke to 8 laboratory /ud5ts or to any "o :o might be wait+ to consult him1 answ]$ "s urg5t lett]1 or gave directions to 8 secret>y2 !n he walk$ or drove to ,:ite's work%op to imm]se himself 9 ! details ( in/rum5t con/ruction until he 0 aga9 due at ! univ]sity = lun*eon1 or to lecture to 8 high] ma!matical class on "s su* subject z ! !ory ( ! tides or ! ,f\ri] analysis4 ,z sci5tific advis] to subm>9e telegraph companies & o!r public bodies1 & m rec5tly z ,presid5t ( ! ,royal ,society ( ,london1 he made frequ5t j\rneys to ,london4 ,^! 7 arrang$ s z to involve ! m9imum exp5diture ( "t4 ,he travell$ by night :5 alone1 & c\ld d s ) com=t1 = he possess$ ! gift ( be+ able to sleep well 9 almo/ any circum/ances4 ,?us he w\ld g to ,london "o night1 sp5d a busy day 9 all k9ds ( bus9ess--sci5tific1 practical1 or political--& return ! next night to ,glasg[1 fre% & eag] = "w on 8 arrival4 ,"h may be notic$ 8 p[] ( deta*+ himself f 8 environm5t1 & ( putt+ aside ?+s :i* might well h be5 anxieties1 & ( becom+ aga9 absorb$ 9 ! problem :i* circum/ances _h made him tempor>ily ab&on4 ,g5ius has be5 said to be ! p[] ( tak+ inf9ite pa9s3 x is t inde$1 b x is also f> m4 ,g5ius means ideas1 intuition1 a faculty ( seiz+ by ?\ght ! hidd5 relations ( ?+s1 & )al ! p[] ( proce$+ /ep by /ep to _! cle> & full expression1 :e!r 9 ! language ( ma!matical analysis or 9 ! diction ( daily life4 ,su* 0 ! g5ius ( ,"l ,kelv92 x 0 l(ty & x 0 practical4 ,he und]/ood--= he _h felt--! fasc9ation ( k ap>t f its application to me*anical devices2 he did n disda9 to devote 8 great p[]s to ! s]vice ( mank9d4 ,8 objects ( daily contemplation 7 ! play ( =ces1 ! actions ( bodies 9 all _! v>i$ manife/ations1 or1 z he pref]r$ to sum up ! realm ( physics1 ! obs]vation & discussion ( prop]ties ( matt]4 ,b 8 eyes 7 ev] op5 to ! be>+ ( all t he saw or discov]$ on ! improvem5t ( indu/rial appliances1 to ! possibility ( us+ x to increase ! com=t & safety ( m51 & s to augm5t ! sum total ( human happ9ess4 ,8 /atem5t1 :i* has be5 s (t5 quot$1 t aft] fifty-five ye>s ( con/ant /udy he knew little m ( electricity & magnetism ?an he did at ! beg9n+ ( 8 c>e]1 is n to be tak5 z a confession ( failure4 ,x 01 l ,newton's fam\s decl>ation1 an indication ( 8 s5se ( ! va/ness ( ! ocean ( tru? & ! manifoldness ( ! treasures :i* /ill lie )9 its deep unfa?om$ caves4 ,l ,newton1 he _h m]ely w&]$ along ! %ore ( t great ocean1 & "h & !re s\nd$ its accessible dep?s1 :ile its inf9ite expanse lay unexplor$4 ,& also l ,newton--inde$ l all great m5--he /ood ) deep rev]5ce be=e ! great problems ( ! s\l & de/9y ( man4 ,he believ$ t ,nature1 :i* he _h s\ght all 8 life to "k & und]/&1 %[$ ev]y:]e ! h&iwork ( an inf9ite & b5efic5t intellig5ce1 & he _h fai? t 9 ! end all t appe>$ d>k & p]plex+ w\ld /& =? 9 fulness ( light4 ,,footnotes3 #a ,"l ,kelv9's address on 8 in/allation z ,*ancellor ( ! ,univ]sity ( ,glasg[1 ,novemb] #bi1 #aijd4 #b ,successor ( ,dr4 ,dick1 ! ,pr(essor ( ,natural ,philosophy :o induc$ ! ,faculty to grant a work%op to ,james ,watt :5 ! ,corporation ( ,hamm]m5 prev5t$ him f />t+ bus9ess 9 ,glasg[1 & = :om ,watt 0 repair+ ! ,newcom5 eng9e :5 he inv5t$ ! sep>ate cond5s]4 #c ,a model /eam-eng9e :i* he made 9 8 y\? 0 c>efully pres]v$ by 8 bro!r 9 ! ,natural ,philosophy ,dep>tm5t4 ,x 0 homely b accurate 9 con/ruction3 ! beam 0 ( wood1 & ! pi/on 0 an old ?ick copp] p5ny6 #d ,proce$+s on ! occasion ( ! ,pres5tation to ! ,univ]sity ( ,glasg[ ( ! ,portrait ( ,em]itus ,pr(essor ,g4 ,g4 ,ramsay4 ,novemb] #f1 #aijg4 #e ,app>5tly = a %ort "t 9 #ahda1 :5 ,dr4 ,meikleham 0 laid aside by illness4 #f ,! ,c4,u4,m4,s4 began z a ,pet]h\se society 9 #ahdc1 & aft] a fir/ conc]t1 :i* 0 foll[$ by a supp]1 & t by c]ta9 op]ations on ! *apel ro(1 ! ,ma/] w\ld only give p]mission to hold a second conc]t 9 ! ,r$ ,lion at ,cambridge1 !re be+ no room 9 ,college1 on condition t ! society call$ itself ! ,univ]sity ,musical ,society4 ,! new society 0 =m$ 9 ,may #ahdd2 ! fir/ presid5t 0 ,g4 ,e4 ,smi?1 ( ,pet]h\se1 ! second 0 ,bl[1 also ( ,pet]h\se1 a viol9 play] & 'celli/1 & ! ?ird 0 ,?omson4 ,see ,cambridge ,*ronicle1 ,july #aj1 #aijc1 & ,! ,cambridge ,review1 ,feb4 #bj1 #aijh4 #g ,x is r /range t ! n9? edition ( ! ,encyclopdia ,britannica conta9s no biography ( ,gre54 ,born 9 ! ye> #agic at ,nott+ham1 ! son ( a bak]1 he assi/$ 8 fa!r1 :o latt]ly acquir$ a mill]'s bus9ess at ! neighb\r+ village ( ,sne9ton4 ,9 #ahbi 8 fa!r di$1 & he dispos$ ( ! bus9ess 9 ord] t he might h leisure to give to ma!matics1 9 :i*1 ?\gh entirely self-taught1 he _h begun to make orig9al rese>*es4 ,8 fam\s ',essay' 0 publi%$ by subscription 9 #ahbh1 & attract$ b little att5tion4 ,9 #ahcc1 at =ty ye>s ( age1 ,gre5 ent]$ at ,gonville & ,caius ,college1 & obta9$ ! f\r? place 9 ! ma!matical tripos ( #ahcg1 ! ye> ( ,griff91 ,sylve/]1 & ,gregory4 ,8 univ]sity c>e]1 :atev] else x may h done1 app>5tly did n t5d to make 8 e>li] "w mu* bett] kn[n to ! g5]al sci5tific public1 & he di$ 9 #ahda )\t ! sci5tific recognition :i* 0 8 due4 ,t came lat] :51 z /at$ bel[1 ,?omson discov]$ him to ! ,fr5* ma!maticians & republi%$ 8 ',essay4' #h ,janu>y #ahfi1 ,repr9t1 etc41 ,article ,,xv4 #i ,repr9t1 ,article ,v4 #aj ,! geometrical idea 01 h[ev]1 giv5 & appli$ at lea/ z e>ly z #ahcf by ,bellavitis1 = a pap] entitl$ ,teoria delle figure inv]sa appe>s 9 ! ,annali delle ,sci5ze del ,regno ,lomb>do-,v5eto = t ye>4 ,x 0 also describ$ z an indep5d5t discov]y by ,mr4 ,john ,wm4 ,/ubbs1 9 a pap] 9 ! ,philosophical ,magaz9e = ,novemb] #ahdc4 ,9 a note on ! hi/ory ( ! trans=mation 9 ,taylor's ,geometry ( ,conics ! date 7)\t ref]5ce7 ( ,bellavitis is giv51 & x is /at$ t ! me?od ( inv]sion 0 giv5 afre% by ,messrs4 ,+ram & ,/ubbs 7,dubl91 ,phil4 ,soc4 ,trans4 ,i74 ,! note also m5tions t inv]sion 0 appli$ by ,dr4 ,hir/ to attractions1 b conta9s no ref]5ce to ,?omson's pap]s6 #aa ,de ,caloris di/ributione p] ,t]r ,corpus 9 ! ,faculty m9ute1 z /at$ above4 #ab ,sic4 ,)\t d\bt a mi/ake ( ! scribe = ,li\ville4 #ac ,nor? ,wales ,*ronicle1 ,report1 ,feb4 #g1 #ahhe4 #ad ,publi%$3 ,treatise on ,natural ,philosophy1 vol4 i 9 #ahfg2 ,elem5ts ( ,natural ,philosophy 9 #ahgc4 #ae ,! exact date at :i* ?is 0 done _c be det]m9$ f ! ,m9utes ( ! ,faculty1 z !y conta9 no ref]5ce to ! appropriation ( space = ! purpose4 ,9 8 ,oration on ,james ,watt1 deliv]$ at ! ,n9? ,jubilee ( ! ,univ]sity ( ,glasg[1 9 #aija1 ,"l ,kelv9 ref]r$ to ! ,glasg[ ,physical ,laboratory z hav+ gr[n up betwe5 #ahdf & #ahef2 & else:]e he has ref]r$ to x z hav+ be5 incipi5t 9 #ahea4 #af ,!re are n[ 9 ,glasg[ 9 ! w9t] session alone ab\t #cfj elem5t>y /ud5ts & #hj advanc$ /ud5ts1 & ab\t #bej tak+ practical laboratory "w4 #ag ,be=e 8 dea? 79 #ahcb7 ,c>not _h obta9$ a cle> p]ception ( ! true /ate ( ! case1 & ( ! complete doctr9e ( ! cons]vatism ( en]gy4 ,see extracts f ,c>not's unpubli%$ writ+s app5d$1 ) a biography1 to ! repr9t$ ,memoir1 by 8 y\ng] bro!r1 ,hippolyte ,c>not4 #ah ,?is equation = ! por\s plug exp]im5t may be e/abli%$ 9 ! foll[+ mann]1 :i* =ms a good example ( ,?omson's second def9ition ( absolute temp]ature4 ,take pressure & volume ( ! gas on ! supply side ( ! plug z p dp & v1 & on ! deliv]y side z p & v dv1 s t dp & dv are positive4 ,! net "w done 9 =c+ ! gas ?r\gh ! plug 7p dp7v p7v dv7 pdv vdp4 ,let a heat+ effect result s t temp]ature is *ang$ f ,t to ,t ,t4 ,let ?is be annull$ by ab/raction ( heat ,cp,t at con/ant pressure4 7,cp sp4 heat press4 con/47 ,x is to be und]/ood t dv is ! total expansion exi/+1 aft] ?is ab/raction ( heat4 ,! en]gy e ( ! fluid has be5 increas$ by de pdv vdp ,cp,t4 ,n[1 s9ce ! orig9al temp]ature has be5 re/or$1 ! same expansion dv if impos$ iso!rmally w\ld involve ! same en]gy *ange de2 b 9 t case heat d,h 7dynamical7 w\ld be absorb$1 & "w pdv w\ld be done by ! gas4 ,h5ce de d,h pdv4 ,?is1 ) ! =m] value ( de1 gives d,h vdp ,cp,t4 ,?omson's "w-ratio is ?us pdv7vdp ,cp,t74 ,n[ suppose dp impos$ )\t *ange ( volume1 & d,t to be ! result+ temp]ature *ange4 ,! temp]ature & pressure ratios are d,t,t1 dpp4 ,?us d,t,t dp dv7vdp ,cp,t71 or 7v,t77d,tdv7 #aa 7,cpv77,tdp7 :i* is ,?omson's equation4 ,! m9us sign on ! "r arises f a heat+ effect hav+ be5 tak5 "h z ! normal case4 ,if ! temp]ature ,t is re/or$ by remov+ ! heat at con/ant volume1 a simil> process gives ! equation 7v,t77d,tdv7 #a 7,tp77,tdp7#a 7,cvv77,tdp7 :]e dp is ! *ange ( pressure be=e ! re/oration ( ! temp]ature ,t1 & ,tp is ! rate ( v>iation ( ,t ) p1 volume con/ant4 #ai ,on a ,univ]sal ,t5d5cy 9 ,nature to ,dissipation ( ,en]gy1 ,proc4 ,r4,s4,e41 #aheb1 & ,phil4 ,mag41 ,oct41 #aheb4 #bj ,to ?is may be add$ ! extremely useful !orem = su* problems1 t if any direct$ quantity ,l1 say1 *>act]i/ic ( ! motion ( a body1 be associat$ ) a l9e or axis ,ol1 :i* is *ang+ 9 direction1 x causes a rate ( production ( ! same quantity = a l9e or axis in/antane\sly at "r angles to ,ol1 t[>ds :i* ,ol is turn+ ) angul> velocity 1 ( am\nt ,l4 ,if ,m be ! am\nt ( ! quantity already exi/+ = ?is latt] l9e or axis1 ! total rate ( gr[? ( ! quantity is !re ,m ,l4 ,= example1 a p>ticle mov+ ) uni=m spe$ v 9 a circle ( radius r1 has mom5tum mv along ! tang5t4 ,b ! tang5t is turn+ r\nd z ! p>ticle moves ) angul> spe$ vr1 t[>ds ! radius4 ,! rate ( gr[? ( mom5tum t[>ds ! c5tre is !re=e mv vr mvr4 #ba ,see ,gray's ,lehrbu* d] ,physik1 s4 #bgh4 ,vieweg u4 ,sohn1 #aijd4 #bb ,gray1 ,royal ,in/itution1 ,friday ,ev5+ ,disc\rse1 ,febru>y #ahih4 #bc ,see ! ,reports ( ! ,committee on ,electrical ,/&>ds1 edit$ by ,pr(4 ,fleem+ ,j5k91 ,f4,r4,s41 ,maxwell's ,electricity & ,magnetism1 & ,gray's ,!ory & ,practice ( ,absolute ,measurem5ts 9 ,electricity & ,magnetism1 ,vol4 ,,ii1 ,"p ,,ii4 #bd ,! writ] once1 on a ?ick night1 9 a pass5g] /eam] 9 ! ,race ( ,ald]ney1 :5 ! eng9es 7 /opp$ & s\nd+s 7 be+ tak51 saw ! reel & cord g ov]bo>d1 ne>ly tak+ "o ( ! m5 ) x4 ,a new hank ( cord _h to be got & b5t on a new reel2 an op]ation t took a long "t1 dur+ :i* ! exact locality ( ! %ip 0 a matt] ( unc]ta9ty4 ,comm5t is ne$less6 #be ,! tun+ ( a major ?ird1 9 ?is way1 is describ$ 9 ! pap] entitl$ ,beats on ,imp]fect ,h>monies1 publi%$ 9 ,popul> ,lectures & ,addresses1 vol4 ii4 #bf ,! writ] well rememb]s meet+ a man ( "s exp]i5ce 9 cable "w :o 0 on 8 way to measure ! alt]nat+ curr5ts 9 a ,jablo*k(f c&le in/allation by ! aid ( an ,ayrton & ,p]ry galvanomet] ) /eel ne$le6 ,,index ,atlantic cables1 #bfg1 #bfh ,atmosph]ic electricity1 #bbf ,atoms1 size (1 #bfa ,ayrton1 ,w4 ,e41 #bif ,baltimore lectures1 #bed-bfc ,b]tr&'s !orem ( maximum k9etic en]gy1 #aeh ,bottomley1 ,james ,?omson1 #caa ,bottomley1 ,william1 #g ,briti% ,association1 electrical /&>ds1 #bdd-bec ,cambridge ,univ]sity ,musical ,society1 #bd ,cambridge & ,dubl9 ,ma!matical ,j\rnal1 #be1 #ca1 #gh ,c>not1 ,sadi1 #gg1 #aja ,c>not's ,?orie ,motrice du ,feu1 #hg1 #aja1 #ajh et seq4 ,cau*y1 #bid ,*asles1 #bh1 #dc ,clapeyron1 #aja1 #aab ,clausius1 #aad et seq4 ,college1 ! old1 ( ,glasg[1 #aj ,compass1 errors (1 #bgc ,dew-drop1 artificial1 #bij ,dynamical !orems1 ,?omson's & ,b]tr&'s1 #aeh et seq4 ,e>?1 ! age (1 #aif1 #bbi-bdc ,e>?1 tidal ret>dation (1 #bcj ,ela/icity1 ,poisson-,navi] !ory (1 #bia2 encyclopdia article on1 #big ,electrical oscillations1 #aha et seq4 ,electricity1 ma!matical !ory (1 #cc ,electrolysis1 me*anical !ory (1 #agf ,electromet]s1 #bbc et seq4 ,electromotive =ces1 e/imation (1 by heats ( comb9ation1 #agh ,electromotive =ces1 measurem5t (1 #agi ,electro/atics & ,magnetism1 #bbb et seq4 ,ellis1 ,rob]t ,leslie1 #bf ,en]gy1 dissipation (1 #aci ,faculty1 !1 ( ! ,univ]sity ( ,glasg[1 #d1 #fc-fg ,f>aday1 #fa ,faure1 ,m41 #ha ,fitz,gerald1 ,g4 ,f41 #cja1 #cje ,f\ri]1 ,?orie ,analytique de la ,*aleur1 #af et seq4 ,gauss1 #bh ,gauss & ,web]1 #bde ,gre51 ,george1 ( ,nott+ham1 #ba1 #cj1 #bid ,gregory1 ,j4 ,w41 #bda ,goodw91 ,h>vey1 #bf ,gyro/ats & gyro/atic action1 #bad1 #bhd-bhf ,hamilton1 ,sir ,william ,r[an1 #aif1 #bid ,heat1 encyclopdia article on1 #big ,heaviside1 ,oliv]1 #bid ,helmholtz1 von1 #aac ,h]tz1 #aia1 #bef ,hopk9s1 ,william1 #bc ,huxley1 #gg1 #aif1 #bdb ,hydrodynamics1 #aec-age ,images1 electric1 #ca1 #ch-ei ,inv]sion1 electrical1 #di et seq4 ,inv]sion1 geometrical1 #ei1 #fj ,j\le1 ,james ,prescott1 #gg1 #hf et seq41 #aja et seq4 ,l>mor1 ,joseph1 #bef ,lectures on ,natural ,philosophy at ,glasg[1 #bgi et seq4 ,li\ville1 #ca ,li\ville's ,j\rnal de ,ma?matiques1 #be1 #bf1 #ca ,los*midt1 #bfb ,lubbock1 ,sir ,john 7,"l ,avebury71 #he ,lum9if]\s e!r1 motion ( planets ?r\gh1 #bef ,magnetism1 !ory (1 #bbg ,m>9]s' compass1 #bgb et seq4 ,maxwell1 #aag1 #aic1 #cje ,may]1 ( ,heilbronn1 #aje ,mc,farlane1 ,donald1 #if1 #bhg1 #bhi ,mc,kichan1 ,dugald1 #aic ,mcanique ,analytique ( ,lagrange1 #aii1 #bje ,mcanique ,cle/e ( ,laplace1 #aii1 #bje ,meikleham1 ,william1 #fa ,mirror galvanomet]1 #bfh ,motivity1 !rmodynamic1 #ach ,natural ,philosophy1 ,*air (1 at ,glasg[1 #fc ,natural ,philosophy1 ,?omson & ,tait's1 #aif et seq4 ,navigational s\nd+ ma*9e1 #bgb ,newton1 #aie1 #bjb ,ni*ol1 ,john1 ,pr(essor ( ,engli% ,language & ,lit]ature1 #e ,ni*ol1 ,john ,pr+le1 ,pr(essor ( ,a/ronomy1 #e1 #bj1 #fa1 #fc ,o]/$1 #fa ,oscillations1 electrical1 #aha et seq4 ,p>k9son1 ,/eph51 #bg ,pelti]1 #adh ,p5dulum1 balli/ic1 #bhh ,p]ry1 ,john1 #bdj1 #bif ,phosphoresc5ce1 dynamical !ory (1 #bei ,physical laboratory1 fir/1 #gj ,pick]+1 #bag ,pol>is$ light1 rotation ( plane (1 #bbj ,pr9cipia1 ,newton's1 #aie1 #bjb ,ramsay1 ,george ,gilb]t1 ,pr(essor ( ,humanity1 #aa ,regnault1 #bi ,royal ,society ( ,ed9burgh1 presid5cy (1 #bii ,royal ,society ( ,london1 presid5cy (1 #bii ,rum=d1 ,c\nt1 #ajc ,seebeck1 #adh ,signall+1 !ory ( telegraphic1 #bfd ,siphon record]1 #bfh1 #bgj ,smi?1 ,ar*ibald1 #bge ,spectrum analysis1 dynamical !ory (1 #hd ,/okes1 ,sir ,george ,gabriel1 #bd1 #gi1 #hj1 #ha1 #he1 #bia1 #bid ,/oney1 ,dr4 ,john/one1 #bfb ,sun's heat1 age (1 #bcb ,tait1 ,pet] ,gu?rie1 #aid et seq4 ,temp]ature1 absolute1 #abe et seq42 comp>ison (1 ) scale ( air !rmomet]1 #ace ,!rmodynamics1 #ii-aeb ,!rmoela/icity1 #adb et seq4 ,!rmoelectricity1 #adg et seq4 ,!rmometry1 absolute1 #aad-aeb ,?omson1 ,david1 #fa ,?omson1 ,james1 ,pr(essor ( ,ma!matics1 #a-d1 #g ,?omson1 ,james1 ,pr(essor ( ,eng9e]+1 #aac1 #bji2 integrat+ ma*9e1 #bji1 #cjc ,?omson & ,tait's ,natural ,philosophy1 #fh1 #aif et seq41 #bah ,?omson's !orem ( m9imum k9etic en]gy1 #aeh ,?omson1 ,?omas1 ,pr(essor ( ,*emi/ry1 #f ,?omson1 preval5ce ( "n at ,glasg[ ,college1 #e ,?omson1 ,william1 ,"l ,kelv93-- ,p>5tage & e>ly education1 #a-ab ,c>e] at ,univ]sities ( ,glasg[ & ,cambridge1 #ac-cb ,e>ly rese>*es1 #af1 #ah1 #ca ,election to ,*air ( ,natural ,philosophy at ,glasg[1 #fd ,sci5tific rese>*es1 passim2 ,jubilee (1 #cja2 ,*ancellor ( ,univ]sity ( ,glasg[1 #cjb ,9 class-room & laboratory1 #bgi-bih ,practical activities1 hon\rs & di/9ctions1 la/ illness & dea?1 #bii-cjd2 fun]al 9 ,we/m9/] ,abbey1 #cjd ,tidal ,analys]1 #baa ,tide ,pr$ict]1 #bjh ,vortex-,motion1 #afa-age ,wald/e9 sonata1 #bd ,web]1 ,w41 #aic ,weights & measures1 ,briti%1 #bhi1 #bij ,:ite1 ,james1 #bgf ,will>d ,gibbs1 #bid ,,ri*>d ,,clay ,,sons1 ,,limit$1 ,,bread ,,/reet ,,hill1 ,e4,c41 ,,& ,,bungay1 ,,suffolk4