file :i* includes ! orig9al illu/rations4 ,see #ededf-;h4htm or #ededf-;h4zip3 7https3_/_/www4gut5b]g4org_/ca*e_/epub_/ #ededf_/pg#ededf-;images4html7 or 7https3_/_/www4gut5b]g4org_/files_/#eded f_/ededf-;h4zip7 ,images ( ! orig9al pages are available ?r\gh ,int]net ,ar*ive4 ,see https3_/_/ar*ive4org_/details_/timeclock sdescri#jj;cuny ,transcrib]'s note3 ,text enclos$ by und]scores is 9 italics 7italics74 ,h[ev]1 to improve readability1 italics notation has be5 omitt$ f equations4 ,if ! v>iables are 9 italics 9 ! surr\nd+ text1 !y 7 9 italics 9 ! equations4 ,,"t ,,& ,,clocks4 ,illu/ration3 ,frontispiece4 ,,nuremb]g ,,clock4 ,,conv]t$ ,,f ,a ,,v]ge ,,escapem5t ,,to ,a ,,p5dulum ,,movem5t4 ,,"t ,,& ,,clocks3 ,a ,description ( ,anci5t & ,mod]n ,me?ods ( ,measur+ ,"t4 by ,h4 ,h4 ,,cunynghame ,m4,a4 ,c4,b4 ,m4,i4,e4,e4 ,) ,_m ,illu/rations4 ,london3 ,ar*ibald ,con/able ,co4 ,ltd4 #af ,james ,/reet ,haym>ket4 #aijf4 ,bradbury1 ,agnew1 ,co4 ,ld41 ,pr9t]s1 ,london & ,tonbridge4 ,,cont5ts4 ,,page ,,introduction #a ,,*apt] ,i4 #g ,,*apt] ,,ii4 #ej ,,*apt] ,,iii4 #ij ,,*apt] ,,iv4 #abc ,,app5dix ,,on ,,! ,,%ape ,,( ,,! ,,tee? ,,( ,,:eels #ahg ,,index #aii ,,"t ,,& ,,clocks4 ,,introduction4 ,:5 we read ! works ( ,hom]1 or ,virgil1 or ,plato1 or turn to ! lat] productions ( ,dante1 ( ,%akespe>e1 ( ,milton1 & ! ho/ ( writ]s & poets :o h done s mu* to in/ruct & amuse u1 & to make our lives good & agreeable1 we are apt to look ) "s disappo9tm5t ^u pres5t times4 ,& :5 we turn to ! field ( art & comp>e ,greek /atues & ,go?ic or ,r5aissance ar*itecture ) our mod]n ef=ts1 we mu/ feel b\nd to admit our inf]iority to our ance/ors4 ,& ?is leads u p]haps to "q :e!r our age is ! equal ( ^? :i* h gone be=e1 or :e!r ! human intellect is n on ! decl9e4 ,?is feel+1 h[ev]1 proce$s f a failure to rememb] t ea* age ( ! _w has its peculi> po9ts ( /r5g?1 z well z ( weakness4 ,dur+ "o p]iod t self-d5y+ patriotism & zeal = ! common good w be develop+1 :i* is necess>y = ! =mation ( society4 ,dur+ ano!r1 ! /udy ( ! pr9ciples ( morality & religion w be 9 ! asc5dant4 ,dur+ ano!r ! arts w take ! lead2 dur+ ano!r1 poetry1 trag$y1 & lyric poetry & prose w be cultivat$2 dur+ ano!r1 music w take its turn1 & out ( rude peasant songs w evolve ! h>mony ( ! op]a4 ,to our age is res]v$ ! glory ( be+ easily ! =emo/ 9 sci5tific discov]y4 ,future ages may despise our lit]ature1 surpass u 9 poetry1 compla9 t 9 philosophy we h done no?+1 & ev5 d]ide & =get our music2 b !y w only be able to look back ) admiration on ! b& ( sci5tific ?9k]s :o 9 ! sev5te5? c5tury r$uc$ to a sy/em ! laws t gov]n ! motions ( worlds no less ?an ^? ( atoms1 & :o 9 ! eighte5? & n9ete5? f\nd$ ! sci5ces ( *emi/ry1 electricity1 s\nd1 heat1 light1 & :o gave to mank9d ! /eam-eng9e1 ! telegraph1 railways1 ! me?ods ( mak+ huge /ructures ( iron1 ! dynamo1 ! telephone1 & ! ?\s& applications ( sci5ce to ! s]vice ( man4 ,& future /ud5ts ( hi/ory :o %all be famili> ) ! conditions ( our life w1 ,i ?9k1 be also /ruck ) surprise at our e/imate ( our own peculi> capabilities & faculties4 ,!y w note ) a/oni%m5t t a g5tleman ( ! n9ete5? c5tury1 an age mighty 9 sci5ce1 & by no means pre-em95t 9 art1 lit]ature & philosophy1 %\ld h consid]$ x disgraceful to be ignorant ( ! acc5t ) :i* a ,greek or a ,roman ?\ght fit to pron\nce a ^w1 %\ld h be5 a%am$ to be unable to con/rue a ,lat9 aphorism1 & yet %\ld h consid]$ x no %ame at all n to "k h[ a telephone 0 made & :y x work$4 ,!y w smile :5 !y obs]ve t our highe/ univ]sity degrees1 our mo/ lucrative rew>ds1 7 giv5 = ! /udy ( dead languages or ar*ological inve/igations1 & t sci5ce1 our glory & t = :i* we h %[n real ability1 %\ld only h occupi$ a second>y place 9 our education4 ,!y w smile :5 !y le>n t we consid]$ t a k ( public affairs c\ld only be acquir$ by a gr\nd+ 9 ,greek p>ticles1 or t x c\ld ev] h be5 ?\ght t m5 c\ld n comm& an army )\t a /udy ( ! tactics employ$ at ! battle ( ,m>a?on4 ,b ! battle betwe5 classical & sci5tific education is n 9 reality s mu* a dispute reg>d+ subjects to be taught1 z betwe5 me?ods ( tea*+4 ,x is possible to tea* classics s t !y become a m5tal tra9+ ( ! highe/ value4 ,x is possible to tea* sci5ce s t x becomes a m]e enslav+ r\t9e4 ,! "o great requirem5t = ! education ( ! future is firmly to grasp ! fact t a /udy ( words is n a /udy ( ?+s1 & t a man _c become a c>p5t] m]ely by le>n+ ! names ( 8 tools4 ,x 0 ! mi/ake ( ! tea*]s ( ! ,middle ,ages to believe t ! fir/ /ep 9 k 0 to get a correct set ( concepts ( all ?+s1 & !n to d$uce or br+ out all k f !m4 ,admirable plan if y c get y\r concepts6 ,b un=tunately concepts d n exi/ ready made--!y mu/ be gr[n2 & z y\r k increases1 s d y\r concepts *ange4 ,a concept ( a ?+ is n a m]e def9ition1 x is a complete hi/ory ( x4 ,& y mu/ build up y\r edifice ( sci5tific k f ! e>?1 brick by brick & /one by /one4 ,!re is no magic process by :i* x c ) a ^w be conjur$ into exi/5ce l a palace 9 ! ,arabian ,nights4 ,= no?+ is m fatal ?an a juggle ) words su* z =ce1 weight1 attraction1 mass1 "t1 space1 capacity1 or gravity4 ,words are l purses1 !y conta9 only z mu* money z y put into !m4 ,y may j+le y\r bag ( p5nies till !y s\nd l sov]eigns1 b :5 y come to pay y\r bills ! diff]5ce is soon discov]$4 ,?is fatal practice ( le>n+ words )\t try+ to obta9 a cle> compreh5sion ( _! mean+1 causes _m tea*]s to use ma!matical =mul n z m]e /eps 9 a logical *a91 b l magical *aldrons into :i* !y put ! premises z ! wit*es put h]bs & babies' ?umbs into _! pots1 & expect ! answ]s to rise l app>itions by "s occult process t !y _c expla94 ,?is t5d5cy is enc\rag$ by fooli% p>5ts :o l to see _! infant prodigies appe> to und]/& ?+s too h>d = !mselves1 & look on at _! *ildr5's lessons 9 ma!matics l ru/ics gap+ at a fair4 ,!y =get t = ! practical purposes ( life "o ?+ well und]/ood is wor? a :ole book-full ( muddl$ ill-dige/$ =mul4 ,un=tunately x is possible to cram boys up & run !m ?r\gh ! exam9ation sieves ) ! appe>ance ( k )\t its reality4 ,if x 7 cricket or golf t 7 be+ te/$ h[ soon w\ld ! fraud be discov]$4 ,no humbug w\ld be p]mitt$ 9 ^? int]e/+ & absorb+ subjects4 ,& really1 :5 "o reflects h[ easy x is to pres5t ! appe>ance ( book k )\t ! reality1 "o c h>dly blame ^? :o select m5 = s]vice 9 ,india & ,egypt a good deal = _! pr(ici5cy 9 sports & games4 ,bett] a good cricket] ?an a silly p$ant /uff$ full ( le>n+ t 8lies l m>l ^u a b>r5 soil encumb]+ :at is n 9 its p[] to f]tilize40 ,ano!r k9dr$ error is to expect too mu* ( sci5ce4 ,= ) all our ef=ts to obta9 a fur!r k ( ! my/]ies ( nature1 we are only l travell]s 9 a =e/4 ,! deep] we p5etrate x1 ! d>k] becomes ! %ade4 ,= sci5ce is 8b an ex*ange ( ignorance = t :i* is ano!r k9d ( ignorance0,a & all our analysis ( incompreh5sible ?+s leads u only to ?+s m incompreh5sible /ill4 ,a ,manfr$1 ,act ,,ii41 sc5e iv4 ,x is1 !re=e1 by ! firm resolution nev] to juggle ) words or ideas1 or to try & p]suade ourselves or o!rs t we und]/& :at we d n und]/&1 t any sci5tific advance c be made4 ,,*apt] ,i4 ,all /ud5ts ( any subject are at fir/ apt to be p]plex$ ) ! numb] & complication ( ! new ideas pres5t$ to !m4 ,! ne$ ( compreh5d+ ^! ideas is felt1 & yet !y are difficult to grasp & to def9e4 ,?us1 = in/ance1 we are all apt to ?9k we "k :at is meant :5 =ce1 weight1 l5g?1 capacity1 motion1 re/1 size1 are spok5 (4 ,& yet :5 we come to exam9e ^! ideas m closely1 we f9d t we "k v little ab\t !m4 ,inde$1 ! m elem5t>y !y are1 ! less we are able to und]/& !m4 ,! mo/ primordial ( our ideas seem to be ^? ( numb] & quantity2 we c c\nt ?+s1 & we c measure !m1 or comp>e !m ) "o ano!r4 ,ari?metic is ! sci5ce :i* deals ) ! numb]s ( ?+s & enables u to multiply & divide !m4 ,! e/imation ( quantities is made by ! application ( our faculty ( comp>ison to diff]5t subjects4 ,! ideas ( numb] & quantity appe> to p]vade all our conceptions4 ,! /udy ( natural ph5om5a ( ! _w ar\nd u is call$ ! /udy ( physics f ! ,greek ^w or 8inanimate nature10 ! t]m physics is usually conf9$ to su* "p ( nature z is n alive4 ,! /udy ( liv+ ?+s is usually t]m$ biology 7f 1 life74 ,9 ! /udy ( natural ph5om5a !re are1 h[ev]1 ?ree ideas :i* occupy a peculi> & important position1 because !y may be us$ z ! means ( measur+ or e/imat+ all ! re/4 ,9 ?is s5se !y seem to be ! mo/ primitive & fundam5tal t we possess4 ,we are n entitl$ to say t all o!r ideas are =m$ f & comp\nd$ ( ^! ideas1 b we are entitl$ to say t our correct und]/&+ ( physics1 t is ( ! /udy ( nature1 dep5ds 9 no slight degree ^u our cle> und]/&+ ( !m4 ,! ?ree fundam5tal ideas are ^? ( space1 "t & mass4 ,space appe>s to be ! univ]sal accompanim5t ( all our impressions ( ! _w ar\nd u4 ,try z we may1 we _c ?9k ( mat]ial bodies except 9 space1 & occupy+ space4 ,?\gh we c imag9e space z empty we _c conceive x z de/roy$4 ,& ?is space has ?ree dim5sions1 l5g?1 bread? measur$ across or at "r angles to l5g?1 & ?ickness measur$ at "r angles to l5g? & bread?4 ,m dim5sions ?an ?is we _c h4 ,= "s inscrutable reason x has be5 arrang$ t space %all pres5t ^! ?ree dim5sions & no m4 ,a f\r? dim5sion is to u unimag9able--,i w n say inconceivable--we c conceive t a _w might be ) space 9 f\r dim5sions1 b we _c imag9e x to ourselves or ?9k :at ?+s w\ld be l 9 x4 ,) difficulty we c p]haps imag9e a _w ) space ( only two dim5sions1 a 8flat l&10 :]e flat be+s ( diff]5t %apes1 l figures cut out ( pap]1 slide or float ab\t on a flat table4 ,!y c\ld n hop ov] "o ano!r1 = !y w\ld only h l5g? & bread?2 to hop up y w\ld want to be able to move 9 a ?ird dim5sion1 b hav+ two dim5sions only y c\ld only slide =w>d & sideways 9 a plane4 ,to su* be+s a r+ w\ld be a box4 ,y w\ld h to break ! r+ to get any?+ out ( x1 = if y tri$ to slide out y w\ld be met by a wall 9 e direction4 ,y c\ld n jump out ( x l a %eep w\ld jump out ( a p5 ov] ! hurdles1 = to jump w\ld require a ?ird dim5sion1 :i* y h n got4 ,be+s 9 a _w ) "o dim5sion only w\ld be 9 a worse plight /ill4 ,l beads on a /r+ !y c\ld slide ab\t 9 "o direction z f> z ! o!rs w\ld let !m4 ,!y c\ld n pass "o ano!r4 ,to su* a be+ two o!r be+s w\ld be a box "o on ea* side ( him1 = if ?us imprison$1 he c\ld n get away4 ,l a waggon on a railway1 he c\ld n walk r\nd ano!r waggon4 ,t w\ld want p[] ( mov+ 9 two dim5sions1 /ill less c\ld he jump ov] !m1 t w\ld want ?ree4 ,we h n ! smalle/ idea :y our _w has be5 ?us limit$4 ,"s philosoph]s ?9k t ! limitation is 9 u1 n 9 ! _w1 & t p]haps :5 our m9ds are free f ! limitations impos$ by _! soj\rn 9 our bodies1 & dea? has set u free1 we may see n only :at is ! l5g? & bread? & height1 b a great deal m also ( :i* we c n[ =m no conception4 ,b ^! speculations lead u out ( sci5ce into ! %ad[y l& ( metaphysics1 ( :i* we long to "k some?+1 b are condemn$ to "k s little4 ,area is got by multiply+ l5g? by bread?4 ,cubic cont5t is got by multiply+ l5g? by bread? & by height4 ,( all ! conceptions respect+ space1 t ( a l9e is ! simple/4 ,x has direction1 & l5g?4 ,! idea ( mass is m difficult to grasp ?an t ( space4 ,x means quantity ( matt]4 ,b :at is matt]8 ,t we d n "k4 ,x is n weight1 ?\gh x is true t all matt] has weight4 ,yet matt] w\ld /ill h mass ev5 if its prop]ty ( weight 7 tak5 away4 ,= consid] su* a ?+ z a p\nd packet ( tea4 ,x has size1 x occupies space1 x has l5g?1 bread?1 & ?ickness4 ,x has also weight4 ,b :at gives x weight8 ,! attraction ( ! e>?4 ,suppose y d\ble ! size ( ! e>?4 ,! e>? be+ bigg] w\ld attract ! package ( tea m /rongly4 ,! weight ( ! tea1 t is1 ! attraction ( ! e>? on ! package ( tea1 w\ld be increas$--! tea w\ld weigh m ?an be=e4 ,take ! package ( tea to ! planet ,jupit]1 :i*1 be+ v l>ge1 has an attraction at ! surface #b times t ( ! e>?4 ,its size w\ld be ! same1 b x w\ld feel to c>ry l a package ( s&4 ,yet !re w\ld be ! same 8mass0 ( tea4 ,y c\ld make no m cups ( tea out ( x 9 ,jupit] ?an on e>?4 ,take x to ! moon1 & x w\ld weigh a little ov] two ounces1 b /ill x w\ld be a p\nd ( tea4 ,we are 9 ! habit ( e/imat+ mass by its weight1 & we d s rightly1 = at any place on ! e>?1 z ,london1 ! weights ( masses are always proportion$ to ! masses1 & if y want to f9d out :at mass ( tea y h got1 y weigh x1 & y "k = c]ta94 ,h5ce 9 our m9ds we confuse mass ) weight4 ,& ev5 9 our ,acts ( ,p>liam5t we h done ! same ?+1 s t x is difficult 9 ! /atutes respect+ /&>d weights to "k :at 0 meant by ^? :o drew !m up1 & :e!r a p\nd ( tea means ! mass ( a c]ta9 am\nt ( tea or ! weight ( t mass4 ,= accurate ?9k+ we mu/1 ( c\rse1 always deal ) masses1 n ) weights4 ,= s f> z we c tell mass appe>s inde/ructible4 ,a mass is a mass :]ev] x is1 & = all "t1 :]eas its weight v>ies ) ! attractive =ce ( ! planet ^u :i* x happ5s to be1 & ) its di/ance f t planet's c5tre4 ,a flea on ?is e>? c skip p]haps eight in*es high2 put t flea on ! moon1 & ) ! exp5diture ( ! same en]gy he c\ld skip f\r feet high4 ,put him on ! planet ,jupit] & he c\ld only skip #c in*es high4 ,a man 9 a /reet 9 ! moon c\ld jump up into a w9d[ on ! fir/ floor ( a h\se4 ,"o p\nd ( tea tak5 to ! sun w\ld be z heavy z tw5ty-eight p\nds ( x at ! e>?'s surface2 & weight v>ies at diff]5t p>ts ( ! e>?4 ,h5ce ! true measure ( quantity ( matt] is mass1 n weight4 ,! mass ( bodies v>ies accord+ to _! size2 if y h ! same nature ( mat]ial1 !n = a d\ble size y h a d\ble mass4 ,"s bodies are m conc5trat$ ?an o!rs1 t is to say1 m d5se2 x is z ?\gh !y 7 m tightly squeez$ toge!r4 ,?us a ball ( lead ( an in* 9 diamet] conta9s =ty-eight times z mu* mass z a ball ( cork an in* 9 diamet]4 ,9 ord] to "k ! weight ( a c]ta9 mass ( matt]1 we %\ld h to multiply ! mass by a figure repres5t+ ! attractive =ce or pull ( ! e>?4 ,9 physics x is usual to employ ! lett]s ( ! alphabet z a sort ( %or?& to repres5t words4 ,s t ! lett] m /&s = ! mass ( a body4 ,s aga9 g /&s = ! attractive pull ( ! e>? at a giv5 place4 w /&s = ! weight ( ! body4 ,h5ce !n1 s9ce ! weight ( a body dep5ds on its mass & also on ! attractive pull ( ! e>?1 we express ?is 9 %ort language by say+1 w m g2 or w is equal to m multipli$ by g2 ! symbol be+ us$ = equality1 & ! sign ( multiplication4 ,9 common use is usually omitt$1 & :5 lett]s are put toge!r !y are int5d$ to be und]/ood z multipli$4 ,s t ?is is writt5 w mg4 ,( c\rse by ?is equation we d n mean t weight is mass multipli$ into ! =ce ( gravity1 we only mean t ! numb] ( units ( weight is to be f\nd by multiply+ ! numb] ( units ( mass into ! numb] ( units ( ! e>?'s =ce ( gravity4 ,9 ! same way1 if :5 e/imat+ ! numb] ( waggons1 w1 t w\ld be want$ = an army ( m51 n1 :i* consum$ a numb] ( p\nds1 p1 ( provisions a day1 we might put w np4 ,b ?is w\ld n mean t we 7 multiply+ soldi]s into food to produce waggons1 b only t we 7 p]=m+ a num]ical calculation4 ,"t is "o ( ! mo/ my/]i\s ( our elem5t>y ideas4 ,x seems to exi/ or n to exi/1 accord+ z we are ?9k+ or n ?9k+4 ,x seems to run or /& /ill & to g fa/ or sl[ly4 ,h[ x drags ?r\gh a we>isome lesson2 h[ x flies dur+ a game ( cricket2 h[ x seems to /op 9 sleep4 ,if we measur$ "t by our own ?\ghts x w\ld be a v unc]ta9 quantity4 ,b o!r consid]ations seem to %[ u t ,nature kn[s no su* unc]ta9ty z reg>ds "t1 t %e produces h] ph5om5a 9 a uni=m mann] 9 uni=m times1 & t "t has an exi/5ce indep5d5t ( our ?\ghts & wills4 ,! idea ( a /ate ( ?+s 9 :i* "t exi/$ no m 0 q famili> to m$ival ?9k]s1 & 0 reg>d$ by _m ( !m z ! condition t w\ld exi/ aft] ! ,day ( ,judgm5t4 ,9 rec5t times ,kant prop\nd$ ! !ory t "t 0 only a necess>y condition ( our ?\ghts1 & _h no exi/5ce ap>t f ?9k+ be+s--9 fact1 t x 0 our way ( look+ at ?+s4 ,sci5tifically1 h[ev]1 we are w>rant$ 9 treat+ "t z p]fectly real & capable ( ! mo/ exact measurem5t4 ,= example1 if we arrange a /ream ( s& to run out ( an orifice1 & obs]ve h[ mu* w run out :ile an egg is be+ boil$ h>d1 we f9d z a fact t if ! same quantity ( s& runs out1 ! /ate ( ! egg is uni=m4 ,if we walk = an h\r by a wat*1 we f9d t we c g half ! di/ance t we %\ld if we walk$ two h\rs4 ,x is ! correspond5ce ( ^! v>i\s exp]im5ts t gives u fai? 9 ! treatm5t ( "t z a ?+ exi/+ indep5d5tly ( ourselves1 or1 at all ev5ts1 indep5d5t ( our transi5t moods4 ,! ideas ( "t acquir$ by ! races ( m5 t fir/ evolv$ f a /ate ( b>b>ism 7 no d\bt d]iv$ f ! obs]vation ( day & night1 ! mon? & ! ye>4 ,illu/ration3 ,,fig4 #a4 ,=1 suppose t a %eph]d 7 on ! pla9s ( ,*aldea1 or p]haps on ^? m\nta9s ( ,india kn[n z ! ro( ( ! _w1 :i* accord+ to "s ar*ologi/s 0 ! site ( ! g>d5 ( ,ed5 & ! e>ly home ( ! ,european race1 :at w\ld he see8 ,he w\ld see ! sun rise 9 ! ea/1 sl[ly m\nt ! heav5s till x /ood ov] ! s\? at middle day1 !n x w\ld s9k t[>ds ! we/ & disappe>4 ,9 summ] ! ris+ po9t ( ! sun w\ld be m to ! nor?w>d ?an 9 w9t]1 & s also w\ld be its po9t ( sett+ ,a4 ,9 w9t] x w\ld rise a little to ! s\? ( ea/1 & set a little to ! s\? ( we/1 & n rise s high 9 ! heav5s at midday1 s t ! summ] day w\ld be long] ?an ! w9t] day4 ,if ! day 7 always divid$ into twelve h\rs1 :e!r x 7 long or %ort1 !n 9 summ] ! h\rs ( ! day w\ld be long2 9 w9t] !y w\ld be %ort4 ,?is mode ( divid+ ! day 0 t us$ by ! ,greeks4 ,! ,egyptians1 on ! o!r h&1 av]ag$ _! day by divid+ ! :ole r\nd ( ! sun into tw5ty-f\r h\rs1 s t ! summ] day conta9$ m h\rs ?an ! w9t] day4 ,h5ce1 = ! ,egyptians1 sun-rise did n always take place at six o'clock4 ,= 9 w9t] x took place aft] six1 & 9 summ] be=e six2 & ?is is ! sy/em t has desc5d$ to u4 ,! moon also w\ld rise at diff]5t places1 v>y+ betwe5 ,a & ,b1 & set at places v>y+ betwe5 ,a & ,b1 b ^! w\ld be indep5d5t ( ^? at :i* ! sun rose & set4 ,moreov]1 ! moon ea* day w\ld appe> to get fur!r & fur!r away f ! sun 9 ! direction ( ! arr[1 z %[n 9 ! sket*4 ,if ! moon rose an h\r aft] ! sun on "o day1 ! next day x w\ld rise m ?an two h\rs aft] ! sun1 & s on4 ,?is delay 9 ris+ ( ! moon w\ld g on day by day till at la/ %e came "r r\nd to ! sun aga91 z %[n at ,m4 ,& 9 h] pa? %e w\ld *ange h] =m f a cresc5t1 z at ,m1 up to a full moon1 :5 %e w\ld be half way r\nd f ! sun1 t is1 :5 %e w\ld rise twelve h\rs aft] him1 or j be ris+ z ! sun set4 ,?is delay & accompany+ *ange ( =m w\ld g on1 till aft] ?ree weeks %e w\ld h got r\nd to a position ,a1 :5 %e w\ld rise eighte5 h\rs aft] ! sun1 & h become a cresc5t ) h] back to ! sun2 9 fact1 %e w\ld always turn h] convex side to ! sun4 ,at l5g?1 :5 tw5ty-eight days _h pass$1 %e w\ld be r\nd aga9 ab\t opposite to ! sun1 & consequ5tly h] pale light w\ld be ext+ui%$ 9 8 beams1 & %e w\ld gradually reappe> z a new moon on ! o!r side ( him4 ,?is s]ies ( *anges ( ! moon takes place once e tw5ty-eight days1 & is call$ a lun> or 8moon0 mon?1 & 0 us$ z a division ( "t by v e>ly nations4 ,! *anges ( ! seasons recurr$ ) ! *anges 9 ! times ( ris+ ( ! sun1 & took a ye> to br+ ab\t4 ,& !re 7 ne>ly ?irte5 moon *anges 9 ! ye>4 ,x 0 also obs]v$ t dur+ its cycle ( *anges1 ! sun 0 sl[ly mov+ r\nd backw>ds among ! />s 9 ! same direction z ! moon1 only x made its retrograde cycle 9 a ye>1 & ?us arose ! division ( "t into mon?s & ye>s4 ,! />s turn$ r\nd 9 ! heav5s once 9 ! complete day4 ,! sun1 !re=e1 appe>$ to move back among !m1 pass+ successively ?r\gh gr\ps ( />s1 s z to make ! circuit ( !m all 9 a ye>4 ,! />s ?r\gh :i* he pass$ 9 a ye>1 & ?r\gh :i* ! moon travell$ 9 a mon?1 7 divid$ by ! anci5ts into gr\ps call$ con/ellations1 & its ye>ly pa? 9 ! heav5s 0 call$ ! zodiac4 ,!re 7 twelve ( ^! con/ellations 9 ! zodiac call$ ! signs4 ,h5ce1 !n1 ! sun pass$ ?r\gh a sign 9 e mon?1 mak+ ! t\r ( !m all 9 ! ye>4 ,to ^! signs fanciful names 7 giv51 su* z 8! ,ram10 8! ,wat]-be>]10 8! ,virg910 8! ,scorpion10 & s on1 & ! sun & moon 7 !n said to pass ?r\gh ! signs ( ! zodiac4 ,h5ce1 s9ce ! pa? ( ! sun m>k$ ! ye>1 y c\ld tell ! seasons by kn[+ :at sign ( ! zodiac ! sun 0 94 ,! age ( ! moon 0 easily kn[n by h] =m4 ,:5 ! w9t] 0 ov]1 !n1 j z ! sun set ! dog /> w\ld be ris+ 9 ! ea/1 & ?is w\ld %[ t ! spr+ 0 at h&4 ,!n ! peasants prep>$ to till ! e>? & s[ ! se$ & lead ! ox5 out to pa/ure1 & celebrat$ ) joyful mir? ! glad adv5t ( ! spr+1 correspond+ to our ,ea/]1 :5 ! sun _h run ?r\gh ?ree con/ellations ( ! zodiac4 ,!n came ! summ] heat1 & ) _m a my/ic rite !y celebrat$ ,midsumm]'s ,day4 ,9 autumn1 aft] ?ree m signs ( ! zodiac h be5 trav]s$ by ! sun1 ! sun aga9 rises exactly 9 ! ea/ & sets 9 ! we/1 & ! days & nights are equal4 ,?is is ! autumnal equ9ox1 & 0 once celebrat$ by ! fea/ :i* we n[ "k z ,mi*aelmas ,day1 & ! goose is ! remnant ( ! anci5t fe/ival4 ,illu/ration3 ,,fig4 #b4 ,& ! great w9t] fea/ ( ! anci5ts is n[ kn[n to u z ,*ri/mas1 & *os5 to celebrate ! bir? ( our ,"l2 = :5 ,*ri/ianity came into ! _w & ! hea!ns 7 conv]t$1 ! old fea/ days 7 delib]ately *ang$ into ,*ri/ian fe/ivals4 ,to u1 !re=e1 ! :ole heav5s1 & ! fix$ />s ) !m1 appe> to turn f ea/ to we/1 or f left to "r1 z we look t[>ds ! s\?1 z %[n by ! big arr[4 ,b ! moon & sun1 ?\gh app>5tly plac$ 9 ! heav5s1 move backw>ds among ! fix$ />s1 z %[n by ! small arr[s4 ,! sun moves at su* a rate t he goes r\nd ! circle ( ! heav5s 9 a ye> ( ?ree hundr$ & sixty-five days4 ,! moon goes r\nd ! circle 9 tw5ty-eight & a half days1 or a lun> mon?4 ,( c\rse1 9 reality ! sun is at re/1 & x is ! e>? t moves r\nd ! sun & sp9s on its axis z x moves4 ,b x w pres5tly be %[n t ! appe>ance to a p]son on ! e>? is ! same :e!r ! e>? goes r\nd ! sun or ! sun r\nd ! e>?4 ,f ! works ( ,greek writ]s we "k a good deal ab\t ! ideas ( ! _w t 7 ent]ta9$ by ! anci5ts4 ,! mo/ e>ly notions 71 ( c\rse1 connect$ ) ! wor%ip ( ! gods4 ,! sun 0 consid]$ z a huge light c>ri$ 9 a *>iot1 driv5 by ,apollo1 ) f\r spirit$ /e$s4 ,x desc5d$ to ! ocean :5 ! day decl9$1 & !n ! horses 7 unyok$ by ! nymphs ( ! ocean & l$ r\nd to ! ea/1 s z to be ready = ! j\rney ( ! foll[+ day4 ,! ,egyptians figur$ ! sun z plac$ 9 a boat :i* sail$ ov] ! heav5s4 ,at night ! sun god desc5d$ into ! inf]nal regions1 c>ry+ ) him ! s\ls ( ^? :o _h di$ dur+ ! day4 ,!re !y pass$ ?r\gh diff]5t regions ( hell1 ) portals gu>d$ by hide\s mon/]s4 ,^? :o _h well le>n$ ! ritual ( ! dead knew ! words ( p[] :]e) to appease ! demons4 ,^? unprovid$ ) ! wat*words 7 subject$ to t]rible dang]s4 ,!n ! s\l appe>$ be=e ,m9os1 & 0 weigh$ & dealt ) accord+ to its des]ts4 ,illu/ration3 ,,fig4 #c4 ,! e>? 0 consid]$ z a huge isl& 9 ! mid/ ( a circul> sea4 ,gradually1 h[ev]1 a/ronomical ideas became subject$ to sci5ce4 ,"o ( ! fir/ tru?s t dawn$ on a/ronom]s 0 ! fact t ! e>? 0 a sph]e4 ,= !y notic$ t z p w5t fur!r & fur!r to ! nor?1 ! elevation ( ! sun at midday above ! horizon became small] & small]4 ,?is c easily be se5 f ! diagram4 ,:5 an obs]v] is at ,a ! sun appe>s at an altitude above ! horizon equal to ! angle 1 b z he goes along ! curv$ surface ( ! e>? to a po9t ,b ne>] to ! nor? pole1 ! sun appe>s to be l[] & only to h an altitude 4 ,f ?is x 0 easy = m5 s skill$ 9 geometry z ! ,greeks to calculate h[ big ! e>? 04 ,!y did s1 & x appe>$ to h ! enorm\s diamet] ( #h1jjj miles4 ,!y only knew q a small portion ( x4 ,!y ?\ght t ! re/ 0 ocean4 ,b !y _h1 ( c\rse1 a cle> idea ( ! 8antipodes0 or up-side-d[n side ( x1 & !y believ$ t if m5 7 on ! o!r side ( x t _! feet mu/ all po9t t[>ds its c5tre4 ,f ?is !y got ! idea ( ! c5tre ( ! e>? z a po9t ( attraction = all ?+s t _h an e>?-seek+ or e>?y nature4 ,fire appe>$ always to desire to g upw>ds1 s !y ?\ght t fire _h an e>?-repell5t1 heav5-seek+ "*4 ,wat] !y ?\ght p>tly e>?-seek+1 p>tly heav5-seek+1 = x appe>$ 9 ! ocean or float$ z cl\ds4 ,air !y ?\ght to be indiff]5t4 ,& out ( ! f\r elem5ts fire1 wat]1 e>?1 & air !y believ$ ! _w 0 made4 ,! e>? !y ?\ght mu/ be at re/2 = if x 0 9 motion ?+s w\ld fly (f f x4 ,!y saw t ei!r ! sun mu/ be mov+ r\nd ! e>?1 or else ! e>? mu/ be turn+ on its axis4 ,!y *ose ! =m] hypo!sis1 because !y argu$ t if ! e>? 7 twi/+ r\nd once 9 tw5ty-f\r h\rs !n su* a c\ntry z ,greece mu/ be fly+ r\nd l a spot on ! surface ( a top1 at ! rate ( ab\t #ah1jjj miles 9 tw5ty-f\r h\rs1 t is1 at ! rate ( ab\t #ahj y>ds 9 a second1 or fa/] ?an an arr[ f a b[4 ,b if t 0 ! case !n a bird t flew up f ! e>? w\ld be left f> beh9d4 ,if a ball 7 ?r[n up x w\ld fall hundr$s ( y>ds beh9d ! p]son :o ?rew x4 ,!y c\ld n conceive h[ x 0 possible = a ball ?r[n up by someone /&+ on a mov+ object n to fall beh9d ! ?r[]4 ,?is decid$ !m 9 _! error4 ,! mi/ak5 a/ronomy ( ! ,greeks 0 also mu* =w>d$ by ,ari/otle1 ! tutor ( ,alex&] ! ,great4 ,?is great g5ius 9 politics & philosophy 0 only 9 ! second rank z a man ( sci5ce1 &1 z ,i ?9k1 h>dly equal to ,ar*im$es or ,hipp>*us1 or ev5 to ,ptolemy4 ,ari/otle wrote a book conc]n+ ! heav5s :i* bri/les ) ! mo/ wantonly errone\s sci5tific ideas1 su* z1 = in/ance1 t ! motion ( ! heav5ly bodies mu/ be circul> because ! mo/ p]fect curve is a circle1 & simil> assumptions z to ! c\rse ( nature4 ,! e>?1 !n1 be+ fix$1 !y ?\ght t ! moon1 ! sun1 & ! sev5 planets 7 c>ri$ r\nd x1 fix$ ea* ( !m 9 an enorm\s cry/al sph]ical %ell4 ,^! sph]es1 l coats ( an onion1 slid r\nd "o ^u ano!r1 ea* c>ry+ 8 cele/ial lum9>y4 ,! moon 0 ! ne>e/1 !n ,m]cury1 !n ,v5us1 !n ! sun1 !n ,m>s1 ,jupit] & ,saturn4 ,outside !m 0 ! sph]e ( ! />s1 & outside all ! 8primum mobile10 or great ,prime ,mov] ( ! univ]se4 ,:5 "o ( ! cele/ial bodies1 su* z ! moon1 got 9 front ( ano!r1 su* z ! sun1 !re 0 an eclipse4 ,!y soon obs]v$ t ! moon d]iv$ its light f ! sun4 ,z !y knew ! size ( ! e>?1 by comp>ison !y got "s vague idea ( ! huge di/ances t ! heav5ly bodies mu/ be f u4 ,9 fact1 !y measur$ ! di/ance ( ! moon ) approximate accuracy1 mak+ x #bdj1jjj miles1 or ab\t ?irty times ! e>?'s diamet]4 ,?is1 ( c\rse1 gave !m ! moon's diamet]1 = !y 7 easily able to calculate h[ big an object mu/ be1 t looks z big z ! moon & is #bdj1jjj miles away4 ,?is l>ge size ( ! moon gave !m "s idea ( ! di/ance ( ! sun1 b !y fail$ to realise h[ big & f> away he really is4 ,sev]al anci5t nations us$ weeks z means ( measur+ "t4 ,!y made f\r weeks to ! lun> mon?4 ,! ord] ( ! days 0 r curi\sly arrang$4 ,=1 assum+ t ! e>? is ! c5tre ( ! planet>y sy/em1 put ! planets 9 a column1 putt+ ! ne>e/ 7! moon7 at ! bottom & ! fur!/ (f at ! top-- ,saturn1 ,jupit]1 ,m>s1 ,! ,sun1 ,v5us1 ,m]cury1 ,! ,moon4 ,!n divide ! day into ?ree wat*es ( eight h\rs ea*1 & let ea* wat* be presid$ ov] by "o ( ! planet-gods3 beg9 ) ,saturn4 ,we !n h ,saturn z ! fir/ god rul+ ,saturday1 & ,jupit] & ,m>s1 ! two o!r gods1 = t day4 ,! fir/ wat* = ,sunday w be ! sun2 ,v5us & ,m]cury w preside ov] ! next two wat*es ( t day4 ,! planet t w preside ov] ! fir/ wat* ( ! next day w be ! moon1 & ! day w1 !re=e1 be call$ ,monday2 ,saturn & ,jupit] w be ! o!r gods = ,monday4 ,! fir/ wat* ( ! next day w be presid$ ov] by ,m>s1 & ! day w1 !re=e1 be call$ ,m>s-day or ,m>di1 or1 9 ! ,teutonic languages1 ,tuesday1 aft] ,tuesco1 a ,sc&9avian god ( w>4 ,m]cury w give a "n to ,m]cr$i1 or to ,w$nesday1 or ,wod9's-day4 ,jupit] to ,jeudi1 or 8,?urs0 day4 ,v5us to ,v5dr$i1 or 9 ! ,sc&9avian1 ,friday1 ! day ( ! ,sc&9avian goddess ,freya1 ! goddess ( love & beauty1 :o corresponds to ,v5us1 & ?us ! week is complet$4 ,illu/ration3 ,,fig4 #d4 ,?is weekly s*eme came probably f ! ,*aldean a/ronom]s4 ,x appe>s probable t ! great t[] ( ,babel1 ! ru9s ( :i* exi/ to ?is day1 consi/$ ( sev5 /ages1 "o ov] ! o!r1 ! top "o pa9t$ :ite1 or p]haps purple1 to repres5t ! ,moon1 ! next l[] blue = ,m]cury1 !n gre5 = ,v5us1 yell[ = ! ,sun1 r$ = ,m>s1 orange = ,jupit]1 & black = ,saturn4 ,un=tunately1 ( ! col\rs no trace n[ rema9s4 ,b nightly on ! long t]races ! ,babylonian prie/s obs]v$ eclipses & o!r cele/ial ph5om5a4 ,_! records 7 aft]w>ds tak5 to ,alex&ria & kept 9 ! great libr>y t 0 subsequ5tly burn$ by ! ,turks4 ,9 t libr>y !y 7 se5 by ! a/ronom] ,ptolemy1 :o us$ !m 9 ! writ+ ( 8 "w on a/ronomy call$ ! 8,great ,syntaxis0 or 8,collection40 ,! orig9al "w p]i%$1 b x _h be5 translat$ into ,arabic by ! ,arab a/ronom]s1 :o call$ x 8,al ,mage/10 ! ,great ,book4 ,x 0 translat$ f ,arabic into ,lat91 & rema9$ ! textbook = a/ronom]s 9 ,europe q d[n to ! "t ( ,que5 ,elizabe?1 :5 a bett] sy/em took its place4 ,= ! use ( m5 engag$ 9 practical a/ronomy1 x is v conv5i5t to consid] ! sun1 moon1 />s1 & planets z go+ r\nd ! e>? at re/4 ,= in/ance1 seam5 use ! heav5ly bodies z 9 a way h&s ( a huge clock f :i* !y c "k ! "t & _! position on ! e>?4 8,! ,nautical ,almanac10 :i* is pr9t$ ye>ly1 gives ! true position ( ^! heav5ly bodies = e h\r1 m9ute1 & second ( ! ye>1 & ,i w pres5tly %[ h[ useful ?is is to sailors4 ,we w deal ) ! sun fir/4 ,f ! motions ( ! sun we c obs]ve ! "t4 ,?is is done 9 e g>d5 by means ( sun-dials1 & ,i w n[ describe h[ !y are con/ruct$4 ,if a light1 su* z ! light ( a c&le1 be mov$ r\nd 9 a circle at a uni=m pace s z to g r\nd once 9 "s giv5 p]iod1 su* z tw5ty-f\r h\rs1 x is obvi\s t x w\ld s]ve to measure "t4 ,?us1 = example1 if a %eet ( :ite pap] be plac$ ^u ! table1 & a p5cil be /uck on to x upright ) "s seal+ wax1 or a p5 propp$ up 9 an ink-pot1 !n a c&le held by anyone w ca/ ! %ad[ ( ! p5 on ! pap]4 ,illu/ration3 ,,fig4 #e4 ,if ! p]son hold+ ! c&le walk r\nd ! table at a uni=m spe$1 ! %ad[ w g r\nd l ! h& ( a clock1 & might be made to m>k ! "t4 ,if ! c&le took tw5ty-f\r h\rs to g r\nd ! table1 z ! sun takes tw5ty-f\r h\rs to g r\nd ! e>?1 !n m>ks plac$ on ! pap] w\ld s]ve to measure ! h\rs1 & ! pap] & p5 w\ld s]ve z a sort ( sun-dial4 ,b ! sun does n g r\nd ! e>? z ! c&le r\nd ! table4 ,its pa? is an incl9$ "o1 l t %[n by ! dott$ l9e4 ,sometimes x is above ! level ( ! table1 sometimes bel[ x4 ,&1 moreov]1 its w9t] pa? is diff]5t f its summ] pa?4 ,:5ce !n x foll[s t ! h\r-m>ks on ! pap] _c be put equidi/ant l ! h\rs on ! dial ( a clock1 & t "s arrangem5t mu/ be made s t ! l9e z %[n by ! summ] sun %all correspond ) ! "t z %[n by ! w9t] sun4 ,illu/ration3 ,,fig4 #f4 ,let u suppose t ,n ,o ,s is ! axis ( ! heav5s1 & ! l9es ,n ,a ,s1 ,n ,b ,s1 ,n ,c ,s1 are m]idian l9es drawn f "o ( ! poles ,n ( ! heav5s r\nd on ! surface ( a cele/ial sph]e ^: c5tre is at ,o4 ,let ,a ,b ,c be a circle also on ?is sph]e1 pass+ ?r\gh ,o1 ! c5tre ( ! sph]e1 9 a plane at "r angles to ,n ,s1 ! axis4 ,!n ,a ,b ,c is call$ ! equatorial4 ,x is a circle 9 ! heav5s correspond+ to ! equator on ! e>?4 ,at ! v]nal & autumnal equ9ox1 namely on ,m>* #be & ,septemb] #be1 ! sun is 9 ! equatorial4 ,9 midsumm] & midw9t] x is on opposite sides ( ! equatorial4 ,9 midsumm] x is ne>] to ,n1 z at ,v2 9 midw9t] x is ne>] to ,s1 z at ,w4 ,suppose we 7 on an isl& 9 ! mid/ ( a surr\nd+ ocean1 we %\ld only h a limit$ range ( view4 ,if ! highe/ po9t on ! isl& 7 #ajj feet1 !n f t altitude we %\ld be able to see ab\t ?irte5 miles to ! horizon4 ,m ?an t c\ld n be se5 on acc\nt ( ! rotundity ( ! e>?4 ,let u suppose !n su* an isl& surr\nd$ = ?irte5 miles di/ant on e side by an ocean1 & let u consid] :at w\ld be ! app>5t motions ( ! sun :5 se5 f su* an isl&4 ,at ! v]nal & autumnal equ9oxes1 :5 ! sun is on ! equatorial1 x w\ld appe> to rise out ( ! ocean at a po9t ,e1 due ea/2 x trav]ses half ! equatorial & sets 9 ! ocean at a po9t ,w1 due we/4 ,! day is twelve h\rs long1 f #f a4m4 to #f p4m4 ,illu/ration3 ,,fig4 #g4 ,9 summ] ! sun is high]1 & ne>] to ! pole ,n1 say at a po9t s4 ,x rises at a po9t a 9 ! ocean m to ! nor? ?an ,e1 ! ea/]n po9t1 & sets at a po9t b1 also m nor? ?an ,w1 ! we/]n po9t1 & trav]ses ! pa? a s b4 ,b to trav]se ?is pa? x takes long] ?an twelve h\rs1 = a s b is m ?an half ! circle a s b4 ,h5ce !n x rises say at #d4cj a4m4 & sets at #g4cj p4m4 ,! night1 dur+ :i* ! sun moves r\nd ! pa? f b to a1 is correspond+ly %ort1 be+ only n9e h\rs 9 l5g?1 f #g4cj p4m4 till #d4cj a4m4 ,s y h a long summ] day & a %ort summ] night4 ,b 9 w9t]1 :5 ! sun gets ne>] to ! s\? pole ( ! heav5s1 x rises at a po9t ,c 9 ! ocean at #g4cj a4m41 & trav]ses ! arc c t d1 & sets at ! po9t d at #d4cj p4m4 ,s t ! w9t] day is only n9e h\rs long4 ,b ! w9t] night la/s f #d4cj p4m4 till #g4cj a4m41 & is !re=e fifte5 h\rs long1 ! sun go+ r\nd ! pa? d r c 9 ! int]val4 ,x is !re=e ! obliquity ( ! poles ,n ,s1 c\pl$ ) ! fact t ! sun's position is ne>] to "o pole1 ,n1 9 summ]1 & ne>] to ! o!r pole1 ,s1 9 w9t]1 t produces ! inequality ( days & nights 9 our latitudes4 ,suppose our isl& 7 on ! equator4 ,! nor? pole & ! s\? pole w\ld appe> to be on ! horizon1 & !n :e!r ! sun mov$ 9 ! circle a s b 9 ! summ]1 or ,e ,s ,w at ! v]nal or autumnal equ9oxes1 or c t d 9 ! w9t]1 9 ea* ( ^! cases1 ?\gh ! places ( ris+ & sett+ 9 ! ocean might v>y 9 summ] f a & b to c & d 9 w9t]1 yet 9 ea* ( ^! cases ! pa? f a to b1 ,a to ,b1 & c to d w\ld /ill always be a half-circle & occupy twelve h\rs4 ,h5ce at ! equator ! days & nights nev] v>y 9 l5g?1 b ! sun always rises at six & sets at six4 ,&1 besides1 x always rises /raight up f ! ocean & plunges d[n v]tically into x1 s t !re is b little twilight & dawn4 ,illu/ration3 ,,fig4 #h4 ,b n[ let u suppose we 7 liv+ at ! nor? pole4 ,9 ?is case ! nor? pole w\ld be directly ov]head1 ! s\? pole directly "u our feet4 ,at ! v]nal & autumnal equ9oxes ! sun w\ld appe> ) half its disc above ! ocean1 & g r\nd ! ocean horizon1 always appe>+ ) half its disc above ! sea4 ,9 summ] x w\ld appe> at a po9t s ne>] to ! pole ,n4 ,x w\ld g r\nd 9 ! heav5s1 always appe>+ above ! horizon1 & w\ld nev] set at all4 ,z ! summ] wan$ ! sun w\ld become l[] & l[]1 /ill1 h[ev]1 go+ r\nd & r\nd )\t sett+ till at ! autumn equ9ox x rea*$ ! horizon4 ,s t = six mon?s x w\ld nev] h set4 ,b :5 x did set1 !re w\ld !n be six mon?s )\t a sun at all4 ,illu/ration3 ,,fig4 #i4 ,?us !n all ov] ! _w ! p]iod ( d>kness & light is equival5t4 ,at ! tropics ! days & nights are always equal4 ,at ! poles light = six mon?s is foll[$ by d>kness = six mon?s4 ,9 ! int]m$iate temp]ate regions nights ( v>y+ l5g?s foll[ days ( v>y+ l5g?s1 a %ort night foll[+ a long day & vice v]s4 ,illu/ration3 ,,fig4 #aj4 ,x is evid5t t = a p]son liv+ on ! nor? pole a sun-dial w\ld be an easy ?+ to make4 ,all t w\ld be ne$ful w\ld be to put a po/ v]tically 9 ! gr\nd1 & obs]ve its %ad[ z ! sun w5t r\nd 7,fig4 #aj74 ,illu/ration3 ,,fig4 #aa4 ,9 latitudes su* z t ( ,engl&1 :]e ! pole ( ! e>? is incl9$ at an angle to ! horizon1 x is necess>y t ! rod1 or 8/yle0 z x is call$1 ( ! sun-dial %\ld be incl9$ to ! horizontal4 ,= if we us$ an upright 8/yle10 z ,o ,a1 !n :5 ! sun 0 9 ! s\?1 at midday1 ! %ad[ w\ld lie along ! same direction1 ,o ,b1 :e!r ! sun 7 high 9 summ]1 z at ,s1 or l[ 9 w9t]1 z at s4 ,b at o!r h\rs1 su* z n9e o'clock 9 ! morn+1 ! %ad[ ( ! 8/yle0 ,o ,a w\ld1 :5 ! sun 0 at its summ] position ,t1 lie along ,o ,d1 :]eas :5 ! sun 0 at its w9t] position t ! %ad[ w\ld lie along ,o ,c4 ,?us ! "t w\ld appe> diff]5t 9 summ] & 9 w9t]2 & ! dial w\ld lead to errors4 ,b if ! 8/yle0 is incl9$ 9 ! direction ( ! poles1 !n1 h[ev]1 ! sun moves f or t[>ds ! pole4 ,z its position v>ies 9 w9t] & summ]1 ! %ad[ /ill rema9s un*ang$ = any p>ticul> h\r1 & x is only ! circul> motion ( ! sun r\nd 9 its daily pa? t affects ! position ( ! %ad[s4 ,illu/ration3 ,,fig4 #ab4 ,!re=e ! fir/ condition ( mak+ a sun-dial is t ! 8/yle0 :i* ca/s ! %ad[ %\ld be p>allel to ! e>?'s axis1 t is to say %\ld po9t to ! pol> />4 ,?is is ! case :e!r ! sun-dial is horizontal or is v]tical1 & :e!r x /&s on a pill> 9 ! g>d5 or is atta*$ to ! wall ( a h\se4 ,to divide ! dial1 we h only to imag9e x surr\nd$ by a sort ( cage =m$ ( tw5ty-f\r arcs drawn f ! nor? pole to ! s\? pole1 & equidi/ant f "o ano!r4 ,9 its c\rse ! sun w\ld cross "o ( !m e h\r4 ,h5ce ! po9ts to :i* ! %ad[s o a1 o b1 o c1 o d1 ( ! incl9$ 8/yle0 ,o ,n w\ld po9t are ! po9ts :]e ^! arcs meet ! horizontal circle4 ,?is consid]ation leads to a simple me?od ( con/ruct+ a sun-dial1 :i* is giv5 at ! end ( ?is *apt] 9 an app5dix4 ,sun-dials 7 l>gely 9 use 9 anci5t times4 ,x is ?\ght t ! circul> r[s ( /ones us$ by ! ,druids 7 us$ to m>k ! sun's pa?1 & indicate ! times & seasons4 ,obelisks are also suppos$ to h be5 us$ to ca/ sun-%ad[s4 ,! ,greeks 7 p]fectly acqua9t$ ) ! me?od ( mak+ sun-dials ) incl9$ 8/yles10 or 8gnomons40 ,illu/ration3 ,,fig4 #ac4 ,small portable sun-dials 7 once mu* us$ be=e ! introduction ( wat*es1 & 7 provid$ ) compasses by :i* !y c\ld be turn$ r\nd1 s t ! 8/yle0 po9t$ to ! nor?4 ,sun-dials 7 only available dur+ ! h\rs ( ! day :5 ! sun 0 %9+4 ,! desire to m>k ! h\rs ( ! night l$ to ! adoption ( wat] clocks1 :i* measur$ "t by ! am\nt ( wat] :i* escap$ f a small hole 9 a level ( wat]4 ,"s c>e1 h[ev]1 is requir$ to secure correct regi/ration4 ,= suppose t we h a vessel ) a small pipe lead+ out ne> ! bottom1 !n ! am\nt ( wat] :i* w run out ( ! pipe 9 a giv5 "t dep5ds ^u ! pressure ( ! wat] at ! pipe1 & ?is dep5ds 9 its turn ^u ,p ,q1 ! head ( wat] 9 ! vessel4 ,:5ce x foll[s t ! division ,q ,r1 due to say an h\r's run ( ! clock at ,q ,r1 w be m ?an q r1 ! division correspond+ to an h\r1 at q1 a po9t l[] d[n betwe5 ,p & ,q1 & h5ce ! divisions m>k$ on ! vessel to %[ ! h\rs by means ( ! level ( ! wat] w\ld be unev51 becom+ small] & small] z ! wat] fell 9 ! vessel4 ,to avoid ! inconv5i5ce ( unequal divisions1 ! wat] to be measur$ 0 all[$ to escape into an empty vessel f a vessel 9 :i* its surface 0 always kept at a con/ant level4 ,inasmu* z ! pressure on ! pipe or orifice 9 ! vessel 9 :i* ! wat] 0 always kept at a con/ant level 0 always con/ant1 x foll[$ t equal volumes ( wat] indicat$ equal times1 & ! vessel into :i* ! wat] fell ne$$ only to be equally divid$4 ,z a measure ( h\rs ( ! day 9 c\ntries su* z ,egypt1 :]e ! h\rs 7 always equal1 & ?us :]e ! long] days conta9$ m h\rs1 ! wat] clock 0 v suitable2 b 9 ,greece & ,rome1 :]e ! day1 :atev] its l5g?1 0 always divid$ into twelve h\rs1 ! simple wat] clock 0 z unsuitable z a mod]n clock w\ld be1 = x always divid$ ! h\rs equally1 & took no acc\nt ( ! fact t by su* a sy/em ! h\rs 9 summ] 7 long] ?an 9 w9t]4 ,9 ord]1 !re=e1 to make ! wat] clock available 9 ,greece & ,italy1 x became necess>y to make ! h\rs unequal1 & to arrange !m to correspond ) unequal h\rs ( ! ,greek day4 ,?is plan 0 accompli%$ z foll[s4 ,^u ! wat] :i* 0 p\r$ into ! vessel t measur$ ! h\rs 0 plac$ a float2 & on ! float /ood a figure made ( ?9 copp]1 ) a w& 9 its h&4 ,?is w& po9t$ to an unequally divid$ scale4 ,a sep>ate scale 0 provid$ = e day 9 ! ye>1 & ^! scales 7 m\nt$ on a drum :i* revolv$ s z to turn r\nd once 9 ! ye>4 ,?us z ! figure rose ea* day by means ( a cog:eel x mov$ ! drum r\nd "o division1 or "o ?ree hundr$ & sixty-fif? "p ( a revolution4 ,by ?is means ! scale correspond+ to any p>ticul> day ( w9t] or summ] 0 br\ght opposite ! w& ( ! figure1 & ?us ! scale ( h\rs 0 kept true4 ,9 fact1 ! wat] clock1 :i* kept true "t1 0 made by artificial means to keep untrue "t1 9 ord] to correspond ) ! unequal h\rs ( ! ,greek days4 ,9 ! picture ,a is ! receiv+ wat] vessel1 ,p ! pipe ?r\gh :i* ! wat] fl[s2 ,b is ! figure1 ,c ! rod2 ,d is ! drum1 made to revolve by ! cog:eel ,e1 conta9+ #cfe tee?1 ( :i* "o too? 0 driv5 =w>d at ! close ( ea* day4 ,a syphon ,g 0 fix$ 9 ! vessel ,a1 s t :5 ! figure _h ris5 to ! top & pu%$ =w>d ! lev] ,f1 ! syphon sudd5ly empti$ ! vessel ?r\gh ! pipe ,h1 & ! figure fell to ! bottom ( ! vessel ,a & became ready to rise & regi/] ano!r day4 ,! divisions on ! drum are1 ( c\rse1 unev54 ,on "o side1 correspond+ to ! summ]1 ! day h\rs w\ld reckon ab\t sev5ty m9utes ea*1 ! night h\rs w\ld be only ab\t fifty m9utes ea*1 s t ! day divisions on ! scale w\ld be long1 & ! night divisions %ort4 ,! rev]se w\ld be ! case 9 w9t]4 ,&1 !re=e1 ! l9es r\nd ! drum w\ld g 9 an unev5 wavy =m4 ,illu/ration3 ,,fig4 #ad4 ,su* wat] clocks z ^! 7 us$ by ! anci5t ,romans4 ,s& 0 also us$ to measure "t4 ,z soon z ! art ( bl[+ glass _h be5 p]fect$ by ! p ( ,byzantium1 f :om ! art pass$ to ! ,v5etians1 s&-glasses 7 made4 ,^! glasses 7 us$ = all sorts ( purposes1 = spee*es & = cook+1 b _! mo/ important use 0 at sea4 ,= x 0 v important 9 ! e>ly days ( navigation to "k ! spe$ at :i* ! vessel 0 proce$+ 9 ord] t "o's place at sea might be calculat$4 ,! e>lie/ me?od 0 to ?r[ ov] a heavy piece ( wood ( a %ape t resi/$ be+ dragg$ ?r\gh ! wat]1 & ) a /r+ ti$ to x4 ,! block ( wood 0 call$ ! log1 & ! /r+ _h knots 9 x4 ,! knots 7 s arrang$ t :5 "o ( !m ran ?r\gh "o's f+]s 9 a half-m9ute measur$ by a s&-glass x indicat$ t ! vessel 0 go+ at ! spe$ ( "o nautical mile 9 an h\r4 ,! nautical mile 0 tak5 s t sixty ( !m con/itut$ "o degree1 t is "o ?ree hundr$ & sixtie? "p ( a great circle ( ! e>?4 ,ea* nautical mile has1 !re=e1 #f1jhj feet4 ,?is is bigg] ?an an ord9>y mile on l&1 :i* has only #e1bhj feet4 ,! knots1 !re=e1 h to be arrang$ s t :5 ! %ip is go+ "o nautical mile--t is to say1 #f1jhj feet--9 an h\r1 a knot %all run out dur+ ! half-m9ute run ( ! m9ute glass4 ,?is is atta9$ by putt+ ! knots #a_/abj #f1jhj #ej feet #g in*es ap>t4 ,z "o sailor heav$ ! log ov] he gave a /amp on ! deck & all[$ ! cord to run out ?r\gh 8 f+]s4 ,ano!r sailor !n turn$ ! s&-glass4 ,:5 ! s& _h all run out1 %[+ t half a m9ute _h pass$1 ! man :o 0 lett+ ! cord run ?r\gh 8 f+]s gripp$ x fa/1 & obs]v$ h[ _m knots or p>ts ( knots ( /r+ _h run out1 & ?us 0 able to tell h[ _m 8knots0 p] half-m9ute ! vessel 0 go+1 t is to say1 h[ _m nautical miles an h\r4 ,! mod]n plan ( obs]v+ ! spe$ ( vessels is diff]5t4 ,n[ we use a pat5t log1 consi/+ ( a m9iature screw propell] ti$ to a /r+ & dragg$ ?r\gh ! wat] aft] ! vessel4 ,z x is pull$ ?r\gh ! wat] x revolves1 & ! numb] ( revolutions x makes %[s h[ mu* wat] x has pass$ ?r\gh1 & ?us :at di/ance x has gone4 ,! numb] ( revolutions is measur$ by a c\nt+ me*anism1 & c be read (f :5 ! log is pull$ 94 ,or sometimes ! screw is atta*$ to a /iff wire1 & ! c\nt+ me*anism is kept on bo>d ! %ip4 ,we use ! expression 8knots an h\r0 q incorrectly4 ,x %\ld be 8knots p] half-m9ute10 or 8nautical miles an h\r40 ,x is easy to use ! fl[ ( s& = all sorts ( purposes to measure "t4 ,?us1 if s& be all[$ to fl[ f a hopp] ?r\gh a f9e hole into a bucket1 ! bucket may be arrang$ s t :5 a giv5 "t has elaps$1 & a giv5 weight ( s& has !re=e fall51 ! bucket %all tip ov]1 & release a cat*1 :i* %all !n all[ a weight to fall & any me*anical op]ation to be done t is requir$4 ,?us1 = example1 we might put an egg 9 a small hold] ti$ to a /r+ & l[] x into a saucepan ( boil+ wat]4 ,! /r+ might h a c\nt]-weight atta*$ to x1 act+ ov] a pulley & ?us always try+ to pull x up out ( ! wat]4 ,b ?is might be prev5t$ by a p9 pass+ ?r\gh a loop 9 ! /r+ & prev5t+ x mov+4 ,a hopp] or funnel might be fill$ ) s& :i* 0 all[$ gradually to escape into a small tip-waggon or o!r simil> device1 s t :5 a giv5 am\nt ( s& _h ent]$ ! tip-waggon w\ld tip ov]1 lur* ! p9 out ( ! loop1 & ?us release ! weight1 :i* 9 its turn w\ld pull ! egg up out ( ! wat] 9 ?ree m9utes or any desir$ "t aft] x _h be5 put 91 or a hole c\ld be made 9 ! saucepan1 furni%$ ) a little tap1 & ! wat] t ran out might be made to fall into a tip-waggon & tip x ov]1 & ?us :5 x _h run out to put an ext+ui%] on to ! _s lamp t 0 heat+ ! saucepan1 & at ! same "t make a contact & r+ an electric bell4 ,by ?is means ! egg w\ld be always exactly cook$ to ! "r am\nt1 w\ld be kept w>m aft] x 0 cook$1 & a signal giv5 :5 x 0 ready4 ,illu/ration3 ,,fig4 #ae4 ,! sket* %[s su* an arrangem5t4 ,! saucepan is ab\t ?ree in*es 9 diamet] & two in*es high4 ,:5 fill$ ) wat] x w hold an egg com=tably4 ,! ext+ui%] ,e1 m\nt$ on a h+e ,q1 is turn$ back1 & ! _s lamp ,l is lit4 ,z soon z ! wat] boils1 ! tap ,t is turn$1 & ! wat] gradually trickles away into ! tip-waggon4 ,z soon z x is full x tips ov] & /rikes ! arm ,x ( ! ext+ui%]1 & turns ! lamp out4 ,! little hot wat] left 9 ! saucepan w keep ! egg w>m = "s "t4 ,! waggon ,w mu/ h a weight ,p at "o end ( x1 & ! fulcrum mu/ be ne>] to t end1 s t :5 empty x re/s ) ! end ,p d[n1 b :5 full x tips ov] on ! fulcrum1 :5 ! waggon has receiv$ ! "r quantity ( wat]4 ,i leave to ! +5i\s read] ! task ( work+ out ! details ( su* a ma*9e1 :i*1 if made prop]ly1 w act v well & may be made = a numb] ( eggs & work$ ) v little tr\ble4 ,illu/ration3 ,,fig4 #af4 ,m]cury has be5 us$ also z an h\r-glass4 ,! orifice mu/ be exce$+ly f9e4 ,or a bubble ( m]cury may be put into a tube :i* conta9s air1 & made gradually z x falls to drive ! air out ?r\gh a m9ute hole4 ,! difficulty is to get ! hole f9e en\gh4 ,all t c be done is to draw out a f9e tube 9 ! bl[-lamp1 break x (f1 & put ! brok5 po9t 9 ! bl[-lamp until x is almo/ completely clos$ up4 ,a tube may ?us be made ab\t twelve in*es long t w take twelve h\rs = a bubble ( m]cury to desc5d 9 x4 ,b ! tr\ble ( mak+ s small a hole is consid]able4 ,illu/ration3 ,,fig4 #ag4 ,k+ ,alfr$ is said to h us$ c&les made ( wax to m>k ! "t4 ,z !y blew ab\t ) ! draughts1 he put !m 9 lant]ns ( horn4 ,!y _h no glass w9d[s 9 ^? days1 b only op5+s clos$ ) heavy wood5 %utt]s4 ,^! l>ge %utt]s 7 = use 9 f9e wea!r4 ,small] %utt]s 7 made 9 !m1 s z to let a little light 9 9 ra9y wea!r )\t lett+ 9 too mu* w9d & ra94 ,rooms mu/ !n h be5 v draughty1 s t p requir$ to we> caps & g[ns1 & b$s _h ?ick curta9s drawn r\nd !m4 ,:5 glass 0 fir/ inv5t$ x 0 only us$ by k+s & pr9ces1 & glass casem5ts 7 c>ri$ ab\t ) !m to be fix$ into ! w9d[s ( ! h\ses to :i* !y came1 & remov$ at _! dep>ture4 ,oil lamps 7 also us$ to m>k ! "t4 ,"s ( !m c]ta9ly z e>ly z ! fifte5? c5tury 7 made l bird-bottles2 t is to say1 !y consi/$ ( a res]voir clos$ at ! top ) a pipe lead+ out ( ! bottom4 ,:5 full1 ! pressure ( ! ext]nal atmosph]e keeps ! oil 9 ! bottle1 & ! oil /&s 9 ! neck & fe$s ! wick4 ,z ! oil is consum$ bubbles ( air pass back along ! neck & rise up to ! top ( ! oil1 ! level ( :i* gradually s9ks4 ,( c\rse ! "t %[n by ! lamp v>ies ) ! rate ( burn+ ( ! oil1 & h5ce ) ! size ( ! wick1 s t ! me?od ( measur+ "t is a v r\gh "o4 ,,app5dix4 ,to make a sun-dial1 procure a circul> piece ( z9c1 ab\t in* ?ick1 & say twelve in*es 9 diamet]4 ,h a 8/yle0 or 8gnomon0 ca/ su* t ! angle ( its edge equals ! latitude ( ! place :]e ! sun-dial is to be set up4 ,?is = ,london w be equal to #ea #cj4 ,a patt]n may be made = ?is 9 wood2 x %\ld !n be ca/ 9 gun-metal1 :i* is mu* bett] = out-(-door exposure ?an brass4 ,on a %eet ( pap] draw a circle ,a ,b ,c ) c5tre ,o4 ,make ! angle ,b ,o ,d equal to ! latitude ( ! place = ,london #ea #cj4 ,f ,a draw ,a ,e p>allel to ,o ,b to meet ,o ,d 9 ,e1 & ) radius ,o ,e describe ano!r circle ab\t ,o4 ,divide ! inn] circle ,a ,b ,c into tw5ty-f\r p>ts1 & draw radii ?r\gh !m f ,o to meet ! l>g] circle4 ,?r\gh any divisions 7say t correspond+ to two o'clock7 draw l9es p>allel to ,o ,b1 ,o ,c1 respectively to meet 9 a4 ,!n ! l9e ,o a is ! %ad[ l9e ( ! gnomon at two o'clock4 ,! l9es ?us drawn on pap] may be transf]r$ to ! dial & engrav$ on x1 or else eat5 9 ) acid 9 ! mann] 9 :i* et*+s are done4 ,illu/ration3 ,,fig4 #ah4 ,! c5tre ,o ne$ n be 9 ! c5tre ( ! z9c disc1 b may be on "o side ( x1 s z to give bett] room = ! h\rs1 etc4 ,a motto may be et*$ ^u ! dial1 su* z 8,horas non num]o nisi s]5as10 or 8,qual 'hom s5za ,dio1 son s5za sol io10 or any suitable inscription1 & ! dial is ready = use4 ,x is be/ put up by turn+ x till ! h\r is %[n truly z comp>$ ) a correctly tim$ wat*4 ,x mu/ be levell$ ) a _s level4 ,x mu/ be rememb]$ t ! sun does n move q uni=mly 9 8 ye>ly pa? among ! fix$ />s4 ,?is is because he moves n 9 a circle1 b 9 an ellipse ( :i* ! e>? is 9 "o ( ! foci4 ,h5ce ! h\rs %[n on ! dial are slightly irregul>1 ! sun be+ sometimes 9 advance ( ! clock1 sometimes beh9d x4 ,! diff]5ce is nev] m ?an a qu>t] ( an h\r4 ,!re is no diff]5ce at midsumm] & midw9t]4 ,illu/ration3 ,,fig4 #ai4 ,civil "t is sol> "t av]ag$1 s z to make ! h\rs & days all equal4 ,! diff]5ce betwe5 civil "t & app>5t sol> "t is call$ ! equation ( "t1 & is ! am\nt by :i* ! sun-dial is 9 advance ( or 9 ret>d ( ! clock4 ,9 sett+ a dial by means ( a wat*1 ( c\rse all[ance mu/ be made = ! equation ( "t4 ,,*apt] ,,ii4 ,9 ! la/ *apt] a %ort description has be5 giv5 ( ! ideas ( ! anci5ts z to ! nature ( ! e>? & heav5s4 ,be=e we pass to ! *anges introduc$ by mod]n sci5ce1 x w be well to devote a %ort space to an exam9ation ( anci5t sci5tific ideas4 ,all sci5ce is really bas$ ^u a comb9ation ( two me?ods1 call$ respectively inductive & d$uctive reason+4 ,! fir/ ( ^! consi/s 9 ga!r+ toge!r ! results ( obs]vation & exp]im5t1 &1 hav+ put !m all toge!r1 9 ! =mulation ( univ]sal laws4 ,hav+1 = example1 long obs]v$ t all heavy ?+s t5d$ to g t[>ds ! c5tre ( ! e>?1 we might conclude t1 s9ce ! />s rema9 up 9 ! sky1 !y c h no weight4 ,! conclusion w\ld be wrong 9 ?is case1 n because ! me?od is wrong1 b because x is wrongly appli$4 ,x is true t all heavy ?+s t5d to g to ! c5tre ( ! e>?1 b if !y are be+ :irl$ r\nd l a /one 9 a sl+ ! c5trifugal =ce w c\nt]act ?is t5d5cy4 ,! fir/ "p ( ! reason+ w\ld be inductive1 ! second d$uctive4 ,all ?is reason+ consi/s1 !re=e1 9 =m+ z complete an idea z possible respect+ ! nature ( a ?+1 & !n conclud+ f t idea :at ! ?+ w d or :at its o!r prop]ties w be4 ,9 fact1 y =m correct ideas1 or 8concepts10 z !y are call$1 & reason f !m4 ,b ! dang] arises :5 y beg9 to reason be=e y are sure ( ! nature ( y\r concepts1 & ?is has be5 ! great s\rce ( error1 & x 0 ?is error t all m5 ( sci5ce s commonly fell into all ?r\gh anci5t & mod]n times up to ! sev5te5? c5tury4 ,( c\rse1 if x 7 possible by m]e obs]vation to d]ive a complete k ( any objects1 x w\ld be ! simple/ me?od4 ,all t w\ld be necess>y to d w\ld be to reason correctly f ?is k4 ,un=tunately1 h[ev]1 x is n possible to obta9 k ( ?is k9d 9 any bran* ( sci5ce4 ,! anci5t me?od resembl$ ! action ( "o :o %\ld cont5d t by obs]v+ & talk+ to a man y c\ld acquire su* a k ( 8 "* z w\ld infallibly enable y to und]/& & pr$ict all 8 actions1 & to take little tr\ble to see :e!r :at he did v]ifi$ y\r pr$ictions4 ,! only diff]5ce betwe5 ! old me?ods & ! new is t 9 mod]n times m5 h le>n$ to give f> m c>e to ! =mation ( correct ideas to />t )1 are mu* m cauti\s 9 argu+ f !m1 & keep te/+ !m aga9 & aga9 on e possible opportunity4 ,! con/ant insi/5ce on ! =mation ( cle> ideas & ! practice (1 z ,"l ,bacon call$ x1 8putt+ nature to ! torture10 is ! ma9 cause ( ! advance ( physical sci5ce 9 mod]n times1 & ! want ( application ( ^! pr9ciples expla9s :y s little progress is be+ made 9 ! s-call$ 8humanit>ian0 /udies1 su* z philosophy1 e?ics1 & politics4 ,! works ( ,ari/otle are full ( ! fallaci\s me?od ( ! old sy/em4 ,9 8 "w on ! heav5s he repeat$ly argues t ! heav5ly bodies mu/ move 9 circles1 because ! circle is ! mo/ p]fect figure4 ,he affects a p]plexity z to h[ a circle c at ! same "t be convex & also its opposite1 concave1 & repeat$ly entangles 8 read]s 9 simil> m]e ^w confusion4 ,reg>d$ z a man ( sci5ce1 he mu/ be plac$1 ,i ?9k1 9 spite ( 8 great g5ius1 bel[ ,ar*im$es1 ,hipp>*us1 & sev]al o!r anci5t a/ronom]s & physici/s4 ,8 errors liv$ aft] him & dom9at$ ! ?\ght ( ! middle ages1 & = a long "t delay$ ! progress ( sci5ce4 ,! o!r great writ] on a/ronomy ( anci5t times 0 ,ptolemy ( ,alex&ria4 ,8 "w 0 call$ ! 8,great ,collection10 & 0 :at we %\ld n[ t]m a comp5dium ( a/ronomy4 ,al?\gh bas$ on a fundam5tal error1 x is a ?or\ghly sci5tific "w4 ,!re is none ( ! false philosophy 9 x t s mu* disfigures ! "w ( ,ari/otle4 ,! reasons = believ+ t ! e>? is at re/ are int]e/+4 ,ptolemy argues t if ! e>? 7 mov+ r\nd on its axis once 9 tw5ty-f\r h\rs a bird t flew up f x w\ld be left beh9d4 ,at fir/ sight ?is argum5t seems v conv9c+1 = x appe>s impossible to conceive a body sp9n+ at ! rate at :i* ! e>? is alleg$ to move1 & yet n leav+ beh9d any bodies t become deta*$ f x4 ,on ! o!r h&1 ! sy/em :i* taught t ! sun & planets mov$ r\nd ! e>?1 & :i* _h be5 adopt$ l>gely on acc\nt ( its suppos$ simplicity1 prov$1 on fur!r exam9ation1 to be exce$+ly complicat$4 ,ea* planet1 in/ead ( mov+ simply & uni=mly r\nd ! e>? 9 a circle1 _h to be suppos$ to move uni=mly 9 a circle r\nd ano!r po9t t mov$ r\nd ! e>? 9 a circle4 ,?is second>y circle1 9 :i* ! planet mov$1 0 call$ an epicycle4 ,& ev5 ?is m complicat$ view fail$ to expla9 ! facts4 ,a sy/em :i*1 l t ( ,ari/otle & ,ptolemy1 0 bas$ on d$uctions f concepts1 & :i* consi/$ r ( draw+ conclusions ?an ( exam9+ premises1 0 v well adapt$ to m$ival ?\ght1 & =m$ ! f\ndation ( a/ronomy & geography z taught by ! s*oolm54 ,illu/ration3 ,,fig4 #bj4 ,! poem ( ,dante accurately repres5ts ! be/ sci5tific k ( 8 day4 ,accord+ to 8 views1 ! c5tre ( ! e>? 0 a fix$ po9t1 su* t all ?+s ( a heavy nature t5d$ t[>ds x4 ,?us ! e>? & wat] collect$ r\nd x 9 ! =m ( a ball4 ,he _h no idea ( ! attraction ( "o p>ticle ( matt] = ano!r p>ticle4 ,! only conception he _h ( gravity 0 ( a =ce draw+ all heavy ?+s to a c]ta9 po9t1 :i* ?us became ! po9t r\nd :i* ! _w 0 =m$4 ,! habitable "p ( ! e>? 0 an isl&1 ) ,j]usalem 9 ! middle ( x ,j4 ,r\nd ?is isl& 0 an ocean ,o4 ,"u ! isl&1 9 ! =m ( a holl[ cone1 0 hell1 ) its sev5 circles ( torm5t1 ea* circle becom+ small] & small]1 till x got d[n into ! c5tre ,c4 ,heav5 0 at ! opposite side ,h ( ! e>? to ,j]usalem1 & 0 beyond ! circles ( ! planets1 9 ! primum mobile4 ,:5 ,lucif] 0 expell$ f heav5 aft] 8 rebellion aga9/ ,god1 hav+ become ( a nature to be attract$ to ! c5tre ( ! e>?1 & no long] drawn heav5w>ds1 he fell f heav51 & imp+$ ^u ! e>? j at ! antipodes ( ,j]usalem1 ) su* viol5ce t he plung$ "r ?r\gh x to ! c5tre1 ?r[+ up beh9d him a hill4 ,on ! summit ( ?is hill 0 ! ,g>d5 ( ,ed51 :]e our fir/ p>5ts liv$1 & d[n ! sides ( ! hill 0 a spiral w9d+ way :i* con/itut$ purgatory4 ,dante1 hav+ desc5d$ into hell1 & pass$ ! c5tre1 f\nd 8 head imm$iately turn$ r\nd s z to po9t ! o!r way up1 &1 hav+ asc5d$ a tortu\s pa?1 came out ^u ! hill ( ,purgatory4 ,hav+ se5 ?is1 he 0 conduct$ to ! v>i\s sph]es ( ! planets1 & 9 ea* sph]e he became put into spiritual communion ) ! spirits ( ! bless$ :o 7 ( ! "* repres5t$ by t sph]e1 & he supposes t he 0 ?us all[$ to proce$ f sph]e to sph]e until he 0 p]mitt$ to come into ! pres5ce ( ! ,almighty1 :o 9 ! primum mobile presid$ ov] ! cele/ial ho/s4 ,! a/ronomical descriptions giv5 by ,dante ( ! ris+ & sett+ ( ! sun & moon & planets are q accurate1 accord+ to ! sy/em ( ! _w z conceiv$ by him1 & %[ n only t he 0 a compet5t a/ronom]1 b t he probably possess$ an a/rolabe & "s tables ( ! motions ( ! heav5ly bodies4 ,our own poet ,*auc] may also be cr$it$ ) accurate k ( ! a/ronomy ( 8 day4 ,8 poems (t5 m5tion ! con/ellations1 & "o ( !m is devot$ to a description ( ! a/rolabe1 an in/rum5t some:at l ! cele/ial globe :i* us$ to be employ$ 9 s*ools4 ,b ) ! revival ( le>n+ 9 ,europe & ! rise ( fre$om ( ?\ght1 ! old !ories 7 que/ion$ 9 m ?an "o qu>t]4 ,x occurr$ to ,cop]nicus1 an ecclesia/ic :o liv$ 9 ! sixte5? c5tury1 to re-exam9e ! !ory t _h be5 />t$ 9 anci5t times1 & to consid] :at explanation ( ! appe>ance ( ! heav5ly bodies c\ld be giv5 on ! hypo!sis put =w>d by ,py?agoras1 t ! e>? mov$ r\nd on its own axis1 & also r\nd ! sun4 ,x may appe> r curi\s t two !ories s diff]5t1 "o t ! sun goes r\nd ! e>? & ! o!r t ! e>? goes r\nd ! sun1 %\ld ea* be capable ( expla9+ ! obs]v$ appe>ances ( ^? bodies4 ,b x mu/ be rememb]$ t motion is relative4 ,if 9 a waltz ! g5tleman goes r\nd ! lady1 ! lady also goes r\nd ! g5tleman4 ,if y take away ! room 9 :i* !y are turn+1 & consid] !m z sp9n+ r\nd l two insects 9 space1 :o is to say :i* ( !m is at re/ & :i* 9 motion8 ,= motion is relative4 ,i c consid] motion 9 a tra9 f ,london to ,york4 ,z ,i leave ,london ,i get ne>] to ,york1 & ,i move ) respect to ,london & ,york4 ,b if bo? ,london & ,york 7 annihilat$ h[ %\ld ,i "k t ,i 0 9 motion at all8 ,or1 aga91 if1 :ile ,i 0 at re/ 9 ! tra9 at a /ation on ! way1 in/ead ( ! tra9 mov+ ! :ole e>? began to move 9 a s\?w>d direction1 & ! tra9 9 "s way 7 left /ation>y1 !n1 ?\gh ! e>? 0 mov+1 & ! tra9 0 at re/1 yet1 s f> z ,i 0 conc]n$1 ! tra9 w\ld appe> to h />t$ aga9 on its j\rney to ,york1 at :i* place x w\ld appe> to arrive 9 due "t4 ,! trees & h$ges w\ld fly by at ! prop] rate1 & :o 0 to say :e!r ! tra9 0 9 motion or ! e>?8 ,! !ory ( ,cop]nicus1 h[ev]1 rema9$ b a !ory4 ,x 0 oppos$ to ! evid5ce ( ! s5ses1 :i* c]ta9ly leads u to ?9k t ! e>? is at re/1 & x 0 oppos$ also to ! ideas ( "s among ! !ologians :o ?\ght t ! ,bible taught u t ! e>? 0 s fa/ t x c\ld n be mov$4 ,!re=e ! !ory f\nd b little fav\r4 ,x 0 9 fact necess>y be=e ! "q c\ld be prop]ly consid]$ on its m]its t m %\ld be kn[n ab\t ! laws ( motion1 & ?is 0 ! pr9cipal "w ( ,galileo4 ,! m]it ( ,galileo is n only to h plac$ on a firm basis ! /udy ( me*anics1 b to h set himself def9itely & consci\sly to rev]se ! anci5t me?ods ( le>n+4 ,he disc>d$ au?ority1 bas+ all k ^u reason1 & prote/$ aga9/ ! !ory t ! /udy ( words c\ld be any sub/itute = ! /udy ( ?+s4 ,allud+ to ! ma!maticians ( 8 day1 8,?is sort ( m510 says ,galileo 9 a lett] to ! a/ronom] ,kepl]1 8fanci$ t philosophy 0 to be /udi$ l ! #8neid' or #8,odyssey1' & t ! true read+ ( nature 0 to be detect$ by ! collat+ ( texts40 ,& mo/ ( 8 life 0 sp5t 9 fight+ aga9/ preconceiv$ ideas4 ,x 0 ma9ta9$ t !re c\ld only be sev5 planets1 because ,god _h ord]$ all ?+s 9 nature by sev5s 78,dianoia ,a/ronomica10 #afaj72 & ev5 ! discov]ies ( ! spots on ! sun & ! m\nta9s 9 ! moon 7 discr$it$ on ! gr\nd t cele/ial bodies c\ld h no blemi%es4 8,h[ great & common an error10 writes ,galileo1 8appe>s to me ! mi/ake ( ^? :o p]si/ 9 mak+ _! k & appreh5sion ! measure ( ! k & appreh5sion ( ,god1 z if t alone 7 p]fect :i* !y und]/& to be s4 ,b 444 nature has o!r scales ( p]fection1 :i* we1 be+ unable to compreh5d1 class among imp]fections4 8,if "o ( our mo/ celebrat$ ar*itects _h _h to di/ribute ! va/ multitude ( fix$ />s ov] ! great vault ( heav51 ,i believe he w\ld h dispos$ !m ) beautiful arrangem5ts ( squ>es1 hexagons1 & octagons2 he w\ld h disp]s$ ! l>g] ones among ! middle-siz$ or less]1 s z to correspond exactly ) ea* o!r2 & !n he w\ld ?9k he _h contriv$ admirable proportions2 b ,god1 on ! contr>y1 has %ak5 !m out f ,8 h& z if by *ance1 & we1 =soo?1 mu/ ?9k t ,he has scatt]$ !m up yond] )\t any regul>ity1 symmetry1 or elegance40 ,9 "o ( ,galileo's 8,dialogues0 ,simplicio says1 8,t ! cause t ! p>ts ( ! e>? move d[nw>ds is notori\s1 & ev]yone kn[s t x is gravity40 ,salviati replies1 8,y are out1 ,ma/] ,simplicio3 y %\ld say t ev]yone kn[s t x is call$ gravity2 ,i d n ask y = ! "n1 b = ! nature1 ( ! ?+ ( :i* nature nei!r y nor ,i "k any?+40 ,too (t5 are we /ill incl9$ to put ! "n = ! ?+1 & to ?9k :5 we use big words su* z art1 empire1 lib]ty1 & ! rights ( man1 t we expla9 matt]s in/ead ( obscur+ !m4 ,n "o man 9 a ?\s& :o uses !m kn[s :at he means2 no two m5 agree z to _! signification4 ,! relativity ( motion m5tion$ above 0 v elegantly illu/rat$ by ,galileo4 ,he call$ att5tion to ! fact t if an arti/ 7 mak+ a draw+ ) a p5 :ile 9 a %ip t 0 9 rapid passage ?r\gh ! wat]1 ! true l9e drawn by ! p5 ) reg>d to ! surface ( ! e>? w\ld be a long /raight l9e ) "s small d5ts or v>iations 9 x4 ,yet ! v same l9e trac$ by ! p5 ^u a pap] c>ri$ along 9 ! %ip made up a draw+4 ,:e!r y saw a long unev5 l9e or a draw+ 9 ! pa? t ! p5 _h trac$ dep5d$ altoge!r on ! po9t ( view ) :i* y reg>d$ its motion4 ,illu/ration3 ,,fig4 #ba4 ,b ! fir/ great /ep 9 sci5ce :i* ,galileo made :5 q a "y pr(essor at ,pisa 0 ! refutation ( ,ari/otle's op9ion t heavy bodies fell to ! e>? fa/] ?an light ones4 ,9 ! pres5ce ( a numb] ( pr(essors he dropp$ two balls1 a l>ge & a small "o1 f ! p>apet ( ! lean+ t[] ( ,pisa4 ,!y fell to ! gr\nd almo/ exactly 9 ! same "t4 ,?is exp]im5t is q an easy "o to try4 ,"o ( ! simple/ ways is z foll[s3 ,into any beam 7! l9tel ( a door w d71 & ab\t f\r in*es ap>t1 drive ?ree smoo? p9s s z to project ea* ab\t a qu>t] ( an in*2 !y mu/ n h any heads4 ,take two unequal weights1 say ( #a lb4 & #c lbs4 ,any?+ w d1 say a boot = "o & pocket-knife = ! o!r2 fa/5 loops ( f9e /r+ to !m1 put ! loops ov] ! c5tre peg ( ! ?ree1 & pass ! /r+s "o ov] ea* ( ! side pegs4 ,n[ ( c\rse if y hit* ! loops (f ! c5tre peg ,p ! objects w be releas$ toge!r4 ,?is c be done by mak+ a loop at ! end ( ano!r piece ( /r+1 ,a1 & putt+ x on to ! c5tre peg beh9d ! o!r loops4 ,if ! /r+ be pull$ ( c\rse ! loop on x pulls ! o!r two loops (f ! c5tral peg1 & all[s ! boot & ! knife to drop4 ,! boot & ! knife %\ld be hung s z to be at ! same height4 ,!y w !n fall to ! gr\nd toge!r4 ,! same exp]im5t c be tri$ by dropp+ two objects f an upp] w9d[1 hold+ "o 9 ea* h&1 & tak+ c>e to let !m g toge!r4 ,illu/ration3 ,,fig4 #bb4 ,?is result is v puzzl+2 "o does n und]/& x4 ,x appe>s z ?\gh two unequal =ces produc$ ! same effect4 ,x is z ?\gh a /rong horse c\ld run no fa/] ?an a weak] "o4 ,! pr(essors 7 s irritat$ at ! result ( ?is exp]im5t1 & inde$ at ! g5]al "* ( "y ,pr(essor ,galileo's attacks on ! "t-hon\r$ ideas ( ,ari/otle1 t !y nev] re/$ till !y worri$ him out ( 8 v poorly paid *air at ,pisa4 ,he !n took a pr(essor%ip at ,padua4 ,let u n[ exam9e ?is result & see :y x is t ! ideas we %\ld at fir/ naturally =m are wrong1 & t ! heavy body w fall 9 exactly ! same "t z ! light "o4 ,we may reason ! matt] 9 ?is way4 ,! heavy body has m =ce pull+ on x2 t is true1 b !n1 on ! o!r h& !re is m matt] :i* has got to be mov$4 ,if a cr[d ( p]sons are ru%+ out ( a build+1 ! total =ce ( ! cr[d w be great] ?an ! =ce ( "o man1 b ! spe$ at :i* !y c get out w n be great] ?an ! spe$ ( "o man2 9 fact1 ea* man 9 ! cr[d has only =ce en\gh to move 8 own mass4 ,& s x is ) ! weights3 ea* "p ( ! body is occupi$ 9 mov+ itself4 ,if y add m to ! body y only add ano!r "p :i* has itself to move4 ,a hundr$ m5 by tak+ h&s _c run fa/] ?an "o man4 ,b1 y w say1 _c a man run fa/] ?an a *ild8 ,yes1 because 8 impell+ p[] is great] 9 proportion to 8 weight ?an t ( a *ild4 ,if x 7 ! fact t ! attraction ( gravity due to ! e>? act$ on "s bodies ) =ces great] 9 proportion to _! masses ?an ! =ces t act$ on o!r bodies1 !n x is true t ^? diff]5t bodies w\ld fall 9 unequal "t4 ,b x is an exp]im5tal fact t ! attractive =ce ( gravity is always exactly proportional to ! mass ( a body1 & ! resi/ance to motion is also proportional to mass1 h5ce ! =ce ) :i* a body is mov$ by ! e>?'s attraction is always proportional to ! difficulty ( mov+ ! body4 ,?is w\ld n be ! case ) o!r me?ods ( sett+ a body 9 motion4 ,if ,i kick a small ball ) all my might1 ,i %all s5d x fur!r ?an a kick ( equal /r5g? w\ld s5d a heavi] ball4 ,:y8 ,because ! impulse is ! same 9 ea* case1 b ! masses are diff]5t4 ,b if ^? balls are pull$ by gravity1 !n1 by ! v nature ( ! e>?'s attraction 7! reason ( :i* we _c expla971 ! small ball receives a little pull1 & ! big ball receives a big pull1 ! e>? exactly apportion+ its pull 9 ea* case to ! mass ( ! body on :i* x has to act4 ,x is to ?is fact1 t ! e>? pulls bodies ) a /r5g? always 9 ea* case exactly proportional to _! masses1 t is due ! result t !y fall 9 equal times1 ea* body hav+ a pull giv5 to x proportional to its ne$s4 ,! error ( ! view ( ,ari/otle 0 n only demon/rat$ by ,galileo by exp]im5t1 b 0 also demon/rat$ by argum5t4 ,9 ?is argum5t ,galileo imitat$ ! ab/ract me?ods ( ! ,ari/otelians1 & turn$ ^? me?ods aga9/ !mselves4 ,= he said1 8,y0 7! ,ari/otelians7 8say t a light] body w fall m sl[ly ?an a heavy "o4 ,well1 !n1 if y b9d a light body on to a heavy "o by means ( a /r+1 & let !m fall toge!r1 ! light body ought to hang beh9d1 & imp$e ! heavy body1 & ?us ! two bodies toge!r ought to fall m sl[ly ?an ! heavy body alone2 ?is foll[s f y\r view3 b see ! contradiction4 ,= ! two bodies ti$ toge!r con/itute a heavi] body ?an ! heavy body alone1 & ?us1 on y\r own !ory1 ought to fall m quickly ?an ! heavy body alone4 ,y\r !ory1 !re=e1 contradicts itself40 ,! tru? is t ea* body is occupi$ 9 mov+ itself )\t tr\bl+ ab\t mov+ its neighb\r1 s t if y put any numb] ( m>bles into a bag & let !m drop !y all g d[n individually1 z x 71 & all 9 ! "t :i* a s+le m>ble w\ld take to fall4 ,= any o!r result w\ld be a contradiction4 ,if y cut a piece ( bread 9 two1 & put ! two halves toge!r1 & tie !m toge!r ) a ?read1 w ! m]e fact t !y are two pieces make ea* ( !m fall m sl[ly ?an if !y 7 "o8 ,yet t is :at y w\ld be b\nd to ass]t on ! ,ari/otelian !ory4 ,hold an egg 9 y\r op5 h& & jump d[n f a *air4 ,! egg is n left beh9d2 x falls ) y4 ,yet y are ! heavi] ( ! two1 & on ,ari/otelian pr9ciples y ought to leave ! egg beh9d y4 ,x is true t :5 y jump d[n a bank y\r /raw hat w (t5 come (f1 b t is because ! air (f]s m resi/ance to x ?an ! air (f]s to y\r body4 ,x is ! d[nw>d ru% ?r\gh ! air t causes y\r hat to be left beh9d1 j z w9d w bl[ y\r hat (f )\t bl[+ y away4 ,= s9ce motion is relative1 x is all "o :e!r y jump d[n ?r\gh ! air1 or ! air ru%es pa/ y1 z 9 a w9d4 ,if !re 7 no air1 ! hat w\ld fall z fa/ z y\r body4 ,?is is easy to see if we h an airpump & are ?us enabl$ to pump out almo/ all ! air f a glass vessel4 ,9 t vessel s exhau/$1 a fea!r & a co9 w fall 9 equal times4 ,if we h n an airpump1 we c try ! exp]im5t 9 a m simple way4 ,= let u put a fea!r into a metal egg-cup & drop !m toge!r4 ,! cup w keep ! air f ! fea!r1 & ! fea!r w n come out ( ! cup4 ,bo? w fall to ! gr\nd toge!r4 ,b if ! light] body fall m sl[ly1 ! fea!r ought to be left beh9d4 ,if1 h[ev]1 y tie "s /r+s across a napk9 r+ s z to make a sort ( r\gh sieve1 & put a fea!r 9 x1 & !n drop ! r+1 !n z ! r+ falls ! air c get ?r\gh ! bottom ( ! r+ & act on ! fea!r1 :i* w be left float+ z ! r+ falls4 ,let u n[ g on to exam9e ! second fallacy t 0 d]iv$ f ! ,ari/otelians1 & t s long imp$$ ! advance ( sci5ce1 namely1 t ! e>? mu/ be at re/4 ,! pr9cipal reason giv5 = ?is 0 t if bodies 7 ?r[n up f ! e>? !y ought1 if ! e>? 7 9 motion1 to rema9 beh9d4 ,n[1 if ?is 7 s1 !n x w\ld foll[ t if a p]son 9 a tra9 :i* 0 mov+ rapidly ?rew a ball v]tically1 t is p]p5dicul>ly1 up into ! air1 ! ball1 in/ead ( com+ back into 8 h&1 ought to hit ! side ( ! c>riage beh9d him4 ,! next "t any ( my read]s travel by tra9 he c easily satisfy himself t ?is is n s4 ,b !re are o!r ways ( prov+ x4 ,= in/ance1 if a little waggon runn+ on rails has a spr+ gun fix$ 9 x 9 a p]p5dicul> position1 s arrang$ t :5 ! waggon comes to a p>ticul> po9t on ! rails a cat* releases ! trigg] & %oots a ball p]p5dicul>ly upw>ds1 x w be f\nd t ! ball1 in/ead ( go+ upw>ds 9 a v]tical l9e1 is c>ri$ along ov] ! waggon1 & ! ball z x asc5ds & desc5ds keeps always above ! waggon1 j z a hawk might hov] ov] a runn+ m\se1 & f9ally falls n beh9d ! waggon1 b into x4 ,s1 aga91 if an article is dropp$ out ( ! w9d[ ( a tra91 x w n simply be left beh9d z x falls1 b :ile x falls x w also p>take ( ! motion ( ! tra91 & t\* ! gr\nd1 n beh9d ! po9t f :i* x 0 dropp$1 b j und]nea? x4 ,! reason is1 t :5 ! ball is dropp$ or ?r[n x acquires n only ! motion giv5 to x by ! ?r[1 or by gravity1 b x takes also ! motion ( ! tra9 f :i* x is ?r[n4 ,if a ball is ?r[n f ! h&1 x d]ives its motion f ! motion ( ! h&1 & if at ! "t ( ?r[+ ! p]son :o does s is mov+ rapidly along 9 a tra91 8 h& has n only ! outw>d motion ( ! ?r[1 b also ! onw>d motion ( ! tra91 & ! ball !re=e acquires bo? motions simultane\sly4 ,h5ce !n x is n correct reason+ to say1 because a ball ?r[n up v]tically falls v]tically back to ! spot f :i* x 0 ?r[n1 t !re=e ! e>? mu/ be at re/2 ! same result w happ5 :e!r ! e>? is at re/ or 9 motion4 ,y c no m tell :e!r ! e>? is at re/ or 9 motion f ! behavi\r ( fall+ bodies ?an y c tell :e!r a %ip on ! ocean is at re/ or 9 motion f ! behavi\r ( bodies on x4 ,b y w say4 ,!n :y d we feel sea-sick on a %ip8 ,! answ] is1 t t is because ! motion ( ! %ip is n uni=m4 ,if ! e>?1 in/ead ( turn+ r\nd uni=mly1 7 to rock to & fro1 ev]y?+ on x w\ld be flung ab\t 9 ! wilde/ fa%ion4 ,= z soon z ! e>? _h communicat$ its motion to a body :i* !n mov$ ) ! e>?1 if ! e>?'s motion 7 rev]s$1 ! body w\ld g on l a pass5g] 9 a tra9 on :i* ! break is quickly appli$1 & he w\ld be %ot up aga9/ ! side ( ! room4 ,nay1 m1 ! h\ses w\ld be %ak5 (f _! f\ndations4 ,*anges ( motion are p]ceptible s long z ! *ange is go+ on4 ,we are !re=e ju/ifi$ 9 inf]r+ f ! behavi\r ( bodies on ! e>?1 n t ! e>? is at re/1 b t x is ei!r at re/1 or else1 if x is 9 motion1 t its motion is uni=m & n 9 j]ks or v>iable4 ,illu/ration3 ,,fig4 #bc4 ,= if x 7 n s1 consid] :at w\ld be happ5+ ar\nd u4 ,! e>? is ab\t #h1jjj miles 9 diamet]1 & a p>allel ( latitude ?r\gh ,london is !re=e ab\t #ai1jjj miles long1 & ?is space is travell$ 9 tw5ty-f\r h\rs4 ,s t ,london is sp9n+ ?r\gh space at ! rate ( ov] #a1jjj feet a second1 due to ! e>?'s rot>y motion alone1 n to speak ( ! motion due to ! e>?'s pa? r\nd ! sun4 ,if a boy jump$ up two & a half feet into ! air1 he w\ld take ab\t half a second to g up & come d[n1 b if 9 jump+ he did n p>take ( ! e>?'s motion1 he w\ld l& m ?an #ejj feet to ! we/w>d ( ! po9t f :i* he jump$ up1 & if he did x 9 a room1 he w\ld be da%$ aga9/ ! wall ) a =ce great] ?an he w\ld exp]i5ce f a drop d[n f ! top ( ,mont ,blanc4 ,he w\ld be n only kill$1 b da%$ into an indi/+ui%able mass4 ,if ! e>? sudd5ly /ood /ill1 ev]y?+ on x w\ld be %ak5 to pieces4 ,x is bad en\gh to h ! concussion ( a tra9 go+ ?irty miles an h\r :5 da%$ aga9/ "s ob/acle4 ,b ! concussion due to ! e>?'s /oppage w\ld be z ( a tra9 go+ ab\t #hjj miles an h\r1 :i* w\ld sma% up ev]y?+ & ev]ybody4 ,?us1 !n1 ! fir/ effect ( ! new ideas =mulat$ by ,galileo 0 to %[ t ! ,cop]nican !ory t ! e>? mov$ r\nd on its axis1 & r\nd ! sun1 0 9 agreem5t ) ! laws ( motion4 ,9 fact1 he introduc$ q new ideas ( =ce1 & ^! ideas ,i mu/ n[ endeav\r to expla94 ,let u consid] :at is meant by ! ^w 8=ce40 ,if ,i press my h& aga9/ ! table1 ,i ex]t =ce4 ,! h>d] ,i press1 ! m =ce !re is4 ,if ,i put a weight on a /&1 ! weight presses ! /& d[n ) a =ce4 ,if ,i squeeze a spr+1 ! spr+ tries to recov] itself & ex]ts a c]ta9 =ce4 ,9 all ^! cases =ce is consid]$ z a pressure4 ,& ,i c measure ! =ce by see+ h[ mu* x w press ?+s4 ,if ,i take a spr+1 & press x 9 an in*1 x takes p]haps a =ce ( #a lb4 ,x w take a =ce ( #b lbs4 to press x 9 ano!r in*4 ,or aga91 if ,i pull x out an in*1 x takes a =ce ( #a lb4 ,if ,i pull x out ano!r in*1 x takes a =ce ( #b lbs4 ,we ?us always get into ! habit ( conceiv+ =ces z produc+ pressures & be+ measur$ by pressures4 ,illu/ration3 ,,fig4 #bd4 ,?is is a p]fectly legitimate way ( look+ at ! matt]1 j z ! cook's me?od ( employ+ a spr+ balance to weigh masses ( meat is a p]fectly legitimate way ( e/imat+ ! =ces act+ ^u bodies at re/4 ,b :5 y come to consid] ! laws ( ! p5dulums ( clocks1 to :i* all t ,i am say+ is a prep>ation1 !n y h to deal ) bodies 9 motion4 ,& = ?is purpose a new idea ( =ce altoge!r is requisite4 ,we %all no long] speak ( =ces z produc+ pressures4 ,we %all treat !m q indep5d5tly ( _! press+ p[]4 ,! sun ex]ts a =ce ( attraction on ! e>?1 b x does n press ^u x4 ,x ex]ts its =ce at a di/ance4 ,h5ce !n we want a new idea ( 8=ce40 ,?is idea is to be ! foll[+4 ,we w consid] t :5 a =ce acts ^u a body x endeav\rs to cause x to move2 9 fact1 x tries to imp>t motion to ! body4 ,we may treat ?is motion z a sort ( ?+ or prop]ty4 ,! long] ! =ce acts on ! body1 ! m motion x imp>ts to x1 provid$ ! body is free to receive t motion4 ,s t we may say t ! te/ ( ! /r5g? ( ! =ce is h[ mu* motion x c give to a body ( a giv5 mass 9 a giv5 "t4 ,x does n matt] h[ ! =ce acts4 ,x may act by means ( a /r+ & pull x2 x may act by means ( a /ick & pu% x2 x may act by attraction & draw x2 x may act by repulsion & repel x2 x may act z a sort ( little _s & fly away ) x4 ,9 all ^! cases x acts4 ,! m x acts1 ! m effect x has4 ,9 d\ble ! "t x produces d\ble ! motion4 ,if ! mass is big1 x takes m =ce to make ! mass move2 if ! mass ( ! body is small1 x is mov$ m easily4 ,!re=e :5 we want to measure a =ce 9 ?is way we d n press x aga9/ spr+s to see h[ mu* x w press !m 94 ,:at we d is to cause x to act on bodies t are free to move & see :at motions x w produce 9 !m4 ,( c\rse we c only d ?is ) ?+s t are free to move4 ,y _c treat =ce 9 ?is way if y h only a pair ( scales2 9 t case y w\ld h to be cont5t ) simply measur+ pressures4 ,x is important cle>ly to grasp ?is idea4 ,if a body has a c]ta9 mass1 !n ! =ce act+ on x is measur$ by ! am\nt ( motion t w 9 a giv5 "t be imp>t$ to t mass1 provid$ t ! mass is free to move4 ,?is is to be our def9ition ( =ce4 ,!re=e1 by ! action ( an attraction or any o!r =ce on a body free to move2 motion is cont9ually be+ imp>t$ to ! body4 ,motion is1 z x 71 p\r$ into x1 & !re=e ! body cont9ually moves fa/] & fa/]4 ,"h is a ball fly+ ?r\gh ! air4 ,let u suppose t =ces are act+ on x4 ,h[ c we measure !m8 ,we _c feel :at pressures are be+ ex]t$ on x4 ,! only ?+ we c d is to wat* its motions1 & see h[ x flies4 ,if x goes m & m quickly1 we say1 8,!re is propell+ =ce act+ on x02 if x beg9s to /op1 we say aga91 8,!re is ret>d+ =ce act+ on x40 ,s long z x does n *ange its spe$ or direction1 we say1 8,!re is no =ce act+ on x40 ,by ?is me?od1 !re=e1 we tell :e!r a body is be+ act$ on by =ce1 simply by obs]v+ its spe$ or its *ange ( spe$4 ,m]ely to say a body is mov+ does n tell u t =ce is act+ on x4 ,all we "k is t1 if x is mov+1 =ce has act$ on x4 ,x is only :5 we see x *ang+ its spe$ or direction1 t is *ang+ its motion1 t we say =ce is act+4 ,e *ange ( motion1 ei!r 9 direction or spe$1 mu/ be ! result ( =ce1 & mu/ be proportional to t =ce4 ,?is is :at we mean :5 we say motion is ! te/ & measure ( =ce4 ,?is mo/ int]e/+ way ( look+ at ! matt] lies at ! root ( ! :ole !ory ( me*anics4 ,x is ! f\ndation ( ! sy/em :i* ! /up5d\s g5ius ( ,newton conceiv$ 9 ord] to expla9 ! motion ( ! sun1 moon1 & />s4 ,=ces 7 treat$ by him z proportional to ! motions1 & ! motions proportional to ! =ces1 & ) ?is idea he solv$ a "p ( ! riddle ( ! univ]se4 ,galileo _h p>tly se5 ! same ?+1 b he nev] saw x s cle>ly z ,newton4 ,great discov]ies are only made by see+ ?+s cle>ly4 ,:at requir$ ! =ce ( a g5ius 9 "o age to see 9 ! next may be und]/ood by a *ild4 ,h5ce !n we say a =ce is t :i* 9 a giv5 "t produces a giv5 motion 9 a giv5 mass :i* is free to move4 ,y mu/ h "t = a =ce to act 92 = h[ev] great ! =ce1 9 no "t !re c be no motion4 ,y mu/ h mass = a =ce to act on2 no mass1 no effect4 ,y mu/ h free space = ! mass to move 92 no fre$om to move1 no movem5t4 ,b :at is ?is 8mass08 ,we d n "k2 x is a my/]y4 ,we call x 8quantity ( matt]40 ,9 uni=m sub/ances x v>ies ) size4 ,d\ble ! volume1 d\ble ! mass4 ,cut a cake 9 half1 ea* half has ! same 8mass40 ,b !n is mass 8weight08 ,no1 x is n4 ,weight is ! action ( ! e>?'s attraction on matt]4 ,no e>? to attract1 & y w\ld h no weight1 b y w\ld /ill h 8mass40 ,:at !n is matt]8 ,( t we h no idea4 ,! greate/ m9ds are n[ at "w ^u x4 ,b mass is quantity ( matt]4 ,knock a brick aga9/ y\r head1 & y w "k :at mass is4 ,x is n ! weight ( ! brick t gives y a bump2 x is ! mass4 ,try to ?r[ a ball ( lead1 & y w "k :at mass is4 ,try to pu% a heavy waggon1 & y w "k :at mass is4 ,weights1 t is e>? attractions on masses1 are proportional to ! masses at ! same place4 ,?is1 z we h se51 is kn[n by exp]im5t4 ,!re=e1 :5 a =ce acts = a c]ta9 "t on a mass t is free to move1 h[ev] small ! =ce & h[ev] small ! "t1 t body w move4 ,:5 a baby 9 a temp] /amps ^u ! e>? x makes ! e>? move--n mu*1 x is true1 b /ill x moves2 nay1 m1 9 !ory1 n a fly c jump into ! air )\t mov+ ! e>? & ! :ole sol> sy/em4 ,only1 z y may imag9e !y d n %[ x appreciably4 ,/ill1 9 !ory ! motion is !re4 ,h5ce !n !re are two diff]5t ways ( consid]+ & e/imat+ =ces1 "o suitable = obs]vations on bodies at re/1 ! o!r suitable = obs]vations ( bodies t are free to move4 ,! =ce ( c\rse always t5ds to produce motion4 ,if1 h[ev]1 motion is impossible1 !n x develops pressures :i* we c measure1 & calculate1 & obs]ve4 ,if ! body is free to move1 !n ! =ce produces motions :i* we c also measure1 calculate1 & obs]ve4 ,& we c comp>e ^! two sets ( effects4 ,we c say1 8,a =ce :i*1 act+ on a ball ( a mass ( "o p\nd1 w\ld produce su* & su* motions1 w\ld if x act$ on a c]ta9 spr+ produce s mu* compression40 ,! attraction ( ! e>? on masses ( matt] t are n free to move gives rise to =ces :i* are call$ weights4 ,?us ! attraction ( gravitation on a mass ( "o p\nd produces a pressure equal to a weight ( "o p\nd4 ,un=tunately ! same ^w 8p\nd0 is us$ to express bo? ! mass & ! weight1 & has come d[n to u f days :5 ! nature ( mass 0 n v well appreciat$4 ,b great c>e mu/ be tak5 n to confuse ^! two mean+s4 ,b ! e>?'s attractions & all o!r =ces act+ ^u matt] :i* is free to move give rise to *anges ( motion4 ,! ^w us$ = a *ange ( motion is 8accel]ation0 or a quick5+4 8,he accel]at$ 8 pace10 we say4 ,t is1 he quick5$ x2 he add$ to 8 motion4 ,s t =ce1 act+ on mass dur+ a "t1 produces accel]ation4 ,f ?is1 !n1 x foll[s t if a =ce cont9ues to act on a body ! body keeps mov+ quick] & quick]4 ,:5 ! =ce /ops act+1 ! motion already acquir$ goes on1 b ! accel]ation /ops4 ,t is to say1 ! body goes on mov+ 9 a /raight l9e uni=mly at ! pace x _h :5 ! =ce /opp$4 ,if1 !n1 a body is expos$ to ! action ( a =ce1 & held tight1 :at w happ58 ,x w1 ( c\rse1 rema9 fix$4 ,n[ let x g--x w !n1 be+ a free body1 beg9 to move4 ,z long z ! =ce acts1 ! =ce keeps putt+ m & m motion into ! body1 l p\r+ wat] into a jug1 ! long] y p\r ! fa/] ! motion becomes4 ,! body keeps all ! motion x _h1 & keeps add+ all ! motion x ga9s4 ,x is l a boy sav+ up 8 weekly pocket-money3 he has :at he _h1 & he keeps add+ to t4 ,s if 9 "o second a motion is imp>t$ ( "o foot a second1 !n 9 ano!r second a motion ( "o foot a second m w be add$1 mak+ toge!r a motion ( two feet a second2 9 ano!r second ( =ce action ! motion w h be5 increas$ or 8accel]at$0 by ano!r foot p] second1 & s on4 ,! spe$ w ?us be always proportional to ! =ce & ! "t4 ,if we write ! lett] ,v to repres5t ! motion1 or spe$1 or velocity2 ,f to repres5t ! accel]ation or ga9 ( motion2 & ,t to repres5t ! "t1 !n ,v ,,ft4 ,"h ,v is ! velocity ! body w h acquir$ at ! end ( ! "t ,t1 if free to move & submitt$ to a =ce capable ( produc+ an accel]ation ( ,f feet p] second 9 a unit ( "t4 ,v is ! f9al velocity4 ,! av]age velocity w be #a_/b ,v1 = x began ) no velocity & increas$ uni=mly4 ,h[ f> w ! body h fall5 9 ! int]val8 ,manife/ly we get t by multiply+ ! "t by ! av]age velocity1 t is ,s #a_/b ,,vt1 :]e ,v1 z ,i said1 is ! f9al velocity1 b we f\nd t ,v ,,ft4 ,h5ce by sub/itution ,s #a_/b ,,ft ,t #a_/b ,,ft4 ,x is to be c>efully borne 9 m9d t ^! lett]s ,v1 ,s1 & ,t d n repres5t velocities1 spaces1 & times1 b m]ely repres5t ari?metical numb]s ( units ( velocities1 spaces1 & times4 ,?us ,v repres5ts ,v feet p] second1 ,s repres5ts ,s feet1 & ,t repres5ts ,t seconds4 ,& :5 we use ! equation ,v ,,ft we d n mean t by multiply+ a =ce by a "t y c produce a velocity4 ,if1 = in/ance1 x be true t y c obta9 ! numb] ( inhabitants 7,h7 9 ,london by multiply+ ! av]age numb] ( p]sons 7,p7 :o live 9 a h\se by ! numb] ( h\ses 7,n71 ?is may be express$ by ! equation ,h ,,pn4 ,b ?is does n mean t by multiply+ p into h\ses y c produce inhabitants4 ,h1 ,p1 & ,n are numb]s ( units1 & !y are numb]s only4 ,!re=e :5 a body is be+ act$ on by an accel]at+ =ce x t5ds to g fa/] & fa/] z x proce$s1 & !re=e its velocity increases ) ! "t4 ,b ! space pass$ ?r\gh increases fa/] /ill1 = z ! "t runs on n only does ! space pass$ ?r\gh increase1 b ! rate ( pass+ also gets bigg]4 ,x goes on increas+ at an increas+ rate4 ,x is l a man :o has an increas+ income & always goes on sav+ x4 ,8 total m\nts up n m]ely 9 proportion to ! "t1 b ! v rate ( increase also increases ) ! "t1 s t ! total increase is 9 proportion to ! "t multipli$ into ! "t1 9 o!r words to ! squ>e ( ! "t4 ,s !n1 if ,i let a body drop f re/ "u ! action ( any =ce capable ( produc+ an accel]ation1 ! space pass$ ?r\gh w be z ! squ>e ( ! "t4 ,n[ let u see :at ! spe$ w be if ! =ce is gravity1 t is ! attraction ( ! e>?4 ,turn+ back to :at 0 said ab\t ,galileo1 x w be rememb]$ t he %[$ t all bodies1 big & small1 light & heavy1 fell to ! e>? at ! same spe$s4 ,:at is t spe$8 ,let u d5om9ate by ,g ! numb] ( feet p] second ( increase ( motion produc$ 9 a body by ! e>?'s action dur+ "o second4 ,!n ! velocity at ! end ( t second w be ,v ,,gt4 ,! space fall5 ?r\gh w be ,s #a_/b ,,gt4 ,:at ,i want to "k !n is ?is3 h[ f> w a body "u ! action ( gravity fall 9 a second ( "t8 ,?is1 ( c\rse1 is a matt] = measurem5t4 ,if we c get a ma*9e to measure seconds1 we %all be able to d x2 b inasmu* z fall+ bodies beg9 by fall+ sixte5 feet 9 ! fir/ second & aft]w>ds g on fall+ quick] & quick]1 ! measurem5ts are difficult4 ,galileo want$ to see if he c\ld make x easi] to obs]ve4 ,he said to himself1 8,if ,i c only wat] d[n ! =ce ( gravity & make x weak]1 s t ! body w move v sl[ly "u its action1 !n ! "t ( fall+ w be easi] to obs]ve40 ,b h[ to d x8 ,?is is "o ( ^? ?+s ! discov]y ( :i* at once m>ks ! inv5tor4 ,illu/ration3 ,,fig4 #be4 ,! idea ( ,galileo 01 in/ead ( lett+ ! body drop v]tically1 to make x roll sl[ly d[n an incl9e1 = a body put ^u an incl9e is n urg$ d[n ! incl9e ) ! same =ce :i* t5ds to make x fall v]tically4 ,c any law be discov]$ t5d+ to %[ :at ! =ce is ) :i* gravity t5ds to drag a mass d[n an incl9e8 ,!re is a simple "o1 & be=e ,galileo's "t x _h be5 discov]$ by ,/ev9us1 an eng9e]4 ,/ev9us' solution 0 z foll[s4 ,suppose t ,a ,b ,c is a w$ge-%ap$ block ( wood4 ,let a loop ( heavy *a9 be hung ov] x1 & suppose t !re is a little pulley at ,c & no friction any:]e4 ,!n ! *a9 w hang at re/4 ,b ! l[] "p1 f ,a to ,b1 is symmetrical2 t is to say1 x is ev5 9 %ape on bo? sides4 ,h5ce1 s f> z any pull x ex]ts is conc]n$1 ! half f ,a to ,d w balance ! o!r half f ,b to ,d4 ,!re=e1 l weights 9 a scale1 y may remove bo?1 & !n ! =ce ( gravity act+ d[n ! plane on ! "p ,a ,c w balance ! =ce ( gravity act+ v]tically on ! "p ,c ,b4 ,n[ ! weight ( any "p ( ! *a91 s9ce x is uni=m1 is proportional to its l5g?4 ,h5ce1 !n1 ! gravitational =ce d[n ! plane ( a piece ^: weight equals ,c ,a is equal to ! gravitational =ce v]tically ( a piece ^: weight equals ,c ,b4 ,9 o!r words1 ! =ce ( gravity act+ d[n a plane is dim9i%$ 9 ! ratio ( ,c ,b to ,c ,a4 ,b :5 a body falls v]tically1 !n1 z we h se51 ,s #a_/b ,,gt1 :]e ,s is ! space x w fall ?r\gh1 ,g ! numb] ( feet p] second ( velocity t gravity1 act+ v]tically on a body1 w produce 9 x 9 a second1 & ,t ! numb] ( seconds ( "t4 ,if !n1 in/ead ( fall+ v]tically1 ! body is to fall obliquely d[n a plane1 in/ead ( ,g we mu/ put z ! accel]at+ =ce ,g 7v]tical height ( ! end ( ! plane7_/7l5g? ( ! plane74 ,to try ! exp]im5t1 he took a beam ( wood ?irty-six feet long ) a groove 9 x4 ,he incl9$ x s t "o end 0 "o foot high] ?an ! o!r4 ,h5ce ! accel]ation d[n ! plane 0 #a_/cf ,g1 :]e ,g is ! v]tical accel]ation due to gravity :i* he want$ to discov]4 ,!n he measur$ ! "t a brass ball took to run d[n ! plane ?irty-six feet long1 & f\nd x to be n9e seconds4 ,:5ce f ! equation giv5 above #cf feet #a_/b accel]ation ( gravity d[n ! plane 7#i seconds74 ,:5ce x foll[s t ! accel]ation ( gravity d[n ! plane is 7#cf #b7_/7i7 feet p] second4 ,b ! slope ( ! plane is "o ?irty-six? to ! v]tical4 ,!re=e ! v]tical accel]ation ( gravity1 i4e41 ! velocity :i* gravity w\ld induce 9 a v]tical direction 9 a second1 is equal to ?irty-six times t :i* x ex]cises d[n ! plane1 i4e41 #cf 7#cf #b7_/7i72 & ?is equals #cb feet p] second4 ,?\gh ?is me?od is +5i\s1 x possesses two defects4 ,"o is ! error produc$ by friction1 ! o!r f failure to obs]ve t ! =ce ( gravity on ! ball is n only ex]t$ 9 gett+ x d[n ! plane1 b also 9 rotat+ x1 & = ?is no all[ance has be5 made4 ,! all[ance to be made = rotation is complicat$1 & involves m k ?an ,galileo possess$4 ,/ill ! result is approximately true4 ,illu/ration3 ,,fig4 #bf4 ,! next attempt to measure ,g1 t is ! velocity t gravity w produce on a body 9 a second ( "t1 0 made by ,attwood1 a ,cambridge pr(essor4 ,8 idea 0 to weak5 ! =ce ( gravity & ?us make ! action sl[1 n by mak+ x act obliquely1 b by all[+ x to act1 n on ! :ole1 b only on a portion ( ! mass to be mov$4 ,= ?is purpose he hung two equal weights ov] a v delicately con/ruct$ pulley4 ,gravity1 ( c\rse1 c\ld n act on ^!1 = any effect x produc$ on "o w\ld be negativ$ by its effect on ! o!r4 ,! weights w\ld !re=e rema9 at re/4 ,if1 h[ev]1 a small weight ,w1 equal say to a hundr$? ( ! comb9$ weight ( ! weights ,a & ,b & ,w1 7 sudd5ly put on ,a1 !n x w\ld desc5d "u an accel]at+ =ce equal to a hundr$? "p ( ord9>y gravity4 ,we %\ld !n h ,s 7! space mov$ ?r\gh by ! weights7 #a_/b ,g_/#ajj t4 ,) su* a sy/em1 he f\nd t 9 #g seconds ! weights mov$ ?r\gh #i feet4 ,:5ce he got #i #a_/b ,g_/#ajj 7#g74 ,f :i* ,g 7#b #i #ajj7_/7g7 #cb feet p] second ne>ly4 ,?us by lett+ gravity only act on a hundr$? "p ( ! total weight mov$1 namely ,a1 ,b1 & ,w1 he weak5$ its action #ajj times1 & ?us made ! "t ( fall+ & ! space fall5 ?r\gh suffici5tly l>ge to be capable ( measurem5t4 ,to sum up1 :5 a body free to move is act$ ^u by ! =ce ( gravity1 its spe$ w increase 9 proportion to ! "t x has be5 act$ ^u1 & ! space x w pass ?r\gh f re/ is proportional to ! squ>e ( ! "t dur+ :i* ! accel]at+ =ce has act$ on x4 ,gravity is1 ( c\rse1 n ! only accel]at+ =ce ) :i* we are acqua9t$4 ,if a spr+ be sudd5ly all[$ to act on a body & pull x1 ! body beg9s to move1 & its action is gradually accel]at$1 j z ?\gh x 7 attract$1 & ! accel]ation ( its motion w be proportional to ! "t dur+ :i* ! accel]at+ =ce acts4 ,simil>ly1 if gunp[d] be explod$ 9 a gun-b>rel1 & ! =ce ?us produc$ be all[$ to act on a bullet1 ! motion ( ! bullet is accel]at$ s long z x is 9 ! b>rel4 ,:5 ! bullet leaves ! b>rel x goes on ) a uni=m pace 9 a /raight l9e1 :i*1 h[ev]1 by ! e>?'s attraction is at once deflect$ into a curve1 & alt]$ by ! resi/ance ( ! air4 ,illu/ration3 ,,fig4 #bg4 ,x has be5 already /at$ t motions may be consid]$ indep5d5tly "o ( ano!r1 s t if a body be expos$ to two diff]5t =ces ! action ( ^! =ces c be consid]$ & calculat$ ea* indep5d5tly ( ! o!r4 ,let u take an example ( ?is law4 ,we h se5 if a body is propell$ =w>ds1 & !n ! =ce act+ on x ceases1 t x proce$s on ) uni=m un*ang+ velocity1 & if no?+ imp$$ x1 or influ5c$ x1 x w\ld g on 9 a /raight l9e at a uni=m spe$4 ,we h also se5 t if a body is expos$ to ! action ( an accel]at+ =ce su* z gravity x con/antly keeps be+ accel]at$1 x con/antly keeps ga9+ motion1 & its spe$ becomes quick] & quick]4 ,illu/ration3 ,,fig4 #bh4 ,let u suppose a body expos$ to bo? ( ^! =ces at ! same "t4 ,%oot x out ( a cannon1 & let an accel]at+ =ce act on x1 n 9 ! direction x is go+1 b 9 "s o!r direction1 say at "r angles4 ,:at w happ58 ,9 ! direction 9 :i* x is go+1 its spe$ w rema9 uni=m4 ,9 ! direction 9 :i* ! accel]at+ =ce is act+1 x w move fa/] & fa/]4 ,?us along ,a ,b x w proce$ uni=mly4 ,if x proce$$ uni=mly also along ,a ,c 7z x w\ld d if a simple =ce act$ on x & !n ceas$ to act71 !n z a result x w\ld g 9 ! oblique l9e ,a ,d1 ! obliquity be+ det]m9$ by ! relative magnitude ( ! =ces act+ on x4 ,b h[ if x w5t uni=mly along ,a ,b1 b at an accel]at$ pace along ,a ,c8 ,!n :ile 9 equal times ! di/ances along ,a ,b w\ld be uni=m ! di/ances 9 ! same times along ,a ,c w\ld be gett+ bigg] & bigg]4 ,x w\ld n describe a /raight l9e2 x w\ld g 9 a curve4 ,?is is v int]e/+4 ,let u take an example ( x4 ,suppose we give a ball a bl[ horizontally2 z soon z x quits ! bat x w\ld ( c\rse g on horizontally 9 a /raight l9e at a uni=m spe$2 b n[ if ,i at ! same in/ant expose x to ! accel]at+ =ce ( gravity1 !n1 ( c\rse1 :ile its horizontal movem5t w g on uni=mly1 its d[nw>d drop w keep increas+ at a spe$ v>y+ z ! "t4 ,& :ile ! total di/ances horizontally w be uni=m 9 equal times1 ! total d[nw>d drop f ,a ,b w be z ! squ>es ( ! times4 ,"h1 !n1 y h a po9t mov+ uni=mly 9 a horizontal direction1 b z ! squ>es ( ! times 9 a v]tical direction4 ,x describes a curve4 ,:at curve8 ,:y1 "o ^: di/ances g uni=mly "o way1 b increase z ! squ>es ! o!r way4 ,illu/ration3 ,,fig4 #bi4 ,?is int]e/+ curve is call$ a p>abola4 ,) a ball simply hit by a bat1 ! motion is s v fa/ t we _c see x well4 ,_c we make x g sl[ly8 ,let u rememb] :at ,galileo did4 ,he us$ an incl9$ plane to wat] d[n 8 =ce ( gravity4 ,let u d ! same4 ,let u take an incl9$ plane & ?r[ on x a ball horizontally4 ,x w g 9 a curve4 ,its spe$ is uni=m horizontally1 b is accel]at$ d[nw>ds4 ,if we desire to trace ! curve x is easy to d4 ,we coat ! ball ) clo? & !n dip x 9 ! inkpot4 ,x w !n describe a visible p>abola4 ,if ,i tilt up ! plane & make ! =ce ( gravity big1 ! p>abola is long & ?92 if ,i weak5 d[n ! =ce ( gravity by mak+ ! plane ne>ly horizontal1 !n x is wide & flat4 ,"o c also %[ ?is by a /ream ( peas or %ot4 ,! little bullets g ea* ) a uni=m velocity horizontally1 & an accel]at$ =ce d[nw>ds4 ,in/ead ( peas we c use wat]4 ,a /ream ( x ru%+ horizontally out ( an orifice w soon b5d d[n into a p>abola4 ,?us !n ,i h tri$ to %[ :at =ce is & h[ x is measur$4 ,i repeat aga91 :5 a body is free to move1 !n1 if no fur!r =ce acts on x1 x w g on 9 a /raight l9e at a uni=m spe$1 b if a =ce cont9ues to act on x 9 any direction1 !n t =ce produces 9 ea* unit ( "t a unit ( accel]ation 9 ! direction 9 :i* ! =ce acts1 & ! result is t ! body goes on mov+ t[>ds ! direction ( accel]ation at a con/antly increas+ spe$1 & h5ce pass+ ov] spaces t are great] & great] z ! spe$ increases4 ,?is is ! notion ( a 8=ce40 ,9 all t has be5 said above x has be5 assum$ t ! attraction ( gravity on a body does n increase z t body gets ne>] to ! e>?4 ,?is is n /rictly true2 9 reality ! attractive =ce ( gravity increases z ! e>?'s c5tre is approa*$4 ,b small di/ances ?r\gh :i* ! weights 9 ,attwood's ma*9e fall make no appreciable diff]5ce1 be+ z no?+ comp>$ to ! radius ( e>?4 ,= practical purposes1 !re=e1 ! =ce may be consid]$ uni=m on bodies t are be+ mov$ )9 a few feet ( ! e>?'s surface4 ,x is only :5 we h to consid] ! motions ( ! planets t consid]ations ( ! *ange ( attractive =ce due to di/ance h to be consid]$4 ,i am glad to say t ! mo/ tiresome1 or r ! mo/ difficult1 "p ( our inquiry is n[ ov]4 ,) ! help ( ! notions already acquir$1 we are n[ ready to get to ! p5dulum1 & to %[ h[ x came ab\t t a boy :o once 9 *ur* amus$ himself by wat*+ ! sw++ ( ! great lamps in/ead ( att5d+ to ! s]vice laid ! f\ndation ( our mod]n me?ods ( measur+ "t4 ,,*apt] ,,iii4 ,we h exam9$ ! action ( a body "u ! accel]at+ or spe$-quick5+ =ce due to gravity1 ! attractive =ce ( :i* on any body is always proportional to ! mass ( t body4 ,let u n[ consid] ano!r =m ( accel]ation4 ,illu/ration3 ,,fig4 #cj4 ,take ! case ( a /rip ( indi>ubb]4 ,if pull$ x resi/s & t5ds to spr+ back4 ,! m ,i pull x out ! h>d] is ! pull ,i h to ex]t4 ,?is is true ( all spr+s4 ,x is true ( spiral spr+s1 :e!r !y are pull$ out or pu%$ 91 & 9 ea* case ! am\nt by :i* ! spr+ is pull$ out or pu%$ 9 is proportional to ! pressure4 ,?is law is call$ ,hooke's law4 ,x 0 express$ by him 9 ,lat91 8,ut t5sio1 sic vis03 8,z ! ext5sion1 s ! =ce40 ,x is true ( all ela/ic bodies1 & x is true :e!r !y are pull$ out or pu%$ 9 or b5t aside4 ,! common spr+ balance is devis$ on ?is pr9ciple4 ,! body to be weigh$ is hung on a hook susp5d$ f a spr+4 ,! am\nt by :i* ! spr+ is pull$ out is a measure ( ! weight ( ! body4 ,if y take a fi%+ rod & put ! butt end ( x on a table & secure x by putt+ some?+ heavy on ! end1 !n ! tip w b5d d[n on acc\nt ( its own weight4 ,m>k ! po9t to :i* x goes4 ,n[1 if y hang a weight on ! tip1 ! tip w b5d d[n a little fur!r4 ,if y put d\ble ! weight ! tip w g d[n d\ble ! di/ance1 & s on until ! fi%+ rod is consid]ably b5t1 s t its =m is alt]$ & a new law ( flexure comes into play4 ,suppose ,i use a spr+ z an accel]at+ =ce4 ,= example1 suppose ,i susp5d a heavy ball by a /r+ & !n atta* a spiral spr+ to x & pull ! spr+ aside4 ,! ball w be drawn aft] ! spr+4 ,if !n ,i let ! ball g1 x w beg9 to move4 ,! =ce ( ! spr+ w act ^u x z an accel]at+ =ce1 & ! ball w g on mov+ quick] & quick]4 ,b ! accel]ation w n be l t ( gravity4 ,!re w be two diff]5ces4 ,! pull ( ! spr+ w 9 no way dep5d on ! mass ( ! ball1 & ! pull ( ! spr+1 in/ead ( be+ con/ant1 l ! pull ( gravity1 w become weak] & weak] z ! ball yields to x4 ,consequ5tly ! equations above giv5 :i* det]m9e ! relations betwe5 ?is space pass$ ?r\gh1 ! velocity1 & ! "t :i* 7 det]m9$ 9 ! case ( gravity are no long] true1 & a diff]5t set ( relations has to be det]m9$4 ,?is c be easily done by ma!matics4 ,b ,i d n propose to g into x4 ,i pref] to (f] a r\gh & ready explanation1 :i*1 ?\gh x does n am\nt to a pro(1 yet enables u to accept ! tru? t c be e/abli%$ bo? by exp]im5t & by calculation4 ,illu/ration3 ,,fig4 #ca4 ,let a heavy ball 7,a7 be susp5d$ by a long /r+1 s t ! action ( gravity sideways on ! ball is v small & may be neglect$1 & to ea* side atta* an indi>ubb] ?read fa/5$ at ,b & ,c4 ,!n :5 ! ball is pull$ aside a little1 say to a position ,d1 x w t5d to fly back to ,a ) a =ce proportion$ to ! di/ance ,a ,d4 ,:at w be ! "t x w take to d ?is8 ,if ! di/ance ,a ,d is small1 ! ball has only a small di/ance to g1 b !n1 on ! o!r h&1 x has only small =ces act+ on x4 ,if ! di/ance ,a ,d is bigg]1 !n x has a long] di/ance to g1 b l>g] =ces to urge x4 ,^! c\nt]act "o ano!r1 s t ! "t 9 ea* case w be ! same4 ,illu/ration3 ,,fig4 #cb4 ,! "q is ?is3--,w y g a long di/ance ) a p[]ful horse1 or a small di/ance ) a weak horse8 ,if ! di/ance 9 ea* case is proportion$ to ! p[] ( ! horse1 !n ! am\nt ( ! di/ance does n matt]4 ,! p[]ful horse goes ! long di/ance 9 ! same "t t ! weak horse goes ! %ort di/ance4 ,& s x is "h4 ,h[ev] f> y pull out ! spr+1 ! accel]ative pull on ! ball is proportion$ to ! di/ance4 ,b ! "t ( pull+ ! ball 9 dep5ds on ! di/ance4 ,s t ea* neutralises ! o!r4 ,:5ce !n we h ?is mo/ important fact1 t spr+s are all iso*ron\s2 t is to say1 any body atta*$ to any spr+ :atev]1 :e!r x is big or small1 /raight or curly1 long or %ort1 has a "t ( vibration q indep5d5t ( ! bigness ( ! vibration4 ,! exp]im5t is easy to try ) a ball m\nt$ on a long arm t c sw+ horizontally4 ,x is atta*$ on ea* side to an ela/ic ?read4 ,if pull$ aside1 x vibrates1 b obs]ve1 ! vibration is exactly ! same :e!r ! bigness ( ! vibration is great or small4 ,if ! pull aside is big1 ! =ce ( re/itution is big2 if ! pull is small1 ! =ce ( re/itution is small4 ,9 "o case ! ball has a long] di/ance to g1 b !n at all po9ts ( its pa? x has a proportionally /rong] =ce to pull x2 if ! ball has a small] di/ance to g1 !n at all ! correspond+ po9ts ( its pa? x has a proportionally weak] =ce to pull x4 ,?us ! "t rema9s ! same :e!r y h ! p[]ful horse = ! long j\rney or ! weak] horse = ! small] j\rney4 ,illu/ration3 ,,fig4 #cc4 ,next take a %ort1 /iff spr+ ( /eel4 ,"o ( ! k9d kn[n z tun+ =ks may be employ$4 ,! read] is probably aw>e t s\nds are produc$ by v rapid pulsations ( ! air4 ,any s]ies ( taps becomes a cont9u\s s\nd if x is only rapid en\gh4 ,= example1 if ,i tap a c>d at ! rate ( #bfd times 9 a second1 ,i %\ld get a cont9u\s s\nd su* z t giv5 by ! middle ,c note ( ! piano4 ,t1 9 fact1 is ! rate at :i* ! piano /r+ is vibrat+ :5 ,c is /ruck1 & t vibration x is t gives ! taps to ! air by :i* ! note is produc$4 ,?is c be v easily prov$4 ,= if y lift up ! end ( a bicycle & cause ! driv+ :eel to sp9 pretty rapidly by turn+ ! p$al ) ! h&1 !n ! :eel w rotate p]haps ab\t ?ree times 9 a second4 ,if a visit+ c>d be held s z to be flipp$ by ! spokes z !y fly by1 s9ce !re are ab\t ?irty-six ( !m1 we %\ld get a s]ies ( taps at ! rate ( ab\t #ajh a second4 ,?is on trial w be f\nd to ne>ly correspond to ! note ,a1 ! l[e/ space on ! bass clef ( music4 ,z ! spe$ ( rotation is l[]$1 ! tone ( ! note becomes l[]2 if ! spe$ is made great]1 ! pit* ( ! note becomes high]1 & ! note m %rill4 ,h[ev] f> or ne> ! c>d is held f ! c5tre ( ! :eel makes no diff]5ce1 = ! numb] ( taps p] second rema9s ! same4 ,s1 aga91 if a bit ( wat*-spr+ be rapidly drawn ov] a file1 y he> a musical note4 ,! f9] ! file1 & ! m rapid ! action1 ! high] ! note4 ,! action ( a tun+ =k & ( a vibrat+ /r+ 9 produc+ a note dep5ds simply on ! beat+ ( ! air4 ,! hum ( insects is also simil>ly produc$ by ! rapid flapp+ ( _! w+s4 ,x is an exp]im5tal fact t :5 a piano note is /ruck1 z ! vibration gradually ceases ! s\nd dies away1 b ! pit* ( ! note rema9s un*ang$4 ,a tune play$ s(tly1 s t ! /r+s vibrate b little1 rema9s ! same tune /ill1 & ) ! same pit* = ! notes4 ,a 8sir50 is an +5i\s app>atus = produc+ a s]ies ( v rapid puffs ( air4 ,x consi/s ( a small :eel ) oblique holes 9 x1 m\nt$ s z to revolve 9 close proximity to a fix$ :eel ) simil> holes 9 x4 ,if air be =c$ ?r\gh ! :eels1 by reason ( ! obliquity ( ! orifices 9 ! movable :eel x is caus$ to rotate4 ,z x does s1 ! air is alt]nately int]rupt$ & all[$ to pass1 s t a s]ies ( v rapid puffs is produc$4 ,z ! air is =c$ 91 ! :eel turns fa/] & fa/]4 ,! rapidity ( succession ( ! puffs increases s t ! note produc$ by !m gradually increases 9 pit* till x rises to a sort ( scream4 ,= /eam]s ^! 8sir5s0 are work$ by /eam1 & make a v l\d noise4 ,x is1 h[ev]1 impossible to make a tun+ =k or a /ret*$ piano spr+ alt] ! pit* ( its note )\t alt]+ ! ela/ic =ce ( ! spr+ by alt]+ its t5sion1 or )\t putt+ weights on ! arms ( ! tun+ =k to make x g m sl[ly4 ,& ?is is because ! tun+ =k & ! piano spr+1 be+ ela/ic1 obey ,hooke's law1 8,z ! deflection1 s ! =ce02 & !re=e ! "t ( back spr+ is 9 ea* case inv>iable1 & ! pit* ( ! note produc$ !re=e rema9s inv>iable1 :atev] ! amplitude ( ! vibration may be4 ,^u ?is law dep5ds ! correct go+ ( bo? clocks & wat*es4 ,wond]ful nature1 t causes ! uni=mity ( s\nds ( a piano1 or a viol91 to dep5d on ! same laws t gov]n ! uni=m go+ ( a wat*6 ,nay1 m1 all creation is vibrat+4 ,! surge ( ! sea ^u ! coa/ t swi%es 9 at regul> int]vals1 ! col\rs ( light1 :i* consi/ ( ripples made 9 an ela/ic e!r1 :i* spr+s back ) a re/itutional =ce proportion$ to its displacem5t1 all dep5d ^u ! same law4 ,?is gr& law by :i* s _m ph5om5a ( nature are gov]n$ has a v beautiful "n1 :i* ,i hope y w rememb]4 ,x is call$ 8h>monic motion10 by :i* is meant t :5 ! atoms ( nature vibrate !y vibrate1 l piano /r+s1 accord+ to ! laws ( h>mony4 ,! anci5t ,py?agorean philosoph]s ?\ght t all nature mov$ to music1 & t dy+ s\ls c\ld beg9 to he> ! tones to :i* ! />s mov$ 9 _! orbits4 ,!y call$ x1 z y "k1 ! music ( ! sph]es4 ,b c\ld !y h se5 :at sci5ce has reveal$ to man's pati5t ef=ts1 !y w\ld h se5 a vision ( h>mony 9 :i* n a ray ( light1 n a /r+ ( a musical in/rum5t1 n a pipe ( an organ1 n an undulation ( all-p]vad+ electricity1 n a w+ ( a fly1 b vibrates accord+ to ! law ( h>mony1 ! simple easy law ( :i* a boy's catapult is ! type1 & :i*1 z we h se51 tea*es u t :5 an ela/ic body is displac$ ! =ce ( re/itution1 9 o!r words1 ! =ce t5d+ to re/ore x to its old position1 is proportional to ! displacem5t1 & ! "t ( vibration is uni=m4 ,! la/ is ! important ?+ = u2 we seem to get a gleam ( a notion ( h[ ! clock & wat* problem is go+ to be solv$4 ,b be=e we get to t we h yet to g back a little4 ,ab\t ! ye> #aehj an inatt5tive y\? 7x 0 our fri5d ,galileo aga97 wat*$ ! sw+ ( "o ( ! great *&eli]s 9 ! ca!dral *ur* at ,pisa4 ,! *&eli]s h be5 r5ew$ s9ce 8 day1 x 0 "o ( ! old lamps t he wat*$4 ,x _h be5 lit1 & all[$ to sw+ ?r\gh a consid]able space4 ,he expect$ t z x gradually came to re/ x w\ld sw+ 9 a quick] & quick] "t1 b x seem$ to be uni=m4 ,?is 0 curi\s4 ,he want$ to measure ! "t ( its sw+4 ,= ?is purpose he c\nt$ 8 pulse-beats4 ,s f> z he c\ld judge1 !re 7 exactly ! same numb] 9 ea* p5dulum sw+4 ,?is greatly int]e/$ him1 & at home he began to try "s exp]im5ts4 ,z he got old] 8 att5tion 0 repeat$ly turn$ to t subject1 & he f9ally e/abli%$ 9 a satisfactory way ! law t1 if a weight is hung to ! end ( a /r+ & caus$ to vibrate1 x is iso*ron\s1 or equal-tim$1 no matt] :at ! ext5t ( ! arc ( vibration4 ,! fir/ use ( ?is t he made 0 to make a little ma*9e ) a /r+ ( :i* y c\ld v>y ! l5g?1 = use by doctors4 ,= ! doctors ( t day _h no gold wat* to pull out :ile ) solemn face !y wat*$ ! ticks4 ,!y 7 delight$ ) ! new inv5tion1 & = ye>s doctors us$ to take out ! little /r+ & weight1 & put "o h& on ! pati5t's pulse :ile !y adju/$ ! /r+ till ! p5dulum beat 9 unison ) ! pulse4 ,by obs]v+ ! l5g? ( ! /r+1 !y 7 !n able to tell h[ _m beats ! pulse made 9 a m9ute4 ,b ,galileo did n /op !re4 ,he proce$$ to exam9e ! laws :i* gov]n ! p5dulum4 ,we w foll[ ^! inve/igations1 :i* w l>gely dep5d on :at we h already le>n$4 ,be=e1 h[ev]1 x is possible to und]/& ! laws :i* gov]n ! p5dulum1 !re are "o or two simple matt]s connect$ ) ! balance & op]ation ( =ces :i* h to be grasp$4 ,suppose t we h a flat piece ( wood ( any %ape l ,fig4 #cd1 & t we put a screw ?r\gh any spot ,a 9 x1 no matt] :]e1 & screw x to a wall1 s t x c turn r\nd ! screw z r\nd a pivot4 ,illu/ration3 ,,fig4 #cd4 ,illu/ration3 ,,fig4 #ce4 ,next we w knock a t9tack into any po9t ,b1 & tie a /r+ on to ,b4 ,!n if ,i pull at ! /r+ 9 any direction ,b ,c ! bo>d t5ds to twi/ r\nd ! screw at ,a4 ,:at w ! /r5g? ( ! twi/+ =ce be8 ,x w dep5d on ! /r5g? ( ! pull1 & on ! 8lev]age10 or di/ance ( ! l9e ,c ,b f ,a4 ,we might imag9e ! /r+1 in/ead ( be+ atta*$ at ,b1 to be atta*$ at ,d2 !n1 if ,i put ,p z ! /r5g? ( ! pull1 ! twi/+ p[] w\ld be repres5t$ by ,p ,a ,d4 ,?is is call$ ! 8mom5t0 ( ! =ce ,p r\nd ! c5tre ,a4 ,x w\ld be ! same z if ,i _h simply an arm ,a ,d1 & pull$ ^u x ) ! =ce ,p4 ,x is an exp]im5tal tru?1 kn[n to ! old ,greek philosoph]s1 t mom5ts1 or twi/+ p[]s1 are equal :5 9 ea* case ! result ( multiply+ ! arm by ! p[] act+ at "r angles to x is equal4 ,n[ suppose ,a ,b is a p5dulum1 ) a bob ,b ( #aj lbs4 weight1 & suppose x has be5 drawn aside out ( ! v]tical s t ! bob is 9 ! position ,b4 ,!n ! weight ( ! bob w act v]tically d[nw>ds along ! l9e ,b ,c4 ,! mom5t1 or twi/+ p[]1 ( ! weight w be equal to #aj lbs4 multipli$ by ,a ,d1 ,a ,d be+ a l9e p]p5dicul> to ,b ,c4 ,illu/ration3 ,,fig4 #cf4 ,n[ suppose t ano!r /r+ 7 ti$ to ! bob ,b1 & pull$ 9 a direction at "r angles to ,a ,b1 ) a =ce ,p j en\gh to hold ! bob back 9 ! position ,b4 ,! pull along ,d ,b ,a ,b w\ld be ! mom5t ( t pull r\nd ! po9t ,a4 ,b1 because ?is mom5t j holds ! p5dulum up1 x foll[s t ! mom5t ( ! weight ( ! p5dulum r\nd ,a is equal to ! mom5t ( ! pull ( ! /r+ ,b ,d r\nd ,a4 ,:5ce ,p ,a ,b #aj lbs4 ,a ,d4 ,:5ce ,p #aj lbs4 7,a ,d7_/7,a ,b74 ,b ,a ,b is always ! same1 :atev] ! side deflection or displacem5t ( ! p5dulum may be4 ,:5ce !n we see t :5 a p5dulum is pull$ aside a di/ance ,e ,b 7:i* is always equal to ,a ,d71 !n ! =ce t5d+ to br+ x back to ,e is always proportional to ,e ,b4 ,b if ! p5dulum be fairly long1 say #ci-a_/g in*es1 & ! displacem5t ,e ,b be small1--9 o!r words1 if we d n drag x mu* out ( ! v]tical1--!n we may say t ! =ce t5d+ to br+ x back to ,f1 its position ( re/1 is n v diff]5t f ! =ce t5d+ to br+ x back to ,e4 ,b ,f ,b is ! 8displacem5t0 ( ! p5dulum1 &1 !re=e1 we f9d t :5 a p5dulum is displac$1 or deflect$1 or pull$ aside a little1 ! am\nt ( ! deflection is always v ne>ly proportional to ! =ce :i* 0 us$ to produce ! deflection4 ,?is important law c be v]ifi$ by exp]im5t4 ,if ,c is a small pulley1 & ,b ,c a /r+ atta*$ to a p5dulum ,a ,b ^: bob is ,b4 ,!n if a weight ,d be ti$ to ! /r+ & pass$ ov] a pulley ,c1 ! am\nt ,f ,b by :i* ! weight ,d w deflect ! bob ,b is almo/ exactly proportional to ,d1 s long z we only make ! deflection ,e ,b small1 t is two or ?ree in*es1 :]e say #ci-a_/g in*es is ! l5g? ,a ,b ( ! p5dulum4 ,if ,f ,b is made too big1 !n ! l9e ,b ,f c no long] be consid]$ ne>ly equal to ! arc ( deflection ,e ,b1 & ! proposition is no long] true4 ,h5ce !n1 bo? by exp]im5t & on !ory1 we f9d t = small di/ances ! displacem5t ( a p5dulum bob is approximately equal to ! =ce by :i* t displacem5t is produc$4 ,b if s1 !n f :at has gone be=e1 we h an example ( h>monic motion4 ,! weight ( ! bob1 t5d+ to pull ! bob back to ,e1 acts j z an ela/ic b& w\ld act1 t is to say pulls m /rongly 9 proportion z ! di/ance ,f ,b is bigg]4 ,9 fact1 if we c\ld remove ! =ce ( gravity /ill leav+ ! mass ,b ( ! p5dulum bob1 ! =ce ( an ela/ic b& act+ s z to t5d to pull ! bob back to re/ might be us$ to replace x4 ,x w\ld be all "o :e!r ! bob 7 br\ght back to re/ by ! d[nw>d =ce ( its own gravity1 or by ! horizontal =ce ( a prop]ly arrang$ ela/ic b& ( suitable l5g?4 ,illu/ration3 ,,fig4 #cg4 ,b ! motion ( ! bob1 "u ! influ5ce ( ! pull ( an ela/ic b& :]e ! /ra9 0 always proportional to ! displacem5t1 w\ld1 z we h se51 be h>monic motion1 & p]=m$ 9 equal times :atev] ! ext5t ( ! sw+4 ,:5ce !n we conclude t if ! sw+s ( a p5dulum are n too big1 say n exce$+ two & a half in*es ea* way1 ! motion may be consid]$ h>monic motion1 & ! sw+s w be made 9 equal times :e!r !y are l>ge or small ones4 ,9 o!r words1 a clock ) a #ci-a_/g in* p5dulum & side sw+ on ea* side if n ov] two in*es w keep "t1 :atev] ! arc ( sw+ may be4 ,?is may be v]ifi$ exp]im5tally4 ,take a p5dulum ( wood #ci-a_/g in*es long1 & affix to its end a bob ( #aj lbs4 weight4 ,! p5dulum w sw+ once 9 ea* second4 ,to pull x aside two in*es we %\ld want a weight su* t its mom5t ab\t ! po9t ( support 0 equal to ! mom5t ( ! =ce ( gravity act+ on ! bob1 ab\t ! po9t ( support4 ,9 o!r words1 ! weight requir$ #ci-a_/g in*es #aj lbs4 #b in*es4 ,:5ce ! weight requir$ #a_/b lb4 7ne>ly74 ,n[ fix a simil> p5dulum ,a ,b #ci-a_/g in*es long1 horizontally1 ) a weight ,b ( #aj lbs4 on x4 ,fa/5 x to a v]tical %aft ,c ,d1 ) a tie rod ( wire or /r+ ,a ,b s z to keep x up1 & atta* to ea* side ( ! rod ,a ,b ela/ic ?reads ,e ,f & ,e ,g4 ,let ^! ?reads be ti$ on at su* a po9t t :5 ,b is pull$ aside two in*es ! =ce t5d+ to br+ x back to re/ is half a p\nd4 ,!n if set vibrat+ ! rod w sw+ backw>ds & =w>ds 9 equal times1 no matt] h[ big1 ! arc ( vibration 7provid$ ! arc is kept small71 & ! "t ( oscillation w be t ( a p5dulum1 namely1 "o sw+ 9 a second4 ,9 fact1 :e!r y put ,a ,b v]tically & let x sw+ on ! pivots ,c & ,d by ! =ce ( gravity1 or put x horizontally1 & ?us prev5t gravity act+ on x1 b make x sw+ "u ! accel]at+ influ5ce ( a pair ( ela/ic b&s s arrang$ z to be equival5t to gravity1 9 ea* case x w sw+ 9 seconds4 ,illu/ration3 ,,fig4 #ch4 ,x is ?is curi\s prop]ty ( ! circle t makes ! v]tical =ce ( gravity on a p5dulum pull x z ?\gh x 7 a horizontally act+ ela/ic b&2 t is ! reason :y a p5dulum is equal-"t-sw++1 or1 z x is call$1 iso*ron\s1 f two ,greek words t mean 8! same0 & 8"t40 ,b x mu/ be rememb]$ t ?is equal sw++ is only approximate1 & only true :5 ! arc ( vibration is small4 ,"h !n we h a pro( :i* %[s u t ! p5dulum ( a clock & ! balance :eel ( a wat* dep5d on exactly ! same pr9ciples4 ,!y are ea* an example ( h>monic motion4 ,! next "q t arises is :e!r ! weight ( ! p5dulum has any influ5ce ^u ! "t ( its vibration4 ,a little reflection w soon conv9ce u t x has none4 ,= we "k t ! "t t bodies take to fall to ! gr\nd "u ! action ( gravity is indep5d5t ( ! weight4 ,a fall+ #b lb4 weight is only equival5t to two p\nd-weights fall+ side by side4 ,9 ! same way & by ! same reason+ we might take two p5dulums ( equal l5g?1 & ea* ) a bob weigh+ #a lb4 ,!y w\ld1 if put side by side close toge!r sw+ 9 equal times4 ,b ! "t w\ld be ! same if !y 7 fa/5$ toge!r1 & made into "o p5dulum4 ,= inasmu* z ! fall ( a p5dulum is due to gravity1 & ! action ( gravity ^u a body is proportional to its mass1 x foll[s t 9 a p5dulum ! "p ( ! gravitational =ce t acts ^u ea* "p ( ! mass is occupi$ 9 mov+ t mass1 & ! :ole p5dulum may be consid]$ z a bundle ( p5dulums ti$ toge!r & vibrat+ toge!r4 ,! same w\ld be ! case ) a p5dulum vibrat+ "u ! influ5ce ( a spr+4 ,if y h two bobs & two spr+s1 !y w vibrate 9 ! same "t z "o bob accel]at$ by "o spr+4 ,9 ?is case1 h[ev]1 ! =ce ( ! "o spr+ mu/ be equal to ! comb9$ =ce ( ! two spr+s4 ,9 o!r words1 ! spr+s mu/ be made proportional 9 /r5g? to ! masses4 ,h5ce1 !n1 y _c increase ! spe$ ( ! vibration ( a p5dulum by add+ weight to ! bob4 ,on ! o!r h&1 if y h a bob vibrat+ "u ! influ5ce ( a spr+1 l ! balance :eel ( a wat*1 !n if y increase ! bob )\t increas+ ! spr+1 s9ce ! mass to be mov$ has increas$ )\t a correspond+ increase 9 ! accel]at+ =ce act+ on x1 ! "t ( sw+ w alt] accord+ly4 ,b 9 ! case ( gravity1 by alt]+ ! mass1 y !reby proportionally alt] ! attraction on x1 & !re=e ! "t ( sw+ is unalt]$4 ,illu/ration3 ,,fig4 #ci4 ,! explanation :i* has be5 giv5 above ( ! reasons :y a p5dulum sw+s backw>ds & =w>ds 9 a giv5 "t indep5d5tly ( ! l5g? ( ! arc ?r\gh :i* x sw+s1 t is to say ( ! am\nt by :i* x sways f side to side1 is only approximate1 because 9 ! pro( we assum$ t ! arc ( sw+ & ! l9e ,f ,b 7 equal1 :i* is n really & exactly true4 ,galileo nev] got at ! real solution1 ?\gh he tri$ h>d4 ,x 0 res]v$ = ano!r ?an he to f9d ! true pa? ( an iso*ron\s p5dulum & completely to det]m9e its laws4 ,huyg5s1 a ,dut* ma!matician1 f\nd t ! true pa? 9 :i* a p5dulum ought to sw+ if x is to be really iso*ron\s is a curve call$ a cycloid1 t is to say ! curve :i* is trac$ out by a p5cil fix$ on ! rim ( a hoop :5 ! hoop is roll$ along a /raight rul]4 ,x is ! curve :i* a nail /ick+ out ( ! rim ( a waggon :eel w\ld scrat* ^u a wall4 ,i w n g into ! ma!matical pro( ( ?is4 ,clocks are n made ) cycloidal p5dulums1 because :5 ! arc ( a p5dulum is small ! sw+ is s v ne> a cycloid z to make no appreciable diff]5ce 9 "t-keep+4 ,i am n[ glad to be able to say t ,i h dealt ) all ! ma!matics t is necess>y to enable ! me*anism ( a clock to be und]/ood4 ,x all leads up to ?is3-- 7#a7 ,a h>monic motion is "o 9 :i* ! accel]at+ =ce increases ) ! di/ance ( ! body f "s fix$ po9t4 7#b7 ,bodies mov+ h>monically make _! sw+s ab\t ?is po9t 9 equal times4 7#c7 ,a spr+ ( any sort or %ape always has a re/itutional =ce proportional to ! displacem5t4 7#d7 ,& !re=e masses atta*$ to spr+s vibrate 9 equal times h[ev] l>ge ! vibration may be4 7#e7 ,! bob ( a p5dulum1 oscillat+ backw>ds & =w>ds1 acts l a weight "u ! influ5ce ( a spr+1 & is !re=e iso*ron\s4 7#f7 ,! "t ( vibration ( a p5dulum is un9flu5c$ by *anges 9 ! weight ( ! bob1 b is influ5c$ by *anges 9 ! l5g? ( ! p5dulum rod4 ,! "t ( vibration ( a mass atta*$ to a spr+ is influ5c$ by *anges 9 ! mass4 ,we h n[ to deal ) ! application ( ^! pr9ciples to clocks & wat*es4 ,clocks _h be5 kn[n be=e ! "t ( ,galileo1 & be=e ! inv5tion ( ! p5dulum4 ,!y _h :at is kn[n z balance1 or v]ge escapem5ts4 ,/rictly 9 ord] ( "t ,i ought to expla9 !m "h4 ,b ,i w n d s4 ,i w g on to describe ! p5dulum clock1 & !n ,i w g back & expla9 ! v]ge escapem5t1 :i*1 we %all see1 is really a sort ( huge wat* ( a v imp]fect "*4 ,z soon z ,galileo _h discov]$ t p5dulums 7 iso*ron\s1 t is1 equi-"t-sw++1 he set to "w to see :e!r he c\ld n contrive to make a timepiece by means ( !m4 ,?is w\ld be easy if only he c\ld keep a p5dulum sw++4 ,:5 a p5dulum is set sw++1 x soon comes to re/4 ,:at br+s x to re/8 ,! resi/ance ( ! air & ! friction ( ! pivots4 ,!re=e :at is obvi\sly want$ is some?+ to give x a kick n[ & !n1 b ! ?+ mu/ kick ) discretion4 ,if x kick$ at ! wrong "t1 x might actually /op ! p5dulum in/ead ( keep+ x go+4 ,y want some?+ t1 j z ! p5dulum is at "o end & has begun to move1 w give x a fur!r pu%4 ,suppose t ,i h a sw+ & t ,i put a boy 9 x1 & ,i sw+ him to & fro4 ,i "t my pu%es4 ,z he comes back aga9/ my h& ,i let him pu% x back1 & !n j z ! sw+ turns ,i give x a fur!r pu%4 ,b ,i _c /& do+ t all day4 ,i mu/ make a ma*9e to d x4 ,n[ :at sort ( a ma*9e8 ,fir/1 ! ma*9e mu/ h a res]voir ( =ce4 ,i c't get a ma*9e to d "w unless ,i w9d x up1 nor a man to d "w unless ,i fe$ him1 :i* is 8 way ( be+ w\nd up4 ,b !n :at d ,i want him to d8 ,i want him1 :5 ,i give him a pu%1 to pu% me back h>d]4 ,i want a res]voir ( =ce su* t :5 a p5dulum comes back & t\*es x1 ! t\*1 l ! pressure ( ! trigg] ( a gun1 %all all[ "s p5t-up p[] to escape & to drive ! p5dulum =w>d4 ,?is is ! case 9 a sw+4 ,ea* "t t ! sw+ returns to my h&s ,i give x a pu%1 :i* s]ves to su/a9 ! motion t w\ld o!rwise be de/roy$ by friction & ! resi/ance ( ! air4 ,su* an arrangem5t1 if x c be contriv$ me*anically1 is call$ an 8escapem5t40 ,an arrangem5t ( ?is k9d 0 contriv$ by ,galileo4 ,he provid$ a :eel1 z is "h %[n1 ) a numb] ( p9s r\nd x4 ,! p5dulum ,a ,b has an arm ,a ,h atta*$ to x1 & !re is a rat*et ,c ,d :i* engages ) ! p9s4 ,! rat*et has a project+ arm ,e ,f4 ,illu/ration3 ,,fig4 #dj4 ,:5 ! p5dulum comes back t[>ds ! end ( its beat1 ! arm ,a ,h /rikes ! arm ,e ,f1 & raises ! rat*et ,c ,d4 ,?is releases ! :eel1 :i* has a weight w\nd up ^u x1 & !re=e at once tries to g r\nd4 ,! consequ5ce is1 t ! p9 ,g /rikes ^u ! arm ,a ,h1 & ?us on its return /roke gives an impetus to ! p5dulum4 ,z ! p9 ,g moves =w>d x slides on ! arm ,a ,h till x slips ov] ! po9t ,h4 ,! :eel n[ be+ free1 w\ld fly r\nd 7 x n t :5 ! p5dulum return$1 & ! arm ,a ,h 0 l[]$1 ! rat*et _h got into position aga9 & its po9t ,d 0 ready to meet & /op ! next p9 t 0 com+ on aga9/ x4 ,at ea* bl[ ( ! p9s aga9/ ! p5dulum a 8tick0 is made1 at ea* bl[ ( a p9 aga9/ ! rat*et a 8tock0 is s\nd$1 s t z x moves ! p5dulum makes ! 8tick-tock0 s\nd ) :i* we are all famili>4 ,h5ce !n a clock consi/s ( a :eel1 or tra9 ( :eels1 urg$ by a weight or spr+1 :i* /rives cont9ually to sp9 r\nd1 b its rotation is controll$ by an escapem5t & p5dulum1 s contriv$ z only to all[ x to g a /ep =w>d at regul> equal int]vals ( "t4 ,b ?is w\ld make only a poor sort ( escapem5t4 ,= ! mode ( driv+ ! p5dulum adds a complication to ! sw+ ( ! p5dulum4 ,in/ead ( ! p5dulum be+ simply "u ! accel]ative =ce ( gravity1 x is also subject$ to ! accel]ation ( ! p9 ,g4 ,?is accel]ation is n ( ! 8h>monic0 ord]4 ,h5ce s f> z x goes x does n t5d to assi/ 9 giv+ a h>monic motion to ! p5dulum1 b1 on ! contr>y1 di/urbs t h>monic motion4 ,besides ?is1 ! impulse ( ! p9 is 9 practice n always uni=m4 ,= if ! :eel is at ! end ( a tra9 ( :eels driv5 by a weight1 ?\gh ! =ce act+ on x is con/ant1 yet1 z t =ce is transmitt$ ?r\gh a tra9 ( :eels1 x is mu* affect$ by ! friction ( ! oil4 ,& on cold] days ! oil becomes m coagulat$1 & (f]s great] resi/ance4 ,moreov]1 z w be expla9$ m 9 detail aft]w>ds1 ! fact t ! impulse is adm9i/]$ by ,g at ! end ( ! /roke ( ! p5dulum is disadvantage\s1 z x int]f]es ) ! free play ( ! p5dulum4 ,f all ^! causes ! above escapem5t is imp]fect 9 "*1 & w\ld n d :]e precision 0 requir$4 ,illu/ration3 ,,fig4 #da4 ,x is n[ "t to return to ! old-fa%ion$ escapem5ts :i* 7 9 use be=e ! "t ( ,galileo4 ,^! consi/$ ( a :eel call$ a cr[n :eel1 ) triangul> tee?4 ,on "o side ( ?is :eel a v]tical axis 0 fitt$1 ) project+ 8pallets0 e f4 ,across ! axis a v]ge or rod e f 0 plac$1 fitt$ ) a ball at ea* end4 ,:5 ! cr[n :eel attempt$ to move on1 "o ( its tee? came 9 contact ) a pallet4 ,?is urg$ ! pallet =w>d1 & !reby caus$ an impulse to be giv5 to ! axis1 on :i* 0 m\nt$ ! v]ge1 c>ry+ ! balls4 ,^! ( c\rse began to move "u ! accel]ation ( ! =ce ?us impress$ ^u ! pallet4 ,meantime1 h[ev]1 ! o!r pallet 0 mov+ 9 ! opposite direction1 & by ! "t ! fir/ pallet _h be5 pu%$ s f> t x escap$ or slid pa/ ! too? ( ! cr[n :eel1 :i* 0 press+ ^u x1 ! o!r pallet _h come into contact ) ! too? on ! o!r side ( ! cr[n :eel4 ,?is t5d$ to arre/ ! motion ( ! v]ge1 to br+ ! balls to a /&/ill1 & ultimately to imp>t a motion 9 a contr>y direction to !m4 ,?us !n ! arrangem5t 0 t ( a p5dulum n act$ on by gravity1 = ! balls neutralis$ "o ano!r4 ,! p5dulum 01 h[ev]1 n subject$ to a h>monic accel]ation1 b alt]nately to a ne>ly uni=m accel]ation f ,a to ,b & ,b to ,a4 ,z a result1 !re=e1 ! "t ( oscillation 0 n indep5d5t ( ! arc ( sw+1 b v>i$ accord+ to x1 z also accord+ to ! driv+ p[] ( ! cr[n :eel4 ,at ea* /roke !re 0 a consid]able 8recoil40 ,= z ea* too? ( ! :eel came into play x 0 unable at fir/ to ov]come & drive back ! pallet aga9/ :i* x 0 press+1 b1 on ! contr>y1 0 = a "t itself driv5 back by ! pallet4 ,illu/ration3 ,,fig4 #db4 ,( c\rse1 s long z ! motions ( ! :eel & v]ge 7 exactly uni=m1 fair "t 0 kept4 ,b ! lea/ inequality ( manufacture produc$ diff]5ces4 ,nev]!less x 0 on ?is pr9ciple t clocks 7 made dur+ ! ?irte5?1 f\rte5? & fifte5? c5turies4 ,!y 7 mo/ly made = ca!drals & mona/]ies4 ,"o 0 put up at ,we/m9/]1 erect$ out ( money paid z a f9e ^u "o ( ! few ,engli% judges :o h be5 convict$ ( tak+ bribes4 ,! "t ( sw+ ( ^! clocks dep5d$ entirely ^u ! ratio ( ! mass ( ! balls at ! end ( ! v]ge z comp>$ ) ! /r5g? ( ! driv+ =ce by :i* ! accel]ation on ! pallets 0 produc$4 ,!y 7 v commonly driv5 by a spr+ in/ead ( a weight4 ,! spr+ consi/$ ( a long /rip ( r poor quality /eel coil$ up on a drum4 ,z x unw\nd x became weak]1 & ?us ! accel]ation on ! v]ge became weak]1 & ! clock w5t sl[]4 ,9 ord]1 !re=e1 to keep ! "t true1 x became necess>y to devise "s arrangem5t by :i* ! driv+ =ce on ! cr[n :eel %\ld be kept m con/ant4 ,?is gave rise to ! inv5tion ( ! fusee4 ,! spr+ 0 put inside a drum or cyl9drical box4 ,"o end ( ! spr+ 0 fa/5$ to an axis1 :i* 0 kept fix$ :ile ! clock 0 go+2 ! o!r 0 fa/5$ to ! inside ( ! drum4 ,r\nd ! drum a cord 0 w\nd1 :i*1 z ! drum 0 mov$ by ! spr+1 t5d$ to be w\nd up on ! surface ( ! drum4 ,ow+ to ! unequal pull ( ! spr+1 ?is cord 0 pull$ by ! drum /rongly at fir/1 & aft]w>ds m feebly4 ,to comp5sate its action a conical :eel 0 provid$1 ) a spiral pa? cut 9 x 9 su* a way & ( su* a size & proportion t z ! :eel 0 turn$ r\nd by ! pull ( ! drum ! cord 0 on diff]5t p>ts ( x1 s t ! lev]age or turn+ p[] on x v>i$1 becom+ great] z ! pull ( ! cord became weak]1 & 9 su* a ratio t "o j comp5sat$ ! o!r1 & ! turn+ p[] ( ! axle 0 kept uni=m4 ,9 ?is mann] small table clocks 7 made :i* kept v tol]able "t4 ,illu/ration3 ,,fig4 #dc4 ,huyg5s conv]t$ ^! clocks into p5dulum clocks 9 a v simple mann]4 ,he remov$ "o ( ! balls1 l5g!n$ ! v]ge1 & slightly increas$ ! weight ( ! o!r ball4 ,by ?is means1 :ile ! cr[n :eel /ill cont9u$ to drive ! v]ge & rema9+ ball1 ! accel]ation on t ball n[ no long] dep5d$ entirely on ! =ce ( ! cr[n :eel4 ,! accel]ation & ret>dation 7 n[ almo/ entirely gov]n$ by ! =ce ( gravity on ! rema9+ ball1 & ?is accel]ation 0 h>monic4 ,! clock1 !re=e1 0 imm5sely improv$ z a "t-keep]4 ,/ill1 h[ev]1 ! accel]ation rema9$ p>tly due to ! driv+ p[]1 & ?is 0 p>tly non-h>monic & introduc$ errors4 ,mo/ ( ! old clocks 7 conv]t$ %ortly aft] ! "t ( ,huyg5s4 ,z !re 0 9 g5]al no room = ! p5dulum inside ! clock-case1 !y usually br\ght ! axle on :i* ! pallets 7 m\nt$ outside ! clock & made x vibrate 9 front ( ! face4 ,_m old clocks exi/1 ( :i* ! engrav+ 9 ! frontispiece is an example1 t h be5 ?us conv]t$4 ,a true old v]ge escapem5t clock is n[ a r>ity4 ,! type ( escapem5t inv5t$ by ,galileo nev] came into vogue = clocks1 on acc\nt ( its imp]fections1 except till aft] a long int]val1 :51 ) c]ta9 modifications1 x became ! basis ( a new improvem5t at ! h&s ( ,sir ,george ,airey4 ,! cr[n :eel fell into disuse & 0 replac$ by ! an*or escapem5t1 :i* 0 employ$ 9 t popul> & excell5t timepiece us$ ?r\gh\t ! eighte5? & ! e>ly "p ( ! n9ete5? c5tury1 & is n[ kn[n z 8,! ,gr&fa!r's ,clock40 ,x 0 aft] all ! cr[n :eel 9 ano!r %ape4 ,! :eel1 h[ev]1 0 flatt5$ out1 ! tee? be+ put 9 ! same plane4 ,?is made x mu* easi] to con/ruct4 ,! pallets 7 fix$ on an axis1 & 7 a little alt]$ s z to suit ! *ang$ arrangem5t ( ! tee?4 ,! p5dulum 0 no long] hung on ! axis :i* c>ri$ ! pallets4 ,a cause ( a good deal ( friction & loss ( p[] 0 ?us remov$4 ,! p5dulum 0 hung f a /rip ( ?9 /eel spr+1 :i* all[$ x to oscillate1 & :i* support$ x )\t friction4 ,?is excell5t mann] ( susp5d+ p5dulums is n[ univ]sal4 ,x enabl$ ! p5dulum to be made v heavy4 ,! bob 0 usually "s eight or n9e p\nds weight4 ,by ?is means ! accel]ation on ! p5dulum 0 due almo/ entirely to gravity act+ on ! bob1 & ?us ! motion ( ! p5dulum became almo/ :olly h>monic4 ,:5ce x foll[$ t v>iations 9 ! p5dulum sw+ became ( second>y importance1 & did n greatly alt] ! go+ ( ! clock4 ,illu/ration3 ,,fig4 #dd4 ,!re=e :5 ! :eels became worn1 & ! pivots *ok$ ) old oil & du/1 ! old clock /ill w5t on4 ,if x %[$ a t5d5cy to /op = want ( p[]1 a little m 0 add$ to ! driv+ weight1 & ! clock kept z good "t z ev]4 ,! sw+ ( ! p5dulum 0 by ?is escapem5t enabl$ to be made small1 s t ! arc ( sw+ ( ! bob diff]$ b little f a cycloid4 ,! secret ( ! "t-keep+ qualities ( ^! old 8,gr&fa!r0 clocks is ! l5g? ( p5dulum4 ,?is r5d]s x possible to h b a small arc ( oscillation1 & !re=e ! motion is kept v ne>ly h>monic4 ,= practical purposes no?+ w ev5 n[ beat ^! old clocks1 ( :i* "o %\ld be 9 e h\se4 ,at pres5t ! t5d5cy is to aboli% !m & to sub/itute ,am]ican clocks ) v %ort p5dulums1 :i* nev] c keep good "t4 ,!y are made ( /amp$ metal4 ,:5 !y get out ( ord] no "o ?9ks ( hav+ !m m5d$4 ,!y are ?r[n into ! a%-pit & a new "o b\ght4 ,9 reality ?is is n economy4 ,good 8,gr&fa!r0 clocks are n n[ (t5 made4 ,! la/ place ,i rememb] to h se5 !m be+ manufactur$ is at ,morez1 9 ! di/rict ( ! ,jura4 ,an excell5t clock1 enclos$ 9 a du/-tight iron case1 ) a tall pa9t$ case ( qua9t old design1 c be b\ght = ab\t #ees4 ,! :eels are well cut1 & ! int]nal me*anism v good4 ,i visit$ ! t[n ( ,morez 9 ! ye> #ahic4 ,! clock indu/ry 0 decl9+4 ,! f>m]s ( ,france seem$ to pref] small clocks ( hide\s appe>ance1 made 9 ,g]many & 9 ,am]ica1 to ! excell5t "w ( _! own c\ntry4 ,probably by n[ ! old clockmak+ indu/ry is ext9ct4 ,"o ,i pur*as$ at t "t has gone well ev] s9ce4 ,,*apt] ,,iv4 ,x is n[ "t to give a description ( ! v>i\s p>ts ( an ord9>y p5dulum clock4 ,we w take ! 8,gr&fa!r0 clock z an example4 ,we %all want an h\r h& & a m9ute h& 9 ! c5tre ( ! face1 & a seconds h& to %[ seconds a little above !m4 ,!re w be a seconds p5dulum #ciad in*es long1 & ! c5tre ( ! face ( ! clock w be ab\t sev5 feet above ! gr\nd1 s z to give practically ab\t five feet ( fall = ! weight4 ,illu/ration3 ,,fig4 #de4 ,9 ! fir/ place1 we h to consid] ! axle :i* c>ries ! m9ute h&1 & :i* turns r\nd once 9 ea* h\r4 ,?is is usually made ( a piece ( /eel ab\t "o-six? ( an in* 9 diamet]4 ,clockmak]s usually call an axle an 8arbor10 or 8tree10 :5ce our ^w axletree4 ,?is 8arbor0 is turn$ 9 ! la!1 s z to h pivots on ea* end1 fitt$ into holes 9 ! clock plates1 t is to say1 ! flat pieces ( brass t s]ve z ! body ( ! clock4 ,! adjo9+ diagram %[s ,s ,t ! clock faces1 & ,c1 ! arbor ( ! m9ute h&4 ,inasmu* z ! seconds h& is to turn r\nd sixty times :ile ! m9ute h& turns r\nd once1 x is obvi\s t ! arbor ( ! m9ute h& mu/ be connect$ to ! arbor ( ! seconds h& by a tra9 ( cog:eels s arrang$ z to multiply by sixty4 ,?is ( c\rse involves u 9 hav+ l>ge & small cog:eels4 ,illu/ration3 ,,fig4 #df4 ,! small cog:eels usually h eight tee?1 & are = conv5i5ce ( manufacture1 z also to /& prolong$ we>1 cut out ( ! solid /eel ( ! arbor4 ,!y are nicely poli%$4 ,! easie/ pair ( :eels to use w be two p9ions ( eight tee?1 or 8leaves10 z !y are call$1 & two cog:eels1 "o ( sixty-f\r tee?1 ! o!r ( sixty tee?4 ,x is !n cle> t if ! arbor ,a turns r\nd once 9 an h\r1 ! arbor ,b w turn r\nd eight times 9 an h\r1 & ,c w turn r\nd 7#fj #fd7_/7h #h7 #fj times 9 an h\r1 or once 9 ea* m9ute4 ,by hav+ #dhj tee? on ! cog:eel on ,a1 y c\ld1 ( c\rse1 make ,c g r\nd once 9 a m9ute )\t ! use ( any int]m$iate arbor su* z ,b4 ,illu/ration3 ,,fig4 #dg4 ,b ?is w\ld n be a v conv5i5t plan4 ,= z ! :eel on ,a is usually ab\t two & a qu>t] in*es 9 diamet]1 to cut #dhj tee? on s small a :eel w\ld involve u 9 cutt+ ab\t sixty tee? to ! in*4 ,! tee? w\ld ?us be microscopically small1 & w\ld h to be set s f9e t ! lea/ dirt w\ld clog !m4 ,moreov]1 ! p9ion ( eight leaves w\ld h to be microscopic4 ,= ^! reasons1 !re=e1 x is usual 9 clocks n to use :eels ) tee? m ?an sixty or sixty-f\r 9 numb]1 & to dim9i% ! motion gradually by means1 :]e ne$ful1 ( int]m$iate arbors4 ,we h next to consid] h[ ! weight is to be arrang$ s z to turn ! arbor ,a once r\nd 9 an h\r4 ,we "k t we h five feet ( space = ! weights to fall 94 ,if we arrange to h :at is call$ a d\ble fall1 z %[n 9 ! sket*1 !n1 all[+ room = pulley :eels1 we %all f9d t our /r+ may be practically ab\t n9e feet 9 l5g?4 ,illu/ration3 ,,fig4 #dh4 ,! clock w be want$ to g = a week )\t w9d+1 & z p may =get to w9d x at ! prop] h\r ( ! day1 we w give x a day extra1 & make an 8eight-day0 clock ( x4 ,h5ce !n1 :ile n9e feet ( cord is be+ pull$ out by a weight :i* falls f\r & a half feet1 ! m9ute h& is to be turn$ r\nd z _m times z !re are h\rs 9 eight days1 viz41 #aib times4 ,?is c\ld be accompli%$1 ( c\rse1 by w9d+ ! cord r\nd ! arbor ( ! m9ute h&4 ,b ?is w\ld require #aib turns4 ,if our cord is to be ord9>y :ipcord1 or catgut1 say "o-twelf? ( an in* 9 diamet]1 9 ord] t ! cord c\ld be w\nd ^u x1 ! arbor w\ld h to be #aib_/ab in*es long #ad in*es long4 ,?is w\ld make ! clock case unnecess>ily deep4 ,we mu/ !re=e aga9 h rec\rse to an int]m$iate :eel4 ,illu/ration3 ,,fig4 #di4 ,if we put a p9ion ( eight leaves on ! m9ute h& arbor c1 & engage x ) a :eel ( sixty-f\r tee? on ano!r arbor b1 !n b w obvi\sly turn r\nd once 9 eight h\rs1 t is to say1 tw5ty-f\r times 9 ! p]iod ( eight days4 ,&1 if we fix on b a 8drum0 or cyl9d] two in*es long1 ! tw5ty-f\r turns ( our cord w j fit ^u x1 s9ce1 z has be5 said1 our cord is to be "o-twelf? ( an in* 9 diamet]4 ,! diamet] ( ! drum mu/ be su* t a cord n9e feet long c be w\nd tw5ty-f\r times r\nd x4 ,t is to say1 ea* lap mu/ take 7#i #ab7_/bd #d in*es ( cord4 ,f ?is x is easy to calculate t ! diamet] ( ! drum mu/ be r less ?an "o & a half in*es4 ,f ?is !n x results t we want = a 8,gr&fa!r's0 clock a drum two in*es long & "o & a half in*es diamet]1 on ?is a cog:eel ( sixty-f\r tee? work+ into a m9ute h& arbor1 ) a p9ion :eel ) eight leaves1 & a cog:eel ( sixty-f\r tee?1 an int]m$iate or idle :eel ) an eight-leav$ p9ion1 & a cog:eel ( sixty tee?1 engag+ ) a seconds h& arbor ) a p9ion ( eight leaves4 ,?is is call$ ! 8tra9 ( :eels40 ,) x a weight su* z c be arrang$ 9 an ord9>y 8,gr&fa!r's0 clock case w cause by its fall dur+ eight days ! second h& arbor to turn r\nd once 9 ea* m9ute dur+ ! :ole "t1 & ! m9ute h& arbor to turn r\nd once 9 ea* h\r4 ,illu/ration3 ,,fig4 #ej4 ,we mu/ next provide an arrangem5t = w9d+ ! clock up4 ,x is obvi\s t we _c d s by twi/+ ! h&s back4 ,x is true t ?is c\ld be done1 b x w\ld take ab\t five m9utes to d ea* "t & be we>isome4 ,9 ord] to save ?is tr\ble1 an arrangem5t call$ a rat*et :eel & pall mu/ be provid$4 ,a rat*et :eel consi/s ( a :eel ) a s]ies ( not*es cut 9 x1 z %[n 9 ! figure ,a4 ,a pall is a piece ( metal1 m\nt$ on a p91 & kept press$ up aga9/ ! rat*et :eel by a spr+ ,c4 ,x is obvi\s t if ,i turn ! :eel ,a r\nd1 & ?us w9d up a weight1 fa/5$ to a cord w\nd r\nd ! drum ,d1 t ! pall ,b w g click-click-click z ! rat*et :eel goes r\nd1 b t ! pall w hold x f slipp+ back aga94 ,:51 h[ev]1 ,i take my h&s away1 & let ! rat*et :eel alone1 !n ! weight ,e w pull on ! drum ,d1 & try & turn ! rat*et :eel back ! opposite way to t 9 :i* ,i twi/$ x at fir/4 ,if ! pall ,b is held fa/1 x is impossible to move x1 b if ! pall is fix$ to a cog:eel ,f1 :i* rides loose on ! arbor ( ! drum ,d1 !n ! pull ( ! weight ,e w t5d to twi/ ! cog:eel ,f r\nd1 & ?is1 if engag$ ) a p9ion :eel on ! m9ute h& arbor1 w !re=e drive ! clock4 ,z ! clock arbors move1 ( c\rse ! weight ,e gradually runs d[n1 &1 at la/ all ! /r+ is unw\nd f ! drum ,d4 ,! clock is said !n to h 8run d[n10 b if ,i take a clock key1 & by means ( x w9d ! /r+ up ^u ! drum ,d1 !n ! pall lets ! drum & rat*et slip2 ! clock h&s are n affect$4 ,:5 ,i h giv5 tw5ty-f\r turns to ! arbor1 ! n9e feet ( cord w !n be w\nd ^u ! drum aga91 & ! clock w be ready to g = eight m days1 & w beg9 to move z soon z ,i cease to press ^u ! clock key4 ,illu/ration3 ,,fig4 #ea4 ,i h ?us describ$ ! w9d+ me*anism4 ,x n[ rema9s to describe ! escapem5t4 ,x is ( c\rse obvi\s t1 if ! weight & tra9 ( :eels 7 simply let g1 ! weight w\ld ru% d[n1 & ! seconds-h& :eel w\ld fly r\nd at a trem5d\s pace2 b we want x to be s re/ra9$ z only to be all[$ to g "o-sixtie? "p ( its j\rney r\nd 9 ea* second4 ,9 fact1 we ne$ an 8escapem5t0 & a p5dulum4 ,! escapem5t usually employ$ 9 8,gr&fa!r0 clocks is ! an*or escapem5t above describ$4 ,x is n by any means ! be/ sort ( escapem5t1 b x is ! easie/ to make2 & h5ce its popul>ity 9 ! days sometimes call$ ! 8de>1 good old days10 :5 p _h to file ev]y?+ out by h&1 & _h to take a day to d badly :at c n[ be done well 9 five m9utes4 ,! escape :eel ( an an*or escapem5t has ?irty %>p angul> tee? on its rim4 ,! :eel is made z light z possible1 s t ! %ock ( /oppage at ea* tick ( ! clock may be z slight z possible1 = a heavy bl[ ( c\rse wa/es p[] & gradually we>s out ! clock4 ,! an*or consi/s ( two arms ( ! %ape %[n 9 ! illu/ration 7,fig4 #dd74 ,z ! escape :eel goes r\nd 9 ! direction ( ! arr[1 ! an*or1 m\nt$ on its arbor1 rocks to & fro4 ,! :eel _c run away1 because ! act ( pu%+ "o arm or 8pallet10 z x is call$1 outw>ds1 & ?us free+ ! too? pulls ! o!r pallet 91 & ?is /ops ! motion ( ! too? opposite to x1 b :5 ! an*or rocks back aga91 s z to dis5gage ! pallet f ! too? t holds x1 !n ! opposite too? is free to fly =w>d aga9/ ! o!r pallet4 ,?is t5ds to rock ! an*or ! o!r way1 b at t in/ant ! pallet j engages ! next too? ( ! :eel1 & s ! action goes on4 ,! an*or rocks f side to side2 ! pallets alt]nately engage ! tee? ( ! :eel1 mak+ at ea* rock ( ! an*or ! tick-tock s\nd ) :i* we are s famili>4 ,if ! an*or 7 free to rock at any spe$ x c\ld1 ! tick+ ( ! clock w\ld be v quick2 s1 to re/ra9 ! vivacity ( ! an*or1 we h a p5dulum4 ,! p5dulum might be simply hung on to ! an*or4 ,b ! disadvantage ( do+ ?is w\ld be t ! heavy bob ( ! p5dulum w\ld cause su* a pressure on ! arbor ( ! an*or t !re w\ld be great friction1 & ! arbor w\ld soon be worn out1 & ! accurate go+ ( ! clock di/urb$4 ,! p5dulum !re=e is hung on a piece ( /eel spr+ on a sep>ate hook1 :i* lets x g backw>ds & =w>ds & c>ries ! weight easily1 :ile a rod project+ f ! an*or has a p91 :i* works 9 a slot on ! p5dulum4 ,! p5dulum is !re=e able to control & regulate ! movem5ts ( ! escapem5t1 & ?us ! "t ( ! clock4 ,( c\rse x is cle> t ! heavi] ! driv+ weight put on ! drum ( ! clock1 & ! bett] ! cut & f9i% ( ! :eels1 & ! great] ! cleanl9ess & oil1 ! m w be ! pressure t5d+ to drive r\nd ! escape :eel1 & ! h>d] ! pressure on ! pallets1 & h5ce ! bigg] ! impulses on ! p5dulum1 & !re=e ! l>g] ! amplitude ( its sw+4 ,if ! amplitude ( ! p5dulum's sw+ affect$ ! "t ( its sw+1 !n ! "t kept by ! clock w\ld v>y ) ! weight1 & ! dirt & friction1 & ! dry+ up ( ! oil4 ,b "h precisely is :]e ! value ( ! beautiful law gov]n+ ! h>monic motion ( ! p5dulum comes 94 ,! "t ( ! p5dulum is 7= small arcs7 indep5d5t ( ! l5g? ( sw+1 & !re=e ( ! driv+ =ce ( ! clock1 & h5ce )9 limits ! clock1 ev5 ?\gh r\ghly made & f\l ) ! dirt ( ye>s1 cont9ues to keep good "t4 ,b ! an*or escapem5t has imp]fections4 ,! only way 9 :i* a p5dulum c be reli$ on to keep accurate "t is by leav+ x unimp$$4 ,b ! pressure ( ! tee? on ! pallets 9 an an*or escapem5t con/antly int]f]es ) ?is4 ,illu/ration3 ,,fig4 #eb4 ,a little consid]ation w easily %[ t !re are "s times dur+ ! sw+ ( a p5dulum at :i* int]f]5ce is f> m fatal to its "t-keep+ ?an at o!rs4 ,?us ! bob ( a p5dulum may be reg>d$ z a weight %ot outw>ds f its position ( re/ aga9/ ! influ5ce ( a ret>d+ =ce v>y+ z its di/ance f re/--9 fact1 %ot out aga9/ a spr+4 ,! "t ( go+ out & com+ 9 aga9 w be q indep5d5t ( ! =ce ex]t$ to ?r[ x out1 q indep5d5t ( its orig9al velocity4 ,!re=e a v>iation 9 ! impulse giv5 to ! bob is ( no consequ5ce1 provid$ t impulse is giv5 :5 ! bob is ne> ! position ( re/4 ,?is foll[s f ! nature ( ! motion4 ,if a ball be atta*$ to a piece ( ela/ic ?read1 & ?r[n f ! h&1 s t x flies out1 & !n /ops & is br\ght back by ! ela/ic =ce ( ! ?read1 ! "t ( ! outw>d motion & ! return is ! same :atev] be ! =ce ( ! ?r[4 ,& s if a p5dulum be impell$ outw>ds f a position ( re/1 ! "t ( ! sw+ out & back is ! same1 h[ev] big 7)9 limits7 is ! impell+ =ce & ! consequ5t l5g? ( ! sw+4 ,! use ( a p5dulum z a measure ( "t is to impel x outw>ds1 & !n let x fly freely out & back4 ,b if its motion is n free1 if =ces o!r ?an gravity act ^u x :ile on its pa?1 !n its "t ( sw+ w be di/urb$4 ,x does n matt] ) :at =ce y orig9ally impel x1 b :at does matt] is1 t :5 x once />ts x %\ld be all[$ to travel unimp$$ & un9flu5c$4 ,n[ t is :at an an*or escapem5t does n d4 ,! impulse is giv5 ! :ole way out on "o ( ! pallets1 & !n :5 x is at its extreme ( sw+1 & ought to be left tranquil1 ! o!r pallet fa/5s on x4 ,b a p]fect escapem5t ought to give its impulse at ! middle po9t ( ! sw+1 :5 ! p5dulum is at ! l[e/1 & !n cease1 & all[ ! p5dulum to adapt its sw+ to ! impulse x has receiv$1 & ?us !re=e to keep its "t con/ant4 ,?is is done by an escapem5t call$ ! dead beat escapem5t1 :i*1 ?\gh 9 an imp]fect way1 realises ^! conditions4 ,! alt]ation is made 9 ! %ape ( ! pallets ( ! an*or4 ,! :eel is mu* ! same4 ,ea* pallet consi/s ( two faces3 a driv+ face a b & a slid+ face b c4 ,illu/ration ,:5 ! too? b has done its "w by press+ on ! driv+ face1 & ?us driv+ ! an*or ov]1 say1 to ! left1 !n ! too? on ! opposite side falls on ! slid+ face ( ! o!r pallet4 ,?is be+ an arc ( a circle1 has no effect 9 driv+ ! an*or "o way or ! o!r2 h5ce ! p5dulum is free to sw+ to ! left z f> z x likes & return :5 x feels incl9$1 always ) ! exception ( a little friction ( ! too? on ! faces ( ! pallets1 b :5 x returns & beg9s to move t[>ds ! "r1 ! too? slides back along ! face ( ! pallet till ! p5dulum is almo/ at ! middle ( its sw+2 !n an impulse is giv5 by ! pressure ( ! too? ^u ! incl9$ plane a b4 ,z soon1 h[ev]1 z ! too? leaves b1 ano!r too? on ! o!r side at once engages ! slid+ face b c ( ! o!r pallet1 & s ! motion goes on4 ,?is beautiful escapem5t is at pres5t us$ = a/ronomical clocks2 ! pallets are made ( agate or sapphire1 & !re=e d n gr9d away ! tee? ( ! :eel p]ceptibly1 & ! loss by friction on ! slid+ surfaces is exce$+ly small4 ,!re are sev]al o!r ways ev5 bett] ?an ?is = secur+ a free p5dulum movem5t4 ,we h n[ to return to our clock4 ,! c5tre arbor moves r\nd once 9 an h\r1 & c>ries ! m9ute h&4 ,9 ord] to provide an h\r h&1 :i* %all turn r\nd once 9 twelve h\rs1 we fa/5 a cog:eel & tube ,n on to ! m9ute h& arbor by means ( a small spr+1 :i* keeps x r tight1 b all[s x to slip if turn$ r\nd h>d 7see ,fig4 #de74 ,?is spr+ is a little b5t plate slipp$ 9 beh9d ! cog:eel on :i* its ends re/2 its c5tre presses on a %\ld] on ! m9ute h& arbor2 x is a sort ( small c>riage spr+4 ,! cog:eel n has ?irty tee?4 ,?is cog:eel engages ano!r cog:eel o ) ?irty tee?1 on a sep>ate arbor1 :i* c>ries a ?ird cog:eel1 p1 ) six tee?1 & ?is aga9 engages a f\r? cog:eel1 q1 ) sev5ty-two tee?1 m\nt$ on a tube :i* slips ov] ! tube to :i* ! cog:eel a is atta*$4 ,x is n[ easy to see t = ea* turn ( ! m9ute h& arbor ! arbor p makes "o turn1 & = ea* turn ( ! arbor p ! cog:eel d1 makes "o-twelf? ( a turn4 ,f :i* x foll[s t = ea* turn ( ! m9ute h& arbor ! cog:eel d ) its tube1 or1 z x is sometimes call$1 its 8slieve10 makes "o-twelf? ( a turn1 & ?us makes a h& fa/5$ to x %[ "o h\r = e complete turn ( ! m9ute h&4 ,! m9ute h& is atta*$ to ! tube or slieve :i* c>ries ! cog:eel ,n4 ,! h\r h& is atta*$ to ! tube or slieve :i* c>ries ! cog:eel ,q1 & "o goes twelve times z sl[ly z ! o!r4 ,b if y want to set ! clock x is easy to d s by reason ( ! fact t ! m9ute h& is n fix$ to ! arbor1 b only to ! slieve on ! cog:eel t fits on ! arbor1 & is held some:at tight to ! arbor by means ( ! spr+4 ,! h&s c ?us be turn$1 b !y are a little /iff4 ,a wa%] on ! m9ute h& arbor keeps ! slieve on ! cog:eel press$ tight aga9/ ! spr+1 be+ secur$ 9 its turn by a v small lyn*-p9 driv5 ?r\gh a hole 9 ! m9ute h& arbor4 ,x rema9s to expla9 a few subsidi>y arrangem5ts1 n always f\nd ^u all clocks1 b :i* are useful4 ,9 ord] to prev5t ! ov]w9d+ ( ! clock 7see ,fig4 #dc71 :i* w\ld cause ! cord to ov]run ! drum1 an arm is provid$1 fitt$ ) a spr+4 ,z ! weight is w\nd up ! free "p ( ! cord travels along ! drum or ! fusee2 & ! cord1 :5 x is ne> ! end ( ! w9d+1 comes up aga9/ ! arm & pu%es x a little aside4 ,?is causes ! end ( ! arm to be pu%$ aga9/ a /op on ! axis ( ! fusee1 & ?us prev5ts ! clock be+ fur!r w\nd up4 ,! /op1 be+ rat*et-%ap$1 does n prev5t ! weight f pull+ ! rat*et :eel r\nd ! o!r way1 & ?us driv+ ! clock2 x only prev5ts ! rotation ( t :eel :5 ! /r+ is ne> x1 & ! w9d+ is f9i%$4 ,ano!r arrangem5t is ! 8ma9ta9+ spr+40 ,x w be rememb]$ t dur+ ! process ( w9d+ ! clock ! h& twi/+ ! key takes ! pressure ( ! rat*et :eel (f ! pall1 s t dur+ t op]ation no =ce is at "w to drive ! clock4 ,9 consequ5ce ! p5dulum receives no impulse1 b sw+s simply by virtue ( its =m] motion4 ,if ! process ( w9d+ 7 done sl[ly en\gh ! clock might ev5 /op4 ,to avoid ?is1 a v +5i\s arrangem5t is made to keep ! cog:eel m\nt$ on ! w9d+ %aft go+ dur+ ! w9d+-up process4 ,?is is call$ a ma9ta9+ spr+4 ,! arrangem5t %[n 9 ,fig4 #ec w expla9 x4 ,illu/ration3 ,,fig4 #ec4 ,! cog:eel a & ! rat*et :eel are bo? m\nt$ loosely on ! arbor c>ry+ ! drum4 a is l9k$ to b by a spr+ c4 ,! rat*et :eel b is engag$ by a pall fix$ to "s conv5i5t place on ! body ( ! clock frame4 ,:5 ! weight pulls on ! drum ! pull is communicat$ to ! rat*et :eel b1 & ?is acts on ! spr+ c & pulls x out a little4 ,z soon z ! spr+ c is pull$ out z f> z its ela/icity p]mits1 a pull is communicat$ to ! cog:eel a1 & ! clock is driv5 r\nd4 ,:5 ! clock is w\nd ! pressure ( ! weight is remov$1 & !re=e ! rat*et :eel e no long] presses on ! pall1 & ?us no pressure is communicat$ to ! rat*et :eel b1 or ?r\gh x to ! clock4 ,b "h ! spr+ c comes into play4 ,= s9ce ! rat*et :eel b is held fa/ by ! pall d1 ! spr+ c pulls at ! :eel a1 & ?us = a m9ute or s w cont9ue to drive ! clock4 ,?is driv+ =ce1 x is true1 is less ?an t caus$ by ! weight1 b x is j en\gh to keep ! p5dulum go+ = a %ort "t1 s t ! go+ ( ! clock is n int]f]$ )4 ,if ! read] c get possession ( a clock1 pref]ably "o t does n /rike1 &1 ) ! aid ( a small pair ( p9c]s & "o or two screwdriv]s1 w take x to pieces & put x toge!r aga91 ! me*anism above describ$ w soon become famili> to him4 ,n e clock is provid$ ) ma9ta9+ spr+ & ov]w9d+ prev5t]4 ,! cause ( /oppage ( a clock g5]ally is dirt4 ,:]e possible1 clocks %\ld always be put "u glass cases4 8,gr&fa!r0 clocks w g mu* bett] if br[n pap] cov]s are fitt$ ov] ! works "u ! cases4 ,9 ?is way a quantity ( du/ may be avoid$4 ,to get a good oil is v important4 ,x w be notic$ t pivot-holes 9 clocks are usually provid$ ) little cup-l depressions4 ,?is is to aid 9 keep+ 9 ! oil4 ,! be/ clock oil is t :i* does n easily solidify or evaporate4 ,ord9>y ma*9e oil1 su* z us$ = sew+ ma*9es1 is good z a lubricant1 b rapidly evaporates4 ,olive oil corrodes ! brass4 ,x is be/ to procure a little clock oil1 or else ! oil us$ = gun locks1 sold by ! gunsmi?s4 ,! holes %\ld be clean$ out ) ! end ( a wood5 lucif] mat*1 cut to a tap]+ po9t4 ,! pivots %\ld be well rubb$ ) a rag dipp$ 9 spirits ( w9e4 ,if ! pivots are worn !y %\ld be repoli%$ 9 ! la!4 ,if ! cogs ( ! :eels are worn1 !re is no rem$y b to get new ones4 ,old clocks sometimes want a little addition to ! driv+ weight to make !m g4 ,! weight necess>y to drive ! clock dep5ds on its goodness ( con/ruction1 & on ! weight ( ! p5dulum4 ,if ! clock is driv5 = eight days ) a cord ( n9e feet 9 l5g? ) a d\ble fall1 !n dur+ ea* beat ( ! p5dulum t weight w desc5d by an am\nt #i_/7b #bd #fj #fj #h7 feet or #a_/abhjj? in*4 ,:5ce1 if ! clock weight is #aj lbs41 ! impulse receiv$ by ! clock at ea* beat is equival5t to a weight ( #aj lbs4 fall+ ?r\gh #a_/abhjj? ( an in*1 or to ! fall ( six gra9s ?r\gh an in*4 ,! p[] ?us exp5d$ goes 9 friction ( ! :eels & h&s1 & 9 ma9ta9+ ! p5dulum 9 spite ( ! friction ( ! air4 ,! "w !re=e t is put into ! clock by ! op]ation ( w9d+ is gradually exp5d$ dur+ ! week 9 movem5t aga9/ friction4 ,! "w is inde/ructible4 ,! friction ( ! p>ts ( ! clock develops heat1 :i* is dissipat$ ov] ! room & gradually absorb$ 9 nature4 ,b ?is heat is only ano!r =m ( "w4 ,am\nts ( "w are e/imat$ 9 pressures act+ ?r\gh di/ances4 ,?us1 if ,i draw up a weight ( #a lb4 aga9/ ! accel]ative =ce ( gravity ?r\gh a di/ance ( "o foot1 ,i am said to d a foot-p\nd ( "w4 ,"o p\nd ( coal consum$ 9 a p]fect eng9e w\ld d eight millions foot-p\nds ( "w4 ,h5ce1 if ! en]gy 9 a p\nd ( coal c\ld be utiliz$1 x w\ld keep ab\t #ajj1jjj gr&fa!r's clocks go+ = a week4 ,z x is consum$ 9 an ord9>y /eam eng9e x w d ab\t half a million foot-p\nds ( "w4 ,"o p\nd ( bread conta9s ab\t ?ree million foot-p\nds ( en]gy4 ,a man c eat ab\t ?ree p\nds ( bread 9 a day1 &1 z he is a v good eng9e1 he c turn ?is into ab\t ?ree-qu>t]s ( a million foot-p\nds ( "w4 ,! re/ ( ! "w conta9$ 9 ! bread goes (f 9 ! =m ( heat4 ,illu/ration3 ,,fig4 #ed4 ,z has be5 previ\sly said1 ! p[] ( ! action ( gravity 9 draw+ back a p5dulum t has be5 pu%$ aside f its position ( re/ becomes less 9 proportion z ! p5dulum is long]1 & h5ce z ! p5dulum is long] ! "t ( vibrations increases4 ,9 ! app5dix to ?is *apt] a %ort pro( w be giv5 %[+ t ! l5g? ( a p5dulum v>ies z ! squ>e ( ! "t ( its vibration4 ,a p5dulum :i* is #ciad in*es 9 l5g? vibrates at ,london once 9 ea* second4 ,( c\rse at o!r p>ts ( ! e>?1 :]e ! =ce ( gravity is slightly diff]5t1 ! "t ( vibration w be diff]5t1 b1 s9ce ! e>? is ne>ly a globe 9 %ape1 ! =ce ( gravity at diff]5t p>ts ( x does n v>y mu*1 & !re=e ! "t ( vibration ( ! same p5dulum 9 diff]5t p>ts ( ! e>? does n v>y v mu*4 ,! l5g? ( a p5dulum is measur$ f its po9t ( susp5sion d[n to a po9t 9 ! bob or weight4 ,at fir/ sight "o w\ld be incl9$ to ?9k t ! c5tre ( gravity ( ! p5dulum w\ld be ! po9t to :i* y mu/ measure 9 ord] to get its l5g?4 ,s t if ,b 7 a circul> bob1 & ! rod ( ! p5dulum 7 v light1 ! di/ance ,a ,b to ! c5tre ( ! bob w\ld be ! l5g? ( ! p5dulum4 ,b if we 7 to fly to ?is conclusion1 we %\ld be mak+ ! same error t ,galileo made :5 he all[$ a ball to roll d[n an incl9$ plane4 ,he =got t ! motion 0 n a simple "o ( a body d[n a plane1 b 0 also a roll+ motion4 ,! p5dulum does n vibrate s z always to keep ! bob immovable ) ! top side ,c always upp]mo/4 ,on ! contr>y1 at ea* beat ! bob rotates on its c5tre & makes1 z x 71 "s sw+s ( its own4 ,!re=e 9 ! total motions ( ! p5dulum ?is rotation ( ! bob has to be tak5 into acc\nt4 ,( c\rse1 if ! p5dulum 7 s arrang$ t ! bob did n rotate1 & ! po9t ,c 7 always upp]mo/1 z1 = in/ance1 if ! p5dulum consi/$ ( two p>allel rods1 ,a ,b & ,c ,d1 susp5d$ f ,a & ,c1 !n we might consid] ! bob z t ( a p5dulum susp5d$ f ,e1 & ! p5dulum w\ld sw+ once 9 a second if ,a ,b ,c ,d ,e ,f 7 equal to #ciad in*es1 = by ?is arrangem5t !re w\ld be no rotation ( ! bob4 ,b z p5dulums are g5]ally made ) ! bob rigidly fix$ to ! rod ,e ,f1 ! rotation mu/ be tak5 into acc\nt4 ,illu/ration3 ,,fig4 #ee4 ,x wants "s r advanc$ ma!matical k to d ?is4 ,b 9 practice clockmak]s take no acc\nt ( x4 ,! correction is n a l>ge "o1 s !y make ! rod z ne>ly true z !y c1 arrange a screw on ! bob to all[ ( adju/m5t1 & !n screw ! bob up & d[n until 9 practice ! "t ( oscillation is f\nd to be correct4 ,illu/ration3 ,,fig4 #ef4 ,! mode ( susp5sion ( a p5dulum ( ! be/ class is t %[n 9 ,fig4 #ef1 :i* all[s ! p5dulum to fall into its true position )\t /ra94 ,a is a temp]$ /eel spr+1 :i* b5ds to & fro at ea* oscillation4 ,x is wond]ful h[ long ^! spr+s c be b5t to & fro )\t break+4 ,inasmu* z l5g!n+ ! p5dulum increases ! "t1 s t ! "t ( vibration t v>ies z ! squ>e ( ! l5g? ( ! p5dulum1 a v small l5g!n+ ( ! p5dulum causes a diff]5ce 9 ! "t4 ,9 practice1 = ea* ?\s&? ( an in* t we l5g!n ! p5dulum we make a diff]5ce ( ab\t "o second a day 9 ! go+ ( ! clock4 ,if we cut a screw ) eighte5 ?reads to ! in* on ! bottom ( ! p5dulum rod1 & put a circul> nut on x1 ) ! rim divid$ into sixty p>ts1 !n ea* turn ?r\gh "o division w raise or l[] ! bob by #a_/ajhj? ( an in*1 & ?is fir/ causes an alt]ation ( "t ( ! clock by "o second 9 ! day4 ,?is is a conv5i5t arrangem5t 9 practice1 = x af=ds an easy means ( adju/+ ! p5dulum4 ,we ne$ only obs]ve h[ _m seconds ! clock loses or ga9s 9 ! day1 & !n turn ! nut ?r\gh a correspond+ numb] ( divisions 9 ord] to rectify ! p5dulum4 ,illu/ration3 ,,fig4 #eg4 ,ano!r ne$ful correction ( ! p5dulum is t due to *anges 9 temp]ature4 ,if ! rod ( ! p5dulum be made ( ?or\ghly dri$ mahogany1 soak$ 9 a weak solution ( %ellac 9 spirits ( w9e1 & !n dri$1 !re w n be mu* v>iation ei!r f heat or moi/ure4 ,b = clocks requir$ to h great precision ! p5dulum rod is usually made ( metal4 ,a rod ( iron exp&s ab\t #a_/afjjjj? ( its l5g? = ea* degree ,fahr5heit2 & !re=e = ea* degree ,fahr5heit a p5dulum rod ( #ciad in*es w exp& ab\t #a_/djjj ?\s&?s ( an in*1 & ?us make a diff]5ce 9 ! go+ ( ! clock ( ab\t "o-f\r? ( a second p] day4 ,! expansion w1 ( c\rse1 make ! clock g sl[]4 ,x w\ld be possible to correct ?is expansion if "s arrangem5t c\ld be made1 :5ev] x occurr$1 to lift up ! bob ( ! p5dulum by an am\nt correspond+ to x1 z1 = in/ance1 to make ! bob ( "s mat]ial :i* exp&$ v mu* m by heat ?an ! mat]ial ( :i* ! p5dulum rod 0 made4 ,illu/ration3 ,,fig4 #eh4 ,?us if we hang on to ! end ( a p5dulum ( iron a bottle ( iron ab\t sev5 in*es long1 & almo/ fill x ) m]cury1 !n1 z soon z ! heat increases1 ! iron ( ! rod & ( ! bottle exp&s1 & ! c5tre ( oscillation ( ! p5dulum is l[]$4 ,b z ! l9e> expansion ( m]cury conta9$ 9 a bottle is ab\t five times t ( iron1 ! m]cury rises 9 ! bottle1 & ?us ! expansion d[nw>ds ( ! p5dulum rod is comp5sat$ by ! expansion upw>ds ( ! m]cury 9 ! bottle4 ,! rod may be fa/5$ to ! m\? ( ! bottle by a screw1 s t z ! bottle is turn$ r\nd x may be rais$ or l[]$ on ! rod1 & ?us ! l5g? ( ! p5dulum may be adju/$4 ,! bottle is made ( /eel tube1 screw$ into a ?9 turn$ iron top & bottom4 ,( c\rse no sold] mu/ be us$ to unite ! iron1 = m]cury dissolves sold]4 ,a little oil & :ite-lead w make ! screw$ jo9ts tight4 ,?is is an excell5t =m ( p5dulum4 ,ano!r plan is to use z9c z ! metal :i* is to c\nt]act ! expansion ( ! iron4 ,! expansion ( z9c is ab\t ?ree times t ( iron4 ,illu/ration3 ,,fig4 #ei4 ,h5ce a z9c tube1 ab\t tw5ty in*es long 7%[n %ad$ 9 ,fig4 #ei71 is made to re/ ^u a disc fa/5$ to ! l[] "p ( ! iron p5dulum rod4 ,on ! top ( ! z9c re/s a flat r+ ,a1 f :i* is susp5d$ an iron tube ,a1 :i* c>ries ! bob ,b4 ,! expansion ( ! z9c tube is l>ge en\gh to comp5sate ! expansion bo? ( ! rod & ! tube1 & ! bob consequ5tly rema9s at ! same dep? bel[ ! po9t ( susp5sion1 :atev] be ! temp]ature4 ,!re is1 h[ev]1 a new me?od :i* is f> sup]ior to all ^!1 & ?is is due to ! discov]y by ,m4 ,guilliaume1 ( ,p>is1 ( a comp\nd ( nickel & /eel :i* exp&s s little t x c be comp5sat$ by a bob ( lead in/ead ( by a bob ( m]cury4 ,?is mat]ial is sold 9 ,engl& "u ! "n ( 8inv>40 ,an inv> rod ) a prop]ly proportion$ lead bob makes an almo/ p]fect p5dulum1 ! expansion ( ! inv> & ! lead go+ on toge!r4 ,! exact expansion ( ! inv> is giv5 by ! mak]s1 :o also supply in=mation z to ! size & susp5sion ( ! bob prop] to use ) x4 ,x has be5 already %[n t ! uni=mity ( "t ( sw+ ( a p5dulum is only true :5 ! arc ?r\gh :i* x sw+s is v small4 ,if ! total sw+ f "o side to ano!r is n m ?an ab\t two in*es v little diff]5ce 9 "t-keep+ is made by putt+ a little m driv+ weight on ! clock1 & ?us increas+ its arc ( sw+2 b :5 ! arc ( sw+ becomes say ?ree in*es1 or "o & a half in*es on ea* side ( ! p5dulum1 !n ! "t ( vibration is affect$4 ,at ?is di/ance ea* t5? ( an in* increase ( sw+ makes ! p5dulum g sl[] by ab\t a second a day4 ,! resi/ance ( ! air1 ( c\rse1 has a great influ5ce on a p5dulum1 & is "o ( ! *ief causes t br+ x ultimately to re/4 ,ev5 ! v>iations ( pressure ( ! atmosph]e :i* ! b>omet] %[s z ! wea!r v>ies h an effect on ! go+ ( a clock4 ,attempts h be5 made by fix+ b>omet]s on to p5dulums ) an +5i\s sy/em ( c\nt] balanc+ to c\nt]act ?is1 b ^! ref9em5ts are n 9 common use1 & are too complicat$ to be susceptible ( effective regulation4 ,,app5dix ,,to ,,*apt] ,,iv4 ,x may be useful to give a simple =m ( pro( ( ! law :i* gov]ns ! "t ( oscillation ( a p5dulum ^: l5g? is giv54 ,un=tunately1 x is impossible to give "o s simple z to be compreh5d$ by ^? :o "k no?+ :atev] ( ma!matics4 ,x is1 h[ev]1 possible to give a pro( t requires v little ma!matical k4 ,we "k t :5 a mass ( matt] is :irl$ r\nd at ! end ( a /r+ x t5ds to fly outw>ds & puts a /ra9 on ! /r+4 ,! fa/] ! spe$ at :i* ! mass is :irl$1 ! /rong] w be ! /ra9 on ! /r+4 ,suppose t ! l5g? ( ! /r+ equals ,r1 ! velocity ( ! mass z x flies r\nd equals ,v4 ,let a be ! body :irl$ r\nd by a /r+ o a f a c5tre at ,o4 ,! body always1 ( c\rse1 t5ds to fly on 9 a /raight l9e f ! po9t at :i* x is at any in/ant4 ,b t t5d5cy is fru/rat$ by ! pull ( ! /r+ :i* con/ra9s x to take a circul> pa?4 ,x is1 ( c\rse1 all "o :e!r ! =ce t t5ds to pull ! body inw>ds t[>ds ,o is a /r+ or an attractive =ce ( any k9d act+ ?r\gh a di/ance )\t any /r+ at all4 ,evid5tly if ! body keeps its place 9 ! circle x mu/ be because ! c5trifugal =ce t5d+ to :irl x out is equal to ! c5tripetal or attractive =ce t5d+ to pull x 94 ,illu/ration3 ,,fig4 #fj4 ,! /ra9 on ! body1 due to ! =ce t5d+ to pull x inw>ds1 we %all designate by ,f1 mean+ by ,f ! numb] ( feet ( velocity t w\ld 9 "o second be imp>t$ to ! body by ! attractive =ce4 ,suppose t at "s giv5 in/ant ( "t ! body is at a po9t a4 ,at t in/ant its direction w be along a b1 tang5tial to ! circle at a1 & t is ! pa? x w\ld take if ! c5tripetal or attractive =ce ceas$ to act j z ! body got to a4 ,9 t case ! body w\ld be :irl$ (f l a /one f a sl+ along ! l9e a b1 & w\ld at ! end ( a giv5 "t1 let u suppose a second1 arrive at b4 ,b x is n s :irl$ (f2 x is attract$ t[>ds ,o & pull$ inw>ds1 & comes to c4 ,h5ce1 !n1 ! attractive =ce act+ dur+ "o second mu/ h be5 suffici5t to pull ! mass 9 f b to c4 ,b we "k t if an accel]at+ =ce 7,f7 acts on a body = a second x produces a f9al velocity equal to ,f at ! end ( ! second1 & an av]age velocity half ,f dur+ ! second4 ,h5ce1 !n1 ! space b c1 by :i* ! body has be5 pull$ 91 is repres5t$ by half ,f1 b a b1 ! space :i* ! body w\ld h travell$ =w>ds1 w be repres5t$ by ,v1 ! velocity ( ! body 9 a second2 b if ! motion be su* t ! di/ance b c travell$ 9 a second is v small1 !n ! triangles a b d & a b c are approximately simil>1 & ! small] a b is ! m ne>ly simil> !y are4 ,:5ce !n 7a b7_/7b c7 7a d7_/7a b71 t is to say 7a b7 a d b c4 ,b a b repres5ts ! space :i* w\ld h be5 trav]s$ by ! body 9 "o second at ! rate x 0 go+1 & h5ce is equal to ,v2 a d is ! diamet] ( ! circle1 & h5ce equals #b ,r2 b c is ! space ?r\gh :i* ! body has be5 drawn 9 ! second by ! attractive =ce ,f1 & !re=e equals half ,f4 ,:5ce !n ,v #b ,r half ,f ,r ,f4 ,we took a second z ! limit ( "t dur+ :i* ! motion 0 to be consid]$4 ,( c\rse any o!r "t c\ld h be5 tak54 ,n[ :at is true ( ! motion ( a body dur+ a v %ort "t is also true ( ! body dur+ ! :ole ( its pa?1 assum+ t ! pa? is a circle1 & t ,f rema9s con/ant1 z x obvi\sly w if ! pa? is a circle1 & ! velocity is uni=m4 ,:5ce !n we may g5]ally say t if a body is be+ :irl$ r\nd at ! end ( a /r+ ! /ra9 ,f on ! /r+ is directly proportional to ! squ>e ( ! velocity1 & is inv]sely proportional to ! l5g? ( ! /r+4 ,! "t ( rotation1 is ( c\rse l5g? ( ! pa? velocity 7#b,r7_/,v 7#b,r7_/7,r ,f7 #b7,r_/,f74 ,:5ce !n we see t = motion 9 a circle ( a mass "u ! attraction ( a c5tripetal =ce1 or pull ( a /r+1 ! "t ( rotation w be uni=m1 provid$ t ! c5tripetal =ce always v>ies z ! radius ( ! pa?4 ,f ?is x is evid5t t a body fix$ on to an ela/ic ?read :]e ! pull v>ies z ! ext5sion w\ld make its rotations always 9 equal times4 ,if y\r sl+ consi/s ( ela/ic1 :irl z y w1 y c only :irl ! body r\nd s _m times 9 a second1 & no m4 ,any increase 9 y\r ef=ts only makes ! /r+ /ret*1 & ! circle get bigg]4 ,! velocity ( ! body 9 its pa? ( c\rse increases1 b ! "t x takes to g once r\nd is inv>iable4 ,x also foll[s t if a body hung by a /r+ ( l5g? l1 "u ! action ( gravity1 be travell+ 9 a circle r\nd & r\nd1 !n1 if ! circle is a small "o comp>$ ) ! l5g? ( ! /r+1 ! inw>d accel]ation f t[>ds ! c5tre w be approximately proportional to ! radius r ( ! circle1 & ! "t ( rotation w be t #b7r_/f74 ,b 9 ?is case f1 ! inw>d accel]ation1 is to g ! accel]ation d[nw>ds ( gravity z ,a ,b3,a ,p or f_/g 7,a ,b7_/7,a ,p7 7,a ,p7_/7,o ,p7 r_/l4 ,illu/ration3 ,,fig4 #fa4 ,illu/ration3 ,,fig4 #fb4 ,:5ce !n ! "t ( rotation ( ?is body w\ld be if ! circle ( rotation 0 small #b7l_/g74 ,& if y try y w f9d t ?is is s4 ,= in/ance1 take a ?read #ci-a_/g in*es long1 t is #cbe feet4 ,hang any?+ heavy f "o end ( x1 & cause x to sw+ r\nd & r\nd 9 a small circle4 ,n[ g ! accel]ation ( gravity #cbb feet p] second4 ! ratio ( ! circumf]5ce ( a circle to its diamet] #cad4 ,f :i* x foll[s t ! "t ( rotation #b #cad7cbe_/cbb7 seconds #b seconds4 ,b if we look at ! rotat+ body sideways1 x appe>s to act z a p5dulum2 x matt]s no?+ :e!r we sw+ x r\nd & r\nd or to & fro4 ,= 9 any case ! accel]ative =ce t5d+ to br+ x back to a position ( re/ is always proportional to ! di/ance ( displacem5t1 &1 !re=e1 its "t ( motion mu/ always be #b7l_/g7 & its motion h>monic4 ,! l5g? ( a seconds p5dulum1 t is a p5dulum t makes its d\ble sw+ 9 two seconds1 w !re=e be l #d_/77b77 g feet 7g #ab7_/ in*es #ciad in*es4 ,,*apt] ,v4 ,i h ?us describ$ ! pr9cipal features ( ord9>y clocks4 ,= ! details _m treatises mu/ be /udi$1 & k acquir$ :i* is n 9 any books at all4 ,i n[1 h[ev]1 pass to wat*es4 ,x w be rememb]$ t a v]ge escapem5t consi/s ( a cr[n :eel ) tee?1 engag+ two pallets fix$ ^u a v]ge1 furni%$ ) balls at its extremities4 ,z ! cr[n :eel 0 urg$ =w>ds ea* pallet 9 succession 0 pu%$ till x slipp$ ov] ! too? :i* 0 engag+ x4 ,!n a too? on ! o!r side came into %>p collision ) ! o!r pallet1 & drove ! v]ge ! o!r way1 & s on4 ,n[ "h we h a driv+ =ce1 & a sort ( p5dulum4 ,b h[ did ! v]ge act z a p5dulum to measure "t8 ,x is n a body rock+ "u ! action ( gravity1 nor "u ! accel]ation ( a spr+4 ,h[ !n c x act z a regulator ( "t1 & :at is ! p]iod ( its sw+8 ,! answ] to ?is is1 t x is "u ! accel]ation ( gravity1 b t gravity does n act freely on ! bobs or weights1 b only ?r\gh ! driv+ weight & tee?4 ,! impulse t drives ! v]ge is really also ! accel]at+ =ce ^u x1 & ! only accel]at+ =ce ^u x4 ,& ! wor/ feature ab\t ! movem5t is1 t z ! tee? & pallets move1 ! lev]age ( ! tee? on ! pallets alt]s1 & ?us ! bobs on ! v]ge are "u ! influ5ce n ( a uni=m or duly regulat$ =ce1 b ( a con/antly v>y+ "o1 & "o t v>ies 9 a v complicat$ & erratic way4 ,x w\ld be hopeless to expect mu* "t-keep+ f su* a contrivance4 ,! mo/ t c\ld be expect$ w\ld be by putt+ on a v big weight to r$uce to comp>ative insignificance ! friction1 & !n hope t ! sw+s w\ld be uni=m1 s t :atev] w5t on 9 "o sw+ w\ld g on 9 ! next1 & ?us ! "t-keep+ be regul>4 ,b any c\rse t5d+ to dim9i% ! driv+ =ce1 su* z ! ?ick5+ ( ! oil1 w\ld greatly affect ! go+4 ,x 0 = ?is reason t ,huyg5s turn$ ! v]ge into a p5dulum by remov+ "o ( ! bobs1 & lett+ gravity ?us act on ! o!r4 ,= wat*es1 h[ev]1 a diff]5t plan 0 contriv$4 ,"o end ( a sl5d] spiral spr+ 0 affix$ to ! v]ge4 ,! o!r end ( ! spr+ 0 made fa/ to ! clock frame4 ,! v]ge 0 n[1 !re=e1 *iefly "u ! action ( ! accel]ation ( ! spr+4 ,to make ! accel]ation ( ! tee? ( ! 'scape :eel less emb>rass+1 ! tee? 7 s %ap$ z only to give a %ort pu% at /at$ int]vals1 & n int]f]e ) ! free sw+ ( ! v]ge "u ! alt]nate to-&-fro accel]ations & ret>dations ( ! spr+4 ,by ?is means ! v]ge became 9 e way an excell5t p5dulum1 n dep5d5t on gravity1 & p]mitt+ ! wat* to be held 9 any position4 ,! v]ge ?us fitt$ 0 turn$ into a :eel1 & became a 8balance :eel40 ,x 0 comp5sat$ = heat expansion by a cunn+ use ( ! unequal expansion ( brass & /eel1 9 a mann] analog\s to ! way ?is unequal expansion ( metals _h be5 employ$ to comp5sate ! p5dulum1 & became ! beautiful & accurate "t-measur] t we see to-day1 ) its pivots m\nt$ 9 jewels to dim9i% friction1 & ) screws r\nd ! rims ( ! balance :eel to enable ! c5tre ( gravity to be exactly adju/$ to its c5tre ( rotation1 & ) a delicate hair-spr+ ( temp]$ /eel t is a m>vel ( microscopic "w4 ,b ! escapem5t ( ! e>ly wat*es left mu* to be desir$4 ,9 ord] to make x cle> h[ imp]fect t e>ly escapem5t 01 we h to turn back & rememb] :at has be5 said ab\t ! dead beat escapem5t4 ,x w !n be rememb]$ t x 0 %[n t = small arcs ! p5dulum w\ld keep good "t provid$ y let x h z mu* sw+ z x want$ to use up ! =ce :i* ! escapem5t _h appli$ to x1 b n o!rwise1 s ! p5dulums only act$ really well :5 ! impulse 0 giv5 ab\t ! middle ( ! sw+1 & !y 7 free to g on & /op :5 !y pleas$1 & turn back at ! end ( x4 ,?is ess5tial condition 0 fairly approximat$ to 9 ! dead beat escapem5t ( clocks :i* left !m at ! end ( _! sw+ ) only a v slight friction to imp$e _! free motion4 ,b :5 y come to deal ) a wat* ! case is q diff]5t4 ,"h ! escapem5t is ( a great size comp>$ ) ! balance :eel1 & ! friction ev5 ( ! mo/ dead beat wat* escapem5t t c\ld be contriv$ 0 s big comp>$ ) ! =ces act+ on ! balance :eel z s]i\sly to d]ange its motion1 & r5d] x f> f a p]fect "t-keep]4 ,n[ ab\t ?is "t--,i am speak+ ( ! e>ly "p ( ! eighte5? c5tury--a dem& ( a v exceptional "* arose = a really p]fect wat*4 ,! dem& did n arise f g5tlem5 :o want$ to keep appo9tm5ts to play at ombre at _! clubs1 or ev5 f m]*ants to "t _! c\nt+ h\se h\rs4 ,= ^! ! old-fa%ion$ wat* did v well4 ,! dem& came f m>9]s4 ,b ! seam5 did n want to "k ! "t m]ely to arrange ! h\rs = meals on ! %ip or to det]m9e :5 ! wat* 0 to be reliev$1 b = a f> m important purpose1 namely1 to f9d out by obs]vation ( ! heav5s _! place ^u ! ocean :5 f> out ( sight ( ! l&4 ,x w be v int]e/+ to see h[ ?is problem arose1 & h[ ! pati5t indu/ry & +5uity ( man has solv$ x4 ,! anci5t navigators nev] w5t v f> f ! %ore1 =1 once out ( sight ( l&1 a %ip 0 out ( all means ( kn[+ :]e %e 04 ,on cle> days & nights ! compass1 & ! sun & />s w\ld tell ! m>9] ! direction he 0 sail+ 91 b x 0 q a problem to det]m9e :]e he 0 on ! surface ( ! e>?4 ,illu/ration3 ,,fig4 #fc4 ,let u consid] ! problem4 ,suppose = conv5i5ce t ! e>? is divid$ up into 8squ>es10 z ne>ly1 at lea/1 z y c consid] a globe to be s m>k$ out4 ,let u suppose t x has be5 agre$ to draw on x f pole to pole #cfj l9es ( longitude1 comm5c+ ) "o ?r\gh say ,gre5wi* ,obs]vatory z a />t+-po9t1 & go+ "r r\nd ! e>? till y come back to ,gre5wi* aga94 ,also suppose t !re h be5 drawn a s]ies ( circles p>allel to ! equator1 b go+ up at equal di/ances ap>t t[>ds ! poles4 ,let u h #agi ( ^! circles1 s z to leave #ahj spaces1 a to b1 b to c1 etc41 f pole to pole4 ,?is w divide ! e>? up l a bird-cage into squ>es1 z if we _h rob$ x 9 a well-fitt+ ,scot* plaid4 ,! l5g? measur$ along ! equator ( ! side p q ( ea* squ>e at ! equator is tak5 z exactly sixty nautical miles 7ap>t f a small error ( measurem5t1 :i* makes x 9 actual practice #eiif74 ,?is is equal to sixty-n9e & a qu>t] ,engli% /atute miles4 ,! side ( ! squ>e lead+ t[>ds ! poles q s w\ld also be sixty nautical miles 7 x n t ! e>? is n truly sph]ical1 :i* introduces a slight error4 ,we may1 h[ev]1 r\ghly say t at ! equator ea* squ>e measures sixty nautical miles ea* way4 ,illu/ration3 ,,fig4 #fd4 ,z we get t[>ds ! poles ! squ>es become rectangul> figures1 ) ! heights ( latitude /ill sixty nautical miles1 b ! wid?s becom+ small]4 ,?us 9 ,engl& our squ>es measure p q #cg nautical miles & q s #fj nautical miles4 ,n[ ( c\rse we c see at once t x is easy at any place on ! e>?'s surface to f9d y\r latitude by a simple obs]vation ( ! sun at noon1 if y "k ! day ( ! ye>1 & h got a nautical almanac4 ,= by an in/rum5t call$ a sextant y c measure ! angle he appe>s to be above ! horizon1 & !n1 z y "k f a nautical almanac ! angle he is above ! equator1 y c soon det]m9e y\r place ,a on ! globe4 ,or at night1 if y measure ! angul> di/ance t ! pol> /> ,p is f ! z5i?1 or po9t exactly ov] y\r head--t is1 ! angle ,p ,o ,z--y c subtract x f a "r angle & get y\r latitude1 ,a ,o ,e1 at once4 ,illu/ration3 ,,fig4 #fe4 ,b h[ are y to det]m9e y\r longitude8 ,! pole-/>1 or sun1 or any o!r /> won't help y1 = z ! e>? is mov+ !y keep %ift+1 & at "o "t or ano!r appe> exactly 9 ! same position to ev]yone on ! same p>allel ( latitude1 z x is easy to see4 ,! fact is t y are on a ball turn+ r\nd4 ,y "k easily :at latitude y are on1 b y _c tell y\r longitude unless y c tell h[ _m h\rs & m9utes y get to a position be=e ,gre5wi* gets to ! same position4 ,if :5 a p>ticul> /> got to ,gre5wi* a gong 7 s\nd$ :i* c\ld be he>d all ov] ! e>?1 !n ( c\rse1 by see+ :at />s 7 ov]head1 ev]yone w\ld "k _! longitude at once4 ,p]haps by means ( ! new electric waves ?is w be=e long be done1 & ! ,gre5wi* h\rs w be s\nd$ all ov] ! _w = ! use ( m>9]s4 ,b till ?is is accompli%$ all t c be done is to keep an accurate clock on bo>d1 s z always to give y ,gre5wi* "t4 ,e>ly attempts 7 made to take a p5dulum clock to sea1 susp5d+ x s z to avoid di/urbance to its motion by ! rock+ ( ! %ip4 ,^! prov$ va94 ,x !re=e became desirable t a wat* ) a balance :eel %\ld be contriv$ to g ) a degree ( accuracy 9 "s respects comp>able ) ! accuracy ( a p5dulum clock4 ,to enc\rage inv5tors an ,act ( ,p>liam5t 0 pass$ 9 ! ?irte5? ye> ( ,que5 ,anne's reign 7*apt] xv47 7#agac7 promis+ a rew>d ( #bj1jjj to anyone :o w\ld inv5t a me?od ( f9d+ ! longitude at sea true to half a degree--t is1 true to ?irty geographical miles4 ,if ! f9d+ ( ! longitude 7 to be accompli%$ by ! inv5tion ( an accurate wat*1 !n ?is involv$ ! use ( a wat* t %\ld n1 9 sev]al mon?s' go+1 h an error ( m ?an two m9utes1 :i* is ! "t :i* ! e>? takes to turn ?r\gh half a degree ( longitude4 ,?is 0 ! problem :i* ,john ,h>rison1 a c>p5t]1 ( ,york%ire1 made x 8 life bus9ess to solve4 ,8 ef=ts la/$ ov] =ty ye>s1 b at ! end he succe$$ 9 w9n+ ! prize4 ,^! in/rum5ts h be5 mu* improv$ by subsequ5t inv5tors1 & h result$ 9 ! con/ruction ( ! mod]n %ip's *ronomet]1 a l>ge wat* ab\t six in*es 9 diamet]1 m\nt$ on axles1 9 a mahogany box4 ,sev]al ( ^! are tak5 to sea by e %ip4 ,! peculi>ity ( ! *ronomet] is its escapem5t4 ,let ,a ,b be ! scape :eel1 & ,c ,d a small lev] atta*$ to ,c1 ! pivot on :i* ! balance :eel & spr+ is fa/5$4 ,let ,e ,g be a lev]1 ) a too? ,f :i* engages ! tee? ( ! scape :eel & prev5ts x mov+ r\nd4 ,let ,h be a spr+ hold+ ! lev] ,e ,g up to its "w4 ,illu/ration3 ,,fig4 #ff4 ,! lev] has a spr+ ,k ,e fa/5$ to x at ! po9t ,k4 ,?is spr+ is v delicate4 ,if ! lev] ,c ,d is turn$ s t ! little projection ,m on x /rikes ! spr+ ,e f left to "r1 !n1 z ! spr+ re/s on ! lev]1 ! :ole lev] is pu%$ ov]1 & ! tee? ( ! scape :eel set free4 ,at t in/ant1 h[ev]1 ! escapem5t is s arrang$ t ! arm ,c ,d is j opposite ! too? ,d ( ! scape :eel1 s t ! scape :eel1 in/ead ( runn+ away1 leaps ) its too? ,d on to ! lev] ,c ,d & sw+s ! balance :eel r\nd4 ,! balance :eel is free to twi/ z mu* z x pleases1 b ! mom5t x has twi/$ s mu* t ! projection ,m passes ! spr+ ,e1 !n ! lev] ,g ,e flies back to its place1 & ! scape :eel is aga9 *eck$4 ,mean:ile ! balance :eel flies r\nd till at la/ x is br\ght to re/ by ! balance spr+4 ,x !n recoils & sets out on its return pa?4 ,?is "t1 h[ev]1 ! projection ,m m]ely flips aside ! spr+ ,e & ! balance :eel goes back1 till aga9 x is br\ght to re/ & returns4 ,z soon z ! lev] comes opposite ,d ! projection ,m !n aga9 hits ! spr+ ,e1 & releases ! cat* at ,f1 & ano!r too? ( ! scape :eel goes by4 ,!re !n y h a completely free escapem5t1 & consequ5tly an accurate "o4 ,_m wat*es are made ) ^! escapem5ts1 b !y are m exp5sive ?an ^? 9 common use4 ,!re is b little rema9+ 9 a wat* t is n 9 a clock1 = ! :eel-tra9s & g5]al arrangem5ts are v simil>4 ,x is possible to apply ! *ronomet]'s deta*$ escapem5t to a clock4 ,?is 0 done by sev]al clock-mak]s 9 ! eighte5? & e>ly "p ( ! n9ete5? c5tury4 ,"o me?od ( do+ x is z foll[s3 ,a is a block ( metal fitt$ to ! bottom ( ! p5dulum1 ,b a light lev] pivot$ on x4 ,c is ! scape :eel1 ) f\r tee?2 ,d a too? ( ! scape :eel1 :i* hops on to ! projection ( ! p5dulum ! mom5t t ! impact ( ! po9t ,e ( ! lev] ,b ,e has pu%$ aside ! lev] ,g ,f1 & ?us releas$ ! scape :eel4 ,! advantage is t x is a v easy escapem5t to make4 ,b x is 9 reality a deta*$ 7t is to say1 a completely free7 *ronomet] escapem5t1 z c easily be se54 ,illu/ration3 ,,fig4 #fg4 ,turret-clocks are op5 to consid]able disadvantages1 = ! w9d bl[+ on ! h&s gives rise to consid]able pressure1 s t ! clocks are sometimes urg+ ! h&s aga9/ ! w9d1 sometimes are be+ help$ by ! w9d4 ,& ?is inequality ( driv+ =ce makes ! p5dulum at "s times make a bigg] arc ( sw+ ?an at o!rs4 ,b we saw above t ?\gh diff]5ce ( arc ( sw+ ought to make no diff]5ce 9 ! "t ( sw+ ( ! p5dulum1 yet ?is 0 only /rictly true if ! arc ( sw+ 7 a cycloid4 ,b z = practical conv5i5ce we are oblig$ to make x a circle1 x foll[s1 z we saw1 t = e t5? ( an in* ( increase ( sw+ ( an ord9>y seconds p5dulum ab\t a second a day ( error is introduc$4 ,to remove ?is difficulty a gravity escapem5t 0 inv5t$ by ,mudge 9 ! eighte5? c5tury1 improv$ by ,bloxam1 a b>ri/]1 & p]fect$ by ! late ,"l ,grim?orpe4 ,! idea 0 to make ! scape :eel1 in/ead ( directly driv+ ! p5dulum1 lift a weight1 :i*1 be+ subsequ5tly releas$1 drove ! p5dulum4 ,! consequ5ce 01 t inequalities 9 w9d pressure1 :i* affect$ ! driv+ =ce ( ! scape :eel1 w\ld n act on ! p5dulum1 :i* w\ld be always driv5 by ! uni=m fall ( a fix$ & def9ite weight4 ,a movem5t ( ?is k9d has be5 fix$ 9 ! great clock at ,we/m9/]1 & has gone admirably4 ,a description ( its details w be f\nd 9 ! ,encyclopdia ,britannica1 writt5 by ,"l ,grim?orpe himself4 ,all sorts ( ecc5tric clocks & wat*es h be5 propos$4 ,= in/ance1 x seems wond]ful to see a pair ( h&s fitt$ to ! c5tre ( a transp>5t %eet ( glass g r\nd & keep "t ) app>5tly no?+ to drive !m4 ,b ! my/]y is simple4 ,! seem+ %eet ( glass is n "o %eet1 b f\r4 ,! two c5tre %eets move r\nd invisibly1 c>ry+ ! h\r h& & m9ute h& ) !m1 be+ urg$ by little roll]s bel[ on :i* !y re/4 ,:5 y t\* ! glass ! outside %eets appe> at re/1 & y d n suspect t x is o!r ?an a s+le %eet4 ,b bew>e ( du/1 = if du/ gets on ! inn] plate y detect ! trick4 ,9 ?is way a me*anical h& 0 made t wrote d[n answ]s to que/ions4 ,?is plan c be appli$ to all sorts ( tricks4 ,sir ,william ,congreve1 an +5i\s inv5tor1 propos$ to make a clock t measur$ "t by lett+ a ball roll d[n an incl9e4 ,:5 x got to ! bottom x hit a lev]1 :i* releas$ a spr+ & tipp$ ! plane up aga91 s t ! ball n[ ran d[n ! o!r way4 ,x is a poor "t-keep]1 & ! idea 0 n orig9al1 = a ball _h be5 previ\sly design$ = ! same purpose4 ,sometimes clocks are con/ruct$ by atta*+ p5dulums to bronze figures1 :i* h s small a movem5t t ! eye is unable to detect x4 ,! figure appe>s to be at re/1 b is 9 reality sl[ly rock+ to & fro4 ,x is necess>y to make ! movem5t z small z ab\t "o f\r hundr$? ( an in* 9 half a second1 if ! movem5t is to escape human obs]vation4 ,= a movem5t ( "o two hundr$? ( an in* p] second is ab\t ! l>ge/ t w c]ta9ly rema9 unp]ceiv$4 ,9 m$ival times clocks 7 con/ruct$ ) all sorts ( que] devices4 ,! p ( ! upp] t[n at ,basle hav+ qu>rell$ ) ^? ( ! l[] t[n1 f\ght & beat !m4 ,to commemorate ?is victory !y put on ! old bridge at ! upp] t[n a clock provid$ ) an iron head1 t sl[ly put out & drew 9 a long tongue ( d]ision4 ,?is clock may /ill be se5 9 ! museum4 ,x is z ?\gh ! c\ncil ( ! city ( ,london put a clock ( d]ision at ,temple ,b> to put out its tongue at ! ,c\nty ,c\ncil4 ,i d n propose "h to describe ! /rik+ me*anism ( clocks4 ,!re are sev]al diff]5t ways ( arrang+ x4 ,!y are r complicat$ to foll[ out1 b !y all resolve !mselves into a few simple pr9ciples4 ,z ! h\r h& revolves x c>ries a cam s arrang$ z to be deep] cut away = ! twelf? h\r1 less = ! elev5?1 & s on4 ,:5 ! m9ute h& comes to ! h\r x releases ! /rik+ me*anism1 :i*1 urg$ by a weight1 beg9s to revolve1 &1 driv+ an arm c>ry+ a p91 raises a hamm]1 :i* goes on /rik+ away z ! arm revolves4 ,?is w\ld cont9ue = ev] if x 7 n t at ! same mom5t an arm is lib]at$ :i* falls aga9/ ! cam4 ,at ea* /roke ! arm is 7by ! /rik+ app>atus7 rais$ a bit back into position4 ,:5 x comes back into position x /ops ! /rik+4 ,x ?us acts z a c\nt]1 or reckon] ( ! bl[s giv51 /opp+ ! movem5t :5 ! clock has /ruck suffici5tly4 ,if ! c\nt+ me*anism fails to act1 we h ! ph5om5on :i* occasionally occurs ( a 8,gr&fa!r0 clock /rik+ ! :ole ( ! h\rs = ! week )\t /opp+4 ,a *im+ clock is simpl] /ill4 ,= "h we h a b>rel cov]$ ) p9s1 l ! b>rel 9 a musical box4 ,z ! p9s g r\nd !y raise hamm]s :i* fall aga9/ bells4 ,! b>rel is w\nd up & driv5 by a spr+ or weight4 ,:5 ! clock comes to ! h\r1 ! b>rel is releas$1 & rotat+1 plays ! tune4 ,if y want to make a clock wake y up 9 ! morn+ x c be done by mak+ ! /rik+ arrangem5t hamm] away ) no c\nt+ me*anism to /op x until ! weight has run d[n4 ,if1 n cont5t ) t1 y want ! %eets pull$ (f ! b$ or ! b$ tilt$ up1 or a c ( wat] empti$ ov] ! p]son :o w n rise1 a me*anical device kn[n z a relay mu/ be us$4 ,x is v simple4 ,:at is want$ is t1 aft] ! lapse ( a "t :i* a clock mu/ measure1 a consid]able =ce mu/ be ex]t$ to pull (f ! b$clo!s4 ,x w\ld be absurd to make ! clock ex]cise ?is pull4 ,x is obvi\sly bett] to atta* ! clo!s by a hook to a rope :i* passes ov] a pulley1 & f :i* hangs a weight4 ,a p9 secures ! weight f fall+1 ! p9 be+ )drawn by ! clock4 ,! "w is ?us done by ! weight :5 releas$ by ! clock4 ,9 l mann]1 if y h a telegraph design$ to pr9t messages at a di/ance1 y d n s5d along ! wires ! :ole =ce necess>y = do+ ! pr9t+4 ,y only s5d impulses1 :i*1 l trigg]s1 release ! =ces by :i* ! lett]s are to be /amp$4 ,electric clocks ( _m k9ds h be5 inv5t$4 ,! pr9ciple ( an electric escapem5t is simil> to t ( an ord9>y escapem5t4 ,illu/ration3 ,,fig4 #fh4 ,! read] no d\bt kn[s t1 :5 a circuit ( wire is jo9$ or complet$ lead+ to a s\rce ( electricity1 electricity fl[s ?r\gh ! wire4 ,if ! wire is w\nd r\nd a piece ( iron1 !n1 :5ev] ! circuit is jo9$1 a curr5t is set 9 motion1 & ! iron becomes an electro-magnet4 ,:5 ! circuit is sev]$ ! iron ceases to be a magnet4 ,if put at a prop] position x w\ld at ea* "t an iron p5dulum approa*$ give x a small impulse provid$ t at t in/ant ! curr5t is turn$ on4 ,?is c easily be made to be done by ! p5dulum itself4 ,= j z ! p5dulum is com+ back to ! c5tral position a flipp] ,p atta*$ to ! rod c be caus$ to make contact ) a piece ( metal fix$ on its pa?4 ,!n ! electro-magnet1 becom+ magnetis$1 ex]ts a pull on ! iron p5dulum4 ,on ! return beat ( ! p5dulum ! o!r side ( ! flipp] ,r /rikes ! ob/ruction4 ,b if t side ,r is cov]$ ) ebonite or "s non-conduct+ mat]ial no curr5t w be set 9 motion1 & ! electro-magnet w n 7z x w\ld o!rwise d7 ret>d ! p5dulum4 ,su* a p5dulum has !re=e an impulse giv5 to x e second beat4 ,su* p5dulums d n act v well1 because x is difficult to keep metallic surfaces l ,q clean1 & !re=e misses (t5 occur4 ,besides1 ! /r5g? ( ! curr5t v>ies ) ! goodness ( ! contact & ) o!r ?+s4 ,:at is n[ pref]r$ is to make an arrangem5t by :i* an electric curr5t w9ds ! clock up e m9ute or s4 ,by ?is means ! impulse :i* drives ! clock is n a v>y+ electric "o1 b is a /eady weight4 ,! mo/ successful clocks h be5 made on ^! pr9ciples4 ,! advantage ( electricity is1 t by means ( ! curr5t t actuates ! clock1 or w9ds x up1 y c at regul> int]vals set ! h&s 9 motion ( a great numb] ( clocks4 ,s t only "o go+ clock ) a p5dulum is ne$$4 ,! o!r clocks di/ribut$ ov] ! build+ h only faces & h&s1 & a v few simple :eels1 to :i* a slight pu% is giv5 by an electro-magnet1 say1 e m9ute or s4 ,! sy/em is !re=e well adapt$ = (fices & hotels4 ,9 ,am]ica1 by means ( electric contacts1 clocks h be5 arrang$ to put gramophones into action4 ,y w rememb] t x 0 po9t$ out t if a wire 7 dragg$ ov] a file a s\nd w\ld be produc$ due to ! little taps made z ! wire click$ aga9/ ! r\gh cuts on ! file1 & t ! tone ( ! note dep5d$ on ! f95ess ( ! cuts1 & h5ce ! rapidity ( ! little taps4 ,y c imag9e t1 if ! r\ghnesses 7 prop]ly arrang$1 we might get ! tones to v>y1 & ?us imitate spee*4 ,?is is ! pr9ciple ( ! gramophone4 ,! r\ghnesses are produc$ by a tool1 :i*1 vibrat+ "u ! influ5ce ( human spee*1 makes small cuts 9 a s(t mat]ial4 ,?is is h>d5$1 & !n1 :5 ano!r wire is dragg$ ov] ! cuts1 ! voice is reproduc$4 ,9 ?is way clocks are made to speak & tell ! *ildr5 :5 d9n] is ready & :5 to g to b$4 ,on ?is simple plan1 too1 dolls c be made to speak4 ,! mod]n me?ods ( clock & wat*-mak+ are v diff]5t f ^? 9 use 9 old5 days4 ,9 =m] times ! pivots 7 turn$ up by h& on small la!s1 & ev5 ! tee? ( ! :eels 7 fil$ out4 ,ea* hole 9 ! clock or wat* frame 0 drill$ out sep>ately1 & ea* :eel sep>ately fitt$ 91 s t ! wat* 0 gradually built up z "o w\ld build a h\se4 ,ea* :eel1 ( c\rse1 only fitt$ its own wat*1 & ! p>ts ( wat*es 7 n int]*angeable4 ,?is has n[ all be5 alt]$4 ,by means ( elaborate ma*9]y ! :ole ( ! "w ( cutt+ out e :eel & ! mak+ ( e s+le "p is done by tools mov$ indep5d5tly ( ! w ( ! workman1 ^: only duty is to sit /ill & see ! ?+s made4 ,he is1 z x 71 ! slave ( ! ma*9e1 wat*+ x & answ]+ to its calls4 ,or %all we r say t he is ! ma*9e's employ] & ma/]8 ,he has "h a s]vant :o nev] tires nor ev] disobeys him4 ,all ! ma*9e requires is t its cutt+ edges %\ld be exactly true & %>p & microscopically p]fect2 !n x w cut away & make :eel aft] :eel4 ,x oils itself4 ,x only wants ! man to act z sup]9t5d5t1 & /op x if any cutt+ edge gets unduly worn4 ,= ?is purpose he measures ! "w x is do+ f "t to "t ) a microscope to see t x is good & true & exact4 ,:5 all ! p>ts h ?us be5 made y h p]haps a hundr$ boxes1 ea* ) a ?\s& wat* p>ts 9 x1 ea* "p exactly l its fell[s4 ,y take "o :eel or bit f ea* box indiscrim9ately1 & y !n h ! mat]ials = a wat*1 screws1 fitt+s1 p9s1 & all4 ,all y h n[ got to d is simply to screw !m all toge!r1 l putt+ toge!r a puzzle4 ,ev]y?+ fits2 !re is no snipp+ or fil+4 ,9 su* a wat* if a bit gets brok5 y simply s5d = ano!r bit ( ! same k9d & fit x into its place4 ,motor c>s1 bicycles1 & _m o!r ma*9es are1 or ought to be1 made 9 ?is mann]1 s t if a driv] at ,york breaks a "p ( ! c> he simply s5ds to ,london = ano!r4 ,x comes & fits into its place at once4 ,b = ?is sort ( plan y mu/ d "w true to mu* less ?an a ?\s&? ( an in*1 &1 ( c\rse1 no "o mu/ want to indulge 8 individual fancy z to ! %ape or appe>ance ( ! wat*4 ,! :ole advantage consi/s 9 dead uni=mity4 ,b ! *eapness is surpris+4 ,y c h a bett] wat* n[ = #cjs4 ?an c\ld h be5 got = #cj tw5ty ye>s ago4 ,arti/ic p are 9 ! habit ( condemn+ ?is uni=mity z ?\gh x 7 in>ti/ic & degrad+4 ,9 tru?1 x is n degrad+ to get a ma*9e to d :at y want at ! exp5se ( z little lab\r z possible4 ,y pay #cjs4 = ! wat*1 b y h #bh #ajs4 left to sp5d on pictures4 ,only "o ought n to confuse indu/ry ) art4 ,wat*es made 9 ?is way h no pret5ce to be arti/ic products4 ,!y are simply useful4 ,to rule !m all ov] ) ma*9e l9es or to put hide\s ma*9e ornam5t on !m is purely & simply base & degrad+4 ,let y\r ornam5t be h& "w1 y\r utility ma*9e "w4 ,?us !n ,i h endeav\r$ to give a v brief sket* ( ! modes ( measur+ "t1 & incid5tally to introduce my read]s to ^? laws ( motion :i* are ! f\ndation ( s l>ge a "p ( mod]n sci5ce4 ,x only rema9s t ,i %\ld %ortly describe mod]n app>atus by means ( :i* x is possible to measure ) accuracy p]iods ( "t s %ort z to appe> impossible4 ,b :5 y see h[ x is done ! me?od seems easy en\gh4 ,x is /ill by means ( a p5dulum1 only a p5dulum beat+ "t n once1 b hundr$s & ev5 ?\s&s ( times 9 a second4 ,& su* p5dulums1 in/ead ( be+ difficult to make1 are rem>kably simple1 & pres5t no difficulty :atev]4 ,= we h only to use ! tun+ =k :i* has be5 previ\sly describ$4 ,! tun+ =k consi/s ( a piece ( /eel b5t into a ,u %ape4 ,! arms are set vibrat+ s z alt]nately to approa* & rec$e f "o ano!r4 ,! reason :y !re are two arms is t1 if !y come toge!r & rec$e1 !y balance1 & h5ce ! in/rum5t z a :ole does n %ake on its base4 ,?is balance ( mov+ p>ts ( a rapidly mov+ ma*9e is v important4 ,"s motor c>s are arrang$ s t ! eng9es are 8balanc$10 & ! mov+ p>ts come 9 & out simultane\sly1 leav+ ! c5tre ( gravity un*ang$ :atev] be ! position ( ! motion4 ,?is makes ! vibration ( ! c> v small4 ,! tun+ =k is !re=e balanc$4 ,be+ ela/ic1 x obeys ,hook's law1 8,z ! =ce1 s ! deflection40 ,& !re=e1 z we h se51 ! vibrations ( ! =k are iso*ron\s4 ,a =k ) arms ab\t six or sev5 in*es long w make ab\t fifty or sixty vibrations 9 a second4 ,h[ are we to record ^? vibrations1 & h[ keep ! tun+ =k vibrat+8 ,illu/ration3 ,,fig4 #fi4 ,a tra9 ( :eels is almo/ an impossibility1 n p]haps s impossible z might be suppos$1 b /ill v difficult4 ,s a diff]5t me?od is adopt$4 ,a little wire projects f "o tun+ =k arm4 ,a piece ( glaz$ pap] is g5tly smok$ by means ( a wax tap]1 & is /ret*$ r\nd a well-made brass drum4 ,! tun+ =k is !n put s t ! little wire j t\*es ! pap]4 ,! tun+ =k is !n made to vibrate by a bl[1 & :ile x is vibrat+ ! drum is revolv$4 ,?us a wavy l9e is =m$ on ! drum by ! wire on ! tun+ =k4 ,if ! tun+ =k made fifty complete vibrations to & fro 9 a second !re w\ld be "o hundr$ su* ind5tations1 fifty to ! "r & fifty to ! left1 & by ^! ! "t c be measur$ z y w\ld measure a l5g? ^u a rule4 ,illu/ration3 ,,fig4 #gj4 ,if an arm a b be fitt$ to move sideways :5 a little /r+ c d is pull$1 & be also provid$ ) a small wire1 s z to t\* ! drum1 !n x also w trace a /raight l9e on ! drum z ! wire lightly scrat*es away ! ?9 coat+ ( smoke4 ,n[1 if x is sudd5ly j]k$ & flips back1 !n a little ind5tation w be made 9 ! l9e1 & if :5 we are to measure a rapid lapse ( "t a j]k is giv5 at ! beg9n+1 & ano!r j]k at ! end ( x1 we %\ld get a diagram l t 9 ! adjo9+ figure1 :]e a is ! trace ( ! tun+ =k1 b t ( ! indicat+ arm4 ,! "t :i* has elaps$ betwe5 ! j]k :i* produc$ ! ind5tation c & t :i* produc$ ! ind5tation d w be ab\t ?ree & ?ree-qu>t] d\ble ind5tations ( ! tun+ =k l9e1 ?us indicat+ ?ree & ?ree-qu>t] fiftie?s ( a second4 ,x is easy to see h[ delicate ?is means ( measurem5t c be made4 ,) small tun+ =ks we c easily measure times to a ?\s&? "p ( a second1 & mu* less if desir$4 ,! j]k may be giv5 by electricity if x is wi%$4 ,:5 ! curr5t is jo9$ a little electro-magnet pulls a bit ( iron & gives a pull to ! /r+4 ,s extremely rapid is ! flight ( electricity t no appreciable "t is lo/ 9 its transit ?r\gh ! wires1 s t ! impulse may be giv5 f a di/ance4 ,?us we may arrange t :5 a cannon ball leaves a gun an electric impulse %all be giv54 ,:5 x rea*es & hits a t>get ano!r electric impulse is giv54 ,^! make nicks 9 ! trac+ l9e on ! drum f :i* we c easily compute ! "t t has elaps$ betwe5 ! leav+ ( ! m\? ( ! gun & ! arrival ( ! %ot at its de/9ation4 ,illu/ration3 ,,fig4 #ga4 ,su* an app>atus is us$ 9 mod]n gunn]y exp]im5ts4 ,x is an elaborate "o1 b is bas$ on ! pr9ciple above describ$4 ,drums are sometimes driv5 by clockwork1 & tun+ =ks are also (t5 kept vibrat+ by electricity1 ?us con/itut+ v rapidly mov+ electric clocks4 ,! arrangem5t is simple4 ,an electro-magnet ,e is put 9 ! vic9ity ( ! arm ( ! tun+ =k4 ,a small piece ( wire f ! arm is 9 contact ) a piece ( metal ,q1 f :i* a wire runs to ! electro-magnet1 !nce to a batt]y1 & f ! batt]y to ! tun+ =k1 ?r\gh :i* ! curr5t runs to ! wire ,r4 ,:5 ! =k vibrates ! arm1 be+ b5t outw>ds1 makes ! wire ,r t\* ,q4 ,?is at once causes ! electro-magnet to give a small pull to ! /eel arm ( ! tun+ =k1 & ?us assi/s ! sw+ ( ! arm4 ,! :ole arrangem5t is exactly analog\s to an electric clock1 z may be se5 by comp>+ ,fig4 #ga ) ,fig4 #fh4 ,!re is ano!r me?od ( measur+ rapid int]vals ( "t :i* also m]its att5tion4 ,x is to let a body drop at ! comm5cem5t ( ! p]iod ( "t to be measur$1 & m>k h[ f> x falls 9 ! "t1 & !n f9d ! "t f ! equation giv5 previ\sly1 ,s #a_/b g t4 ,x is practically done by lett+ a piece ( smok$ glass fall & mak+ a small po9t] make two dots ^u x1 "o at ! beg9n+1 ano!r at ! end1 ( ! "t to be measur$4 ,an int]e/+ adaptation ( ?is me?od c s]ve z a basis ( a curi\s toy4 ,take a crossb[1 ) a bolt ) a spike on x2 fix x firmly 9 a vice s t ! b>rel po9ts at a spot a on a wood5 wall4 ,on ! spot a hang a c>dbo>d figure ( a cat on to a nail s contriv$ t :5 an electro-magnet acts ! nail is pull$ aside1 & ! cat drops4 ,?us let a be ! cat1 b ! loop by :i* x is hung ov] ! nail c1 t is fix$ to ano!r piece ( iron furni%$ ) a h+e at c1 s t :5 ! electric curr5t is turn$ on ! nail c is )drawn & ! cat drops4 ,c>ry ! wires f ! electro-magnet & batt]y to ! crossb[1 & s arrange !m t :5 ! bolt leaves ! muzzle "o is press$ aga9/ ! o!r1 & contact made4 ,n[ "h y h an app>atus su* t exactly z ! bolt leaves ! crossb[1 ! cat drops4 ,n[ :at w happ58 ,illu/ration3 ,,fig4 #gb4 ,:5 ! bolt leaves ! b[ x is subject to two motions1 "o a motion ( projection at a uni=m pace 9 ! direction ( b a f ! b[ to ! t>get4 ,b x is also subject to ano!r =ce1 namely t ( gravity1 :i* acts on x v]tically1 & deflects x 9 a v]tical direction exactly z mu* & z fa/ z a body w\ld d if dropp$ f re/ at ! same in/ant z ! bolt leaves ! b[4 ,b ! cat is su* a body4 ,h5ce1 !n1 s9ce by ! electric arrangem5t !y are bo? let g toge!r1 !y w bo? drop simultane\sly1 & ?us w always be on ! same level1 & :5 ! bolt rea*es ! wood5 wall & has fall5 v]tically f a to c1 ! cat w also h fall5 v]tically f a to c1 & ! bolt w p9 him to ! wall4 ,x does n matt] h[ f> y take ! b[ f ! wall1 nor h[ /rong ! b[ is1 nor h[ heavy ! bolt is1 nor h[ heavy ! cat is1 nor :e!r a b is horizontal or po9t+ upw>ds or d[nw>ds4 ,illu/ration3 ,,fig4 #gc4 ,9 e case1 if only ! b>rel is po9t$ directly at ! cat1 !n ! bolt & cat fall simultane\sly & at ! same rate1 & ! bolt w p9 ! cat to ! wall4 ,9 try+ ! exp]im5t ! bolt %\ld be pretty heavy1 say half a p\nd1 & h a good spike2 b if c>efully done ! exp]im5t w succe$ e "t4 ,x enables y also to measure ! spe$ ( flight ( ! bolt4 ,= if ! di/ance ( ! b[ f ! wall be ?irty feet1 & ! cat h fall5 ?ree feet :5 x is /ruck1 !n ! "t ( fall is ,t 77#b,s7_/g7 7#f_/;g7 #dc seconds4 ,b ! bolt 9 ?is "t w5t ?irty feet2 h5ce its velocity 0 ?irty feet 9 #dc seconds1 or sev5ty feet p] second4 ,( c\rse if y make ! bolt heavi] ! velocity ( projection w become sl[]1 ! "t long]1 & h5ce ! cat w fall fur!r be=e x is transfix$ by ! bolt4 ,my task is n[ at a close4 ,i h endeav\r$ n m]ely to give a description ( clocks & v>i\s app>atus = measur+ "t1 b to expla9 ! fundam5tal pr9ciples ( me*anics :i* lie at ! root ( ! subject4 ,may ,i end ) a ^w ( advice to p>5ts8 ,!re is a c]ta9 numb] ( boys1 b only a c]ta9 numb]1 :o h a real love = me*anical sci5ce4 ,su* boys %\ld be enc\rag$ 9 e way by ! possession ( tools & app>atus1 b 9 ! selection ( ?is app>atus ! foll[+ pr9ciples %\ld be borne 9 m9d3-- ,fir/1 t almo/ ev]y?+ a boy wants c be made ) wood1 & metal1 & wire1 & /r+1 if he has someone to give him a little in/ruction h[ to d x4 ,a b5t bit ( /eel jamm$ 9 a vice makes an excell5t tun+ =k4 ,second1 t he wants n toy tools1 b good tools4 ,if an exp]t wants a good tool1 h[ mu* m a beg9n]4 ,?ird1 t he ought to h a reasonably dry & com=table place to "w 91 & ! help & advice ( ! village c>p5t] or blacksmi?4 ,f\r?1 t he ought n to be all[$ to pott] ) 8 tools1 b to make some?+ really s5sible & useful1 & n beg9 a doz5 ?+s & f9i% none4 ,fif?1 t ! mak+ ( app>atus to %[ sci5tific facts is m useful ?an mak+ bootjacks = 8 fa!r or workboxes = 8 "m4 ,&1 la/ly1 t a little money sp5t 9 ?is way w keep _m a "y rascal f worry+ 8 si/]s & /on+ ! cat2 & :5 ! inevitable "t comes at :i* he mu/ face ! "y man's fir/ trial1 ,,! ,,exam9]1 he w (t5 ?ank 8 />s t he le>n$ 9 play ! fundam5tal =mula ,s #a_/b g t1 & t he kn[s ! nature ( 8h>monic motion10 ! two mo/ important pr9ciples 9 ! measurem5t ( "t4 ,,! ,,end4 ,,app5dix ,,on ,,! ,,%ape ,,( ,,! ,,tee? ,,( ,,:eels4 ,illu/ration3 ,,fig4 #gd4 ,! tee? ( :eels = wat*es & clocks ne$ p>ticul> c>e 9 %ap+1 & x may be ( int]e/ if ,i describe briefly ! pr9ciples ^u :i* ^! :eels are made4 ,:at is requir$ is t ! motion %all n be communicat$ by j]ks z ! tee? successively engage "o ano!r1 b t ! motion %all be p]fectly smoo?4 ,! problem !re=e becomes ?is3 ,h[ are we to arrange ! tee? ( ! :eels s t z "o ( !m turns & drives ! o!r r\nd ! lev]age or turn+ p[] ex]cis$ by ! driv+ :eel on ! driv5 :eel %all always be uni=m8 ,n[ if ! tee? 7 simple spikes "o c easily see t ?is w\ld n be ! case4 ,= in/ance1 z ! arm a c turn$ r\nd1 driv+ be=e x ! arm b d1 ! po9t c w\ld scrape along1 & ! lev]age betwe5 ! two tee? w\ld con/antly alt]4 ,evid5tly "s o!r con/ruction mu/ be adopt$4 ,be=e we c det]m9e :at x is to be1 we mu/ inquire :at ! lev]age w\ld be betwe5 two rods1 a c & d b1 m\nt$ on pivots at a & d4 ,! answ] to ?is "q is1 t :5 a lev] su* z a c presses ) its end aga9/ ano!r1 d b1 ! p[] is ex]cis$ 9 a direction c e at "r angles to d b4 ,h5ce ! lev]age betwe5 ! two arms is 9 ! ratio ( a e to d c4 ,! sy/em is j z if we _h a lev] a e unit$ to a lev] d c by a rigid rod e c at "r angles to bo? ( !m4 ,illu/ration3 ,,fig4 #ge4 ,:5ce !n ! ratio ( ! p[] is z a e is to d c4 ,illu/ration3 ,,fig4 #gf4 ,b s9ce ! triangles a e f1 d c f1 are simil>1 a e is to d c z a f to f d4 ,:5ce !n we get ?is g5]al proposition3 ,if "o body m\nt$ on an axis is press+ ^u ano!r body m\nt$ on an axis1 ! pressure ex]t$ betwe5 !m is always ex]cis$ 9 a direction1 %[n by ! dott$ l9e1 at "r angles to ! two surfaces 9 contact2 & ! ratio ( ! lev]age is f\nd by draw+ a l9e f "o axis to ! o!r1 s z to cut ! l9e ( direction ( pressure 9 f4 ,! lev]age ( "o on ! o!r is !n z a f to f d4 ,our problem has n[ become ! foll[+3 ,giv5 a rod b d1 suppose t x is press$ ^u by a curv$ surface m\nt$ on an axis at a4 ,!n ! direction ( ! pressure t ! curv$ surface 7call$ 9 eng9e]+ language a cam7 w ex]cise on ! rod b d is %[n by ! dott$ l9e2 & ! ratio ( ! driv+ p[] to ! driv5 p[] is z d f to a f4 ,n[ h[ c we %ape ! cam s t z x moves r\nd1 & diff]5t p>ts ( its surface come successively into contact ) b c1 ! ratio ( ! lev]age is always ! same2 t is to say1 ! ratio ( a f to f d %all always be con/ant2 t is to say1 ! l9e drawn ?r\gh ! po9t ( contact p]p5dicul> to ! curve at t po9t1 %all always pass ?r\gh ! po9t f8 ,illu/ration3 ,,fig4 #gg4 ,illu/ration3 ,,fig4 #gh4 ,evid5tly1 if ?is is to be s1 ! po9t d mu/ be on a semicircle1 ^: diamet] is f b1 = 9 t case ! angle f d b w always be a "r angle4 ,illu/ration3 ,,fig4 #gi4 ,! surface mu/ !n be s arrang$ t1 :atev] be ! position ( ! cam & ( ! rod b d1 ! po9t ( contact betwe5 !m mu/ always be on ! semicircle f c d2 t is to say1 z ! cam moves r\nd ! axis a its %ape mu/ be su* t a l9e drawn f f to ! po9t :]e x cuts ! circle f d b is always p]p5dicul> to ! curve4 ,n[ suppose t we move a circle ^: c5tre is at a1 & radius a f1 s z to roll ! circle f d b by simple surface friction r\nd its c5tre o1 !n any po9t d on x w\ld m>k out a curve on a piece ( pap] atta*$ to ! mov+ circle ^: c5tre is at a1 & ! direction ( motion ( ! curve w\ld always be su* t ! po9t d on x w\ld at any in/ant be describ+ a circle r\nd f1 & ! direction ( ! curve w\ld ?us at any po9t always be at "r angles to ! l9e d f = ! "t be+4 ,illu/ration3 ,,fig4 #hj4 ,?is curve1 caus$ by ! roll+ ( "o circle on ano!r1 is call$ an epicycloid4 ,h5ce1 !n1 = a clock1 if we make ! p9ion :eel ) /raight spokes & ! driv+ :eel ) its tee? cut 9 ! =m ( epicycloids1 caus$ by roll+ a circle ) a diamet] equal to ! radius ( ! p9ion ^u ! driv+ :eel1 we %all get a uni=m ratio ( lev]age "o ^u ! o!r4 ,! circles ) radii a f1 b f1 are call$ ! 8pit* circles10 & ^! radii are 9 ! ratio ( ! movem5t t is requir$ = ! :eels1 usually six to "o or eight to "o1 z ! case may be4 ,! sides ( ! tee? ( ! p9ion :eels are /raight l9es radiat+ f ! c5tre1 & r\nd$ (f at ! ends s z to avoid accid5tal jamb+4 ,! tee? ( ! cog:eel h epicycloidal sides4 ,! tips are cut (f s z to be out ( ! way1 & spaces are left betwe5 !m = ! wid? ( ! leaves ( ! p9ion :eel4 ,illu/ration3 ,,fig4 #ha4 ,bo? p9ion :eels & cog:eels are cut by cutt]s rotat+ at a high spe$1 ab\t #c1ejj times 9 a m9ute1 ! cutt]s be+ c>efully %ap$ = ! p9ion :eels ) /raight edges1 = ! cog:eels 9 epicycloids4 ,x is a pretty ?+ to see a :eel-cutt+ eng9e at "w1 ! cutt] fly+ r\nd ) a hum1 cutt+ ! rim ( a brass :eel into tee?1 ! brass com+ (f 9 flakes ?9n] ?an f9e hairs & fall+ 9 f9e du/4 ,:5 a too? is cut1 ! :eel is mov$ r\nd "o division ( an app>atus call$ a 8divid+ plate10 s z to pres5t a new "p ( ! :eel to ! cutt]4 ,( c\rse1 ! cutt] & :eels mu/ all be prop]ly proportion$4 ,cutt]s are sold 9 sets duly %ap$ = ! "w !y h to d4 ,:eel-cutt+ is a special bran* ( ! clockmak+ indu/ry4 ,! reason ! spe$ ( cutt+ is s high is because x is desir$ to take (f small portions ( metal at a "t1 & ?us n /ra9 ! :eel & ! cutt+ ma*9]y4 ,if bigg] cuts 7 made1 !n ! ma*9e w\ld h to g sl[]1 = x is a pr9ciple 9 ! con/ruction ( cutt+ ma*9]y t ! spe$ ( ! cut mu/ always be proportion$ to ! dep? ( x4 ,if y want to take deep cuts y mu/ move ! cutt+ edge sl[ly1 & vice v]s4 ,! mo/ mod]n me?od ( mak+ cog:eels ( brass1 & ! be/1 is to /amp !m out ( solid %eet metal at a s+le pun* ( a pun*+ ma*9e1 & *eap wat*es are always made 9 ?is way4 ,9 fact1 ! :ole me?od ( wat* & clock-mak+ is und]go+ a trans=mation4 ,be=e ! "t ( ! great eng9e]+ developm5t :i* took place t[>ds ! end ( ! eighte5? c5tury1 ! mak+ ( ma*9es 0 a sort ( f9e art4 ,cog:eels 7 cut by h&4 ,! circumf]5ce 0 m>k$ out by means ( compasses4 ,!n holes 7 drill$ r\nd ! rim1 & tee? cut out lead+ into !m1 & %ap$ by means ( special files con/ruct$ = ! purpose 7,fig4 #hb74 ,big ma*9]y 0 all %ap$ out at ! =ge & by ! file4 ,! eng9e]s compla9$ t y c\ld n get big "w made true ev5 to ! eigh? ( an in*4 ,b wat*es & clocks 7 beautifully made1 ?\gh only at ! co/ ( h\rs ( pati5t measur+ & fil+4 ,! ta/e = ornam5t /ill exi/$4 ,! :eels & backs ( wat*es 7 *as$ ov] ) ! mo/ beautiful patt]ns2 ! frames ( ! clocks 7 wr\ght into beautiful figures & =ms4 ,ev5 a/ronomical in/rum5ts 7 embelli%$4 ,illu/ration3 ,,fig4 #hb4 ,!n came ! era ( sev]e accuracy4 ,m5 ( sci5ce took ! gov]nm5t ( ma*9e-mak+ ^: feel+s 7 repugnant to art 9 any =m4 ,!y hat$ to see any ef=t exp5d$ 9 ornam5t4 ,) sev]ely utilit>ian aims1 !y bani%$ all appe>ance ( beauty f in/rum5ts & tools ( all sorts1 s t our mod]n ma*9es1 f a /eam eng9e d[n to a wat*1 are n[ models ( precise b p]fectly unornam5t$ workman%ip4 ,!y are ! fitt+ implem5ts ( a nation t we>s tr\s]s & tall hats4 ,"o has only to comp>e an old vessel ( w>1 ) its sculptur$ pr[ & /ream]s1 ) a mod]n ironclad to take note ( ! diff]5ce4 ,! art ( ornam5tation is n[ little m ?an a spasmodic imitation ( ! pa/1 ) a hi/orical int]e/ only4 ,z a liv+ entity x has almo/ ceas$ to exi/4 ,b 9 precision ( manufacture ! pres5t age is )\t a rival 9 ! hi/ory ( ! _w4 ,p believe no long] 9 ! old me?ods ( scrap+ & fil+1 & h&-"w directly ex]cis$ on metal is rapidly fall+ into desuetude4 ,x is possible1 ( c\rse1 ) a file & scrap] & days ( lab\r to get two flat surfaces ( metal s p]fect t :5 put toge!r "o w lift ! o!r l a suck] on a /one1 b x is wa/e lab\r4 ,a small ma*9e w d x z well 9 a few m9utes4 ,no long] is a wat* built up z "o w\ld build a h\se1 fitt+ "p to "p4 ,by exp5sive ma*9es ?\s&s ( wat* p>ts are /amp$ & cut out to patt]n1 & !n a wat* is made by tak+ "o ( ea* indiscrim9ately & j putt+ !m into _! places4 ,comp>atively unskill$ workm5 c d ?is4 ,:]e ! skill is want$ is to design & make ! ma*9]y & wat* ! cutt]s1 measur+ !m ) microscopic gauges f "t to "t1 & at once rem$y+ !m if an edge is f\nd to be a t5-?\s&? "p ( an in* out ( place4 ,s t ! lab\r ( man is becom+ m & m a lab\r ( design & ( sup]vision4 ,ma*9es are ! slaves t d ! "w1 = 9 a good ma*9e we h an eye & an arm t nev] tires1 & only ne$s to be kept 9 work+ ord]4 ,b ma*9es are n arti/ic1 & ?us art is lo/ :ile precision is ga9$4 ,at pres5t a desp]ate attempt is be+ made to supply by means ( ma*9]y ! crav+ ( ! human m9d = art4 ,b x is de/9$ to failure4 ,art ( ?is k9d is g5]ally produc$ by ! same bra9 t designs ma*9es1 & !re=e pres5ts an appe>ance ( rigid accuracy & uni=mity1 :i*1 :ile ess5tial to an eng9e1 is out ( place 9 an arti/ic product4 ,! great manufactur]s ( our ,midl&s d n seem to und]/& t !re is no object 9 mak+ a t[el-horse z geometrically accurate z a turn+ la!4 ,x w app>5tly be ye>s be=e !y le>n to put art & precision ea* 9 ! place :]e x is want$--precision 9 ! works ( ! wat*1 art 9 ! face & ! case ( x2 ma*9e "w 9 ! inside ( a wat*1 h& "w on ! outside4 ,:5 ! public ta/e is educat$ s z to see ! odi\s "* ( ! jumble ( ,go?ic1 ,egyptian1 & mean+less ornam5t on su* an article z ! case ( an ,am]ican organ1 "o /ep w h be5 made t[>ds ! revival ( arti/ic ta/e4 ,b to propose z a means ( reviv+ art t we %\ld discont9ue ! use ( ma*9]y or ab&on our mod]n cutt]s ( precision to g back to a hack-saw & file is ridicul\s1 & c\ld only be sugge/$ by m5 q de/itute ( sci5tific ideas4 ,art & precision ea* has its place3 !re is room = bo?2 let nei!r intrude on ! doma9 ( ! o!r4 ,,index4 ,accel]ation1 #gc1 #gg ,almage/1 #ec ,an*or escapem5t1 #abj ,anci5t sci5ce1 #ej ,ari/otle's ideas1 #bc1 #eb ,attwood's ma*9e1 #hc ,babylon1 temple (1 #bd ,balance :eel1 #aei ,c&les to measure "t1 #df ,*aldean day1 #ae ,*auc]1 #ef ,*ronographs1 #agi ,*ronomet]1 #afe ,*ronomet] escapem5t1 #aff ,clock movem5t1 #abc ,cop]nicus1 #ef ,crossb[ exp]im5t1 #ahc ,cr[n :eel1 #aae ,cycloid1 !1 #aji ,dante's ,inf]no1 #ed ,day1 l5g? (1 #bi ,dead beat escapem5t1 #ace ,d5sity1 #ab ,driv+ weight1 #abg1 #ada ,e>?1 a sph]e1 #ba ,e>?'s motion1 #eg1 #fi ,e>? n at re/1 #fg ,egg-boil]1 #dc ,electric clocks1 #agi ,epicycloidal :eels1 #aia ,escapem5ts1 an*or1 #abj cr[n1 #aae *ronomet]1 #aff dead beat1 #ace gravity1 #afi ,fall+ bodies1 laws (1 #fb ,=ce1 #gf ,=ces1 revolution (1 #hi ,fusee1 !1 #aag ,galileo's 8,dialogues10 #eh clock1 #aaa ,gr&fa!r's clock1 #aai ,gravity1 action (1 #ac1 #fe ,gravity escapem5t1 #afi ,greek day1 #af ,h>monic motion1 #ig ,hooke's law1 #ga ,iso*ronism ( spr+s1 #ic ,lamps to measure "t1 #df ,latitude & longitude1 #afa f9d+1 #afc ,mass1 nature (1 #aj ,m]cury clock1 #de ,mod]n me?ods1 #agg1 #aig ,mom5ts1 #aja ,moon's appe>ance1 #ag ,motion1 reliability (1 #eg ,musical notes1 #ie ,nor? pole1 days at1 #cc ,oscillations1 law (1 #aea ,p>abola1 !1 #hg ,p5dulum1 !1 #ajc1 #ade susp5sion1 #ade m]cury1 #adg gridiron1 #adi !ory (1 #aee free1 #acc ,pisa1 lean+ t[] (1 #fa ,planets1 names (1 #aa ,pulse measur]1 #ii ,rat*et :eels1 #abi ,roman clocks1 #dj ,s&-glasses1 #da ,space1 nature (1 #h ,spe$ ( fall+ bodies1 #gi ,spr+ balance1 #ajg ,/ev9us' !ory1 #ha ,/yle ( sun-dials1 #ce ,sun-dials1 #bg to make1 #dh ,syn*ron\s clocks1 #age ,"t1 #ac ,too!d :eels1 #abe1 #acg ,tun+ =k1 #id1 #aha ,velocities1 composition (1 #he ,wat] pressure1 #cg ,wat] clocks1 #ci ,wat*es1 #aef ,week days1 names (1 #bd ,:eels1 %ape ( tee?1 #aij ,:eel-cutt+ ma*9es1 #aic ,w9d+ drum1 #aca ,w9t] sun1 #ca ,zodiac1 #ah ,,bradbury1 ,,agnew1 ,,co4 ,,ld41 ,,pr9t]s1 ,,london ,,& ,,tonbridge4 99 99 99 99 99 99 ,transcrib]'s note3 ,punctuation1 hyph5ation1 & spell+ 7 made consi/5t :5 a pr$om9ant pref]5ce 0 f\nd 9 ?is book2 o!rwise !y 7 n *ang$4 ,simple typographical errors 7 correct$2 occasional unpair$ quotation m>ks 7 reta9$4 ,ambigu\s hyph5s at ! ends ( l9es 7 reta9$4 ,squ>e roots are repres5t$ z 7values74 ,index n *eck$ = prop] alphabetization or correct page ref]5ces4 ,page #af3 8six o'clock0 0 pr9t$ z 8six clock02 *ang$ "h4