,transcrib]'s ,notes3 ,und]scores 80 be=e & aft] a ^w or phrase indicate italics 9 ! orig9al text4 ,equal signs 80 be=e & aft] a ^w or phrase indicate bold 9 ! orig9al text4 ,small capitals h be5 conv]t$ to ,,solid capitals4 ,typographical & punctuation errors h be5 sil5tly correct$4 ,,e9/e9 ,,& ,,! ,,univ]se ,a ,popul> ,exposition ( ! ,fam\s ,!ory ,by ,,*>les ,,nordmann ,a/ronom] to ! ,p>is ,obs]vatory4 ,translat$ by ,,joseph ,mc,c,a,b,e ,) a ,preface by ! ,rt4 ,hon4 ,,! ,,visc\nt ,,haldane1 ,o4,m4 ,t4 ,,fi%] ,,unw9 ,,ltd4 ,,london3 ,,adelphi ,,t]race ,fir/ publi%$ 9 ,engli% ,april #aibb ,second ,impression ,june #aibb ,all rights res]v$ ,,preface ,a di/+ui%$ ,g]man au?ority on ma!matical physics1 writ+ rec5tly on ! !ory ( ,relativity1 decl>$ t if 8 publi%]s _h be5 will+ to all[ him suffici5t pap] & pr9t he c\ld h expla9$ :at he wi%$ to convey )\t us+ a s+le ma!matical =mula4 ,su* success is conceivable4 ,ma!matical me?ods pres5t1 h[ev]1 two advantages4 ,_! t]m9ology is precise & conc5trat$1 9 a fa%ion :i* ord9>y language _c af=d to adopt4 ,fur!r1 ! symbols :i* result f _! employm5t h implications :i*1 :5 br\ght to light1 yield new k4 ,?is is d$uctively rea*$1 b x is none ! less new k4 ,) great] precision ?an is usual1 ord9>y language may be made to d "s1 if n a great deal1 ( ?is "w = :i* ma!matical me?ods are alone q appropriate4 ,if ord9>y language c d "p ( x an advantage may be ga9$4 ,! difficulty t att5ds ma!matical symbolism is ! accompany+ t5d5cy to take ! symbol z exhau/ively descriptive ( reality4 ,n[ x is n s descriptive4 ,x always embodies an ab/raction4 ,x accord+ly leads to ! use ( metaphors :i* are inadequate & g5]ally untrue4 ,x is only qualification by descriptive language ( a wid] range t c keep ?is t5d5cy 9 *eck4 ,a new s*ool ( ma!matical physici/s1 /ill1 h[ev]1 small 9 numb]1 is beg9n+ to appreciate ?is4 ,b = ,engli% & ,g]man writ]s ! new task is v difficult4 ,nei!r ,anglo-,saxon nor ,saxon g5ius l5ds itself readily 9 ?is direction4 ,nor has ! task z yet be5 tak5 9 h& completely1 s f> z ,i am aw>e1 9 ,france4 ,/ill1 9 ,france !re is a _s & a gift ( expression :i* makes ! approa* to x easi] ?an ei!r = u or = ! ,g]mans4 ,lucidity 9 expression is an end[m5t :i* ! be/ ,fr5* writ]s possess 9 a high] degree ?an we d4 ,"s ( u h accord+ly await$ ) deep int]e/ ,fr5* r5d]+s ( ! difficult doctr9e ( ,e9/e94 ,m4 ,nordmann1 9 addition to be+ a highly qualifi$ a/ronom] & ma!matical-physici/1 possesses ! gift ( 8 race4 ,! ,lat9 capacity = elim9at+ ab/ractness f ! description ( facts is ev]y:]e app>5t 9 8 writ+4 ,individual facts take ! places ( g5]al conceptions1 ( ,begriffe4 ,! language is t ( ! ,vor/ellung1 9 a way t w\ld h>dly be practicable 9 ,g]man4 ,nor is our own language equal to t ( ,france 9 delicacy ( di/9ctive description4 ,?is book c\ld h>dly h be5 writt5 by an ,engli%man4 ,b ! difficulty 9 8 way w\ld h be5 "o z mu* ( _s z ( lett]4 ,x is ! lucidity ( ! ,fr5* au?or1 9 comb9ation ) 8 own gift ( expression1 t has made x possible = ! translator to succe$ s well 9 ov]com+ ! ob/acles to giv+ ! exposition 9 our own tongue ?is book conta9s4 ,! r5d]+ seems to me1 aft] read+ ! book bo? 9 ,fr5* & 9 ,engli%1 admirable4 ,m4 ,nordmann has pres5t$ ,e9/e9's pr9ciple 9 words :i* lift ! av]age read] ov] _m ( ! difficulties he mu/ enc\nt] 9 try+ to take x 94 ,rememb]+ ,goe!'s maxim t he :o w\ld accompli% any?+ mu/ limit himself1 he has n aim$ at cov]+ ! full field to :i* ,e9/e9's tea*+ is direct$4 ,b he succe$s 9 mak+ _m ab/ruse ?+s intelligible to ! layman4 ,p]haps ! mo/ brilliant ( 8 ef=ts 9 ?is direction are ,*apt]s ,v & ,,vi1 9 :i* he expla9s ) extraord9>y lucidity ! new !ory ( gravitation & ( its relation to in]tia4 ,i ?9k t ,m4 ,nordmann is p]haps less successful 9 ! c\rage\s attack he makes 9 8 ?ird *apt] on ! obscurity :i* att5ds ! notion ( ! 8,int]val40 ,b t is because ! f\r-dim5sional _w1 :i* is ! basis ( exp]i5ce ( space & "t = ,e9/e9 & ,m9k[ski1 is 9 itself an obscure conception4 ,ma!maticians talk ab\t x gaily & ?r[ its qualities into equations1 despite ! ess5tial exclusion f x ( ! measurem5t & %ape :i* actual exp]i5ce always 9 "s =m involves4 ,!y lapse on t acc\nt into unconsci\s metaphysics ( a dubi\s "*4 ,?is does n de/roy ! practical value ( _! equations1 b x does make !m v unreliable z guides to ! "* ( reality 9 ! mean+ :i* ! pla9 man atta*es to x4 ,"h1 accord+ly1 we f9d ! au?or ( ?is little treatise to be a good man /ruggl+ ) adv]sity4 ,if he c\ld make ! topic cle> he w\ld4 ,b !n no "o has made x cle> except+ z an ab/raction :i* works1 b :i*1 despite sugge/ions made to ! contr>y1 _c be clo!d = u 9 images4 ,?is1 h[ev]1 is ! fault1 n ( ,m4 ,nordmann himself1 b ( a phase ( ! subject4 ,) ! subject 9 its o!r aspects he deals ) ! incomp>able lucidity ( a ,fr5*man4 ,i "k no book bett] adapt$ ?an ! "o n[ translat$ to give ! av]age ,engli% read] "s und]/&+ ( a pr9ciple1 /ill 9 its infancy1 b de/9$1 z ,i believe1 to trans=m op9ion 9 m regions ( k ?an ^? m]ely ( ma!matical physics4 ,haldane ,,cont5ts ,,preface ,,by ,,! ,,rt4 ,,hon4 ,,visc\nt ,,haldane1 ,o4,m4 pp4 #e-h ,,introduction pp4 #ac-ae ,,*apt] ,i ,,! ,,metamorphoses ,,( ,,space ,,& ,,"t ,remov+ ! ma!matical difficulties--,! pill>s ( k--,absolute "t & space1 f ,ari/otle to ,newton--,relative "t & space1 f ,epicurus to ,po9c> & ,e9/e9--,classical ,relativity--,ant9omy ( /ell> ab]ration & ! ,mi*elson exp]im5t pp4 #ag-ca ,,*apt] ,,ii ,,sci5ce ,,9 ,a ,,no-,,?or\ghf>e ,sci5tific tru? & ma!matics--,! precise function ( ,e9/e9--,mi*elson's exp]im5t1 ! ,gordian knot ( sci5ce--,! hesitations ( ,po9c>--,! /range1 b necess>y1 ,fitzg]ald-,lor5tz hypo!sis--,! contraction ( mov+ bodies--,philosophical & physical difficulties pp4 #cb-eb ,,*apt] ,,iii ,,e9/e9',s ,,solution ,provisional rejection ( e!r--,relativi/ int]pretation ( ,mi*elson's exp]im5t--,new aspect ( ! spe$ ( light--,explanation ( ! contraction ( mov+ bodies--,"t & ! f\r dim5sions ( space--,e9/e9's 8,int]val0 ! only mat]ial reality pp4 #ec-gb ,,*apt] ,,iv ,,e9/e9',s ,,me*anics ,! me*anical f\ndation ( all ! sci5ces--,asc5d+ ! /ream ( "t--,! spe$ ( light an impassable limit--,! addition ( spe$s & ,fizeau's exp]im5t--,v>iability ( mass--,! balli/ics ( electrons--,gravitation & light z atomic microcosms--,matt] & en]gy--,! dea? ( ! sun pp4 #gc-ajj ,,*apt] ,v ,,g5]alis$ ,,relativity ,weight & in]tia--,ambiguity ( ! ,newtonian law--,equival5ce ( gravitation & accel]at$ movem5t--,jules ,v]ne's projectile & ! pr9ciple ( in]tia--,:y rays ( light are subject to gravitation--,h[ light f ! />s is weigh$--,an eclipse z a s\rce ( light pp4 #aja-abc ,,*apt] ,,vi ,,! ,,new ,,conception ,,( ,,gravitation ,geometry & reality--,euclid's geometry & o!rs--,cont+5cy ( ,po9c>'s crit]ion--,! real univ]se is n ,euclidean b ,riemannian--,! avat>s ( ! numb] --,! po9t ( view ( ! drunk5 man--,/raight & geodetic l9es--,! new law ( univ]sal attraction--,explanation ( ! anomaly ( ! planet ,m]cury--,e9/e9's !ory ( gravitation pp4 #abd-adg ,,*apt] ,,vii ,,is ,,! ,,univ]se ,,inf9ite8 ,kant & ! numb] ( ! />s--,ext9ct />s & d>k nebul--,ext5t & aspect ( ! a/ronomical univ]se--,diff]5t k9ds ( univ]ses--,po9c>'s calculation--,physical def9ition ( ! inf9ite--,! inf9ite & ! unlimit$--,/ability & curvature ( cosmic space-"t--,real & virtual />s--,diamet] ( ! ,e9/e9ian univ]se--,! hypo!sis ( globes ( e!r pp4 #adh-aei ,,*apt] ,,viii ,,sci5ce ,,& ,,reality ,! ,e9/e9ian absolute--,revelation by sci5ce--,discussion ( ! exp]im5tal bases ( ,relativity--,o!r possible explanations--,argum5ts 9 fav\r ( ,lor5tz's real contraction--,newtonian space may be di/9ct f absolute space--,! real is a privileg$ =m ( ! possible--,two attitudes 9 face ( ! unkn[n pp4 #afj-agb ,,*apt] ,,ix ,,e9/e9 ,,or ,,newton8 ,rec5t discussion ( ,relativism at ! ,academy ( ,sci5ces--,traces ( ! privileg$ space ( ,newton--,! pr9ciple ( causality1 ! basis ( sci5ce--,exam9ation ( ,m4 ,pa9lev's objections--,newtonian argum5ts & ,relativi/ replies--,m4 ,pa9lev's =mulas ( gravitation--,fecundity ( ,e9/e9's !ory--,two conceptions ( ! _w--,conclusion pp4 #agc-ahe ,,introduction ,?is book is n a romance4 ,nev]!less4444 ,if love is1 z ,plato says1 a so>+ t[>d ! inf9ite1 :]e %all we f9d m love ?an 9 ! impassion$ curiosity :i* impels u1 ) b[$ heads & beat+ he>ts1 aga9/ ! wall ( my/]y t environs our mat]ial _w8 ,beh9d t wall1 we feel1 !re is some?+ sublime4 ,:at is x8 ,sci5ce is ! outcome ( ! se>* = t my/]i\s some?+4 ,a giant bl[ has rec5tly be5 /ruck1 by a man ( consummate ability1 ,alb]t ,e9/e91 ^u ?is wall :i* conceals reality f u4 ,a little ( ! light f beyond n[ comes to u ?r\gh ! brea* he has made1 & our eyes are en*ant$1 almo/ dazzl$1 by ! rays4 ,i propose "h to give1 z simply & cle>ly z is possible1 "s fa9t reflex ( ! impression x has made ^u u4 ,e9/e9's !ories h br\ght ab\t a pr(\nd revolution 9 sci5ce4 ,9 _! light ! _w seems simpl]1 m co-ord9at$1 m 9 unison4 ,we %all h5ce=w>d realise bett] h[ gr&iose & coh]5t x is1 h[ x is rul$ by an inflexible h>mony4 ,a little ( ! ineffable w become cle>] to u4 ,m51 z !y pass ?r\gh ! univ]se1 are l ^? specks ( du/ :i* dance = a mom5t 9 ! gold5 rays ( ! sun1 !n s9k into ! d>kness4 ,is !re a f9] or nobl] way ( sp5d+ ?is life ?an to fill "o's eyes1 "o's m9d1 "o's he>t ) ! immortal1 yet s elusive1 rays8 ,:at high] pleasure c !re be ?an to contemplate1 to seek1 to und]/&1 ! magnific5t & a/\nd+ spectacle ( ! univ]se8 ,!re is 9 reality m ( ! m>vell\s & ! romantic ?an !re is 9 all our poor dreams4 ,9 ! ?ir/ = k1 9 ! my/ic impulse :i* urges u t[>d ! deep he>t ( ! ,unkn[n1 !re is m passion & m sweetness ?an 9 all ! trivialities :i* su/a9 s _m lit]atures4 ,i may be wrong1 aft] all1 9 say+ t ?is book is n a romance4 ,i w endeav\r 9 ^! pages to make ! read] und]/&1 accurately1 yet )\t ! aid ( ! esot]ic app>atus ( ! te*nical writ]1 ! revolution br\ght ab\t by ,e9/e94 ,i w try also to fix its limits2 to /ate precisely :at1 at ! mo/1 we c really "k to-day ab\t ! ext]nal _w :5 we reg>d x ?r\gh ! transluc5t scre5 ( sci5ce4 ,e revolution is foll[$ by a reaction1 9 virtue ( ! rhy?m :i* seems to be an inh]5t & et]nal law ( ! m9d ( man4 ,e9/e9 is at once ! ,sieys1 ! ,mirabeau1 & ! ,danton ( ! new revolution4 ,b ! revolution has already produc$ its fanatical ,m>ats1 :o w\ld say to sci5ce3 8,?us f> & no f>!r40 ,h5ce we f9d "s resi/ance to ! pret5sions ( ov]-zeal\s apo/les ( ! new sci5tific gospel4 ,9 ! ,academy ( ,sci5ces ,m4 ,paul ,pa9lev takes 8 place1 ) all ! /r5g? ( a vigor\s ma!matical g5ius1 betwe5 ,newton1 :o 0 suppos$ to be ov]?r[n1 & ,e9/e94 ,9 my f9al pages ,i w exam9e ! p5etrat+ criticisms ( ! great ,fr5* geometrician4 ,!y w help me to fix ! precise position1 9 ! evolution ( our ideas1 ( ,e9/e9's magnific5t syn!sis4 ,b ,i w\ld fir/ exp\nd ! syn!sis itself ) all ! affection :i* "o mu/ be/[ ^u ?+s t "o w\ld und]/&4 ,sci5ce has n complet$ its task ) ! "w ( ,e9/e94 ,!re rema9s _m a dep? t is = u unfa?omable1 wait+ = "s g5ius ( to-morr[ to ?r[ light into x4 ,x is ! v ess5ce ( ! augu/ & l(ty gr&eur ( sci5ce t x is p]petually advanc+4 ,x is l a tor* 9 ! sombre =e/ ( my/]y4 ,man enl>ges e day ! circle ( light :i* spreads r\nd him1 b at ! same "t1 & 9 virtue ( 8 v advance1 he f9ds himself confront+1 at an increas+ numb] ( po9ts1 ! d>kness ( ! ,unkn[n4 ,few m5 h borne ! %aft ( light s deeply into ! =e/ z has ,e9/e94 ,9 spite ( ! sordid c>es :i* h>ass u to-day1 amid s _m grave cont+5cies1 8 sy/em reveals to u an elem5t ( gr&eur4 ,our age is l ! noisy & unsub/antial fro? t cr[ns1 & hides = a mom5t1 ! gold ( "s g5]\s w9e4 ,:5 all ! transitory murmur t n[ fills our e>s is ov]1 ,e9/e9's !ory w rise be=e u z ! great ligh?\se on ! br9k ( ?is sad & petty tw5tie? c5tury ( ours4 ,,*>les ,,nordmann4 ,,e9/e9 ,,& ,,! ,,univ]se ,,*apt] ,i ,,! ,,metamorphoses ,,( ,,space ,,& ,,"t ,remov+ ! ma!matical difficulties--,! pill>s ( k--,absolute "t & space1 f ,ari/otle to ,newton--,relative "t & space1 f ,epicurus to ,po9c> & ,e9/e9--,classical ,relativity--,ant9omy ( /ell> ab]ration & ! ,mi*elson exp]im5t4 8,h y read ,b>u*80 ,la ,fonta9e us$ to cry1 en?usia/ically4 ,to-day he w\ld h tr\bl$ 8 fri5ds ) ! "q 8,h y read ,e9/e980 ,b1 :]eas "o ne$s only a little ,lat9 to ga9 access to ,sp9oza1 frightful mon/]s keep gu>d be=e ,e9/e91 & _! horrible grimaces seem to =bid u to approa* him4 ,!y /& beh9d /range mov+ b>s1 sometimes rectangul> & sometimes curvil9e>1 :i* are kn[n z 8co-ord9ates40 ,!y be> names z frightful z !mselves--8contrav>iant & cov>iant vectors1 t5sors1 scal>s1 det]m9ants1 or?ogonal vectors1 g5]alis$ symbols ( ?ree signs10 & s on4 ,^! /range be+s1 br\ght f ! wilde/ dep?s ( ! ma!matical jungle1 jo9 toge!r or "p f ea* o!r ) a rem>kable promiscuity1 by means ( "s a/oni%+ surg]y :i* is call$ integration & diff]5tiation4 ,9 a ^w1 ,e9/e9 may be a treasure1 b !re is a fe>some troop ( ma!matical reptiles keep+ inquisitive folk away f x2 ?\gh !re c be no d\bt t !y h1 l our ,go?ic g>goyles1 a hidd5 beauty ( _! own4 ,let u1 h[ev]1 drive !m (f ) ! :ip ( simple t]m9ology1 & approa* ! spl5d\r ( ,e9/e9's !ory4 ,:o is ?is physici/ ,e9/e98 ,t is a "q ( no importance "h4 ,x is en\gh to "k t he refus$ to sign ! infam\s manife/o ( ! pr(essors1 & ?us br\ght ^u himself p]secution f ! ,pan-,g]mani/s4#a ,ma!matical tru?s & sci5tific discov]ies h an intr9sic value1 & ?is mu/ be judg$ & appreciat$ imp>tially1 :oev] _! au?or may *ance to be4 ,_h ,py?agoras be5 ! l[e/ ( crim9als1 ! fact w\ld n 9 ! lea/ detract f ! validity ( ! squ>e ( ! hypot5use4 ,a !ory is ei!r true or false1 :e!r ! nose ( its au?or has ! aquil9e cont\r ( ! nose ( ! *ildr5 ( ,sem1 or ! flatt5$ %ape ( t ( ! *ildr5 ( ,*am1 or ! /raightness ( t ( ! *ildr5 ( ,japhet4 ,d we feel t humanity is p]fect :5 we he> x said occasionally3 8,tell me :at *ur* y frequ5t1 & ,i w tell y if y\r geometry is s\nd40 ,tru? has no ne$ ( a civil /atus4 ,let u get on4 #a ,alb]t ,e9/e91 born 9 #ahgi1 is a ,g]man ,jew ( ,wrtemb]g4 ,he /udi$ 9 ,switz]l&1 & 0 an eng9e] !re until #aiji1 :5 he became pr(essor at ,zuri* ,univ]sity4 ,9 #aiaa he pass$ to ,prague ,univ]sity1 9 #aiab to ! ,zuri* ,polyte*nic1 & 9 #aiad to ! ,prussian ,academy ( ,sci5ce4 ,he refus$ to give 8 "n to ! manife/o 9 :i* n9ety-?ree pr(essors ( ,g]many & ,au/ria def5d$ ,g]many's w>-action4--,trans4 99 99 99 99 99 ,all our ideas1 all sci5ce1 & ev5 ! :ole ( our practical life1 are bas$ ^u ! way 9 :i* we picture to ourselves ! successive aspects ( ?+s4 ,our m9d1 ) ! aid ( our s5ses1 *iefly ranges ^! "u ! head+s ( "t & space1 :i* ?us become ! two frames 9 :i* we dispose all t is app>5t to u ( ! mat]ial _w4 ,:5 we write a lett]1 we put at ! head ( x ! "n ( ! place & ! date4 ,:5 we op5 a newspap]1 we f9d ! same indications at ! beg9n+ ( ea* piece ( telegraphic news4 ,x is ! same 9 ev]y?+ & = ev]y?+4 ,"t & space1 ! situation & ! p]iod ( ?+s1 are ?us se5 to be ! tw9 pill>s ( all k1 ! two columns :i* su/a9 ! edifice ( m5's und]/&+4 ,s felt ,leconte de ,lisle :51 address+ himself to 8div9e dea?10 he wrote1 9 8 pr(\nd1 philosophic way3 ,free u f "t1 numb]1 & space3 ,grant u ! re/ t life ha? spoil$4 ,he ins]ts ! ^w 8numb]0 only 9 ord] to def9e "t & space quantitatively4 ,:at he has f9ely express$ 9 ^! fam\s & sup]b l9es is ! fact t all t !re is = u 9 ?is va/ univ]se1 all t we "k & see1 all ! ineffable & agitat$ fl[ ( ph5om5a1 pres5ts to u no def9ite aspect1 no precise =m1 until x has pass$ ?r\gh ^? two filt]s :i* are int]pos$ by ! m9d1 "t & space4 ,! "w ( ,e9/e9 d]ives its importance f ! fact t he has %[n1 z we %all see1 t we h entirely to revise our ideas ( "t & space4 ,if t is s1 ! :ole ( sci5ce1 includ+ psy*ology1 w h to be recon/ruct$4 ,t is ! fir/ "p ( ,e9/e9's "w1 b x goes fur!r4 ,if t 7 ! :ole ( 8 "w x w\ld be m]ely negative4 ,once he _h remov$ f ! /ructure ( human k :at _h be5 reg>d$ z an indisp5sable wall ( x1 ?\gh x 0 really only a frail scaffold+ t hid ! h>mony ( its proportions1 he began to recon/ruct4 ,he made 9 ! /ructure l>ge w9d[s :i* all[ u n[ to see ! treasures x conta9s4 ,9 a ^w1 ,e9/e9 %[$1 on ! "o h&1 ) a/oni%+ acut5ess & dep?1 t ! f\ndation ( our k seems to be diff]5t f :at we _h ?\ght1 & t x ne$s repair+ ) a new k9d ( cem5t4 ,on ! o!r h&1 he has recon/ruct$ ! edifice on ?is new basis1 & he has giv5 x a bold & rem>kably beautiful & h>moni\s =m4 ,i h n[ to %[ 9 detail1 concretely1 & z accurately z possible1 ! mean+ ( ^! g5]alities4 ,b ,i mu/ fir/ insi/ on a po9t :i* is ( consid]able importance3 if ,e9/e9 _h conf9$ himself to ! fir/ "p ( 8 "w1 z ,i h describ$ x1 ! "p :i* %att]s ! classical ideas ( "t & space1 he w\ld nev] h atta9$ ! fame :i* n[ makes 8 "n great 9 ! _w ( ?\ght4 ,! po9t is important because mo/ ( ^?--ap>t f exp]ts--:o h writt5 on ,e9/e9 h *iefly1 (t5 exclusively1 emphasis$ ?is m or less 8de/ructive0 side ( 8 "w4 ,b1 z we %all see1 f ?is po9t ( view ,e9/e9 0 n ! fir/1 & he is n alone4 ,all t he has done is to %>p51 & press a little deep] betwe5 ! badly jo9$ /ones ( classical sci5ce1 a *isel :i* o!rs1 especially ! great ,h5ri ,po9c>1 _h us$ long be=e him4 ,my next po9t is to expla91 if ,i c1 ! real1 ! immortal1 title ( ,e9/e9 to ! gratitude ( m53 to %[ h[ he has by 8 own p[]s rebuilt ! /ructure 9 a new & magnific5t =m aft] 8 critical "w4 ,9 ?is he %>es 8 glory ) none4 99 99 99 99 99 ,! :ole ( sci5ce1 f ! days ( ,ari/otle until our own1 has be5 bas$ ^u ! hypo!sis--prop]ly speak+1 ! hypo!ses--t !re is an absolute "t & an absolute space4 ,9 o!r words1 our ideas re/$ ^u ! supposition t an int]val ( "t & an int]val ( space betwe5 two giv5 ph5om5a are always ! same1 = e obs]v] :atsoev]1 & :atev] ! conditions ( obs]vation may be4 ,= in/ance1 x w\ld nev] h occurr$ to anybody z long z classical sci5ce 0 pr$om9ant1 t ! int]val ( "t1 ! numb] ( seconds1 :i* lies betwe5 two successive eclipses ( ! sun1 may n be ! fix$ & id5tically same numb] ( seconds = an obs]v] on ! e>? z = an obs]v] 9 ,sirius 7assum+ t ! second is def9$ = bo? by ! same *ronomet]74 ,simil>ly1 no "o w\ld h imag9$ t ! di/ance 9 metres betwe5 two objects1 = in/ance ! di/ance ( ! e>? f ! sun at a giv5 mom5t1 measur$ by trigonometry1 may n be ! same = an obs]v] on ! e>? z = an obs]v] 9 ,sirius 7! metre be+ def9$ = bo? by ! same rule74 8,!re is10 says ,ari/otle1 8"o s+le & inv>iable "t1 :i* fl[s 9 two movem5ts 9 an id5tical & simultane\s mann]2 & if ^! two sorts ( "t 7 n simultane\s1 !y w\ld nev]!less be ( ! same nature4444 ,?us1 9 reg>d to movem5ts :i* take place simultane\sly1 !re is "o & ! same "t1 :e!r or no ! movem5ts are equal 9 rapidity2 & ?is is true ev5 if "o ( !m is a local movem5t & ! o!r an alt]ation4444 ,x foll[s t ev5 if ! movem5ts diff] f ea* o!r1 & arise indep5d5tly1 ! "t is absolutely ! same = bo?40#b ,?is ,ari/otelic def9ition ( physical "t is m ?an two ?\s& ye>s old1 yet x cle>ly repres5ts ! idea ( "t :i* has be5 us$ 9 classic sci5ce1 especially 9 ! me*anics ( ,galileo & ,newton1 until q rec5t ye>s4 ,x seems1 h[ev]1 t 9 spite ( ,ari/otle1 ,epicurus outl9$ ! position :i* ,e9/e9 w\ld lat] adopt 9 antagonism to ,newton4 ,to translate lib]ally ! words 9 :i* ,lucretius exp\nds ! tea*+ ( ,epicurus3 8,"t has no exi/5ce ( itself1 b only 9 mat]ial objects1 f :i* we get ! idea ( pa/1 pres5t1 & future4 ,x is impossible to conceive "t 9 itself indep5d5tly ( ! movem5t or re/ ( ?+s40#c #b ,physics1 bk4 iv1 *4 xiv4 #c ,de ,natura ,r]um1 bk4 i1 vv4 #dfj ff4 ,bo? space & "t h be5 reg>d$ by sci5ce ev] s9ce ,ari/otle z inv>iable1 fix$1 rigid1 absolute data4 ,newton ?\ght t he 0 say+ some?+ obvi\s1 a platitude1 :5 he wrote 9 8 celebrat$ ,s*olion3 8,absolute1 true1 & ma!matical "t1 tak5 9 itself & )\t relation to any mat]ial object1 fl[s uni=mly ( its own nature4444 ,absolute space1 on ! o!r h&1 indep5d5t by its own nature ( any relation to ext]nal objects1 rema9s always un*angeable & immovable40 ,! :ole ( sci5ce1 ! :ole ( physics & me*anics1 z !y are /ill taught 9 our colleges & 9 mo/ ( our univ]sities1 are bas$ entirely ^u ^! propositions1 ^! ideas ( an absolute "t & space1 tak5 by !mselves & )\t any ref]5ce to an ext]nal object1 indep5d5t by _! v nature4 ,9 a ^w--if ,i may v5ture to use ?is figure--"t 9 classical sci5ce 0 l a riv] be>+ ph5om5a z a /ream be>s boats1 fl[+ on j ! same :e!r !re 7 ph5om5a or n4 ,space1 simil>ly1 0 r l ! bank ( ! riv]1 indiff]5t to ! %ips t pass$4 ,f ! "t ( ,newton1 h[ev]1 if n f ! "t ( ,ari/otle1 any ?\ghtful metaphysician might h notic$ t !re 0 some?+ wrong 9 ^! def9itions4 ,absolute "t & absolute space are 8?+s 9 !mselves10 & ^! ! human m9d has always reg>d$ z n directly accessible to x4 ,! specifications ( space & "t1 ^? numb]$ labels :i* we atta* to objects ( ! mat]ial _w1 z we put labels on p>cels at ! /ation s t !y may n be lo/ 7a precaution t does n always suffice71 are giv5 u by our s5ses1 :e!r aid$ by in/rum5ts or n1 only :5 we receive concrete impressions4 ,%\ld we h any idea ( !m if !re 7 no bodies atta*$ to !m1 or r to :i* we atta* ! labels8 ,to answ] ?is 9 ! affirmative1 z ,ari/otle1 ,newton1 & classical sci5ce d1 is to make a v bold assumption1 & "o t is n obvi\sly ju/ifi$4 ,! only "t ( :i* we h any idea ap>t f all objects is ! psy*ological "t s lum9\sly /udi$ by ,m4 ,b]gson3 a "t :i* has no?+ except ! "n 9 common ) ! "t ( physici/s1 ( sci5ce4 ,x is really to ,h5ri ,po9c>1 ! great ,fr5*man ^: dea? has left a void t w nev] be fill$1 t we mu/ accord ! m]it ( hav+ fir/ prov$1 ) ! greate/ lucidity & ! mo/ prud5t audacity1 t "t & space1 z we "k !m1 c only be relative4 ,a few quotations f 8 works w n be out ( place4 ,!y w %[ t ! cr$it = mo/ ( ! ?+s :i* are curr5tly attribut$ to ,e9/e9 is1 9 reality1 due to ,po9c>4 ,to prove ?is is n 9 any way to detract f ! m]it ( ,e9/e91 = t is1 z we %all see1 9 o!r fields4 ,?is is h[ ,po9c>1 ^: ideas /ill dom9ate ! m9ds ( ?\ghtful m51 ?\gh 8 mortal frame p]i%$ ye>s ago1 express$ himself1 ! triumphant sweep ( 8 w+s rea*+ fur!r e day3 8,"o _c =m any idea ( empty space4444 ,f t foll[s ! und5iable relativity ( space4 ,any man :o talks ( absolute space uses words :i* h no mean+4 ,i am at a p>ticul> spot 9 ,p>is--! ,place du ,pan?on1 let u suppose--& ,i say3 #8,i w come back "h to-morr[4' ,if anyone asks me :e!r ,i mean t ,i w return to ! same po9t 9 space1 ,i am tempt$ to reply1 #8,yes4' ,i %\ld1 h[ev]1 be wrong1 because betwe5 ?is & to-morr[ ! e>? w h travell$1 tak+ ! ,place du ,pan?on ) x1 s t to-morr[ ! squ>e w be m ?an #b1jjj1jjj kilometres away f :]e x is n[4 ,& x w\ld be no use my attempt+ to use precise language1 because ^! #b1jjj1jjj kilometres are "p ( our e>?'s j\rney r\nd ! sun1 b ! sun itself has mov$ 9 relation to ! ,milky ,way1 & ! ,milky ,way 9 turn is d\btless mov+ at a spe$ :i* we _c le>n4 ,?us we are entirely ignorant1 & always w be ignorant1 h[ f> ! ,place du ,pan?on %ifts its position 9 space 9 a s+le day4 ,:at ,i really meant to say 03 #8,to-morr[ ,i %all aga9 see ! dome & faade ( ! ,pan?on4' ,if !re 7 no ,pan?on1 !re w\ld be no mean+ 9 my words1 & space w\ld disappe>40 ,po9c> works out 8 idea 9 ?is way3 8,suppose all ! dim5sions ( ! univ]se 7 increas$ a ?\s&fold 9 a night4 ,! _w w\ld rema9 ! same1 giv+ ! ^w #8same' ! mean+ x has 9 ! ?ird book ( geometry4 ,nev]!less1 an object t _h measur$ a metre 9 l5g? w h5ce=w>d be a kilometre 9 l5g?2 a ?+ t _h measur$ a millimetre w n[ measure a metre4 ,! b$ on :i* ,i lie & ! body :i* lies on x w increase 9 size to exactly ! same ext5t4 ,:at sort ( feel+s w ,i h :5 ,i awake 9 ! morn+1 9 face ( su* an amaz+ trans=mation8 ,well1 ,i %all "k no?+ ab\t x4 ,! mo/ precise measurem5ts w\ld tell me no?+ ab\t ! revolution1 because ! tape ,i use = measur+ w h *ang$ to ! same ext5t z ! objects ,i wi% to measure4 ,z a matt] ( fact1 !re w\ld be no revolution except 9 ! m9d ( ^? :o reason z if space 7 absolute4 ,if ,i h argu$ = a mom5t z !y d1 x 0 only 9 ord] to %[ m cle>ly t _! position is contradictory40 ,x w\ld be easy to develop ,po9c>'s argum5t4 ,if all ! objects 9 ! univ]se 7 to become1 = in/ance1 a ?\s& times tall]1 a ?\s& times broad]1 we %\ld be q unable to detect x1 because we ourselves--our ret9a & our measur+ rod--w\ld be trans=m$ to ! same ext5t at ! same "t4 ,inde$1 if all ! ?+s 9 ! univ]se 7 to exp]i5ce an absolutely irregul> spatial de=mation--if "s invisible & all-p[]ful _s 7 to di/ort ! univ]se 9 any fa%ion1 draw+ x out z if x 7 rubb]--we %\ld h no means ( kn[+ ! fact4 ,!re c\ld be no bett] pro( t space is relative1 & t we _c conceive space ap>t f ! ?+s :i* we use to measure x4 ,:5 !re is no measur+ rod1 !re is no space4 ,po9c> pu%$ 8 reason+ on ?is subject s f> t he came to say t ev5 ! revolution ( ! e>? r\nd ! sun is m]ely a m conv5i5t hypo!sis ?an ! contr>y supposition1 b n a tru] hypo!sis1 unless we imply ! exi/5ce ( absolute space4 ,x may be rememb]$ t c]ta9 unw>y controv]siali/s h tri$ to inf] f ,po9c>'s argum5t t ! condemnation ( ,galileo 0 ju/ifi$4 ,no?+ c\ld be m amus+ ?an ! way 9 :i* ! di/+ui%$ ma!matician-philosoph] def5d$ himself aga9/ ?is int]pretation1 ?\gh "o mu/ admit t 8 def5ce 0 n :olly conv9c+4 ,he did n take suffici5tly into acc\nt ! agno/ic elem5t4 ,po9c>1 9 any case1 is ! lead] ( ^? :o reg>d space z a m]e prop]ty :i* we ascribe to objects4 ,9 ?is view our idea ( x is only1 s to say1 ! h]$it>y outcome ( ^? ef=ts ( our s5ses by means ( :i* we /rive to embrace ! mat]ial _w at a giv5 mom5t4 ,x is ! same ) "t4 ,"h aga9 ! objections ( philosophic ,relativi/s 7 rais$ long ago1 b x 0 ,po9c> :o gave !m _! def9itive %ape4 ,8 lum9\s demon/rations are1 h[ev]1 well kn[n1 & we ne$ n reproduce !m "h4 ,x is en\gh to obs]ve t1 9 reg>d to "t z well z space1 x is possible to imag9e ei!r a contraction or an enl>gem5t ( ! scale :i* w\ld be completely imp]ceptible to u2 & ?is seems to %[ t man _c conceive an absolute "t4 ,if "s malici\s _s 7 to amuse itself "s night by mak+ all ! ph5om5a ( ! univ]se a ?\s& times sl[]1 we %\ld n1 :5 we awake1 h any means ( detect+ ! *ange4 ,! _w w\ld seem to u un*ang$4 ,yet e h\r record$ by our wat*es w\ld be a ?\s& times long] ?an h\rs _h previ\sly be54 ,m5 w\ld live a ?\s& times z long1 yet !y w\ld be unaw>e ( ! fact1 z _! s5sations w\ld be sl[] 9 ! same proportion4 ,:5 ,lam>t9e appeal$ to "t to 8susp5d its flight10 he said a v *>m+1 b p]haps mean+less1 ?+4 ,if "t _h obey$ 8 passionate appeal1 nei!r ,lam>t9e nor ,elvire w\ld h kn[n & rejoic$ ov] ! fact4 ,! boatman :o conduct$ ! lov]s on ! ,lac du ,b\rget w\ld n h ask$ paym5t = a s+le additional h\r2 yet he w\ld h dipp$ 8 o>s into ! pleasant wat]s = a f> long] "t4 ,i v5ture to sum up all ?is 9 a s5t5ce :i* w at fir/ sight seem a p>adox3 9 ! op9ion ( ! ,relativi/s x is ! measur+ rods :i* create space1 ! clocks :i* create "t4 ,all ?is 0 ma9ta9$ by ,po9c> & o!rs long be=e ! "t ( ,e9/e91 & "o does inju/ice to tru? 9 ascrib+ ! discov]y to him4 ,i am q aw>e t "o l5ds only to ! ri*1 b "o does an inju/ice to ! weal?y !mselves 9 attribut+ to !m :at does n belong to !m1 & :at !y ne$ n 9 ord] to be ri*4 ,!re is1 moreov]1 "o po9t at :i* ,galileo & ,newton1 = all _! belief 9 ! exi/5ce ( absolute space & "t1 admitt$ a c]ta9 relativity4 ,!y recognis$ t x is impossible to di/+ui% betwe5 uni=m movem5ts ( translation4 ,!y ?us admitt$ ! equival5ce ( all su* movem5ts1 & !re=e ! impossibility ( prov+ an absolute movem5t ( translation4 ,t is :at is call$ ! ,pr9ciple ( ,classic ,relativity4 99 99 99 99 99 ,an unexpect$ fact s]v$ to br+ ^! que/ions ^u a new plane1 & l$ ,e9/e9 to give a rem>kable ext5sion to ! ,pr9ciple ( ,relativity ( classic me*anics4 ,?is 0 ! issue ( a fam\s exp]im5t by ,mi*elson1 ( :i* we mu/ give a brief description4 ,x is well kn[n t rays ( light travel across empty space f /> to />1 o!rwise we %\ld be unable to see ! />s4 ,f ?is physici/s long ago conclud$ t ! rays travell$ 9 a m$ium t is devoid ( mass & in]tia1 is inf9itely ela/ic1 & (f]s no resi/ance to ! movem5t ( mat]ial bodies1 into :i* x p5etrates4 ,?is m$ium has be5 nam$ e!r4 ,light travels ?r\gh x z waves spread ov] ! surface ( wat] at a spe$ ( some?+ l #ahf1jjj miles a second3 a velocity :i* we w express by ! lett] ,v4 ,! e>? revolves r\nd ! sun 9 a v]itable ocean ( e!r1 at a spe$ ( ab\t #ah miles a second4 ,9 ?is respect ! rotation ( ! e>? on its axis ne$ n be notic$1 z x pu%es ! surface ( ! globe ?r\gh ! e!r at a spe$ ( less ?an two miles a second4 ,n[ ! "q _h (t5 be5 ask$3 ,does ! e>?1 9 its orbital movem5t r\nd ! sun1 take ) x ! e!r :i* is 9 contact ) x1 z a sponge ?r[n out ( a w9d[ takes ) x ! wat] :i* x has absorb$8 ,exp]im5t--or r1 exp]im5ts1 = _m h be5 tri$ ) ! same result--has %[n t ! "q mu/ be answ]$ 9 ! negative4 ,?is 0 fir/ e/abli%$ by a/ronomical obs]vation4 ,!re is 9 a/ronomy a well-kn[n ph5om5on discov]$ by ,bradley :i* is call$ ab]ration4 ,x consi/s 9 ?is3 :5 we obs]ve a /> ) a telescope1 ! image ( ! /> is n precisely 9 ! direct l9e ( vision4 ,! reason is t1 :ile ! lum9\s rays ( ! /> :i* h ent]$ ! telescope are pass+ d[n ! l5g? ( ! tube1 ! in/rum5t has be5 slightly displac$1 z x %>es ! movem5t ( ! e>?4 ,on ! o!r h&1 ! lum9\s ray 9 ! tube does n %>e ! e>?'s motion1 & ?is gives rise to ! v slight deviation :i* we call ab]ration4 ,?is proves t ! m$ium 9 :i* light travels1 ! e!r :i* fills ! in/rum5t & surr\nds ! e>?1 does n %>e ! e>?'s motion4 ,_m o!r exp]im5ts h settl$ beyond "q t ! e!r1 :i* is ! vehicle ( ! waves ( light1 is n borne along by ! e>? z x travels4 ,n[1 s9ce ! e>? moves ?r\gh ! e!r z a %ip moves ov] a /ation>y lake 7n l "o float+ on a mov+ /ream71 x ought to be possible to detect "s evid5ce ( ?is spe$ ( ! e>? 9 relation to ! e!r4 ,"o ( ! devices t may be imag9$ = ! purpose is ! foll[+4 ,we "k t ! e>? turns on itself f we/ to ea/1 & travels r\nd ! sun 9 ! same way4 ,x foll[s t 9 ! middle ( ! night ! revolution ( ! e>? r\nd ! sun means t ,p>is w be displac$1 9 ! direction f ,auteuil t[>d ,*>5ton1 at a spe$ ( ab\t ?irty kilometres a second4 ,dur+ ! day1 ( c\rse1 x is precisely ! opposite4 ,p>is *anges its place r\nd ! sun 9 ! direction f ,*>5ton t[>d ,auteuil4 ,well1 let u suppose t at midnight a physici/ at ,auteuil s5ds a lum9\s signal4 ,a physici/ receiv+ ?is ray ( light at ,*>5ton1 & measur+ its velocity1 ought to f9d t ! latt] is ,v #cj kilometres4 ,we "k t1 z a result ( ! e>?'s motion1 ,*>5ton rec$es be=e ! ray ( light4 ,consequ5tly1 s9ce light travels 9 a m$ium1 ! e!r1 :i* does n %>e ! e>?'s motion1 ! obs]v] at ,*>5ton ought to f9d t ! ray rea*es him at a less spe$ ?an x w\ld if ! e>? 7 /ation>y4 ,x is mu* ! same z if an obs]v] 7 travell+ on a bicycle 9 front ( an express tra94 ,if ! express travels at ?irty metres a second & ! cycli/ at ?ree metres a second1 ! spe$ ( ! tra9 9 relation to ! cycli/ w be #cj-c #bg metres a second4 ,x w\ld be nil if ! tra9 & ! cycli/ 7 travell+ at ! same rate4 ,on ! o!r h&1 if ! cycli/ 7 go+ t[>d ! tra91 ! spe$ ( ! tra9 9 relation to him w\ld be #cj #c #cc metres a second4 ,simil>ly1 :5 ! physici/ at ,*>5ton s5ds out a lum9\s message at midnight1 & ! physici/ ( ,auteuil receives x1 ! latt] ought to f9d t ! ray ( light has a velocity ( ,v #cj kilometres4 ,all ?is may be put 9 a diff]5t way4 ,suppose ! di/ance betwe5 ! obs]v] at ,auteuil & ! man at ,*>5ton 7 exactly twelve kilometres4 ,:ile ! ray ( light emitt$ at ,auteuil spe$s t[>d ,*>5ton1 t t[n is rec$+ be=e x to a small ext5t4 ,x foll[s t ! ray w h to travel a little m ?an twelve kilometres be=e x rea*es ! man ( sci5ce at ,*>5ton4 ,x w travel a little less ?an t di/ance if we imag9e x proce$+ 9 ! opposite direction4 ,n[ ! ,am]ican physici/ ,mi*elson1 borr[+ an +5i\s idea f ! ,fr5* physici/ ,fizeau1 succe$$1 ) a high degree ( accuracy1 9 measur+ di/ances by means ( ! int]f]5ce-b&s ( light4 ,e v>iation 9 ! di/ance measur$ betrays itself by ! displacem5t ( a c]ta9 numb] ( ^! b&s1 & ?is may easily be detect$ by a microscope4 ,let u next suppose t our two physici/s "w 9 a laboratory in/ead ( betwe5 ,*>5ton & ,auteuil4 ,let u suppose t !y are1 by means ( ! int]f]5ce-b&s1 measur+ ! space trav]s$ by a ray ( light produc$ 9 ! laboratory1 accord+ z x travels 9 ! same direction z ! e>? or 9 ! opposite direction4 ,t is ,mi*elson's fam\s exp]im5t1 r$uc$ to its ess5tial elem5ts & simplifi$ = ! purpose ( ?is essay4 ,9 ^? circum/ances ,mi*elson's delicate app>atus ought to reveal a di/9ctly measurable diff]5ce accord+ z ! light travels ) ! e>? or 9 ! opposite direction4 ,b no su* diff]5ce 0 f\nd4 ,contr>y to all expectation1 & to ! pr(\nd a/oni%m5t ( physici/s1 x 0 f\nd t light travels at precisely ! same spe$ :e!r ! man :o receives x is rec$+ be=e x ) ! velocity ( ! e>? or is approa*+ x at ! same velocity4 ,x is an und5iable consequ5ce ( ?is t ! e!r %>es ! motion ( ! e>?4 ,we h1 h[ev]1 se5 t o!r exp]im5ts1 n less precise1 _h settl$ t ! e!r does n %>e ! motion ( ! e>?4 ,out ( ?is contradiction1 ?is conflict ( two irreconcilable yet indubitable facts1 ,e9/e9's spl5did syn!sis1 l a sp>k ( light issu+ f ! cla% ( fl9t & /eel1 came into be+4 ,,*apt] ,,ii ,,sci5ce ,,9 ,a ,,no-,,?or\ghf>e ,sci5tific tru? & ma!matics--,! precise function ( ,e9/e9--,mi*elson's exp]im5t1 ! ,gordian knot ( sci5ce--,! hesitations ( ,po9c>--,! /range1 b necess>y1 ,fitzg]ald-,lor5tz hypo!sis--,! contraction ( mov+ bodies--,philosophical & physical difficulties4 ,x w\ld be fooli% to pret5d t we c p5etrate ! mo/ obscure corn]s ( ,e9/e9's !ories )\t ! aid ( ma!matics4 ,i believe1 h[ev]1 t we c give 9 ord9>y language--t is to say1 by means ( illu/rations & analogies--a fairly satisfactory idea ( ^! ?+s1 ! intricacy ( :i* is usually due to ! inf9itely subtle & supple play ( ma!matical =mul & equations4 ,aft] all1 ma!matics is n1 nev] 01 & nev] w be1 any?+ m ?an a p>ticul> k9d ( language1 a sort ( %or?& ( ?\ght & reason+4 ,! purpose ( x is to cut across ! complicat$ me&]+s ( long tra9s ( reason+ ) a bold rapidity t is unkn[n to ! m$ival sl[ness ( ! syllogisms express$ 9 our words4 ,h[ev] p>adoxical ?is may seem to p :o reg>d ma!matics z ( itself a means ( discov]y1 ! tru? is t we c nev] get f x any?+ t 0 n implicitly inh]5t 9 ! data :i* 7 ?ru/ betwe5 ! jaws ( its equations4 ,if ,i may use a some:at trivial illu/ration1 ma!matical reason+ is v l c]ta9 ma*9es :i* are se5 9 ,*icago--s bold explor]s 9 ! ,unit$ ,/ates tell u--into :i* "o puts liv+ animals t em]ge at ! o!r end 9 ! %ape ( appetis+ prep>$ meats4 ,no spectator c\ld h1 or w\ld wi% to h1 eat5 ! animal alive1 b 9 ! =m 9 :i* x issues f ! ma*9e x c at once be dige/$ & assimilat$4 ,yet ! meat is m]ely ! animal conv5i5tly prep>$4 ,t is :at ma!matics does4 ,by means ( a m>vell\s ma*9]y ! ma!matician extracts ! valuable m>r[ f ! giv5 facts4 ,x is a ma*9]y t is p>ticul>ly useful 9 cases :]e ! :eels ( v]bal argum5t1 ! *a9 ( syllogisms1 w\ld soon be br\ght to a halt4 ,does x foll[ t1 prop]ly speak+1 ma!matics is n a sci5ce8 ,does x foll[ at lea/ t x is only a sci5ce 9 s f> z x is bas$ ^u reality1 & f$ ) exp]im5tal data1 s9ce 8exp]i5ce is ! sole s\rce ( tru?40 ,i refra9 f answ]+ ! "q1 z ,i am "o ( ^? :o believe t ev]y?+ is mat]ial = sci5ce4 ,/ill1 x 0 wor? :ile to raise ! "q because _m are too mu* dispos$ to reg>d a purely ma!matical education z a sci5tific education4 ,no?+ c\ld be fur!r f ! tru?4 ,pure ma!matics is1 9 itself1 m]ely an abbreviat$ =m ( language & ( logical ?\ght4 ,x _c1 ( its own nature1 tea* u any?+ ab\t ! ext]nal _w2 x c d s only 9 proportion z x ent]s into contact ) ! _w4 ,x is ( ma!matics 9 p>ticul> t we may say3 ,natur non imp]atur nisi p>5do4 ,are n ,e9/e9's !ories1 z "s imp]fectly in=m$ writ]s h sugge/$1 only a play ( ma!matical =mul 7tak+ ! ^w 9 ! mean+ giv5 to x by bo? ma!maticians & philosoph]s78 ,if !y 7 only a t[]+ ma!matical /ructure 9 :i* ! x's %oot out _! volutes 9 bewild]+ arabesques1 ) swan-neck integrals describ+ ,l\is ,,xv patt]ns1 !y w\ld h no int]e/ :atev] = ! physici/1 = ! man :o has to exam9e ! nature ( ?+s be=e he talks ab\t x4 ,!y w\ld1 l all coh]5t s*emes ( metaphysics1 be m]ely a m or less agreeable sy/em ( ?\ght1 ! tru? or fals5ess ( :i* c\ld nev] be demon/rat$4 ,e9/e9's !ory is v diff]5t f t1 & v mu* m ?an t4 ,x is bas$ ^u facts4 ,x also leads to facts--new facts4 ,no philosophical doctr9e or purely =mal ma!matical con/ruction ev] enabl$ u to discov] new ph5om5a4 ,x is precisely because x has l$ to su* discov]y t ,e9/e9's !ory is nei!r ! "o nor ! o!r4 ,t is ! diff]5ce betwe5 a sci5tific !ory & a pure speculation1 & x is t :i*1 ,i v5ture to say1 makes ! =m] s sup]ior4 ,l "s susp5sion bridge boldly ?r[n across an abyss1 ,e9/e9's !ory re/s1 on ! "o side1 on exp]im5tal ph5om5a1 & x leads1 at ! o!r side1 to o!r1 & hi!rto unsuspect$1 ph5om5a1 :i* x has enabl$ u to discov]4 ,betwe5 ^! two solid exp]im5tal columns ! ma!matical reason+ is l ! m>vell\s network ( ?\s&s ( /eel b>s :i* repres5t ! elegant & transluc5t /ructure ( ! bridge4 ,x is t1 & no?+ b t4 ,b ! arrangem5t ( ! beams & b>s might h be5 diff]5t1 & ! bridge--?\gh less light & graceful1 p]haps--/ill h be5 able to jo9 toge!r ! two sets ( facts on :i* x re/s4 ,9 a ^w1 ma!matical reason+ is only a k9d ( reason+ 9 a special language1 f exp]im5tal premises to conclusions :i* are v]ifiable by exp]i5ce4 ,n[ !re is no language :i* _c 9 "s degree be translat$ into ano!r language4 ,ev5 ! hi]oglyphics ( ,egypt _h to give way be=e ,*ampollion4 ,i am !re=e conv9c$ t ! ma!matical difficulties ( ,e9/e9's !ories w "s day be replac$ by simpl] & m accessible =mul4 ,i believe1 inde$1 t x is ev5 n[ possible to give by means ( ord9>y spee* an idea1 r sup]ficial p]haps1 b accurate & sub/antially complete1 ( ?is wond]ful ,e9/e9ian /ructure :i* ranges all ! conque/s ( sci5ce1 z 9 "s well-ord]$ museum1 9 a new & sup]b unity4 ,let u try4 99 99 99 99 99 ,we may resume 9 ! few foll[+ words ! /ory ( ! orig91 ! />t+-po9t1 ( ,e9/e9's sy/em4 #a4 ,obs]vation ( ! />s proves t int]planet>y space is n empty1 b is fill$ ) a special m$ium1 e!r1 9 :i* ! waves ( light travel4 #b4 ,! fact ( ab]ration & o!r ph5om5a seems to prove t ! e!r is n displac$ by ! e>? dur+ its c\rse r\nd ! sun4 #c4 ,mi*elson's exp]im5t seems to prove1 on ! contr>y1 t ! e>? be>s ! e!r ) x 9 its movem5t4 ,?is contradiction betwe5 facts ( equal au?ority 0 = ye>s ! despair & ! wond] ( physici/s4 ,x 0 ! ,gordian knot ( sci5ce4 ,long & fruitless ef=ts 7 made to untie x until at la/ ,e9/e9 cut x ) a s+le bl[ ( 8 rem>kably acute intellig5ce4 ,9 ord] to und]/& h[ t 0 done--:i* is ! vital po9t ( ! :ole sy/em--we mu/ retrace our /eps a little & exam9e ! precise conditions ( ,mi*elson's fam\s exp]im5t4 ,i po9t$ out 9 ! prec$+ *apt] t ,mi*elson propos$ to /udy ! spe$ ( a ray ( light produc$ 9 ! laboratory & direct$ ei!r f ea/ to we/ or we/ to ea/3 t is to say1 9 ! direction 9 :i* ! e>? itself moves1 at a spe$ ( ab\t eighte5 miles a second1 z x travels r\nd ! sun1 or 9 ! opposite direction4 ,z a matt] ( fact1 ,mi*elson's exp]im5t 0 r m complicat$ ?an t1 & we mu/ return to x4 ,f\r mirrors are plac$ at an equal di/ance f ea* o!r 9 ! laboratory1 9 pairs :i* face ea* o!r4 ,two ( ! oppos+ mirrors are arrang$ 9 ! direction ea/-we/1 ! direction 9 :i* ! e>? moves 9 consequ5ce ( its revolution r\nd ! sun4 ,! o!r two are arrang$ 9 a plane p]p5dicul> to ! prec$+1 ! direction nor?-s\?4 ,two rays ( light are !n />t$ 9 ! respective directions ( ! two pairs ( mirrors4 ,! ray com+ f ! mirror to ! ea/ goes to ! mirror 9 ! we/1 is reflect$ !refrom1 & returns to ! fir/ mirror4 ,?is ray is s arrang$ t x crosses ! pa? ( ! light :i* goes f nor? to s\? & back4 ,x int]f]es ) ! latt] light1 caus+ 8fr+es ( int]f]5ce0 :i*1 z ,i said1 enable u to le>n ! exact di/ance trav]s$ by ! rays ( light reflect$ betwe5 ! pairs ( mirrors4 ,if any?+ br\ght ab\t a diff]5ce betwe5 ! l5g? ( ! two di/ances1 we %\ld at once see ! displacem5t ( a c]ta9 numb] ( int]f]5ce-fr+es1 & ?is w\ld give u ! magnitude ( ! diff]5ce4 ,an analogy w help u to und]/& ! matt]4 ,suppose a viol5t /eady ea/ w9d blew across ,london1 & an aviator propos$ to cross ! city ab\t twelve miles f extreme we/ to ea/ & back3 t is to say1 go+ ) ! w9d on 8 outw>d j\rney & aga9/ x on ! return j\rney4 ,suppose ano!r aviator1 ( equal spe$1 propos$ at ! same "t to fly f ! same />t+-po9t to a po9t twelve miles to ! nor? & back1 ! second aviator w fly bo? ways at "r angles to ! direction ( ! w9d4 ,if ! two />t at ! same "t1 & are imag9$ z turn+ r\nd in/antane\sly1 w !y bo? rea* ! />t+-po9t toge!r8 ,&1 if n1 :i* ( !m w h complet$ 8 d\ble j\rney fir/8 ,x is cle> t if !re 7 no w9d1 !y w\ld get back toge!r1 z we suppose t !y bo? d tw5ty-f\r miles at ! same spe$1 :i* we may r\ghly /ate to be #bjj y>ds a second4 ,b x w be diff]5t if1 z ,i po/ulat$1 !re is a w9d bl[+ f ea/ to we/4 ,x is easy to see t 9 su* circum/ances ! man :o flies ea/ to we/ w take long] to complete ! j\rney4 ,9 ord] to get x q cle>ly1 let u suppose t ! w9d is travell+ at ! same spe$ z ! aviator 7#bjj y>ds a second74 ,! man :o flies at "r angles to ! w9d w be bl[n twelve miles to ! we/ :ile he is do+ 8 twelve miles f s\? to nor?4 ,he w !re=e h trav]s$ 9 ! w9d a real di/ance equal to ! diagonal ( a squ>e measur+ twelve miles on ea* side4 ,in/ead ( fly+ tw5ty-f\r miles1 he w really h fl[n ?irty-f\r 9 ! w9d1 ! m$ium 9 relation to :i* he has any velocity4 ,on ! o!r h&1 ! aviator :o flies ea/w>d w nev] rea* 8 de/9ation1 because 9 ea* second ( "t he is driv5 we/w>d to precisely ! same ext5t z he is travell+ ea/w>d4 ,he w rema9 /ation>y4 ,to accompli% 8 j\rney he w\ld ne$ to cov] 9 ! w9d an inf9ite di/ance4 ,if1 in/ead ( imag9+ a w9d equal 9 velocity to ! aviator 7an extreme supposition 9 ord] to make ! demon/ration cle>]71 ,i _h ?\ght ( x z less rapid1 we %\ld aga9 f9d1 by a v simple calculation1 t ! man :o flies nor? & s\? has less di/ance to cov] 9 ! w9d ?an ! man :o flies ea/ & we/4 ,n[ take rays ( light in/ead ( aviators1 ! e!r in/ead ( ! w9d1 & we h v ne>ly ! conditions ( ! ,mi*elson exp]im5t4 ,a curr5t or w9d ( e!r--s9ce ! e!r has be5 already %[n to be /ation>y 9 relation to ! e>?'s movem5t--proce$s f "o to ! o!r ( our ea/-we/ mirrors4 ,!re=e ! ray ( light :i* travels betwe5 ^! two mirrors1 =? & back1 mu/ cov] a long] di/ance 9 e!r ?an ! ray :i* goes f ! s\? mirror to ! nor? & back4 ,b h[ are we to detect ?is diff]5ce8 ,x is c]ta9ly v m9ute1 because ! spe$ ( ! e>? is t5 ?\s& times less ?an ! velocity ( light4 ,!re is a v simple means ( do+ ?is3 "o ( ^? +5i\s devices :i* physici/s love1 a diff]5tial device s elegant & precise t we h entire confid5ce 9 ! result4 ,let u suppose t our f\r mirrors are fix$ rigidly 9 a sort ( squ>e frame1 some?+ l ^? 8:eels ( =tune0 ) numb]s on !m t "o sees 9 c\ntry fairs4 ,let u suppose t we c turn ?is frame r\nd z we wi%1 )\t j]k+ or displac+ x1 :i* is n difficult if x floats 9 a ba? ( m]cury4 ,i !n take a l5s & obs]ve ! p]man5t int]f]5ce-fr+es :i* def9e ! diff]5ce betwe5 ! pa?s trav]s$ by my two rays ( light1 nor?-s\? & ea/-we/4 ,!n1 )\t los+ sight ( ! b&s or fr+es1 ,i turn ! frame r\nd a qu>t] ( a circle4 ,ow+ to ?is rotation ! mirrors :i* 7 ea/-we/ n[ become nor?-s\?1 & vice v]sa4 ,! d\ble j\rney made by ! nor?-s\? ray ( light has n[ tak5 ! direction ea/-we/1 & has !re=e sudd5ly be5 l5g!n$2 ! d\ble j\rney ( ! ea/-we/ ray has become nor?-s\?1 & has be5 sudd5ly %ort5$4 ,! int]f]5ce-fr+es1 :i* indicate ! diff]5ce 9 l5g? betwe5 ! two pa?s1 :i* has sudd5ly *ang$1 mu/ necess>ily be displac$1 & t1 z we c calculate1 to no slight ext5t4 ,well1 we f9d no *ange :atev]6 ,! fr+es rema9 unalt]$4 ,!y are z /ation>y z /umps ( trees4 ,x is bewild]+1 "o w\ld almo/ say revolt+1 because ! delicacy ( ! app>atus is su* t1 ev5 if ! e>? mov$ ?r\gh ! e!r at a rate ( only ?ree kilometres a second 7or t5 times less ?an its actual velocity71 ! displacem5t ( ! fr+es w\ld be suffici5t to indicate ! spe$4 99 99 99 99 99 ,:5 ! negative result ( ?is exp]im5t 0 ann\nc$1 !re 0 some?+ l con/]nation among/ ! physici/s ( ! _w4 ,s9ce ! e!r 0 n borne along by ! e>?1 z obs]vation _h e/abli%$1 h[ c\ld x possibly behave z if x did %>e ! e>?'s motion8 ,x 0 a ,*9ese puzzle4 ,m ?an "o v5]able grey head 0 9 despair ov] x4 ,x 0 absolutely necess>y to f9d a way out ( ?is inexplicable contradiction1 to end ?is p>adoxical mock]y :i* ! facts seem$ to oppose to ! mo/ rigor\s results ( calculation4 ,?is ! m5 ( sci5ce succe$$ 9 do+4 ,h[8 ,by ! me?od :i* is g5]ally us$ 9 su* circum/ances--by means ( supplem5t>y hypo!ses4 ,hypo!ses 9 sci5ce are a k9d ( s(t cem5t :i* h>d5s rapidly 9 ! op5 air1 ?us enabl+ u to jo9 toge!r ! sep>ate blocks ( ! /ructure1 & to fill up ! brea*es made 9 ! wall by projectiles1 ) artificial /uff :i* ! sup]ficial obs]v] pres5tly mi/akes = /one4 ,x is because hypo!ses are some?+ l t 9 sci5ce t ! be/ sci5tific !ories are ^? :i* include lea/ hypo!ses4 ,b ,i am wrong 9 us+ ! plural 9 ?is connection4 ,9 ! end x 0 f\nd t "o s+le hypo!sis conv5i5tly expla9$ ! negative result ( ! ,mi*elson exp]im5t4 ,t is1 by ! way1 a r>e & rem>kable exp]i5ce4 ,hypo!ses usually spr+ up l mu%rooms 9 e d>k corn] ( sci5ce4 ,y get a score ( !m to expla9 ! slighte/ obscurity4 ,?is s+le hypo!sis1 :i* seem$ to be capable ( extricat+ physici/s f ! dilemma into :i* ,mi*elson _h put !m1 0 fir/ advanc$ by ! di/+ui%$ ,iri% ma!matician ,fitzg]ald1 !n tak5 up & develop$ by ! celebrat$ ,dut* physici/ ,lor5tz1 ! ,po9c> ( ,holl&1 "o ( ! mo/ brilliant ?9k]s ( our "t4 ,e9/e9 w\ld no m h atta9$ fame )\t him ?an ,kepl] w\ld )\t ,cop]nicus & ,ty*o ,brahe4 ,let u n[ see :at ?is ,fitzg]ald-,lor5tz hypo!sis1 z /range z x is simple1 really is4 ,b we mu/ fir/ glance at a prelim9>y matt] ( "s importance4 ,a numb] ( able m5 h decl>$--aft] ! issue1 let x be said--t ! result ( ! ,mi*elson exp]im5t c\ld only be negative a priori4 ,9 po9t ( fact1 !y argue 7m or less71 ! ,classic ,pr9ciple ( ,relativity1 ! pr9ciple kn[n to ,galileo & ,newton1 implies t x is impossible = an obs]v] :o %>es ! motion ( a vehicle to detect ! motion ( t vehicle by any facts he obs]ves :ile he is 9 x4 ,?us1 :5 two %ips or two tra9s pass ea* o!r1#d x is impossible = ! pass5g]s to say :i* ( ! two is mov+1 or mov+ ! m rapidly4 ,all t !y c p]ceive is ! relative spe$ ( ! tra9s or %ips4 #d ,x is assum$ t ! %ip is n roll+ or pit*+1 & t !re is no vibration 9 ! tra94 ,! m5 ( sci5ce to :om ,i h ref]r$ say t1 if ,mi*elson's exp]im5t _h _h a positive result1 x w\ld h giv5 u ! absolute velocity ( ! e>? 9 space4 ,?is result w\ld h be5 contr>y to ! ,pr9ciple ( ,relativity ( classical philosophy & me*anics1 :i* is a self-evid5t tru?4 ,!re=e ! result c\ld only be negative4 ,?is is1 z we %all see1 ambigu\s4 ,!re is1 if ,i may say s1 a flaw 9 ! argum5t :i* has escap$ ! notice ev5 ( di/+ui%$ m5 ( sci5ce l ,pr(essor ,edd+ton1 ! mo/ erudite ( ! ,engli% ,e9/e9ians4 ,x 0 he :o organis$ ! obs]vations ( ! sol> eclipse ( ,may #bi1 #aiai1 :i* h1 z we %all see1 furni%$ ! mo/ /rik+ v]ification ( ,e9/e9's d$uctions4 ,9 ! fir/ place1 if ,mi*elson's exp]im5t _h _h a positive result1 :at x w\ld h indicat$ is ! velocity ( ! e>? 9 relation to ! e!r4 ,b1 = ?is to be an absolute velocity1 ! e!r w\ld h to be id5tical ) space4 ,?is is s f> f be+ necess>y t we c easily conceive a space--to put x bett]1 a discont9uity--betwe5 two />s t conta9s no e!r & across :i* nei!r light nor any o!r kn[n =m ( en]gy w\ld travel4 ,:5 ,edd+ton says t 8x is legitimate & reasonable10 t x is 8inh]5t 9 ! fundam5tal laws ( nature10 t we _c detect any movem5t ( bodies 9 relation to e!r1 & t ?is is c]ta9 8ev5 if ! exp]im5tal evid5ce is inadequate10 he affirms some?+ :i* w\ld be evid5t only if space & e!r 7 evid5tly id5tical4 ,b ?is is f> f be+ ! case4 ,if ,mi*elson's exp]im5t _h _h a positive result1 if we _h detect$ a velocity on ! "p ( ! e>?1 %\ld we h discov]$ a velocity 9 relation to an absolute /&>d8 ,c]ta9ly n4 ,x is q possible t ! /ell> univ]se :i* is kn[n to u1 ) its hundr$s ( ?\s&s ( galaxies :i* x takes light millions ( ye>s to cross1 may be conta9$ 9 a sph]e ( e!r t rolls 9 an abyss :i* is devoid ( e!r1 & is s[n "h & !re ) o!r univ]ses1 o!r giant drops ( e!r1 f :i* no ray ( light or any?+ else may ev] rea* u4 ,x is1 at all ev5ts1 n inconceivable4 ,& 9 t case1 assum+ t ! e!r has ! prop]ties attribut$ to x by classic physics1 ev5 if we _h detect$ ! movem5t ( ! e>? 9 relation to x1 we %\ld n h discov]$ an absolute movem5t1 b at ! mo/ a movem5t 9 relation to ! c5tre ( gravity ( our p>ticul> univ]se1 a /&>d :i* we c\ld n ref] to "s o!r :i* w\ld be absolutely /ation>y4 ,! ,classical ,pr9ciple ( ,relativity w\ld n be violat$4 ,h5ce1 :atev] may h be5 said to ! contr>y1 ! issue ( ,mi*elson's exp]im5t might1 9 ^! hypo!ses1 be ei!r positive or negative )\t any detrim5t to ,classical ,relativism4 ,z a matt] ( fact1 x 0 negative1 s no?+ fur!r ne$ be said4 ,exp]im5t has pron\nc$1 & x alone _h ! "r to pron\nce4 ,^! di/9ctions 7 n unkn[n to ,po9c>1 & he wrote3 8,by ! real velocity ( ! e>? ,i und]/&1 n its absolute velocity1 :i* is mean+less1 b its velocity 9 relation to ! e!r40 ,!re=e ! possibility ( ! exi/5ce ( a velocity discov]able 9 relation to ! e!r 0 n reg>d$ z an absurdity by ,po9c>4 ,he said3 8,any man :o speaks ( absolute space uses a ^w t has no mean+40 ,x is wor? :ile notic+ t 9 all ?is ! developm5t ( ,po9c>'s ideas betrays a c]ta9 hesitation4 ,speak+ ( exp]im5ts analog\s to ^? ( ,mi*elson1 he said3 8,i "k t x w be said t we are n measur+ its absolute velocity1 b its velocity 9 relation to ! e!r4 ,t is sc>cely satisfactory4 ,is x n cle> t1 if we conceive ! pr9ciple 9 ?is fa%ion1 we c make no d$uctions :atev] f x80 ,f ?is x is evid5t t ,po9c>1 9 spite ( himself & all 8 ef=ts to avoid x1 0 dispos$ to f9d ! di/9ction betwe5 space & e!r 8sc>cely satisfactory40 ,i mu/ admit t ,po9c>'s own argum5t seems to me n :olly satisfactory1 or at lea/ n conv9c+4 8,nature10 says ,fresnel1 8c>es no?+ ab\t analytical difficulties40 ,i imag9e t x c>es j z little ab\t philosophical or purely physical difficulties4 ,x is h>dly an inconte/able crit]ion to suppose t a conception ( ph5om5a is s mu* ne>] to reality ! m 8satisfactory0 x is to u1 or ! bett] x is f\nd adapt$ to ! weakness ( ! human m9d4 ,o!rwise we %\ld h to hold1 :e!r we lik$ or no1 t ! univ]se is necess>ily adapt$ to ! categories ( ! m9d2 t x is con/itut$ ) a view to giv+ u ! lea/ possible intellectual tr\ble4 ,t w\ld be a /range return to an?ropoc5tric f9alism & conceit6 ,! fact t vehicles d n pass !re1 & t p$e/rians h to turn back1 does n prove t !re are no su* ?+s z no-?or\ghf>es 9 our t[ns4 ,x is possible1 ev5 probable1 t ! univ]se also1 consid]$ z an object ( sci5ce1 has its no-?or\ghf>e4 ,cle>ly "o may reply to me t x is n ! univ]se t is adapt$ to our m9d1 b ! m9d t has become adapt$ to ! univ]se 9 ! evolution>y c\rse ( _! relations to ea* o!r4 ,! m9d ne$s 9 its evolution to adapt itself to ! univ]se1 9 con=mity ) ! pr9ciple ( m9imum action =mulat$ by ,f]mat3 p]haps ! mo/ pr(\nd pr9ciple ( ! physical1 biological1 & moral _w4 ,9 t respect ! simple/ & mo/ economical ideas are ! ne>e/ to reality4 ,yes1 b :at pro( is !re t our m5tal evolution is complete & p]fect1 especially :5 we are deal+ ) ph5om5a ( :i* our organism is ins5sible8 99 99 99 99 99 ,exp]im5t alone has prov$1 & _h ! "r to prove1 t x is impossible to measure ! velocity ( an object relatively to ! e!r4 ,at all ev5ts1 ?is is n[ settl$4 ,aft] all1 s9ce x is evid5tly 9 ! v nature ( ?+s t we _c detect an absolute movem5t1 is x n because ! velocity ( ! e>? 9 relation to ! e!r is an absolute velocity t we h be5 unable to detect x8 ,possibly2 b x _c be prov$4 ,if x is s--:i* is n at all c]ta9--x is 9 ! la/ resort exp]i5ce1 ! "o s\rce ( tru?1 :i* ?us t5ds to prove1 indirectly1 t ! e!r is really id5tical ) space4 ,9 t case1 h[ev]1 a space devoid ( e!r1 or "o conta9+ sph]es ( e!r1 w\ld no long] be conceivable1 & !re c be no?+ b a s+le mass ( e!r ) />s float+ 9 x4 ,9 a ^w1 ! negative result ( ,mi*elson's exp]im5t c\ld n be d$uc$ a priori f ! problematical id5tity ( absolute space & ! e!r2 b ?is negative result does n ju/ify u 9 d5y+ ! id5tity a po/]iori4 ,let u return to our prop] subject1 ! ,fitzg]ald-,lor5tz hypo!sis :i* expla9s ! issue ( ! ,mi*elson exp]im5t1 & :i* 0 9 a s5se ! spr+-bo>d = ,e9/e9's leap4 ,! hypo!sis is z foll[s4 ,! result ( ! exp]im5t is t1 :]eas :5 ! pa? ( a ray ( light betwe5 two mirrors is transv]se to ! e>?'s motion ?r\gh e!r1 & x is !n made p>allel to ! e>?'s motion1 ! pa? ought to be long]1 we actually f9d no su* l5g!n+4 ,accord+ to ,fitzg]ald & ,lor5tz1 ?is is because ! two mirrors approa*$ ea* o!r 9 ! second "p ( ! exp]im5t4 ,to put x diff]5tly1 ! frame 9 :i* ! mirrors 7 fix$ contract$ 9 ! direction ( ! e>?'s motion1 & ! contraction 0 su* 9 magnitude z to comp5sate exactly = ! l5g!n+ ( ! pa? ( ! ray ( light :i* we ought to h detect$4 ,:5 we repeat ! exp]im5t ) all k9ds ( diff]5t app>atus1 we f9d t ! result is always ! same 7no displacem5t ( ! fr+es74 ,x foll[s t ! "* ( ! mat]ial ( :i* ! in/rum5t is made--metal1 glass1 /one1 wood1 etc4--has no?+ to d ) ! result4 ,!re=e all bodies und]go an equal & simil> contraction 9 ! direction ( _! velocity relatively to ! e!r4 ,?is contraction is su* t x exactly comp5sates = ! l5g!n+ ( ! pa? ( ! rays ( light betwe5 two po9ts ( ! app>atus4 ,9 o!r words1 ! contraction is great] 9 proportion z ! velocity ( bodies relatively to ! e!r becomes great]4 ,t is ! explanation propos$ by ,fitzg]ald4 ,at fir/ x seem$ to be v /range & arbitr>y1 yet !re 01 app>5tly1 no o!r way ( expla9+ ! result ( ,mi*elson's exp]im5t4 ,moreov]1 :5 y reflect on x ?is contraction is f\nd to be less extraord9>y1 less />tl+1 ?an "o's common s5se at fir/ pron\nces x4 ,if we ?r[ "s non-rigid object1 su* z "o ( ^? little balls ) :i* *ildr5 play1 quickly aga9/ an ob/acle1 we see t x is slightly pu%$ 9 at ! surface by ! ob/acle1 precisely 9 ! same s5se z ! ,fitzg]ald-,lor5tz contraction4 ,! ball is no long] r\nd4 ,x is a little flatt5$1 s t its diamet] is %ort5$ 9 ! direction ( ! ob/acle4 ,we h mu* ! same ph5om5on1 ?\gh 9 a m viol5t =m1 :5 a bullet is flatt5$ aga9/ a t>get4 ,!re=e1 if solid bodies are ?us capable ( de=mation--z !y are1 = cold is suffici5t ( itself to conc5trate _! molecules m closely--!re is no?+ absurd or impossible 9 suppos+ t a viol5t w9d ( e!r may press !m out ( %ape4 ,b x is f> less easy to admit t ?is alt]ation may be exactly ! same1 9 ! giv5 conditions1 = all bodies1 :atev] be ! mat]ial ( :i* !y are compos$4 ,! little ball we ref]r$ to w\ld by no means be flatt5$ s mu* if x 7 made ( /eel in/ead ( rubb]4 ,moreov]1 !re is 9 ?is explanation some?+ q improbable1 some?+ t %ocks bo? our good s5se & t c>icature ( x :i* we call common s5se4 ,is x possible to admit t ! contraction ( bodies always exactly comp5sates = ! optic effect :i* we seek1 :atev] be ! conditions ( ! exp]im5t 7& !y h be5 greatly v>i$78 ,is x possible to admit t nature acts z if x 7 play+ hide-&-seek ) u8 ,by :at my/]i\s *ance c !re be a special circum/ance1 provid5tially & exactly comp5sat+ = e ph5om5on8 ,cle>ly !re mu/ be "s aff9ity1 "s hidd5 connection1 betwe5 ?is my/]i\s mat]ial contraction ( ,fitzg]ald & ! l5g!n+ ( ! light pa? = :i* x comp5sates4 ,we %all see pres5tly h[ ,e9/e9 has illum9$ ! my/]y1 reveal$ ! me*anism :i* connects ! two ph5om5a1 & ?r[n a broad & brilliant light ^u ! :ole subject4 ,b we mu/ n anticipate4 ,! contraction ( ! app>atus 9 ,mi*elson's exp]im5t is extremely slight4 ,x is s slight t if ! l5g? ( ! in/rum5t 7 equal to ! diamet] ( ! e>?--t is to say1 #h1jjj miles--x w\ld be %ort5$ 9 ! direction ( ! e>?'s motion by only six & a half c5timetres6 ,9 o!r words1 ! contraction w\ld be f> too small to be 9 any way measurable 9 ! laboratory4 ,!re is a fur!r reason = ?is4 ,ev5 if ,mi*elson's app>atus 7 %ort5$ by sev]al in*es--t is to say1 if ! e>? travell$ ?\s&s ( times z rapidly z x does r\nd ! sun--we c\ld n detect & measure x4 ,! measur+ rods :i* we w\ld use = ! purpose w\ld contract 9 ! same proportion4 ,! de=mation ( any object by a ,fitzg]ald-,lor5tz contraction c\ld n be e/abli%$ by any obs]v] on ! e>?4 ,x c\ld be discov]$ only by an obs]v] :o did n %>e ! movem5t ( ! e>?3 an obs]v] on ! sun1 = in/ance1 or on a sl[-mov+ planet l ,jupit] or ,saturn4 ,micromegas w\ld1 be=e he left 8 planet to visit u1 h be5 able to discov]1 by optical means1 t our globe is %ort5$ by sev]al in*es 9 ! direction ( its orbital movem5t2 suppos+ t ,voltaire's g5ial h]o 7 provid$ ) trigonometrical app>atus inf9itely m delicate ?an t us$ by our surveyors & a/ronom]s4 ,b :5 he rea*$ ! e>?1 ,micromegas1 ) all 8 precise app>atus1 w\ld h f\nd x impossible to detect ! contraction4 ,he w\ld h be5 greatly surpris$--until he met ,e9/e9 & he>d1 z we %all he>1 ! explanation ( ! my/]y4 ,i h1 un=tunately1 nei!r ! "t nor ! space--x is "h1 especially1 t space is relative1 & is con/antly %ort5$ by ! fl[ ( ! p5--to give ! dialogue :i* w\ld h tak5 place betwe5 ,micromegas & ,e9/e94 ,p]haps1 inde$1 if we are to be fai?ful to ! ,voltairean orig9al1 ! dialogue w\ld h be5 v sup]ficial1 =--to speak confid5tially--,i believe t ,voltaire nev] q und]/ood ,newton1 ?\gh he wrote mu* ab\t him1 & ,newton 0 less difficult to und]/& ?an ,e9/e9 is4 ,nei!r did ,mme4 du ,*telet1 = all ! praise t has be5 lavi%$ ^u h] translation ( ! immortal ,pr9cipia4 ,x sw>ms ) mean+less passages :i* %[ t1 :e!r %e knew ,lat9 or no1 %e did n und]/& ,newton4 ,b all ?is is ano!r /ory1 z ,kipl+ w\ld say4 ,! movem5t ( ! app>atus 9 ! e!r v>ies 9 spe$ accord+ to ! h\r & ! mon? 9 :i* ! ,mi*elson & simil> exp]im5ts are made4 ,z ! comp5sation is always precise1 we may try to calculate ! exact law :i* gov]ns ! contraction z a function ( velocities1 & makes x1 z we f9d1 a precise comp5sation = ! latt]4 ,lor5tz has done ?is4 ,tak+ ,v z ! velocity ( light & v z ! velocity ( ! body mov+ 9 e!r1 ,lor5tz f\nd t1 9 ord] to h comp5sation 9 all cases1 ! l5g? ( ! mov+ body mu/ be %ort5$1 9 ! plane ( its progress1 9 ! proportion ( 7 v 7 #a to 7#a ---------------- 74 7 ,v 7 ,if we take by way ( illu/ration ! case ( ! orbital movem5t ( ! e>?1 :]e v is equal to ?irty kilometres1 we f9d t ! e>? contracts 9 ! plane ( its orbit 9 ! proportion 7 #a 7 7#a ---------------------- 74 7 #ajj1jjj1jjj 7 ,! diff]5ce betwe5 ^! two numb]s is _/111 & ! two hundr$ million? "p ( ! e>?'s diamet] is equal to #f c5timetres4 ,x is ! figure we _h already f\nd4 ,?is =mula1 :i* gives ! value ( ! contraction 9 all cases1 is elem5t>y4 ,ev5 ! inexp]t c easily see ! mean+ ( x4 ,x enables u to calculate ! ext5t ( contraction = e rate ( velocity4 ,we c easily d$uce f x t if ! e>?'s orbital motion 71 n #cj kilometres1 b #bfj1jjj kilometres a second1 x w\ld be %ort5$ by "o-half its diamet] 9 ! plane ( its motion 7)\t any *ange 9 its dim5sions 9 ! p]p5dicul>74 ,at t spe$ a sph]e becomes a flatt5$ ellipsoid1 ( :i* ! small axis is only half ! l5g? ( ! l>g] axis2 a squ>e becomes a rectangle1 ( :i* ! side p>allel to ! motion is twice z small z ! o!r4 ,^! de=mations w\ld be visible to a /ation>y spectator1 b !y w\ld be imp]ceptible to an obs]v] :o %>es ! movem5t1 = ! reason already giv54 ,! measur+ rods & in/rum5ts1 & ev5 ! eye ( ! obs]v]1 w\ld be equally & simultane\sly alt]$4 ,?9k ( ! di/ort+ mirrors :i* "o sees at times 9 places ( amusem5t4 ,"s %[ y a greatly elongat$ picture ( y\rself1 )\t alt]+ y\r bread?4 ,o!rs %[ y ( y\r normal height1 b grotesquely enl>g$ 9 wid?4 ,try1 n[1 to measure y\r height & bread? ) a rule1 z !y are giv5 9 ^! de=m$ reflections 9 ! mirror4 ,if y\r real height is #e feet #f in*es1 & y\r real wid? #b feet1 ! rule w1 :5 y apply x to ! /range reflection ( y\rself 9 ! glass1 m]ely tell y t ?is figure is #e feet #f in*es 9 height & #b feet 9 bread?4 ,! rule z se5 9 ! mirror und]goes ! same di/ortion z y\rself4 ,h5ce x is t1 ev5 if ! globe ( ! e>? _h ! fanta/ic spe$ :i* we sugge/$ above1 its inhabitants w\ld h no means ( discov]+ t !y & x 7 %ort5$ by "o-half 9 ! plane ea/ to we/4 ,a man #e feet #f in*es 9 height1 ly+ 9 a l>ge squ>e b$ 9 ! direction nor?-s\?1 !n *ang+ 8 position to ea/-we/1 w\ld1 q unkn[n to himself1 h 8 l5g? r$uc$ to #b feet #i in*es4 ,at ! same "t he w\ld become twice z /\t z be=e1 because previ\sly 8 bread? 0 ori5tat$ f ea/ to we/4 ,b ! e>? travels at ! rate ( only ?irty kilometres a second1 & its entire contraction is only a matt] ( a few c5timetres4 ,9 contra/ ) ! e>?'s velocity1 ! spe$ ( our mo/ rapid means ( transport is only a small fraction ( a kilometre a second4 ,an a]oplane go+ at #cfj kilometres an h\r has a spe$ ( only #ajj metres a second4 ,h5ce ! maximum ,fitzg]ald-,lor5tz contraction ( our spe$ie/ ma*9es c only be su* an inf9itesimal fraction ( an in* t x is entirely imp]ceptible to u4 ,t is :y--t is ! only reason :y--! solid objects ) :i* we are famili> seem to keep a con/ant %ape1 at :atev] spe$ !y pass be=e our eyes4 ,x w\ld be q o!rwise if _! spe$ 7 hundr$s ( ?\s&s ( times great]4 ,all ?is is v /range1 v surpris+1 v fanta/ic1 v difficult to admit4 ,yet x is a fact1 if !re really is ?is ,fitzg]ald-,lor5tz contraction1 :i* has s f> prov$ ! only possible explanation ( ! ,mi*elson exp]im5t4 ,b we h already se5 "s ( ! difficulties t we f9d 9 ent]ta9+ ! exi/5ce ( ?is contraction4 ,!re are o!rs4 ,if all t we h j said is true1 only objects :i* are /ation>y 9 ! e!r w\ld reta9 _! true %apes1 = ! %ape is alt]$ z soon z !re is movem5t ?r\gh ! e!r4 ,h5ce1 among/ ! objects :i* we ?9k sph]ical 9 ! mat]ial _w 7planets1 />s1 projectiles1 drops ( wat]1 & s on71 !re w\ld be "s t really are sph]es1 :il/ o!rs w\ld1 on acc\nt ( ! spe$ or sl[ness ( _! movem5ts1 be m]ely elongat$ or flatt5$ ellipsoids1 alt]$ 9 %ape by _! velocity4 ,among/ ! v>i\s squ>e objects1 "s w\ld be really squ>e1 :ile o!rs1 travell+ at diff]5t spe$s relatively to ! e!r1 w\ld be r rectangles1 %ort5$ on _! long] sides ow+ to _! velocity4 ,& x is suppos$ t we w\ld h no means ( kn[+ :i* ( ^! objects mov+ at diff]5t spe$s are really %ap$ z we ?9k & :i* are %ap$ o!rwise1 because1 z ! ,mi*elson exp]im5t proves1 we _c detect a velocity relatively to ! e!r4 ,?is we utt]ly decl9e to believe1 say ! ,relativi/s4 ,!re are too _m difficulties ab\t ! matt]4 ,:y speak p]si/5tly1 z ,lor5tz does1 ( velocities 9 relation to ! e!r1 :5 no exp]im5t c detect su* a velocity1 yet exp]im5t is ! sole s\rce ( sci5tific tru?8 ,:y1 on ! o!r h&1 admit t "s ( ! objects we p]ceive h ! privilege ( appe>+ to u 9 _! real %ape1 )\t alt]ation1 :ile o!rs d n8 ,:y admit su* a ?+ :5 x is1 ( its v nature1 repugnant to ! _s ( sci5ce1 :i* is always oppos$ to exceptions 9 nature--sci5ce deals only ) g5]al laws--especially :5 ! exceptions are imp]ceptible8 ,t 0 ! /ate ( affairs--v advanc$ f ! po9t ( view ( ! ma!matical expression ( ph5om5a1 b v confus$1 deceptive1 contradictory1 & tr\blesome f ! physical po9t ( view--:5 8at l5g? ,malh]be arriv$0 444 ,i mean ,e9/e94 ,,*apt] ,,iii ,,e9/e9',s ,,solution ,provisional rejection ( e!r--,relativi/ int]pretation ( ,mi*elson's exp]im5t--,new aspect ( ! spe$ ( light--,explanation ( ! contraction ( mov+ bodies--,"t & ! f\r dim5sions ( space--,e9/e9's 8,int]val0 ! only mat]ial reality4 ,e9/e9's fir/ act ( intellig5t audacity 0 t1 )\t relegat+ ! e!r to ! category ( ^? obsolete fluids1 su* z phlogi/on & animal spirits1 :i* ob/ruct$ ! av5ues ( sci5ce until ,lavoisi] appe>$--)\t d5y+ all reality to e!r1 = !re mu/ be "s sort ( support = ! rays :i* rea* u f ! sun--he obs]v$ t1 9 all t we h z yet se51 !re is always "q ( velocities relatively to ! e!r4 ,we h no means :atev] ( e/abli%+ su* velocities1 & p]haps x w\ld be simpl] to leave out ( our argum5ts ?is entity1 real or o!rwise1 :i* is inaccessible & m]ely plays ! futile & tr\blesome "p ( fif? :eel to ! electro-magnetic *>iot 9 ! progress ( physici/s along ! ruts ( _! difficulties4 ,! fir/ po9t is !n3 ,e9/e9 beg9s1 provisionally1 by omitt+ ! e!r f 8 l9e ( reason+4 ,he nei!r d5ies nor affirms its exi/5ce4 ,he beg9s by ignor+ x4 ,we w n[ foll[ 8 example4 ,we %all no long]1 9 ! c\rse ( our demon/ration1 speak ab\t ! m$ium 9 :i* light travels4 ,we %all consid] light only 9 relation to ! be+s or mat]ial objects :i* emit or receive x4 ,we %all f9d t our progress becomes at once mu* easi]4 ,= ! mom5t we w relegate ! e!r ( ! physici/s to ! /ore ( useless accessories1 along ) ! suave1 =mless1 vague--b s preci\s arti/ically--e!r ( ! poets4 99 99 99 99 99 ,%ortly1 :at does ,mi*elson's exp]im5t prove8 ,only t a ray ( light travels at ! surface ( ! e>? f we/ to ea/ at exactly ! same spe$ z f ea/ to we/4 ,let u imag9e two simil> guns 9 ! middle ( a pla91 bo? fir+ at ! same mom5t1 9 calm wea!r1 & dis*>g+ _! %ells ) ! same initial velocity1 b "o t[>d ! we/ & ! o!r t[>d ! ea/4 ,x is cle> t ! two %ells w take ! same "t to trav]se an equal am\nt ( space1 "o go+ t[>d ! we/ & ! o!r t[>d ! ea/4 ,! rays ( light :i* we produce on ! e>? behave 9 ?is respect1 z reg>ds _! progress1 exactly z ! %ells d4 ,!re w\ld !re=e be no?+ surpris+ 9 ! result ( ! ,mi*elson exp]im5t1 if we knew only :at exp]i5ce tells u ab\t ! lum9\s rays4 ,b let u pu% ! comp>ison fur!r4 ,let u consid] ! %ell fir$ by "o ( ! guns1 & imag9e t x hits a t>get at a c]ta9 spot1 & t1 :5 x rea*es ! t>get1 ! residual velocity ( ! %ell is1 let u say1 fifty metres a second4 ,i imag9e ! t>get m\nt$ on a motor tractor4 ,if ! latt] is /ation>y ! velocity ( ! %ell 9 relation to ! t>get w be1 z we said1 fifty metres a second at ! po9t ( impact4 ,b let u suppose t ! tractor & ! t>get are mov+ at a spe$ (1 = in/ance1 t5 metres a second t[>d ! gun1 s t ! t>get passes to its prec$+ position exactly at ! mom5t :5 ! %ell /rikes x4 ,x is cle> t ! velocity ( ! %ell relatively to ! t>get at ! mom5t ( impact w n n[ be fifty metres1 b #ej #aj #fj metres a second4 ,x is equally evid5t t ! spe$ w fall to #ej-aj #dj metres a second if 7o!r ?+s be+ equal7 ! t>get is travell+ away f ! gun1 in/ead ( t[>d x4 ,if1 9 ! latt] case1 ! velocity ( ! t>get 7 equal to t ( ! %ell1 x is cle> t ! relative velocity ( ! %ell w\ld n[ be nil4 ,s mu* is cle> en\gh4 ,t is h[ juggl]s 9 ! music-halls c cat* eggs fall+ f a height on plates )\t break+ !m4 ,x is en\gh to give ! plate1 at ! mom5t ( contact1 a slight d[nw>d velocity1 :i* less5s by s mu* ! velocity ( ! %ock4 ,t is also h[ skill$ box]s make a movem5t backw>d be=e a bl[1 & ?us less5 its effective =ce1 :]eas ! bl[ is all ! h>d] if !y advance to meet x4 ,if ! lum9\s rays behav$ 9 all respects l ! %ells1 z !y d 9 ! ,mi*elson exp]im5t1 :at w\ld be ! result8 ,:5 "o advances v rapidly to meet a ray ( light1 "o ought to f9d its velocity increas$ relatively to ! obs]v]1 & less5$ if ! obs]v] rec$es be=e x4 ,if ?is 7 ! case1 all w\ld be simple2 ! laws ( optics w\ld be ! same z ^? ( me*anics2 !re w\ld be no contradiction to s[ discord 9 ! peaceful army ( our physici/s1 & ,e9/e9 w\ld h _h to sp5d ! res\rces ( 8 g5ius on o!r matt]s4 ,un=tunately--p]haps we ought to say =tunately1 because1 aft] all1 x is ! un=ese5 & ! my/]i\s t l5d "s *>m to ! way ( ! _w--?is is n ! case4 ,bo? physical & a/ronomical obs]vation %[ t1 "u all conditions1 :5 an obs]v] advances rapidly t[>d lum9\s waves or rec$es rapidly f !m1 !y /ill %[ always ! same velocity relatively to him4 ,to take a p>ticul> case1 !re are 9 ! heav5s />s :i* rec$e f u & />s :i* approa* u2 t is to say1 />s f :i* we rec$e1 or :i* we approa*1 at a spe$ ( t5s1 & 9 "s cases hundr$s1 ( miles a second4 ,b an a/ronom]1 de ,sitt]1 has prov$ t ! velocity ( ! light :i* rea*es u is1 = u1 always exactly ! same4 ,?us1 up to ! pres5t x has prov$ q impossible = u1 by any device or movem5t1 to add to or less5 9 ! lea/ ! velocity ) :i* a ray ( light rea*es u4 ,! obs]v] f9ds t ! rate ( spe$ ( ! light is always exactly ! same relatively to himself1 :e!r ! light comes f a s\rce :i* rapidly approa*es or rec$es f him1 :e!r he is advanc+ t[>d x or retreat+ be=e x4 ,! obs]v] c always increase or less51 relatively to himself1 ! spe$ ( a %ell1 a wave ( s\nd1 or any mov+ object1 by pu%+ t[>d or mov+ away f ! object4 ,:5 ! mov+ object is a ray ( light1 he c d no?+ ( ! k9d4 ,! spe$ ( a vehicle _c 9 any case be add$ to t ( ! light x receives or emits1 or be subtract$ f x4 ,?is fix$ spe$ ( ab\t #ahf1jjj miles a second1 :i* we f9d always 9 ! case ( light1 is 9 _m respects analog\s to ! temp]ature ( #bgc bel[ z]o :i* is kn[n z 8absolute z]o40 ,?is also is1 9 nature1 an impassable limit4 ,all ?is proves t ! laws :i* gov]n optical ph5om5a are n ! same z ! classic laws ( me*anical ph5om5a4 ,x 0 = ! purpose ( reconcil+ ^! app>5tly contradictory laws t ,lor5tz1 foll[+ ,fitzg]ald1 gave u ! /range hypo!sis ( contraction4 99 99 99 99 99 ,b we %all n[ f9d ,e9/e9 %[+ u1 9 lum9\s fa%ion1 t ?is contraction is se5 to be p]fectly natural :5 we ab&on c]ta9 conceptions--p]haps errone\s1 ?\gh classical--:i* rul$ our habitual & traditional way ( e/imat+ l5g?s ( space & p]iods ( "t4 ,take any object--a measur+ rod1 = in/ance4 ,:at is x t settles = u ! app>5t l5g? ( ! rod8 ,x is ! image made ^u our ret9a by ! two rays t come f ! two ends ( ! rod1 & :i* rea* our eye simultane\sly4 ,i italicise ! ^w1 because x is ! key ( ! :ole matt]4 ,if ! rod is /ation>y be=e u1 ! case is simple4 ,b if x is mov$ :ile we are look+ at x1 ! case is less simple4 ,x is s mu* less simple t be=e ! "w ( ,e9/e9 mo/ ( our le>n$ m5 & ! :ole ( classic sci5ce ?\ght t ! in/antane\s image ( an object t 0 n subject to *ange ( %ape 0 necess>ily & always id5tical1 & indep5d5t ( ! velocities ( ! object & ! obs]v]4 ,! :ole ( classical sci5ce argu$ z if ! spread ( light 0 itself in/antane\s--z if x _h an inf9ite velocity--:i* is n ! case4 ,i /& on ! bank by ! side ( a railway4 ,on ! l9e is a h&some ,pullman c>1 9 :i* x is s pleasant to ?9k t space is relative1 9 ! ,galileian s5se ( ! ^w4 ,close to ! l9e ,i h two pegs fix$1 "o blue1 ! o!r r$1 & !y exactly m>k ! ends ( ! coa* & indicate its l5g?4 ,!n1 )\t leav+ my obs]vation-po/ on ! bank1 my face turn$ t[>ds ! middle ( ! coa*1 ,i give ord]s = ! coa* to be drawn back & c\pl$ to a locomotive ( unhe>d-( p[]1 :i* is to c>ry ! coa* pa/ me at a fanta/ic spe$1 millions ( times fa/] ?an ! spe$ any m]e eng9e] c\ld provide4 ,su* is ! pot5tial sup]iority ( ! imag9ation ov] sob] reality6 ,i assume fur!r t my ret9a is p]fect1 & is s con/itut$ t ! visual impressions w rema9 on x only z long z ! light :i* causes !m4 ,^! some:at arbitr>y suppositions c\nt = no?+ 9 ! ess5ce ( ! demon/ration4 ,!y are only = ! sake ( conv5i5ce4 ,n[ = ! "q4 ,w ! coa* 7:i* ,i assume to be ( "s rigid metal71 z x passes be=e me at full spe$1 seem to me to be exactly ! same l5g? z x did :5 x 0 at re/8 ,to put x diff]5tly1 at ! mom5t :5 ,i see its front end co9cide ) ! blue peg ,i _h plant$1 %all ,i see its back end co9cide at ! same "t ) ! r$ peg8 ,to ?is "q ,galileo1 ,newton1 & all ! support]s ( classic sci5ce w\ld reply yes4 ,yet accord+ to ,e9/e9 ! answ] is no4 ,"h is ! simple pro(1 z we d$uce x f ,e9/e9's g5]al idea4 ,i am1 recollect1 on ! edge ( ! track1 at an equal di/ance f bo? pegs4 ,:5 ! front end ( ! coa* co9cides ) ! blue peg1 x s5ds t[>d my eye a c]ta9 ray ( light 7:i*1 = conv5i5ce1 we w call ! front ray71 & ?is co9cides ) ! lum9\s ray com+ to me f ! blue peg4 ,?is front ray rea*es my eye at ! same "t z a c]ta9 ray t comes f ! back end ( ! coa* 7:i* we w call ! back ray74 ,does ! back ray co9cide ) ! ray :i* comes to me f ! r$ peg8 ,cle>ly n4 ,! front ray leaves ! front end ( ! coa* at ! same spe$ z ! back ray leaves ! back end2 z any obs]v] 9 ! coa* w\ld f9d :o c>$ to try ! ,mi*elson exp]im5t on !m4 ,b ! front end ( ! coa* is rec$+ f me :ile ! back end is approa*+ me4 ,h5ce ! front ray travels t[>d my eye m sl[ly ?an ! back ray1 ?\gh ,i _c p]ceive ?is1 z1 :5 !y rea* me1 ,i f9d t !y bo? h ! same velocity4 ,h5ce ! back ray1 :i* rea*es my eye at ! same "t z ! front ray1 mu/ h left ! back end ( ! coa* lat] ?an ! front ray left ! front end ( ! coa*4 ,!re=e1 :5 ,i see ! front end ( ! coa* co9cide ) ! blue peg1 ,i at ! same "t see ! back end ( ! c>riage aft] x has pass$ ! r$ peg4 ,!re=e ! l5g? ( a coa* travell+ at full spe$1 & su* z x appe>s to me1 is %ort] ?an ! di/ance betwe5 ! two pegs1 :i* indicat$ ! l5g? ( ! coa* at re/4 ,q4,e4,d4 ,v little att5tion is ne$$ = any p]son to und]/& ?is argum5t1 ?\gh its elem5t>y simplicity has n be5 atta9$ )\t difficulty4 ,x is "p ( ,e9/e9's ma!matical argum5t & ( 8 conception ( simultaneity4 99 99 99 99 99 ,x foll[s t ! coa*1 or1 9 g5]al1 any object1 seems to be contract$ 9 virtue ( its velocity1 & 9 ! direction ( t velocity1 relatively to ! spectator4 ,! same ?+ happ5s1 obvi\sly1 if ! obs]v] moves 9 relation to ! object1 because we c "k only relative velocities1 9 virtue ( ! ,classical ,pr9ciple ( ,relativity ( ,newton & ,galileo4 ,9 ?is new light ! ,lor5tz-,fitzg]ald contraction becomes intelligible1 or at lea/ admissible4 ,! contraction1 ?us consid]$1 is n ! cause ( ! negative result ( ! ,mi*elson exp]im5t3 x is an effect ( x4 ,x is n[ q cle>1 & we see t !re 0 some?+ wrong ) ! classical way ( e/imat+ ! in/antane\s dim5sion ( objects4 ,c]ta9ly ! fact t lum9\s rays1 />t+ out f _! s\rces at diff]5t spe$s1 %\ld h ! same spe$ :5 !y rea* our eye1 is /range4 ,x upsets our habitual way ( look+ at ?+s4 ,if ,i may v5ture to use a comp>ison simply = ! purpose ( provok+ reflection1 n at all 9 ! way ( explanation1 we h "h some?+ analog\s to :at happ5s ) ! bombs ( aviators4 ,bombs ( a giv5 type1 :e!r releas$ at a height ( #e1jjj or ( #aj1jjj metres1 :i* !re=e h v diff]5t d[nw>d velocities at #e1jjj metres f ! gr\nd1 h always ! same residual velocity :5 !y rea* ! gr\nd4 ,?is is due to ! mod]at+ & equalis+ influ5ce ( ! atmosph]ic resi/ance1 :i* prev5ts ! spe$ f increas+ indef9itely1 & makes x con/ant :5 x has atta9$ a c]ta9 value4 ,mu/ we suppose t !re is r\nd our eye & r\nd objects a sort ( field ( resi/ance :i* sets a simil> limit to ! light8 ,:o kn[s8 ,b p]haps su* que/ions h no mean+ = ! physici/4 ,he c "k no?+ ab\t ! behavi\r ( light except :5 x leaves its s\rce or :5 x rea*es ! eye1 :e!r arm$ ) in/rum5ts or no4 ,he _c le>n h[ x behaves dur+ its passage across ! int]m$iate space1 9 :i* !re is no matt]4 ,inde$1 ! m deeply we /udy ! new physics1 ! m we see t x d]ives almo/ all its /r5g? f its sy/ematic disda9 ( all t is beyond ph5om5a1 all t _c fall "u exp]im5tal obs]vation4 ,x is because x is solely bas$ ^u facts 7h[ev] contradictory !y may be7 t our pro( ( ! necess>y contraction ( objects ow+ to _! velocity relatively to ! obs]v] is s /rong4 99 99 99 99 99 ,we mu/ und]/& ! pr(\nd significance ( ! ,fitzg]ald-,lor5tz contraction4 ,?is app>5t contraction is by no means due to ! movem5t ( objects relatively to ! e!r4 ,x is ess5tially ! effect ( ! movem5ts ( objects & obs]v]s relatively to ea* o!r1 or relative movem5ts 9 ! s5se ( ! old] me*anics4 ,! greate/ relative velocities to :i* we are accu/om$ 9 our daily life are less ?an a few kilometres a second4 ,! initial velocity ( ! %ell fir$ by 8,b]?a0 0 only ab\t #a1cjj metres a second4 ,= movem5ts s sl[ z ?is ! ,relativi/ contraction is entirely negligible4 ,h5ce1 z ! classical me*anics _h nev] obs]v$ su* contraction1 x reg>d$ ! %apes & dim5sions ( rigid objects z indep5d5t ( sy/ems ( ref]5ce4 ,x 0 v ne>ly true2 & t makes all ! diff]5ce betwe5 true & false4 ,to say t #iii1iij #i #a1jjj1jjj1 is to say some?+ t is v ne>ly true1 & is !re=e false4 ,:5 x 0 discov]$ t ! e>? 0 r\nd no *ange 0 made 9 _! proc$ure by ar*itects4 ,!y cont9u$ to build z if ! direction indicat$ by ! plumb-l9e 0 always p>allel to itself4 ,9 ! same way ^? :o make our locomotives & a]oplanes w n h to consid] ! =ms ( ! ma*9es z dep5d5t on _! velocities4 ,:at does x matt]8 ,! practical po9t ( view is n1 & _c be1 t ( sci5ce except indirectly4 ,s mu* ! worse if !re is no indirect influ5ce1 or if x is sl[ 9 com+4 ,"s ye>s ago1 h[ev]1 we discov]$ ?+s :i* move at spe$s1 relatively to u1 ( t5s or hundr$s ( ?\s&s ( kilometres a second2 ! projectiles ( ! ca?ode rays & ( radium4 ,9 ?is case ! ,relativi/ contraction is v consid]able4 ,we %all see h[ x has be5 obs]v$4 ,b let u fir/ recapitulate :at we h se54 ,objects seem to alt] _! %ape 9 ! direction ( _! movem5t & n 9 ! direction p]p5dicul> to ?is4 ,!re=e _! =ms1 ev5 if !y be compos$ ( an ideal & p]fectly rigid mat]ial1 dep5d on _! velocity relatively to ! obs]v]4 ,?is is ! ess5tially new po9t ( view :i* ,e9/e9's 8,special ,relativity0 sup]imposes ^u ! ,relativity ( classical me*anics & philosoph]s4 ,= ^! ! absolute dim5sions ( a rigid object or a geometrical figure 7 n absolute2 x 0 only ! relations ( ^! dim5sions :i* 7 real4 ,! new po9t ( view is t ^! relations are !mselves relative1 because !y are a function ( ! velocity ( ! obs]v]4 ,x is a sort ( ,relativity 9 ! second degree1 ( :i* nei!r ! philosoph]s nor ! classic physici/s _h dream$4 ,spatial relations !mselves are relative1 9 a space :i* is already relative4 ,9 ! case ( our ,pullman c> & ! two pegs :i* m>k its l5g? :5 x is /ation>y1 an obs]v] situat$ 9 ! c>riage w\ld f9d ! di/ance betwe5 ! two pegs %ort5$ z he passes !m4 ,! coa* w\ld seem to him long] ?an ! di/ance betwe5 ! pegs4 ,i :o rema9 beside ! pegs obs]ve ! contr>y4 ,yet ,i h no means ( prov+ to ! pass5g] t he is wrong4 ,i see q pla9ly t ! ray ( light :i* comes f ! back peg runs beh9d ! coa*1 & has !re=e1 relatively to x1 a spe$ ( less ?an #ahf1jjj miles a second4 ,i "k t ?is is ! reason = ! pass5g]'s error1 b ,i h no means ( conv9c+ him t he is wrong4 ,he w always say1 & rightly3 8,i h measur$ ! spe$ at :i* ?is ray rea*es me1 & ,i h f\nd x #ahf1jjj miles a second40 ,ea* ( u is really "r4 ,9 v rapid motion a squ>e w\ld seem to ! obs]v] a rectangle2 a circle w\ld appe> to be an ellipse4 ,if ! e>? travell$ "s ?\s&s ( times fa/] r\nd ! sun1 we %\ld see x elongat$1 l a giant lemon susp5d$ 9 ! heav5s4 ,if an aviator c\ld fly at a fanta/ic spe$ ov] ,trafalg> ,squ>e1 9 ! direction ( ! ,/r&--& if ! impressions on 8 ret9a 7 in/antane\s--he w\ld see ! ,squ>e z a v flatt5$ rectangle4 ,if he flew 9 a diagonal l9e ab\t x1 he w\ld f9d x %ap$ l a loz5ge4 ,if ! same aviator flew across a road on :i* fat cattle 7 be+ driv5 to ! slaught]-h\se1 he w\ld be a/oni%$1 = ! bea/s w\ld seem to him extraord9>ily lean1 :ile !re w\ld be no *ange 9 _! l5g?4 ,! fact t ^! alt]ations ( %ape ow+ to velocity are reciprocal is "o ( ! mo/ curi\s consequ5ces ( all ?is4 ,a man :o c\ld pass 9 e direction among/ 8 fell[s at ! fanta/ic spe$ ( "o ( ,%akespe>e's spirits--let u put x at ab\t #agj1jjj miles an h\r1 ?\gh !re w\ld be no limit--w\ld f9d t 8 fell[s _h become dw>fs only half z l>ge z himself4 ,w\ld he h become a giant1 a sort ( ,gulliv] among/ ! ,lilliputians8 ,n 9 ! lea/4 ,su* is ! ju/ice ( ! s*eme ( e>?ly ?+s t he himself w\ld seem a dw>f to ! p :om he ?\ght small] ?an himself1 & :o are q sure ( ! contr>y4 ,:i* is "r1 & :i* wrong8 ,bo?4 ,ea* po9t ( view is accurate1 b !re are only p]sonal po9ts ( view4 ,aga91 any obs]v] :atev] w only see ?+s t are n connect$ ) him z small]--nev] l>g]--?an ! ?+s :i* are connect$ ) 8 movem5t4 ,if ,i might v5ture to relieve ?is sob] exposition by a reflexion r less au/]e ?an is usual 9 physics1 ,i w\ld say t ! new sy/em af=ds a supreme ju/ification ( egoism1 or1 r1 ( egoc5tricism4 ,x is ! same ) "t z ) space4 ,by simil> reason+ to t :i* has %[n u h[ ! di/ance ( ?+s 9 space is connect$ ) _! velocity relatively to ! obs]v]1 x c be %[n t _! di/ance 9 "t likewise dep5ds ^u ?is4 ,x w\ld be useless to reproduce "h ! :ole ( ! ,e9/e9ian argum5t z to duration4 ,x is analog\s to t :i* we h us$ 9 reg>d to l5g?1 & ev5 simpl]4 ,! result is z foll[s4 ,! "t express$ 9 seconds :i* a tra9 takes to pass f "o /ation to ano!r is %ort] = ! pass5g]s on ! tra9 ?an = u :o wat* x pass1 ?\gh our wat*es may be j ! same z !irs4#e ,simil>ly1 all ! ge/ures ( m5 :o are on mov+ vehicles w seem to a /ation>y obs]v] sl[$ d[n1 & !re=e prolong$1 & vice v]sa4 ,b ! velocity w\ld1 z 9 ! case ( v>iation 9 l5g?1 h to be fanta/ic to make ^! v>iations 9 "t p]ceptible4 #e ,! be/ def9ition ( ! second t c be giv5 is ! foll[+3 x is ! "t :i* light takes to cov] #ahf1jjj miles 9 empty space & f> f any /rong gravitational field4 ,?is def9ition1 ! only /rict def9ition1 is fur!r ju/ifi$ by ! fact t !re is no bett] means ( regulat+ clocks ?an lum9\s or ,h]tzian 7:i* h ! same spe$7 signals4 ,x is n less true t ! "t betwe5 ! bir? & ! dea? ( any creature1 its life1 w seem long] if ! creature moves rapidly & fanta/ically relatively to ! obs]v]4 ,9 ?is _w1 :]e appe>ance is almo/ ev]y?+1 ?is is n )\t importance1 & x foll[s t1 philosophically speak+1 to move on is to la/ long]2 b = o!rs1 n = oneself2 j z o!rs may seem to me to la/ long]4 ,a /rik+1 a pr(\nd1 an un=ese5 ju/ification ( ! words ( ! sage3 immobility is dea?6 99 99 99 99 99 ,=m]ly1 be=e ! ,e9/e9ian hegira1 be=e ! ,relativi/ ,era op5$1 ev]ybody 0 conv9c$ t ! portion ( space occupi$ by an object 0 suffici5tly & explicitly def9$ by its dim5sions--l5g?1 bread?1 & height4 ,^! are :at are call$ ! ?ree dim5sions ( an object2 j z we speak1 to use a diff]5t expression1 ( ! longitude1 latitude1 & altitude ( ea* ( its po9ts1 or z we speak 9 a/ronomy ( its "r asc5sion1 decl9ation1 & di/ance4 ,x 0 q und]/ood t we _h1 9 addition1 to indicate ! epo*1 ! mom5t1 to :i* ^! data correspond4 ,if ,i def9e ! position ( an a]oplane by its longitude1 latitude1 & altitude1 ^! indications are only correct = a c]ta9 mom5t1 because ! a]oplane is mov+ relatively to ! obs]v]1 & ! mom5t also mu/ be indicat$4 ,9 ?is s5se x has long be5 kn[n t space dep5ds ^u "t4 ,b ! ,relativi/ !ory %[s t x dep5ds ^u "t 9 a mu* m intimate & deep] mann]1 & t "t & space are z closely connect$ z ^? tw9 mon/]s :i* ! surgeon _c sep>ate )\t kill+ bo?4 ,! dim5sions ( an object1 its %ape1 ! app>5t space occupi$ by x1 dep5d ^u its velocity3 t is to say1 ^u ! "t :i* ! obs]v] takes to trav]se a c]ta9 di/ance relatively to ! object4 ,"h we h space already dep5d+ ^u "t4 ,9 addition1 ! obs]v] measures ! "t ) a *ronomet]1 ! seconds ( :i* are m or less accel]at$ accord+ to 8 velocity4 ,h5ce x is impossible to def9e space )\t "t4 ,t is :y we n[ say t "t is ! f\r? dim5sion ( space1 or t ! space 9 :i* we live has f\r dim5sions4 ,x is rem>kable t !re 7 able m5 9 ! pa/ :o _h a m or less cle> intuition ( ?is4 ,?us we f9d ,did]ot1 9 #aggg1 writ+ 9 ! ,encyclopdie1 9 ! article 8,dim5sion03 8,i h already said t x is impossible to conceive m ?an ?ree dim5sions4 ,a le>n$ man ( my acqua9tance1 h[ev]1 believes t "o might reg>d duration z a f\r? dim5sion1 & t ! product ( "t by solidity w\ld be1 9 a s5se1 a product ( f\r dim5sions4 ,! idea may n be admitt$1 b x seems to be n )\t m]it1 if x be only ! m]it ( orig9ality40 ,x 0 algebra1 und\bt$ly1 t gave rise to ! idea ( a space ) m ?an ?ree dim5sions4 ,s9ce1 9 po9t ( fact1 l9es or spaces ( "o dim5sion are repres5t$ by algebraical expressions ( ! fir/ degree1 surfaces or spaces ( two dim5sions by =mul ( ! second degree1 & volumes or spaces ( ?ree dim5sions by expressions ( ! ?ird degree1 x 0 natural to ask oneself if =mul ( ! f\r? & high] degrees are n also ! algebraical repres5tation ( "s =m ( space ) f\r or m dim5sions4 ,! f\r-dim5sional space ( ! ,relativi/s is1 h[ev]1 n q :at ,did]ot imag9$4 ,x is n ! product ( "t by ext5sion1 = a dim9ution ( "t is n comp5sat$ 9 x by an increase ( space4 ,q ! contr>y4 ,take two ev5ts1 su* z ! successive passage ( our ,pullman c> ?r\gh two /ations4 ,= a pass5g] 9 ! c> ! di/ance betwe5 ! two /ations1 measur$ by ! l5g? ( ! track cov]$1 is1 z we saw1 %ort] ?an = a p]son :o is /&+ /ation>y beside ! l9e4 ,! "t betwe5 pass+ ?r\gh ! two /ations is likewise less = ! fir/ obs]v]4 ,! numb] ( seconds & fractions ( seconds m>k$ by 8 *ronomet] is small] = him1 z we saw4 ,9 a ^w1 di/ance 9 "t & di/ance 9 space dim9i% simultane\sly :5 ! velocity ( ! obs]v] increases1 & bo? increase :5 ! velocity ( ! obs]v] less5s4 ,?us velocity 7velocity relatively to ! ?+s obs]v$1 we mu/ always rememb]7 acts 9 a s5se z a d\ble brake less5+ durations & %ort5+ l5g?s4 ,if a diff]5t illu/ration be pref]r$1 velocity enables u to see bo? spaces & times m obliquely1 at an increas+ly %>p angle4 ,space & "t are !re=e only *ang+ effects ( p]spective4 ,c we conceive space ( f\r dim5sions8 ,t is to say1 c we imag9e or visualise x8 ,ev5 if we _c1 x proves no?+ z reg>ds ! reality ( su* space4 ,dur+ ages no "o conceiv$ su* a ?+ z ! ,h]tzian waves1 & ev5 to-day we h no direct s5se-impression ( !m4 ,!y exi/ none ! less4 ,z a matt] ( fact1 we f9d x difficult to conceive space ( ?ree dim5sions4 ,if x 7 n = our muscul> *anges1 we %\ld "k no?+ ab\t x4 ,a p>alys$ & "o-ey$ man1 t is to say1 a man )\t ! s5sation ( relief :i* we get f b9ocul> vision--& ev5 ?is is1 9 ! fir/ place1 a muscul> s5sation--w\ld1 ) 8 s+le eye1 see all objects on ! same plane1 z on ! drop-sc5e ( a !atre4 ,he c\ld h no p]ception ( ?ree-dim5sional space4 ,i believe !re are p :o c =m an idea ( f\r-dim5sional space4 ,! successive appe>ances ( a fl[] 9 its v>i\s phases ( gr[?1 f ! day :5 x is b a frail gre5 bud until ! "t :5 its exhau/$ petals fall sadly to ! gr\nd1 & ! successive *anges ( its corolla "u ! influ5ce ( ! w9d1 give u a globul> image ( ! fl[] 9 f\r-dim5sional space4 ,are !re any :o c see all ?is toge!r8 ,i believe t !re are1 especially among/ good *ess-play]s4 ,:5 a skilful play] plays well1 x is because he c take 9 ) a s+le glance ( 8 m5tal eye ! :ole *ronological & spatial s]ies ( moves t may foll[ ! fir/ move1 ) all _! effects on ! bo>d4 ,he sees ! :ole s]ies simultane\sly4 ,! words ,i h italicis$ look contradictory4 ,t is because we are 9 a prov9ce :]e x is all b impossible to express ! f9e %ades ( ?+s 9 words4 ,"o might j z well attempt to def9e v]bally all t !re is 9 a symphony ( ,bee?ov54 8,! translator is a traitor40 ,if !re is any tru? 9 ! prov]b1 x is because words are ! organ ( translation4 99 99 99 99 99 ,we h rea*$ a po9t 9 our gradual progress into ,relativi/ physics :]e we h be=e our eyes m]ely a battlefield /rewn ) corpses & ru9s4 ,we _h reg>d$ "t & space z hooks solidly fa/5$ to ! wall beh9d :i* lurks reality1 & on ^! we hang our float+ ideas ( ! mat]ial _w1 j z we hang our coats on ! rack4 ,n[ !y lie1 torn d[n & crumpl$1 among/ ! rubbi% ( anci5t !ories1 victims ( ! hamm]-bl[s ( ! new physics4 ,we knew q well1 ( c\rse1 t ! s\ls ( m5 7 inscrutable to u1 b we did ?9k t we saw _! faces4 ,n[1 z we approa* !m1 we f9d t x is only masks we saw4 ,! mat]ial _w1 z ,e9/e9 %[s x to u1 is a sort ( mask$ ball1 &1 by a deceptive irony1 x is we ourselves :o h made ! black velvet masks & ! gay co/umes4 ,in/ead ( reveal+ reality to u1 space & "t are1 accord+ to ,e9/e91 only mov+ veils1 wov5 by ourselves1 :i* hide x f u4 ,yet--/range & melan*oly reflection--we c no m conceive ! _w )\t space & "t ?an we c obs]ve c]ta9 microbes "u ! microscope )\t fir/ inject+ col\r+ matt] into !m4 ,are "t & space1 !n1 m]ely halluc9ations8 ,&1 if s1 :at is real8 ,no4 ,once ! ,relativi/ has ?r[n d[n ! tott]+ ru9s1 he beg9s to recon/ruct4 ,beh9d ! veils1 n[ torn d[n & trodd5 "u foot1 a new & m subtle reality is ab\t to appe>4 ,if we describe ! univ]se 9 ! usual way1 9 sep>ate categories ( space & "t1 we see t its aspect dep5ds ^u ! obs]v]4 ,happily1 x is n ! same :5 we describe x 9 ! unique category ( ! f\r-dim5sional cont9uum 9 :i* ,e9/e9 locates ph5om5a1 & 9 :i* space & "t are insep>ably unit$4 ,if ,i may v5ture to use ?is illu/ration1 "t & space are l two mirrors1 "o convex1 ! o!r concave1 ! curvature ( :i* is acc5tuat$ 9 proportion to ! velocity ( ! obs]v]4 ,ea* ( ^! mirrors gives u1 sep>ately1 a di/ort$ picture ( ! succession ( ?+s4 ,b ?is is =tunately comp5sat$ = by ! fact t1 :5 we comb9e ! two mirrors s t "o reflects ! rays receiv$ by ! o!r1 ! picture ( ! succession ( ?+s is re/or$ 9 its unalt]$ reality4 ,! di/ance 9 "t & ! di/ance 9 space ( two giv5 ev5ts :i* are close to ea* o!r bo? increase or decrease :5 ! velocity ( ! obs]v] decreases or increases4 ,we h %[n t4 ,b an easy calculation--easy on acc\nt ( ! =mula giv5 previ\sly to express ! ,lor5tz-,fitzg]ald contraction--%[s t !re is a con/ant relation betwe5 ^! concomitant v>iations ( "t & space4 ,to be precise1 ! di/ance 9 "t & ! di/ance 9 space betwe5 two contigu\s ev5ts are num]ically to ea* o!r z ! hypot5use & ano!r side ( a rectangul> triangle are to ! ?ird side1 :i* rema9s inv>iable4#f #f ,9 ! geometrical calculus or repres5tation t may be sub/itut$ = ?is ! hypot5use ( ! triangle is ! di/ance 9 "t1 ea* second be+ repres5t$ by #cjj1jjj kilometres4 ,tak+ ?is ?ird side = base1 ! o!r two w describe1 above x1 a triangle m or less elevat$ accord+ z ! velocity ( ! obs]v] is m or less r$uc$4 ,?is fix$ base ( ! triangle1 ( :i* ! o!r two sides--! spatial di/ance & ! *ronological di/ance--v>y simultane\sly ) ! velocity ( ! obs]v]1 is1 !re=e1 a quantity indep5d5t ( ! velocity4 ,x is ?is quantity :i* ,e9/e9 has call$ ! ,int]val ( ev5ts4 ,?is 8,int]val0 ( ?+s 9 f\r-dim5sional space-"t is a sort ( conglom]ate ( space & "t1 an amalgam ( ! two4 ,its compon5ts may v>y1 b x rema9s itself inv>iable4 ,x is ! con/ant resultant ( two *ang+ vectors4 ,! 8,int]val0 ( ev5ts1 ?us def9$1 gives u = ! fir/ "t1 accord+ to ,relativi/ physics1 an imp]sonal repres5tation ( ! univ]se4 ,9 ! /rik+ words ( ,m9k[ski1 8space & "t are m]e phantoms4 ,all t exi/s 9 reality is a sort ( intimate union ( ^! entities40 ,! sole reality accessible to man 9 ! ext]nal _w1 ! "o really objective & imp]sonal ?+ :i* is compreh5sible1 is ! ,e9/e9ian ,int]val z we h def9$ x4 ,! ,int]val ( ev5ts is to ,relativi/s ! sole p]ceptible "p ( ! real4 ,ap>t f t !re is some?+1 p]haps1 b no?+ t we c "k4 ,/range de/9y ( human ?\ght6 ,! pr9ciple ( relativity has1 9 virtue ( ! discov]ies ( mod]n physics1 spread its w+s mu* f>!r ?an x did be=e1 & has rea*$ summits :i* 7 ?\ght beyond ! range ( its so>+ flight4 ,yet x is to ?is we owe1 p]haps1 our fir/ real p]ception ( our weakness 9 reg>d to ! _w ( s5se1 9 reg>d to reality4 ,e9/e9's sy/em1 ( :i* we h n[ to see ! con/ructive "p1 w disappe> "s day l ! o!rs1 = 9 sci5ce !re are m]ely !ories ) 8provisional titles10 nev] !ories ) 8def9itive titles40 ,possibly t is ! reason ( its _m victories4 ,! idea ( ! ,int]val ( ?+s w1 no d\bt1 survive all ^! *anges4 ,! sci5ce ( ! future mu/ be built ^u x4 ,! bold /ructure ( ! sci5ce ( our "t rises ^u x daily4 ,x mu/1 9 f9e1 be cle>ly und]/ood t ! ,e9/e9ian ,int]val tells u no?+ ab\t ! absolute1 ab\t ?+s 9 !mselves4 ,x1 l all o!rs1 %[s u only relations betwe5 ?+s4 ,b ! relations :i* x discloses seem to be real & unv>y+4 ,!y %>e ! degree ( objective tru? :i* classic sci5ce attribut$1 )1 p]haps1 unf\nd$ assurance1 to ! *ronological & spatial relations ( ph5om5a4 ,9 ! view ( ! new physics ^! 7 b false scales4 ,! ,e9/e9ian ,int]val alone %[s u :at c be kn[n ( reality4 ,e9/e9's sy/em1 !re=e1 takes pride 9 hav+ lift$ = all future "t a corn] ( ! veil :i* conceals f u ! sacr$ nudity ( nature4 ,,*apt] ,,iv ,,e9/e9',s ,,me*anics ,! me*anical f\ndation ( all ! sci5ces--,asc5d+ ! /ream ( "t--,! spe$ ( light an impassable limit--,! addition ( spe$s & ,fizeau's exp]im5t--,v>iability ( mass--,! balli/ics ( electrons--,gravitation & light z atomic microcosms--,matt] & en]gy--,! dea? ( ! sun4 ,:5 ,baudelaire wrote3 ,i hate ! movem5t t displaces l9es1 he ?\ght only1 l ! physici/s ( 8 "t1 ( ! /atic de=mations :i* h be5 kn[n z long z !re h be5 m5 to obs]ve !m4 ,:at we h se5 ab\t ,e9/e9ian "t & space has taught u t !re mu/ be1 9 addition to ^!1 k9ematic de=mations1 to :i* e mat]ial object1 h[ev] rigid x seems1 is liable4 ,movem5t1 !re=e1 displaces l9es mu* m ?an ,baudelaire suppos$1 ev5 ! l9es ( ! h>de/ ( m>ble /atues4 ,?is k9d ( de=mation1 :i* is pleasant r ?an hateful1 s9ce x br+s u ne>] to ! he>t ( ?+s1 has upset ! :ole ( me*anics4 ,me*anics is at ! f\ndation ( all ! exp]im5tal sci5ces1 because x is ! simple/1 & because ! ph5om5a x /udies are always pres5t--if n exclusively pres5t--among/ ! ph5om5al objects ( ! o!r sci5ces1 su* z physics1 *emi/ry1 & biology4 ,! conv]se ( ?is is n true4 ,= in/ance1 !re is n a s+le ph5om5on 9 *emi/ry or biology 9 :i* "o has n to /udy bodies 9 movem5t1 objects end[$ ) mass & giv+ out or absorb+ en]gy4 ,on ! o!r h&1 ! peculi> aspects ( a biological1 *emical1 or physical ph5om5on1 su* z ! exi/5ce ( a diff]5ce ( pot5tial1 an oxidation1 or an osmotic pressure1 are n always f\nd 9 ! /udy ( ! movem5ts ( a pond]able mass & ( ! =ces :i* act ^u & ?r\gh x4 ,comp>$ ) me*anics1 ! sci5ces ( physics1 *emi/ry1 & biology h1 9 ! ord] 9 :i* we "n !m1 objects ( increas+ complexity & g5]ality1 or1 to put x bett]1 ( decreas+ univ]sality4 ,^! sci5ces are mutually dep5d5t 9 ! way t ! trunk1 bran*es1 leaves1 & fl[]s ( a tree are4 ,!y are to "s ext5t relat$ to ea* o!r z are ! v>i\s p>ts ( ! jo9t$ ma/s on :i* milit>y telegraphi/s fix _! ant5n4 ,! l[] "p ( ! ma/1 ! l>g] "p1 su/a9s ! :ole2 b x is ! upp] p>ts :i* be> ! delicate & complicat$ organs4 ,! object ( ! great syn!ti/s 9 sci5ce has always be51 & is1 to r$uce all ph5om5a to me*anical ph5om5a1 z ,desc>tes attempt$4 ,:e!r ^! attempts are well-gr\nd$ or no1 :e!r !y w "s day succe$ or are condemn$ a priori to failure because physico-biological ph5om5a involve elem5ts t are ess5tially incapable ( r$uction to me*anical elem5ts1 is a "q t has be51 & w cont9ue to be1 mu* discuss$4 ,b1 h[ev] ?9k]s may diff] on t po9t1 !y are agre$ on ?is3 9 all natural ph5om5a1 9 all ph5om5a t are objects ( sci5ce1 !re is ! me*anical elem5t--exclusive 9 "s1 ! pr9cipal elem5t 9 o!rs4 ,all ?is leads to ! conclusion t :atev] modifies me*anics1 modifies at ! same "t ! :ole /ructure ( ideas f\nd$ !reon--t is to say1 ! o!r sci5ces1 ! :ole ( sci5ce1 our entire conception ( ! univ]se4 ,b we are n[ go+ to see t ,e9/e9's !ory1 z a direct effect ( :at x tea*es 9 reg>d to space & "t1 completely upsets ! classical me*anics4 ,x is 9 ?is way1 p>ticul>ly1 t x has %ak5 ! r somnol5t frame ( traditional sci5ce1 & ! vibration is n yet ov]4 ,9 approa*+ ! ,e9/e9ian me*anics we %all h ! pleasure ( pass+ f ideas ( "t & space t are r too exclusively geometrical & psy*ological to ! direct /udy ( mat]ial realities1 ( bodies4 ,"h we c comp>e !ory & reality1 ! ma!matical premises & ! sub/antial v]ifications2 & we %all be pleas$ to see :at ! facts1 giv5 9 exp]i5ce1 h to say on ! matt]4 ,we %all be able to make our *oice1 ) in=m$ m9ds & s\nd crit]ia1 betwe5 ! old & ! new ideas4 ,9 a ^w1 if ,i may use ?is illu/ration1 z long z we 7 deal+ ) ideas ( space & "t--:i* are empty frames 9 !mselves1 vases t w\ld int]e/ u *iefly by ! liquids !y conta9--we 7 r l ! "y m5 :o h to *oose a fiance solely by ! description ( h] :i* has be5 giv5 !m4 ,we are n[ go+ to see ) our own eyes1 & see at "w ! two aspirants to our affection3 classical sci5ce & ,e9/e9's !ory4 ,we %all see bo? ( !m take up ! pa/e ( facts1 & we %all be able to comp>e ! delici\s di%es :i* !y respectively make f x = ! n\ri%m5t ( ! m9d4 ,!ories h no value except z functions ( facts4 ,^? :i*1 l s _m 9 metaphysics1 h no real crit]ion by :i* we may te/ !m1 are all ( ! same value4 ,exp]i5ce1 ! sole s\rce ( tru? ( :i* ,lucretius said long ago3 unde omnia cr$ita p5d5t1 or ! mat]ial facts1 is go+ to judge ,e9/e9's sy/em = u4 99 99 99 99 99 ,! result ( ! ,mi*elson exp]im5t1 ! impossibility ( prov+ any velocity ( ! e>? 9 relation to ! m$ium 9 :i* light is propagat$1 am\nts to ?is3 we h no means :atev] ( detect+ a spe$ high] ?an t ( light4 ,?is consequ5ce ( ! ,mi*elson exp]im5t w be bett] und]/ood1 p]haps1 if we put x 9 a tangible =m4 ,"h is an illu/ration t w s]ve our purpose4 ,9 "s a/ronomical novel an imag9>y obs]v] is suppos$ to rec$e f ! e>? at a spe$ great] ?an t ( light--at #cjj1jjj miles a second1 let u say--yet to keep 8 eyes 7arm$ ) prodigi\s glasses7 /eadily fix$ on ?is little globe ( ours4 ,:at w happ58 ,evid5tly1 our obs]v] w see ! tra9 ( e>?ly ev5ts 9 inv]se ord]1 because 9 ! c\rse ( 8 voyage he w cat* up 9 succession ! lum9\s waves :i* left ! e>? be=e him4 ,! f>!r away !y are1 ! long] x mu/ be s9ce !y left ! e>?4 ,aft] a "t our man1 or our sup]man1 w witness ! ,battle ( ! ,m>ne4 ,he w fir/ see ! field /rewn ) ! dead4 ,gradually ! dead m5 w rise & jo9 _! regim5ts1 & pres5tly !y w be se5 9 gr\ps 9 ,galli5i's taxis1 :i* w travel backw>ds at full spe$ to ,p>is1 arriv+ 9 ! mid/ ( a population t is extremely anxi\s ab\t ! issue ( ! /ruggle1 & ! soldi]s w1 naturally1 be unable to give !m any news4 ,9 a ^w1 our obs]v] w1 if he rec$es f ! e>? at a spe$ great] ?an t ( light1 see t]re/rial ev5ts happ5+ z if he 7 asc5d+ ! /ream ( "t4 ,x w\ld be v diff]5t if ! obs]v] rema9$ /ation>y1 & ! e>? rec$$ f him at a spe$ ( #cjj1jjj miles a second4 ,:at w\ld happ5 !n8 ,x is cle> t 9 ?is case our obs]v] w see t]re/rial ev5ts1 n 9 inv]se ord]1 b z !y are3 except t !y w\ld seem to him to take place ) maje/ic sl[ness1 because ! rays ( light :i* leave ! e>? at ! end ( "s p>ticul> ev5t w take a mu* long] "t to rea* him ?an ! rays :i* left ! e>? at ! beg9n+ ( ! ev5t4 ,9 sum1 ! ph5om5a obs]v$ by him be+ ess5tially diff]5t 9 ! two cases1 our imag9>y obs]v] w\ld be able to say :e!r x is he :o is rec$+ f ! e>? or ! e>? t is rec$+ f him2 to detect ! real movem5t ( ! ev5t ?r\gh space4 ,?is means1 ( c\rse1 movem5t relatively to ! m$ium ( ! propagation ( light1 n necess>ily1 z we saw1 movem5t 9 relation to absolute space4 ,! exp]im5t we h imag9$ c\ld n v well be c>ri$ out ) ! actual res\rces ( our laboratories4 ,we _c atta9 ^! fanta/ic spe$s1 & ev5 if we c\ld ! obs]v] w\ld n di/+ui% mu*4 ,b we h *os5 a colossal in/ance1 & ! results ( x w\ld be colossal1 z !re w\ld be "q ( no?+ less ?an a rev]sal ( ! ord] ( "t4 ,if we 7 to use m mode/ means1 ! results w be m mode/1 b accord+ to ! old] !ories !y ought to be record$ 9 our in/rum5ts4 ,b ! ,mi*elson exp]im5t--a m9iature v]sion ( :at we h j describ$--%[s t ! diff]5ces we %\ld expect are n obs]v$4 ,!re=e ! premise we laid d[n--t !re c be velocities great] ?an t ( light 9 empty space--does n h>monise ) reality4 ,h5ce ?is velocity ( light is a wall1 a limit t _c be pass$4 99 99 99 99 99 ,n[ let u see :at foll[s4 ,!re is at ! base ( classical me*anics1 z x 0 f\nd$ by ,galileo1 ,huygh5s1 & ,newton1 & z x is taught ev]y:]e1 a pr9ciple :i* is 9 ! long run1 l all ! pr9ciples ( me*anics1 gr\nd$ ^u exp]i5ce4 ,x is ! pr9ciple ( ! composition ( velocities4 ,if a boat1 :i* makes t5 miles an h\r 9 smoo? wat]1 sails d[n a riv] :i* fl[s at five miles an h\r1 ! spe$ ( ! boat 9 relation to ! bank w be1 z we may f9d by actual measur+1 equal to ! sum ( ! two spe$s1 or fifte5 miles an h\r4 ,?is is ! rule ( ! addition ( velocities4 ,9 a m g5]al way1 if a body />ts f a /ate ( re/1 & "u ! action ( "s =ce takes on 9 a second ! velocity ,v1 :at w x d if ! action ( ! =ce is prolong$ = ano!r second8 ,accord+ to classical me*anics x w take on ! velocity #b,v4#g ,let u imag9e an obs]v] :o is travell+ at ! velocity ,v1 yet ?9ks he is at re/4 ,x w seem to him1 at ! end ( ! fir/ second1 t ! body is at re/ 7because x has ! same velocity z ! obs]v]74 ,9 virtue ( ! ,classical ,pr9ciple ( ,relativity1 ! app>5t movem5t ( ! body mu/ be ! same = our obs]v] z if ! re/ 7 real4 ,?is means t at ! end ( ! second second ! relative velocity ( ! body 9 ref]5ce to ! obs]v] w be ,v1 &1 z ! obs]v] already has ! velocity ,v1 ! absolute velocity ( ! body w be #b,v4 ,9 ! same way x w be #c,v at ! end ( ?ree seconds1 #d,v at ! end ( f\r seconds1 & s on4 ,c\ld x increase indef9itely if ! =ce cont9ues to act long en\gh8 ,classical me*anics says 8yes40 ,e9/e9 says 8no10 because !re _c be a great] velocity ?an t ( light4 #g ,z an example ( an id5tical =ce act+ dur+ p]iods ( "t successively equal to #a1 #b1 or #c1 we may take ?ree guns ( ! same calibre1 b ( l5g?s equal to #a1 #b1 & #c1 & ( :i* ! *>ges1 or r1 _! propulsive =ces1 are id5tical & con/ant4 ,x is f\nd t ! initial velocities ( ! %ells are1 9 relation to ea* o!r1 #a1 #b1 & #c4 ,we h imag9$ an obs]v] :o has ! velocity ,v relatively to u1 & :o believes t he is at re/4 ,= him ! body obs]v$ 0 likewise at re/ at ! beg9n+ ( ! second second1 because its velocity 0 ! same z t ( ! obs]v]4 ,f ! fact t ! app>5t movem5t ( ! body is = ! obs]v]1 dur+ ! second second1 ! same z x 0 = u dur+ ! fir/1 classical me*anics conclud$ t its velocity d\bles dur+ ! second second4 ,x did n "k :at ,e9/e9 has n[ taught u3 t ! "t & space ( ?is obs]v] are diff]5t f ours4 ,:at is a velocity8 ,x is ! space trav]s$ 9 ! c\rse ( a second4 ,b ! space ?us measur$ by our mov+ obs]v]1 :i* he believes to be ( a c]ta9 l5g?1 is 9 reality1 = u :o are /ation>y1 small] ?an he ?9ks1 because ! rules he uses are1 z ,e9/e9 has %[n1 %ort5$ by velocity )\t 8 p]ceiv+ x4 ,!re=e ! velocities are n add$ toge!r 9 equal proportions & indef9itely = a giv5 obs]v]1 z classical me*anics ma9ta9$4 ,"u ! action ( ! same =ce1 ! old me*anics said1 a body w always exp]i5ce ! same accel]ation1 :atev] be ! velocity already acquir$4 ,"u ! action ( ! same =ce1 ! new me*anics says1 ! motion ( ! body w be accel]at$ less & less 9 proportion to its velocity4 ,take1 = in/ance1 "s movable object hav+1 relatively to me1 a velocity ( #bjj1jjj kilometres a second4 ,let u place an obs]v] on ?is object4 ,! obs]v] w !n />t1 9 ! same direction & "u ! same conditions z we h done1 a second movable object1 :i* w ?us h1 relatively to him1 a spe$ ( #bjj1jjj kilometres4 ,! ,relativi/ says t ! resultant velocity ( ! second object relatively to u w n be1 z ! classical addition ( velocities w\ld make x1 #bjj1jjj #bjj1jjj #djj1jjj kilometres a second4 ,x w be only #bgg1jjj kilometres a second4 ,:at ! second mov+ obs]v] took to be #bjj1jjj kilometres 7because 8 measur+ rod 0 %ort5$ ow+ to velocity7 0 really only #gg1jjj ( our kilometres4 ,h[ is x possible to calculate t8 ,simply by us+ ! =mula ( ,lor5tz :i* ,i gave 9 ,*apt] ,,ii1 :i* gives u ! value ( ! contraction due to velocity4 ,we !n easily f9d t1 if we h two velocities1 v & v1 & if we call ! resultant w1 classical me*anics /at$ t w v v ,! ,e9/e9 me*anics says t ?is is n correct1 & t :at we really h 7,c be+ ! velocity ( light7 is v v w -------------------------- 7 vv 7 7#a ------------------7 7 ,c 7 ,i apologise = aga9 introduc+--x %all be ! la/ "t--an algebraical =mula into my "w4 ,b x sp>es me a l>ge numb] ( words1 & x is s simple t e read] :o has ev5 a t9cture ( elem5t>y ma!matics w at once see its great significance & ! consequ5ces ( x4 ,! =mula expresses 9 ! fir/ place ! fact t ! resultant ( ! velocities1 h[ev] great x may be1 _c be great] ?an ! spe$ ( light4 ,x conveys also t1 if "o ( ! compon5t velocities is t ( light1 ! resultant velocity mu/ h ! same value4 ,x means1 9 f9e1 t 9 ! case ( ! slight velocities we h to d ) 9 actual life 7t is to say1 :5 ! compon5t velocities are mu* small] ?an t ( light7 ! resultant is v ne>ly equal to ! sum ( ! two compon5ts1 z ! classical me*anics says4 ,! classical me*anics 01 we mu/ rememb]1 f\nd$ ^u exp]i5ce4 ,we und]/& h[1 9 ^? circum/ances1 ,galileo & 8 successors1 deal+ only ) relatively sl[ly mov+ bodies1 rea*$ a pr9ciple :i* seem$ to be true = !m1 b is only a fir/ approximation4 ,= in/ance1 ! resultant ( two velocities1 ea* equal to a hundr$ kilometres a second 7:i* is f> high] ?an any velocities obta9able by ,galileo & ,newton71 am\nts to1 n #bjj kilometres1 b #aiiiiiigh kilometres4 ,! diff]5ce is sc>cely tw5ty-two millimetres 9 #bjj kilometres6 ,we c q und]/& t ! e>li] exp]im5t]s c\ld n detect diff]5ces ev5 less m9ute ?an t4 99 99 99 99 99 ,among/ ! v]ifications ( ! new law ( composition ( velocities we may quote "o1 ! outcome ( an e>ly exp]im5t ( ! great ,fizeau1 :i* is v /rik+4 ,imag9e a pipe full ( "s liquid1 su* z wat]1 & a ray ( light travell+ along x4 ,we "k ! spe$ ( light 9 wat]3 x is mu* l[] ?an 9 air or 9 empty space4 ,suppose1 fur!r1 t ! wat] is n /ation>y1 b fl[s ?r\gh ! pipe at a c]ta9 spe$4 ,:at w be ! velocity ( ! ray ( light :5 x leaves ! pipe aft] trav]s+ ! mov+ liquid8 ,t 0 :at ,fizeau1 ) _m v>iations ( ! conditions ( ! exp]im5t1 tri$ to asc]ta94 ,! velocity ( light 9 wat] is ab\t #bbj1jjj kilometres a second4 ,!re is "q "h ( s rapid a propagation t !re is a great diff]5ce betwe5 ! law ( addition ( ! old classical me*anics & ( ,e9/e9ian me*anics4 ,n[ ! results ( ,fizeau's exp]im5t are 9 complete h>mony ) ,e9/e9's =mula1 & are n 9 h>mony ) t ( ! old] me*anics4 ,_m obs]v]s1 includ+1 rec5tly1 ! ,dut* physici/ ,zeeman1 h repeat$ ,fizeau's exp]im5t ) ! greate/ c>e1 b ! result 0 ! same4 ,:5 ,fizeau made ! exp]im5t 9 ! la/ c5tury1 attempts 7 made to int]pret 8 results 9 ! light ( ! old] !ories4 ,?is1 h[ev]1 l$ to v improbable hypo!ses4 ,fresnel1 = in/ance1 try+ to expla9 ,fizeau's results1 _h be5 compell$ to admit t ! e!r is p>tially borne along by ! wat] z x fl[s1 & t ?is p>tial displacem5t v>ies ) ! l5g? ( ! lum9\s waves s5t ?r\gh1 or t x is n ! same = ! blue z = ! r$ waves6 ,a v />tl+ d$uction1 & "o v difficult to admit4 ,! new law ( composition ( velocities giv5 to u by ,e9/e91 on ! o!r h&1 imm$iately & ) p]fect accuracy expla9s ,fizeau's results4 ,!y are oppos$ to ! classical law4 ,! facts1 ! sov]eign judges & crit]ia1 %[ 9 ?is case t ! new me*anics corresponds to reality2 ! e>li] me*anics does n1 at lea/ 9 its traditional =m4 ,"h is some?+1 !re=e1 :i* enables u to see at once ! pr(\nd tru? 7sci5tific tru? be+ :at is v]ifiable71 ! beauty1 ( ! doctr9e ( ,e9/e93 some?+ :i* %[s u1 sup]bly1 h[ a sci5tific1 a physical1 !ory diff]s f an arbitr>y & m or less consi/5t philosophical sy/em4 ,exp]i5ce1 ! supreme judge1 decides 9 fav\r ( ! ,e9/e9ian me*anics aga9/ ! old] me*anics4 ,we %all see fur!r examples2 & we %all n f9d a s+le case 9 :i* ! v]dict is ! o!r way4 99 99 99 99 99 ,let u turn n[ to a diff]5t matt]4 ,! new law ( composition ( velocities & ! resi/ance ( a velocity-limit equal to t ( light may be express$ 9 a diff]5t language f t we h hi!rto us$4 ,up to ?is we h spok5 only ( velocities & movem5ts4 ,let u see h[ ^! ?+s look :5 we at ! same "t exam9e ! p>ticul> qualities ( ! mov+ objects1 ( bodies1 ( matt]4 ,ev]ybody kn[s t ! *>act]i/ic feature ( matt] is :at we call in]tia4 ,if matt] is at re/1 a =ce is ne$$ to set x 9 motion4 ,if x is 9 motion1 x ne$s a =ce to /op x4 ,x ne$s "o to accel]ate ! movem5t & "o to alt] ! direction4 ,?is resi/ance :i* matt] (f]s to ! =ces :i* t5d to modify its condition ( re/ or movem5t is :at we call in]tia4 ,b diff]5t bodies may (f] a diff]5t degree ( resi/ance to ^! =ces4 ,if a =ce is appli$ to an object1 x w give x a c]ta9 accel]ation4 ,b ! same =ce appli$ to ano!r object w1 z a rule1 give x a diff]5t accel]ation4 ,a race-horse mak+ a supreme ef=t w get along mu* m quickly "u a small jockey ?an "u a man ( fifte5 /one4 ,a draught-horse w run m quickly if ! c>t x draws is empty ?an if x is full ( goods4 ,y c />t a p]ambulator ) a pu% t w\ld be useless 9 ! case ( a heavy truck4 ,:5 a locomotive ) a few coa*es sudd5ly />ts1 ! velocity imp>t$ to ! tra9 dur+ ! fir/ second is :at we call its accel]ation4 ,if ! same locomotive />ts1 9 ! same conditions1 ) a mu* long] tra91 we see t ! accel]ation is less4 ,h5ce ! idea1 introduc$ into sci5ce by ,newton1 ( ! mass ( bodies1 :i* is ! measure ( _! in]tia4 ,if 9 our example ! locomotive produces 9 ! second case an accel]ation only half z great1 we express ?is by say+ t ! mass ( ! second tra9 is d\ble t ( ! fir/4 ,if we f9d t ! accel]ation produc$ by ! locomotive is ! same = ?ree trucks load$ ) :eat z = a s+le truck load$ ) metal1 we see t ! two tra9s are equal 9 mass4 ,9 a ^w1 ! masses ( bodies are conv5tional data def9$ by ! fact t !y are proportional to ! accel]ations caus$ by "o & ! same =ce4 ,to put x diff]5tly1 ! mass ( a body is ! quoti5t ( ! =ce :i* acts ^u x by ! accel]ation giv5 to x4 ,po9c> us$ to say picturesquely3 8,masses are coeffici5ts :i* x is conv5i5t to use 9 calculations40 ,if !re is "o prop]ty ( bodies :i* comes )9 ! range ( our s5ses1 a prop]ty ( :i* e man has "s sort ( in/9ct or intuition1 x is mass4 ,yet c>eful analysis %[s u t we are unable to def9e x o!rwise ?an by disguis$ conv5tions4 ,po9c>'s def9ition seems p>adoxical 9 its admission ( p[]lessness4 ,b x is correct4 ,mass is only a 8coeffici5t10 a conv5tional outcome ( our weakness6 ,nev]!less1 some?+ rema9$ ^u :i* we ?\ght we c\ld base1 if n our crav+ = c]ta9ty--g5u9e m5 ( sci5ce gave up ! idea ( c]ta9ty long ago--at lea/ our desire = accuracy ( d$uction 9 our classification ( ph5om5a4 ,we believ$ 9 ! con/ancy ( mass1 ( ?is conv5i5t & s cle>ly def9$ coeffici5t4 ,"h aga91 un=tunately1 we h to recant--or1 p]haps1 we %\ld say =tunately1 z !re is no pleasure l t ( novelty4 ,! old] me*anics taught u t mass is con/ant 9 "o & ! same body1 & is !re=e indep5d5t ( ! velocity :i* ! body acquires4 ,f :i* x foll[$1 z we h already expla9$1 t1 if a =ce cont9ues to act1 ! velocity acquir$ at ! end ( a second w be d\bl$ at ! end ( two seconds1 tripl$ at ! end ( ?ree seconds1 & s on indef9itely4 ,b we h j se5 t ! velocity increases less dur+ ! second second ?an dur+ ! fir/1 & s on1 cont9u\sly dim9i%+ until1 :5 ! velocity ( light is atta9$1 t ( ! mov+ body c increase no fur!r1 :atev] =ce may act ^u x4 ,:at does t mean8 ,if ! velocity ( a body increases less dur+ ! second second1 x mu/ be because x (f]s an increas+ resi/ance to ! accel]at+ =ce4 ,ev]y?+ happ5s z if its in]tia1 its mass1 _h *ang$6 ,:i* am\nts to say+ t ! mass ( bodies is n con/ant3 x dep5ds ^u _! velocity1 & increases ) an increase ( velocity4 ,9 ! case ( feeble velocities ?is influ5ce is imp]ceptible4 ,x 0 because ! f\nd]s ( classical me*anics1 an exp]im5tal sci5ce1 _h exp]i5ce only ( relatively feeble velocities t !y f\nd t mass 0 p]ceptibly con/ant1 & believ$ !y might conclude t x 0 absolutely con/ant4 ,9 ! case ( great] velocities t is n s4 ,simil>ly1 9 ! case ( feeble velocities1 9 ! new me*anics z well z ! old1 bodies p]ceptibly oppose ! same resi/ance ( in]tia to ! =ces :i* t5d to accel]ate _! movem5t z to ^? :i* t5d to alt] ! direction1 to give a curve to _! trajectories4 ,9 ! case ( great velocities t is n s4 ,mass1 !re=e1 increases rapidly ) velocity4 ,x becomes inf9ite :5 ! velocity equals t ( light4 ,no body :atev] c atta9 or surpass ! velocity ( light1 because1 9 ord] to pass t limit1 x w\ld ne$ to ov]come an inf9ite resi/ance4 ,9 ord] to make x q cle>1 let u give c]ta9 figures :i* %[ h[ mass v>ies ) velocity4 ,! calculation is easy1 ?anks to ! =mula :i* we h previ\sly se51 giv+ ! values ( ! ,fitzg]ald-,lor5tz con/ruction4 ,a mass ( #a1jjj grammes w weigh an additional two grammes at ! velocity ( #a1jjj kilometres a second4 ,x w weigh #a1jfj grammes at ! velocity ( #ajj1jjj kilometres a second2 #a1cda grammes at ! velocity ( #bjj1jjj kilometres a second2 #b1jjj grammes 7or d\ble7 at ! velocity ( #bei1hjf kilometres a second2 #c1ije grammes at ! velocity ( #bij1jjj kilometres a second4 99 99 99 99 99 ,t is :at ! new !ory tells u4 ,b h[ c we v]ify x8 ,x w\ld h be5 impossible only fifty ye>s ago1 :5 ! only velocities kn[n 7 ^? ( our vehicles & projectiles1 :i* !n did n rise1 ev5 9 ! case ( %ells1 above "o kilometre a second4 ,! planets !mselves are f> too sl[ = ! purpose ( v]ification4 ,m]cury1 = in/ance1 ! swifte/ ( !m1 travels at a spe$ ( only a hundr$ kilometres a second1 :i* is n en\gh4 ,if we _h at our disposal no high] velocities ?an ^!1 we %\ld h no means ( settl+ :i* 0 "r1 ! classical me*anics ) its con/ancy ( mass or ! new me*anics ) its ass]tion ( v>iability4 ,x is ! ca?ode rays & ! ,beta rays ( radium :i* h provid$ u ) velocities great en\gh = ! purpose ( v]ification4 ,^! rays consi/ ( an un9t]rupt$ bomb>dm5t by small & v rapid projectiles1 ea* ( a mass less ?an ! two-?\s&? "p t ( an atom ( hydrog51 & *>g$ ) negative electricity4 ,!y are ! electrons4 ,! ca?ode tubes ( radium give out a cont9u\s bomb>dm5t ( ^! m9ute projectiles1 *>g$1 n ) mel9ite1 b electricity3 f> small] ?an ! %ells ( our artill]y1 b animat$ ) inf9itely great] initial spe$s4 ,! velocity ( 8,b]?a's0 %ells is contemptible 9 comp>ison4 ,b h[ 0 x possible to measure ! spe$ ( ^! projectiles8 ,we "k t electrifi$ bodies act ^u ea* o!r4 ,!y attract or repel ea* o!r4 ,n[ our electrons are *>g$ ) electricity4 ,if1 !re=e1 we put !m 9 an electric field1 betwe5 two plates connect$ at ! edges by an electrical ma*9e or an induction coil1 !y w be subject$ to a =ce t w cause !m to *ange _! direction4 ,! ca?ode rays1 9 o!r words1 w *ange _! direction "u ! influ5ce ( an electric field4 ,! am\nt ( div]sion w dep5d ^u ! spe$ ( ! projectiles & ^u _! mass2 t is to say1 ^u ! resi/ance ( in]tia :i* ! mass opposes to ! causes :i* t5d to div]t x4 ,b ?is is n all4 ,! electric *>ges borne by ! projectiles are 9 movem5t1 ev5 rapid movem5t4 ,n[1 electricity 9 movem5t is an electric curr5t1 & we "k t curr5ts are div]t$ by magnets or magnetic fields4 ,!re=e ! ca?ode rays w be div]t$ by ! magnet4 ,?is div]sion w1 l ! =m]1 dep5d ^u ! velocity & ! mass ( ! projectile2 b n q 9 ! same way4 ,o!r ?+s be+ equal1 ! magnetic div]sion w be great] ?an ! electrical div]sion1 if ! velocity is high4 ,z a matt] ( fact1 ! magnetic div]sion is due to ! action ( ! magnet on ! curr5t4 ,x w be great] 9 proportion to ! int5sity ( ! curr5t2 & ! curr5t w be m int5se 9 proportion to ! height ( ! velocity1 s9ce x is ! movem5t ( ! projectile :i* causes ! curr5t4 ,on ! o!r h&1 ! trajectory ( our little projectiles w be less influ5c$ by ! electrical attraction 9 proportion z ! velocity ( ! projectile is great4 ,h5ce x is easy to see t :5 we subject a ca?ode ray to ! action ( an electric field1 !n to t ( a magnetic field1 we may1 by comp>+ ! two deviations1 measure at "o & ! same "t ! velocity ( ! projectile & its mass 7relat$ to ! kn[n electric *>ge ( ! electron74 ,9 ?is way we f9d enorm\s velocities1 ris+ f a few t5s ( kilometres to #aej1jjj kilometres a second1 & ev5 m4 ,z to ! ,beta rays ( radium1 !y are /ill m rapid4 ,9 cases !y atta9 velocities n f> %ort ( t ( light1 & high] ?an #bij1jjj kilometres a second4 ,"h are j ! velocities we ne$ 9 ord] to te/ :e!r or no mass increases ) !m4 99 99 99 99 99 ,9 ord] to und]/& cle>ly ! progress ( ! exp]im5ts1 x rema9s to say a few words ab\t ! curi\s ph5om5on ( electrical in]tia :i* is call$ self-induction4 ,:5 we want to set up an electric curr5t1 we f9d a c]ta9 initial resi/ance :i* ceases z soon z ! curr5t beg9s4 ,if aft]w>ds we want to break ! curr5t1 x t5ds to ma9ta9 itself1 & we h j ! same tr\ble to /op x z to /op a vehicle 9 motion4 ,x is a matt] ( daily exp]i5ce4 ,sometimes ! trolley ( a tramc> leaves = a mom5t ! wire :i* conducts ! curr5t1 & we !n see sp>ks4 ,:y8 ,!re 0 a curr5t pass+ f ! wire to ! trolley1 & if ! trolley breaks away f ! wire = a mom5t1 leav+ an int]val ( air :i* ob/ructs ! passage ( electricity1 ! curr5t w n /op4 ,x has be5 set go+1 z x 71 & x leaps ! ob/acle 9 ! =m ( a sp>k4 ,?is ph5om5on is :at we call self-induction4 ,self-induction--or 8self0 z ! electrical work]s call x--is a real in]tia4 ,! surr\nd+ m$ium (f]s resi/ance to ! =ce :i* t5ds to e/abli% an electric curr5t1 & to t :i* t5ds to /op a curr5t already set up2 j z matt] resi/s ! =ce :i* t5ds to cause x to pass f re/ to movem5t1 or f movem5t to re/4 ,!re is1 !re=e1 a real electrical in]tia z well z me*anical in]tia4 ,b our ca?odic projectiles1 our electrons1 are *>g$4 ,:5 !y beg9 to move1 !y />t an electric curr5t2 :5 !y come to re/1 ! curr5t ceases4 ,besides me*anical in]tia1 !n1 !y mu/ also h electrical in]tia4 ,!y h1 s to speak1 two in]tias2 t is to say1 two in]t masses1 a real & me*anical mass1 & an app>5t mass due to ! ph5om5a ( electro-magnetic self-induction4 ,by /udy+ ! two deviations1 electric & magnetic1 ( ! ,beta rays ( radium or ( ! ca?ode rays1 x is possible to det]m9e ! respective p>ts ( ea* ( ^! masses 9 ! total mass ( ! electron4 ,! electro-magnetic mass due to ! causes :i* we h expla9$ v>ies ) ! velocity1 accord+ to c]ta9 laws :i* we ga!r f ! !ory ( electricity4 ,h5ce1 by obs]v+ ! relation betwe5 ! total mass & ! velocity1 we c see :at "p belongs to ! real & inv>iable mass & :at to ! app>5t mass ( electro-magnetic orig94 ,! exp]im5t has be5 made repeat$ly by physici/s ( di/9ction4 ,! result ( x is surpris+3 ! real mass is nil1 & ! :ole mass ( ! p>ticle is ( electro-magnetic orig94 ,"h is some?+ t is calculat$ to modify entirely our ideas ( ! ess5ce ( :at we call matt]4 ,b t is ano!r /ory4 ,physici/s !n ask$ !mselves--?is is :at we 7 com+ to1 aft] cle>+ ! way ( v>i\s difficulties--:e!r ! relation betwe5 ! mass & ! velocity ( ! ca?odic projectiles 0 ! same z t :i* we f\nd 9 virtue ( ! ,pr9ciple ( ,relativity4 ,! result ( ! exp]im5ts is absolutely cle> & consi/5t1 & "s ( !m h dealt ) ,beta rays correspond+ to a mass-value t5 times great] ?an ! orig9al mass4 ,?is result is3 mass v>ies ) velocity1 & 9 exact accord ) ! num]ical laws ( ,e9/e9's dynamics4 ,"h is a new & valuable exp]im5tal confirmation4 ,?is 9 turn t5ds to %[ t classical me*anics 0 m]ely a r\gh approximation1 valid at ! mo/ only = ! comp>atively slight velocities ) :i* we h to deal 9 ! v re/rict$ c\rse ( daily life4 ,?us ! mass ( bodies1 ! ,newtonian prop]ty :i* 0 believ$ to be ! v symbol ( con/ancy1 ! equival5t ( :at loyalty to treaties is 9 ! moral ord] ( ?+s1 is n[ m]ely a small coeffici5t1 v>iable1 undulat+1 & relative to ! po9t ( view4 ,9 virtue ( ! reciprocity :i* we h describ$1 :5 !re is "q ( contraction due to velocity1 ! mass ( an object increases 9 ! same way1 n only if ! object is displac$1 b if ! obs]v] is displac$1 & )\t any o!r obs]v]1 connect$ ) ! object1 be+ able to detect ! diff]5ce4 ,= in/ance1 a measur+ rod t moves at a velocity ( ab\t #bfj1jjj kilometres a second w n only h its l5g? %ort5$ by "o-half1 b w h its mass d\bl$ at ! same "t4 ,h5ce its d5sity1 :i* is ! relation ( its mass to its volume1 w be quadrupl$4 ,! physical ideas :i* 7 believ$ to be mo/ solidly e/abli%$1 mo/ con/ant1 mo/ un%akeable1 h be5 uproot$ by ! /orm ( ! new me*anics4 ,!y h become s(t & pla/ic ?+s m\ld$ by velocity4 99 99 99 99 99 ,fur!r confirmations ( ! new =mula1 q indep5d5t ( ! "o we h j describ$1 h rec5tly be5 provid$ by physici/s4 ,"o ( ! mo/ a/oni%+ ( ^! is giv5 9 spectroscopy4 ,z is well kn[n1 :5 we cause a ray ( sunlight1 admitt$ ?r\gh a n>r[ slit1 to pass ?r\gh ! edge ( a glass prism1 ! ray exp&s1 z x issues f ! prism1 l a beautiful fan1 ! successive blades ( :i* consi/ ( ! diff]5t col\rs ( ! ra9b[4 ,:5 we exam9e closely ?is col\r$ fan1 we notice c]ta9 f9e discont9uities1 n>r[ l9es or gaps1 9 :i* !re is no light4 ,!y look l cuts made ) a pair ( scissors 9 our poly*rome fan4 ,!y are ! d>k l9es ( ! sol> spectrum4 ,ea* ( ^! l9es1 or ea* gr\p ( !m1 corresponds to a special *emical elem5t1 & s]ves to id5tify ?is1 :e!r 9 our laboratories or 9 ! sun & ! />s4 ,x 0 expla9$ long ago t ^! l9es are due to electrons :i* revolve rapidly r\nd ! nuclei ( ! atoms4 ,_! sudd5 *anges ( velocity give rise to a wave 7l ^? caus$ 9 wat] :5 y drop a pebble into x7 9 ! surr\nd+ m$ium1 & ?is is "o ( ! *>act]i/ic lum9\s waves ( ! atom4 ,x reveals itself 9 "o ( ! l9es ( ! spectrum4 ,! ,dani% physici/ ,bohr has rec5tly develop$ ?is !ory 9 detail1 & has %[n t x accurately expla9s ! v>i\s spectral l9es ( ! diff]5t *emical elem5ts4 ,^!1 ,i may note1 diff] f ea* o!r 9 ! numb] & arrangem5t ( ! electrons :i* revolve )9 _! atoms4 ,n[ ,somm]feld has argu$ z foll[s4 ,! electrons :i* gravitate ne> ! c5tre ( an atom mu/ h a high] velocity ?an ^? :i* revolve 9 its out] "p2 j z ! small] planets1 ,m]cury & ,v5us1 revolve r\nd ! sun f> m rapidly ?an ! l>g] planets1 ,jupit] & ,saturn4 ,x foll[s if ,lor5tz & ,e9/e9 are "r t ! mass ( ! int]ior electrons ( ! atoms mu/ be great] ?an t ( ! ext]ior electrons3 appreciably great]1 z ! =m] revolve ) enorm\s velocities4 ,we c calculate t1 9 ^? conditions1 ea* l9e 9 ! spectrum ( a *emical elem5t mu/ 9 reality consi/ ( a numb] ( f9e l9es jo9$ toge!r4 ,?is is precisely :at ,pas*5 aft]w>ds 7#aiaf7 f\nd4 ,he discov]$ t ! /ructure ( ! f9e l9es is /rictly su* z ,somm]feld _h pr$ict$4 ,x 0 an a/oni%+ confirmation ( an hypo!sis3 a pro( ( ! s\ndness ( ! new me*anics4 ,b t is n all4 ,we "k t ! ,x-rays are vibrations analog\s to light1 ! same 9 orig91 b consi/+ ( mu* %ort] waves1 or waves ) a f> high] frequ5cy4 ,h5ce1 :ile light comes f ! ext]nal electrons ( ! m9iature sol> sy/em :i* we call an atom1 ! ,x-rays come f ! mo/ rapid electrons--^? ne>e/ to ! c5tre4 ,x foll[s t ! special /ructure ( ! f9e l9es1 due to ! v>iation ( ! mass ( ! electron ) its velocity1 mu/ be mu* m m>k$ 9 ! case ( ! ,x-rays ?an 9 ! case ( ! spectral l9es ( light4 ,?is1 aga91 0 confirm$ by exp]im5t4 ,! figures express+ ! obs]v$ facts correspond exactly ) ! calculations ( ! new me*anics1 z reg>ds ! pr$ict$ v>iation ( mass ) velocity4 ,x is !re=e settl$ t ! ph5om5a :i* take place 9 ! microcosm ( ea* atom are subject to ! laws ( ! new me*anics1 n ! old1 & t1 9 p>ticul>1 masses 9 motion v>y z ! new me*anics dem&s4 ,exp]i5ce1 8sole s\rce ( tru?10 has giv5 its v]dict4 ,we are n[ v f> f ! ideas :i* 7 once preval5t4 ,lavoisi] taught u t matt] c nei!r be creat$ nor de/roy$4 ,x rema9s always ! same4 ,:at he meant 0 t mass is inv>iable1 z he prov$ by means ( scales4 ,n[ x appe>s t1 p]haps1 bodies h no mass at all--if x is entirely ( electro-magnetic orig9--& t1 9 any case1 mass is n inv>iable4 ,?is does n mean t ,lavoisi]'s law has n[ no mean+4 ,!re rema9s some?+ t corresponds to mass at l[ velocities4 ,our idea ( matt] is1 h[ev]1 revolutionis$4 ,by matt] we p>ticul>ly meant mass1 :i* seem$ to u to be at once ! mo/ tangible & mo/ endur+ ( its prop]ties4 ,n[ ?is 8mass0 has no m reality ?an ! "t & space 9 :i* we ?\ght we locat$ x6 ,our solid realities 7 b phantoms4 ,! read] mu/ p>don me = :atev] difficulties he f9ds 9 ?is exposition4 ,! new me*anics op5s out to u su* /range new horizons t x is wor? f> m ?an a rapid & sup]ficial glance4 ,if y want to see a va/ prospect 9 an unexplor$ _w1 y mu/ n hesitate to d "s r\gh climb+1 h[ev] brea?less x may leave y = ! "t4 99 99 99 99 99 ,!re is1 9 f9e1 ano!r fundam5tal idea ( me*anics1 t ( en]gy1 :i* takes on a new aspect 9 ! light ( ,e9/e9's !ory3 an aspect :i*1 9 turn1 is l>gely ju/ifi$ by exp]im5t4 ,we saw t a body *>g$ ) electricity & 9 motion makes a c]ta9 resi/ance to int]f]5ce1 on acc\nt ( ! electrical in]tia :i* is kn[n z self-induction4 ,calculation & exp]im5t %[ t1 if we r$uce ! dim5sions ( a body t is *>g$ ) a c]ta9 quantity ( electricity1 )\t alt]+ ! *>ge1 ! electrical in]tia increases4 ,z a matt] ( fact1 9 our hypo!ses1 & if ! in]tia is entirely electro-magnetic 9 orig91 ! electrons are n[ m]ely a sort ( electric trails mov+ 9 ! propagat+ m$ium ( electrical & lum9\s waves :i* we call e!r4 ,! electrons are no long] any?+ 9 !mselves4 ,!y are m]ely1 9 ! words ( ,po9c>1 a sort ( 8holes 9 e!r10 r\nd :i* ! e!r presses mu* z a lake makes eddies :i* *eck ! progress ( a boat4 ,9 t case1 h[ev]1 ! small] ! holes 9 ! e!r are1 ! m important w be ! agitation ( ! e!r r\nd !m2 &1 consequ5tly1 ! great] w be ! in]tia ( ! 8hole 9 e!r0 :i* repres5ts ! corpuscle "u inve/igation4 ,:at w foll[8 ,we "k f measurem5ts we h made t ! mass ( ! t9y sun ( ea* atom1 ! positive nucleus1 r\nd :i* ! planet-electrons revolve1 is great] ?an t ( an electron4 ,if ?is mass & ! correspond+ in]tia are electro-magnetic 9 orig91 x foll[s t ! positive nucleus ( ! atom is mu* small] ?an ! electron4 ,let u consid] ! atom ( hydrog51 ! lighte/ & simple/ ( ! gases4 ,we "k t x consi/s ( "o planet only1 "o s+le negative electron revolv+ r\nd ! m9ute c5tral sun1 ! positive nucleus4 ,we "k also t ! mass ( ! electron is two ?\s& times z small z t ( ! hydrog5 atom4 ,x foll[s1 z we c calculate1 t ! positive nucleus mu/ h a radius two ?\s& times small] ?an t ( ! electron4 ,n[1 ! exp]im5ts ( ! ,engli% physici/s h prov$ t ! l>ge ,alpha p>ticles ( ! radium emanation c pass ?r\gh hundr$s ( ?\s&s ( atoms )\t be+ appreciably div]t$ by ! positive nucleus4 ,we conclude t ! latt] is 9 reality mu* small] ?an ! electron1 z !ory pr$ict$4 ,all ?is irresi/ibly compels u to ?9k t ! in]tia ( ! v>i\s compon5t p>ts ( atoms--t is to say1 ( all matt]--is exclusively electro-magnetic 9 orig94 ,!re is n[ no matt]4 ,!re is only electrical en]gy1 :i*1 by ! reactions ( ! surr\nd+ m$ium ^u x1 leads u to ! fallaci\s belief 9 ! exi/5ce ( ?is sub/antial & massive some?+ :i* hundr$s ( g5]ations h be5 wont to call 8matt]40 ,& f all ?is x also foll[s1 by calculation & by ! simple & elegant reason+ ( ,e9/e91 ( :i* ,i "h convey only ! fa9te/ adumbration1 t mass & en]gy are ! same ?+1 or are at lea/ ! two diff]5t sides ( "o & ! same co94 ,!re is1 !n1 no long] a mat]ial mass4 ,!re is no?+ b en]gy 9 ! ext]nal univ]se4 ,a /range--9 a s5se1 an almo/ spiritual--turn = mod]n physics to take6 ,accord+ to all ?is ! great] "p ( ! 8mass0 ( bodies mu/ be due to a consid]able & conceal$ int]nal en]gy4 ,x is ?is en]gy :i* we f9d gradually dissipat$ 9 radio-active bodies1 ! only res]voirs ( atomic en]gy :i* h z yet op5$ ext]nally4 ,if ?is is true1 if en]gy & mass are synonym\s1 if mass is m]ely en]gy1 x foll[s t free en]gy mu/ possess ! prop]ty ( mass4 ,z a matt] ( fact1 light1 = in/ance1 has mass4 ,c>eful exp]im5ts h %[n t :5 a ray ( light /rikes a mat]ial object1 x ex]ts ^u x a pressure :i* has be5 measur$4 ,light has mass2 !re=e x has weight1 l all masses4 ,:5 we come to consid] ! new =m giv5 by ,e9/e9 to ! problem ( gravitation1 we %all see a fur!r & beautiful pro( t light has weight4 ,we c calculate t ! light receiv$ f ! sun by ! e>? 9 ! space ( a ye> is r m ?an #eh1jjj tons4 ,x seems v little :5 "o ?9ks ( ! =midable weight ( coal t w\ld be ne$$ to ma9ta9 our globe at ! temp]ature at :i* ! sun keeps x--9 ! ev5t ( a sudd5 ext9ction ( our lum9>y4 ,! reason = ! diff]5ce is t1 :5 we produce heat f a c]ta9 am\nt ( coal1 we use only a small proportion ( its total en]gy1 its *emical en]gy4 ,its intra-atomic en]gy is inaccessible to u4 ,x is a pity1 z o!rwise we %\ld ne$ only a few ounces ( coal to supply heat = a :ole ye> to all ! t[ns & work%ops ( ,engl&6 ,h[ _m problems t w\ld simplify6 ,:5 humanity em]ges f ! ignorance & ! clumsy b>b>ism 9 :i* x lives to-day--t is to say1 9 "s hundr$s ( c5turies--?is w be accompli%$4 ,yes1 x w "o day be done4 ,x w be a glori\s spectacle1 "o 9 :i* we may ju/ly rejoice 9 advance4 ,meantime1 our sun1 l all ! o!r />s1 l e inc&esc5t body1 loses its weight 9 proportion z x radiates4 ,b ?is happ5s s sl[ly t we ne$ n fe> to see x disappe> at "s e>ly date1 l ! ephem]al ?+s :i* die because !y gave !mselves too freely4 99 99 99 99 99 ,to f9i% ) ,e9/e9's me*anics1 let me reproduce a v sugge/ive application ( ^! ideas ab\t ! id5tity ( en]gy & mass4 ,!re is 9 *emi/ry a well-kn[n elem5t>y law :i* is call$ 8,pr\t's ,law40 ,x /ates t ! atomic masses ( all ! elem5ts mu/ be :ole multiples ( ! mass ( hydrog54 ,s9ce hydrog5 has ! lighte/ atoms among/ all kn[n bodies ,pr\t's ,law />t$ f ! hypo!sis t all ! atoms are built up ( a fundam5tal elem5t1 ! atom ( hydrog54 ,?is suppos$ unity ( matt] seems to be m & m confirm$ by ! facts4 ,on ! "o h&1 x is prov$ t ! electrons :i* come f diff]5t *emical elem5ts are id5tical4 ,on ! o!r h&1 9 ! trans=mation ( radio-active bodies we f9d heavy atoms simplify+ !mselves by successively emitt+ atoms ( helium gas4 ,la/ly1 ! great ,briti% physici/ ,sir ,erne/ ,ru!r=d %[$ 9 #aiai t by bomb>d+ ! atoms ( nitrog5 gas1 9 c]ta9 circum/ances1 by means ( radium emanation1 we c deta* hydrog5 atoms f !m4 ,?is exp]im5t1 ! importance ( :i* has n be5 fully realis$--x is ! fir/ in/ance ( transmutation really effect$ by man--also t5ds to prove ! s\ndness ( ,pr\t's hypo!sis4 ,yet1 :5 we accurately measure & comp>e ! atomic masses ( ! v>i\s *emical elem5ts1 we f9d t !y d n /rictly con=m to ,pr\t's ,law4 ,= in/ance1 :ile ! atomic mass ( hydrog5 is #a1 t ( *lorium is #cedf1 :i* is n a :ole multiple ( #a4 ,b we c calculate t1 if ! =mation ( complex atoms f hydrog5 upw>ds is accompani$1 z is probable1 by v>iations ( int]nal en]gy1 z a consequ5ce ( ! radiation ( a c]ta9 am\nt ( en]gy dur+ ! comb9ation1 x necess>ily foll[s 7s9ce ! lo/ en]gy has weight7 t !re w be v>iations 9 ! mass ( ! body compos$1 & ^! w expla9 ! kn[n dep>tures f ,pr\t's ,law4 99 99 99 99 99 ,9 our some:at hurri$ & in=mal excursion into ! bu% ( ! new facts :i* confirm ! me*anics outl9$ by ,lor5tz & complet$ by ,e9/e9 our progress has be5 r difficult4 ,x is because1 s9ce we c\ld n use t]m9ology & te*nical =mul :i* w\ld be unsuitable 9 ?is "w1 we h _h to be cont5t ) bold & rapid moves into ! di/ricts we wi%$ to reconnoitre4 ,p]haps !y h suffic$ to enable ! read] to und]/& :at a revolution 9 ! v bases ( sci5ce1 :at an explosion amid/ its age-old f\ndations1 ! brilliant syn!sis ( ,e9/e9 has caus$4 ,new light n[ /reams ^u all :o sl[ly climb ! slopes ( k3 ^u all :o1 wisely r5\nc+ ! desire to "k 8:y10 w\ld at lea/ le>n ! 8h[0 9 _m ?+s4 ,a little be=e 8 dea?1 =esee+1 ) ! intuition ( g5ius1 t a new era op5$ 9 me*anics1 ,po9c> advis$ pr(essors n to tea* ! new tru?s to ! "y until !y 7 /eep$ to ! v m>r[ ( _! bones 9 ! old] me*anics4 8,x is10 he add$1 8) ord9>y me*anics t _! life is conc]n$3 x is t alone t !y w ev] h to apply4 ,:atev] spe$ our motor-c>s may atta91 !y w nev] rea* a spe$ at :i* ! old me*anics ceases to be true4 ,! new is a luxury1 & we mu/ ?9k ( luxuries only :5 x c be done )\t injury to necess>ies40 ,i w\ld appeal f ,po9c>'s text to ! man himself4 ,= him ?is luxury1 ! tru?1 0 a necess>y4 ,on ! day 9 "q1 x is true1 he ?\ght ( ! "y4 ,b d m5 ev] cease to be *ildr58 ,to t ! ma/]1 too e>ly tak5 f u1 w\ld h repli$1 9 8 grave1 smil+ mann]3 8,yes--at all ev5ts1 x is bett] to suppose s40 ,,*apt] ,v ,,g5]alis$ ,,relativity ,weight & in]tia--,ambiguity ( ! ,newtonian law--,equival5ce ( gravitation & accel]at$ movem5t--,jules ,v]ne's projectile & ! pr9ciple ( in]tia--,:y rays ( light are subject to gravitation--,h[ light f ! />s is weigh$--,an eclipse z a s\rce ( light4 ,we are n[ on ! ?re%old ( ! great my/]y ( gravitation4 ,9 ! prec$+ *apt] we saw h[ ,e9/e9 br\ght "u "o magnific5t law bo? ! sl[ movem5ts ( massive objects & ! f> m rapid movem5ts ( light4 ,!y _h hi!rto be5 sep>ate & an>*ic prov9ces ( ! univ]se4 ,we n[ "k t ! same laws gov]n me*anics & optics4 ,if = a "t x appe>$ o!rwise1 x 0 because at velocities :i* approa* t ( light ! l5g?s & masses ( objects exp]i5ce 9 ! eyes ( ! obs]v] an alt]ation :i* is imp]ceptible at famili> spe$s4 ,x is 9 its p[] ( syn!sis t ,e9/e9's me*anics is s spl5did4 ,?anks to x1 we p]ceive m unity1 m h>mony1 m beauty1 ?an =m]ly 9 ?is a/\nd+ univ]se1 9 :i* our ?\ghts & our anxieties are s ephem]al4 ,! !ory ( ,relativity1 h[ev]1 has up to ! pres5t n t\*$ a ph5om5on t is fundam5tal1 ess5tial1 ubiquit\s 9 our cosmos4 ,i mean gravitation1 ! my/]i\s prop]ty ( bodies :i* rules ! t9y atom no less ?an ! mo/ gigantic />1 & directs _! pa?s 9 maje/ic curves4 ,! univ]sal attraction :i*1 z f> z e>? is conc]n$1 we call weight 0 a k9d ( /eep-cliff$ isl& 9 ! sea ( ph5om5a1 some?+ unrelat$ to ! re/ ( natural philosophy4 ,! ,e9/e9ian me*anism1 z we h describ$ x up to n[1 pass$ by ?is isl&1 tak+ no notice ( x4 ,= t reason x 01 9 ?is =m1 kn[n z 8! !ory ( ,special ,relativity40 ,9 ord] to conv]t x into a p]fect in/rum5t ( syn!sis1 ! ph5om5on ( gravitation _h to be introduc$4 ,x is ?us t ,e9/e9 cr[n$ 8 "w1 & 8 sy/em assum$ ! =m :i* is well call$ 8! !ory ( ,g5]al ,relativity40 ,e9/e9 has drawn gravitation f its 8spl5did isolation10 & has annex$ x1 docile & vanqui%$1 to ! triumphal *>iot ( 8 me*anics4 ,he has1 moreov]1 giv5 ,newton's fam\s law a m correct =m1 & exp]im5t1 ! supreme judge1 has decl>$ ?is ! only j =m4 ,h[ he did ?is1 by :at subtle & p[]ful *a9 ( reason+1 by :at calculations bas$ ^u facts1 ,i w n[ endeav\r to tell2 & ,i w aga9 d my be/ to avoid ! network ( b>b$ wire ( ma!matical t]m9ology4 ,:y did ,newton1 foll[$ by ! :ole ( classical sci5ce1 believe t gravitation1 ! fall ( bodies1 did n belong to ! me*anics ( :i* he =mulat$ ! laws8 ,:y1 9 a ^w1 did he reg>d gravitation z a =ce or--to use a vagu] b m g5]al t]m--an action :i* prev5ts heavy bodies f *ang+ _! positions freely 9 space8 ,because ( ! pr9ciple ( in]tia4 ,?is pr9ciple1 ! f\ndation ( ! :ole ,newtonian me*anics1 may be express$ ?us3 a body :i* is n act$ ^u by any =ce ma9ta9s its velocity & direction un*ang$4 ,:y d we equip /eam-eng9es ) ! heavy :eels :i* we call 8fly-:eels10 :i* "w no?+8 ,because ! pr9ciple ( in]tia is c]ta9ly ne>ly true4 ,:5 ! eng9e exp]i5ces a sudd5 & %>p *eck1 or an accel]ation1 ! fly-:eel s]ves to keep x /eady4 ,driv5 by ! spe$ x has acquir$1 & driv+ ! eng9e 9 its turn1 x t5ds to pres]ve its velocity1 & x prev5ts or modifies accid5tal *ecks or accel]ations4 ,! pr9ciple is !re=e bas$ ^u exp]i5ce1 especially on ! exp]im5ts ( ,galileo1 :o v]ifi$ x by roll+ balls d[n planes incl9$ at diff]5t angles4 ,= in/ance1 we f9d t a ball set 9 motion on a highly poli%$ horizontal plane keeps its direction1 & w\ld pres]ve its velocity if ! resi/ance ( ! atmosph]e & ! friction ( ! plane did n gradually r$uce x to z]o4 ,we f9d t1 9 proportion z we r$uce ! friction1 ! ball t5ds to ma9ta9 its spe$ s mu* ! long]4 ,newton's pr9ciple ( in]tia is bas$ ^u a numb] ( ^! exp]im5ts4 ,x is by no means 9 ! nature ( a self-evid5t ma!matical tru?4 ,?is is s true t anci5t ?9k]s believ$1 contr>y to classical me*anics1 t ! movem5t ceases z soon z ! cause ( x is remov$4 ,c]ta9 ( ! ,greek philosoph]s ev5 ?\ght t all bodies travel 9 a circle1 if no?+ int]f]es ) !m1 because ! circul> is ! noble/ ( all movem5ts4 ,we %all see lat] h[ ! pr9ciple ( in]tia ( ,e9/e9's g5]alis$ me*anics has a /range aff9ity to ?is idea1 & at ! same "t to ! curi\s decl9ation1 ! cl9am51 :i* ! great & pr(\nd ,lucretius attribut$ to ! free pa? ( ! atoms4 ,b we mu/ n anticipate4 99 99 99 99 99 ,?is belief1 t an object left freely to itself & n act$ ^u by any =ce pres]ves its velocity & direction1 _c pret5d to be m ?an an exp]im5tal tru?4 ,b ! obs]vations on :i* x is bas$1 especially ^? ( ,galileo1 b any t may be imag9$ by physici/s1 c\ld n possibly be conclusive1 because 9 practice x is impossible to protect a mov+ body f e ext]nal =ce1 su* z atmosph]ic resi/ance1 friction1 or o!r4 ,i am aw>e t ,newton gr\nd$ 8 pr9ciple on a/ronomical z well z t]re/rial obs]vations4 ,he notic$ t1 ap>t f any attraction by o!r cele/ial bodies1 & z f> z we c see1 ! planets seem to ma9ta9 _! direction & velocity relatively to ! vault ( heav54 ,b ,relativi/s ?9k t ! words ,i h italicis$ 9 ! prec$+ s5t5ce1 :i* reflect ,newton's idea1 really beg ! "q4 ,8 argum5t assumes t ! planets d n circulate freely2 t !y are gov]n$ 9 _! motions by a =ce :i* he call$ univ]sal attraction4 ,we %all see h[ ,e9/e9 came to ?9k t ?is is n a =ce1 & 9 t case ! issue ( ! argum5t is v diff]5t4 ,h[ev] t may be1 ! classical pr9ciple ( in]tia is a tru? bas$ ^u 7imp]fect7 exp]i5ce1 & x is !re=e subject to ! con/ant control ( facts4 ,all t we c say ab\t x is t practically--t is to say1 approximately--x h>monises ) :at we f9d4 ,newton did n reg>d x z su*1 n z a m or less precise approximation1 b z a /rict tru?4 ,t is :y1 :5 he saw t ! planets d n travel 9 /raight l9es b 9 curv$ orbits1 he conclud$--:i* is a petitio pr9cipii--t !y 7 subject to a c5tral =ce1 gravitation4 ,t is :y heavy bodies did n seem to him am5able to ! me*anical laws :i* he _h =mulat$ = bodies left freely to !mselves4 ,t is :y1 9 a ^w1 ,newton's law ( gravitation & 8 laws ( dynamics are two di/9ct & sep>ate ?+s4 ,! great g5ius1 ! m9d :i* _h no equal1 0 nev]!less human4 ,! immortal ,desc>tes put =w>d /range /atem5ts & v occult hypo!ses 7ab\t ! p9eal gl& & animal spirits71 aft] he _h expressly resolv$ to affirm no?+ t he did n p]ceive cle>ly & di/9ctly4 ,9 ! same way ,newton1 aft] lay+ d[n z 8 pr9ciple ,hypo!ses non f+o1 put ! hypo!ses ( absolute "t & space at ! v basis ( 8 me*anics4 ,at ! basis ( 8 ma/]ly !ory ( gravitation he put ! hypo!sis--:i* is a priori easi] to admit--t !re is a special =ce ( gravitation4 ,^! are weaknesses :i* ! greate/ ( m5 d n escape4 ,!y ought to make u admire all ! m ! f9] aspects ( _! "w4 ,s deep is ! furr[ pl\gh$ by ^! great /ud5ts ( ! unkn[n t1 ev5 :5 x is n /raight1 x takes two c5turies & a half be=e m5 dream ( inquir+ afre% :e!r ,newton's di/9ction betwe5 purely me*anical & gravitational ph5om5a 0 j4 ,x is ! signal di/9ction ( ,e9/e9 t he successfully accompli%$ ?is3 t1 aft] eras+ _m ?+s :i* 7 suppos$ to be f9ally settl$1 he bl5d$ me*anics & gravitation 9 a sup]b syn!sis1 & enabl$ u to see m cle>ly ! sublime unity ( ! _w4 99 99 99 99 99 ,to tell ! tru?--let u premise ?is be=e we g fur!r into ! pr(\nd & m>vell\s tru?s ( ,g5]al ,relativity--x is a priori evid5t t ,newton's law ( univ]sal attraction c no long] be consid]$ satisfactory4 ,x says3 ,bodies attract ea* o!r 9 direct proportion to _! masses & 9 inv]se proportion to ! squ>e ( _! di/ances4 ,:at does t mean8 ,we saw t ! mass ( a body v>ies ) its velocity4 ,:51 = in/ance1 we introduce ! mass ( our planet into calculations :i* involve ,newton's law1 :at precisely d we mean8 ,d we mean ! mass :i* ! e>? w\ld h if x did n revolve r\nd ! sun8 ,or d we mean ! l>g] mass :i* x has 9 virtue ( its motion8 ,?is motion1 h[ev]1 is n always ( ! same spe$1 because ! e>? travels 9 an ellipse1 n a circle4 ,:at value %all we give to ?is v>iable mass 9 ! calculation8 ,t :i* corresponds to p]ihelion or aphelion1 ! p]iod :5 ! e>? travels mo/ rapidly or mo/ sl[ly8 ,moreov]1 ought we n also to take into acc\nt ! velocity ( translation ( ! sol> sy/em1 :i* 9 turn increases or dim9i%es accord+ to ! season8 ,aga91 "u ,newton's law :at %all we make ! di/ance f ! e>? to ! sun8 ,is x to be ! di/ance relatively to an obs]v] on ! e>? or on ! sun1 or to a /ation>y obs]v] 9 ! middle ( ! ,milky ,way :o does n %>e ! motion ( our sy/em across x8 ,"h aga9 we %all h diff]5t values 9 ea* case1 because spatial di/ances v>y1 z we saw ) ,e9/e91 accord+ to ! relative velocity ( ! obs]v]4 ,h5ce ,newton's law is1 9 spite ( its simple & arti/ic =m1 ambigu\s & f> f cle>4 ,i am aw>e t ! diff]5ces ,i h j not$ are n v important1 b our calculations %[ t !y are by no means negligible4 ,e9/e9ians !re=e reg>d x z indisputable1 ap>t f ! consid]ations :i* we %all see pres5tly1 t ,newton's law1 9 its classical =m1 is obscure1 & mu/ be modifi$ & complet$4 ,^! prelim9>y rem>ks w s]ve to at lea/ put u 9 ! frame ( m9d t is requir$ ( iconocla/s2 & 9 sci5ce ! iconocla/s are (t5 ! mak]s ( progress4 ,! p>ticul> idols at :i* we are prep>+ to deal a few audaci\s bl[s are ! conception ( ! ,newtonian law & gravitation4 ,laplace wrote1 9 8 ,exposition du ,sy/me du ,monde3 8,x is impossible to d5y t no?+ is m fully prov$ 9 natural philosophy ?an ! pr9ciple ( univ]sal gravitation 9 virtue ( mass & 9 inv]se proportion to ! squ>e ( ! di/ance40 ,no?+ c bett] %[ u ?an ?is s5t5ce ( ! great ma!matician ! importance ( ! /ep tak5 by ,e9/e9 :5 he1 z we %all see1 improv$ :at _h be5 reg>d$ z ! v type1 ! mo/ p]fect example1 ( sci5tific tru?3 ! fam\s ,newtonian law4 99 99 99 99 99 ,gravitation1 or weight1 has ?is 9 common ) in]tia1 t x is a q g5]al ph5om5on4 ,all mat]ial objects1 :atev] may be _! physical & *emical condition1 are bo? in]t 7t is to say1 accord+ to _! mass !y resi/ =ces :i* t5d to displace !m7 & heavy 7!y fall :5 !y are left to !mselves74 ,b x is a /range ?+1 not$ by ,newton1 ?\gh he did n realise ! significance ( x--he reg>d$ x m]ely z an extraord9>y co9cid5ce--t ! same figure :i* def9es ! in]tia ( a body also def9es its weight4 ,?is figure is ! mass ( ! body4 ,let u return to ! illu/ration :i* ,i us$ 9 a previ\s *apt] 9 deal+ ) ,e9/e9's me*anics4 ,if two tra9s drawn by two simil> locomotives />t 9 ! same conditions1 & if ! velocity communicat$ to ! fir/ tra9 at ! end ( a second is d\ble t communicat$ to ! second1 we conclude t ! in]tia1 ! in]t mass1 ( ! second tra9 7leav+ out ( acc\nt ! friction ) ! rails7 is twice z great z t ( ! fir/4 ,if we aft]w>ds weigh our two tra9s1 we f9d t ! weight ( ! second is simil>ly twice z great z t ( ! fir/4 ,?is exp]im5t1 ?\gh crude en\gh 9 our illu/ration1 has be5 made ) great precision by physici/s1 :o us$ delicate me?ods :i* we ne$ n describe "h4 ,! result 0 ! same4 ,! in]t mass & ! weight ( bodies are exactly express$ by ! same figures4 ,newton saw 9 ?is a m]e co9cid5ce4 ,e9/e9 f\nd 9 x ! key to ! h]metically seal$ & inviolate dungeon 9 :i* gravitation 0 isolat$ f ! re/ ( nature4 ,let u see h[4 ,!re is "o rem>kable feature ( weight or gravitation3 :atev] be ! nature ( ! objects1 !y always fall at ! same spe$ 7ap>t f atmosph]ic resi/ance74 ,?is is easily prov$ by caus+ a numb] ( diff]5t objects to fall1 9 ! same p]iod ( "t1 d[n a long tube 9 :i* a vacuum has be5 creat$4 ,!y all rea* ! bottom ( ! tube at ! same "t4 ,a ton ( lead & a %eet ( pap] w1 if !y are laun*$ into ! void simultane\sly f ! summit ( a t[]1 rea* ! gr\nd simultane\sly1 ) a velocity ! accel]ation ( :i* is1 ne> ! gr\nd1 #iha c5timetres a second4 ,?is fact 0 kn[n to ,lucretius4 ,two ?\s& ye>s ago t pr(\nd & immortal poet wrote3 ,nulli1 de nulla p>te1 neque ullo ,tempore1 inane pote/ vacuum subsi/]e rei1 ,qu9 sua quod natura petit conc$]e p]gat4 ,omnia quapropt] deb5t p] inane quietum que pond]ibus non quis concita f]ri4#h #h ,de ,natura ,r]um1 bk4 ii1 vv4 #bce-dj4 ,n[ if weight 7 a =ce analog\s to electrical attraction1 to ! propulsion ( a locomotive1 or ev5 to ! propulsive action ( a *>ge ( p[d]1 ?is ought n to be ! case4 ,! velocities :i* x communicates to diff]5t masses ought to be diff]5t f ea* o!r4 ,! two tra9s ( unequal mass 9 our illu/ration receive unequal accel]ations f ! same locomotive4 ,nev]!less1 if a great tr5* sudd5ly op5$ be=e !m1 !y w\ld fall into x ) ! same velocity4 ,f ?is x is only "o /ep to conclude t gravitation is n a =ce1 z ,newton ?\ght1 b simply a prop]ty ( space 9 :i* bodies move freely4 ,e9/e9 took ?is /ep )\t hesitation4 ,imag9e ! cable ( ! lift 9 "s colossal skyscrap] sudd5ly break+4 ,! lift w fall ) an accel]at$ movem5t1 ?\gh less rapidly ?an x w\ld 9 a vacuum1 on acc\nt ( ! atmosph]ic resi/ance & ! friction ( ! cage ( ! app>atus4 ,b let u suppose1 fur!r1 t ! electrical eng9e :i* works ! lift has its commutator rev]s$ at ! same "t1 & ?is accel]ates ! fall to su* an ext5t t ! velocity ( ! desc5t increases #iha c5timetres 9 e second4 ,x w\ld be q easy = our eng9e]s to c>ry out ?is exp]im5t1 ?\gh ! int]e/ ( x has n up to ! pres5t seem$ great en\gh to ju/ify x4 ,b we h ! "r1 :5 x is necess>y to make a subject cle>1 to say ) ! poet3 ,an ?\ wilt1 let u dream a dream4 ,let u suppose our dream fulfill$4 ,! lift falls f above ) precisely ! accel]at$ velocity ( an object fall+ 9 a vacuum4 ,if ! pass5g]s h kept cool en\gh 9 _! giddy ru% d[nw>d to obs]ve :at happ5s1 !y w notice t _! feet cease to press aga9/ ! floor ( ! lift4 ,!y c imag9e !mselves l ,la ,fonta9e's *>m+ & poetic pr9cess3 ,no blade ( grass _h felt ,! light traces ( h] /eps4 ,our pass5g]s' purses w1 ev5 if !y are full ( gold1 no long] be heavy 9 _! pockets--:i* may give !m a mom5t>y anxiety4 ,if _! hats are releas$ f _! h&s1 !y w rema9 susp5d$ 9 ! air beside !m4 ,if !y happ5 to h scales ) !m1 !y w notice t ! pans rema9 pois$ at equal height1 ev5 if v>i\s weights are put 9 "o pan4 ,all ?is is because ! objects1 z a natural effect ( _! weight1 fall t[>d ! gr\nd ) ! same velocity z ! lift itself4 ,_! weight has disappe>$4 99 99 99 99 99 ,jules ,v]ne describ$ ?is /ate ( ?+s 9 ! projectile :i* he imag9$ tak+ 8 h]oes f ! e>? to ! moon1 at ! mom5t :5 ! romantic projectile rea*es ! 8neutral po9t03 t is to say1 ! po9t :]e x leaves ! e>?'s sph]e ( gravitation1 b has n yet ent]$ t ( ! moon4 ,we might add t ,jules ,v]ne p]petrat$ a few little sci5tific h]esies 9 connection ) 8 projectile4 ,9 p>ticul>1 he =got t1 9 compliance ) :at is mo/ conspicu\sly evid5t 9 ! pr9ciple ( in]tia1 ! un=tunate pass5g]s ought to h be5 flatt5$ l pancakes aga9/ ! bottom ( ! projectile :5 ! *>ge 0 fir$4 ,he also wrongly suppos$ t objects ceas$ to h weight 9 ! projectile only at ! po9t :]e x 0 exactly betwe5 ! two sph]es ( attraction1 t ( ! e>? & t ( ! moon4 ,b let u ov]look ^! trifles & return to ! admirable illu/ration he has prophetically provid$ = our conv5i5ce 9 expla9+ ,e9/e9's sy/em4 ,let u take ! projectile :5 x beg9s to fall freely t[>d ! moon4#i ,x is evid5t t f ?is po9t onw>d1 until x l&s on ! moon1 x w behave exactly l ! lift :i* we h describ$4 #i ,x is obvi\s t we assume ! projectile to be )\t rotation3 t is to say1 ! ,columbia cannon mu/ n1 9 our hypo!ses1 be rifl$4 ,?is is indisp5sable1 = if ! projectile turn$1 !re w\ld be c5trifugal effects :i* w\ld greatly complicate bo? ! ph5om5a & our argum5t4 ,dur+ ?is fall ^u ! moon ! pass5g]s1 if !y h miracul\sly escap$ be+ flatt5$ at ! />t1 w see ! v>i\s objects ab\t !m sudd5ly depriv$ ( _! weight1 float+ 9 ! air1 &1 at ! slighte/ %ake1 adh]+ to ! walls or ! vault$ ro( ( ! projectile4 ,!y w feel !mselves extraord9>ily light1 & !y w be able to make prodigi\s leaps )\t any ef=t4 ,?is is because !y & all ! objects ab\t !m fall t[>d ! moon ) ! same velocity z ! projectile4 ,h5ce ! disappe>ance ( weight or gravitation1 :i* vani% z if spirit$ away by "s magician4 ,! magician is ! prop]ly accel]at$ movem5t1 ! unimp$$ fall ( ! obs]v]s4 ,9 a ^w1 to get rid ( ! app>5t effects ( gravitation 9 any place :atev] x is en\gh = ! obs]v] to acquire a prop]ly accel]at$ velocity4 ,t is :at ,e9/e9 calls ! 8pr9ciple ( equival5ce03 equival5ce ( ! effects ( weight & ( an accel]at$ movem5t4 ,! "o _c be di/+ui%$ f ! o!r4 ,let u imag9e ,jules ,v]ne's projectile & its un=tunate pass5g]s transport$ a long di/ance f ! moon1 ! e>?1 & ! sun1 to "s des]t$ & glacial region ( ! ,milky ,way :]e !re is no matt]1 & s remote f ! />s t !re is no long] any weight or attraction4 ,let u suppose t our projectile is ab&on$ !re1 & motionless4 ,x is cle> t 9 ^! circum/ances !re w be no su* ?+ z high or l[--no su* ?+ z weight--= ! pass5g]s4 ,!y w f9d !mselves reliev$ ( e inconv5i5ce ( weight4 ,!y may1 if !y *oose1 /& on ! inn] wall ( ! upp] "p ( ! projectile or on ! floor1 z x 0 :5 !y 7 fall+ ^u ! moon4 ,n[ let u suppose t ! wiz>d ,m]l9 quietly approa*es &1 fa/5+ a cord to ! r+ on ! top ( ! projectile1 beg9s to drag x ) a uni=mly accel]at$ movem5t4 ,:at w happ5 to ! pass5g]s8 ,!y w notice t !y h sudd5ly recov]$ _! weight1 & t !y are rivet$ to ! floor ( ! projectile1 mu* z !y 7 drawn to ! surface ( our planet be=e !y left x4 ,inde$1 if ! motion ( ,m]l9 is accel]at$ #iha c5timetres a second1 !y w h exactly ! same s5sations ( weight z !y _h on ! e>?4 ,!y w notice t if !y ?r[ a plate into ! air at a giv5 mom5t1 x w fall ^u ! floor & be brok54 8,?is is10 !y w ?9k1 8because we are aga9 subject to weight4 ,! plate falls 9 virtue ( its weight1 its in]t mass40 ,b ,m]l9 w say3 8,! plate falls because1 on acc\nt ( its in]tia1 x has reta9$ ! increas+ velocity :i* x _h at ! mom5t :5 x 0 ?r[n4 ,imm$iately aft]w>ds1 z ,i drew ! projectile ) an accel]at$ movem5t1 ! asc5d+ velocity ( ! projectile 0 great] ?an t ( ! plate4 ,t is :y ! bottom ( ! projectile1 9 its accel]at$ asc5d+ c\rse1 knock$ aga9/ ! plate & broke x40 ,?is proves t ! weight or gravitation ( a body is indi/+ui%able f its in]tia4 ,in]t mass & heavy mass are n1 z ,newton suppos$1 two ?+s :i* happ5 by "s extraord9>y co9cid5ce to be equal2 !y are id5tical & insep>able4 ,! two ?+s are really "o4 ,& we are ?us l$ to believe t ! laws ( weight & ! laws ( in]tia1 ! laws ( gravitation & ^? ( me*anics1 mu/ be id5tical1 or mu/ at lea/ be two modalities ( "o & ! same ?+3 mu* z ! full face & ! pr(ile ( ! same man are ! same face se5 "u two diff]5t angles4 ,ev5 if ! travell]s 9 ! projectile--:o look r l gu9ea-pigs--peep out ( ! w9d[ & see ! cord t is draw+ !m1 x w n alt] _! illusion4 ,!y w believe t !y are at re/ & float+ at a po9t ( space :]e weight has be5 re/or$3 t is to say1 9 ! language ( ! exp]ts1 at a po9t ( space :]e !re is a 8gravitational field40 ,?is phrase is analog\s to ! famili> 8magnetic field10 :i* ref]s to a "p ( space 9 :i* !re is magnetic action1 a "p 9 :i* ! ne$le ( ! compass has a def9ite direction impos$ ^u x4 ,9 sum1 we c at any po9t replace a gravitational field1 or ! effects ( weight1 by a prop]ly accel]at$ movem5t ( ! obs]v]1 & vice v]sa4 ,!re is a complete equival5ce betwe5 ! effects ( weight & ^? ( an appropriate movem5t4 99 99 99 99 99 ,?is n[ enables u to e/abli% v simply ! foll[+ fundam5tal fact1 unkn[n only a few ye>s ago1 b n[ brilliantly prov$ by exp]im5t3 ,light does n travel 9 a /raight l9e 9 ^? p>ts ( ! univ]se :]e !re is gravitation1 b its pa? is curv$ l t ( heavy objects4 ,we %[$ 9 "o ( ! prec$+ *apt]s t 9 ! f\r-dim5sional cont9uum 9 :i* we live1 :i* we might call 8space-"t0 b :i* we m simply call ! univ]se1 !re is some?+ t rema9s con/ant1 id5tical = obs]v]s :o move at giv5 & diff]5t velocities4 ,x is ! 8,int]val0 ( ev5ts4 ,x is natural to suppose t ?is 8,int]val0 w rema9 id5tical ev5 if ! velocity ( ! obs]v]s *anges--ev5 if x is accel]at$ l ! velocity ( ! lift 9 our illu/ration1 or ( ,jules ,v]ne's projectile1 dur+ _! fall4 ,9 po9t ( fact1 if some?+ 9 ! univ]se is an inv>iant1 z physici/s say1 or inv>iable1 = ! obs]v]s :o move at diff]5t spe$s1 ?is some?+ mu/ naturally rema9 ! same = a ?ird obs]v] ^: velocity *anges gradually f t ( ! fir/ to t ( ! second obs]v]1 & :o is !re=e 9 a /ate ( uni=mly accel]at$ movem5t4 ,f ?is we d$uce c]ta9 consequ5ces ( a fundam5tal "*4 ,9 ! fir/ place1 "o ?+ is evid5t1 & is unanim\sly admitt$ by physici/s3 9 a vacuum1 & 9 a region ( space :]e !re is no =ce act+ & no su* ?+ z weight1 light travels 9 a /raight l9e4 ,t is c]ta9 = _m reasons--9 ! fir/ place1 on ! m]e gr\nd ( symmetry1 because 9 a region ( isotropic vacuum a ray :i* is un9flu5c$ w n dep>t f its rectil9e> pa? 9 any direction :atev]4 ,t is evid5t1 :atev] hypo!sis we adopt z to ! nature ( light1 & ev5 if1 l ,newton1 we suppose t x consi/s ( pond]able p>ticles4 ,admitt+ t1 let u n[ suppose t at "s po9t 9 ! univ]se :]e !re is weight--at ! moon's surface1 = in/ance--!re is a rem>kable gun :i* c fire a ball t has & reta9s 7along its :ole pa?7 ! velocity ( light4 ,! trajectory ( ?is ball w be v ext5sive1 on acc\nt ( its great velocity1 yet curv$ t[>d ! surface ( ! moon on acc\nt ( its weight4 ,z we may make our *oice 9 ! field ( hypo!ses1 !re is no?+ to prev5t u f suppos+ t ! ball is ( su* a nature z to disclose its pa? by a fa9t lum9\s trail4 ,!re 7 projectiles ( ?is "* dur+ ! ,great ,w>4 ,z ! ball advances1 x also falls e second t[>d ! moon's surface1 to ! same ext5t z any o!r projectile w\ld :i* 0 fir$ at any velocity :atev]1 or _h no velocity4 ,all objects ne> ! surface ( ! gr\nd 79 a vacuum7 fall at ! same v]tical velocity1 & ?is is indep5d5t ( _! motion 9 ! horizontal direction4 ,t is1 9 fact1 ! reason :y ! pa?s ( projectiles are ! m curv$ ! less initial spe$ !y h4 ,se5 f ! w9d[s ( ,jules ,v]ne's projectile 7:i* is itself fall+ t[>d ! moon71 ! trajectory ( ! ball w seem to ! pass5g]s to be a /raight l9e1 because x falls ) ! same velocity z !y4 ,n[ let u suppose t a lum9\s ray1 f ! flame ( ! gun1 />ts at ! same "t & 9 ! same direction z ! ball4 ,?is lum9\s ray w obvi\sly be rectil9e> = ! pass5g]s 9 ! projectile1 because light travels 9 a /raight l9e :5 !re is no weight4 ,consequ5tly1 s9ce x has ! same =m1 direction1 & velocity z ! lum9\s ball1 ! pass5g]s w see ! ray ( light co9cide 9 its :ole c\rse ) ! trajectory ( ! ball4 ,x fur!r foll[s t ! 8,int]val0 7bo? 9 "t & space7 ( ! lum9\s ray & ( ! ball is1 & rema9s1 z]o4 ,n[ ?is 8,int]val0 mu/ rema9 ! same1 :atev] be ! velocity ( ! obs]v]4 ,h5ce1 if ,jules ,v]ne's projectile ceases to fall1 & is /opp$ at ! moon's surface1 its pass5g]s w cont9ue to see ! lum9\s ray co9cide at e po9t ) ! trajectory ( ! ball4 ,?is trajectory is1 z !y n[ notice1 curv$ on acc\nt ( weight4 ,!re=e1 ! lum9\s ray is simil>ly curv$ 9 its pa? on acc\nt ( weight4 ,?is %[s t light does n travel 9 a /raight l9e1 b falls1 "u ! influ5ce ( gravitation1 l all o!r objects4 ,! reason :y ?is 0 nev] kn[n be=e1 & x 0 always ?\ght t light travels 9 a /raight l9e1 is t on acc\nt ( ! enorm\s velocity ( light its trajectory is only v slightly curv$ by weight4 ,t is easy to und]/&4 ,at ! e>?'s surface1 = in/ance1 light mu/ fall 7l all o!r objects7 ) a velocity equal to #iha c5timetres at ! end ( a second4 ,n[ by ! end ( a second a lum9\s ray has travell$ #cjj1jjj kilometres4 ,suppose we c\ld obs]ve a horizontal lum9\s ray #cjj kilometres long ne> ! e>?'s surface--a v f>-fet*$ supposition--dur+ ! ?\s&? "p ( a second1 :i* x w take ! ray to pass f "o obs]v] to ! o!r1 x w fall to ! ext5t ( only ab\t ! five-?\s&? ( a millimetre4 ,we c und]/& h[ x 0 t a lum9\s ray t deviates only to ?is imp]ceptible ext5t f its initial direction 9 ! c\rse ( ?ree hundr$ kilometres 0 always consid]$ rectil9e>4 ,is !re no means ( v]ify+ :e!r light is or is n b5t out ( its pa? by gravitation8 ,!re is su* a means 9 a/ronomy1 z we %all n[ see4 99 99 99 99 99 ,x is impossible to detect ! curvature ( a lum9\s ray travell+ f "o po9t to ano!r on ! e>?'s surface1 ma9ly because weight on ! e>? is too slight to b5d ! ray mu*4 ,a fur!r reason is t our planet is s ridicul\sly small t we _c foll[ ! light ov] a suffici5t di/ance4 ,b :at _c be done on ?is little globule ( ours1 ! entire diamet] ( :i* light c cov] 9 ! tw5ty-fif? ( a second1 may possibly be done 9 ! gigantic laboratory ( cele/ial space4 ,we h1 almo/ )9 our rea*--a m]e matt] ( #ic1jjj1jjj miles away1 t is to say--a /> on :i* weight is tw5ty-sev5 times great] ?an on ! e>?4 ,we mean ! sun4 ,on ! sun a body left to itself falls #acb metres 9 ! fir/ second4 ,its fall is tw5ty-sev5 times z rapid z on ! e>?4 ,h5ce1 ne> ! sun1 light w be mu* m b5t out ( its pa? by gravitation4 ,! deviation w be all ! great] f ! fact t ! sun is #hjj1jjj miles 9 diamet]1 & a lum9\s ray ne$s a mu* long] "t to cov] ?is di/ance ?an to travel ! l5g? ( ! e>?'s diamet]4 ,h5ce gravitation acts ^u ! ray ( light dur+ a mu* long] "t ?an ^u a ray t rea*es ! e>?1 & x w be all ! m curv$4 ,take a lum9\s ray t comes f a /> at a great di/ance beh9d ! sun4 ,if x rea*es u aft] pass+ ne> to ! sun1 x w behave l a projectile4 ,its pa? w no long] be rectil9e>4 ,x w be slightly curv$ t[>d ! sun4 ,9 o!r words1 ! ray w deviate f a /raight l9e1 & ! direction x has :5 our eyes receive x on ! e>? is a little diff]5t f ! direction x _h :5 x left ! />4 ,x has be5 div]t$4 ,calculation %[s t ?is deviation1 ?\gh v slight1 c be measur$4 ,x is equal to an angle ( a second & ?ree-qu>t]s3 an angle :i* ! delicate me?ods ( our a/ronom]s are able to measure4 ,c]ta9ly su* an angle is v f> f consid]able1 = x takes #cbd1jjj angles ( "o second to make a "r angle4 ,9 o!r words1 an angle ( "o second is t at :i* we %\ld see ! two ends ( a rod1 a metre 9 l5g?1 fix$ 9 ! gr\nd1 at a di/ance ( #bjf kilometres4 ,if our eyes 7 %>p en\gh to see a man ( normal height /&+ #bjj kilometres away f u1 our glance1 9 pass+ f 8 head to 8 feet1 w\ld h a v small angle ( deviation4 ,well1 ?is angle accurately repres5ts ! deviation exp]i5c$ by ! light t comes to u f a /> :5 x has pass$ close to ! gold5 globe ( ! sun4 ,m9ute z ?is angle is1 ! me?ods ( ! a/ronom] are s delicate & precise t he c det]m9e x4 ,! t9y measurem5t is by no means to be despis$4 ,disda9 ( ! m5 :o devote !mselves to su* ref9$ subtleties is v mu* out ( place1 because our mod]n sci5ce has be5 revolutionis$ by ?is measurem5t4 ,e9/e9 is "r1 & ,newton wrong1 because we h be5 able to measure ?is m9ute angle & e/abli% ! curvature ( light4 ,a great difficulty arose :5 we wi%$ to v]ify ?is4 ,h[ c we obs]ve 9 full daylight a ray ( light t comes to u f a /> & passes close to ! sun8 ,x _c be done4 ,ev5 if we use ! mo/ p[]ful glasses ! />s on ! f>!r side ( ! sun are completely dr[n$ 9 its blaze--to speak m correctly1 9 ! light :i* is diffus$ by our atmosph]e4 ,to say ! tru?--if we may v5ture ^u a p>5!tic rem>k at ?is juncture--night has taught u mu* m ?an day ab\t ! my/]ies ( ! univ]se4 ,9 lit]>y symbolism1 9 politics1 ! light ( day is ! v symbol ( progress & k3 night is ! symbol ( ignorance4 ,:at folly6 ,x is a blasphemy aga9/ night1 ! sweetness ( :i* we ought r to v5]ate4 ,i d n ref] to its romantic *>m1 b to ! mighty progress 9 k :i* x has enabl$ u to make4 ,midnight is n m]ely ! h\r ( crime4 ,x is also ! h\r ( prodigi\s flight t[>d remote worlds4 ,dur+ ! day we see only "o sun3 by night we see millions ( suns4 ,! bl9d+ veil :i* ! sunlight draws across ! heav5s may be wov5 ( ! mo/ brilliant rays1 b x is none ! less a veil1 = x makes u z bl9d z ! mo?s :i*1 9 a /rong light1 c see no fur!r ?an ! tips ( _! w+s4 ,9 ord] to solve our problem1 !re=e1 we h to obs]ve 9 complete d>kness />s :i* are nev]!less ne> ! edge ( ! sun's disk4 ,is t impossible8 ,no4 ,nature has met our ne$ by provid+ total eclipses ( ! sun :i* may at times be se5 f v>i\s /ations on ! e>?4 ,at ^? times ! bright disk is hidd5 = a few m9utes beh9d ! disk ( ! moon4 ,midday is turn$ into midnight4 ,we see />s %9e out close to ! mask$ face ( ! sun4 99 99 99 99 99 ,=tunately1 a total eclipse1 visible 9 ,africa & ,s\? ,am]ica1 0 due on ,may #bi1 #aiai1 %ortly aft] ,e9/e9 _h1 on ! /r5g? ( an argum5t l t we h j exp\nd$1 ann\nc$ ! deviation ( ! light ( ! />s :5 x pass$ ! sun4 ,two exp$itions 7 organis$ by ! a/ronom]s ( ,gre5wi* & ,ox=d4 ,"o proce$$ to ,sobral1 9 ,brazil1 ! o!r to ! small ,portuguese isl& ,pr9cipe1 9 ! ,gulf ( ,gu9ea4 ,"s ( ! ,engli% a/ronom]s 7 r sceptical ab\t ! issue4 ,h[ c\ld we1 until x 0 prov$1 admit t ,newton 0 wrong1 or _h at lea/ fail$ to =mulate a p]fect law8 ,b ?is 0 prov$1 & v decisively1 by ! obs]vations4 ,^! obs]vations consi/$ 9 tak+ a c]ta9 numb] ( photographs dur+ ! few m9utes ( total eclipse ( ! />s ne> ! sun4 ,!y _h be5 photograph$ ) ! same in/rum5ts "s weeks be=e1 at a "t :5 ! region ( ! sky 9 :i* !y %9e 0 visible at night & f> f ! sun4 ,z ev]ybody kn[s1 ! sun passes successively1 9 its annual c\rse1 ?r\gh ! diff]5t con/ellations ( ! zodiac4 ,if ! light ( ! />s :i* 7 photograph$ 7 n b5t out ( its pa? 9 pass+ ! sun1 x is cle> t _! di/ances ought to be ! same on ! plates expos$ dur+ ! eclipse z on ! negatives tak5 dur+ ! night "s "t previ\sly4 ,b if ! light f !m 7 b5t out ( its c\rse dur+ ! eclipse by ! gravitational influ5ce ( ! sun1 x w\ld be q o!rwise4 ,! reason is z foll[s4 ,:5 ! moon rises on "o ( our pla9s1 x is n r\nd1 z ev]ybody w h notic$1 b flatt5$ at top & bottom1 some:at l a giant tang]9e lift$ above ! horizon = "s magic supp]4 ,! moon has1 ( c\rse1 n ceas$ to be r\nd4 ,x m]ely seems to be flatt5$ because ! rays :i* come f its l[] edge1 & h to pass ?r\gh a ?ick /ratum ( ! atmosph]e be=e !y rea* u1 are b5t t[>d ! gr\nd by ! refraction ( ! d5s] atmosph]e mu* m ?an are ! rays com+ f ! moon's upp] edge1 :i* pass ?r\gh a less d5se mass ( air4 ,our eyes see ! edge ( ! moon 9 ! direction f :i* its rays come to u1 n 9 ! direction f :i* !y />t$4 ,t is :y ! l[] edge ( ! moon seems to u to be rais$ high] above ! horizon ?an x really is4 ,?is deviation is due to refraction4 ,9 ! same way a /> situat$ a little to ! ea/ ( ! sun 7! rays 9 ?is case be+ curv$ by weight1 n by refraction7 w seem to u fur!r away f x4 ,x w look z if x 7 fur!r ea/ ?an x really is4 ,simil>ly1 a /> to ! we/ ( ! sun w seem to u /ill fur!r f ! sun's we/]n edge4 ,h5ce ! />s on ei!r side ( ! sun w1 if ,e9/e9 is "r1 be m widely sep>at$ f ea* o!r 9 ! negatives tak5 dur+ ! eclipse4 ,9 _! normal position1 on ! photographs tak5 dur+ ! night1 !y w seem ne>] to ea* o!r4 ,?is is precisely :at 0 f\nd :5 ! photographs tak5 at ,sobral & ,pr9cipe 7 /udi$ ) ! aid ( ! micromet]4 ,n only 0 x ?us prov$ t ! light ( ! />s is b5t out ( its pa? by ! sun1 b x 0 f\nd t ! deviation _h exactly ! ext5t :i* _h be5 pr$ict$ by ,e9/e94 ,x am\nts to an angle ( "o second & ?ree-qu>t]s 7#age7 9 ! case ( a /> t is q close to ! sun's disk1 & ! angle decreases rapidly 9 proportion to ! di/ance ( />s f ! sun4 ,x 0 a great triumph = ! !ory ( ,e9/e91 & = ! fir/ "t x gave u "s connect+ l9k betwe5 light & gravitation4 ,on ! prec$+ page ,i comp>$ ! curvature ( light ow+ to its weight ) ! deviation t is caus$ by atmosph]ic refraction4 ,z a matt] ( fact1 !re 7 a/ronom]s :o wond]$ :e!r ! agreem5t betwe5 ,e9/e9's !ory & ! results obta9$ dur+ ! eclipse 0 n m]ely a co9cid5ce3 :e!r ! deviation t 0 record$ 0 n due to refractive action by ! sun's atmosph]e4 ,x seems impossible to admit ?is4 ,sometimes we see comets pass+ q close to ! surface ( ! sun dur+ _! j\rney ?r\gh space4 ,_! movem5t w\ld be consid]ably di/urb$ if ! sun's atmosph]e 7 refractive en\gh to acc\nt = ! deviations obs]v$ at ,sobral & ,pr9cipe4 ,p]turbations ( comet>y orbits ( ?is nature1 ne> ! sun1 h nev] be5 record$4 ,! only possible int]pretation1 !re=e1 is t ! ph5om5a are due to ! effect ( weight ^u light4 ,?us ! light ( ! />s1 weigh$ 9 a balance ( ! mo/ exquisite delicacy1 has giv5 u a decisive confirmation ( ,e9/e9's !oretical d$uctions4 ,by its fruit we "k ! tree4 ,,*apt] ,,vi ,,! ,,new ,,conception ,,( ,,gravitation ,geometry & reality--,euclid's geometry & o!rs--,cont+5cy ( ,po9c>'s crit]ion--,! real univ]se is n ,euclidean b ,riemannian--,! avat>s ( ! numb] --,! po9t ( view ( ! drunk5 man--,/raight & geodetic l9es--,! new law ( univ]sal attraction--,explanation ( ! anomaly ( ! planet ,m]cury--,e9/e9's !ory ( gravitation4 ,does ! univ]se con=m to ! laws ( geometry8 ,x is a "q t has be5 mu* discuss$ by philosoph]s & s*ol>s1 b ! deviation ( light ow+ to its weight n[ enables u to approa* x ) confid5ce4 ,9 our s*ools we are taught a magnific5t s]ies ( geometrical !orems1 all solidly int]connect$1 ! pr9cipal ( :i* 7 creat$ by ! great ,greek g5ius1 ,euclid4 ,t is :y classical geometry is kn[n z ,euclidean geometry4 ,its !orems are bas$ ^u a c]ta9 numb] ( axioms & po/ulates1 ?\gh ^! are really only affirmations or def9itions4 ,! mo/ important ( ^! def9itions is3 8,a /raight l9e is ! %orte/ di/ance betwe5 two po9ts40 ,t seems to s*oolboys q simple1 because !y "k t ! y\? :o amuses himself by runn+ 9 a zigzag on ! rac+ track w be ! la/ to rea* ! tape2 & at ! sports gr\nd "o is n 9 a mood or has n "t to bo!r ab\t ! validity ( ! axioms ( geometry4 ,:at is ! precise mean+ ( ?is def9ition ( a /raight l9e8 ,!re has be5 a great deal ( discussion ( t po9t4 ,h5ri ,po9c> has writt5 a numb] ( f9e & pr(\nd pages on x1 yet 8 conclusions are n entirely )\t an elem5t ( unc]ta9ty4 ,9 practice we all "k :at we mean by a /raight l9e3 x is ! l9e t we make by means ( a good rul]4 ,b h[ d we "k t a rul] is good & correct8 ,by hold+ x up be=e ! eye1 & see+ t bo? ends ( x & all ! int]m$iate po9ts 9 its edge m]ge toge!r :5 we look along x4 ,t is h[ a c>p5t] tells if a bo>d is smoo?ly plan$4 ,9 a ^w1 9 practice we mean by a /raight l9e ! l9e :i* is tak5 by ! eye ( ! rifleman look+ along 8 sights4 ,all ?is am\nts to say+ t a /raight l9e is ! direction 9 :i* a ray ( light travels4 ,h[ev] we look at ! matt]1 we always come back to ! same po9t--to say t ! edge ( an object is /raight means t ! delimit+ l9e co9cides 9 its :ole l5g? ) a ray ( light4#aj ,we may !re=e say t practically a /raight l9e is ! pa? foll[$ by light 9 a homog5e\s m$ium4 #aj ,x goes )\t say+ t 9 all ?is we assume t ! lum9\s ray travels 9 a homog5e\s m$ium4 ,& t gives rise to a "q4 ,is ! _w 9 :i* we live1 ! univ]se1 9 con=mity ) ,euclid's geometry8 ,is x ,euclidean8 ,x mu/ be und]/ood t ,euclid's geometry is n ! only "o t has be5 creat$4 ,9 ! n9ete5? c5tury !re 7 bold & pr(\nd ma!maticians--,riemann1 ,bolyay1 ,lobat*ewski1 ev5 ,po9c>--:o f\nd$ new & diff]5t & r /range geometries4 ,!y are j z logical & coh]5t z ! classical geometry ( ,euclid1 b !y are bas$ ^u diff]5t axioms & po/ulates--9 a ^w1 diff]5t def9itions4 ,= in/ance1 8p>allels0 are said to be two /raight l9es1 be+ 9 ! same plane1 :i* c nev] meet4 ,! geometry :i* we le>n$ 9 our boyhood says3 8,?r\gh a giv5 po9t !re c be only "o /raight l9e p>allel to a giv5 /raight l9e40 ,?is is said to be ,euclid's po/ulate4 ,riemann1 h[ev]1 does n admit ?is & wi%es to replace x by3 8,?r\gh a giv5 po9t !re _c be any /raight l9e p>allel to a giv5 /raight l9e0--t is to say1 any l9e :i* nev] meets x4 ,^u ?is ,riemann f\nds a q consi/5t sy/em ( geometry4 ,:o w v5ture to say t ,euclid's geometry is true & t ( ,riemann false8 ,z !oretical ideal con/ructions !y are bo? equally true4 99 99 99 99 99 ,a "q t we may legitimately ask is3 ,does ! real univ]se correspond to ! classical geometry ( ,euclid or to t ( ,riemann8 ,x 0 long believ$ t x correspond$ to ,euclid's geometry4 ,po9c> himself1 speak+ ( ,euclid's sy/em1 said3 8,x is1 & w rema91 ! mo/ conv5i5t1 7#a7 because x is ! simple/2 7#b7 because x agrees v well ) ! prop]ties ( natural solids1 ! bodies ) :i* our limbs & our eyes are conc]n$1 & out ( :i* we make our measur+ in/rum5ts40 ,:5 p us$ to say 9 e>li] ages t ! e>? is flat1 !y argu$ pretty mu* z ,po9c> does3 8,?is !ory is ! mo/ conv5i5t1 7#a7 because x is ! simple/2 7#b7 because x agrees v well ) ! prop]ties ( ! natural objects ) :i* we are 9 contact40 ,b :5 m5 came into t\* ) m remote objects1 :5 navigators & a/ronom]s multipli$ ^! remote objects1 ! idea ( a flat e>? ceas$ to be ! mo/ conv5i5t1 ! simple/1 & ! be/ suit$ to ! facts ( exp]i5ce4 ,!n appe>$ ! idea t ! e>? is r\nd1 & ?is 0 f\nd inf9itely m conv5i5t1 simpl]1 & bett] adapt$ to ! mat]ial univ]se4 8,conv5i5ce10 :i* ,po9c> makes a crit]ion ( sci5tific tru?1 is a cont+5t & ela/ic ?+4 ,a po9t ( view may be conv5i5t 9 ,london & n 9 ,b$=d4 ,a !ory may be conv5i5t 9 an area ( a hundr$ y>ds & no long] conv5i5t = an area ( a hundr$ million miles4 ,! hypo!sis ( a flat e>? has be5 replac$ by ! !ory ( ! e>?'s rotundity4 ,! /ation>y e>? has be5 replac$ by a revolv+ globe4 ,9 ! same way1 x seems t 9 our "t ,euclid's geometry mu/ give way to ano!r z a conv5i5t repres5tation ( ! real _w4 ,c !re be1 9 our univ]se1 our space1 a p>allel to a /raight l9e8 ,t is to say1 is x true t two /raight l9es be+ 9 ! same plane w nev] meet8 ,! real mean+ ( ! "q is3 ,is x impossible = two lum9\s rays1 travell+ 9 empty space & be+ 9 :at 7= ea* fraction ( ! rays7 we w call ! same plane1 ev] to meet8 ,! answ] to ?is "q is 9 ! negative4 ,z ^! two lum9\s rays are b5t out ( _! pa?s 9 space by ! gravitation ( ! />s1 & z !y are diff]5tly affect$ 9 ?is way because !y are at diff]5t di/ances f ! />s1 x foll[s necess>ily t !y w cease to be p>allel 79 ! ,euclidean s5se ( ! ^w7 & w f9ally meet2 or at lea/ t !y cease to realise ! fir/ condition ( p>allelism--coexi/5ce--9 ! same local plane4 ,9 a ^w1 if we consid] ! matt]1 n )9 ! ridicul\sly limit$ field ( exp]im5t 9 ! laboratory1 b 9 ! va/ field ( cele/ial space1 ! real univ]se is n ,euclidean1 because 9 x light does n travel 9 a /raight l9e4 ,kant reg>d$ ! tru?s--to be accurate1 ! d$uctive affirmations--( ! ,euclidean geometry z 8syn!tic judgm5ts a priori10 or self-evid5t propositions4 ,z we h se51 ,kant 0 wrong1 n only f ! po9t ( view ( !oretical geometry1 b also f ! po9t ( view ( real geometry4 ,! etymology ( ! ^w 8geometry0 7:i* means 8measur+ ! e>?07 is en\gh ( itself to %[ t x 0 orig9ally1 & *iefly1 a practical sci5ce4 ,t is a suffici5t ju/ification = our ask+ :i* geometry is mo/ 9 accord ) ! real univ]se4 ,gauss1 a pr(\nd ?9k]1 ask$ ! "q long ago1 9 ! la/ c5tury1 & he made c]ta9 delicate exp]im5ts to measure if ! sum ( ! angles ( a triangle is really equal to two "r angles1 z ! ,euclidean geometry says4 ,) ?is view he took a va/ triangle1 ! apices ( :i* 7 =m$ by ! highe/ peaks ( ?ree widely sep>at$ m\nta9s4 ,"o ( !m 0 ! fam\s ,brock54 ,) 8 assi/ants he took simultane\s sights ( ea* peak 9 relation to ! o!r two1 & he f\nd t ! sum ( ! ?ree angles ( ! triangle only diff]$ f #ahj degrees to an ext5t t might be put d[n to error 9 obs]vation4 ,!re 7 _m philosoph]s :o ridicul$ ,gauss & 8 exp]im5ts4 ,) ! a priori dogmatism t "o s (t5 enc\nt]s among/ ^! p !y said t 8 measurem5ts1 ev5 if !y _h _h a diff]5t result1 w\ld h prov$ no?+ to ! detrim5t ( ,euclid's !orems1 b w\ld m]ely h %[n t "s di/urb+ cause b5t ! lum9\s rays betwe5 ! ?ree apices ( ! triangle4 ,?is is true1 b x does n matt]4 ,if ,gauss _h f\nd t ! sum ( ! angles ( ! triangle 9 "q 0 l>g] ?an two "r angles1 x w\ld h prov$ t real geometry is n ! geometry ( ,euclid4 ,! "q :i* ,gauss ask$ 0 pr(\nd & reasonable4 ,! philosoph]s :o ridicul$ x might h be5 *all5g$ to def9e real /raight l9es1 natural /raight l9es1 9 any o!r t]ms ?an ^? ( ! passage ( light4 ,gauss did n f9d ! sum ( ! angles diff]5t f two "r angles because 8 measurem5ts 7 n suffici5tly precise4 ,if !y _h be5 mu* m rigor\s1 or if he c\ld h us$ a mu* l>g] triangle--) ! e>?1 ,jupit] 9 opposition1 & ano!r planet z its apices--he w\ld h f\nd a consid]able diff]5ce4 ,! real univ]se is n ,euclidean4 ,x is only approximately ,euclidean 9 ^? p>ts ( space :]e light travels 9 a /raight l9e3 t is to say1 9 ! p>ts :i* are f> f any gravitational mass1 su* z t 9 :i*1 on an e>li] page1 we left ,jules ,v]ne's projectile4 ,!re are _m o!r reasons :y ! univ]se1 9 consequ5ce ( gravitation1 does n con=m to ! laws ( ,euclid's geometry4 ,= in/ance1 9 ! ,euclidean geometry ! ext5t ( ! circumf]5ce has a well-kn[n proportion to its diamet]1 & ?is is indicat$ by ! ,greek lett] 4 ,?is proportion1 express+ h[ _m times ! diamet] is conta9$ 9 ! circumf]5ce1 is equal to #cadaeibfe 444 etc41 b ,i pass ov] ! re/1 z has an inf9ite numb] ( decimals4 ,we !n ask3 ,9 practice is ! proportion ( circumf]5ces to _! diamet]s really equal to ! classic value ( 8 ,= in/ance1 is ?is precisely ! proportion ( ! e>?'s circumf]5ce to its diamet]8#aa ,e9/e9 says t x is n1 & he gives u ! foll[+ pro(4 ,imag9e two v clev] & quick & wiz>d-l surveyors sett+ out to measure ! circumf]5ce & diamet] ( ! e>? at ! ,equator4 ,!y bo? use ! same scales ( measurem5t4 ,!y beg9 measur+ at ! same mom5t1 & !y />t f ! same po9t on ! ,equator4 ,b "o goes we/w>d & ! o!r ea/w>d1 & _! spe$s are equal1 & su* t ! "o :o goes we/w>d keeps up ) ! e>?'s rotation1 & ?us sees ! sun all day long /ation>y at ! same height above ! horizon4 ,9 music-halls1 = in/ance1 "o sometimes sees an acrobat walk+ on a roll+ ball & keep+ to ! top ( ! ball1 because ! pace ( 8 /eps is exactly equal & contr>y to ! displacem5t ( ! sph]ical surface4 #aa ,we are1 ( c\rse1 imag9+ ! e>? z p]fectly circul>1 )\t irregul>ities4 ,a /ation>y obs]v] 9 space--on ! sun1 let u say--w\ld ?us see our surveyor :o is go+ we/w>d1 /ation>y "r opposite to him4 ,on ! o!r h&1 ! surveyor :o goes ea/w>d w seem to him to g r\nd ! e>?1 & twice z quickly z if he _h rema9$ at ! />t+-po9t4 ,:5 ea* ( our surveyors1 bo? go+ at ! same spe$1 has f9i%$ 8 task ( measur+ ! r\nd ( ! e>?1 w !y bo? h ! same result8 ,evid5tly n4 ,z ! sup]-obs]v] 9 ! sun w see1 ! y>d ( ! surveyor :o travels ea/w>d is %ort5$ by velocity 9 virtue ( ! ,fitzg]ald-,lor5tz contraction4 ,on ! o!r h&1 ! y>d ( ! surveyor :o travels we/w>d does n exp]i5ce ?is contraction1 z ! sup]-obs]v] on ! sun1 9 ref]5ce to :om he rema9s /ation>y1 w\ld see4 ,consequ5tly ! two surveyors rea* diff]5t figures = ! e>?'s circumf]5ce1 ! "o :o travels we/w>d f9d+ a result a few y>ds less ?an t ( ! o!r4 ,yet x is obvi\s t :5 !y proce$ to measure ! e>?'s diamet]1 travell+ at ! same spe$1 ! two obs]v]s w rea* ! same figure = x4 ,h5ce ! :i* expresses ! proportion ( ! e>?'s circumf]5ce to its diamet] on ! gr\nd ( actual measurem5t diff]s accord+ z ! measur] travels 9 ! direction ( ! e>?'s rotation or 9 ! opposite direction4 ,!re=e1 z ! real values ( are diff]5t1 !y _c be ! unique & q def9ite figure ( classical geometry4 ,!re=e ! real univ]se does n con=m to ?is geometry4 ,^! diff]5ces1 9 ! illu/ration we h giv51 are due to ! e>?'s rotation4 ,f ! /&po9t ( gravitation ! e>?'s rotation has c5trifugal effects :i* modify ! c5tripetal influ5ce ( weight4 ,we h se51 moreov]1 t = ! surveyor ^: spe$ equals t ( ! e>?'s rotation ! value ( is small] ?an = ! obs]v] ^: spe$ seems to be d\ble t ( ! rotation4 ,?us ! effects ( weight be+ ! rev]se ( ^? ( rotation1 or ( c5trifugal =ce1 x foll[s 7x w\ld be j z easy to prove ?is z ! prec$+7 t ! effect ( weight is to give some?+ less ?an its classical value4 ,9 a ^w1 9 ! univ]se real circumf]5ces trac$ ^u gravitat+ masses1 su* z />s1 are1 9 proportion to _! diamet]s1 less ?an !y are 9 ! ,euclidean geometry4 ,! diff]5ce is g5]ally v slight1 x is true4 ,b !re is a diff]5ce4 ,if we put a mass ( a ?\s& kilogrammes 9 ! c5tre ( a circle t is t5 metres 9 diamet]1 ! figure w diff] 9 reality f its ,euclidean value by less ?an "o-?\s&-million-billion?4 ,9 ! neighb\rhood ( su* =midable masses ( matt] z ! />s are1 ! diff]5ce may be f> great]1 z we %all see4 ,?is is ! orig9 ( ! div]g5ces betwe5 ,newton's law ( gravitation & t ( ,e9/e93 div]g5ces :i* obs]vation has settl$ 9 fav\r ( ! latt]4 ,b we w n anticipate4 99 99 99 99 99 ,we %[$ 9 a previ\s *apt] t ! real univ]se ( ! ,relativi/s is a f\r-dim5sional cont9uum--n ?ree-dim5sional1 z classic sci5ce ?\ght--& t 9 ?is cont9uum di/ances 9 "t & space are relative4 ,! only ?+ t has a value indep5d5t ( ! conditions ( obs]vation--t has an absolute1 or at lea/ objective1 value--is :at we call$ ! 8,int]val0 ( ev5ts1 ! syn!sis ( ! spatial & *ronological data4 ,yet1 9 spite ( its f\r dim5sions1 ! univ]se1 z we discuss$ x 9 connection ) ! ,mi*elson exp]im5t & ! ,special ,relativity :i* ?is discloses1 0 nev]!less a ,euclidean cont9uum1 9 :i* ! classical geometry 0 v]ifi$1 & light travell$ 9 a /raight l9e4 ,z we h j se51 we h to recant ?is4 ,! univ]se n only has f\r dim5sions1 b x is n ,euclidean4 ,) :at geometry does ! univ]se accord be/--or mo/ conv5i5tly1 to use ! language ( ,po9c>8 ,probably t ( ,riemann4 ,:5 we take ! compasses & draw a small circle on a %eet ( pap] spread on ! table1 ! radius ( ! circle is f\nd by ! di/ance betwe5 ! po9ts ( ! compasses1 & ! circle is ,euclidean4 ,b if we draw ! circle on an egg1 ! fix$ po9t ( ! compasses be+ /uck 9 ! top ( ! egg1 & aga9 get ! radius by ! di/ance betwe5 ! po9ts1 ! circle we h n[ drawn is n ,euclidean4 ,! proportion ( ! circumf]5ce to ! radius z ?us def9$ is small] ?an 1 j z x is small] ?an :5 ! circle is trac$ r\nd a massive />4 ,well1 !re is ! same diff]5ce betwe5 ! non-,euclidean real univ]se & a ,euclidean cont9uum z !re is betwe5 our flat %eet ( pap] & ! surface ( ! egg1 tak+ into acc\nt ! fact t ^! surfaces h only two dim5sions :ile ! univ]se has f\r4 ,two-dim5sional space may be flat l ! %eet ( pap] or curv$ l ! surface ( ! egg4 ,by leav+ ! %eet ( pap] flat or roll+ x up we c make ! geometry ( ! figures drawn on x correspond ) or diff] f ! ,euclidean geometry4 ,9 j ! same way space ) m ?an two dim5sions may or may n be ,euclidean4 ,z a matt] ( fact1 ! univ]se is1 z we saw1 only approximately ,euclidean 9 ^? regions :i* are remote f all heavy masses4 ,x is n ,euclidean1 b curv$ or w>p$ 9 ! vic9ity ( ! />s2 & ! curvature is ! great] 9 proportion z we approa* ! />s4 ,h5ce ! geometry ( curv$ space1 z f\nd$ by ,riemann1 seems to be ! be/ adapt$ to ! real univ]se4 ,x is ! "o us$ by ,e9/e9 9 8 calculations4 99 99 99 99 99 ,:5 we s\ght to prove1 on a previ\s page1 t rays ( light fall j z projectiles ( ! same velocity w\ld1 we us$ ! foll[+ argum5t3 ,s9ce ! 8,int]val0 ( two ev5ts is ! same = two obs]v]s mov+ at uni=m & diff]5t velocities1 x is natural to ?9k t x w be ! same = a ?ird obs]v] ^: velocity increases f t ( ! fir/ to t ( ! second--t is to say1 ^: velocity is uni=mly accel]at$4 ,!re is1 9 fact1 no reason :y ! pass5g]s 9 a tra9 :i* runs at a uni=m spe$ ( sixty miles an h\r %\ld obs]ve an 8inv>iant0 elem5t 9 ph5om5a j z d ^? 9 ano!r tra9 mov+ at half ! spe$1 yet ?is 8inv>iant0 %\ld cease to be su* = ! pass5g]s 9 a ?ird tra9 :i* passes gradually f ! velocity ( ! fir/ tra9 to t ( ! second4 ,to admit ! contr>y w\ld be to grant a privileg$ position 9 ! univ]se to ! fir/ two & o!rs l !m4 ,if !re is any e/ate 9 ! _w t has _h its unju/ privileges suppress$ by ! new physics1 x is ! /udy ( ! mat]ial _w4 ,?is privilege ( obs]v]s mov+ at a uni=m velocity w\ld be ! less ju/ifi$ z1 if we g to ! root ( ! matt]1 x is v difficult to say exactly :at a uni=m movem5t is4 ,:at d we mean :5 we say t a tra9 has a uni=m velocity ( sixty miles an h\r8 ,we mean t ! tra9 has ?is velocity 9 ref]5ce to ! rails or ! gr\nd4 ,b 9 ref]5ce to an obs]v] 9 a balloon1 or :o passes 9 ano!r tra91 ! velocity has n ! same value1 & x may cease to be a uni=m velocity4 ,we "k only relative movem5ts1 or1 to be q accurate1 movem5ts relative to "s mat]ial object or o!r4 ,accord+ to our *oice ( ?is object1 ?is /&>d ( comp>ison1 ! same velocity may be uni=m or accel]at$4 ,9 ! long run1 x is cle>1 we %\ld h to h rec\rse to ,newton's hypo!sis ( absolute space to be able to say :e!r a giv5 velocity is really uni=m or accel]at$4 ,t is ! pr(\nd reason :y ! ,e9/e9ian 8,int]val0 ( ?+s1 ! inv>iable quantity or 8,inv>iant10 mu/ be ! same = all obs]v]s :atev] be _! velocity1 & 9 p>ticul> = obs]v]s mov+ at velocities equival5t1 9 a giv5 place1 to ! effects ( gravitation4 ,b 9 t case ! inf]5ces we draw f ! ,mi*elson exp]im5t1 9 reg>d to ! aspect ( ph5om5a = obs]v]s 9 uni=m diff]5t movem5ts ( translation1 no long] suffice to expla9 to u ! :ole ( reality4 ,!y ne$ to be complet$ 9 su* fa%ion t ! univ]sal inv>iant1 ! 8,int]val0 ( ?+s1 rema9s ! same = an obs]v] :o is mov+ 9 any way :atev]4 ,if ,i pass along a /reet at "s unhe>d-( spe$1 b ) a uni=m motion1 its g5]al aspect may1 on acc\nt ( ! contraction caus$ by my velocity1 be a little diff]5t f :at x w\ld seem to me if ,i 7 /ation>y4#ab ,! h\ses1 = in/ance1 w seem n>r[] 9 proportion to _! height4 ,nev]!less ! g5]al aspect & proportions ( objects w be mu* ! same 9 bo? cases1 & !y w h some?+ 9 common4 ,?us ! gas-lights w seem to me ?9n]1 b !y w be /raight4 #ab ,x goes )\t say+ t we assume ! obs]v] to h a ret9a ) in/antane\s impressions4 ,x w be q o!rwise if ! obs]v]'s movem5ts are v>i$3 if1 = in/ance1 we imag9e him a drunk5 giant1 reel+ ab\t at a prodigi\s spe$4 ,= su* an obs]v] ! /reet w h q a new aspect4 ,! gas-jets w no long] be /raight1 b zigzag1 reproduc+ 9 an inv]se way ! zigzags :i* he himself makes z he reels along4 ,?is is s true t c>icaturi/s g5]ally repres5t ! trees & lamp-po/s & h\ses se5 by a drunk5 man by ridicul\sly wav+ l9es4 ,our obs]v] w be conv9c$ t objects really h ! zigzag =ms :i* he sees1 & t ! =ms *ange at e /ep he takes4 ,try to tell him t x is he :o is danc+1 n ! objects2 t x is he :o is n walk+ /raight1 n ! dog he has on lea%4 ,he w n believe x--& f ! po9t ( view ( ,g5]al ,relativity he is nei!r m nor less "r ?an y4 ,yet !re is some?+ 9 ! aspect ( ! _w t mu/ be common to ! drunk>d & ! dr9k] ( wat]4 ,if ! :ole univ]se 7 sudd5ly plung$ 9 a mass ( gelat9e :i* has set1 & "o 7 to squeeze or alt] ! %ape 9 any way ( ?is gelat9\s mass1 !re w\ld /ill be some?+ un*ang$ 9 ! coagulat$ /uff4 ,:at is ?is some?+8 ,& :at is ! calculus to use = x8 ,! answ] to ^! que/ions 0 ! la/ /age = ,e9/e9 to cov] 9 ord] to e/abli% ! equations ( gravitation & ,g5]al ,relativity4 99 99 99 99 99 ,"h x 0 ! p5etrat+ g5ius ( ,h5ri ,po9c> t indicat$ ! pa?4 ,x is v necess>y to insi/ on ?is1 z ju/ice has n be5 done 9 ! matt] to ! great ,fr5* ma!matician4 ,if all ! bodies 9 ! univ]se 7 to be simultane\sly dilat$1 & to an id5tical ext5t1 we %\ld h no means ( kn[+ x4 ,our in/rum5ts & our own bodies be+ simil>ly dilat$1 we %\ld n p]ceive ?is =midable hi/orical & cosmic ev5t4 ,x w\ld n di/ract u = a mom5t f ! trivialities ( ! h\r4 ,:at is m1 n only w x be unrecognisable if worlds are modifi$ 9 su* a fa%ion z to alt] ! scale ( l5g?s & "t1 b x w\ld be impossible to di/+ui% betwe5 two worlds1 if "o s+le po9t ( ! fir/ corresponds to ea* po9t ( ! second2 if to ea* object or ev5t ( ! "o _w !re corresponds "o ( ! same "*1 plac$ exactly 9 ! same position1 9 ! o!r4 ,n[ ! successive & div]se de=mations :i* we impose ^u ! gelat9\s mass 9 :i* we metaphorically enclos$ our entire univ]se 9 an e>li] p>agraph give u precisely indi/+ui%able worlds f ?is po9t ( view4 ,po9c> has ! di/9ction ( fir/ call+ our att5tion to ?is & prov+ t ! relativity ( ?+s mu/ be und]/ood 9 ?is v broad s5se4 ,! amorph\s & pla/ic cont9uum 9 :i* we place ! univ]se has a c]ta9 numb] ( prop]ties :i* are exempt f all idea ( measurem5t4 ,! /udy ( ^! prop]ties is ! "w ( a special geometry1 a qualitative geometry4 ,! !orems ( ?is geometry h ?is peculi>ity1 t !y w\ld /ill be true ev5 if ! figures 7 copi$ by a clumsy draughtsman :o made gross errors 9 ! proportions & sub/itut$ irregul> & wavy l9es = /raight l9es4 ,?is is ! geometry :i*1 z ,po9c> ably indicat$1 mu/ be us$ = ! f\r-dim5sional &1 accord+ to its regions1 m or less ,euclidean cont9uum :i* is ! ,e9/e9ian univ]se4 ,x is precisely ?is geometry :i* /ates :at !re is 9 common betwe5 ! =ms ( objects se5 by ! drunk5 man & ^? se5 by ! wat]-dr9k]4 ,x is along ?is r\te1 or a r\te analog\s to ?is1 t ,e9/e9 at la/ rea*$ success4 ,! univ]se be+ a m or less w>p$ cont9uum1 he propos$ to apply to x ! geometry creat$ by ,gauss = ! /udy ( surfaces ( v>iable curvature3 a geometry g5]alis$ by ,riemann4 ,x is by means ( ?is special geometry t we express ! fact t ! 8,int]val0 ( ev5ts is an inv>iant4 ,"h is an illu/ration :i* w1 ,i ?9k1 lead u to ! he>t ( ! problem ( gravitation & to ! solution ( x4 99 99 99 99 99 ,let u consid] a surface ( v>iable curvature--= in/ance1 ! surface ( any l>ge di/rict ) its hills1 m\nta9s1 & valleys4 ,:5 we travel 9 ?is region1 we c proce$ 9 a /raight l9e z long z we are on ! level pla94 ,a /raight l9e on a level pla9 has ! rem>kable feature ( be+ ! %orte/ di/ance betwe5 two po9ts4 ,x has also ?is peculi>ity1 t x is ! only "o ( its k9d & its l5g?1 :]eas we may draw a great numb] ( l9es t are n /raight unit+ ! two po9ts1 long] ?an ! /raight l9e b all ( equal l5g?4 ,b we h rea*$ ! hilly di/rict4 ,x is n[ impossible = u to foll[ a /raight l9e f "o po9t to ano!r if !re is a hill betwe5 !m4 ,:atev] pa? we take1 x w be curv$4 ,b among/ ! v>i\s possible pa?s :i* lead f "o po9t to ! o!r on ! f>!r side ( ! hill1 !re is "o--& only "o1 z a rule--:i* is %ort] ?an any ( ! o!rs1 z we c\ld prove by means ( a tape4 ,?is %orte/ pa?1 ! only "o ( its k9d1 is :at is call$ ! geodetical ( ! surface cov]$4 ,9 ! same way no vessel c g 9 a /raight l9e if x is sail+ f ,lisbon to ,new ,york4 ,x mu/ foll[ a curv$ pa?1 because ! e>? is r\nd4 ,b among/ ! possible curv$ pa?s !re is a privileg$ "o :i* is %ort] ?an ! o!rs3 ! "o :i* foll[s ! direction ( ! great circle ( ! e>?4 ,9 go+ f ,lisbon to ,new ,york1 ?\gh !y are ne>ly 9 ! same latitude1 vessels are c>eful n to head /raight we/w>d1 9 ! direction ( ! p>allels4 ,!y sail a little to ! nor?-we/1 s t :5 !y rea* ,new ,york !y come f ! nor?-ea/1 hav+ foll[$ pretty closely a t]re/rial great circle4 ,on our globe1 z on all sph]es1 ! geodetical1 ! %orte/ r\te betwe5 two po9ts1 is ! arc ( a great circle pass+ ?r\gh ! two po9ts4 ,n[ ! 8,int]val0 ( two po9ts 9 ! f\r-dim5sional univ]se precisely repres5ts ! geodetical1 ! m9imum pa? ( progress betwe5 ! two po9ts trac$ 9 ! univ]se4 ,:]e ! univ]se is curv$1 ! geodetic is a curv$ l9e4 ,:]e ! univ]se is approximately ,euclidean1 x is a /raight l9e4 ,i may be told t x is v difficult to imag9e z curv$ a ?ree-dim5sional space1 & /ill m a f\r-dim5sional4 ,i agree4 ,we h already se5 t x is difficult en\gh to imag9e f\r-dim5sional space ev5 :5 x is n curv$4 ,b :at does t prove8 ,!re are _m o!r ?+s 9 nature :i* we _c visualise or =m a m5tal picture (4 ,! ,h]tz waves1 ! ,x-rays1 & ! ultra-violet waves exi/ all ! same1 ?\gh we _c imag9e !m1 or at lea/ only by giv+ !m a visible =m :i* does n belong to !m4 ,x is j "o ( our human infirmities t we _c conceive :at we _c picture to ourselves4 ,h5ce our t5d5cy to--if "o may use an inelegant b expressive ^w--visualise ev]y?+4 ,let u !re=e return to our geodetics4 ,^! we c v well picture to ourselves1 because 9 ! univ]se1 9 spite ( its f\r dim5sions1 !y are l9es ( only "o dim5sion1 l all o!r l9es t we "k4 99 99 99 99 99 ,! exi/5ce ( geodetics1 ( %orte/-di/ance l9es1 w n[ beautifully expla9 to u ! connection betwe5 in]tia & weight1 :i* did n appe> 9 ! ,euclidean _w ( classic sci5ce4 ,h5ce ! ,newtonian di/9ction betwe5 ! pr9ciple ( in]tia & ! =ce ( gravitation4 ,we ,relativi/s f9d ?is di/9ction no long] necess>y4 ,mat]ial masses1 l light1 travel 9 a /raight l9e :5 !y are f> f a gravitational field1 & 9 a curv$ l9e :5 !y are ne> gravitational masses4 ,9 virtue ( symmetry a free mat]ial po9t c only foll[ a geodetic 9 ! univ]se4 ,if we n[ reflect t ! =ce ( gravitation introduc$ by ,newton does n exi/--su* action at a di/ance is v problematical--& t 9 empty space !re are only objects freely left to !mselves1 we are driv5 to ! foll[+ conclusion1 :i* unites 9 a simple way ! previ\sly sep>at$ si/]s1 in]tia & weight3 ,e mov+ body freely left to itself 9 ! univ]se describes a geodetic4 ,f> f ! massive />s ?is geodetic is a /raight l9e1 because !re ! univ]se is almo/ ,euclidean4 ,ne> ! />s x is a curv$ l9e1 because !re ! univ]se is n ,euclidean4 ,a f9e conception1 comb9+ 9 a s+le rule ! pr9ciple ( in]tia & ! law ( gravitation6 ,a brilliant syn!sis ( me*anics & gravitation1 putt+ an end to ! s*ism :i* s long kept !m sep>ate & non-correspond+ sci5ces6 ,9 ?is bold & simple !ory gravitation is n a =ce4 ,! planets h curv$ pa?s because ne> ! sun1 j z 9 ! neighb\rhood ( e conc5tration ( matt] ! univ]se is curv$ or w>p$4 ,! %orte/ pa? f "o po9t to ano!r is a l9e t only seems /raight to u--poor pygmies t we are--because we measure x ) v small rods & ov] small di/ances4 ,if we c\ld foll[ ! l9e ov] millions ( miles1 & dur+ a suffici5t p]iod1 we %\ld f9d x curv$4 ,9 a ^w--to use an illu/ration t mu/ be reg>d$ only z an analogy--! planets describe curv$ pa?s because !y foll[ ! %orte/ pa? 9 a curv$ univ]se1 j z at a sports gr\nd cycli/s h no ne$ to turn ! h&les :5 !y rea* ! corn]1 b p$al /raight on1 because ! slope ( ! gr\nd compels !m ( itself to turn4 ,9 ! sports gr\nd1 z 9 ! sol> sy/em1 ! curvature is great] 9 proportion z ! ma*9e is ne>] to ! inn] edge ( ! track4 ,all t n[ rema9s is to assign to ! univ]se1 to space-"t1 su* a curvature at its v>i\s po9ts t ! geodetics w exactly repres5t ! pa?s ( ! planets & ( fall+ bodies1 admitt+ t ! curvature ( ! univ]se is caus$ at ea* po9t by ! pres5ce or vic9ity ( mat]ial masses4 ,9 ?is calculation we h to take into acc\nt ! fact t ! 8,int]val0--t is to say1 ! "p ( ! geodetic betwe5 two po9ts t are v ne> ea* o!r--mu/ be an inv>iant :oev] may be ! obs]v]4 ,9 ?is way ! same geodetic w be a curv$ or ev5 wavy l9e = ! drunk5 man we introduc$ & a /raight l9e = a /ation>y obs]v]4 ,! l5g? ( ! l9e is ! same1 :e!r x appe>s /raight or curv$4 ,tak+ all ?is into acc\nt1 & do+ prodigies ( ma!matical skill ( :i* we h suffici5tly indicat$ ! object1 ,e9/e9 has succe$$ 9 express+ ! law ( gravitation 9 a completely inv>iant =m4 ,9 calculat+1 on ! gr\nd ( ,newton's law1 ! 8,int]val0 ( two a/ronomical ev5ts--= in/ance1 ! successive falls ( two meteorites into ! sun--we %\ld f9d t ! 8,int]val0 has n precisely ! same value = obs]v]s :o are mov+ at diff]5t velocities4 ,) ! new =m giv5 to ! law by ,e9/e9 ! diff]5ce disappe>s4 ,! two laws1 h[ev]1 diff] little f ea* o!r1 z 0 to be expect$ 9 view ( ! accuracy ) :i* a/ronom]s f\nd ,newton's law v]ifi$ dur+ a c\ple ( c5turies4 ,! improvem5t made 9 ,newton's law by ,e9/e9 means1 9 a ^w 7& to use ! old language ( ! ,euclidean univ]se71 t we consid] ! law accurate ) ! res]ve t ! di/ances ( ! planets f ! sun are measur$ by a scale :i* decreases slightly 9 l5g? z ! sun is approa*$4 99 99 99 99 99 ,x is surpris+ t ,newton & ,e9/e9 agree 9 express+ ! movem5ts ( gravitat+ />s 9 an almo/ id5tical =m1 because _! />t+-po9ts are v diff]5t4 ,newton />ts f ! hypo!sis ( absolute space1 ! empirical laws ( ! motions ( ! planets express$ 9 ,kepl]'s laws1 & ! belief t gravitational attraction is a =ce proportional to mass4 ,e9/e91 on ! o!r h&1 9 mak+ 8 calculations />ts f ! conditions ( inv>iance :i* we indicat$4 ,he />ts1 9 a s5se1 f ! philosophical pr9ciple or po/ulate or impulse to hold t ! laws ( nature are inv>iant & indep5d5t ( ! po9t ( view--irrelative1 if ,i may use ! ^w4 ,e9/e9 ev5 ab&ons ! hypo!sis :i* ascrib$ ! curv+ ( gravitational pa?s to a di/9ct =ce ( attraction4 ,yet1 />t+ f a po9t ( view s diff]5t f t ( ,newton1 & "o t seems at fir/ less ov]load$ ) hypo!ses1 ,e9/e9 rea*es a law ( gravitation :i* is almo/ id5tical ) ,newton's4 ,?is 8almo/0 is ( imm5se int]e/1 because x enables u to te/ :i* is ! accurate law1 t ( ,newton or t ( ,e9/e94 ,!y give ! same results :5 !re is "q ( velocities t are feeble 9 comp>ison ) t ( light1 b _! results diff] a little :5 !re is "q ( v high velocities4 ,we h already se5 t1 ne> ! sun1 light itself is b5t out ( its c\rse 9 exact con=mity ) ,e9/e9's law1 & 9 a way t ,newton's law did n pr$ict z su*4 ,b !re is ano!r div]g5ce betwe5 ! two laws4 ,accord+ to ! ,newtonian law ! planets revolv+ r\nd ! sun describe ellipses :i*--neglect+ ! small p]turbations due to ! o!r planets--h a rigor\sly fix$ position4 ,suppose we put on a table a slice ( lemon cut ?r\gh ! long] diamet] ( ! fruit1 & imag9e t ! *ief />s1 ! nor!rn con/ellations1 are pa9t$ on ! vault$ ro( ( ! va/ hemisph]ical room 9 ! middle ( :i* we place our table4 ,! slice ( lemon has v ne>ly ! =m ( an ellipse1 &1 if we take "o ( ! pips to repres5t ! sun1 x w /& = ! orbit ( "o ( our planets4 ,newton's law says t--aft] mak+ due corrections--! planet>y orbit keeps a fix$ position relatively to ! />s z long z ! planet cont9ues to revolve4 ,?is means t ! slice ( lemon rema9s /ation>y4 ,e9/e9's law says1 on ! contr>y1 t ! orbital ellipse turns v sl[ly among/ ! />s :ile ! planet trav]ses x4 ,?is means t our slice ( lemon mu/ turn slightly on ! table1 9 su* wise t ! two ends ( ! lemon d n rema9 opposite ! same />s pa9t$ on ! wall4 ,if we calculate1 9 virtue ( ,e9/e9's law1 ! ext5t to :i* ! elliptical orbits ( ! planets mu/ ?us turn1 we f9d x s small z to be impossible ( obs]vation except 9 ! case ( "o planet1 ! swifte/ ( all1 ,m]cury4 ,m]cury revolves completely r\nd ! sun 9 ab\t eighty-eight days1 & ,e9/e9's law %[s t its orbit mu/ at ! same "t turn by a small angle :i* am\nts to =ty-?ree seconds ( an arc 7#dc7 at ! end ( a c5tury4 ,small z ?is quantity is1 ! ref9$ me?ods ( ! mod]n a/ronom] c easily measure x4 ,z a matt] ( fact1 x _h be5 notic$ dur+ ! la/ c5tury t ,m]cury 0 ! only "o ( ! planets to %[ a slight anomaly 9 its movem5ts1 :i* c\ld n be expla9$ by ,newton's law4 ,le ,v]ri] made prodigi\s calculations 9 connection ) x1 z he ?\ght t ! anomaly might be due to ! attraction ( an unkn[n body ly+ betwe5 ,m]cury & ! sun4 ,he hop$ t he w\ld ?us discov]1 by calculation1 an intra-,m]curial planet1 j z he _h discov]$ ! trans-,uranian planet ,neptune4 ,b no "o ev] obs]v$ 8 planet1 & ! anomaly ( ,m]cury cont9u$ to be ! despair ( a/ronom]s4 ,n[1 9 :at did ! anomaly consi/8 ,precisely 9 an abnormal rotation ( ! planet>y orbit2 a rotation :i* ,le ,v]ri]'s calculations %[$ to be =ty-?ree seconds ( an arc 9 a c5tury4 ,t is exactly ! figure t we d$uce1 )\t us+ any hypo!sis1 f ,e9/e9's law ( gravitation6 ,x is true t1 accord+ to ! rec5t calculations ( ,grossmann1 ! a/ronomical obs]vations collect$ by ,newcomb give z ! record$ value ( ! secul> displacem5t ( ! p]ihelion ( ,m]cury1 n #dc z ,le ,v]ri] believ$1 b #ch at ! mo/4 ,! agreem5t ) ,e9/e9's !oretical result is1 !re=e1 n p]fect 7:i* w\ld h be5 extraord9>y71 b x is /rik+1 & is )9 ! limits ( possible error ( obs]vation4 ,e9/e9's law is j z exact z ,newton's = ! sl[] planets4 ,= fa/] bodies1 ! motion ( :i* c be obs]v$ ) a high] degree ( precision1 ,newton's law is wrong1 & ,e9/e9's triumphs once m4 99 99 99 99 99 ,?is improvem5t ( :at _h be5 consid]$ p]fect--! "w ( ,newton--is a great victory = ! human m9d4 ,a/ronomy & cele/ial me*anics d]ive additional precision & p[] ( =eca/ f x4 ,we c n[ foll[ ! gold5 orbs1 on ! triumphal w+s ( calculation1 bett] ?an we c\ld be=e1 or ant$ate _! movem5ts by c5turies4 ,b !re is ano!r te/ ( ,e9/e9's law ( gravitation4 ,if x is s\nd1 ! duration ( a ph5om5on increases1 accord+ to ,e9/e91 :5 ! gravitational field becomes m int5se4 ,x foll[s t ! duration ( ! vibration ( a giv5 atom mu/ be long] on ! sun ?an on ! e>?4 ,! wave-l5g?s ( ! spectral l9es ( ! same *emical elem5t ought to be a little great] 9 sunlight ?an 9 light :i* orig9ates on ! e>?4 ,rec5t obs]vations t5d to confirm ?is1 b ! v]ification is less satisfactory ?an 9 ! case ( ,m]cury because o!r causes may int]v5e to modify ! wave-l5g?s4 ,on ! :ole1 ! p[]ful syn!sis :i* ,e9/e9 calls ! !ory ( ,g5]al ,relativity1 :i* we h "h rapidly outl9$1 is a l(ty & beautiful m5tal con/ruction z well z a sup]b in/rum5t ( exploration4 ,to "k is to =eca/4 ,?is !ory =eca/s1 & bett] ?an its pr$ecessors did4 ,= ! fir/ "t x comb9es gravitation & me*anics4 ,x %[s h[ matt] imposes ^u ! ext]nal _w a curvature or w>p+ ( :i* gravitation is b a symptom3 j z ! we$s "o sees float+ on ! sea are b indications ( ! curr5t :i* be>s !m along4 ,:atev] modifications x may und]go 9 ! future--= ev]y?+ 9 sci5ce is op5 to improvem5t--x has %[n u a little m ( ! h>mony t is born ( unity 9 ! laws ( nature4 ,b ,i h suffici5tly %[n t if ,i h succe$$ 9 enabl+ ! read] to und]/&--to feel1 at lea/--^! matt]s )\t invok+ ! aid ( ! pure light :i* geometry p\rs ^u ! invisible4 ,,*apt] ,,vii ,,is ,,! ,,univ]se ,,inf9ite8 ,kant & ! numb] ( ! />s--,ext9ct />s & d>k nebul--,ext5t & aspect ( ! a/ronomical univ]se--,diff]5t k9ds ( univ]ses--,po9c>'s calculation--,physical def9ition ( ! inf9ite--,! inf9ite & ! unlimit$--,/ability & curvature ( cosmic space-"t--,real & virtual />s--,diamet] ( ! ,e9/e9ian univ]se--,! hypo!sis ( globes ( e!r4 ,is ! univ]se inf9ite8 ,x is a "q t m5 h ask$ 9 all ages1 ?\gh !y h n def9$ its mean+ v accurately4 ,! !ory ( ,relativity enables u to approa* x f a new & subtle po9t ( view4 ,kant--! g5ial grumbl] :o f\nd x s horribly monoton\s to see ! same sun %9+1 & ! same spr+ blossom+1 e ye>--took 8 /& on metaphysical consid]ations :5 he affirm$ t space is inf9ite1 & is s[n ) simil> />s 9 all p>ts4 ,x is1 p]haps1 bett] to conf9e ourselves 9 su* a matt] to ! results ( rec5t obs]vation1 & close ! doors ( our debat+-room aga9/ ! fog ( metaphysics4 ,inde$1 ! latt] w\ld compel u to def9e pure space1 ab\t :i* we "k no?+--n ev5 if !re is su* a ?+4 ,! pro( t we "k little ab\t x is ! fact t ! ,newtonians believe 9 x1 :ile ! ,e9/e9ians reg>d x m]ely z an insep>able attribute ( mat]ial ?+s4 ,!y def9e space by matt]2 & !y !n h to def9e ! latt]4 ,desc>tes1 on ! contr>y1 def9$ matt] 9 t]ms ( ext5sion1 :i* is ! same ?+ z space4 ,x is a vici\s circle4 ,x is !re=e bett] to leave ,kant's metaphysical argum5ts out ( our discussion1 & adh]e /rictly to exp]i5ce1 to :at is measurable4 ,to simplify matt]s1 we w admit ! reality ( ?is cont9uum 9 :i* ! />s float1 :i* is trav]s$ by _! radiations1 :i* common s5se calls space4 ,if !re 7 />s ev]y:]e--if !y 7 inf9ite 9 numb]--!re w\ld also be space & matt] ev]y:]e4 ,newtonians might f9d ?is a triumph equally ) ,e9/e9ians4 ,^? :o believe 9 absolute space & ^? :o d5y x--,absoluti/s & ,relativi/s--w\ld equally rejoice4 ,x w\ld be =tunate if a/ronomical obs]vation 7 to %[ t ! numb] ( ! />s is inf9ite1 & ?us ! hold]s ( contr>y op9ions c\ld bo? *ant a victory 9 _! writ+s4 ,b :at does a/ronomical obs]vation actually report8 ,!re are ^? :o d5y a priori t ! numb] ( ! />s c be inf9ite4 ,t numb]1 !y said1 is capable ( increase2 x is !re=e n inf9ite1 because no?+ c be add$ to ! inf9ite4 ,! argum5t is speci\s1 b uns\nd2 al?\gh ,voltaire himself 0 s$uc$ by x4 ,"o ne$ n be a great ma!matician to see t x is always possible to add to an inf9ite numb]1 & t !re are inf9ite quantities :i* are !mselves inf9itely small 9 comp>ison ) o!rs4 ,let u get on to ! facts4 ,if ! /ell> univ]se has no limits1 !re is no visual l9e drawn f ! e>? to ! heav5s :i* w n enc\nt] "o ( ! />s4 ,! a/ronom] ,olb]s has said t ! :ole nocturnal sky w\ld 9 t case %9e ) ! brilliance ( ! sun4 ,b ! total brilliance ( all ! />s put toge!r is only ?ree ?\s& times great] ?an t ( a /> ( ! fir/ magnitude1 or ?irty million times less ?an ! light ( ! sun4 ,b t proves no?+1 z ,olb]s' argum5t is wrong1 = two reasons4 ,on ! "o h&1 !re are necess>ily a good _m ext9ct or d>k />s 9 ! heav5s4 ,"s ( !m h be5 closely /udi$1 ev5 weigh$4 ,!y betray _! exi/5ce by p]iodically eclips+ bright] />s1 ) :i* !y revolve4 ,on ! o!r h&1 x 0 discov]$ "s "t ago t cele/ial space is occupi$ ov] l>ge /ret*es by d>k gase\s masses & cl\ds ( cosmic du/1 :i* absorb ! light ( m di/ant />s4 ,we ?us see t ! exi/5ce ( an inf9ite numb] ( />s is q compatible ) ! poorness ( ! light ( ! heav5s at night4 99 99 99 99 99 ,n[ let u put on our spectacles--our telescopes1 ,i mean--& turn f ! prov9ce ( possibility to t ( reality1 & we %all see t rec5t a/ronomical obs]vation has yield$ a numb] ( rem>kable facts :i* lead irresi/ibly to ! foll[+ conclusions4 ,! numb] ( ! />s is n1 z 0 long suppos$1 limit$ by ! range ( our telescopes alone4 ,z we get fur!r away f ! sun1 ! numb] ( />s conta9$ 9 a unity ( space1 ! frequ5ce ( ! />s1 ! d5sity ( ! /ell> population1 d n rema9 uni=m1 b decrease 9 proportion z we approa* ! limits ( ! ,milky ,way4 ,! ,milky ,way is a va/ ar*ipelago ( />s1 our sun ly+ 9 its c5tral region4 ,?is mass ( />s1 to :i* we belong1 has1 r\ghly1 ! %ape ( a wat*-case1 ! ?ickness be+ only ab\t half ! wid? ( ! /ructure4 ,light1 :i* travels f ! e>? to ! moon 9 little ov] a second1 f ! e>? to ! sun 9 eight m9utes1 & f ! e>? to ! ne>e/ /> 9 ?ree ye>s1 ne$s at lea/ #cj1jjj ye>s--?ree hundr$ c5turies--to pass f end to end ( ! ,milky ,way4 ,! numb] ( />s 9 ! ,milky ,way is some?+ betwe5 #ejj & #a1ejj millions4 ,x is a small numb]3 sc>cely equal to ! human population ( ! e>?1 mu* small] ?an ! numb] ( molecules ( iron 9 a p9's head4 ,9 addition to ^! we h discov]$ d5se masses ( />s1 su* z ! ,magellanic ,cl\ds1 ! clu/] 9 ,h]cules1 & s on1 :i* seem to belong to ! fr+es ( our ,milky ,way--to be suburbs ( x1 s to say4 ,^! suburbs seem to /ret* a consid]able di/ance1 p>ticul>ly on "o side ( ! ,milky ,way4 ,! fur!/ away is1 p]haps1 n less ?an #bjj1jjj light-ye>s f u4 ,beyond ^!1 space seems to be des]t$1 devoid ( />s ov] expanses :i* are enorm\s 9 comp>ison ) ! dim5sions ( our galactic univ]se z we h describ$ x4 ,:at is beyond ?is8 ,well1 beyond ?is we f9d ^? /range bodies1 ! spiral nebul1 ly+ l silv] snails 9 ! g>d5 ( ! />s4 ,we h discov]$ sev]al hundr$ ?\s& ( !m4 ,"s a/ronom]s believe t ^! spiral masses ( />s may be annexes ( ! ,milky ,way1 r$uc$ models ( x4 ,mo/ a/ronom]s incl9e to ?9k1 = v good reason1 t ! spiral nebul are sy/ems l ! ,milky ,way1 & comp>able to x 9 _! dim5sions4 ,if ! =m] view is correct1 ! entire sy/em ( />s accessible to our telescopes c\ld be trav]s$ by light 9 "s hundr$s ( ?\s&s ( ye>s4 ,on ! second hypo!sis ! dim5sions ( ! /ell> univ]se to :i* we belong mu/ be multipli$ by t51 & light w\ld take at lea/ millions ( ye>s to trav]se x4 ,on ! fir/ view ! entire /ell> univ]se1 9 s f> z x is accessible to u1 consi/s ( ! ,milky ,way & its annexes3 t is to say1 a local conc5tration ( />s1 beyond :i* we c see no?+4 ,! /ell> univ]se is1 9 o!r words1 practically limit$1 or at lea/ f9ite4 ,on ! second view our ,milky ,way is simply "o ( ! myriads ( spiral univ]ses we see4 ,! spiral nebula 7) its hundr$s ( millions ( />s7 plays ! same "p 9 ?is va/] univ]se t a /> has 9 ! ,milky ,way4 ,we h ! same problem z be=e1 b on a va/] scale3 if ! ,milky ,way consi/s ( a conc5tration ( a f9ite numb] ( />s1 z obs]vation proves1 does ! accessible univ]se consi/ ( a f9ite numb] ( spiral nebul8 ,exp]i5ce has z yet n pron\nc$ on ?is po9t4 ,b 9 my op9ion x is probable t1 :5 our in/rum5ts are p[]ful en\gh to tackle su* a problem--9 sev]al c5turies1 p]haps--sci5ce w answ] 8yes40 ,if x 7 o!rwise1 if ! spiral nebul 7 fairly ev5ly di/ribut$ z we g outw>d1 we c %[ by calculation t1 attraction be+ 9 inv]se proportion to ! squ>e ( ! di/ance1 gravitation w\ld h an inf9ite int5sity 9 su* a univ]se1 ev5 9 ! "p 9 :i* we live4 ,b ?is is n ! case4 ,x foll[s t1 ei!r ! attraction ( two masses decreases at great di/ances r m rapidly ?an 9 inv]se proportion to ! squ>e ( ! di/ance 7:i* is n :olly impossible71 or t ! numb] ( /ell> sy/ems & />s is f9ite4 ,p]sonally ,i fav\r ! second hypo!sis1 b x is incapable ( pro(4 ,9 su* matt]s !re is always an alt]native1 always a way ( escap+ 9 accordance ) "o's bias1 & !re is really no?+ t compels u to say t ! />s are f9ite 9 numb]4 99 99 99 99 99 ,/>t+ f ! mean value1 z x has be5 obs]v$1 ( ! prop] motions ( ! ne>] />s1 ,h5ri ,po9c> has calculat$ t ! total numb] ( />s 9 ! ,milky ,way mu/ be ab\t "o ?\s& million4 ,! figure agrees fairly well ) ! results ( ! />-gauges effect$ by a/ronom]s by means ( photographic plates4 ,he has also %[n t ! prop] motions ( />s w\ld be great] if !re 7 _m m />s ?an ^? :i* we see4 ,?us ,po9c>'s calculations are oppos$ to ! hypo!sis ( an indef9ite ext5sion ( ! /ell> univ]se1 z ! numb] ( />s 8c\nt$0 agrees fairly closely ) ! numb] 8calculat$40 ,we %\ld add1 h[ev]1 t ^! calculations prove no?+ if ! law ( attraction is n q ! inv]se proportion ( ! squ>e at enorm\s di/ances4 ,on ! o!r h&1 if ! univ]se is f9ite 9 space z x is conceiv$ 9 classic sci5ce1 ! light ( ! />s1 & isolat$ />s !mselves1 w\ld gradually drift away into ! inf9ite1 & ! cosmos w\ld disappe>4 ,our m9d res5ts ?is consequ5ce1 & a/ronomical obs]vation discov]s no trace :atev] ( su* a dislocation4 ,9 a ^w1 9 ! space ( ! 8,absoluti/s0 ! /ell> univ]se c only be inf9ite if ! law ( ! squ>e ( di/ances is n q exact = v remote masses2 & x _c be f9ite except on ! condition t x is ephem]al 9 po9t ( "t4 ,= ,newton1 inde$1 ! /ell> univ]se might be f9ite )9 an inf9ite univ]se1 because 9 8 view !re c be space )\t matt]4 ,= ,e9/e91 on ! contr>y1 ! univ]se & ! mat]ial or /ell> univ]se are "o & ! same ?+1 because !re is no space )\t matt] or en]gy4 99 99 99 99 99 ,^! difficulties & obscurities disappe> 9 great "p :5 we consid] space1 or space-"t1 f ! ,e9/e9ian /&po9t ( ,g5]al ,relativity4 ,:at is ! mean+ ( ! s5t5ce1 8,! univ]se is inf9ite08 ,f ei!r ! ,e9/e9ian1 ! ,newtonian1 or ! ,pragmati/ po9t ( view x means3 ,if ,i g /raight ahead1 go+ on et]nally1 ,i %all nev] get back to my />t+-po9t4 ,is x possible8 ,newton is compell$ to say yes1 because 9 8 view space /ret*es out indef9itely1 indep5d5t ( ! bodies t occupy "p ( x1 :e!r ! numb] ( ! />s is or is n limit$4 ,b ,e9/e9 says no4 ,= ! ,relativi/ ! univ]se is n necess>ily inf9ite4 ,is x !re=e limit$1 f5c$ 9 by "s sort ( rail+s8 ,no4 ,x is n limit$4 ,a ?+ may be unlimit$ )\t be+ inf9ite4 ,= in/ance1 a man :o moves on ! surface ( ! e>? may travel ov] x indef9itely 9 e direction )\t ev] rea*+ a limit4 ,! surface ( ! e>?1 ?us reg>d$1 or ! surface ( any sph]e :atsoev]1 is !re=e bo? f9ite & unlimit$4 ,well1 we h only to apply to space ( ?ree dim5sions :at we f9d 9 two-dim5sional space 7a sph]ical surface71 to see h[ ! univ]se may be at "o & ! same "t f9ite & unlimit$4 ,we saw t1 9 consequ5ce ( gravitation1 ! ,e9/e9ian univ]se is n ,euclidean1 b curv$4 ,x is1 z we said1 difficult1 if n impossible1 to visualise a curvature ( space4 ,b ! difficulty exi/s only = our imag9ation1 :i* is re/rict$ by our life ( s5se1 n = our reason1 :i* goes f>!r & high]4 ,x is "o ( ! commone/ ( errors to suppose t ! w+s ( ! imag9ation are m p[]ful ?an ^? ( reason4 ,if "o wants pro( ( ! contr>y1 "o has only to comp>e :at ! mo/ poetic ( anci5t ?9k]s made ( ! />ry heav5s ) :at mod]n sci5ce tells ab\t ! univ]se4 ,"h is ! way to approa* our problem4 ,let u n notice = ! mom5t ! r irregul> di/ribution ( />s 9 our /ell> sy/em1 & take x z fairly homog5e\s4 ,:at is ! condition requir$ = ?is di/ribution ( ! />s "u ! influ5ce ( gravitation to rema9 /able8 ,calculation gives u ?is reply3 ,! curvature ( space mu/ be con/ant1 & su* t space is b5t l a sph]ical surface4 ,rays ( light f ! />s may travel et]nally1 indef9itely1 r\nd ?is unlimit$1 yet f9ite1 univ]se4 ,if ! cosmos is sph]ical 9 ?is way1 we c ev5 imag9e ! rays :i* emanate f a />--! sun1 = in/ance--cross+ ! univ]se & conv]g+ at ! diametrically opposite po9t ( x4 ,9 su* case we might expect to see />s at opposite po9ts 9 ! heav5s1 ( :i* "o w\ld be ! image1 ! spectre1 ! 8d\ble0 ( ! o!r--9 ! s5se :i* ! anci5t ,egyptians gave to ! ^w4 ,prop]ly speak+1 ?is 8d\ble0 w\ld repres5t1 n ! g5]at+ /> z x is1 b z x 0 at ! "t :5 x emitt$ ! rays :i* =m ! d\ble1 or millions ( ye>s e>li]4 ,if we obs]ve ! orig9al & ! d\ble />1 ! reality & ! mirage1 simultane\sly f "s remote "p ( ! /ell> sy/em1 su* z our planet1 we %all see a great diff]5ce betwe5 !m1 s9ce ! 8copy0 w %[ u ! orig9al z x 0 ?\s&s ( c5turies be=e4 ,x may1 9 fact1 happ5 t ! second /> is m brilliant ?an ! fir/1 because 9 ! meantime ! fir/ has gradually cool$1 & may ev5 be ext9ct4 99 99 99 99 99 ,x is improbable t we %\ld f9d _m ( ^! phantom-/>s1 or virtual />s1 lum9\s & unreal daught]s ( heavy suns4 ,! reason is t ! rays 9 _! passage ?r\gh ! univ]se w g5]ally be div]t$ by ! />s ne> :i* !y pass4 ,conc5tration or conv]g5ce ( !m at ! antipodes ( ! real /> mu/ be r>e4 ,moreov]1 ! rays are to "s ext5t absorb$ by ! cosmic /uff !y meet 9 space4 ,x is1 h[ev]1 n impossible t ! a/ronom]s ( ! future may discov] su* ph5om5a4 ,x is1 9 fact1 n impossible t we h already obs]v$ su* ?+s )\t kn[+ x4 ,9 any case1 :at obs]v]s h n done 9 ! pa/ !y may v well d 9 ! future1 ?anks to ! sugge/ions ( ! new sci5ce4 ,possibly x is go+ to h a great effect on obs]vational a/ronomy & induce x to furni% brilliant new v]ifications ( !ory4 ,!re may be a/oni%+ results1 un=ese5 by our folly1 ( ! new conceptions1 surpass+ 9 _! fanta/ic poetry ! mo/ romantic con/ructions ( ! imag9ation4 ,reality1 or at lea/ ! possible1 is ris+ to giddy heights t 7 f> beyond ! rea* ( ! gold5 w+s ( fantasy4 ,i spoke on a previ\s page ( ! millions ( ye>s :i* light takes to travel r\nd our curv$ univ]se4 ,/>t+ f ! fairly well-asc]ta9$ value ( ! quantity ( matt] compris$ 9 ! ,milky ,way1 x is possible to calculate ! curvature ( ! _w & its radius4 ,we f9d t ! radius has a value equal to at lea/ #aej1jjj1jjj light-ye>s4 ,x !re=e takes light at lea/ #ijj1jjj1jjj ye>s1 at a spe$ ( #ahf1jjj miles a second1 to travel r\nd ! univ]se1 assum+ t x consi/s only ( ! ,milky ,way & its annexes4 ,! figure is q consi/5t ) ! figures we get f a/ronomical obs]vation = ! dim5sions ( ! galactic sy/em1 & also ) ! mu* l>g] figures :i* we f9d if we reg>d ! spiral nebul z ,milky ,ways4 ,?us = ! ,relativi/ ! univ]se may be unlimit$ )\t be+ inf9ite4 ,z to ! ,pragmati/1 :o goes /raight ahead--:o foll[s :at he calls a /raight l9e1 or ! pa? ( light--he w get back 9 ! end to ! body f :i* he />t$1 provid$ t he has "t en\gh at 8 disposal4 ,he w !n say t1 if t is ! nature ( ?+s1 ! univ]se is n inf9ite4 ,h5ce ! "q ( ! inf9ity or f9it5ess ( ! univ]se c be controll$ by exp]i5ce1 & "s day x w be possible to prove :e!r ! :ole cosmos & space are ,newtonian or ,e9/e9ian4 ,un=tunately1 x w h to be a v long exp]i5ce1 ) v>i\s little practical difficulties to ov]come4 ,we may !re=e pref] n to commit ourselves )\t fur!r in/ructions4 ,we may n feel ourselves oblig$ to *oose betwe5 ! two conceptions1 & we may leave ! b5efit ( ! d\bt to :i*ev] ( ! two is false4 99 99 99 99 99 ,moreov]1 !re is p]haps a ?ird issue3 if n = ! ,pragmati/1 at lea/ = ! philosoph]--,i mean1 see+ t 9 ,engl& physics comes "u ! head ( 8,natural ,philosophy10 = ! physici/4 ,"h x is4 ,if all ! heav5ly bodies we "k belong to ! ,milky ,way1 o!r & v remote univ]ses may be inaccessible to u because !y are optically isolat$ f u2 possibly by ! ph5om5a ( ! cosmic absorption ( light1 to :i* we h already ref]r$4 ,b ?is might also be due to some?+ else :i* w1 p]haps1 %ock ,relativi/s1 b w seem to ,newtonians q possible4 ,! e!r1 ! m$ium t transmits ! lum9\s waves1 & :i* ,e9/e9 has end$ by admitt+ once m 7refus+1 h[ev]1 to give x its famili> k9ematic prop]ties71 & matt] seem m & m to be m]ely modalities4 ,we expla9$ ?is1 on ! /r5g? ( ! mo/ rec5t physical discov]ies1 9 a previ\s *apt]4 ,!re is no?+ to prove t ^! two =ms ( sub/ance are n always associat$4 ,does ?is n give me ! "r to ?9k t p]haps our :ole visible univ]se1 our local conc5tration ( matt]1 is only an isolat$ clump or sph]e ( e!r8 ,if !re is su* a ?+ z absolute space 7:i* does n mean t x is accessible to u71 x is indep5d5t ( e!r z well z matt]4 ,9 t case !re w\ld be va/ empty spaces1 devoid ( e!r1 all r\nd our univ]se4 ,possibly o!r univ]ses palpitate beyond ^!2 & = u su* worlds w\ld be = ev] z if !y did n exi/4 ,no ray ( k w\ld ev] rea* u f !m4 ,no?+ c\ld cross ! black1 dumb abysses :i* environ our /ell> isl&4 ,our glances are conf9$ = ev] )9 ?is giant--yet too small--monad4 8,are !re1 !n10 "s w cry 9 a/oni%m5t1 8?+s :i* exi/1 yet we w nev] "k !m80 ,naive pret5sion--to want to embrace ev]y?+ 9 a few cubic c5timetres ( grey bra9-/uff6 ,,*apt] ,,viii ,,sci5ce ,,& ,,reality ,! ,e9/e9ian absolute--,revelation by sci5ce--,discussion ( ! exp]im5tal bases ( ,relativity--,o!r possible explanations--,argum5ts 9 fav\r ( ,lor5tz's real contraction--,newtonian space may be di/9ct f absolute space--,! real is a privileg$ =m ( ! possible--,two attitudes 9 face ( ! unkn[n4 ,we approa* ! end ( our "w4 ,has reality1 se5 ?r\gh ! prism ( sci5ce1 *ang$ its aspect ) ! new !ories8 ,yes1 c]ta9ly4 ,! ,relativi/ !ory claims to h improv$ ! a*romatism ( ! prism & by ?is means improv$ ! picture x gives u ( ! _w4 ,"t & space1 ! two poles ^u :i* ! sph]e ( empirical data turn$1 :i* 7 believ$ to be un%akeable1 h be5 dislodg$ f _! /rong positions4 ,in/ead ( !m ,e9/e9 (f]s u ! cont9uum 9 :i* be+s & ph5om5a float3 f\r-dim5sional space-"t1 9 :i* space & "t are yok$ toge!r4 ,b ?is cont9uum is itself only a flabby =m4 ,x has no rigidity4 ,x adapts itself docilely to ev]y?+4 ,!re is no?+ fix$1 because !re is no def9ite po9t ( ref]5ce by means ( :i* we c\ld di/ribute ph5om5a2 because on ! %ores ( ?is great ocean 9 :i* ?+s float !re are none left ( ^? solid r+s to :i* m>9]s once fa/5$ _! vessels4 ,up to ?is po9t ! !ory ( ,relativity well des]ves its "n4 ,b n[1 9 spite ( x & its v "n1 !re rises some?+ :i* seems to h an indep5d5t & det]m9$ exi/5ce 9 ! ext]nal _w1 an objectivity1 an absolute reality4 ,?is is ! 8,int]val0 ( ev5ts1 :i* rema9s con/ant & inv>iable ?r\gh all ! fluctuations ( ?+s1 h[ev] inf9itely v>i$ may be ! po9ts ( view & /&>ds ( ref]5ce4 ,f ?is datum1 :i*1 speak+ philosophically1 /rangely %>es ! intr9sic qualities ) :i* ! old] absolute "t & absolute space 7 s mu* reproa*$1 ! :ole con/ructive "p ( ,relativity1 ! "p :i* leads to ! spl5did v]ifications we describ$1 is d]iv$4 ,?us ! !ory ( ,relativity seems to d5y its orig91 ev5 its v "n1 9 all t makes x a useful monum5t ( sci5ce1 a con/ructive tool1 an in/rum5t ( discov]y4 ,x is a !ory ( a new absolute3 ! ,int]val repres5t$ by ! geodetics ( ! quadri-dim5sional univ]se4 ,x is a new absolute !ory4 ,s true is x t ev5 9 sci5ce y c build no?+ on pure negation4 ,= creation y ne$ affirmation4 ,! !ory ( ,relativity has won brilliant victories1 cr[n$ by ! decisive sanction ( facts4 ,we h giv5 "s a/oni%+ in/ances ( ^! 9 our e>li] *apt]s4 ,b to say t ! !ory is true because x has pr$ict$ ph5om5a t 7 aft]w>ds v]ifi$ w\ld be to judge x f too n>r[ly ,pragmati/ a /&po9t4 ,x w\ld also--!re is real dang] 9 ?is--be to close aga9/ ! m9d o!r pa?s :]e !re are /ill fl[]s to cull4 ,we w n d t4 ,x is !re=e important1 9 spite ( its successes--nay1 on acc\nt ( !m--to turn ! light ( criticism ^u ! f\ndations ( ! new doctr9e4 ,ev5 ,cs>1 z he m\nt$ ! ,capitol1 _h to li/5 to ! jokes ( ! soldi]s r\nd 8 *>iot & l[] 8 pride4 ,! !ory ( ,relativity also1 z x advances 9 all its magnific5ce along ! ,triumphal ,way1 mu/ le>n t x has its limits1 p]haps its weaknesses4 99 99 99 99 99 ,b be=e we g fur!r into x1 be=e we turn ! raw light ^u x1 let u make "o obs]vation4 ,:atev] be ! obscurities ( physical !ories1 :atev] be ! et]nal & fat$ imp]fection ( sci5ce1 "o ?+ may be positively laid d[n "h3 sci5tific tru?s are ! be/ e/abli%$1 ! mo/ c]ta91 ! lea/ d\btful ( all ! tru?s we c "k 9 reg>d to ! ext]nal _w4 ,if sci5ce _c reveal to u ! nature ( ?+s 9 its entirety1 !re is no?+ else t c d x z well4 ,! tru?s ( s5tim5t1 ( fai?1 ( intuition1 h no?+ to d ) ^? ( sci5ce z long z !y rema9 /rictly tru?s ( ! int]ior _w4 ,!y are on ano!r plane4 ,b ! mom5t !y claim to be measures ( ! ext]nal _w--:i* w\ld be _! only cause ( weakness--!y subject !mselves to ! mat]ial reality1 to ! sci5tific inve/igation ( ! tru?4 ,x is !re=e nons5se to speak ( a 8bankruptcy ( sci5ce0 z contra/$ ) ! c]ta9ty :i* o!r discipl9es may give u respect+ ! ext]nal _w4 ,! bankruptcy ( "o w\ld make all ! o!rs bankrupt4 ,:5 x is n a "q ( ! intimate oasis 9 :i* ! s]5e realities ( s5tim5t fl\ri%1 b ( ! arid & imp]fectly explor$ des]t ( ! mat]ial _w1 ! sci5tific facts are ! basis ( all con/ructions4 ,de/roy ^? & y de/roy ev]y?+4 ,if y ram ! gr\nd floor ( a h\se & br+ x d[n1 y br+ d[n also ! upp] /ories4 ,to say ! tru?1 x w\ld seem t no?+ "h bel[ s mu* reveals ! my/ic pres5ce ( ! div9e z does ! et]nal & inflexible h>mony t unites ph5om5a1 & t f9ds expression 9 ! laws ( sci5ce4 ,is n ?is sci5ce :i* %[s u ! va/ univ]se well-ord]$1 coh]5t1 h>moni\s1 my/]i\sly unit$1 organis$ l a great mute symphony1 dom9at$ by law in/ead ( caprice1 by irrefragable rules in/ead ( individual wills--is ?is n a revelation8 ,!re y h ! only means ( reconcil+ ! m9ds :i* are devot$ to ext]nal realities & ^? :i* b[ to metaphysical my/]y4 ,to talk ( bankruptcy ( sci5ce--if x means any?+ m ?an to po9t out human weakness1 :i* is1 alas6 obvi\s en\gh--is really to calumniate t "p ( ! div9e :i* is accessible to our s5ses1 ! "p :i* sci5ce reveals4 99 99 99 99 99 ,9 sum1 ! :ole ,e9/e9ian syn!sis fl[s f ! issue ( ! ,mi*elson exp]im5t1 or at lea/ f a p>ticul> int]pretation ( t issue4 ,! ph5om5on ( /ell> ab]ration proves t ! m$ium :i* transmits ! light ( ! />s to our eyes does n %>e ! motion ( ! e>? z x revolves r\nd ! sun4 ,?is m$ium is kn[n to physici/s z e!r4 ,"l ,kelv91 :o 0 hon\r$ by be+ buri$ 9 ,we/m9/] ,abbey n f> f ! tomb ( ,newton1 rightly reg>d$ ! exi/5ce ( int]/ell> e!r z prov$ z fully z ! exi/5ce ( ! air we brea!2 = )\t ?is m$ium ! heat ( ! sun1 "m & nurse ( all t]re/rial life1 w\ld nev] rea* u4 ,9 8 !ory ( ,special ,relativity1 ,e9/e91 z we saw1 int]prets ph5om5a )\t introduc+ ! e!r1 or at lea/ )\t introduc+ ! k9ematic prop]ties :i* are usually attribut$ to x4 ,9 o!r words1 ,special ,relativity nei!r affirms nor d5ies ! exi/5ce ( ! classic e!r4 ,x ignores x4 ,b ?is indiff]5ce to or disda9 ( ! e!r disappe>s 9 ! !ory ( ,g5]al ,relativity4 ,we saw 9 a previ\s *apt] t ! trajectories ( gravitat+ bodies & ( light are directly due1 on ?is !ory1 to a special curvature & ! non-,euclidean "* ( ! m$ium :i* lies close to massive bodies 9 ! void--t is to say1 e!r4 ,?is1 !re=e1 ?\gh ,e9/e9 does n give x ! same k9ematic prop]ties z classic sci5ce did1 becomes ! sub/ratum ( all ! ev5ts 9 ! univ]se4 ,x resumes its importance1 its objective reality4 ,x is ! cont9u\s m$ium 9 :i* spatio-temporal facts evolve4 ,h5ce 9 its g5]al =m1 & 9 spite ( ! new k9ematic attitude :i* is ascrib$ to x1 ,e9/e9's g5]al !ory admits ! objective exi/5ce ( e!r4 ,/ell> ab]ration %[s t ?is m$ium is /ation>y relatively to ! orbital motion ( ! e>?4 ,! negative result ( ,mi*elson's exp]im5t t5ds1 on ! contr>y1 to prove t x %>es ! e>?'s motion4 ,! ,fitzg]ald-,lor5tz hypo!sis solves ?is ant9omy by admitt+ t ! e!r does n really %>e ! e>?'s motion1 b say+ t all bodies sudd5ly displac$ 9 x are contract$ 9 ! direction ( ! movem5t4 ,?is contraction increases ) _! velocity 9 ! e!r1 :i* expla9s ! negative result ( ! ,mi*elson exp]im5t4 ,lor5tz's explanation seem$ to ,e9/e9 inadmissible on acc\nt ( c]ta9 improbabilities :i* we po9t$ out1 & especially because x assumes t !re is 9 ! univ]se a sy/em ( privileg$ ref]5ces :i* recalls ,newton's 8absolute space40 ,e9/e91 tak+ 8 /& on ! pr9ciple t all po9ts ( view are equally relative1 does n admit t !re are 9 ! univ]se privileg$ spectators--spectators :o are /ation>y 9 ! e!r--:o c\ld see ?+s z !y are1 :]eas ^! ?+s w\ld be de=m$ = e o!r obs]v]4 ,!n1 :ile pres]v+ ! ,lor5tz contraction & ! =mul 9 :i* x is express$1 ,e9/e9 says t ?is contraction1 :ile x really exi/s1 is only an appe>ance1 a sort ( optical illusion1 due to ! fact t ! light :i* %[s u objects does n travel in/antane\sly1 b ) a f9ite velocity4 ,?is spread ( light foll[s laws ( su* a nature t app>5t space & "t are *ang$ 9 precise accordance ) ! =mul ( ,lor5tz4 ,t is ! f\ndation ( ,e9/e9's ,special ,relativity4 ,h5ce ! two imm$iate possible explanations ( ! negative result ( ! ,mi*elson exp]im5t are3 #a4 ,mov+ objects are contract$ 9 ! /ation>y e!r1 ! fix$ sub/ratum ( all ph5om5a4 ,?is contraction is real1 & x increases ) ! velocity ( ! body relatively to ! e!r4 ,t is ,lor5tz's explanation4 #b4 ,mov+ objects are contract$ relatively to any obs]v] :atsoev]4 ,?is contraction is only app>5t1 & is due to ! laws ( ! propagation ( light4 ,x increases ) ! velocity ( ! mov+ body relatively to ! obs]v]4 ,t is ,e9/e9's explanation4 99 99 99 99 99 ,b !re is at lea/ "o o!r possible explanation4 ,x introduces new & /range hypo!ses1 b !y are by no means absurd4 ,inde$1 x is especially 9 physics t tru? may at times seem improbable4 ,?is explanation w %[ h[ we may acc\nt = ! result ( ! ,mi*elson exp]im5t ap>t f ei!r ,lor5tz or ,e9/e94 ,?is ?ird explanatory hypo!sis is z foll[s4 ,e mat]ial body be>s along ) x1 z a sort ( atmosph]e1 ! e!r t is b\nd up ) x4 ,!re is1 9 addition1 a /ation>y e!r 9 ! int]/ell> spaces2 an e!r ins5sible to ! motion ( ! mat]ial bodies t move 9 x1 & :i* we may1 to di/+ui% x f ! e!r b\nd up ) bodies1 call ! 8sup]-e!r40 ,?is sup]-e!r occupies ! :ole ( int]/ell> space1 & ne> ! heav5ly bodies x is sup]impos$ ^u ! e!r :i* !y be> along4 ,! e!r & ! sup]-e!r int]p5etrate ea* o!r j z !y p5etrate matt]1 & ! vibrations !y transmit spread indep5d5tly4 ,:5 a mat]ial body s5ds out s]ies ( waves 9 ! e!r :i* surr\nds x1 ^! move relatively to x ) ! con/ant velocity ( light4 ,b :5 !y h trav]s$ ! relatively ?9 /ratum ( e!r b\nd up ) ! mat]ial body1 :i* m]ges gradually 9 ! sup]-e!r1 !y spread 9 ! latt]1 & x is relatively to ?is t !y progressively take _! velocity4 ,x is l a boat cross+ ! ,lake ( ,g5eva at a c]ta9 spe$4 ,ab\t ! middle ( ! lake x has ?is spe$ relatively to ! n>r[ curr5t :i* ! ,riv] ,rhone makes !re1 & !n x resumes x relatively to ! /ation>y lake4 ,9 ! same way ! lum9\s rays ( ! />s1 al?\gh !y come f bodies :i* are approa*+ or rec$+ f u1 h ! same velocity :5 !y rea* u1 & ?is w be ! common velocity :i* ! sup]-e!r imposes ^u !m4 ,?us also1 on ! o!r h&1 ! /ell> rays t rea* our telescopes w be transmitt$ to u by ! sup]-e!r1 )\t ! v ?9 /ratum ( mobile e!r b\nd up ) ! e>? be+ able to di/urb _! propagation4 ,^! hypo!ses expla9 & reconcile all ! facts3 7#a7 ! fact ( /ell> ab]ration1 because ! rays :i* rea* u f ! />s are transmitt$ to u unalt]$ by ! sup]-e!r2 7#b7 ! negative result ( ! ,mi*elson exp]im5t1 because ! light :i* we produce 9 ! laboratory travels 9 ! e!r t is borne along by ! e>?1 :]e x orig9ates2 7#c7 ! fact t1 9 spite ( ! approa* or recession ( ! />s1 _! light rea*es u ) ! common velocity :i* x _h acquir$ 9 ! sup]-e!r1 %ortly aft] x />t$4 ,h[ev] /range ?is explanation may seem1 x is n absurd1 & x raises no insurm\ntable difficulty4 ,x %[s t1 if ! result ( ! ,mi*elson exp]im5t is a sort ( no-?or\ghf>e1 !re are o!r ways out ( x besides ,e9/e9's !ory4 ,to resume ! matt]1 we h (f]$ to u ?ree diff]5t ways ( escap+ ! difficulties1 ! app>5t contradictions1 involv$ 9 our exp]i5ce--! ant9omy aris+ f ab]ration & ! ,mi*elson result--& !y are r$uc$ to ^! alt]natives3 #a4 ,! contraction ( bodies by velocity is real 7,lor5tz74 #b4 ,! contraction ( bodies by velocity is only an appe>ance due to ! laws ( ! propagation ( light 7,e9/e974 #c4 ,! contraction ( bodies by velocity is nei!r real nor app>5t3 !re is no su* ?+ 7hypo!sis ( sup]-e!r connect$ ) e!r74 ,?is %[s t ! ,e9/e9ian explanation ( ph5om5a is by no means impos$ ^u u by ! facts1 or is at lea/ n absolutely impos$ by !m to ! exclusion ( any o!r explanation4 99 99 99 99 99 ,is x at lea/ impos$ by reason1 by pr9ciples1 by ! evid5tial "* ( its rational premises1 or because x does n conflict ) our good s5se & m5tal habits z ! o!rs d8 ,"o w\ld suppose ?is at fir/1 :5 "o comp>es x ) ! tea*+ ( ,lor5tz2 &1 9 ord] to relieve ?is discussion1 ,i w = ! mom5t leave out ( acc\nt ! ?ird !ory :i* ,i sket*$1 t ( a sup]-e!r4 ,:at seem$ mo/ difficult to admit 9 ,lor5tz's hypo!sis ( real contraction 0 t ! contraction ( bodies 0 suppos$ to dep5d entirely ^u _! velocity1 n 9 any way ^u _! nature2 t x 0 suppos$ to be ! same = all bodies1 no matt] :at 0 _! *emical composition or physical condition4 ,a little reflexion %[s t ?is /range sugge/ion is n s cle>ly inadmissible4 ,we "k t ! atoms are all =m$ ( ! same electrons1 & !y diff]1 & diff]5tiate bodies1 only 9 _! numb] & arrangem5t4 ,if1 !n1 ! electrons common to all matt] & _! relative di/ances exp]i5ce simultane\sly a contraction due to velocity1 x is natural en\gh to suppose t ! result maybe ! same = all objects4 ,:5 an iron grat+ ( a giv5 l5g? is dilat$ by heat1 ! ext5t to :i* a temp]ature ( a hundr$ degrees dilates x w be ! same :e!r x c\nts t5 or a hundr$ /eel b>s to ! squ>e y>d1 provid$ !y are id5tical4 ,h5ce x is n really "h t we f9d ! improbability :i* caus$ ,relativi/s to reject ! ,lor5tz !ory4 ,x is 9 ! pr9ciples ( ! !ory4 ,x is because ! !ory admits 9 nature a sy/em ( privileg$ ref]5ce--! /ation>y e!r relatively to :i* bodies move4 ,let u exam9e ?is m closely4 ,x has be5 said t ,lor5tz's /ation>y e!r is m]ely a resuscitation ( ,newton's absolute space1 :i* ! ,relativi/s h s vigor\sly attack$4 ,t is v f> f ! tru?4 ,if1 z we suppos$ 9 ! prec$+ *apt]1 our /ell> univ]se is only a giant globe ( e!r roll+ 9 a space t is devoid ( e!r--"o ( _m su* globes t w rema9 = ev] unkn[able to man--x is obvi\s t ! drop ( e!r :i* repres5ts our univ]se may v well be mov+ 9 ! environ+ space1 :i* w\ld !n be ! real 8absolute space40 ,f ?is /&po9t ! ,lor5tzian e!r _c be id5tifi$ ) absolute space4 ,to d s am\nts to say+ t ! space call$ 8absolute0 by ,newton does n des]ve ! "n4 ,if ,newtonian space is only ! physical cont9uum 9 :i* ! ev5ts ( our univ]se happ51 x is any?+ b /ation>y4 ,9 t case ! :ole fault "o has to f9d ) ,newton is t he us$ a wrong expression3 t he call$ some?+ absolute :i* is m]ely privileg$ = a giv5 univ]se4 ,x w\ld be a qu>rel ab\t gramm>2 & su* ?+s h nev] succe$$ 9 revolutionis+ sci5ce4 ,b ! ,relativi/s--at lea/ ^? imp5it5t ,relativi/s1 ! ,e9/e9ians--w n be cont5t ) t4 ,x is n en\gh = !m t ! ,newtonian space ) all its privileges may n be absolute space4 ,our conception ( ! univ]se1 z a mov+ isl& ( e!r1 is well calculat$ to reconcile ! pre-em95ce ( ,newtonian space ) t agno/icism :i* =bids u to hope to atta9 ! absolute4 ,b ?is aga9 is n en\gh = ! ,e9/e9ians4 ,:at !y mean to d is to /rip ( all its privileges ! ,newtonian space on :i* ! /ructure ( classical me*anics has be5 re>$4 ,!y mean to r$uce ?is space to ! ranks1 to make x no m ?an analog\s to any o!r spaces t c be imag9$ & :i* move arbitr>ily 9 ref]5ce to x4 99 99 99 99 99 ,f ! agno/ic1 ! sceptical1 po9t ( view ?is is a f9e & /rong attitude4 ,b 9 ! c\rse ( ?is volume we h s mu* admir$ ,e9/e9's p[]ful !oretical syn!sis & ! surpris+ v]ifications to :i* x l$ t we are n[ entitl$ to make "s res]ves4 ,x is legitimate to call into "q ev5 ! d5ials ( d\bt]s1 because1 aft] all1 !y are really !mselves affirmations4 ,we believe t 9 face ( ?is philosophic attitude ( ! ,e9/e9ians--9 face ( :at ,i %\ld l to call _! absolute relativism--we are ju/ifi$ 9 rebell+ a little & say+ some?+ l ?is3 8,yes1 ev]y?+ is possible2 or1 r1 _m ?+s are possible1 b all ?+s are n4 ,yes1 if ,i g into a /range h\se1 ! draw+-room clock may be r\nd1 squ>e1 or octagonal4 ,b once ,i h ent]$ ! h\se & se5 t ! clock is squ>e1 ,i h a "r to say3 #8,! clock is squ>e4 ,x has ! privilege ( be+ squ>e4 ,x is a fact t x is nei!r r\nd nor octagonal4' 8,x is ! same 9 nature4 ,! physical cont9uum :i* conta9s1 l a vase1 all ! ph5om5a ( ! univ]se1 might h1 relatively to me--& z long z ,i h n obs]v$ x--any =ms or movem5ts :atev]4 ,b z a matt] ( fact1 x is :at x is4 ,x _c be diff]5t ?+s at ! same "t4 ,! draw+-room clock _c at "o & ! same "t be compos$ entirely ( gold & entirely ( silv]4 8,!re is !re=e "o privileg$ possibility among/ ! v>i\s possibilities :i* we imag9e 9 ! ext]nal _w4 ,x is t :i* has be5 effectively realis$3 t :i* exi/s40 ,! complete relativism ( ! ,e9/e9ians am\nts to mak+ ! univ]se ext]nal to u to su* an ext5t t we h no means ( di/+ui%+ betwe5 :at is real & :at is possible 9 x1 z f> z space & "t are conc]n$4 ,! ,newtonians1 on ! o!r h&1 say t we c recognise real space & real "t by special signs4 ,we w analyse ^! signs lat]4 ,9 a ^w1 ! pure ,relativi/s h tri$ to escape ! necessity ( suppos+ t reality is inaccessible4 ,x is a po9t ( view t is at once m mode/ & mu* m presumptu\s ?an t ( ! ,newtonians1 ! ,absoluti/s4 ,x is m mode/ because accord+ to ! ,e9/e9ian we _c "k c]ta9 ?+s :i* ! ,absoluti/ reg>ds z accessible3 real "t & space4 ,x is m presumptu\s because ! ,relativi/ says t !re is no reality except t :i* comes "u obs]vation4 ,= him ! unkn[able & non-exi/5t are ! same ?+4 ,t is :y ,h5ri ,po9c>1 :o 0 ! mo/ pr(\nd ( ,relativi/s be=e ! days ( ,e9/e91 us$ to repeat con/antly t que/ions ab\t absolute space & "t h 8no mean+40 ,"o might sum x up by say+ t ! ,e9/e9ians h tak5 z _! motto ! words ( ,augu/e ,comte3 8,ev]y?+ is relative1 & t is ! only absolute40 ,newton1 ^: spatio-temporal premises ,h5ri ,po9c> vigor\sly refus$ to admit1 & classical sci5ce take up an attitude1 on ! contr>y1 :i* ,newton himself well describ$ :5 he wrote3 8,i am b a *ild play+ on ! %ore1 rejoic+ t ,i f9d at times a well-poli%$ pebble or an unusually f9e %ell1 :ile ! great ocean ( tru? lies unexplor$ be=e me40 ,newton says t ! ocean is unexplor$1 b he says t x exi/s2 & f ! features ( ! %ells he f\nd he d$uc$ c]ta9 qualities ( ! ocean1 especially ^? prop]ties :i* he calls absolute "t & space4 ,e9/e9ians & ,newtonians are agre$ 9 ?9k+ t ! ext]nal _w is n 9 our "t entirely am5able to sci5tific rese>*4 ,b _! agno/icism diff]s 9 its limits4 ,! ,newtonians believe t1 h[ev] ext]nal to u ! _w may be1 x is n to su* an ext5t z to make 8real "t & space inaccessible to u40 ,! ,e9/e9ians hold a diff]5t op9ion4 ,:at sep>ates !m is only a "q ( degree ( scepticism4 ,! :ole controv]sy is r$uc$ to a fronti] qu>rel betwe5 two agno/icisms4 ,,*apt] ,,ix ,,e9/e9 ,,or ,,newton8 ,rec5t discussion ( ,relativism at ! ,academy ( ,sci5ces--,traces ( ! privileg$ space ( ,newton--,! pr9ciple ( causality ! basis ( sci5ce--,exam9ation ( ,m4 ,pa9lev's objections--,newtonian argum5ts & ,relativi/ replies--,m4 ,pa9lev's =mul ( gravitation--,fecundity ( ,e9/e9's !ory--,two conceptions ( ! _w--,conclusion4 ,:at are ^! 8special signs0 by :i* ! ,newtonian conception ( nature recognises t we are 9 t\* ) ! privileg$ space :i* ,newton call$ absolute space1 & :i* seem$ to him ! real1 intr9sic1 exclusive frame ( ph5om5a8 ,^! signs or crit]ia are implicitly at ! root ( ! developm5t ( classic sci5ce1 b !y = a "t rema9$ 9 ! %ades ( ! discussions provok$ by ,e9/e9's !ory4 ,leav+ aside = a mom5t o!r1 & p]haps less noble1 c>es1 ,m4 ,paul ,pa9lev1 address+ ! ,academy ( ,sci5ces at ,p>is1 has ) brilliant success drawn att5tion to ! argum5ts1 anci5t yet ev] robu/1 :i* con/itute ! /r5g? ( ! ,newtonian conception ( ! _w4 ,let u f ?is po9t speak ( ! absolute "t & space ( ,newton & ( ,galileo z privileg$ space & privileg$ "t1 9 ord] n to expose our flanks fur!r to ! metaphysical objections--n )\t ju/ification--:i* ! qualification 8absolute0 provokes4 ,:y is classical sci5ce1 ! me*anics ( ,galileo & ,newton1 f\nd$ ^u privileg$ space & privileg$ "t8 ,:y d !y ref] all ph5om5a to ^! unique /&>ds1 & consid] !m adequate to reality8 ,x is on acc\nt ( ! pr9ciple ( causality4 ,! pr9ciple may be =mulat$ ?us3 ,id5tical causes produce id5tical effects4 ,t means t ! initial conditions ( a ph5om5on det]m9e its ult]ior modalities4 ,x is briefly a /atem5t ( ! det]m9ism ( ph5om5a1 & )\t t sci5ce is impossible4 ,x is1 ( c\rse1 possible to be capti\s on ! po9t4 ,conditions entirely id5tical ) giv5 initial conditions c nev] be reproduc$ or discov]$ at a diff]5t "t or 9 a diff]5t place4 ,!re is always "s circum/ance t w be diff]5t2 = in/ance1 ! fact t 9 ! int]val betwe5 ! two exp]im5ts ! ,nebula 9 ,&rom$a w h come sev]al ?\s& miles ne>] to u4 ,& we h no influ5ce on ! ,nebula 9 ,&rom$a4 ,happily--?is saves ! situation--di/ant bodies h1 x seems1 only a negligible influ5ce on our exp]im5ts4 ,t is :y we c repeat !m4 ,= in/ance1 if we to-day put a gramme ( sulphuric acid 9 t5 grammes ( soda-solution 7"o-t5?71 !y w 9 ! same p]iod ( "t produce ! same quantity ( sulphate ( sodium t !y w\ld h done a ye> previ\sly 9 ! same conditions ( temp]ature & pressure2 9 spite ( ! fact t meantime ,m>%al ,fo* sail$ = ! ,unit$ ,/ates4 ,?us ! pr9ciple ( causality 7l causes1 l effects7 is always v]ifi$1 & nev] f\nd at fault4 ,x is !re=e an empirical tru?1 b 9 addition to ?is x imposes itself on our m9d ) irresi/ible =ce4 ,x ev5 imposes itself ^u animals4 8,! scald$ cat avoids hot wat]10 is pro( en\gh4 ,9 any case1 n sci5ce only b ! :ole life ( man & animals is bas$ ^u x4 ,x is a consequ5ce ( ! pr9ciple t if ! initial conditions ( a movem5t pres5t a symmetry1 ?is w appe> aga9 9 ! movem5t4 ,m4 ,paul ,pa9lev insi/$ /rongly on ?is 9 ! c\rse ( ! rec5t discussion ( ,relativism at ! ,academy ( ,sci5ces4 ,! pr9ciple ( in]tia 9 p>ticul> foll[s f ?is /atem5t3 a body left to itself f> f any mat]ial mass w1 by reason ( symmetry1 rema9 at re/ or travel 9 a /raight l9e4 ,x w c]ta9ly foll[ a /raight l9e = a giv5 obs]v] 7or = obs]v]s mov+ ) uni=m velocities relatively to ! fir/74 ,! ,newtonians say t ! space ( ^! obs]v]s is privileg$4 ,on ! o!r h&1 = ano!r obs]v] :o is1 relatively to !m1 mov+ at an accel]at$ velocity1 ! pa? ( ! mov+ body w be a p>abola1 & w no long] be symmetrical4 ,!re=e ! space ( ?is new obs]v] is n privileg$ space4 ,x seems to me t ! ,relativi/s might reply to ?is z foll[s4 ,y h no "r to def9e ! initial conditions = a giv5 obs]v]1 !n ! subsequ5t movem5t = ano!r obs]v] :o is mov+ ) accel]at$ velocity4 ,if y ?us def9e y\r initial conditions relatively to ! latt]1 ! mov+ body at ! mom5t :5 x is releas$ is n free = ?is obs]v]1 b falls 9 a gravitational field4 ,x is !re=e n surpris+ t ! motion produc$ seems to him accel]at$ & dissymmetrical4 ,! pr9ciple ( causality is n wrong = ei!r obs]v]4 ,"o might also give a diff]5t def9ition ( ! privileg$ sy/em1 say+3 x is t relatively to :i* light travels 9 a /raight l9e 9 an isotropic m$ium4 ,b 9 t case ! rays f ! />s travel 9 a spiral = an obs]v] fix$ on a turn+ e>?1 & ! ,newtonians w\ld inf] f ?is t ! e>? turns relatively to _! privileg$ space4 ,e9/e9ians w reply t ! space 9 :i* ! rays travel is n isotropic1 & t !y are div]t$ f ! /raight l9e 9 x by ! turn+ gravitational field :i* causes ! c5trifugal =ce ( ! e>?'s rotation4 ,!y w always f9d an escape :i* w leave ! pr9ciple ( causality intact4 ,x seems difficult1 !re=e1 to give unansw]able pro( ( ! exi/5ce ( ! privileg$ sy/em :5 we />t f ! pr9ciple ( causality4 ,ea* p>ty reta9s its position4 99 99 99 99 99 ,on ! o!r h&1 !re is evid5tial value1 a ke5 & conv9c+ p5etration1 9 ! second "p ( ! criticism :i* ,m4 ,pa9lev directs aga9/ ! pr9ciples ( ,e9/e9's !ory4 ,let u sum up ! argum5t ( ! di/+ui%$ geometrician4 ,y1 he says to ! ,e9/e9ians1 d5y all privilege to any sy/em ( ref]5ce :atev]4 ,b :5 y want to d$uce1 by calculation1 ! law ( gravity f y\r g5]al equations1 y _c d x1 & y really d n d x1 except by introduc+ sc>cely disguis$ ,newtonian hypo!ses & privileg$ axes ( ref]5ce4 ,y only rea* ! result ( y\r calculation by %>ply sep>at+ "t & space z ,newton does1 & by ref]r+ y\r gravitat+ mov+ objects to purely ,newtonian privileg$ axes1 9 ! case ( :i* c]ta9 conditions ( symmetry are realis$4 ,to ?is f9e & pr(\nd criticism :i* ,m4 ,pa9lev raises may be add$ t ( ,wie*]t1 :o has po9t$ out v>i\s o!r hypo!ses introduc$ by ,e9/e9 9 ! c\rse ( 8 calculations4 ,9 a ^w1 ,e9/e9 seems n to h kept entirely cle> ( ! ,newtonian premises :i* he repudiates4 ,he has n ! disda9 = !m t "o w\ld suppose1 & he does n hesitate to h rec\rse to !m occasionally = ! purpose ( help+ out 8 calculations4 ,t is r to pay a little rev]5ce to ! idols y h burn$4 ,9 reply ! ,e9/e9ians w d\btless say t1 if !y introduce ,newtonian axes 9 ! c\rse ( _! argum5ts1 x is to make ! results ( calculation comp>able to ! result ( exp]im5tal measurem5ts4 ,! axes introduc$ into _! equations h = ! ,relativi/s ! sole privilege ( be+ ^? to :i* exp]im5t]s ref] _! measurem5ts4 ,b we mu/ admit t t is no small privilege4 99 99 99 99 99 ,t is n all4 ,! pr9ciple ( ,g5]al ,relativity am\nts to ?is3 ,all sy/ems ( ref]5ce are equival5t = express+ natural laws1 & ^! laws are inv>iant to any sy/em ( ref]5ce to :i* !y are relat$4 ,t means 9 effect3 ,!re are relations betwe5 objects ( ! mat]ial _w :i* are indep5d5t ( ! "o :o obs]ves !m1 & p>ticul>ly ( 8 velocity4 ,?us1 :5 a triangle is drawn on pap]1 !re is some?+ 9 ! triangle :i* *>act]ises x & :i* is id5tical1 :e!r ! obs]v] passes v quickly or v sl[ly1 or at any spe$ & 9 any direction :atev]1 beside ! pap]4 ,m4 ,pa9lev obs]ves1 ) "s reason1 t 9 ?is =m ! pr9ciple is a sort ( truism4 ,x is a sev]e v]dict1 yet x expresses a c]ta9 fact4 ,! real relations ( ext]nal objects _c be alt]$ by ! /&po9t ( ! obs]v]4 ,e9/e9 replies t x is at all ev5ts some?+ to h provid$ a sieve by :i* we may sift ! laws & =mul :i* s]ve to repres5t ! ph5om5a t h be5 empirically obs]v$3 a crit]ion :i* !y mu/ pass be=e !y are recognis$ z correct4 ,?is is true4 ,newton's law1 9 its classic =m1 did n meet ?is crit]ion4 ,?is proves t x 0 n q s obvi\s4 ,a tru? t 0 unkn[n ye/]day has become to-day a truism4 ,s mu* ! bett]4 ,9 express+ "o ( ! conditions :i* mu/ be satisfi$ by natural laws ! !ory ( ,relativity at lea/ has :at is call$ 9 philosophical j>gon a 8heuri/ic0 value4 ,b x is none ! less true1 z ,m4 ,pa9lev po9ts out ) great =ce & cle>ness1 t ! pr9ciple ( ,g5]al ,relativity1 consid]$ 9 ?is light1 w\ld be unable to provide precise laws4 ,x w\ld be q consi/5t ) a law ( gravity 9 :i* ! attraction w\ld be 9 inv]se proportion1 n to ! squ>e1 b to ! sev5te5? or hundr$? p[]1 or any p[] :atev]1 ( ! di/ance4 ,9 ord] to extract ! correct law ( gravitation f ! pr9ciple ( ,g5]al ,relativity we h to add to x ! ,e9/e9ian int]pretation ( ! result ( ! ,mi*elson exp]im5t--to wit1 t relatively to any obs]v] :atsoev] light travels locally ) ! same velocity 9 e direction4 ,we h also to add v>i\s hypo!ses :i* ,m4 ,pa9lev reg>ds z ,newtonian4 ,to ! critical discussion ( ,relativity :i* he s brilliantly pres5t$ at ! ,academy ( ,sci5ces ,m4 ,paul ,pa9lev add$ a valuable ma!matical contribution ( :i* ! *ief result is ! foll[+3 ,x is possible to excogitate o!r laws ( gravitation ?an t (f]$ by ,e9/e91 & all ( !m w fulfil ! ,e9/e9ian conditions4 ,! le>n$ ,fr5* geometrician indicat$ sev]al ( ^!1 especially "o ( :i* ! =mula diff]s consid]ably f t ( ,e9/e91 yet equally & precisely expla9s ! motions ( ! planets1 ! displacem5t ( ! p]ihelion ( ,m]cury1 & ! deviation ( rays ( light ne> ! sun4 ,?is new =mula corresponds to a space t is indep5d5t ( "t1 & x does n involve ! consequ5ce t ,e9/e9's =mula does 9 reg>d to ! %ift+ t[>d ! r$ ( all ! l9es 9 ! sol> spectrum4 ,! v]ification or non-v]ification ( ?is consequ5ce ( ,e9/e9's equation1 ( :i* we po9t$ out ! difficulties 7p]haps insurm\ntable7 9 a previ\s *apt]1 ?us acquires a new importance4 ,x is a rem>kable ?+ t _m ( ! =mul ( gravitation giv5 by ,m4 ,pa9lev lead to ! conclusion1 diff]5tly f t ( ,e9/e91 t space rema9s ,euclidean ev5 ne> ! sun1 9 ! s5se t measures are n necess>ily contract$4 ,all ?is light on ! a/ronomical horizon seems l ! dawn ( a new era 9 :i* obs]vations ( unprec$5t$ delicacy w provide te/s t are calculat$ to give a m precise & less ambigu\s =m to ! law ( gravitation4 ,!re are great days--or1 r1 great nights--9 /ore = ! a/ronom]4 99 99 99 99 99 ,z f> z ! pr9ciples are conc]n$1 ! controv]sy w g on4 ,x mu/ end 9 some?+ l ! foll[+ dialogue3 ,! ,newtonian3 ,d y admit t at a po9t 9 ! univ]se t is f> away f all mat]ial masses a mov+ object left to itself mu/ foll[ a /raight l9e8 ,if s1 y recognise ! exi/5ce ( privileg$ obs]v]s--^? = :om ! l9e is /raight4 ,= ano!r obs]v] ! l9e is a p>abola4 ,!re=e 8 po9t ( view is wrong4 ,! ,relativi/3 ,yes1 ,i grant x2 b 9 po9t ( fact !re is no po9t 9 ! univ]se :]e !re is no influ5ce ( di/ant mat]ial masses4 ,!re=e y\r mov+ object left to itself is a m]e fiction1 & ,i am n go+ to base sci5ce ^u an unv]ifiable piece ( imag9ation4 ,! :ole aim ( ! ,relativi/ is to rid sci5ce ( ev]y?+ t has no exp]im5tal significance4 ,z to ! obs]v] :o sees ! mov+ object 9 "q describe a p>abola1 he w int]pret 8 obs]vation to mean t ! object is 9 a gravitational field4 ,! ,newtonian3 ,y are !re=e compell$ to admit t f> away f all matt]1 f> f all heav5ly bodies1 !re c be :at y call a gravitational field1 t x v>ies accord+ to ! velocity ( ! obs]v]1 & t x c be v int5se 9 spite ( ! di/ance ( ! heav5ly bodies1 & ev51 at times1 increase ) t di/ance4 ,^! are /range & absurd hypo!ses4 ,! ,relativi/3 ,!y are /range1 b ,i defy y to prove t !y are absurd4 ,!y are less absurd ?an to localise & set 9 motion a po9t t is isolat$ & indep5d5t ( any mat]ial mass4 ,! ,newtonian3 ,= my "p1 ,i c easily imag9e a s+le mat]ial po9t 9 ! univ]se hav+ a c]ta9 position & a c]ta9 velocity 9 x4 ,! ,relativi/3 ,= my "p1 on ! contr>y1 if su* a mat]ial po9t exi/$1 x w\ld be absurd & impossible to speak ( its position & its motion4 ,x w\ld h nei!r position nor motion nor re/4 ,su* ?+s c exi/ only ) ref]5ce to o!r mat]ial po9ts4 ,! ,newtonian3 ,t is n my op9ion4 ,! ,imp>tial ,spectator3 ,9 ord] to "k :i* ( y is "r we %\ld ne$ to try an exp]im5t on a mat]ial po9t t is )drawn f ! influ5ce ( ! re/ ( ! univ]se4 ,c y try ?is exp]im5t8 ,! ,newtonian & ! ,relativi/ 7toge!r73 ,no1 unhappily4 ,! ,metaphysician 7com+ up l ! ?ird ?ief 9 ! fable73 ,!n1 g5tlem51 ,i advise y to return to y\r telescopes1 y\r laboratories1 & y\r tables ( log>i?ms4 ,! re/ is my affair4 ,! ,newtonian & ! ,relativi/ 7toge!r73 ,9 t case we are q sure we %all nev] le>n any?+ fur!r ab\t x ?an we "k or believe n[4 99 99 99 99 99 ,meantime1 x is impossible to exagg]ate ! importance ( ! new light ?r[n on ! "q ( ,relativity by ! int]v5tion ( ,m4 ,paul ,pa9lev at ! ,academy ( ,sci5ces4 ,x w h a la/+ & prodigi\s e*o4 ,w ,e9/e9's f9e syn!sis be defeat$8 ,%all we see x s9k 9 ! controv]sies1 d\bts1 & obscurities ( :i* we h giv5 a %ort acc\nt8 ,i ?9k n4 ,:5 ,*ri/oph] ,columbus discov]$ ,am]ica1 x 0 all v well to tell him t 8 premises 7 wrong1 & t if he _h n believ$ t he 0 sail+ = ! ,indies he w\ld nev] h rea*$ a new cont95t4 ,he might h repli$1 aft] ! /yle ( ,galileo3 8,i discov]$ x1 = all t40 ,! me?od t gives good results is always a good me?od4 ,:5 we h to plunge into ! dep?s ( ! unkn[n to discov] some?+ new1 :5 we h to le>n m & bett]1 ! end ju/ifies ! means4 ,:5 he rem9ds u ( optics1 me*anics1 & gravitation1 n[ b\nd up toge!r 9 a new %eaf1 ( ! deviation ( light by gravity :i* he =etold aga9/ all expectation1 ( ! anomalies ( ,m]cury :i* he 0 ! fir/ to expla91 & ( 8 improvem5t ( ! ,newtonian law1 ,e9/e9 has ! "r to say1 ) "s pride3 8,!re is :at ,i h done40 ,x is said t ! pa?s by :i* he atta9$ all ^! f9e results are n devoid ( unpleasant false turns & quagmires4 ,well1 !re are _m ways to ,rome & to tru?1 & "s ( !m are n p]fect4 ,! ma9 ?+ is to get !re4 ,& 9 ?is case ! tru? means anci5t facts br\ght into a new h>mony1 & new facts set =? 9 prophetic equations & v]ifi$ 9 ! mo/ surpris+ mann]4 ,if discussion ( pr9ciples--if !ory1 :i* is only ! s]vant ( k--%rugs its s]vile & disloyal %\ld]s a little ov] ,e9/e9's "w1 at all ev5ts exp]i5ce1 ! sole s\rce ( tru?1 has ju/ifi$ him4 ,brilliant =mul t ,e9/e9 _h n =ese5 are n[ discov]$ to expla9 ! anomaly ( ,m]cury & ! deviation ( light4 ,x is good3 b we mu/ n =get t ! fir/ ( ^! correct =mul1 t ( ,e9/e91 w5t boldly 9 advance ( ! v]ification4 ,new tr5*es h be5 won 9 ! w> aga9/ ! et]nal enemy1 ! unkn[n4 ,c]ta9ly we h n[ to organise !m & create m direct roads to !m4 ,b to-morr[ we %all h to advance aga91 to ga9 m gr\nd4 ,we %all h1 by any !oretical device t we c1 to /ate o!r new facts1 unkn[n b v]ifiable facts4 ,t is :at ,e9/e9 did4 ,if x is a weakness ( ,e9/e9's tea*+ to d5y all objectivity1 all privilege1 to any sy/em ( ref]5ce :atev]1 :ile utilis+ su* a sy/em = ! necessities ( calculation1 x 0 at all ev5ts a weakness %>$ by ! great ,po9c>4 ,to ! day ( 8 dea? he rebell$ en]getically aga9/ ! ,newtonian conception4 ,! support ( su* a g5ius1 :om "o f9ds involv$ 9 all our mod]n discov]ies1 is en\gh to secure "s respect = ! ,relativi/ !ory4 ,if we h on ! "o side ,newton & 8 ard5t & p]suasive apologi/1 equipp$ ) a f9e ma!matical g5ius1 ,paul ,pa9lev1 we h on ! o!r side ,e9/e9 & ,h5ri ,po9c>4 ,ev5 9 e>li] hi/ory we h ,ari/otle aga9/ ,epicurus1 ,cop]nicus aga9/ ! ,s*ola/ics1 at ! same b>ricade4 ,x is an et]nal w> ( ideas1 & x may be endless if1 z ,po9c> believ$1 ! ,pr9ciple ( ,relativity is at ! bottom only a conv5tion ) :i* exp]i5ce _c qu>rel because1 :5 we apply x to ! entire univ]se1 x is incapable ( v]ification4 ,x is ! f]tility ( ! ,e9/e9ian sy/em :i* proves t x is /rong & s\nd4 ,are ! new be+s ) :i* x has peopl$ sci5ce--! discov]ies pr$ict$ by x--legitimate *ildr58 ,! ,newtonians say t !y are n4 ,b 9 prop]ly ord]$ sci5ce1 z 9 an ideal ,/ate1 x is ! *ildr5 t matt]1 n _! legitimacy4 ,at all ev5ts ! vigor\s c\nt]-(f5sive ( ,m4 ,pa9lev has driv5 back to _! l9es ! ov]-zeal\s apo/les ( ! new gospel1 :o ?\ght t !y _h pulv]is$ classic sci5ce beyond hope ( recov]y4 ,ea* side n[ rema9s 9 its positions4 ,!re is no long] any "q ( reg>d+ ! ,newtonian conception ( ! _w z a piece ( *ildlike b>b>ism4 ,a diff]5t conception is n[ oppos$ to x--t is all4 ,! w> betwe5 !m is z yet undecid$1 & may rema9 = ev] undecid$1 z ! weapons ) :i* x might be possible to br+ x to an issue are seal$ up = ev] 9 ! ars5al ( metaphysics4 99 99 99 99 99 ,:atev] may happ51 ,e9/e9's tea*+ has a p[] ( syn!sis & pr$iction :i* w inevitably incorporate its maje/ic sy/em ( equations 9 ! sci5ce ( ! future4 ,m4 mile ,pic>d1 p]petual secret>y ( ! ,academy ( ,sci5ces1 & "o ( ! lum9\s & pr(\nd ?9k]s ( our "t1 has ask$ if x is an advance 8to try1 z ,e9/e9 has done1 to r$uce physics to geometry40 ,)\t l+]+ ov] ?is "q1 :i* may be insoluble1 l all speculative que/ions1 we w conclude ) ! di/+ui%$ ma!matician t ! only ?+s :i* matt] are ! agreem5t ( ! f9al =mul ) ! facts & ! analytic m\ld 9 :i* ! !ory ca/s ! ph5om5a4 ,consid]$ f ?is angle1 ,e9/e9's !ory has ! solidity ( bronze4 ,its correctness consi/s 9 its explanatory =ce & 9 ! exp]im5tal discov]ies pr$ict$ by x & at once v]ifi$4 ,:at *anges 9 !ories are ! pictures we =m ( ! objects betwe5 :i* sci5ce discov]s & e/abli%es relations4 ,sometimes we alt] ^! pictures1 b ! relations rema9 true1 if !y are bas$ ^u obs]v$ facts4 ,?anks to ?is common fund ( tru?1 ev5 ! mo/ ephem]al !ories d n :olly die4 ,!y pass on to ea* o!r1 l ! anci5t runn]s ) _! tor*1 ! "o accessible reality3 ! laws t express ! relations ( ?+s4 ,to-day x happ5s t two !ories toge!r clasp ! sacr$ tor*4 ,! ,e9/e9ian & ! ,newtonian vision ( ! _w are two fai?ful reflections ( x3 j z ! two images1 pol>is$ 9 opposite directions1 :i* ,icel& sp> %[s u 9 its /range cry/al bo? %>e ! light ( ! same object4 ,tragically isolat$1 imprison$ 9 8 own 8self10 man has made a desp]ate ef=t to 8leap beyond 8 %ad[10 to embrace ! ext]nal _w4 ,f ?is ef=t 0 born sci5ce1 & its m>vell\s ant5n subtly prolong our s5sations4 ,?us we h 9 places approa*$ ! brilliant raim5t ( reality4 ,b 9 comp>ison ) ! my/]y t rema9s ! ?+s we "k are z small z are ! />s ( heav5 comp>$ ) ! abyss 9 :i* !y float4 ,e9/e9 has discov]$ new light = u 9 ! dep?s ( ! unkn[n4 ,he is1 & w rema91 "o ( ! light-h\ses ( human ?\ght4 ,pr9t$ 9 ,great ,brita9 by ,hazell1 ,watson amp2 ,v9ey1 ,ld41 ,london & ,aylesbury4