,page images provid$ by ,case ,we/]n ,res]ve ,univ]sity's ,digital ,pres]vation ,dep>tm5t ,exp]im5tal ,det]m9ation ( ! ,velocity ( ,light ,made at ! ,u4,s4 ,naval ,academy1 ,annapolis4 ,by ,alb]t ,a4 ,mi*elson1 ,ma/] ,u4,s4 ,navy4 ,note4 ,! probability t ! mo/ accurate me?od ( det]m9+ ! sol> p>allax n[ available is t re/+ on ! measurem5t ( ! velocity ( light1 has l$ to ! acceptance ( ! foll[+ pap] z "o ( ! s]ies hav+ 9 view ! increase ( our k ( ! cele/ial motions4 ,! rese>*es describ$ 9 x1 hav+ be5 made at ! ,unit$ ,/ates ,naval ,academy1 ?\gh at private exp5se1 7 report$ to ! ,honorable ,secret>y ( ! ,navy1 & ref]r$ by him to ?is ,(fice4 ,at ! sugge/ion ( ! writ]1 ! pap] 0 recon/ruct$ ) a full] g5]al discussion ( ! processes1 & ) ! omission ( "s ( ! details ( individual exp]im5ts4 ,to prev5t a possible confusion ( ?is det]m9ation ( ! velocity ( light ) ano!r n[ 9 progress "u (ficial auspices1 x may be /at$ t ! cr$it & responsibility = ! pres5t pap] re/s ) ,ma/] ,mi*elson4 ,simon ,newcomb1 ,pr(essor1 ,u4,s4 ,navy1 ,sup]9t5d5t ,nautical ,almanac4 ,nautical ,almanac ,(fice1 ,bureau ( ,navigation1 ,navy ,dep>tm5t1 ,wa%+ton1 ,febru>y #bj1 #ahhj4 ,table ,( ,cont5ts4 ,introduction ,!ory ( ! ,new ,me?od ,arrangem5t & ,description ( ,app>atus ,det]m9ation ( ! ,con/ants ,! ,=mul ,obs]vations ,sep>ate results ( ,gr\ps ( ,obs]vations ,discussion ( ,errors ,objections ,consid]$ ,po/script ,exp]im5tal ,det]m9ation ( ! ,velocity ( ,light4 ,by ,alb]t ,a4 ,mi*elson1 ,ma/]1 ,u4,s4,n4 ,introduction4 ,9 ,cornu's elaborate memoir ^u ! det]m9ation ( ! velocity ( light1 sev]al objections are made to ! plan foll[$ by ,f\cault1 :i* w be consid]$ 9 ! latt] "p ( ?is "w4 ,x may1 h[ev]1 be /at$ t ! mo/ important among ^! 0 t ! deflection 0 too small to be measur$ ) ! requir$ degree ( accuracy4 ,9 ord] to employ ?is me?od1 !re=e1 x 0 absolutely necess>y t ! deflection %\ld be increas$4 ,9 ,novemb]1 #ahgg1 a modification ( ,f\cault's arrangem5t sugge/$ itself1 by :i* ?is result c\ld be accompli%$4 ,betwe5 ?is "t & ,m>* ( ! foll[+ ye> a numb] ( prelim9>y exp]im5ts 7 p]=m$ 9 ord] to famili>ize myself ) ! optical arrangem5ts4 ,! fir/ exp]im5t tri$ ) ! revolv+ mirror produc$ a deflection consid]ably great] ?an t obta9$ by ,f\cault4 ,?us f> ! only app>atus us$ 0 su* z c\ld be adapt$ f ! app>atus 9 ! laboratory ( ! ,naval ,academy4 ,at ! exp5se ( #aj a revolv+ mirror 0 made1 :i* c\ld execute #abh turns p] second4 ,! app>atus 0 in/all$ 9 ,may1 #ahgh1 at ! laboratory4 ,! di/ance us$ 0 #ejj feet1 & ! deflection 0 ab\t tw5ty times t obta9$ by ,f\cault4#a ,footnote #a3 ,see ,proc4 ,am4 ,assoc4 ,adv4 ,sci5ce1 ,sa9t ,l\is meet+4 ,^! exp]im5ts1 made ) v crude app>atus & "u great difficulties1 gave ! foll[+ table ( results = ! velocity ( light 9 miles p] second3 #ahfgcj #ahhhbj #ahfccj #aheccj #ahgijj #ahdejj #ahfggj #ahejjj #ahehjj #ahgidj ------ ,mean #ahfejj #cjj miles p] second1 or #cjjadj kilomet]s p] second4 ,9 ! foll[+ ,july ! sum ( #b1jjj 0 plac$ at my disposal by a private g5tleman = c>ry+ out ^! exp]im5ts on a l>ge scale4 ,be=e ord]+ any ( ! in/rum5ts1 h[ev]1 x 0 necess>y to f9d :e!r or n x 0 practicable to use a l>ge di/ance4 ,) a di/ance 7betwe5 ! revolv+ & ! fix$ mirror7 ( #ejj feet1 9 ! prelim9>y exp]im5ts1 ! field ( light 9 ! eye-piece 0 some:at limit$1 & !re 0 consid]able indi/9ctness 9 ! image1 due to atmosph]ic di/urbances4 ,accord+ly1 ! same l5s 7#ci feet focus7 0 employ$1 be+ plac$1 toge!r ) ! o!r pieces ( app>atus1 along ! nor? sea-wall ( ! ,academy gr\nds1 ! di/ance be+ ab\t #b1jjj feet4 ,! image ( ! slit1 at noon1 0 s confus$ z n to be recognizable1 b t[>d sunset x became cle> & /eady1 & measurem5ts 7 made ( its position1 :i* agre$ )9 "o "o-hundr$? ( a millimet]4 ,x 0 ?us demon/rat$ t ) ?is di/ance & a deflection ( #ajj millimet]s ?is measurem5t c\ld be made )9 ! t5-?\s&? "p4 ,9 ord] to obta9 ?is deflection1 x 0 suffici5t to make ! mirror revolve #bej times p] second & to use a radius ( ab\t #cj feet4 ,9 ord] to use ?is l>ge radius 7di/ance f slit to revolv+ mirror71 x 0 necess>y t ! mirror %\ld be l>ge & optically true2 also1 t ! l5s %\ld be l>ge & ( great focal l5g?4 ,accord+ly ! mirror 0 made #a in*es 9 diamet]1 & a new l5s1 #h in*es 9 diamet]1 ) a focal l5g? ( #aej feet 0 procur$4 ,9 ,janu>y1 #ahgi1 an obs]vation 0 tak51 us+ ! old l5s1 ! mirror mak+ #abh turns p] second4 ,! deflection 0 ab\t #dc millimet]s4 ,! micromet] eye-piece us$ 0 sub/antially ! same z ,f\cault's1 except t "p ( ! incl9$ plate ( glass 0 silv]$1 ?us secur+ a mu* great] quantity ( light4 ,! deflection hav+ rea*$ #dc millimet]s1 ! incl9$ plate ( glass c\ld be disp5s$ )1 ! light go+ pa/ ! obs]v]'s head ?r\gh ! slit1 & return+ #dc millimet]s to ! left ( ! slit1 :]e x c\ld be easily obs]v$4 ,?us ! micromet] eye-piece is mu* simplifi$1 & _m possible s\rces ( error are remov$4 ,! field 0 q limit$1 ! diamet] be+1 9 fact1 b little great] ?an ! wid? ( ! slit4 ,?is w\ld h prov$ a mo/ s]i\s objection to ! new arrangem5t4 ,) ! new l5s1 h[ev]1 ?is difficulty disappe>$1 ! field be+ ab\t tw5ty times ! wid? ( ! slit4 ,x 0 expect$ t1 ) ! new l5s1 ! image w\ld be less di/9ct2 b ! diff]5ce1 if any1 0 small1 & 0 fully comp5sat$ by ! great] size ( ! field4 ,! fir/ obs]vation ) ! new l5s 0 made ,janu>y #cj1 #ahgi4 ,! deflection 0 #gj millimet]s4 ,! image 0 suffici5tly bright to be obs]v$ )\t ! slighte/ ef=t4 ,! fir/ obs]vation ) ! new micromet] eye-piece 0 made ,april #b1 ! deflection be+ #aae millimet]s4 ,! fir/ ( ! f9al s]ies ( obs]vations 0 made on ,june #e4 ,all ! obs]vations previ\s to ?is1 ?irty sets 9 all1 7 reject$4 ,aft] ?is "t1 no set ( obs]vations nor any s+le obs]vation 0 omitt$4 ,!ory ( ,new ,me?od4 ,illu/ration3 ,,fig4 #a4 ,let ,s1 ,fig4 #a1 be a slit1 ?r\gh :i* light passes1 fall+ on ,r1 a mirror free to rotate ab\t an axis at "r angles to ! plane ( ! pap]2 ,l1 a l5s ( great focal l5g?1 ^u :i* ! light falls :i* is reflect$ f ,r4 ,let ,m be a plane mirror ^: surface is p]p5dicul> to ! l9e ,r1 ,m1 pass+ ?r\gh ! c5t]s ( ,r1 ,l1 & ,m1 respectively4 ,if ,l be s plac$ t an image ( ,s is =m$ on ! surface ( ,m1 !n1 ?is image act+ z ! object1 its image w be =m$ at ,s1 & w co9cide1 po9t = po9t1 ) ,s4 ,if1 n[1 ,r be turn$ ab\t ! axis1 s long z ! light falls ^u ! l5s1 an image ( ! slit w /ill be =m$ on ! surface ( ! mirror1 ?\gh on a diff]5t "p1 & z long z ! return+ light falls on ! l5s an image ( ?is image w be =m$ at ,s1 not)/&+ ! *ange ( position ( ! fir/ image at ,m4 ,?is result1 namely1 ! production ( a /ation>y image ( an image 9 motion1 is absolutely necess>y 9 ?is me?od ( exp]im5t4 ,x 0 fir/ accompli%$ by ,f\cault1 & 9 a mann] diff]+ app>5tly b little f ! =ego+4 ,illu/ration3 ,,fig4 #b4 ,9 8 exp]im5ts ,l1 ,fig4 #b1 s]v$ simply to =m ! image ( ,s at ,m1 & ,m1 ! return+ mirror1 0 sph]ical1 ! c5t] co9cid+ ) ! axis ( ,r4 ,! l5s ,l 0 plac$ z ne> z possible to ,r4 ,! light =m+ ! return image la/s1 9 ?is case1 :ile ! fir/ image is sweep+ ov] ! face ( ! mirror1 ,m4 ,h5ce1 ! great] ! di/ance ,,rm1 ! l>g] mu/ be ! mirror 9 ord] t ! same am\nt ( light may be pres]v$1 & its dim5sions w\ld soon become inord9ate4 ,! difficulty 0 p>tly met by ,f\cault1 by us+ five concave reflectors in/ead ( "o1 b ev5 !n ! greate/ di/ance he f\nd x practicable to use 0 only #bj met]s4 ,return+ to ,fig4 #a1 suppose t ,r is 9 ! pr9cipal focus ( ! l5s ,l2 !n1 if ! plane mirror ,m h ! same diamet] z ! l5s1 ! fir/1 or mov+ image1 w rema9 ^u ,m z long z ! axis ( ! p5cil ( light rema9s on ! l5s1 & ?is w be ! case no matt] :at ! di/ance may be4 ,:5 ! rotation ( ! mirror ,r becomes suffici5tly rapid1 !n ! fla%es ( light :i* produce ! second or /ation>y image become bl5d$1 s t ! image appe>s to be cont9u\s4 ,b n[ x no long] co9cides ) ! slit1 b is deflect$ 9 ! direction ( rotation1 & ?r\gh twice ! angul> di/ance describ$ by ! mirror1 dur+ ! "t requir$ = light to travel twice ! di/ance betwe5 ! mirrors4 ,?is displacem5t is measur$ by ! tang5t ( ! arc x subt5ds4 ,to make ?is z l>ge z possible1 ! di/ance betwe5 ! mirrors1 ! radius1 & ! spe$ ( rotation %\ld be made z great z possible4 ,! second condition conflicts ) ! fir/1 = ! radius is ! diff]5ce betwe5 ! focal l5g? = p>allel rays1 & t = rays at ! di/ance ( ! fix$ mirror4 ,! great] ! di/ance1 !re=e1 ! small] w be ! radius4 ,!re are two ways ( solv+ ! difficulty3 fir/1 by us+ a l5s ( great focal l5g?2 & secondly1 by plac+ ! revolv+ mirror )9 ! pr9cipal focus ( ! l5s4 ,bo? means 7 employ$4 ,! focal l5g? ( ! l5s 0 #aej feet1 & ! mirror 0 plac$ ab\t #ae feet )9 ! pr9cipal focus4 ,a limit is soon rea*$1 h[ev]1 = ! quantity ( light receiv$ dim9i%es v rapidly z ! revolv+ mirror approa*es ! l5s4 ,arrangem5t & ,description ( ,app>atus4 ,site & ,plan4 ,! site select$ = ! exp]im5ts 0 a cle>1 almo/ level1 /ret* along ! nor? sea-wall ( ! ,naval ,academy4 ,a frame build+ 0 erect$ at ! we/]n end ( ! l9e1 a plan ( :i* is repres5t$ 9 ,fig4 #c4 ,illu/ration3 ,,fig4 #c4 ,! build+ 0 #de feet long & #ad feet wide1 & rais$ s t ! l9e along :i* ! light travel$ 0 ab\t #aa feet above ! gr\nd4 ,a helio/at at ,h reflect$ ! sun's rays ?r\gh ! slit at ,s to ! revolv+ mirror ,r1 !nce ?r\gh a hole 9 ! %utt]1 ?r\gh ! l5s1 & to ! di/ant mirror4 ,! ,helio/at4 ,! helio/at 0 "o k9dly furni%$ by ,dr4 ,woodw>d1 ( ! ,army ,m$ical ,museum1 & 0 a modification ( ,f\cault's =m1 design$ by ,kei?4 ,x 0 f\nd to be accurate & easy to adju/4 ,! light 0 reflect$ f ! helio/at to a plane mirror1 ,m1 ,fig4 #c1 s t ! =m] ne$ n be di/urb$ aft] be+ once adju/$4 ,! ,revolv+ ,mirror4 ,! revolv+ mirror 0 made by ,fau? ,co41 ( ,wa%+ton4 ,x consi/s ( a ca/-iron frame re/+ on ?ree level+ screws1 "o ( :i* 0 connect$ by cords to ! table at ,s1 ,fig4 #c1 s t ! mirror c\ld be incl9$ =w>d or backw>d :ile mak+ ! obs]vations4 ,illu/ration3 ,,fig4 #d4 ,two b9d+ screws1 ,s1 ,s1 ,fig4 #d1 t]m9at+ 9 h>d5$ /eel conical sockets1 hold ! revolv+ "p4 ,?is consi/s ( a /eel axle1 ,x1 ,y1 ,figs4 #d & #e1 ! pivots be+ conical & h>d5$4 ,! axle exp&s into a r+ at ,r1 :i* holds ! mirror ,m4 ,! latt] 0 a disc ( plane glass1 made by ,alvan ,cl>k ,sons1 ab\t #a in* 9 diamet] & #j4b in* ?ick4 ,x 0 silv]$ on "o side only1 ! reflection tak+ place f ! out] or front surface4 ,a species ( turb9e :eel1 ,t1 is held on ! axle by friction4 ,?is :eel has six op5+s = ! escape ( air2 a section ( "o ( !m is repres5t$ 9 ,fig #f4 ,illu/ration3 ,,fig4 #e4 ,illu/ration3 ,,fig4 #f4 ,adju/m5t ( ! ,revolv+ ,mirror4 ,! air ent]+ on "o side at ,o1 ,fig4 #e1 acquires a rot>y motion 9 ! box ,b1 ,b1 c>ry+ ! :eel ) x1 & ?is motion is assi/$ by ! reaction ( ! air 9 escap+4 ,! disc ,c s]ves ! purpose ( br++ ! c5t] ( gravity 9 ! axis ( rotation4 ,?is 0 done1 foll[+ ,f\cault's plan1 by all[+ ! pivots to re/ on two incl9$ planes ( glass1 all[+ ! arrangem5t to come to re/1 & fil+ away ! l[e/ "p ( ! disc2 try+ aga91 & s on1 till x w\ld re/ 9 indiff]5t equilibrium4 ,! "p correspond+ to ,c1 9 ,f\cault's app>atus1 0 furni%$ ) ?ree v]tical screws1 by mov+ :i* ! axis ( figure 0 br\ght into co9cid5ce ) ! axis ( rotation4 ,?is adju/m5t 0 v tr\blesome4 ,=tunately1 9 ?is app>atus x 0 f\nd to be unnecess>y4 ,:5 ! adju/m5t is p]fect ! app>atus revolves )\t giv+ any s\nd1 & :5 ?is is accompli%$1 ! motion is regul> & ! spe$ great4 ,a slight deviation causes a s\nd due to ! rattl+ ( ! pivots 9 ! sockets1 ! spe$ is v mu* dim9i%$1 & ! pivots beg9 to we>4 ,9 ,f\cault's app>atus oil 0 furni%$ to ! pivots1 ?r\gh small holes runn+ ?r\gh ! screws1 by pressure ( a column ( m]cury4 ,9 ?is app>atus x 0 f\nd suffici5t to t\* ! pivots occasionally ) a drop ( oil4 ,illu/ration3 ,,fig4 #g4 ,fig4 #g is a view ( ! turb9e1 box1 & supply-tube1 f above4 ,! quantity ( air ent]+ c\ld be regulat$ by a valve to :i* 0 atta*$ a cord lead+ to ! obs]v]'s table4 ,! in/rum5t 0 m\nt$ on a brick pi]4 ,! ,micromet]4 ,illu/ration3 ,,fig4 #h4 ,! app>atus = measur+ ! deflection 0 made by ,grun[1 ( ,new ,york4 ,?is in/rum5t is %[n 9 p]spective 9 ,fig4 #h1 & 9 plan by ,fig4 #i4 ,! adju/able slit ,s is clamp$ to ! frame ,f4 ,a long millimet]-screw1 n %[n 9 ,fig4 #h1 t]m9at+ 9 ! divid$ head ,d1 moves ! c>riage ,c1 :i* supports ! eye-piece ,e4 ,! frame is furni%$ ) a brass scale at ,f = c\nt+ revolutions1 ! head c\nt+ hundr$?s4 ,! eye-piece consi/s ( a s+le a*romatic l5s1 ^: focal l5g? is ab\t two in*es4 ,at its focus1 9 ,h1 & 9 ne>ly ! same plane z ! face ( ! slit1 is a s+le v]tical silk fib]4 ,! app>atus is furni%$ ) a /&>d ) rack & p9ion1 & ! base furni%$ ) level+ screws4 ,mann] ( ,us+ ! ,micromet]4 ,9 measur+ ! deflection1 ! eye-piece is mov$ till ! cross-hair bisects ! slit1 & ! read+ ( ! scale & divid$ head gives ! position4 ,?is measurem5t ne$ n be repeat$ unless ! position or wid? ( ! slit is *ang$4 ,!n ! eye-piece is mov$ till ! cross-hair bisects ! deflect$ image ( ! slit2 ! read+ ( scale & head are aga9 tak51 & ! diff]5ce 9 read+s gives ! deflection4 ,! screw 0 f\nd to h no lo/ motion1 s t read+s c\ld be tak5 ) ! screw turn$ 9 ei!r direction4 ,measurem5t ( ,spe$ ( ,rotation4 ,to measure ! spe$ ( rotation1 a tun+-=k1 be>+ on "o prong a /eel mirror1 0 us$4 ,?is 0 kept 9 vibration by a curr5t ( electricity f five gravity cells4 ,! =k 0 s plac$ t ! light f ! revolv+ mirror 0 reflect$ to a piece ( plane glass1 9 front ( ! l5s ( ! eye-piece ( ! micromet]1 incl9$ at an angle ( #de1 & !nce to ! eye4 ,:5 =k & revolv+ mirror are bo? at re/1 an image ( ! revolv+ mirror is se54 ,:5 ! =k vibrates1 ?is image is drawn out into a b& ( light4 ,:5 ! mirror comm5ces to revolve1 ?is b& breaks up into a numb] ( mov+ images ( ! mirror2 & :51 f9ally1 ! mirror makes z _m turns z ! =k makes vibrations1 ^! images are r$uc$ to "o1 :i* is /ation>y4 ,?is is also ! case :5 ! numb] ( turns is a submultiple4 ,:5 x is a multiple or simple ratio1 ! only diff]5ce is t !re are m images4 ,h5ce1 to make ! mirror execute a c]ta9 numb] ( turns1 x is simply necess>y to pull ! cord atta*$ to ! valve to ! "r or left till ! images ( ! revolv+ mirror come to re/4 ,! electric =k made ab\t #abh vibrations p] second4 ,no dep5d5ce 0 plac$ ^u ?is rate1 h[ev]1 b at ea* set ( obs]vations x is comp>$ ) a /&>d ,ut =k1 ! temp]ature be+ not$ at ! same "t4 ,9 mak+ ! comp>ison ! s\nd-beats produc$ by ! =ks 7 c\nt$ = #fj seconds4 ,x is int]e/+ to note t ! electric =k1 z long z x rema9$ unt\*$ & at ! same temp]ature1 did n *ange its rate m ?an "o or two hundr$?s vibrations p] second4 ,illu/ration3 ,,fig4 #i4 ,! ,obs]v]'s ,table4 ,fig4 #i ,repres5ts ,! ,table ,at ,:i* ,! ,obs]v] ,sits4 ,! ,light ,f ,! ,helio/at ,passes ,?r\gh ,! ,slit ,at ,s1 ,goes ,to ,! ,revolv+ ,mirror1 c41 ,&1 ,on ,its ,return1 ,=ms ,an ,image ,( ,! ,slit ,at ,d1 ,:i* ,is ,obs]v$ ,?r\gh ,! ,eye-piece4 ,e ,repres5ts ,! ,electric ,=k 7! ,prongs ,be+ ,v]tical7 ,be>+ ,! ,/eel ,mirror ,m4 ,k ,is ,! ,/&>d ,=k ,on ,its ,resonator4 ,c ,is ,! ,cord ,atta*$ ,to ,! ,valve ,supply+ ,air ,to ,! ,turb9e4 ,! ,l5s4 ,! l5s 0 made by ,alvan ,cl>k ,sons4 ,x 0 #h in*es 9 diamet]2 focal l5g?1 #aej feet2 n a*romatic4 ,x 0 m\nt$ 9 a wood5 frame1 :i* 0 plac$ on a support mov+ on a slide1 ab\t #af feet long1 plac$ ab\t #hj feet f ! build+4 ,z ! diamet] ( ! l5s 0 s small 9 comp>ison ) its focal l5g?1 its want ( a*romatism 0 inappreciable4 ,= ! same reason1 ! effect ( p>allax 7due to want ( co9cid5ce 9 ! plane ( ! image ) t ( ! silk fib] 9 ! eye-piece7 0 too small to be notic$4 ,! ,fix$ ,mirror4 ,! fix$ mirror 0 "o ( ^? us$ 9 tak+ photographs ( ! transit ( ,v5us4 ,x 0 ab\t #g in*es 9 diamet]1 m\nt$ 9 a brass frame capable ( adju/m5t 9 a v]tical & a horizontal plane by screw motion4 ,be+ w$ge-%ap$1 x _h to be silv]$ on ! front surface4 ,to facilitate adju/m5t1 a small telescope furni%$ ) cross-hairs 0 atta*$ to ! mirror by a univ]sal jo9t4 ,! heavy frame 0 m\nt$ on a brick pi]1 & ! :ole surr\nd$ by a wood5 case to protect x f ! sun4 ,adju/m5t ( ! ,fix$ ,mirror4 ,! adju/m5t 0 effect$ z foll[s3 ,a !odolite 0 plac$ at ab\t #ajj feet 9 front ( ! mirror1 & ! latt] 0 mov$ ab\t by ! screws till ! obs]v] at ! !odolite saw ! image ( 8 telescope reflect$ 9 ! c5t] ( ! mirror4 ,!n ! telescope atta*$ to ! mirror 0 po9t$ 7)\t mov+ ! mirror itself7 at a m>k on a piece ( c>d-bo>d atta*$ to ! !odolite4 ,?us ! l9e ( collimation ( ! telescope 0 plac$ at "r angles to ! surface ( ! mirror4 ,! !odolite 0 !n mov$ to #a1jjj feet1 &1 if f\nd necess>y1 ! adju/m5t 0 repeat$4 ,!n ! mirror 0 mov$ by ! screws till its telescope po9t$ at ! hole 9 ! %utt] ( ! build+4 ,! adju/m5t 0 complet$ by mov+ ! mirror1 by signals1 till ! obs]v]1 look+ ?r\gh ! hole 9 ! %utt]1 ?r\gh a good spy-glass1 saw ! image ( ! spy-glass reflect$ c5trally 9 ! mirror4 ,! :ole op]ation 0 complet$ 9 a little ov] an h\r4 ,not)/&+ ! wood5 case ab\t ! pi]1 ! mirror w\ld *ange its position betwe5 morn+ & ev5+2 s t ! la/ adju/m5t _h to be repeat$ be=e e s]ies ( exp]im5ts4 ,app>atus = ,supply+ & ,regulat+ ! ,bla/ ( ,air4 ,fig4 #aj repres5ts a plan ( ! l[] floor ( ! build+4 ,e is a ?ree-horse p[] ,lovegrove eng9e & boil]1 re/+ on a /one f\ndation2 ,b1 a small ,roots' bl[]2 ,g1 an automatic regulator4 ,f ?is ! air goes to a deliv]y-pipe1 up ?r\gh ! floor1 & to ! turb9e4 ,! eng9e made ab\t #d turns p] second & ! bl[] ab\t #ae4 ,at ?is spe$ ! pressure ( ! air 0 ab\t half a p\nd p] squ>e in*4 ,illu/ration3 ,,fig4 #aj4 ,! regulator1 ,fig4 #aa1 consi/s ( a /rong bell[s support+ a weight ( #cgj p\nds1 p>tly c\nt]pois$ by #hj p\nds 9 ord] to prev5t ! bell[s f sagg+4 ,:5 ! pressure ( air f ! bl[] exce$s ! weight1 ! bell[s comm5ces to rise1 &1 9 s do+1 closes ! valve ,v4 ,illu/ration3 ,,fig4 #aa4 ,illu/ration3 ,,fig4 #ab4 ,?is arrangem5t 0 f\nd 9 practice to be insuffici5t1 & ! foll[+ addition 0 made3 ,a valve 0 plac$ at ,p1 & ! pipe 0 tapp$ a little f>!r on1 & a rubb] tube l$ to a wat]-gauge1 ,fig #ab4 ,! column ( wat] 9 ! small] tube is depress$1 &1 :5 x rea*es ! horizontal "p ( ! tube1 ! slighte/ v>iation ( pressure s5ds ! column f "o end to ! o!r4 ,?is is *eck$ by an assi/ant at ! valve2 s t ! column ( wat] is kept at ab\t ! same place1 & ! pressure ?us r5d]$ v ne>ly con/ant4 ,! result 0 satisfactory1 ?\gh n 9 ! degree anticipat$4 ,x 0 possible to keep ! mirror at a con/ant spe$ = ?ree or f\r seconds at a "t1 & ?is 0 suffici5t = an obs]vation4 ,/ill x w\ld h be5 m conv5i5t to keep x s = a long] "t4 ,i am incl9$ to ?9k t ! v>iations 7 due to *anges 9 ! friction ( ! pivots r ?an to *anges ( pressure ( ! bla/ ( air4 ,x may be m5tion$ t ! te/ ( uni=mity 0 v delicate1 z a *ange ( spe$ ( "o or two hundr$?s ( a turn p] second c\ld easily be detect$4 ,me?od ,foll[$ 9 ,exp]im5t4 ,x 0 f\nd t ! only "t dur+ ! day :5 ! atmosph]e 0 suffici5tly quiet to get a di/9ct image 0 dur+ ! h\r aft] sunrise1 or dur+ ! h\r be=e sunset4 ,at o!r times ! image 0 boil+ s z n to be recognizable4 ,9 "o exp]im5t ! electric light 0 us$ at night1 b ! image 0 no m di/9ct ?an at sunset1 & ! light 0 n /eady4 ,! me?od foll[$ 9 exp]im5t 0 z foll[s3 ,! fire 0 />t$ half an h\r be=e1 & by ! "t ev]y?+ 0 ready ! gauge w\ld %[ #dj or #ej p\nds ( /eam4 ,! mirror 0 adju/$ by signals1 z be=e describ$4 ,! helio/at 0 plac$ & adju/$4 ,! revolv+ mirror 0 incl9$ to ! "r or left1 s t ! direct reflection ( light f ! slit1 :i* o!rwise w\ld fla% into ! eye-piece at e revolution1 fell ei!r above or bel[ ! eye-piece4#b ,footnote #b3 ,o!rwise ?is light w\ld ov]p[] t :i* =ms ! image to be obs]v$4 ,z f> z ,i am aw>e1 ,f\cault does n speak ( ?is difficulty4 ,if he all[$ ?is light to int]f]e ) ! brightness ( ! image1 he neglect$ a mo/ obvi\s advantage4 ,if he did incl9e ! axis ( ! mirror to ! "r or left1 he makes no all[ance = ! error ?us introduc$4 ,! revolv+ mirror 0 !n adju/$ by be+ mov$ ab\t1 & incl9$ =w>d & backw>d1 till ! light 0 se5 reflect$ back f ! di/ant mirror4 ,?is light 0 easily se5 ?r\gh ! coat ( silv] on ! mirror4 ,! di/ance betwe5 ! front face ( ! revolv+ mirror & ! cross-hair ( ! eye-piece 0 !n measur$ by /ret*+ f ! "o to ! o!r a /eel tape1 mak+ ! drop ( ! cat5>y ab\t an in*1 z !n ! error caus$ by ! /ret* ( ! tape & t due to ! curve j c\nt]balance ea* o!r4 ,! position ( ! slit1 if n det]m9$ be=e1 0 !n f\nd z be=e describ$4 ,! electric =k 0 />t$1 ! temp]ature not$1 & ! s\nd-beats betwe5 x & ! /&>d =k c\nt$ = #fj seconds4 ,?is 0 repeat$ two or ?ree times be=e e set ( obs]vations4 ,! eye-piece ( ! micromet] 0 !n set approximately#c & ! revolv+ mirror />t$4 ,if ! image did n appe>1 ! mirror 0 incl9$ =w>d or backw>d till x came 9 sight4 ,footnote #c3 ,! deflection be+ measur$ by its tang5t1 x 0 necess>y t ! scale %\ld be at "r angles to ! radius 7! radius drawn f ! mirror to "o or ! o!r end ( t "p ( ! scale :i* repres5ts ?is tang5t74 ,?is 0 done by sett+ ! eye-piece approximately to ! expect$ deflection1 & turn+ ! :ole micromet] ab\t a v]tical axis till ! cross-hair bisect$ ! circul> field ( light reflect$ f ! revolv+ mirror4 ,! axis ( ! eye-piece be+ at "r angles to ! scale1 ! latt] w\ld be at "r angles to radius drawn to ! cross-hair4 ,! cord connect$ ) ! valve 0 pull$ "r or left till ! images ( ! revolv+ mirror1 repres5t$ by ! two bright r\nd spots to ! left ( ! cross-hair1 came to re/4 ,!n ! screw 0 turn$ till ! cross-hair bisect$ ! deflect$ image ( ! slit4 ,?is 0 repeat$ till t5 obs]vations 7 tak51 :5 ! mirror 0 /opp$1 temp]ature not$1 & beats c\nt$4 ,?is 0 call$ a set ( obs]vations4 ,usually five su* sets 7 tak5 morn+ & ev5+4 ,illu/ration3 ,,fig4 #ac4 ,fig4 #ac repres5ts ! appe>ance ( ! image ( ! slit z se5 9 ! eye-piece magnifi$ ab\t five times4 ,det]m9ation ( ,! ,con/ants4 ,comp>ison ( ! ,/eel ,tape ) ! ,/&>d ,y>d4 ,! /eel tape us$ 0 "o ( ,*e/]man's1 #ajj feet long4 ,x 0 comp>$ ) ,wurdeman's copy ( ! /&>d y>d1 z foll[s3 ,temp]ature 0 #ee ,fahr4 ,! /&>d y>d 0 br\ght "u ! microscopes ( ! comp>ator2 ! cross-hair ( ! unm>k$ microscope 0 made to bisect ! division m>k$ o1 & ! cross-hair ( ! microscope1 m>k$ ,i1 0 made to bisect ! division m>k$ #cf4 ,! read+ ( microscope ,i 0 tak51 & ! o!r microscope 0 n t\*$ dur+ ! exp]im5t4 ,! /&>d 0 !n remov$ & ! /eel tape br\ght "u ! microscopes & mov$ along till ! division m>k$ #j4a 7feet7 0 bisect$ by ! cross-hair ( ! unm>k$ microscope4 ,! screw ( microscope ,i 0 !n turn$ till its cross-hair bisect$ ! division m>k$ #c4a 7feet71 & ! read+ ( ! screw tak54 ,! diff]5ce betwe5 ! orig9al read+ & t ( ea* measurem5t 0 not$1 c>e be+ tak5 to reg>d ! direction 9 :i* ! screw 0 turn$1 & ?is gave ! diff]5ce 9 l5g? betwe5 ! /&>d & ea* succesive portion ( ! /eel tape 9 t]ms ( turns ( ! micromet]-screw4 ,to f9d ! value ( "o turn1 ! cross-hair 0 mov$ ov] a millimet] scale1 & ! foll[+ 7 ! values obta9$3 ,turns ( screw ( microscope ,i 9 #amm-- #g4fh #g4gc #g4fj #g4fg #g4fh #g4fb #g4fe #g4eg #g4gb #g4gj #g4fd #g4fi #g4fe #g4ei #g4fc #g4fd #g4ee #g4fe #g4fa #g4fc ,mean #g4fe ,h5ce "o turn #j4acjgmm4 or #j4jjea in*4 ,! l5g? ( ! /eel tape f #j4a to #ii4a 0 f\nd to be great] ?an #cc y>ds1 by #g4d turns 4#ifmm 4#jjc feet4 ,correction = temp]ature 4#jjc feet4 ,l5g? #ajj4jjj feet4 -------------- ,correct$ l5g? #ajj4jjf feet4 ,det]m9ation ( ! ,value ( ,micromet]4 ,two pairs ( l9es 7 scrat*$ on "o slide ( ! slit1 ab\t #chmm ap>t1 i4e41 f ! c5t] ( fir/ pair to c5t] ( second pair4 ,?is di/ance 0 measur$ at int]vals ( #amm ?r\gh ! :ole l5g? ( ! screw1 by bisect+ ! int]val betwe5 ea* two pairs by ! v]tical silk fib] at ! end ( ! eye-piece4 ,) ^! values a curve 0 con/ruct$ :i* gave ! foll[+ values = ?is di/ance1 :i* we %all call ,d3 ,turns ( screw4 ,at #j ( scale ,d #ch4aee #aj ( scale ,d #ch4aee #bj ( scale ,d #ch4aej #cj ( scale ,d #ch #aej #dj ( scale ,d #ch4ade #ej ( scale ,d #ch4adj #fj ( scale ,d #ch4adj #gj ( scale ,d #ch4acj #hj ( scale ,d #ch4acj #ij ( scale ,d #ch4abe #ajj ( scale ,d #ch4abj #aaj ( scale ,d #ch4aaj #abj ( scale ,d #ch4aje #acj ( scale ,d #ch4ajj #adj ( scale ,d #ch4ajj ,*ang+ ! =m ( ?is table1 we f9d t1-- ,= ! fir/ #aj turns ! av]age value ( ,d is #ch4aee #bj turns #ch4aec #cj turns #ch4aeb #dj turns #ch4aea #ej turns #ch4adi #fj turns #ch4adh #gj turns #ch4adf #hj turns #ch4add #ij turns #ch4adb #ajj turns #ch4adj #aaj turns #ch4ach #abj turns #ch4ace #acj turns #ch4acb #adj turns #ch4acj ,on comp>+ ! scale ) ! /&>d met]1 ! temp]ature be+ #af4e ,c41 #adj divisions 7 f\nd to #aci4dfbmm4 ,?is multipli$ by 7#a 4#jjjjahh #af4e7 #aci4ejemm4 ,"o hundr$ & =ty divisions 7 f\nd to be equal to #adj4jbb turns ( ! screw1 :5ce #adj turns ( ! screw #aci4dhcmm1 or #a turn ( ! screw #j4iifcjemm4 ,?is is ! av]age value ( "o turn 9 #adj4 ,b ! av]age value ( ,d1 = #adj turns is1 f ! prec$+ table1 #ch4acj4 ,!re=e1 ! true value ( ,d1 is #ch4acj 4#iifcjemm1 & ! av]age value ( "o turn = #aj1 #bj1 #cj1 etc41 turns1 is f\nd by divid+ #ch4acj 4#iifcje by ! values ( ,d21 giv5 9 ! table4 ,?is gives ! value ( a turn-- mm4 ,= ! fir/ #aj turns #j4iiegj #bj turns #j4iiegj #cj turns #j4iiegc #dj turns #j4iiegg #ej turns #j4iiehj #fj turns #j4iiehc #gj turns #j4iiehi #hj turns #j4iieif #ij turns #j4iifja #ajj turns #j4iifjf #aaj turns #j4iifab #abj turns #j4iifah #acj turns #j4iifbe #adj turns #j4iifcj ,,note4--,! micromet] has be5 s5t to ,pr(essor ,may]1 ( ,hobok51 to te/ ! screw aga91 & to f9d its value4 ,! /eel tape has be5 s5t to ,pr(essor ,rog]s1 ( ,cambridge1 to f9d its l5g? aga94 7,see page #ade47 ,measurem5t ( ! ,di/ance betwe5 ! ,mirrors4 ,squ>e lead weights 7 plac$ along ! l9e1 & measurem5ts tak5 f ! =w>d side ( "o to =w>d side ( ! next4 ,! tape re/$ on ! gr\nd 7:i* 0 v ne>ly level71 & 0 /ret*$ by a con/ant =ce ( #aj p\nds4 ,! correction = l5g? ( ! tape 7#ajj4jjf7 0 #j4ab ( a foot4 ,to correct = ! /ret* ( ! tape1 ! latt] 0 /ret*$ ) a =ce ( #ae p\nds1 & ! /ret* at int]vals ( #bj feet measur$ by a millimet] scale4 mm4 ,at #ajj feet ! /ret* 0 #h4j #hj feet ! /ret* 0 #e4j #fj feet ! /ret* 0 #e4j #dj feet ! /ret* 0 #c4e #bj feet ! /ret* 0 #a4e --- --- #cjj #bc4jj ,weight$ mean #g4g mm4 ,= #aj p\nds1 /ret* #e4a mm4 #j4jafg feet4 ,correction = :ole di/ance #j4cc feet4 ,! foll[+ are ! values obta9$ f five sep>ate measurem5ts ( ! di/ance betwe5 ! caps ( ! pi]s support+ ! revolv+ mirror & ! di/ant reflector2 all[ance made 9 ea* case = effect ( temp]ature3 #aihe4ac feet4 #aihe4ag feet4 #aihd4ic feet4 #aihe4ji feet4 #aihe4ji feet4 ------- ,mean #aihe4jhb feet4 4#gj4 ,cap ( pi] to revolv+ mirror4 4#cc4 ,correction = /ret* ( tape4 4#ab4 ,correction = l5g? ( tape4 -------- #aihf4bc4 ,true di/ance betwe5 mirrors4 ,rate ( ,/&>d ,ut ,=k4 ,! rate ( ! /&>d ,ut =k 0 f\nd at ! ,naval ,academy1 b z s mu* dep5d$ on its accuracy1 ano!r s]ies ( det]m9ations ( its rate 0 made1 toge!r ) ,pr(essor ,may]1 at ! ,hobok5 ,in/itute ( ,te*nology4 ,set ( det]m9ations made at ,naval ,academy4 ,! =k 0 arm$ ) a tip ( copp] foil1 :i* 0 lo/ dur+ ! exp]im5ts & replac$ by "o ( plat9um hav+ ! same weight1 #d4f mgr4 ,! =k1 on its resonator1 0 plac$ horizontally1 ! plat9um tip j t\*+ ! lampblack$ cyl9d] ( a ,s*ultze *ronoscope4 ,! "t 0 giv5 ei!r by a sid]eal break-circuit *ronomet] or by ! break-circuit p5dulum ( a mean-"t clock4 ,9 ! =m] case ! break-circuit work$ a relay :i* int]rupt$ ! curr5t f ?ree ,grove cells4 ,! sp>k f ! second>y coil ( an inductorium 0 deliv]$ f a wire ne> ! tip ( ! =k4 ,frequ5tly two sp>ks ne> toge!r 7 giv51 9 :i* case ! fir/ alone 0 us$4 ,! rate ( ! *ronomet]1 ! record ( :i* 0 kept at ! ,obs]vatory1 0 v regul>1 & 0 f\nd by obs]vations ( transits ( />s dur+ ! week to be #a4c seconds p] day1 :i* is ! same z ! record$ rate4 ,specim5 ( a ,det]m9ation ( ,rate ( ,ut ,=k4 ,temp4#bg ,c4 ,column #a gives ! numb] ( ! sp>k or ! numb] ( ! second4 ,column #b gives ! numb] ( s9uosities or vibrations at ! correspond+ second4 ,column #c gives ! diff]5ce betwe5 #a & #aa1 #b & #ab1 #c & #ac1 etc4 ,july #d1 #ahgi4 #a #j4a #beeb4j #b #bee4c #beea4g #c #eaj4e #beea4i #d #gfe4f #beea4i #e #ajbj4g #beeb4a #f #abge4g #beeb4j #g #aecj4g #beea4h #h #aghf4e #beea4d #i #bjda4f #beea4g #aj #bbig4j #beea4e ------- #aa #beeb4a #bee4ahj mean #aj4 #ab #bhjg4j 4#fii r$uction = mean "t4 #ac #cjfb4d 4#jjc correction = rate4 #ad #ccag4e 4#ahg correction = temp]ature4 ------- #ae #cegb4h #bef4jfi numb] ( vibrations p] second at #fe ,fahr4 #af #chbg4g #ag #djhb4e #ah #dcce4i #ai #deic4c #bj #dhdh4e ,! correction = temp]ature 0 f\nd by ,pr(essor ,may] by c\nt+ ! s\nd-beats betwe5 ! /&>d & ano!r ,ut =k1 at diff]5t temp]atures4 ,8 result is 4#jab vibrations p] second = a dim9ution ( #a ,fahr4 ,us+ ! same me?od1 ,i arriv$ at ! result 4#jabe4 ,adopt$ 4#jab4 ,rsum ( det]m9ations made at ,naval ,academy4 ,9 ! foll[+ table ! fir/ column gives ! date1 ! second gives ! total numb] ( seconds1 ! ?ird gives ! result uncorrect$ = temp]ature1 ! f\r? gives ! temp]ature 7c5tigrade71 ! fif? gives ! f9al result1 & ! six? ! diff]5ce betwe5 ! greate/ & lea/ values obta9$ 9 ! sev]al det]m9ations = int]vals ( t5 seconds3 ,july #d #bj #bee4hhb #bg4j #bef4jfi #j4jg #e #ai #bee4iae #bf4d #bef4jhi #j4je #e #ah #bee4iaa #bf4j #bef4jgg #j4jb #f #ba #bee4hgd #bd4g #bef4jab #j4ac #f #i #bee4idh #bd4h #bef4jhg #j4bd #g #bb #bee4ich #bd4f #bef4jgd #j4je #g #ba #bee4iaa #be4c #bef4jfa #j4jd #h #bj #bee4iba #bf4f #bef4ajj #j4jb #h #bj #bee4ije #bf4f #bef4jhd #j4jf #h #bj #bee4hhg #bf4f #bef4jff #j4jc ------- ,mean #bef4jgb ,9 "o ( ! prec$+ exp]im5ts1 ,i comp>$ ! two ,vt =ks :ile ! /&>d 0 trac+ its record on ! cyl9d]1 & also :5 x 0 9 position z = use 9 ! obs]vations4 ,! diff]5ce1 if any1 0 less ?an 4#ja vibration p] second4 ,second det]m9ation4 7,jo9t "w ) ,pr(essor ,a4,m4 ,may]1 ,/ev5s ,in/itute1 ,hobok547 ,! =k 0 w$g$ into a wood5 support1 & ! plat9um tip all[$ to re/ on lampblack$ pap]1 w\nd ab\t a metal cyl9d]1 :i* 0 rotat$ by h& ,"t 0 giv5 by a break-circuit clock1 ! rate ( :i* 0 asc]ta9$1 by comp>isons ) ,we/]n ,union "t-ball1 to be #i4hg seconds4 ,! sp>k f second>y coil ( ! inductorium pass$ f ! plat9um tip1 pi]c+ ! pap]4 ,! size ( ! sp>k 0 regulat$ by resi/ances 9 prim>y circuit4 ,! foll[+ is a specim5 det]m9ation3 ,column #a gives ! numb] ( ! sp>k or ! numb] ( seconds4 ,column #b gives ! correspond+ numb] ( s9uosities or vibrations4 ,column #c gives ! diff]5ce betwe5 ! #a/ & #g? #f1 #bnd & #h? #f1 etc4 #a #j4c #bee4hc #b #bef4a #bee4ij #c #eaa4g #bee4ij #d #gfg4i #bee4ic #e #ajbc4e #bee4ib #f #abhi4b #bef4ja #g #aece4c #bee4ie ------- #h #agia4e #bee4ibj mean4 #i #bjdg4a - 4#jbh correction = rate4 ------- #aj #bcjc4e #bee4hib #aa #beei4j 4#ahj correction = temp]ature4 ------- #ab #bhbe4c #bef4jgb numb] ( vibrations p] second at #fe ,fahr4 #ac #cjga4j ,9 ! foll[+ rsum1 column #a gives ! numb] ( ! exp]im5ts4 ,column #b gives ! total numb] ( seconds4 ,column #c gives ! result n correct$ = temp]ature4 ,column #d gives ! temp]ature ,fahr5heit4 ,column #e gives ! f9al result4 ,column #f gives ! diff]5ce betwe5 ! greate/ & lea/ values3 #a #ac #bee4hib #hj #bef4jgb #j4ah #b #aa #bee4icd #ha #bef4abf #j4ag #c #ac #bee4hii #ha #bef4jia #j4ab #d #ac #bee4ihh #ge #bef4ajh #j4ac #e #aa #bee4idh #ge #bef4jfh #j4je #f #ab #bee4igj #ge #bef4jij #j4je #g #ab #bee4iib #ge #bef4aab #j4bj #h #aa #bee4iib #gf #bef4abd #j4jc #i #aa #bee4hhh #ha #bef4jhj #j4ac #aj #ac #bee4hgh #ha #bef4jgj #j4ac ------- ,mean #bef4jid ,effect ( ,support & ( ,scrap+4 ,! /&>d ,vt =k held 9 its wood5 support 0 comp>$ ) ano!r =k on a resonator load$ ) wax & mak+ ) /&>d ab\t five beats p] second4 ,! /&>d 0 free f ! cyl9d]4 ,! beats 7 c\nt$ by co9cid5ces ) ! second beats ( a wat*4 ,specim54 ,co9cid5ces 7 m>k$-- ,at #cb seconds4 #cg seconds4 #dc4e seconds4 #di seconds4 #ed4e seconds4 #fa4e seconds4 #fa4e - #cb #bi4e4 #bi4e #e #e4i "t ( "o int]val4 ,rsum4 #a #e4i #b #f4b #c #f4b #d #f4b ---- ,mean #f4ac "t ( "o int]val betwe5 co9cid5ces4 ,9 ?is "t ! wat* makes #f4ace #cj4fe beats1 & ! =ks make #cj4fe #a #ca4fe beats4 ,h5ce ! numb] ( beats p] second is #ca4fe #f4ac #e4afc4 ,specim54 ,circum/ances ! same z 9 la/ case1 except t /&>d ,vt =k 0 all[$ to trace its record on ! lampblack$ pap]1 z 9 f9d+ its rate ( vibration4 ,co9cid5ces 7 m>k$ at-- #ei seconds4 #jd seconds4 #aj4e seconds4 #ag seconds4 #gg - #ei #ah4 #ah #c #f4j "t ( "o int]val4 ,rsum4 ,no4 #a #f4j seconds4 #f4ca #e #ca4ee #b #f4j seconds4 #a4jj #c #f4g seconds4 ---- #d #f4c seconds4 #e #f4e seconds4 #cb4ee #f #f4g seconds4 #cb4ee #f4ca #e4aei #g #f4j seconds4 ,) =k free #e4afc ---- ----- ,mean #f4ca seconds ,effect ( scrape - 4#jdd ,specim54 ,circum/ances z 9 fir/ case1 except t bo? =ks 7 on _! resonators4 ,co9cid5ces 7 obs]v$ at-- #ba seconds4 #bh seconds4 #cf seconds4 #dd seconds4 #ea seconds4 #fj seconds4 #fj - #ba #ci #ci #e #g4h "t ( "o int]val4 ,rsum4 ,no4 #a #g4h seconds4 #g4db #e #cg4aj #b #g4a seconds4 #a4jj #c #g4f seconds4 ----- #d #g4d seconds4 #ch4aj #e #g4b seconds4 #ch4aj #g4db #e4acc ---- 7,above7 #e4aei ----- ,mean #g4db seconds4 ,effect ( support & scrape - 4#jbf ,mean ( second det]m9ation 0 #bef4jid ,apply+ correction 7scrape1 etc47 - 4#jbf ------- ,correct$ mean #bef4jfh ,result ( fir/ det]m9ation #bef4jgb ------- ,f9al value #bef4jgj ,,note--,! result ( fir/ det]m9ation excludes all "w except ! s]ies comm5c+ ,july #d4 ,if previ\s "w is includ$1 & also ! result fir/ obta9$ by ,pr(essor ,may]1 ! result w\ld be #bef4jhi4 #bef4ahj #bef4jcf #bef4jgb #bef4jfh ------- ,mean #bef4jhi ,! previ\s "w 0 omitt$ on acc\nt ( v>i\s inaccuracies & want ( practice1 :i* made ! sep>ate results diff] widely f ea* o!r4 ,! ,=mul4 ,! =mul employ$ are-- d 7#a7 tan ----- r #beibjjj ,d n 7#b7 ,v ----------------- angle ( deflection4 d correct$ displacem5t 7l9e>74 r radius ( measurem5t4 ,d twice ! di/ance betwe5 ! mirrors4 n numb] ( revolutions p] second4 incl9ation ( plane ( rotation d deflection z read f micromet]4 ,b numb] ( beats p] second betwe5 electric ,vt =k & /&>d ,vt ,cor correction = temp]ature ( /&>d ,vt#c4 ,v velocity ( light4 ,t value ( "o turn ( screw4 7,table1 page #abf47 ,sub/itut+ = d1 its value or d,tsec 7log sec 4#jjjjh71 & = ,d its value #cigb4df1 & r$uc+ to kilomet]s1 ! =mul become-- d,t 7#c7 tan c ----2 log c 4#eafjg r n 7#d7 ,v c ---2 log c 4#difgj ,d & r are express$ 9 feet & d 9 millimet]s4 ,vt =k makes #bef4jgj vibrations p] second at #fe ,fahr4 ,d #cigb4df feet4 tan tang5t ( angle ( incl9ation ( plane ( rotation #j4jb 9 all b ! la/ twelve obs]vations1 9 :i* x 0 #j4jae4 log c 4#eafjg 74#eafjc 9 la/ twelve obs]vations474 log c 4#difgj4 ,! electric =k makes 7#bef4jgj ,b cor47 vibrations p] second1 & n is a multiple1 submultiple1 or simple ratio ( ?is4 ,obs]vations4 ,specim5 ,obs]vation4 ,june #ag4 sunset4 ,image good2 be/ 9 column 7#d74 ,! columns are sets ( read+s ( ! micromet] = ! deflect$ image ( slit4 #aab4ha #aab4hj #aab4hc #aab4gd #aab4gi #ha #ha #ha #gf #gh #gi #gh #gh #gd #gd #hj #ge #gd #gf #gd #gi #gg #gd #gf #gg #hb #gi #gb #gh #ha #hb #gc #gf #gh #gg #gf #gh #ha #gi #ge #hc #gi #gd #hc #hb #gc #gc #gf #gh #hb ------- ------- ------- ------- ------- ,mean #aab4hja #aab4ggc #aab4gfi #aab4ggb #aab4ggi ,z]o #j4bfj #j4bfj #j4bfj #j4bfj #j4bfj ------- ------- ------- ------- ------- d #aab4dea #aab4eac #aab4eji #aab4eab #aab4eai ,temp #gg #gg #gg #gg #gg ,b #a4ejj ,corr - 4#add ------- #a4cfe #bef4jgj ------- n #beg4dbf #beg4dc #beg4dc #beg4dc #beg4dc r #bh4aeg #bh4aeg #bh4aeg #bh4aeg #bh4aeg ,! above specim5 0 select$ because 9 x ! read+s 7 all tak5 by ano!r & not$ d[n )\t divulg+ !m till ! :ole five sets 7 complet$4 ,! foll[+ is ! calculation = ,v3 #b;d1 #c;d1 #a/ set4 & #d? sets4 #e? set4 log c #eafjg #eafjg #eafjg ,t #iihcb #iihcb #iihcb d #jeaca #jeaai #jeabc ------- ------- ------- #efegj #efeeh #efefb r #ddieh #ddieh #ddieh ------- ------- ------- tan #aafab #aafjj #aafjd #bfid4g #bfid4a #bfid4c c #difgj #difgj #difgj n #dajff #dajff #dajff ------- ------- ------- #ijgcf #ijgcf #ijgcf #dcjeb #dcjdb #dcjdf ------- ------- ------- ,v #dgfhd #dgfid #dgfij ,v #biihjj #biihhj #biihej ,9 ! foll[+ table1 ! numb]s 9 ! column head$ ,di/9ctness ( ,image are ?us translat$3 #c1 good2 #b1 fair2 #a1 poor4 ,^! numb]s d n1 h[ev]1 %[ ! relative weights ( ! obs]vations4 ,! numb]s conta9$ 9 ! columns head$ ,position ( ,deflect$ ,image1 ,position ( ,slit1 & displacem5t ( image 9 divisions 7 obta9$ z describ$ 9 ! p>agraph head$ ,micromet]1 page #abj4 ,! column head$ ,b conta9s ! numb] ( beats p] second betwe5 ! electric ,vt =k & ! /&>d ,vt z expla9$ 9 ! p>agraph head$ ,measurem5t ( ! ,spe$ ( ,rotation4 ,! column head$ ,cor4 conta9s ! correction ( ! rate ( ! /&>d =k = ! diff]5ce 9 temp]ature ( exp]im5t & #fe ,fahr41 = :i* temp]ature ! rate 0 f\nd4 ,! numb]s 9 ! column head$ ,numb] ( revolutions p] second 7 f\nd by apply+ ! corrections 9 ! two prec$+ columns to ! rate ( ! /&>d1 z expla9$ 9 ! same p>agraph4 ,! radius ( measurem5t is ! di/ance betwe5 ! front face ( ! revolv+ mirror & ! cross-hair ( ! micromet]4 ,! numb]s 9 ! column head$ ,value ( "o turn ( ! screw 7 tak5 f ! table1 page #abg4 ,date4 ,di/9ctness ( image4 ,temp]ature1 ,fahr4 ,position ( deflect$ image4 ,position ( slit4 ,displacem5t ( image 9 divisions4 ,diff]5ce betwe5 greate/ & lea/ values4 ,b4 ,cor4 ,numb] ( revolutions p] second4 ,radius ( measurem5t1 9 feet4 ,value ( "o turn ( ! screw4 ,velocity ( light 9 air1 9 kilomet]s4 ,rem>ks4 ,june #ecgfaad4he #j4cjjaad4eej4aga4dbc-j4acbbeg4cfbh4fgbj 4iifadbiihej;,electric light4 ,june #gbgbaad4fd #j4jgdaad4efj4aja4ecc-j4jhdbeg4ebbh4feej 4iifadbiigdj,p4,m4 ,frame incl9$ at v>i\s angles ,june #gbgbaad4eh #j4jgdaad4ejj4jha4ecc-j4jhdbeg4ebbh4fdgj 4iifadbiiijj,p4,m4 ,frame incl9$ at v>i\s angles ,june #gbgb #he4ia #j4jgd #he4hdj4aba4ecc-j4jhdaic4adbh4fdgj4iieih cjjjgj,p4,m4 ,frame incl9$ at v>i\s angles ,june #gbgb #he4ig #j4jgd #he4hi,o4#jga4ecc-j4jhdaic4adbh4fejj4iie ihbiiicj,p4,m4 ,frame incl9$ at v>i\s angles ,june #gbgbaad4fa #j4jgdaad-ecj4jga4ecc-j4jhdbeg4dbbh4fejj 4iifadbiihej,p4,m4 ,frame incl9$ at v>i\s angles ,june #ichcaad4ed #j4jgdaad4dgj4jga4ecc-j4bafbeg4cibh4fehj 4iifadbiiiej,p4,m4 ,frame incl9$ at v>i\s angles ,june #ichcaad4ed #j4jgdaad4dfj4aja4ecc-j4bafbeg4cibh4fehj 4iifadbiiihj,p4,m4 ,frame incl9$ at v>i\s angles ,june #ichcaad4eg #j4jgdaad4dgj4jha4ecc-j4bafbeg4cibh4ffbj 4iifadbiiihj,p4,m4 ,frame incl9$ at v>i\s angles ,june #ichcaad4eg #j4jgdaad4ejj4jfa4ecc-j4bafbeg4cibh4ffjj 4iifadbiihhj,p4,m4 ,frame incl9$ at v>i\s angles ,june #ibhcaad4fa #j4jgdaad4ecj4aca4ecc-j4bafbeg4cibh4fghj 4iifadcjjjjj,p4,m4 ,frame incl9$ at v>i\s angles ,june #ajbijaad4fj #j4jgdaad4ebj4aaa4eag-j4cjjbeg4bibh4fhej 4iifadbiiihj,p4,m4 ,june #ajbijaad4fb #j4jgdaad4edj4jha4eag-j4cjjbeg4bibh4fhej 4iifadbiiicj,p4,m4 ,june #abbgaaad4ha #j4jgdaad4gdj4jia4dej-j4jgbbeg4debh4fijj 4iifadbiifej;,a4,m4 ,june #abbgaaad4gh #j4jgdaad4gjj4jea4dej-j4jgbbeg4debh4fijj 4iifadbiigfj;,a4,m4 ,june #abagaaad4gf #j4jgdaad4fhj4jia4dej-j4jgbbeg4debh4fijj 4iifadbiihaj;,a4,m4 ,june #accgbaab4fd #j4jgdaab4efj4jia4ejj-j4jhdbeg4dibh4agbj 4iifadcjjjjj;,a4,m4 ,june #accgbaab4fc #j4jgdaab4efj4aja4ejj-j4jhdbeg4dibh4agbj 4iifadcjjjjj;,a4,m4 ,june #acbgbaab4fe #j4jgdaab4egj4jha4ejj-j4jhdbeg4dibh4agbj 4iifadbiiifj;,a4,m4 ,june #accgiaab4hb #j4bfjaab4efj4jfa4eag-j4afhbeg4dbbh4aghj 4iifadbiiifj,p4,m4 ,june #accgiaab4hb #j4bfjaab4efj4aca4eag-j4afhbeg4dbbh4aghj 4iifadbiiifj,p4,m4 ,june #accgiaab4hc #j4bfjaab4egj4jga4eag-j4afhbeg4dbbh4aghj 4iifadbiiidj,p4,m4 ,june #accgiaab4hb #j4bfjaab4efj4jfa4eag-j4afhbeg4dbbh4aghj 4iifadbiiifj,p4,m4 ,june #accgiaab4hc #j4bfjaab4egj4aaa4eag-j4afhbeg4dbbh4aghj 4iifadbiiidj,p4,m4 ,june #accgiaac4da #j4bfjaac4aeaa #a4eag-j4afhbeh4gjbh4aebj4iifadbiihhj,p4 ,m4 ,set micromet] & c\nt$ oscillations4 ,june #accgiaab4ad #j4bfjaaa4hhf #a4eag-j4afhbee4fibh4aebj4iifadbiihjj,os cillations ( image ( revolv+ mirror4 ,june #adafdaab4hc #j4bfjaab4egj4aba4ejjj4jabbeg4ehbh4aebj4 iifadbiihej;,a4,m4 ,june #adafdaab4hc #j4bfjaab4egj4jea4eagj4jabbeg4fjbh4aebj4 iifadbiihhj;,a4,m4 ,june #adafeaab4ha #j4bfjaab4eej4aaa4eag #j4jjjbeg4eibh4aebj4iifadbiiijj;,a4,m4 ,june #adaffaab4hc #j4bfjaab4egj4jia4eag-j4jabbeg4egbh4aebj 4iifadbiihdj;,a4,m4 ,june #adafgaab4hc #j4bfjaab4egj4aba4eag-j4jbdbeg4efbh4aebj 4iifadbiihcj;,a4,m4 ,june #adahdaab4gh #j4bfjaab4ebj4jfa4eag-j4bbhbeg4cfbh4aeij 4iifadbiigij,p4,m4 ,read+s tak5 by ,lieut4 ,nazro4 ,june #adaheaab4gf #j4bfjaab4ejj4jha4ejj-j4bdjbeg4ccbh4aeij 4iifadbiihaj,p4,m4 ,read+s tak5 by ,lieut4 ,nazro4 ,june #adahdaab4gb #j4bfjaab4dfj4jha4dhc-j4bbhbeg4cbbh4aeij 4iifadbiihhj,p4,m4 ,read+s tak5 by ,lieut4 ,nazro4 ,june #adahdaab4gc #j4bfjaab4dgj4jia4dhc-j4bbhbeg4cbbh4aeij 4iifadbiihhj,p4,m4 ,june #adahdaab4ge #j4bfjaab4dij4jia4dhc-j4bbhbeg4cbbh4abij 4iifadbiihcj,p4,m4 ,june #agbfbaab4he #j4bfjaab4eij4jia4eagj4jcfbeg4fbbh4adij4 iifadbiihjj;,a4,m4 ,june #agbfcaab4hd #j4bfjaab4ehj4jfa4ejjj4jbdbeg4eibh4adij4 iifadbiigij;,a4,m4 ,june #agafdaab4he #j4bfjaab4eij4jga4ejjj4jabbeg4ehbh4adij4 iifadbiigfj;,a4,m4 ,june #agcggaab4hj #j4bfjaab4edj4jga4ejj-j4addbeg-dcbh4aegj 4iifadbiihjj,p4,m4 ,read+s tak5 by ,mr4 ,clason4 ,june #agcggaab4gg #j4bfjaab4eaj4jha4ejj-j4addbeg4dcbh4aegj 4iifadbiihhj,p4,m4 ,read+s tak5 by ,mr4 ,clason4 ,june #agcggaab4gg #j4bfjaab4eaj4aaa4ejj-j4addbeg4dcbh4aegj 4iifadbiihhj,p4,m4 ,read+s tak5 by ,mr4 ,clason4 ,june #agcggaab4gg #j4bfjaab4eaj4jia4ejj-j4addbeg4dcbh4aegj 4iifadbiihhj,p4,m4 ,read+s tak5 by ,mr4 ,clason4 ,june #agcggaab4gh #j4bfjaab4ebj4jha4ejj-j4addbeg #dcbh4aegj4iifadbiihfj,p4,m4 ,read+s tak5 by ,mr4 ,clason4 ,june #ahaehaab4ij #j4bfeaab4fdj4jga4ejjj4jhdbeg4febh4aejj4 iifadbiigbj;,a4,m4 ,june #ahaehaab4ij #j4bfeaab4fdj4aja4ejjj4jhdbeg4febh4aejj4 iifadbiigbj;,a4,m4 ,june #ahaeiaab4ib #j4bfeaab4ffj4jga4dhcj4jgbbeg4fbbh4aejj4 iifadbiifbj;,a4,m4 ,june #ahbgeaab4gi #j4bfeaab4ebj4jia4dhc-j4abjbeg-dcbh4aehj 4iifadbiihfj,p4,m4 ,june #ahbgeaab4ge #j4bfeaab4dhj4aja4dhc-j4abjbeg-dcbh4aehj 4iifadbiiigj,p4,m4 ,june #ahbgeaab4gf #j4bfeaab4dij4jha4dhc-j4abjbeg-dcbh4aehj 4iifadbiiiej,p4,m4 ,june #bjcfjaab4id #j4bfeaab4fgj4jga4eagj4jfcbeg4febh4agbj4 iifadbiihhj;,a4,m4 ,june #bjcfaaab4ib #j4bfeaab4fej4jia4eagj4jdhbeg4fcbh4agbj4 iifadbiiiaj;,a4,m4 ,june #bjbfbaab4id #j4bfeaab4fgj4jga4eagj4jcfbeg4fbbh4agbj4 iifadbiihej;,a4,m4 ,june #bjbfcaab4ic #j4bfeaab4ffj4jca4eagj4jbdbeg4fabh4agbj4 iifadbiihgj;,a4,m4 ,june #bjbghacc4dh #j4bfeacc4baj4aca4dej-j4aefbeg4cfcc4cdej 4iifbgbiihdj,p4,m4 ,june #bjbgiacc4di #j4bfeacc4bcj4jia4ejj-j4afhbeg4djcc4cdej 4iifbgbiihdj,p4,m4 ,june #bjbhjacc4di #j4bfeacc4bbj4jga4ejj-j4ahjbeg4cicc4cdej 4iifbgbiihej,p4,m4 ,june #bjbgiacc4ej #j4bfeacc4bdj4aca4dhc-j4afhbeg4cicc4cdej 4iifbgbiihdj,p4,m4 ,june #bjbgiacc4di #j4bfeacc4bbj4jfa4dhc-j4afhbeg4chcc4cdej 4iifbgbiihdj,p4,m4 ,june #bjbgiacc4di #j4bfeacc4bbj4aja4dhc-j4afhbeg4chcc4cdej 4iifbgbiihdj,p4,m4 ,june #babfaacc4ef #j4bfeacc4bij4aba4eccj4jdhbeg4fecc4ccbj4 iifbgbiihij;,a4,m4 ,june #babfbacc4eh #j4bfeacc4caj4jha4eccj4jcfbeg4fdcc4ccbj4 iifbgbiihaj;,a4,m4 ,june #babfcacc4eg #j4bfeacc4caj4jia4eccj4jbdbeg4fccc4ccbj4 iifbgbiihaj;,a4,m4 ,june #babfdacc4eg #j4bfeacc4cjj4aaa4eccj4jabbeg4facc4ccbj4 iifbgbiihbj;,a4,m4 ,june #babfeacc4ef #j4bfeacc4cjj4aca4ecc #j4jjjbeg4fjcc4ccbj4iifbgbiihjj;,a4,m4 ,june #bachjacc4dh #j4bfeacc4baj4jfa4ecc-j4ahjbeg4dbcc4ccjj 4iifbgbiiggj,p4,m4 ,june #bachaacc4df #j4bfeacc4aij4aja4ejj-j4aibbeg4chcc4ccjj 4iifbgbiigfj,p4,m4 ,june #bachbacc4df #j4bfeacc4bjj4jea4ejj-j4bjdbeg4cgcc4ccjj 4iifbgbiigdj,p4,m4 ,june #bachbacc4df #j4bfeacc4bjj4jha4eag-j4bjdbeg4chcc4ccjj 4iifbgbiigej,p4,m4 ,june #bachaacc4df #j4bfeacc4aij4jha4ejj-j4aibbeg4chcc4ccjj 4iifbgbiigfj,p4,m4 ,june #bcchiacc4dc #j4bfeacc4afj4jha4edb-j4bhhbeg4cbcc4cdej 4iifbgbiiiaj,p4,m4 ,june #bcchiacc4db #j4bfeacc4aej4jfa4eej-j4bhhbeg4cccc4cdej 4iifbgbiiibj,p4,m4 ,june #bccijacc4dc #j4bfeacc4agj4jia4eej-j4cjjbeg4cbcc4cdej 4iifbgbiihij,p4,m4 ,june #bccijacc4dc #j4bfeacc4afj4jga4ecc-j4cjjbeg4cjcc4cdej 4iifbgbiihfj,p4,m4 ,june #bccijacc4db #j4bfeacc4afj4jga4eag-j4cjjbeg4bicc4cdej 4iifbgbiihhj,p4,m4 ,june #bdcgbacc4dg #j4bfeacc4bjj4aea4eag-j4jhdbeg4ejcc4caij 4iifbgbiigbj;,a4,m4 ,june #bdcgcacc4dd #j4bfeacc4agj4jda4eag-j4jifbeg4dicc4caij 4iifbgbiihdj;,a4,m4 ,june #bdcgdacc4db #j4bfeacc4afj4aaa4eag-j4ajhbeg4dhcc4caij 4iifbgbiihej;,a4,m4 ,june #bdcgeacc4db #j4bfeacc4afj4jfa4eag-j4abjbeg4dgcc4caij 4iifbgbiihej;,a4,m4 ,june #bdcgfacc4dd #j4bfeacc4ahj4aja4eag-j4acbbeg4decc4caij 4iifbgbiighj;,a4,m4 ,june #bfbhfacc4db #j4bfeacc4aej4jea4ejh-j4bebbeg4cccc4ccij 4iifbgbiihij,p4,m4 ,june #bfbhfacc4dd #j4bfeacc4agj4jha4ejh-j4bebbeg4cccc4ccij 4iifbgbiihdj,p4,m4 ,june #bgcgcacc4di #j4bfeacc4bbj4aaa4dhc-j4jifbeg4dfcc4cbhj 4iifbgbiighj;,a4,m4 ,june #bgcgdacc4dg #j4bfeacc4bjj4jfa4dhc-j4ajhbeg4ddcc4cbhj 4iifbgbiihaj;,a4,m4 ,june #bgcgeacc4dg #j4bfeacc4baj4jia4dhc-j4abjbeg4dccc4cbhj 4iifbgbiigfj;,a4,m4 ,june #bgcgeacc4de #j4bfeacc4aij4jia4dfg-j4abjbeg4dbcc4cbhj 4iifbgbiihaj;,a4,m4 ,june #bgcgfacc4dg #j4bfeacc4bjj4jha4dhc-j4acbbeg4dbcc4cbhj 4iifbgbiigij;,a4,m4 ,june #bgcgfacc4de #j4bfeacc4aij4aja4dhc-j4acbbeg4dbcc4cbhj 4iifbgbiihaj;,a4,m4 ,june #cjbhe #ce4cbace4jj #ii4fhj4jea4ejj-j4bdjaic4jjcc4bgdj4iifde biihbj,p4,m4 ,mirror inv]t$4 ,june #cjbhf #ce4cdace4jj #ii4fgj4jfa4ejh-j4bebaic4jjcc4bgdj4iifde biihej,p4,m4 ,mirror inv]t$4 ,june #cjbhf #ce4cdace4jj #ii4ffj4aja4ejh-j4bebaic4jjcc4bgdj4iifde biihgj,p4,m4 ,mirror inv]t$4 ,june #cjbhf #ce4cdace4jj #ii4ffj4jia4eag-j4bebaic4jjcc4bgdj4iifde biihgj,p4,m4 ,mirror inv]t$4 ,july #abhc #jb4agace4adeacb4ihj4jga4ejj-j4bafbeg4ce cc4bhbj4iifbgbiihaj,p4,m4 ,mirror inv]t$4 ,july #abhd #jb4aeace4adeacc4jjj4jia4ejj-j4bbhbeg4cd cc4bhbj4iifbgbiigdj,p4,m4 ,mirror inv]t$4 ,july #abhf #jb4adace4adeacc4jaj4jfa4dfg-j4bebbeg4bh cc4caaj4iifbgbiihaj,p4,m4 ,mirror inv]t$4 ,july #abhf #jb4adace4adeacc4jjj4jha4dfg-j4bebbeg4bh cc4caaj4iifbgbiiidj,p4,m4 ,mirror inv]t$4 ,july #bchf #ii4he #j4djj #ii4dej4jea4dej-j4bebaib4iecc4bjej4iifjf biiiej,p4,m4 ,mirror erect4 ,july #bchf #ff4gd #j4djj #ff4cdj4jca4dej-j4bebabh4fccc4bjej4iiehf biihjj,p4,m4 ,mirror erect4 ,july #bchf #ej4af #j4djj #dg4ifj4jga4dfg-j4beb #if4dhcc4bjej4iiehjbiihaj,p4,m4 ,mirror erect4 ,july #bche #cc4eg #j4djj #cc4agj4jfa4dej-j4bdj #fd4cbcc4bjej4iiegdbiihgj,p4,m4 ,mirror erect4 ,9 ! la/ two sets ( ,june #ac1 ! micromet] 0 fix$ at #aac4da & #aab4ad respectively4 ,! image 0 bisect$ by ! cross-hair1 & kept z ne>ly z possible 9 ?is place1 meantime c\nt+ ! numb] ( seconds requir$ = ! image ( ! revolv+ mirror to complete #fj oscillations4 ,9 o!r words1 in/ead ( measur+ ! deflection1 ! spe$ ( rotation 0 measur$4 ,9 column #g = ^! two sets1 ! numb]s #aa & #f are ! diff]5ces betwe5 ! greate/ & ! smalle/ numb] ( seconds obs]v$4 ,9 f9d+ ! mean value ( ,v f ! table1 ! sets are all giv5 ! same weight4 ,! diff]5ce betwe5 ! result ?us obta9$ & t f any sy/em ( weights is small1 & may be neglect$4 ,! foll[+ table gives ! result ( diff]5t gr\p+s ( sets ( obs]vations4 ,necess>ily "s ( ! gr\ps include o!rs3 ,electric light 7#a set7 #biihej ,set micromet] c\nt+ oscillations 7#b7 #biihdj ,read+s tak5 by ,lieut5ant ,nazro 7#c7 #biihcj ,read+s tak5 by ,mr4 ,clason 7#e7 #biihfj ,mirror inv]t$ 7#h7 #biihdj ,spe$ ( rotation1 #aib 7#g7 #biiiij ,spe$ ( rotation1 #abh 7#a7 #biihjj ,spe$ ( rotation1 #if 7#a7 #biihaj ,spe$ ( rotation1 #fd 7#a7 #biihgj ,radius1 #bh4e feet 7#ed7 #biihgj ,radius1 #cc4c feet 7#df7 #biihcj ,highe/ temp]ature1 #ij ,fahr4 7#e7 #biiiaj ,mean ( l[e/ temp]atures1 #fj ,fahr4 7#g7 #biihjj ,image1 good 7#df7 #biihfj ,image1 fair 7#ci7 #biihfj ,image1 poor 7#ae7 #biihaj ,frame1 incl9$ 7#e7 #biiifj ,greate/ value #cjjjgj ,lea/ value #biifej ,mean value #biiheb ,av]age diff]5ce f mean #fj ,value f\nd = #c4bf ,probable error #e ,discussion ( ,errors4 ,! value ( ,v dep5ds on ?ree quantities ,d1 n1 & 4 ,^! w n[ be consid]$ 9 detail4 ,! ,di/ance4 ,! di/ance betwe5 ! two mirrors may be 9 error1 ei!r by an errone\s det]m9ation ( ! l5g? ( ! /eel tape us$1 or by a mi/ake 9 ! measurem5t ( ! di/ance by ! tape4 ,! fir/ may be caus$ by an error 9 ! copy ( ! /&>d y>d1 or 9 ! comp>ison betwe5 ! /&>d & ! tape4 ,an error 9 ?is copy1 ( 4#jjjcf in*1 :i*1 = su* a copy1 w\ld be consid]$ l>ge1 w\ld produce an error ( only 4#jjjja 9 ! f9al result4 ,suppos+ t ! bisections ( ! divisions are correct to 4#jjje in*1 :i* is a lib]al e/imate1 ! error caus$ by suppos+ ! error 9 ea* y>d to be 9 ! same direction w\ld be only 4#jjjjad2 or ! total error ( ! tape1 if bo? errors 7 9 ! same direction1 w\ld be #jjjjbd ( ! :ole l5g?4 ,! calculat$ probable error ( ! five measurem5ts ( ! di/ance 0 4#jjjjae2 h5ce ! total error due to ,d w\ld be at mo/ 4#jjjjd4 ,! tape has be5 s5t to ,pr(essor ,rog]s1 ( ,cambridge1 = comp>ison1 to confirm ! result4 ,! ,spe$ ( ,rotation4 ,?is quantity dep5ds on ?ree conditions4 ,x is affect$1 fir/1 by an error 9 ! rate ( ! /&>d2 second1 by an error 9 ! c\nt ( ! s\nd beats betwe5 ! =ks2 & ?ird1 by a false e/imate ( ! mom5t :5 ! image ( ! revolv+ mirror is at re/1 at :i* mom5t ! deflection is measur$4 ,! calculat$ probable error ( ! rate is 4#jjjjaf4 ,if ?is rate %\ld be que/ion$1 ! =k c be aga9 rat$ & a simple correction appli$4 ,! =k is c>efully kept at ! ,/ev5s ,in/itute1 ,hobok51 & comp>isons 7 made ) two o!r =ks1 9 case x 0 lo/ or injur$4 ,9 c\nt+ ! s\nd beats1 exp]im5ts 7 tri$ to f9d if ! vibrations ( ! /&>d 7 affect$ by ! o!r =k1 b no su* effect c\ld be detect$4 ,9 ea* case ! numb] ( beats 0 c\nt$ correctly to 4#jb1 or less ?an 4#jjja "p1 & 9 ! great numb] ( comp>isons made ?is s\rce ( error c\ld be neglect$4 ,! error due to an incorrect e/imate ( ! exact "t :5 ! images ( ! revolv+ mirror came to re/ 0 elim9at$ by mak+ ! measurem5t sometimes :5 ! spe$ 0 sl[ly increas+1 & sometimes :5 sl[ly decreas+4 ,fur!r1 ?is error w\ld =m "p ( ! probable error d$uc$ f ! results ( obs]vations4 ,we may !n conclude t ! error1 9 ! measurem5t ( n1 0 less ?an 4#jjjjb4 ,! ,deflection4 ,! angle ( deflection 0 measur$ by its tang5t1 tan d_/r2 d 0 measur$ by ! /eel screw & brass scale1 & r by ! /eel tape4 ,! value ( "o turn ( ! screw 0 f\nd by comp>ison ) ! /&>d met] = all p>ts ( ! screw4 ,?is measurem5t1 includ+ ! possible error ( ! copy ( ! /&>d met]1 ,i e/imate to be correct to 4#jjjje "p4 ,! in/rum5t is at ! ,/ev5s ,in/itute1 :]e x is to be comp>$ ) a millimet] scale made by ,pr(essor ,rog]s1 ( ,cambridge4 ,! deflection 0 read to )9 ?ree or f\r hundr$?s ( a turn at ea* obs]vation1 & ?is error appe>s 9 ! probable error ( ! result4 ,! deflection is also affect$ by ! incl9ation ( ! plane ( rotation to ! horizon4 ,?is incl9ation 0 small1 & its secant v>ies sl[ly1 s t any slight error 9 ?is angle w\ld n appreciably affect ! result4 ,! measurem5t ( r is affect$ 9 ! same way z ,d1 s t we may call ! greate/ error ( ?is measurem5t 4#jjjjd4 ,x w\ld probably be less ?an ?is1 z ! mi/akes 9 ! individual measurem5ts w\ld also appe> 9 ! probable error ( ! result4 ,! measurem5t ( 0 n correct$ = temp]ature4 ,z ! corrections w\ld be small !y may be appli$ to ! f9al result4 ,= an increase ( #a ,f4 ! correction to be appli$ to ! screw = unit l5g? w\ld be -4#jjjjjff4 ,! correction = ! brass scale w\ld be 4#jjjjaje1 or ! :ole correction = ! micromet] w\ld be 4#jjjjjd4 ,! correction = ! /eel tape us$ to measure r w\ld be 4#jjjjjff4 ,h5ce ! correction = tan4 w\ld be -4#jjjjjc t4 ,! av]age temp]ature ( ! exp]im5ts is #ge4f ,f4 #ge4f-fb4e #ac4a4 -4#jjjjjcac4a -4#jjjjd ,h5ce %\ld be divid$ by #a4jjjjd1 or ! f9al result %\ld be multipli$ by #a4jjjjd4 ,?is w\ld correspond to a correction ( #ab kilomet]s4 ,! greate/ error1 exclud+ ! "o j m5tion$1 w\ld probably be less ?an 4#jjjji 9 ! measurem5t ( 4 ,summ+ up ! v>i\s errors1 we f9d1 !n1 t ! total con/ant error1 9 ! mo/ unfavorable case1 :]e ! errors are all 9 ! same direction1 w\ld be 4#jjjae4 ,add+ to ?is ! probable error ( ! result1 4#jjjjb1 we h = ! limit+ value ( ! error ( ! f9al result 4#jjjag4 ,?is corresponds to an error ( #ea kilomet]s4 ,! correction = ! velocity ( light 9 vacuo is f\nd by multiply+ ! spe$ 9 air by ! index ( refraction ( air1 at ! temp]ature ( ! exp]im5ts4 ,! error due to neglect+ ! b>ometric height is exce$+ly small4 ,?is correction1 9 kilomet]s1 is #hj4 ,f9al ,result4 ,! mean value ( ,v f ! tables is #biiheb ,correction = temp]ature #ab ------------ ,velocity ( light 9 air #biihfd ,correction = vacuo #hj ------------ ,velocity ( light 9 vacuo #biiiddea ,! f9al value ( ! velocity ( light f ^! exp]im5ts is !n--#biiidj kilomet]s p] second1 or #ahfchj miles p] second4 ,objections ,consid]$4 ,measurem5t ( ! ,deflection4 ,! *ief objection1 namely1 t 9 ! me?od ( ! revolv+ mirror ! deflection is small1 has already be5 suffici5tly answ]$4 ,! same objection1 9 ano!r =m1 is t ! image is m or less indi/9ct4 ,?is is answ]$ by a glance at ! tables4 ,^! %[ t 9 ea* individual obs]vation ! av]age error 0 only ?ree t5-?\s&?s ( ! :ole deflection4 ,unc]ta9ty ( ,laws ( ,reflection & ,refraction 9 ,m$ia 9 ,rapid ,rotation4 ,:at is probably h9t$ at "u ! above head+ is t !re may be a possibility t ! rapid rotation ( ! mirror ?r[s ! reflect$ p5cil 9 ! direction ( rotation4 ,grant+ t ?is is ! case1 an inspection ( ,fig4 #ad %[s t ! deflection w n be affect$4 ,9 ?is figure let m m be ! position ( ! mirror :5 ! light fir/ falls on x f ! slit at a1 & m m ! position :5 ! light returns4 ,illu/ration3 ,,fig4 #ad4 ,f ! axis o draw op op1 p]p5dicul> to m m & to m m1 respectively4 ,!n1 suppos+ !re is no su* effect1 ! c\rse ( ! axis ( ! p5cil ( light w\ld be a o c mirror c o a4 ,t is1 ! angle ( deflection w\ld be a o a1 d\ble ! angle p o p4 ,if n[ ! mirror be suppos$ to c>ry ! p5cil ) x1 let o c be ! direction ( ! p5cil on leav+ ! mirror m m2 i4e41 ! motion ( ! mirror has *ang$ ! direction ( ! reflect$ ray ?r\gh ! angle c o c4 ,! c\rse w\ld !n be a o c1 mirror c o4 ,f o ! reflection w\ld take place 9 ! direction a1 mak+ ! angles c o p1 & p o a equal4 ,b ! angle c o c mu/ be add$ to p o a1 9 consequ5ce ( ! motion ( ! mirror1 or ! angle ( deviation w be a o a c o c2 or a o a c o c d4 7#a7 ,by con/ruction-- c o p p o a 7#b7 c o p p o a 7#c7 ,subtract+ 7#c7 f 7#b7 we h-- c o p - c o p p o a - p o a1 or c o c a o a ,sub/itut+ a o a = c o c 9 7#a7 we h-- a o a a o a a o a d4 ,or ! deflection has rema9$ unalt]$4 ,ret>dation ,caus$ by ,reflection4 ,cornu1 9 answ]+ ! objection t !re may be an unkn[n ret>dation by reflection f ! di/ant mirror1 says t if su* exi/$ ! error x w\ld introduce 9 8 own "w w\ld be only #a_/gjjj t ( ,f\cault1 on acc\nt ( ! great di/ance us$1 & on acc\nt ( !re be+ 9 8 own exp]im5ts b "o reflection in/ead ( twelve4 ,9 my own exp]im5ts ! same reason+ %[s t if ?is possible error made a diff]5ce ( #a p] c5t4 9 ,f\cault's "w 7& 8 result is correct )9 t am\nt71 !n ! error w\ld be b 4#jjjjc "p4 ,di/ortion ( ! ,revolv+ ,mirror4 ,x1 has be5 sugge/$ t ! di/ortion ( ! revolv+ mirror1 ei!r by twi/+ or by ! effect ( c5trifugal =ce1 might cause an error 9 ! deflection4 ,illu/ration3 ,,fig4 #ae ,! only plane 9 :i* ! deflection might be affect$ is ! plane ( rotation4 ,di/ortions 9 a v]tical plane w\ld h simply ! effect ( rais+1 l[]+1 or ext5d+ ! slit4 ,aga91 if ! mean surface is plane !re w be no effect on ! deflection1 b simply a blurr+ ( ! image4 ,ev5 if !re be a di/ortion ( any k9d1 !re w\ld be no effect on ! deflection if ! rays return$ to ! same portion :5ce !y 7 reflect$4 ,! only case :i* rema9s to be consid]$1 !n1 is t giv5 9 ,fig4 #ae1 :]e ! light f ! slit a1 falls ^u a di/ort$ mirror1 & ! return light ^u a diff]5t portion ( ! same4 ,! "o p5cil takes ! c\rse a b c d e f a1 :ile ! o!r foll[s ! pa? a f g h i b a4 ,9 o!r words1 besides ! image co9cid+ ) a1 !re w\ld be two images1 "o on ei!r side ( a1 & 9 case !re 7 m ?an two portions hav+ diff]5t incl9ations !re w\ld be =m$ z _m images to correspond4 ,if ! surfaces are n plane1 ! only effect is to produce a di/ortion ( ! image4 ,z no multiplication ( images 0 obs]v$1 & no di/ortion ( ! "o image1 x foll[s t ! di/ortion ( ! mirror 0 too small to be notic$1 & t ev5 if x 7 l>g] x c\ld n affect ! deflection4 ,! figure repres5ts ! di/ort$ mirror at re/1 b ! reason+ is ! same :5 x is 9 motion1 save t all ! images w be deflect$ 9 ! direction ( rotation4 ,imp]fection ( ! ,l5s4 ,x has also be5 sugge/$ t1 z ! p5cil goes ?r\gh "o-half ( ! l5s & returns ?r\gh ! opposite half1 if ^! two halves 7 n exactly simil>1 ! return image w\ld n co9cide ) ! slit :5 ! mirror 0 at re/4 ,?is w\ld und\bt$ly be true if we consid] b "o-half ( ! orig9al p5cil4 ,x is evid5t1 h[ev]1 t ! o!r half w\ld pursue ! contr>y c\rse1 =m+ ano!r image :i* falls on ! o!r side ( ! slit1 & t bo? ^! images w\ld come into view1 & ! l9e midway betwe5 !m w\ld co9cide ) ! true position4 ,no su* effect 0 obs]v$1 & w\ld be v unlikely to occur4 ,if ! l5s 0 imp]fect1 ! faults w\ld be all ov] ! surface1 & ?is w\ld produce simply an indi/9ctness ( ! image4 ,moreov]1 9 ! latt] "p ( ! obs]vations ! mirror 0 inv]t$1 ?us produc+ a positive rotation1 :]eas ! rotation 9 ! prec$+ sets 0 negative4 ,?is w\ld correct ! error m5tion$ if x exi/$1 & %[s also t no con/ant errors 7 introduc$ by hav+ ! rotation con/antly 9 ! same direction1 ! results 9 bo? cases be+ almo/ exactly ! same4 ,p]iodic ,v>iations 9 ,friction4 ,if ! spe$ ( rotation v>i$ 9 ! same mann] 9 ea* revolution ( ! mirror1 ! *ances w\ld be t1 at ! p>ticul> "t :5 ! reflection took place1 ! spe$ w\ld n be ! same z ! av]age spe$ f\nd by ! calculation4 ,su* a p]iodic v>iation c\ld only be caus$ by ! influ5ce ( ! frame or ! pivots4 ,= in/ance1 ! frame w\ld be clos] to ! r+ :i* holds ! mirror twice 9 e revolution ?an at o!r times1 & x w\ld be m difficult = ! mirror to turn "h ?an at a position #ij f ?is4 ,or else !re might be a c]ta9 position1 due to want ( tru5ess ( %ape ( ! sockets1 :i* w\ld cause a v>iation ( friction at c]ta9 p>ts ( ! revolution4 ,to asc]ta9 if !re 7 any su* v>iations1 ! position ( ! frame 0 *ang$ 9 azimu? 9 sev]al exp]im5ts4 ,! results 7 un*ang$ %[+ t any su* v>iation 0 too small to affect ! result4 ,*ange ( ,spe$ ( ,rotation4 ,9 ! la/ f\r sets ( obs]vations ! spe$ 0 l[]$ f #bef turns to #aib1 #abh1 #if1 & #fd turns p] second4 ,! results ) ^! spe$s 7 ! same z ) ! great] spe$ )9 ! limits ( errors ( exp]im5t4 ,bias4 ,f9ally1 to te/ ! "q if !re 7 any bias 9 tak+ ^! obs]vations1 eight sets ( obs]vations 7 tak51 9 :i* ! read+s 7 made by ano!r1 ! results be+ writt5 d[n )\t divulg+ !m4 ,five ( ^! sets are giv5 9 ! specim51 pages #acc-acd4 ,x rema9s to notice ! rem>kable co9cid5ce ( ! result ( ^! exp]im5ts ) t obta9$ by ,cornu by ! me?od ( ! too!d :eel4 ,cornu's result 0 #cjjdjj kilomet]s1 or z int]pret$ by ,helm]t #biiiij kilomet]s4 ,t ( ^! exp]im5ts is #biiidj kilomet]s4 ,po/script4 ,! comp>ison ( ! micromet] ) two scales made by ,mr4 ,rog]s1 ( ! ,h>v>d ,obs]vatory1 has be5 complet$4 ,! scales 7 bo? on ! same piece ( silv]1 m>k$ ,scales ,no4 #be1 on silv]4 ,half in* at #eh ,f41 too %ort 4#jjjjji in*4 ,c5timet] at #fg ,f41 too %ort 4#jjjjh cm4 ,x 0 f\nd t ! ratio 4#cicgjgi c\ld be obta9$ almo/ exactly1 if1 in/ead ( ! c5timet] be+ too %ort1 x 7 too long by 4#jjjjh cm4 at #fg4 ,on ?is supposition ! foll[+ tables 7 obta9$4 ,!y repres5t ! value ( "o turn ( ! micromet] 9 millimet]s4 ,table #a is ! result f c5timet] scale4 ,table #b is ! result f half-in* scale4 ,table #c is ! result f page #ca4 ,x is se5 f ! correspond5ce 9 ^! results1 t ! previ\s "w is correct4 7#a7 7#b7 7#c7 ,f #j to #ac 4#iiefc 4#iiefb 4#iiegj #be 4#iiefb 4#iiefd 4#iiega #ch 4#iiefj 4#iiegb 4#iiegf #ea 4#iiefg 4#iiegh 4#iiehj #fd 4#iiegg 4#iiehf 4#iiehe #gf 4#iiehb 4#iieij 4#iieib #hi 4#iieij 4#iieih 4#iifja #ajb 4#iieif 4#iifjh 4#iifje #aae 4#iifjf 4#iifad 4#iifae #abh 4#iifah 4#iifbb 4#iifbc #adj 4#iifbi 4#iifcc 4#iifcj