Download - Fizeau (1859)-Hypotheses on Luminous Ether and on an Experiment.pdf

7/28/2019 Fizeau (1859)-Hypotheses on Luminous Ether and on an Experiment.pdf

1/20

NASA TECHNICAL TRANSLATION NASA F-13,423

HYPOTHESES ON LUMINOUS ETHER AND ON AN EXPERIMENTTHAT APPEARS TO DEMONSTRATE THAT THE MOTION OF BODIES CHANGES

THJ3 VELOCITY WITH WHICH LIGHT PROPAGATES IN THEIR INTERIOR

H . F i z e a u

T r a n s l a t i o n of "Sur les h y p o t h e s e s relatives al'ether lumiaeux", Annales de Chemie e t d e P h y s i q u e ,3rd Series, Vol. 57 , December 18 59 , pp. 3 85-404.

386(THRU)L? -J

Y (PAGES,5 -__- L/s ( N A S A CR OR IMX OR AD NUMBER) (CATEGORY)

NATIONAL AERONAUTICS AND SPACE ADMINISTRATIONWASHINGTON, D. C . 20546 APRIL 1 9 7 1


2/20

HYPOTHESES ON LUMINOUS ETHER-4ND ON AN EXPERIMENT THAT APPEARS TO DEMONSTRATE THAT

THE MOTION OF BODIES CHANGES THE VELOCITY WITHWHICH LIGHT PWPAGATES I N THEIR INTERIOR

I.izeau

ABSTRACT. The author d iscusses F resnel 's hypothesist o e x pl a in l i g h t a b be r at i on and l i g h t waves.t o de termine the poss ib l e changes in t he speed of l i gh tt ravel ing through t ransparent bodies is discussed , as w e l las the a pparatus used fo r such experiments. The authorpresents c a lcul a t io ns and d iscusses re su l t s and poss i b lesou rces of e r ro r .

An experiment

Several theor ies on w a v e systems have been proposed t o attempt t o expl ainthe abbera t ion of l i g h t . F i r s t , F r e sn e l a nd , m re recently, Doppler, Stokes,Cha l l i s and sever a l o the rs have publ ished papers on th is subject, but i t doesnot seem th a t any of the theor ies so f a r proposed have been able t o completelys a t i s f y t h e p h y s i c i s t s .p rope r t i e s of the luminous ether and i t s re la t ionsh ip t o ponde rable matter,i t has been nec essa ry t o i ntr oduc e hypotheses, amoag which are those whichare more o r less probable, b ut none t ha t can be considered as proven.

Because of a lack of de fi ni te knowledge about the

These can be reduced t o th re e main hypotheses, a l l of which refer t o t h es ta te i n which the e the r in s ide a tran spar ent body should be considered:

~ ~ ~- ~ ~*Numbers i n the margin ind ica te the pag ina tion i n the o r ig i na l fo re ign tex t .1


3/20

The ethe r adheres, o r i s fix ed, to th e molecules of the body, and,consequently, sha res i n the motion th at may be imposed on the body;

O r , the e the r is fr ee and independent, and is not ca rri ed along by th ebody i n i t s motion;

O r , f i n a l l y , a t hi r d hypoth esi s which borrows from each of t he two above,/386n which onl y a port ion of t he e t he r would be f ree , while th e o ther por t ion -

ould be fixed t o th e molecules of th e body and would so le ly shar e i n i t smotion.

This last hypothesis , po stu la ted by Fresnel , w a s conceived i n o r d er t os a t i s f y a t t h e same time th e phenomenon of a bbe ra ti on, and a famous experimentby Arago, i n which he had shown th a t the motion of the Ear th d id not have anye f f ec t upon the re f rac t ion va lue of s t a r l i g h t in a prism.could be explained through Fres nel 's hypothes is wit h admirable prec isio n.However, Fresnel's hypothesis is not regarded today as abso lu te t ru th , and therel ati ons hip s between eth er and ponderable matter are s t i l l genera l ly consi-dered as uncer ta in and hard t o unders tand. This i s because Fresnel's mechac.--c a l conception seems too unusual t o be accepted without d ir ec t proof , orperhaps because i t seemed equal ly po ssi ble t o sa t i s f y th e observed phenomenaw i t h e i t h e r of t he two other hypotheses . Perhaps , f i na l l y , as o the r phys ic i s t shave thought , c er ta i n results from th i s theory seemed contrar y t o experience.

These two phenomena

The following considerations have led me t o t r y an experiment, th e rest l tsof which, I b e l i ev e , s ho ul d c l a r i f y t h i s matter.

I t is poss ib le in th e thr ee hypotheses enumerated above th at , i f the bodyis in motion, the vel oci ty a t which light w i l l go through i t w i l l be d if ferent :from tha t observed i f the body were a t rest.th e motion of t he body would have a d i f f e r e n t e f f e c t u pon t h e l i g h t v e lo c i t y.

For each of these hypotheses,

Thus, i f e t h e r is supposed be fixe d t o t he body Curing the l a t t e r ' smotion, t h e v e lo c i t y of l i g h t w i l l be augmented by t h a t of the body, i f t he2


4/20

dir ec t ion of t he l i gh t ray and of th e motion are t h e same.

I f t h e e t h e r is supposed to be f re e , the ve loc i t y of l i g h t w i l l notchange.

F i n a ll y , i f o n l y p a r t of t h e e t h e r is at tached t o the body, the ve loc i tyo f l i g h t w i l l be augmented only by a f ra c t i on of t he ve loci ty of the body,and not by th e t o t a l amount as i n t h e f i r s t h yp ot he si s.as evident as in t he f i r s t two hypotheses, but Fresnel has made i t clear t h a ti t may be upheld by very cr ed ib le mechanical consid eration s.

This result i s notI 387-

I t i s supposed tha t th e speed or l i g h t i n a body a t rest o r i n motion maybe determined exactly.corresponding t o t he s ta te of rest incre ases by the t o t a l speed of motion ofthe body, t h i s w i l l conform with t he f i r s t hypothesis .

I f th e body is i n motion, and i f the speed of l i gh t

I f the speed o f l i gh t i s the same in both cases (body a t rest o r i nmotion), th e second hypothes is w i l l b e s a t i s f i e d .

I f , on the o ther hand, the speed of l i gh t corresponding to the s t a t e ofrest i s augmented by a f rac t ion o f t he speed o f the body, the re su l t w i l l b ei n agreement with the th ir d hypothesis .

It is t r u e t h a t l i g h t t ravels a t such a gr ea t spee d -when compared t othe speeds tha t w e may impart to th e bodies- hat the change in the speedof l i g h t i s too s m a l l t o be observable. Nonetheless, by choosing the mostfavorable circumstances, it ha s seemed t o me poss ib le to submi t two media, air andand water, t o a dec is ive test.th ei r components o r molecules, can be acc eler ated t o gre at speeds.

These two media, because of th e mob ili ty of

W owe t o Arago a method of observation, based on interference, whichreveals the smallest v a r i a ti o n s i n t h e r e f r a c t i v e i n d i ce s of bodies. Aragoan d Fresnel have demons trated th e ex t rao rd ina ry se ns i t iv i t y of th i s

3


5/20

procedure through sev era l d e l i ca t e observat ions , such as t h e d i f f e r e n c e i nrefraction between dry and humid air.

I t has seemed to me t h a t a mode of observation based on t h i s p r i n c i p l e i sthe only one th at reve als the changes i n speed due t o motion.producing in terference f r inges with tw o l i gh t r ays , a f t e r they have passedthrough two paral le l tubes i n which air and water may f l o a t a t grezt speedsand i n opposi te d irec t ion s .needed several innovations, which I w i l l ind ica te .

I t c o n s i st s i n

The special goa l t h a t I ha ve t r i e d t o a t t a i n ha s

Great d i f f i c u l t i e s were encountered relat ive t o t h e l i g h t i n t e ns i t y. Thetubes, with an i n t e r i o r d i a m e t e r of 5.3 mm, had t o be t r ave rsed by the l ig h tnea r th e i r cen te r and no t nea r the i r s ides .more e longated than usual , and , consequent ly, t he l i gh t in t ens i t y a t thepo in t of o r i g in of the f r inges w a s very l ow.

Thus, th e tw o s l i t s had t o be

This inconvenience w a s overcome by placing a convergent l ens behind thes l i t s .t h e l i g h t i n t e n s i t y i s f a i r l y g r e a t .

Then the fringes were observed a t the point of th e beam junctio n where

Since the length of th e tubes w a s f a i r l y l a r g e , 1. 487 m , i t was fearedtha t any d if feren ce i n temperature or pressure between t he tw o tubes wouldi n i t i a t e a considerable d isp lacement of the f r i nge s , which i n tu rn couldccmq-letely mask the displacement due to motion.

This d if f ic ul t y has been obviated by means of a telescope having amirror a t i t s fo ca l point. This way each beam is fo rced to t r ave rse the twotubes success ive ly , so th at both beams covered exac tly th e same d js tance , bu t i nopposi te d i rec t ion . The ef fe ct s produced by pressure o r temperature ar e thuscompensated. I have sa t i s f ie d myself , through several experiments, that t h ecompensation is complete, and regardless of any changes i n den sity o r tempera-tu re intr oduced upon th e medium i n one of th e tubes, th e fri nge s keep th ei rsame exact posi t ion . In th i s type of a rrangement, th e f r inges should be

I 3 8 8-

/389-4


6/20

observed a t t h e same poin t of depart ure of the beams; su nl ig ht i s ac-s i t iedla te ra l l y , and d irec t ed toward the tubes by i t s r e f l e c t i o n o n a mirror. Thebeams, a f t e r th i s double passage through the tu bes, r e t u r n t o set up the iri n t e r f e r e n c e p a t t e r n a sho rt d is tan ce beyond th e mirror t rave rsed by themo r i g i n a l l y . I t i s h e r e t h a t t h e f r i n g e s ar e observed with the a id of ano c u l a r h a v h g a divided scale.

Another advantage of th e double t r a j ec t ory by t he beam i s thz t o f inc reas -ing the probable effec t of motion; i t i s j u s t as i f t h e tu be s were twice aslong.

This arrangeme.it al so permit s t he use of a very simple means t o m a k e t hef r i n g e s larger than they should be a t t h e d i s t a n ce s e p a r a t i n g t h e two s l i t s( t h i s d i s t a n c e w a s 9 mil l ime te r s ) .g l a s s i n f ro nt of one of the s l i t s i n c l i n e d i n s uc h a way th at , because ofr e f r a c t i o n e f f e c t s , the two s l i t s would appear very c l o s e t o e a ch o t h e r .f r i n g e s are then as l a r g e as they would be i f t h e s l i t s were r e a l l y a l o tcloser. Also, t h e r e is no apprec iable loss i n in t ens i ty , and , on the con-t ra ry , the in ten s i t y can be g rea t l y inc reased by inc reas ing the l i gh t source .The s i z e of the f r inges can be va r ied a t w i l l by changing th e inc l in a t i on ofthe g la s s , and s o i t i s p o s s i b l e t o o b t a i n t h e f r i n g e s i z e most convenientfo r observ ing the d isplacement with pr ec is i on .

This i s done by placing a very th ick

The

I w a n t to des cri be now 2 arrangement of the tubes and apparatus to se tt he water i n Eo tion.

The tw o tubes , p laced s id e by s id e , were closed at e i the r end wi th as i n g l e p i ec e of gla ss g lued i n t o p lace with gum l ac , i n a pasi t ion perpendi-cular t o t he common di re ct io n. Near each end a branch, shaped as a roundedelbow, establishes communication with a l a r ge r tube t ha t goes t o the bo ttomof a f l a s k .the two tubes.

/390onsequently, there were four f lasks connected to the ends of -5


7/20

One of t h e two f lasks connected to a tube is f u l l of water; a piece oftubing allows th e intro duct ion of compressed a i r coming from a reservoir con-nected t o an a i r pump. The pr es su re fo i es the water t o rise in to the tube ,traverse it completely, and go i n t o t h e f l a s k a t the opposi te end .fl as k may, i n tur n, be pressu rize d wit h compressed a i r , and t he water w i l lr e t u r n t o t h e f i r s t f l a s k , t r a v e r s i ng t h e t u b e i n t h e op p o si t e d i r e c t i o n.Water speeds over seven meters per second may be obtained.p lace s imultaneously i n the two tubes , a l though in opposi te d ire c t i on t o oneanother.

This l a t t e r

The same flow took

The observer ha s two handy stopcocks connected t o th e a i r re se rvo i r ; i fThei t h e r one i s open, water flow is es tab l i shed a t once i n both tubes.

d i r e c t i o n of flow is reversed with th e other stopcock.

The air reservoir , where the air i s usua l ly a t two atmospheres of pres-s u r e , has a 15 l i t e r capacity.l i t e r s . They are cal ibr a te d i n equal volumes, and the dura t ion fo r the f lowof 0.5 l i te r s p l u s t h e water i n t h e s e c t i o n o f t h e t u b es are subtrac ted f romthe speed of t h e water.

The capacity of t h e f l a s k s i s about two

The apparatus arrangement, which I have jus t t r i e d t o d e s cr i b e , h a s on l ybeen used f o r experimentation with water i n motion .a i r , provided some modifications ar e made.w a s made previously with a somewhat different apparatus, which w i l l b e d e a l twith l a te r , and with which conclusive r es ul ts were obtained.

I t i s al so convenient f orThe experiment with a i r i n mot ion

I have determined that a ir motion does not produce a pe rcep t ib le d i s -placement of t he fring es.d e t a i l .

Later I s h a l l go o v er t h e s e r e s u l t s i n g r e a t e r

I n t h e case of water, the re is an evident displacement.

6


8/20

/391hen th e water flows away from t h e obse rve r i n the tube on h i s r ig h t ,and toward the obse rve r i n the tube on h i s l e f t , the f r in ges are d isp lacedtoward the r ight .

-When t h e water f low takes p lace i n a d i r e c t i o n o pp o s it e t o t h e o n e

descr ibed above, the f r i nge s are d i sp l ac e d t o t h e l e f t .

The fringes remain very clear whi le the water is i n motion. They movep a r a l l e l t:, themselves, without disturbances, i n amounts p erc ept ibl y propor-t i o n a l t o t h e s p e e d of t h e water. At a speed of two meters per second, th edisplacement i s a l ready fa i r ly no t iceab le , and is pe rf ec tl y measq?y-.bie a twater speeds between 4 and 7 meters per second.

I t has been found experimentally that the displacement of a f r i n g eoccupying f ive nicrometer d i v i s i o n s is 1 .2 d i v i s i o n s t o t h e r i g h t or 1. 2d iv i si o ns t o t h e l e f t , a t a water ve loc i ty o f 7.059 meters per second.

Thc sum of both displacements is 2.4 divisions, which means a s e n s i t i v i t yof 1 / 2 f r inge .

In o rde r to avo id ce r t a in ob jec t ions , I should say tha t the sys tem oftubes and fl as ks i n which t he motion of t he water took place was completelyis o la ted f rom the o ther por t ion of th e apparatus .i n o rde r t o p reven t t he p re ssu re o r the shock of the water from producingacc iden ta l f l exu ra l changes i n certain po rt io ns of th e app ara tus whose move-ments could have inf luenced the pos i t i on of the f r inges . On the o ther hand,I have assure d myself t h a t motion imposed by t h e desi gn upon th e two-tubesystem had :io inf l uence upon th e posi t ion of t he f r inges .

This precaut ion w a s taken

Af te r having ve r i f i ed the existence of t h e phenomenon, I t r i e d t odetermine the va lue with th e gre a t es t poss i b le accuracy .

In o rde r t o avoid a cause f or e rr or which, I thought, would exert anin f luence on the re s u l t s , I have changed th e widt h of t h e f r i n g e s , the speed -3927


9/20

of the water, and even t he nat ure o f the mic-ometer di vi si ons , s o as t oobscrve the d if fer ent d isplacements without be ing able to presuppose t he va lue .I n f a c t , t h e g r e a t e s t i n f l u e nc e t o b e f ea r e d was th a t of preoccupat ion whilemeasuring small qua nt it ie s which involved a grea t dea l of e s t ima t ion .b e l i e ve t h a t the r e s u l t s I have obta ined have been fr ee of t h i s cause of e rr or .

I

The g r e a t e r p o r ti o n of t h e observat ions were made a t a speed of 7.059A c e rt a i n number of them were made a t a spead of 5.515eters p e r second.

meters per second, and some were made a t 3 .7 meters p e r second. :be observedvalues wcre reduce d t o t h e maximum spee d of 7.059 meters pe r second, andr e l a t e d t o t h e l en g t h of a f r in ge taken as un i ty .

Fringe displacement valuesf o r an average water speed of7.059 m per second.

Differ ences between th eobserved values and theaverage.

- , 0 30- ,010+0,010- , 059- ,063- , 005.- 0,oo- ,orF,L. 0,006

- , 006+o,oT,t-I-0,077-I- 0 ,0264- 0 ,010+0 ,010- ,041

0,000

3- 0 ,017

I393y doubling the average value,0.46 is obtained, which is ve ry c lo se t o -a l f a f r i n g e , and which represents the displacement value produced when the

f low in t he tubes is reversed.8


10/20

The dif fe re nc e between th e observed and th e average valu es w a s added t othe observed values i n order to de termine the devia t ion a t e i t h e r s i d e of t i eaverage. I t was observed t ha t they gen era lly repres ent a very minute f racdonof the width of the f r i nge; the gre a t es t devia t ion d id not exceed 1/13 of af r inge .

A d i f f ic u l t y , imposs ible to avoid , fu rn i shed the exp lana t ion fo r thesed i f fe rences .and, conse quently, th e obse rva tion must be done rap idl y. I f i t were poss ib let o ma inta in a constant flow speed of t he water f o r a longer t i m e , the measure-ments would be more prec ise . But t h i s has not been poss ib le without in tro -ducing considerable changes i n the appara tus .th is exper iment t o a time of th c yea r when experiments r equ iri ng th e use ofsun lig ht become almost impossible t o perform.

The maximum displacem ent ta ke s pl ac e d uri ng a ve ry sho r t time,

Such changes would have retarded

I want now t o compare th e va lu e found fo r t h e displacement of t he f r i nge st o th at which would be the r es ul t of each of the hypotheses i i i quest ion .

To s t a r t with , i t su f f ic e s tha t the mo tion o f the water d isp laces thefr in ge s i n any amount to exc lude the suppos i tion tha t the e the r is completelyf r e e and independent of th e motion of the body.

I t is al so necessary t o ca l cul a te what the d isp lacement of th e f r i nge swould beth at they would shar e i n each ot he r ' s motion.

assuming tha t the e ther is at tached t o the molecules of the body s o

L e t v = speed of l i g h t i n vacuum,1394v' = speed of l i g h t in s t i l l water, and -

= speed of water paral le l t o t h e d i r e c t i o n of t h e l i g h t r ay s.

The speed of light in water, when th i s l i qu id is i n motion, w i l l be forbotb rays ,

9


11/20

The motion take s p lace i n a r e l a t iv e d ire c t i ou which i s opposed t o each of th erays

I f w e c a l l A the d if ference in speeds be ing sovght , E the length of thecolumn of water t raversed by t h e rays, by applyingof in te rfe rences ,we f ind tha t

!..? pr inc i p le s o f the theo ry

0'" a l s o ,

' tSince u i s so small i n r 2 1a t io n t o v,reduced,wlthovt apprec iable e rro r , t o

), this express ion may be33 00 0 00 0

VVReplacing the expression -, by m , t h e r e f r a c t i v e i nd e x of water, i n t he aboveformula w e have

uQA f 2 E m * .

Each ray t ia ve rse s the tubes twice, an d so the l e -g th E is twice t h e a c t u a lLength of t he tubes.meters j , the previous

By c a l l i n g L the a ctus . leng th of each tube (1.4875express o n b e omes

Numerical ca lcu la t ion y ie ld s :A = 0.0002418 millimeters

This is the d i f fe rence i n d is tance tha t shou ld ex i s t between t h e two rays - 2the f i r s t hypothesiE were true.10


12/20

This number i s a c t u a ll y i n r e l a t i o n t o v e l o c it y i n a vacuum. I n o r d er t orelate i t t o a i r , i t should be divided by t he r ef ra ct io n index of t h i s medium.But, t h i s index is so c l o s e t o un it y t h a t , f o r t h e sa k e of s i m p l i f i c a t i o n , i t i sposs ib l t t o igno re the t r ansfo rma tion wh i le in t roducing an e r r o r n o g r e a t e r.han un i ty i n the l a s t f igu re .

The value for the f r inge d isp lacement ,as a funct ion of the width of af r i nge , is obta ined by d iy id ing the above quant i ty by t he va lue of a wavelength.As a matter of f a c t , f o r a d i f fe rence i n speed o f 1, 2 , 3, m wavelengths, thefrizlge system i s displaced by 1, 2, 3, m f r inges .

Tki2 wavelength for ray E i s h = O.Cd0526. These ar e t h e r a ys t h a t seemt o m ai nt a in t h e g r e a t e s t i n t e n s i t y , s i n c e t h e l i g h t m u s t t ravel through ara t he r cons ide rab le thickness o f water.

Final17 th e Fringe displacement i s found,A '5= 14597:

I f t h e r e were agreement with :he hypothesis i n quest ion , th e e th er wouldbe placed i n motion at a speed equal to th a t o f the water, which , i n the pre-ceding experimeat would have caused a displacement of 0.46 fringes.

But,the average of the observations has been only 0.23, and observat ionof t he indiv idu al va lues h igher than the average shows thar: none of the n ap-proaches th e number 0.46. I should a ls o add t ha t t h i s number should be s t i l lg r e a t e r because of a sma l l e r r o r in the eva lua t ion of the speed of water.s ou r ce o f t h i s e r r o r is known, as w i l l be seen l a t e r , bu t i t has not beenpqss ib le to co r rec t the e r ro r exac t ly .

The

I t is ev iden t th a t t h i s hypothes i s is not i n agreement i :h th e experiment./396-Ox? the o the r harrd, we s h a l l see t h a t t h e : ird hypothesis p *

Fresnel , leads t o a displacement value very cl ose t o the obsex. 1 8 *11


13/20

I t i s known t h a t the ordinary phenomenon of refraction i s d ue t o t h e f a c ttha t the speed of p ropaga t ion o f l ig h t in th e in t e r io r o f bod ies i s less thani n a vacuum. Fresnel admiLs tha t t h i s change in speed takes p lace because th ee ther possesses a g r e a t e r tensity i n t h e i n t e r i o r of b o d ie s than i n vacuum. I nt h e case of two media wi th th e same e l a s t i c i t y bu t d i f f e r e n t d e n s i t i e s , t h esquared powers of the speeds of propagation are in inve rse p roport ion t o thedensi t ies . Thus w e have

i n which D and D' are the d ens i t ies of th e e t he r i n vacuum and i n the body,and v and v' are the corresponding propagation speeds, respectively.Consequently ,

and

This l a s t express ion g ives the excess d e n s i t y o f t h e i n t e r i o r e t h e r .

I f the body is se t in motion, only a p a r t o f t h e i n t e r i o r e t h e r i s se t i nmotion with the body; t h i s i s t h e p o r t i o n t h a t h a s a g r e a t e r d e n s i t y t ha n t h a tof the surrounding e ther .D' - D.motion takes piace , has a dens i ty D.

The density of t h i s mob ile po r t ion is expressed byThe o the r por t io n of the ether, which remains immobile while the

What is th e speed of propagat ion of t h e waves i n ch i s type of medium-a port ion i n motion and a port ion motionless - uppos ing , fo r s imp l ic i t y ' ssake, th at th e body moves i n th e di re ct io n of propagation of th e waves?

Fresnel considers t ha t the speed assumed by t he ce nter of gra vi t y of the -397system i s added t o th e speed of propagation of t he waves.

If u is the speed of the body, '4 (%2) i l l be the speed of the cen te rof grav i ty of t h e s y s t e m , and from preceding con sid cra tio ns, thi s expressioni s equa l to12


14/20

which is t h e amount by which t he speed of p ropag ation of t he waves should beincreased .

Also, if th e speed of p ropagation in t h e sta te of rest i s v ' , i n t h es t a t e of motion i t w i l l be

Now, wi th the help of t h i s expressions 1 am g oi ng t o c a l c u l a t e t h e f r i n g edisplacement that should be observed in the exper iment i n quest ion .

The speed of propagation of l i gh t i n moving water, fo r each of t he tworays tha t have to i n t e r f e r e , i s one of t he values expressed by the precedingformula. Using the same no ta t ion as i n t he previous example , the d i f fe rencei n v e l o c i t i e s w i l l b e

By doing t he c al cu la ti on s and some transformations, i t i s found

This express ion may be s impl if ied by tak ing in to considera t ion th a t u i s) , nd t h a t t h e c o e f f i c i e n t of u i s22v, ("=eAy small i n r e l a t i o n t oalways smaller than uni ty , which permits the can cela t ion of the term i n uwithout apprec iable err or ; m i s the index of r e f r a c t i o n , E is twice t h e l e n gt hL of the tubes , and the f i na l formula is

/398-3300000013


15/20

By making th e numerical cm ce la ti on , i t i s found:A = 0.00010634 millimeters

This i s the d i f fe rence in speeds between the tw o r a y s t h a t i n t e r f e r e ,es ta bl ish ed by th e motion of the water.of a wave, A, the f r inge d isp lacement i s obtpiceo

Dividing ' - l i s re s u l t by the l ength

The experimental result w a s 0.23.

These two values ar e almost i d e n t i c a l . I a lso want to demonstrate thatthe d if feren ce be tween the observed and the ca l cula t ed va lues can very l i ke lybe descr ibed by an e r r o r i n t he eva lua t ion of t h e water speed, w i t h a sourceeasy to assign, and whose value can be assumed by an~ iogy o be very s m a l l .

The speed of water i n each tube has been ca lcula ted by d i v id ing thevolume of water flowing in one second by t he t ube sec tion .median speed of th e water has been obtai ned, which would be t he ac tu al one i fth e motion of the l i qui d threads were t h e same through the cross sec t ion ofthe tube , a long the center as w e l l as along the w a l l s . But, reaso ning showst h a t t h i s i s not the case, and that t h e res is tance exper ienced by t h e l i q u i dalong the walls has an immediate effect upon the neighiooring layers closer tothe center .a t d i f f e ren t d i s tances f rom the w a l l .is in te rmed ia te t o these d i f f e ren t speeds.gr ea te r than the median speed, which i n tur n is grea te r than the speed nearthe walls.

I n t h i s way, t h e

This means tha t the speed is d i f f e r a t f o r l i q u i d th re ad s f lo wi ngThe speed value obta ined by ca lcu la t io n

The speed nea r t he center i s much

Also, t h s s l i t s , placed in f r ont of each tube to admit t h e l i g h t r a yst h a t w i l l eventual ly cause the in te r fe rence , are loca ted i n the middle of thec i rcu lar end of t he tubes , so tha t the rays t raverse the centra l zones wheret h e speed of the water s hould be g re at er than th e media? speed. (Each s l i t

1 4


16/20

has the shape of a rec tang le , 3 mm by 1.5 mm , and i t s su r face i s 1/5 of thec ross sec t i on o f t h e tube.)

Laws governing the flow of water i n tubes,t hat would follow thes e speedvariati ons,have ye t t o be dLcerrmned, and thus it i s no t poss ib le t o in t roducethe necessary correc t ions . A t t he same t i m e , a n a l y s i s i n di c a t e s t h a t t h eposs ib le error cannot be too gres+water flow in open canals has been determined, and in t h i s case t h e samecause produces a similar e f f e c t .near the burface , t h e water has a greater speed than the median.found t h a t . when th e median speed varies between 1 and 5 meters per second,the m a x i m u m speed i s obtaine d by multip lying th e median speed by a f a c t o rvarying from 1.23 t o 1.11. By an al ogy, i t i s poss ib le t o assume t h a t t h eco r rec t ion to use would be on th e ord er of this magnitude.

As a matter o f f a c t , a l a w governing the

I t is s e en t h a t in th e middle of the canal ,I t has been

I f u i s mult ip l ied by 1.1, 1.15, o r 1 . 2 , and the corresponding fr ingedisplacement i s calc ulat ed, values of 0.22, 0.23 and 0 .24 are found i n placeof 0.20. I t is seen tha t th e corre c t ion tends t o become closer t o the ca lcu-l a t e d ratLer than the observed resul t .the small difference between these two values i s due t o a small e r r o r i n t h e

Thus, i t is poss ib le to assume t h a t

/400c tua l vater veloci ty : an er ro r th a t cannot be correc ted i n a s a t i s f a c t o r y -anner because of a l a c k o f s u f f i c i e n t l y precise data .

Thus, th e fr in ge displacem ent by t he movement of t he water, and t h eamount of displacement, are sa t i s f ac to r i ly expla ined by the theory proposedby Fresnel.

I sa id be fo re that, where the rays t ravel through a i r in s tead of water,This f ac t haso f r i nge d isplacement is observed when the a i r is i n motion .

been proven by means of the apparatus whick. I w i l l b r i e f l y d e s c ri b e.

A bello ws, count erpois ed wit h weigh ts and moved by a lev er , for ces t hea i r through tw o copper tubes c losed with g la ss a t th e i r ends; the a i r movesi n opposi te d i rec t ion s in each tube. These tubes had an e f f e c t i v e l e ng t h of

15


17/20

1.495 meters and a diameter of 1a.a i r flow w a s measured with a manometer connected a t the en t rance to the tubes ;a t tines i t would go as high as 3 cm of mercury.

The pressur e necess ary t o produce t he

The air speed w a s calc ulat ed from the pr essu re and th e dimensions of th etubes , according t o the known laws p e r t a i n i n g t o gas flow.w a s contro l led by the known capacit y of th e bellows,aud t he speed a t which i thad t o be ac tua ted i n order t o produce a fa i r ly cons tan t p re s su re a t t heen t rance t o t he tubes .25 meters pe r second and, on rare occasio ns, much gr ea te r speeds of unc erta invalue.

The found value

I t w a s r e l a t i v e l y e a s y t o ob ta in air speeds of up to

No apprec iable d isp lacement of the f r inges w a s detec ted i n any of th eexperiments.o r moving a t speeds of 25 meters p e r second or b e t t e r .

They always occupied the same pos i t i on whether t he air was s t i l l ,

When t h i s experimen t w a s being conducted, I had not yet thought of thep o s s i b i l i t y of using a ref lec t in g te lescope , which makes i t possib le to double -401the va lue of th e d isplacements by f u l ly compensat ing fo r the e ffe c ts due t oacc iden ta l d i f fe rences i n t empera tu re o r p re ssu re i n the two tubes.sure way t o dis t i nguis h between the ef fe c t s due t o motion and the o theracc iden ta l e f fec t s tha t cou ld occu r .

I used a

This cons i s t s of making two succ essi ve obs erva tio ns by passin g throughThis w a s done by placinghe apparatus beams going i n opposite d ire cti ons .

t h e l i g h t s o u r ce a t the point where the cent ra l fringe had formed in the p re-cedi ng exper imen t, and th e new fr in ge s would form a t t h e exact point wherethe source had been before.

With the d ir ec t ion of air f low constant i n both cases , i t is e a s y t o seetha t acc id enta l e ff ec ts should have produced d isp lacement a t t h e s i d e of t h esame tube dur ing both observat ions , while the d isplacement due t o a i r motionshould have taken place f i r s t to the s ide of one tube , and then to the s i de ofthe opposi te OG. I n t h i s way, a d i s p l a c e m e n t due t o motion would have been16


18/20

recognized, even i f i t had been accompanied by an acci denta l d isplacement duemainly t o some defe ct of symmetry i n th e d iamete rs o r i n t h e o r i f i c e of t h etubes.gas,and , onsequently, i n a d i f f e r e n c e i n d e n s i t y .

This would have re sul ted i n unequal resistance t o the passage of t he

But i t has been poss ib le to g ive the appara tus such a high degree ofsymmetry th at t he re were no appa ren t dens i ty d i f fe rences in the t w o tubesduring the f low of a i r . Thus, th e double observ ati on would not have beennecessary. Nonetheless, t h i s second obse rvat ion ha s been done fcr added assur-ance, and to a l l ay th e f ea r th a t the d isp lacement be ing looked fo r could havebeen accidentally compensated by a small dif fer enc e i n densi ty , which wouldhave masked it completely.

In sp i t e of the se p recau t ions , no f r inge d isp lacement by a i r motioncould be found.

I estimate t h a t a displacement as s m a l l as 1/14 of a fringe, produced by -402th e motion of th e air , would have been noticed.

Here are the ca lcu la t ion s re l a ted to t h i s exper imen t.

Consider ing t he hypcthesis where the e t he r is completely affixed to theair i n motion,

where m2 i s 1.00G567 a t a temperature of 10C.Since the experiment w a s conducted on ai r , t h e m a x i m u m l i g h t i n g i s ob-

ta ined from yel low l i gh t rays , and th is m a x i m u m is the one th at determinesthe width of t he f r i nges .corresponding t o ray D.

Thus, i t i s convenient t o use fo r A , the va lueThus, w e have

17


19/20

or some o t h e r similar displacement which could be daubled by reversing thedi rec t io n of t he f low. This d isp lacement cer ta in l y could not have escapedobservat ion .

Following are t h e results of t he ca lc u la t i on accord ing t o Fre sne l ' shypothesis:

This is a displacement of 2/10,000 of t he width of a f r i ng e which i sunobservable, even i f i t were 100 t i m e s grea te r .p l a in s t he apparent inrmodbil i ty of th e f r i nges i n th e exper iment made withair i n motion .so weak that i t cannot be noticed.

Thus, F resn el 's theory ex-

The displacement of t h e f r i n g e s i s n o t r e a l l y z e ro , b u t it i s

After o b t ai n i ng t h i s n e g a t iv e f a c t , I s t i l l continued t o search fo r anexplanat ion f or the hypotheses re la t ive to e the r tha t wou ld ,a t the same t i m e ,exp lai n th e phenomenon of abb era tio n and Arago's experiment. I t seemed t o m et h a t i t was necessary t o admit with Fresnel tha t th e motion of bodies producesa change i n the speed of l i gh t , and t ha t th e magnitude of t h i s change of speeddepends upon th e energy with which the d i f f er en t media r ef ra c t l i gh t .f a i r l y l a r g e f o r hi g h ly r e f r a c t i v e b o d ie s , and v er y small f o r t h o s e t h a tr e f r a c t v e r y l i t t l e , such as a i r .

/ 4 0 3

It i s

This r e su l ted in the f r inge s no t be ing d i sp laced when l i gh t t r ave ledthrough the a i r i n motion.ta in ed i f the exper imenr. were performed i n water, whose r efr ac t ive index ismuch gre at er than t ha t of a i r .

An appreciable displacement should have been ob-

One experi ment per formed by Babi net and mentioned i n Volume 9 of theAcademy's Comptes Rendus, seemed t o co nt ra di ct tile hyp ot hes is of the speedchange i n conformance with Fresnel's law. But upon consi deri ng the18


20/20

circumstances of th e experiment, I have not iced the exis tence or a compensatingcause tha t d i sgu ise s the e f fec t o f mo t ion .su f fe red by th e l i gh t in th i s exper imen t.th at when th er e i s a d i f f e r e n c e i n t h e v e l o c i t y o f two r a y s , t h i s d i f f e r e nc ei s changed when the rays are re f lec ted by a mirror i n motion.c u l a t i o n of the e ff ec ts i n Babinet 's exper iment shows th a t they have f a i r l yequal va lues , but with opposi te s igns .

This cause i s t h e r e f l e c t i o nI n f a c t , i s i s possib le to show

A separats cal-

This expla nation renders even more probable t he hypoth esis of th e changeof speed, and i t has seemed t o m e t h a t an expe rim ent made i n moving watershould he lp t o dec ide the ques t ion wi th c e r ta in ty .

I b e l i e v e t h a t t h e s uc c es s of t h is exper iment should br ing about th e/ 4 0 4doption of Fresnel 's hypothesis , o r a t l east of the l a w he d i scove red t ha t -xpla ins the change in the speed of l i gh t because of motion of bodies .this law i s t r u e , i t c o n s t i t u t e s a ve ry s t r ong p roo f i n f avo r of the hypo thes i s ,of which th i s l a w is only a consequence.

t i o n w i l l seem s o extraordinary,and s o hard t o admit i n c e r t a i n r e s p e c t s , t h a taddi t io nal proofs might s t i l l be required .goemetricians i s required , before th is can be considered t o be v a l i d .

Since

I t might be that Fresnel 's concep-

A thorough examination by t he

Transl ated fo r National Aeronautics and Space Administration under cmr*.z+.c:No. NASw 2035, by SCITRAN, P.O. Box 5456, Santa Barbara, Cali for nia Q J . ~ ) !