No. 203. VOL. XXXIV.

TOVEMBEU, 1887.

B1tabli1hed by BB1'1AKI1' SD.LI•.&.1' in 1818.

THE
AMERICAN
• JOU· RNAL OF SCIENCE.
.EDITORS
JAMES D. AND EDWARD S. DANA.
A.88001.A:TB BDITOBS
PJIOJ'BSSOBS ASA GRAY, JOSIAH P. COOKE, AND JOHN TROWBRIDGE, OP CAllBJUDGX,
Pa•ol'Bssoas B. A. NEWTON ill> A. E. VERRILL, o.tr NBW HAVBN'
Pao•BBSOR GEORGE F. BARKER, OJ!' Pa1LADBLPHll.
TlllBD SB•BIBS.
VOL. XXXIV. -[rWHOLE NUMBER, OXXXIV.J
WlTll PLA.l'E8 II ro IX.
No. 203-NO'VEMBER, 1887.
NEW HAVEN, OONN.: J. D. & E. S. DANA. 1887.
TtJTTLB, MOBlltBOUIIIB • TAYLOR, PBilfTBB8, l'n B'tAT.llli 8'l'U.ltT,
'° aaz. dollan per 7f11tZ (poalace prepaid). $6.40 fore:lp. aubecriben of oountriea in
&ha Poalal Union. Remlu.Doea ab.ould be made either bJ mon.e;r orden, r•si•fiei.d -...,.,orbuakollMb.

THE
AMERICAN JOURNAL OF SCIENCE.
[THIRD SERIES.)

ART. XXXVI.-On the Relative Motion of the Earth and the

w. Lumi'niferous Eiher; by ALBERT A. MICHELSON and

EDWARD

MORLEY.*

THE discovery of the aberration of light was soon folJowed
by an explanation according to the emission theory. Tbe effect was attributed to a simple composition of the velocity of light with the velocity of the earth in its orbit. The difficulties in this apparently sufficient explanation were overlooked until after an explanation on the undulatory theory of light was proposed. This new explanation was at first almost as simple as tbe former. But it failed to account for the fact proveJ by
experiment that the aberration was unchanged when observa• tion1 were made with a telescope filled with water. For if the
tangent of the angle of aberration is the ratio of the velocity of the earth to the velocity of light, then, since the latter velocity in water is three fourths its velocity in a vacuum, the aberration observed with a water telescope should be four. thirds of its true valne.t
* Thia research was carried out with the aid of the Bache Fund. t lt may be noticed that IQ.Ost writers admit the aul'fl.ciency ot tbe explanation
according to the earlasiou theory of light; while in fact the dlt!lculty ia QVen greater than according to ihe undulatory theory. For on the emi11ion theory the velocity of light must be gre,.ter io the water tele8COpe, and therefore the an«l~ of aberratioo lhould be lea; hence, in order to reduce it to ite I.rue nlue,,we muat make the abaurd hypotbe11i11 that the inotion of the water in the teleeeope e&rriee tbe ray of ligbt in &he oppoeite direc&ion !
AM. Jon. SoL-TB.llU> Snucs, Vor.. XXXIV, No. 203.-Nov., 188T.
22

as, MicA.l!uon and .Morky-lJ.otion. of the Earth, de.

. On the undulatory theory acco~ding to_Fr~nel, first, th_e ether 18 euppoeed to be,at rest exc,ept. m the mter1or of transparent

media, in wbiob secondly, it is supposed to move with a velo ci y

1, less than the velocity of t.he medium in the ratio nn'; where

n is the index of .refractioo. These two hypotheses give a com•

plete and sn.ttisfactory explanation of aberration. The second

hypothesis, notwithstanding its seeming improbability, must be

considered as fully proved, firat, by the celebrated experiment of

Fizeau1* and secondly, by the ample confirmation of our own
work.t The experimental trial of the firat hypothesis forms

the suhjeot of the preseut paper.

If tl,-e earth were a transparent body, it might perhaps be

conceded, in view of the experiments just cited, that the inter•

molecular ether was at rest in space, notwithstanding the mo•

tion of the earth in its orbit; hut we have no right to ex-

t.end tbe conclusion from these experiments to opaque bodies.

But there can hardly be question that the ether can and doee

pass through metit,ls. Lorentz cites .tb.e il_l.ustrut.ion of a m~tallio

barometer tube. When the tube 1s mc1rned the ether m the

space above the mercury is certainly forced out, for it is im-

oompressible.f But again we huve no right to assume thnt it makes its escape with perfect freedom, and if there bi:, any resist■

ance, however slight, we certainly could not assume an opaque

1,ody such as the whole earth to offer free passage through its

a entire mami. But .as Lorent.z aptly remarks: "quoi qui'I en
soit,t on ·fera bien, moo avis, de ne pas se laisser guider, dans

une question aus.si import.ante, par des c-0nsiderations sur .Je

a deg~ de probahilite OU de simp1icite de l'une OU de J'nutre
hypot~ese, mais de s'addrf'sser a. !'experience pour appre'ndre

a conna1tre 1'6tnt, . de repo-s oo de mouvement, dans lequel se
trouve !'ether la surface terrestre. 11§

I~ April, 1881! a methO?, was prorosed and carried out for

testmg the gnestmn experrmentaUy.

.

Io deducrng tbe formula for toe quantity to be measured,

the effect of tee motion of the earth through the ethl'r on the

path of the ray at right angles to this motion. was overlooked.,.

• Oomptee Rendus, xmli, a.t9, 1861; Pogg. AhD. Erginzungeband, ,ii, -i5i,

l

H
t

S; Aon . Chim. .Pby1J..1 ln.fl.~nce of Motion o

I f

II, lvil, 3851 the M:edium

1859. on the

Velocity

of

'Light.

Thia Journal,

Dlt,

x:ut, S'f'l, 1886. It may be objected

tbat

it-may

escape

by

the

space

between

the

mel'CUry

ancl

the walls; but tb.ie could be prevented by amalgamating lhe walle..

§ Arebm• NeerlandaiMa., n:i, 2•• livr.

lllcIhTehlaeorne,lathtiiv$eJomuort.i,onrrro.fnt"hiie,

earth 120.

and

the

luminileroue

ether,

by

Albett

A.

, 1' ma.:, be mentioned here that the.error was pointed o'llt-to the author ot ihe

former paper by M.A. Potier, of Paris, iu the win.tar of 1881.

.Miohelao-n anuJ, Morky-Re«LWV8 Motu>n of tM 835
The disco888ioo of this oversight and of the entire ex.periment forms the enbject of a very searching analysis by H. A. Lorentz,* who ftnds that this effect can by no means be disregarded.
In consequence, the quantity t.o be measured had in foot bnt
one-half the value supposed, and as it was already barely beyond the limits of errors of experiment, the conclusion drawn from the result of the experiment might well be questioned; since, however, the main portion of the theory remains unqu~ione~, it was deoid~ t.o repeat the ~xperiment with such modlfioat.tons as would maure a theoret1oal result much t.oo large to be masked by experimental errors. The theory of the method may be briefly stated as follows :
Let sa, fig. 1, be a ray of light which is partly reflected
in ab, and partly transmitted in ac, being returned by the mirrors band c, along ba and ca. ba is partly transmitted along ad,

"', b

I

b

I

I

I

I

I

~

I

8

I

d

8

1.
C
C

2.

and c:a is partly :reffected along ad. If then the paths ab and ac are equal, the two rays interfere along ad. Suppose now, the ether being a& reat, that the whole apparatus moves in the direction ac, with the velocity of the earth in its orbit, the direc-

* De l'Influenoe du Moavement
Ju,deilN, m, 2- livr., 1886.

de

la

Terre

1111'

lea Phen.

Lum.

ArehiYee

N-,.

886

.&rlA and tM .Ltvmimferow Etlu,r.

tions and distances traversed by the rays will be altered thus:TbA ray sa is reflected along ab, fig. 2; the angle bab, being
eqaal to the aberration =a, is returned along ba,, (aba, =2a), and
goes to the focus of the telescope, whose direction is unaltered. The transmitted ray goes along ac, is returned along ca,, and is reflected at a0 making ca,e equal 90-a, and therefore still coin• ciding with tbe first ray. It may be remarked that the rays l>a, and ca,, do not now meet exactly in the same point a,, though the difference is of the second order ; this does not affect th.e validity of the reasoning. Let it now be required to find the difference in the two paths aba,, and a.car
= Let V velocity of light. v = velocity of the earth in its orbit. D=distance ab or a.c, fig. 1. T=time light occupies to pass from a to c. T =time light occupies to retarn from c to a,1. (fig. 2.)

Then

T

=

v

D
-t,

,

I

T,=vD+v.

The whole time of going and com·

vY ., ing is T+T,=2D -v and the distance traveled in this time

v• ( is 2DV'-v'= 2D 1 + Vv''), neglecting terms of the fourth order.

The length of the other path is evidently 2D✓1+;,, or to the

same degree of accuracy, 2n(1+2~ 1). The difference is there•
.fore Dytt',· If now the whole apparatus be turned through 90°,

the difference placement of

will be in the opposite the interference fringes

dsihroecutlidonb, eh2ennc;e.•.theOdoine-•

eidering only the velocity of the earth in its orbit, this would
be 2Dx10-•. If, as was the ca.se in the first experiment,
D=2Xl0• waves of yellow light, the displacement to be
expected would be 0·04 of the distance between the interference
fringes. In the first experiment one of the principal difficulties en-
counte~ was that of revolving the apparatus without produ• oing distortion; and snot.her was its extreme sensitiveneea to vibration. This was so great that it was impossible to see the interference fringes e:&eept at brief int.erva.ls when working in
the city, even at two o'~lock in the morning. Finally~ as be· fore remarked, the qaant1ty to be observed, namely, a d1splaoement of something less than a twentieth oi the distance between the int.erferenoe fringes may have been too small to be detected when masked by experiment.al errors.

MicMlaon and J[()'l'ley-Relaltiw Motion of the 387
The firat named difficulties were entirely overcome by mounting the apparatus on a massive stone floating on mercury; and theaecond by increasing, by repeated reflection, the path of the light to about ten times its former value.
Tbe apparatus is represented in perspective in fig. 3, in p1an in fig. 4, and in vertical section in fig. 5. The stone a (6g. o)is about 1·5 metier square and ·0·3 meter thick. It rests on an annular wooden float bb, 1·5 meter out.side diameter, 0-7 meter inside diameter, and 0·25 meter thick. Tbe Boat rests on mercury contained io the cast-iron trough cc, l ·5 centimeter thick, and of such dimensions as to leave a clearance of about one centimeter around the float. A pin d, ~aided by arms gggg, flt.a into a socket e attached to the float. The pin may be pushed into the socket or be withdrawn, by a lever pivoted at/. This pin keeps tbe float concentric with tbe trough, but does not bear any part of the weight of the stone. The annular iron troagh rests on a bed of cemen, on a low brick pier bailt. in the form of a hollow octagon.
a.
At each corner of th_e atone were p1aoed four mirrors d d ee fig. 4. Near the center of the stone was a plane~parallel gl&88 b. These were so disposed that light from an argand burner a, passing through a lens, fel) on b so as to be in part reflected to d,; tbe two pencils followed the paths indfoated in the figure, bdedbf and bd,e1d,b/respectively, and were observed by tbti telescope /. Both / and a revolved with the stone. The mirrors were of speculum metal carefully worked to optically plane 11urfaces five centimeters in diameter, and the glasaee I, and o were plane-paralJel and of the same thickness. l ·25 centimeter;

838

Etwe/. am,d fM Lumi,mifwou, Etk,r.

their surfaces measured 5·0 by 7·5 centimeters. The second of these waa placed in the path of one of the pencils to compensate for the puaage of the other through the same thickness of glass. The whole of the optical portion of the apparatus was kept covered with a wooden cover to prevent air carrente and r&J!!d changes of temperature.
The adjustment was effected as follows: The mirrors having been adjusted by screws in the castings which held the
'-

/
Q, I
mirrors, against which they were pressed by springs, till light from both pencils could be seen in the teJescope, the lengths of the two paths were measured by a light wooden rod reaching diagonally from mirror to mirror, the distance being read from a smaH et.eel scale to tenlbe of millimeters. The difference in the lengths of the two paths was then annulled by moving the minor~" This mirror bad three adjustments; it had an adjust• meot in alLitude and one in azimuth, like all the other mirrora,

Michelson.and MO'rley-.Rdative Motion of the 889

but finer; it also had an adjustment in the direction of the

incident ray, eliding forward or backward. b11t keeping very

aconrateJy parallel to its form~r plane. The three a_djust~~nt.a

of this m1rror could be made with the wooden cover m pos1t1on.

The paths being now approximately equal, the two images

of the source of light or of some well-defined object placed in

front of the condensing lens, were made to coincide, the teles-

cope was now adjusted for distinct vision of the expected inter-

ference bands, and sodium light was substituted for white light,

when the interfereooe bands appeared. These were now made

as clear as possible by adjusting the mirror e,; then white light

was restored, the sca·ew altering the length of path was very

slowly moved (one turn of a ~crew of one hundred threads to the

6

inch altering the path

•

nearlyl000 wave-lengLhs)

a

till the colored interfer-

ence fringes reappeared

!!.

in white light. These

e b
I
I I

Cg d gC
I g ◄ >-o
I

b c were now given a con-

I venient width and posi -

I

tion, and the apparatus

I

I

was ready for observa-

I
I

I I

tion.

I

I

Tbe observations were

I

I

I

I conducted as follows :

'

I

Around the cast-iron

trough were sixteen equidistant marks. The apparatus was

revolved very slowly (one turn in six minutes) and after a

few minutes the cross wire of tbe micrometer was set on the

olearest of the interference fringes at the instant of passing

one of the marks. The motion was so slow tbat this could be

done readily and accurately. Tbe reading of the screw-head

on the micrometer was noted, and a very slight and gradual

impulse was given to keep up the motion of the stone; on

passing the second mark, the same process was repeated, and

t.his was continued till the apparatus had completed aix revolu-

tions. It was found that by keeping the apparatus in slow

uniform motion, the results were much more uniform and con-

sistent than when the stone was brought to rest for every ob-

servation; for the effecte of strains could be noted for at least

half a minute after the atone came to r:est, and ~uring this time

effects of change of temperature came rnto action.

The following tables give, the means of the six readings; the

first, for observations ma.de near noon, the second, those near

ai:r. o'clock in the evening. The reapings are divisions of the

screw-bead& The width of the fringes varied from 40 to 60

<livisiona, the mean value being near 60, so that one division

340

Earth and ths Ltvminif61"0'U8 Ether.

means 0·02 wave-length. The rotation in the observations at noon was contrary to, and in the evening observations. with, that of the hands of a watch.

NOON' OBSBRVATI0!!.8.

I 2::.. 16. I ). •• 2. 3. 4, ~ 6. II ,. 8. 9. ]0. ~ 12. 13. It 14.

]I•

July 8 ...... . i-n· .u·o 43·,'> 39'7 a.">·2 3'·7 M·a! az-r. 28'2 20-2 23·9· ZJ"2 20·3 1s·1I 17·1, 1e·s IB·T

July 9 . ... .. . 57•4 6i '3 58'2 59•2 55·; 00·2 60'81 62-0 01·5 63-3 65·81 6i"3 60'"7 70"'i! 73'0 'i'O".! 12·2

July ll ... . . 21•3 zi-5 22·0 19-s 10·2 19·3 1 •i i 1 • 10-2 u-a 13·3; 12· 13·3 :12-a, 10-2 7·3 0•5

Mean....... . Mean in w. l.

4~ -3·1· 4~ 1"6' 4- 1'2 3~ 9-41 ~ 37•; ~ 38·] . 1 37"9 ~ 37· ~ 35"3 ~ 3'"6 ~ M"3;~ M·t ~ M·,i d 331>'~ ~-6~ fil•.t~ oo·s

·700 . "6'{12 '686 "6881 '688 "67 ·012j ·628 '6 6

I

I

:

Final mean. ·,sf •7112! '755 '738 'i21 '720 "715 ·692 "661

I

P. M. OBSERVATION'S.

July 8 ... ... 6l'!?l 63•31 6.1"3 68'2 6j·j 69'3 'i0'3 69'8 69-0 il'3 il-:J 70·5 Tl·2, 'il"2j 70'5 7'i-"5 75'T

July 9 .. .. ... 26·01' 26·01 28'2, 29·2 3l"l~ 32·0 31·3 an aa·o 35"8 36·3 37-3 38·8 u·o, l2"1 '3"'i -0

" July 12 ......

oo·s

00•51 66·0 1

st·3

62·2

ai-o

o '3

oo·,

58"2

M·'i

53"7 • sn

55•0

58"2

M·s

57-0

56· 0

' Mean . . . . . .. 51'3 _51"9' 52•5 53·9 63"8 sn M·S M·, 63·{. M-11- 53"8 M"! 55·0 56"81 5'j·2 5'i"t 58•6

Mean

tow.

1.

1]'·0000861"10-m86s1,11r"o0o7o6. _1]·.·«mws,.

1•07a 1_·OS2 t1186 1·1001"1001'1«

t1JT• Iil68.1-oeo 1•15-11·112

11r.61-0M

1·1001·18611

"1"

1·

w

1·1 'm

Final mean. liM7 11llrllI'063°l 'OJI 1'08811'1091·116 l·lH 1·12<il

Tbe rePults of the observations are expressed graphically in fig. 6. The upper is the curve for the observations at ooon, and tbe lower that for the eveniug observations. The dotted corves represent one-eighth of the theoretical displacements. It seems fair to conclude from the figure that if there is any dis•

6.
- o-osJ

r.lacement due to the relative motion of the earth and the
uminiferous ether, this cannot be much greater than 0·0l of the distanee between the fringes.
Considering the motion of \be earth in ita orbit only, this

Michilaon and, .MQ'rky-Relatilve lifotion of tM 841
diaplacement should be 2Dvy',=2Dx10-•. The distance D was
about eleven meters, or 2X10' wave-lengths of yellow light; hence the displacement to be expected was 0·4 fringe. Tbe aotaal displacement was cert.ainly less than the twen~ietb part of this, and probably less than the fortieth part. But since the displacement is proportional to the square of the velocity, the relative velocity of the earth and the ether is probably less than one l'ixth the earth's orbital velocity, and certainly less than one-fourth.
In what precedes, only the orbital motion of the earth is considere<l If this is combined with tbe motion of the solar system, concerning which but little is known with certainty, the resuh would have to be modified; and it is just possible that ihe reenhant velocity at the time of the observations was small though the chances are much against it. The experiment will therefore be repeated at intervals of three months, and thus all uncertainty will be avoided.
It appears, from all that precedes, reasonably certain that if
there be any relative moti9n between the earth nnd the lnminif. erous et.her, it must be small; quite small enough entirely to refute Fresnel's explanation of aberration. Stokes has given a theory of aberration which assumes the ether at the earth's surface t.o be at rest with regard to the latt.er, and only requires in addition that the relative velocity have a potential; but Lorentz shows that these conditions are incompatible. Lorentz then proposes a modification which combiaes some ideas of Stokes and Fresnel, and assumes the existence of a potential, together with Fresnel's coefficient.. If now it were legitimate to conclude from the present work that the ether is at rest with regard to the earth's surface, according to Lorentz there could not be a velocity potential, and his own theory also fails.
Supplement.
It is obvious from what bas gone before that it would be hopeless to attempt to solve the question of the motion of the eolar system by observations of OP.tieal phenomena at 'the ,urface of the earth. But it is not impossible that at even moderate distances above the level of-the sea, at the top of an isolated mountain peak, for instance, the relative motion might be perceptible in an apparatus like that used in these experiments. Per• haps if the experiment should ever be tried in these oircums'8ooes, the cover should be of glass, or should be removed.
It may be worth while to notice another method for multip]ying the square of the aberration aofficiently to bring it within the range of observation, which bas presented itself during the

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would be about one-millionth of the original intensity, so that if sunlight or the electric arc were used it could still be readily seen. The mirrors bb, and cc, would differ from parallelism sufficiently to separate the successive images. Finally, Lbe apparatus need not be mounted so as to revolve, as the earth's
rotation would be sufficient. If it were possible to measure with sufficient accara-0y the
velocity of light without returning the ray to its start.fog pointt tbe problem of measuring the first power of the relative velocity
of the earth with respect to the ether would be solved. This may not be as hopeless as might appear at first sight, since the difficulties are entirely mechanical and may possibly be sur-
mounted in tbe cour e of time. For example, suppose (fig. 8) m and m, two mirrors revolving
with equal velocity in opposite directions. It is evident that light from s will form a stationary image at s, and similarly light
from s, will form a stationary image at s. If now tbe velocity of the mirro~ be increased sufficiently, their phases stiJl being exactly the same, botb images will be deflected from 8 and s,
i~ inverse P.roportion to the .velocities o. f hght in the two ~ireet10ns; or, 1f tbe two deflections are made equalt and the difference of phase of the mirrors be simultaneously measured, this will evidently be proportional to the difference of velocity in
the two directions. The only real difficolt.v lies in this measuremeat. The following is perhaps a possible solution: gg, _(fig.,
4) are two gratings on which sunlight is concentrated. These are placed so that after falling on the revolviag mirrors m and
m1, the light forms images of the ~ratings at a and s", two very senshive selenium ce1ls in circuit with a battery and a telephone. If everything be symmetrical, the sound in the telephone will be a maximum. If now one of the slits s be displaced through half the distance between the image of the grating bars, there
will be silence. Suppose now that the two deflections having been made exactly equal, the slit is adjusted for silence. Then if the experiment be repeated when the earth's rotation bas turned the whole apparatus through 180°, and the deflections are again made equa4 there will no longer be silence, and the angular distance through which s must be moved to restore silence will measure the required difference in phase.
There remain three other methods, all astronomical, for attacking the problem of the motion of the solar system through space.
1. The ~elescopi~ obaervatio1; of the proper motio!1e <?f the
st.a.rs.. This has gtven us a highly probably determ1nat1on of the direction of this motion, bot only a guess as to its amount.
2. :rhe spectroscopic observation of the motion of stars in the hoe of sigh,. Thia could furnish data for the relative

Mich&oo anul, Murley-Motion of th8 Emrth, et,c. 345
motions only, though it seems likely that by the immense improvements in. the p~otograpby of stellar spectra, the information thus obt.amed will be far more accurate than any other.
8. Fina1ly there remains the determination of the velocity of light by observations of. the eclipses of J ~piter's satellites. If the improved photometric methods practiced at the Harvard observatory make it possible to observe these with sufficient accuracy, the difference io the results found for the velocity of light when Jupiter is nearest to and farthest from the line of mbtion will give, not merely the motion of ·the solar system with reference to the stars, but with reference to the luminiferoaa ether itse1f.