120 A. A. Michelson- 'l'l,e 1'elllttoe mot/on oj tile' Earth

ART. XXI.-The relulive motLim oj the Earth mul the LUTm:nij emus ether j by AI,BKR'r A. MICHELSON~ Mastel', U. S, Navy.

THE undulatory theor.Y of light assumes the existence of a

medium called the ethel', whose vibrations produce the phe-

nomena of heat and light, and which is supposed to fill all

space. According to Fresnel, the ethel', which is enclosed in

optical media, partakes of the motion of these media, to an ex-

tent depending on their indices of refraction. For ail', this

motion would be but a small fmction o£ that of the air itself

and will be neglected.

.Assuming then that the ether. is at rest, the earth moving

through it, the time required fol' light to pass £l'Om one point

to another on the earth's surface, would depend on the direc-

tion in which it travels,

Let V be the velocity of light,
v = the speed of the earth with respect to the ethel'. D = the distance between the two points. cl = the distance through which the earth moves, while

light travels from one point to the other.

d, = the distanee earLh moves, while light passes in the

opposite direction.

Suppose the direction of the line joining the two points to

coincide with the direction of eal'th's motion, and let T = time

required fOI' light to pass f!'Om the one point to the other, and
'1', = time required £01' it to pass in the opposite direction.

Further, let To = time required to perform the joul'lley if the

Dtd earth were at rest. 'l'hen '1'=

= ~; aud T,= Dv!! = ~

From

these

relations

we

Hnd

d=Dv~
-'1)

und

d'=. D-'+,'1.')1c)

whence T=vD-1'

and

T'=vD+ ; T~T,=2To-v'1) v

nearly,

and

T-T

v=V"2'j'\

If now "it were possible to measure T-T, since V and '1'0 are knowp, we could find v the velocity of the earth's inotion through the ethel'.
In a letter, published in "Nature" shortly after his death, Olerk Maxwell pointed out that T-T, could be calculated by measuring the velocity of light by means of the eclipses of Jupiter's satellites at pel'iods when that planet lay in <liffeI'ent directio)1s f!'Om earth j but that fOI' this pnrpose the observations of these coli pses rn nAt gl'C:1.tl'y exceerl in acclll'ac'y those

and the Lwninij.'erous Ethel'"

121

which have thus far been obtained" In the same letter it was also stated that the reason why such measurements coul.1 not be made at the eal"th's surface was that we have thus far no method for measLuing the velocity of light which does not involve the necessity of returning the light ovel" its path, wbm"eby it would lose nearly as much as -.yas gained in going"
The difference depending on the square of the !"atio of the two velocities, according to Maxwell, is fa'" too small to
measure" The following is intended to show that, with a wave-length
of yellow light as a standard, the quantity-if it exists-is easily measurable"
D Using the same notation as befo,"e we have rr=_y _ and
-v
'l\=V~v" The whole time occupied thel"efol"e in going and

.'!..," returning T+'l\=2Dy -v If, howevm", the light had trav"
eled in a direction at right angles to the earth's motion it
would be entirely unaffected and the time of going and return-
ing would be, therefOl"e, 2~=2To" The (lifference between the

times T+'l\ and 2To is

zDY

(

Y

1
'-v

'

-

1 )
Y'

,
= T ; T = 2 D V V. ( ;•.:....v.)

v' 01" nearly 2ToV'" In the time -r the light would t,"avel a dist·

1)'

v'

ance Y-r=2YToV.=2DV'"

That is, the actual distance the light tl"ftvels in the first case
is greater than in the second, by the quantity 2D~."

Considering only the velocity of the earth in its orbit, the

ratI"O vY=100100

approxi"ma1 te y,

1
am

Yv·'=100

0010

000"

If D =

1200 millimeters, or in wave-lengths of yellow light, 2000000,
then in terms of the same unit, 2D~.= 1~O"

If, therefore, an apparatus is so constructed as to permit two

pencils of light, which have traveled over paths at right anglcs

to each other, to interfe,"e, the pencil which has traveled in the

direction

of

the earth's

motion,

will

in

realit"y

travel

~
100

of

a

wave-length fa,"the," than it would have done, were the ea,"th at

rest" The other pencil heing at right angles to the motion

would not be H tll'uLell.

122 A. A. JHc/i,·lson - '/1,e 1'elative mot£on of the Earth

If, now, the appamtus be revolved through 900 so that the

second pencil is brought into the direction of the earth's mo-

tion, its path will have lengthened ~ wave-lengths. The to-

100

8

tal change in the position of the interference bands would be 100

of the distance between the bands, a quantity easily measurable.

The conditions for producing interference of two pencils of

light which had traversed paths at right angles to each other

were realized in the following simple manner.

Light from a lamp a, fig. 1, passed through the plane par-

allel glass plate b, part going to the mirror e, and part being

1.

- reflected to the mirror d. The

mirrors e and d were of plane

glass, and silvered on the front

surface. From these the light

was reflected to b, where the

one was reflected and the other

refracted, the two coinciding

along be.

:::.a_ _ _~9f1l---;{L____---!LCn

The distance equal to bd, and

be being made a plate of glass

U.g being interposed in the path

of the ray be, to compensate for

the thickness of the glass b,

which is traversed by the ray

e

.bd, the two rays wi1l have

traveled over equal paths and al'e in condition to interfere.

'rhe instrument is represented in plan by fig. 2, and in per-

spective by fig. 3. The same letters refer to the same parts in

the two figures.

The source of light, a small lantern provided with a lens,

the flame being in the focus, is represented at a. band g are

the two plane glasses, both being cut from the same piece; d

and e are the silvered glass mirrors; m is a micl'ometer screw

which moves the plate b in the direction be. The telescope e,

for observing the interference bands, is provided with a micro-

meter eyepiece. w is a counterpoise.

Tn the experiments the arms, bd, be, were covered by long

paper boxes, not represented in the figures, to guard against

changes in temperature. 'rhey wem supported at the outer

ends by the pins k, l, and at the other by the circular plate o.

The adjustments were effected as follows:

The mirrors e and d were moved up as close as possible to

the plate b, and by means of the screw m the distances between

a point on the surface of b and the two mi....ors were made

approximately equal by a pair of compasses. The lamp being

and the LWllinIel'olis Ethel'.

123

lit, a small hole made in a screen placed before it served as a point of light; and the plate b, wbich was adjustable in two planes, was moved about till the two images of the point of light, which were reflected by the minol's, coillcirlecl. Then a sodium flame placed at a pl'oduced at once the intcrfel'cnce bands, rrhese could then be altered in width, position, or direction, by 11 slight movement of tlIe plate b, and when they were of convenient width and of maximum sharpness, the

.,<.,.

i, :

:

Fi!J'.2.

I I

I

-----~I
sodium flame was remove(l allel thc lamp again substituted. :;he screw 1n was then slowly tUl'l1ed till the bands reappeared, I hey were then of course colored, except the central band, which was nearly black. The observing telescope had to be focussed on the surface of the mirror d, where the fringes were most distinct. The whole apparatus, including the lamp and the telescope, was movable about a vertical axis,
It will be observed that this apparatus can very easily be

124 A.. 1. Jhchelson-The relative motion of the Earth
made to serve as an "intel'ferential refmctor," and has the two important advantages of small cost, and wide separation of tIle two pencils.
The apparatus as above descriheJ was constructed by Schmidt and Hmnsch of Berlin. It was placed 011 a stone pie]' in the Physical Institute, Berlin. '{'he first observation showed, however, that owing to the ext]'eme sensitiveness of the instrument to vibrations, the work could not be carried on durillg the day. The experiment was next tried at night. 'Vhell the mirrors were placed half-way on thc arms the fringes were visible, hut their position could not he rneasurec1 till aftcr twelve o'clock, ana then only at intervals. 'Vhen the mirrors were moved ont to thc ends of the arms, the fringes were only occasionally visible.
It th us appeared that the experiments could not be performed in Berlin, and the apparatus was accordingly removed
d
to the Astrophysicalisches Obserualoriwn ill Potsdam. Even here the ordinar'y stone piers did not su/lke, and the apparatus was again transferl'ed, this time to a cellar whose circulal' walls formed the foundation for the piel' of the equatoriaL
Here, the fringes uncleI' ordinary circumstances were sufficiently quiet to measure, but so extraordinaril'y sensitivc was the instl'l1rnent that the stamping of the pavement, about 100 meters from the obscl'v[ttory, made the fringes disappear entirely!
If this was the case with the instrument cOllstmcted with a view to avoid sensitiveness, what may we not expect f!'Om one made as sensitive as possible!
At this time of the year, early in Apl'il, the earth's motion in its orbit coincides roughly in longitude with the estimated direction of the motion of the solar s'ystelt1-llamel'y, toward the eonstellatioll Hercules, The direction of this motion is inclined at an angle of about +260 to the plane of the equator,

amt the Lwniniferults Ether.

125

and at this time of the year the tangellt of the earth's motion ill its orbit makes [tIl angle of -23±0 with the plane of the equfltOJ"; hence we may say the I'esultant would lie within 25° of the equator.
rPhe nearer the two components aI'e in magnitude to each other, the more nearly woulel their resultant coincide with the plane of the eq nator..
In this case, if the apparatus be so placed that the arms point north and east at nooI), the arm 'pointing east would coincide with· the resultant motion, and the other would be at right angles. Therefore, if at this time the apparatus be rotated 90°, the displacement of the fl'ioges should be twice
~ or 0'16 of the distance between the fringes.
100
If, on the other hand, the proper motion of the sun is small
compared to the earth':.; motion, the displacement should be To
of '08 or 0'048. Taking the mean of these two numbers as the most probable, we may say that the displacement to be looked for is not far from one,tenth the distance between the fi·inges.
The principal difficulty which was to be feared in making these experiments, was that arising from changes of temperature of the two arms of the instrument. These being of brass whose coefficient of expansion is 0'000019 and having a length of about 1000 mm. 01' 1 700000 wave-lengths, if one arm should have a temperature only one one-hundredth of a degree highet: than the other, the fringes would thereby expel'ience a displacement three times as great as that which would result from the rotation. On the other hand, since the changes of temperature me independent of the direction of the arms, if these changes were not too great their effect could be eliminated.
It was found, however, that the displacement on account of bending of the arms during rotation was so considerable that the instrument had to be returned to the maker, with instructions to make it revolve as easily as possible. It will be seen from the tables, that notwithstanding this precaution a large displacement was observed in one particular direction. That this was due entirely to the support was proved by turning the latter through 90°, when the direction in which the displacement appeared was also (loanged 90°.
On account of the sensitiveness of the instrument to vibration, the' micrometei' screw of the observing telescope could not be employed, and a scale ruled on glass was substituted. The distance between the fringes covered three scale divisions, and the position of the center of the dark fringe was estimated to fourths of a division, so that the separate estimates were
correct to within rt.
It freqL1ently occurred that from some slight cause (among

126 A. A. M£chelson-The relative l1tOt£on vf the Earth

others the springing of the tin lantern by heating) the frillges would suddenly change their position, in which case the series of observations was rejected and a new series begu,n.
In making the adjustment befol'e the third series of observations, the direction in which the fringes moved, 011 moving the glass plate b, was reversed, so that the displacement 111 the third and fourth series are to be taken with the opposite sign.
At the end of each sel'ies the SUppOl't was turned 90°, a11(1 the axis was carefully adjusted to the vel'tical by means of the foot-screws and a spirit level.

N,

-N,-E.

E,
--

S,K
--

S,
--

S,W,
--

W,
--

NW,

Remal'ks,

I st revolution 1)'0 0'0 0'0 -8'0 -1'0 -1'0 -2'0 -3'0 Series I, footscrew

2d " 3d " 4th " 5th "

1.6'0 16'0 16'0 9'0 16'0 16'0 10'0 13'0

17'0 17'0 17'0 10'0 1'7'0 16'0 16'0 17'0

15'0 15'0 15'n 8'0 14'5 14'5 14'0 14'0

13'5 61'0

13'5 61'0

i3'o 61'0

-x5-'0

12'0 58'5

13'0 58'0

13'0 5(;'5

13'0 54'0

marked B. toward East,

S, 58'5 120'0

W, -11586-''O5

N,E, 61'5 S,E. -60-'0

120'0

114'0

Excess,

-118-'0
+2'0

-114-'O
+6'0

1st revolution 10'0 11'0 12'0 13'0 13'0 0'0 14'0 10'0 Serie.~ '~}, B t.oward

2d " 3d " 4th " oth "

16'0 16'0 16'0 17'0 17'0 2'0 ]7'0 17'0 17'0 17'0 17'5 17'5 17'0 4'0 18'0 17'5 17'0 17'(; 17'(1 17'0 17'0 4'0 17'() 17'0
- - 17'0 17'0 17'0 17'0 16'0 3'0 16'0 16'0
78'0 79'0 79'0 81'0 80'0 x 82'0 82'5

SOllth,

S, -80-'5 W, 82'0

158'5

161'5

N,E. -79-'0 S,1£, -81-'5

160'0

164'0

- Excess,

--1361-'0'5

164'0 -4'0

I ...

1st revolution ;J'O 3'0 3'0 iI'O 2'5 2·5 2'5 10'0 Series 3, B toward

2d

"

18'1) 1.7'5 17'5 18'0 18'5 19'0 19'5 26'0 West,

3d " 4th " 5th "

11'0 H'O 13'0 12'0 13'0 13'5 lil'5 21'0 1'0 0'0 0'0 0'0 0'0 0'0 0'0 14'0
- - 4'0 4'0 5'0 5'0 5'0 5'0 5'5 16'0
37'0 35'0 39'0 a8'5 39'0 40'5 71'0 x

S, 39'5 76'0

W, -4810-''00

N,E, 35'5 SIt 38'5

76'0

79'5

Excess,

76'5 +3'5

-7(-;'0
+3'0

'lst revolution 14'0 21'0 15'5 17'0 14'0 14'0 14'5 1(;'0 Series 4, B toward

2d

::

10'0 20'0 12'0 12'0 13'0 13'0 li1'O 13'5 North,

3d "

14'0 25'0 15'0 16'0 16'0 16'0 16'0 17'0

4th 5th

,".

18'O 27'0 IS'5 18'5 IS'5 19'() 20'0 21'0

- - - - - - - - - - 15'0 71'0

-2x4-'0

15'0 76'0

15'0 78'5

15'0 -16-'0
76'5 7S'5

](j'O 79'0

1(;'5 84"0

S, 76'5 W, 79'5

N,E, 73'0 S'K 78'5

14~~

155'5

152'0

162'5

147'5

152'0

Excess,

+S'O

+10'51

awl the Lum£/1 ifel'olls Ellter.

127

The heading of the columns in the table gives the direction

toward which the telescope pointed.

The footing of the erl"Oneous column is marked x, and in the

calculations the mean of the two adjacent footings is sub-

stituted.

The numbers in the columns are the positions of the center

of the dark fringe in twelfths of the distance between the

fringes.

In the first two series, when the footings of the columns N.

and S. exceed those of columns E. and W., the excess is called

positive. The excess of the. footings of N.E., S.W., over

those of N.W., S.E., are also called positive. In the third

and fourth series this is reversed.

The numbers marked "excess" are the sums of ten observa-

tions, Dividing therefore by .10, to obtain the mean, and also

by :..2 (since the numbers are twelfths of the distance between

the fringes), we find for

N.S.
Series I .• _••...•.•• + 0'0 I7
.. 2 ............ -0'025
;1- .. ____ ..... +0'030
4 ........ __ .. + 0'067

N.K,S.W. +0'050 -0'033 +0'030 +0'087

4) 0'089

0'137

Mean

+0'()~2

rfhe displacement is, therefore,

In favor of the columns N.S.... __ ....... __ • +0'022

"

.. N.E., S.W... ______ ... + 0'034

The former is too small to be considered as showing a dis· placement due to the simple change in direction, and the latter should have been zero.
The numbers are simply outstanding enol'S of experiment. It is, in fact, to be seen from the footings of the columns, that the numbers increase (or decrease) with more or less regularity from left to right.
This gradual change, which should not in the least affect the pet'iodic variation for which we are searching, would of itself necessitate an outstanding errol', simply because the sum of the two columns fmthet' to the left must be less (or greater) than the sum of those farther to the right,
This view is ampl'y confirmed b.y the fact that where the ex· cess is positive for the column N.S., it is also positive for N.E., S. W., and where negative, negative. If, therefore, we can eliminate this gradual change, we ma'y expect a much smaller C1't'or. This is most readil'y accomplished as follows:
Adding together all the footings of the four series, the third and fonrth with negative sign, we obtain

~

RK

K

&~

&

&~

~

~~

31'5 31'5

~6'0

24'5

23'0

20'S

18'0 11'0

128 A. A. J11'iclic1son-1'he relative motivil C!l ti,e fj,'a'l'lh, etc.

01' dividing by 20x12 to ohtaill the mcallS ill terms of the distance betweell the fri nges,

N. 0'131

N.K
0'] :ll

E. 0'108

S.K 0'102

S. 0'0%

S.W. 0'08G

W. 0'075

N.W.
0'046

If x is the numbcr of the colnmn cUllllting fl"Om the right and !.I the corresponding footing, tLCll the rnetllOtl of least squal'es gives as the eqnation of tlw stmight lille which passes nearest the points x, !.I-
+ V = 9'25x 64',5

If, now, we construct a curve with ol'llillates efJ.unl to the differencc of the values of V found frolll thc eq uation, and the actual value of ?I, it will rcpresent the r1ic;plaeeltlellts observed, freecl f!"Olll the error in (I uestioll.
'rhese ordinates are:

N.

N.E.

g.

S.E.

S.

S.W.

W.

N.W.

-'002 -'011 +'003 -'001 -'004 -'003 -'001 +'018

N.

-'002

S.

-'004

Mean= -'OOil +'00]

!i:xcess= -·OQ4.

liJ. +'003 W. -'(JOI
+ '001

N.K
S.W.

-'011 -'OO:!

Mean= -'007 + '008

Excess=-'OllJ

N.W. +'018 S.I·;. -'001
+'008

'rhe small displaceillents -0'004 and -0'015 are simply errors of experiment.
The results obtftined are, however, Illore strikingly showll by constructing thc actual cUI've togethcl' with the curve that should have been fOHn!1 if the theory had been COlTect, This is shown in fig, 4.
4.

j 0.0'

___ ---'

o.oo~

"""

0.05 t----

"'",-----,//

The dotterl Cl1l've is dmwn on the supposition that the displacement to be expecte(l is one·tenth of the distance betwecn
the fringes, but if this displacement were only Th, the broken
line would still coincide more nearly WIth the straight line than with the Clleve.
The intel'pl'etalion of these results is that thCl'e is no displacement of the illterferenee bamhi. The rcsult of the hypothesis of a stational'y ethel' is thus shown to be incoreect, and tIle necessary conclusion follows that the hypothesis is
el'eoneous. This conclusion dieeetly contradicts the explanation of the
phcllomenon of aberration which hac; been hitheeto generall'y accepted, and which presupposes that the earth moves thl'Ough tbe ether, the latter remaining at rest.

129
It may not be out of place to add an extract from an article published ill the Philosopllical Magal':ine by Stokes in 1846.
" All these results would follow immediately from the theory of abelTation which I pl'Ojlosed in the July number of this magazine: nor have I been able to obtain any result admitting of being compared with experiment, which would be different according to which theory we a(lopted. rl'his affords a cmiolls instance of two totally difl"et'ellt tbeories running pandlel to each other in the explanation of phenomena. I do not sup' pose that many would be disposed to maintain Fresnel's tbeory, when it is shown that it may be dispensed with, inasmuch as we would not be disposed to believe, without good evidence, that the ether moved quite freely throngh the solid mass of the earth. Still it would have been, satisfactory, if it had been possible to have put the two theories to the test of some decisive experiment"
In conclusion, I take this opportunity to thank Mr. A. Gra· ham BelL who has provided the means for canyillg out this work, and Professor Vogel, the Director of the ASI'l'ophysi· calisches Observatorium, for bis courtesy in placing the resources of his laboratory at my disposal.