# The relative Motion of the Earth and the Ether

The relative Motion of the Earth and the Ether
by Albert A. Michelson

To account for the phenomenon of aberration Fresnel supposes the luminiferous ether at rest, the earth moving through this medium without communicating any perceptible part of its motion. On this theory it has been shown[1] that it should be possible to detect a difference of the velocity of light in two directions at right angles. As no such difference was observed, it would seem to follow that Fresnel's hypothesis is incorrect.

Another theory is that of Stokes, in which the aberration is accounted for if the relative velocity of the earth and the ether have a potential. This requirement, however, is inconsistent with the results of the experiment just cited, which indicates that at the earth's surface the relative motion is zero.

In the hope of detecting a relative motion corresponding to a difference of level, the following experiment was undertaken.

I take this opportunity of gratefully acknowledging the faithful and efficient services rendered in the execution of this work by Professor S. W. Stratton and Mr. C. R. Mann.

Light from the source s, a calcium light or an electric arc lamp, separated into two pencils at a plane-parallel glass plate, o, lightly silvered. The two pencils were reflected by double mirrors along the paths oabcoe, and ocbaoe, respectively. The two paths being equal, interference fringes could be observed with the aid of the telescope at e. Fig. 2 shows details of the corner at ${\displaystyle c:pq}$ are plane-parallel glass disks, cemented to the ends of the iron pipes; mn, plane glass plates silvered on front surface, and provided with adjustments in two planes; omnb. the path of the pencil of light. The apparatus was set up in the vertical east and west plane, the light traversing the entire circuit of the Ryerson Laboratory, a path about 200 feet long and 50 feet high.

It was found that under ordinary conditions the temperature disturbances in this length of air made it impossible to measure the position of the fringes; and the difficulty was only slightly remedied by enclosing the whole path of the light in a wooden box. By making this enclosure an iron pipe and exhausting the air to within a hundredth of an atmosphere, it was found possible to measure the position of the central bright fringe to within something like a twentieth of the fringe-width.

A difficulty is encountered in the selection of a fiducial mark. The double image of the source does not remain on the cross hairs of the observing telescope for any great length of time, notwithstanding the precaution of the double reflections at the corners, but by using this double image itself as the fiducial mark, any possible errors due to daily temperature changes, etc., are eliminated. This double image and the interference fringes are not in focus at the same time, but by sacrificing a very little in the definition of each, the measurements maybe made with very considerable precision.[2]

The observations were taken in the morning, at noon, evening and night; no special care being taken as to the exact hour. The results are summed up in the table containing the observations taken and reduced by Mr. Mann, as follows:—

The micrometer was set on one spot, then on the central fringe, then on the other spot, giving three readings of the micrometer. The first reading was subtracted from the third, giving the distance between the spots in divisions of the micrometer head. The second reading was subtracted from the third, giving the distance of the central fringe from the lower in divisions of the micrometer head. This last remainder was divided by the first, giving the distance n of the central fringe from the lower spot in fractions of the distance between the spots regarded as unity.

Each reading was reduced this way and the mean of ten taken as the result for any given time. The weights p were calculated as usual from the formula: ${\displaystyle p=c/e^{2}}$.

 Date. 6 A.M. 12 Noon. 6 P.M. 11 P.M. n p pn n p pn n p pn n p pn March 11 .500 67 33.50 .515 40 20.60 .503 12 6.03 .480 20 9.60 .513 38 19.49 .506 10 5.06 .490 32 15.68 March 13 .495 11 5.44 .530 33 17.49 March 16 .507 55 27.88 .490 50 24.95 .492 13 6.40 .479 60 28.74 .509 120 61.08 .491 45 22.09 .488 40 49.52 .487 22 10.71 March 17 .490 40 19.60 .504 80 40.32 .500 35 17.50 .488 105 51.24 .488 50 24.40 .502 60 30.12 .498 30 14.94 .496 100 49.60 March 18 .501 80 40.08 .492 80 39.36 .493 40 19.72 .498 25 12.45 .507 50 25.35 .488 25 12.20 .498 35 17.43 Sums. 461 231.47 438 220.28 205 101.37 399 195.45 Means .502 ± .002 .503 ± .003 .494 ± .002 .490 ± .002

12 Noon - 11 P. M. = .013
1 fringe = .250      ${\displaystyle \therefore }$ maximum displacement ${\displaystyle {\frac {13}{250}}={\frac {1}{20}}}$ fringe.

The conclusion from these results is that if there is any displacement of the fringes it is less than one-twentieth of a fringe.

If we consider the times occupied by the two pencils in completing their paths at noon and at midnight (when the horizontal parts of the path are parallel with the earth's motion in its orbit), we find the difference is ${\displaystyle 4s{\frac {v}{V^{2}}}}$ where s is the length of the horizontal part of the path, v the difference of relative velocities above and below, and V the velocity of light. This corresponds to a displacement ${\displaystyle \Delta =4{\frac {s}{\lambda }}{\frac {v}{V}}}$ fringes.

If the relative motion be assumed to follow an exponential law it may be represented by

${\displaystyle v=v_{0}(1-e^{-kh})}$

where ${\displaystyle v_{0}}$ is the velocity of the earth and h, the height above the surface.

Suppose ${\displaystyle {\frac {v_{0}-v}{v}}}$ falls to ${\displaystyle {\frac {1}{e}}}$ of its surface value in one hundred kilometers. Then in fifteen meters, which is the difference of level of the two horizontal pipes

${\displaystyle v_{0}-v_{1}=.00015\ v_{0}}$.

Substituting this for v in the equation for ${\displaystyle \Delta }$ we have

${\displaystyle \Delta =.0006{\frac {s}{\lambda }}{\frac {v_{0}}{V}}}$.

Putting ${\displaystyle {\frac {s}{\lambda }}=12\times 10^{7}}$ and ${\displaystyle {\frac {v_{0}}{V}}=10^{-4}}$ we find ${\displaystyle \Delta =7.2}$ fringes.

As the actual displacement was certainly less than a twentieth of a fringe, it would follow that the earth's influence upon the ether extended to distances of the order of the earth's diameter.[3]

Such a conclusion seems so improbable that one is inclined to return to the hypothesis of Fresnel and to try to reconcile in some other way the negative results obtained in the experiment cited in the first paragraph.

The only attempt of this character is due to H. A. Lorentz.[4] It involves the hypothesis that the length of bodies is altered by their motion through the ether.

In any case we are driven to extraordinary conclusions, and the choice lies between these three:—

1. The earth passes through the ether (or rather allows the ether to pass through its entire mass) without appreciable influence.
2. The length of all bodies is altered (equally?) by their motion through the ether.
3. The earth in its motion drags with it the ether even at distances of many thousand kilometers from its surface.

1. This Journal, November, 1887.
2. On account of the inequality of the angles of incidence and reflection there will be a slight difference between the real and apparent positions of the double image. This difference will be altogether too minute to produce any appreciable error. Again, this difference in direction produces a difference in the length of the two paths—which is however of the second order and can also be neglected.
3. Of course this will depend on the law assumed for the rate of diminution of relative velocity with distance from the earth's surface; and possibly an exponential law is far from the truth. It may be desirable to repeat the experiment with a much greater difference of level, and perhaps to bury the lower tube some distance underground.
4. "Versuch einer Theorie der El. u. Op. Erscheinungen in bewegten Körpern," H. A. Lorentz.

This work is in the public domain in the United States because it was published before January 1, 1923.

The author died in 1931, so this work is also in the public domain in countries and areas where the copyright term is the author's life plus 80 years or less. This work may also be in the public domain in countries and areas with longer native copyright terms that apply the rule of the shorter term to foreign works.