The relative Motion of the Earth and the Ether
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 planeparallel 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 are planeparallel 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 fringewidth.
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 may be 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: .
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 
The conclusion from these results is that if there is any displacement of the fringes it is less than onetwentieth 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 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 fringes.
If the relative motion be assumed to follow an exponential law it may be represented by
where is the velocity of the earth and h, the height above the surface.
Suppose falls to of its surface value in one hundred kilometers. Then in fifteen meters, which is the difference of level of the two horizontal pipes
Substituting this for v in the equation for we have
Putting and we find 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:—
 The earth passes through the ether (or rather allows the ether to pass through its entire mass) without appreciable influence.
 The length of all bodies is altered (equally?) by their motion through the ether.
 The earth in its motion drags with it the ether even at distances of many thousand kilometers from its surface.
 ↑ This Journal, November, 1887.
 ↑ 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.
 ↑ 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.
 ↑ "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.