In general the two sets of fringes will not coincide in position, entirely aside from any question of ether drift or the earth’s rotation, unless the two direct images and the two reflected images of the source are exactly superposed. The central fringes of the set formed by the mirrors of the short circuit will be halfway between the direct and reflected images of the source, and the central fringe of the long line would be halfway between the direct and reflected images if there were no difference due to the earth’s rotation.
To correct for any lack of superposition of the two sets of rays, the observing telescope (a six-inch achromatic objective, and two-inch micrometer eyepiece) was focused on the images of the source (arc or slit) and the apparent displacement of the central fringe of the long circuit, compared with the central fringe of the short circuit, was corrected by an amount equal to the difference in the mean positions of the two images for the two light circuits. The fringes are most conveniently observed in the overlapping cones of light an inch or so inside or outside of the focal plane.
About half of the determinations were made with the arc placed directly in front of the window at A, and about half with a condensing lens, slit, and collimating lens. The second arrangement gave much more light than the first, but there was no apparent difference in the measured displacements.
The calculated value of the displacement on the assumption of a stationary ether as well as in accordance with relativity is
where A is the displacement in fringes, A the area in square kilometers, φ the latitude (41°46′), V the velocity of light, ω the angular velocity of the earth, and X the effective wave-length of the light used. Measurements were made in the laboratory, comparing the fringes produced by the same set of mirrors and the same 20-ampere alternating-current arc, with fringes produced by sodium light from a bit of glass in an oxyhydrogen flame. The light from the arc was reduced to approximately the same intensity as in the experiment at Clearing, by transmitting it through a rather narrow slit in a
rotating disk. The mean of ten determinations gave λ = 5700± 50 angstroms.
The displacement of the fringes due to the earth’s rotation was measured on many different days, with complete readjustments of the mirrors, with the reflected image sometimes on the right and sometimes on the left of the transmitted image, and by different observers. The deflections were averaged usually in sets of twenty, in the order in which they were taken. The resulting means are given in Table I. The entire set of two hundred and sixty-nine determina-
TABLE I
|
Observation* |
Displacement in Fringes |
Number of Observations |
Deviation from Mean |
|
1 |
0.252 |
20 |
0.022 |
|
2 |
.255 |
20 |
.025 |
|
3 |
.193 |
20 |
.037 |
|
4 |
.246 |
20 |
.016 |
|
5 |
.235 |
20 |
.005 |
|
6 |
.207 |
26 |
.023 |
|
7 |
.232 |
20 |
.002 |
|
8 |
.230 |
20 |
.000 |
|
9 |
.217 |
20 |
.013 |
|
10 |
.198 |
20 |
.032 |
|
11 |
.252 |
20 |
.022 |
|
12 |
.237 |
20 |
.007 |
|
13 |
0.230 |
23 |
0.000 |
|
Mean 0.230 |
Total 269 |
Av. dev. from Mean 0.016 |
* Observations 1 and 2 corrected for direct image only; 1-6 inclusive, without collimator; 7-13 inclusive, with collimator.
tions and their distribution about the mean value is shown graphically in Figure 3. The final displacement, expressed as a fraction of a fringe, is
0.230±.005 obs. 0.236±.002 calc.
In view of the difficulty of the observations, this must be taken to mean that the observed and calculated shifts agree within the limits of observational error.
The successful completion of this experiment is due in no small measure to the friendly co-operation of the officials of the City of
|
Obs. |
Calc. | |
|
Displacement... |
0. 230± .002 |
0. 236± .002 |