372
ROY J. KENNEDY
Now
Similarly,
Therefore
dlx , 47rka2 . 47ra d# X X
dl2 —dirka2 . 4xa -r-= - sin .
dx X X
. I"87rka2 . 47ral .
a7=±b^sinVr’
the sign being of no importance.
The perceptibility of the variation is determined not by 37 alone, but by the ratio of 37 to the total intensity, 7t or I2. According to the Weber-Fechner law, if hi is taken to be the least perceptible variation in intensity, the foregoing ratio is nearly constant for a considerable range of intensities. With this meaning of 37, Sx becomes the least detectable change of position of M2.
If initially we have uniformity of illumination, we have from the equations above,
. 47ra
37 8tt
^ = ÔX
I X , 47ra
I ± COS -7—
or
47ra
, X 8/,±COS X
bx = — —
8w I . 4xa sin ——
If now 37/7 were a true constant, we should have for the case of negative sign, which corresponds to dim illumination of the field, the sensibility of the apparatus increasing indefinitely as the factor a was made smaller. 7 decreases with a, however, and the Fechner “constant” soon diminishes rapidly. Nevertheless, the conditions of illumination and contrast here are similar to those in the halfshade polariscope, and from the theory of the Lippich instrument it appears that 37/7 equals about 8X10“3. The lack of perfect planeness in the mirrors and of equality of intensity in the interfering beams is a further limiting factor; a little experimenting indicated
CONFERENCE ON MICHELSON-MORLEY EXPERIMENT 373
that a should not be much less than 0.025 X, which was the value finally used. Substituting these values in the last equation, we get
ôx = 5Xio“s\
as the least detectable change in position of one of the mirrors. This corresponds to a change of optical length of path
81= 20x= io-4 X .
To take full advantage of the possibilities of the arrangement would have required perfect mirrors and an intenser and, therefore, hotter source of light than would have been desirable near the sensitive apparatus, as well as lengthening the interval between observations, thus allowing greater chance for any steady temperature shift to show itself. No attempt was made in the experiment, therefore, to go below values of hi equal to 2 X io“3 X; such variations were detectable without the least uncertainty.
With this apparatus the velocity of 10 km/sec. found by Professor Miller would produce a shift corresponding to 8X10-3 wavelengths of green light, which is four times the least detectable value.
The experiment was performed in a constant-temperature room in the Norman Bridge Laboratory at various times of day, but oftenest at the time when Miller’s conclusions require the greatest effect. The sensitiveness of the eye was tested for each trial by the placing or removal of a small weight on the slab before and after rotating it. There being no fluctuations in the field of view, it was unnecessary to take the average of a number of readings. As has been shown, a shift as small as one-fourth that corresponding to Miller’s would have been perceived. The result was perfectly definite. There was no sign of a shift depending on the orientation.
Because an ether drift might conceivably depend on altitude, the experiment was repeated on Mount Wilson, in the 100-inch telescope building. Here again the effect was null.
[Note added April, 1928.—Illingworth at the California Institute of Technology has continued the work with Kennedy’s apparatus, using improved optical surfaces and a method of averaging. He concludes1 that no ether drift as great as 1 km/sec. exists.]
1 Physical Review, 30, 692, 1927.