CONFERENCE ON MICHELSON-MORLEY EXPERIMENT 397
was right, his observations were spoiled by temperature effects. His errors were thirty times greater than the effect he was looking for. The second time he got rid of his errors, but there was no effect to be expected at the sidereal time chosen for this observation.
Miller: I agree with Hedrick that the theory of the instrument used for the experiments should be thoroughly studied. The theory of Lorentz is exact ; but it is general, and does not take into account the special conditions of the apparatus used. What actually happens to the fringes is dependent on the adjustment of the mirrors. When I became interested in the experiment in 1900, there existed no really adequate theory of the instrument. A theoretical study of the apparatus was then undertaken by W. M. Hicks, which was published in the Philosophical Magazine for January, 1902. We [Miller and Morley] thought it necessary to take up the question again, as Hicks had suggested that there was an additional term in the expression for the effect which had not previously been considered. This term represents an effect of appreciable magnitude, which is periodic in each full turn of the interferometer, while the ether-drift effect is periodic in each half-turn. In the Philosophical Magazine for May, 1905, we gave a review of the theory, showing that Hicks’s calculations did not affect the conclusions previously drawn. The full-period effect is actually present in the experiments of 1887, as well as in all those that have followed. In Comptes rendus, 168, 837, 1919, Righi began a series of articles, setting forth the theory in detail. He thought that our conclusions were not justified by the theory. It seems to me that Righi’s theory is correct in the abstract; but it does not deal with the actual things happening in the interferometer, as Hicks’s theory does. The question needs still further investigation, as suggested by Professor Hedrick. Hicks’s theory takes into account the fact that in practice the image c (Fig. 23) of mirror a with regard to a is slightly oblique to mirror b. This is necessarily true when straight-line fringes of finite width are obtained. Righi’s calculations are based on the assumption that b and c are exactly parallel, which would produce fringes of infinite width; thus, his criticism does not apply to the actual case. When b and c are oblique to each other, an actual ether drift will produce the additional effect predicted by Hicks, which is periodic in a full turn of the apparatus. Hicks has calculated its magnitude, showing that it
39^
DISCUSSION
depends on the angle between b and c. The effect increases with increasing angle and decreasing width of fringes. As the effect we are looking for (ether drift) must be periodic in each half-turn, we are justified in eliminating the full-period effect. This is done by plotting the single observations, turn by turn of the interferometer; these curves are analyzed by the mechanical harmonic analyzer, and the second harmonic (half-turn effect) is taken as representing the ether drift. If there is an ether-drift effect, the full-turn effect is
necessarily produced, according to Hicks, and its presence may be taken as further evidence of the ether drift. The magnitude and phase of the full-period effect is variable, because it depends upon the adjustment of the mirrors as well as the ether drift. [Slides were shown representing the full-period effect.] It is evident that the magnitude is very different for different sets of observations. The half-period effect, on the other hand, is characterized by a constant magnitude. The full-period effect is small when the width of the fringes is such that five of them cover the mirror (10 cm in diameter). Under other conditions, however, it may be very large. The full-period effect is not new, but has always been present in all the experiments. It is present in Professor Michelson’s original observations.
Kennedy: Are the effects the same in case you use a concrete frame instead of an iron frame?
Miller: Yes, they are essentially the same. The concrete instrument showed smaller temperature effects than did the one with the steel frame, but its mechanical strength was also less. I have always used (as did Kennedy) the method of shifting the fringes by putting weights on the end of the frame; to produce a shift of one fringe, approximately 325 g was necessary. This is less than the corresponding weight in Dr. Kennedy’s apparatus, because
Fig. 23