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DISCUSSION
order effect would be different from that which Michelson calculated. My procedure seems to me still to be the easiest and most straightforward one. Still it must be found out where the discrepancy between the two ways lies. In case a method other than Fermat’s is chosen, one has to do considerable work. One must distinguish, for instance, very carefully between the rays of light and the normals to the wave trains. Another difficult point is involved in the treatment of the reflection from moving mirrors. Fermat’s principle, of which I have made use, gives in any case a much simpler treatment. But as there exists a discrepancy between the results obtained by the two methods, I intend to go through the detailed calculations as soon as possible. In the meantime I still hope, of course, that my general considerations are right.
I should now like to make some remarks on Mr. Miller’s experiment. It seems to me that there is a serious problem connected with the effect which is periodic for a full turn of the apparatus and which is discarded by Mr. Miller, who emphasizes the importance of the half-period effect (periodic with half-turns of the apparatus) in regard to the question of an ether drift. In many cases the full-period effect is much larger than the half-period effect. According to Mr. Miller, the full-period effect is dependent on the width of the fringes and would become zero for infinitely wide fringes.
Although Mr. Miller says that he was able to eliminate this effect to a great extent in his Cleveland measurements, and that it is to be explained easily by the experimental arrangement, I should like to understand its cause somewhat more clearly. Speaking now for a moment as an adherent of the relativity theory, I should contend that no such effect whatever could exist. Indeed, a rotation of the entire apparatus as a whole, the source of light included, should not give any shift at all from the standpoint of relativity. No effect would be expected were the earth and the apparatus at rest. According to Einstein, then, the same absence of an effect is to be expected for the moving earth. The full-period effect is thus in contradiction with the theory of relativity and of main importance. If then Mr. Miller has found some systematic effects whose existence cannot be denied, it is also important to know the cause for the full-period effect.
CONFERENCE ON MICHELSON-MORLEY EXPERIMENT 391
Let us discuss now the half-period effect. After having seen the different diagrams I think there can hardly exist any doubt that there is an actual displacement of the fringes with Mr. Miller’s setup. There arises, then, the question as to its possible cause. Mr. Miller himself has offered some suggestions which are very interesting. His conclusion is that the effect found corresponds to an absolute velocity of 10 km/sec. and for a definite sidereal time is the same throughout the year. It is certainly not connected with the orbital motion of the earth, but indicates a motion of the solar system relative to the stellar system of the same kind as found by Mr. Strömberg from a quite different point of view. The velocity of this motion is estimated to be at least 200 km/sec. For some reason or other, the full relative velocity between ether and earth
does not come into action. Otherwise, one cannot account for the lack of an effect related to the orbital motion of the earth. There is, however, the following point to be mentioned. One could assume as Mr. Miller does that the entrainment is only partial, because the earth, for instance, is not completely impermeable to the ether.' But then the following consideration would have to be taken into account. Suppose w to be the velocity of the earth relative to the ether (which is at rest at C). Then if the ether behaves as an ideal fluid, there will be a relative velocity in it at A with respect to B amounting to w/z. Miller accounts for the daily variation in amplitude of his effect, in a way which is immediately understood from Figure 20. According to the consideration given above, however, w could not be considered as a vector of constant length but would itself vary during one day. This would of course make the interpretation of the drift more complicated.
Fig. 19
my vacation Fig. 20