344
A. A. MICHELSON
and back. If white light is used, the central fringe will be white and the side fringes will be colored. A motion of the apparatus with the velocity w through the ether should have much the same effect on the light as a stream of water would have on a boat trying to go once forth and back across the stream, and once down and then back up the stream. The time for getting forth and back a given distance will be different for the two cases. This is easily seen, because, however swift the current, the boat in its transverse journey could always return to the bank from which it started, whereas, in the second case, it might be unable to get back up stream against the current.
I tried the experiment at Berlin in Helmholtz’ laboratory, but the vibrations of the city traffic made it impossible to get steady fringes. The apparatus was transferred to the observatory at Potsdam. I have forgotten the name of the director (I think it was Vogel), but I remember with pleasure that he was immediately interested in my experiment. Though he had never seen me before, he put the whole observatory with its staff at my disposition. I got a zero result in Potsdam. The accuracy was not very high, because I had a light-path of only about i m. Still it is interesting that the results were quite good. Coming back to America, I had in Cleveland the good fortune to secure the co-operation of Professor Morley. The apparatus then used was the same in principle as that used in Berlin, although the light-path was made longer by introducing a number of reflections instead of a single one. The path was in fact about io-ii m long, which should have yielded a displacement of half a fringe, due to the orbital motion of the earth. But no displacement was found. The shift of fringes was certainly less than 1/20 and may be even 1/40 of that predicted by the theory. The result could be accounted for by the assumption that the earth drags the ether along nearly at its full speed, so that the relative velocity between the ether and the earth at the surface is zero or very small. This assumption, however, is a very dubious one because it contradicts some other important theoretical considerations. Lorentz then suggested another explanation (Lorentz contraction) which in its final form yielded as a result the famous Lorentz transformation equations. These contain the gist of the whole relativity theory. The Michelson-Morley experiment was continued by Morley and
CONFERENCE ON MICHELSON-MORLEY EXPERIMENT 345
Miller, who again obtained a negative result. Miller then continued alone, and seems now to get some positive effect. This effect, however, has nothing to do with the orbital motion of the earth. It seems to be due to a velocity of the solar system relative to stellar space, which may be much greater than the orbital velocity.
The observations of Mr. Miller have stimulated new interest in the problem. An excellent piece of work has already been done by Mr. Kennedy, whose report you will hear. I intend myself to go over the experiments again, but several months may pass before I shall be able to give my results, which, I hope, will shed more light on the subject.
n. PROFESSOR H. A. LORENTZ (LEIDEN, HOLLAND)
The motion of the earth through a hypothetical ether (talking in historical terms) might have an effect on different phenomena. The first relevant phenomenon found experimentally was the aberration of fight. It was discussed on the basis of the emission theory and also on the wave theory in the form Fresnel had given it. From Fresnel’s point of view we may argue as follows: We draw our diagrams in a system of co-ordinates which is fixed to the earth. In this system all ponderable matter is at rest. But the ether may move through it. Say the velocity of the ether is w. If the ether does not move, then the velocity of light through matter would be u = c//j, (/x = index of refraction ; c = velocity of light). Now let an elementary wave be formed around P. This after the time dt will be a sphere of radius udt. The center 0 of this wave will, however, not coincide with P, being displaced over a distance kwdt, where i—k is FresnePs coefficient 1 —1 /m2 = P- Thus k = i/p2. PQ is a ray of light. (We denote by v the velocity of the rays of light.)
We have then from Figure 4, in which PQ = vdt, PO = kwdt, and OQ = udt, the relation
PQ:PO:OQ = v:kw:u. p 0
Thus
U2 = V2-\-k2W^—2kv COS Û (1) IG’ 4
The derivation of this formula is based on Huyghens’ principle and FresnePs entrainment. Huyghens’ principle can be used in any