E. A. LORENTZ
beams. This effect has been observed by Professors Michelson and Gale.
In the following there will be no question of the rotation of the earth; the annual aberration only will be considered. For the explanation of this the foregoing considerations suffice. If, at a point at some distance from the earth, the direction of the rays coming from a star is given in a system of co-ordinates in which the earth is moving, one can deduce from that the direction of the rays in a system of co-ordinates fixed to the earth, and the further course of these relative rays is determined by the ordinary laws of optics.
We proceed with the discussion of some special theories. In Fresnel’s theory the ether is supposed to be at rest; its motion relative to the earth may be considered as a uniform translation, which, obviously, is irrotational. It is necessary to introduce the dragging coefficient because the ether moves through the ponderable bodies (lenses) contained in our instruments of observation.
Stokes proposed a theory in which the ether was supposed to have an irrotational motion, such that at all points of the earth’s surface its velocity is equal to that of the earth. By this latter assumption he could avoid the introduction of Fresnel’s coefficient.
However, at least when the ether is supposed to be incompressible, Stokes’s assumptions contradict each other. If a sphere moves with a constant velocity in an incompressible medium, the motion of the medium is completely determined by the condition that it is irrotational and that, in the direction of the normal to the surface, a point of the sphere and the adjacent medium have the same velocity. In a tangential direction the two velocities will necessarily be different.
So far as aberration is concerned, a modification of Fresnel’s theory is certainly admissible. When we admit his value of the dragging coefficient, we may assume the existence of any motion of the ether, provided that it be irrotational. In fact, this is a necessary condition. Suppose, for instance, that over a part of the earth’s surface which may be considered as plane the ether flows in a horizontal direction x with a velocity wx increasing with the height y above the earth. This motion would not be irrotational and would not lead to the observed aberration. Since the existence of a velocity
CONFERENCE ON MICHELSON-MORLEY EXPERIMENT 349
potential requires the equality of the derivatives dwx/dy and dwv/dx, the observed aberration can exist only when, in addition to the supposed motion in a horizontal direction, there is a vertical velocity of the ether of sufficient magnitude, varying from one point of the surface to the other.
So far there was question of first-order effects only, i.e., of effects that would be proportional to the first power of the ratio between the velocity of the earth and the speed of light. In almost all cases in which astronomers and physicists have tried to detect an influence of the earth’s motion on optical and electromagnetic phenomena, only effects of this order of magnitude could have been observed. The fact that all these attempts have been fruitless, and that this could be accounted for by theoretical considerations of the kind just preceding, led by and by to the conviction that the motion of the earth can never produce a first-order effect. This conviction was greatly strengthened when Einstein developed his theory of relativity and simply postulated that the result of all experiments which we perform in our laboratories must be independent of the motion of the earth, whatever may be the refinement of our measurements and the order of the effects which we can reach by them. To the experimental evidence which we already had, the charm of a beautiful and self-consistent theory was then added.
. Historically, I might add that before the relativity theory was developed the situation was somewhat similar to that which now characterizes the quantum problem. There were, of course, not so many people working in the field as there are now. Nevertheless, we had often very lively discussions about the subject. I remember especially the assembly of the German Society of Natural Sciences in Düsseldorf in 1898, at which numerous German physicists were present, Planck, W. Wien, Drude, and many others. We discussed especially the question of the first-order effects. Some devices with which such an effect might be observed were proposed, but none of these attempts was ever made, so far as I know. The conviction that first-order effects do not exist became by and by too strong. We even got, finally, into the habit of looking only at the summary of experimental papers which dealt with such effects. In case the result was properly negative we felt perfectly satisfied.