CONFERENCE ON MICHELSON-MORLEY EXPERIMENT 347 This has the same value for all paths, and the condition (2) becomes simply ## a C
| 34^ 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 w |