810 Prof. H. A. Wilson on the Relative 



produce, at any rate, second order optical effects, so that such 

 motion, if it exists, will be extremely difficult to detect. 



If we do not admit that bodies change in length when set 

 in molion relatively to the sether, then the experiments such 

 as Michelson and Morley's referred to above *, in which the 

 apparatus was turned about a vertical axis, show that at the 

 surface of the earth the motion of the sether relative to the 

 earth has no component in a horizontal plane. Let us regard 

 the earth as at rest and suppose that the velocity of the aether 

 at a great distance away is parallel to the axis of x and equal 

 to v. Take the centre of the earth as the origin and denote 

 its radius by a. We require then to find a distribution of 

 velocity having a velocity potential (</>) such that <j> r=a is a 

 constant and that when r = 00 —dfyjdx — v, dcj)/di/ = d(p/dz = 0. 



Regarding the sether as an incompressible fluid, it will be 

 seen at once that this problem is precisely analogous to the 

 problem of finding the electric field in the space surrounding 

 a conducting sphere placed in an electric field which is 

 uniform at a great distance from the sphere. The solution is 



(f) — v(a^/r 2 — r) cos 6, 

 where is the angle between r and the axis of x. 



At the surface of the sphere cf> = 0, so that the velocity has 

 no component parallel to the surface while 



— d(p/dr r=za = 3« cos $> 

 so that the velocity perpendicular to the surface varies from 

 3v where = to where = 7r/2. It appears, therefore, 

 that the stream-lines crowd into the earth just as the lines of 

 electric force crowd into a sphere of very high specific 

 inductive capacity or into a conductor. It will now be 

 shown that a physical explanation of this crowding in of the 

 stream-lines can be given which is consistent with some 

 modern ideas as to the nature of matter. 



Let us suppose that the sether near an atom is in motion 

 as though the atom contained a point source of sether and a 

 point sink of equal strength, so that the sether entering the 

 atom at the sink comes out again at the source. If the source 

 and sink are very near together they will form a doublet. 

 We may, if we like, imagine many such doublets in each 

 atom. 



It is easy to see that two sources will move away from 

 each other, and by considering the hydrodynamical analogue 

 of the Cavendish experiment in electrostatics it is easy to 

 prove that the force between them is inversely proportional 



* Other such experiments are those of Rayleigh and Brace : also 

 Trouton's experiments on a suspended charged condenser, and on the 

 resistance of a wire. 



