270 Prof. Challis on a Theory of the Disjiersion of Light* 



effective accelerative force of the aether. Hence putting /c' 2 « 2 / 

 for the latter force, K/c' 2 aY for the retarding force, and K 2 crf for 

 the accelerative force of the sether due to the actual variations 

 of density, we have 



a:'V/=A 2 /-K^V/, or *' 2 (1 + K) = ^. 



Putting, therefore, /jl for the ratio of k to k', which is the ratio 

 of the rate of propagation outside the medium to the rate within, 

 it follows that 1 + K=^ 2 . Hence, since the retardation must 

 vary ceteris paribus as the number of atoms in a given space 

 (that is, as the density of the medium), if we put 8 for the den- 

 sity, and HS for K, we get/^ 2 = l -fHS. The constant K, being 

 by hypothesis the same for different parts of the same wave, will 

 also be the same for waves of different breadths. 



In this reasoning the atoms are regarded as fixed. Supposing, 

 as must be the case, that they are moveable about their mean 

 positions of equilibrium, the retardation due to the reflections 

 from each atom will be altered in the ratio of the velocity of the 

 sether relative to the atom to the actual velocity of the sether. 

 That is, x being the distance at the time t of the centre of the 

 atom from a fixed plane perpendicular to the direction of the 

 propagation of the waves, and V the velocity of the sethereal par- 

 ticles at that distance, we shall have 



the medium being supposed at present to be a simple one. In 



order, therefore, to obtain a formula for /jl it is necessary to cal- 



, . due 

 culate -=-« 



dt dx 



Now the velocity -=- of the vibrating atom may be considered 



to result from three different actions : — (1) the distribution about 

 the surface of the atom of the condensation and pressure due to 

 the incidence of a given series of sethereal waves, which, in fact, 

 is the primary cause of its movement ; (2) the resistance of the 

 sether to the motion of the atom ; (3) the action of the proper 

 molecular forces of the medium called into play by the displace- 

 ment of the atom. In my original researches I supposed that 

 the first of these actions depended on the relative motion of the 

 atom and the sether ; but afterwards it occurred to me to reason 

 as follows. The atom being supposed to have a vibratory mo- 

 tion from any cause, conceive to be impressed upon it and upon 

 the whole of the fluid at each instant this motion in the opposite 

 direction. The atom will thus be brought to rest ; and as the 

 motion and propagation of the waves will in no manner be 



