through Space occupied by Ether. 183 



(5) in (3) we find 



and the components of the resultant force are still expressed 

 by (2). We may suppose a to be either positive or negative 

 (positive for attraction and negative for repulsion) ; and in 

 fact in our first and simplest illustration of the problem we 

 suppose it to be positive in some parts and negative in other 

 parts of the atom, in such quantities as to fulfil the condition 



lff A "=° (7). 



§ 5. As a first and very simple illustration, suppose the 

 atom to be spherical, of radius unity, with concentric interior 

 spherical surfaces of equal density. This gives, for the 

 direction of the resultant force on any particle of the ether, 

 whether inside or outside the spherical boundary of the atom, 

 a line through the centre of the atom. The further assump- 

 tion of (7) may now be expressed by 



i 



drr 9 -cc = 0. . (8); 



and this, as we are now supposing the forces between every 

 particle of the atom and every particle of the ether to be 

 subject to the Newtonian law, implies, that the resultant of 

 its attractions and repulsions is zero for every particle of 

 ether outside the boundary of the atom. To simplify the 

 case to the utmost, we shall further suppose the distribution 

 of positive and negative density of the atom, and the law of 

 compressibility of the ether, to be such, that the average 

 density of the ether within the atom is equal to the un- 

 disturbed density of the ether outside. Thus the attractions 

 and repulsions of the atom in lines through its centre pro- 

 duce, at different distances from its centre, condensations 

 and rarefactions of the ether, with no change of the total 

 quantity of it within the boundary of the atom ; and there- 

 tore produce no disturbance of the ether outside. To fix 

 the ideas, and to illustrate the application of the suggested 

 hypothesis to explain the refractivity of ordinary isotropic 

 transparent bodies such as water or glass, I have chosen a 

 definite particular case in which the distribution of the ether 

 when at rest within the atom is expressed by the following 

 formula, and partially shown in the accompanying diagram 

 (p. 186), and tables of calculated numbers : — 



7 * = l + K(l-r')* (9) * 



02 



