220 Proceedings of Royal Society of Edinburgh. [sess. 
and simplest illustration of tlie 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 
|JjAa = 0 (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 assumption of (7) may now be 
expressed by 
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 undisturbed density of the ether outside. Thus the 
attractions and repulsions of the atom in lines through its centre 
produce, 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 therefore 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, and tables of calculated numbers : — 
1 + K(1 - r') 2 
• (9)- 
Here, r denotes the undisturbed distance from the centre 
of the atom, of a particle of the ether which is at distance 
