Prof. Challis on the Dispersion of Light, 453 



pose it is necessary to take account of the proper elasticity of the 

 refractive medium in investigating au expression for the accele- 

 ration of an individual atom due to the dynamical action of the 

 sethereal waves. In seeking for such an expression, I supposed at 

 first that the atoms were fixed, and assumed that the condensa- 

 tion or rarefaction of the aether in contact with any atom is always 

 proportional to the condensation or rarefaction of the wave at the 

 position where the atom is situated, but is distributed unequally 

 about the surface, the excess being on the hemisphere on which 

 the waves are incident, and the distribution being symmetrical 

 about an axis drawn through the centre in the direction of inci- 

 dence. As the resulting accelerative force in that direction would 

 thus be proportional to the condensation, and consequently to the 

 velocity of the incident waves, the expression assumed for it was 



km sin—- (tcat — cc + c), 



A 



k being a constant factor multiplying the velocity. At this 

 point of the reasoning I omitted to inquire whether that factor 

 is a function of X, and subsequently treated it as if it were inde- 

 pendent of that quantity. This inquiry I now propose to enter 

 upon. 



The whole investigation, it will eventually appear, turns upon 

 the solution of the following hydrodynamical problem : — A series 

 of waves defined by the equations 



V = /cacr = m sin — (fcat—x + c), 



is incident in a given direction on a fixed smooth sphere of given 

 radius : it is required to find the condensation at any point of the 

 surface of the sphere at any instant. Since in the view I take of 

 theoretical physics this problem is of the utmost importance, I 

 have given to it especial consideration ; and though I seem to have 

 succeeded to a considerable extent in solving it, I do not profess 

 to have completely overcome the difficulties. The process I have 

 adopted depends in part on the new general hydrodynamical 

 equation, which I have deduced from the principle of the conti- 

 nuity of successive surfaces of displacement of a given element 

 in successive instants. I am aware that the solution might be 

 attempted without reference to that equation by a process ana- 

 logous to that employed by Poisson in determining the simulta- 

 neous movements of a ball pendulum and the surrounding air. 

 But with every disposition to find that that method is exact and 

 sufficient, I have been compelled, for reasons which will appear in 

 the sequel, to have recourse to inferences drawn from the new 

 equation. My previous researches having demonstrated that the 



