spherical Wave of Light. yg 



The solution is still left indefinite ; to make it definite 

 in the last part of this paper I shall consider values of 

 g<\. It is needless to consider the general case of dis- 

 placement of a sphere, it offers no further difficulties and 

 gives no further conditions. 



If we had, in what precedes, integrated only over that 

 part of the spherical surface which presents itself to P (a case 

 which in the limit corresponds to the integration over an 

 infinite plane), we should have obtained in addition to the 

 principal terms already treated, terms arising from the 

 boundary of which the only part sensible would be 



— cos/{^(T + /) - c-y + /}, 



which corresponds to the value 2 of n, and in which y stands 

 for the length of the tangent from the point to the 

 sphere. This term is of the same order of quantities as the 

 terms which we have called principal terms. In the last 

 part of this paper I attempt to show that b^ = 0. 



Note. — It might be objected that the displacement, but 

 not the velocity of displacement has been here considered. 

 But our expressions will give the requisite velocity of dis- 

 placement, as may be easily proved. It must be remembered 

 that we are attempting to satisfy the conditions of motion 

 by expressions into which the time enters only in the form 



<Py-i\ in other words by a divergent wave. Hence, if the 

 expressions which we obtain do not satisfy the conditions, 

 we should infer that the problem could not be solved by 



expressions of the form <^( ^-^)- We have in this case one 



function only to be introduced, and the displacement and 

 velocity of displacement initially satisfy the equations of 

 motion which we are solving. 



Taking Poisson's solution of the equation (^. - ^V W = 0, 



and expanding it (noticing that cos0.sin0cos^ and sinOsin^, 



