1884.] Mr Leahy, On the pulsation of Spheres, &c. 153 



where P, Q and R are any constants ; Fresnel's construction Avill 

 be satisfied if 



LI + Mm + Nn = 0, 



that is if the displacement is in the wave front. This condition is 

 equivalent to 



^/ + ^ + ^ = o 



dx dy dz ' 



which of course is Maxwell's fundamental assumption. 



Thus in order to deduce Fresnel's construction from the electro- 

 magnetic theory of light the condition 



dx dy dz 



is necessary and sufficient. Maxwell himself had of course shewn 

 the sufficiency of the condition, but I am not aware that the 

 problem has been treated previously quite so generally as in the 

 present paper. 



(2) On. the pulsations of Spheres in an Elastic Medium. 

 By A. H. Leahy, B.A. 



[Abstract.'} 



The problem of two pulsating spheres in an incompressible 

 fluid has been discussed by several writers. The author considers 

 the analogous problem in the case in which the medium surround- 

 ing the spheres has the properties of an elastic solid. He finds 

 that the most important term in the expression of the law of force 

 between the two spheres varies inversely as the square of the 

 distance between them. This force will be an attraction if the 

 spheres be in unlike phases, a repulsion if they be in like phases 

 at any instant. The next term in the expression varies inversely 

 as the cube of the distance between the two spheres and is always 

 a repulsion. 



The paper is being published in full in the Transactions of the 

 Society. 



