642 Mr. G. H. Livens on the Initial Accelerated 



We try a solution involving the first order harmonics only. 

 We add on to the initial field the first harmonic solution of 

 the general equations, and attempt to satisfy the boundary 

 conditions. We take 



X = ~ 2 + — p- 0/ +/), Y= -^- (r 2 / ' + r/+/) f 



sin# „ 



/is now interpreted as a function of (c£ — r + a). 



As Prof. Love points out, there are two conditions to be 

 satisfied, one at the front of the advancing wave boundary, 

 which started out from the sphere at the initial instant, and 

 the other one at the surface of the sphere itself. The con- 

 ditions at the wave front can easily be seen to be 



X = X , Y— cy=Y at ?* = a + ct, 



the initial field (X , Y , Z , a , /3 , y ) existing undisturbed 

 outside this boundary. These give 



/'(0)=0, /(0)=0. 



The condition at the surface of the sphere is that the 

 tangential electrodynamic force is zero. In the case under 

 discussion this is the same as that the tangential electric 

 force should be zero, the magnetic part of the former, con- 

 taining the product of two small quantities, being zero to the 

 first order. 



This leads to the condition that 



Y _ gsinflX 



a 



account being taken of the fact that the centre of the sphere 

 is not at the origin of the coordinates ; this is equivalent to 



aV"(rt) + af(ct) +f(ct) - e£= 0. 



We now use a = ct and A — ^ and then the equation for 

 /is Zc 



a?f"{x) + «/» +/(*)-A* > .= 0. 



The solution subject to the wave-boundary conditions is 



4Aa 2 * x v/3 



