186 DR. T. J. I'A. BROMWICH ON THE 



Similarly the scattered waves will be given by the two functions 



ri 

 (4'5) <J and 



+ sin0sin^ - 2n+l_ 

 I K n = i n (n + 1 ) 



The boundary conditions are given by the continuity of the tangential components 

 of electric and magnetic force at the sphere r = a. 



It is evident from. the form of equations (2'l), (2'2) that these conditions will be 

 satisfied if we take 



( au, au au rt 



L = -+ 



dr or or 

 (4'6) { and 



- + . ,, 



I cr or or 



Thus we find that A, and C n (the coefficients in the scattered waves) are given by 



f {S. M + A.E. M I ^ - S'. M + A n E' n 



(47) ^ and 



IS.M +C.E.M} s ^- - S'. 



The special case of a perfectly conducting sphere is given by making the tangential 

 electric force zero at the sphere r a ; and this condition is satisfied if 



(4-61) o- + ", = V+V . 



cr cr 



Thus we find the simpler formulas 

 (471) S'.M+A.E'.M = S.M + C.E.M = 0, 



which may be regarded as limiting forms of (47), when K | -> oo and /UL -> 0. 



The forinulaB (4*5) and (471 ) lead at once to those quoted by Dr. J. PROUDMAN* 

 in calculating the pressure of radiation due to a plane wave incident on a small 

 conducting sphere. 



In all the applications with which we shall be concerned at present the point at 

 which the disturbance is to be calculated will be at a distance large compared with 



* ' Monthly Notices of the Royal Astronomical Society,' vol. 73, 1913, p. 535, 



