174 MR. GEORGE W. WALKER ON THE INITIAL ACCELERATED 



Inside the sphere we may have both converging and diverging disturbances, and 

 hence we assume at all points inside 



(X, Y, Z) = '(-1. 0, 0){^ 1 ff (C't,-r)+r^ H (C f t+ 



+ ~-(x, y, z){^ 



Now the field must not become infinite at the origin, and this requires as a primary 

 condition that 



Neglecting squares of velocity, &c. (X, Y, Z) = (X', Y', Z'), and the tangential 

 component of electric force must be continuous at r = a, and hence we get 



Further, the surface density of electricity a- - -- ; and the difference of normal 



4-rr a 1 



flux must equal 



We thus get the additional condition 



The components of electric force at the surface are 

 Along normal outside N t = + - J '. A l (a^' 



d ff> 



rri vy . Sill U / >> tf 



tangent f, = --- - 3 (a- x " 



9Q' p 



., normal inside N 3 = ~ - J j - {a(i/// ^a)+^ii 



Of 



tangent T 2 = - ^^ {a 2 



Now the resultant tractions are 



Along normal - {N, 2 + (K-l) T a 2 -KN 3 2 }, 



eT 



tangent 



Hence the force per unit area in the direction of x is 



. {N 1 2 + (K-l) T^-KN, 8 } cos 0+ sin 0. 



