252] ELECTROMAGNETIC WAVES. 529 



parallel to the radius, and the second, equal to 



parallel to the ^-axis. At the surface of the sphere, r = R, if the 

 conductivity is large,, the lines of force are normal to the surface, 

 so that this second component vanishes, and we have 



-- o -, 



r dr dr 2 r dr 



that is 



When t 0, the electric forces are derivable from a potential, 

 which is, by (i), equal to ~ (since A$ = 0). But by 194 (7) 

 the potential is, in the case supposed, proportional to 



z 9 



r*=- 

 Consequently initially 



Introducing the value of <j> from (2) this gives 



Consequently the function / is constant for all values of its argu- 

 ment greater than R. Hence the value of <, 



remains equal to (7/r so long as r at>R, and the field remains 

 unchanged. When t = (r - ^)/a, the wave arrives at the distance r, 

 and to determine the field at subsequent instants we must deter- 

 mine the values off for values of its argument less than R. 



Let us make use of equation (5). 

 Differentiating <f) by r gives 



d<f> = f(r-at) f(r-at) 

 dr r r* 



?* = /> - at) _ 2/(r-aQ 2/(r-<rt) 

 ar 2 r r 2 r^ 



w. E. 34 



