424 THE ELECTROMAGNETIC FIELD. [PT. III. CH. XI. 



SO that 



( I4 ) _( l a aw a a avi 



dhdn V 9a?i 8^ 8^/ V 8^ ^8^ 'faJ\r 



a.(i) 3^(1) a- (1) 



^aS + ^ + ^>8 



Now since 1/r satisfies the equation 



I ; . - 



we may write 



with similar substitutions for 8 2 (l/r)^ 2 and 8 2 (l/r)/8^ 2 . Making 

 these substitutions, and arranging the terms differently, we obtain 



* 



dhdn 



(15) 



'1\ /! 



a(- 



,r/ V^ 



pVH 



Consequently if we put 



