97] MOTION OF TWO SPHERES. 141 



The value of N may be written down from symmetry, viz. it is 



N= ?,7Tpb* (1+3 -%,-n + 3 jj^r-r 



\ c 3 /! 3 cPfi* (< 

 where 



/ 3 ' = '- 2 // 2 '> f*=/fa, } (xi), 



and so on. 



To calculate M we require the value of 0' near the surface of the sphere A ; 

 this is due to double-sources //, /*/, /* 2 'j Ms',.-- at distances c, c //, c-/ 2 ', 

 c-/ 3 ', ... from ^1, where 



(xii), 



and so on. This gives, for points near the surface of A, 



..f, , , / N COS^ 



9 = \\ i \ +^3 +M5 +) "~2~ 



Hence 



When the ratios a/c and b/c are both small we have 



.. (xv) # 



approximately. 



* To this degree of approximation these results may also be obtained by the 

 method of the next Art. 



