97] MOTION OF TWO SPHERES. 



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



*-) 



141 



where 



and so on. 



To calculate M we require the value of near the surface of the sphere A \ 

 this is due to double-sources //, p,/, p 2 &amp;gt; Psi-- a ^ distances c, cf^ c /&quot; 2 , 

 c-/ 3 , ... from A, where 



(xii), 



and so on. This gives, for points near the surface of .4 

 &amp;lt; / )/ = C/^i + /*s + /*B + .2^ 



Hence 



L CT3&3 6&6 I 



^(^ / )3V/ 3 ^ 3 7^ 2 T(^^ 



When the ratios a/c and 6/c are both small we have 



approximately. 



(xv),* 



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

 method of the next Art. 



