496 Lord Rayleigh on the Influence of Obstacles 



£= + v, where v is finally to be made infinite ; and, as we 

 have just seen, we may exclude the space bounded by 



!j=±v, v=±v, £=± u ; 



so that ^S 2 will be obtained from the space bounded by 



Now when p is sufficiently great, the summation may be 

 replaced by an integration ; thus 



- . s *=-JK(?) wr - 



In this, 



d 1 d t- • 



vdi) 2v' 



and finally 



J: 



J_„ (« 2 + D OH? 2 )' Jo V (S + tanV) 



i: 



S 2 = ^ (65) 



P = ^r, (66) 



*W US _TT 



Thus 



2tt 

 3 



If we neglect a 10 /* 10 , and write /> for the ratio of volumes, 

 viz. 



4?ra 3 



we have by (60) for the conductivity 



(*+v)/(l-v)-2p (m , 



(Z + v )l{l-v)+p> • ■• ■■•■■• ■' 1°'' 



or in the particular case of non-conducting obstacles (V = 0) 



rr£' •. (68) 



In order to carry on the approximation we must calculate 

 S 4 &c. Not seeing any general analytical method, such as 

 was available in the former problem, I have calculated an 



* Compare Maxwell's ' Electricity,' § 314. 



