JEolotropic Potential. 459 



The value of 7^ given directly is 

 oX 



ptftbcC dw r 3(Z«e + my + nz) 2 l 



- 4 JlSrV-' + AHL 1- 2a 2 / 2 +\ J 



or using (137) and (138) it is 



V (« 2 + A.) (lr + X) ^c- + X) L ~ a 2 + X J ' 

 and this gives immediately the usual form 



J A v / («'" > + X)(/r + X)(c- + X) L a- + XJ 



The potential of a conductor is § of the first term of this 

 formula and 



2 J a V ; (a 2 + X)(6 2 + X) (c 2 +X)' 



The formula for ^ the potential for a density 

 p(ax+(fy+b'z) is 



OVJ Mp(ttA"+7*Wp)i L Ux + flUp J' 



The verification will be merely sketched for this case. 

 Setting out from a member of (138) we derive by 

 differentiation 



5A. 2 ' /<U r? (Z 4 , J 2 ** 2 , J 3 m, or Pmn) 



4?r _ 

 = ., - - [3a 2 , a/3+27'-, 3a 7 '. or aa' + 2^V] respectively, 



and thence 



- A i' P or Im) (lx+my + nz) 2 da > _ \ir !>(143) 



J «#A+/*tip)i ~VA( M ) X 



and 



where of course 1 may be written for u v These values make" 



^X =(, - an ' 1 1/f- ajT> J* } ^e the valuer due to explicit 



2 II 2 



