180 Lord Rayleigh on the Electrical Capacity of 

 Accordingly, 



io g u 2=-2iog a +f(cv+cy+cy ! + . . .), 



and (11) becomes 



fc/Q = 21og(£/a)-C 2 2 -2C 3 2 - . . . -0-l)C/, . (13) 



the term in Ci disappearing, as was to be expected. 



The potential energy of the charge is i^Q 2 . I£ the 

 change of potential energy due to the deformation be called 

 P', we have 



p'=_!Q'{cy+2C3 8 +...+(p-i)cv 2 },. . (U) 



in agreement with my former results. 



There are so few forms of surface for which the electric 

 capacity can be calculated that it seems worth while to 

 pursue the approximation beyond that attained in (11), 

 supposing, however, that all the e's vanish, everything being 

 symmetrical about the line # = 0. Thus from (4), as an 

 extension of (7) with inclusion of C 2 , 



0=(H„ Uo »-H C n )JgF„ 2 



+ f^F„(C 1 F 1 + C 1! F 2 + . . .)(H,« Fi + 2H 2 « 2 F 2 



+3H,u »F,+ . . .) 



+ ^°r^F„(C 1 F 1 + C 2 F 2 + C 3 F 3 +...) 2 , . • • (15) 



or with use of (8) 



u »H n /H =a-J o ^F % (C 1 F 1 + C 2 F 2 + C 8 F 3 + . . .) 



(3C 1 F 1 + 5C 2 F 8 + 7C 3 F 8 + ...),. (16) 



by which H„ is determined by means of definite integrals of 

 the form 



27r F„F p F^<9, (17) 



o 



I 



n, p 9 q being positive integers. It will be convenient to 

 donote the integral on the right of (16) by I B , I« being of 

 the second order in the O's. 



