706  Mr.  J.  W.  Nicholson  on  the  Symmetrical 
of  electric  force  at  any  point  normal  to  two  of  the  surfaces 
through  that  point  are  zero  ;  and  (2)  a  type  in  which  the 
same  property  is  true  of  the  magnetic  force.  As  a  particular 
case,  one  of  the  surfaces  of  revolution  may  be  absent. 
The    components    of    force    are,    in     the    most    general 
oscillation, 
^=P2p3^|?       y=  ~PiP*^> 
*=^&,       -^|fby(3)to(6).     (8) 
Now  the  element  of  arc  in  any  direction  A,  is 
Taking  \  =  a,{3,(o  successively, 
by  a  property  of  conjugate  functions, 
similarly  -,  7 
J  dns  =  pcla>. 
Thus 
B(*,£) 
— g  =  —s  =  ^,P,~o[  an(i  Vz—  ->      •     •     •     C9) 
Pi        7>2         d(«,/3)  P 
and  (7)  becomes 
d^  OP         P\0«da       dp  0/5/  ^0(«,Pj 
In  order  to  obtain  the  electrical  periods  between  two 
perfectly  conducting  surfaces  of  the  family,  it  is  necessary 
to  find  solutions  of  the  form  A  (a)  B(/3),  which  is  possible, 
provided  that 
!M=/i(a)+/2(/S)' (11) 
-  ~  —function  of  a  only, 
p  0«  J 
-  ^  =  function  of  8  only. 
p¥  J 
