﻿Potential 
  of 
  Two 
  Conducting 
  Spheres. 
  287 
  

  

  &c, 
  and 
  V/, 
  V 
  2 
  ', 
  V 
  3 
  ', 
  &c. 
  its 
  potentials 
  at 
  J 
  1? 
  J 
  2 
  , 
  J 
  s 
  , 
  &c, 
  

   Let 
  the 
  charge 
  on 
  A 
  be 
  unity, 
  and 
  let 
  B 
  have 
  no 
  charge. 
  

  

  We 
  have, 
  then, 
  the 
  two 
  sets 
  of 
  equations,- 
  

   c 
  U=l 
  + 
  a(V-V 
  1 
  '), 
  

  

  BJ.V^rr 
  6(U-U 
  2 
  '). 
  

  

  AJ 
  s 
  .U 
  2 
  ' 
  = 
  l 
  + 
  a(V-V,'), 
  

   BJ 
  3 
  .V 
  3 
  ' 
  = 
  /<U-U 
  4 
  '), 
  

   AJ 
  4 
  .TT 
  4 
  '=l+.fl(V-V 
  '). 
  

  

  cV= 
  k 
  u 
  -Ui), 
  

  

  Alj.U^l 
  + 
  aCV-Vg), 
  

   BI 
  2 
  .V 
  2 
  = 
  6(U-U 
  8 
  ), 
  

   AT 
  3 
  .U 
  3 
  =l 
  + 
  a(V-V 
  4 
  ), 
  

   &(U-U 
  5 
  ). 
  

  

  BI 
  4 
  .V 
  4 
  

  

  The 
  first 
  .set 
  gives 
  at 
  once 
  

  

  

  a 
  3 
  6 
  3 
  

  

  - 
  rt 
  ' 
  U 
  [i 
  

  

  ' 
  BJ! 
  . 
  BJ 
  3 
  . 
  BJ 
  5 
  . 
  AJ 
  2 
  . 
  AJ 
  4 
  . 
  A 
  J 
  ( 
  

  

  ab 
  

  

  ...] 
  

  

  + 
  

  

  BJi 
  . 
  BJ 
  3 
  . 
  AJ 
  2 
  

  

  a 
  2 
  h 
  2 
  

  

  + 
  BJj 
  . 
  BJ 
  3 
  . 
  BJ 
  5 
  . 
  AJ 
  2 
  . 
  AJ 
  4 
  + 
  J 
  

   or 
  cV 
  = 
  (1 
  + 
  aV) 
  G,- 
  - 
  a&UF,-, 
  

  

  