﻿that 
  of 
  Three 
  Electrified 
  Spherical 
  Conductors. 
  391 
  

  

  The 
  centres 
  of 
  the 
  spheres 
  are 
  the 
  points 
  A, 
  B, 
  Q, 
  and 
  we 
  

   shall 
  use 
  these 
  letters 
  to 
  denote 
  also 
  their 
  potentials 
  ; 
  a, 
  /3, 
  7 
  

   are 
  the 
  lengths 
  of 
  the 
  radii 
  of 
  the 
  spheres, 
  and 
  a, 
  b, 
  <rthe 
  

  

  Fig. 
  2. 
  

  

  lengths 
  of 
  the 
  sides 
  of 
  the 
  triangle. 
  The 
  potential 
  due 
  to 
  

   the 
  sphere 
  A 
  at 
  any 
  point, 
  say 
  K 
  41 
  , 
  will 
  be 
  denoted 
  by 
  A^ 
  41 
  , 
  

   the 
  potential 
  due 
  to 
  B 
  at 
  L 
  31 
  by 
  Bj 
  31 
  , 
  and 
  so 
  on. 
  The 
  object 
  

   of 
  the 
  problem 
  is 
  to 
  find 
  B 
  a 
  -f- 
  C? 
  a 
  . 
  

   We 
  have 
  

  

  c.B 
  a 
  + 
  /3(A 
  il 
  + 
  C 
  il 
  )=/3B, 
  

  

  b.C 
  a 
  + 
  y(A 
  kL 
  +B 
  kl 
  )=ryC. 
  

  

  /3 
  

  

  .-. 
  B 
  a 
  +c 
  a 
  -reA,-+|A 
  Al 
  +^a 
  1+ 
  X=-B+7.a 
  

  

  p. 
  

  

  Thus 
  the 
  first 
  two 
  terms 
  of 
  the 
  expression 
  for 
  B^ 
  + 
  a 
  are 
  

  

  c 
  b 
  

  

  2 
  E 
  2 
  

  

  