﻿290 
  Coefficients 
  of 
  Potential 
  of 
  Ttco 
  Conducting 
  Spheres. 
  

   or, 
  if 
  we 
  write 
  for 
  c 
  2 
  —a 
  2 
  — 
  b'\ 
  a: 
  2 
  , 
  and 
  for 
  ab, 
  p 
  2 
  , 
  

   P\2 
  = 
  k\ 
  

  

  K^—p^ 
  

  

  i>56^ 
  

  

  k 
  4 
  —2 
  P 
  * 
  

  

  i>78 
  — 
  ^2 
  ' 
  

  

  /e 
  4 
  -3p 
  4 
  

  

  K 
  

   &C... 
  

  

  The 
  series 
  is, 
  therefore, 
  

  

  ,.p\ 
  p* 
  . 
  «Y. 
  

  

  1 
  + 
  K 
  2 
  "I" 
  ^^4 
  + 
  (rf*-^) 
  (^_2p 
  4 
  ) 
  

  

  « 
  4 
  » 
  8 
  

  

  + 
  (> 
  -^4) 
  ( 
  „4 
  _ 
  2p*) 
  (^ 
  _ 
  3jp 
  4) 
  + 
  • 
  • 
  • 
  

  

  ir- 
  1 
  />« 
  /»* 
  _ 
  A* 
  

  

  or, 
  denoting 
  _ 
  9 
  or 
  , 
  by 
  a, 
  

  

  1 
  1 
  a 
  a 
  2 
  

  

  Hence 
  we 
  have 
  

  

  a&/- 
  1 
  1 
  a 
  \ 
  

  

  2 
  C 
  \ 
  a 
  a 
  2 
  — 
  1 
  (a 
  2 
  — 
  l)( 
  a 
  2) 
  / 
  

   Similarly, 
  for 
  the 
  second 
  series, 
  we 
  can 
  show 
  that 
  

  

  _ 
  p>23 
  (c 
  2 
  — 
  a 
  2 
  — 
  b 
  2 
  ) 
  — 
  a 
  2 
  b 
  2 
  

  

  ^45 
  — 
  - 
  — 
  > 
  

  

  ^23 
  

  

  _. 
  «>23 
  — 
  P 
  4 
  

   ^23 
  

  

  Pt7— 
  - 
  , 
  

  

  &C...., 
  

  

  AT 
  c 
  2 
  -6 
  2 
  . 
  (c 
  2 
  -/> 
  2 
  + 
  a6')(c 
  2 
  -/> 
  2 
  -ac) 
  

  

  also 
  Alx 
  = 
  , 
  and 
  p 
  23 
  = 
  ^-^ 
  . 
  

  

  c 
  M 
  c—b* 
  

  

  Let 
  ^>23 
  he 
  denoted 
  by 
  h 
  

  

  