﻿Potential 
  of 
  Two 
  Conducting 
  Spheres. 
  289 
  

  

  We 
  have, 
  then, 
  writing 
  G 
  for 
  G» 
  and 
  G 
  j} 
  

  

  1 
  c 
  J 
  

  

  *(i 
  + 
  ?*)(l 
  + 
  ?*)-?a 
  

  

  G 
  

  

  ab^ 
  

  

  1 
  1 
  + 
  T 
  F 
  < 
  

  

  It 
  will 
  be 
  seen 
  that 
  

  

  (l 
  + 
  ?*)(l 
  + 
  **,)-** 
  

  

  ab 
  

  

  q 
  u 
  = 
  — 
  --br, 
  

  

  ? 
  22 
  =M1+-F 
  J 
  

  

  It 
  has 
  thus 
  been 
  shown 
  that 
  the 
  values 
  of 
  the 
  coefficients 
  

   of 
  induction, 
  capacity, 
  and 
  potential 
  depend 
  on 
  the 
  sums 
  o£ 
  

   two 
  series, 
  

  

  ab 
  . 
  a 
  2 
  b 
  2 
  

  

  + 
  AI 
  X 
  . 
  BI 
  2 
  + 
  Al! 
  . 
  AI 
  8 
  . 
  BI 
  2 
  . 
  BI 
  4 
  

  

  a^ 
  3 
  

  

  + 
  AI^AIe.AIs.BI^B^.BIe 
  4 
  "-- 
  

   which 
  we 
  have 
  denoted 
  by 
  G, 
  and 
  

  

  1 
  ab 
  a 
  2 
  l> 
  2 
  

  

  AIT 
  + 
  AIx 
  . 
  BI 
  2 
  • 
  AI 
  3 
  AIx 
  . 
  AI 
  3 
  . 
  AJ 
  5 
  . 
  BI 
  2 
  . 
  BI 
  4 
  + 
  " 
  * 
  ' 
  

  

  which 
  we 
  have 
  denoted 
  hj 
  F. 
  Both 
  of 
  these 
  series 
  can 
  be 
  

   expressed 
  in 
  terms 
  of 
  a, 
  b, 
  c. 
  

  

  Taking 
  the 
  first 
  series 
  and 
  denoting 
  

  

  All 
  • 
  BI 
  2 
  by 
  p 
  12} 
  AI 
  3 
  . 
  BI 
  4 
  by 
  p 
  34 
  , 
  AJ 
  5 
  . 
  BI 
  6 
  by 
  ^ 
  56 
  , 
  &c. 
  . 
  ., 
  

  

  it 
  can 
  be 
  shown 
  that 
  

  

  ^-a 
  2 
  -b 
  2 
  )2) 
  l2 
  -a 
  2 
  b 
  2 
  

   p 
  Zi 
  — 
  - 
  - 
  , 
  

  

  ( 
  c 
  2-. 
  a 
  2 
  ~b 
  2 
  )p 
  u 
  -a 
  2 
  b 
  2 
  ■ 
  

  

  