﻿Resistance 
  of 
  a 
  Conductor 
  of 
  Uniform 
  Thickness. 
  735 
  

   into 
  the 
  axis 
  of 
  f 
  in 
  the 
  f 
  plane 
  fig. 
  2, 
  the 
  corresponding 
  

  

  Fig. 
  2. 
  — 
  £ 
  plane. 
  

   P 
  

  

  I 
  I 
  r~ 
  

  

  -^ 
  -j 
  o 
  

  

  points 
  being 
  indicated 
  by 
  the 
  lettering 
  in 
  the 
  figures. 
  

  

  •-VMS* 
  

  

  r+i_i 
  

  

  write 
  

  

  and 
  the 
  integral 
  becomes 
  

  

  (a-l)dd 
  

  

  H£ 
  

  

  <9 
  2 
  )(l-0 
  2 
  j 
  

  

  where 
  the 
  origin 
  in 
  the 
  z 
  plane 
  is 
  taken 
  at 
  the 
  point 
  corre- 
  

   sponding 
  to 
  f 
  = 
  — 
  a, 
  77 
  = 
  in 
  the 
  f 
  plane, 
  and 
  tanh 
  or 
  coth 
  is 
  

   taken 
  according 
  to 
  whether 
  the 
  quantity 
  under 
  the 
  root 
  sign 
  

   is 
  less 
  than 
  or 
  greater 
  than 
  unity. 
  

  

  In 
  order 
  to 
  show 
  the 
  connexion 
  between 
  the 
  z 
  and 
  £ 
  planes 
  

   graphically, 
  we 
  write 
  

  

  where 
  r 
  a 
  , 
  a 
  , 
  r 
  l3 
  #x 
  are 
  the 
  coordinates 
  of 
  the 
  point 
  £77, 
  with 
  

   respect 
  to 
  the 
  points 
  —a 
  and 
  —1 
  (fig. 
  2), 
  and 
  

  

  cos 
  -f 
  - 
  

  

  ?' 
  a 
  2 
  = 
  ? 
  >2 
  + 
  2a 
  r 
  cos 
  + 
  a 
  2 
  , 
  cot 
  #„ 
  = 
  . 
  A 
  - 
  , 
  

  

  sin# 
  

  

  COS0 
  + 
  - 
  

  

  t\ 
  = 
  r 
  2 
  + 
  2r 
  cos 
  + 
  1, 
  cot 
  X 
  = 
  — 
  t—^- 
  

  

  sin 
  

  

  Resolving 
  each 
  term 
  of 
  the 
  above 
  equation 
  into 
  its 
  norm 
  and 
  

  

  * 
  The 
  form 
  argtanli 
  lias 
  been 
  retained 
  throughout 
  because 
  of 
  the 
  

   symmetry 
  of 
  the 
  norm 
  and 
  amplitude 
  when 
  this 
  is 
  done. 
  

  

  