﻿Resistance 
  in 
  Telephone 
  and 
  other 
  Circuits. 
  427 
  

  

  writing, 
  as 
  an 
  ordinary 
  value 
  for 
  iron, 
  a 
  — 
  10,000 
  C.G.S., 
  

  

  ■^ 
  = 
  J/*, 
  (36) 
  

  

  ii 
  fjb 
  = 
  100. 
  Thus 
  even 
  when 
  / 
  = 
  10,000 
  per 
  second, 
  neglect 
  

   of 
  x^l^i^ 
  only 
  affects 
  the 
  third 
  figure 
  of 
  CD, 
  and 
  therefore 
  at 
  

   most 
  the 
  fourth 
  of 
  L, 
  when 
  the 
  ratio 
  a^/c^ 
  is 
  noticed. 
  This 
  

   process 
  is 
  justifiable 
  whether 
  the 
  ascending 
  or 
  descending 
  

   series 
  are 
  used 
  for 
  (a, 
  yS, 
  7). 
  

   In 
  a 
  similar 
  manner, 
  

  

  + 
  V5l0g/,c; 
  

  

  and 
  after 
  some 
  reduction, 
  

  

  AE-BF 
  . 
  1 
  /. 
  ^ 
  2r 
  

  

  CD 
  

  

  = 
  l+l(2 
  + 
  /3p.-^'-^.logf) 
  

  

  /* 
  V 
  or 
  oL 
  or 
  J 
  

  

  /A 
  c 
  

  

  En 
  the 
  extreme 
  case 
  above, 
  ~ 
  > 
  77^^ 
  , 
  and 
  the 
  final 
  error 
  

  

  /t^ 
  -^ 
  600 
  

  

  consequent 
  upon 
  its 
  neglect 
  is 
  of 
  order 
  (6000) 
  "^ 
  relative 
  to 
  

   unity 
  CA'en 
  when 
  the 
  wires 
  have 
  limiting 
  practical 
  closeness. 
  

   Accordingly, 
  

  

  -(-^j3-j=l+-(^2 
  + 
  /3p..-^-^..log-j 
  

  

  + 
  ^,(2^y..2-«pV 
  + 
  5^'- 
  ^' 
  +.,2^(«-2^^) 
  log^). 
  

  

  Consider 
  now 
  the 
  case 
  in 
  which 
  ^>8. 
  In 
  the 
  coefficient 
  

   of 
  /A~2, 
  the 
  first 
  order 
  values 
  of 
  (a/37) 
  ^^7 
  ^® 
  used, 
  with 
  the 
  

   second 
  order 
  in 
  that 
  of 
  /x~^. 
  

  

  Under 
  these 
  conditions, 
  the 
  coefficient 
  of 
  //-"^ 
  is 
  found 
  to 
  

   vanish, 
  leading 
  to 
  the 
  very 
  simple 
  result^ 
  to 
  order 
  //<~^, 
  

  

  = 
  l 
  + 
  (A--l)(logAc-2)/2/*, 
  

  

  