﻿422 
  Dr. 
  J. 
  W. 
  Nicholson 
  on 
  Inductance 
  and 
  

  

  parison 
  with 
  unity. 
  In 
  the 
  most 
  unfavourable 
  case 
  furnished 
  

   by 
  the 
  telephone, 
  /=1600, 
  a 
  = 
  3 
  millimetres, 
  leading 
  to 
  

   li^a^ 
  z= 
  10 
  - 
  1* 
  approximately. 
  

  

  Thus 
  this 
  source 
  of 
  error 
  needs 
  no 
  further 
  consideration 
  in 
  

   such 
  a 
  case. 
  But 
  in 
  fact, 
  the 
  neglect 
  of 
  this 
  quantity 
  is 
  

   always 
  legitimate. 
  For 
  if 
  / 
  be 
  the 
  frequency, 
  li^a^ 
  = 
  4/^1 
  0~ 
  ^^ 
  

   for 
  a 
  wire 
  of 
  a 
  centimetre 
  radius. 
  It 
  can 
  only 
  therefore 
  

   affect 
  the 
  fourth 
  figure 
  if 
  /=20 
  million, 
  and 
  the 
  second 
  if 
  

   y=200 
  million, 
  and 
  such 
  a 
  frequency 
  is 
  never 
  used 
  in 
  

   combination 
  with 
  so 
  thick 
  a 
  wire. 
  

  

  Secondly, 
  a^jd^ 
  was 
  neglected 
  in 
  comparison 
  with 
  unity. 
  

   Now 
  even 
  in 
  ordinary 
  telephone 
  construction 
  there 
  is 
  usually 
  

   about 
  2J 
  millimetres 
  of 
  paper 
  and 
  air 
  between 
  the 
  wires, 
  so 
  

   that 
  in 
  the 
  case 
  of 
  the 
  cable, 
  taking 
  an 
  extreme 
  radius 
  of 
  

   1*3 
  millimetres, 
  c 
  = 
  4a, 
  and 
  only 
  the 
  third 
  figure 
  is 
  affected. 
  

   For 
  overhead 
  wires, 
  the 
  distance 
  apart 
  is 
  about 
  30 
  centimetres. 
  

  

  The 
  limiting 
  practical 
  closeness 
  of 
  the 
  wires, 
  when 
  a 
  

   knowledge 
  of 
  the 
  self-induction 
  is 
  required, 
  is, 
  I 
  believe, 
  

   attained 
  in 
  Mr. 
  A. 
  Campbell's 
  experiments 
  on 
  variable 
  

   mutual 
  inductances 
  *. 
  The 
  error 
  may 
  then 
  be 
  so 
  great 
  as 
  

   one 
  or 
  two 
  per 
  cent. 
  

  

  Effect 
  of 
  a 
  Small 
  Capacity. 
  

  

  Heaviside 
  f 
  has 
  divided 
  circuits 
  into 
  five 
  classes, 
  with 
  the 
  

   following 
  determining 
  properties: 
  — 
  

  

  (1) 
  Submarine 
  cables 
  proper, 
  in 
  which 
  the 
  capacity 
  is 
  the 
  

   main 
  factor, 
  and 
  whose 
  treatment 
  must 
  follow 
  the 
  electro- 
  

   static 
  theory. 
  

  

  (2) 
  Short 
  lines 
  of 
  low 
  frequency, 
  in 
  which 
  self-induction 
  

   and 
  resistance 
  determine 
  the 
  effects. 
  This 
  class 
  includes 
  the 
  

   majority 
  of 
  short 
  telephone 
  circuits. 
  

  

  (3) 
  A 
  class 
  in 
  which 
  capacity 
  and 
  self-induction 
  are 
  

   equally 
  important. 
  These 
  circuits 
  are 
  very 
  difficult 
  in 
  

   theory. 
  

  

  (4) 
  Circuits 
  of 
  high 
  frequency, 
  but 
  small 
  capacity 
  and 
  

   resistance, 
  and 
  with 
  the 
  inductance 
  so 
  chosen 
  that 
  signals 
  

   may 
  travel 
  without 
  distortion. 
  For 
  this 
  class 
  the 
  electro- 
  

   static 
  theory 
  cannot 
  be 
  applied 
  however 
  long 
  the 
  circuit. 
  

  

  (5) 
  Circuits 
  in 
  which 
  distortionless 
  propagation 
  is 
  obtained 
  

   by 
  allowing 
  an 
  electric 
  leakage. 
  

  

  The 
  effect 
  of 
  leakage 
  is 
  small 
  in 
  all 
  but 
  the 
  fifth 
  case, 
  

   and 
  will 
  be 
  ignored. 
  

  

  Let 
  an 
  impressed 
  force 
  Ee''^^ 
  act 
  at 
  one 
  end 
  of 
  a 
  circuit 
  

   consisting 
  of 
  two 
  parallel 
  wires, 
  with 
  terminal 
  apparatus 
  

  

  * 
  PMl. 
  Mag. 
  Jan. 
  1008. 
  

  

  t 
  * 
  Electrical 
  Papers/ 
  toI 
  ii. 
  

  

  