﻿424 
  Dr. 
  J. 
  W. 
  Nicholson 
  on 
  Inductance 
  and 
  

  

  If 
  \j 
  be 
  the 
  equivalent 
  induction 
  when 
  this 
  small 
  capacity- 
  

   is 
  taken 
  into 
  account, 
  

  

  I12 
  + 
  L'V= 
  (R2 
  + 
  LV)(l--iPn2LC) 
  

  

  or 
  (L^-L)/L= 
  ~ro(;R2^LV)/6L 
  approximately. 
  (27) 
  

  

  This 
  equation 
  serves 
  to 
  limit 
  the 
  types 
  of 
  circuit 
  to 
  which 
  

   the 
  uncorrected 
  inductance 
  formulae 
  may 
  be 
  applied, 
  in 
  so 
  

   far 
  as 
  error 
  due 
  to 
  capacity 
  is 
  concerned. 
  For 
  example, 
  if 
  

   a 
  three-figure 
  accuracy 
  is 
  required, 
  it 
  is 
  necessary 
  that 
  

  

  ro(R2+LV)/6L 
  > 
  10-S 
  . 
  . 
  . 
  (28) 
  

  

  where 
  I 
  is 
  the 
  length 
  of 
  either 
  wire 
  of 
  the 
  circuit. 
  

  

  We 
  have 
  also 
  neglected 
  

  

  in 
  comparison 
  with 
  unity. 
  This 
  restricts 
  the 
  capacity 
  for 
  

   which 
  the 
  correction 
  (27) 
  may 
  be 
  used. 
  Thus, 
  for 
  low 
  

   resistance, 
  

  

  4ZVC2 
  > 
  9 
  . 
  10-^. 
  

  

  This 
  equation 
  will 
  ordinarily 
  supply 
  the 
  lower 
  limit 
  for 
  C. 
  

   Thus 
  for 
  frequencies 
  such 
  that 
  

  

  ?iC> 
  (5P)-ilO-2 
  . 
  ... 
  (29) 
  

  

  3apacity) 
  formulae 
  may 
  be 
  used 
  provided 
  

   1 
  as 
  to 
  make 
  

  

  C7i2L>6Z-nO-S 
  . 
  . 
  . 
  . 
  (30) 
  

  

  again 
  neglecting 
  R. 
  

  

  For 
  a 
  capacity 
  of 
  one 
  microfarad 
  per 
  kilometre, 
  C 
  = 
  10~^^. 
  

   In 
  a 
  case 
  like 
  that 
  of 
  the 
  Atlantic 
  cable 
  the 
  capacity 
  is 
  about 
  

   a 
  quarter 
  of 
  this 
  amount, 
  and 
  the 
  limiting 
  frequency, 
  with 
  

   I 
  in 
  centimetres, 
  is 
  about 
  l~^ 
  10^^. 
  This 
  excludes 
  such 
  a 
  

   cable 
  altogether 
  from 
  the 
  investigation, 
  although 
  a 
  shorter 
  

   cable 
  of 
  the 
  same 
  radius 
  of 
  wire 
  and 
  capacity 
  gradient 
  can 
  

   be 
  within 
  its 
  scope. 
  For 
  example, 
  a 
  frequency 
  of 
  so 
  much 
  

   as 
  10 
  million 
  can 
  be 
  treated 
  if 
  I 
  is 
  not 
  greater 
  than 
  1*2 
  kilo- 
  

   metres, 
  for 
  a 
  suitable 
  range 
  of 
  inductance 
  given 
  by 
  (30). 
  

   The 
  range 
  of 
  inductance 
  is 
  of 
  course 
  dependent 
  mainly 
  on 
  

   the 
  distance 
  between 
  the 
  wires. 
  

  

  Obviously 
  all 
  short 
  telephone 
  circuits 
  satisfy 
  both 
  (29) 
  

   and 
  (30), 
  and 
  their 
  capacity 
  needs 
  no 
  consideration. 
  

  

  the 
  uncorrected 
  (for 
  capacity) 
  formulae 
  may 
  be 
  used 
  provided 
  

   that 
  C 
  is 
  also 
  so 
  small 
  as 
  to 
  make 
  

  

  