﻿CD 
  

   P 
  

  

  426 
  Dr. 
  J. 
  W. 
  Nicholson 
  on 
  Inductance 
  and 
  

  

  i£ 
  f 
  is 
  the 
  frequency, 
  then 
  

  

  . 
  , 
  c 
  4 
  /, 
  2 
  5 
  \ 
  

   L 
  = 
  41og.- 
  + 
  -(1- 
  ^ 
  + 
  ^,) 
  + 
  ^, 
  j^g^^^ 
  

  

  -«-$('' 
  + 
  ^'''°sf+ 
  3 
  log 
  f) 
  

  

  where 
  p 
  = 
  \ogelia^ 
  and 
  the 
  limiting 
  capacity 
  is 
  given 
  by 
  (29). 
  

   For 
  most 
  useful 
  purposes 
  it 
  may 
  be 
  greatly 
  shortened, 
  

   according 
  to 
  the 
  value 
  of 
  X. 
  

  

  Iron 
  Wires 
  ivit/i 
  High 
  Frequence/. 
  

  

  When 
  iron 
  is 
  used, 
  there 
  is 
  no 
  object 
  to 
  be 
  served 
  in 
  

   obtaining 
  so 
  accurate 
  a 
  formula, 
  on 
  account 
  of 
  the 
  vagaries 
  

   in 
  the 
  magnetic 
  behaviour 
  of 
  the 
  metal. 
  But 
  the 
  approximate 
  

   value 
  of 
  fjL 
  is 
  known, 
  for 
  Lord 
  Rayleigh 
  * 
  has 
  shown 
  that 
  for 
  

   feeble 
  magnetizing 
  forces 
  of 
  periodic 
  character, 
  yu, 
  usually 
  

   lies 
  between 
  90 
  and 
  100, 
  and 
  becomes 
  much 
  greater 
  as 
  the 
  

   forces 
  are 
  increased. 
  It 
  is 
  therefore 
  lawful 
  to 
  take 
  fi 
  as 
  of 
  

   order 
  10^. 
  In 
  the 
  formulae 
  (20), 
  (a, 
  /3, 
  y) 
  never 
  become 
  

   large, 
  and 
  therefore 
  whatever 
  the 
  value 
  of 
  x 
  (or 
  X), 
  the 
  

   approximation 
  may 
  be 
  conducted 
  by 
  expanding 
  the 
  functions 
  

   in 
  inverse 
  powers 
  of 
  /jl. 
  

  

  Thus 
  if 
  /J 
  = 
  log 
  ha 
  as 
  before^ 
  

  

  _4/3w;--^-^^i'-«pV). 
  (35) 
  

  

  This 
  neglects 
  the 
  ratio 
  ic^/fJ. 
  Taking 
  a 
  wire 
  of 
  gauge 
  

   J 
  cm., 
  an 
  approximate 
  practical 
  limit 
  for 
  overhead 
  wires, 
  and 
  

  

  * 
  Scientific 
  Papers; 
  iii. 
  

  

  