﻿420 
  Dr. 
  J. 
  W. 
  Nicholson 
  on 
  Inductance 
  and 
  

  

  Moreover, 
  

  

  AE-BF 
  / 
  , 
  a, 
  , 
  llB. 
  ha^ 
  "^x 
  / 
  2 
  

  

  = 
  (.log^log;.a-^^log^ 
  + 
  y(^^ 
  

   27\ 
  2yL62^7, 
  , 
  

  

  + 
  1 
  

  

  27\ 
  

  

  (16) 
  

  

  The 
  succeeding 
  reduction 
  depends 
  upon 
  the 
  particular 
  

   circumstances 
  of 
  the 
  wires. 
  We 
  now 
  write 
  /a=1, 
  and 
  

   suppose 
  that 
  the 
  wires 
  are 
  of 
  copper. 
  The 
  only 
  case 
  needing 
  

   separate 
  treatment 
  is 
  that 
  of 
  iron, 
  where 
  (jl 
  is 
  very 
  large. 
  

  

  Inductance 
  when 
  fjL 
  = 
  l. 
  High 
  frequency 
  . 
  

  

  Quoting 
  the 
  value 
  of 
  M 
  in 
  (14), 
  the 
  inductance 
  becomes, 
  

   when 
  fJL^l, 
  

  

  where 
  

   AE-BF 
  

  

  -BF 
  r 
  . 
  a, 
  -, 
  ff, 
  ha^ 
  ^ 
  1\ 
  

   p—- 
  (-log-log 
  7.a--log- 
  + 
  -,j 
  

  

  CD 
  ,2, 
  2^, 
  ^ 
  ^ 
  1 
  

   p-=alogVw-— 
  log7ia+^. 
  

  

  Asymptotic 
  formulae 
  for 
  the 
  functions 
  (a, 
  y8, 
  7) 
  have 
  been 
  

   developed 
  by 
  Dr. 
  A. 
  Russell 
  *. 
  

  

  When 
  the 
  argument 
  a? 
  is 
  not 
  less 
  than 
  8, 
  then 
  to 
  four 
  

   significant 
  figures, 
  if 
  \ 
  = 
  /r 
  \^2f, 
  so 
  that, 
  in 
  terms 
  of 
  the 
  

   characteristics 
  of 
  the 
  two 
  wires^ 
  

  

  we 
  may 
  write 
  

  

  ,=2af-^y, 
  

  

  (19) 
  

  

  

  0^/•2 
  = 
  l 
  

  

  1_ 
  J^ 
  

  

  * 
  Proc. 
  Phys. 
  Soc. 
  vol. 
  xxii. 
  

  

  t 
  This 
  modification 
  is 
  more 
  convenient 
  for 
  purposes 
  of 
  printing. 
  

  

  (20) 
  

  

  