﻿430 
  Dr. 
  J. 
  W. 
  Nicholson 
  on 
  Inductance 
  and 
  

  

  II. 
  Effective 
  Kesistance. 
  

   Copper 
  Wires 
  with 
  High 
  Frequency. 
  

  

  The 
  limitations 
  o£ 
  all 
  the 
  formulae 
  below, 
  except 
  when 
  

   otherwise 
  stated, 
  are 
  the 
  same 
  as 
  in 
  the 
  corresponding 
  induc- 
  

   tance 
  formulae. 
  With 
  the 
  previous 
  notation, 
  the 
  effective 
  

   resistance 
  per 
  unit 
  length 
  of 
  the 
  two 
  wires 
  is 
  

  

  -p 
  _ 
  4w/>fc 
  ber 
  x 
  bei' 
  x—h&i 
  x 
  ber' 
  x 
  -^ 
  

   ~C 
  {hQv' 
  xf 
  + 
  {hQi'xy 
  

  

  ='-F-MS(^^+s^) 
  (^*) 
  

  

  where 
  CD/P 
  has 
  the 
  value 
  in 
  (15), 
  and 
  on 
  reduction 
  

  

  + 
  ^logAo(l-5 
  + 
  JW?). 
  . 
  (45) 
  

  

  When 
  At 
  = 
  1, 
  and 
  the 
  frequency 
  is 
  high, 
  so 
  that^ 
  if 
  x 
  s/2 
  — 
  \ 
  

   the 
  formulae 
  (20) 
  may 
  be 
  employed, 
  then 
  after 
  further 
  

   reduction, 
  

  

  AF 
  + 
  BE 
  2 
  , 
  a. 
  . 
  (. 
  2 
  5 
  \ 
  4 
  , 
  , 
  /, 
  2\ 
  

   — 
  P— 
  = 
  -log-logAa(^l-- 
  + 
  -,j-^log/.a^l--j 
  

  

  and 
  with 
  the 
  help 
  of 
  (32), 
  we 
  ultimately 
  obtain 
  

  

  ^(AF 
  + 
  BE) 
  = 
  2plogf+p-log^-i{p' 
  + 
  log^(2-3p 
  + 
  2p^)} 
  

  

  where 
  p=\ogeTia. 
  

  

  Finally, 
  for 
  a 
  pair 
  of 
  copper 
  wires, 
  with 
  high 
  frequency, 
  

   and 
  with 
  the 
  limitations 
  of 
  (34), 
  

  

  ^=$(^+^ 
  + 
  4T^)-w{''^'V-l)logf} 
  

  

  + 
  )^{^^ 
  + 
  ^2-3, 
  + 
  2,^)logi} 
  

  

  -^p\^P-^P" 
  + 
  ^p'-^^-^P-^^P'' 
  + 
  ^-p')^^S.~}- 
  (46) 
  

  

  