﻿428 
  Mr. 
  C. 
  A. 
  Chant 
  : 
  An 
  Experimental 
  Investigation 
  

  

  Suppose, 
  now, 
  the 
  periodic 
  current 
  at 
  the 
  surface 
  to 
  be 
  

   represented 
  by 
  

  

  io 
  = 
  I 
  sin 
  pt 
  (6) 
  

  

  We 
  have 
  to 
  solve 
  (5) 
  subject 
  to 
  the 
  conditions 
  

  

  io=Ismp>t, 
  when 
  a? 
  = 
  0, 
  .... 
  (7) 
  

  

  w=0, 
  „ 
  t=0. 
  . 
  . 
  . 
  (») 
  

  

  The 
  solution 
  is 
  

  

  I 
  sinjctfl 
  e~& 
  2 
  cos 
  -r^Y^d/3 
  — 
  cosptfl 
  e~P 
  2 
  sin 
  f 
  2R2 
  d$ 
  L 
  . 
  (9) 
  

  

  2 
  

  

  s/ir 
  

  

  2K 
  A 
  Jt 
  2Kjt 
  

  

  wherein 
  « 
  2 
  = 
  o-/47r^. 
  

  

  As 
  t 
  increases 
  the 
  condition 
  of 
  affairs 
  approaches 
  a 
  ' 
  \ 
  per- 
  

   manent 
  ' 
  state, 
  and 
  then 
  (9) 
  reduces 
  to 
  * 
  

  

  , 
  t 
  =I^ 
  S 
  in( 
  ?1 
  -V 
  2 
  7). 
  • 
  (10) 
  

   At 
  the 
  surface, 
  i.e. 
  when 
  w 
  = 
  0, 
  the 
  maximum 
  value 
  of 
  the 
  

   current 
  is 
  I. 
  It 
  becomes 
  - 
  of 
  this 
  value 
  at 
  a 
  depth 
  

  

  / 
  a 
  = 
  1 
  /*_ 
  

  

  V 
  2l7fXp 
  2tT 
  V 
  fM)l 
  

  

  (11) 
  

  

  This 
  depth 
  J. 
  J. 
  Thomson 
  t 
  and 
  Poincare 
  J 
  take 
  as 
  the 
  thick- 
  

   ness 
  of 
  the 
  ' 
  skin.' 
  The 
  difference 
  in 
  phase 
  between 
  the 
  

   current 
  at 
  the 
  surface 
  and 
  that 
  at 
  this 
  depth 
  is 
  easily 
  obtained 
  

   from 
  (10), 
  and 
  is 
  

  

  1 
  (radian) 
  = 
  57°'3. 
  

  

  For 
  high 
  frequencies 
  this 
  thickness 
  becomes 
  exceedingly 
  

   small, 
  and 
  an 
  object 
  of 
  the 
  present 
  investigation 
  was 
  to 
  see 
  

   whether 
  an 
  oscillator 
  behaved 
  differently 
  when 
  the 
  metal 
  con- 
  

   stituting 
  it 
  was 
  thinner 
  than 
  this 
  ' 
  skin'; 
  and 
  if 
  so, 
  what 
  was 
  

   the 
  critical 
  thickness 
  in 
  any 
  particular 
  case. 
  

  

  In 
  the 
  experiments 
  to 
  be 
  described, 
  oscillators 
  were 
  used 
  

   with 
  frequencies 
  approximately 
  375, 
  825, 
  2000, 
  3200 
  millions 
  

   per 
  second, 
  respectively. 
  Substituting 
  these 
  values 
  for 
  n 
  in 
  

   the 
  above 
  value 
  (11) 
  for 
  a?; 
  and 
  taking 
  /*=1, 
  <r~1600, 
  

   approximately, 
  for 
  copper 
  or 
  gold, 
  13,500 
  for 
  platinum, 
  and 
  

  

  * 
  See 
  Byerly's 
  'Fourier's 
  Series 
  and 
  Spherical 
  Harmonics/ 
  Art 
  51. 
  

   t 
  Recent 
  Researches, 
  pp. 
  260, 
  281. 
  

   % 
  Oscillations 
  Fdectriques, 
  p, 
  252. 
  

  

  