﻿into 
  the 
  ' 
  'Skin 
  '-effect 
  in 
  Electrical 
  Oscillators. 
  427 
  

  

  A 
  calculation 
  of 
  the 
  superficial 
  shell 
  effective 
  in 
  the 
  re- 
  

   flexion 
  of 
  Hertzian 
  oscillations 
  is 
  given 
  by 
  Poincare 
  *, 
  who 
  

  

  finds 
  the 
  thickness 
  at 
  which 
  the 
  effect 
  is 
  - 
  of 
  its 
  amount 
  at 
  

   the 
  surface, 
  ' 
  e 
  

  

  for 
  frequency, 
  7i 
  = 
  50 
  X 
  10 
  6 
  , 
  thickness 
  = 
  0002 
  cm.; 
  

   „ 
  „ 
  n 
  = 
  500 
  X 
  10 
  6 
  , 
  thickness=0'0006 
  cm. 
  

  

  This 
  estimate 
  is 
  probably 
  too 
  high. 
  

  

  J. 
  J. 
  Thomson 
  has 
  treated 
  the 
  ' 
  skin 
  '-effect 
  with 
  consider- 
  

   able 
  fulness. 
  In 
  a 
  note 
  appended 
  by 
  him 
  to 
  Art. 
  690 
  of 
  the 
  

   third 
  edition 
  of 
  Maxwell 
  f, 
  he 
  obtains 
  as 
  the 
  resistance 
  per 
  

   unit 
  length 
  of 
  the 
  conductor 
  

  

  B'-(g)* 
  ......... 
  oo 
  

  

  where 
  the 
  symbols 
  have 
  the 
  meanings 
  given 
  above. 
  This, 
  

   again, 
  is 
  the 
  same 
  as 
  the 
  values 
  obtained 
  by 
  Rayleigh 
  and 
  

   Stefan 
  . 
  

  

  We 
  can 
  obtain 
  the 
  relative 
  current-densities 
  at 
  different 
  

   depths 
  below 
  the 
  surface 
  for 
  any 
  given 
  frequency 
  in 
  the 
  

   following 
  way. 
  Stefan 
  % 
  has 
  shown 
  that 
  if 
  id 
  be 
  the 
  com- 
  

   ponent 
  of 
  the 
  current 
  in 
  the 
  direction 
  of 
  the 
  axis 
  of 
  z, 
  and 
  if 
  

   it 
  does 
  not 
  vary 
  with 
  z, 
  the 
  equation 
  

  

  div 
  _ 
  a 
  /d 
  2 
  iv 
  d 
  2 
  w\ 
  , 
  . 
  

  

  Tt~l7TfM\d? 
  + 
  df) 
  W 
  

  

  must 
  be 
  satisfied. 
  

  

  When 
  the 
  depth 
  to 
  which 
  the 
  action 
  penetrates 
  is 
  small, 
  the 
  

   effect 
  of 
  curvature 
  of 
  the 
  surface 
  may 
  usually 
  be 
  neglected, 
  

   in 
  which 
  case 
  (4t) 
  may 
  be 
  replaced 
  by 
  

  

  dw 
  _ 
  a 
  d?w 
  

  

  ~d~t~ 
  A^'dx 
  2 
  W 
  

  

  This 
  is 
  Fourier's 
  well-known 
  equation 
  of 
  diffusion 
  which 
  

   Lord 
  Kelvin 
  § 
  has 
  shown 
  to 
  be 
  applicable 
  to 
  the 
  motion 
  of 
  a 
  

   viscous 
  fluid, 
  of 
  closed 
  electric 
  currents 
  within 
  a 
  homo- 
  

   geneous 
  conductor, 
  of 
  heat, 
  of 
  substances 
  in 
  solution, 
  of 
  electric 
  

   potential 
  in 
  the 
  conductor 
  of 
  a 
  submarine 
  cable 
  ; 
  and, 
  indeed, 
  

   to 
  every 
  case 
  of 
  diffusion 
  in 
  which 
  the 
  substance 
  concerned 
  is 
  

   in 
  the 
  same 
  condition 
  at 
  all 
  points 
  of 
  any 
  one 
  plane 
  parallel 
  

   to 
  a 
  given 
  plane. 
  

  

  * 
  Oscillations 
  Electriques, 
  p. 
  246 
  & 
  fol. 
  

   f 
  See 
  also 
  ' 
  Recent 
  Researches,' 
  p. 
  246 
  & 
  fol. 
  

  

  \ 
  SitzungsbericMe 
  der 
  Wiener 
  Ahad. 
  der 
  Wiss. 
  xcv. 
  2 
  Abth. 
  p. 
  917 
  

   (1887). 
  

  

  § 
  Report 
  of 
  British 
  Assoc. 
  1888, 
  p. 
  571. 
  

  

  2 
  F 
  2 
  

  

  