﻿in 
  Iron 
  by 
  liapidly 
  Oscillating 
  Current-fields. 
  501 
  

  

  and 
  his 
  results 
  show 
  that 
  the 
  permeability 
  of 
  the 
  iron 
  is 
  still 
  

   very 
  great 
  with 
  rapid 
  oscillations. 
  

  

  Since 
  the 
  very 
  early 
  experiments 
  first 
  mentioned, 
  none 
  

   have 
  been 
  described 
  showing 
  directly 
  that 
  iron 
  is 
  magnetized 
  

   in 
  a 
  rapidly 
  alternating 
  field, 
  or 
  showing 
  how 
  the 
  induced 
  

   magnetization 
  depends 
  on 
  the 
  frequency 
  of 
  oscillation. 
  The 
  

   present 
  research 
  was 
  undertaken 
  to 
  show, 
  by 
  a 
  direct 
  method, 
  

   how 
  the 
  magnetization 
  induced 
  in 
  iron 
  by 
  such 
  oscillatory 
  

   fields 
  depends 
  on 
  the 
  strength 
  and 
  frequency 
  of 
  the 
  field, 
  

   and 
  on 
  the 
  diameters 
  of 
  the 
  wire 
  used. 
  

  

  The 
  relations 
  between 
  these 
  quantities 
  will 
  be 
  most 
  clearly 
  

   displayed 
  by 
  considering 
  the 
  alteration 
  in 
  the 
  magnetization 
  

   produced 
  by 
  (1) 
  altering 
  the 
  frequency 
  while 
  keeping 
  the 
  

   magnetizing 
  field 
  constant, 
  (2) 
  altering 
  the 
  magnetizing 
  

   field 
  while 
  keeping 
  the 
  frequency 
  constant 
  ; 
  or 
  if 
  B 
  repre- 
  

   sents 
  the 
  maximum 
  induced 
  magnetism, 
  n 
  the 
  frequency 
  of 
  

   oscillation, 
  H 
  the 
  maximum 
  intensity 
  of 
  the 
  magnetizing 
  

  

  field 
  ; 
  (1) 
  ( 
  J- 
  B 
  ) 
  and 
  (2) 
  (||) 
  

  

  \ 
  O 
  n 
  / 
  H 
  = 
  const. 
  \ 
  O 
  Jo. 
  / 
  n 
  = 
  const. 
  

  

  2. 
  When 
  a 
  leyden-jar 
  of 
  capacity 
  C 
  is 
  discharged 
  through 
  

   a 
  circuit 
  containing 
  self-induction 
  L 
  and 
  resistance 
  E, 
  the 
  

   oscillatory 
  current, 
  i, 
  at 
  any 
  time 
  t 
  is 
  given 
  by* 
  

  

  Rf 
  

  

  2Q 
  

   ^ 
  . 
  e 
  2L 
  . 
  sin 
  

  

  / 
  V'4L(J-K 
  2 
  C 
  2 
  A 
  

  

  where 
  Q 
  is 
  the 
  quantity 
  of 
  electricity 
  in 
  the 
  condenser 
  at 
  

   time 
  £ 
  = 
  0. 
  -d 
  2 
  , 
  < 
  

  

  If, 
  as 
  is 
  the 
  case 
  in 
  all 
  the 
  following 
  experiments, 
  —r- 
  

  

  ' 
  4L 
  

   is 
  very 
  small 
  compared 
  with 
  unity, 
  we 
  can 
  write 
  the 
  equation 
  

   in 
  the 
  usual 
  form 
  

  

  . 
  e 
  ^ 
  L 
  . 
  sin 
  

  

  •nr 
  vEtr 
  

  

  which 
  shows 
  that 
  i 
  goes 
  through 
  harmonic 
  oscillations 
  of 
  

   frequency 
  n= 
  ~r=- 
  and 
  of 
  decreasing 
  amplitude. 
  For 
  

  

  di 
  

  

  the 
  first 
  and 
  greatest 
  amplitude 
  -=- 
  = 
  0, 
  whence 
  

  

  ^LCtan-'dy^), 
  

  

  7 
  SM 
  

  

  R 
  2 
  C 
  

  

  or 
  practically, 
  since 
  *-— 
  is 
  very 
  small, 
  

  

  2 
  ' 
  

  

  * 
  See 
  Bedell 
  & 
  Crehore's 
  ' 
  Alternating- 
  Currents/ 
  p. 
  107. 
  

  

  