﻿on 
  the 
  Hysteresis 
  Loss 
  in 
  Iron 
  in 
  a 
  Rotating 
  Field. 
  869 
  

  

  current 
  of 
  '31 
  amp. 
  a 
  rotating 
  field 
  of 
  about 
  20 
  C.G.S. 
  units 
  

   was 
  produced 
  at 
  the 
  point 
  0. 
  A 
  small 
  coil, 
  made 
  up 
  with 
  

   200 
  turns 
  of 
  no. 
  46 
  wire 
  (140 
  ohms 
  resistance) 
  5 
  cms. 
  long 
  

   and 
  1 
  cm. 
  broad, 
  is 
  suspended 
  in 
  the 
  central 
  space 
  between 
  

   the 
  coils, 
  and 
  is 
  connected 
  to 
  the 
  search-coil 
  on 
  the 
  iron 
  

   specimen. 
  In 
  the 
  galvanometer-coil 
  there 
  are 
  two 
  E.M.F.'s, 
  

   one, 
  E 
  cos 
  pt 
  (say) 
  due 
  to 
  the 
  flux 
  in 
  the 
  iron 
  specimen, 
  and 
  

   one 
  due 
  to 
  the 
  rotating 
  field 
  of 
  the 
  galvanometer 
  itself. 
  

   Referring 
  to 
  fig. 
  2, 
  let 
  H 
  H' 
  be 
  the 
  direction 
  of 
  the 
  rotating 
  

   field 
  of 
  maximum 
  value 
  H 
  when 
  E 
  cos 
  pt 
  is 
  a 
  maximum. 
  

   The 
  angle 
  between 
  it 
  and 
  the 
  coil 
  at 
  a 
  time 
  t 
  will 
  be 
  6-{-pt, 
  

   and 
  the 
  component 
  along 
  the 
  coil 
  H 
  cos 
  pi 
  H-^. 
  The 
  flux 
  

   normal 
  to 
  the 
  coil 
  is 
  Hsinj9i 
  + 
  ^, 
  and 
  the 
  E.M.F. 
  induced 
  is 
  

   proportional 
  to 
  

  

  Hp 
  cos 
  pt-\-0 
  = 
  El 
  cos 
  pt-\-0. 
  

  

  If 
  R 
  be 
  the 
  resistance 
  of 
  the 
  coil 
  and 
  the 
  self-induction 
  is 
  

   negligible, 
  the 
  resultant 
  current 
  is 
  equal 
  to 
  

  

  ^(Ecospi 
  + 
  Ei 
  cos 
  pt-\- 
  6). 
  

  

  The 
  torque 
  at 
  a 
  time 
  t 
  will 
  be 
  proportional 
  to 
  

  

  H 
  cos 
  pt 
  + 
  6 
  I 
  TJ 
  (E 
  COS 
  jyt 
  + 
  El 
  cos 
  pH^) 
  > 
  . 
  

  

  Hence 
  the 
  mean 
  torque 
  acting 
  on 
  the 
  coil 
  is 
  proportional 
  to 
  

  

  |{Ecos^ 
  + 
  Ei}. 
  

  

  This 
  deflecting 
  torque 
  therefore 
  consists 
  of 
  two 
  parts, 
  one 
  

   constant 
  and 
  one 
  which 
  depends 
  on 
  the 
  position 
  of 
  the 
  four 
  

   magnetizing-coils 
  A 
  B 
  C 
  D. 
  In 
  the 
  apparatus 
  used 
  these 
  

   coils 
  were 
  fixed 
  to 
  a 
  turntable, 
  which 
  could 
  be 
  rotated 
  until 
  

   the 
  deflexion 
  was 
  a 
  maximum. 
  The 
  deflecting 
  torque 
  would 
  

  

  then 
  be 
  proportional 
  to 
  ^(E 
  + 
  Ei). 
  Another 
  way 
  of 
  using 
  

  

  the 
  instrument 
  is 
  to 
  get 
  E 
  and 
  Ei 
  in 
  opposition, 
  in 
  which 
  

   case 
  the 
  minimum 
  deflexion 
  is 
  proportional 
  to 
  (E, 
  — 
  E) 
  ; 
  and 
  

   this 
  is 
  the 
  better 
  method 
  because 
  the 
  total 
  deflexion 
  is 
  

   smaller, 
  and 
  greater 
  sensitiveness 
  is 
  obtained. 
  

  

  The 
  instrument 
  was 
  calibrated 
  by 
  putting 
  a 
  resistance 
  of 
  

   4000 
  ohms 
  in 
  series 
  with 
  the 
  coil 
  and 
  applying 
  a 
  measured 
  

   pressure 
  of 
  1*95 
  R.M.S. 
  volts 
  to 
  it. 
  The 
  derfexion, 
  after 
  

   deducting 
  that 
  obtained 
  by 
  shortcircuiting 
  the 
  coil 
  through 
  

   the 
  4000 
  ohms, 
  equalled 
  22*4 
  centimetres, 
  consequently 
  one 
  

  

  Fhil 
  Mag. 
  S. 
  6. 
  Vol. 
  18. 
  No. 
  108. 
  Dec. 
  J 
  909. 
  3 
  N 
  

  

  