﻿68 
  ProL 
  T. 
  R. 
  Lyle 
  on 
  the 
  Theory 
  of 
  

  

  and 
  induced 
  field-currents 
  determined 
  above, 
  correctly 
  a& 
  

   regards 
  both 
  their 
  relative 
  amplitudes 
  and 
  phases. 
  

  

  23. 
  In 
  designing 
  the 
  field 
  o£ 
  an 
  alternator 
  attention 
  should 
  

   be 
  given 
  to 
  the 
  fact 
  that 
  the 
  conductor 
  has 
  to 
  carry 
  not 
  only 
  

   the 
  exciting 
  current, 
  but 
  also 
  the 
  induced 
  field-current, 
  

   which, 
  as 
  we 
  have 
  seen, 
  may 
  at 
  full 
  load 
  attain 
  a 
  relatively 
  

   large 
  value. 
  In 
  addition 
  it 
  should 
  not 
  be 
  forgotten 
  that 
  in 
  

   the 
  field-magnet 
  cores 
  there 
  is 
  the 
  associated 
  alternating 
  flux 
  

   which 
  causes 
  some 
  additional 
  heat. 
  

  

  It 
  is 
  well 
  known 
  that 
  in 
  a 
  case 
  o£ 
  excessive 
  heating 
  in 
  the 
  

   field, 
  reduction 
  o£ 
  the 
  heating 
  is 
  effected 
  by 
  the 
  employment 
  

   of 
  heavy 
  closed 
  copper 
  conductors, 
  called 
  dampers, 
  embracing 
  

   the 
  field-magnet 
  poles. 
  

  

  To 
  explain 
  this 
  action, 
  let 
  us 
  consider 
  a 
  two-pole 
  machine 
  

   on 
  each 
  field 
  pole 
  o£ 
  which 
  is 
  a 
  damper. 
  

  

  Neglecting 
  magnetic 
  leakage 
  and 
  iron 
  loss, 
  if 
  f 
  be 
  the 
  

   current 
  in 
  each 
  damper, 
  the 
  magnetic 
  flux 
  through 
  the 
  

   armature 
  windings 
  is 
  

  

  ^1 
  ?2A' 
  + 
  (vf 
  4- 
  2?") 
  cos 
  ft)i|- 
  , 
  

  

  and 
  that 
  through 
  the 
  field 
  windings 
  and 
  the 
  dampers 
  is 
  

  

  ^ 
  { 
  vf 
  -f- 
  2 
  f 
  + 
  n.i' 
  cos 
  ft)^ 
  } 
  , 
  

  

  so 
  that 
  the 
  equations 
  connecting 
  x, 
  f 
  , 
  and 
  f 
  are 
  

  

  Tx 
  +gn 
  -J- 
  {nx 
  + 
  (j'f 
  + 
  2f) 
  cos 
  cot} 
  = 
  0, 
  

   p^-^-gvj^{y^+2^+7ixcos(Dt}==v, 
  K 
  . 
  (VII.) 
  

  

  z^+g 
  -T.{v^+ 
  ^2^ 
  -\-nx 
  cos 
  cot} 
  = 
  0, 
  j 
  

  

  where 
  z 
  is 
  the 
  resistance 
  of 
  each 
  damper 
  and 
  the 
  other 
  

   symbols 
  have 
  the 
  same 
  significations 
  as 
  in 
  the 
  previous 
  

   sections 
  of 
  this 
  paper. 
  

  

  Obviously 
  there 
  is 
  no 
  constant 
  term 
  in 
  f, 
  and 
  considering 
  

   only 
  the 
  variable 
  terms 
  (harmonics) 
  in 
  f, 
  we 
  see 
  at 
  once 
  that 
  

  

  from 
  which 
  it 
  follows 
  that 
  

  

  v^ 
  + 
  2f=vf(l4-.t:) 
  = 
  vf 
  say, 
  

   where 
  

  

  and 
  that 
  

  

  