﻿64 
  Prof. 
  T. 
  R. 
  Lyle 
  on 
  the 
  Theory 
  of 
  

  

  20. 
  In 
  § 
  16 
  it 
  was 
  shown 
  that 
  the 
  iron 
  loss 
  (i. 
  e. 
  energy 
  

   dissipated 
  per 
  sec. 
  in 
  the 
  iron) 
  in 
  a 
  magnetic 
  circuit 
  is 
  

  

  hence 
  the 
  loss 
  due 
  to 
  the 
  flux 
  A^ 
  § 
  18 
  is 
  

  

  ^cdSo— 
  sinS„; 
  

   9q 
  ^ 
  

  

  ^(otqgq 
  sin 
  ^jTia^-f- 
  ^ 
  (a^_i 
  + 
  ^^+i) 
  

   and 
  that 
  due 
  to 
  the 
  flux 
  Ay 
  is 
  

  

  Adding 
  these 
  we 
  find 
  that 
  the 
  total 
  iron 
  loss 
  in 
  the 
  generator 
  

  

  13 
  

  

  ia)X^^^sinS^|72a^+|(a^_l 
  + 
  a2+l) 
  + 
  ^ 
  (a^_i-<5tg+l) 
  |. 
  

  

  Expanding 
  and 
  remembering 
  that 
  

  

  2 
  _ 
  _ 
  A 
  

  

  cc 
  + 
  13 
  = 
  u^ 
  + 
  13^ 
  + 
  2ul3 
  cos 
  c^^y 
  

  

  and 
  that 
  

  

  ^q-l+<^g+l=-iq(^q^q 
  (see 
  § 
  19) 
  

  

  we 
  find 
  that 
  the 
  total 
  iron 
  loss 
  is 
  equal 
  to 
  

  

  S 
  ^iqcogg 
  sin 
  Bq 
  -|^~ 
  {al_^ 
  + 
  a^^^) 
  - 
  n'^^j 
  — 
  -Ir 
  sin^ 
  8^ 
  + 
  qcol' 
  sin 
  B^ 
  cos 
  Bgj 
  a^J 
  

  

  where 
  5' 
  is 
  odd. 
  

  

  21. 
  An 
  approximate 
  determination 
  of 
  the 
  effect 
  of 
  iron 
  

   loss 
  on 
  the 
  performance 
  of 
  an 
  alternator 
  can 
  be 
  obtained 
  by 
  

   taking 
  all 
  the 
  G 
  operators 
  for 
  its 
  magnetic 
  circuit 
  as 
  equal 
  

   to 
  Gi, 
  that 
  is, 
  equal 
  to 
  the 
  one 
  for 
  the 
  fundamental 
  harmonic 
  

   of 
  the 
  armature 
  flux. 
  

  

  Making 
  this 
  simplification 
  in 
  the 
  equations 
  of 
  § 
  19, 
  we 
  

   find 
  that 
  aj, 
  ag, 
  as, 
  &c., 
  uq, 
  ag? 
  <^c., 
  are 
  connected 
  by 
  the 
  two 
  

   series 
  of 
  equations 
  

  

  a^_i 
  + 
  Tpa^-f 
  a^^i 
  = 
  

  

  