﻿the 
  Alternate 
  Current 
  Generator, 
  65 
  

  

  with 
  Uq 
  = 
  27;/o, 
  in 
  which 
  

  

  ^ 
  ?ivGr 
  I 
  qw 
  J 
  nv 
  (. 
  g 
  qwg 
  ) 
  

  

  Tp 
  = 
  r^^ 
  v-U 
  + 
  X 
  — 
  '^ 
  r 
  V 
  = 
  —^ 
  K+ 
  ^^'^ 
  f^i^ 
  J- 
  

  

  ^ 
  ?zvGr 
  t 
  2^co 
  ' 
  J 
  nv 
  I. 
  p 
  pcog 
  } 
  

  

  as 
  G 
  = 
  gir^» 
  

  

  Putting 
  I 
  for 
  gn^^ 
  X 
  for 
  gv^, 
  m 
  for 
  gnv, 
  and 
  — 
  remembering 
  

   that 
  S 
  is 
  a 
  small 
  angle 
  (see 
  § 
  17) 
  — 
  unity 
  for 
  cos 
  8, 
  we 
  find 
  

   that 
  

  

  where 
  

  

  D^ 
  = 
  4{G 
  + 
  0'+-!^+2-sinS| 
  

  

  qco 
  

  

  2r 
  . 
  

  

  qcom 
  m 
  

  

  'Dq 
  sin/^ 
  = 
  ^373; 
  — 
  7^ 
  sin 
  ^ 
  

  

  A« 
  sm 
  d)^ 
  = 
  — 
  sm 
  o. 
  

  

  ^ 
  pwm 
  m 
  

  

  The 
  t 
  and 
  t 
  operators 
  having 
  been 
  calculated 
  from 
  these 
  

   formulse, 
  the 
  rest 
  of 
  the 
  solution 
  for 
  this 
  case 
  follows 
  in 
  

   every 
  particular 
  the 
  course 
  for 
  the 
  simple 
  case 
  fully 
  ex- 
  

   plained 
  in 
  §§8, 
  9. 
  

  

  ^2. 
  In 
  order 
  to 
  illustrate 
  the 
  practical 
  application 
  of 
  the 
  

   foregoing 
  theory, 
  I 
  will 
  determine 
  the 
  performance 
  of 
  a 
  small 
  

   two-pole 
  alternator 
  when 
  carrying 
  a 
  rather 
  heavy 
  non- 
  

   inductive 
  load* 
  

  

  The 
  details 
  of 
  the 
  alternator 
  are 
  as 
  follows 
  : 
  — 
  

  

  ! 
  diameter 
  12 
  cm, 
  

   leno-th 
  8 
  cm. 
  

   turns 
  n 
  = 
  lUU. 
  

   resistance 
  '25 
  ohm. 
  

  

  Air-gap 
  =1 
  mm. 
  

  

  r 
  turns 
  v 
  = 
  400. 
  

   Field 
  < 
  resistance 
  p 
  = 
  ?> 
  ohms. 
  

  

  (^exciter, 
  three 
  storage-cells 
  ; 
  r 
  — 
  ^'^ 
  volts. 
  

  

  Frequency 
  IOO/tt, 
  t. 
  e. 
  « 
  = 
  200. 
  

   Magnetic 
  leakage 
  =5 
  per 
  cent. 
  

   Flux 
  operator 
  Gr 
  = 
  5000i~^^ 
  

   PUl. 
  Mag. 
  S. 
  6. 
  Vol. 
  18. 
  No. 
  103. 
  July 
  1909. 
  F 
  

  

  