﻿66 
  Prof. 
  T. 
  H. 
  Lyle 
  on 
  the 
  Theory/ 
  of 
  

  

  Let 
  the 
  external 
  resistance 
  in 
  the 
  armature 
  circuit 
  in 
  the 
  

   case 
  in 
  hand 
  be 
  4*75 
  ohms 
  so 
  that 
  ^ 
  = 
  5 
  ohms. 
  

   Hence 
  (see 
  § 
  21) 
  

  

  / 
  = 
  5 
  . 
  10^ 
  V 
  = 
  -05 
  Z 
  = 
  '25 
  . 
  10^ 
  

  

  X 
  = 
  8 
  . 
  10^ 
  X' 
  = 
  •05X 
  = 
  4 
  . 
  10^ 
  

  

  m 
  = 
  2. 
  W, 
  r 
  = 
  5, 
  10^ 
  p 
  = 
  3 
  . 
  10^ 
  

  

  CO 
  = 
  200, 
  8 
  = 
  3° 
  and 
  

  

  Zq 
  = 
  2r)/p 
  ~ 
  '4:4 
  (absolute). 
  

  

  Using 
  these 
  values 
  for 
  the 
  constants 
  and 
  the 
  formulse 
  in 
  

   § 
  21 
  we 
  obtain 
  the 
  t 
  and 
  r 
  operators 
  which 
  are 
  given 
  in 
  the 
  

   following 
  table 
  : 
  — 
  

  

  tq 
  = 
  J)qi-fq' 
  

  

  rp=Apc 
  "^r 
  

  

  Q- 
  

  

  D,. 
  

  

  /«. 
  

  

  V' 
  

  

  Ap. 
  

  

  (pp. 
  

  

  1 
  

  

  •592 
  

  

  24° 
  51' 
  

  

  2 
  

  

  8-4 
  

  

  0° 
  22' 
  

  

  3 
  

  

  •535 
  

  

  8 
  48 
  

  

  4 
  

  

  8-4 
  

  

  8' 
  

  

  5 
  

  

  •530 
  

  

  5 
  18 
  

  

  6 
  

  

  8-4 
  

  

  1' 
  

  

  7 
  

  

  •528 
  

  

  3 
  45 
  

  

  8 
  

  

  8-4 
  

  

  -r 
  

  

  9 
  

  

  •527 
  

  

  2 
  54 
  

  

  10 
  

  

  8-4 
  

  

  -2' 
  

  

  11 
  

  

  •526 
  

  

  2 
  21 
  

  

  ]2 
  

  

  8-4 
  

  

  -3' 
  

  

  13 
  

  

  •526 
  

  

  1 
  57 
  

  

  14 
  

  

  8-4 
  

  

  -4' 
  

  

  15 
  

  

  •526 
  

  

  1 
  40 
  

  

  16 
  

  

  8-4 
  

  

  -5' 
  

  

  17 
  

  

  •526 
  

  

  1 
  28 
  ! 
  

  

  1 
  

  

  18 
  

  

  8-4 
  

  

  -5' 
  

  

  [Note 
  that 
  the 
  r 
  operators 
  are 
  all 
  practically 
  equal 
  and 
  

   simple 
  numerical 
  multipliers 
  (see 
  § 
  8).] 
  

  

  And 
  from 
  these, 
  by 
  the 
  method 
  explained 
  in 
  § 
  8 
  we 
  obtain 
  

   the 
  S, 
  S, 
  continued 
  fraction 
  operators 
  which 
  are 
  given 
  in 
  the 
  

   following 
  table 
  : 
  — 
  

  

  Bq=Sql-h' 
  

  

  2p=(rpi~rp- 
  

  

  Q- 
  

  

  Sq. 
  

  

  b,. 
  

  

  p. 
  

  

  (Tp. 
  

  

  f^p. 
  

  

  1 
  

  

  3 
  

   5 
  

   7 
  

   9 
  

   11 
  

   13 
  

  

  •457 
  

   •366 
  

   •353 
  

   •350 
  

   •348 
  

   •346 
  

   •346 
  

  

  36° 
  32' 
  

   15 
  32 
  

   9 
  50 
  

   7 
  9 
  

   5 
  34 
  

   4 
  30 
  

   3 
  42 
  

  

  2 
  

  

  4 
  

  

  6 
  

  

  8 
  

  

  10 
  

  

  12 
  

  

  14 
  

  

  5-82 
  

   5-63 
  

   5-57 
  

   5-55 
  

   5-53 
  

   5-51 
  

   5-50 
  

  

  7° 
  46' 
  

   5 
  8 
  

   3 
  40 
  

   2 
  54 
  

   2 
  18 
  

   1 
  51 
  

   1 
  21 
  

  

  And 
  from 
  these 
  as 
  explained 
  in 
  § 
  9 
  we 
  obtain 
  the 
  different 
  

   harmonics 
  of 
  both 
  the 
  armature 
  current 
  and 
  the 
  induced 
  

   field 
  current. 
  These 
  also 
  are 
  given 
  in 
  tabular 
  form: 
  — 
  

  

  