﻿the 
  Alternate 
  Current 
  Generator, 
  61 
  

  

  Hence, 
  following 
  the 
  assumption 
  already 
  made, 
  if 
  the 
  

   mao-netizino- 
  current-turns 
  

  

  nx 
  = 
  ?i(a] 
  + 
  as 
  + 
  aj 
  -h 
  &c.) 
  

   produce 
  in 
  a 
  magnetic 
  circuit 
  the 
  flux 
  

  

  then 
  A 
  = 
  nGi&u 
  /s 
  = 
  nGi&z, 
  &c. 
  

  

  where 
  the 
  G's 
  are 
  operators 
  of 
  the 
  type 
  given 
  by 
  G^=g^L-^q, 
  

   In 
  the 
  above 
  the 
  back 
  E.M.F., 
  e 
  say, 
  in 
  the 
  magnetizing 
  

   coils 
  due 
  to 
  variation 
  of 
  flux 
  is 
  

  

  e 
  = 
  n-^j=ncoL^Xqf^ 
  

  

  and 
  the 
  power 
  absorbed, 
  that 
  is 
  the 
  total 
  iron 
  loss 
  per 
  sec. 
  

   in 
  the 
  magnetic 
  circuit, 
  is 
  the 
  mean 
  value 
  of 
  ex, 
  that 
  is 
  of 
  the 
  

   product 
  

  

  Sa 
  into 
  nwL^^^qfq 
  

   which 
  (see 
  § 
  11) 
  = 
  Jn&)X($S/^ 
  . 
  a 
  ) 
  

  

  17. 
  As 
  an 
  example 
  let 
  us 
  determine 
  the 
  G 
  operator 
  for 
  a 
  

   magnetic 
  circuit 
  of 
  uniform 
  cross 
  section 
  = 
  100 
  cm.^, 
  made 
  

   up 
  of 
  40 
  cm. 
  length 
  of 
  laminated 
  iron 
  and 
  two 
  air-gaps 
  each 
  

   1 
  mm. 
  when 
  B 
  maximum 
  = 
  5000 
  and 
  the 
  frequency 
  30. 
  

  

  In 
  the 
  paper 
  already 
  quoted 
  we 
  find 
  for 
  a 
  sample 
  of 
  

   No. 
  2^ 
  iron 
  well 
  insulated 
  between 
  the 
  laminae 
  when 
  Bmax 
  

   = 
  5000 
  and 
  frequency 
  = 
  30 
  q.p. 
  that 
  

  

  yL. 
  = 
  2500fc-^^° 
  (nearly). 
  

   Now 
  G= 
  ^"^ 
  

  

  

  , 
  ^ 
  L 
  1 
  r 
  40 
  50° 
  , 
  ^^ 
  

  

  A/x 
  100 
  L 
  2500 
  ' 
  "^'-^J 
  

   = 
  l,{l6.^«°-|-200} 
  

  

  2106 
  3°18' 
  

  

  L 
  

  

  10^ 
  

   Hence 
  G 
  = 
  5968 
  6"^°!^' 
  

  

  