﻿74 
  Prof, 
  H. 
  A. 
  Rowland 
  on 
  Electrical 
  

  

  Method 
  4. 
  

  

  Li 
  [B!(r 
  + 
  B„) 
  + 
  R" 
  (B/ 
  + 
  B 
  /f 
  ) 
  ] 
  [B' 
  (B" 
  + 
  B„) 
  + 
  B" 
  (B, 
  + 
  B„) 
  ] 
  

   c 
  "~~ 
  R'B" 
  

  

  Method 
  5. 
  

  

  Li_ 
  [B,(B" 
  + 
  B„) 
  + 
  B„ 
  (B' 
  + 
  B")] 
  [B' 
  (B" 
  + 
  B„) 
  + 
  r(B' 
  + 
  B") 
  ] 
  

   c 
  " 
  (B' 
  + 
  B")(B" 
  + 
  B„) 
  

  

  Method 
  6. 
  

  

  ^or^=(B 
  + 
  B')(B" 
  + 
  r). 
  

  

  We 
  can 
  correct 
  for 
  self-inductions 
  I/, 
  L" 
  in 
  the 
  circuits 
  

   B', 
  B" 
  by 
  using 
  the 
  exact 
  equation 
  

  

  tf 
  ["[1/ 
  (r 
  + 
  B") 
  + 
  (L" 
  - 
  ^W] 
  [i/ 
  (B 
  + 
  B') 
  + 
  B"(L 
  4- 
  L')] 
  + 
  

  

  B 
  r 
  R"(r 
  + 
  B")(B+B'), 
  

  

  or 
  approximately 
  

  

  L 
  /T> 
  , 
  -on 
  m 
  „ 
  , 
  ^ 
  _ 
  L' 
  _ 
  L" 
  R 
  + 
  R' 
  ^ 
  u 
  L[L'(r 
  + 
  B") 
  + 
  L"B'] 
  

  

  c 
  c 
  

   + 
  &c. 
  

  

  = 
  (B 
  + 
  E')(B» 
  + 
  r)--- 
  -Jr 
  +# 
  

  

  Method 
  7. 
  

  

  R 
  3 
  R 
  3 
  M 
  12 
  M 
  13 
  + 
  & 
  2 
  [L 
  3 
  M 
  12 
  -M 
  23 
  M 
  13 
  ] 
  [L 
  2 
  M 
  13 
  -M, 
  3 
  M 
  1S 
  ] 
  = 
  0. 
  

  

  For 
  a 
  coil 
  containing 
  three 
  twisted 
  wires, 
  M 
  ]2 
  = 
  M 
  13 
  = 
  M 
  23 
  

   and 
  the 
  self-inductions 
  of 
  the 
  coils 
  are 
  also 
  equal 
  to 
  each 
  other 
  

   and 
  nearly 
  equal 
  to 
  the 
  mutual 
  inductions. 
  Put 
  an 
  extra 
  self- 
  

   induction 
  L 
  3 
  in 
  R 
  3 
  and 
  a 
  capacity 
  C 
  2 
  in 
  R 
  2 
  . 
  Replace 
  L 
  3 
  by 
  

  

  L 
  + 
  L 
  3 
  and 
  L 
  3 
  by 
  L— 
  prr 
  and 
  we 
  can 
  write 
  

  

  Ii 
  3+ 
  ^~ 
  M 
  =R 
  2 
  R 
  3 
  + 
  ^(L-M)(L 
  3 
  + 
  L-M). 
  

  

  ^2 
  

  

  As 
  L 
  — 
  M 
  is 
  very 
  small 
  and 
  can 
  be 
  readily 
  known, 
  the 
  

   formula 
  will 
  give 
  -J 
  . 
  When 
  L 
  — 
  M 
  = 
  we 
  have 
  

  

  L 
  2 
  L 
  3 
  

  

  77" 
  or 
  TT 
  —-^2^3- 
  

  

  U3 
  \Ji 
  

  

  -rr 
  Or 
  -ft- 
  =RoRa. 
  

  

  