﻿Measurement 
  by 
  Alternating 
  Currents, 
  81 
  

  

  Method 
  19. 
  

   & 
  2 
  (L'J-M 
  2 
  ) 
  = 
  ^ 
  [E'E 
  // 
  -B 
  // 
  E 
  / 
  ], 
  

   L' 
  R' 
  + 
  R, 
  ulll-Wfl 
  Ll 
  \ 
  R' 
  + 
  R, 
  BMg//, 
  t 
  \ 
  

  

  This 
  is 
  useful 
  in 
  obtaining 
  the 
  constants 
  of 
  an 
  induction 
  

   standard. 
  For 
  twisted 
  wires 
  L'l— 
  M 
  2 
  should 
  be 
  nearly 
  0, 
  de- 
  

   pending, 
  as 
  it 
  does, 
  on 
  the 
  magnetic 
  leakage 
  between 
  the 
  

  

  coils. 
  Yt 
  * 
  s 
  often 
  known 
  sufficiently 
  nearly 
  for 
  substitution 
  

  

  in 
  the 
  right 
  hand 
  member. 
  It 
  can, 
  however, 
  be 
  found 
  by 
  

   reversing 
  the 
  inductance 
  standard. 
  

  

  

  

  Method 
  20. 
  

  

  

  

  

  R'R„-R"R,=0, 
  

  

  

  M 
  

   L 
  = 
  

  

  R" 
  M 
  

   R, 
  + 
  R 
  7/ 
  ' 
  L' 
  

  

  any 
  value. 
  

  

  W 
  R, 
  2 
  L 
  

  

  R'^R^ 
  + 
  RJ' 
  25 
  L'- 
  

  

  W 
  

  

  ~R' 
  + 
  R" 
  

  

  L>M: 
  V 
  

  

  In 
  case 
  of 
  a 
  standard 
  inductance, 
  M 
  and 
  L 
  are 
  known, 
  

   especially 
  when 
  the 
  wires 
  are 
  twisted. 
  

  

  The 
  method 
  can 
  then 
  be 
  used 
  for 
  determining 
  any 
  other 
  

   inductance, 
  I/, 
  and 
  is 
  very 
  convenient 
  for 
  the 
  purpose. 
  

  

  R 
  y/ 
  and 
  R 
  / 
  + 
  R 
  // 
  are 
  first 
  calculated 
  from 
  the 
  inductance 
  

   standard. 
  The 
  Wheatstone 
  bridge 
  is 
  then 
  adjusted 
  and 
  W 
  

   varied 
  until 
  a 
  balance 
  is 
  obtained. 
  This 
  balance 
  is 
  indepen- 
  

   dent 
  of 
  the 
  current 
  period, 
  as 
  also 
  in 
  the 
  next 
  two 
  methods. 
  

  

  Method 
  21. 
  

   R'R^-R^R^O, 
  

  

  J_ 
  R'+R, 
  I/_(R/ 
  + 
  R 
  Z 
  ) 
  2 
  L'_ 
  R' 
  + 
  R 
  

  

  M~ 
  R, 
  ; 
  M~ 
  rR 
  y 
  ; 
  I 
  ~~ 
  r 
  L 
  

  

  This 
  is 
  Niven's 
  method 
  adapted 
  to 
  alternating 
  currents. 
  

   See 
  remarks 
  to 
  method 
  20. 
  

  

  Methods 
  20 
  and 
  21 
  are 
  specially 
  useful 
  when 
  one 
  wishes 
  to 
  

   set 
  up 
  an 
  apparatus 
  for 
  measuring 
  self-induction, 
  as 
  the 
  

   resistances 
  R', 
  R", 
  R 
  /} 
  R 
  y/ 
  can 
  be 
  adjusted 
  once 
  for 
  all 
  in 
  

   case 
  of 
  a 
  given 
  inductance 
  standard 
  and 
  only 
  W 
  or 
  r 
  need 
  be 
  

   varied 
  afterwards. 
  

  

  Phil. 
  Mag. 
  S. 
  5. 
  Vol. 
  45. 
  No. 
  272. 
  Jan. 
  1898. 
  G 
  

  

  