﻿Measurement 
  by 
  Alternating 
  Currents. 
  79 
  

  

  The 
  first 
  equation 
  is 
  satisfied 
  by 
  adjusting 
  the 
  Wheatstone 
  

   bridge 
  so 
  as 
  to 
  make 
  

  

  (R,R"-R 
  /;/ 
  R') 
  =0 
  ; 
  R/'-R„r' 
  = 
  ; 
  

  

  R 
  l 
  (B 
  ll 
  +0-B 
  IJ 
  (B' 
  + 
  r')=a 
  

  

  That 
  is 
  

  

  JL 
  i?l_ 
  r 
  - 
  

   R,, 
  - 
  R" 
  ~ 
  r 
  ,r 
  

  

  We 
  can 
  then 
  adjust 
  W 
  with 
  alternating 
  currents. 
  This 
  is 
  a 
  

   very 
  good 
  method 
  and 
  easy 
  of 
  application, 
  but 
  requires 
  many 
  

   resistances 
  of 
  known 
  ratio. 
  Many 
  of 
  these, 
  however, 
  may 
  be 
  

   equal 
  without 
  disadvantage. 
  A 
  well-known 
  case 
  is 
  given 
  by 
  

   making 
  r' 
  and 
  r 
  f/ 
  =0. 
  

  

  (B) 
  By 
  placing 
  self-inductions 
  or 
  condensers 
  in 
  R, 
  and 
  r" 
  

   instead 
  of 
  the 
  above 
  we 
  have 
  the 
  following 
  

  

  ^ 
  or 
  -PL 
  e" 
  or 
  h 
  - 
  R, 
  (W 
  + 
  R") 
  - 
  R'R„ 
  

   tf 
  ' 
  I" 
  ~ 
  R" 
  ("W 
  + 
  / 
  + 
  r") 
  Wr" 
  

  

  ( 
  W" 
  + 
  r' 
  + 
  r")(R 
  y 
  R" 
  - 
  R„RQ 
  + 
  W 
  (R/' 
  - 
  R,/) 
  

   W 
  + 
  R" 
  

  

  Making 
  R 
  ;/ 
  = 
  0, 
  we 
  have 
  

  

  c" 
  72T 
  „ 
  L, 
  R.W-R'R,, 
  

   g- 
  or 
  -PL/' 
  or 
  ^ 
  = 
  w?y/ 
  " 
  

  

  -pC/' 
  or 
  7^ 
  or 
  -PV 
  , 
  =R%, 
  + 
  * 
  / 
  R//(i+ 
  f 
  ) 
  

   -^(R 
  y 
  W-R'R„). 
  

  

  In 
  case 
  we 
  adjust 
  the 
  bridge 
  to 
  R 
  ; 
  W 
  — 
  R 
  / 
  R 
  // 
  = 
  and 
  a 
  

   condenser 
  is 
  in 
  v" 
  so 
  that 
  we 
  can 
  make 
  r 
  f/ 
  =0, 
  the 
  value 
  of 
  

  

  — 
  6 
  2 
  L 
  / 
  c 
  // 
  will 
  be 
  indeterminate, 
  and 
  we 
  can 
  find 
  —~ 
  by 
  the 
  

  

  6 
  

  

  adjustment 
  of 
  W 
  alone. 
  

  

  This 
  is 
  an 
  excellent 
  method, 
  apparently, 
  as 
  only 
  one 
  adjust- 
  

   ment 
  is 
  required. 
  

  

  However, 
  see 
  the 
  remarks 
  on 
  method 
  15. 
  This 
  present 
  

  

  method 
  with 
  r-" 
  = 
  0for 
  — 
  is 
  Anderson's, 
  with, 
  however, 
  alter- 
  

  

  o 
  

  

  nating 
  currents 
  instead 
  of 
  direct 
  as 
  in 
  his. 
  

  

  The 
  other 
  two 
  values 
  are 
  imaginary 
  in 
  this 
  case. 
  Indeed 
  

  

  