﻿42 
  Howland 
  and 
  Penniraan 
  — 
  Electrical 
  Measurements, 
  

   c' 
  R"R-R'R, 
  

  

  C; 
  ~"R'(R" 
  + 
  R,,)+r(R' 
  + 
  R'y 
  

  

  lotive 
  force 
  is 
  appliec 
  

   lis 
  case 
  is 
  

  

  When 
  a 
  periodic 
  electromotive 
  force 
  is 
  applied 
  to 
  a 
  and 
  d, 
  the 
  

   ratio 
  of 
  the 
  currents 
  in 
  this 
  case 
  is 
  

  

  C^ 
  ""R'(R" 
  + 
  RJ+r(R' 
  + 
  R'')+^^/(R' 
  + 
  R") 
  

   Separating 
  the 
  real 
  and 
  imaginary 
  parts 
  

   ^ 
  (R'R,-R^R 
  ')[ 
  R^(R" 
  + 
  R,) 
  + 
  y 
  (R' 
  + 
  R,)] 
  + 
  6VLR^'(R^ 
  + 
  R^^) 
  

  

  4. 
  

  

  If 
  now 
  the 
  fixed 
  coils 
  of 
  the 
  electrodjnamometer 
  are 
  placed 
  

   in 
  the 
  R^ 
  arm 
  of 
  the 
  bridge, 
  and 
  the 
  hanging 
  coil 
  is 
  placed 
  in 
  

   cross 
  connection 
  of 
  the 
  bridge, 
  as 
  in 
  fig. 
  4, 
  the 
  different 
  resist- 
  

   ances 
  may 
  be 
  adjusted 
  until 
  there 
  is 
  no 
  deflection, 
  in 
  which 
  

   case 
  ^ 
  = 
  90° 
  or 
  cos 
  </> 
  = 
  0, 
  therefore 
  

  

  (R"R^ 
  — 
  R'RJ 
  [R'(R" 
  + 
  RJ+r(R' 
  + 
  R")]+^VLR"(R'4-R") 
  = 
  

  

  . 
  R"R, 
  =:R'R 
  -6^/L 
  

  

  R"(R' 
  + 
  R") 
  

  

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

   If 
  in 
  connection 
  with 
  L' 
  a 
  capacity 
  C 
  is 
  added, 
  the 
  formula 
  

   becomes, 
  substituting 
  for 
  L^, 
  L/ 
  

  

  R''R, 
  = 
  RR,-(5^/L^-^) 
  

  

  b'c 
  

  

  (R"R' 
  + 
  RO 
  

  

  R'(ir 
  + 
  HJ— 
  r(R' 
  + 
  R") 
  

  

  In 
  most 
  cases 
  since 
  I 
  and 
  L^ 
  are 
  generally 
  the 
  self-inductances 
  

   of 
  the 
  instruments 
  the 
  term 
  If 
  I 
  L 
  can 
  be 
  neglected 
  in 
  compari- 
  

   son 
  with 
  - 
  and 
  the 
  equation 
  becomes 
  

  

  c 
  R'(H" 
  + 
  K,) 
  + 
  r(K'4-R") 
  

  

  In 
  this 
  equation 
  R^ 
  includes 
  both 
  the 
  ohmic 
  and 
  the 
  absorption 
  

   resistance. 
  The 
  value 
  of 
  R^ 
  is 
  determined 
  in 
  terms 
  of 
  known 
  

   quantities, 
  that 
  is 
  the 
  resistance 
  and 
  I 
  and 
  C. 
  It 
  was 
  not 
  

  

  