﻿Roioland 
  and 
  Penniman 
  — 
  Electrical 
  Measurements. 
  39 
  

  

  In 
  this 
  method 
  the 
  hanging 
  coil 
  is 
  shunted 
  off 
  the 
  fixed 
  coils 
  

   circuit, 
  and 
  this 
  with 
  a 
  non-inductive 
  resistance 
  in 
  circuit 
  with 
  

   the 
  hanging 
  coils 
  is 
  made 
  the 
  same 
  as 
  that 
  of 
  a 
  certain 
  induc- 
  

   tive 
  resistance 
  in 
  circuit 
  with 
  the 
  hanging 
  coil. 
  The 
  connec- 
  

   tions 
  are 
  made 
  as 
  in 
  the 
  figs. 
  1, 
  2, 
  where 
  CoC*'^^, 
  C^e^^'CSi^+^i), 
  

   C^e^■(6# 
  + 
  (?».2) 
  are 
  currents. 
  K, 
  R', 
  ?', 
  resistancec. 
  Thev 
  represent 
  

   the 
  entire 
  resistance 
  of 
  their 
  respective 
  branches. 
  L 
  represents 
  

   self 
  -inductance 
  of 
  the 
  .coil 
  by 
  which 
  it 
  is 
  placed. 
  The 
  outer 
  

   circle 
  in 
  fig. 
  1 
  represents 
  the 
  fixed 
  coils 
  and 
  the 
  small 
  circle 
  the 
  

   hanging 
  coil 
  of 
  the 
  electrodjnamometer. 
  In 
  fig. 
  2 
  the 
  termi- 
  

   nals 
  of 
  the 
  fixed 
  and 
  hanging 
  coils 
  are 
  represented 
  by 
  F 
  and 
  H. 
  

   D 
  is 
  a 
  reversing 
  commutator. 
  K 
  is 
  a 
  key 
  to 
  send 
  the 
  current 
  

   first 
  through 
  the 
  inductive 
  and 
  then 
  through 
  the 
  non-inductive 
  

   resistance. 
  Ij 
  = 
  27r?i, 
  n 
  = 
  complete 
  alternation 
  per 
  sec. 
  This 
  

   is 
  the 
  general 
  notation 
  adopted 
  throughout 
  the 
  article. 
  

  

  The 
  quantity 
  to 
  be 
  found 
  is 
  QS^\ 
  cos 
  (/)^, 
  which 
  is 
  proportional 
  

   to 
  the 
  deflection 
  of 
  the 
  hanging 
  coil 
  in 
  the 
  two 
  positions 
  of 
  E, 
  

  

  In 
  one 
  position 
  

  

  Therefore 
  

  

  In 
  the 
  other 
  position 
  of 
  K 
  

  

  C/ 
  ^^^ 
  R' 
  =: 
  Q\ 
  P^ 
  r— 
  (C/*^-(C; 
  i^^) 
  r 
  

   Therefore 
  

  

  (/) 
  = 
  0, 
  as 
  (/) 
  is 
  an 
  angle 
  whose 
  tangent 
  is 
  ^y 
  and 
  C 
  = 
  nearly. 
  

   In 
  the 
  case 
  of 
  equal 
  deflection 
  D 
  = 
  D' 
  and 
  therefore 
  

   ^^L'=(R'-R) 
  (R 
  + 
  r) 
  

  

  If 
  capacity 
  had 
  been 
  used 
  in 
  the 
  place 
  of 
  self-inductance 
  the 
  

   formula 
  would 
  be 
  

  

  j^ 
  = 
  (R'-R)(K+'-) 
  

  

  If 
  self-inductance 
  and 
  capacity 
  were 
  used 
  in 
  series 
  

  

  ■ 
  *'(L-:^y 
  = 
  (R'-R)(R+'-) 
  

  

  The 
  application 
  of 
  this 
  formula 
  to 
  the 
  measurement 
  of 
  self- 
  

   inductance 
  gave 
  results 
  that 
  agreed 
  to 
  within 
  the 
  accuracy 
  with 
  

   which 
  the 
  period 
  of 
  the 
  alternations 
  could 
  be 
  determined. 
  

  

  