﻿Measurement 
  by 
  Alternating 
  Currents. 
  83 
  

  

  Method 
  25. 
  

  

  In 
  fig. 
  6 
  remove 
  the 
  shunt 
  R/ 
  and 
  self-induction 
  L. 
  

  

  This 
  method 
  then 
  depends 
  upon 
  the 
  measurement 
  of 
  the 
  

   angular 
  deflexion 
  when 
  a 
  self-induction 
  or 
  a 
  capacity 
  is 
  put 
  

   in 
  the 
  circuit 
  of 
  the 
  small 
  coil 
  of 
  the 
  electrodynamometer, 
  and 
  

   comparing 
  this 
  with 
  the 
  deflexion 
  when 
  the 
  circuit 
  only 
  

   contains 
  resistance. 
  

  

  The 
  resistance 
  of 
  the 
  circuit, 
  r, 
  is 
  supposed 
  to 
  be 
  so 
  great 
  

   compared 
  with 
  R 
  that 
  the 
  current 
  in 
  the 
  main 
  circuit 
  remains 
  

   practically 
  unaltered 
  during 
  the 
  change. 
  

  

  There 
  is 
  also 
  an 
  error 
  due 
  to 
  the 
  mutual 
  induction 
  of 
  the 
  

   electrodynamometer-coils 
  which 
  vanishes 
  when 
  r 
  is 
  great. 
  

  

  These 
  formulas 
  assume 
  that 
  the 
  deflexion 
  is 
  proportional 
  

   to 
  6. 
  This 
  assumption 
  can 
  be 
  obviated 
  by 
  adjusting 
  6=0 
  f 
  , 
  

   when 
  we 
  have 
  

  

  Qr 
  w= 
  (r 
  + 
  B")(r,R"-rR 
  / 
  ") 
  > 
  

  

  6V 
  R 
  

  

  These 
  can 
  be 
  further 
  simplified 
  by 
  making 
  R 
  // 
  = 
  R/ 
  / 
  . 
  

  

  The 
  method 
  thus 
  becomes 
  very 
  easy 
  to 
  apply 
  and 
  capable 
  

   of 
  considerable 
  accuracy. 
  As 
  the 
  absolute 
  determination 
  

   depends 
  on 
  the 
  current 
  period, 
  however, 
  no 
  great 
  accuracy 
  

   can 
  be 
  expected 
  for 
  absolute 
  values 
  except 
  where 
  this 
  period 
  

   is 
  known 
  and 
  constant, 
  a 
  condition 
  almost 
  impossible 
  to 
  be 
  

   obtained. 
  The 
  comparison 
  of 
  condensers 
  or 
  of 
  inductances 
  is, 
  

   however, 
  independent 
  of 
  the 
  period 
  and 
  can 
  be 
  carried 
  out, 
  

   however 
  variable 
  the 
  period, 
  by 
  means 
  of 
  a 
  key 
  to 
  make 
  the 
  

   change 
  instantaneously. 
  

  

  Method 
  26. 
  

  

  Similar 
  results 
  can 
  be 
  obtained 
  by 
  putting 
  the 
  condenser 
  

   or 
  inductance 
  in 
  R 
  x/ 
  instead 
  of 
  r, 
  but 
  the 
  current 
  through 
  the 
  

   electrodynamometer 
  suspension 
  is 
  usually 
  too 
  great 
  in 
  this 
  

   case 
  unless 
  r 
  is 
  enormous. 
  We 
  have 
  in 
  this 
  case 
  for 
  equal 
  

   deflexions, 
  

  

  ^ 
  or 
  OT/««R"(B"+r) 
  ( 
  ri 
  \ 
  /R 
  !T 
  ) 
  

  

  where 
  r, 
  and 
  R/' 
  are 
  the 
  resistances 
  without 
  condenser 
  or 
  

   self-induction. 
  

  

  This 
  is 
  a 
  very 
  good 
  method 
  in 
  many 
  respects. 
  

  

  G2 
  

  

  