﻿Measurement 
  by 
  Alternating 
  Currents. 
  73 
  

  

  Electric 
  absorption 
  in 
  a 
  condenser 
  acts 
  as 
  a 
  resistance 
  

   varying 
  with 
  the 
  square 
  of 
  the 
  period, 
  the 
  capacity 
  also 
  

   varying, 
  as 
  I 
  have 
  shown 
  above. 
  

  

  In 
  general 
  any 
  circuit 
  containing 
  resistances, 
  inductances, 
  

   and 
  capacities 
  combined 
  acts 
  as 
  a 
  resistance 
  and 
  inductance 
  or 
  

   capacity, 
  both 
  of 
  which 
  vary 
  with 
  the 
  current 
  period, 
  the 
  

   square 
  of 
  the 
  current 
  period 
  alone 
  entering. 
  For 
  symmetry 
  

   the 
  square 
  of 
  the 
  current 
  period 
  can 
  alone 
  enter 
  in 
  all 
  these 
  

   cases 
  and 
  those 
  above. 
  

  

  Hence 
  only 
  inductances 
  containing 
  no 
  iron 
  or 
  not 
  near 
  any 
  

   closed 
  metallic 
  circuits 
  have 
  a 
  fixed 
  value. 
  The 
  same 
  may 
  be 
  

   said 
  of 
  condensers, 
  as 
  they 
  must 
  be 
  free 
  from 
  electric 
  absorp- 
  

   tion 
  or 
  electrolytic 
  action 
  to 
  have 
  constants 
  independent 
  of 
  the 
  

   period. 
  There 
  is 
  no 
  apparent 
  hysteresis 
  in 
  condensers 
  and 
  the 
  

   constants 
  do 
  not 
  apparently 
  vary 
  with 
  the 
  electrostatic 
  force. 
  

  

  In 
  Plate 
  XIX. 
  I 
  have 
  drawn 
  the 
  diagrams 
  for 
  the 
  various 
  

   methods, 
  which 
  are 
  nearly 
  self-explanatory. 
  In 
  methods 
  1 
  to 
  

   14 
  inclusive, 
  the 
  concentric 
  circles 
  are 
  the 
  coils 
  of 
  the 
  electro- 
  

   dynamometer. 
  Either 
  one 
  is 
  the 
  fixed 
  coil 
  and 
  the 
  other 
  the 
  

   hanging 
  coil. 
  Oblong 
  figures 
  are 
  inductances, 
  and 
  when 
  near 
  

   each 
  other 
  are 
  mutual 
  inductances. 
  A 
  pair 
  of 
  cross-lines 
  is 
  

   a 
  condenser. 
  When 
  a 
  condenser 
  and 
  inductance 
  are 
  on 
  the 
  

   same 
  circuit, 
  we 
  may, 
  in 
  general, 
  leave 
  out 
  one 
  or 
  the 
  other. 
  

  

  The 
  following 
  numbers 
  indicate 
  both 
  the 
  number 
  of 
  the 
  

   method 
  and 
  the 
  figures 
  in 
  Plate 
  XIX. 
  

  

  Method 
  1. 
  

   I/„ 
  [Kfy 
  + 
  R") 
  +R 
  // 
  (r 
  + 
  R 
  / 
  )][R 
  / 
  (R 
  / 
  + 
  B„) 
  + 
  R"(R, 
  + 
  RQ] 
  

   c 
  (R 
  y 
  + 
  R" 
  + 
  R„) 
  3 
  

  

  — 
  or6 
  2 
  LL'or- 
  

  

  Method 
  2. 
  

  

  b 
  2 
  cc' 
  " 
  

  

  [^R'-^R'nCR/r 
  + 
  R'') 
  + 
  R> 
  + 
  R,)1 
  ^ 
  

   R 
  ii 
  (R 
  i 
  +R 
  /i 
  ) 
  

  

  Method 
  3. 
  

   In 
  (1) 
  make 
  R^R'^R^O, 
  or 
  in 
  (2) 
  make 
  R" 
  = 
  R,=0, 
  

  

  R..=oo 
  . 
  Hence 
  — 
  =rW. 
  

   " 
  c 
  

  

  In 
  case 
  the 
  circuit 
  r 
  contains 
  some 
  self-inductance, 
  / 
  ; 
  we 
  

   can 
  correct 
  for 
  it 
  by 
  the 
  equation 
  

  

  f-'^-i} 
  

  

  