﻿46 
  Roidand 
  and 
  Penniman 
  — 
  Electrical 
  Measurements. 
  

  

  In 
  these 
  experiments 
  great 
  care 
  was 
  taken 
  that 
  the 
  measure- 
  

   ments 
  of 
  the 
  resistances 
  were 
  performed 
  immediately 
  after 
  the 
  

   adjustment. 
  In 
  this 
  way 
  the 
  actual 
  resistances 
  at 
  the 
  time 
  of 
  

   the 
  experiment 
  were 
  obtained, 
  and 
  so 
  the 
  effect 
  of 
  the 
  heating 
  

   by 
  the 
  current 
  was 
  somewhat 
  eliminated. 
  

  

  Methods 
  26, 
  9 
  and 
  3 
  give 
  good 
  results, 
  but 
  the 
  methods 
  that 
  

   gave 
  the 
  most 
  satisfaction 
  were 
  Methods 
  12 
  and 
  6, 
  Method 
  12 
  

   being 
  for 
  the 
  comparison 
  of 
  two 
  self-inductances 
  and 
  Method 
  

   6 
  for 
  the 
  comparison 
  of 
  a 
  self-inductance 
  with 
  a 
  capacity. 
  

   These 
  give 
  some 
  remarkable 
  results, 
  the 
  theory 
  and 
  deductions 
  

   of 
  the 
  methods 
  being 
  as 
  follows 
  : 
  

  

  Method 
  12 
  — 
  Zero 
  method 
  for 
  the 
  comparison 
  of 
  two 
  self- 
  

  

  mductances. 
  

  

  Let 
  the 
  connections 
  be 
  made 
  as 
  in 
  the 
  figure 
  where 
  the 
  

   hanging 
  coil 
  and 
  the 
  fixed 
  coils 
  are 
  in 
  two 
  distinct 
  circuits. 
  

  

  r^^r^? 
  

  

  

  R" 
  C,e- 
  

  

  

  )0 
  

  

  i(bt-tfj 
  

  

  'c^W^) 
  

  

  Let 
  C^B^^^ 
  etc. 
  be 
  the 
  currents. 
  A' 
  and 
  A" 
  reversing 
  commuta- 
  

   tors, 
  R''', 
  R 
  and 
  r 
  the 
  resistance 
  of 
  the 
  different 
  circuits, 
  L'^ 
  and 
  L 
  

   the 
  self-inductances, 
  M 
  the 
  mutual 
  inductance 
  of 
  the 
  coils 
  B, 
  

   and 
  B^ 
  by 
  which 
  it 
  is 
  placed. 
  When 
  a 
  periodic 
  electromotive 
  

   force 
  aei'bt 
  is 
  applied 
  to 
  A, 
  B 
  the 
  quantity 
  to 
  be 
  found 
  is 
  C, 
  Cg 
  

   cos 
  (fg— 
  (p^ 
  where 
  cp^—ipi 
  is 
  the 
  difference 
  of 
  phase. 
  

  

  The 
  current 
  in 
  the 
  W 
  circuit 
  is 
  then 
  

  

  Q^{U 
  + 
  (f)^ 
  

  

  micj^* 
  

  

  R"-\-ibL" 
  

   The 
  current 
  in 
  the 
  R 
  circuit 
  is 
  

  

  C/&< 
  + 
  <^^)(R-f-^^L) 
  = 
  C/^^ 
  + 
  ^») 
  r 
  

  

  a) 
  

  

  ...c3.^-(^^+^3)r^±r±!^_=c. 
  

  

  ibt 
  

  

  