﻿B'lfilar 
  Vibration 
  Galvanometer. 
  Ill 
  

  

  Let 
  E 
  = 
  the 
  R.M.S. 
  value 
  of 
  the 
  E.M.F. 
  impressed 
  on 
  the 
  

   circuit 
  consisting 
  of 
  the 
  vibration 
  galvanometer 
  

   and 
  its 
  added 
  resistance 
  ; 
  

  

  d 
  = 
  the 
  corresponding 
  amplitude 
  of 
  deflexion 
  in 
  

   millimetres 
  ; 
  

  

  r 
  = 
  the 
  total 
  resistance 
  of 
  the 
  circuit 
  ; 
  

  

  e 
  = 
  the 
  back 
  E.M.F. 
  (R.M.S. 
  value 
  per 
  millimetre 
  

   of 
  deflexion) 
  ; 
  

  

  c 
  = 
  the 
  true 
  value 
  in 
  microamperes 
  of 
  the 
  current 
  

   through 
  the 
  vibration 
  galvanometer; 
  

  

  k 
  = 
  the 
  true 
  sensibility 
  in 
  millimetres 
  per 
  micro- 
  

   ampere 
  ; 
  

   then 
  d 
  = 
  ch. 
  

  

  If 
  the 
  mechanical 
  friction 
  of 
  the 
  instrument 
  is 
  small, 
  then, 
  

   when 
  it 
  is 
  tuned 
  to 
  resonance, 
  the 
  motion 
  of 
  the 
  wires 
  will 
  be 
  

   nearlv 
  90° 
  out 
  of 
  phase 
  with 
  the 
  force, 
  i. 
  e. 
  the 
  current 
  ; 
  and 
  

   the 
  E.M.F. 
  induced 
  in 
  the 
  wires 
  due 
  to 
  their 
  cutting 
  the 
  

   magnetic 
  field 
  will 
  also 
  be 
  90° 
  out 
  of 
  phase 
  with 
  their 
  motion, 
  

   so 
  that 
  the 
  back 
  E.M.F. 
  will 
  be 
  approximately 
  at 
  180° 
  to 
  the 
  

   current. 
  Tlie 
  E.M.F. 
  sendino^ 
  the 
  current 
  throuu^h 
  the 
  

   vibration 
  galvanometer 
  may 
  therefore 
  be 
  approximately 
  

   taken 
  as 
  Yj 
  — 
  ed^ 
  and 
  the 
  current 
  

  

  ^-ed 
  , 
  

   c 
  =i 
  , 
  whence 
  

  

  r 
  + 
  ek 
  = 
  k 
  

   B 
  

  

  r 
  

   E 
  

  

  If 
  therefore 
  -j 
  be 
  plotted 
  against 
  r 
  the 
  resistance 
  of 
  the 
  

  

  vibration 
  galvanometer 
  circuit, 
  the 
  graphs 
  obtained 
  should 
  be 
  

   straight 
  lines 
  which 
  should 
  not 
  pass 
  through 
  the 
  zero 
  but 
  

   should 
  cut 
  the 
  zero 
  line 
  at 
  a 
  yo'mtek 
  which 
  gives 
  the 
  apparent 
  

   resistance 
  of 
  the 
  instrument 
  due 
  to 
  its 
  back 
  E.M.F. 
  

  

  This 
  test 
  has 
  been 
  carried 
  out 
  and 
  the 
  graphs 
  are 
  given 
  in 
  

   fig. 
  10. 
  From 
  these 
  graphs 
  the 
  following 
  results 
  were 
  

   obtained 
  : 
  — 
  

  

  ! 
  

  

  1 
  Free 
  length 
  

   1 
  in 
  cm. 
  

  

  1 
  

  

  Frequency. 
  

  

  Intercept 
  

   in 
  ohms. 
  

  

  Back 
  E.M.F. 
  in 
  

  

  microvolts 
  per 
  

  

  millimetre. 
  

  

  5 
  

  

  10 
  

   13 
  

   16 
  

  

  538 
  

   502 
  

   530 
  

   228 
  

  

  SO 
  

   130 
  

   1G5 
  

   205 
  

  

  48 
  

   14-8 
  

   184 
  

  

  8-4 
  

  

  Phil. 
  Mag. 
  !S. 
  6. 
  Vol. 
  18. 
  No. 
  103. 
  Jidy 
  1909. 
  

  

  N 
  

  

  