﻿110 
  Barus 
  — 
  Trial 
  of 
  Interferential 
  Induction 
  balance. 
  

  

  are 
  cut 
  off 
  by 
  both 
  and 
  the 
  interference 
  fringes 
  will 
  not 
  be 
  dis- 
  

   placed 
  however 
  fast 
  the 
  mirrors 
  may 
  vibrate. 
  If 
  an 
  appreciable 
  

   time 
  is 
  spent 
  by 
  the 
  effective 
  current 
  in 
  passing 
  from 
  helix 
  A 
  

   to 
  helix 
  JB, 
  then 
  with 
  increasing 
  retardation 
  the 
  fringes 
  will 
  

   gradually 
  vanish 
  and 
  gradually 
  reappear 
  when 
  the 
  time 
  of 
  

   delay 
  has 
  reached 
  the 
  period 
  of 
  vibration 
  of 
  the 
  mirrors. 
  Let 
  

   the 
  motion 
  of 
  the 
  mirrors 
  m, 
  n 
  be 
  given 
  by 
  a 
  x 
  sin 
  wt 
  and 
  a^ 
  sin 
  

   (tot 
  +6). 
  Then 
  the 
  motion 
  of 
  the 
  fringes 
  is 
  proportional 
  to 
  

   a 
  1 
  &m(tot— 
  1 
  ) 
  ; 
  where 
  

  

  a 
  1 
  = 
  ^/a 
  l 
  * 
  + 
  a 
  i 
  *—2a 
  1 
  a 
  a 
  cos 
  6 
  and 
  tan 
  l 
  = 
  a 
  2 
  sin 
  6 
  / 
  (a 
  x 
  + 
  a 
  2 
  cos0). 
  

   If 
  the 
  amplitudes 
  are 
  equal 
  

  

  a 
  1 
  = 
  2a 
  sin 
  6/ 
  2 
  (I) 
  

  

  If 
  the 
  self-inductions 
  L 
  x 
  and 
  Z 
  2 
  of 
  the 
  two 
  helices 
  are 
  not 
  

   equal, 
  if, 
  for 
  instance, 
  the 
  cores 
  are 
  chosen 
  of 
  different 
  diame- 
  

   ters, 
  the 
  currents 
  in 
  the 
  helices 
  will 
  lag 
  behind 
  the 
  correspond- 
  

   ing 
  electromotive 
  forces 
  by 
  different 
  amounts. 
  The 
  result 
  

   will 
  bring 
  the 
  interference 
  fringes 
  to 
  vanish 
  more 
  and 
  more 
  

   fully 
  at 
  first, 
  and 
  finally 
  less 
  and 
  less 
  so, 
  as 
  the 
  difference 
  of 
  self- 
  

   induction 
  increases, 
  till 
  the 
  dephasing 
  approaches 
  one 
  com- 
  

   plete 
  period. 
  If 
  6^ 
  and 
  2 
  be 
  the 
  current 
  lag 
  in 
  each 
  helix 
  and 
  

   if 
  their 
  ohmic 
  resistance 
  R 
  is 
  the 
  same, 
  then 
  

  

  ten 
  *="* 
  /; 
  w 
  < 
  2) 
  

  

  There 
  are 
  thus 
  two 
  equations, 
  (1) 
  and 
  (2), 
  for 
  6. 
  If 
  Z 
  3 
  be 
  

   made 
  very 
  small 
  tan0 
  = 
  ©Z 
  1 
  /i?. 
  Similar 
  results 
  may 
  be 
  

   obtained 
  for 
  different 
  amplitudes 
  a 
  x 
  and 
  a„ 
  and 
  different 
  values 
  

   fori?. 
  

  

  Equation 
  (1), 
  however, 
  may 
  be 
  supposed 
  to 
  include 
  the 
  

   retardation 
  due 
  to 
  the 
  external 
  resistances 
  as 
  well 
  as 
  the 
  lag 
  in 
  

   equation 
  (2). 
  From 
  this 
  wider 
  point 
  of 
  view 
  the 
  fringes 
  will 
  

   be 
  at 
  rest 
  if 
  a 
  1 
  = 
  or 
  if 
  is 
  an 
  even 
  multiple 
  of 
  it. 
  The 
  

   motion 
  of 
  the 
  interference 
  fringes 
  will 
  be 
  a 
  maximum 
  or 
  they 
  

   will 
  vibrate 
  to 
  and 
  fro 
  with 
  greatest 
  intensity 
  when 
  6 
  is 
  an 
  odd 
  

   multiple 
  of 
  it. 
  

  

  The 
  criterion 
  is, 
  therefore, 
  visibility 
  and 
  clearness 
  of 
  the 
  

   fringes, 
  and 
  the 
  method 
  of 
  observation 
  is 
  not 
  continuous. 
  

  

  §4. 
  With 
  the 
  object 
  of 
  obtaining 
  a 
  continuous 
  series 
  of 
  data 
  

   the 
  above 
  stroboscopic 
  disc 
  G 
  was 
  introduced. 
  It 
  is 
  made 
  of 
  

   very 
  thin 
  tin 
  plate 
  about 
  40 
  cm 
  in 
  diameter, 
  with 
  a 
  sufficient 
  

  

  