﻿C. 
  Bancs 
  — 
  Excursions 
  of 
  a 
  Telephone 
  Diaphragm. 
  221 
  

  

  The 
  induction 
  coil 
  was 
  now 
  removed 
  and 
  replaced 
  with 
  a 
  

   microphone 
  (dust 
  transmitter 
  with 
  a 
  small 
  transformer) 
  placed 
  

   over 
  a 
  small 
  music 
  box 
  playing 
  into 
  the 
  mouth-piece 
  of 
  the 
  

   microphone. 
  All 
  this 
  was 
  removed 
  to 
  a 
  distant 
  room. 
  The 
  

   tinkling 
  of 
  the 
  music 
  could 
  be 
  heard 
  in 
  the 
  telephone 
  but 
  the 
  

   fringes 
  remained 
  clear. 
  Finally 
  I 
  placed 
  a 
  small 
  siren 
  under 
  

   the 
  trumpet 
  of 
  the 
  microphone 
  and 
  produced 
  the 
  usual 
  suc- 
  

   cession 
  from 
  low 
  to 
  high 
  pitch. 
  As 
  a 
  rule, 
  the 
  fringes 
  were 
  

   only 
  slightly 
  affected. 
  At 
  certain 
  stages, 
  however, 
  a 
  loud 
  cry 
  

   was 
  heard 
  in 
  the 
  telephone 
  and 
  the 
  fringes 
  vanished 
  : 
  but 
  

   these 
  stages 
  seemed 
  clearly 
  to 
  be 
  harmonics. 
  Similarly 
  an 
  

   organ 
  pipe, 
  f" 
  (n 
  = 
  TOO), 
  produced 
  strong 
  resonance 
  and 
  a 
  

   blank 
  interference 
  field. 
  

  

  It 
  follows, 
  therefore, 
  that 
  if 
  attention 
  be 
  confined 
  to 
  tele- 
  

   phonic 
  sounds 
  of 
  faint 
  but 
  distinct 
  audibility, 
  the 
  excursions 
  

   of 
  the 
  diaphragm 
  must 
  be 
  small 
  as 
  compared 
  with 
  the 
  wave- 
  

   length 
  of 
  sodium 
  light. 
  Since 
  a 
  single 
  fringe 
  corresponds 
  to 
  

   30xl0" 
  6 
  cm 
  , 
  and 
  since 
  a 
  shifting 
  or 
  tremor 
  of 
  less 
  than 
  1/10 
  

   fringe 
  is 
  discernible, 
  the 
  excursions 
  of 
  the 
  plate 
  of 
  an 
  ordinary 
  

   Bell 
  telephone 
  cannot, 
  in 
  the 
  case 
  in 
  question, 
  be 
  greater 
  than 
  

   3xl0 
  -6 
  cm> 
  The 
  y 
  are 
  p 
  r0 
  J3 
  a 
  bly 
  even 
  below 
  10 
  ~ 
  6 
  cm 
  . 
  

  

  3. 
  The 
  result 
  with 
  two 
  telephones 
  in 
  circuit 
  was 
  not 
  as 
  1 
  

   expected 
  to 
  find 
  it, 
  viz 
  : 
  a 
  retention 
  of 
  clearness 
  of 
  the 
  field 
  

   throughout 
  greater 
  intensities 
  of 
  vibration. 
  If 
  anything, 
  the 
  

   fringes 
  vanished 
  sooner, 
  and 
  under 
  like 
  conditions 
  were 
  more 
  

   blurred 
  than 
  for 
  the 
  case 
  of 
  a 
  single 
  telephone 
  in 
  circuit. 
  The 
  

   reason 
  of 
  this 
  one 
  would 
  naturally 
  seek 
  in 
  a 
  difference 
  in 
  the 
  

   self 
  inductions 
  of 
  the 
  two 
  telephones, 
  one 
  of 
  which 
  was 
  a 
  

   morje 
  recent 
  Bell 
  telephone 
  and 
  the 
  other 
  an 
  older 
  instrument 
  

   which 
  had 
  been 
  used 
  by 
  Profs. 
  Blake 
  and 
  Peirce 
  in 
  their 
  early 
  

   telephone 
  investigations. 
  The 
  plates 
  in 
  diameter, 
  thickness 
  

   and 
  material 
  were 
  alike, 
  but 
  not 
  the 
  coils. 
  If, 
  however, 
  one 
  

   inquires 
  specifically 
  into 
  the 
  matter 
  the 
  case 
  is 
  not 
  so 
  clear. 
  

   Let 
  6 
  be 
  the 
  difference 
  between 
  the 
  lags 
  of 
  the 
  two 
  telephones 
  

   behind 
  the 
  electromotive 
  force. 
  Let 
  L 
  1 
  and 
  Z 
  2 
  be 
  their 
  self- 
  

   inductions, 
  R 
  x 
  and 
  _i? 
  2 
  their 
  resistances. 
  Let 
  co 
  be 
  proportional 
  

   (27r) 
  to 
  the 
  frequency 
  of 
  the 
  note. 
  Then 
  as 
  shown 
  in 
  my 
  last 
  

   paper, 
  

  

  tan 
  

  

  l 
  + 
  (Z 
  1 
  (o/i?J(Z: 
  2 
  a 
  J 
  /i2 
  2 
  )* 
  

  

  The 
  quantity 
  L.L^yi^P, 
  will 
  usually 
  be 
  large 
  as 
  compared 
  

   with 
  1. 
  Thus 
  

  

  tan0 
  = 
  {RJL-RJL^Iu. 
  

  

  Since, 
  therefore, 
  tan 
  6 
  increases 
  inversely 
  with 
  frequency, 
  and 
  

   since 
  self-induction 
  is 
  not 
  small 
  as 
  compared 
  with 
  resistance, 
  

  

  