﻿222 
  C. 
  Bar 
  us 
  — 
  Excursions 
  of 
  a 
  Telephone 
  Diaphragm. 
  

  

  will 
  not 
  usually 
  exceed 
  a 
  few 
  degrees. 
  Its 
  effect 
  will 
  thus 
  be 
  

   negligible 
  in 
  view 
  of 
  the 
  usually 
  large 
  values 
  of 
  co. 
  

  

  Hence 
  it 
  seems 
  more 
  probable 
  that 
  the 
  vibration 
  figures 
  of 
  

   the 
  two 
  diaphragms 
  are 
  not 
  identical, 
  or 
  that 
  the 
  mirrors 
  do 
  

   not 
  (with 
  increasing 
  amplitude) 
  move 
  parallel 
  to 
  themselves. 
  

   There 
  would 
  thus 
  be 
  a 
  rotation 
  of 
  fringes, 
  and 
  the 
  effect 
  is 
  

   accentuated 
  with 
  two 
  telephones. 
  A 
  decision 
  of 
  the 
  matter 
  

   must, 
  however, 
  be 
  reserved 
  for 
  stroboscopic 
  work 
  with 
  spec- 
  

   trum 
  monochromatic 
  light. 
  

  

  4. 
  Returning 
  again 
  to 
  the 
  small 
  induction 
  coil, 
  I 
  put 
  an 
  

   additional 
  telephone 
  in 
  circuit, 
  which 
  throughout 
  the 
  experi- 
  

   ment 
  was 
  held 
  to 
  the 
  ear, 
  and 
  then 
  inserted 
  enough 
  resistance 
  

   (20,000 
  ohms 
  with 
  a 
  weak 
  primary 
  current) 
  to 
  obtain 
  vibrations 
  

   only 
  just 
  discernible 
  by 
  the 
  interference 
  method. 
  The 
  effect 
  

   in 
  general 
  is 
  a 
  widening 
  of 
  the 
  bands 
  (for 
  the 
  elongations 
  are 
  

   specially 
  visible) 
  together 
  with 
  a 
  blurring 
  of 
  the 
  field 
  as 
  a 
  

   whole. 
  Under 
  these 
  conditions 
  I 
  observed 
  a 
  permanent 
  dis- 
  

   placement 
  of 
  the 
  fringes, 
  which 
  changed 
  sign 
  with 
  the 
  sign 
  of 
  

   the 
  current, 
  the 
  shifting 
  being 
  about 
  a 
  half 
  fringe 
  or 
  equivalent 
  

   to 
  15xl0~ 
  6 
  cm 
  along 
  the 
  central 
  normal 
  of 
  the 
  diaphragm. 
  

   The 
  latter 
  is 
  thus 
  more 
  attracted 
  in 
  one 
  case 
  and 
  less 
  in 
  the 
  

   other, 
  or 
  the 
  position 
  of 
  equilibrium 
  of 
  the 
  vibrating 
  plate 
  

   does 
  not 
  apparently 
  coincide 
  with 
  its 
  position 
  for 
  no 
  current. 
  

   Hence 
  the 
  forced 
  vibrations 
  must 
  have 
  been 
  more 
  rapid 
  than 
  

   the 
  natural 
  frequency 
  of 
  the 
  plate. 
  

  

  It 
  is 
  interesting 
  to 
  compute 
  the 
  increment 
  of 
  force 
  tugging 
  

   at 
  the 
  plate 
  in 
  these 
  cases. 
  Having 
  given 
  a 
  circular 
  plate 
  of 
  

   radius 
  r 
  and 
  thickness 
  s, 
  fixed 
  at 
  the 
  edges, 
  the 
  force 
  P 
  in 
  dynes 
  

   will 
  produce 
  a 
  displacement 
  of 
  f 
  centimeters, 
  where 
  

  

  0-6825 
  r^P 
  

  

  E 
  being 
  Young's 
  modulus 
  (2 
  XlO 
  12 
  dynes). 
  Putting 
  r 
  = 
  2 
  cm 
  , 
  

   s 
  = 
  0'016 
  cm 
  , 
  /= 
  15X 
  10- 
  6 
  cm 
  (as 
  just 
  found), 
  the 
  value 
  of 
  P 
  

   becomes 
  

  

  P— 
  140 
  dynes. 
  

  

  This 
  unexpectedly 
  large 
  result 
  for 
  the 
  force 
  at 
  the 
  center 
  

   of 
  the 
  plate 
  is 
  an 
  explanation 
  of 
  the 
  unexpectedly 
  small 
  excur- 
  

   sions 
  of 
  the 
  diaphragm 
  discussed 
  above 
  : 
  for 
  even 
  if 
  the 
  

   given 
  minimum 
  amplitude 
  of 
  10~ 
  6Cm 
  be 
  taken, 
  the 
  force 
  at 
  

   the 
  center 
  in 
  case 
  of 
  static 
  flexure 
  would 
  exceed 
  10 
  dynes. 
  

  

  Brown 
  University, 
  Providence, 
  R. 
  I. 
  

  

  