﻿76 
  Prof. 
  Barton 
  and 
  Miss 
  Browning 
  on 
  

  

  When 
  the 
  coupling 
  vanishes 
  the 
  frequencies 
  of 
  the 
  separate 
  

   vibrations 
  are 
  of 
  course 
  undisturbed. 
  Thus 
  for 
  equal 
  lengths, 
  

   but 
  any 
  ratio 
  of 
  masses, 
  we 
  have 
  for 
  7 
  = 
  0, 
  p 
  : 
  q 
  equals 
  unity. 
  

   But 
  for 
  different 
  separate 
  frequencies 
  (i. 
  e., 
  tj 
  not 
  equal 
  to 
  

   unity) 
  we 
  have 
  for 
  7 
  = 
  0, 
  p 
  : 
  q 
  greater 
  than 
  unity. 
  But 
  with 
  

   large 
  couplings 
  the 
  effect 
  of 
  unequal 
  separate 
  frequencies 
  

   gradually 
  disappears. 
  

  

  V. 
  Experimental 
  Results. 
  

  

  Masses 
  20 
  : 
  1. 
  — 
  The 
  bobs 
  used 
  in 
  these 
  experiments 
  were 
  

   of 
  the 
  order 
  1000 
  gms. 
  and 
  50 
  gms. 
  respectively. 
  Figs. 
  1-11 
  

   of 
  Plate 
  I. 
  give 
  photographic 
  reproductions 
  of 
  the 
  double 
  

   sand 
  traces 
  simultaneously 
  obtained 
  when 
  the 
  masses 
  of 
  the 
  

   bobs 
  Q 
  and 
  P 
  were 
  as 
  20 
  : 
  1, 
  i. 
  e. 
  } 
  p 
  = 
  20. 
  

  

  The 
  couplings 
  vary 
  from 
  1 
  per 
  cent, 
  in 
  the 
  first 
  to 
  a 
  little 
  

   over 
  30 
  per 
  cent, 
  in 
  the 
  last, 
  and 
  are 
  shown 
  as 
  percentages 
  

   on 
  every 
  figure. 
  

  

  Figs. 
  1-8 
  were 
  obtained 
  by 
  drawing 
  the 
  heavy 
  bob 
  aside 
  

   horizontally, 
  the 
  light 
  bob 
  being 
  allowed 
  to 
  hang 
  at 
  rest 
  in 
  

   its 
  more 
  or 
  less 
  displaced 
  position 
  according 
  as 
  the 
  coupling 
  

   was 
  tight 
  or 
  loose. 
  In 
  figs. 
  9-11, 
  while 
  the 
  heavy 
  bob 
  was 
  

   pulled 
  aside, 
  the 
  light 
  one 
  was 
  held 
  in 
  its 
  undisplaced 
  posi- 
  

   tion. 
  Figs. 
  1-6 
  show 
  a 
  very 
  marked 
  effect 
  due 
  to 
  the 
  

   inequality 
  of 
  the 
  masses. 
  For, 
  as 
  the 
  resultant 
  vibrations 
  of 
  

   the 
  light 
  bob 
  wax 
  and 
  wane 
  in 
  amplitude, 
  those 
  of 
  the 
  heavy 
  

   bob 
  scarcely 
  change. 
  Thus 
  showing 
  that 
  with 
  masses 
  20 
  : 
  1 
  

   we 
  have 
  in 
  this 
  respect 
  almost 
  reached 
  the 
  limiting 
  case 
  of 
  

   forced 
  vibrations 
  in 
  which 
  the 
  reaction 
  of 
  the 
  driven 
  on 
  the 
  

   driver 
  is 
  negligible. 
  The 
  frequencies, 
  however, 
  are 
  still 
  

   appreciably 
  affected. 
  The 
  contrast 
  with 
  the 
  case 
  of 
  equal 
  

   masses 
  may 
  be 
  seen 
  by 
  referring 
  to 
  figs. 
  1-5 
  in 
  Plate 
  V. 
  of 
  

   the 
  October 
  paper, 
  where 
  the 
  waxings 
  and 
  wanings 
  occur 
  

   equally 
  and 
  alternately 
  in 
  both 
  traces. 
  Figs. 
  1-8 
  show 
  that 
  

   as 
  the 
  coupling 
  increases 
  the 
  inequality 
  of 
  the 
  frequencies 
  

   of 
  the 
  superposed 
  vibrations 
  increases 
  also. 
  Hence 
  there 
  are 
  

   fewer 
  vibrations 
  in 
  the 
  beat 
  cycle 
  and 
  this 
  fulfils 
  the 
  theory. 
  

  

  In 
  fig. 
  9 
  the 
  initial 
  displacement 
  of 
  the 
  heavy 
  bob 
  was 
  so 
  

   great 
  that 
  a 
  collision 
  occurred 
  between 
  the 
  two 
  as 
  indicated. 
  

   But 
  its 
  effect 
  passed 
  away 
  after 
  a 
  few 
  vibrations. 
  This 
  may 
  

   be 
  seen 
  by 
  fig. 
  10, 
  in 
  which 
  with 
  a 
  slightly 
  smaller 
  displace- 
  

   ment 
  the 
  collision 
  was 
  avoided. 
  

  

  Fig. 
  11 
  shows 
  appreciable 
  damping 
  of 
  the 
  vibration 
  of 
  

   the 
  light 
  bob 
  which 
  was 
  held 
  undisplaced 
  while 
  the 
  heavy 
  

   one 
  was 
  drawn 
  aside, 
  whereas 
  that 
  of 
  the 
  heavy 
  bob 
  is 
  not 
  

   appreciably 
  damped. 
  This 
  is 
  exactly 
  what 
  might 
  be 
  expected 
  

  

  