﻿78 
  Coupled 
  Vibrations 
  : 
  Unequal 
  Masses 
  or 
  Periods. 
  

  

  This 
  again 
  is 
  in 
  accord 
  with 
  theory, 
  for 
  the 
  frequencies 
  of 
  

   the 
  superposed 
  vibrations 
  are 
  then 
  more 
  unequal 
  and 
  there- 
  

   fore 
  gain 
  more 
  quickly 
  on 
  each 
  other. 
  

  

  Lengths 
  3 
  : 
  4. 
  — 
  Figs. 
  20-28 
  show 
  double 
  traces 
  simul- 
  

   taneously 
  obtained 
  with 
  the 
  masses 
  of 
  the 
  bobs 
  equal, 
  but 
  

   the 
  lengths 
  of 
  the 
  suspensions 
  as 
  3 
  : 
  4. 
  The 
  lower 
  trace 
  on 
  

   each 
  figure 
  is 
  that 
  made 
  by 
  the 
  shorter 
  pendulum. 
  In 
  the 
  

   case 
  of 
  fig. 
  20, 
  the 
  short 
  pendulum 
  was 
  pulled 
  aside, 
  the 
  

   long 
  one 
  hanging 
  still 
  in 
  its 
  slightly 
  displaced 
  position. 
  In 
  

   the 
  cases 
  of 
  figs. 
  21-25, 
  the 
  long 
  one 
  was 
  drawn 
  aside 
  while 
  

   the 
  short 
  one 
  hung 
  at 
  rest 
  in 
  its 
  more 
  or 
  less 
  displaced 
  

   position. 
  In 
  figs. 
  26-28 
  the 
  long 
  pendulum 
  was 
  pulled 
  

   aside 
  while 
  the 
  short 
  one 
  was 
  held 
  in 
  its 
  zero 
  position, 
  as 
  

   this 
  favoured 
  the 
  exhibition 
  of 
  the 
  compound 
  harmonic 
  trace 
  

   which 
  it 
  was 
  then 
  sought 
  to 
  obtain. 
  

  

  The 
  couplings 
  in 
  this 
  set 
  vary 
  from 
  about 
  5 
  per 
  cent, 
  to 
  

   over 
  60 
  per 
  cent. 
  In 
  the 
  5 
  and 
  10 
  per 
  cent, 
  couplings 
  the 
  

   response 
  of 
  the 
  second 
  pendulum 
  is 
  feeble 
  and 
  the 
  beat 
  

   cycles 
  contain 
  very 
  few 
  vibrations. 
  These 
  are 
  the 
  effects 
  of 
  

   the 
  inequality 
  of 
  lengths. 
  But 
  as 
  the 
  coupling 
  is 
  further 
  

   increased 
  these 
  effects 
  of 
  the 
  inequality 
  of 
  the 
  separate 
  

   frequencies 
  are 
  seen 
  to 
  be 
  overpowered. 
  This 
  is 
  exactly 
  

   in 
  accord 
  with 
  the 
  theory 
  as 
  exhibited 
  in 
  the 
  graphs 
  on 
  

   fig. 
  2. 
  

  

  Fig. 
  26 
  shows 
  an 
  accidental 
  collision 
  of 
  the 
  lighter 
  bob 
  

   with 
  the 
  releasing 
  apparatus. 
  But 
  the 
  effect 
  of 
  the 
  blow 
  is 
  

   seen 
  to 
  pass 
  away 
  after 
  a 
  few 
  vibrations, 
  as 
  shown 
  by 
  com- 
  

   parison 
  with 
  fig. 
  27, 
  which 
  is 
  a 
  repetition 
  of 
  the 
  conditions 
  

   first 
  intended. 
  Figs. 
  26 
  and 
  27 
  are 
  seen 
  to 
  present 
  almost 
  

   the 
  appearance 
  of 
  the 
  compound 
  harmonic 
  motion 
  of 
  a 
  tone 
  

   and 
  its 
  octave, 
  the 
  latter 
  being 
  too 
  sharp. 
  Fig. 
  28 
  shows 
  

   the 
  coupling 
  reduced 
  to 
  60 
  per 
  cent., 
  and 
  this 
  gives 
  the 
  

   relation 
  of 
  frequencies 
  almost 
  exactly 
  2 
  : 
  1. 
  

  

  The 
  pair 
  of 
  simultaneous 
  traces 
  in 
  fig. 
  28 
  is 
  almost 
  

   identical 
  in 
  type 
  with 
  those 
  in 
  fig. 
  11 
  of 
  Plate 
  V. 
  in 
  the 
  

   October 
  paper, 
  in 
  which 
  latter 
  case 
  the 
  lengths 
  were 
  equal. 
  

   It 
  may 
  well 
  seem 
  surprising 
  that 
  the 
  effect 
  of 
  the 
  present 
  

   mistuning 
  (in 
  which 
  the 
  frequency 
  ratio 
  exceeds 
  8:7) 
  should 
  

   be 
  so 
  completely 
  obliterated 
  by 
  this 
  coupling. 
  But 
  experi- 
  

   ment 
  and 
  theory 
  agree 
  that 
  it 
  should 
  be 
  so. 
  

  

  VI. 
  Summary. 
  

  

  1. 
  This 
  second 
  paper 
  describes 
  further 
  experiments 
  with 
  

   the 
  double-cord 
  pendulum, 
  but 
  with 
  the 
  masses 
  unequal 
  as 
  

   20 
  : 
  1 
  and 
  as 
  5:1, 
  or 
  the 
  lengths 
  unequal 
  as 
  3:4. 
  These 
  

  

  