﻿Waves 
  generated 
  by 
  Impact. 
  Ill 
  

  

  material. 
  The 
  relative 
  intensities 
  of 
  the 
  sound 
  in 
  different 
  

   directions 
  have 
  been 
  measured 
  by 
  the 
  aid 
  of 
  the 
  ballistic 
  

   phonometer, 
  and 
  in 
  order 
  to 
  exhibit 
  the 
  results 
  in 
  an 
  effective 
  

   manner, 
  they 
  have 
  been 
  plotted 
  in 
  polar 
  coordinates, 
  the 
  

   point 
  at 
  which 
  the 
  spheres 
  impinge 
  being 
  taken 
  as 
  the 
  origin, 
  

   and 
  the 
  line 
  of 
  collision 
  as 
  the 
  axis 
  of 
  x. 
  As 
  might 
  be 
  ex- 
  

   pected, 
  the 
  curves 
  thus 
  drawn 
  show 
  marked 
  asymmetry 
  in 
  

   respect, 
  of 
  the 
  plane 
  perpendicular 
  to 
  the 
  line 
  of 
  impact. 
  

  

  A 
  detailed 
  mathematical 
  discussion 
  of 
  the 
  nature 
  of 
  the 
  

   results 
  to 
  be 
  expected 
  is 
  possible 
  by 
  considering 
  the 
  analogous 
  

   case 
  of 
  two 
  rigid 
  spheres 
  nearly 
  in 
  contact 
  which 
  vibrate 
  

   bodily 
  along 
  their 
  line 
  of 
  centres. 
  By 
  choosing 
  an 
  appro- 
  

   priate 
  wave-length 
  for 
  the 
  resulting 
  motion, 
  intensity 
  curves 
  

   similar 
  to 
  those 
  found 
  experimentally 
  for 
  the 
  case 
  of 
  impact 
  

   are 
  arrived 
  at. 
  A 
  further 
  confirmation 
  is 
  thus 
  obtained 
  of 
  

   the 
  hypothesis 
  regarding 
  the 
  origin 
  of 
  the 
  sound 
  suggested 
  

   by 
  the 
  work 
  of 
  Hertz 
  and 
  of 
  Lord 
  Rayleigh 
  on 
  the 
  theory 
  of 
  

   elastic 
  impact. 
  

  

  When 
  the 
  impinging 
  spheres, 
  though 
  not 
  equal 
  in 
  size, 
  are 
  

   of 
  the 
  same 
  or 
  nearly 
  the 
  same 
  density, 
  the 
  intensity-curve 
  

   drawn 
  for 
  the 
  plane 
  of 
  observation 
  shows 
  the 
  sound 
  to 
  be 
  a 
  

   maximum 
  along 
  the 
  line 
  of 
  impact 
  in 
  either 
  direction, 
  and 
  

   also 
  along 
  two 
  directions 
  making 
  equal 
  acute 
  angles 
  with 
  

   this 
  line. 
  The 
  sound 
  is 
  a 
  minimum 
  along 
  four 
  directions 
  in 
  

   the 
  plane. 
  In 
  practically 
  all 
  other 
  cases, 
  that 
  is 
  when 
  the 
  

   spheres 
  differ 
  considerably 
  either 
  in 
  density 
  alone, 
  or 
  both 
  

   in 
  diameter 
  and 
  density, 
  the 
  intensity 
  is 
  found 
  to 
  be 
  a 
  

   maximum 
  along 
  the 
  line 
  of 
  impact 
  in 
  either 
  direction, 
  and 
  

   to 
  be 
  a 
  minimum 
  along 
  directions 
  which 
  are 
  nearly 
  but 
  not 
  

   quite 
  perpendicular 
  to 
  the 
  line 
  of 
  impact. 
  The 
  form 
  of 
  the 
  

   intensity 
  curve 
  is 
  practically 
  determined 
  by 
  the 
  diameters 
  

   and 
  the 
  masses 
  of 
  the 
  spheres. 
  

  

  The 
  investigation 
  was 
  carried 
  out 
  in 
  the 
  Physical 
  Labora- 
  

   tory 
  of 
  the 
  Indian 
  Association 
  for 
  the 
  Cultivation 
  of 
  Science. 
  

   It 
  is 
  hoped 
  when 
  a 
  suitable 
  opportunity 
  arises 
  to 
  study 
  also 
  

   the 
  case 
  of 
  oblique 
  impact. 
  The 
  writer 
  has 
  much 
  pleasure 
  

   in 
  acknowledging 
  the 
  helpful 
  interest 
  taken 
  by 
  Prof. 
  C. 
  V. 
  

   Raman 
  in 
  the 
  progress 
  of 
  the 
  work 
  described 
  in 
  the 
  present 
  

   paper. 
  

  

  Calcutta, 
  

   15th 
  June, 
  1917. 
  

  

  