﻿110 
  Prof. 
  Sudhansukumar 
  Banerji 
  on 
  Aerial 
  

  

  attached 
  to 
  it 
  ceases 
  to 
  touch 
  the 
  mirror 
  of 
  the 
  indicator 
  

   would 
  no 
  doubt 
  depend, 
  to 
  some 
  extent, 
  on 
  the 
  relation 
  

   between 
  its 
  natural 
  frequency 
  and 
  the 
  frequency 
  of 
  the 
  

   sound-waves 
  set 
  up 
  by 
  the 
  impact. 
  The 
  best 
  results 
  were 
  

   obtained 
  with 
  a 
  disk 
  neither 
  so 
  thick 
  as 
  to 
  be 
  relatively 
  

   insensith 
  r 
  e 
  nor 
  so 
  thin 
  as 
  to 
  remain 
  with 
  its 
  pointer 
  in 
  contact 
  

   with 
  the 
  indicator 
  longer 
  than 
  absolutely 
  necessary. 
  

  

  4. 
  The 
  general 
  case 
  of 
  spheres 
  of 
  any 
  diameter 
  

   and 
  density. 
  

  

  When 
  the 
  impinging 
  spheres 
  are 
  both 
  of 
  different 
  diameter 
  

   and 
  of 
  different 
  density, 
  the 
  result 
  generally 
  obtained 
  is 
  that 
  

   the 
  sound 
  is 
  a 
  maximum 
  on 
  the 
  line 
  of 
  impact 
  in 
  either 
  

   direction, 
  and 
  a 
  minimum 
  which 
  approaches 
  zero 
  in 
  direc- 
  

   tions 
  asymmetrically 
  situated 
  with 
  reference 
  thereto. 
  

   Generally 
  speaking, 
  no 
  maxima 
  in 
  lateral 
  directions 
  are 
  

   noticed, 
  that 
  is, 
  the 
  curve 
  consists 
  of 
  two 
  nearly 
  closed 
  loops. 
  

   The 
  difference 
  of 
  the 
  intensity 
  of 
  the 
  sound 
  in 
  the 
  two 
  

   directions 
  of 
  the 
  line 
  of 
  impact 
  may 
  sometimes 
  be 
  very 
  con- 
  

   siderable. 
  As 
  a 
  typical 
  case, 
  the 
  results 
  obtained 
  by 
  the 
  

   impact 
  of 
  a 
  sphere 
  of 
  wood 
  3 
  inches 
  in 
  diameter 
  with 
  a 
  brass 
  

   sphere 
  only 
  1§- 
  inch 
  in 
  diameter 
  are 
  shown 
  in 
  fig. 
  8. 
  It 
  is 
  

   observed 
  that 
  the 
  sound 
  due 
  to 
  impact 
  is 
  actually 
  of 
  greater 
  

   intensity 
  on 
  the 
  side 
  of 
  the 
  small 
  brass 
  ball. 
  As 
  a 
  matter 
  

   of 
  fact, 
  the 
  result 
  generally 
  obtained 
  is 
  that 
  the 
  intensity 
  is 
  

   greater 
  on 
  the 
  side 
  of 
  the 
  ball 
  of 
  the 
  denser 
  material 
  even 
  if 
  

   its 
  diameter 
  be 
  the 
  smaller. 
  

  

  The 
  mathematical 
  treatment 
  of 
  the 
  general 
  case 
  is 
  precisely 
  

   on 
  the 
  same 
  lines 
  as 
  in 
  the 
  two 
  preceding 
  sections. 
  Jt 
  is 
  

   found 
  in 
  agreement 
  with 
  the 
  experimental 
  result 
  that 
  in 
  

   practically 
  all 
  cases 
  in 
  which 
  both 
  the 
  densities 
  and 
  the 
  

   diameters 
  are 
  different, 
  the 
  zonal 
  harmonic 
  of 
  the 
  first 
  

   order 
  is 
  of 
  importance 
  and 
  that 
  the 
  intensity 
  curve 
  consists 
  

   of 
  two 
  nearly 
  closed 
  loops, 
  as 
  in 
  the 
  case 
  of 
  two 
  spheres 
  of 
  

   the 
  same 
  diameter 
  but 
  of 
  different 
  density. 
  

  

  5. 
  Summary 
  and 
  Conclusion, 
  

  

  The 
  investigation 
  of 
  the 
  origin 
  and 
  characteristics 
  of 
  the 
  

   sound 
  due 
  to 
  the 
  direct 
  impact 
  of 
  two 
  similar 
  solid 
  spheres 
  

   which 
  was 
  described 
  in 
  the 
  Phil. 
  Mag. 
  for 
  July, 
  1916, 
  has 
  

   been 
  extended 
  in 
  the 
  present 
  paper 
  to 
  the 
  cases 
  in 
  which 
  the 
  

   impinging 
  spheres 
  are 
  not 
  both 
  of 
  the 
  same 
  diameter 
  or 
  

  

  