﻿On 
  Aerial 
  Waves 
  generated 
  by 
  Impact. 
  97 
  

  

  they 
  may 
  be 
  entirely 
  separated. 
  When 
  this 
  is 
  the 
  case, 
  the 
  

   fringes 
  of 
  the 
  ordinary 
  Fresnel 
  type 
  due 
  to 
  the 
  edge 
  of 
  the 
  

   cylinder 
  may 
  be 
  observed, 
  and 
  inside 
  the 
  shadow 
  we 
  have 
  also 
  

   an 
  entirely 
  separate 
  system 
  of 
  fringes 
  due 
  to 
  the 
  reflected 
  rays, 
  

   the 
  first 
  and 
  principal 
  maximum 
  of 
  which 
  lies 
  alongside 
  the 
  

   virtual 
  caustic 
  formed 
  by 
  oblique 
  reflexion 
  ; 
  the 
  distribution 
  

   of 
  intensity 
  in 
  this 
  system 
  can 
  be 
  found 
  from 
  the 
  well-known 
  

   integral 
  due 
  to 
  Airy; 
  (d) 
  but 
  when 
  the 
  focal 
  plane 
  is 
  only 
  a 
  

   little 
  in 
  advance 
  of 
  the 
  edge, 
  the 
  caustic 
  and 
  the 
  reflecting 
  

   surface 
  are 
  nearly 
  in 
  contact, 
  and 
  Airy's 
  investigation 
  of 
  

   the 
  intensity 
  in 
  the 
  neighbourhood 
  of 
  a 
  caustic 
  requires 
  

   modification. 
  It 
  is 
  then 
  found 
  that 
  only 
  a 
  finite 
  number 
  of 
  

   bands 
  (one, 
  two, 
  three, 
  or 
  more 
  according 
  to 
  the 
  position 
  

   of 
  the 
  plane 
  of 
  observation) 
  is 
  formed 
  within 
  the 
  limits 
  of 
  

   the 
  shadow, 
  and 
  not 
  an 
  indefinitely 
  large 
  number 
  as 
  con- 
  

   templated 
  by 
  Airy's 
  theory. 
  The 
  rest 
  of 
  the 
  fringes 
  seen 
  in 
  

   the 
  field 
  are 
  due 
  to 
  the 
  interference 
  of 
  the 
  direct 
  and 
  reflected 
  

   rays, 
  but 
  modified 
  by 
  diffraction 
  at 
  the 
  edge 
  of 
  the 
  cylinder. 
  

  

  The 
  Indian 
  Association 
  

  

  for 
  the 
  Cultivation 
  of 
  Science, 
  

  

  Calcutta, 
  8th 
  May, 
  1917. 
  

  

  X. 
  On 
  Aerial 
  Waves 
  generated 
  by 
  Impact. 
  Part 
  II. 
  By 
  

   Sudhansukumar 
  Baneeji, 
  M.Sc, 
  Assistant 
  Professor 
  of 
  

   Applied 
  Mathematics, 
  University 
  of 
  Calcutta 
  *. 
  

  

  [Plate 
  IV.] 
  

  

  1. 
  Introduction. 
  

  

  THE 
  origin 
  and 
  characteristics 
  of 
  the 
  sound 
  produced 
  by 
  

   the 
  collision 
  of 
  two 
  solid 
  spheres 
  were 
  discussed 
  by 
  me 
  

   at 
  some 
  length 
  in 
  the 
  first 
  paper 
  under 
  the 
  same 
  title 
  that 
  

   was 
  published 
  in 
  the 
  Philosophical 
  Magazine 
  for 
  July, 
  1916. 
  

   It 
  was 
  shown 
  in 
  that 
  paper 
  that 
  the 
  sound 
  is 
  not 
  due 
  to 
  the 
  

   vibrations 
  set 
  up 
  in 
  the 
  spheres, 
  which 
  in 
  any 
  ordinary 
  

   material 
  are 
  both 
  too 
  high 
  in 
  pitch 
  to 
  be 
  audible 
  and 
  too 
  faint 
  

   in 
  intensity, 
  but 
  to 
  aerial 
  waves 
  set 
  up 
  by 
  the 
  reversal 
  of 
  the 
  

   motion 
  of 
  the 
  spheres 
  as 
  a 
  whole. 
  The 
  intensity 
  of 
  the 
  sound 
  

   in 
  different 
  directions 
  for 
  the 
  case 
  in 
  which 
  the 
  two 
  spheres 
  

   were 
  of 
  the 
  same 
  material 
  and 
  diameter, 
  was 
  investigated 
  by 
  

   the 
  aid 
  of 
  a 
  new 
  instrument 
  which 
  will 
  be 
  referred 
  to 
  as 
  

  

  * 
  Communicated 
  by 
  Prof. 
  C. 
  V. 
  Raman. 
  

   Phil. 
  Mag. 
  S. 
  6. 
  Vol. 
  35. 
  No. 
  205. 
  Jan. 
  1918. 
  H 
  

  

  