﻿Waves 
  generated 
  by 
  Impact. 
  109 
  

  

  that 
  the 
  directions 
  of 
  minimum 
  intensity 
  are 
  not 
  quite 
  in 
  the 
  

   plane 
  perpendicular 
  to 
  the 
  line 
  of 
  impact, 
  being 
  nearer 
  the 
  

   side 
  of 
  the 
  lighter 
  ball. 
  

  

  

  

  Table 
  III. 
  

  

  

  Angles 
  

   (in 
  degrees). 
  

  

  F 
  X 
  const. 
  

  

  Gr 
  X 
  const. 
  

  

  (F 
  2 
  4-G 
  2 
  ) 
  X 
  const. 
  

  

  

  

  4- 
  786000 
  

  

  - 
  1415000 
  

  

  2620021 
  

  

  10 
  

  

  4- 
  793732 
  

  

  -1374897 
  

  

  2521061 
  

  

  20 
  

  

  + 
  813819 
  

  

  -1256037 
  

  

  2240132 
  

  

  30 
  

  

  + 
  835068 
  

  

  -1068615 
  

  

  1839986 
  

  

  40 
  

  

  4- 
  845629 
  

  

  - 
  826059 
  

  

  1397992 
  

  

  50 
  

  

  + 
  828667 
  

  

  - 
  549652 
  

  

  989741 
  

  

  60 
  

  

  4- 
  768690 
  

  

  - 
  262257 
  

  

  660005 
  

  

  70 
  

  

  4- 
  654594 
  

  

  4- 
  7901 
  

  

  427780 
  

  

  80 
  

  

  4- 
  482433 
  

  

  4- 
  237049 
  

  

  288493 
  

  

  90 
  

  

  + 
  252125 
  

  

  4- 
  403500 
  

  

  225913 
  

  

  100 
  

  

  4- 
  228907 
  

  

  4- 
  495515 
  

  

  297466 
  

  

  110 
  

  

  - 
  331298 
  

  

  4- 
  509107 
  

  

  368642 
  

  

  120 
  

  

  - 
  647986 
  

  

  4- 
  454821 
  

  

  626929 
  

  

  130 
  

  

  - 
  954405 
  

  

  4- 
  347884 
  

  

  1031220 
  

  

  140 
  

  

  -1229335 
  

  

  + 
  211923 
  

  

  1555385 
  

  

  150 
  

  

  -1458496 
  

  

  4- 
  71667 
  

  

  2130948 
  

  

  160 
  

  

  -1629521 
  

  

  - 
  47667 
  

  

  2655850 
  

  

  170 
  

  

  -1734880 
  

  

  - 
  128811 
  

  

  3026866 
  

  

  180 
  

  

  -1770000 
  

  

  - 
  157000 
  

  

  3157549 
  

  

  A 
  result 
  of 
  some 
  importance 
  indicated 
  by 
  theory 
  is 
  that 
  

   when 
  one 
  of 
  the 
  spheres 
  is 
  much 
  heavier 
  than 
  the 
  other, 
  

   replacing 
  the 
  former 
  by 
  a 
  still 
  heavier 
  sphere 
  of 
  the 
  same 
  

   diameter 
  should 
  not 
  result 
  in 
  any 
  important 
  alteration 
  in 
  

   the 
  distribution 
  of 
  the 
  intensity 
  of 
  sound 
  in 
  different 
  direc- 
  

   tions 
  due 
  to 
  impact. 
  This 
  is 
  clear 
  from 
  expression 
  (16). 
  

   For 
  when 
  U 
  a 
  is 
  much 
  larger 
  than 
  U 
  6 
  , 
  any 
  diminution 
  in 
  the 
  

   value 
  of 
  Uj 
  should 
  not 
  appreciably 
  affect 
  the 
  value 
  of 
  the 
  

   expression. 
  This 
  indication 
  of 
  theory 
  is 
  in 
  agreement 
  with 
  

   experiment. 
  Several 
  series 
  of 
  measurements 
  have 
  been 
  

   made 
  with 
  various 
  pairs 
  of 
  balls 
  of 
  the 
  same 
  size 
  but 
  of 
  

   different 
  densities, 
  e. 
  g., 
  wood 
  and 
  marble, 
  wood 
  and 
  iron, 
  

   billiard 
  ball 
  and 
  iron 
  ball, 
  and 
  so 
  forth. 
  Generally, 
  similar 
  

   results 
  are 
  obtained 
  in 
  all 
  cases. 
  It 
  was 
  noticed 
  also 
  that 
  

   the 
  form 
  of 
  the 
  intensity 
  distribution 
  as 
  shown 
  by 
  the 
  ballistic 
  

   phonometer 
  was 
  not 
  altogether 
  independent 
  of 
  the 
  thickness 
  

   of 
  the 
  mica 
  disk 
  used 
  in 
  the 
  instrument. 
  This 
  is 
  not 
  sur- 
  

   prising, 
  as 
  the 
  behaviour 
  of 
  the 
  mica 
  disk 
  before 
  the 
  pointer 
  

  

  