﻿Waves 
  generated 
  by 
  Impact, 
  105 
  

  

  of 
  different 
  character 
  in 
  different 
  directions, 
  and 
  not 
  all 
  

   throughout 
  the 
  same 
  as 
  in 
  the 
  periodic 
  case. 
  

  

  Now 
  taking 
  k(a 
  + 
  b) 
  = 
  2, 
  we 
  find 
  (neglecting 
  a 
  constant 
  

   factor) 
  

  

  F=-0992 
  P 
  2 
  (cos 
  0) 
  + 
  -2840 
  P 
  2 
  (cos 
  0)- 
  -0354 
  P 
  3 
  (cos 
  0) 
  

   -•0146 
  P 
  4 
  (cos 
  0)+&c, 
  

  

  G 
  = 
  '0496 
  Pi 
  (cos 
  0)-'4O4O 
  P 
  2 
  (cos 
  0) 
  -'0177 
  P 
  3 
  (cos 
  0) 
  

  

  + 
  -0315 
  P 
  4 
  (cos 
  0) 
  + 
  &c. 
  . 
  . 
  . 
  (12) 
  

  

  The 
  values 
  of 
  F 
  and 
  G 
  for 
  different 
  directions 
  have 
  been 
  

   calculated 
  and 
  are 
  shown 
  in 
  the 
  following 
  table 
  : 
  — 
  

  

  

  

  Table 
  I. 
  

  

  

  Angles 
  

   (in 
  degrees). 
  

  

  F 
  X 
  const. 
  

  

  G- 
  X 
  const. 
  

  

  (F 
  2 
  +G 
  2 
  ) 
  X 
  const. 
  

  

  

  

  +329000 
  

  

  -338000 
  

  

  223144 
  

  

  10 
  

  

  +325908 
  

  

  -326525 
  

  

  212552 
  

  

  20 
  

  

  +297435 
  

  

  -273545 
  

  

  162738 
  

  

  30 
  

  

  +251537 
  

  

  -214337 
  

  

  109300 
  

  

  40 
  

  

  +189095 
  

  

  -114659 
  

  

  48946 
  

  

  50 
  

  

  +114215 
  

  

  - 
  24167 
  

  

  13572 
  

  

  60 
  

  

  + 
  33341 
  

  

  + 
  74407 
  

  

  6565 
  

  

  70 
  

  

  - 
  43647 
  

  

  +155306 
  

  

  25961 
  

  

  80 
  

  

  -107073 
  

  

  +205212 
  

  

  53574 
  

  

  90 
  

  

  - 
  147250 
  

  

  +213625 
  

  

  67405 
  

  

  100 
  

  

  -158815 
  

  

  +178920 
  

  

  57322 
  

  

  110 
  

  

  -140329 
  

  

  + 
  106238 
  

  

  30836 
  

  

  120 
  

  

  - 
  95149 
  

  

  + 
  8675 
  

  

  9106 
  

  

  130 
  

  

  - 
  34099 
  

  

  - 
  99267 
  

  

  10957 
  

  

  140 
  

  

  + 
  35677 
  

  

  -202159 
  

  

  42100 
  

  

  150 
  

  

  + 
  102819 
  

  

  -289237 
  

  

  94130 
  

  

  160 
  

  

  + 
  157869 
  

  

  -353605 
  

  

  150280 
  

  

  170 
  

  

  + 
  192648 
  

  

  -392229 
  

  

  190913 
  

  

  180 
  

  

  +201000 
  

  

  -404000 
  

  

  203617 
  

  

  180 
  +201000 
  -404000 
  203617 
  

  

  Now 
  taking 
  Jc(a 
  + 
  b)=3, 
  we 
  find 
  (neglecting 
  a 
  constant 
  

   factor) 
  

  

  F= 
  '105 
  P 
  a 
  (cos 
  0) 
  + 
  1*060 
  P 
  2 
  (cos 
  0) 
  + 
  '016 
  P 
  3 
  (cos 
  0) 
  

   - 
  •281P 
  4 
  (cos(9)-&c. 
  

  

  G= 
  - 
  -122 
  Pj 
  (cos 
  0) 
  + 
  -186 
  P 
  3 
  (cos 
  0)-*O24 
  P 
  4 
  (cos 
  0) 
  

  

  -Ac 
  (13) 
  

  

  