﻿Decay 
  of 
  Waves 
  in 
  a 
  Canal. 
  487 
  

  

  where 
  

  

  I£ 
  we 
  neglect 
  the 
  squares 
  of 
  velocities, 
  these 
  equations 
  are 
  

   satisfied 
  by 
  

  

  M 
  BH 
  ^a 
  

  

  ^^=B^-+^y 
  ""Be' 
  

   _'d± 
  BF 
  ^ 
  

  

  B0 
  BG 
  BF 
  

  

  where 
  

  

  provided 
  

  

  and 
  

  

  p 
  _ 
  

   p 
  

  

  ^t 
  

  

  — 
  

  

  OV' 
  

  

  V'<t> 
  = 
  

  

  --0, 
  

  

  

  

  vv-F 
  = 
  

  

  BF 
  

  

  &c 
  

  

  

  It 
  - 
  

  

  Vif=0' 
  

  

  

  

  Consider 
  

  

  ^ 
  = 
  (Ai 
  cosh 
  my-h 
  Ao 
  sinh 
  my) 
  cos'-^ 
  e^^+''\ 
  

  

  nirz 
  

  

  G 
  = 
  (Gi 
  cosh 
  m'y 
  + 
  G2 
  sinh 
  ;>z^//) 
  sin 
  ''-^e^'''+^\ 
  

  

  H 
  = 
  (Hi 
  cosh 
  m'y 
  + 
  Ho 
  sinh 
  »z» 
  cos 
  "pe^^'^+'^^ 
  

  

  nr 
  = 
  /r 
  + 
  n-Tr-ju-, 
  

  

  These 
  are 
  not 
  the 
  most 
  general 
  expressions 
  of 
  the 
  type 
  

   which 
  might 
  have 
  been 
  written 
  down, 
  but 
  they 
  are 
  the 
  only 
  

   ones 
  which 
  satisfy 
  the 
  conditions 
  of 
  the 
  problem. 
  

  

  