﻿360 
  Mr. 
  C. 
  Godfrey 
  on 
  Discontinuities 
  of 
  Wave-motion 
  

   For 
  2=1 
  we 
  have 
  

  

  sin 
  ?r(sin 
  ■?■ 
  +^ 
  cos^J 
  =0. 
  

  

  The 
  factor 
  sin 
  ^ 
  gives 
  yjr 
  = 
  2s7r, 
  where 
  s 
  is 
  integral. 
  The 
  

  

  other 
  factor 
  gives 
  roots 
  lying 
  between 
  it 
  and 
  2-7T, 
  37r 
  and 
  47r, 
  

   &c. 
  It 
  will 
  be 
  seen 
  that 
  they 
  lie 
  beyond 
  the 
  zeros 
  of 
  the 
  

   corresponding 
  regions. 
  

   For 
  z= 
  — 
  1 
  we 
  have 
  

  

  cos 
  ~ 
  ( 
  cos 
  -~ 
  — 
  fjisfr 
  sin 
  ~ 
  ) 
  = 
  0. 
  

  

  "\tp 
  

   The 
  factor 
  cos 
  J- 
  gives 
  ^r=(2a 
  + 
  l)7r. 
  The 
  other 
  factor 
  gives 
  

  

  roots 
  between 
  and 
  7r, 
  27T 
  and 
  37T, 
  &c. 
  ; 
  and 
  again 
  lyino- 
  

   beyond 
  the 
  zeros 
  of 
  the 
  corresponding 
  regions. 
  

  

  Fi°\ 
  2. 
  

  

  It 
  is 
  also 
  clear 
  that 
  the 
  maxima 
  and 
  minima 
  become 
  more 
  

   marked 
  as 
  yjr 
  increases. 
  With 
  these 
  data 
  it 
  is 
  easy 
  to 
  see 
  that 
  

   the 
  general 
  shape 
  of 
  the 
  curve 
  is 
  as 
  above. 
  

  

  