﻿Ripple 
  Formation 
  in 
  KamWs 
  Tube 
  Experiment. 
  185 
  

  

  (the 
  1st 
  being 
  supposed 
  to 
  be 
  at 
  the 
  antlnode) 
  as 
  follows, 
  if 
  

   we 
  consider 
  

  

  ?2, 
  = 
  7?-=;i.= 
  =nr 
  

  

  \«23/ 
  ^2/ 
  

  

  ©■-©■ 
  

  

  A^r.r+l\ 
  _ 
  AV+l 
  V 
  

   \ar-l.rj 
  ~ 
  \^0-l/ 
  

  

  Forming 
  the 
  product 
  of 
  all 
  the 
  terms 
  on 
  the 
  left, 
  and 
  of 
  

   those 
  on 
  the 
  right, 
  and 
  equating, 
  we 
  get 
  

  

  \ai.2 
  J 
  \lCl. 
  102/ 
  

  

  Xow 
  fxv-j.1 
  is 
  approximately 
  = 
  t^V, 
  

  

  and 
  iCo 
  is 
  „ 
  =ifi. 
  

  

  Therefore 
  we 
  can 
  write 
  

  

  \ 
  «1.2 
  / 
  ~~\l^l) 
  ' 
  

  

  If 
  Wr 
  is 
  distant 
  k 
  from 
  the 
  antinode, 
  we 
  have 
  

  

  (TT 
  ^\^ 
  

   IVq 
  cos 
  ^ 
  -y 
  \ 
  , 
  

  

  Wq 
  / 
  2 
  1 
  

  

  This 
  gives 
  approximately 
  the 
  law 
  of 
  variation 
  of 
  the 
  dis- 
  

   tances 
  between 
  the 
  ripples 
  on 
  the 
  above 
  assumptions. 
  

  

  From 
  this 
  we 
  see 
  that 
  this 
  distance 
  gets 
  smaller 
  as 
  we 
  go 
  

   from 
  the 
  antinode 
  to 
  the 
  node. 
  This 
  statement 
  will 
  not 
  be 
  

   affected 
  if 
  we 
  consider 
  variations 
  in 
  the 
  value 
  of 
  n, 
  for 
  if 
  n 
  

   varies, 
  it 
  can 
  only 
  diminish 
  as 
  we 
  go 
  from 
  the 
  antinode 
  to 
  

   the 
  node. 
  This 
  is 
  readily 
  seen 
  when 
  we 
  remember 
  that 
  the 
  

   width 
  of 
  the 
  ripples, 
  i. 
  e. 
  the 
  chord 
  of 
  the 
  segment 
  in 
  fig. 
  2, 
  

   gets 
  smaller 
  as 
  we 
  go 
  away 
  from 
  the 
  antinode. 
  Then 
  going 
  

  

  