﻿184 
  Mr. 
  J. 
  Robinson 
  on 
  Konig's 
  Theori/ 
  of 
  the 
  

  

  particle 
  at 
  the 
  centre 
  of 
  A2 
  are 
  Fj 
  and 
  F3 
  respectively, 
  where 
  

  

  J^i= 
  r-3— 
  

  

  F.,= 
  

  

  «12 
  

  

  For 
  equilibrium 
  of 
  this 
  particle 
  in 
  A 
  we 
  have 
  Fj^Fg 
  

   and 
  therefore 
  n-iWi^ 
  n^w^^ 
  

  

  I. 
  e. 
  

  

  ai2 
  «23 
  

  

  Vai2/ 
  n^io^' 
  

  

  which 
  pives 
  the 
  ratio 
  of 
  the 
  distances 
  between 
  successive 
  

   ripples. 
  

   Now 
  

  

  TT 
  h 
  

   W^^WqCOS^. 
  J 
  

  

  TT 
  h 
  + 
  2a 
  

  

  = 
  l(/'0COSg 
  . 
  T- 
  

  

  ( 
  where 
  a 
  is 
  the 
  mean 
  of 
  oi 
  and 
  a^)^ 
  

   n^ 
  cos^ 
  

  

  /TT 
  h-\-2a 
  \ 
  

  

  nicos^^.^ 
  

  

  If 
  we 
  consider 
  ni 
  = 
  n^, 
  i. 
  e., 
  that 
  the 
  distribution 
  of 
  powder 
  

   along 
  the 
  ripples 
  is 
  the 
  same 
  for 
  all 
  of 
  them, 
  then 
  

  

  \«12/ 
  

  

  oTT 
  /i 
  

  

  cos^2-T 
  

  

  And 
  we 
  see 
  that 
  a^^ 
  is 
  smaller 
  than 
  a-^^, 
  i- 
  e.^ 
  that 
  the 
  

   farther 
  we 
  get 
  from 
  the 
  antinode 
  the 
  smaller 
  is 
  the 
  distance 
  

   between 
  the 
  ripples. 
  

  

  We 
  can 
  find 
  the 
  ratio 
  of 
  the 
  distance 
  apart 
  of 
  the 
  rth 
  and 
  

   r 
  + 
  lth 
  ripples, 
  and 
  of 
  that 
  between 
  the 
  1st 
  and 
  2nd 
  ripples 
  

  

  