﻿186 
  Ripiile 
  Formation 
  in 
  Kandt's 
  T'ahe 
  E^r,perlment. 
  

   back 
  to 
  the 
  equation 
  

  

  we 
  have 
  

  

  

  <1 
  

  

  and 
  W3 
  can 
  only 
  be 
  less 
  than 
  n^. 
  

   Therefore 
  we 
  have 
  

  

  Now 
  

  

  ^3 
  

   ^1 
  • 
  

  

  \«23/ 
  

  

  which 
  means 
  that 
  

  

  IS 
  >1, 
  

  

  (£)' 
  >'■ 
  

  

  Some 
  experimental 
  results 
  in 
  connexion 
  with 
  this 
  point 
  

   lijive 
  been 
  obtained. 
  The 
  distance 
  between 
  two 
  nodes 
  was 
  

   divided^ 
  into 
  three 
  parts, 
  left, 
  middle, 
  and 
  right, 
  and 
  the 
  

   mean 
  distance 
  between 
  the 
  ripples 
  in 
  each 
  part 
  measured 
  by- 
  

   means 
  of 
  a 
  travelling 
  microscope. 
  It 
  would 
  be 
  desirable 
  to 
  

   make 
  such 
  measurements 
  whilst 
  the 
  tone 
  is 
  being 
  emitted, 
  

   but 
  as 
  I 
  used 
  the 
  ordinary 
  method 
  of 
  producing 
  the 
  figures 
  * 
  

   by 
  means 
  of 
  stroking 
  a 
  glass 
  rod, 
  this 
  was 
  not 
  done 
  for 
  the 
  

   results 
  here 
  given. 
  The 
  results 
  are 
  given 
  for 
  different 
  

   powders 
  and 
  for 
  different 
  frequencies, 
  and 
  in 
  every 
  case 
  it 
  is 
  

   seen 
  that 
  the 
  distance 
  between 
  the 
  ripples 
  is 
  greater 
  at 
  the 
  

   antinodes 
  than 
  near 
  the 
  nodes, 
  which 
  is 
  quite 
  in 
  agreement 
  

   with 
  the 
  above 
  investigation. 
  

  

  Distance 
  

  

  between 
  

  

  two 
  nodes. 
  

  

  Fre- 
  

   quency. 
  

  

  Distance 
  between 
  consecutive 
  ripples. 
  

  

  Fine 
  iron 
  

   powder. 
  

  

  Coarse 
  iron 
  

   powder. 
  

  

  Emery 
  powder 
  

  

  Sand. 
  

  

  Left. 
  

  

  Mid. 
  

  

  Rigbt. 
  

  

  L. 
  

  

  M. 
  

  

  E. 
  

  

  L. 
  

  

  M. 
  

  

  R. 
  

  

  L. 
  

  

  M. 
  

  

  E. 
  

  

  3-63 
  

   cm. 
  

  

  5-03 
  

   cm. 
  

  

  4545 
  

   3208 
  

  

  mm. 
  

   0-90 
  

  

  1-01 
  

  

  mm. 
  

   0-94 
  

  

  1-25 
  

  

  mm. 
  

   086 
  

  

  107 
  

  

  mm. 
  

   1-11 
  

  

  1-64 
  

  

  mm. 
  

   1-50 
  

  

  2-33 
  

  

  mm. 
  

   131 
  

  

  1-64 
  

  

  mm. 
  

   1-43 
  

  

  1-68 
  

  

  mm. 
  

   1-91 
  

  

  1-76 
  

  

  mm. 
  

   1-57 
  

  

  1-48 
  

  

  mm. 
  

   1-23 
  

  

  1-34 
  

  

  mm. 
  

   1-72 
  

  

  1-82 
  

  

  mm. 
  

   1-06 
  

  

  1-22 
  

  

  * 
  Phys. 
  ZeiL 
  1908, 
  p. 
  

  

  