﻿162 
  

  

  Bucher 
  — 
  Origin 
  of 
  Ripples, 
  and 
  

  

  Increasing 
  viscosity 
  reduces 
  the 
  energy 
  of 
  the 
  whole 
  

   system 
  which, 
  in 
  the 
  first 
  line, 
  decreases 
  the 
  height 
  of 
  the 
  

   vortices 
  and 
  with 
  it, 
  of 
  course, 
  the 
  wave-length 
  of 
  the 
  

   ripples. 
  

  

  A 
  comparison 
  of 
  the 
  range 
  of 
  wave-lengths 
  obtained 
  

   by 
  Hahmann 
  in 
  his 
  experiments 
  15 
  with 
  that 
  of 
  current- 
  

  

  FlG. 
  l. 
  

  

  Fig. 
  1. 
  Contour 
  map 
  representing 
  the 
  ideal 
  form 
  of 
  linguoid 
  current- 
  

   ripples. 
  L 
  = 
  lowest 
  point; 
  dotted 
  lines 
  = 
  lines 
  of 
  flow 
  of 
  water. 
  (Copied 
  

   from 
  H. 
  Blasius, 
  1910, 
  fig. 
  3.) 
  

  

  ripples 
  observed 
  in 
  nature 
  brings 
  out 
  a 
  remarkable 
  dis- 
  

   crepancy. 
  Between 
  the 
  extremes 
  of 
  velocity 
  (0-313- 
  

   0*525 
  in 
  sec.) 
  and 
  of 
  grain 
  (average 
  diameter 
  from 
  below 
  

   0-1 
  mm. 
  to 
  2-8 
  mm.) 
  the 
  wave-length 
  varies 
  between 
  124 
  

  

  15 
  Cf. 
  tables 
  2 
  and 
  3; 
  for 
  complete 
  data 
  see 
  original 
  paper. 
  

  

  