﻿192 
  Bucher 
  — 
  Origin 
  of 
  Ripples, 
  and 
  

  

  obviously 
  determined 
  by 
  that 
  of 
  the 
  preexisting 
  set 
  of 
  

   ripples. 
  

  

  A 
  simple 
  experiment 
  confirmed 
  the 
  suspicion, 
  aroused 
  

   by 
  this 
  specimen, 
  that 
  cross-ripples 
  result 
  from 
  the 
  inter- 
  

   section 
  of 
  an 
  oscillation 
  with 
  a 
  preexisting 
  set 
  of 
  ripples. 
  

   A 
  vessel, 
  containing 
  a 
  fine 
  grade 
  of 
  carborundum 
  powder 
  

   as 
  sediment, 
  was 
  rocked 
  by 
  hand. 
  After 
  one 
  to 
  two 
  hun- 
  

   dred 
  oscillations 
  a 
  set 
  of 
  good 
  ripples 
  had 
  formed. 
  Then 
  

   the 
  direction 
  of 
  oscillation 
  was 
  changed. 
  Up 
  to 
  a 
  differ- 
  

   ence 
  of 
  45°, 
  as 
  Forel 
  had 
  already 
  observed, 
  no 
  important 
  

   change 
  in 
  the 
  shape 
  and 
  orientation 
  of 
  the 
  ripples 
  first 
  

   formed 
  was 
  observed. 
  At 
  90°, 
  rectangular 
  interference 
  

   ripples 
  were 
  produced, 
  that 
  is, 
  a 
  new 
  set 
  of 
  ripples 
  was 
  

   set 
  up 
  in 
  the 
  troughs 
  between 
  the 
  old 
  ones. 
  At 
  inter- 
  

   vening 
  angles 
  of 
  intersection, 
  however, 
  the 
  crests 
  of 
  the 
  

   first 
  ripples 
  quickly 
  changed 
  to 
  a 
  zigzag 
  line, 
  while 
  the 
  

   growing 
  new 
  ripples 
  shifted 
  to 
  alternating 
  positions 
  in 
  

   adjoining 
  troughs, 
  producing 
  the 
  hexagonal 
  interference 
  

   pattern. 
  

  

  In 
  fig. 
  1 
  the 
  processes 
  involved 
  are 
  shown 
  in 
  diagram- 
  

   matic 
  form. 
  The 
  lines 
  A-A 
  represent 
  the 
  first 
  set 
  of 
  rip- 
  

   ples. 
  The 
  long 
  arrows 
  at 
  the 
  upper 
  end 
  of 
  each 
  diagram 
  

   indicate 
  the 
  direction 
  of 
  the 
  oscillation 
  which 
  tends 
  to 
  

   produce 
  the 
  ripples 
  B-B. 
  These 
  can 
  exist 
  only, 
  if 
  they 
  

   intersect 
  A-A 
  at 
  right 
  angles. 
  (Fig. 
  la.) 
  If 
  formed 
  at 
  

   a 
  smaller 
  angle, 
  as 
  in 
  figure 
  lb, 
  they 
  are 
  rapidly 
  trans- 
  

   formed 
  into 
  the 
  hexagonal 
  pattern, 
  figure 
  1c. 
  The 
  

   small, 
  curved 
  arrows 
  indicate 
  the 
  horizontal 
  components 
  

   of 
  the 
  vortices 
  in 
  the 
  lee 
  of 
  the 
  growing 
  second 
  set 
  of 
  

   ripples 
  (B-B) 
  and 
  their 
  deflection 
  by 
  A-A. 
  The 
  arrows 
  

   drawn 
  with 
  dotted 
  lines 
  correspond 
  to 
  the 
  second 
  half 
  

   of 
  an 
  oscillation, 
  when 
  the 
  current 
  is 
  reversed. 
  

  

  In 
  figures 
  la 
  and 
  1c, 
  these 
  arrows 
  are 
  grouped 
  sym- 
  

   metrically 
  on 
  both 
  sides 
  of 
  B-B, 
  not, 
  however, 
  in 
  lb. 
  

   This 
  explains, 
  why 
  a 
  diagonal 
  pattern 
  of 
  cross-ripples 
  

   does 
  not 
  form. 
  The 
  unequal 
  power 
  of 
  the 
  vortices 
  on 
  

   opposite 
  sides 
  of 
  the 
  growing 
  ripples 
  must 
  cause 
  a 
  shift- 
  

   ing 
  of 
  the 
  lines 
  of 
  attack, 
  until 
  the 
  difference 
  no 
  longer 
  

   exists. 
  We 
  recognize 
  therefore 
  in 
  this 
  transformation 
  

   again 
  the 
  tendency 
  to 
  establish 
  a 
  state 
  of 
  equilibrium. 
  

  

  Since 
  ripples 
  in 
  nature 
  are 
  neither 
  strictly 
  parallel 
  nor 
  

   straight, 
  the 
  cross-ripples 
  are 
  usually 
  very 
  irregular 
  and 
  

   the 
  typical 
  forms 
  confined 
  to 
  small 
  portions 
  of 
  the 
  rippled 
  

   surfaces 
  only 
  (cf. 
  fig. 
  8). 
  

  

  Cross-ripples, 
  therefore, 
  may 
  form 
  anyivhere, 
  in 
  shal- 
  

  

  