﻿166 
  Bucher 
  — 
  Origin 
  of 
  Ripples, 
  and 
  

  

  2. 
  The 
  first 
  appearance 
  of 
  regressive 
  sand-waves. 
  

   Concerning 
  their 
  first 
  appearance, 
  when 
  observed 
  in 
  

  

  shallow 
  streams 
  of 
  sandy 
  tidal 
  fore-shores, 
  Cornish 
  

   writes 
  (1901, 
  tidal, 
  p. 
  198) 
  : 
  19 
  "Almost 
  as 
  soon 
  as 
  the 
  

   velocity 
  .... 
  is 
  attained 
  at 
  which 
  the 
  water 
  becomes 
  

   notably 
  turbid, 
  a 
  train 
  of 
  sand-waves 
  arises 
  with 
  start- 
  

   ling 
  suddenness, 
  the 
  wave-fronts 
  quickly 
  extend 
  across 
  

   the 
  stream 
  at 
  right 
  angles 
  to 
  the 
  current, 
  and 
  the 
  ampli- 
  

   tude 
  of 
  the 
  sand-wave 
  sometimes 
  becomes 
  so 
  great 
  that 
  

   the 
  surface 
  of 
  the 
  sand 
  at 
  its 
  crest 
  is 
  nearly 
  on 
  a 
  level 
  

   with 
  the 
  surface 
  of 
  the 
  water 
  above 
  its 
  trough. 
  

  

  Pierce 
  (1916, 
  p. 
  43) 
  describes' 
  the 
  appearance 
  of 
  water- 
  

   waves 
  connected 
  with 
  regressive 
  sand-waves 
  in 
  the 
  lower 
  

   San 
  Juan 
  as 
  follows 
  : 
  "At 
  one 
  moment 
  the 
  stream 
  is 
  run- 
  

   ning 
  smoothly 
  for 
  a 
  distance 
  of 
  perhaps 
  several 
  hundred 
  

   yards. 
  Then 
  suddenly 
  a 
  number 
  of 
  waves, 
  usually 
  from 
  

   6 
  to 
  10, 
  appear. 
  They 
  reach 
  their 
  full 
  size 
  in 
  a 
  few 
  sec- 
  

   onds, 
  flow 
  for 
  perhaps 
  two 
  or 
  three 
  minutes, 
  then 
  sud- 
  

   denly 
  disappear. 
  ' 
  ' 
  

  

  3. 
  Data 
  concerning 
  regressive 
  sand-waves. 
  

  

  1. 
  Ground-plan. 
  — 
  The 
  axes 
  of 
  regressive 
  sand-waves 
  

   lie 
  transverse 
  to 
  the 
  direction 
  of 
  the 
  current. 
  In 
  the 
  

   experimental 
  trough 
  they 
  occupied 
  its 
  full 
  width; 
  in 
  

   natural 
  streams 
  Gilbert 
  observed 
  them 
  reaching 
  either 
  

   from 
  side 
  to 
  side 
  of 
  the 
  channed 
  or 
  else 
  forming 
  well- 
  

   defined 
  rows 
  in 
  the 
  direction 
  of 
  the 
  current 
  (cf. 
  also 
  

   Pierce, 
  1. 
  a). 
  

  

  2. 
  Profile. 
  — 
  In 
  profile 
  these 
  sand-waves 
  differ 
  from 
  

   current-ripples 
  in 
  being 
  symmetrical 
  with 
  flat, 
  gently 
  

   rounded 
  crests. 
  

  

  3. 
  Lines 
  of 
  flow. 
  — 
  There 
  are 
  no 
  vortices 
  ; 
  the 
  flow 
  

   lines 
  of 
  the 
  water 
  in 
  general 
  are 
  everywhere 
  essentially 
  

   parallel 
  to 
  the 
  bed 
  surface. 
  The 
  surface 
  of 
  the 
  water 
  

   follows 
  the 
  gentle 
  swell 
  of 
  the 
  sand 
  surface 
  underneath, 
  

   so 
  that 
  the 
  depth 
  of 
  water 
  is 
  approximately 
  the 
  same 
  

   over 
  crest 
  and 
  hollow. 
  "The 
  velocity 
  in 
  a 
  wave-trough 
  

   is 
  greater 
  than 
  near 
  the 
  crest. 
  The 
  sand 
  grains 
  flow 
  

   nearly 
  parallel 
  to 
  the 
  bed 
  as 
  they 
  pass 
  through 
  the 
  

   trough, 
  but 
  at 
  the 
  crest 
  they 
  have 
  an 
  up 
  and 
  down 
  motion, 
  

   as 
  well 
  as 
  a 
  forward 
  motion. 
  On 
  the 
  crest 
  of 
  the 
  larger 
  

   waves 
  their 
  forward 
  motion 
  is 
  small 
  compared 
  with 
  their 
  

   vertical 
  motion' 
  7 
  (Gilbert, 
  1914, 
  p. 
  32). 
  

  

  10 
  For 
  a 
  good 
  photograph 
  of 
  the 
  water-waves 
  connected 
  with 
  regressive 
  

   sand-waves, 
  see 
  Cornish, 
  1899, 
  pi. 
  1, 
  fig. 
  A. 
  

  

  