﻿Related 
  Sedimentary 
  Surface 
  Forms. 
  

  

  177 
  

  

  described 
  above, 
  but 
  to 
  exclude 
  any 
  other 
  forms. 
  Sand- 
  

   waves, 
  in 
  this 
  sense, 
  can 
  not 
  exist 
  with 
  velocities 
  smaller 
  

   than 
  those 
  creating 
  them. 
  With 
  a 
  decrease 
  of 
  velocity 
  

   they 
  either 
  disappear 
  or 
  are 
  transformed. 
  Theyform 
  

   above 
  the 
  third 
  critical 
  point 
  of 
  velocity, 
  are 
  slightly 
  

   asymmetrical 
  or 
  symmetrical, 
  have 
  flat, 
  gently 
  rounded 
  

   crests 
  and 
  no 
  eddy 
  on 
  the 
  lee-side. 
  28 
  In 
  all 
  these 
  fea- 
  

   tures 
  they 
  differ 
  fundamentally 
  from 
  current-ripples, 
  

   which 
  form 
  below 
  the 
  second 
  critical 
  point 
  of 
  velocity, 
  

   are 
  strongly 
  asymmetrical, 
  with 
  rather 
  sharp 
  project- 
  

   ing 
  crests 
  sheltering 
  an 
  eddy. 
  

  

  Fig. 
  5. 
  

  

  Fig. 
  5. 
  Longitudinal 
  section 
  of 
  a 
  progressive 
  sand-wave, 
  to 
  illustrate 
  the 
  

   increase 
  in 
  velocity 
  of 
  the 
  bottom 
  current 
  at 
  the 
  crests 
  and 
  its 
  decrease 
  in 
  

   the 
  troughs, 
  abed 
  represents 
  the 
  quantity 
  of 
  water 
  which 
  passes 
  the 
  cross- 
  

   sections 
  A-A 
  and 
  B-B 
  in 
  the 
  unit 
  of 
  time. 
  The 
  velocity 
  is 
  proportional 
  to 
  

   the 
  horizontal 
  distances 
  ab 
  and 
  a'b' 
  . 
  

  

  Eegressive 
  and 
  progressive 
  sand-waves 
  differ 
  in 
  the 
  

   direction 
  of 
  traveling 
  and 
  in 
  their 
  mode 
  of 
  appearance. 
  

   Both 
  characteristics 
  seem, 
  however, 
  to 
  be 
  of 
  a 
  secondary 
  

   nature, 
  not 
  essential 
  for 
  the 
  production 
  of 
  the 
  wave-form. 
  

  

  The 
  up-stream 
  motion 
  of 
  the 
  regressive 
  sand-waves 
  is 
  

   due 
  to 
  the 
  fact 
  that 
  the 
  small 
  amount 
  of 
  water, 
  often 
  

   hardly 
  sufficient 
  to 
  cover 
  their 
  crests 
  when 
  at 
  rest, 
  liter- 
  

   ally 
  has 
  to 
  climb 
  up 
  the 
  weather-slope 
  of 
  the 
  sand-wave 
  

   and 
  fall 
  down 
  its 
  lee-slope. 
  Consequently, 
  it 
  is 
  retarded 
  

   by 
  gravity 
  on 
  the 
  weather-side, 
  causing 
  sediment 
  to 
  be 
  

   dropped, 
  and 
  accelerated 
  on 
  the 
  lee-side, 
  causing 
  erosion. 
  

   Thus, 
  while 
  all 
  grains 
  are 
  moving 
  down-stream, 
  the 
  wave- 
  

   form 
  moves 
  up-stream. 
  29 
  

  

  This 
  process, 
  however, 
  is 
  only 
  a 
  function 
  of 
  the 
  depth 
  

   of 
  the 
  water. 
  30 
  There 
  is 
  no 
  reason 
  why 
  at 
  a 
  greater 
  

   depth 
  sand-waves 
  should 
  not 
  form 
  also. 
  Cornish 
  

   remarks 
  : 
  l 
  ' 
  The 
  commencement 
  of 
  the 
  smaller 
  sand- 
  

  

  28 
  This 
  is 
  at 
  least 
  highly 
  probable 
  for 
  the 
  large 
  sand-waves 
  of 
  rivers. 
  

  

  29 
  Gilbert, 
  1914, 
  p. 
  34; 
  Cornish, 
  1901 
  (Tidal), 
  p. 
  198. 
  

  

  30 
  According 
  to 
  Gilbert 
  (1914, 
  p. 
  34) 
  the 
  second 
  and 
  third 
  critical 
  points 
  

   are 
  reached 
  "when 
  the 
  depth 
  of 
  water 
  bears 
  a 
  certain 
  numerical 
  relation 
  

   to 
  a 
  power 
  of 
  the 
  mean 
  velocity 
  near 
  the 
  cube. 
  ' 
  ' 
  

  

  