﻿Related 
  Sedimentary 
  Surface 
  Forms. 
  161 
  

  

  increase 
  of 
  the 
  height 
  of 
  the 
  vortices, 
  other 
  things 
  being 
  

   equal, 
  increases 
  the 
  wave-length 
  of 
  the 
  ripples. 
  

  

  The 
  velocity 
  at 
  the 
  lower 
  boundary 
  is 
  affected 
  by 
  the 
  

   bed 
  resistance, 
  which 
  is 
  a 
  function 
  of 
  the 
  size 
  of 
  the 
  

   grains. 
  An 
  increase 
  in 
  the 
  size 
  of 
  the 
  grain 
  means 
  

   reduction 
  of 
  the 
  velocity 
  of 
  the 
  bottom 
  current. 
  This 
  

   must 
  disturb 
  the 
  equilibrium, 
  since 
  owing 
  to 
  this 
  retard- 
  

   ation, 
  the 
  same 
  volume 
  of 
  water 
  can 
  not 
  pass 
  the 
  crest 
  

   of 
  the 
  vortices. 
  

  

  I 
  suggest 
  that 
  the 
  inclination 
  of 
  the 
  gentle 
  slope 
  of 
  the 
  

   current-ripple 
  regulates 
  the 
  discharge 
  of 
  water 
  across 
  

   the 
  crest 
  and 
  thus 
  counteracts 
  the 
  retardation 
  of 
  the 
  bot- 
  

   tom 
  current. 
  Its 
  effect 
  is 
  probably 
  analogous 
  to 
  that 
  of 
  

   the 
  approach 
  to 
  a 
  weir 
  on 
  its 
  discharge. 
  In 
  a 
  series 
  of 
  

   experiments 
  made 
  by 
  Rafter 
  14 
  in 
  1898 
  for 
  the 
  U. 
  S. 
  Deep 
  

   Waterways 
  Commission 
  at 
  the 
  Canal 
  of 
  the 
  Cornell 
  

   Hydraulic 
  Laboratory, 
  the 
  following 
  values 
  of 
  the 
  vari- 
  

   able 
  factor 
  M 
  of 
  the 
  formula 
  for 
  the 
  discharge 
  of 
  a 
  weir 
  

   were 
  found: 
  

  

  Up-stream 
  Head 
  on 
  crest 
  in 
  feet 
  

  

  slope 
  

  

  1-0 
  2-0 
  JB-0 
  4-0 
  5-0^ 
  

  

  26° 
  344 
  31)6 
  3-68 
  3-70 
  3-71 
  

  

  18° 
  3-82 
  3-69 
  3-55 
  3-55 
  3-55 
  

  

  14° 
  3-44 
  3-48 
  3-48 
  3-48 
  3-48 
  

  

  11° 
  3-33 
  3-35 
  3-38 
  3-39 
  3-39 
  

  

  The 
  crest 
  of 
  this 
  weir 
  was 
  0-66 
  feet 
  wide 
  and 
  had 
  a 
  ver- 
  

   tical 
  down-stream 
  slope. 
  Although 
  a 
  submerged 
  weir 
  

   would 
  offer 
  a 
  closer 
  analogy 
  to 
  the 
  case 
  of 
  current-rip- 
  

   ples, 
  these 
  experiments 
  suffice 
  to 
  illustrate 
  the 
  effect 
  of 
  

   the 
  up-stream 
  slope 
  on 
  the 
  discharge. 
  In 
  this 
  case, 
  the 
  

   most 
  favorable 
  angle 
  for 
  low 
  velocities 
  (1-2 
  feet 
  head) 
  is 
  

   smaller 
  than 
  that 
  for 
  higher 
  velocities 
  (3-5 
  feet 
  head). 
  

  

  The 
  coarser 
  the 
  grain, 
  and 
  therefore, 
  the 
  smaller 
  the 
  

   velocity 
  of 
  the 
  bottom 
  current, 
  the 
  smaller 
  the 
  inclination 
  

   of 
  the 
  gentle 
  slope 
  of 
  the 
  ripple 
  has 
  to 
  be, 
  in 
  order 
  to 
  give 
  

   the 
  same 
  discharge 
  as 
  with 
  finer 
  grains. 
  Such 
  a 
  reduc- 
  

   tion 
  of 
  the 
  inclination 
  of 
  the 
  gentle 
  slope, 
  other 
  things 
  

   being 
  equal, 
  necessarily 
  increases 
  the 
  wave-length 
  of 
  the 
  

   ripples. 
  It 
  is 
  thought 
  that 
  the 
  gentle 
  slope 
  of 
  the 
  cur- 
  

   rent-ripple 
  adjusts 
  itself 
  automatically 
  to 
  the 
  needs 
  of 
  

   the 
  whole 
  system 
  and 
  thereby 
  increases 
  the 
  wave-length, 
  

   when 
  the 
  size 
  of 
  the 
  grains 
  of 
  the 
  sediment 
  increases. 
  

  

  "Quoted 
  from 
  M. 
  Merriman, 
  Treatise 
  on 
  Hydraulics, 
  1912, 
  p. 
  163-164. 
  

  

  