﻿180 
  Bucher 
  — 
  Origin 
  of 
  Ripples, 
  and 
  

  

  we 
  turn 
  to 
  Humphreys 
  and 
  Abbot's 
  Report 
  of 
  the 
  Mis- 
  

   sissippi 
  River. 
  Here 
  we 
  find, 
  for 
  instance, 
  the 
  following 
  

   sub-surface 
  velocity 
  observations 
  34 
  made 
  at 
  Vicksburg, 
  

   1858. 
  

  

  At 
  the 
  highest 
  stage 
  of 
  the 
  river 
  (depth 
  about 
  23 
  m.) 
  

   the 
  velocity 
  was 
  : 
  

  

  May 
  13 
  Aug. 
  7 
  

  

  Surface 
  2-35 
  m./sec. 
  2-65 
  m./sec. 
  

  

  Depth 
  of 
  21 
  in 
  2-25 
  m./sec. 
  1-80 
  m./sec. 
  

  

  At 
  a 
  medium 
  stage 
  (depth 
  about 
  16 
  m.) 
  : 
  

  

  Sept. 
  28 
  Sept. 
  28 
  

  

  Surface 
  1-59 
  m./sec. 
  1-59 
  m./sec. 
  

  

  Depth 
  of 
  15 
  m 
  1-45 
  m./sec. 
  1-00 
  m./sec. 
  

  

  Using 
  these 
  figures 
  as 
  examples, 
  we 
  are 
  justified 
  in 
  

   assuming 
  that 
  the 
  currents 
  at 
  the 
  bottom 
  of 
  the 
  27 
  m. 
  

   section 
  as 
  to 
  all 
  probability 
  at 
  the 
  very 
  most 
  were 
  four 
  

   times 
  as 
  strong 
  as 
  those 
  in 
  the 
  11 
  m. 
  section, 
  probably 
  

   much 
  less. 
  

  

  In 
  case 
  of 
  a 
  ratio 
  of 
  velocities 
  of 
  1 
  : 
  4 
  at 
  the 
  two 
  points, 
  

   which 
  at 
  least 
  lies 
  within 
  the 
  range 
  of 
  possibility, 
  the 
  

   lengths 
  of 
  the 
  sand-waves 
  should 
  be 
  in 
  the 
  ratio 
  1 
  : 
  16, 
  

   which 
  would 
  give 
  for 
  the 
  27 
  m. 
  section 
  a 
  wave-length 
  of 
  

   208 
  m. 
  The 
  wave-length 
  actually 
  found 
  was 
  228 
  m. 
  

  

  The 
  ratio 
  of 
  velocities, 
  however, 
  in 
  all 
  probability, 
  was 
  

   very 
  much 
  smaller. 
  Another 
  factor 
  of 
  at 
  least 
  equal 
  

   importance 
  must 
  therefore 
  influence 
  the 
  wave-length. 
  

  

  In 
  Gilbert's 
  experiments, 
  ' 
  ' 
  anti-dunes 
  ' 
  ' 
  of 
  0-6-0-9 
  m. 
  

   length 
  were 
  produced 
  with 
  currents 
  of 
  ±1-00 
  m./sec. 
  

   velocity, 
  at 
  a 
  depth 
  measured 
  in 
  centimeters. 
  The 
  veloc- 
  

   ity 
  of 
  the 
  current 
  that 
  produced 
  the 
  13 
  m. 
  sand-waves 
  

   was 
  as 
  to 
  all 
  probability 
  hardly 
  much 
  greater. 
  This, 
  as 
  

   Gilbert 
  has 
  pointed 
  out 
  already, 
  seems 
  to 
  indicate 
  that 
  

   depth 
  is 
  an 
  important 
  factor 
  in 
  the 
  formation 
  of 
  sand- 
  

   waves. 
  This 
  is 
  to 
  be 
  expected 
  in 
  the 
  case 
  of 
  friction 
  

   waves, 
  while 
  in 
  the 
  case 
  of 
  current-ripples 
  a 
  direct 
  influ- 
  

   ence 
  of 
  an 
  increase 
  of 
  depth 
  on 
  the 
  size 
  of 
  the 
  vortices, 
  

   etc., 
  would 
  hardly 
  seem 
  intelligable 
  and 
  was 
  never 
  

   observed. 
  Depth 
  does 
  not 
  appear 
  in 
  Helmholtz's 
  

   formula, 
  because, 
  owing 
  to 
  the 
  great 
  difficulties 
  of 
  treat- 
  

   ing 
  such 
  a 
  complex 
  problem 
  mathematically, 
  it 
  was 
  

  

  1 
  Humphreys 
  an. 
  I 
  Abbot, 
  Report 
  upon 
  the 
  Physics 
  and 
  Hydraulics 
  of 
  the 
  

   Mississippi 
  River, 
  1861, 
  p. 
  258. 
  In 
  the 
  figures 
  quoted, 
  feet 
  were 
  transformed 
  

   into 
  meters, 
  to 
  the 
  nearest 
  centimeter. 
  

  

  