﻿Related 
  Sedimentary 
  Surface 
  Forms. 
  245 
  

  

  2. 
  The 
  following 
  relations 
  exist 
  between 
  the 
  dimen- 
  

   sions 
  of 
  a 
  water-body 
  and 
  the 
  oscillation 
  ripples 
  formed 
  

   in 
  it: 
  

  

  (a) 
  A 
  ripple 
  of 
  a 
  given 
  wave-length 
  owes 
  its 
  formation 
  

   to 
  an 
  oscillating 
  current 
  of 
  definite 
  velocity. 
  The 
  size 
  

   of 
  the 
  water 
  wave 
  which 
  sets 
  up 
  the 
  oscillation 
  determines 
  

   the 
  depth 
  at 
  which 
  this 
  velocity 
  would 
  exist 
  and 
  be 
  effec- 
  

   tive. 
  The 
  relation 
  is 
  very 
  complex 
  and 
  not 
  known 
  quan- 
  

   titatively. 
  As 
  the 
  orbital 
  velocity 
  of 
  the 
  particles 
  of 
  

   water 
  decreases 
  with 
  depth, 
  we 
  may 
  state 
  in 
  a 
  general 
  

   way 
  that 
  the 
  greatest 
  depth 
  at 
  which 
  the 
  velocity 
  neces- 
  

   sary 
  for 
  the 
  formation 
  of 
  a 
  given 
  set 
  of 
  ripples 
  is 
  found, 
  

   is 
  the 
  greater 
  the 
  larger 
  the 
  waves 
  creating 
  it. 
  

  

  Any 
  set 
  of 
  oscillation-ripples 
  may, 
  therefore, 
  have 
  been 
  

   produced 
  in 
  shallow 
  water 
  by 
  smaller, 
  or 
  in 
  deeper 
  water 
  

   by 
  larger 
  waves. 
  

  

  As 
  was 
  demonstrated 
  by 
  Kindle 
  's 
  observations 
  (p. 
  

   188), 
  there 
  exists 
  also 
  a 
  minimum 
  depth 
  for 
  each 
  size 
  of 
  

   ripples. 
  For 
  each 
  size 
  of 
  oscillation 
  ripples 
  there 
  must 
  

   exist, 
  therefore, 
  a 
  range 
  of 
  depth 
  within 
  which 
  it 
  may 
  

   form. 
  This 
  range 
  is 
  very 
  large 
  for 
  small 
  ripples. 
  I 
  

   have 
  frequently 
  observed 
  oscillation 
  ripples 
  with 
  1, 
  5 
  cm. 
  

   wave 
  length 
  on 
  the 
  silt 
  of 
  floodplains 
  of 
  the 
  Ohio 
  and 
  

   Little 
  Miami 
  Rivers, 
  in 
  places 
  where 
  the 
  water 
  could 
  not 
  

   possibly 
  have 
  been 
  more 
  than 
  a 
  few 
  cm. 
  deep. 
  Udden 
  10 
  

   observed 
  ripples 
  of 
  6 
  mm. 
  wave-length 
  in 
  a 
  small 
  water 
  

   pool 
  in 
  a 
  hollow 
  of 
  the 
  surface 
  of 
  a 
  rock, 
  at 
  a 
  depth 
  of 
  

   water 
  of 
  but 
  1 
  to 
  2 
  cm. 
  Siau 
  found 
  oscillation-ripples 
  of 
  

   small 
  size 
  at 
  the 
  depth 
  of 
  188 
  m. 
  off 
  the 
  island 
  of 
  Bourbon. 
  

   They 
  may 
  form, 
  and 
  certainly 
  do, 
  at 
  any 
  time 
  at 
  any 
  

   depth 
  in 
  between. 
  From 
  very 
  small 
  ripples, 
  therefore, 
  

   no 
  inference 
  of 
  any 
  kind 
  can 
  be 
  drawn 
  concerning 
  the 
  

   dimensions 
  of 
  the 
  waterbody 
  in 
  which 
  they 
  formed. 
  Of 
  

   statements 
  based 
  on 
  such 
  insufficient 
  evidence, 
  I 
  quote 
  

   only 
  that 
  of 
  Zimmermann. 
  11 
  He 
  found 
  small 
  ripples 
  of 
  a 
  

   little 
  less 
  than 
  2 
  cm. 
  wave-length 
  on 
  one 
  of 
  the 
  layers 
  of 
  

   salt 
  separated 
  by 
  very 
  thin 
  laminae 
  of 
  anhydrite 
  in 
  a 
  drill 
  

   core 
  from 
  the 
  Zechstein 
  of 
  Hesse. 
  From 
  this 
  he 
  con- 
  

   cluded 
  that 
  these 
  ripples 
  could 
  have 
  formed 
  only 
  under 
  

   a 
  very 
  thin 
  cover 
  of 
  water, 
  perhaps 
  but 
  a 
  few 
  decimeters 
  

  

  10 
  J. 
  A. 
  Tdden, 
  Jour. 
  Geol., 
  1916, 
  p. 
  123. 
  

  

  11 
  E. 
  Zimmermann, 
  Steinsaltz 
  mit 
  Wellenfurchen 
  von 
  Schlitz 
  in 
  Hessen, 
  

   Zs. 
  Deutsch. 
  Geol. 
  Ges., 
  vol. 
  60, 
  Monatsber., 
  y. 
  70, 
  190S. 
  

  

  