﻿206 
  Bucher 
  — 
  Origin 
  of 
  Ripples, 
  and 
  

  

  geology 
  refer 
  to 
  the 
  shoals 
  on 
  the 
  inner 
  side 
  of 
  meanders 
  

   and 
  the 
  " 
  crossings" 
  between 
  two 
  bends. 
  It 
  seems 
  to 
  

   be 
  less 
  well 
  known, 
  however, 
  that 
  a 
  depositing 
  stream 
  

   will 
  distribute 
  its 
  load 
  in 
  a 
  straight 
  channel 
  in 
  a 
  similar 
  

   way, 
  80 
  with 
  shoals 
  on 
  alternating 
  sides, 
  connected 
  by 
  

   "crossings," 
  so 
  that 
  the 
  main 
  current 
  flowing 
  from 
  the 
  

   deep 
  on 
  one 
  side 
  in 
  order 
  to 
  pass 
  over 
  to 
  following 
  deep 
  

   on 
  the 
  other 
  side 
  has 
  to 
  traverse 
  the 
  shallow 
  "crossing." 
  

  

  Compare 
  with 
  this 
  the 
  lines 
  of 
  flow 
  on 
  fig. 
  2. 
  The 
  

   similarity 
  of 
  the 
  arrangement 
  is 
  striking. 
  The 
  conclu- 
  

   sion 
  drawn 
  by 
  Blasius 
  seems 
  inevitable 
  that 
  the 
  forma- 
  

   tion 
  of 
  both 
  is 
  governed 
  by 
  the 
  same 
  principle. 
  

  

  One 
  might 
  consider 
  rhomboid 
  and 
  linguoid-ripples 
  as 
  

   transitional 
  forms 
  leading 
  to 
  the 
  other 
  extreme, 
  that 
  of 
  

   longitudinal 
  ridges 
  and 
  furrows 
  of 
  which 
  the 
  longitudinal 
  

   dunes 
  are 
  the 
  most 
  remarkable 
  examples. 
  

  

  According 
  to 
  Johnston's 
  investigations, 
  81 
  beach 
  cusps 
  

   represent 
  a 
  peculiar 
  special 
  case 
  of 
  longitudinal 
  ridges. 
  

   They 
  are 
  of 
  a 
  certain 
  interest 
  in 
  this 
  connection 
  since 
  

   Johnston's 
  interpretation 
  of 
  the 
  method 
  of 
  formation 
  

   of 
  these 
  cusps 
  as 
  due 
  to 
  the 
  establishment 
  of 
  a 
  state 
  of 
  

   equilibrium 
  through 
  gradual, 
  more 
  or 
  less 
  fortuitous 
  

   changes, 
  is 
  exactly 
  analogous 
  to 
  that 
  given 
  for 
  ripples. 
  

   He 
  writes 
  : 
  ' 
  ' 
  The 
  tendency 
  of 
  wave 
  action 
  will 
  be 
  to 
  

   develop 
  from 
  initial 
  irregularities 
  a 
  smaller 
  number 
  of 
  

   broad 
  and 
  shallow 
  depressions 
  on 
  that 
  portion 
  of 
  the 
  

   beach 
  traversed 
  by 
  the 
  swash." 
  "Equilibrium 
  will 
  be 
  

   established 
  when 
  adjacent 
  channels 
  are 
  of 
  approximately 
  

   the 
  same 
  size, 
  and 
  at 
  the 
  same 
  time 
  of 
  a 
  size 
  appropriate 
  

   to 
  the 
  volumes 
  of 
  water 
  traversing 
  them." 
  S2 
  

  

  A 
  closer 
  analogy 
  with 
  longitudinal 
  ridges 
  is 
  offered 
  

   by 
  the 
  drumlins, 
  the 
  origin 
  of 
  which 
  must 
  probably 
  be 
  

   explained 
  along 
  some 
  such 
  lines. 
  Their 
  origin 
  as 
  friction 
  

   phenomena 
  is 
  emphasized 
  by 
  Fairchild's 
  statement, 
  that 
  

   "one 
  important 
  and 
  essential 
  factor" 
  is 
  "the 
  movement 
  

   of 
  the 
  ground 
  contact 
  ice 
  due 
  to 
  thrust 
  or 
  push 
  of 
  the 
  

   rearward 
  ice." 
  83 
  

  

  80 
  Cf 
  . 
  the 
  beautifully 
  illustrated 
  paper 
  by 
  H. 
  Engels, 
  Untersuchungen 
  uber 
  

   die 
  Bettausbildung 
  gerader 
  oder 
  schwach 
  gekrummter 
  Flusstrecken 
  mit 
  

   beweglicher 
  Sohle, 
  Zs. 
  Bauwesen, 
  vol. 
  55, 
  p. 
  663 
  ff. 
  (plates 
  63-67), 
  1905. 
  

  

  81 
  D. 
  W. 
  Johnston, 
  Beach 
  Cusps, 
  Bull. 
  Geol. 
  Soc. 
  Am., 
  vol. 
  21, 
  pp. 
  599-624, 
  

   1910. 
  

  

  "'Ibid., 
  p. 
  621. 
  

  

  83 
  H. 
  L. 
  Fairchild, 
  in 
  discussion 
  of 
  W. 
  C. 
  Alden 
  's 
  paper 
  on 
  Radiation 
  of 
  

   glacial 
  flow 
  as 
  a 
  factor 
  in 
  drumlin 
  formation, 
  Bull. 
  Geol. 
  Soc. 
  Am., 
  vol. 
  22, 
  

   p. 
  734, 
  1911. 
  

  

  