﻿106 
  Messrs. 
  R. 
  M. 
  Deeley 
  and 
  P. 
  H. 
  Parr 
  on 
  

  

  Generally 
  speaking, 
  the 
  form 
  of 
  well 
  glaciated 
  valleys 
  

   very 
  closely 
  approximates 
  to 
  a 
  parabola. 
  Fig. 
  12 
  gives 
  two 
  

   sections 
  across 
  valley 
  No. 
  7 
  in 
  the 
  Bighorn 
  Mountains 
  of 
  

   Wyoming. 
  This 
  form 
  may 
  be 
  described 
  as 
  a 
  lop-sided 
  para- 
  

   bola. 
  Unfortunately 
  the 
  conditions 
  of 
  viscous 
  flow 
  have 
  

   not 
  been 
  ascertained 
  for 
  a 
  parabolic 
  channel. 
  

  

  For 
  the 
  curve 
  we 
  have 
  referred 
  to, 
  which 
  we 
  have 
  called 
  

   Parr's 
  curve, 
  the 
  d^pth 
  at 
  the 
  centre 
  is 
  

  

  sj 
  

  

  /3-^//3 
  2 
  -4 
  

  

  .... 
  (19) 
  

  

  2 
  ■ 
  J 
  

  

  If 
  a 
  be 
  the 
  semi-width 
  of 
  the 
  channel, 
  and 
  b 
  its 
  depth 
  at 
  

   the 
  centre, 
  we 
  have 
  

  

  and 
  Y 
  =vvra) 
  s 
  .- 
  (20) 
  

  

  a 
  2 
  > 
  ^ 
  a 
  4 
  b- 
  

  

  4/4 
  

  

  Y 
  being 
  the 
  velocity 
  at 
  the 
  centre. 
  

  

  The 
  curves 
  given 
  by 
  the 
  equation 
  (see 
  Appendix) 
  will 
  be 
  

   found 
  to 
  approximate 
  very 
  closely 
  indeed 
  to 
  natural 
  glaciated 
  

   valleys, 
  most 
  of 
  which 
  can 
  be 
  fitted 
  very 
  accurately 
  by 
  a 
  

   proper 
  choice 
  of 
  the 
  constants 
  /3 
  and 
  c. 
  ft 
  settles 
  the 
  depth 
  

   of 
  the 
  section 
  and 
  c 
  the 
  amount 
  of 
  lopsidedness. 
  

  

  In 
  fig. 
  13 
  a 
  curve 
  aaa 
  of 
  this 
  nature 
  has 
  been 
  fitted 
  to 
  

   the 
  section 
  of 
  the 
  Hintereis 
  Glacier. 
  It 
  will 
  be 
  seen 
  that 
  it 
  

   has 
  the 
  same 
  area 
  as 
  the 
  actual 
  section, 
  and 
  that 
  the 
  deepest 
  

   parts 
  of 
  the 
  two 
  sections 
  coincide. 
  Here 
  /3 
  = 
  3*5 
  and 
  c=2. 
  

  

  According 
  to 
  this 
  curve 
  

  

  = 
  P 
  / 
  3580O 
  2 
  x 
  19900 
  \ 
  2 
  

   V 
  ~2V'\35800 
  2 
  + 
  19900 
  2 
  j 
  

  

  79-46 
  / 
  35800 
  2 
  x 
  19900 
  \ 
  / 
  35800 
  2 
  \ 
  

  

  2x0-0000654: 
  x 
  \35800 
  2 
  + 
  199007 
  X 
  \35800 
  2 
  + 
  19900V* 
  

  

  (21) 
  

  

  Here 
  .35800 
  2 
  _ 
  y 
  

  

  35800 
  2 
  + 
  19900 
  2 
  ~~ 
  p 
  ' 
  

  

  Correcting 
  the 
  value 
  of 
  F 
  p 
  in 
  the 
  same 
  manner 
  as 
  was 
  

   a 
  lop 
  ted 
  for 
  F 
  e 
  , 
  we 
  have 
  

  

  F,xg=-764x;fg=-685, 
  . 
  . 
  . 
  (22) 
  

  

  