﻿98 
  Messrs. 
  R. 
  M. 
  Deeley 
  and 
  P. 
  H. 
  Parr 
  on 
  

  

  Very 
  little 
  is 
  known 
  concerning 
  the 
  coefficient 
  of 
  friction 
  

   of 
  glaciers 
  upon 
  their 
  beds. 
  Indeed 
  it 
  is 
  not 
  clear 
  why 
  a 
  

   glacier 
  slips 
  at 
  all 
  upon 
  its 
  bed 
  when 
  we 
  consider 
  how 
  slight 
  

   the 
  slope 
  generally 
  is. 
  

  

  In 
  most 
  glacier 
  valleys 
  there 
  are 
  hollows 
  and 
  hummocks, 
  

   into 
  which 
  and 
  over 
  which 
  the 
  ice 
  moves. 
  When 
  this 
  is 
  the 
  

   case 
  the 
  viscosity 
  of 
  the 
  ice 
  assists 
  to 
  prevent 
  the 
  glacier 
  

   from 
  slipping 
  forwards 
  bodily 
  ; 
  for 
  the 
  glacier 
  has 
  to 
  undergo 
  

   change 
  of 
  form 
  to 
  enable 
  it 
  to 
  slip. 
  The 
  viscosity, 
  therefore, 
  

   influences 
  the 
  slip 
  to 
  some 
  extent. 
  If 
  clean 
  ice 
  which 
  was 
  

   melting 
  at 
  the 
  surface 
  of 
  contact 
  rested 
  upon 
  smooth 
  rock, 
  

   the 
  coefficient 
  of 
  friction 
  would 
  be 
  small. 
  But 
  the 
  bottoms 
  

   of 
  glaciers 
  are 
  charged 
  with 
  stones, 
  sand, 
  and 
  mud, 
  and 
  it 
  is 
  

   probable 
  that 
  the 
  resistance 
  to 
  slipping 
  is 
  mainly 
  due 
  to 
  the 
  

   stony 
  condition 
  of 
  the 
  bottom 
  surface, 
  where, 
  as 
  in 
  the 
  case 
  

   of 
  the 
  Hintereis 
  Glacier, 
  the 
  valley 
  is 
  of 
  fairly 
  regular 
  

   section 
  and 
  slope. 
  

  

  In 
  the 
  case 
  of 
  an 
  elliptical 
  channel, 
  such 
  as 
  that 
  shown 
  

   in 
  fig. 
  7, 
  the 
  shear 
  force 
  at 
  any 
  point 
  &•, 
  y 
  is 
  

  

  >-*V*+£ 
  

  

  V 
  being 
  the 
  central 
  velocity. 
  

  

  The 
  pressure 
  at 
  the 
  same 
  point 
  is 
  p 
  = 
  dy, 
  d 
  being 
  the 
  

   density. 
  

  

  Now 
  the 
  slip 
  may 
  be 
  reasonably 
  expected 
  to 
  be 
  directly 
  

   proportional 
  to 
  the 
  force 
  f 
  producing 
  it, 
  and 
  inversely 
  pro- 
  

   portional 
  to 
  the 
  frictional 
  resistance, 
  which 
  latter 
  will 
  be 
  

   directly 
  proportional 
  to 
  the 
  pressure, 
  so 
  that 
  

  

  slip 
  cc 
  

  

  dy 
  

  

  2 
  Vg 
  

  

  dy 
  

  

  (10) 
  

  

  or, 
  as 
  2, 
  y, 
  V, 
  and 
  d 
  are 
  constants, 
  they 
  may 
  be 
  ignored, 
  

   and 
  

  

  ***■&£+$ 
  (11) 
  

  

  In 
  fig. 
  7 
  the 
  slip-curve 
  cc, 
  calculated 
  according 
  to 
  this 
  

   formula, 
  has 
  been 
  plotted. 
  It 
  will 
  be 
  seen 
  that 
  it 
  makes 
  

   the 
  slip 
  somewhat 
  less 
  at 
  the 
  centre 
  than 
  at 
  the 
  sides. 
  At 
  

   the 
  point 
  c 
  (fig. 
  6), 
  where 
  the 
  extrapolated 
  curve 
  leaves 
  the 
  

   actual 
  speed 
  curve 
  bb, 
  the 
  slip 
  is 
  24 
  per 
  cent, 
  greater 
  than 
  

  

  