﻿the 
  Viscosity 
  of 
  Glacier 
  Ice. 
  103 
  

  

  a 
  

  

  If 
  s 
  = 
  fr 
  

  

  •6 
  s 
  

  

  then 
  * 
  = 
  2V(£ 
  + 
  1 
  )' 
  (13) 
  

  

  so 
  that 
  the 
  velocity 
  as 
  determined 
  for 
  a 
  definite 
  thickness 
  

   /», 
  and 
  a 
  definite 
  velocity 
  V, 
  will 
  be 
  affected 
  by 
  the 
  ratio 
  of 
  

   semi-widfh 
  to 
  depth 
  according 
  to 
  

  

  F, 
  

  

  We 
  thus 
  obtain 
  

  

  

  v=^-V„ 
  (14) 
  

  

  F 
  6 
  being 
  the 
  ratio 
  of 
  the 
  true 
  viscosity 
  to 
  the 
  viscosity 
  

   obtained 
  by 
  considering 
  the 
  section 
  to 
  be 
  of 
  infinite 
  width 
  ; 
  

  

  <* 
  v 
  = 
  V^e, 
  

  

  where 
  rj 
  = 
  true 
  viscosity, 
  

  

  V 
  x 
  = 
  viscosity 
  for 
  infinite 
  width, 
  

  

  F 
  e 
  = 
  factor 
  depending 
  on 
  proportions 
  of 
  the 
  ellipse. 
  

  

  "We 
  will 
  suppose 
  (fig. 
  11) 
  that 
  the 
  effect 
  of 
  each 
  portion 
  of 
  

  

  the 
  glacier 
  bed 
  affects 
  the 
  central 
  velocity 
  V 
  in 
  the 
  proportion 
  

  

  x 
  2 
  

   of 
  -g, 
  and 
  that 
  the 
  total 
  effect 
  is 
  proportional 
  to 
  the 
  mean 
  

  

  value 
  of 
  a 
  number 
  of 
  radials 
  calculated 
  in 
  this 
  way 
  = 
  F 
  a 
  . 
  

   On 
  a 
  flat 
  bottom, 
  for 
  instance, 
  all 
  radials 
  will 
  have 
  the 
  value 
  

   ,/-. 
  whilst 
  the 
  effect 
  of 
  radials 
  high 
  up 
  on 
  the 
  sides, 
  when 
  the 
  

   glacier 
  is 
  broad, 
  will 
  be 
  very 
  small. 
  The 
  method 
  gives 
  

   accurate 
  results 
  for 
  a 
  semicircular 
  channel, 
  and 
  is 
  fairly 
  

   accurate 
  for 
  ellipses. 
  For 
  some 
  other 
  sections, 
  such 
  as 
  V., 
  it 
  

   is 
  not 
  so 
  accurate. 
  

  

  But 
  although 
  the 
  method 
  does 
  not 
  give 
  correct 
  results, 
  

   except 
  for 
  certain 
  sections, 
  it 
  gives 
  exceedingly 
  good 
  com- 
  

   parisons 
  between 
  sections 
  which 
  do 
  not 
  differ 
  much 
  from 
  

   each 
  other 
  in 
  shape. 
  

  

  In 
  fig. 
  5 
  the 
  lower 
  section 
  shows 
  the 
  glacier 
  bed, 
  and 
  

  

  x 
  2 
  

   above 
  it 
  are 
  the 
  values 
  of 
  F„, 
  calculated 
  by 
  the 
  — 
  2 
  mean 
  

  

  radial 
  method, 
  the 
  value 
  of 
  F„ 
  for 
  the 
  centre 
  of 
  the 
  glacier 
  

   being 
  0'f)51. 
  Above 
  the 
  section 
  of 
  the 
  glacier 
  are 
  drawn 
  the 
  

   surface-velocity 
  curve 
  bb 
  and 
  Weinberg's 
  curve 
  aa 
  Eor 
  

   pitch. 
  

  

  