the  Descent  of  Glaciers  by  their  Weight  only,  39 
one  another,  not  only  upon  the  surface  but  beneath  it,  those  on 
the  surface  that  are  nearer  to  the  axis  moving  faster  than  those 
more  remote,  and  those  below  the  surface  that  are  nearer  to  it 
moving  faster  than  those  deeper  down*. 
This  differential  motion  supposes  the  displacement  of  infinitely 
thin  longitudinal  strips  of  the  ice  in  the  direction  of  the  length  of 
the  glacier  side  by  side  and  over  and  under  one  another.  The  force 
(in  the  nature  of  pressure)  which  opposes  itself  tothis  displacement 
I  call  shear ;  and  I  obtain  the  unit  of  shear  by  a  direct  experiment 
of  the  resistance  to  the  shearing  of  two  parts  of  the  same  piece  of 
ice  upon  one  another  by  means  of  an  apparatus  specially  con- 
structed for  that  purpose  t,  precisely  as  in  this  glacier  contiguous 
strips  of  ice  are  in  their  differential  motion  supposed  to  be  sheared. 
I  have  not  found  this  unit  of  shear  to  be  in  any  case  more  than 
3  lbs.  less  than  75  lbs.  per  square  inch  in  ice  presumably  of  the 
temperature  of  32°  Fahr.;  but  I  have  found  it  to  be  considerably 
greater  in  ice  of  a  lower  temperature  J. 
The  unit  of  shear  being  known,  and  the  differential  motion  of 
the  glacier,  it  is  possible  to  determine  the  work  expended  on 
shearing  through  any  distance  of  its  descent.  If  its  weight  be 
the  only  force  which  causes  it  to  descend,  then  the  work  of  its 
weight  through  this  descent  must  at  least  equal  the  work  of  its 
shearing.  But  it  is  actually  far  less  than  it ;  it  is  less  than  one 
thirtieth  of  it.  It  is  impossible,  therefore,  that  a  glacier  of  uni- 
form section  and  slope  and  direction  should  descend  by  its  weight 
only ;  and  being  impossible  with  such  a  glacier,  it  is  a  fortiori  im- 
possible with  a  glacier  of  variable  section  and  direction.  This  is  my 
*  If  proof  were  needed  of  this  fact,  the  ribboned  structure  of  the  interior 
supposes  it  to  be  maintained  throughout  such  a  glacier,  and  the  dirt-bands 
of  the  surface  would  be  sufficient  evidence.     See  Phil.  Mag.  April  18/0. 
t  See  Phil.  Mag.  January  1870. 
+  See  my  paper  in  trie  Philosophical  Magazine  for  August  1871.  In 
describing  an  experiment  made  on  February  15,  1870,  I  have  spoken  of 
a  cylinder  of  ice  when  placed  in  the  shearing-apparatus  at  6  j  o'clock  in  the 
evening  as  having  yielded,  under  a  pressure  of  63'6  lbs.  per  square  inch  on 
its  upper  surface,  at  8  o'clock  by  -fa  inch,  and  of  its  having  been  examined 
at  lUj  the  next  morning  and  found  not  to  have  sheared  during  the  night. 
I  have  failed  to  express  myself  clearly,  and  Mr.  Mathews  has  misunderstood 
me.  I  should  have  explained  that  the  yielding  of  the  upper  surface  was 
accompanied  by  no  shearing  of  one  portion  of  the  ice  over  the  other.  Be- 
fore shearing  begins  in  my  apparatus,  the  pressure  on  the  upper  surface  of 
the  ice  being  greater  than  elsewhere,  and  the  apparatus  being  warmer  than 
the  ice,  the  ice  is  melted  there  more  than  elsewhere.  It  was  by  this  melt- 
ing, and  not  by  sheaiing,  that  the  upper  surface  yielded.  In  experiments 
under  an  external  temperature  above  freezing  the  warmth  of  the  shearing- 
apparatus  and  its  conductivity  cause  a  continual  melting  of  the  ice  and  di- 
minution of  its  cross  section.  "When  the  ice  once  begins  to  shear,  as  the 
shearing-pressure  remains  constant  while  the  section  continually  dimi- 
nishes, the  shearing  motion  cannot  but  be  kept  up. 
