44         Canon  Moseley  on  the  Mechanical  Impossibility  of 
direction  of  what  has  been  called  its  thickness  or  depth  (but 
which,  now  that  it  is  laid  down  in  the  channel  of  a  glacier,  must 
be  called  its  length),  and  that,  in  some  way  which  has  not  been 
explained,  it  would  bend  continually  more  and  more  and  so  de- 
scend. For  if  it  would  not  do  so  under  these  conditions,  then 
a  fortiori  it  would  not  do  so  under  the  actual  conditions  of  a 
glacier,  in  which  the  stops — instead  of  being  placed  at  the  end 
only,  and  the  sides  and  bottom  being  elsewhere  without  resistance 
— are  distributed  over  the  whole  surface  of  the  channel,  sides, 
and  bottom.  Now  it  is  my  object  to  show  that  this  imagi- 
nary glacier  would  not  bend  by  its  own  weight  only  in  the  di- 
rection of  its  length  under  these  conditions,  and  therefore  a  for- 
tiori that  it  would  not  descend  by  bending  under  the  conditions 
of  an  actual  glacier. 
For  the  sake  of  argument,  I  will  suppose  that  the  deflection 
of  my  imaginary  glacier  along  its  sloping  channel  in  the  direc- 
tion of  its  length,  and  that  of  Mr.  Mathews's  ice-plank  in  the  ver- 
tical direction  of  its  thickness,  are  neither  of  them  carried  beyond 
what  is  called  the  elastic  limit,  so  that  neither  of  them  takes  a 
set  in  the  act  of  deflecting.  This  being  supposed,  it  is  possible 
to  determine  by  well-known  formulae  what  ratio  the  bendings  or 
deflections  of  the  two  masses  of  ice  would  have  to  one  another. 
It  will,  I  hope,  put  no  great  mathematical  strain  on  my  readers  to 
follow  the  investigation  of  this  ratio,  which  I  have  subjoined  in 
a  note*.  It  results  from  it  that  the  bending  downwards  of  the 
glacier  will  not  be  -019122,  or  not  the  fiftieth  part  of  the  bend- 
ing of  the  ice-plank. 
When  the  bending  of  a  body  is  carried  beyond  certain  limits, 
known  as  the  limits  of  its  elasticity,  it  takes  a  set.    The  ice-plank 
*  If  D  represent  the  deflection,  by  its  weight  alone,  of  a  solid  having  a 
rectangular  cross  section  whose  depth  is  c,  and  the  distance  of  the  two 
points  on  which  it  is  supported  a,  and  its  breadth  b,  and  ifwbethc 
weight  of  a  cubic  unit  of  it,  and  E  its  modulus  of  elasticity,  and  if  it  be 
borne  in  mind  that  the  weight  of  such  a  mass  produces  the  same  effect  in 
causing  it  to  deflect,  as  five  eighths  of  its  weight  would  do  if  collected  in 
its  centre,  then  (see  Morin,  vide  Memoire  de  Mecanique  Pratique,  p.  481, 
ed.  5,  or  '  Mechanical  Principles  of  Engineering/  by  the  author  of  this 
paper,  p.  510,  ed.  2) 
t)_    a3(i-aal)c)   _/5co\ft4 
~  WE^bc*)  ~\32E/  c*' 
But  if,  instead  of  being  placed  vertically,  the  solid  had  been  laid  upon  a 
smooth  incline  whose  inclination  was  i,  the  pressure  of  each  cubic  unit  of 
its  mass  tending  to  cause  it  to  deflect  would  have  become  w  sin  i  instead  of 
w.     In  this  case,  therefore, 
whence  it  follows  that  in  respect  of  different  solids  so  placed,  having  equal 
