235.  The  moment  of  this  force  cannot  be  accurately  or  ap-
proximately estimated  ;  the  strongest  kinds  of  timber  frames,
faced  with  iron  rails,  are  simply  crushed  and  splintered  into
kindling-wood.
236.  Mr.  Weisbach  and  others  give  formulae  for  the  amount
of  force  exerted  ;  but  the  elements  of  it  are  unknown,  and  all
that  can  be  done  is  to  assume  a  certain  value  for  the  area  of
surface  pressed,  velocity  of  current,  and  some  unknown  factor
depending  on  the  shape  of  the  pier,  and  obtaining  a  result
which  could  have  no  practical  value.
237*  By  observing  the  actual  result  and  determining  the  re-
sistance to  splitting  of  the  ice  for  a  distance  above  the  pier,  we
will  have  part  of  the  resistance  to  the  moving  force.  Much  of
it,  however,  is  taken  up  by  friction  of  the  ice  as  it  moves  along
the  shore  lines,  wider  at  some  and  narrower  at  other  parts.  The
writer  has  therefore  simply  determined  the  extent  of  the  force
on  the  pier  by  multiplying  the  area  of  the  split  surface  by  10
tons  to  the  square  foot,  this  figure  being  simply  assumed  (it
may  be  very  far  from  the  correct  value,  as  so  much  depends
upon  the  temperature  and  the  condition  of  freezing;  from  some
actual  experiments  the  tensile  strength  has  been  found  to  vary
from  140  to  200  pounds  per  square  inch),  in  order  to  illustrate
the  manner  of  arriving  at  the  actual  force  exerted.
