The  total  friction  will  be  the  sum  of  two  components  exerted  at
the  two  parts  of  the  bearing-surface  respectively,  and  will  be  pro-
portional to  the  arithmetical  sum  of  the  two  components  of  the
bearing-pressure ;  that  is,  to  the  force

Q  (c  +  2  ;g)

c         '

whereas,  if  the  plane  of  action  of  the  resultant  of  the  given  force
and  the  effort  had  not  overhung  the  bearings,  the  friction  would
have  been  simply  proportional  to  Q.  Hence  the  effect  of  that
plane's  overhanging  the  bearings  by  the  distance  0,  is  to  increase
the  friction  approximately  in  the  ratio  of

1       2«    ,
1  +  —  :  1.
c

III.  As  to  the  condition  that  the  bearing-surfaces  should  fit
each  other  easily,  it  is  necessary  in  order  that  the  bearing-pressure
may  not  contain,  to  any  appreciable  extent,  pairs  of  components
which  balance  each  other,  being  transverse  to  the  direction  of  ithe


426


DTITAMIGS  OF  UACHINEBT.
resultant  bearing-pressore ;  for  each  components  cause  an  un-
necessary addition  to  the  friction.  The  ratio  in  which  the  fridion
of  a  tighi-fitUng  heming  exceeds  that  of  an  easy-fitting  bearing  of
the  same  dimensions  and  figure,  is  yerj  nearly  equal  to  that  in
which  the  whole  area  of  the  bearing-scur&ce  exceeds  the  area  of
the  projection  of  that  sui&ce  on  a  plane  normal  to  the  direction  of
the  resultant  bearing-pressure.
When  the  use  of  beanngnsurfaces  in  pairs,  oblique  to  the  plane
of  the  pressure  and  motion,  is  unavoidable  (as,  for  example,  in  the
case  of  the  Y-shaped  bearings  of  a  planing  machine),  their  efieet
may  be  allowed  for  by  increasing  the  co-efficient  of  Motion  in  the
ratio  above-mentioned;  which  m  expressed  by  the  secant  of  the
equal  angles  which  the  normals  to  the  bearing-surfiuses  make  with
iJiat  plane.
