How  are  the  last  two  uses  illustrated  in
Figure    96  ?      The    pulleys    employed    are
called  fixed  pulleys,  i.e.  they  have  no  motion
except  that  of  rotation.      Is  any  mechani-
cal   advantage    gained    by    fixed    pulleys  ?
What  is  the  use  of  a  fixed  pulley  ?     Pulley
B   (Fig.  94)  is  a   movable  pulley.     What
kind  of  advantage  is  gained  by
means  of  a  movable  pulley  ?


Fig.  96.
95.  General  Law  of  Machines.
—  From  the  experiments  and  dis-
cussion above  we  derive  the  following  formula  for  ma-
chines :  —

FS  =  RS'  +  w,


MACHINES.  Ill

in  which  F  represents  the  force  applied,  and  S  the  distance
through  which  F  acts ;  R  represents  the  resistance  over-
come, and  S'  the  distance  through  which  its  point  of  ap-
plication is  moved ;  w  represents  the  wasted  work.  A
machine  in  which  there  is  no  wasted  work  is  a  perfect
machine.  Such  a  machine  is  purely  ideal,  as  none  exists.
If  in  our  calculations  we  regard  a  machine  as  perfect
(though  subsequently  suitable  allowance  must  be  made
for  the  wasted  work),  then  our  formula  becomes

FS  =  RS'.
Whence  R  :  F  :  :  S  :  S' ;  i.e.  the  force  and  resistance  vary
inversely  as  the  distances  which  their  respective  points  of  ap-
plication move.  In  other  words,  the  ratio  of  the  resistance
to  the  force  is  the  reciprocal  of  the  ratio  of  the  distances
which  these  points  move.
R  :  F  -  4,  then  S' :  S  -  J.
