At  any  point  in  the  stroke  after  the  steam-valve  is  closed,
the  volume  and  pressure  of  steam  in  the  cylinder  can  be
determined  from  the  indicator-diagram  if  the  dimensions  of
the  engine  and  its  clearance  are  known.  If  the  weight  of  steam
used  is  known  from  an  engine-test,  there  can  be  determined
from  the  indicator-diagram  both  the  quality  and  amount  of
heat  in  the  cylinder  at  any  point,  with  the  single  exception  of
the  steam  remaining  in  the  clearance  spaces.  Thus  let  Vc
equal  volume  of  clearance;  V,  -f-  Vct  volume  at  admission,
usually  equal  to  Vc ;  Vx  +  Ve ,  volume  at  cut-off  ;  V%  +  Vc ,  at
release  ;  V%  +  Vc,  at  compression  ;  M,  the  weight  of  steam
used;  M9t  the  weight  of  steam  caught  and  retained  in  the
clearance  spaces.     Then,  by  method  used  in  equation  (12),

Vc  =  M9(xcuc  +  <rc) ; (15)

V.  +  Vc  =  M.(x.u0  +  <r.) ; (16)

Vi  +  K={Mo+M){x1ul+<rl);    .     .     .  (17)

Vi+Vc  =  (M9  +  M)(x9u9+<r9);    .     .     .  (18)

K+K=(Af.  +  M)(xiui  +  (rt).     .     .    .  (19)

In  the  above  equations  we  know  the  volumes  and  pressures
for  each  point,  and  the  weight  of  steam,  M,  passing  through
the  engine.  So  that  in  the  five  equations  there  are  six  un-
known quantities :  M% ,  xe  9  x0 ,  xx ,  x\ ,  and  x% ,  of  which  x9  may
be  assumed  as  1.00  without  sensible  error.  In  the  above  equa-
tions, (15)  and  (16)  are  usually  identical ;  they  differ  from  each
other  only  when  there  is  a  sensible  lead  which  shows  on  the
diagram.
