Mechanical Theory of Heat to the Steam Engine. 371 
The whole quantity of heat which may be called Q, is conse- 
quently : 
(36.) Q=m,7r,-—mgr + Me(T,-T.) + 4, 1, -ue(T,-T>). 
The quantities of work are found in the following manner : 
. In order to determine the space described by the surface of 
the piston during the influx, we know that the Whole space oc- 
cupied by the mass M-+-#, at the end of this time, is 
My Uy +(M+xn)o. 
From this the injurious space must be subtracted. As this was 
led in the beginning at the temperature 7’, for the mass y, of 
which the portion “, was in the form of steam, it may be ex- 
pressed. by My Uy + HO. 
If we subtract this quantity from the previous one and multiply 
the prnndes by the mean pressure, p, we obtain as the first 
work : 
(m2 Uz + Mo-u, uy) p'. é 
2. The work, by the condensation of the mass m,, is: 
eae : 
3. By forcing back the mass m into the boiler 
r 
—Mop,. 
4, By the evaporation of the portion », : 
Ho Uo Po- 
By the addition of these four quantities, we obtain for the 
whole work W, the expression, 
(87.) Wamu, (pj, —P2)—Mo(p,—Pi)— Mo %o (P1 ~Po)- 
If we substitute these values of Q, and W, in equation (1), 
namely, = ALW : 
and bring the terms containing m, together on one side, he have 
(xin. Mo|r Au ,— =m, ,+Me(T ,-T.)+ Mo? Hel ’,-T,) 
) m,[r.4+Au,(p} sige a Gp! ny alle =p) 
By means of this equation, we can calculate the quantity m, 
from the quantities supposed to be known. 2 : 
35. In Bins cases in which the mean pressure p; is considera- 
bly greater than the final pressure 7., for instance, if we assume 
that during the greater part of the period of influx, nearly the 
Same pressure has taken place in the cylinder as in the boiler, 
and that the pressure has first diminished to the lesser value p,, 
y the expansion of the steam already in the cylinder, it may 
happen that we find for m, a value which is smaller than m, + 
“,, that consequently a portion of the steam originally present is 
Ae pieted. f on the other hand, p) be but little greater or In 
smaller than p,, we find for m, a value which is greater 
nm,+#,. This last is to be considered as the rule in the 
Steam engine, and holds good in particular also for the special 
Case assumed by Pambour that p)=p,- 
