Mechanical Theory of Heat to the Steam Engine. — 25 
Art. VII—On the Application of the Mechanical Theory of Heat 
to the Steam Engine; by R. CLaustus. 
[Concluded from vol. xxii, p, 374.] 
39. I believe that it will not be without interest, if before I at- 
tempt to make these equations more convenient for application, 
Ishow how we may-also, for an imperfect. steam engine, arrive 
at the same expressions by the inverse method formerly pointed 
out as by that previously followed. In order, however, not to 
be too prolix in this digression, I will take into consideration 
only two of the imperfections which are considered in the fore- 
going equations, namely, the presence of the injurious space, 
and the less pressure of the steam in the cylinder than in the 
boiler during the influx. On the other hand I will assume that 
the expansion is complete, in which case we must put 7,=7', and 
that also the quantities T,, T’, and 7”, are equal to each other. 
¢ have to apply in this determination the equation (2), which 
we will here write in the following form: 
710 T 
»_ 1 Ly 
| W=3(@-7, Bes ae! 
The first term on the right side signifies the work which we 
should obtain by means of the applied quantity of heat Q,, which 
°F our case is represented by m, r,+4€c(7,—T,), if these im- 
Perfections did not take place. This term is already calculated 
in $23 where the following expression was found: 
1 Mi 
amir tie (7, ~L,)=T, (Aye Mc log 7)| 
=e Second term signifies the loss of work which is occasioned 
by these two imperfections. The quantity NV which occurs 1n it, 
th also already calculated, namely, in § 36, and is represented by 
© €xpression cited in equation (38). : : 
We substitute these two expressions in the foregoing equa- 
ave 
tion, We h 
l Zr 
(44) W=A|m Re = Mat o4+Me(T ,- o- (AM u)eT log For | 
1 
We easily see that this equation corresponds in fact with equa- 
tions (XIV) if we introduce into the first of them the mass m, 
for the mass m,, which may be done by means of the third 
“qnation, and by then putting 7,=7,=T',=7",. 
In the same manner we can take into account the loss of work 
Which arises from the incomplete expansion, by calculating the 
“compensated transformation which occurs during the passage 
SECOND SERIES, VOL. XXIII, NO. 67.—JAN., 1857, 
4 
