_* 
Mechanical Theory of Heat to the Steam Engine. 187 
Qy 
’ 1 d 
(2) W=5 (0-7, f B-7,.m), 
If we assume specially that the whole circular process is inverta- 
Mei according to the above N=0, and the foregbinig equation 
ecomes 
We Le,-2,.f 9) 
‘ 0 
This expression is only distinguished from the previous one by 
the term —-—°. WN. Since WV can only be positive this term can 
when the whole circular process is invertable, and that the quan- 
‘tity of work is diminished by every circumstance which causes 
one of the special processes occurring in the cireular process to 
be uninvertable. 
Equation (2) leads accordingly to the sought value of the work 
in a manner which is directly opposed to the usual one, inasmuch 
as we do not, as formerly, determine singly the quantities of 
work performed during the different processes and then add them 
together, but set out from the maximum work, and subtract from 
it the losses of heat which have arisen from the single incom- 
plete parts of the process. 
If we make the limiting condition with respect to the commu- 
nication of the heat that the whole quantity of heat Q, is com- 
municated to the body at a determined temperature 7’,, the 
rtion of the integration embracing this quantity of heat may 
at once Sxevuted, and gives 
1 
1 
by which equation (3), which holds good for the maximum of 
the work, talkes the following form, 
sa Q, T 1-7 
| (4) Wa di 
In this special form the equation was already deduced by W. 
Thomson and Rankine from the combination of Carnot’s theo- 
rem, modified by me, with the theorem of the equivalence of 
-. heat and work.* 
10. Before we can pass from these considerations, which hold 
good for all thermo-dynamic machines, to the treatment of the 
steam engine, some remarks with respect to the behavior of va- 
pors at a maximum density must first be brought forward. 
* Phil. Mag., July, 1851. 
