Mechanical Theory of Heat to the Steam Engine. 191 
cand h, only functions of 7, and the quantity m only a function 
of Zand v we obtain 
d (dQ 1 dr eo du 
C9) a ie) = aah op 
d (dQ So fg oe du\dm 
arya is sara 
: dm . 1 
or, if we put for Tp 8 value m 
d (dQ _h-c r du 
“ za : 
By substituting the expressions given in (10), (11), and (8), in 
(m1) and (1v) we obtain the sought equations, which represent 
€ two principal theorems of the mechanical theory of heat for 
_ Vapors at a maximum density, namely 
dr dp 
(v.) ap teh 4 4. 
dp 
(v1.) r= A. Pur 
and from the combination of the two, we also obtain ae te 
dr fies 
(12) art ¢—h= Via 
14. With the help of these equations we will now consider a 
case which will so often occur in what follows, that it is advan- 
eous to fix, a priori, the results which refer to it. 
8 assumed that the previously considered vessel 
_ the form of vapor will change, and besides, a a or negative 
ternal wo vy P 
roduces the pres- 
Sure of the vapor, since in the change of volume the pressure of 
the form of vapor, the volume v and the work W are 
termi i ¥. 
ad 
roe dv + [(—mebmh-br Fle7. 
