Mechanical Theory of Heat to the Steam Engine. 189 
depends only on the temperature 7 It only remains to decide 
whether the quantity of the two parts which are present in dif- 
ferent conditions is determined. For this purpose the condition 
is given, that these two parts must together exactly fill up the 
content of the vessel. we therefore denote the volume of the 
unit of weight of steam, at its maximum density, at the tempera- 
sare T by s, and that of a unit of weight of fluid by o, we must 
ave: 
v=m.s+(M—m)e 
=m(s—o)+ Mo, 
The quantity s occurs in what follows, only in the combination 
(s—<), and we will therefore introduce a special letter for this 
difference, putting 
uUu=s—9, 
by which the previous equation becomes 
6) | v=mu+M, 
and hence i 
(7) m= RBA : 
sac : m : | 
By this equation, m is determined as a function of 7 and », since 
u and o are functions of 7. : 
12. In order now to be able to apply equations (111) _ o 
our case, we must first determine the quantities Ty nd oH 
Let us first assume that the vessel expands so much that its 
content increases by dv, then a quantity of heat must be thereb 
communicated to the mass, which will in general, be represented 
b 404 
vy or V. 
Now since this quantity of heat is only consumed in the forma- 
tion of vapor which takes ~~ during the ee ee it may 
also be represented, if the heat of ev be denoted for 
the unit of mass by 7, by the expression 
pay 
and we may also put 
dQ dm 
“dv dv 
whence, since according to (7), 
dm 
we find (8) Toa’ 
Tf we assume in the‘second Ree that the ‘temperature of the 
mass, while the content of the vessel remains constant, is in- 
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