188 _ R. Clausius on the Application of the 
I have already in my former paper of 1850, on the motive 
power of heat, developed the equations which represent the two 
incipal theorems of the mechanical theory of heat in their ap- 
plications to vapors at a maximum density, and have applied 
them to deduce various conclusions. 
As I have however introduced in my last memoir “on a 
change in the form of the second principal theorem of the me- 
chanical theory of heat,” a somewhat different mode of repre- 
senting the whole subject, I consider it, as already mentioned, 
more advantageous for the sake of greater simplicity and breadth 
of view, to sup only this last memoir as known. : 
therefore again deduce in a different way the equations referred 
to from the results obtained in it. 
In this memoir it was assumed, in order to apply the general | 
equations first established to a somewhat more special case, that — 
the only foreign force acting upon the variable body which de- 
rves consideration in determining the external work, was an ~ 
external pressure, the force of which was equal at all points of 
the surface, and whose direction was every where perpendicular — 
to it, and that further this pressure always changed only so — 
slowly, and consequently was at every instant only so little dif — 
ferent from the expansive force of the body acting opposite to it, 
that in calculation the two might be considered as equal. If 
then we denote by p the pressure, by v the volume, cide T the — 
absolute temperature of the body, which last we will introduce | 
into the formulas instead of the temperature as estimated from — 
the freezing point, because they take a simpler form in this way, — 
this be acakinlibek: a 
jules 
the equations deduced for 
d (dQ\_ a (dQ\_, dp 
oy AS) £(8)aadt 
dQ dp 
(rv) ds =A.T or 
case of vapors at a maximum density, 
11. Let the given mass of the substance whose vapor is to be ~ 
considered be M, and let this be contained in a completely closed 
extensible vessel, the part m in a state of vapor, and the re- _ 
maining part, M—m, in a fluid state. This mixed mass is now 
to form the variable body to which the previous equations are 
to be applied. sigs a 
If the temperature 7’ of the mass and its volume v—that is — 
to say, the content of the vessel—are given, then the condition — 
of the mass, so far as it here comes under consideration, is thereby — 
completely determined. Since ome the vapor by supposition 
always remains in contact with the liquid, and consequently at 
a maximum density; its condition, as well as that of the liquid, — 
