192 R. Clausius on the Application of the 
must be equated to zero, in consequence of the condi- 
tion now laid down that heat must neither be communicated to 
nor taken from the mass. In this way we obtain, if we simply 
write dm for 
4 v5 a Fe ys 
the equation 
18 rdm+m(h-c)d T+ Mcd T= 0. 
If we substitute in this, according to (12) 
nga dr) F-. 
a ti doe 
and again write simply dr for iA 
of 7, we have 
rdm4mdr-dT4+Med T=0, 
a7? T, since ris only a fancting 
or (14) d(mr) - 7d T-4+Med T=0. 
If we divide this equation by 7, and remember that 
(mr MP) (mr 
ae id T=i(F), 
we obtain 
(15) a(") +Mc 70: 
As the specific heat of a liquid changes but slowly with the 
temperature, we will in what follows, always consider the que 
tity c as constant. Then the previous eps may | 
grated at once, and Bt 
7 = ae Me log 7’=const, 
or if the initial values of 7, ee m, be ee by 71,7, m1, 
(vu) pets 
By this equation, m is also pen oi as a fanotion of the tem- 
perature, if r, as a function of the temperature, can be a poe 
considered as known. 
In order to give an approximate view of the behavior of this 
function, I have collected together in the apa table some — 
“ | 
values calculated for a particular case, 
that the vessel at the beginning contains no guid water, but 38 
exactly filled with steam at the maximum density, so th 
at f 
he previous equation m, is to be put equal to M, and let now 
an expansion of the vessel take place. the vessel should be 
