ee oe ee eee scr an 
ae ee ee 
Mechanical Theory of Heat to the Steam Engine. 198 
compressed, we could not make the assumption that in the be- 
ginning no fluid water is present, because then the vapor would 
hot remain at a maximum density, but would be overheated b 
the heat produced during the compression. In the expansion 
on the other hand, the steam remains not only at a maximum 
density, but a part of it is in fact condensed, and it is precisely 
the diminution of m produced thereby, to which the table re- 
fers. The initial temperature is assumed as 150° C., and corres- 
ponding values of 7 are given for the times when the tempera- 
ture has sunk by the expansion to 125°, 100°, ete. The tem- 
eeatnre estimated from the freezing point is denoted by 4, as 
eretofore, to distinguish it from the absolute temperature repre- 
sented by 7. 
| t | 150° | 195° | 100° | 50 | 50° | 95° 
| on | 1 | 0°956 | oo | 0°866 | 0'821 | 0-776 | 
M | 
For this purpose we only need to substitute in the equation (vi1,) 
for r, the expression given in (vi,) whereby we obtain 
i hs od ) _ bo lo a 
(v11.) atet k  mmong u,(35 ; oa z F . 
The differential coefficient oe which occurs here is to be looked 
on as known; p itself is known as a function of the temperature, 
and consequently by this equation, the product mu is determined, 
and from it we obtain by addition of Mo the sought quantity v. 
In the following sable; there is again collected a series ¢ 
values of the fraction aa which are deduced from this equation, 
for the same case to which the foregoing table relates, For the 
Sake of comparison, those values of = are also added, which we 
should obtain if the two assumptions usually made heretofore in 
the theory of the steam engine were correct. (1.) that the stean 
SECOND SERIES, VOL, XXII, NO, 65.—-SEPT., 1856, 
25 
