sae Co et ccd i ah go ee oe i ge OI RG a 
Mechanical Theory o Heat to the Steam Engine. 199 
If on the other hand, we hake the assumption, that the ex- 
gp is driven until the steam by the expansion has cooled 
om the temperature of the boiler to that of the condenser, 
which, it is true, it is not completely possible to do, but whic 
still forms the limiting case to which we must approximate as 
closely as possible, we need only put T',=7', whereby we obtain 
(24) W'=-[m,r,—myro+ Me(T,-7,)]. 
If we also eliminate from this m,r, by means of the before- 
cited Siuktion, in which also we must put T,=T,, we have 
* 
(x) We= “[™. Big 5 pal °+ MT, - -T, +7, log f »)|: 
22. If we write the tren equation in the allowing form, 
(25) W=m eee pit Me(2- ye Ait oz los 7°), 
~ two pone whi = occur herein, Me (7,- r. >) and m mts 
comes from the pesmi in the fluid state, with the temperature 
o up to 7’, and the last represents the quantity of heat which 
is required to convert the portion m, at the temperature 7’, into 
m, is little smaller than i, the last quantity of heat 
is far , Breaier than the first. 
will bring the factor belonging to Mc(T,-T,) into a 
soca hat different form, in order to be able to compare with 
one other more conveniently the two factors, with which these 
0 quantities of heat are multiplied in equation (25). If then, 
for the sone of abbreviation, we introduce the letter z with the 
Significatio 
Taomit~, 
T, 
_ * The foregoing equations, which represent k under the two simplifying 
an is te osushastnet $14, bad bed develo loped by m along 
(26) z= 
nded 
comp that Rankine had not considered the circumstance t 
wat liquid i oo a with ~ steam at its entrance into the cylinder. By 
the earlier te ea of this paper t eating J was ee for this rior of my inves- 
nevertheless the correspondence was in so far a gratification to me, as it 
ave me a guarantee that the mode of oteettng the subject employed was really 
& natural one. 
