RY si a a ey 
/ 
Mechanical Theory of Heat to the Steam Engine. 378 
consider as before the particular portions of the same in succes- 
sion. 
The mass U/ flows from the boiler in which the pressure p, is 
assumed, into the cylinder, the part m, as steam, and the remain- 
der as liquid. Let the mean pressure acting in the cylinder dur- 
ing this time be denoted as above by p', and the final pressure 
Pa: 
The steam now expands until its pressure has sunk from p, to 
a@ given value, p, and consequently its temperature from 7, to 
T,. The cylinder is thereupon put into communication with the 
condenser in which the pressure p, is exerted and the piston 
makes the whole motion just completed again in the opposite 
direction. The counter pressure which it thereby undergoes, is 
during a somewhat more rapid motion greater than p,, and we 
will iheoetire, to distinguish it from this value, denote the mean 
counter pressure by p’,. ‘ 
steam which remains at the end of the motion of the pis- 
ton in the injurious space, which must be considered for the next 
stroke, is under a pressure which in like manner need be neither 
may be greater or smaller than p{, according as the cutting off 
from the condenser takes place somewhat before or after the end 
of the motion of the piston, inasmuch as the steam in the first 
place is compressed somewhat further, in the last case, on the 
contrary, has time to expand somewhat more by the partial influx 
into the condenser. 
Finally the mass M must be brought back from the condenser 
into the owe whereby as before the pressure p, acts to produce 
the effect and the pressure p, must be overcome. 
88. The quantities of work done in these processes are repre- 
Sented by expressions apie similar to those in the simpler case 
y considered, only that the indices of the letters are 
hanged in a manner which is easily understood, and the quan- 
tities which relate to the injurious space must be added. We 
thus obtain the following equations: 
For the period of influx according to § 34, in which however 
» must be written instead of w,. 
(39.) W,=(m,u,+Mo—4, wu!) Pi 
For the expansion from the pressure p, to the p Ps 
cording to equation (rx) if M+ is put mm the place of W: 
(40.) W,=m, U3 P3- mata Pat lms 5 ms? g{M+u)e( T2- s)] 
For the return of the piston, in which the space described by 
ac- 
= surface of the aca is equal to the whole space occupied by 
he mass M+ under the pressure Ps, less the injurious space 
represented by Mg UP Ho- 
(41.) W,=—(m, Ugt+ Mo —, u"y) Po 
