Mechanical Theory of Heat to the Steam Engine. 197 
It is moreover to be remarked with respect to the friction of 
the piston in the cylinder, that the work consumed in overcomin 
it is not to be considered as entirely lost, for by this friction heat 
is generated, and thereby the interior of the cylinder kept warmer 
than it otherwise would be, and consequently the force of the 
steam is increased. 
Finally, as it is advantageous to learn in the first place the 
action of the most complete machine possible before we study 
the influence of the particular imperfections which naturally 
a go is present 
during a circular process, may be expressed without further cal- 
culation, with the help of the results obtained above, and give a 
simple expression as the sum. Let the whole mass which passes 
during the ascent of the piston from the boiler into the cylinder, 
be called UM, and let the part m, be in the form of vapor, and 
the part M—m, liquid. the space which this mass occupies is, 
if m, signifies the value of « belonging to 7',, 
m,u,+Me. 
The piston is accordingly lifted as high as this space underneath 
it becomes free, and as this happens under the action of the pres- 
sure p, pepe 7, the work done during this first process, 
which we may W,, is 
(18) W,=m,u, p,+Mop,. 
Let the expansion which now follows be so far continued, 
until the temperature of the mass enclosed in the cylinder has 
sunk from the value 7, to a second given value, 7,. The work 
which is done hereby, which we may call W,, is found immedi- 
ately from equation (1x), if 7, is assumed in it, as the final tem- 
, and also if the corresponding values are substituted for 
the other quantities occurring in the equation, namely : 
