Mechanical Theory of Heat to the Steam Engine. 39 
state, subsequently evaporates, and the more so the greater the 
expansion. 
55. We will now in a similar manner consider a machine 
which works expansively, and we will for this purpose choose a 
machine with a condenser. With reference to the amount of 
expansion, we will assume that the cut-off from the boiler takes 
place when the piston has passed through one-third of its stroke. 
We have then to determine e the equation 
‘ e—e=4 (1 wi &), 
and hence we find, if we retain for ¢ the value 0-05, 
c= ~~ 808666... 
in the cylinder somewhat exceeds the pressure in the condenser, 
We will assume for the mean counter pressure p,, in round num- 
bers, one-fifth of an atmosphere, or 152™™, to which the tempera- 
ture ¢,=60°46 belongs. If we retain finally for 7 the value 
Previously assumed, the quantities which come into application 
m this example are the following: 
e = 0°36667. 
oa 152. : 
Putting p, in the second of equations (xvit) in the place of p,, 
and changing in like manner the other quantities connected with 
P. We find in this manner for our case the value 
‘ 1-010. - \ 
Setting out from this we will assume as a first example that the 
actual velocity of the machine exceeds the least le velocity 
i about the ratio of 3: 2, putting in round numbers 
7 ih, 
and we will determine the work for this velocity. 
56. In the first place, the two temperatures, ¢, and ¢,, must 
be determined b substituting this value of V m the last two of 
€quations (xyrr), The determination of ¢, has already been 
¢ 
