Mechanical Theory of Heat to the Steam Engine. 365 
by vand p. In this equation we need only substitute for p the 
known values from the tension series, in order to be able to cal- 
culate for every temperature the correct volume under these 
suppositions, 
29. As, however, the integral 45 pdv plays a principal part in 
(29) v= b+? ’ 
inwhich Band } are constants. He now sought to determine 
these constants in such a manner, that the volumes calculated 
from this formula corresponded as accurately as possible with 
those calculated from the previous formula. As this however, is 
hot possible with sufficient accuracy for all the pressures whic 
occur in steam engines, he calculated two different formulas, for 
Machines with and without condensers. 
The first is as follows: 
20000 
(2 9a) = 1200 +p ; 
and agrees best with the above formula (28) between } and 34 
atmospheres, is applicable however also in a somewhat wider in- 
terval, perhaps between 4 and 5 atmospheres. 
e second formula determined for machines without conden- 
Sers, is on the other hand as follows: 
__ 21232 
(29b) 9 et 
It is most accurate between 2 and 5 atmospheres, and the whole 
al of its applicability, extends about from 1} to 10 atmos- 
eres, : 
380. The magnitudes depending upon the dimensions of the 
engine thick occur draleternsdiy the work, shall here be 
denoted in the following manner, somewhat different from that 
of Pambour. Let the whole space which becomes free for the 
Steam during a stroke in the cylinder, including the injurious 
* ae be called vw’. Let the injurious space form the fraction « of 
@ whole Space, so that thus the injurious space 1s separated by 
7) and the described by the surface of the piston by (1—¢) 0’. 
Further let the portion of the whole space which has become 
