Mechanical Theory of Heat to the Steam Engine. 365 



by v and 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 J* pdv plays a principal part in 



the formulas for the work of the steam engine, it was necessary 

 to have the simplest possible formula between v and p alone, in 

 order to be able to calculate this in a convenient manner. 



The equations, which we should obtain if we were to eliminate 

 the temperature t from the foregoing equation, by means of one 

 of the empirical formulas for jp, would prove too complicated, 

 and Pambour therefore proposed to form a special empirical form- 

 ula for this purpose, to which he gave, according to the process 

 of Navier, the following general form 



( 29 ) »=Fry 



in which B and b 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 

 not possible with sufficient accuracy for all the pressures which 

 occur in steam engines, he calculated two different formulas, for 

 machines with and without condensers. 

 The first is as follows : 



20000 



and agrees best with the above formula (28) between f and 3 J 

 atmospheres, is applicable however also in a somewhat wider in- 

 terval, perhaps between -J- and 5 atmospheres. 



The second formula determined for machines without conden- 

 sers, is on the other hand as follows : 



, ftn , N 21232 

 (29b) v — . 



It is most accurate between 2 and 5 atmospheres, and the whole 

 interval of its applicability, extends about from 1-J- to 10 atmos- 

 pheres. 



30. The magnitudes depending upon the dimensions of the 

 steam engine which occur in determining 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 

 space, be called v'. Let the injurious space form the fraction s of 

 the whole space, so that thus the injurious space is separated by 

 ev' and the space described by the surface of the piston by (1 - £ ) v'. 

 Further let the portion of the whole space which has become 



