Mechanical Theory of Heat to the Steam Engine. 371 



The whole quantity of heat which may be called Q } is conse- 

 quently : 



(36.) Q = m 1 r 1 -m 2 r 2 +Mc(T ir T 2 ) + fi 0 r 0 -fie (T 2 - T 0 ). 

 The quantities of work are found in the following manner : 



1. In order to determine the space described by the surface of 

 the piston during the influx, we know that the whole space oc- 

 cupied by the mass M+p, at the end of this time, is 



From this the injurious space must be subtracted. As this was 

 filled in the beginning at the temperature T 0 for the mass <«, of 

 which the portion p 0 was in the form of steam, it may be ex- 

 pressed by iu 0 u 0 -f (Mo-. 



If we subtract this quantity from the previous one and multiply 

 the remainder by the mean pressure, p\, we obtain as the first 

 work : 



(m 2 u 2 + M(7-fi 0 u 0 )p\. 



2. The work, by the condensation of the mass m 2 , is: 



-m 2 u 2 p 2 . 



3. By forcing back the mass m into the boiler 



— M(jp 1 . 



4. By the evaporation of the portion 0 : 



By the addition of these four quantities, we obtain for the 

 whole work the expression, 



(37.) W—m 2 u 2 (p[ -p 2 )-Mo{p 1 -p[)-l* Q u Q (p[ -p 0 ). 

 If we substitute these values of Q, and W, in equation (1), 

 namely, Q — A . W 



and bring the terms containing m 2 together on one side, we have 



(xm.) m 2 [r 2 +Au 2 (p' 1 -p 2 )]=m 1 r 1 +Mc{T 1 -T 2 )+^ 



+A[* 0 u 0 (p / l -p 0 )+AMa(p 1 -p[). 



By means of this equation, we can calculate the quantity m a 

 from the quantities supposed to be known. 



35. In those cases in which the mean pressure p\ is considera- 

 bly greater than the final pressure p 2 , for instance, if we assume 

 that during the greater part of the period of influx, nearly the 

 same pressure has taken place in the cylinder as in the boiler, 

 and that the pressure has first diminished to the lesser value p 2J 

 by the expansion of the steam already in the cylinder, it may 

 happen that we find for m 2 a value which is smaller than m, + 

 /w 0 , that consequently a portion of the steam originally present is 

 precipitated. If on the other hand, p[ be but little greater or in 

 fact smaller than p 2 , we find for m 2 a value which is greater 

 thaum 1 +^ 0 . This last is to be considered as the rule in the 

 steam engine, and holds good in particular also for the special 

 case assumed by Pambour that p[ =p 2 . 



