Mechanical Theory of Heat to the Steam Engine. 367 



If we multiply this quantity by the space described by the 

 surface of the piston up to the same moment, namely (e— e) v', 

 we obtain for the first part of the work, the expression : 



(31.) W 1 — mB. € —^- - v'(e-s)b. 



The law according to which the pressure varies during the ex- 

 pression which now follows, is also given by equation (29). Let 

 the variable volume at any moment be denoted by and the 

 corresponding pressure by p, and we have 



m . B ^ 



We must substitute this expression in the integral J* pdv and 



and then execute the integration from v=ev' to v= v' by. which 

 means we obtain as the second part of the work 



(32.) W 2 = m B . log - e -v' b. 



In order to determine the negative work done during the return 

 of the piston, by the counter pressure, the counter pressure itself 

 must be known. Without for the present entering upon the 

 question how this counter pressure is related to the pressure 

 which takes place in the condenser, we will denote the mean 

 counter pressure hj p Q) so that the work done by it, is repre- 

 sented by 



(33.) W s =-v'(l-8) Po . 



Finally, there still remains the work which must be applied to 

 force the quantity of liquid M, again into the boiler. Pambour 

 has not specially considered this work, but has included it in the 

 friction of the machine. As I have however, taken it into con- 

 sideration in my formulas, in order to have the cyclus of the op- 

 erations complete, I will add it here also for the sake of a more 

 easy comparison. If p , denotes the pressure in the boiler, and 

 p 0 the pressure in the condenser, this work is represented as a 

 whole by 



(34.) Wt=-.Ma( Pl -p 0 ), 



as is deduced from equations (21) and (22) established in the ex- 

 ample formerly considered. For our present case, in which we 

 understand by p, not the pressure in the condenser itself, but in 

 the part of the cylinder which is in connection with the con- 

 denser. This expression it is true, is not quite accurate ; as how- 

 ever in consequence of the smallness of the quantity the whole 

 expression has so small a value that it scarcely deserves consid- 

 eration, we may neglect the more freely a small inaccuracy in 

 comparison with the small value, and will therefore here also, re- 

 tain the expression in the same form. 



