W^w^ Theory of Heat to the Steam^enffine*^ *"'^^ 347 



86. According to what was said in § 8, we can easily deter- 

 mine the uncompensated transformation which occurs in the ex- 

 pansion by referring the integral contained in the equation 



N=-J$ 



to the several quantities of heat expressed in § 34. 



The quantities of heat m^r^, —m^r^, and /jlqTq are imparted at 

 the constant temperatures Tj, Tg, and Tq, so that these parts of 

 the integral are, respectively, 



^1^1 ^2^9 and '^0^*0 



Ty' T^' ^"""^ To' 



The parts of the integral arising from the quantities of heat 

 Mc(Ti — Tg) and /u-c(Tg— Tq), are found, by the method adopted 

 in § 23, to be 



T T 



Mclog^ and - fic log rfr- 



ig ■'•0 ^ 



By putting the sum of these magnitudes in place of the above 

 integral, we obtain for the uncompensated transformation the 

 value 



N=-^' + ^_Mclog^-^ + ^logJ. . (38) 



■■■1 -*-2 ^2 ■•^O ■*^0 



37. We can now return to the complete circular process which 

 occurs in an acting steam-engine, and consider the several parts 

 of the same in the same manner as before. 



The mass M, of which the part m^ is vaporous and the rest 

 liquid, issues from the boiler, where the pressure is supposed to 

 be jOp into the cylinder. As before, the mean pressure acting in 

 the cylinder during this time shall hep'^, and the final pressure jo^. 



The vapour now expands until its pressure sinks from p^ to a 

 given value p,^j and consequently its temperature from Tg to Tg. 



After this the cylinder is put in communication with the con- 

 denser, where the pressure is jOq, and the piston returns through 

 the whole of the space it has just described. When the motion 

 is somewhat quick, the reaction which it now experiences will be 

 somewhat greater thanjOQ ; to distinguish it from the latter value, 

 we will represent the mean reaction by ^0- 



Similarly, the pressure of the vapour which remains in the 

 vicious space after the piston^s motion is completed will not ne- 

 cessarily be equal either to p^ or to jo'q, and must consequently 

 be represented by another symbol jo%. It may be greater or less 

 than p'q, according as the communication with the condenser is 

 cut off somewhat before, or somewhat after the conclusion of the 

 piston's motion ; for in the first case the vapour would be a little 



3A2 



