\'to^$kw\i>Hll]n^goyy of Heat to the Steam-engine. 259 



siderable ; and as it is for the most part distributed throughout 

 the vapour in small drops^ so that it can readily participate in 

 any changes of temperature which the vapour may suffer during 

 expansion, we shall incur no great inaccuracy if, in calculation, 

 we consider the temperature at any moment as the same through- 

 out the whole of the mass in the cylinder. 



Further, in order to avoid complicating our formulas too much, 

 we will for the present determine the total amount of work 

 done by the vapour pressure, without taking into consideration 

 how much of this work is useful, and how much is again con- 

 sumed by the machine itself in overcoming friction, and in work- 

 ing any pumps, which, besides the one in the figure, may be 

 necessary to the efficiency of the machine. This part of the 

 work may be afterwards determined and deducted, as will sub- 

 sequently be shown. 



With respect to the friction of the piston in the cylinder, how- 

 ever, we may remark, the work consumed in overcoming it can 

 scarcely be considered as lost. For heat is generated by this 

 friction, and consequently the interior of the cylinder kept warmer 

 than it would otherwise be, and thus the force of the vapour 

 increased. 



Lastly, inasmuch as it is advisable first to study the actions 

 of the most perfect machines before examining the influence of 

 the several imperfections which practically are always unavoidable, 

 we will add to these preliminary considerations two more sup- 

 positions, which shall afterwards be again relinquished. First, 

 the canal from the boiler to the cylinder, and that from the 

 cylinder to the condenser, or to the atmosphere, shall be so wide, 

 or the speed of the machine shall be so slow, that the pressure 

 in the part of the cylinder in connexion with the boiler shall be 

 equal to that in the boiler itself, and similarly the pressure on the 

 other side of the piston shall be equal to the pressure in the 

 condenser or to the atmospheric pressure; and secondly, no 

 vicious space shall be present. 



20. Under these circumstances, the quantities of work done 

 during a circular process can be written down, without further 

 calculation, by help of the results above attained ; and for their 

 sum they give a simple expression. 



Let M be the whole mass which passes from the boiler into 

 the cylinder during the ascent of the piston, and of it let m, be 

 the vaporous, and M— m^ the liquid part. The space occupied 

 by this mass is , ^i^ 



where u^ is the value of u corresponding to T^. The piston is 

 raised therefore until this space is left free under it ; and as this 

 takes place jOi^der. the,^tioii of the pressure jOj, corresponding to 



