240 Mr. W. J. M. Rankmc on the Mechanical Action of Heat. 



Those equations are Nos. (50) and (51) of the original paper, 

 I shall now express them in a form more convenient for practical 

 use, the notation being as follows : — 



Let A be the area of the piston. 



I, the length of stroke. 



n, the number of double strokes in unity of time. 



c, the fraction of the total bulk of steam above the piston 



when down, allowed for clearance and for filling steam -passages ; 



so that the total bulk of steam at the end of the eflfective stroke is 



/A 



13^ ('^^ 



I' , the length of the portion of the stroke performed when the 

 steam is cut off. 



s, the ratio of expansion of the steam, so that 



[b) 



Let W be the weight of steam expended in unity of time. 



P,, the pressure at which it enters the cylinder. 



Vj, the volume of unity of weight of steam at saturation at 

 the pressure P,, which may be found from Table L* 



F, the sum of all the resistances not depending on the useful 

 load reduced to a pressure per xuiit of area of piston ; whether 

 arising from imperfect vacuum in the condenser, resistance of 

 the air-pump, feed-pump, and cold water pump, friction, or any 

 other cause. 



R, the resistance arising from the useful load, reduced to a 

 pressure per unit of area of piston. 



Z, the ratio of the total action of steam working at the expan- 

 sion s to its action without expansion. Values of this ratio are 

 given in Table IL 



Then the following are the two fundamental equations of the 

 motion of the steam-engine, as comprehended in equation (50) 

 of the original paper. 



First. Equality of power and eflfect, 



RA/ra=WV,{P,(Z-cs)-F(l-c)s}. . . . (c) 

 Secondly . Equality of two expressions for the weight of steam 



* The volumes thus fouud (as has been already stated), though near 

 enough the truth for practical purposes, are onl)' approximately correct, 

 having been computed on the assumption that steam is a perfect gas. 



