196 MR W. J. M. RANKINE ON THE POWER AND ECONOMY 
express them in a form more convenient for practical use, the notation being as 
follows :— 
Let A be the area of the piston. 
/, 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 effective stroke is 
tA 
7 P ri OO: s sn) 

l’, 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 

Let W be the weight of steam expended in unity of time. 
P,, the pressure at which it enters the cylinder. 
V,, the volume of unity of weight of steam at saturation at the pressure P, ; 
which may be found from Table I. of the Appendix to the original paper. 
F, the sum of all the resistances not depending on the useful load, reduced to 
a pressure per unit of area of piston; whether arising from imperfect vacuum in 
the condenser, resistance of the air-pump, feed-pump, and cold-water pump, fric- 
tion, or any other cause. 
R, the resistance arising from the wseful load, reduced to a pressure per unit 
of area of piston. 
Z, the ratio of the total action of steam working at the expansion s, to its 
action without expansion. Values of this ratio are given in the second Table of 
the Appendix to the original paper. ; 
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 effect,— 
RAIn=WV, {P,(Z—cs)—F(1%c)s}- - (6) 
Secondly, Equality of two expressions for the weight of steam expended in 
unity of time,— 
Ain 
W=y 29s re) 

