
OF SINGLE-ACTING EXPANSIVE STEAM-ENGINES. 197 
From these two equations is deduced the following, expressing the ratio of the 
mean load on the piston to the initial pressure of the steam :— 
R+F Z—cs 
ap = Ges ; : 5 5 CO} 
being equivalent to equation (51). 
In computing the effect of Cornish engines these formule require to be modi- 
fied, owing to the following circumstances. 
The terms depending on the clearance c have been introduced into equations 
(c), (2), on the supposition that the steam employed in filling the space above the 
piston at the top of its stroke is lost, being allowed to escape into the condenser, 
without having effected any work; so that a weight of steam Wcs is wasted, 
and an amount of power WV, (P,—F)es lost, in unity of time. But in Cornish 
engines this is not the case; for by closing the equilibrium-valve at the proper 
point of the up or out-door stroke, nearly the whole quantity of steam necessary 
to fill the clearance and valve-boxes may be kept imprisoned above the piston so 
as to make the loss of power depending on it insensible in practice. This portion 
of steam is called a cushion, from its preventing a shock at the end of the up- 
stroke; and as Mr Pots in his valuable work on the Cornish engine has observed, 
its alternate compression and expansion compensate each other, and have no 
effect on the duty of the engine. The proper moment of closing the equilibrium- 
valve is fixed by trial, which is, perhaps, the best way; but if it is to be fixed by 
theory, the following is the proper formula. Let /’ be the length of the portion of 
the up-stroke remaining to be performed after the equilibrium-valve has been 
closed : then— 

Wl” _e(s—1) 
= ee ; : : : (Sf) 
A slight deviation from this adjustment will produce little effect in practice, if the 
fraction c is small. 
In forming the equations of motion, therefore, of the Cornish engine, we may, 
without material error in practice, omit the terms denoting a waste of steam and 
loss of power due to clearance and filling of steam-passages; and the results are 
the following :— 
Equation of effect and power in unity of time :— 
Useful effect E=RAZn=WV,{P,Z—-F} .  (87.) 
Weight of steam expended in unity of time :— 
Aln 
W=7— (58.) 

1 
From those two fundamental equations the following are deduced :— 
Ratio of mean load on piston to maximum pressure,— 
es 
B= (59.) 
