The Steam Engine Explained and Illustrated (Seventh Edition) / With an Account of Its Invention and Progressive Improvement, and Its Application to Navigation and Railways; Including Also a Memoir of Watt

by Dionysius Lardner

[Pg513]

which, taken between the limits s = S′ and s = S, becomes

E″ = a log.	S	− b(S − S′).(12.)
	S′

But by (11.) we have

E′ = a − bS′,

E = a − bS;

∵ E′ − E = b(S − S′);

∵ E″ = a log.	S	− E′ + E;
	S′

∵ E = E″ + E′ = a log.	S	+ E.(13.)
	S′

Or,

E = a (1 + log.	S	) − bS.(14.)
	S′

Hence it appears that the mechanical effect of a cubic foot of water evaporated under the pressure P may be increased by the quantity a log. ^S/_S′, if it be first evaporated under the greater pressure P′, and subsequently expanded to the lesser pressure P.