61 



The moment of closing the equilibrium-valve is supposed to be 

 so adjusted, whether by trial or by calculation, as to prevent any 

 sensible loss of power from clearance and steam passages. Let I" 

 be the portion of up-stroke, remaining to be performed at the proper 

 moment for closing this valve, then 



I " 1-c 



This adjustment being made, the two following are the funda- 

 mental equations of motion of the engine : — 

 E = R A Z »z = W V^ (P^ Z -F) = useful effect in unity of time. 



„-, A Z n , , , . . - . 



W = == — = steam expended in unity of time. 

 Vj s 



The following are deduced from them. Ratio of mean load to 



maximum pressure : — 



R + F _Z 



Pi ~~-' 



Duty of unity of weight of steam — 



|=V,(P,Z-F); 



Weight of steam expended per stroke — 



W_A Z ^ 

 n Vj « 



The results of the last two formulae are compared with the expe- 

 riments made by Mr Wicksteed on a large Cornish pumping-engine 

 at Old Ford at five different ratios of expansion ; and the agreement 

 is found to be so close as to prove that the results of the theory are 

 practically correct. 



The results of experiment generally shew a somewhat less expen- 

 diture of steam for a given duty than theory indicates. This is con- 

 ceived to arise from the cylinder being heated by a jacket commu- 

 nicating with the boiler, in which the temperature is much higher 

 than the highest temperature in the cylinder. 



The theory is next applied to the solution of the problem of the 

 economy of Cornish engines. The merit of first proposing this pro- 

 blem is believed to belong to the Artizan Club, who have offered 

 premiums for its solution, " with a view," as they state, " to enable 



F 2 



