Mr. W. J. M. Rankine on the Mechanical Action of Heat. 241 

 expended iu unity of time, 



^^=vi^ W 



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 



~p7" "(1-0)5 ^'> 



being equivalent to equation (51). 



In computing the effect of Cornish engines, these formulae 

 require to be modified, owing to the following circumstances. 



The terms depending on the clearance c have been introduced 

 into equations (c), [d), 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,(Pj — r)cs lost, in unity of time. But 

 in Cornish engines this is not the case ; for by closing the equi- 

 librium-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. Pole, in his valu- 

 able 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 



l_c{s-\) 



l~ \-c' ^■'' 



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 clear- 

 ance and filling of steam-passages, and the results are the fol- 

 lowing : — 



* The same etjuation will serve to determine the proper moment for 

 clo»in(> tlie exliaust-port in non-condensing engines, so as nearly to pre- 

 vent loss of jKtwer from clearance. 



