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



engine, and corresponds with equation A of M. de Pambour's 

 theory. 



(26.) Dividing both sides of equation (50) by the space tra- 

 versed by the piston in unity of time WV,(1 — e)s, and trans- 

 ferring the pressure of the waste steam, Pg, to the first side, we 

 obtain this equation : — 



1 o- ,_' 

 _ s <^ —cs 



R+P3.-.P. -" ^^z:-,, — . • ■ (51) 



which gives the means of determining the pressure Pj at which 

 the steam must enter the cylinder, in order to overcome a given 

 resistance and counter-pressure with a given expansion ; or sup- 

 posing the expansion s to be variable at pleasure, and the initial 

 pressure Pj fixed, the equation gives the means of finding, by 

 approximation, the expansion best adapted to overcome a given 

 resistance and couuter-pressiire. 



The next step is to determine, from equations (XV.) of the 

 Introduction and (38) of this section, the volume Vj of unity of 

 weight of steam corresponding to the maximum pressure Pj. 

 Then equation (48) gives the space traversed by the piston in 

 unity of time, which, being multiplied by the resistance R per 

 unit of area of piston, gives the gross effect of the engine. 



(27.) If, on the other hand, the space traversed by the piston 

 in unity of time is fixed, equation (48) gives the means of deter- 

 mining, from the evaporating power of the boiler W, either the 

 volume Vj of unity of weight of steam required to work the 

 engine at the given velocity with a given expansion, or the ex- 

 pansion s proper to enable steam of a given initial density to 

 work the engine at the given velocity. The initial pressure Pj 

 being then determined from the volume V,, the resistance which 

 the engine is capable of overcoming with the given velocity is to 

 be calculated by means of equation (51). 



(28.) This calculation involves the determination of the pres- 

 sure P, from the volume Vj of unity of weight of steam at satu- 

 ration, which can only be done by approximation. The following 

 formula will be found useful for this purpose : — 



.... (53) 



'MW' 



where w represents the pressure of one atmosphere, Vq the 

 volume of steam of saturation at that pressure (being 1696 times 

 the volume of water at 4°-l Cent., or 27" 166 cubic feet per pound 

 avoirdupois), and V, the volume of steam of saturation at the 

 pressure Pj. This formula is only applicable between the pres- 

 sures of one and eight atmospheres ; that is to say, when the 

 volume of steam is not greater than 27 cubic feet per pound. 



