Mr. W. J. M. Rankine on the Mechanical Action of Heat. 177 



Secondly. For the pressure on the opposite side of the piston, 

 of the steam which escapes into the condensei-, or into the atmo- 

 sphere, as the case may be. Let P3 be the pressure of this 

 steam ; the deduction to be made for its action is 



P3S,(1-C)=P3V,(1-C).. 



These deductions having been made, there is obtained for the 

 effect of unity of weight of water evaporated, 



(35.) The effect of the engine in unity of time is found by 

 multiplying the above quantity by the number of imits of weight 

 of water evaporated in unity of time. 



If this number be denoted by W, 



WS2(l-c)=WVi(l-e)s=AM . . . . (48) 



will represent the cubical space traversed by the piston in unity 

 of time, A denoting the area of the piston, and u its mean 

 velocity. 



Now let the whole resistance to be overcome by the engine be 

 reduced by the principles of statics to a certain equivalent pres- 

 sure per unit of area of piston, and let this pressure be denoted 

 by R. Then 



RAm = RWVj(1-c)s (49) 



expresses the effect of the engine in terms of the gross resistance. 



We have now the means of calculating the circumstances 

 attending the working of a steam-engine according to the prin- 

 ciple of the conservation of vis viva, or, in other words, of the 

 equality of power and effect, which regulates the action of all 

 machines that move with a uniform or periodical velocity. 



This principle v.'as first applied to the steam-engine bytheCount 

 de Pambour ; and accordingly, the formulse which I am about to 

 give only differ from those of his work in the expressions for the 

 maximum pressure at a given temperature, and for the expansive 

 action of the steam, which are results peculiar to the theory of 

 this essay. 



In the first place, the effect, as expressed in terms of the pres- 

 sure, is to be equated to the effect as expressed in terms of the 

 resistance, as follows : — 



RAm = RW V, (1 - c)s = W Vi 



Hr^-r^ 



-P3(l-C).sj. 



This is the fundamental equation of the action of the steam- 



