Mr. W. J. M. Rankiue on the Mechanical Action of Heat. 175 



equal to the heat required to expand m. Heuce making, accord- 

 ing to equation (30), 



and 



we obtain 



Sts-^SV 



"To ••■ 



m h\ 



yS' 2 

 — + - 



-1 





^^; . (43) 



8V 



and denoting the coefficient of -^ by — v, 



rfbgV 



and because 



dlosV 



rflogm _ 



f/logS 

 (/lo^V 



= l-v; 



rfloaP 



^^=-a-<>-g-V)= 



rflogP 



+ 



(44) 



As the mean temperature of the liquid thus produced more or 

 less exceeds that of the remaining vapour, a small fraction of it 

 will be reconverted into vapour if the expansion is carried on 

 slowly enough; but its amount is so small, that to take it into 

 account would needlessly complicate the calculation, without 

 making it to any material extent more accurate. 



(23.) The extreme complexity of the exponent o", considered 

 as a function of the pressure P, would render a general formula 

 for the expansive action y"P<;S very cumbrous in its application, 

 for practical purposes, it is sufficient to consider the exponent a 

 as constant daring the expansion which takes place m any given 

 engine, assigning it an average value suitable to the part ot the 

 scale of pressures in which the expansion takes place. ±or 

 engines in which the steam is introduced at pressures not exceed- 

 ing four atmospheres, I conceive that it will be sufficiently accu- 

 rate to make 6 



