Mr. W. J. M. Rankiue on the Mechanical Action of Heat. 183 



If I be the entire length of stroke, /' the portion performed at 

 full pressure, and c the fraction of the entire capacity of the 

 cylinder allowed for clearance, then 



1_ 



and — = (1 — c) y + c. 



/ \-c' s ^ 'I 



The entire capacity of the cylinder is to be understood to in- 

 clude clearance at one end only. 



The second column gives the reciprocals of the quantities in 

 the first, or the values of the I'atio of expansion s. 



The third and fourth coluQins, headed Z, give the values of 



i^ 



the quantity tj s '^ of article 23, which represents 



the ratio of the entire gi'oss action of the steam to its action at 

 full pressui-e, without allowing for clearance. The third column 

 is to be used for initial pressures of from one to fom* atmo- 

 spheres ; and the fourth for initial pressures of from four to 

 eight atmospheres. 



The deduction to be made from the quantity Z for clearance 

 is cs, or the product of the fraction of the cylinder allowed for 

 clearance by the ratio of expansion. Hence, to calculate from 

 the tables the net mechanical action of unity of weight of steam, 

 allowing for the countez'-pressure of the waste steam P3, as well 

 as for clearance, we have the formula 



P,V,(Z-c.)-P3V,(l-c)., 



being equivalent to the formula (47) of this paper. 



Note. — The third, fourth, and fifth columns of the first of the 

 following tables may be relied on as showing the pressures of 

 steam and their logarithms with a degree of accuracy limited 

 only by that of M. Regnault's experiments, from which the 

 formula used in computing them was deduced. 



On the other hand, the sixth, seventh, eighth, and ninth 

 columns of the first table, relating to the volume of one pound 

 of steam and its action at full pressure, are to be considered as 

 merely sufficiently accurate, in the absence of more precise data, 

 for the calculation of the power of steam-engines to an a])proxi- 

 mation near enough for practical purposes, and are not to be 

 relied upon, in theoretical computations, above the temperature 

 of aljout 60'' Centigrade, or 140° Fahrenheit. 



