Properties of Gases and Vapours, &c. 285 



to take account of the small terms in equation (35), we obtain the well- 

 known empirical formula of Kankine (1849), which is very convenient 

 and accurate. A nearly equivalent formula is that of Unwin,* log p = 

 A 4- B0 6 , in which the same effect is empirically secured by an arbitrary 

 exponent. These formulae are purely empirical, but it is interesting to 

 observe how they are related to the correct thermodynamical expres- 

 sion (35). 



Saturation-Pressures of Steam. 



In employing equation (35) to calculate the numerical values of the 

 saturation-pressure in the case of steam, we have only one empirical 

 constant, namely, p, which is determined by the condition that the 

 saturation-pressure at 100 C. is 760 mm. The values of the other 

 constants which occur in this equation have been already given, 

 namely, 



S - 04966 cal./deg. L = 593-5 cals. R = 0-11037 cal./deg. 



The value of 6, which is also one of the fundamental data, is taken as 

 being 273, but is uncertain to the extent of 0'1. Dividing the equa- 

 tion by R, and reducing to common logarithms by the modulus log e 10 

 = 2-3026 = m, we obtain the numerical formula 



log lo pfp = 



- (d<}> - dh/0)/mR ...... (36). 



in which F(#) stands for the function logio 0/B - t/mO. I have used this 

 form for calculation, and have -given the values of the separate terms in 

 Table V so as to show their relative importance. It is also possible to 

 write the formula in the shape, log p = A + ~B/6 + C log 6 + small 

 terms, but this does not show so clearly the relative effect and im- 

 portance of L and S. 



The values of the saturation-pressure in the column headed p are 

 calculated by the complete thermodynamic formula (36). The values 

 given in the column headed Regnault are those of Regnault, recalcu- 

 lated by Peabody and reduced to latitude 45. The difference expressed 

 in degrees of temperature is given in the last column, and is probably 

 within the limits of error of Regnault's observations and of the empirical 

 formulae employed to represent them. If we refer to the actual obser- 

 vations of Regnault, we find that the discrepancies of individual 

 observations at any point, expressed in degrees of temperature, exceed 

 the values of the differences shown in the last column. We also find 

 that in most cases the actual observations agree better with the single 

 formula (36) than they do with the two empirical formulae, each with 

 five arbitrary constants, from which the values in the column headed 



* ' Phil. Mag.,' Tol. 21, p. 300. 



