Prof. II. L. ('allrndar. On ih< Tin /?/*'/////"/// /<// 



The various terms of this equation have l.ccn already calculated, and 

 are given in equations (18), (24), (26), and in Table IV. The last three 

 terms of the equation are small, and represent the effect of the \ 

 tion of the specific heat of water, and of the deviation of the properties 

 of steam from the ideal state, as expressed by the characteiisti. 

 equation (6). Neglecting the small terms, the equation is identical 

 with one given by Bertrand, on the assumption that steam may be 

 treated as an ideal gas. It is evident that the values of the saturation- 

 pressure may l)e calculated from this equation by means of the values 

 of the latent heat already found. It is better, however, to eliminate L 

 by means of the energy equation (32) already given. 



Equation of the Saturation-Pressure. 



If we substitute H - H = L - L + h = L - L + / + dh, in the energy 

 equation (32), and divide by 0, and subtract from the entropy equation 

 (34) above given, we obtain the equation of saturation-pressure, which 

 may be reduced to the form 



R lo&p/p" = (L/0 + np o c o /ey/e - (i - s) (log. e/e - t/e) 



+ (pc -pc)/e - (d<j> - dh/B) (35). 



Neglecting the terms depending on the co-aggregation, and on the 

 variation of the specific heat of water, this equation is equivalent to 

 one given by Dupr and Bertrand, and rediscovered in various ways by 

 many other observers (e.g., Pictet and Hertz).* If the correct values 

 of S, L, and R are inserted in the formula, the equation thus simplified 

 gives very accurate values of the saturation-pressure at low pressures 

 where the properties of steam satisfy approximately the fundamental 

 assumptions made in deducing the formula. Bertrand, t although of 

 course he was well aware that the formula thus obtained was not accu- 

 rate at high pressures, has calculated numerical formulae of this type 

 for a large number of vapours, choosing the constants empirically so as 

 to obtain the best agreement over the whole range. The values of the 

 constants so found do not, of course, agree with the correct values of 

 L or S. The numerical values chosen by Bertrand in the case of 

 water, for instance, give L = 573 calories, S = 0*575 cal. per deg., 

 and the value of the steam pressure found is 763 mm. at 100 C. At 

 low temperatures the first term in formula (35) is the most important, 

 since log djB" is very nearly equal to t\B when t is small. The formula 

 then reduces to the simple type, \ogp = A + B/0, which has often been 

 employed for approximate work, and is the basis of the useful relation 

 of Ramsay and Young.J Adding a second term, C/0 2 , to this formula 



* Pictet, ' Comptes Rendus,' vol. 90, p. 1070, 1880 (proof invalid) ; Hertz, 

 ' Wied. Ann.,' vol. 17, p. 177, 1832. 

 t ' Thermodjnamique,' p. 93. 

 j ' Phil. Mag.,' vol. 21, p. 33. 



