1'SO Prof. H. L Callendar. On the Tkirmodjriumieal 



This simple formula agrees very nearly with Regnault's observations 

 in the rate of variation above 60, and also with the table of values of h 

 given by Callendar and Barnes.* 



The accurate relation between the Total Heat and the Specific Heat 

 of the Vapour is readily obtained by equating the intrinsic energy of 

 steam evaporated at C. at a pressure p", and then heated at constant 

 pressure p up to any temperature 0, to that of steam obtained by heat- 

 ing the liquid up to the same temperature 0, evaporating it at 6 under the 

 constant saturation pressure p, and expanding the vapour at constant 

 temperature down to the pressure p" of saturation at C. The 

 various changes of intrinsic energy involved in these processes are 

 given by equations (20) and (22). After a few simple reductions we 

 obtain the Equation of Total Heat, 



H-H = S(0-0)-(n+l)(cp-cy) (32), 



which is simply the expression of the first law of thermodynamics as 

 applied to the problem, and might also have been obtained in various 

 other ways. If we omit the small terms depending on the co-aggrega- 

 tion c, the equation is identical with that given by Kankine in 1850, 

 on the assumption that saturated steam could be treated as an ideal 

 gas. The small terms represent the effect of the deviations of steam 

 from the ideal state, and become important at high pressures. The 

 equation neglects the external work of expansion of the liquid, but 

 this is less than one-thirtieth of a calorie at 200 C., although it may 

 become important as the critical temperature is approached. 



Equation (32) gives only the variations of the total heat of the 

 saturated vapour. In order to find the absolute values, it is neces- 

 sary to know the actual value of the total heat at some particular 

 temperature. The obvious value to select would be that given by 

 Regnault at 100 C., namely 637 calories. His methods do not appear, 

 however, to have been sufficiently exact, and I prefer to rely on a 

 more recent determination by Joly, with his steam calorimeter (described 

 by Griffiths), t Joly determined the mean specific heat of water between 

 12 and 100 C 'in terms of the latent heat of steam at 100 C. Now 

 the mean specific heat of water between 12 and 100 C. is known in 

 terms of the specific heat at 20 C. by the results quoted above. We 

 can therefore reverse the calculation, and find the latent heat of steam 

 at 100 C. The result of the calculation gives L at 100 = 540 - 2 

 calories at 20 C. This is considerably in excess of Regnault's value, 

 but it is quite within the limits of probable error of his experiments, 

 and it possibly still errs in the direction of being too low. Assuming 

 this value as a starting point, I have calculated the following table of 



* 'Brit. Aasoc. Hep.,' 1899. 



t ' Phil. Trans.,' A, 1895, p. 322. 



