130 Starkweather — Thermodynamic Relations for Steam. 



But Yan Laar's equation does not satisfy the saturation vol- 

 umes. The writer has shown in a previous paper* that the 

 saturation volumes as calculated from Kegnault's latent heats 

 are entirely out of accord with those directly measured by 

 Battelli,f and has given reasons for preferring the former. 

 From these Yan Laar's equation deviates 2*5 per cent. Even 

 should we assume Battelli's experiments to be correct instead 

 of Regnault's the deviations would still exceed 1 per cent. 



Were it certain that the equation were necessarily of 

 Clausius' form, holding for the liquid as well as the vapor, the 

 method would be exact, and we should simply have to say so 

 much the worse for the experiments. But all we know con- 

 cerning the last term of the second member is that at large 



c 

 volumes at any given temperature it must be sensibly — , as 



has been shown by Yan der Waals. If we replace ^-„ 



J . i F (*>+£) 2 



by some other function of v which is sensibly -j at large volumes, 



the application of Clausius' method becomes very complicated, 

 if not, indeed, impossible. The failure of Yan Laar's equation 



f(T) 

 to satisfy the facts would seem to show that the form / ' is 



\ (v+P) 



not sufficiently correct for the water line, at least. 



Abandoning the attempt to satisfy the water line throughout, 



f(T) 

 we might still consider ' as sufficiently accurate for it in 



the vincinity of the critical point, the relations for that point 

 still holding true. The equation would thus apply to steam 

 for all states. In this case, if we give the equation Clausius' 

 general form, his method for determining f(T) does not apply, 

 and we are free to choose it so as to satisfy the saturation 

 volumes. This has apparently never been done. The writer 

 has attempted it, but without success. /(T) would necessarily 

 decrease very rapidly with increasing temperature. Thus at 

 100° C, 200° C. and 365° C. (the critical temparature) f(T) 

 would have the respective values 59*5, 21*5 and 13*5. More- 

 over, the great fall from 100° to 200° is out of accord with the 

 change from 200° to 365°. This seems to indicate that the 

 type of formula selected will not satisfy the facts. 



There remains the following problem, to obtain equations 

 which shall satisfy the experiments within ordinary limits. 

 Such equations would suffice for most purposes, and moreover 

 the writer hopes to draw from them some theoretical conclu- 



* This Journal, Jan. 1899, p. 13. 



fMem. R. Ace. Sc. di Torino (ii), 43, 1893. 



