Properties of Gases and Vapours, &c. 273 



the change is effected, and equal to the values calculated by combining 

 isothermal expansion with heating at constant pressure. We thus 

 obtain the following general expressions for the change of energy and 

 the change of entropy in any transformation from the state p, 0, to 

 the state p, : 



E-E = i(d-B}- n (pc-pc} (25). 



$ - <f> = S log 0/0 - E logjp// - n(cp/6 - cp/e) (26). 



These expressions are true for any value of n. 



Calculation of the Specific Volume of Saturated Steam. 



As an illustration of the numerical application of this method, I 

 propose to take the case of steam, as the most important and interest- 

 ing. But the methods and reasoning would be equally applicable to 

 any other gases or vapours for which the requisite experimental data 

 were available. 



The deviations of the specific volume from the ideal state are imme- 

 diately given by the values of the co-aggregation- volume c, which are 

 easily calculated. It is quite a mistake to suppose, as is frequently 

 stated, that there is any sudden or rapid change in the co-aggregation 

 as the saturation point is approached. This idea has arisen merely 

 from experimental errors due to surface condensation. Under certain 

 conditions it is well known that the vapour can exist in stable equi- 

 librium at pressures greatly in excess of the saturation value, provided 

 that there is no liquid present, or any nuclei, or other aids to con- 

 densation. I have not, for obvious reasons, succeeded in investigating 

 the properties of supersaturated steam by the method of throttling ; but 

 there does not appear to be any reason to suppose that its behaviour 

 could not be predicted with great probability by assuming that the 

 co-aggregation volume remains constant at constant temperature, 

 which is certainly a very close approximation to the behaviour of 

 steam in the superheated condition down to the temperature of satura- 

 tion. 



In the following table, which contains a few sample values of the co- 

 aggregation c and the specific volume v, the ideal specific volume of 

 steam at 100 C. and 760 mm. pressure is taken as 1698O c.c., which 

 is calculated by assuming the density of oxygen, corrected for its 

 probable co-aggregation, and taking the ratio of the molecular weight 

 of steam to that of oxygen to be 18/32. The value of c for steam at 

 100 C. is taken as 26 '5 c.c., and the values at other temperatures are 

 calculated by the formula (6) : 



VOL. LXVII. 



