270 l'i !'. If. L C.ill'Midar. <>,i ?// Tl //,/</////"////' 



tion, which is equal to 3/x ~1 per unit mass ;it any tempt- 

 follows from this assumption that the limiting value of the SJH-. -iti<- heat 

 of a gas in the ideal state (p 0, v = oc ), cither at constant ]> 

 or at constant volume, must IKJ constant, if the molecule is stable, since 

 it is directly proportional to />//#, which tends to a constant limit \\lien 

 p = 0, even in the case of vapours at temperatures far below their 

 boiling points. These constant limiting values of the two fundamental 

 specific heats will l>e denoted by the symbols S and a" respectively. 

 As a further simplification we may a-sumc that the kinetic energy of a 

 vapour is proportional top (v - f>) at all stages and not only in the limit. 

 On this assumption it is also necessary to suppose that the index of 

 in the small term /R#- in the Joule-Thomson equation is not 2, but 

 n = */R, the ratio of the limiting value of the specific heat at constant 

 volume to the limiting value of prjd. If we adopt the hypothesis of 

 Clerk Maxwell with regard to the distribution of energy between the 

 various degrees of freedom of a molecule, which, in the absence of 

 certain knowledge with regard to the exact nature of a molecule, 

 appears to be the only practical working hypothesis, the theoretical 

 value of this limiting ratio should be 1'5 for a monatomic gas like 

 argon, 2*5 for a diatomic gas like oxygen or hydrogen, 3*5 for a tri- 

 atomic gas like steam or COo, and so on, increasing by unity for each 

 additional atom in the molecule. The value 3*5 for the index is closely 

 verified in the case of steam by the experiments to be described on the 

 Joule-Thomson effect, and also by the experiments on the specific heat, 

 by which this relation was first suggested. 



Adopting these two modifications, of which the second is the more 

 important, the equation may be written in the form, 



v-b = R6Jp-c(6 /6) n = V-r (6), 



in which V is taken as a convenient abbreviation for the ideal volume 

 ~RO/p, and the co-volume b is taken as constant and equal to the volume 

 of the liquid. The small correction c, representing the state of co- 

 aggregation of the molecules, is called the "co-aggregation volume," 

 and is a function of the temperature only, varying inversely as the //th 

 power of the absolute temperature, where the index n is used as an 

 abbreviation for .<; /R. It is a quantity of the same dimensions as a 

 volume, and is measured in cubic centimetres. The numerical value of 

 f in the case of steam at 100 C. is 26'5 c.c., as deduced from the 

 experiments on the Joule-Thomson effect and the specific heat. The 

 calculated value of c at 6 = 273'0 is 79*0 c.c. It is obvious on the 

 simplest considerations that the co-aggregation volume r cannot remain 

 accurately constant at high pressures, since there is an obvious limit to 

 the possible co-aggregation of the molecules. If, for instance, the 

 molecules are simply paired, the pairing must cease when v-b = c. 

 But it is certain from the differential experiments that the modified 



