I 

 340 KEYES ART. J 



are believed to be limiting laws valid for infinitely extended 

 volumes it is desirable to review briefly the circumstances 

 surrounding the behavior of important functions along the 

 path by which reduction of pressure to zero takes place. Con- 

 sider in this connection, for example, the Joule-Thomson ex- 

 periment. The effect is given by the thermodynamic equation, 



where Cp designates the constant-pressure heat capacity, x the 

 "heat content" (e + pv) and t = t~^. The existing data show 

 that the right hand member does not vanish as p goes to zero 

 but on the contrary becomes constant and independent of the 

 pressure. Joule and Thomson deduced, however, that the 

 effect varied inversely as f at low pressures, which requires the 

 following relation between p, v, and t: 



V = fip)t - J, (VI) 



or 



p)t -y^ th) 



fiv)t 



Clearly the condition that (II) be applicable at every tem- 

 perature is that /(p), as is possible, may be taken to be R/p 

 for t; -^ 00 . 



On the other hand, the change of energy with volume, 



\dv/t \ Bt /v 



has been shown in the case of one substance'' to vary as the 

 density squared (at low pressures), which may be regarded as 

 a verification by experiment of equation (IV) since {de/dv)t — > 

 as the density diminishes. The consequence of this is that 

 6 = f{t) and that p = f(v)t. Taking into account the validity 

 of Boyle's law as an exact expression of physical behavior for 

 p -^ the latter relation leads to equation (II). The quantity 



