Laics of Molecular Force. '227 



4. Establishment of Characteristic Equation below the 

 region of the Critical Volume. — Now that we have practically 

 exhausted the available data of the gaseous state, we see that 

 by themselves they do not give much scope for generalization ; 

 but if we can secure an equation applicable from the critical 

 volume down to the volumes of liquids in the ordinary state, 

 then, with two equations covering almost the whole range of 

 fluidity, we shall have a much larger experimental area laid 

 under contribution for information on the characters of mole- 

 cules. 



Already we have secured one important fact towards the 

 acquisition of such an equation, namely that below the critical 

 volume the internal virial term varies inversely as the volume ; 

 and in the case of ethyl oxide we know its actual amount l/2v 

 with Z = 5514. We have therefore only to add to l/2v Ramsay 

 and Young's values of pv at different temperatures for different 

 volumes below the critical, and we obtain the values of the 

 kinetic-energy term in the desired equation ; we can then 

 proceed to study how this quantity depends on temperature 

 and volume, and express the resulting conclusions in a 

 formula. 



As to the form we have this clue, that it must join on con- 

 tinuously with the previous one where that ceases to be appli- 

 cable. Now the first fact to notice is that our form for 

 compounds above the critical region cannot, like that for the 

 elements, give a critical point by itself at all ; for given p 

 and T it is not a cubic but a quadratic in v, and hence cannot 

 give us the three equal roots which are adopted as charac- 

 teristic of the critical point when we apply the conditions 



■d P fdv = 0, B 2 iV^ 2 = 0. 



This emphasizes the discontinuity in compounds as contrasted 

 with elements. However, we know as an experimental fact 

 that at the critical point "dpfdv^Q, which with the charac- 

 teristic equation gives us only two relations between the 

 critical temperature, pressure, and volume. As a third relation 

 that would perfectly define these three quantities I was led to 

 believe that the critical volume is proportional to k, and found 



critical volume v e = 7k/6 



is the relation which, with the two others, gives successfully 

 the numerics of the critical state in agreement with ex- 

 periment. As this will be proved subsequently (Section 10) 

 for a large number of substances, I will not delay at present to 

 give examples, except for those compounds for which we have 

 already found k and /. 



