MOLECULAR VOLUME 669 



vibration space, or by the more simple one of compact structure. 

 The latter is capable of explaining all the known properties of 

 liquids, many of which are inconsistent with the first alternative. 



Since V° = 2n(V°) = the sum of the combined A.V.'s 

 V p m = V° [1 + eftp)] - 2n(V°) [1 + ftp)]. 



The space V£, — £n(V°) is thus a function of the composition and 

 constitution of the molecules because it is proportional to 

 2n(V°). 



So also is the whole volume V^ proportional to 2n(V°). 



On the assumption of compact structures 



V^ 2n(V°) L ^ 9{y,i 

 and (VS) = (V°) [1 + <£(?)]. 



If p represents some fraction of the critical pressure, or when the 

 pressure is sufficiently low some common pressure, then we suppose 

 that the atomic volumes change under the different physical conditions 

 in the same ratio as the whole molecular volumes. This constitutes, 

 at least in part, a physical interpretation of the Law of Coincident 

 States as it applies to liquids. 



Such a ratio is probably independent of the chemical com- 

 position and constitution of the substances, and depends mainly 

 on the physical conditions of comparison. 



A 



This is the first of three lines of investigation which form 

 the experimental basis of this theory, and may be called a proof 

 of the existence of the Law of Coincident States in liquids. 



Suppose that the two reference points for the volumes of a 

 number of liquids are the equal or reduced pressure p and p lf 



Then for Substance I. 



V£_ Vm[i + 4>'(Pi)] _ [i + 4>'(Pi)] 

 V& V£[i+#p)] [i+*(p)] 



For Substance II. 



V'£ _ VS, [1 + *'(Pi)] _ [1 + *'(Pi)] 



vg, " v° [1 + </>(?)] [i + <Kp)] ( Re § ularit y 1.) 



and so on for a number of substances. 



These ratios are thus the same for all. 



(a) Young has made the Critical Molecular Volume, or rather 

 Density, the basis of comparison, and has shown that the 



