664 SCIENCE PROGRESS 



just mentioned is to cause the atom to occupy a space consider- 

 ably larger than that of its own substance, so that the volume 

 of the molecule at any temperature above absolute zero is 

 greater than XA. V._ 273 . The enlarging effect of the heat forces, 

 combined with the attractive intermolecular forces, still pre- 

 serves the compact arrangement, but in such a way as to allow 

 of the slow diffusion of the molecules through the mass. One 

 possibility of this unstable equilibrium is the alternate formation 

 and dissolution of molecular aggregates. At any rate, this view 

 accounts for the undoubted rigidity which has been found 

 characteristic of liquids, the possibility of the formation of 

 liquid crystals, and the enormous resistances to pressure which 

 distinguish the liquid from the vapour states. 



The passage of a substance into the solid state is easily 

 accounted for, because the diminishing temperature causes the 

 intermolecular forces to assume greater relative importance, 

 owing to the gradual approximation of the molecular centres. 

 Under such conditions a point is found where the relative 

 movement which involves slipping becomes impossible, and 

 there may also result an orientation of the molecules. 



This compact condition of matter is involved in the theory 

 of Barlow and Pope on the Morphotropic Relationships of 

 Crystalline Structures, and it has been deduced by Richards 

 as a result of his work on the Compressibilities of Solids and 

 Liquids. 



(b) As an alternative to the above, there exists the con- 

 ception of space only partly occupied by matter. The molecules 

 under the circumstances are not in contact, but are separated 

 from each other by a molecular vibration space, which is 

 maintained against the enormous internal attractions by com- 

 paratively feeble vibratory movements. This space is called 

 the co-volume — a term borrowed from Van der Waals' theory. 



(i) Co-volume Constant at Equal Temperatures. — Traube con- 

 siders that the co-volume is the same for all non-associated 

 substances at the same temperature (Ueber den Raum der 

 A tome, Stuttgart, 1899, and Berichte, 1892-5). 



Thus V m = £nV a -f <£, <f> being constant at t° say. At 15 , <£ is 

 25 — 26 for different non-associated compounds. This volume is 

 a considerable fraction of the total volume, and it is difficult to 

 make this circumstance coincide with the existence of the Law 

 of Coincident States. 



