668 SCIENCE PROGRESS 



We believe that both the central nuclei and the external 

 dielectric shells together constitute the physical atoms, and that 

 it is this physical atom which vibrates as a whole when the 

 temperature is raised. 



It is quite possible that, as Traube shows, both the sum of 

 these central nuclei which make up MRa, and the sum of the 

 external shells b — MRa, are proportional to n the number of 

 valencies : 



MR a .„ ,b -MR .. 



= 790 ana — = 175 on the average. 



At any rate, MRa, b , V K , V BP , and the molecular volumes under 

 equally reduced pressures, show constant relations with each 

 other in the different substances examined, and thus the additive 

 relations which apply to one apply to all. 



It consequently seems one-sided to refer to MRa only 

 when for spatial relations volumetric standards are available. 

 Moreover, as just indicated, it does not seem justifiable to 

 consider the atom as being just that portion which happens 

 to be impermeable to light and is conducting, and to neglect the 

 remainder b — MRa. It leads to results which are imperfect, 

 although in themselves of utility and interest. Molecular 

 Volume relations introduce another aspect which is of equal 

 importance. 



(ii) In the second place, the existence of the co-volume has 

 been shown to be connected with an external vapour pressure. 

 T\\e vapour and solid phases can, however, exist together 

 independently of the liquid phase, and the solid can even be 

 transformed into the vapour without the appearance of liquid. 

 Are we, then, to suppose that a vibration space separates the 

 molecules in solids, which manifest the property of rigidity? 

 This is inconceivable, and we conclude that in the solid state 

 the molecules are in contact. 



Since expansion is a well-known property of solids, we must 

 suppose that augmentations in volume with temperature are 

 due to the increased vibration spaces of the atoms. It cannot 

 be supposed that this mode of expansion extends only as far as 

 the melting point, but must persist in the liquid state. 



We are thus left with the alternative of supposing that the 

 extra-atomic space is occupied partly by vibrating atoms, which 

 increase the molecular magnitude, and partly by a molecular 



