348 Prof. J. Traube on the 



changes in the hardness, elastic modulus*, and coefficient of 

 friction f . 



It was further found % that the length of free path of the 

 metallic atoms as calculated from the difference between the 

 diameter of the total volume and that of the true volume 

 (the quantity b) was in agreement with that found from the 

 diffusion- coefficient ; also, the atomic coefficient of compressi- 

 bility of the metals was the greater the greater the co-volume. 



Van der Waals' equation leads to the value - for the heat 



v 



of vaporization §, if, as in the case of lnonatomic substances, 

 it is permissible to neglect the work connected with the 

 passage from a fluidon to a gason. I have shown that in the 

 case of mercury, observation and calculation are in agreement. 

 In the case of poly-atomic substances, the heat of vaporization 



came out to be 2 — . Since according to Deprez-Trouton's 



\1 ox 



rule the heat of vaporization is proportional to the absolute 

 temperature of ebullition for non-associated substances, it 

 follows that the boiling-point also becomes a simple calculable 

 function of the volume, and finally I showed that in the case 

 of metals the absolute boiling-point is inversely proportional to 

 the expansion-coefficient || . 



(c) Internal and External Atomic Volumes. 



So far we have only considered two volumes : the true 

 volume and the co-volume, or the quantities b and v—b. 



According, however, to the calculations of van der Waals, 

 the quantity b is by no means the space which is completely 

 filled by the mass of the atoms, but the four-fold multiple of 

 this space. We may, following Clausius, picture to ourselves 

 the quantity b as the space occupied by the atom together 

 with the gether envelope into which no other atom can 

 penetrate. The internal atomic volume would thus be pro- 

 portional to the external volume, or to the space occupied by 

 the envelope of u bound " sether. Now the theories of 

 Clausius, Mossotti, and Exner lead to the conclusion that an 

 approximate measure of the internal volume is furnished by 



* J. Traube, Zeitschr. anora. Chem. Bd. xxxiv. p. 413 (1903). 

 t J. Traube, ibid. Bd. xl. p. 377 (1905). 

 X J. Traube, ibid. Bd. xxxiv. p. 425 (1903). 



§ J. Traube, Ann. der Plnjs. Bd. viii. p. 298 (1902) : and Zeitschr. 

 anorg. Chem. Bd. xxxiv. p. 423. 



|| J. Traube, Zeitschr. anon/. Chem. Bd. xxxiv. p. 422 (1903). 



