342 Prof. J. Traube on the 



modified gaseous laics are applicable to all three states of matter 

 — was first given by myself*. 



Now the method which I first adopted in investigating the 

 volume relations of liquids was to compare, according to 

 Kopp's method, at the ordinary temperature, the molecular 

 volumes (molecular weight -~ density) of such organic sub- 

 stances as had the same composition-difference, e. g. CH 2 , 

 H 2 , &c. It appeared that — as a first approximation — cor- 

 responding to equal composition -difference there was equal 

 volume-difference. On comparing, for a given compound, 

 the atomic volumes so determined with the molecular volume, 

 it appeared, contrary to Kopp's calculations, that the sum 

 of the former was less than the molecular volume. 



Thus the molecular volume of a liquid consists of a sum of 

 atomic volumes SV a , but in addition to this also of a second 

 term, which obviously represents the co-volume. The values 

 calculated by the above method of this co-volume, per gramme- 

 molecule, mostly oscillated about 25 c.c. at 0° as a rough 

 approximation, and only in the case of associated substances 

 were the calculated values considerably less, for reasons which 

 are easy to understand, when the simple molecular weight 

 was made the basis of calculation. 



The values v ± and v 2 of the volumes corresponding to two 

 neighbouring temperatures T 1 and T 2 , calculated by means of 

 the coefficient of expansion of the liquid, were next substituted 

 in the equation of van der Waals, and thus the values of b and 

 v — b calculated. The values of b so obtained were found to 

 be in agreement t with the %Y a calculated according to 

 Kopp's method — i. e. with the sum of the atomic volumes. 

 Thus the equation of van der Waals was found to hold good 

 for homogeneous liquids. 



The same two methods led to the desired result in the case 



of solids. Kopp's method!, as in the case of liquids, led to 



m ^ m 



an equation of the form — =2V + <£>, where — denotes the 



^ 8 a S 



joolecular volume, SV a the sum of the atomic volumes, and 

 <l> the co-volume. When, on the other hand, by using the 

 coefficients of expansion of the elements the volumes b — XVa 

 and <E> = v — b were calculated by means of van der Waals 

 equation, the following result was obtained § : — 



On the supposition that when a solid element is heated 



* Drude's Ann. d. Phys. Bd. v. p. 548 (1901) ; and Zeitschr. anorg. 

 Client Bd. xxxiv. p. 413 (1903). 



t J. Traube, Drude's Ann. Phys. Bd. v. p. 552 (1901). 



% See the author's Grundriss der Physik. Chemie, Enke, Stuttgart 

 1904, p. 207. 



§ Zeitschr. anorg. Chem. Bd. xxxiv. p. 413 (1903). 



