Space occupied by Atoms. 343 



only the co-volume expands — as in gases — and not the total 

 volume, the coefficient of expansion was referred to the former 

 instead of the latter, and it appeared that this coefficient of 

 expansion is equal to -^jg for all the elements (halogens 

 excepted). Therewith a proof was obtained that van der Waals' 

 equation applies to all three states of aggregation, and that it 

 enables us to calculate the true volume and the co-volume for 

 all three states. 



Now the separate consideration of each volume leads to 

 remarkable consequences. 



(a) The true volumes (the quantities b). 



The atomic volumes as calculated by Kopp's method and 

 by means of van der Waals' equation are only mean values y 

 which may be used for purposes of calculation much in the 

 same way as the mean molecular velocities are used in the 

 kinetic theory of gases. The volume of an oxygen atom is, 

 e. <:/., least when it is in combination with hydrogen, it is 

 appreciably larger in combination with carbon, and increases 

 in homologous series, in combinations such as methyl, 

 ethyl, &c. The contraction, e. g., undergone by chlorine 

 when combined with the atoms of various metals depends on 

 the chemical affinity of the metal concerned for chlorine. 



I was the first — several years before Mr, Richards* — to 



* In the Zeitschr. Physik. Chem. Bd. xlix. p. 19, Richards remarks : — 



tl It is a pleasure to me here to draw attention to the entirely independent 

 investigation of J. Traube in this direction. It is remarkable that quite 

 simultaneously he published in Drude's Ann. Bd. v. p. 555 (20 June, 

 1901) the following proposition : — 



' The atomic volume of an element changes from one compound to 

 another ; it decreases as its attraction for the neighbouring 1 atoms 

 increases ' — while on June 15 of the same year my version of this relation 

 appeared in the Proc. of the Amer. Acad. lvii. p. 17 : 



'The atomic volume is not constant, but is a function of pressure and 

 temperature, and probably of electric strength.' " 



Mr. Kichards has evidently overlooked the fact that in my monograph, 

 which appeared already in 1899, quoted by him and published in Ahrens, 

 Samml. chem. u. chem.-techn. Vortrage, Bd. iv. p. 22, there is contained 

 the following proposition : — 



"The vibration space (the quantity b) changes, according to the 

 nature of the atom, more or less from one compound to another, and in 

 accordance with the mutual influence which the various atoms contained 

 in the compound exert on each other. The less the attraction of 

 neighbouring atoms, the more nearly does the vibration space approach 

 its maximum value (maximum vibration volume), and, on the other 

 hand, the vibration volumes decrease the more the greater the mutual 

 attraction of the atoms." 



I may also remark that I undoubtedly have the claim to priority in 

 the matter of the doctrine of the compressibility of atoms (the quan- 

 tities b) as against J. D. van der Waals (cf. my statements in Zeitschr. 

 anorg. Chem. Bd. xxxvii. p. 242, 1903). 



