Space occupied by Atoms. 351 



later than myself, yet independently, at the important relation 

 between contraction and affinity. By means of the equation 

 Gdt = ¥Ldv he calculates the u energy-quotient " K as a 

 quantity which is proportional to the intrinsic pressure calcu- 

 lated by me from van der Waals' equation. In accord with 

 myself, Richards points out that hardness, elasticity, and other 

 properties vary in accordance with this intrinsic pressure. 

 To Richards is, as already pointed out, due the great credit 

 of having verified for the first time, in a large number of 

 cases, the relations, among others, between the heats of for- 

 mation and the atomic contractions already recognized by 

 myself. As regards the relations connecting electromotive 

 force, solution-pressure, and atomic contraction, Richards has 

 arrived at results which accord with my own. Of fundamental 

 interest is the already quoted memoir on the change of free 

 energy, as well as the recently commenced experimental 

 investigations on the coefficient of compressibility. Although 

 I regret that Mr. Richards did not make himself acquainted 

 with my work before commencing his own, yet, on the other 

 hand, it is satisfactory to find that he has, on the whole, inde- 

 pendently arrived at similar conclusions. 



On one very important point only do we differ. 



Richards remarks, I. c. vol. xlix. p. 17: "The bulk of 

 Traube's reasoning is rendered difficult to follow by his hypo- 

 thetical assumptions of ' co-volume/ t core-volume/ ' bound ' 

 and ' free 9 aether, but nevertheless to him is due the credit of 

 having recognized the importance of many of the facts/'' 



In my opinion, the value of my views lies precisely in what 

 Richards reproaches me with. 



While I distinguish three volumes : internal, external, and co- 

 volume, Richards assumes for the liquid and solid states only a 

 single volume. He regards the atoms as something in the 

 nature of elastic spheres, which are in contact and undergo 

 contraction, without any intervention of a free space between 

 them. The effect of heat manifests itself in condensations 

 and rarefactions within the atom. 



While I have proved the generality of the gaseous laws as 

 expressed by van der Waals' equation, and their applicability 

 to all three states of aggregation, from the assumptions made 

 by Richards it would follow that this equation is not applicable 

 to the liquid and solid states, since Richards equates the 

 co-volume v — b for both these states to zero, not only at the 

 absolute zero of temperature, but at all temperatures. 



But if Richards is right, how are we to account for the 

 fact that the coefficient of expansion of the solid elements 



= 9^0? provided the total expansion be referred not to the 



2 B 2 



