Space occupied by Atoms. 341 



and in a series of memoirs has arrived at conclusions and 

 results which substantially agree with my own, which partly 

 form extensions of them, but which partly also, in one 

 essential point, present so characteristic a difference in the 

 point of view that it may be worth while to compare the two 

 theories. 



More especially, however, do I wish, by a brief resume of 

 my work, to establish my priority in regard to many of the 

 problems treated of by Richards. Although Mr. Richards 

 is good enough, in a concluding note, /. c. vol. xiix. p. 17, 

 to refer in terms of approval ? to my work, I am never- 

 theless of opinion that the note in question is liable to be 

 misleading. 



The space occupied by matter may be regarded as con- 

 sisting of 



(1) The true volume of the atoms and molecules; 



and (2) The co-volume, or space within which the atoms are 

 free to move. 



Now while in the case of the " ideal " gases the true volume 

 is negligible in comparison with the co-volume, Budde and 

 especially J. D. van der Waals have shown how, from the 

 behaviour of gases under high pressures and near the con- 

 densation-point, the coefficient b in van der Waals'equation 



(*+ £)(-*)?= 



RT 



may be taken into consideration *, and how, by the aid of this 

 w T ell-known equation, the cohesion coefficient a, the true 

 volume b, and the co-volume v — b may be calculated, as a 

 first approximation, by taking into account the deviations of 

 strongly compressed gases from the ideal gaseous laws. 



It is sufficiently well known with what success van der Waals 

 applied this equation to the transition from the gaseous to the 

 liquid state, and further to the theory of corresponding states; 

 and how, by means of the coefficient b, it became possible to 

 determine the absolute dimensions of the atoms. 



The proof that the equation of van der Waals also holds 

 good for homogeneous liquids and even for solids — so that the 



* I may take this opportunity of remarking that I regard the establish- 

 ment of van der Waals' state equation as one of the greatest advances in 

 physical chemistry. If we take into consideration the fact that a and b 

 are not constants, then the equation holds with much greater accuracy 

 than has hitherto been supposed ; in any case, it is in general much to 

 be preferred to those complicated equations which have been proposed in 

 place of it, and which, perhaps, come nearer the truth, but are far less well 

 adapted to purposes of calculation. 



