Chemistry arid Physics. 375 



point of the aluminium. In each case pure hydrogen was pro- 

 duced in the theoretical amount, while the carbon was partly 

 deposited in the free state on the surface of the metal, and partly 

 formed a carbide. The latter by the action of water gave off 

 methane which was contaminated with other hydrocarbons. — 

 Berichte, xl, 2871. h. l. w. 



5. Studies on the Mode of Growth of Material Aggregates. 

 II [Addendum] Distribution of Variations;* by A. J. Lotka. 

 — It was pointed out in the body of the paper, under the above 

 heading, that the distribution of the molecules amongst the three 

 classes : stable, metastable and transitional, must bear a close 

 relation to reaction velocity and equilibrium, and the influence of 

 temperature on the same. 



A perusal of Arrhenius' paper on the influence of temperature 

 on reaction velocity, published in the Zeitschr. f. phys. Chem , 

 1889, iv, 226-234,f suggests that his " inactive " and " active " 

 molecules correspond to the "stable" and "metastable" mole- 

 cules of our presentation. We may then directly apply Arrhe- 

 nius' theory. 

 If we denote 



by N the total number of molecules of A 



by N ff the number of stable molecules of A 



by N„ the number of metastable molecules of A 



by N r the number of transitional molecules (of A > B) 



then, by Arrhenius, 



n„ - m a (i) 



where ® is very small and follows Van't Hoff's relation 



® T = ®o« 



£^ T -T 

 R ' T„T 



On the other hand we have 



~n t = m{t'-t) 



= Jc~N a (t' — t) very nearly. 



Hence, N ff : N^ : N T : : 1 : ® T : Jc(t'—i) 



This proportion then expresses the distribution of the molecules 

 amongst the three classes at a given temperature T, in those 

 cases in which Arrhenius' theory is applicable, viz: in reactions 

 whose velocity coefficient varies with the temperature according 

 to the relation : 



D. T -T 

 , _ , B * ToT 



*See this Journal, Sept., 1907, p. 214. 



f Compare also Arrhenius, loc. cit., 1899, v. xxviii, p. 317, et seq. and 

 Kothmund, loc. cit., 1896, v. xx, pp. 168-179. 



