A. J. Lotka — Mode of Growth of Material Aggregates. 211 



this change. Hence, the aggregate can never contain any 

 molecules for which E > E ; , except those 'Nkty' — t), which are 

 actually undergoing the change from A to A'; this number 

 we saw is always negligible for any ordinary chemical change 

 going on with measurable velocity. 



Therefore, A can never, for any length of time, exist except 

 in equilibrium with A'. This conclusion agrees with the facts 

 observed in the case of change of physical state unimpeded by 

 supercooling or superheating, and, perhaps, with certain types 

 of chemical reaction (e.g., dissociation); but it does not corre- 

 spond to the characteristics of an ordinary chemical reaction 

 taking place with measurable velocity. 



(j3) Next, suppose that the path is of type (b) for all mole- 

 cules for which E > E'. In that case no spontaneous change 

 from A to A' will take place, although the aggregate may not 

 be in stable equilibrium with A' ; and this condition will con- 

 tinue indefinitely. 



Cases of this kind are : Physical change arrested by super- 

 heating or supercooling ; also, in practice, every " unstable " 

 chemical compound, which may be preserved (practically) 

 unchanged indefinitely under certain conditions. 



(7) Next suppose the path A A ; is of type (a) for some 

 molecules, of type (0) for others. Then the former will be 

 actually undergoing change, while the latter, although having 

 E > E', will remain in the form of A. 



Such an aggregate may, therefore, for an undetermined 

 length of time, contain molecules for which E > E', i.e., it 

 may have a prolonged existence in a state in which it is not in 

 equilibrium with A 7 , but is undergoing gradual change towards 

 that equilibrium. 



This description evidently fits the case of the typical chem- 

 ical time-reaction,* and to its more detailed study we will 

 return presently, after we have briefly considered some of the 

 remaining types of the path A A'. 



(8) A path of type (c) or (d) for some of the molecules 

 would imply that they were more stable in their transitional 

 state than in the form A or A 7 . 



Such a state of affairs is imaginable — the "stable" form A., 

 would then correspond, not to an ordinary chemical compound, 

 but to a condition of the molecule intermediate between two 

 compounds. A case of this kind is perhaps presented by the 

 phenomenon of tautomerism.f 



* The presence of a maximum in the path of chemical change is indicated 

 in many eases by the increased reactivity (i.e.. increased free energy) of 

 substances in the " nascent " state. But the mere fact that the transitional 

 state is evanescent implies such a maximum. 



f In this case then the "transitional" state would be prolonged, and we 

 might expect to be able to detect the material present in that state. In this 

 connection note the work of Baly and his collaborators. Compare also 

 G. Oddo, Tiber Mesohydrie Chem. Centr. Blatt, 1906, p. 1811. 



