A. J. Loika — Mode of Growth of Material Aggregates. 215 



ferences in concentration, and other unknown effects, may be of 

 this character. 



The effect of the catalyser would in this case be closely analo- 

 gous to that of " nuclei, " or " crystals " in supercooled systems, 

 or of gas bubbles in a superheated liquid. In these cases change 

 of state is arrested because in the absence of " germs " the sys- 

 tem would have to pass through a stage in which its free 

 energy had a value greater than its actual value,* in order 

 to reach the final lower value. The introduction of the germ 

 furnishes another path requiring no such maximum value to be 

 passed, and the change then takes place spontaneously. 



But the catalyser might also produce its effect in another 

 way, namely, by providing mechanism through which a portion 

 of the energy set free by one molecule during its descent along 

 the downward limb of the path A A' is diverted into such a 

 channel that it raises another molecule up the ascending limb 

 of that path.f This possibility is of some interest because a 

 large class of natural phenomena, especially in the living world, 

 depend on an action of this kind. We may only mention here 

 the phenomenon presented by an organism which obtains its 

 food by a series of (muscular) efforts, the energy for which is 

 derived from food previously ingested. The phenomenon as 

 a whole takes place spontaneously, although for each portion of 

 food there is a stage in the process through which it passes when 

 it requires the application of external energy. Another exam- 

 ple of the same kind taken from the world of mechanics is the 

 continuous operation of a heat engine in which the working sub- 

 stance goes through a cycle. 



Lastly we note that according to the view developed above, 

 such agencies as elevation of temperature, or the introduction 

 of a catalyser, which increase k, will shorten the life of the 

 molecule, since we found that the probability at the moment 

 of formation that a given molecule will reach age a is given 

 by e~ ka . 



This brings ns to the close of our consideration of the system 

 A + A'. A similar treatment might of course be applied to 

 more complicated chemical systems, but, although the results 

 obtained would of course differ in form from those deduced 

 above, the underlying principles would be the same. Indeed, 

 the development outlined in this paper appears to promise per- 

 haps more interesting suggestions in the treatment of aggre- 

 gates, the elements of which, unlike the molecules in chemical 



* Owing to the dependence of vapor -pressure, solubility, or melting-point 

 on the form of the surface of contact between the two phases. 



f A somewhat similar idea has been expressed by Raschig (Zeitschr. f . ang. 

 Chem. , 1906, p. 1761), who compares the action of the molecules on one another 

 to that of the consecutive members of a file of dominos set up on end, and 

 overthrown in a body by the fall of the first in the file. 



