64 



and that, when we pass on to the molecules themselves, the ordi- 

 nary attractive forces — the a,2 in van der WAALs'-equation — 

 must be able to explain the phenomena in first approximation. 



Of course, in this conception we are breaking to a certain extent 

 with homogeneity as a necessary element of the notion "phase". 

 But, as I pointed out above, homogeneous is only relative, and so 

 it is only the limits, which are removed. An emulsion too may 

 after all be homogeneons, as long as we do not divide it in parts 

 of too small a size. It depends on the circumstances, how far one 

 may go on with that. As long as we have in the separated part so 

 many molecules — either "really" dissolved, or suspended granules or 

 droplets of liquid — that statistical methods are applicable, that 

 therefore mean values of velocity, energy etc. may be calculated, 

 so long are we allowed to speak of homogeneity. If we go further 

 so that finally one granule in a quantity of liquid is left, then we 

 must call this heterogeneous. A system, for instance, consisting of 

 one drop of oil, floating in a mixture of water and alcohol, is 

 decidedly heterogeneous. For the rest, the remarks just made turn 

 out to be the same in principle as the question, how to consider 

 a gas in such extreme dilution, that there is only one molecule in 

 the unity of volume. 



To summarize, my opinion is, that when we desire to treat the 

 questions, usually dealt with by means of the phase rule, for the 

 case, that any one of the phases is a colloidal solution, we have 

 to apply the rule in its ordinary form ; only when making quanti- 

 tave determinations, we have to paj attention to the size of the 

 molecules. When, however, we wish to investigate as to whether 

 the so-called suspended granules exclusively consist of one component 

 or — as probably the ions do — condense a mantle of liquid-molecules 

 around themselves, we are not likely to succeed with the phase rule, 

 and we shall be obliged to have recourse to other methods, as for 

 instance those in use for the electrolytic or gaseous ions just mentioned. 



Although I have restricted myself to sols, I see no objection at 

 present — - in connexion with the results of a previous investigation ^) — 

 to extending the given considerations to gels. 



After the above paper had been written, the April number of the 

 Journal of the American Chemical Society came into my hands, in 

 which Tolman treats the same question in an analogous manner as 

 Pavlov did, though he obtains different results. 1 shall return to this 

 point shortly in another periodical. 



Inorg. Chem. Lab. University of Amsterdam. 



1) Wolff and Büghner, These Proc. 15, 1078. 



