THE PROBLEMS OF SOLUTION 119 



Let us suppose that, in order to produce the 

 aggregation of colloidal particles which constitute 

 coagulation, a certain minimum electric charge has 

 to be brought within reach of a colloidal group, 

 and that such conjunctions must occur with a 

 certain minimum frequency throughout the solu- 

 tion. Since the electric charge on an ion is 

 proportional to its valency, we shall get equal 

 charges by the conjunction of 211 triads, 37^ diads, 

 or 6n monads, where n is any whole number. 



The chance conjunctions of a large number 

 of particles moving like the ions of an electrolytic 

 solution can be investigated by the principles of 

 the kinetic theory of gases. If ifx denote the 

 chance of one ion colliding with a colloidal particle, 

 the chance that two ions should collide with it is 

 the product of their separate chances, or \\x^, and 

 so on. When applied to the case in hand, these 

 principles lead to the conclusion that the relative 

 coagulative powers of univalent, divalent, and 

 trivalent ions will be proportional to the ratios 

 I \ n \ n^. The value of n, which depends on a 

 number of unknown factors, remains arbitrary. 

 If we assume that n is 32, n^ is 1024, and we get 

 the numbers i : 32 : 1024 to compare with the 

 experimental values of the relative coagulative 

 powers I : 35 : 1023. 



This theoryis, of course, only a first approxima- 

 tion. It takes no account of the action of the other 

 ion, or of differences in the effect of different ions 

 of the same valency. Experiments by Oden on 

 colloidal sulphur show these differences to a degree 

 that in some instances masks the effect of valency. 

 Butthisextremespecific effecthas not been found in 

 any other case, and it seems that the simple theory 



