﻿Distribution of Particles in Colloidal Suspensions. G47 



Writing this in the form Adn = n(C— *Bn)dh, and solving, 



he gets 



C 

 "~~B + K*- CAA ' 



in which K = (0— Bn () )/n and n is the concentration when 

 7i = 0. To obtain Perrin's formula B must be put equal to 

 zero. The ratio VjA can therefore be obtained from Perrin's 

 experiments. Calculation shows that e~ Ch/A tends rapidly to 

 zero. as h increases, and ultimately n becomes 



_ C _ V(d-w)g 

 ?l -~B~ " ke 2 ' 



The depth at which this uniform concentration is practi- 

 cally attained will depend upon the relative values of K and 

 B ; it will be nearer the surface the larger the electrical 

 forces are compared with the gravitational. 



Now there are serious objections to the theory as thus 

 stated. 



In the first place, if the particles really contained charges 

 all of one sign only they would tend to move toward the 

 boundary. This is the equivalent of the fundamental 

 electrical fact that statical charges reside close to the surface 

 of conductors. When we are dealing with large particles 

 instead of electrons, there is no doubt that they would occupy 

 a larger region, instead of a thin superficial area, but still 

 there would be an accumulation at the boundary. This is the 

 opposite to what is observed. 



Bat the charges in the solution are not only of one sign. 

 The solution, as a whole, is uncharged ; consequently an equal 

 opposite charge is to be looked for. This opposite charge is 

 the second member of the double layer close to the surface 

 of each particle. When the existence of this double layer 

 is recognized, the electric forces between the particles become 

 zero, except in so far as relative displacement takes place by 

 induction between two members of a layer so as to give it an 

 electrical movement. In this case the force between two 

 such doublets in the equilibrium state will, on the average, 

 be an attraction and not a repulsion. 



Now Ave have fitted a curve calculated from Burton's 

 equation to the experimental points. They are shown by 

 large circles on the figure and are seen to fit the experiments 

 remarkably well. In view of the above objections to the 



