326 Scientific Proceedings, lioyal Dublin Society. 
produce flocculation, but flocculation stops the pedetic motion of 
the majority of the particles. 
On the basis that in order to produce the aggregation of 
colloidal particles a certain minimum electric charge has to be 
brought within reach of the colloidal groups, and that the con- 
junction of ions necessary to supply this charge must occur with 
a certain minimum frequency throughout the solution; and, 
further, that the electric charge on the ion is proportional to its 
valency, Whetham!' arrives at the expression for the relative 
coagulative powers of equivalent solutions of monovalent, divalent, 
and trivalent solutions 
JD. 8 (Oy 8 fn SIL 8 OS &- 
From this it follows that the coagulative powers rise rapidly 
with the valency. If, for instance, in order to compare the for- 
mula with the experiments of Linder and Picton,’ x is put equal 32, 
then the rise with the valency is given by the series 1 : 382 : 1028. 
This series involves the principle that the probability of an ion 
being within effective reach of a fixed point is expressed by a 
fraction having the volume of “the ionic sphere of influence ”’ as 
nominator, and the entire volume of the liquid as denominatoy, 
certainty being expressed in this case by unity. Then for” ions 
the probability of conjunction is the product of the separate chances 
n times, or is given by (AQ)” where A is a constant and C the 
concentration. | 
This theoretical consideration appears, judging from the 
numerical agreement with experiments, to afford legitimate 
grounds for believing that its physical postulates are approxima. 
tions to the truth; that, in short, such a minimum electric charge 
is required to bring about coagulation, and also that this charge 
is only attained in the case of the very small colloidal particles by 
the haphazard conjunction of ions in themselves not competent to 
effect the coagulative change. What this charge may be, we 
cannot now do more than guess. If the double-electric layer of 
Helmholtz and Quincke, the existence of which appears involved 
in the explanation of electric endosmose and the electric phenomena | 
1 Phil. Mag., v. 48, 1899, p. 74. 
* Chemical Soc. Journ., vol. 67, 1895, p. 63. 
