﻿Distribution of Particles in Colloidal Suspensions. 649 



for speculation. A sugar molecule is tied in a more or less 

 rigid way with at most a single layer of water molecules*. 

 Molecules, however, attract one another with forces which 

 vary according to a high power of their distance apart. 

 But the very large particles of gamboge have a far greater 

 range of action. Large masses attract according to the law 

 of gravitation. The particles in question may be assumed to 

 attract molecules of water with a force varying according 

 to some intermediate law, and have in consequence an inter- 

 mediate range of action. Thus they can form a loose com- 

 bination with comparatively large masses of water, each 

 such agregate moving as a single molecule, so far as kinetic 

 theory is concerned. Hence the large value of b, which is 

 determined by the mean radius at which such units bounce 

 off one another. 



Nothing that is said here must be taken as excluding the 

 action of other intermoleeular forces besides those concerned 

 with collisions. If analogy with a van der Waals' substance 

 is made use of, the osmotic pressure could be written 



p -+- an 2 = nrT/(l — bn), 



where it may be left an open question as to whether a is 

 positive (attraction) or negative (repulsion). 

 The equation for dnjdy then becomes 



hence 



dn f 1 2a"1 ^ 



dy \ w(l - hi) 2 ~~ rfj = ; 



i n , 1 2an xr A 



°l — un 1 — on ri 



The limiting volume of n is still determined, not by a, but 

 by b, and this is so whether a is positive or negative. 



Further light is thrown upon the phenomenon by taking 

 suspensions of various limiting concentrations. In fig. 3 

 .are shown experimental curves for two cases; in curve 2 the 

 limiting concentration (i. e., the concentration in all except 

 the upper layers) is twice the value tor curve 1. Hence, 

 according to the equation given, the value of b in the latter 

 (i. e., the dilute solution) is twice the value it has for the 

 stronger solution. This, again, is quite in accordance with 

 the behaviour of sugar, for which substance more molecules 

 of water were found to be attached to each molecule of 

 sugar in the case of a dilute solution than in the case of a 

 strong one. 



* Porter, loc. cit. 



