﻿Distribution of Particles in Colloidal Suspensions. 645 



If we assume that there is no contraction when gamboge 

 and water are intermingled 



cr = cy-h (1 — c)u and s=u, 



where y = density of solid gamboge. Hence 



a — s = c(y — u) = nm(ry — u) . 



Further writing K= ^ "^T 



±i l ir 



and, putting cr in denominator as equal to u [which is justi- 

 fiable, because even the strongest suspensions of gamboge 

 are fairly dilute] , 



^=Ktt(l-6>n) 2 - 

 dy 



The integral of this equation is 



where A is the constant of integration which can be expressed 

 in terms of (the unknown) concentration when 7 = 0. This 

 is a curve which tends asymptotically for large values of 7 

 to the value n w = l/b ; and which has a point of inflexion for 



A curve of this kind can be fitted to the experimental 

 curve within the limits of experimental accuracy (fig. 2). 

 The following values are obtained by taking 



5 = 10-2 xlO" 8 cm. 3 and K=121 :— 



y (in cms.) -024 "032 "0375 "047 '061 -089 115 



wxlu- 6 12 3 5 7 9 9-7 



A closer fit could, of course, be obtained by allowing b to 

 vary with the concentration, as was done in examining the 

 osmotic pressure of sugar solutions *. It is difficult, however, 

 in the present problem, to give anything but an empirical 

 significance to this constant. It enters into the osmotic 

 pressure in the same way as the least volume of the liquid 

 enters into the gas equation. But in this case it would 

 mean that even in the fairly dilute concentrated suspension of 

 gamboge the effective volume of the particles is the volume 

 of the solution itself — that is to say, that the suspensoid 



* Porter, loc. cit. 



