330 



ANDREWS 



ART. I 



convenient to modify equation (4) slightly. Since the osmotic 

 pressure p will be related to the number of particles per 

 cu. cm n by 



RT 



(5) 



in which N is Avogadro's number, we may substitute n for p, 

 and no for po- We must also bear in mind that in this case the 

 force of gravity enters because of the difference in density of 

 the particles and the solvent. The depressant force will 

 therefore be not Mg but f irr^Nipp - Ps)g, where r is the ra- 

 dius of the particle and Pp and p<, the densities of the particle 



TABLE I 



Sedimentation Equilibrium in a Gamboge Suspension 



and solvent. Equation (4) then becomes 



N 4 



n = noe "^ ^ • vo; 



Table I shows the variation in the number of particles over a 

 microscopic range as determined by actual counting and as 

 calculated from equation (6). Westgren^ made similar 

 measurements with gold sols and obtained even better agree- 

 ment. His results are given in Table II. 



It is evident from an examination of the derivation of equa- 

 tions [233] and (4) that the force involved does not neces- 

 sarily have to be that of gravity. A system of particles acting 

 under any uniform field of force will obey the same laws. For 

 example, the distribution of particles under a centrifugal force 

 provides a means of studying this sort of phenomenon. 



