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LVI. The Law of Distribution of Particles in Colloidal 

 Suspensions, with Special Reference to Perrin s Investi- 

 gations. By Alfred W . Porter, D.Sc, F.R.S., F. Inst.P., 

 President of the Faraday Society, and J. J. Hedges, 

 B.Sc* 



IN the Proceedings of the Royal Society for January last 

 (A, vol. 100, No. 705) E. F. Burton criticises Perrin's 

 work on the law of distribution of particles in colloidal 

 solutions. In the course of his work Perrin shows that, at 

 any rate when the solution is dilute, we should expect a law 

 of distribution of the particles analogous to that which 

 characterises the distribution of the molecules in an 

 atmosphere. By balancing the osmotic pressure of the 

 particles against the effect of gravity he deduces the 

 equation 



^-log e ^ =V(pi-p2)g(h-h), 



where n and n are the numbers of particles present per unit 

 volume (i. e., the numerical concentration) at depths h and A , 

 V is the volume of each particle, p Y and p 2 the densities of 

 the material of the particles and of the medium respectively. 

 Experimentally, for example, Perrin obtains for particles of 

 gamboge, 2*12 x 10~ 5 cm. diameter, the number of particles 

 at four depths differing successively by 3 X 10" 3 cm. and 

 finds values proportional to the numbers 12, 22*6, 47, and 

 100, which numbers are almost in the same proportion as the 

 members of the geometric progression 11*1, 23, 48, 100. 

 Burton's criticism amounts to saying that if this law of 

 doubling continued as the depth increases then at 3 cms. 

 depth the concentration should become 2 1000 times the first 

 value given (viz., 12). Now this ratio is a number containing 

 more than 300 digits ; and even casual observation shows 

 that no such increase occurs. In fact, Burton makes experi- 

 ments to show that throughout most of a tall column of 

 suspensoid there is no sensible change in the concentration. 



Perrin's own observations were confined to very small 

 ranges near the top of the suspensoid where the concentration 

 was very small, in order that his theoretical and experimental 

 work might correspond to one another. He says in " Les 

 Atomes/' § 61, " Ce n'est pas sur une hauteur de quelques 

 centimetres ou meme de quelques millimetres, mais sur des 



* Communicated by the Authors. A paper read before the Faraday 

 Society, Monday, June 26th, 1922. 



PHI. Mag. S. 6. Vol. 44. No. 261. Sept. 1922. 2 T 



