JOHN H. NORTHROP . 783 



It may be seen from the foregoing brief description that the phenomenon can be 

 divided into two distinct steps: first, the collection of the small particles into larger 

 aggregates; and, second, the settling of these aggregates to the bottom of the vessel. 

 In regard to the latter effect, the small and large particles differ from each other both 

 in the rate of settling and in the final condition of equilibrium, although under ordinary 

 conditions the difference in the rate is of the greater significance. 



EFFECT OF THE SIZE OF PARTICLES ON THE RATE OF SETTLING 



The formula for the steady rate of fall of a small body in a viscous medium was 

 given by Stokes as 



^a^ (D-d) s 



V=^ (I) 



2 



where a is the radius, D the density of the particle, d the density of the solution, z the 

 viscosity of the solution, and g the acceleration due to gravity. This formula was 

 tested by Perrin' for small particles by comparing the radius calculated from the rate 

 of fall with that determined by direct measurement or calculated from the weight and 

 size. 



RADIUS IN H DETERMINED BY 



Direct Measurement Weighing From Stokes's Law 



0.371 0.3667 0.3675 



The experiment shows that the particles obey Stokes's law with the greatest exact- 

 ness. This result is of special importance, since the validity of Stokes's law is assumed 

 in all calculations concerning the Brownian movement. It follows, therefore, that the 

 speed of settling of different size particles, other conditions being the same, will in- 

 crease with the square of the radius and the difference in rate between visible and 

 microscopic particles will be enormous. In Perrin 's experiments the rate was a few 

 millimeters a day. 



EFFECT OF THE SIZE OF PARTICLES ON THE FINAL EQUILIBRIUM 



The English botanist, Brown, noted that pollen grains as seen under the micro- 

 scope possessed rapid irregular movements. This peculiar constant motion has be- 

 come known as the "Brownian movement." It was soon found that the motion was 

 independent of the nature of the particles and could not be ascribed to any outside 

 influence. It is less in viscous liquids and very rapid in gases. The motion is less in 

 large particles. It follows from the doctrine of equipartition of energy that the mean 

 kinetic energy (| mv^) of the particles must remain constant. The velocity decreases, 

 therefore, as the size increases.^ Svedberg has shown that it is not affected by the po- 

 tential of the particle nor by the addition of electrolytes.^ It was suggested by Wiener 



' Perrin, J.: Die Atome, p. 90. Dresden, 1914. 



* Lewis, W. C. McC: A System of Physical Chemistry, Vol. i, chap. i. London, New York, 

 Bombay, Calcutta, and Madras, 1920. 



3 For a thorough discussion of the Brownian movement, see Burton, E. F.: op. cit., p. 50; Perrin, 

 J.: op. cit., p. 83. Dresden, 1914; Freundlich, H.: op. cit., p. 469. Leipzig, 1922. 



