80 SCIENCE PROGRESS 



within the limits of experimental error, with the numbers 

 representing the geometrical progression. Thus Perrin con- 

 cludes that the distribution of the granules in the preparation, 

 and probably in all colloidal solutions, is such that, as 

 the height changes arithmetically, the concentration changes 

 geometrically ; in other words, the distribution is exponential. 

 If a curve be drawn, in which the abscissae represent heights 

 in the liquid and the ordinates the logarithm of the concen- 

 tration, a straight line is obtained. 



Now it is known that in a gas in equilibrium under gravity 

 a similar distribution obtains, the density varying exponentially 

 with the height. We have a familiar example in the atmosphere, 

 the density of which falls off according to the same law as 

 the height increases. Here the concentration falls to half its 

 value in a distance of 6 kilometres ; in the solution this occurs 

 for a change of level of only o'l mm. The distribution in this 

 case is readily explained by considering the partial pressure 

 of the gaseous molecules. 



Explanation of Distribution. — Perrin explains this law of 

 distribution in a similar manner. The granules are supposed 

 identical (probably not quite correct); they are in motion, and 

 by their collisions against the walls which arrest them they 

 exert an osmotic pressure proportional to their concentration. 

 The osmotic pressure will thus vary with the height; and by 

 considering that the granules in a given small volume are kept 

 in suspension by the sum of the thrust of Archimedes, and the 

 difference of osmotic pressure on the two faces, he deduces 

 a relation giving the variation of concentration with the height. 

 In this calculation Perrin assumes that the granules behave 

 like the molecules in a perfect gas. 



He finds the relation 2-3 log n/n — mgh (1 — l /p)/k, where 

 n and n are the number of particles in unit volume at the 

 standard height, and at another height h, respectively, m is the 

 mass of a particle, p its density, g the acceleration of gravity, 

 and k is the average osmotic pressure due to each particle. 

 This would represent an exponential distribution such as is 

 found experimentally. 



So far there is a qualitative agreement between Perrin's 

 hypothesis and the experimental results. It still remains to 

 consider whether the quantitative agreement is equally good. 



It can be seen from the above relation that if the concen- 



