MOLECULAR MAGNITUDES 273 



cule. The factor K involves the ratio 1 of the concen- 

 trations at the two levels, and hence may be expressed 

 in terms of the number of particles in equal areas at 

 these levels. These numbers, n and n , Perrin deter- 

 mined by direct count, viewing different layers of the 

 emulsion through a microscope. 



The kinetic energy of translation, wT, may be ex- 

 pressed by using the perfect gas equation, which we 

 saw from our study of osmosis is applicable to such 

 cases. From page 218 we have w = 3R/2N. Using 

 these values of K and w in the expression of the energy 

 relations at equilibrium, gives 



(1) 



where N is the number of molecules per mole. The 

 other terms on the right-hand side of this equation are 

 known. The density, d, was easily measured. The 

 density, Z>, of the mastic Perrin determined from a 

 solid piece before forming the emulsion and checked 

 after the main experiment by evaporating the liquid 

 and measuring the density of the residue. The dis- 

 tance, h, was directly measured. There remained to 

 be determined only the radius r. The granules which 

 he used were about 2X10~ 5 cm. in diameter, much too 

 small for an accurate direct measurement. The radius 

 was obtained by making use of an equation developed 

 by Stokes which states the rate at which small spherical 



1 This factor, which is conveniently derived by using integral 

 calculus, involves the logarithm of the ratio no/n. The expression 

 is K = (2/3) log e (noAO- A "calculus dodging" derivation is given 

 by Perrin in " Les Atomes," an interesting book, published in trans- 

 lation by D. Van Nostrand Company, 1916. 

 T 



