614 The Earl of Berkeley and Dr. C. Y. Burton on 



For airy values of m x and m 2 attained in diffusion experi- 

 ments (with a reservation to be explained immediately), we 

 may regard F x as proportional to m x (and therefore F 2 to m 2 ) 

 to a high order of accuracy, and may write 



Fi = hm-iy F 3 = —hm 1 = km 2 , 



where k is independent of m, but depends on the nature of 

 solute and solvent and on the temperature, as well as on the 

 concentration and hydrostatic pressure at the point considered. 

 We may call k the " internal viscosity," and for very dilute 

 solutions it becomes proportional to the molecular viscosity 

 as ordinarily defined. 



The reservation made in the last paragraph refers to 

 the case where two portions of solution differing finitely in 

 concentration are in immediate contact. Our elementary 

 theory would indicate, initially, an infinite rate of diffusion 

 across the interface ; but the circumstances are not com- 

 pletely realizable even in imagination, when the discrete 

 structure of liquids is taken into account ; and the nearest 

 imaginable approach to discontinuity of concentration would 

 take us far from our original assumption, namely, that a 

 volume element anywhere in the system may be taken small 

 enough for its content to be treated as of uniform concen- 

 tration, without reduction to dimensions so minute that the 

 aggregate of molecules can no longer be treated statistically. 



Appendix 1. 



Consider the annexed diagram, which represents a solution 

 under an external pressure^ separated from the solvent which 

 is under an external pressure c/=p — P, by a semi-permeable 

 membrane, and let there be osmotic equilibrium. 



Fisr. 8. 



J 9 



Solution, 

 Mccss-M 



Solvent 



°f 



Mass -M 



r^ P -p 



Let there be M grams of solution containing c 2 grams of 

 solute per gram. Let there be M grains of solvent, and let 

 the specific volumes of solution and solvent be w and u 

 respectively. 



Carry out the following isothermal thermodynamic cycle. 



