782 Mr. W. Sutherland on a Dynamical Theory 



where ft is the coefficient of sliding friction if there is slip 

 between the diffusing molecule and the solution. For N 

 molecules of solute per c.c. of solution the total resistance 

 win be N times this, and in the steady state of diffusion will 

 equilibrate the driving force due to variation of the osmotic 

 pressure of the solute, namely dp/ da, which by the osmotic 

 laws is JiTdc/dx, if c is the concentration of the solute at 

 x and R is the gas constant. Hence 



r 4:=^Hw:= • • • <» 



and the required formula for the coefficient of diffusion with 

 C for the number of molecules in a gramme-molecule is 



_ RT l + 3V/3a 



GTrrjaQ l + 2 v /pa w 



If /3 = oo , that is, if there is no slipping of solution at surface 

 of molecule, aD is the same for all molecules diffusing through 

 a given solvent at a given temperature. Now for a Lirge 

 molecule of solute moving amongst smaller ones of solvent, 

 we can see that the slipping is probably small. But in the 

 other extreme case of a small molecule of solute moving 

 amongst larger ones of solvent, an effect analogous to slipping 

 will occur, since the small molecule will travel a good deal in 

 the gaps which would be left if the molecules of solvent were 

 forced almost into permanent contact. We have thus two 

 extreme cases of the formula. 



RT 



When £=0, D = 





and when /3= x> , D = - 



4:7T7jaC I 

 RT 



(4) 



67T7}aC 



Thus with increasing values of a we should have aD 

 diminishing from the upper limit RT/47r?;0, when a is small, 

 to the lower limit RT/67r??C, when a is large. This is 

 analogous to the actual behaviour of B^D obtained from 

 experiment, B being the volume of the molecules in a gramme- 

 molecule of solute. The first of the following tables contains 

 the coefficients of diffusion for various gases through water 

 determined by Hiifner *. I have reduced these all to a tem- 

 perature of 16° C, and expressed them with the second as unit 

 of time instead of the day. The values of B are taken mostly 

 from "Further Studies on Molecular Force" (Phil. Mag. [6] 

 xxxix.). In the second last row are given the values of 



* Wied. Ann. 1897, vol. xl., and Zeit.f. Fhys. Chem. xxvii. 



