Dynamical Theory of Diffusion for yon- Electrolytes. 781 



integral passes from to 1//3, as a passes through the 

 value /3*. 



If the aperture of LL be reduced to a narrow annulus, the 

 integral to be considered is 



Jo 

 This assumes an infinite value when a = /3f, 



If the apertures be rectangular, the integrals take still 

 simpler forms. 



LXXV. A Dynamical Theory of Diffusion for Non-Electro- 

 lytes and the Molecular Mass of Albumin. By William 

 Sutherland %. 



IX a paper communicated to the Australian Association for 

 the Advancement of Scienee at Dunedin, 190-1, on the 

 Measurement of Large Molecular Masses, a purely 

 dynamical theory of diffusion was outlined, with the aim of 

 getting a formula for calculating from the data of diffusion 

 those large molecular masses for which the ordinary methods 

 fail. The formula obtained made the velocity of diffusion of 

 a substance through a liquid vary inversely as the radius a of 

 its molecule and inversely as the viscosity of the liquid. On 

 applying it to the best data for coefficients of diffusion D it 

 was found that the products aD, instead of being constant, 

 diminished with increasing a in a manner which made extra- 

 polation with the formula for substances like albumin seem 

 precarious. After looking a little more closely into the 

 dynamical conditions of the problem, it seems to me that the 

 diminution of aD can be accounted for, and can be expressed 

 by an empirical formula which enables us to extrapolate with 

 confidence for a value of a for albumin, and so to assign for 

 the molecular mass of albumin a value whose accuracy 

 depends on that with which D is measured. 



The theory is very similar to that of " Ionization, Ionic 

 Velocities and Atomic Sizes" (Phil. Mag. Feb. 1902;. Let 

 a molecule of solute of radius a move with velocity V parallel 

 to an x axis through the dilute solution of viscosity rj. Then 

 the resistance F to its motion is given by Stokes's formula 



* A theorem attributed to Weber. See Gray and Matthews' ' Bessel's 

 Function?.* p. 22 



Theory of Sound,' § 203, equations (14), (16). 

 | Communicated by the Author. 



Phil. Man. S. 6. Vol. 9. No. 54. June 1905. 3 F 



