250 H, K. SCHACHMAN AND R. C. WILLIAMS 



where kT is the kinetic energy of the molecules, k is the Boltzniann constant 

 and T is the absolute temperature. This relation shows how the diffusion 

 coefl&cient varies with temperature. An additional term is required for 

 solutions at finite concentrations. It is customary, therefore, to perform 

 experiments at several concentrations and to obtain the diffusion coefficient 

 at infinite dilution by extrapolation. The frictional coefficient is a fimction 

 of the size, shape, permeability, and flexibility of the kinetic miit. According 

 to Stokes (1851), the frictional coefficient for rigid, spherical particles can be 

 written 



/= 67717^ (15) 



where iq is the viscosity of the solvent and r is the radius of the spherical 

 particle. Thus an evaluation of a diffusion coefficient provides a direct 

 measure of the radius of a diffusing sphere. It should be noted that radii 

 calculated in this way correspond to the hydrodynamic miit. If a virus 

 particle imbibes a large amount of water and the swollen particle acts as a 

 rigid unit, with its imbibed water immobilized, the diffusion coefficient 

 yields the radius of the hydrated unit. Comparisons of the radii derived in 

 this manner with the values from electron microscopy are to be discouraged, 

 unless special efforts are made to preserve the size and shape of the kinetic 

 units by special desiccating procedures prior to electron microscopic obser- 

 vation. For bushy stunt virus (Neurath and Cooper, 1940), southern bean 

 mosaic virus (MiUer and Price, 1946), and turnip yeUow mosaic virus 

 (Markham, 1951), all of which have been shown by electron microscopy to 

 be essentially spherical, the radii calculated from diffusion can best be 

 compared with those evaluated by low-angle X-ray scattering. 



A more general treatment of the frictional coefficient must include particles 

 of other shapes as well as spheres. For this purpose it is customary to write 



/= {IJfo)fo (16) 



where (///o) is the frictional ratio which expresses the frictional resistance 

 for ellipsoids of revolution relative to that for a sphere of the same volume, 

 and/o is the frictional coefficient for a hypothetical spherical particle of the 

 same volume as the real particle. If it is known that the macromolecule acts 

 as a rigid, anhydrous miit in solution and the molecular weight, M, is avail- 

 able from other data, the frictional ratio can be calculated from combination 

 of Equations 14, 15, and 16 with the equivalent radius, r^, being replaced 

 by {ZMVfiTTNy^^, where N is the Avogadro number. This procedure assumes 

 that the density of the particle is given by the reciprocal of the partial 

 specific volume. From the value oi fffo, the axial ratio of the ellipsoid of 

 revolution is calculated directly from hydrodynamic theories which, in 



