THE PHYSICAL PROPERTIES OF INFECTIVE PARTICLES 251 



effect, are extensions of Stokes' law. Tlie results of these elaborate, theo- 

 retical investigations are given in tabular form, ///„ as a function of axial 

 ratio, for prolate and oblate ellipsoids of revolution (see Table I). 



Most macromolecules in solution are solvated to some extent and there 

 is generally some interaction with the solvent; for them, calculation of the 

 equivalent radius from the molecular weight and the partial specific volume 

 is invalid. Some factor must be included so as to accomit for any swelling 

 which results from imbibing of water into the kmetic unit. Alternately, the 

 effective volume of the kmetic unit is considered as an unknown and written 

 as Vg. The former method is that suggested and used by Oncley (1941) and 

 others, while the latter is the procedure employed by Scheraga and Mandel- 

 kern (1953). According to Oncley (1941), the frictional ratio due to the 

 swelling upon hydration of the macromolecules can be written: 



(l + 4 



V vpJ 



vo/ hydration 



Combination of this with the previous equations relating D to f and / to 

 ifffo) gives: 



D = ^^ = (18) 



6777^(3 Flf/477iV)i/3(i -f ivIYpY'Hflf,) 



Scheraga and Mandelkern obtained a similar equation which is \\Titten: 



Both forms of Equation 18 show that the diffusion coefficient cannot be 

 interpreted in terms of an axial ratio for an ellipsoid unless the hydration 

 (or effective volume of the kinetic unit) is known. Alternatively, knowledge 

 of the shape permits a ready determination of the hydration. This dilemma 

 can be handled, in principle, by coupling diffusion measurements with other 

 hydrodynamic data like the intrinsic viscosity, since this, too, is dependent 

 upon the effective volume and shape of the hydrodynamic unit. If the theo- 

 retical expressions for the intrinsic viscosity (in units of deciliters per gram) 

 the diffusion are combined, the following expression results (Scheraga and 

 Mandelkern, 1953): 



^ ~ kf ^^^^ 



The parameter, ^, is a function only of the axial ratio for ellipsoids of revolu- 

 tion. Table I shows this relationship as calculated from the Simha equation 

 (1940) for viscosity and the Perrin equation (1936) for the frictional coeffi- 

 cient. Insertion of the measured quantities into Equation 19 gives /3 and 

 thence the axial ratio. This is the procedure suggested by Scheraga and 



