44 THE PHYSICS OP VIRUSES 



of hydrodyiiamic equations and so can be handled mathe- 

 matically. The application of these results to diffusion was made 

 by Herzog, Illig, and Kudar (1934) and F. Perrin (1936). Their 

 results are equivalent and lead to the expressions below. The 

 ratio of the diffusion constant D, for an ellipsoid of revolution 

 (semi-axis of revolution of length a, the other, h) to that, Dq, 

 for a sphere of the same mass and volume is 



D Vl - {b/aY 



Do /h\\ /I + Vl - {b/ay 



:;)"'"( 



(^2.25) 



b/a 



for prolate ellipsoids, and 



D /b 



.(I 



arc tan \/{b/ay - 1 



(^2.^26) 



for oblate ellipsoids. We can consider these as measurements 

 of the ratio ///o, where / and fo are the frictional constants for 

 ellipsoids and spheres. 



The extension of this idea to the calculation of the viscosity 

 is much harder. Guth (1936) and Simha (1940) have derived 

 expressions for the viscosity of solutions of prolate and oblate 

 particles. These are not as firmly established as the Einstein 

 equation but they represent the best available. The relations 

 express viscosity in terms of concentration and the force con- 

 stant for the particular shape, which can accordingly be found. 

 The shape is, however, only determined as far as the ratio to 

 spherical is concerned, and this depends on the true mass of the 

 hydrated particle. There is thus no clear separation of hydration 

 and shape. 



Now, in the measurement of / from diffusion studies, it will 

 be remembered that the viscous-drag term corresponds to what- 

 ever actual particle is being pushed through the medium. If some 

 water is bound to the particle and changes its radius or surface, 

 this must be included. So the measurement of /by the diffusion 

 measurement will not yield b/a unless the proper hydrated 



