THE PHYSICAL PROPERTIES OF INFECTIVE PARTICLES 235 



"hydration" is necessary. Hydration is customarily expressed in terms of 

 the hydrodynamic volume fraction, 0, by the following 



= Fc(l + wIVp) (7) 



where w is the number of grams of solvent of density, p, associated with 

 one gram of dry solute. Combination of this with the Einstein equation, 

 which for dilute solutions can be written 



Vsv = ^^ (8) 



gives 



[r?] = vV{l + WJVp) (9) 



In Equations (8) and (9), v is the value of the viscosity increment caused by 

 rigid particles of different axial ratios, the so-called shape factor, and it is 

 evaluated theoretically by Simha. If it is known that the particles are spheres, 

 V = 2.5 and the value of w, the hydration, is directly calculable from the 

 measured value of [tj]. Alternatively, knowledge of the hydration and the 

 measured value of [17] permits the calculation of v for the material under in- 

 vestigation. From Table I, relating the function v to axial ratio, the shape of 

 the hydrodynamic unit is determined. Since various types of data led to the 

 view that tobacco mosaic virus was only slightly hydrated, Lauffer (1938a, 

 1944a) calculated the axial ratio of the particles directly from the viscosity 

 data. 



It is clear from the above discussion that the intrinsic viscosity depends 

 on both the shape and the volume of the solute molecules and evaluation of 

 either depends on knowledge of the other. Scheraga and Mandelkern (1953) 

 considered the problem in a different way by writing the effective volume, 

 T^, of a molecule as an unknown without any reference to the partial 

 specific volume. This is no doubt a more rigorous treatment and is to be pre- 

 ferred, since the hydrodynamic volume cannot be expressed as a function of 

 the partial specific volume by any theoretical consideration. In conjunction 

 with other data, both Fe and the shape of the hydrodynamic unit can be 

 evaluated. This is treated more fully in the discussion of sedimentation and 

 diffusion. 



In the case of both PR8 influenza A virus (Lauffer and Stanley, 1944) 

 and rabbit papilloma virus (Schachman, 1951a), electron microscopic 

 evidence indicated that the virus particles were essentially spherical. In 

 principle, therefore, the viscosity data provided a value of the volume con- 

 centration. In both cases the experimental values of [17] mdicated hydrations 

 which seemed moderately large. Upon close inspection it became clear that 

 the high viscosities were attributable to small amounts of impurities which 

 were difficult to detect by other methods. The impurities were apparently 



