THE PHYSICAL PROPERTIES OF INFECTIVE PARTICLES 277 



value of M will be distinctly greater than the number-average molecular 

 weight. For example, a solution containing equal numbers of tobacco mosaic 

 virus particles of molecular weights 1 X 10^ and 10 X 10' would yield a 

 value of 5.5 X 10'^ as the number-average molecular weight and a weight- 

 average molecular weight of 9.2 X 10'. 



While the methods of light scattermg yield highly reproducible results 

 under favorable conditions (dilute solutions of spherical particles that are 

 small with respect to the wavelength of light), caution is to be exercised in 

 the acceptance of results for those cases where the absolute values of M of 

 large, elongated particles have been reported. The determination of the 

 value of M depends upon an absolute determination of Rg, a quantity 

 involving the ratio of scattered to incident light intensities. The direct 

 measurement of this ratio is quite uncertain, and recourse is generally taken 

 in using other calibration methods, i.e., the relation between turbidity and 

 light scattering, as a fmiction of wavelength, for suspensions of small, 

 spherical particles such as polystyrene latex. But the most likely absolute 

 error due to calibration difficulties remains hard to assess. 



In deriving values of M from light scattering the most likely source of 

 error lies in the dnjdc term (see Equation 32), because its value is squared 

 when used in the equation. 



It is now almost universal practice to use Zimm plots in evaluating 31 

 for large, anisometric particles. Here the handlmg of the data is particularly 

 susceptible to systematic error owing to the nature of the extrapolations. It 

 is necessary to extrapolate the data to = 0° in order to determine M. 

 Unfortunately, in the region of 6 near zero, direct measurements cannot be 

 made, but it is just in this region that effects of contaminating dust and 

 large aggregates of solute particles become the greatest. A large dust particle 

 will scatter much more light in the ^ = 0° direction than in the 6 = 45° 

 direction, and an extrapolation that must go from, say, 6 = 20° to ^ = 0° is 

 inevitably hazardous. 



2. Low- Angle X-ray Scattering 



It has been seen that the methods of light scatteriiig will provide an 

 evaluation of the molecular weight of particles in suspension whether they 

 be large or small compared with the wavelength of light. However, it is to 

 be noted that the shape of the envelope of scattered intensity is quite insensi- 

 tive to particle size and shape when the particles are smaller than about 

 500A in their characteristic dimension. Many virus particles are smaller than 

 this, and if the sizes and shapes are to be determined by radiation scattering 

 it is evident that shorter wave lengths must be employed. For an object of a 

 given size the dissymmetry of the scattering envelope (which is dependent 



