THE PHYSICAL PROPERTIES OF INFECTIVE PARTICLES 279 



measuring the scattering envelope over a range of 6 and by noting the 

 positions of the maxima and minima, one can calculate the particle radius, a. 



Since there are two equations relating to a, it is possible to estimate 

 whether or not an assumption of sphericity is valid. From Equation 34 a 

 value of R is directly obtained, from which a can be calculated on the 

 assumption that the scattering particles are spherical. If this value of a 

 agrees with that obtained from the positions of the maxima and minima by 

 use of Equation 35, the assumption is likely to be valid. 



The radius of particles calculated from low-angle X-ray scattering is that 

 dimension within which the electron density is, on the average, larger than 

 that of water. If a virus particle contains water of internal hydration its 

 calculated radius will include the resulting enlargement of the particle. A 

 shell of external hydration wiU not show as an increased a, since any water 

 bound to the surface of the particle wiU have the same X-ray scattering 

 power as will the general aqueous environment. An interesting case is en- 

 countered when the particle is a spherical shell, believed to be the form of 

 turnip yellow mosiac virus. The shape of the scattering curve is then very 

 nearly like that of a solidly spherical particle of the same diameter, but the 

 maximum and minimum points are shifted in a direction that would corres- 

 pond to a larger particle. This is in accord with the relation between the 

 outer radius and the radius of gyration of a shell; these radii are more nearly 

 equal for a shell than for the case of a solid sphere. 



Low-angle X-ray scattering, like light scattering, can be affected by high 

 concentrations of solute molecules. Since the wavelengths are much shorter, 

 however, considerably higher concentrations can be tolerated before inter- 

 particle interference effects become appreciable. But interaction phenomena, 

 such as aggregation and orientation of the particles, raise equally serious 

 problems of interpretation. In these cases it is necessary to plot measured 

 scattering intensities as a function of concentration and extrapolate to zero 

 concentration. 



3. X-ray Diffraction 



Some of the smaller, spherical viruses have been found to be crystalhzable, 

 i.e., to form into fuUy ordered, three-dimensional arrays. Tobacco mosaic 

 virus, which is rod-shaped, has not been fuUy crystallized in vitro but it can 

 be oriented into a paracrystalline array in which all rods are parallel and 

 equidistant. In both kinds of crystals the internal orderly arrangement of 

 the virus particles has made it possible for the methods of X-ray analysis to 

 be used to disclose certain aspects of their structures (see review by Low, 1953). 



a. The Simple Lattice. A crystal is characterized by having within itself a 

 regular, repeating three-dimensional pattern of particles, such as molecules 

 or atoms. If the crystal is illuminated with X-rays, each atom wiU act as a 



