THE PHYSICAL PROPERTIES OF INFECTIVE PARTICLES 259 



to the equation of Scheraga and Mandelkern (1953), to calculate the para- 

 meter, jS. From ^ the shape and volume of the equivalent ellipsoid are 

 evaluated in the manner described earlier. 



M2'3(l - Vp) 



Use of the procedure suggested by Oncley (1941), who considered the ob- 

 served frictional ratio, ///<„ as the product of two terms, one for solvation 

 and one for shape, is facihtated by contour diagrams showing the various 

 combinations of hydration and shape compatible with any single value of 

 flfg. These contour diagrams are simultaneous plots of Equation 17 and the 

 Perrin equation. Again it should be noted that ^ is insensitive to shape for 

 globular materials; therefore molecular weights can be calculated from [17] 

 and s according to Equation 24. 



in. Partial Specific Volume. In all ultracentrifugal methods the term, 

 (1 — Vp), appears as one of the important factors. Since the partial specific 

 volume of viruses is about 0.70 ml./gm. (slight variations occur depending 

 upon the composition), errors in the determination of V are effectively 

 doubled in the calculation of molecular weights. It is imperative, therefore, 

 that this quantity should be evaluated with great precision. There are, in 

 effect, three different ways of determining the partial specific volume, 

 defined as the increase in volume of an infinite amount of solution caused by 

 the addition of one gram of solute. 



First of these is the classic method which mvolves a series of density 

 measurements on solutions of varying concentrations and the solvent (Lewis 

 and Randall, 1923). From the density of each solution paired with the value 

 for the solvent, the apparent specific volume is calculated (this assumes 

 additivity of the volumes and weights of the solvent and the solute). Almost 

 invariably for macromolecules of the size of viruses the apparent specific 

 volume is independent of concentration, and the average of the individual 

 values is taken as the partial specific volume. More elaborate treatments are 

 required if the apparent specific volume is dependent on concentration. 

 There are many different methods for the density measurements, and a 

 choice among them is dictated mainly by the availability of material. Often 

 the limited amounts of the substance preclude the use of techniques involv- 

 ing pycnometers, and the density gradient column of Linderstrom-Lang and 

 Lanz (1938) is recommended. It is important to note that the density differ- 

 ence between the solution and solvent is very small (about 0.003 gm./ml. for 

 a 1 % solution). Measurements of high precision are therefore mandatory. 

 The computation of the partial specific volume involves knowledge of the 

 concentration. Because this is invariably determined on the basis of the dry 

 weight, the molecular weight refers to the anhydrous material. If the viruses 



