THE PHYSICAL PROPERTIES OF INFECTIVE PARTICLES 237 



BroMaiian motion. Less well-known, although described in 1909 (Pcrrin, 

 1909), is the rapid rotational motion during the course of which an individual 

 particle is exposed to various orientations relative to a fixed direction. If a 

 given particle is observed over a long time period, the average angular dis- 

 placement per unit time can be evaluated, and from this the rotational 

 diffusion coefficient is determined. This is, of course, directly analogous to 

 the determmation of the translational diffusion coefficient by measurement 

 of the displacement of a particle with time. In both cases it is the average 

 of the squares of the displacement, translational or rotational, that leads to 

 a diffusion coefficient. Observation of a given particle during either its trans- 

 lational or rotational motion is very tedious and, in fact, is not feasible for 

 particles as small as many viruses. Therefore, alternative methods are 

 mandatory if such motions are to be followed experimentally. For both 

 types of movements, techniques have now been developed whereby some 

 property of the system which is readily measurable in quantitative terms is 

 used in an indirect way to provide details about the motion of the solute 

 molecules. Just as the number of molecules in a given volume element is 

 termed the concentration, so we can express the angular concentration as a 

 representation of the number (or weight) of particles having a fixed orienta- 

 tion relative to certain coordinates. If all of the particles were oriented by 

 some device and the restraining force were suddenly removed, the ensuing 

 Brownian motion would lead quickly to a state in which the various orienta- 

 tions among the many molecules would be completely random. The mole- 

 cules would continue, of course, to rotate vigorously after the random 

 condition had been achieved; but such motions then would be difficult to 

 detect. On the other hand, the motion immediately after the release of the 

 restraint might be followed by investigating some property that is a function 

 of the degree of orientation of macromolecules. From measurement of the 

 rate of decay of that property, a rotational diffusion coefficient can be 

 determined. The driving force for the rotational motion is thermal energy 

 usually expressed as kT, where k is the Boltzmami constant and T is the 

 absolute temperature. Opposing the rotational motion is the viscous drag 

 of the liquid; this resistance to motion is usually expressed in terms of a 

 rotary frictional coefficient. By means of the same type of hydrodynamic 

 treatment employed in the interpretation of the viscosity of solutions, the 

 frictional coefficients can be expressed, for example, in terms of the size and 

 shape of rigid ellipsoids. For very elongated particles the diffusion coefficient 

 for rotation about the short axis is inversely proportional to the third power 

 of the length of the long axis. Therefore the study of rotational diffusion 

 constitutes a powerful and sensitive method for the examination of the 

 length (and homogeneity with regard to length) of elongated macromolecules. 

 Workers in this field are confronted with the same dilemma facing those 



