18 VIRUSES 



^c=eijnj,-me) (1) 



rr=vf (2) 



Fq=Fj, when the particle moves along at a uniform rate. 

 Therefore, ▼f=g(mp-mB) (3) 



Hence, _ g(mp-mB) = ^*x(mp-mg) (4) 



'^~ f f 



The symbols o) and x represent the angular velocity of the centrifuge and the 

 distance of the particle from the axis of rotation, respectively. This equation 

 can be simplified if the particles are unhydrated spheres, for Stoke's law 

 states that f = 6lrri^ , where r is the radius and /7f is the coefficient of 

 viscosity. Also, for a sphere mp = 4/3Krr'dp and mg = 4/3wr'd8, where mp and 

 fflg represent the masses, smd dp and dg the densities of the par- 

 ticles and the displaced solvent, respectively. 



Therefore, for a spherical particle with radius r, 



T= ^'^ (4/3'gr'dp - 4/3iTr*da) or 

 6trr^ 



^ 2/9 (o'^x r^idp-da) (5) 



V 



Most Investigators reporting sedimentation studies talk about sedimentation 

 constants. This latter is defined as the sedimentation rate in unit centrifugal 

 field and is designated as 



S = jr_ = ar^Cdp-dg) 



UJ* 9'*! (6) 



In a centrifugatlon experiment. If all of the particles move at about the same 

 rate, a boundary between solvent and solution is formed, which moves at the 

 rate of each particle. As was seen previously, the ideal boundary would be an 

 Infinitely sharp one, but in practice more or less fuzzy ones are always obtain- 

 ed. Figure 9 shows graphic6illy the sedlmenting boundary at various times in an 

 experiment on bushy stunt virus. The position of the center of the curves tells 

 us how foggy it is. Prom the rate of displacement of this boundary in a known 

 centrifugal field, the sedimentation constant of bushy stunt virus can be cal- 

 culated. It is, on the average, I32 x 10"13 cm. /sec. in unit field. 



If it is assiuned that the particles are unhydrated spheres, one cam com- 

 pute their size directly by substituting this sedimentation constant in 

 equation (6J. The only additional information needed is the viscosity of the 

 solvent and the densities of the solvent and the particles. The first two 

 quantities can be measured directly and the third can be computed from the den- 

 sity of a solution of known composition. Ordinarily one speaks in terms of the 

 partial specific volume of a virus particle, this Is essentially the recipro- 

 cal of the anhydrous density. licParlane and Kekwick determined the partial 

 specific volume of the particles to be 0.74 . This corresponds to a density 

 of 1.36 . Prom these data the radius can be obtained. Then, from the radius, 

 it is a simple matter to compute the molecular weight. Calculated in this man- 

 ner, the molecular weight is 7 .4 x 10 . The size of a spherical particle can 

 also be obtained from diffusion data. According to the Einstein-Sutherland 

 equation. 



