30 THE PHYSICS OF VIRUSES 



appears to be a centrifugal motion. The outward motion would 

 be accelerated, but the acceleration is modified by the viscosity 

 of the liquid, and so what occurs is a uniform rate of drift. This 

 rate of drift is of the right size to provide the viscous force 

 necessary to hold the particle in place, although slowly drifting. 

 Thus, in the equation describing the motion we must take 

 account of (a) the mass of the particle, (6) the density of the 

 liquid, (c) the viscous drag, and (d) the angular velocity and 

 radius. 



Doing this, we get the following expression for the force acting 

 on the particle, and which must be balanced by viscous drag 



Force = xo)^m — xccWp 



where m is the mass of the particle, V its volume, x the radius 

 from the axis of rotation, and p the density of the liquid. 



It is customary to express T^ in terms of the mass of the 

 particle and the partial specific volume, Vo- This is defined as 

 the volume increase produced in a large volume of solution by 

 1 gm of solute. When pure material is available, Vo can be found 

 by straightforward change in volume measurements. Using 

 this idea, we have V, the particle volume, = mVo- So the 

 expression for the force to be balanced becomes 



mo3^x{l — Vop) 



Now the viscous drag force is proportional to the velocity 

 of drift and can be written as / dx/dt, so that the equilibrium 

 drift will occur when 



mcolT(l - Fop) =/^' (2.10) 



dt 



This can be rewritten as 



Q dx / , m(l - Top) 



^ dt/ ""^ ^ J ^^•^^■> 



The quantity *S is called the sedimentation constant, and if 

 centimeters and seconds are the basic units, *S is around 10~^^ 

 cm/sec per unit acceleration. The value 10~^^ in such units is 

 called a Svedberg unit and is designated by S. 



