SIZE, SHAPE, AND HYDRATION OF VIRUSES 59 



fine slits. The scattered beam is observed through two slits which 

 can be rotated around the scatterer. The whole equipment is 

 al)out () ft in dimensions. 



Two theoretical features of the experiment need to be con- 

 sidered. At very small angles of scattering, <^, the theoretical 

 scattered intensity is /((/)), where 



/((/)) = Nn^e e"^^ (2.28) 



In this expression, A^ is the total number of particles irradiated, 

 n is the number of electrons per particle, J^ is the "radius of 

 gyration"* of the electrons in the particle, X is the X-ray wave- 

 length, and Ig is the normal scattering by a free electron. This 

 theory has been developed by Guinier (1939). A measurement of 

 /(<^), therefore, gives the value of R^. Note that this concerns 

 the electron distribution. Hence if there is any curious structural 

 distribution of phosphorus, a high-electron element, and hydro- 

 gen, a low-electron element, this should show up in the radius-of- 

 gyration measurements. So far this feature has not been exploited, 

 but it has promise. 



The second theoretical point involves larger angles, for which 

 interference from the various internal sections of the virus plays 

 a part. If the virus is spherical, the intensity has maxima and 

 minima given by the expression 



/-tTrZ) sin 6i\ iirD sin e /iirD sin dV 



/W = constX/„| = M^Dsine y "^ ( ^^'"''^ 



where /o is the intensity at zero angle, and D is the diameter 

 of the virus particle 6 is the half-angle of scattering. A more 

 elaborate expression can be derived for spheroids. 



One very important feature of this type of scattering experi- 

 ment is that the essential scattering element is the electron 

 distribution, which differs from water. Thus any hydration 



* This "radius of gyration" is taken about the center and not about an axis of 

 rotation. It is defined as R^ = Xpdvr^/Xpdv, where p is density, v is volume, and r is 

 radius, and so is formally like the mechanical radius of gyration. 



