THE SIZE AND SHAPE OP 7IRU8ES 



23 



diffusion measurements, and the Einstein-Sutherland equation (7), one obtains 

 the true friction coefficient of a particle, and with this value and the value 

 for the friction ratio, one can compute the friction ratio the particle would 

 have if it were an unhydrated sphere. Then, by using Stoke *s law, one can get 

 the radius this particle would have if it were a sphere and from that and the 

 partial specific volume, the molecular weight. Knowing the molecular weight 

 In addition to the shape as determined by viscosity, one can calculate the 

 actual dimension of the particle, 'ilais computation gives us the molecular 

 weight and the particle dimension from diffusion and viscosity data tsUcen in 

 conjunction with the partial specific volume. With known values for the frict- 

 ion ratio and the partial specific volume, one can also determine the molecular 

 weight and particle dimensions from sedimentation and partial specific volume 

 data. The sedimentation rate depends upon the particle mass and upon the co- 

 efficient of friction, as may be seen in equation (4). It is already known for 

 the tobacco mosaic virus that the true coefficient of friction is equal to just 

 twice the coefficient of friction of the hypothetical sphere. Thus, one can 

 substitute into the sedimentation equation (4) for the value of the true co- 

 efficient of friction, twice the value it would be if the particle were an un- 

 hydrated sphere. This latter coefficient of friction is known by Stoke 's law 

 to be a function of the rsulius the particle would have if it were a sphere. The 

 mass of the particle is a function of the radius and the known partial specific 

 volume. Therefore, through the use of an equation similar to 15)» it is pos- 

 sible to solve in terms of the hypothetical particle radius. Ji'rom this value 

 it is simple to calculate the molecular weight. Here again the actual dimen- 

 sions of the particle can be settled by solid geometry. We have here, then, a 

 method of determining the dimensions of a particle from i>artial specific volume, 

 viscosity and sedimentation. 



In Table III, the results of all these methods are presented along with 

 the values obtained directly with the electron microscope and X-ray diffraction. 



TABLE III 

 THE DIMENSIOITS OF TOBACCO MOSAIC VIRUS PARTICLES 



Methods 



Diameter 



Length 



Mol.Wt. 

 (x 10-7) 



Sedimentation and viscosity 13 .6 



Sedimentation and diffusion I3.8 



Viscosity and diffusion 14.0 



Electron microscope and X-ray 15*2 



276 



256 

 283 



270 



3.32 

 3.16 

 3.60 

 4.0 



It csm be seen that, allowing a reasonable margin of error, all of the methods 

 give essentially the same value for the length and thickness of the tobacco 

 mosaic virus particle, and these values agree with those obtained by direct 

 methods. All of these considerations are complicated, however, by the neces- 

 sity of assuming the absence of hydration. Preliminary evidence recently ob- 

 tained by the author and associates makes it appear quite likely that tobacco 

 mosaic virus is hydrated to at least the extent of other viruses which have 

 been studied. The X-ray data of Bernal and Fankuchen show that the distance 

 between tobacco mosaic virus rods oriented parallel in a gel varies exactly 

 with the reciprocal of the square root of the virus concentration. This result 



