22 



VIRUSES 



the ratio of the length of the long semi-axis to that of the short semi-axis 

 from the friction ratio. Jfor a rod-like ellipsoid of revolution, this is ap- 

 proximately the equivalent of the ratio of length to diameter. When the 

 friction ratio of tobacco mosaic virus, 2.0, is substituted into the equation 

 obtained for rod-like particles, one obtains a value of 18.6 for the ratio of 

 length to thickness. The molecular volvune of the tobacco mosaic virus parti- 

 cle is already known. Therefore, since we know the ratio of length to thick- 

 ness and the volume, it is a simple problem in solid geometry to calculate 

 the actual dimensions of the virus particle. Values of 2^6 millimicrons for 

 the length and I3.8 millimicrons for the thickness are obtained. 



According to recent theories also developed from hydrodynaraic consider- 

 ations, it is possible to determine the shape of suspended particles from 

 measurements of the intrinsic viscosities of solutions of those particles. The 

 intrinsic viscosity is a measure of the increase in relative viscosity impart- 

 ed to a solution by dissolving unit volume of a solute. Several such theo- 

 retical developments are summarized in Figure 17. 



Hf 



10 



20 30 



40 50 60 

 AXIAL RATIO 



70 80 



90 



100 



B-IGUSE 17 - GRAPHICAL REPRESENTATION OP SEVERAL THEORETICAL 

 RELATIONSHIPS BETWEEN INTRINSIC VISCOSITY AND THE SHAPE OF 

 SUSPENDED PARTICLES. (li.A.Laiif fer, Chem. Rev. 3I, 56I (1942) ;. 



It seems, at present, that the most adequate treatment is that of Onsager and 

 of Slmha. The intrinsic viscosity of the tobacco mosaic virus solution was 

 found to be 39. If it is assumed that this virus particle is unhydrated and 

 that the treatment of Onsager and of Simha is adequate, one can calculate a 

 ratio of length to thickness for the tobacco mosaic virus particle of 20 to 1. 

 It is possible to pursue this result obtained from viscosity measurements even 

 further. Since one can compute the ratio of length to thickness of a particle 

 from the friction ratio by means of the Gana-Herzog-Perrin equation, one can 

 also do the reverse, that is, calculate the friction ratio from the ratio of 

 length to thickness of a particle. Then, when the friction ratio and the par- 

 tial specific volume are known, it is possible to determine the molecular 

 weight from either diffusion or sedimentation measurements taken singly. JTrom 



