SIZE, SHAPE, AND HYDRATION OF VIRUSES 41 



where cf) is the fraction of the volume occupied by the spherical 

 particles, and r] and rjo are the viscosities of the solution and the 

 medium, respectively. This method, combined with diffusion, 

 was suggested by Einstein as a method of measuring molecular 

 radii and so of obtaining Avogadro's number. In Einstein's 

 first paper, published when Avogadro's number was still in 

 process of being determined, the constant 2.5 was given as 

 unity. The resulting low values of Avogadro's number deter- 

 mined by this useful method were thought of as in reasonable 

 enough agreement. The later paper corrected the figure, and 

 accurate values of Avogadro's number resulted. 



Notice that the essential character of the study of viscosity 

 is the study of a total volume which interferes with the sliding 

 of planes of water over one another. This total volume is, of 

 course, the number of particles times the volume of each, but 

 the volume concerned is basically the volume due to each 

 particle which does not enter into slipping. So any water held 

 by the particle is to be included in the volume (j). Thus viscosity 

 measurements differ from sedimentation measurements in that, 

 although bound water can be argued as equivalent to buoyant 

 water for centrifugal action, and so not concerned in the motion, 

 there is no question of buoyant action in viscosity. So one can 

 turn a dark and a light shade of gray into black and white and 

 assert that the particle mass determined by sedimentation and 

 diffusion is the dry mass, while the volume determined by 

 viscosity is the hydrated volume. This is probably true for 

 protein molecules but is not so apt to be true where viruses of 

 complex internal morphology are concerned. Nevertheless we are 

 going to continue with the black and white idea because all 

 that can be done is to try out reasonable hypotheses in the 

 hope that a fairly large category of viruses will fit them to the 

 first approximation. From there, as measurements improve, the 

 second approximation can be made. So we point out the value 

 of viscosity studies as measuring the size of a particle which 

 fails to slip and which is, therefore, the virus plus its hydration. 



There are many ways of measuring viscosity. An absolute 

 value can be obtained by measuring streamline flow in a capillary 



