THE PHYSICAL PROPERTIES OF INFECTIVE PARTICLES 243 



absolute values for the diffusion coefficient, it is particularly valuable for the 

 virologist who can use the method for the examination of viruses which as 

 yet have not been purified. The second, more popular method of studying 

 diffusion, known as the free diffusion method, is based on another equation 

 derived by Fick and known as Fick's second law. This relates the change of 

 concentration with time to the rate at which the concentration gradient is 

 changing with position, x, in the cell. To derive this equation it is necessary 

 to formulate the so-called continuity equation, which is an expression of the 

 conservation of mass of the diffusing substance. Continuity equations are 

 basic to any theoretical consideration of experiments involving transport of 

 one component. Consider a volume element bounded by the walls of the cell 

 and two hypothetical planes separated by an infinitesimal distance. The 

 accumulation of solute within the volume element can be expressed readily 

 as the difference between the net flow of solute through the first surface and 

 that across the second plane. It is as if observers were stationed at the two 

 planes and each counted the number of molecules crossing the respective 

 planes during a given time period. Clearly any difference recorded by the 

 observers must involve an accumulation or depletion of solute within the 

 volume element, and this would be detected readily by an independent 

 observation, within the selected volume, of the concentration change with 

 time. From a mathematical statement of this principle and Equation (10), 

 Fick's second law emerges 



':=^^ (11) 



U 7)X^ 



This equation applies only to systems in which the diffusion coefficient is 

 independent of concentration. In performing measurements by this method, 

 a sharp boundary is created between the solvent and the solution, and the 

 change in concentration of the solute as a function both of distance and of 

 time is followed by any one of a variety of optical methods. This method is 

 sensitive in the detection of impurities either much larger or smaller than 

 the main component, or in the determination of the homogeneity with 

 respect to size of the principal diffusing species. 



b. Measurement of Diffusion Coefficients, i. Diffusion through a Porous Disk. 

 This method, introduced by Northrop and Anson (1929) and applied by 

 them and others to the measurement of the diffusion coefficient of enzymes, 

 viruses, and hormones, is elegantly simple. Despite some limitations, it 

 should find wide application in the study of the size of an infectious agent 

 whether the agent has been purified or not, as long as a sensitive and specific 

 bioassay is available. It should therefore prove invaluable in attemjjts to 

 establish the identity of an infectious agent as some particular characteristic 

 macromolecule. If purification procedures are not completely successful and 



