VIRUS GENETICS, MULTIPLICATION, AND PHYSICS 205 



taining ions. This charge distribution is conditioned by the fact 

 that an electrical potential energy is possessed by an ion near the 

 virus surface, and this potential energy is a factor in the Boltz- 

 mann distribution of the ions. Thus, if we consider the virus 

 surface to be a plane, there will be a potential V at a point near 

 the plane, and so for an ion of charge multiplicity (valence) m, 

 where the elementary charge is e, the ratio of the number of 

 positive or negative ions, ??+ or «_, per unit volume to the average 

 number, ii, is 



+ _. „—mev/kT 



n 



~ __ „mevikT 



n 



These are not the same, which is an elaborate mathematical way 

 of saying that a double-layer will form. 



Now the charge density, p, at any point can be calculated 

 from ??+ and n_ and is simply 



p = me{iij^ — n_) 



However, the charge density, p, is itself related to the potential 

 by Poisson's equation: 



d^ ,dW dW _ 4xp 

 dx^ dy^ dz^ K 



so that we can, in principle, use these equations to calculate the 

 electrical potential due to this ionic distribution. If we make 

 some simplifications, which limit the range of operation of the 

 result but do not fundamentally alter the theoretical processes 

 involved, we can assume that all ions have the same valence, 

 so m is the same (as indeed has already been written above), 

 and can assume T' is small, so that the first two terms of the 

 exponential series are sufficient to describe the Boltzmann 

 exponentials given above. 

 Then 



»4- = 71 



/ meJ'\ 



