VIRUS GENETICS, MULTIPLICATION, AND PHYSICS "^ll 



and vo is the lowest possible frequency of such a transition, 

 London deduces that the factor {^Qhvo is also involved. The 

 mutual potential energy, U, is then 



^ ~ 4R' 



Actually this calculation is difficult to make, and other ver- 

 sions exist. In general we can put I = B/ 11'^, where 5 is a con- 

 stant for any pair of atoms. 



From our point of view, two vital considerations exist. The 

 first is that these forces are additive, so that one fluctuating 

 atomic dipole influences and attracts all other j)olarizable atoms. 

 The second is that the size of viruses on the molecular scale is 

 large, and the electric field accordingly takes time to travel to 

 all points in the virus, a time which is admittedly very short 

 but not short compared to the rate of fluctuation of the inducing 

 dipole. This means that remote atoms in the virus may be 

 influenced by a field which does not correspond to the existing 

 dipole and so will be out of phase with it and thus much less 

 attracted. The first consideration leads to the remarkable result 

 that between large molecules the attractive potential diminishes 

 quite slowly with their distance apart, d; in fact, over a small 

 range, the potential varies as 1/d^. The second consideration 

 limits the range in which forces can be treated as additive and, 

 indeed, may require that repulsive forces be considered. So 

 for distances exceeding 100 A, the attractive potential varies 

 more rapidly with distance and, in fact, falls very quickly in 

 value. 



The forces between plane surfaces of infinite extent and finite 

 thickness, neglecting the finite-velocity effect mentioned above, 

 were calculated by de Boer (1936), and Hamaker (1937) has 

 considerably extended the calculation to include spherical 

 particles. For the case of two parallel plates of thickness y, the 

 additive feature of the forces is readily exploited, and by 

 two quite simple integrations (see Verwey and Overbeek, 1948, 

 p. 101) an expression for the potential, U, can be derived. It is 



