562 Prof. 0. W. Richardson on a Theory of the 



It will be noticed that the forces perpendicular to the pr- 

 axis vanish, by symmetry. 



The lower limit « of integration with respect to dr l may 

 be taken to represent the radius of the sphere within which 

 it is impossible for the centre of an atom of class B to lie. 

 This interpretation will only be exact provided that each 

 atom contains only one electron, and that placed at its centre. 

 In general v would have to be replaced by pv , where p is 

 the probability that an electron of type s will be found at 

 the point r^u,(j>. The quantity p would then come within 

 the integral which would range from <x>, — 1 and 2-7? to 

 0, + 1 and 0. It will, however, be sufficient for our present 

 purpose to suppose that a represents a kind of average formed 

 in the above way. It is evident that a will be of the order 

 of magnitude of the radius of the atom A and have the sum 

 of the radii of A and B as an upper limit. 



In carrying out the integration we have assumed that v 

 the number of molecules per unit volume is constant. This 

 will not be true if the potential energy of B in A's field of 

 force is comparable with the kinetic energy of B. In this 



to 



case we should have to replace v by v e~mWe inside the in- 

 tegral, where w is the potential energy of a molecule of B 

 of mass m, 6 is the absolute temperature, and R. the gas 

 constant. This, however, is a refinement which does not 

 seem to be required by the facts at present. 



So far we have entirely ignored magnetic effects. It is, 

 however, easy to show that, on this view of the atom, they 

 are small compared with the electrostatic effects already 

 considered. Let £ be the maximum excursion from the 

 equilibrium position of the electron A, then if t is its periodic 

 time the maximum velocity is equal to 27r f /t. The maximum 



velocity of B is evidently of the order 27r -^ £ / T - The force 



on A due to magnetic terms is therefore of order not greater 



f °° L £ 2 e 2 

 than 167T 3 1 -\ — a -^dr h where e is the velocity of light. 



The order of the electrostatic force is given by the first term 



of equation (9). The ratio of the latter to the former is 



2 t'V 



k —2-y* Putting t=10 -15 , and 3 x 10~ 8 and 10 ~ 8 as superio 



limits for a and f respectively, the ratio is approximately 

 2 x 10 5 . The forces of electrostatic are evidently enormous 

 compared with those of electromagnetic origin. The possi- 

 bility of magnetic effects on other views of atomic structure 

 will be considered later. 



