Atoms and Molecules. 



901 



may be treated as a point charge for all external points, and 

 the rest of the spheroid approximates a ring or circle of a 

 certain unknown radius, say a, and may be treated as a single 

 ring uniformly charged, the solution for which is known. In 

 view of the uncertainty as to the precise shape of the electron, 

 this substitution of a ring and a point as the equivalent 

 of the negative electron electrostatically may be just as 

 appropriate as to use the solution for the spheroid were it 

 known. 



2. The Electrostatic Force of One Non- spherical Electron 

 upon Another Coaxial with it. 



Represent the meridian section of the two coaxial electrons 

 as in fig. 5 by ellipses of semi-major axis a and semi- minor 



Fig. 5. — Representing the meridian section of two* coaxial electrons, 

 the charge in the inscribed sphere being electrostatically equivalent 

 to a point, and of the rest equivalent to a ring. 



axis h, and imagine the inscribed sphere to be replaced by a 

 point of charge E x and the rest by a ring of unknown radius, a. 

 The fundamental problem is to find the electrostatic force 

 between two coaxial rings of different radii. Although the 

 radii of the rings for the two electrons are equal, yet to find 

 the force between a ring and a point it is convenient to 

 use the same expression and equate one of the radii to zero 

 for the point. 



The complete general expression for the average electro- 

 static force resolved along the centre line, ?\ between two point 

 charges in circles of different radii but having parallel axes is 

 given by equation (42) of a former pnper *. In the special case 



* Phil. Mag. July 1913, eq. (42). 



