RECENT ADVANCES IN SCIENCE 201 



e being the Napierian base, r distance from the " centre " of 

 the electron, p Q being density at the centre, and X being a 

 constant whose dimension is a reciprocal length. Although this 

 electron has no definite boundary (since p only vanishes if 

 r is infinite) yet practically the whole of its charge is con- 

 tained within a sphere whose radius is a small multiple of V 1 , 

 so that the electron might be said to possess a radius compar- 

 able with the length X" 1 . Expressions for electric field and 

 energy are worked out. They degenerate to the usual ex- 

 pression, based on the inverse square law, for distances from 

 the " centre " which are large compared to X" 1 . The field due 

 to two such distributions of charge with their centres near one 

 another is also dealt with, with the following striking conclu- 

 sions. Whereas according to the ordinary conception of the 

 finite electron, the repulsive force between two electrons 

 would increase enormously on close approach, two such dis- 

 tributions as Nicholson considers would not behave in such 

 manner. The repulsive force would tend to zero and not to 

 infinity as the distance between the electron centres diminishes. 

 For example, when the distance separating the centres is twice 

 the linear constant X -1 , the force is only '05 of the force de- 

 manded by the usual inverse square law, and, as already 

 stated, the limit is zero as the separation tends to zero. Such 

 a coalescence of two electrons would of course be unstable, 

 and the electronic charge e would have to be regarded as a 

 constant of ethereal structure, just as X ; and no doubt 

 Planck's constant would also be involved in a similar way, on 

 account of the undoubted relation between this constant 

 and e. 



The tendency of the force between two such electric 

 charges to vanish is of course true for charges of opposite sign. 

 The large inertia of the positive charge involves of course 

 very small values for the linear constant X" 1 , and therefore 

 large values for X — values which must be at least of the 

 order 1,000 times as great as in the case of the negative elec- 

 tron. But the practical evanescence of the force (of attrac- 

 tion in this case) does not depend on the values of X, and 

 would remain. It is even possible that with a suitable law of 

 density replacing the merely illustrative suggestion of ex- 

 ponential decrease outwards, there might be a reversal in the 

 sign of the force. Hence a positive and negative electron would 



