526 PROCEEDINGS OF THE AMERICAN ACADEMY. 



+ 



vector H becomes a hydrokinetic flow-function for the motion of the 

 positive net; and where there is any positive charge it is a flow-func- 

 tion for the motion of the net plus that of the charge. Similarly the 



vector H is the negative of a flow-function of the motion of the nega- 

 tive net and charges. And in each case, equations (5) and (6) tell 

 us that it is the solenoidal flow-function that is required. 



The equation of motion is, as we expected, one which we have some 

 difficulty in applying. But if we split it up into equations (5) to 

 (10), and then combine them properly, we may use in electrical 

 problems on^v the vectors E and H, representing the relative displace- 

 ment of the positive net from the negative, and the flow-function of 

 the relative motion. And in gravitational problems the vectors E and H 

 disappear entirely. 



Collisions of Electrons. — An interesting application of this model 

 is to the problem of collisions of electrons, of the same or opposite signs, 

 as in the case of a cathode particle striking an electron in the metal 

 it hits. If they are of the same kind they will evidently become 

 flattened as they come together. But as soon as they are within 

 about their own length of each other, the side of either of them nearest 

 the other will be efi^ected not only by the displacement due to the 

 presence of the other, but also by the displacements, radiated from 

 the other on account of its acceleration. To make the vectors bal- 

 ance, as required by equations (9) and (10), its acceleration must 

 therefore be so much greater than that required by the inverse square 

 law that they can never collide. 



In the case of two electrons of difi^erent kinds, both are lengthened, 

 and they come together faster than the inverse square law would 

 demand. But since they may go right through each other perfectly 

 freely, there need not be any of the destructive effects that one might 

 expect from other theories. 



Retarded Potentials.^ — In calculating the values of the retarded 

 potentials due to moving electrons it is found necessary to treat each 

 electron as if its charge were not the same as when at rest, but changed 

 in the ratio (1 — Pr)~S where P^ is the component of P in the direction 

 towards the point at which we wish to know the potential. This has 

 been interpreted by some writers ^ as indicating that all electromag- 

 netic actions are due to some sort of pulsation of the electrons, and are 



8 For information about retarded potentials, see Lorentz, "Theory of 

 Electrons," Chap. 1. 



9 L. de la Rive, Phil. Mag., 13, p. 279. 



