1014 Dr. E. H. Kennard on a Simplified Proof for 



does not perhaps of itself involve its capture and retention 

 as a constituent part of a negatively charged atom. Never- 

 theless there must be a correspondence and perhaps a rough 

 proportionality between the two classes of phenomena — free 

 electrons with a velocity distribution about the critical 

 value, and the number of negatively charged atoms found in 

 tubes under the conditions of discharge. It would seem 

 that an experimental estimate of the number of such atoms 

 is desirable in relation to the velocity distribution in the 

 free electrons of which we have some definite knowledge. 

 The Quantum Theory of atoms itself, proceeding as it does 

 by the elaboration of successive hypotheses, still requires a 

 hypothesis regarding the capture of electrons and the 

 formation of negatively charged atoms. It would be of 

 interest if it could be shown that a stray electron which by 

 the foregoing analysis could not leave the system really 

 became " bound " as a constituent part of the atomic : we 

 may, indeed, perhaps anticipate that this phenomenon 

 usually occurs. 



CIV. On a Simplified Proof for the Retarded Potentials and 

 Huyghenss Principle. By E. H. Kennard, Ph.D.* 



THE proof usually given in deducing the retarded 

 potentials and Huyghens's Principle seems to the 

 author, as it must to many physicists, peculiarly abstract 

 and indirect. This objection is only partly met in Professor 

 Mason's f modification. The following proof seems to be at 

 least as short and as rigorous as any other, while, at the same 

 time, it seems more natural and easier for a physicist to 

 follow. 



§ 1. New Proof. 



The scalar potential $ satisfies the differential equation 



J**ivy+*r* a) 



where p = density of electricity (the units being " ordinary"). 



To find <£ at time t at any point P, let us surround P by 



any closed surface S and then, following Abraham, let us 



* Communicated by the Author. 



t Max Mason, Phys. Kev. vol. xy. p. 312 (1920). 



