300 



SCIENCE 



[N. S. Vol. XL VI. No. 1187 



by forces of an admittedly mysterious 

 character, Coulomb's law, in the ordinary 

 sense, would fail when two electron centers 

 approach within one electron diameter of 

 each other. If, on the other hand, we 

 aibandon the rather artificial spherical model 

 of the electron, and if we assume that the 

 electron has all its charge concentrated at 

 its center, then also it has been well recog- 

 nized that Coulomb's law must fail, for 

 otherwise we could not account for the finite 

 mass of the electron. In this case also we 

 might, if we chose, speak of the size of the 

 electron, meaning thereby the distance from 

 the center at which the electric force differs 

 by a certain amount from that calculated 

 by Coulomb's law. Now in either sense 

 of the word we must agree with Ruther- 

 ford that the positive nucleus of an atom 

 is far smaller than the electron. In other 

 words, two such positive nuclei will repel 

 each other according to Coulomb's law 

 even at distances so small that the law 

 would have quite lost its validity for two 

 electrons or for a positive particle and an 

 electron. In other words, an atom com- 

 posed of a single positive particle and an 

 electron is to be regarded as though the 

 positive particle were imbedded in the elec- 

 tron and not the electron in the positive 

 nucleus, as in the older theory of J. J. 

 Thomson. 



Some years ago I was led, through con- 

 sideration of electron theory alone, and by 

 the aid of plausible assumptions, to an 

 equation for the field of force about an 

 electron, which, at that time, seemed to me 

 a reasonaJble first approximation to the 

 equation which we must substitute for 

 Coulomb's law. If / is the force acting on 

 an equal positive charge at the distance r 

 from the point charge electron, if £ is the 

 charge of the electron, e the base of natural 

 logarithms, and r^ a characteristic distance 

 which does not differ much numerically 



from the radius which is ascribed to the 

 spherical electron, the equation reads 



r' 



At large values of r this obviously re- 

 duces to Coulomb's law; at small values 

 it would correspond to a curve such as that 

 given in Fig. 2, where / is the ordinate 

 and r the abcissa. 



If now we assume that this is only a sug- 

 gestion of the true equation and that the 

 exponential term should be replaced by a 

 similar function of periodic character, say 

 a trigonometrical function of 1/r, we might 

 obtain an equation roughly represented by 

 the curve given in Fig. 3. Any ordinary 



periodicity with respect to 1/r will make 

 the curve which is plotted with respect to 

 r intersect the axis of abscissae an infinite 

 number of times as r approaches zero. A 

 positive particle (which we may regard as 

 negligible in size but greatly preponder- 

 ating in mass) situated at any of the inter- 

 sections /"i, r^, etc., where with diminishing 

 r the force of attraction goes over into one 

 of repulsion, is in a state of equilibrium with 

 respect to the electron. Let us assume that 



