664 



BELL SYSTEM TECILMCIL JOURNAL 



All this is geometry. We must now prove that a particle moving 

 under the influence of an inverse-square attraction, drawing it towards 

 a fixed point, will describe an ellipse with that fixed point in one of 

 its foci — will descrilie. otherwise expressed, a cur\e defined by equa- 

 tion (31). 



As the particle is an electron, and the fixed point is occupied b\- a 

 nucleus of charge is, the mutual attraction is eR r when their (lis- 



9 — 2-n 



V\%. 2— Diagram to illustrate the notation used in describing clli|)tiial orbits 



tance apart is r. Equating this attraction to the product of the 

 mass of the electron into the sum of its accelerations, linear and 

 "centrifugal," we ha\e 



eE/r^=~,nY,i^»>r{^^)' 



(32) 



It is necessary to assume tlu' law nt c(insiT\atinn of ant;iilar mo- 

 mentum; the angular momentum of the electron mrd4>^dt about 

 the centre of attraction iiniains constant in time: 





(33) 



inserting which into (32) we have 



<Pr 



eE/r- = — ni-jji ■\-p'^/mr^ 



(34) 



