. The Bell System technical journal . leus are without per-ceptible effect (C. (J. Darwin. Phil. Mag. 30, pp. 537-551; 1920). The correctionwhich would be required if the nucleus or the electron were o<ldly shaped, if thenucleus were a magnet, or if there were entrainnient of the (jotential energy of thesvstem bv the moving electron, have been evaluated bv various people; consult.■\. K. Kuark, .\stroph. 58, pp. 46-58 (1923). [he ambiguitv of sign which arises in the course of the development may beres lived by thinkmg of the limiting case of the circle f« = 0). 664 BELL SYSTEM TECILMCI
. The Bell System technical journal . leus are without per-ceptible effect (C. (J. Darwin. Phil. Mag. 30, pp. 537-551; 1920). The correctionwhich would be required if the nucleus or the electron were o<ldly shaped, if thenucleus were a magnet, or if there were entrainnient of the (jotential energy of thesvstem bv the moving electron, have been evaluated bv various people; consult.■\. K. Kuark, .\stroph. 58, pp. 46-58 (1923). [he ambiguitv of sign which arises in the course of the development may beres lived by thinkmg of the limiting case of the circle f« = 0). 664 BELL SYSTEM TECILMCIL JOURNAL All this is geometry. We must now prove that a particle movingunder the influence of an inverse-square attraction, drawing it towardsa fixed point, will describe an ellipse with that fixed point in one ofits 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\- anucleus 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 themass of the electron into the sum of its accelerations, linear andcentrifugal, 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 aboutthe centre of attraction iiniains constant in time: (33) inserting which into (32) we have <Pr eE/r- = — ni-jji ■\-p^/mr^ (34) ; ^ .un\i.\ ix I/ivsics-ix fiti,il \\.i\ . li\ iiiuliipK iiii; r,i( li icim\\ill« •-((//• (//); llii result is {,.] = -1> iii>-+2ir — C. ) iIr- last symbol for a constant of intCKralioii. (dr di>)- = ((lr (it)- {(l(t>;dl)- = {dr/dty-(m-r*/p-) = - Cinr /) + 2eEmr\p- - r. (3(5) \\c nro^iiizi- at oiuc the iilentical form of this equa
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