s(K\ir. coxTr.Mi'OR.tKV .iiH'.ixcr.s i\ riiysics-i.\ 66i 



sMtf corresiMuids to a certain circular orbit of the electron; the Angiildr 

 MomenUi of the two atoms are identical xchen they are in corresponding 

 stationary states. As a test, it is fa\-or.il)lc. It does not invoke the 

 rel.iiion between angular momenta and inle^er multiples of // '2v 

 which was stressed in the forejjoiti); section. It is independent of 

 tii.it relation, and may fairly be considered as the second numerical 

 ajjreenient offered by this atom-model, if that relation be considered 

 the first. The idea is due to Sommerfeld; the data whereby the test 

 was made were obtained by Paschen, as a b\-product of the work 

 cited in footnote 12. 



Although the statements in the foregoing; paraj;raphs are literally 

 true, they do not pro\e that the condition Antiiilar Momentum = nh 2w 

 is the distincti\e feature par excellence of the permissible circular orbits. 

 The result would have been cxacth' the same if I had defined the sla- 

 tionar>' states of the ionized helium atom as thr)se for which / = ;;/; or 

 as those for which Lim w = Lim v. 



J. Tk.\( INl. OI' Okiuts 



W'c must now seek for opportunities to make and test generaliza- 

 tions of the notions about the h\drogen atom explained in section H. 



I began by saying that the electron should be supposed to re\(jKe 

 in the in\-erse-square electrostatic field of the nucleus, according to the 

 laws of dynamics, without spending energA" in radiation; and con- 

 tinued by saying that I shf)uld speak of circular orbits only. \ow the 

 laws of dynamics prescribe elliptical orbits, of which the circular 

 orbits are but special cases. In fact, for each one of the sequence 

 of energy-values —Rh «- corresponding to the sequence of Stationar\- 

 States, there is an infinity of elliptical orbits possessing that energy- 

 \ alue, of which the circle of radius specified by equation (7) is only one. 

 Suppose we should inquire what, if any, are the distinctive features of 

 these elliptical orbits which set them apart from all others? 



Again : when radiating hydrogen is exposed to a strong electric field, 

 new stationan.- states appear, and their energy-values are known. 

 The orbit of an electron, in a field compounded of an inverse-square 

 central field and another field uniform in magnitude and direction, 

 is no longer a circle nor even an ellipse nor even a closed orbit (except 

 in special cases). Could the orbits having energv-values equal to 

 those of the stationary states l)e identified and traced, and could dis- 

 tinctive features be found which mark them out from among all the 

 others? 



Again: when radiating hydrogen is exposed to a strong magnetic 



