SOME coMii.MroR.iiK'y .ini'.iXii.s i\ rinsns i\ r>«.i 



wliiili mii>l (H>>x'ss l\V(i iir mi>ri- v.iliu-- -.iMccd .il iiilt-rv.ils of luw 

 iiiiii '■. 



'I'lif ,iti>m-ni(Klrl wliicli vvc luno lircii discussing ,it sucli Icnvjtli 

 (•(insists of an t'li-ctroii ('irculalin^ in an clliplical orbit aboiil a sta- 

 tionary nucleus; the minor \ariations diii- to the variation of.thu 

 lu.iss m of the electron with its sjK-ed, and to the motion of the nucleus, 

 are now of comparatively little importance. An electron circulating 

 in a dosetl orliit with fretjuency f passes c times per second throujjh 

 my |K)int of its orbit, so thai the charge passing per secf)nd ihrouKh 

 my such point is e(|ual to that which would pass, if a continuous 

 rurrent I = ev c (measured in electromagnetic units) were flowinv; 

 around the orbit. Now a current / flowing continuously around the 

 curve lK)unding an area A is equivalent — so far as its field at a dis- 

 tance goes — to a magnet, of which the magnetic moment .1/ is directed 

 norntally to the plane of the curve and is ec|ual in magnitude to I A. 

 The area of an ellipse of which the major a.\is is denoted by a and the 

 minor axis b = a\/\—t- is equal to wab = ira- y/ \ — i" . Hen( e the 

 magnetic moment of the atom-m(xlel is equal to 



M =evwa-\/\—t- c (74) 



Further we have seen, by equations (:^7) and (42), that the angular 

 monienium of the electron in its orbit is equal to 



p = 2Trmva.-yy\—t- {l-y) 



('onse(|uently 



.U, p = e 2mc (7fi) 



a rather surprisingly simple relation! 



Now when a magnet of m(jment .1/ is placed in a magnetic field 

 of field-strength //, it acquires a certain potential energy At' — in 

 addition to the intrinsic energy which it possesses when oriented 

 normally to the field — which depends on the angle 6 between the 



" Unlike sonic of the preceding derivations, this theor>' is not essentially limited 

 to the rase of an atoni-mrHJel t-onsisting of a niiileus and one ekrtron. It there 

 .ire several electrons describing closed orbits, the l.armor precession atTects them 

 iilcniically; or, otherwsc put, the magnetic field treats the at<)m as a unit having 

 an angular momentum and a magnetic moment e(|ual respectively to the v("ctorial 

 sums of the angular momenta and the magnetic moments of the individual electrons. 

 In fact the l>est verification of (7.?i is obtained from the lines l>elonging to the singlet 

 systems of certain metals, which display "normal" Zeeman cflect— the effect to 

 which this theory is adapted. With anomalous Zeeman effect, against which this 

 theory is powerless, we are not now c(jncerned. In the case of hydrogen, the effect 

 is complicatetl fiy the fine structure of the lines. With small magnetic fields it is 

 normal, at least so far as the observations go. Kach of the two stationary states 

 of which the energy-values are given by '02i and (65i is replace«l by two or more, 

 conforming to (73). 



