MM//. (. (>.\ I I.Mnih-.IK) //'( /\i/s l\ I'll) SliS l\ 675 



Lit us now reverse the prfKcdtire of the forenoiiiK paraKr.ii)hs. 

 Instead of asking what is the anjjular inotnentiini of the atom when 

 the electron is revolxing in such an orl)it tliat the energy of the atom 

 is —Rli 4, let us ask what is the energy of the atom when the electron 

 is revolving in a rosette such that the angular momentum of the 

 atom is 2// 2ir. It is liesl to put the question thus: what is the energy 

 of the atom when the electron is revolving in a rosette'" such that the 

 integral cf the angular momentum around a re\'olution is 2/;? 



} f}0 ({<i> = 2li. (01) 



The energy-\alue in question, which I designate by ]\\« for a reason 

 which will presently appear, is found by calculation to be 



11'.,,= -Rli -i-Rha- (i4 (62) 



in which a is ,1 symbol meaning 



a = -lire- he = 7.20 K)-'. (63) 



(This expression incidentally is not the exact consequence of the 

 equations of the motion, but an approximation to it, quite suffi- 

 ciently accurate under these circumstances). Next let us ask what 

 is the energy of the atom when the electron is rc\()h-ing in a rosette'" 

 such that 



\p4,d4> = h. (64) 



Calling this energ\-value H'ji, it is calculated that 



Wi I = - Rh/4 - Rhoa'/M . (65) 



Incidentally it is found, as in the pre\ious simpler case, that when 

 I p4,d<t> = It , then also ) p,dr = It . 



The energy-values corresponding to the two orbits dehned by (68) 

 and (71) therefore differ by the very small amount 



ir.j- \\\i=-Rha\'lQ= -.R//(3..3210-«). (60) 



I said at first that the various "lines" of the Balmer series in the 

 spectrum of hydrogen correspond to transitions into the stationary 

 state of energy-\alue —Rli 4 from other stationary states; and that 

 unusually good spectroscopes show each of these lines to be a pair of 

 lines \ery close together. May this be explained by the theory 

 culminating in equation (66)? If so, the frequency-difference be- 

 tween the two lines of each doublet must be the same, and equal to 



'" This rosette is degenerated into a circle; the precession amounts effectively to 

 an additional term in the expression for the angular velocity of the electron. 



