so,\n-: COM liMi'ou.iK) iin .i.mi.s rx rnv.'^ics—rx 677 



quanlum-ntimhers k=\, 2, . . . «; iiUMiiin.u l>y aziimilhal (|uantum- 

 luimlier the (iiiotii'iU of j p^il<i> 1>> /'. If m>\v wt- taki- arcoimt of ihi- 

 variation of tlie mass of the eieclron with its speed, and calculate 

 the enerv;y-valiies for the n rosettes obtained l)y assi^nin^ the values 

 I, 2, 3 . . . w successively to the syinl)ol k in ((')7), we shall find that 

 these « energy-values are all distinct, deviatinij slijjhtly from —Rh'ri^ 

 and from each other. Therefore, there should he three stationary 

 states of energy-values \\\^, Wi2, VFji, all differing by a little from 



— Rli •.) and from each other; there should he four stationary states 

 of energy-values ll'4i, ll'ia, Wu, Ww, all nearly hut not ciiiile equal to 



— Rh It) and each other; and so forth. (The reason for such symbols 

 as Il'n will now appear; the first subscript represents the total, the 

 second the azimuthal quantum-number of the orbit in question.) 

 In general there are n stationary states in the group corresponding 

 nearly to the mean energy-value —Rh ;/-; and the expressions for 

 their several values are obtained by putting k equal to the various 

 \ahies 1, 2, H . . . « in tiie formula. 



£=-«*, .[,+5(:4)]. m 



Owing to these complexities the lines of the Balmer series should 

 be not doublets, but groups of man>' more lines; e.g., the transitions 

 from what I had called the stationary state of energy-value —Rli/9 

 to the stationary* state of energy-value —Rh/A are transitions of six 

 sorts, from each of three initial states to each of two final; and the 

 first "line" of the Balmer series might he expected to be sextuple. 



The trial of these ideas is best made upon the spectrum of ionized 

 "aelium. The separation between the energy-values of stationary 

 states sharing the same total quantum-number and differing in 

 azimuthal quantum-number is increased, when we pass from an 

 atom-model in which the charge on the nucleus is e to one in which 

 it is Ze, in the ratio Z^:l; in this instance 16:1. The system of com- 

 ponent lines, or the so-called "fine structure" to be expected for any 

 "line" of the hydrogen spectrum should he spread out on a scale 

 sixteenfold as great for the corresponding "line" of the ionized- 

 helium spectrum. The trial was made by Paschen; the comparison 

 between the fine structure of several of the "lines" of ionized helium 

 and the components to be expected from the foregoing theory, yielded 

 what appear to be very satisfactory- results. This matter I discussed 

 over several pages of the First Part of this article; and for economy 

 of space I refer the reader back to them, and at this place say only 

 that the "other numerical agreements between the production and 



