SOMi: ( (».V// .U/'(iA'. (AT .//>( ./.\( 7 V I .\ I'llVSUS /V (<■'" 



— Rh — Rli M-. wliicli art- the ciUTny valiu-s for llu- (tl)str\i(l 



stationary statt-s of liydro^cii. If this is not an acrick-ntal roinridt-nct', 

 llit-n by itnaKining tlial the clrrtron of tin- ioni/i'<l lii-liuin atom lilct-- 

 wisi- ran rf\ol\i' only in orliits for whirli tiu- angular nionu-ntuin 

 of tlu' ati>ni is some intt'^or multiple of li '2w, anri hy raiciilaliiin tlii- 

 corrt'sponiliiiK t'nerjjy-valui-s for the aloni-niodel, we should arriw 

 at the enerRy-valiies of the observed stationary states of ionized 

 helium. Now the charge on the nucleus of the helium atom is 2e, 

 twice the charge of the hydrogen nucleus; the force which it exerts 

 on an electron at distance r is 2e- >'-, instead of r >-. If the reader 

 will work through the equations of Section H, making this alteration 

 wherever appropriate, he will find for the energ>'-values of the sta- 

 tionary states the sequence 



-ARIi,-^RIi '.).-AKIi It), . . . -ARh >r. . . . 

 in wiiicii 



Ir' 



as heretofore. Tile (iuantil\' yu will be dilferent from what it was 

 for hydrogen; but the difference will be \ery slight. Therefore if the 

 condition that the electron may revoke about the nucleus only in 

 circular orbits for which the angular momentum of the atom is «//, 2jr 

 is an essential condition, and governs the atoms of hydrogen and 

 ionized helium alike, the stationar\' states of ionized helium corre- 

 spond one-to-one with those of hydrogen, but with energy-values 

 almost e.xactly four times as great. So also with the lines of the 

 spectrum; to each line of the hydrogen spectrum should correspond 

 a line of fourfold frequency in the ionized-helium spectrum; the 

 spectrum of ionized helium should be the spectrum of hydrogen on a 

 quadrupled frequency-scale. 



This conclusion is verified. The historical sequence of observa- 

 tions and theories is rather interesting. Certain lines of ionized 

 helium were earliest observed in stars; their simple numerical rela- 

 tions with hydrogen lines being noticed, they were naturally ascribed 

 to hydrogen, and when they were generated in mixtures of hydrogen 

 and helium within a labf)ratory they were still attributed to the first- 

 named of these gases. Bohr in his first published paper reasoned 

 in the manner I have followed in this section, and inferred that these 

 lines really belonged to helium; which was shortly after%vards \erihed 

 by seeking and finding them in the spectrum of helium made as pure 

 as possible. A number of additional lines of the spectrum ha\e since 

 been found, although the lines corresponding to transitions into the 



