1U4 



that the frequencies of the lines in all the usual series in the visible spectra of the 

 elements may be represented by r = /'j.,(n") — frW) where t' and r" differ by one unit. 

 Thus in case of the arc spectra of the alkali metals the socalled Principal series may 

 be represented by y = /i(l) — fo(n) (n = 2, 3. . .), the Sharp Subordinate series by 

 v = fi{2)—fAn){n = 2,2,. . .) the Diffuse Subordinate series by j^ = /a (2)— /"sW (n = 3, 4. . .) 

 and the Fundamental series (Bergmann series) by v = f3{3) — fi{n) (n = 4, 5...)- 



The same holds for the great number of lines observed by Fowler in his de- 

 tailed investigation of the magnesium spark spectrum-^). Looking apart from the 

 doubling of the lines, the combinations denoted by Fowler by P, S, D, p, C and the 

 series denoted by s, d, f,A, B may in our notation be represented bj' the following scheme: 



p 



= hW- 



-m) 



s = /2(3)- 



-hin) (n 



= 4, 5 . 



• 7) 



s 



= hm- 



-/i(2) 



d = h (3) - 



-hin) (n 



= 4, 5 . 



•8) 



D 



= /-2(2)- 



-/a (3) 



f=U&)- 



-A(n) (n 



= 4, 5 . 



• 11) 



P -- 



= /i(2)- 



-hii) 



A = /3(4)- 



-U{n) (« 



= 6, 7 . 



.12) 



C - 



= /'3(3)- 



-/2(4) 



ß = /4(4)- 



-U{n) (n 



= 6, 7 . 



. 12) 



The connection between the different series represented in this scheme, which 

 is seen to be in agreement with the above considerations, coincides with that given 

 by Fowler on the basis of the combination principle with the exception only of 

 the B series the frequencies of which, according to Fowler, in our notation should 

 be given by the combinations f^iA) — fiin). This would if correct be in disagreement 

 with the rule that r must change by one unit, and it is therefore interesting to note 

 that according to Fowler's calculations the B series was the only series for which 

 apparently the frequencies observed showed deviations from the values deduced from 

 the combination principle which surpassed the experimental errors (loc. cit. p. 253). 

 All disagreement, however, disappears completely on the above interpretation of 

 this series by introducing a fifth series of stationary states which according to the 

 general theory must be expected to exist and to have values for the total energy 

 corresponding to a function ^5(73) which differs still less from unity than 94 (n). 



The considerations about the probabilities of transition seem not only to account 

 for the appearance of the observed series but seem also to be in general agreement 

 with the relative intensities of these series. Thus the fact, that the amplitudes of the 

 harmonic circular rotations into which the motion of an electron moving in a central 

 field may be resolved will in general be larger if the direction of rotation is the 

 same as that of the revolution of the electron than if it is opposite, offers a simple 

 interpretation of the observation that the series in which the angular momentum 

 during the transitions decreases are in general more intense than the series for 

 which the angular momentum increases, and may explain that certain series of the 

 latter type the existence of which should be expected on the theorj- have hitherto not 

 been recorded. For a detailed discussion of this question, however, it would be 



^) A. Fowler, loc. cit. 



