342 



58 



il is of interest lo notice that for a transition where one of the r's is negative,' /. e. 

 during which one of the n's increases, the value of R' is always either very small 

 or equal to zero, and that in agi-eement with this the corresponding component, if 

 observed at all, is very weak^). It is easily seen that, from a mathematical point of 

 view, the reason for the small values of R' in such cases lies in the circumstance 

 that the coefficients Crj, . r., in a convergent trigonometric series of the type (12) 

 not only converge to zero when the numerical value [r^-j- • • of the sum of the 

 r's increases, but also when the sum + •■ rj of the numerical values of the 

 r's increases, + ... r,,: remaining constant. 



Special interest is afforded by transitions of the type {n[, 0, n'.. -^0, ii^, /j^). For 

 these transitions both R' and R" are equal to zero, but, as mentioned in the former 

 section, it is not allowable from this to conclude that such transitions are impossible, 

 in intimate connection with the fact that the amplitude of the vibration of fre- 

 (juency n' Wj — n" + — "'sO^s» although equal to zero for the motion in the 

 initial state and in the final state, is different from zero in the mechanically pos- 

 sible states which lie "between" these states and which are characterised by /j = 

 /n'j, /, = (1 — Å)n", = n'g + Å{n[ — n") (0 < / < 1). As seen from the tables 

 weak components corresponding to transitions of the type under consideration seem 

 actually to have been observed-). 



For transitions of the type (a, a, c — h, b, c) the amplitude of the vibration 

 of frequency (a — fc)(t»j + (a — b)(02 equal to zero, not only in the initial state 

 and in the final state, but also in the states characterised by 1^ = 1^= b ^ Å(a — b), 

 /j = c, due to the symmetry of the motion of a state for which /j = I^- From this 

 we may probably conclude that a transition of the type under consideration is 

 impossible. In the tables we meet with two examples of such a transition, uiz. 

 (112^002) in Hß and (222-^002) in H^. In no corresponding component has 

 been observed, but in Hß a weak component has been recorded. The appearance of 

 this component, however, (if not due to "Gittergeister") does not necessarily mean a 

 disagreement with the theory, but is possibly due to the influence of the relativity 

 modifications, as it will be discussed below. 



When we consider the values of R"^ and R" '^ as affording an estimate for the 

 intensities of the components it must be remembered that in § 3 these values are 

 calculated with neglect of small terms proportional to the first and higher powers 

 of the electric force. It is easily seen, however, that we may look apart from these 

 small terms, not only on account of the preliminary and approximative character of 

 the discussion, but also because errors of at least the same order of magnitude are 



') It will be observed that the point under consideration has an interesting connection with 

 Sommerfeld's suggestion that only such transitions would be possible for which all n's in (99) decrease 

 or remain unaltered (hypothesis of the "Quantenungleichungen Compare A Sommerfeld, Ann. d. Phys. 

 LI p. '24 (1916). Compare also Epsi ein s discussion of the intensities of the Stark effect components). 



^1 (202 ^011) in Hß; i;i02 ^ Ü11) in H)- ; (402 ^011) in H^. Components corresponding to (401 -^011 

 in H/ and (501^011) in H,) are recorded by Stark as questionable. 



