92 PEOF. W. M. HICKS: A CEITICAL STUDY OF SPECTEAL SEEIES. 



P, (oo)- 16947 6 = 4 1446 '76 1-69 -16947 6 = 24500 7 '5, say. This, of course, 

 suggests the same limit as the S. and D. series, which is 24472'll3-84. But the 

 limits of error show that this is not the case, but that the difference is real. The 

 limit of S 3 is 17'1 higher, or 24489'21 3'84. Another 17"! higher would give 

 24506-31 3'8. In view of the actual limit 24 500 7 '5, we might provisionally fix it 

 at 24506. The second line of the doublet would then be 24523'!. An additional 

 17'1 lands us on 24 5 40 - 1, which is close to the 24550+ ? of the two series considered 

 above. These results can hardly be fortuitous. The limit of S, is generated by the 

 P, series, being VP,(l); the limit of S 2 is found from this by deducting the atomic 

 weight term, 2W, from the p of P,(l). The limits will therefore be generated by 

 writing /j. = '148678 2pW in P,, where p has integral values from to 5, and 

 possibly to 7 (LENARD'S series), both inclusive. RITZ has given the doublet series 

 just considered as VP, (l)-VP, (m), VP 2 (l) VP, (m). We have seen, however, that 

 this cannot be the case.* Moreover, VP, (l) VP, (m) for m = 1 would give an 

 infinite time of vibration, and would suggest instability. In fact, the configuration 

 giving this series, containing one very long period, is apparently very slightly stable. 

 It is possible that the VP, (m) ought also to be slightly different, but the observations 

 are far too inexact to settle this. 



Again, RYDBERG'S tables show that 7418 S., 5100 LE., 4472 S. have denominators 

 about 2-845, 3'845, and 4'845, with a limit 27026. Working from this they satisfy 

 the formula 



n = 27034'5-N/(m+ -8358 +wT 1 x -0148). 



27034 is not far from the value of VD(1), which is 27282 52. But the interest 

 of this allocation lies chiefly in this, that its /A is of the form we should expect for the 

 real D series, if NaD were formed on the same plan as for K, Rb, Cs, in which we 

 have seen that the JJL is 1W-sb = '8505 with undetermined. The closeness of 

 the agreement is chance ; the errors in observation are too great to give p with 

 certainty, but it is suggestive. 



It will be convenient, for reference, to attach letters to the various series just 

 considered. In the list the LENARD series is denoted by A, the second by B, the third 

 by C, although a very doubtful one, that parallel to P by E and the last by G. 



Collecting, we find 



VP, (2)- VI) (3) VP 2 (2)-VS (2) 



VP 2 (2)- VD (3) VP, (2)- VS (2) 



F = 12275-3 {VD (2)}-N/{m+ -998613} 3 (m = 3"4) 



A = 24570-6 AT /f -2819061 2 , 



N/ \m+ T013864+ V (m = 2 3 4 5 6 7) 

 / I m J 



* Unless 4472-5 S. is 4 A.U. in error, which is not likely. 



