DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 419 



separations become normal also, but as they stand Fj and F give the true mean limit. In other words 

 they have the same sequent, or the sequent is modified in the same way for both. The normal FI should 

 be as much greater as the normal F! is smaller, and we do find such indications. The value given for Fj 

 was found as the mean of two observed lines 32211-10 and 32213-80, supposed as displacements from 

 the true line. If 32213-80 be taken as normal FI it gives as mean limit with X ...92-80. The whole set 

 of F and F in this order affords good illustrations of the remarks on p as to the general properties 

 of these series. All the F lines show link connections. Thus F 2 , -(M- -1), u- -1; F 3 , +u- -73- 

 F 4 , -(- -32), M-2-33, v- -9; F 5 , +t>+l-7; F ft + M+-2. 



21456, 21462 e.X, e.X(2/t) 



e--292-38 



24638 32912 w.X X(2A).w 



u + 1 87 u + 1 86 



v--70 v + 2-06 



2434G 33203 i'.X(/;) X(2k).v 



e-44-0 

 36083 X ( - k).e 



In the preceding table the wave-numbers where deduced are entered as depending 

 on one given line. But in nearly all cases these are substantiated also by links or 

 other displaced limit lines. Although in an exhaustive treatment of the spectrum all 

 these must be considered, this is not required for the illustration of general theory, 

 and the notes do not go beyond m = 7. The number of the associated lines is 

 remarkable. The proof of the existence of these lines depending on other d sequents 

 as limits is so important, as a matter of general theory, that a large number have been 

 adduced up to m = 7. To go beyond would be to overload the present communication 

 with detail. The prevalence of the u.v. links over e may be noted in the F series. 



In dealing with the 1864 series the mean of the common F and F limits for different 

 orders was treated as giving the true value within a very small possible error of 

 about = '3. It may be interesting to see how in the present cases the corresponding 

 averages deviate from the values which have been established on the 1864 basis. 

 The mean values found from the tables and expressed in terms of differences from the 

 adopted ones are '26, '24, '33, '06, '05, '15 and justify the supposition of the small 

 limit of error in The mean separations as found from the same 10 F lines deviate 

 from the correct values by '02, '86, '05, '06, '11. The large deviation '86 is due 

 chiefly to the uncertainty of the displacement in F 3 (3). 



The preceding discussion is sufficient to show the excessive number and 

 complication of the lines belonging to the F systems in this neighbourhood and that 

 the complete problem has only been touched upon. As however the allocation of the 

 extrapolated lines 16013 and 16044 as extreme satellites of D series based respectively 

 on D ( oo ) = g ( oo ) and ( 3^) S ( ) is important, it will be well to consider shortly 

 if corresponding F series can be indicated. The two lines referred to give the same 

 d sequence, depending on a denominator 1_+70A 2 . This makes d(l) = 35012'30. 



