

DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 409 



The mantissas of both lines differ by an exact 3<J. This is the natural conclusion, viz., 

 same limit, sequents differ by 3S, but then the value of 1785 remains unexplained, 

 and we should not expect to find two D n lines of the same group so close together. A 

 possible explanation is to allot 20559 to the alternative displacement of 35, which 

 gives K, = 1776'30 and to take 2<5, in the sequent of the second line. This would give 

 a modified separation 1776'30 + 2x 4'91 = 1786'12 or '48 greater than that observed. 

 It may be noted that as they stand the four lines (18 to 21 of list) requiring -3<J, 

 displacement have their sequence mantissae equally spaced by l|c5. The line 20041 

 also comes into the system with an exact S sequence displacement from 20021. 



In an analogous position to the 16013 line in the D(oo) set appears the 

 (-3J,)D(oo)set 



[16044'OS] 1785-37 (l) 17829'41 810'13 (2) 18631T54 



in which the 16044 is extrapolated from 18639 by the 1/, + v, = 2595'5. As the oun 

 displacement on the sequent here produces 6'06, the modified v } should be 1779'50 

 + 6'06 = 1785'56, and the modified v t = 816'02-6'06 = 809'96 which agree with the 

 observed. We may regard the 16044 as subject to the observation errors of 18639, 

 say d\. The mantissa of 16044 is 769863 = 70 ( 10998 '04 - - 36dx), or 70A 2 as in the 

 case of D ( oo ). 



With the examples here given the arguments from the capability test and the 

 observed separation agree. Complete sets for ( 3(5,) D() series are obtainable 

 but are not here adduced. 



(2) The line of 19942 has already been considered on (p. 396) as a (4(5,) D (oo ). It 

 again is a case where the capability test and i/, separation both point to the limit 

 displacement of 4(5, or S. The list also gives 19959 as requiring the same displacement. 

 But it is w.F 4 (3) of the series below and shows a forward link 1 864 in analogy with 

 these F series. 



(3) The line 20312 is clearly of special importance. It gives the source of the 1864 

 separations. As is seen the capability test reqires 4(5, but there are many difficulties 

 in the way of properly placing it. It forms part of a strong doublet (6)20312 

 1783'72 (5) 22096 in which the intensities are not in normal order. If 178372 is 

 the usual modified ,, the sequence oun displacement is here 4 "98 and the true i/, 

 = 178372-4-178 = 177874. This differs only by '13 from that proper to (-25,) D( oo), 

 instead of to the 45,. The 1864 separations are greater than in the F series, being 

 1865'51, 832'13 against those found from the F above 1865'10, 829'64. . The latter 

 were based on the limit 30725"30 on which a displacement of (5, produces "45 in 1864 

 and "22 in 829. There is clearly here some triplet modification as the ratio of the 

 separations is not correct. With 1865 "51 should go 830" 15 or with the given sum 

 1866'87, 830'77. Now -3^ on the limit produces 1865'45 and increase the limit 

 itself to 30740'21. This should be the d sequent for 20312. If so the D limit should 



3 K 2 



