DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
409 
The mantissfe of both lines differ by an exact This is the natural conclusion, viz., 
same limit, sequents differ by 3(5, but then the value of 1785 remains unexplained, 
and we shoidd not expect to find two lines of the same group so close togethei’. A 
possible explanation is to allot 20559 to the alternative displacement of 3^i which 
gives vi = 1776 30 and to take 2(5, in the sequent of the second line. This would give 
a modified separation 1776’30 + 2 x 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^i 
displacement have their sequence mantissse equally spaced by l|-^. The line 20041 
also comes into the system with an exact (5 sequence displacement from 20021. 
In an analogous position to the 16013 line in the D(cxi) set appears the 
( —3(5i) D ( oo) set 
[16044-05] 1785-37 (l) 17829-41 810-13 (2) 18639-54 
in which the 16044 is extrapolated from 18639 by the vy + v.^ = 2595-5. As the oun 
displacement on the sequent here prodiices 6-06, the modified yj should be 1779-50 
+ 6-06 = 1785-56, and the modified i '2 = 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 dX. The mantissa of 16044 is 769863 = 70 (l0998-04--36d\), or 7 OA 2 as in the 
case of D ( cx >). 
With the examples here given the arguments from the capability test and the 
observed separation agree. Complete sets for ( — 3(5]) D(qo) series are obtainable 
but are not here adduced. 
( 2 ) The line of 19942 has aheady been considered on (p. 396) as a (4(5j) H (), It 
again is a case where the capability test and t/y separation both point to the limit 
displacement of 4^i 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 1864 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 1783-72 is 
the usual modified i^y, the sequence oun displacement is here 4-98 and the true V] 
= 1783-72 — 4-178 = 1778-74. This differs only by -13 from that proper to (-2(5]) D( co), 
instead of to the —4(5]. The 1864 separations are greater than in the F series, being 
1 865 - 5 I, 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 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(5] 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 
