404 
DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
common in the middle set of a triplet, but in the opposite direction to the usual one, 
i.e., the sequent to the second line is d (—(ij) instead o^ d (Si). 
The preceding considerations have shown the existence of a complete set of D ( 1 ) 
satellites. But further, the D suitability test shows that 20305'60 may be a line 
with normal limit and that with it may go two sets of extrapolated triplets in which 
the mantissa of the first is a multiple of As- They are 
r 1777-90 (I) 17791-35 
[16013-45] 
[1784-83 ( 1 ) 17798-28 
[17725-39] 1777-90 (3) 19503-29 
(1) 20305-60 
The first set, however, involves for the D 33 the line 18607, which belongs to the 
1864 F set discussed above, and is stronger than we should expect. Provisionally we 
will suppose the true D 33 is hidden by the F line. The line 20320 has been already 
adduced (p. 383) as showing connection with the 1864 separations in a similar way to 
20312. The mantissm of the Dj lines are (p^ indicating extrapolated lines), 
769890 = 70 X 10998-2 + 16 + 3-2p' - 25-2^^ = 70 A 2 + 16 + 3-2p' - 70x - 25-2£, 
814815 + 4-2jo' — 27 - 25 ^, and 889493 + 6p —30-75^. They differ successively by 44925 
= 4 X 10998-2+1^(1+16 + 4-2 {p'2-_p'i)-2-0^ = 73iS+16 + 4-2 (p'2-p\-4:X-2-0i and 
74679 = 122^S—l7 + 6p — 4'2p'^ — 7x — 3'5^. The conditions are satisfied within error 
limits that the mantissa of the extreme satellite is 70 Ao, and that the differences for 
the satellites are due to 122^(1 and 73jS. Since 122|-x 3 = 366-7 and 73^ x 5 = 367-2, 
the normal ratio of satellite separations is again reproduced. The evidence is clear, 
therefore, for two groups of normal diffuse series depending on fOA^ and 70A 2 
respectively. 
The fact that 20320 is connected with 1864 in the same way as 20312, that the 
^2 separation is not good, and that we shoidd expect a doublet here in place of a triplet 
rather point to the supposition that it is not a member of the set. For the line 
the sequent is 51025-29 — 16013-45 = 35011-84, on this the oun displacement produces 
a change of 6-04 which accounts for the modified I'l = 1784-83 in the usual way. The 
mantissas of the two groups 20581, 20320 differ by Ifd. 
It will be sufficient here to attempt the allocation of the corresponding satellites for 
m = 2 only. They should be at about the same oun multiple distance from the 
Dji line as for m = 1. The Dii(2) has been taken as 38366 with denominator 
1 - 943447 . Taking the first group, the satellites should have denominators about 29f(J 
and 47f(i less than this. These would correspond to 38208-61 and 38111-69. With 
regard to the first the lines in this neighbourhood are (l) 38199-58, (l) 38203-51, 
( 1 ) 38217-68, of which the first and third are respectively 9-03 less and 9-07 greater 
than 38208, and suggest equal displacements on either side. They are found to 
correspond to 3l|-(i, 28(5 from D^, or ±7(5i on either side of 38208, with errors 
816-44] 
[ ( 8 ) I86O7-79 
809-51J 
816-96 ( 4 ) 20320-25 
