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 ( S } ) instead of d (^). 



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 Dj 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 A 2 . They are 



T1777-90 (1) 1779T35 816'44] 



[16013-45] 1 > (8) 1860779 



[1784-83 (1) 17798-28 809'5lJ 



[17725-39] 1777-90 (3) 19503'29 816'96 (4) 20320'25 



(1) 20305'GO 



The first set, however, involves for the Dg, 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 mantissas of the Dj lines are (p 1 indicating extrapolated lines), 

 769890 = 70 x 10998'2 + 16 + 3"2p' - 25'2 = 70A 2 + 16 + 3'2p' - 70z - 25'2 

 814815 + 4'2p'-27-25 and 889493 + 6j-3075 They differ successively by 44925 

 = 4x16998-2+1^+16 + 4-2 (p'.,-p\}-W = 73^+16 + 4'2 (p' a -p\-4x-2-0 and 

 74679 = l22%817 + 6p4 c '2p' a 7x3'5g. The conditions are satisfied within error 

 limits that the mantissa of the extreme satellite is 70A a , and that the differences for 

 the satellites are due to 122^5 and 73^. Since 122x 3 = 3667 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 79A 2 and 70A 2 

 respectively. 



The fact that 20320 is connected with 1864 in the same way as 20312, that the 

 i/ 2 separation is not good, and that we should 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 D 1$ line 

 the sequent is 51025"29 16013"45 = 3501T84, on this the oun displacement produces 

 a change of 6'04 which accounts for the modified ^ = 1784'83 in the usual way. The 

 mantissse of the two D n groups 20581, 20320 differ by 14 



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 

 D n line as for m = 1. The D n (2) has been taken as 38366 with denominator 

 1 "943447. Taking the first group, the satellites should have denominators about 29f<J 

 and 47f<5 less than this. These would correspond to 38 208 '61 and 38111-69. With 

 regard to the first the lines in this neighbourhood are (l) 38199'58, (l) 38203'51, 

 (l) 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|<5, 28<S from D u , or +7^ on either side of 38208, with errors 



