18 Prof. W. M. Hicks on the 



if the ouns calculated from S and D are the same, but may 

 be anything between ±6 it' not. 



This makes A = 113951 -6*60p, 



from which N/(9 A) 2 = 26731'03 + l'56p. 



It will be noied that allowance being made for uncertainty 

 in w this is the mean limit given by the observations. Jt 

 points to the fact that the link is not modified and the 

 observed line 18217 has suffered no displacement in the 

 linking. If so, any differences occurring can only arise 

 through observation errors. Take the natural supposition 

 that the tvvo determinations of the oun are the same. Then, 

 as we have seen, p is about 1, say "9. so that a' = 10. The 

 link v is increased by *98 or say 1. The possible error in 

 18217 is -Up'. Hence F 2 = -3282-00-'15p' and the mean 

 limit is now 26732*66 — '07 p', as against the value directly 

 calculated from N/(9 A) 2 of 26732-43, or exact equality. 



This is not a mere meticulous refinement. The analysis is 

 exact when the data are definite. The difficulty in general 

 is that on account of the numerous displacements in two 

 sequents, modified links, and other changes, the data them- 

 selves are subject to indefiniteness. 



Before attempting to allot lines for higher orders it may 

 be advisable to consider what we are to expect. The D and 

 F systems of lines have much in common — indeed, it may 

 ultimately be found on more complete knowledge that thef- 

 are only another set of ^-sequences. There is considerable 

 evidence* that the ^-sequences are not representable by a. 

 continuous mathematical expression, but that they may 

 approximate to values so represented. In the F system, 

 wherever they have been discussed in detail, this tendency is 

 still more marked. There is indisputable evidence that what 

 we should regard as a normal line is often accompanied by a 

 number of others displaced in definite ways, (hat its intensity 

 is then diminished, and, indeed, that it is itself, in that case, 

 frequently absent. In some instances the whole set for a 

 given order (m) may be absent and represented either by 

 another strong set related to it by a displacement of several 

 multiples of A "|\ or by a congery of membra disjecta dis- 

 placed by various oun multiples. One is even tempted to 

 suspect that the possible lines of a spectrum — at least in the 

 D and F systems — are built up by the addition to the 

 mantissa of successive multiples of the oun, and that the 



* See, for instance, Astro. J. xliv. p. 229 (1916). 



t E. g. alkaline earths [III. p. 383 seq.~], the rare gases [V.]. 



