DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
393 
are more likely to be (5^) F (30) and (- S^) F (30). In fact, in this neighbourhood, the difference of two 
successive orders in a series is comparable with the change produced by a displacement in the limit, and 
so introduces some uncertainty in allocation. It will be noticed also that, in a few cases, the same line is 
adduced to fit two cases, which can only happen if a line happens to be a close doublet, an unlikely 
supposition to happen often. 
We are now in a position to determine the limits with considerable accuracy. 
Taking the average means where they are deduced from actual or displaced actual 
values, we find the limits come to 30725-340, 32589-443, 33419-079. In the first 
attack on the problem values of unobserved lines were deduced from observed linked 
lines. The corresponding mean values for the limits then found had for the last digits 
5 292, 9 161, 8- 9 18, very close to those determined from the displacements. The 
individual deviations from the mean are quite small for Fj(co^^ considerably smaller 
than for the others. It is, therefore, the more reliable. The mean deviation in 
magnitude is 28 and the maximum is —-97 in m = 7. We may take it therefore 
that the true value of the limit is 30725-30 within a few decimals. The 
separations given by the deduced limits above are 1864-10 and 829-64. 
These very accurate values afford a means of testing as to their source. If the 
limit were known to be a single number there could be no doubt as to its belonging to 
the d sequences, or as to the series being of the F type. But there is just the 
possibility that it may be a composite number, comprising one or more links—say, p or s 
terms; and that the separations may be due to 01111 displacements in one of them. 
The suspicion that this may be the case is aroused by the fact that the triplet 17615, 
18447, 20312, which would be the origin of the d or F(coj term, and in which 
therefore the first two lines should behave as satellites do not show complete sets with 
the separation 1778, 815, as they should do if normal satellites. Moreover, the 
intensity order with the middle line much more intense than the other is not normal. 
There is no test for the composite nature of 30725, but if it be really so, the most 
probable source would be p = S(co), or some near collateral of this. We vdll 
therefore test this as 51025-26+ f, where f may be considerable, so as to include near 
collaterals, and also test 30725 as a d sequent. We will take the latter first. 
At the start it may be noted that it is an argument in favour of 30725 being 
directly the source, that displacements by small multiples of the oun have fitted in so 
remarkably closely and frequently in the formation of the list of lines above. 
Taking then the limits as 30725-30 + ^, 32589-40 + ^+cAi, 33419-04+ f+cAi + dvo the 
denominators are found to be 
1-889322-30-74^ 
54831-2-60^+28-14di^i 
1-834491-28-14 
22 914 -1 - 14^-1 -1 + 27 cZi /2 
1-811577-27 [i+dv;)-27dv.. 
In these ^ cannot be greater than a few decimals and will produce no effect on the 
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