DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 393 



are more likely to be (SJ F (30) and ( - 8J F (30). In fact, in this neighbourhood, the difference of two 

 successive orders in a series is comparable with the change produced by a 8, 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, 8'918, very close to those determined from the displacements. The 

 individual deviations from the mean are quite small for F 1 (oo), 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 m7. We may take it therefore 

 that the true value of the F a 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 oun 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(<) 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 ( oo ) ( or some near collateral of this. We will 

 therefore test this as 51025'26 + where 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 + ^+c^,, 334 19 '04 + +^ + 6^, the 

 denominators are found to be 



1'889322-3074^ 



54831-2 > 60+28'14d.' 1 

 l'834491-28'14(+di/ I ) 



1 '8 1 1 577 - 27 (+ d Vl ) - 



In these cannot be greater than a few decimals and will produce no effect on the 



3 H 2 



