3SO DE. W. M. HICKS: A CEITICAL STUDY OF SPECTRAL SERIES. 



The mantissa of (l), using F ( oo) = 30678'93 + ' is 



ll-5 =195 



This requires '014 x '577+ '05 p '002 = 0, or combined with the condition for 

 /(2), '112 + '003 '086j9+'05p!'002 = and can be satisfied within error limits. 



The mantissa of (2) 895149-110'63^ + llp, which differs from that of / (2) by 

 29701-3 < 37'+ll#,-16p / = 7 (4243-00-'48 + l'6p-2'3p'). 



This requires 1'61 '907x '48+ l'6p 2'3p' =0 easily satisfied for both cases 

 within observation errors. 



The mantissa of (3) is 937966-115'6'+ll^ 3 , differing from that off (2) by 72518 

 -8'35+llp 3 -16jp. With f = -'58 and -170 this becomes 72523'!... and 72532..., 

 or 17A' 2 +lf<?-23... and 17A' 2 +lf^-24... on their respective values of D'* The 

 amount 23 is perhaps excessive to be covered by the various possible errors but it just 

 comes within. It may be noted that 17A' 2 + lf-(5 = 16A' 2 + A 2 . These three data do not 

 decisively distinguish between the two cases. This, however, is not to be unexpected 

 because the two arise from a S r displacement in d lb , the sequents in this neighbourhood 

 are such that S l on the limit and 25, on the sequent are nearly equivalent, and the 

 multiples involved 185, 189, 195 are too close to produce contrasts. Incidentally, also, 

 the discussion strengthens the allocation of the lines to the displacements given. 



The only further test with our present knowledge is to obtain some independent 

 evidence as to the exact value of the limit, and naturally we turn for this to the mean 

 of the F and F series. The series however in Kr is not nearly so well developed as in 

 X. As has been already seen there are only three sets of observed pairs (m = 2, 3, 4) 

 and these give for F ( co ) respectively values of 3067477, ... 7'27, ... 7'16. Since a 

 displacement of <\ produces a change of 2'03 in F ( o) the first may be due to the fact 

 that the line taken for F (2) is really (3<J,) F (2), when the true mean would be 

 30677 '81. It is natural to seek further as to the existence of summation lines 

 corresponding to our last three examples. The result shows a most remarkable 

 agreement. The sets are shown in the following list together with those obtained 

 from the normal F and F. 



m. F. F(oo). P. 



2 (1)17321'51 30677'82 (4403413) (-3<S,) (2) 44028'04 



3 (In) 23353'84 30677'27 (2) 3800071 



4 (2n) 26067'66 30677'16 (6) 35286'68 



F,(2)(7A',) (5)17594-17 3067776 (l) 43761'38 F t (2) (7A' 2 ) 



F 1 (2){10A 2 ) (6)17747-14 3067773 (l) 43608'33 F, (2) (10A S ) 



F 1 (2)(16A' 2 + A 2 ) (2)1797278 3067770 (l) 43382'63 P,(2) 



These are remarkably concordant, especially when it is noted that the F (3, 4) are 

 diffuse lines and not so susceptible of exact measurement as the others. The mean 



