DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 423 



leaving out for the moment the extrapolated lines, indicated by *, and weighting No. 9 

 with three times the possible error of the others, the mean value of A 2 = 10998 '198 

 '37 the same as from No. 10 alone which is exact. They all, with the exception of 

 No. 5, satisfy this within observation errors < d\ = '04. No. 5 requires that the 

 observation error shall be 'OGAand the true wave-number 19942'47 in place of... 2'53. 

 With this the v l separation = 1775'69 and is brought into practically the exact (d) v l 

 value (see p. 396) required, which is 177576. The outstanding '07 (d\ = '017) would 

 be attached to the strong second line of the doublet (10) 21717. This is in very 

 striking support of the general argument. We have already seen good grounds for 

 putting a small fraction of the order '25. To determine it with greater exactness 

 a corresponding mantissa differing from the above by considerable multiples is 

 necessary : e.g. with mantissa of order '5 the coefficient of is 15'4f The differences 

 equated to A 2 multiples would then give an equation to find in which the error 

 term would have little effect. We get this different coefficient in No. 9, but it is 

 due to an order 2 in which the effect of an error is multiplied to the same extent. 

 The extrapolated lines do not help us as their limits of error are too large. On the 

 contrary the argument enables us to determine their values more correctly : e.g. in 

 No. (2) the error is dependent as the line 21400 from which the line is extrapolated. 

 To make the multiple correct requires p = 2 '7, dn = '42. This reduces the observed 

 v 2 = 809'53 to 809'11. It is supposed modified by a (5, shift on the sequent which 

 here produces a change of 6 '3 pointing to an original v., = 809'11 + 6'03 = 815'14, 

 practically exact. Applying the method to Nos. 3, 9 gives 



= 06 '24 

 with 



A 2 = 1099814- '064p 9 +'043p 3 = 10998'14'10 



But the preferable choice is to use the fact that (10) is the limit to (9), the same 

 value of must enter, and the result depends only on the observation error. 

 The result is now 



'98= '03 + '18p 9 , ='03 + '18^ 9 , A 2 = 10998'187-'06p 9 . 



Thus with maximum error d\ = '04 maximum uncertainty in A 2 is '06, but the 

 line (9) is a good one for measures and the probable error will not exceed '02. 

 Hence as the definitive value A 2 = 10998 '18 is probably within '03 and certainly within 



'06. Hence 



A 2 = 10998'187'03, 3 = 611'0104'0017. 



The value of obtained from the i/ t displacement = 610'87 + 76^ '04 to make 

 these the same requires di/, = '19, Vl = 1778'09. This is possible though not probable. 

 We cannot say definitely here therefore as in Kr that the triplet modification produces. 

 VOL. ccxx. A. 3 M 



