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 tlie others, the mean value of = 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 'OOA and the true wave-number 19942'47 in place of... 2'53. 
With this the separation = 1775'69 and is brought into practically the exact (S) i/j 
value (see p. 396) required, which is 177576. The outstanding ’07 {dX = ’017) would 
be attached to the strong second line of the doublet (lO) 21717. This is in very 
sinking suppoit of the general argument. AVe have already seen good grounds for 
putting f 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 . Q.g. with mantissa of order 5 the coefficient of ^ is 15'4^. 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 = 27, dn = '42. This reduces the observed 
V 2 — 809 5o to 809 11 . It is supposed modified by a dj shift on the sequent which 
here produces a change of 6 '3 pointing to an original 1 / 3 = 809‘ll + 6'03 = 81514, 
practically exact. Applying the method to Nos. 3 , 9 gives 
'98^= '06 -I-18^3—‘06^)3 
^ = -06-1-18^9- -06^3 = 06 + -24 
with 
A 2 = 1099814--064p9+-043^3 = 1099814±10 
But the preferable choice is to use the fact that (lO) is the limit to ( 9 ), the same 
\ alue of ^ must enter, and the result depends only on the observation error. 
The result is now 
■98^ = '03-t 18^9, .^=-03 + 18^9, A 2 = 10998187--06p9. 
Thus with maximum error dX = '04 maximum uncertainty in Ag 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 = 1099818 is probably within '03 and certainly within 
’06. Hence 
A 2 = 10998187±'03, d = 6ir0104±'0017. 
The value of 8 obtained from the displacement = 610-87 + 76di/i-'04^, to make 
these the same requires dj'i = '19, = 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 
