464 
DR. W, M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
The discussion of the two F separations has given A 2 = 267713 —'0126^+‘01, 
S= 14'4710 —■00068^±'0005. Let x denote the correction required on this value 
of A 2 . Then 
36A2+16f(5= 9880-057--4653^+36-90a: 
4.2Ao + 2^S = 11280T23--5306f+4213a: 
150A2 + 9(5 = 4028719-l-896^+150-48x 
Supposing that the true multiples of the oun are y greater, and putting 
di'i = —’0031 + di/j 
36-90a:--017^ + 27 {dv^-dv,)-%Q + Z-&2ij^ = 0 
42-13a;--025^-27c?r2+lT3 + 3-62^2 = 0 
150-48ic--040£-27(7.i + 75 + 3-62^i = 0 
or 
.X = '010 +'00046^-73(71^3--0972/3 
x= --027+ -00057^^+-64(71/2-- 0862/2 
X = --0050 +-00026 ^+-18di/i--0242/1 
In these ^ cannot be more than a few units, dv <- 02 . and.x <- 01 . This can only 
happen if all the y = 0. Thus again there is the very important fact that the oun 
multiples are quite definite and are those used in the actual calculations. ^ is not large 
enough to affect the limits of accuracy in x. The separation 1070 is not so well 
determined as the others and dv^ may well be >- 01 . Thus the first and third can 
easily give the same values of x, but the second would require dv 2 of the order "03, 
inadmissible if the v.^ were accurately determined. But as a fact the average vo as we 
have seen does not enter in the line here considered and it may be so large as to alter 
the multiple. The second may therefore be considered as not at disposal, and the 
third then gives very close limits, viz., with dv^ >'01 
A 2 = 267-708--0124^^±-002 
= 14-4708--0007t^±-0001 
the same value, though with closer limits of accuracy, as was ol)tained from the 265 
separation. With maximum ^ = '33, ^ — 14-4708 +'0003. 
But further, in addition to Watson’s separations, we have found affixed to the 
F series, another =—1932, and this must be tested. The linked line is given by 
B.M.M. as 0593-953 LA. Still using 9-figure logarithims, the wave-number is 
15149-7338 giving the separation 1932-2902, and corresponding to a limit 31852-1816 
— 1932-2902 = 29919-8914 + ^—(7i/. The mantissa of this is 914613-17 —31-997 {^—dv). 
The displacement on 31852 is therefore 58982-87 —2-867^ + 32(7z/. With the above 
values of A 2 , 8, 220 A 2 + 6^ = 58982-58 —2-728^± '44. This again is an exact agreement. 
The foregoing does not give A 2 with the desired definiteness unless the value of f is 
determined. The reason is that it has been based on displacements on the same limit. 
