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



The discussion of the two F separations has given A 2 = 267713 "0126 '01, 

 = 14'4710 '00068'0005. Let x denote the correction required on this value 



of A* Then 



= 9880-057--4653+36'90x 



= 11280-123--5306+42-13:r 

 150A 2 +9<$ = 40287'19-r896+150'48a; 



Supposing that the true multiples of the oun are y greater, and putting 

 d Vl = --0031 + c^, 



3fi'90a:--017f + 27 (d^-dv^-^O + S^y., = 



42'13x- '025^-27^2+1 '13 + 3'G2^ = 



150'48o;--040-27<&< l +75+3 1 62y ] = 

 or 



x= 010+ t 00046f- 1 78d 8 - I 097y a 



x= - '027 + > 00057+ > 64ok s - '086ft, 



x = - 



In these cannot be more than a few units, dv <'02 and a 1 <'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 3 may well be >'01. Thus the first and third can 

 easily give the same values of x, but the second would require di> 2 of the order '03, 

 inadmissible if the v. 2 were accurately determined. But as a fact the average v. 2 as w r e 

 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 l >'01 



A. = 267708-'()124f'()02 

 3= 14-4708-'0007f-0001 



the same value, though with closer limits of accuracy, as was obtained from the 265 

 separation. With maximum f = '33, S = 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 6598'953 LA. Still using 9-figure logarithims, the wave-number is 

 151497338 giving the separation 1932'2902, and corresponding to a limit 318521816 

 -1932'2902 =29919-8914 + ^-^. The mantissa of this is914613M7-3r997 (g-dv). 

 The displacement on 31852 is therefore 58982'87 2'867+32dv. With the above 

 . values of A z , S, 220A 2 + 6^= 58982'58-2728^'44. This again is an exact agreement. 



The foregoing does not give A 2 with the desired definiteness unless the value of is 

 determined.. The reason is that it has been based on displacements on the same limit. 



