404 DR. W. M. HICKS: A CRITICAL STUDY OF Sl'KCTlfAL SKKIKS. 



than for D n . Using D 21 v for D J2 and calculating the formula constants from the 

 first three, there results for the D 12 series 



n = 30644'60-N/L + '994354- 



m I 



with the large possible variation in D(oo) of = 12'23. Using this value of the 

 limit and calculating the formula for D n , the line D n (5) is reproduced with 

 O C = '22, O being '5. If, however, the S lines be used with /u. =f the limit comes 

 to S(oo) = 30614'603"60 and the fourth line is reproduced within limits. S(oo) 

 and D ( QO ) cannot be the same within error limits. If /a = 1 +f, S ( co ) = 30633 '47 3, 

 and the limits can be the same, viz., with = 9732'50 on D(oo) 5 but /a. cannot 

 be 1 +y* if the doublet usually assigned to P belongs really to a P series. I had 

 intended to supplement the direct determination of A from v by a discussion of 

 collaterals, of which both Ag and Cu afford a large number. The doubt however about 

 the form M = 1 +f, and the presence of the numerous collaterals, gives a suspicion 

 that the series are related to the F series with limits based on the typical S ( co ), that 

 they are analogous to the F terms in the high melting-point elements of Group II., 

 and that the doublet usually allocated to the P series is really analogous to the 

 F triplets with negative wave numbers found in Ca and Sr. That discussion is 

 therefore held back for the present.* But certain points not open to doubt and 

 forming a portion of the work of the accurate determination command a place here. 



The D (2) lines are sharp. F and P have measured the lines D n (2) and D 21 (2) 

 with their interferometer. Their measures give a separation of 900'3419'0070. 

 In order to get full advantage of their accuracy, and to avoid the uncertainty due to 

 the last significant figure it is necessary to use logarithmic tables with more than 

 7 figures. This has been done on the supposition that F and P's errors are not 

 larger than '001 A.U., i.e., unity in the seventh significant figure. The old measures 

 are sufficient to show with certainty that the satellite difference is 23^, and 

 the old approximation to A will give 23^ with an inappreciable error, whence D 12 

 can be found. Taking D ( GO) = 30644'6000 + the mantissa of D n (2) = 5465'671 is 

 979596'44-120'59 and 23^ = 2421'18-'15 Hence the mantissa of D 12 is the 

 difference or 977175'2G-120'44f VD 12 calculated from this is 12373'6789 + 1'0045 

 giving with VD 21 the value v = 920'4431 + 0045 in which the correction for is only 

 effective if > 10. The value of A calculated from this is 27786'80-l'473f'20, in 

 which the uncertainty of '20 is due to the uncertainty '001 in A. This value is 4 

 less than that of Table I. obtained by supposing K.Il.'s values for D 12 and D 21 had no 

 errors. It gives S = (361'754'0026-'0152f )iv 2 . With the mean value = -975 

 suggested above this becomes S = (361'902'0026)w 2 . 



The foregoing is interesting also because it shows how the application of the laws 

 developed in the present discussion can help towards more accurate determinations of 



* The value obtained for q from the collaterals was 361-708 -0026 - 0169, which with = - 10, as 

 indicated in the text, gives a value surprisingly close to that deduced from all the elements combined. 



