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



These differences may be written 

 72624 = 40f(l782'18-050+ -31.il/,) 32076= 18 (l782'00--047^ 



= 40^(1793-18... ) =17|(18071... ) 



The first consequence to be drawn from these numbers is that as S is to be of the 

 same order of magnitude as calculated from A, and A 2 it can only take place in the 

 first arrangement since the co-efficients of (the only variable capable of large values) 

 are practically equal. In other words A,= 40fc$, A 2 = ISS, the same multiples as in X. 

 This is OIK; quite definite conclusion of importance. 



But further we know that S must l>e one of the following sets 1783'5, 84"4, 85"3, 

 80" 1 , 87 '(), of which the first two though perhaps possible are improbable and the last 

 three equally probable. We will state the results for the first, third, and fifth, the 

 others being intermediate. The values of dv t , dv 2 being uncertain to about unity, the 

 values of f can only be estimated to the same order. Taking A,, in order to produce 

 the required values of S, must have the respective values of 27, 64, 100 within 

 a few units, and the numbers inside the brackets for A 1; A 2) become 



1 783-53 - '050 + '31^, 1783'27 -047- '047^, 



1785-38-... 1785'OQ ... 



1787-18-... 178G7... 



where now f cannot exceed a few units. The respective limits become 50473, 50436, 

 50400. One of these is close to a S limit. There is another corresponding to the J, 

 displacement about 31 ahead and giving i>, = 5375 about. We already have an 

 accurate value of one d sequence, viz., the F (co) = 29964'20. Combined with the 

 limit this should give a I.) line = S(oo) -29964'20, i.e., near 20509, 20472, or 20435, or 

 the 31 higher values. We only find the following possible lines, viz. (2)20515 and 

 (4) 20*138-8 (W.), (0) 20446-38 (It. II.), 20473, the first and fourth being C.R's copper 

 electrode lines. The first is one of a chain of 2680 separations, or ^-i/, stretching 

 hack to 15136 and by 2689 to the strong line (10) 23204'6 (R.) or 7'57 (W). It has 

 none of the signs of a D line. The line 20438 is one of the strongest in this neighbour- 

 hood has no /, separation link, but 5625"8 back to 148132 (W) to which also 20446 

 has the (<$,) 5649 link, viz., 5633. Again the 14813 shows a D modified lt i> 2 set, viz., 



(0) 14813 (W) 5382-71 (4) 2019571 (W) 2672'41 (5) 2286812 (W), 

 5385-91 (0) 20198-91 (R) 2669-16 (l) '07 (R). 



Hence here we have all the signs of a D n line in 20438 with the above as a satellite 

 set, at the F separation (56...) behind. Now it is a very striking fact that the 

 measures of W. and of R.It, for these lines not only differ by amounts larger than 

 can be attributed to observation errors, but also that their intensities are not 



