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



With the value of v above the value of A calculates with this limit to 7140 = 

 with <^ = 70 '34. The denominator differences of S n and S 13 for m = 1 and 2 are 

 respectively 4188 and 3964, i.e., close to 59S = 4150 and 57^ = 4010, with errors in 

 d\ of '31 and 0, divided between the two sets of lines. It is possible they may be 

 the same within limits of error (59<?), when the value of d\ in the second would 

 be -'16. 



The formula for P, calculated from the first three lines, is 



n = 22281'97-N/(m + '828585- 



.'97-N/l 



m 



This formula gives the following values of O C for the lines for m = 7, 8, 9, 10, 

 viz., '55, '85, '26, 1'86. If the denominator be treated in the same way as 

 Al,* i.e., deducting the group constant '043761, it may be put into the form 



-'043761 + '872346(l- 21480 ) ) which reproduces the '215 constant. Also 



m 



m 



VS(l) = 22277'80 = P( QO) within error limits. 



If 8^3) had been taken as S 12 (3) this would not have been the case. But VP(l) 

 extrapolates to 40717'20 with a denominator 1'641213, whilst S ( <*>) = 39749'90 

 with a denominator 1 '699998, and they cannot be the same even approximately if 

 the typical formula holds. The extrapolated value of VP(l) requires A = 6428 to 

 give v = 320'8 or 91<5, again giving a multiple of 7<^ and at the same time more in 

 line with other elements as being a multiple of S itself, and a multiple more in step 

 with them. It points to the likelihood that the series chosen for S is a parallel series 

 to the true S, i.e., the VS (m) is correct. If so, using the values of VS(l, 2) with 

 S ( oo ) = the extrapolated limit 40717, we should expect doublets with the first lines 

 at 18440 and 30217. There is a doublet at 18457'31, no line observed at 30217, but 

 the doublet companion expected at 30537 is found at 30537 '33. Also 18457 appears 

 as a satellite to a stronger line 18539'91 in a corresponding position 82' 60 a-head. 

 The second set of lines above is, therefore, probably the true S series, the first being 

 a parallel one. With limit 40717'20 and v = 319'45, the mean of all the doublets, 

 the value for A is 6404 = QlS with S = 361'89it' 2 . The value of 361'89 is subject to 

 considerable uncertainty owing to uncertainties in the limit value and the atomic 

 weight, and its agreement with the final estimate for the oun is a mere coincidence. 

 The spectrum of Sc is a most interesting one, but its discussion must be postponed. 

 The object of touching upon it here is to obtain some indication of the nature of its 

 oun as Sc occupies the first place in its sub-group. It would clearly appear that the 

 multiple of the oun in A contains 7 as a factor, viz., 13 x 7^ = 52 x 7(V 



The separation of PI() and P 2 (4) is 11 '26, corresponding to a denominator 

 difference of 5607 = 80<5. This is in fair agreement with the case of other P series in 

 which the differences for orders below the first are about '8 A. 



* [II., p. 46.] 



