108 PEOF. W. M. HICKS: A CEITICAL STUDY OF SPECTRAL SERIES. 



N not constant. In this case the values of N are supposed to be different for both 

 the P and S series. Each series, therefore, requires as before three lines to determine 

 its constants, and the relations P(co) = VS(l) and S(co) = VP(l) give two 

 additional equations to determine the two values of N say, N p and N,. Unfortunately 

 the values of the first lines are so uncertain (with exception of NaP(l)) that the 

 values of N ? N and N, N vary very largely with the errors in the observed lines. 

 For instance, in the case of Kb, if L.'s values for P (1) and S (3) be used, N P -N = -12, 

 N S -N= 1300. If S.'s values for P(l) and S (3.4) are used, N P -N = 141,N.-N = 651. 

 In the first case P is reproduced as well as the original, but S not so well ; in fact, 

 S( oo ) comes out too large. In the second, P is not so good, and S is better than 

 with the 1300 difference. The discussion shows, however, that within easy limits of 

 error the N of P may be taken as constant, and for a provisional value the usual 

 value of N will do -very well. 



For Na, using K.R.'s values for 8(3.4.5), SN, = 215, p = "661089, a = -'032760, 

 and the calculated lines for S agree better than the original except, however, S (2), 

 which is 4"28 wrong in place of 1'37. If, however, PASCHEN'S S (2) is used and 

 K.R.'s 8(3.4), then SN 7 , = 306, SN, = 588, the limits are considerably altered, and 

 the calculated results bad. If we make SN P = and use PASCHEN'S S (2) and K.K.'s 

 S (3), SN, = 342, and the other calculated lines are all outside the limits. The most 

 reliable result appears, therefore, to be that calculated from K.R.'s values for S (3.4.5), 

 which improves all the other lines but requires S (2) to be 4 "28 A.U. larger than 

 PASCHEN'S observation, which can hardly be the case. 



For K, using K.Il.'s 8 (3.4.5), SN, = 609, /A = "841460, a = -"066494. This brings 

 8(2) within "22 of PASCHEN'S value (original difference 16'20), and all the others 

 within limits. 



For Reusing S.'s values for S (3.4) and K.R.'s for S (5), gives SN P = 141, SN, = 651, 

 p. = -894830, a = -"085235, but the P series is bad, although S is better than that 

 referred to above where SN, = 1300. It is probable that a value between 651 and 

 1300 would be preferable. 



For Cs, using L.'s for P (l), K.R.'s for P (2.3), and S.'s for S (3.4.5), gives SN P = 369, 

 SN, = 1286, ^=1-458005, = -"092888, /t. = -992400, a, = -"112079. These 

 bring all the lines within limits, P better than the ordinary. 



It is to be noticed that although N p may be kept constant by giving permissible 

 variations to the lines from which the constants are determined, yet there is a tendency 

 shown to an increase with increasing atomic weight. In all cases N, increases with 

 increasing atomic weight, but the calculated values vary so much with the actual 

 errors of observation, that it is useless to attempt to find any relation between them. 

 SN, for Na is probably not far from 220 ; for the others it is larger. The values of 

 SN, for K, Rb, Cs might be the same, but in view of the smaller value required for 

 Na, this is not likely. One important fact brought out, however, is the raising the 

 value of a for S, so that its ratio to /u. '5 becomes much closer to that for the P series. 



