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



separation occurs with 18447 or v l} v 2 with 17615. But provisionally that was set aside 

 for the moment. If they represented a special D set, the separations ought to 

 reappear in a triplet series of the F type, and in the reverse order. From the sets 

 already excerpted the lines (8) 1860779, (10) 2391572, (5) 26365'19 appeared to 

 have all the signs (RYDBERG'S tables) of belonging to one series. The formula 

 calculated from them brought to light a whole long series of observed lines. The 

 limit found was 30724, close to the value already found (30713) as of the 

 order of magnitude to be expected. This so far supported the supposition of the 

 D relation, but there also came to light another result of evident importance in 

 general theory viz., the F series already referred to. The ordinary form of a series 

 is one in which successive lines obey a formula of the type A (m). In this case 

 we find series associated with it whose successive lines are given by A + (m). 

 This holds for each of the triplet sets, so that the complete series are given by 

 A0wi, B0 (m), C<f> (m}, where B = A+1864, C = A+ 1864 + 830. Quite apart 

 from the importance of this fact in the theory of spectral series the phenomenon is of 

 special use in calculating the various constants on which the series depends. For 

 instance the sum of the wave-numbers of two corresponding lines gives 2 A, 2B, 2C, 

 thus determining the values of the limits quite independently of the nature of the 

 series formula used. Moreover, the displacements which so frequently occur in the 

 F and I) series in the sequence term introduces uncertainties. This happens in two 

 ways. First through the modified i/, values in which it is not always possible to say 

 whether the displacement is produced in the D, or the D 2 line. Secondly because 

 the typical line in any order is often wanting and only appears with a very large 

 displacement of multiples of A a on the sequence term. This effect, however, 

 provided it occurs for both sets (F, P), does not influence the values of A, B, C 

 thus determined. Cases in point are the Kr sets F (2) (7A' a ), F (2) (lOA 2 ). 

 F! (2) (l6A' a + A a ) given on p. 380. In consequence it is possible to determine the 

 separations B A, C B independently of satellite or other displacements. That such 

 sequence displacements occur in these 1864 series is shown by separations which 

 deviate from the normal by more than observation errors. 



But, further, the difference of two corresponding F and F lines, say Fj F ]( P 2 F a , 

 F 3 F 3 , should each give 2f(m), if as is t^ie normal rule the sequence term is the 

 same for each line of a triplet. When however as we have seen in Kr, and shall 

 find even more markedly in X there are displacements in/(m) for successive lines 

 in a triplet, these differences will not be the same, and the observed separations will 

 vary from the normal values. For instance, suppose f(m) becomes f(m)x for the 

 second set, and/(m) y for the third. The lines are A/(m), B + (/(m) x},.. . 

 The values of A, B, C calculated from the sums are not affected, and the real values 

 of the separations given by A-B, C-B are not affected although the observed 

 separations are v+x, v' + y and vx, v -y. In some cases we shall find evidence from 

 close lines with different x or y but the results are quite definite. If, however, in 



