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



407 



but even should it be in error the doubt does not affect the argument as to the 

 relative displacements of the different lines, as ySi denotes the displacements relative 

 to 19889. The final results are given in the following table : 



Of the above (14, 18) must be set aside at once: (14) because it belongs to the 

 triplet set linked by 2e to the parallel set F (l), and (18) because it is F 3 (2). It may 

 also be noted that neither have the prevalent separation 1780 to lines of higher 

 frequency. Of the numbers on the right of the list, those in thick type give the values 

 of y which bring the outstanding differences to the corresponding number in ordinary 

 type. These differences must be due to errors either in or observation. Since is 

 small, it is seen that they must be capable of annulment by the observation errors 

 6(q p), and must, therefore, at the maximum be <12. The smallness of can be 

 seen from the following considerations which connect it with the corresponding f 

 (say ') for the 1864 F series. The limit of the F is 30725'30 + / with mantissa 

 889322-3074^. It is a d (l} sequent. If 19989 is a D line with y = 0, its sequent 

 is 51025-29 + ^-1998972 = 32035'57 + / . The mantissa of this is 8 798 53- 30'29' + 6g. 

 Both being d sequents must differ by a multiple of the oun. Their difference is 

 9469 + 30'29^- 3074^- 6q and 15%S = 9470. Hence 



30'29-3074' = 

 or, 



Thus = ^'3. Since the 1864 limit is determined as the mean of F and P series 

 its value is subject to a very small uncertainty and g will be a small fraction. 

 VOL. ccxx. A. 3 K 



