Frequency Differences in Spectral Series. 341 



o£ regularity. This consists in the recurrence of constant 

 frequency differences between corresponding members of 

 certain groups of lines, so that if A r be the frequency for 

 any line r in group A, then we have the frequency B r in 

 group B by adding a constant frequency /3 (say). Using 

 this notation the groups for As are A r + 461, and A,. + 8058. 

 It is plain that besides the intervals 461 and 8058 there 

 exists also 8058—461 = 7597. For Sb, Kayser and Runge 

 give A'+2069, A'+8613, A'+9955, A' + 12460, and 

 A' + 15023, and for Bi, A" +6225, A" +10245, and 

 A" + 21667. By subtraction we have in Sb, 1342 and 

 in Bi, 4020. In fig. 1 it is seen that these values, viz. 461, 

 1342, and 4020 for As, Sb, and Bi resp. lie on a line 

 (very exactly as appears from the calculation below) passing 

 nearly through a zero value for ]S T and indicating a value 

 41*2 cm. -1 for P. Examining Grautier's spectral measure- 

 ments in P as quoted in Kayser's Spehtroscopie we find 

 the set 



4649-23 (4) 41*83 4658-29 (6r) 

 4575-08 (3) 41-88 4583-86 (0) 

 4475-43 (3r) 41*86 4483-83 (3) 

 4102-3 (0) 41-8 4109-34 (5) 



The interval 41*8 cm. is in good agreement, but the number 

 of cases is too small to warrant any great confidence. There 

 are about 150 differences within the range 40 cm. -1 to 

 50 cm." 1 , so that the odds against four of these falling 

 within a given region of '05 cm. -1 is * 



1 ^q5y e _. 75=16a 



4 ! 

 Hence the odds against this group being within '60 cm. -1 

 on either side of the given line is only about 13 to 1. 



In the Oxygen column triplet series occur again and the 

 values for \/vi and s/v^ for 0, S, Se are shown in fig. 1. 

 Collinearity exists in vj but not in v 2 . For the remainder of 

 the column we have no data. 



For the halogen column, again, the data are insufficient. 



In the last column frequency differences have been found 

 by Kayser f for Ru, Pd, and Pt, but none in the first row 

 Fe, Co, and Ni, so that it is not possible to apply a test. 



Turning now to the first column, He, Ne, &c, there is a 

 further possibility of linearity. Rydberg J has found in 



* Using the formula ~^e~ x , where x is the average density. 



t Abh. Berl. Akad. 1897. 



% Astroph. Journal, vi. p. 239 (1897). 



