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



349 



It is most important to get evidence which can carry conviction as to the reality of 

 displaced lines, especially where the displacements occur simultaneously on both limit 

 and sequent. A numerical coincidence in this case can have little weight by itself. 

 In fact, it can have weight only in each particular case provided it is known from 

 other considerations that such displacements are a common and universal rule. For 

 this purpose it is instructive to adduce here some striking evidence afforded by certain 

 sets of lines connected with the S series. The lines in question are arranged in the 

 two following schemes, expressed in wave-numbers : 



-(1) 42844 



123-00 



-(2) 42721 252-37 Si(l) 

 300-11 



-(1) 42421 



-(3) 42059 



124-53 

 -(1) 41935 252-94 S,,(l) 



-(8) 41496 



122-92 

 -(1) 41625 252-30 S' 8 (l) 



(In) 26407 35 '23 



17-31 

 (10) 26424 35-31 



299-56 

 (2) 26724 35-47 



(1) 26442 (2) 27175 



17-29 22-53 



Si (2) (1)27207 38-70 S 2 (2) (1)27520 35-17 [S' s (2)] 



299-72 298-15 



(5) 26759 (2w) 27506 



These lines are numerically displaced with reference to the S by amounts 

 represented by the following parallel schemes : 



S 2 (l)(-98) 



BJ (2) (-68), 

 (-17J8JS! (2) (-68), 



S,(2)(-38), 

 S 1 (2), 



(-17J8)S 1 (2), 



S a (2)(-9S) 



82 (2) (-68), 

 (-17i8)S 2 (2)(-68). 



8* (2), S's (2) (-68), 



In addition, for m 3, we have seen that in place of normal S a (3) the displaced 

 S 2 (3)( 9$) is seen. The parallelism in spite of lacunae show that the set are 

 definitely related, and the fact that the same displacement on the. sequents for 

 m = 1, 2, 3 are required to represent the observed separations is specially striking, it 

 being remembered that a displacement on the limit gives constant separation for 

 different orders, whilst one on a sequent gives different for different orders. Here, 

 for instance, 252 in m = 1, 35 in m = 2, and 16 in m = 3, all depend on the same 

 oun multiple, 9<5, displacement in the sequences. Also 123 in m = 1 and 17 in m = 2 

 on the same 6(5, whilst the constant displacement 300 is explained by 17^ = 69(J a 

 on the limit. 



