DR. 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 simidtaneously on l)oth 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 aflPorded 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 -(3) 42059 
123-00 124-53 
-( 2 ) 42721 252-37 Si(l) -( 1 ) 41935 252-94 82 ( 1 ) 
300-11 
-(1) 42421 
-( 8 ) 41496 
122-92 
-(1) 41625 252-30 S' 3 (l) 
(In) 26407 35-23 
17-31 
(10) 26424 35-31 
299-56 
(2) 26724 35-47 
(1) 26442 
17-29 
Si (2) 
299-72 
(5) 26759 
( 2 ) 27175 
22-53 
(1) 27207 38-70 82 ( 2 ) 
298-15 
(2n) 27506 
(1) 27520 35-17 [S'3(2)] 
These lines are numerically displaced with reference to the S by amounts 
represented by the following parallel schemes :— 
Si(l)(-96) 
Si(l)(- 68 ), Si(l), 
(-l7i8)Si(l)(-68) 
82 ( 1 ) (-98) 
82(1) (-68), 
8'3(1)(-98) 
8,(1), S'3(1)(-68), S'3(1) 
Si (2) (-98), Si (2) (-38), 
Si (2) (-68), Si (2), 
(-17f8)Si(2)(-68), (-17|8)Si(2), 
82 (2) (-98) 
82 ( 2 ) (- 68 ), 82 ( 2 ), S' 3 ( 2 )(- 6 S), 
(-1718) 82 ( 2 ) (- 68 ). 
[S'b(2 )] 
In addition, for m = 3, we have seen that in place of normal 82 ( 8 ) the displaced 
82 ( 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^, displacement in the sequences. Also 123 in m = 1 and 17 in m = 2 
on the same 6 (^', whilst the constant displacement 300 is explained by — = —69(li 
on the limit. 
