38 
DR. W. HICKS; A CRITICAL STUDY OF SPECTRAL SERIES. 
order as the a. But the difficulty may be met as follows: If D denotes the 
denominator of s (l) and D' that of P (Qo), the values of D-D' instead of being zero 
are respectively (see Part L, p. 76)— 
Na . . 
. •002772±(8390); 
Rb . . 
. •010696 + (16119), 
-(3210); 
K . . 
. •009150 + (8716); 
Cs . . 
. •01672± ? 
The values of 2W or A are given at the bottom of p. 80, viz. ; 
Na. K. Rb. Cs. 
•000744, -002933, -012887, -032435, 
whence* 
8W = -002976 = -002772 + 1/41 x possible error for Na, 
6W =-008799 == -009151-1/25 X „ „ K, 
2W = -012887 = -010696 + 1/8 x „ „ Kb, 
W = -016217 = -016712- ? „ „ Cs. 
It is thus possible to assert the truth of Rydberg’s relations if they are referred 
to the sequences—but not if referred to the series. The value of the first line of the 
S series is found by adding a multiple of the atomic weight term to the sequence 
term for that line, viz., 8W for Na, 6W for K, 2W for Rb, and W for Cs. The 
essential point now is that the term in does not enter. In any case the 
multiple is to be obtained l^y first determining the real limit of the series and then 
the change in the denominator calculated for m = 1 to correct it to the observed 
value. This suggests a similar explanation for the appearance of the terms in 
the Ca group, either an addition of an atomic multiple to the first term of the 
p-sequence, or the deduction of the same multiple from every term after the first, 
and this suspicion is intensified when we notice that the values of tlie /3 are them¬ 
selves multiples of the atomic weight terms. If we compare the values of /3 and of 
Ao, given in Table I., this is at once clear. We find with extreme closeness 
Mg. Ca. Sr. 
/8 =- 20A,„ I 4 A 2 , 3 A 2 . 
To obtain the proper values for the limit it is found necessary to deduct from the 
observed denominators respectively 5 A 2 , 5 A 2 , A 2 . Ba is too uncertain to get definite 
results from. If all Saunders’ lines belong to BaS and the modification de23ends on 
an addition to the first term only, it is necessary to deduct I 2 A 2 from the first and 
the // and a become so large in comparison with the values for the other elements as 
to render the explanation very doubtful. It can, of course, be met by deducting 
multiples from the second line as well as the first, but we can have no certain grounds 
* Too much weight must not be given to these as the possible errors are so large. 
