48 
DR. W. M. HICKS; A CRITICAL STUDY OF SPECTRAL SERIES. 
for the succeeding terms and calculate the value of N required to lepioduce the 
observed value. These were then corrected so that the separations of the Sj, Sg, and 
S-i lines should have the constant value found for p^, p.j. As an example, the case of 
Zn may he taken. The limit is 42876'42 and T)„, = w + l+ 290534(1— 2l520«i ^). 
The results, with possible errors due to possible ol)servational errors, are as follows :— 
m. 
2 109790'5±5-6 
3 109783-8± 12-39 
4 1098l7-7±42-0 
5 109836-7 ±94-5 
G 109618-0 ±220 
These numbers require correction to make the values of p^, p.j correct, viz., 389-19, 
190-20. For ni = 2 the observed values are 388-75, 190-09, i.e., dilference of —-44 
and —-10 . Least squares give as the most probable corrections —-33 to tq, -11 to n.^, 
and -21 to This adds a correction of -6 x possible variation, %.e., 3-3 to the N, 
making N = 109793-8. Similarly for m = 3, I'l is -46 too small and p.^ is -33 too small. 
Treated in the same way a correction of ]A the possiljle must be added, making 
N = 109791-1. It is clear that the value of N can easily be constant and 
= 109790 ±5 within limits of error. In fact, with this value the errors in X are 
respectively about 0, i, L y, f possible ones. The results are given in the 
following table:— 
N. 
p. 
3N. 
Zn (5). 
109792 (3) 
0 
•290534 
117 (3) 
Cd(4). 
110022 (2) 
0 
•359856 
346 
2) 
Hg(9). 
109G07 (4) 
0 
•307463 
- 68(4) 
Mg (5). 
110457 (3) 
- 1 
• 400856 
782 
Ca (5). 
111406 (4) 
- 1 
•617130 
1737 
Sr (4). 
111704 (2) 
- - -6 
•697845 
2030 
Ba(2). 
113023 (3) 
- 19 
•789911 
3348 
A1(4). 
tla(2). 
109267 (4) 
0 
•238500 
-398 
I»(6). 
109348 (6)I 
109400 J 
0 
•277705 
-3321 
- 175 J 
T1. 
109088 1 
109200 / 
0 
•247083 
-577 1 
-475 
1 he numbers alter the chemical symbol {ejj., Zii(5)) give the number of lines 
involved; ^ is a small alteration in the limit S(oo) as determined from the three 
first lines ol a series. It is unnecessary to give a, as the formula for is 
m+ 1 + p. (l— 21520ui”^). The slight uncertainty in the last two digits of the number 
21520 will not appreciably modily the result. It is noticeable that the limits in the 
cases of the Mg group, in which a term was found to be necessary, are close to 
