568 DR J. HALM ON 
those of the series to be compared vy and A. From the considerable number of series 
belonging to this group we select here the following: He, 3rd S.8.; In, 1st SS. ; 
(2nd comp.); Tl, 1st 8.8. (1st comp.); Zn, Ist 8.8. (2nd comp.); Li, Ist SS. The 
following table contains the results of the comparison. By using equation (8) and 
adopting for \, in each case the wave-lengths. which I have bracketed in the table, 
we find the following values of log a, and log #6, : 
log a;. log B;. 
He: 9:99165 — 10 450246, — 10 
‘In: 0°43927 6°31899 —10 
Tl: 0°35204 6°13701 —10 
Zn; 0°39819 625993 —10 
Tei © 0:03893 505185 — 10 
while the computed wave-lengths as well as their discrepancies (Obs. — Comp.) are given 
as follows : 
In, Ist 8.8. Tl, Ist S.S. Zn, 1st 8.8. i 
ES SGD eHTSES. (2nd Comp.) (1st Comp.) (2nd Comp.) te 
6563-07 6678°37 0:00 3039°5 0:0 3529°6 0:0 3302°8 0:0 6103°3 0:0 
4861°52 492210 0:00 2560°2 0:0 29216 0:0 2771:0 0:0 4602°4 0:0 
4340°63 4388:07 + 0:03 2389°6 0:0 2711:1 —0°3 2582°7 —0°1 4132°3+0:1 
4101:90 4143:90 + 0:02 2307:0 —0°2 2610°2 —0°3 2491'7 0:0 3915°14+071 
3970°22 4009°41+0-01 2260°2 + 0°4 2553°3 — 0:2 2440:2 —0°3 [3794°9] 
3889-20 3926°70 — 0:02 [2230°9] 2517-9 --0°4 [24080] ... 3720°8 — 1:9 
3835°53 3871-96 — 0:01 2211°3-0'1 2494-2 —0°2 3671°6 - 1:0 
3798 04 383369 + 0:02 2197:5 0-0 [2477-6] 
3770°77 3805°88 + 0°02 2187:4+01 2465°44+0°1 
3750°30 378501 + 0°02 2179:9+0°1 2456°3 + 0:2 
373451 3768:91 + 0°04 2449°2+0°4 
3722°08 [3756-24] 2443°7+0°3 
3712°11 2439°2 + 0:4 
| 
Although the method of computation scarcely needs an explanation, I will never- 
theless illustrate it by one example. Suppose we want to find the 3rd _helium-line 
(from the top). The corresponding H-line is /=4340°63, further \,=3756'24 and 
L, = 8722°08, hence 
{ a; 
X— 3756-24 ~ 434063 — 3722-08 * Ps 
= 3756°24 + 631°83 = 4388°07, 
= 00015859 — 0:0000032 = 0:0015827 
The existence of so remarkable a relation between the line-series of different 
elements is a novel and certainly important feature, the discovery of which we owe 
to the application of the Rypserc-TureLte formula. In some cases the relation 
