570 DR J. HALM ON 
(4) Lithium, Ist 8.8., and Hydrogen, Ist 8.S. 
[voi [yn 
12211 12189 
6867 6856 
4396 4388 
3053 3047 
2243 2238 
1705 1714 
1351 1354 
1-00177[¥ Ju 
12211 
6868 
4395 
3052 
2242 
akcalcg 
1356 
The RypBeRG-THIELE equation in the form given in (9) presents some striking regu- 
larities of the constants which deserve to be mentioned. 
{by far the most frequent) where b, is negative, we may write the equation in the form; 
[vo —v]}*=a,(m+pt+c)(m+p-—c)=a,(m+d)(m+e) 
Now it appears that in a certain group of elements, such for instance as the alkalis, 
the constants d and e may be represented by common fractions having the same 
denominator. Thus we find for the subsidiary series the following numerical equations : 
Li 1.88.:  [v,-v]}*=[4:95899 — 10}m- in 
2, SS: =[4-96101 — 10](m — 3;)(m — 3%) 
Na “IEs.S:: = [4°95748 — 10](m+%)(m — i%& 
2. 8.8.: = [4°95512 — 10](m+ =3,)(m — 42 
Ko) aeSis:: = [4:94046 — 10](m +44)(m— 44 
2. Si8i: = [4°92668 — 10](m + 42)(m — 32) 
Rb 1sSise = [490881 — 10](m +43)(m — 43 
Cs SHEE == [4°90432 — 10](m + 23)(m — 22 
The coefficients a, are given as logarithms. 
means of these equations leave the following errors in the observations : 
The wave-frequencies computed by 
If we consider first the cases 
14 
C.) 
(10) 
= 28595 
= 28580 
= 24481 
= 24481 
= 22049 
= 22005 
= 21202 
= 19746 
iL | Li, | Na, 
0; + 2 0 
ae 2) ||) = al —1 
0 0 0 
Oo; +1 0 
— 1) -13 —8 
+12 +3 
+ 6 =I 
Na, HS K, Rb Cs 
0 +1|]+ 41 +1 +2 
0 -3 0 —2 —7 
+ 1 Oo; + 2 +3 -2 
0) +2! 4 3 +1 +2 
+ 3 —2 0) a | +1 
+10 -l1'! —-16 -2 0 
—8 |} —10 +1 
+3 
These errors are sufficiently small to be explained by the uncertainties of the 
measurements; they are indeed of the same order as those previously met with and 
considerably less than the corresponding residuals of Kaysmr’s equation. Turning to 
