558 DR J. HALM ON 
| Li. Na. | K. 
| KR. RyTh K-R. By-Th.| KR. Ry-Th. 
O00) Stl |). 000 400 00 28 
| + 44:4 +04 +431°5 0:0 + 26:0 +2°3 
00 +421 0-0 +02 00 -26 
Bee Ree ee) a] SS 
QO E26) 80-0 | or 00 -18 
208; Sl Gaghece D4 ue salen, |e oo Meee 
00 +402 0-0 +05 0:0 +03 
| =4q) 29:9 -2:0 +08 
-~88 —55 E63). 209 
The enormous discrepancies in the second lines show that Kayserr’s formula is 
still far from representing the actual phenomena, and hence, even in this extended 
form, is inferior to the Rypserc-THIELE equation. To give full justice to the 
former I have repeated the computations by excluding the first lines, but I have come 
to the conclusion that while the fourth constant produces on the whole a slight 
improvement in the shorter wave-lengths, the discrepancies in the first lines are even 
increased. All these computations have convinced me that no general improvement 
can be expected by adding a further term to Kayssr’s formula. 
But besides we find other facts which speak in favour of the equation here employed. 
There exists a certain empirical law, first pronounced by RypBERG and Kaysmr, that 
if for a given element two or more subsidiary series exist, these series converge into one 
common tail. This law has now been confirmed approximately in so many instances, 
that we may accept its correctness. The presumption is warranted, therefore, that — 
the better formula should also bear out this law more precisely. Now let us compare 
in this respect KayseEr’s formula with the RypBeRG-THIELE equation. We find for the 
wave-frequencies of the tails of the 1st components : 
K-R. Ditt, .| Ry-Th: Diff. 
Lithium 1. S.S. 28586°7 | 28594°7 | 
| | +80°7 =i 
De Shs). 28666°7 28583°3 
Sodium 1.8.8. | 24492°3 | 24481-2 
+ 56'8 +9:2 | 
2.5.8 245491 | | 24490:4 zea 
Potassium 1.8.8 21991°2 | | 21991°8 
| +30°6 +51 | 
2s 22021°8 21996-9 | 
These ficures leave no doubt that the law is represented much better by our formula 
than by that of Kayser and Runar. We shall see later on that this applies to other 
spectra as well. 
= AS 
