31 
Physics. — “Series in the spectra of Tim and Antimony’. By T. 
VAN LOHUIZEN. (Communicated by Prof. P. Zrrman). 
(Communicated in the meeting of April, 26 1912). 
In my Thesis for the Doctorate, which will shortly appear, I have 
used a spectral formula, which expresses this fundamental thought: 
“For every series the curve obtained by using the parameters (1, 2, 
3, ete.) as abscissae and the reciprocal values of the wave-lengths 
as ordinates, is exactly the same, only referring to anotber system of 
axes’, This curve is the curve of the third degree: 
= 
x? 
in which y= 10°)—!, .# is successively: 1, 2, 3 etc, and N is 
the universal constant which occurs in the formulae of RypBera, 
Ritz, and Mocrnporrr—Hicks, the universality of which, somewhat 
more intelligible after the physical meaning which Rurz *) has given 
to it, can hardly be doubted any more. Transferred to one and the same 
system of axes the general spectral formula becomes for all series : 
TEN LEE ONE 
[(w—a) cos y—b sin y—10® A—! sin y]}? 
in which a and 5 are the ordinates of the origin of the original 
system of axes, and y the angle of rotation. As I shall demonstrate 
more at length in my Thesis, the formula may be reduced to: 
NG 
jp ea eee ee 
[re Ha! Hed}? 
for small values of y. 
This approximated form closely resembles Rrrz’s formuia, which 
may, therefore, be considered as an approximation of the one given 
by me. Also the formulae of Rypprre (ce =0) and of Baumer for 
the hydrogen series (a = 0 and c= 0) are implied in it as special 
cases. Accordingly it is also further closely related to the original 
_ formula of Rypserc. This, too, expresses that the curve is the same 
for all series, but the important difference is that RypBerG gives the 
system of axes only a translation, whereas according to my formula 
there generally appears a — mostly small — rotation of the curve. 
The thought of one curve for all series has been embodied in a 
model which I have had constructed for this purpose, aud which 
contains the ‘most important part of the curve: 
*) Magnetische Atomfeider und Serienspektren. Ann. d. Phys. 25 p, 660 et seq. 1908. 
