( 436 ) 



iVfl changes little from element to element '). The supposition lies at 

 hand, that a constant of nature will occur in the rational formula. 

 For the first associated series of Aluminium calculation gives a con- 

 siderable deviation. Calculating from the first terms of this series we 

 find iV„ = 207620 calculating from the middle lines 7\^„ = 138032, 

 and from the lines with smaller X JST^ = 125048. 



The first asssociated series of aluminium behaves therefore quite 

 abnormally. 



In Rydberg's formula another function than (m -|- a)~^ must be 

 used to get a better harmony, specially with the first terms of a series. 



In my thesis for the doctorate, which will shortly appear, I have 

 examined the formula: 



109675 



ti = A 



> 



in which 7i represents the wave frequency reduced to vacuo, A, a 

 and b are constants which are to be determined, m passes through 

 the series of the positive integers, starting with m = l. In most 

 cases with this formula a good agreement is obtained, also with the 

 first lines of a series. The associated series converge pretty well to 

 the same limit, while also the law of Rydberg — Schuster is satisfied 

 in those cases where besides associated series, also a principal series 

 is observed. 



A spectral formula has also been proposed by Ritz ^). 



In my thesis for the doctorate I ha^e adduced some objections to 

 the formula of Ritz, as it gives rise to highly improbable combinations 

 of lines. Moreover for the metals of the 2"^ column of Mendelejeff's 

 system his views are not at all in harmony with observation. 



In the following tables the observed wavelength in A. E. is given 

 under X^ , the limit of error of observation under F, the deviation 

 according to the formula proposed by me under A, the deviation 

 according to the formula of Kayser and Runge under A. K. R. The 

 mark * on the right above a wavelength indicates that these lines 

 were used as a basis for the calculation of the constants A, a and b. 



The constants are calculated from the wave frequencies reduced 

 to vacuo "'*). 



1) The B in Kayser and Runge's formula varies within considerably wider limits 

 than the N„ of Rydberg's formula. 



2) Ann. d. Phys. Bd. 12, 1903, p. 264. W. Ritz, Zur Theorie der Serienspectren. 

 2) Where it was possible, 1 have always taken these values from the "Index of 



Spectra" from Marshall Watts. 



