See Ritz, Die iiltere Geschichte des Veste and der Stadt Recklinghausen (Erzen, 1904).
The fact that the addition of the term introduced by Ritz not only gives a more satisfactory representation of each series, but verifies the above relationship with a much closer degree of approximation, proves that Ritz's equation forms a marked step in the right direction.
Trunk series: t N = [s +al +b/s 1 [1 5 +a1 +b'/(I.5)2}2 Main Branch Series: t ytr' - I I N [2 + al + 6/29 2 [r+al Side Branch Series: t nT = N [2 +al+6,/22]2 [s+c+d,s92 Here s stands for an integer number beginning with 2 for the trunk and 3 for the main branch, and r represents the succession of numbers 1 5, 5, 3 5, &c. As Ritz points out, the first two equations appear only to be particular cases of the form n I I N +1)2 in which s and r have the form given above.
Hicks 1 has modified Rydberg's equation in a way similar to that of Ritz as shown by (5) above.
If we compare Balmer's formula with the general equation of Ritz, we find that the two can be made to agree if the ordinary hydrogen spectrum is that of the side branch series and the constants a', b, c and d are all put equal to zero.'