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(4) n=A (r+a+b/r2)2 (Ritz).
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.