These forms all agree in making the frequency negative when s falls below a certain value sp. Rydberg's second law states that if the main branch series is taken, the numerical value of np_I corresponding to sp_ I is equal.
As has already been mentioned, the law is only verified very roughly, if Rydberg's form of equation is taken as correctly representing the series.
Hicks 1 has modified Rydberg's equation in a way similar to that of Ritz as shown by (5) above.
Now it follows from Rydberg's second law put on a more accurate basis by Ritz that in one case at any rate a negative period has reality and must be interpreted just as if it were positive.