On the structure of the Balmer series of hydrogen lines

Abstract

It is well known that the spectrum of hydrogen comprises the series of lines generally known as the Balmer series, which is a prominent feature in the spectra of the stars and nebulæ, and the secondary spectrum, consisting of a vast number of lines whose presence in celestial spectra has not yet been established. The co-ordination of the secondary spectrum would appear to present great difficulties on account of its complexity, but it is perhaps remarkable that a precise knowledge of the Balmer series, which was at one time considered to be the most simple series known in spectroscopy, should still be wanting. Balmer showed, at a time when the complexity of the lines was not yet known, that the wave-lengths could be represented with considerable accuracy by the formula λ = 3646·14 m 2 /( m 2 – 4), where m takes successive integral values. Balmer’s formula is a special case of the formula of Rydberg for the wave-number v = N [1/(2 + p ) 2 – 1/( m + q ) 2 ], where v is the wave-number, N Rydberg’s “universal” constant, and p and q are fractions appropriate to the series; this is identical with Balmer’s formula when p and q are put equal to zero. Curtis has deduced from a series of accurate measurements of the leading lines of the Balmer series that the value of Rydberg’s constant N is equal to 109678·3, and that the wave-numbers of the lines cannot be represented to the degree of accuracy attained in his measurements by the simple Balmer formula. Curtis was able to represent his experimental values accurately by the formula v = N [1/(2 + p ) 2 – 1/( m + q ) 2 ], where p = –0·00000383, and q takes the value 0·0000021.