From arguments in connection with the work of the Swedish scientist, Rydberg, in the spectra of other elements, Ritz, a fellow countryman of Balmer’s, has made it seem probable that the hydrogen spectrum contains other lines besides those corresponding to Balmer’s formula. He assumed that the hydrogen spectrum, like other spectra, contains several series of lines and that Balmer’s formula corresponds to only one series. Ritz then enunciated a more comprehensive formula, the Balmer-Ritz formula: ( 1 1 ) ν = K( ------- - -----), ( _n″_² _n′_²) where K has the same value as before, and both _n′_ and _n″_ are integers which can pass through a series of different values. For _n″_ = 2, the Balmer series is given; to _n″_ = 1, and _n′_ = 2, 3 ... ∞ there corresponds a second series which lies entirely in the ultra-violet region, and to _n″_ = 3, _n′_ = 4, 5 ... ∞ a series lying entirely in the infra-red. Lines have actually been found belonging to these series. Formulæ, similar to the Ritz one, have been set up for the line spectra of other elements, and represent pretty accurately the distribution of the lines. The frequencies are each represented by the difference between two terms, each of which contains an integer, which can pass through a series of values. But while the hydrogen formula, except for the _n_′s, depends only upon one constant quantity K and its terms have the simple form K/_n_², the formula is more complicated with the other elements. The term can often be written, with a high degree of exactness, as K/(_n_ + α)², where K is, with considerable accuracy, the same constant as in the hydrogen formula. For a given element α can assume several different values; therefore the number of series is greater and the spectrum is even more complicated than that of hydrogen. All these formulæ are, however, purely empirical, derived from the values of wave-lengths and frequencies found in spectrum measurements. They represent certain more or less simple bookkeeping rules, by which we can register both old and new lines, enter them in rows, arrange them according to a definite system. But from the beginning there could be no doubt that these rules had a deeper physical meaning which it was not yet possible to know. There was no visible correspondence between the spectral line formulæ and the other physical characteristics of the elements which emitted the spectra; not even in their form did the formulæ show any resemblance to formulæ obtained in other physical branches. CHAPTER III IONS AND ELECTRONS Early Theories and Laws of Electricity.