FIG. 12.—Spectra produced by discharges of different character through a glass tube containing nitrogen at a pressure of ¹/₂₀ that of the atmosphere. Above, a band spectrum; below, a line spectrum.] Since the line spectra are most important in the atomic theory, we shall examine them here more carefully. The line spectra of the various elements differ very much from each other with respect to their complexity. While many metals give a great number of lines (iron, for instance, gives more than five thousand), others give only a few, at least in a simple spectroscope. With a more powerful spectroscope the simplicity of structure is lost, since weaker lines appear and other lines which had seemed single are now seen to be double or triple. Moreover, the number of lines is increased by extending the investigation to the ultra-violet and infra-red regions of the spectrum. The sodium spectrum, at first, seemed to consist of one single yellow line, but later this was shown to be a double line, and still later several pairs of weaker double lines were discovered. The kind and number of lines obtained depends not only upon the efficiency of the spectroscope, but also upon the physical conditions under which the spectrum is obtained. The eager attempts of the physicists to find laws governing the distribution of the lines have been successful in some spectra. For instance, the line spectra of lithium, sodium, potassium and other metals can be arranged into three rows, each consisting of double lines. The difference between the frequencies of the two “components” of the double lines was found to be exactly the same for most of the lines in one of these spectra, and for the spectra of different elements there was discovered a simple relationship between this difference in frequency and the atomic weight of the element in question. But this regularity was but a scrap, so to speak; scientists were still very far from a law which could exactly account for the distribution of lines in a single series, not to mention the lines in an entire spectrum or in all the spectra. The first important step in this direction was made about 1885 by the Swiss physicist, Balmer, in his investigations with the hydrogen spectrum, the simplest of all the spectra. In the visible part there are just three lines, one red, one green-blue and one violet, corresponding to the Fraunhofer lines C, F and _h_. These hydrogen lines are now generally known by the letters Hα, Hᵦ and Hᵧ. In the ultra-violet region there are many lines also. Balmer discovered that wave-lengths of the red and of the green hydrogen line are to each other exactly as two integers, namely, as 27 to 20, and that the wave-lengths of the green and violet lines are to each other as 28 to 25. Continued reflection on this correspondence led him to enunciate a rule which can be expressed by a simple formula. When frequency is substituted for wave-length Balmer’s formula is written as