The atomic spectrum of hydrogen is characterized by lines corresponding to radiation quanta of sharply defined energy. A graph of the frequencies at which these lines occur against the ordinal number that characterizes their position in the series of lines produces a smooth curve, indicating that they obey a formal law. In 1885 Johann Jakob Balmer (1825–98) discovered the law, having the form
This law gives the so-called Balmer series of lines in the visible spectrum, in which n1=2 and n2=3,4,5,…, λ is the wavelength associated with the lines, and R is the Rydberg constant.
In the Lyman series, discovered by Theodore Lyman (1874–1954), n1=1 and the lines fall in the ultraviolet. The Lyman series is the strongest feature of the solar spectrum as observed by rockets and satellites above the earth’s atmosphere. In the Paschen series, discovered by Friedrich Paschen (1865–1947), n1=3 and the lines occur in the far infrared. The Brackett series (n1=4), Pfund series (n1=5), and Humphreys series (n1=6) also occur. See also Fock degeneracy.
http://web.lemoyne.edu/~giunta/balmer.html A translation of Balmer’s 1885 paper on the spectral lines of hydrogen in Annalen der Physik und Chemie