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 J. J. Balmer (1825–98) discovered the law having the form:1/λ=R(1/n12+1/n22) 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 F. 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 in the far infrared.
http://web.lemoyne.edu/~giunta/balmer.html Balmer's paper