Johann Balmer's doctorate from Basel was for a dissertation on the cycloid. He taught in Basel all his life both as a school teacher and as a university lecturer at the University of Basel. His main field of interest was geometry.
However Balmer is best remembered for his work on spectral series and his formula, given in 1885, for the wavelengths of the spectral lines of the hydrogen atom. The reason why the formula holds was not understood until the work of Niels Bohr in 1913.
Bron: http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Balmer.html