Balmer's Manuscripts and the Construction of His Series

An earlier regeneration of the Balmer series was difficult, because Balmer's publications omitted some of his steps and only presented fragments of others. After a search, the author located a collection of Balmer's papers which include two preliminary manuscripts and traced Balmer's steps on the basis of his own statements. It was found that initially Balmer used three coefficients of cubic integers and a basic wavelength of 30.38 Å; he then related a fourth, visible line in a similar manner as the first three. Subsequently, he rejected these unpublished equations and developed his final formula on the basis of an unrecorded geometrical construction. The origin and nature of this construction, which served as a model for the series, is documented and analyzed. Balmer's verification of his formula and his conclusions are described. In addition, it is shown that the Balmer series played a direct role in the formation of the Rydberg constant and the atomic theory of Bohr.