It is shown how Holtsmark's theory is related to first principles of line broadening, and its connection with other so-called "statistical" theories is indicated. The quantum-mechanical derivation is restricted to perturbations by a single ion but retains the terms which correspond to the nonuniformity of the field. Ions and electrons are treated simultaneously, and the shifts caused by the electrons are computed in a simple manner. Unpublished work dealing with line broadening by electrons, not included in this paper, is briefly summarized; it is noted that broadening as well as shifts by electrons amount to only a few per cent of the ion width. While the method employed is applicable to all hydrogen lines, the details are given only for the Lyman-a line.