In view of the recent experimental determination of the dispersion by atomic hydrogen it seems interesting to apply the theory of dispersion developed by Schrodinger to this case. In this paper we restrict ourselves to an approximation in which terms of the order of relativistic correction are neglected. For this purpose it is simpler to obtain our wave equation by the operational method of Schrodinger and Eckart, as extended by Epstein, for in this way we immediately obtain an equation free of relativistic terms. In what follows, in order to preserve a continuity of the discussion, details of calculations are omitted from the main text and are given as Supplementary Notes at the end of the paper. References will be found immediately preceding the Supplementary Notes.