Peters v. Roseau: Resolution of a conflict on the classical beach problem

A discrepancy is uncovered between two well documented solutions, to the uniquely solvable classical linearised sloping beach problem, by Peters in 1952 and independently by Roseau also in 1952 (though subsequently adjusted by personal correspondence from Roseau and Lehman to authors Wehausen & Laitone in 1960). The source of the main error (and other more minor errors) is identified, quantified and corrected and a consequence is that a study by Morris in 1976 (on a generalisation where the line source is no longer confined to the origin) will also have suffered from this deficiency. That problem therefore requires a re-visit.