Periodic irrotational waves of finite height

Abstract 1. The method of Stokes for waves of finite height on deep water consists in working upwards by successive steps from the infinitesimal wave towards the highest possible wave. Although lacking formal proof of convergence, it is generally accepted that the method is valid, but that it does not include the highest possible wave when the crests form wedges of 120°. For the highest wave itself we have Michell’s analysis by a distinct method, also involving an infinite series whose convergence has to be assumed.*