  This paper is concerned with two-dimensional, steady, periodic water waves
propagating at the free surface of water either in a flow of finite depth and
constant vorticity over an impermeable flat bed or in an irrotational flow of
great depth. In both cases, the motion of these waves is assumed to be governed
both by surface tension and gravitational forces. By considering a particular
scaling regime, it can be shown that both these schemes approach a limiting
form, corresponding to flows of great depth where the effect of gravity is
neglected. An application of the Implicit Function Theorem demonstrates that
Crapper's explicit solutions to this latter problem can be perturbed by means
of the aforementioned scaling to yield capillary-gravity waves of any finite
(or infinite) depth and any constant vorticity.
