The Equivalence of Bernoulli's Equation and a Set of Integral Relations for Periodic Waves

In a recent paper Longuet-Higgins (1978) discovered some newrelations between Stokes' coefficients in the theory of periodicgravity waves. These were shown to give rise to a set of integralrelations. In this paper we show that this set is complete inthe sense that it is equivalent to Bernoulli's equation. Wealso show that a suitably redefined set exists in the theoryof the solitary wave.