An equatorially trapped westward propagating wave that moves due to isentropic gradients of potential vorticity. The meridional velocity of the n'th mode of these waves has the form exp(-y²/2R²) H_n(y/R), in which y is the meridional distance from the equator, R is the equatorial rossby deformation radius, and H_n is the n'th Hermite polynomial. In the shallow water approximation R²=(gH)^(1/2)/eta in which, eta is the meridional gradient of the Coriolis parameter at the equator, g is the acceleration of gravity, and H is the mean fluid depth. The dispersion relation for the n'th mode (n>0) with zonal wavenumber k is given by those roots of the equation, cubic in the frequency omega, ((gH)^(1/2)/eta) - k² + omega²/(gH) =2n+1 for which the frequency is less than Reta.