The eigenfunctions of a linearized form of the governing equations of motion on a sphere, i.e. Laplace's tidal equations, as first discovered by Hough (1898). Each Hough mode is a function of latitude and longitude and has three components: (1) a zonal (eastward) wind component, (2) a meridional (northward) wind component, and (3) a geopotential component. A distinct horizontal scale and frequency is associated with each mode, and the modes are orthogonal over the sphere in the continuous case. They are sometimes divided into two classes: (1) low-frequency Rossby-Hough modes that tend to satisfy the geostrophic relation and (2) higher frequency Hough modes that correspond to inertia-gravity waves. They can also be thought of as a generalised Fourier series in which the basis functions are the normal modes of a resting atmosphere.