(1) A correction applied to the average of a series of observations on a star or planet, to take account of the divergence of the apparent path of the star or planet from a straight line. Any star which is not an equatorial star does not strictly run along the horizontal wire of a transit instrument as it crosses the meridian of the observer. This phenomenon was first observed by Cassini and was explained by him in 1719. Observations on a star for the purpose of calibrating a micrometre are subject to correction for the apparent curvature of the star's path during observation, as also are some observations for azimuth. The correction to reduce an observation for latitude on a star close to but not on the meridian to what it would be if the star were on the meridian may be considered a curvature correction. (2) The correction applied to some geodetic data to take into account the divergence of the surface of the Earth (or its representing ellipsoid) from a plane. In geodetic leveling, the curvature correction and the effect of atmospheric refraction are considered together, and tables have been prepared from which combined corrections can be taken. In aerotriangulation, the curvature correction is also usually combined with the correction for refraction.