The annexed tables are intended to facilitate the computation of the corrections for refraction which have to be applied to differential measures, such as are made with the micrometer or heliometer.

Differential measures are of two kinds :—(1) Direct measures of differences of right ascension and declination; and (2) measures of position angle and distance. In either case the observer only seeks to determine the relative positions of the objects under observation; and the correction for refraction consists in the applying to each reading a quantity representing the difference of the separate effects of refraction on the apparent places of the two stars, whose relative positions are to be determined.