In text books on astro navigation, the fact that the Earth is not spherical in shape is seldom discussed and therefore one presumes it does not have a significant effect on the accuracy of sight reduction, and yet it is quite remarkable that it is not uncommon to find discussions of the phenomenon of augmentation (a correction to the altitude or semi-diameter of the Moon that amounts to about 0·25 at an altitude of 60°) in these books. It will be shown that discrepancies of the same order of magnitude as augmentation may be present in the calculated altitude of the Moon because of neglecting to take into account the shape of the Earth.

In the following (1) rigourous expressions for correcting the observed altitude and geocentric declination of a body close to the Earth are derived, (2) simple expressions which are sufficiently exact for the purpose of sight reduction for the Moon are given, and (3) an example, using different methods of reduction, is shown in detail to illustrate the theory.