This paper describes two methods of determining whether a sextant observation of the Moon should be of the upper or lower limb. The first method requires the use of a celestial globe or planisphere; the second is mathematical and requires a certain amount of computation, but is exact.

The line which separates the dark portion of the Moon's disk from the illuminated portion is known as the terminator, and the straight line joining the ends of the terminator is that used in this problem. This line is always perpendicular to a line from the Moon to the Sun (the horns being always turned away from the Sun), so that its position can be predicted from the geometrical relations of the Earth, Sun and Moon. This enables the limb to observe to be determined.