The device consists of an arc of a circle, marked off in degrees, and a movable radial arm pivoted at the center of the circle. A telescope or sight, mounted rigidly to the framework, is lined up with the horizon. The radial arm, on which a mirror is mounted, is moved until the star is reflected into a half-silvered mirror in line with the telescope and appears, through the telescope, to coincide with the horizon.
The sextant has the advantage that even though the ship rolls or you have an unsteady hand, the images of the two objects that you are looking at stay in alignment.
The angular distance of the star above the horizon is then read from the graduated arc of the sextant. From this angle and the exact time of day as registered by a chronometer, a Line of position (LOP, similar to a Sumner line) can be determined. By taking measurements on two or more astronomical objects, two or more LOP's are drawn on a chart or plotting sheet and the location of the observer will be at the intersection of the lines.
Another method that can be used is to measure the height of the sun at local apparent noon, or the transit of any astronomical body as it crosses the observers meridian. In this case, only one measurement is required to determine position.
The name "sextant" comes from the Latin sextus, or "one-sixth", for the sextant's arc spans 60 degrees, or one-sixth of a circle. Octants, with 45 degree arcs, were first used to calculate latitude. Sextants were first developed with wider arcs for calculating longitude from lunar observations, and they replaced octants by the second half of the 18th century.
Tables for determining the corrections for dip and refraction can be found in the Nautical Almanac. The corrections for refraction are found on pages A2, A3, and A4 of the Nautical Almanac and are labeled as ALTITUDE CORRECTION TABLES.
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