Excerpt from Bairnson's Ex-Meridian Tables: Being the Shortest Method Yet Offered to the Public

To facilitate this computation these Tables have been compiled, so that the required correction can be taken out by inspection for the purpose of finding the number of minutes of Altitude which the sun has to rise when the observation is made before noon, or what he has fallen when made in the afternoon. In both cases this correction is additive to the sun's observed Altitude, which will give his meridian Altitude, or what it would have been if observed at that place.

It will be perceived that in low latitudes the observation must be made nearer to noon than in high latitudes; these Tables are, therefore, of the greatest utility in high latitudes, and where also it is most probably required, on account of the stormy weather which generally prevails there, when the meridian Altitude can seldom be obtained.

This method of finding the latitude will, therefore, be found very useful when an Altitude can be obtained near noon (but which is generally considered by seamen as useless after their meridian Altitude has been lost), and although a ship at sea is almost continually changing her time, if the time of the observation be noted by a good watch, which may have been regulated previously to apparent time at the ship, then the difference of longitude made in the interval since it was last regulated, turned into time and subtracted from the time by watch, if the ship has been sailing west, or added to it when sailing east, will give the apparent time of the observation; which if before noon, subtracted from 12 hours, will give the time from noon a.m., otherwise it will be the time from noon p.m., or the watch may be regulated by equal altitudes.

But the most correct mode, and that in general use, is to find the apparent time at ship from the chronometer, the ship's longitudebeing generally known within a few minutes of the truth, which, turned into time and applied to the Greenwich time, furnishes the apparent time of the observation as follows.

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