Relatively slight though the perturbations may be, however, they are sufficient to make noteworthy changes in the apparent position of the sun and moon as viewed with modern astronomical instruments; and they can by no means be ignored by the navigator who will determine the position of his ship within safe limits of error. And so it has been the work of the practical astronomers to record thousands on thousands of observations, giving with precise accuracy the location of sun, moon, planets, and various stars at given times; and these observations have furnished the basis for the elaborate calculations of the mathematical astronomers upon which the tables are based that in their final form make up the _Nautical Almanac_, to which we have already more than once referred. These calculations take into account the precise nature of the perturbing influences that are exerted on the earth and on the moon on any given day, and hence lead to the accurate prediction as to the exact relative positions of these bodies on that day. Stated otherwise, they show the precise position in the heavens which will be held at any given time by the sun for example, or by the important planets, as viewed from the earth. How elaborate these computations are may be inferred from the statement that the late Professor Simon Newcomb used about fifty thousand separate and distinct observations in preparing his tables of the sun. Once calculated, however, these tables of Professor Newcomb are so comprehensive as to supply data from which the exact position of the sun can be found for any day between the years 1200 B.C. and 2300 A.D., a stretch of some thirty-five centuries.