The whys and wherefores of navigation

by Gershom Bradford

The circum-meridian, as well as the straight meridian altitude, is available for use of stars near the meridian below the pole, and, as one proceeds into higher latitudes, the pole becomes more and more elevated, offering thereby more opportunities for practicing this phase of the problem. The only feature to be remembered in this case is that the body is higher at the time of a circum-meridian than when it transits, so the correction to be applied to the observed altitude must be subtracted (-) in order to obtain the meridian altitude.

The planets, too, are used by the ex-meridian altitude method, but being wanderers in the heavens their right ascensions and declinations must be determined for the Greenwich date from the Nautical Almanac.

The amended altitude of any body is assumed to be the meridian altitude and is used in the familiar formula z + d = latitude (see Latitude by meridian altitude); but it must be borne in mind that the result is not the latitude at noon but at the time of sight. If the observation was made say 9 minutes before noon and the latitude considered to be the position at local apparent noon as in an ordinary meridian altitude, there would be an error of 3 miles from the correct position for a 20-knot steamer.

Another point to be guarded against is that when taking several altitudes and their corresponding times their mean cannot be obtained in the ordinary way, but each altitude must be separately reduced and the mean taken of the results.

It is again necessary to diverge from the subject to impress on the mariner an urgent warning against anything but the most untiring vigilance in the care of his chronometer, and the keeping of accurate time. If this element cannot be depended upon there will be many hours of anxiety coming to him and probably sooner or later downright disaster. The almost universal establishment of time signals in all good-sized sea ports of the world together with radio time signals sent broadcast allows but little excuse for not obtaining a good rate by the time a vessel is ready for sea. Every well-known work on navigation deals with the subject of rating chronometers and so no space will here be given to it. After reading this talk on one of the most important and up-to-date observations where so much depends upon the accuracy of the time, the reader cannot fail to appreciate this earnest admonishment.

Polaris

The process of finding the latitude by means of Polaris is valuable, comparatively short and the result, if the conditions are favorable, is accurate. We will consider it first in a general way.

The imaginary line representing the earth’s axis, if extended indefinitely, is presumed to pierce the celestial sphere at the celestial pole, therefore for an observer standing at our north pole this imaginary point would be exactly in the zenith and hence 90° from the horizon just as the pole is 90° from the equator, these amounts evidently bear a relation to one another. Should the person at the pole leave his frigid surroundings and proceed toward the equator, he would note that the pole had dropped lower and lower in the heavens, precisely in proportion to his progress southward, until at length, when the equator (latitude 0°) was reached, the pole would be observed to be exactly in the horizon (altitude 0°). From this it is easy to deduce the statement that the altitude of the celestial pole is equal to the latitude of the place of observation.

The object of this problem then is to obtain the altitude of the celestial pole. This point, unfortunately, is marked by no star of which a direct altitude may be observed to aid the navigator in reaching this desired result. There is, however, a star of the 2d magnitude, called Polaris (because of its proximity to the pole) with a polar distance of only 1¼°. As all fixed stars are apparently revolving in circles around the celestial pole, this star joins the grand procession with its little radius of 1¼°.

It is plain that at no time can this star be more than the amount of this radius (1¼°) from the pole, and when on the meridian either above or below the pole the full amount of the radius is subtracted from or added to the corrected altitude of the star to obtain the true altitude of the pole. When the star is on a line passing through the pole and parallel to the horizon at its elongations as it is called, the altitude is then equal to the latitude, for its elevation is the same as that of the pole.