The whys and wherefores of navigation

by Gershom Bradford

There are two methods of calculating an azimuth, one known as the time azimuth and the other as the altitude azimuth. The former is the most popular owing to the tables that have been compiled, an inspection of which facilitates the navigator in quickly obtaining the true azimuth of a body. Before entering the tables, it is necessary to have as arguments the latitude and declination, and, if using the sun, the local apparent time, or for stellar work the hour angle. Should the star’s hour angle exceed 12 hours, 12 hours should be subtracted from it, and the remainder used as P.M. time. A planet may be employed precisely in the same manner as a star.

One of the simplest and most expeditious methods of securing the azimuth is by means of a diagram. Upon this convenient invention the bearing of a body can very quickly be taken off with a pair of rulers. Weir’s Azimuth Diagram is sold by the Hydrographic Office for a very small sum. The only argument that can be used against its use is that it requires a small table to lay it upon. Simple and complete directions are printed on the diagram.

The altitude azimuth is often computed at the same time as the ordinary A.M. and P.M. time sights, utilizing the altitude of the body for both operations. The principle involved in computing both an altitude azimuth and a time azimuth is the solution of the same astronomical triangle for the same angle, but in the case of the altitude azimuth three sides are given (the co-latitude, the zenith distance, and polar distance) to find the angle at the zenith. In the time azimuth, two sides and the included angle are given (the polar distance, co-latitude and local apparent time or hour angle) to find also, the angle at the zenith.

The azimuth found by computation should be named North if in north latitude, or South if in south latitude.

It has been customary to add up the logs, divide by 2 and the cosine will be half the azimuth named from the elevated pole, but a more expeditious way is after adding the logs seek in the log haversines and find the azimuth directly but named from the opposite pole to the latitude.

With the correct bearing of the sun, and its simultaneous bearing by standard compass at hand, the compass error is found by merely taking their difference. Now this error, as said before, is composed of the sum or difference of the deviation and the variation, so, if either is subtracted from their sum, or added to their difference the remainder is the other quantity. The variation being always known is subtracted from or added to the compass error to obtain the deviation, thus checking the deviation card for that particular course the vessel was steering at the time of observation.

With the compass error at hand, many students become perplexed as to the proper manner of dealing with this error, and finding from it the deviation. The compass error is first named, by considering the two bearings (compass and true) from the center of the compass; if the true is to the right of the compass bearing, the error is easterly, if to the left, westerly.

Now should the variation happen to be identical with the compass error, both in amount and in name, there is no deviation; if the variation is 0°, then the whole error is deviation. If by chance the compass error is 0°, it indicates that the variation and deviation are equal in amount and opposed to each other in their influence on the needle. The deviation, in such a case, naturally takes the opposite name from the variation.

In separating the variation from the compass error, it is necessary to exercise a little thought and to consider what deviation applied to the given variation will produce that compass error. This will be readily seen after a little practice. There are, however, some rules which are here given, by which the deviation can be obtained mechanically.

The deviation is the difference between the variation and the compass error if they are of the same name or adding them if of different names. It is given the same name as the compass error unless the compass error is subtracted from the variation, when the deviation takes the opposite name.