There are several pamphlets and books on the market from which the correction to the observed altitude may be obtained. All are simple in form and with their explanations are readily understood. Notable among these Ex-meridian Tables are those by Capt. Armisted Rust, U. S. N.
The circum-meridian is a reliable method of finding the latitude, but the time used should be accurate to produce satisfactory results. If, however, the conditions be favorable, it is not necessary to discard this observation even if the correctness of the time is somewhat in doubt, for in Towson’s Ex-meridian Tables is found this note:
“If equal altitudes be taken before and after the meridian passage, half the elapsed time may be employed as the hour angle for determining the reduction. Or, when the altitudes before and after noon differ by only a few minutes, the mean of the two may be reduced by employing half the elapsed time as the hour angle for reducing the mean altitude.”
In practicing this suggestion it is necessary, in order to preserve accuracy, to put the vessel on the nearest east or west course during the run between these equal altitude observations. This is imperative in a swift vessel.
The stars and planets offer themselves for use in this problem as in all others, and here they possess special advantages of which the mariner may well avail himself. Indeed, it may be said in truth that when a horizon can be obtained the latitude is always available through this problem.
And right here should be impressed upon the navigator the great advantage of becoming familiar with the stars, not merely those of greatest brilliancy, but the “lesser lights” that can be observed. Among the latter, especial acquaintance should be sought with those whose right ascensions place them in the gaps between the larger stars, thus almost the entire heavens are included in the scope of operations, making the latitude and longitude practically always available, provided again there is a horizon.
Star charts, planispheres, and globes are for sale everywhere and no study is more interesting than that of the ways of these celestial travelers. They appear and pass each day, year after year, until you consider them as old friends, and, as you come on deck for the mid-watch, you look for Orion, for instance, the same as you look for the members of your watch at their proper stations.
But we are off our course. The increasing popularity of the circum-meridian and its undoubted accuracy when used with time obtained from a carefully rated chronometer, is breaking the hold of the time-honored meridian altitude. There is no waiting with cold fingers, perhaps, for the body to dip for this sight, just shoot the star, note the time and duck for the chart room to work it up.
The most favorable position of a body for a circum-meridian altitude is one in which the rise and fall near the meridian are slow. In the case of the sun, it was explained that a low altitude proved the best, but, in the case of the stars, we find another condition; those near the pole, or in other words, of large declinations, describe such small diurnal circles that here also the change in altitude is correspondingly small, thus fulfilling a desired condition for the successful working of this problem. To illustrate this point the reader is referred to Polaris. Now this star has an extremely small diurnal circle and it will be remembered that the altitude is for all practical purposes the same for a half hour either side of the meridian, showing the extreme slowness of its movement of revolution.
The stars are used in the same way as the sun except, of course, that the distance from the meridian becomes the star’s hour angle instead of local apparent time. This is readily obtained as follows: Adding to the Greenwich mean time the sidereal time of the preceding Greenwich mean noon (Nautical Almanac), together with the acceleration of Greenwich mean time (Table 9 Bowditch), gives the right ascension of the meridian. Taking the difference between this latter quantity and the right ascension of the star, we have the star’s hour angle, west, if the right ascension of the meridian is greater than that of the star, and east, if contrary conditions exist.