The whys and wherefores of navigation

by Gershom Bradford

An inspection of the table of dip will show that the rate of increase of this error becomes more rapid as the height of the eye is diminished. To illustrate: The reader will note that between an elevation of 4 feet and one of 9 feet there is a difference of 1 minute in the dip, while higher up, say between 26 feet and 38 feet, a difference of 1 minute is likewise found, yet in the first instance there was a range of 5 feet and in the second a range of 12 feet. This fact in itself is an argument in favor of observing altitudes at a good height above the water.

In calculating a meridian altitude, an error in the dip directly affects the result by a corresponding amount, so extra care should be exercised in this respect. In this instance, we endeavor to locate the body relative to our zenith and anything that affects its altitude directly affects the latitude. In a time sight, a different principle is involved. Here the position of the body as defined by the latitude locates the apex of one angle of the astronomical triangle and hence a small error in the altitude will very likely cause a greater effect on the longitude.

An allusion was made under the caption of Refraction to the displacement of the visible horizon by terrestrial refraction to detect which requires watchfulness on the navigator’s part. The familiar “loom” seen along the coast is an example of the workings of variable refraction. Now imagine this distortion less aggravated with no land to show its existence and you have a good illustration of this error.

Refraction of this nature is usually found during light airs and calms when the different layers of air arrange themselves according to their temperatures. The heated air over land below the horizon in hot weather will displace the intervening horizon; moreover, when the air is warmer than the sea, the horizon is elevated above the normal and, when the conditions are reversed, the horizon is unduly depressed. Thus lights become visible a little sooner after a hot day ashore. The Red Sea, Gulf Stream, mouth of the Amazon, and other large rivers are places where the horizon should be especially distrusted. Capt. Lecky, in his famous Wrinkles in Practical Navigation, refers to an experience he once had with this error. The latitude had been found “by an excellent meridian altitude of the sun to be as much as 14´ in error. The time was mid-winter—the day a clear cloudless one—the sea smooth, and the horizon clean-cut. Five observers at noon agreed within the usual minute or half minute of arc, nevertheless, on making Long Island (U. S. A.) in less than two hours afterwards, the latitude was found wrong to the amount stated. Many such cases have come under the writer’s notice, but this one alone is cited on account of the magnitude of the phenomenon.”

What Captain Lecky said in his work on navigation is reliable and this should serve to make an impression as to the dangers of such occurrences.

In clear weather this displacement of the horizon may be lessened somewhat by observing from aloft. By extending the horizon, such disturbing influences as the motion of the vessel and an irregular horizon caused by rough sea are minimized. In hazy weather, however, it is recommended to observe low, bringing the horizon as close as possible.

Parallax

In calculating the true altitude of a body the distance of its center above the horizon is supposed to be measured from the center of the earth, or what is the same thing, the altitude above the rational horizon.

The application of semi-diameter adjusts the measured angle with the center of the body, while parallax corrects the error due to our observing from the surface of the earth to the sensible horizon, instead of from the center to the rational horizon.

Parallax, in other words, is the angle formed at the body by the lines drawn from the observer’s position, and from the center of the earth, respectively. This angle is subtended by the radius of the earth, and it is obvious that the farther away a body is, the smaller the angle, and consequently the less the parallax. So when dealing with planets or fixed stars, it becomes insignificant and no parallax is considered.