The whys and wherefores of navigation

by Gershom Bradford

There are three systems of circles, each designed to fulfil a different requirement.

The first system depends upon the position of the observer and changes its whole imaginary structure to correspond with his movements. The plumb-line, if extended to the heavens overhead, will determine the zenith, the point of origin of this system on the celestial sphere. The corresponding point directly beneath us is known as the nadir.

The great circle of the celestial sphere everywhere equally distant from both the zenith and the nadir is the horizon. It is plain that a new zenith and new horizon are created with every movement of the observer. The facts that man is on the surface and not at the center of the earth, and that his eye is elevated above its surface, each creates another horizon.

The rational horizon is marked by a plane, perpendicular to a plumb-line and passing through the earth’s center; while the sensible horizon is determined by a plane, also perpendicular to the plumb-line, but passing through the eye of the observer. It will therefore be seen that these two parallel horizons are some 4000 miles apart, the semi-diameter of the earth; but this distance when projected on the celestial sphere becomes insignificant when compared with the infinite distance of this sphere from the earth, and the rational and sensible horizons shrink into a single line so far as we can perceive.

While this statement is true when dealing with the stars, it needs modifying when dealing with the sun and moon, and in very accurate observations of planets, as their distances are insufficient to eliminate the angle formed between the line from the body to the center of the earth, and that from the body to the observer. This is allowed for when observing these bodies by applying the correction of parallax to the observed altitude.

The visible horizon is the boundary seen between the sea and sky. If the observer’s eye were at the level of the sea, his visible horizon would coincide with the sensible horizon, defined above; but the elevation above the surface from which sights are taken causes the line of vision, tangent to the sea, to be depressed below the plane of the sensible horizon making an angle with it called the dip of the horizon. In practice all altitudes of heavenly bodies taken from a vessel are measured to the visible horizon and corrected for the dip to reduce them to the sensible horizon, then again corrected for parallax to obtain the true altitude of the body above the rational horizon; or what is the same thing, the altitude as observed at the center of the earth.

From the zenith, an infinite number of great circles, known as vertical circles, sweep around the celestial sphere, cutting the horizon at right angles and passing through the nadir. The one which cuts the north and south points is called the celestial meridian, and is evidently a projection of the terrestrial meridian. The vertical circle passing through the east and west points is called the prime vertical, and has a distinction above other vertical circles by virtue of its being the most favorable position for a body in observations for longitude. The heavens are further swept by an infinite number of parallels of altitude which are, as their name implies, parallel to the horizon.

The azimuth of a body is its angular distance from the north or south points of the horizon, determined by the angle formed at the zenith, or by the arc of the horizon between the meridian of the observer and the vertical circle passing through the body. Amplitude is the angle at the zenith formed by the prime vertical and the vertical circle passing through the body or it is the angular distance from the east or west points, measured on the horizon, and is measured similarly to the azimuth.

The system of laying off the heavens just described is well enough for the momentary locating of a body, which is a very important feature in navigation, but for some purposes a more stable point than the zenith, which on shipboard is ever changing, is needed, from which to form a system that is constant the world over. To meet this demand we take the point in the sky penetrated by the prolongation of the earth’s northern axis—the celestial pole—and from this point meridians and parallels are developed upon the celestial sphere as has been done on the earth. In fact, it is as though these terrestrial coordinates were projected to the heavens where they hold the same relative positions as upon the earth. The northern celestial pole is in the zenith at our north pole. The same is true of the south pole. The celestial equator, or equinoctial, is a great circle, which is midway between the poles and everywhere 90° from them. It marks the termination of the plane of our equator extended to the celestial sphere, or in other words, it is always directly over our equator.

The parallels of the celestial sphere evolved by this system, corresponding to those of latitude upon the earth are called parallels of declination, while the celestial meridians having as their point of origin the prolongation of the earth’s axis, are known as hour circles. The particular hour circle passing through the zenith is one and the same with the celestial meridian. It will be seen that this circle must pass through the zenith, nadir and the poles.