in the direction S and is immediately over the point A of the earth's surface. Its altitude there is 90°. As we pass along the earth's surface away from A, the direction of the horizon continually changes and the altitude of the sun continually diminishes until we reach the great circle, BC, which divides the light from the dark hemisphere, and there the sun is on the horizon and its altitude is zero degrees.
As the earth is spherical, and therefore symmetrical round the line OS, if we draw a circle DE on its surface, with its plane at right angles to this line, the altitude of the sun, as seen from all parts of this circle, will be the same; at the point D this altitude will be represented by h, the angle between the direction of the sun DS'and the horizon; for the sun is so distant from the earth, that its direction is the same from the center of the earth and from any point of the surface, to the degree of accuracy required by explorers. Every part of the circle DE is at right angles to the direction of the sun. The altitude of the sun changes with, and is determined by, the distance of the circle DE from A; and, vice versa, if the altitude is known, the distance of the circle from A is determined. The point A, itself, is fixed when we know Greenwich time and the angular height d of the sun above the equator; this latter is called the declination; it is continually changing, but its value at any time can be found in the "Nautical Almanac." An explorer would always take with him a copy of this work or an abbreviation of it; and he would also be supplied with chronometers keeping Greenwich time.
If an explorer has measured the altitude of the sun, and has at the same time observed the Greenwich time by his chronometer, he has merely determined that he is somewhere on a certain circle, whose position he could plot on his map; but other considerations, such as his last determined location, and the approximate distance he had traveled from it, would make known more or less roughly in what part
