The altitude of the celestial pole is found from the culminations of circumpolar stars. Correction is required for atmospheric refraction; it increases the apparent altitude of a celestial object, especially when near the horizon. Terrestrial latitude is found: 1. By culminations of circumpolar stars; 2. By meridian altitude of the sun declination. Twilight is caused by reflection of light from upper region of atmosphere; it lasts until the sun is 18° below the horizon. CHAPTER VIII. SHAPE OF THE EARTH. GRAVITATION. 146. Public surveys.-The construction of accurate maps is a matter of national importance. When a boundary line between two states or nations is not fixed by some natural landmark, as the channel of a stream or the crest of a mountain, it is often made at lines of latitude and longitude; these must be determined astronomically. The bounds of many of the states and territories, as well as those between the United States and the British Provinces and Mexico, are fixed at astronomical lines. Our sea-coast is long and dangerous. The ships which annually enter our harbors, or leave for foreign or domestic ports, bear hundreds of thousands of lives, and nearly a thousand millions of merchandise. The nation should employ every means, practical or scientific, by which danger may be avoided, and safety insured. To this end, it is necessary to determine the coast-line, and to observe the changes going on there and at the seabottom within soundings; to ascertain the laws which govern currents, tides, and winds; to locate light-houses, and other signals; and to publish results in reliable maps and charts. For many years our government has conducted such a survey along the entire coast. TRIANGULATION. 147. It is first necessary to determine the latitude and longitude of prominent points along the coast, as hills, spires, and head-lands, and to find the distances between them. A base line is measured on a piece of level ground, usually from six to ten miles long, and the ends of this line are located astronomically. This line is made the base of a triangle whose vertex is on a distant hill; the angles at the base are observed, and the two opposite sides are found by the principles of trigonometry. These lines are used as bases of other triangles, which are solved in the same way. Thus the triangulation continues until every conspicuous object in the whole country is included in the system. 148. Example.-Suppose that signals have been erected, and a base line 12, has been measured, six miles long. From the stations 1 and 2, the angles 213, and 123 have been observed, and the distances 13 and 23 are computed. 23 is now the base of the triangle 234; 43 is BASE LINE Fig. 49. found, which becomes the base of 345, and so on to stations 6 and 7. The line 23 may also be the base of the triangle 236, and thus the station at 6 will be located by two operations which should prove each other. 149. Another proof.— After the work has progressed over a large district a new base is measured, or the triangles are made to connect with those begun at another line; the agreement of the computed and meas ured lengths tests the accuracy of the work, including ob*servations, measurements, and computations. A base line in Massachusetts, on the Boston and Providence Railway, 10.76 miles long, has been connected by triangulation with base lines at Epping, in Maine, and at Fire Island, south of Long Island. The distance from Epping Base to Mass. Base is 295 miles. Length of Mass. Base, measured, 66 66 computed from Epping Base, 66 56846.09 feet. 56846.59 66 66 Fire Island Base, 56846.32 First difference, in 10.76 miles, 6 inches. Second 66 66 66 3.2 66 150. Measuring apparatus.-The base lines of the U. S. Coast Survey have been measured with the greatest accuracy by an apparatus devised by Prof. A. D. Bache. The rod is a compound bar of iron and brass, so adjusted that the change of length in one part, on account of heat or cold, is exactly counterbalanced by a change of length in the other. The rod is inclosed in a spar-shaped case, painted white to reflect the heat of the sun. Two such rods are laid in line upon tripods, properly placed, and the contact between their ends is shown by the motion of a very delicate index. Any necessary deviation from a straight or level line is observed and corrected by computation. a, a, the iron rod; b, b, the brass rod; c, the lever of compensation, hinged to the brass and resting against the iron; d, d', sliding rods, which meet in agate surfaces at E; the rod d' pushes at ƒ against the lever of contact, which brings the spirit-level g into a horizontal position. The slope is shown by the graduated scale i, which is moved by the screw k, until the spirit-level h is horizontal. The screw brings the rods together. 151. Completion of survey.—After the principal triangulation has located the prominent points, minor places are determined in a similar way, and are located on a map. The coast line is then filled in, soundings are taken off shore, rocks, reefs, and shoals are marked, suitable channels are indicated, and sailing directions added, by which the mariner may steer his craft to a safe anchorage. Similar surveys have been made in Great Britain and in continental Europe, and have been commenced in India and in South America. THE SHAPE OF THE EARTH. 152. The length of a degree of latitude.-A degree of latitude is such a distance, measured on the meridian, as shall increase the altitude of the pole one degree (40). By the methods described, the length of a degree of latitude has been found in various places, and at various distances from the equator, from Peru, lat. 1° 31', to Lapland, lat. 66° 20'. Among the results are the following: 153. The earth flattened at the poles.-From the table it appears that a degree of latitude is shortest near the equator, and becomes longer as we approach the pole. But since near the equator the altitudes of the pole mark degrees by measuring shorter spaces, it is evident that we must be moving on a smaller circle, with a sharper curvature; near the pole the measured degree is longer, |