758 COAST SURVEY any two points are situated in a north and south or an east and west line ; nor whether its site is near the equator or near the poles, or to the east or west of the first meridian. These wants are supplied by astronomical ob- servations, by which the latitude and longitude of some point, and the directions of the lines with reference to the meridian, are determined. The system of triangles which we have de- scribed may be extended over large areas, or along a coast for several hundred miles, de- pending upon one measured base line. By de- termining the positions of the extremities of the base line and its direction by astronomical observations, .the positions of all the other points of the system and the direction of the lines may be computed after the angles have been accurately measured. Accuracy requires that the computed positions should be fre- quently verified by actual observation, and the computed lengths of the lines occasionally veri- fied also by the introduction of a measured base of verification. The geodetic work thus involves the measurement of the base line, the measurement of the angles of the triangles, and astronomical determination of the latitude and longitude of the different points, and of the di- rections of the lines with reference to the me- ridian. This last is called the measurement of an azimuth. Reconnoissance is the first ope- ration in order. An experienced officer first travels over the country to be surveyed, and makes a preliminary examination for the pur- pose of selecting tbe trigonometrical points which will best fulfil the required conditions. Elevated positions are generally chosen, from which extended views can be taken. A site for a base line is selected on some level plain for convenience of measurement, and from which the triangulation can easily be expand- ed. In the selection of geodetic points great judgment is required ; as upon this depends in a great measure the economy, accuracy, and success of the work. Base Line. For the measurement of the base line a standard must be adopted. The English use the yard, which is also the legal standard of length in the Uni- ted States. But in the coast survey measure- ments the French metre is used, which is more convenient on account of bearing a certain' relation to the magnitude of the earth, being equal to the ten millionth part of the earth's quadrant. The metre bar used as standard in the coast survey is one of those originally made by the French committee of weights and meas- ures. For the actual measurement of base lines rods of wood, metal, or glass have been used ; but the changes of length caused by changes of temperature in a simple bar of any material have rendered it desirable to construct a special apparatus for the purpose, upon a compensating principle, which will retain the same length under all temperatures. The base apparatus of the coast survey, devised by the late Prof. Bache, is considered the best known. It has not only the same length at all stationary tem- peratures, but preserves it also while the tem- perature is changing. Bars of different metal, having the same dimensions and exposed to the same source of heat, will not heat equally in equal times. The thickness and surface of the bars are therefore so proportioned to their relative power of conducting and absorbing heat, that they will equally follow changes of temperature. The principle of the level of contact has been applied to the apparatus ; and the exactness of its operations is so great that lines of seven or eight miles in length may be measured with a probable error of only a frac- tion of an inch. Two sets of compensating bars are used, each 6 metres (nearly 20 feet) in length. Mounted on trestles, provided with every mechanical movement for adjusting the bars in height and direction, this apparatus is- handled with such facility that on favorable ground a mile may be measured in an ordinary working day. Triangulation. For the mea- surement of the angles theodolites of the most accurate construction are used. In the prima- ry work on the Atlantic coast a large theodo- lite with a circle 30 inches in diameter is em- ployed. This is carried to the summit of the hill or mountain where the angles are to be measured, and established carefully ovej the station point, where it is left standing until the measurements at that point are completed. The party having this work in charge live in tents, or in some convenient dwelling near at hand, so as to take advantage of the occurrence of favorable weather for the observation of dis- tant signals. The instrument is furnished with a powerful telescope, which will give a distinct view of such signals. The signals are usually straight poles supported by a tripod, erected at the various points ; but on the long lines an instrument for giving signals is used, called a heliotrope. This is simply a round mirror about the size of a silver dollar, so mounted on a telescope that an assistant at any distant sta- tion is able to reflect the rays of the sun in the direction of the observer. The telescope is used to direct the instrument correctly toward the central position at which the observer is stationed. It is not unusual to see the helio- trope on the summits of mountains 80 or 90 miles distant, when the outlines of the moun- tains are not visible. The measurement of the angles at a primary station occupies three or four weeks. It is found to be impossible to work during the middle of the day, on account of the agitation of the atmosphere caused by the heat of the sun ; and hence only about two hours in the morning and evening can generally be devoted to this work. Each angle is deter- mined by about 30 measurements ; and as at each station there are from 10 to 20 angles to be measured, only two or three primary stations can be occupied in one season. Depending upon the primary triangulation, and controlled by it, a network of secondary and tertiary tri- angles is formed along the seacoast, extending- up the bays and rivers. The angles are mea-
