Compass use of the azi muth compass is considerably restricted for several reasons, namely: The magnetic needle points north at but few places on the earth, the disagreetnent varying from 1° to 50" from true north. This disagreement, or the angle between true north and the magnetic needle, is called the 4declination of the needle.* The declination does not remain constant, however, there being diurnal, atmual and local variations from the normal declination which introduce unknown errors into the compass survey. The diurnal variation is usually not more than 6 minutes but may reach 20 minutes. It is usually zero at 11 o'clock A.M. ; the annual, I to 2 minutes, and the local variation amounts to as much as several degrees in some localities, owing to deposits of iron ore near the surface. Errors from this source may be avoided by back sights at each station. There are also secular variations in the declination, so that when retracing the lines of a compass survey made several years previously, the surveyor must use the same declination used in the original survey. In making a compass survey it is necessary to determine the declina tion of the needle by an observation on a polar star, or on the sun with the aid of a solar attachment (see below). The stellar observation is usually made on Polaris which, however, is not precisely at the north pole. It is necessary, therefore, to make the observation exactly at the time of upper or lower culmina tion, or at eastern or western elongation; a correction being required in the later case. Tables have been published, however, by the United States Land Office for taking the obser vations on Polaris at any convenient time.
where surveyed correctly — hence the necessity for correction lines every 24 miles as noted above. The distances between the meridians at certain latitudes are in proportion to the cosines of the respective latitudes concerned.
There are several methods of surveying north and south boundary lines of townships and sections so as to make them conform to a parallel of latitude, but the secant method. is the one commonly employed (Fig. 4). Briefly stated it is as follows: A straight line, for con venience called a secant, is run upon a certain course, precisely calculated (nearly due west)., and dependent upon the latitude, and from such a point as will cause it to intersect the curve of the parallel of latitude (boundary line) at the mile and five mile points. From this secant line offsets, as previously calculated, are measured north or south as required at the mile and half mile points, to points in the curve or boundary line where monuments are placed. Convenient tables are published by the United States Land Office which show the azimuths Government Land The first public surveys in the United States were made in the State of Ohio under an ordinance of the Continental Congress passed 20 May 1785. This ordinance was slightly modified by an act of Congress, passed 18 May 1796. This act, which is still in force, provided that all public land, except certain private land grants shall be divided into townships six miles square, and that sections shall be subdivided into one-fourth sections one-half mile square.
The act further provides that all lines of pub lic land surveys shall be run on either true meridians or true parallels of latitude. The method of surveying townships and sections is as follows: First —In each State, or convenient group of States, there is established a principle (true) meridian, and, at right angles thereto, a base line conforming to a true parallel of latitude. Second — Standard parallels or cor rection lines, also conforming to parallels of latitude, are established at intervals of 24 miles north and south of the base line. Third— Guide meridians conforming to true meridians are initiated at intervals of 24 miles along all standard parallels, and run due north to the intersection of the next standard parallel. Fourth —The rectangles thus formed by the guide meridians and standard parallels are sub divided into 16 townships. As meridians con verge toward the north pole the north boundary lines of townships are less than six miles long and offsets required at any latitude in the United States.
This is a method of survey ing a polygon by surveying its perimeter only, as distinguished from the method of cutting the polygon up into triangles (Fig. 5). In a traverse survey the transit is usually oriented at each station, thus referring all bearings to a magnetic meridian. In mapping such surveys the "north shows the magnetic north at the date of the survey and a skeleton arrow is drawn through it showing the needle's declina tion at that time and place from true north. It is not necessary to take convergence of the meridians into account except in geodetic work. The method of procedure is as follows: The transit is set up at station No. 1 and the bear ing and distance of the first course determined. The transit is then removed to station No. 2. With vernier still at the previous reading, the lower spindle is undamped and a plumbed rod bisected at station No. 1, with the telescope inverted. The telescope is then revolved to its normal position, undamped, and the bearing and distance to station No. 3 ascertained. The transit is then removed to station No. 3 and the operations repeated. To illustrate this import ant branch of surveying the tabling of a tra verse and the rules governing the same are given in the table on the preceding page.
In the foregoing the latitude and departure of each course is found by multiply ing the distance by the cosine and sine of the angle expressed by the bearing. The latitude of making a topographical survey. First, by the use of a tape, level and transit. Second, by the use of the plane-table. Third, by the use of a transit and stadia rod. The last-named method alone will be discussed here, it being the method usually adopted, on account of its celerity and low cost. Stadia wires are two horizontal wires placed in an adjustable ring so that they appear at equal distances above and below the horizontal cross-wire when look ing through the telescope.