branch of surveying has for its object the exact location of points and lines with reference to the true form of the earth. In most geodetic work the earth is as sumed to be an oblate spheroid, all measured angles and distances being reduced to spheroi dal angles and distances. The United States Coast and Geodetic Survey had adopted the °Clarks spheroid of 1866.° The foundation of a geodetic survey is a base line. This is most carefully measured with specially constructed bars of invar steel (q.v.) encased in wood, called a °Base line Base lines can be measured with steel tapes with an accuracy of one in 1,000,000 under favorable circum stances. These tapes have a screw adjustment for temperature as shown by a thermometer in the handle and there is also a helical spring attachment for regulating exactly the pull used in stretching the tape. Two tapes are used in each measurement and, in case of disagreement are compared with a third and fourth tape. An accuracy of one in 300,000 is generally accepted as satisfactory. With a base line as a nucleus, a system of triangles is laid out over the sur rounding country, additional base lines being measured from time to time to serve as a check upon the work. In a primary triangulation the sides of the triangles are very to 100 miles. The first series of triangles laid from the base line are as nearly equilateral as they can be made. This conduces to accuracy in the larger triangles. Within the primary tri angles secondary and tertiary triangles are laid out, the lines of which are from 1 to 20 miles in length. Angles are measured with specially constructed transits, average results of several readings by the °continuous readingx' method being necessary. The unknown sides and an gles of the spheroidal triangles are calculated and, when possible, the angles are checked by actual observation. Vertical angles are also read at each station and corrected for refrac tion and curvature of the earth. The permis sible error in a primary triangulation by the United States Coast and Geodetic Survey is one-fourth inch per mile or one in about 250,000; the permissible error in the measure ment of an angle is three-tenths of a second and the closing error must not exceed five sec onds, or one in about 260,000. As it is impos sible to measure angles with absolute accuracy it is necessary to adjust the angular measure ment by a system of averaging errors. In de termining the azimuth of any geodetic line the convergence of the meridians has also to be taken into account.
Hydrographic Surveying.— This includes surveys for determining the depths of water in rivers, bays and harbors for purposes of navi gation; the determination of velocity and di rection of currents; the location of hidden rocks or shoals and buoys, lights, etc.; and the determination of the amount of silt or sedi ment carried by streams and deposited in bays. Permanent bench-marks and stations are gen erally made on shore, and the points at which soundings are taken located by triangulation. There are several methods of locating sounding points. First, an observer with a transit is sta tioned at each end of a base line. At the in stant the man on the water makes a sounding he signals the two transitmen to take their ob servations for azimuth. Second, by the °three point problem.° That is, by reading from the boat two angles to three points on shore whose relative positions are known. Of course, sex tants only can be used for measuring angles from the boat.
Soundings are talcen in feet.or fathoms, the mean water level being talcen as the datum plane. For tide waters the average sea-level is ascertained by means of a tide-gauge. In some cases automatic tide-gauges are kept in oper ation for one or more years to determine an average sea-level.
The velocity of water currents in large streams is ascertained by means of a current metre, several styles being in use. The flow of the water in small streams is best determined by means of a weir.
Photographic The use of the camera in surveying is comparatively recent and, though its use is restricted in many ways, it has come into quite general use. It may be called a successful rival to the plane-table. Photo-surveying has been used with success in Italy, India, France, United States and Canada. In the latter country it has supplanted the plane-table almost entirely.
The advantages of a photo-transit are that with it more rapid and cheaper work can be done than by any other means. The results,
however, are not as satisfactory as with the plane-table. The photo-topographer must have a thorough knowledge of perspective drawing, descriptive geometry and photography. The in strument used consists of a compass or a hori zontal, graduated plate with a vernier, to which is attached a camera having a sensitive level and a means of very accurately measuring the focal length at the time each view is taken. If a box camera having a universal lens is used this latter requirement is not necessary. There is also attached to the top or side of the camera a telescope having stadia wires and a vertical circle. Some styles have a scale so placed in the box that it is photographed on the plate when the view is talcen. In any case four pro jecting needles or two cross-wires are so placed in the box that they will indicate the horizon and line of sight in the developed negative. The stadia rod is also photographed as a part of the record. The topographical map is drawn in accordance with the principles of perspective drawing and descriptive geometry, from meas urements taken from the photograph, the com pass bearing and stadia measurements being taken into account.
A con sists essentially of a drawing board mounted upon a tripod together with an alidade, an ali dade being a graduated ruler carrying a tele scope. (Fig. 3). A graduated vertical circle for measuring vertical angles is attached to the telescope, and stadia wires for measuring dis tances are often inserted in it. In operation, the drawing board is covered with a sheet of drawing paper and the alidade telescope sighted consecutively to the various objects which are to be represented in the drawing, pencil lines being drawn upon the paper along the edge of the ruler at each sightinw. The plane-table is then set up over another station whose relative position has been fixed by survey with respect to the first station, and sights taken to all the points sighted from the first station. The pen cil lines will intersect at the points which repre sent the respective objects. Stadia readings are often taken with the alidade telescope, the true elevation and horizontal distances being taken from a slide rule constructed for that purpose. The plane-table is much used by the United States Coast Survey and the United States Geological Survey, as more topographical work can be done in less time by its use than by any other means except photo-topography. Errors in azimuth are impossible and more complete work can be done by making the drawing in the field than by plotting from field notes in the office.
Railroad Railroad surveys are either preliminary, for the study of the terrain, or for the purpose of actual location. A pre liminary survey is often nothing more than a topographical survey of a comparatively wide strip of country through which it is expected to run the line, a paper location being made in the office and the location survey of the paper location afterward made upon the ground. While a topographical survey gives little or no information regarding cuts and fills it is of great value in deciding upon the most advan tageous location.
Briefly stated a railroad location survey con sists of a survey of curves, the tangents joining them and the grades. Tangents and curves are laid out with a transit, the grades and cross sections being worked out with a level. From the cross-section field notes the cubic yards of earth or rock in the cuts and the volume of the fills is computed in the office. The grade line is so located that the material talcen from cuts will furnish enough material to make the fills. All straight portions of a railroad are called "tangents," and the curves are surveyed as the sides of an inscribed polygon of equal sides, each side being 100 feet. (Fig. 6). The "degree of curve," D, is the angle at the centre (of the circumscribed circle) subtended by a chord of 100 feet The "length of curve," L, is the sum of the sides of the inscribed poly gon. The "central angle," Ai is the angle at the centre included between the radii which pass through the tangent points. It is equal to the external angle of the polygon, that is, the de flection angle of the tangents. The "tangent distance," T, is the distance from the vertex to either tangent point. The conditions are such that in any simple railroad curve: 5o I. = — 4. Sin — sinIAD R 100