Page:The New International Encyclopædia 1st ed. v. 18.djvu/827

* SURVEYING. 725 SURVEYING. at A, the surveyor proceeds around the field, ob- taining by his compass the bearings, and by measurement with a surveyor's cliain, the lengtlis, of the lines A B, B C, C D, D E, and E A, one after the other in the order named. This being done he states these bearings and distances on papci', giving the figure ABODE shown by the sketch. He next draws a meridian line NS through the westernmost corner of his boundary, and draws the various perpendiculars shown by the broken lines. These perpendiculars represent what are known as the latitudes of the several lines; thus for line DC, (/D is the latitude, Dc is the departure, and (/D + dC) is the double meridian distance. Knowing the bearings and lengths of the various courses by simple trigo- nometrical calculation, the surveyor is enabled to calculate the latitudes, departures, and double meridian distances. This being known, the fol- lowing rule is used for calculating the area: Twice the area of the figure is equal to the algebraic sum of the products of the double me- ridian distances of the several courses into the corresponding latitudes, north latitude being reckoned positively and south latitude negative- Iv. Expressed svmbolicallv, for the figure shown, this rule is as "follows: '2A = (6B-f cC) Be + (cC-f /■D) Dd— (6B) A6— (oE) Ad— (aE + fD) Eff. It may often happen that one boundary of a field is not a right line, but is an irregular curved line such as the course of a stream C F B instead of by the right line B C. The area of this field is then the area of A B C D E ])lus the area of C F B ; the surveyor when measuring the line B C measures two or more perpendiculars such as xx, yy, zz, and tew, known as oft'sets and extend- ing from the line B C to the stream. These per- pendiculars divide the area C F B into a number of small areas each of which approximates close- ly a simple trapezoid or triangle whose area is easily determined and the sum of who.se areas is the area of the total tract. There is of course a slight error in this method, but it can be made so small by an experienced surveyor as to be practically negligible. Systematic methods have been devised for making field notes so as to in- clude a register of the topographical features incident to the chain lines, the relation of these lines one to another, and a description of monu- ments sufficient to identify the lines in the field. A column is usually taken in the centre of each page of the field-book to represent the chain line, and the necessary notes are entered on either side. These notes if properly kept enable the surveyor to execute a topographical map of the territory survejed, and to calculate its area. Topographical Surveying. The topographical surveying of a region includes not only the char- acter and geographical distribution of the sur- face covering, but also the exact configuration of that surface with reference to its elevations and depressions. Thus any point is geographi- cally located when its position with reference to any chosen point and a meridian through it is found, but to be topographically located its ele- vation above a chosen level must also be known. In making a topographical survey, therefore, the following processes are carried out. First, one or more reference points, according to the area, are geographically located ; second, a series of precise levels are run to establish marks at cer- tain intervals whose elevations are computed with reference to a common datum; third, from these established points and elevations the loca- tions and elevations of the surface points are es- tablished by one of several metliods. The final process is to plat on a map by means of conven- tional symbols the location of all surface objects and the elevations and dp]jressions of the general surface. See Topograpliical Map, accompanying Map. In the topographic work of the Geological Survey, and in fact in the work of all the United States Ciovernnicnt Survc.ys, the reference point for geographical location is astronomical ])Osition and the datum for all elevations is mean sea level. The various reference points are connected by means of a system of triangulation, by which intermediate points are geographically located. Elevations are established by means of lines of precise levels starting from datum. On these as a skeleton the topographical survey proper is hung. The operation of determining an astronom- ical position consists, first, in tlie measurement of zenith distances of stars by means of delicate transit instruments for the determination of lati- tude; second, the exchange of telegraphic time signals between a known astronomical position and an unknown one for the determination of time difference, and hence the difference of longi- tude ; and, third, the determination by astronomic observations on close circumpolar stars of the azimuth of a line, presumably a base line or side of a triangle. The measurement of a base line consists, first, in the selection of a site, the ex- tremities of which are so situated as to permit of easy expansion by primary triangulation ; sec- ond, the laj'ing out of a site by running a line of spirit levels over it and of setting plugs or other stable measuring marks at fixed intervals ; third, the ranging out of a straight line by transit or theodolite; and finallj', the measurement of the length of the base by means of base bars, iced bars or steel tapes. The expansion of a system of primary triangulation consists, first, in a reconnaissance to select stations from which others are intervisible in such manner as to per- mit of the formation of a series of quadrilateral, pentagonal, or similar figures composed of well- conditioned triangles ; second, the erection of signals and the marking of station positions by monuments; and third, the measurement of the angles at any one station to the others which are intervisible therefrom, by means of theodolites of high power. Finally, there remains the office computation whereliy the lengths of the sides of the various triangles are determined, and by the aid of this and their connection with a known astronomic position and azimuth the geodetic po- sition and coordinates of the various triangula- tion stations are computed. These or equivalent coiirdinatcs at important points on a traverse line are then platted on the topographic map sheets, and this furnishes the primary control for the, extension of the secondary detail of the map. The datum on which all of the representation of the relief by contours is based is mean sea level. In order that pieces of work separated by distances of 100 or 1000 miles may ultimately meet on sheet lines with homogeneity of verti- cal location, it has been necessary, first, to plan out series of primary triangulation for the con- trol of the whole. These precise levels are con- nected with tidal gauges referred to the mean level of the sea. With these primary data in ex-