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Surveying

lines, triangles, earth, angle, cb, science and dc

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SURVEYING, the science of determining accurately the relative locations of points and lines on the earth's surface and of recording the same on maps; it includes also the reverse operation of discovering and locating on the ground points and lines depicted on a surveyoes map.

Two principal kinds of surveying are recog nized, plane and geodetic. In plane surveying the area which is the subject of survey is re garded as a plane surface, the curvature of the earth being disregarded. In geodetic survey ing, which deals with areas of large extent, the curvature of the earth is considered and given its proper drcumstance.

Platte surveying consists essentially of the lineal measurement of lines and the spacial measurement of angles, either vertical or hori zontal; together with the subsequent calcula tion of the content of areas to which such lines and angles appertain. It includes as classes (1) land surveys— the defining of the bound aries of land areas; (2) topographical surveys —the determining of variations in altitude and the denotation of physical characteristics; as, for instance, roads, rivers, forests, swamps, etc.; (3) construction surveys —the staking out of bridges, buildings, sewers, railways, etc. As the earliest records of man refer to slcilful measurements and calculations, it is impossible to assign the birth of the science of surveying to any particular year or even century. Foreip states that, according to the Chaldmans, 4,000 camel steps malce one mile, 66%3 miles one degree., from which the circumference of the earth is 24,000 miles. A papyrus in the British Museum, written 1700 B.C., gives rules for cal culating the areas of triangles, trapezoids and circles and the works of Hero of Alexandria (283 Lc.) mention mine surveying and the relatively crude instruments used at that time.

In 1617 Snellius, in Holland, made one of the first attempts to determine accurately the earth's radius. Picard, in 1667, adapted cross-wires to a telescope. In 1735 the French Academy of Scientists sent out two surveying expedi tions, one to Peru and one to Lapland. The latter resulted in the first demonstration that the earth is not a sphere but an oblate spheroid.

The invention of the vernier by Vetnerus in 1631 and of the transit by Roemer in 1672 gave an impetus to the science of surveying, the final results of which are yet to be achievecL Chain great variety. of work can be done by the use of a chain or tape alone, as, with the measuring of straight lines, the areas of triangles, rectangles and even poly gons can be ascertaincd by dividing the polygon into triangles which are then measured. Angles can be ascertained by laying off equal lengths, b, from the vertex, A, on the two lines, then measuring the third side, a (base of isosceles), and using either of the following formulz: a A a Tan A or Sine -- V4b2 —a2 2 — 2b• The angle may then be looked up in a table of sines and tangents. The measurement of inaccessible lines can also be accomplished with the use of only an accurate tape line, as shown in the accompanying Fig. 1. Assume CB to represent the distance to be determined. Lay out from C a perpendicular line (CD) to the point D, from which also the point B is visible; and .from D lay DC off DC perpendic ular to DB, cutting the extension of the line BC at E. There are then the two similar triangles whose corresponding sides are pro portional; and we have the proportion — DC:CB: :CE:DC — from which we find C13==.

DC2 — It remains craly to measure DC and CB CB' with the closest accuracy possible and to substi tute their values in the proportion. The laying of the perpendicular is a simple application of the pons asinortem of the geometry --4The square of the hypothenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.* In surveying practice this becomes the striking of two curves from the points X and Y respectively, these two points being eight feet apart. The radius of the curve from X is to be six feet, and that from Y 10 feet. The point Z where these curves intersect will be in a perpendicular to XY from the point X, the angle YXZ being a right angle. But such measurements are not comparable with work done with the aid of the transit.

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