determining the magnetic meridian on the drawing. The plumbing arm e p p'e' serves for suspending a plumb-bob, so that it will be directly under a point e on the paper representing the point determined on the ground by the plumb-bob.

The plane table is used for preparing topographical maps. In the survey of larger areas, reference lines forming a network of triangles are run with a transit and platted on the drawing of the plane table; the vertexes of these triangles, called

triangulation stations, are used for determining other points of the survey by means of the plane table.

Orienting. When the plane table set up over a point has each line platted on it parallel to the corresponding line in the field, it is said to be oriented.

Let ab, Fig. 2, be the platted position of the line AB on the ground, and assume that the plane table is to be oriented at A. First, orient the table approximately by the eye and at the same time, by means of the plumbing arm, bring the point a over A. Then level the table and, with the edge of the alidade ruler

along the line ab, move the table horizontally until the telescope is accurately directed to B. The table is then clamped and another point, as c, may be platted by directing the telescope to C and at the same time having the edge of the alidade ruler in contact with the point a; the line ax is then drawn and the distance AC, measured by stadia or otherwise, is laid off to scale, giving the point c.

Plotting by Intersection.-After the line ax in the preceding example has been drawn, the point c can be located without measuring the distance ac. This is done by moving the table

to B, platting the line by in a manner similar to line ax, and then bringing these two lines to intersection.

Platting by Resection.-When the plane table is set up on a point C, Fig. 3, not platted on the board, and the points A and B have already been platted, measure the distances CA and CB. Then, with these distances, to the scale of the map, as radii, swing arcs from a and b as centers. The point of intersection of these arcs is the platted position of the point C, and the table can then be oriented in the usual manner.

The Three-Point Problem.-Let the plane table be set over

a point P, Fig. 4, not platted on the board, from which three points A, B, and C platted at a, b, and c, respectively, are visible, but whose distances from P cannot conveniently be measured. To plat this point fasten a piece of tracing cloth over the plane-table paper; orient the table approximately with the eye, and select on the tracing cloth a point p' approximately corresponding to the true position of with regard to a, b, and c, plat the lines p'c', p'b', and p'a' as if p' were the correct point p. Then unfasten the tracing cloth and QA

shift it to the position p"a", "b", and p"c", in which each of the lines p'a', p'b', and p'c' pass, respectively, through the points a, b, and c. The point p" is then over the exact position of p and can be pricked through with a needle point. The plane table can then be oriented accurately by means of any of the lines pa, pb, or pc.

The Two-Point Problem.-When only two points A and B, Fig. 5, platted at a and b are visible, but inaccessible, the platted position of a third point C may be determined by establishing through it a line parallel to AB and orienting the table by means of that line. The field work is as follows: First, set up the plane

table at D, Fig. 5; orient it approximately by the eye, and plat the point d and the lines dc', da', and db'. Then move the table to C and orient it with reference to the line CD by placing the edge of the ruler on the line c'd and directing the telescope to station D. Through any point c" on the line c'd plat the lines of sight to B and A, the intersections of which with da' and db' give, respectively, the points a" and b". The line a'b' is then parallel to AB. Now place the edge of the ruler on the

line a"b" and set in this line a mark at a point at least 500 ft. from C, thereby establishing a long line parallel to AB. The board is now unclamped, and, with the edge of the ruler on the line ab, it is turned horizontally until the line of sight bisects the mark, thereby making ab parallel to AB. The table is then again clamped, and, with the ruler edge in contact with a and b in turn, the telescope is directed to the points A and B and the lines ca and cb are drawn. The intersection of these lines will give the platted position of the point c.

TOPOGRAPHIC SURVEYING

METHODS EMPLOYED

In a topographic survey, the relative elevations or depressions of points and objects are determined in addition to their positions. Three methods, differing with regard to the instruments used, are employed in making topographic surveys; These are the transit method, the stadia method, and the plane-table method.

TRANSIT METHOD

The transit method is well adapted to surveys for the location of railroads and to similar surveys that relate to lines rather than to areas, and in which the topography is required to cover only comparatively narrow strips of country contiguous to the lines. In such surveys, the entire process is based on the line of the survey, which is usually alined with a transit and measured with a chain or tape. Along with the survey, a line of levels is run with a leveling instrument and at suitable intervals, generally every 100 ft., cross-sections are taken at right angles to the line. For the latter purpose the hand level and the clinometer are often used.

Hand Level and Clinometer.-The hand level, also called the Locke level, is shown in Fig. 1. The bubble of the level tube C can be seen through the opening D by means of a

reflecting prism. A cross-hair placed in the main tube AB serves to fix the object observed, and when this hair at the same time bisects the bubble the line of sight is horizontal.

By means of a clinometer, one form of which is shown in Fig. 2, the angle that a slope makes with a horizontal can be