The mechanical solution requires the setting of the instru ment at an unknown point P (Fig. 20 not plotted on the board, from which three points, A, B, and C, platted at a, b, and c, respectively, are visible but whose distances from our selected point cannot be measured conveniently. A piece of tracing cloth is fastened over the plane table; and the table oriented approximately with the eye; and a point p' is selected on the tracing cloth which approximately corresponds to the true position of p. Lines p'c', p'b' and p'a' are platted as if p' were the correct point p. have two angles subtended by three points plotted graphically on a tracing cloth, and the point sought is located by placing the tracing cloth over the plotted points as follows: unfasten the cloth and move it to the position p"a" , p"b" , and p"c", in which each line 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, which is to be marked on the board. The plane table can then be oriented accurately by means of any one of the lines pa, pb, or pc.
The Bessel's solution (Fig. 3o) necessitates the use of the three plotted or known points a, b, and c, and the random point P. Construct an angler with vertex at point c as follows: sight along the line ca at the point A on the ground, clamp the vertical axis. Center the alidade on c and sight at B and draw a line along the fiducial edge. Construct the angle 2 with vertex at point a in the same manner. The line joining b and e will pass through the point p required. Orient the board by sighting at B with the line of sight along the line eb and locate p by resection.
Two-point Problem. When two points A and 13 (Fig. 31) on the ground are platted on the plane table at a and b, are visible, the platted position of a third or required point P may be determined by establishing through it a line parallel to AB and orienting the table by means of that line. Set up the plane
table at D, orient it approximately by the eye and plat the point d and the lines dp' , da', and db' . Pick up the table and set up at P and orient it with reference to the line PD by placing the fiducial edge on the line p'd and sight station D. Through any point p" on the line p'd plat the lines of sight to B and A, the intersection of which with da' and db' will be points a" and b" respectively. The line a"b" is then parallel to AB. Placing the fiducial edge on the line a"b" and make a mark along this line about Soo feet from P, in this way establishing a line parallel to AB. The board is now unclamped and with the fiducial edge on line ab and turned until the line of sight bisects the mark, making ab parallel to AB. The table is then clamped and the fiducial edge in contact with a and b in turn, the telescope is directed to points A and B and the lines pa and pb are drawn. The intersection of these lines will give the platted position of the point p.
Adjustments. The necessary adjustments for the plane table are (I) the plate level, (2) line of collimation, (3) the horizontal axis, (4) the attached level. The adjustments are made similarly to those of a transit.
Summary. Preliminary surveys are made by the use of approximate methods and the resulting work will not be accurate for all purposes, but for certain work it has the advantage of being rapidly made and with small expense. The preliminary survey is usually followed by the precise methods which involve the use of the various instruments, and for all important geo logical work they should be used, and all elevations should be referred to sea level and level work checked in all the starting B.M. or at any other point, where elevations may be known.