As you learned from the above example, plotting of detail points cannot begin until the plane-table drawing board or table is oriented. Orientation consists of rotating the leveled table around its vertical axis until the plotted information is in exactly the same relationship as the data on the ground. There are several methods of orienting the plane table. Some of these methods are discussed below.

In figure 9-3, points a and b are the previously plotted locations of points A and B on the ground. First, you set up and level the table at point B. Then you place the straightedge of the alidade along line ba and rotate the table until the alidade is sighted on point A. Once the alidade is sighted on A, the table is clamped and the orientation is checked by sighting on another visible and previously plotted point. The direction to any other visible point can be plotted as a ray from the plotted position of the occupied station.

For rough mapping at a small scale, you can use a magnetic compass to orient the plane table. If the compass is fixed to the table, you orient by rotating

the table about its vertical axis until the established bearing (usually magnetic north) is observed. If the compass is attached to the alidade, you first place the straightedge along a previously drawn line that represents a north-south line. The table is then oriented by rotating it until the compass needle points north.

As you should recall from your study of the EA3 TRAMAN, you know that the earths magnetic field and local attraction will greatly affect the pointing of the compass needle. For these reasons, you should avoid using the compass to orient the plane table when orientation by backlighting can be accomplished.

Orienting a plane table by backlighting or by compass requires occupying a station whose position has been plotted. Resection, however, enables you to orient the plane table without setting up at a previously plotted station. This technique uses two or more visible points whose positions are plotted on the plane table. From these plotted points, rays are drawn back toward the occupied but unplotted point.

TWO-POINT METHOD. The two-point method of resection is used to orient the plane table and establish the position of a station when two previously plotted points cannot be occupied. A description of the two-point method is as follows: In figure 9-4, A and B are visible, but inaccessible, control points. Points a and b are the plotted positions of A and B. The location of unplotted point C is approximately estimated and marked c. D is a selected

and marked point when rays from A and B will give a strong intersection (angle ADB is greater than 300). First set up and level the plane table at point D (first setup, fig. 9-4). Using plotted points a and b, draw resection rays from A and B. These rays intersect at d which is the tentative position of D. Draw a ray from d toward C. Plot c on this line at the estimated distance from D to C.

Next, set up the plane table at C (second setup, fig. 9-4) and orient by backlighting on D. Sight on A and draw a ray through c intersecting line ad at a. In a like manner, sight on B to establish b. You now have a quadrilateral abdc that is similar to ABDC. Since, in these similar quadrilaterals, line ab should always be parallel to line AB, the error in orientation is indicated by the angle between ab and ab.

To correct the orientation, place the alidade on line ab and sight on a distinctive distant point. Then move the alidade to line ab and rotate the table to sight on the same distant point. The plane table is now oriented, and resection lines from A and B through a and b plot the position of point C.

THREE-POINT METHOD. The three-point method involves orienting the plane table and plotting a station when three known plotted stations can be seen but not conveniently occupied.

Set up the plane table at the unknown point P (fig. 9-5) and approximately orient the table by eye or compass. Draw rays to the known points A, B, and C. The point ab denotes the intersection of the ray to A with the ray to B. Points bc and ac are similar in their notation. If the plane table is oriented properly, the

three rays will intersect at a single point. Usually, however, the first orientation is not accurate, and the rays intersect at three points (ab, bc, and ac) forming a triangle, known as the triangle of error.

From the geometry involved, the location of the desired point, P, must fulfill the following three conditions with respect to the triangle:

1. It will fall to the same side of all three rays; that is, either to the right or to the left of all three rays.

2. It will be proportionately as far from each ray as the distance from the triangle to the respective plotted point.

3. It will be inside the triangle of error if the triangle of error is inside of the main plotted triangle and outside the triangle of error if it is outside the main triangle.

In figure 9-5, notice that the triangle of error is outside the main triangle, and almost twice as far from B as from A, and about equally as far from C as from B. The desired point, P, must be about equidistant from the rays to B, and to C, and about one half as far from the ray to A, and the three measurements must be made to the same side of the respective rays. As drawn, only one location will fulfill all these conditions and that is near P. This is assumed as the desired location. The plane table is reoriented using P and back-lighting on one of the farther points (B). The new rays (a, b, and c) are drawn. Another (smaller) triangle of error results. This means that the selected position, P, was not quite far enough. Another point, P, is selected using the above conditions, the table is reoriented, and the new rays are drawn. If the tri- angle had become larger, a mistake was made and the selected point was on the wrong side of one of the rays. The directions should be rechecked and the point reselected in the proper direction.

The new point, P, shows no triangle of error when the rays are drawn. It can be assumed to be the desired location of the point over which the plane table is set. In addition, the orientation is correct. Using a fourth known and plotted point as a check, a ray drawn from that point should also pass through P. If not, an error has been made and the process must be repeated.

Normally the second or third try should bring the triangle of error down to a point. If, after the third try, the triangle has not decreased to a point, you should draw a circular arc through one set of intersections (ab, ab) and another arc through either of the other sets (bc, bc, or ac, ac). The intersections of the two arcsP. This intersection is used to orient the plane table. A check on a fourth location will prove the location.

TRACING-CLOTH METHOD. Another method you can use to plot the location of an unknown point from three known points is the tracing-cloth method of resection. Figure 9-6 illustrates this method.

In the figure, points a, b, and c are the plotted positions of three corresponding known stations (A, B, and C). P is the point of unknown location over which the plane table is set. To plot the location of P you first place a piece of tracing paper (or clear plastic) over the map and select any convenient point on the paper as P. Then you draw rays from P toward the three known stations. Next, you loosen the tracing paper and shift it until the three rays pass through the corresponding plotted points a, b, and c. The intersection of the rays marks the location of P, which can be pricked through the tracing paper to locate the point on the map.