If, arriving at any station, any other station already located is visible, a check on the work may be had by sighting upon it after orienting the table. Thus, after arriving at B and orienting the table on Y, if the ruler is placed on 6 and a, and the line of sight passes through A, it proves the work is correct; but if not, the amount and direction of deviation show the amount of error introduced in the traverse, which may be here thrown out by orienting on A instead of Y, if the traverse is to continue from B.

Orienting by the needle. When traversing through woods, or along winding roads, or over undulating ground, it may often be more convenient to orient the table by means of the declinator or compass; hence the value of the magnetic meridian which was marked on the paper when beginning work.

The table might even be oriented at each station by the compass, instead of back-sighting, but this method would not be so accurate on account of magnetic disturbances of the needle, and the shortness of the needle line compared to the distance between check dots. Any single inaccuracy in orienting the table with the compass in a series of settings would produce less effect in the end, however, than a like error of the same amount at the same place made in orienting by back-sights. This will be understood by reference to the following figures:

FIG. 122.

F16. 123.

In Fig. 122, by using the compass to orient the table each time, no reference is had to the line 1-2; therefore the only

error, if subsequent settings are correct, will be the first one made.

In Fig. 123, to orient the table at 2, reference must be had to the line 1-2, which being in error, the setting here will also be in error, as also at all the other points, not in themselves, perhaps, but because of an indirect reference back to 1-2.

LOCATION BY RESECTION.-This consists in finding the point on the map or plot which corresponds to the point on the ground over which the table is set, and is done by pointing to known and plotted points, after the table has been oriented. All problems under Resection consist of two partsviz., the orientation and the resection.

In this determination the difficulty that arises is, how to orient the table

1st method: By use of the magnetic needle.

Orientation. If the magnetic meridian has been marked on the plot, then by using the compass the table may be oriented at any place where it may be set up, as described under Traversing.

Resection. The point occupied may be plotted by selecting two points (already plotted) about 90° apart, pivoting the ruler on the plotted position of one, sighting the object, and drawing a line back; then pivoting the ruler on the plotted position of the second object, sighting it, and drawing a line back, intersecting the previous line drawn; this intersection will be the plotted position of the point occupied.

Magnetic disturbances of the needle will, of course, affect the accuracy of this method, which may be tested by sighting, as before, on any other visible plotted point and seeing if the line passes through the point found. If not, it proves that the table was not exactly oriented.

2d method: By use of one known and plotted point and a line drawn from a plotted station through the unknown point. If one sighting has been taken to a point from a station and a line drawn towards it, the point may be occupied with the

table and its position plotted. Thus, from
station S (Fig. 128) the object D was sighted
and the line towards it drawn. The plotted
position of D will be somewhere on this line, ...
but its exact position is not known.

Orientation. The table is set up over D,

KA

FIG. 128

leveled and approximately oriented. The edge of the ruler is placed on the line ds so that the check dots are just visible along the edge, and the table turned until S is bisected, when the table it oriented.

Resection. The ruler is then pivoted on the plotted point k of an object K that will give a good intersection and moved until K is bisected. Where the ruler intersects the line sd will be the plotted position of D. Resection upon any other plotted point will verify its position.

3d method: By use of two known and plotted points (the twopoint problem).

1st. solution: Orientation. The occasion may arise where it is desirable to orient the table and begin work at a point from which only

ated that the intersections from C and D on A and B make sufficiently large angles for good determinations. But the

table approximately in position at D, by estimation or by com. pass, and draw the lines Aa and Bb intersecting d; through d draw a line towards C. Then set up at C and assuming the point c on the line dC, at an estimated distance from d, and putting the table in a position parallel to that which it occupied at D by the line cd, draw lines from c towards A and c towards B. These will intersect the lines dA and dB in the points a' and ', which form with c and d a quadrilateral similar to the true one, but erroneous in size and position.

The angle which the lines ab and a'b' make with each other is the error in position. By now constructing through c a line cď making the same angle with cd as that which ab makes with a'b', and directing this line cď to D, the table will be oriented. Or, to orient instead of transferring the angle of error by construction as above, proceed as follows: As the table stands, a'b' is parallel to AB, but to orient the table, ab must be parallel to AB. Therefore, place the alidade on a'd and set a mark in that direction, then place the alidade on ab and turn the table until it again points to this mark; then ab will be parallel to AB and the table oriented.

Resection. The true plotted position of C may now be found by resection on A and B.

2d solution: Instead of performing the above operations on the actual plot-sheet, if a piece of tracing-linen or tracing. paper is at hand, it may be fastened on the table, and the aux. iliary quadrilateral constructed upon it, by assuming a point d over D and drawing dA, dB, and dC, and completing as above. Then loosen the tracing and place the line a'b' on ab, and with the alidade on ca', cb', or cd revolve the table until the line of sight comes on A, B, or D. The table will then be oriented. (Fig. 133). Set up the

3d solution:

table at C as nearly oriented as can be done by eye, and resect upon A and B, intersecting at d. The angle adb being the true angle at C subtended by AB, the true point c must be on the circumference of the circle through acb. Construct this circle. Meas

FIG. 133.

ure off a base CD at least half the length of CB at right angles, or nearly so, to bd in the direction most convenient. Set up a signal at D and with the alidade draw the line c'd. Take the table to D, and by the line de sighting on C bring the table into a position parallel to that which it had at C. With the ruler pivoted on d, sight B and draw the line dỡ intersecting db at b'. 'b' is the plotted distance of C from B, which distance laid off on the circle as a chord from 6 will give c, the true plotted position of C. A fourth point may then be occupied, and by resection on A, B, and C the accuracy of the determination of C verifled.

If the auxiliary point D can be taken in range with A and B, either between them or in prolongation of the line joining them, the table may be set up there and oriented on them, and then a line drawn towards C from any point on this range line on the plot. The table is then taken to C, oriented by the line just drawn and the position of c found by resection on A and B. One can place himself on the line joining two points, when he is between them, by observing them alternately from opposite ends of the ruler laid on the table and moving the whole table to one side or the other until the ruler viewed from either end bisects the objects.

4th method: By use of three known and plotted points (the three-point problem).

136

Orientation. The table may be at once oriented at any unknown point from which three known plotted points are visible, except when it lies on the circumference of a circle passing through the three known plotted points. In Figs. 134, 135, 136, and 137 let a, b, and c be the plotted positions of A, B, and C respectively, and D the unknown point. The table is set up over D and leveled. The ruler is set on the line ca, and a directed, by revolving the table, to its corresponding signal A and the table clamped. Then with the ruler pivoted on c, the middle signal B is sighted and the line ce drawn. The ruler is then set