and unclamping the vernier plate, direct the telescope on the signal at E. The reading will evidently be equal to twice the angle BAE, and if we repeat the operation, the reading will be three times the angle, and so on. After ten repetitions, if we add 360° each time the 0 of the vernier passes the 0 of the limb, the final reading will be ten times the angle BAE, affected with the joint errors of the ten observations, and one-tenth of this will be the reading required, to a greater degree of accuracy than could probably be attained by a single observation.

20. The method of reading angles, by this mode, is as follows:

Angles at station A, between signals B (left), and E (right.)

21. After the triangulation is completed, the interior may be filled up by the aid of the Compass, or the planetable.

USE OF THE COMPASS.

22. When the secondary and tertiary triangles, have been considerably multiplied, the compass is taken in hand. The field-notes may be kept in the following manner. Divide a page of the note-book into two equal parts, by two parallel lines near to each other, and consider each part as

spaces, and the middle space is generally smaller than either of the others, which are equal.

The notes begin at the bottom of the first page, and run up the page to the top. They then commence again at the bottom of the next page, and run up to the top; thence to the bottom of the third page, and thus, for as many pages as the work may require.

When the compass is used in the way we are about to explain, the distances to objects which lie on the right or left of the courses, are determined by means of offsets.

The beginning of every course is designated in the middle column by 0, and the bearing is entered directly above. The other figures of the middle column, express the distances from the beginning of each course to the offsets, and those in the side columns indicate the lengths of the offsets, or the distances to objects on the right or left of the compass lines.

To explain more definitely the manner of using the compass on the field, let us suppose that we have determined the prominent points and longer lines with the theodolite. Place the compass at A (Plate 6), and take the bearing of the line AE, which is S 12° W.

AE any distance, as Aa equal to 130 yards, and make an offset to the lake, which we measure and find to be 50 yards. Enter the 130 in the middle column, and as the lake lies on the right (in going from A to E), we insert the 50 in the right hand column.

We then measure along the line AE to b, 350 yards from A. Here we make a second offset to the lake, and find it to be equal to 100 yards. Having entered the distances in the notes, we measure to q, the point where the line AE crosses the creek, and we enter the distance from A, 415 yards.

At d, we lay off an offset on the left, to the pond, 70 yards: at e, an offset to the mouth of the creek, 150 yards: and at E, where the course terminates, an offset to the lake, of 160 yards. The entire distance from A to E is 800 yards.

At E, we take the bearing to H, which is N 50° E. Having measured along this line to f, 315 yards, we make an offset to the pond, on the left, of 50 yards, and to the shore, on the right, of 90 yards. Having entered these distances, we recommence the notes at 315 below, which we suppose to be at the bottom of the second page. Having reached H, the extremity of the course, we enter the entire distance from E, 680 yards. We next take the bearing to I, S 52° E. We then measure the distances to m, n, p, and I, and enter them, together with the offsets, as in the notes.

23. It is also well to make, in the columns on the right and left, such sketches of the ground, fields, houses, creeks and rivers, as will afford the means of making an accurate delineation on paper.

THE PLANE-TABLE-ITS USES.

24. Pl. 3, Fig. 1. The plane-table consists of two parts; a rectangular board CDBA, and a tripod EHG, to which it is firmly secured.

Directly under the rectangular board are four milled

brass plate these screws are worked against a second horizontal plate, for the purpose of levelling the table; the table having a ball and socket motion, similar to the limb of the theodolite.

For the purpose of levelling the table, a small detached spirit-level is used. This level being placed over the centre, and also over two of the levelling screws, the screws are turned contrary ways until the level is horizontal; after which, it is placed over the other two screws, and made horizontal in the same manner.

Between the upper horizontal plate and the table, there is a clamp-screw, similar to the clamp-screw of the theodolite, which being loosened, the table can be turned freely about its axis. There is, also, a small tangent-screw, by which the smaller motions of the table are regulated, after the clamp-screw is made fast. Neither of these screws can be seen in the figure.

The upper side of the table is bordered by four brass plates, about one inch in width, and the centre of the table is marked by a small pin, F. About this centre, and tangent to the sides of the table, conceive a circle to be described. Suppose the circumference of the circle to be divided into degrees and parts of a degree, and radii to be drawn through the centre and the points of division. The points 'in which these radii intersect the outer edge of the brass border, are marked by lines on the brass plates, and the degrees are numbered in the direction from left to right, from the point I to the point I, 180°, and from the point I to the point L, 180°. In some plane-tables, how

ever, they are numbered from 0 to 360°.

There are, generally, diagonal scales of equal parts cut on the plates DLC and AIB, the use of which will be explained hereafter.

Near the two other edges of the table, two small grooves are made, into which the plates of brass DB and CA are fitted, and these plates are drawn to their places by means of milled screws, which pass through the table from the

of two of the screws, and S, are seen in the figure, as also one of the plates and its two screws in Fig. 3. The object of these plates is to confine a sheet of paper on the table. By loosening the screws, and pressing them upwards, the plates are raised above the surface of the table; the edges of the paper can then be placed under them: then, by turning the screws back again, the plates are drawn down and the paper held tightly. Fig. 1 represents the table with the paper partly put upon it: one edge of the paper has been placed under the plate DB, and the screws S and Q, tightened. The paper, before being put on, should be moistened, in order to expand it; and then, after it has been dried, it will fit closely to the table.

A ruler, AB (Fig. 2), with open vertical sights, is used with the plane-table. This ruler has a fiducial edge, which is in the same vertical plane with the hairs of the sights. A ruler with a telescope, and a vertical limb, similar to the vertical limb of the theodolite, is sometimes used with the plane-table. A compass, also, is often attached to the table, to show the bearings of the lines.

The plane-table is used for two distinct objects.

1st. For the measurement of horizontal angles.

2dly. For the determination of the shorter lines of a survey, both in extent and position.

TO MEASURE A HORIZONTAL ANGLE.

25. Place, by means of a plumb, the centre of the table directly over the angular point: then level the table; after which, place the fiducial edge of the ruler against the small pin at the centre: direct the sights to one of the objects, and note the degrees on the brass plate; then turn the ruler and sights to the other object, and note the degrees as before. If the ruler has not passed over the 0 point, the difference of the readings is the angle sought; but, if it has, the larger taken from 180°, and the remainder added to the smaller, gives the required angle.

TO DETERMINE LINES IN EXTENT AND POSITION.