For this purpose, after having levelled the instrument, add 180° to the direction from A to B, and place the o of the eyeglass vernier at the point so found. Then clamp the vernier plate, after which direct both the telescopes to station A. It is now plain that the line of the limb drawn through o and 180° will coincide with the base line AB, the 0 being towards 4, as before; hence the theodolite is like placed.

Having clamped the limb, loosen the clamp-screw of the vernier plate, and sight to stations E and C, and enter the directions as below.

Having sighted to all the stations which can be seen from B, replace the station-staff and remove the instrument to station C. To the direction BC=57° 12′ add 180°, and the sum is 237° 12'. Having levelled the instrument, place the 0 of the eyeglass vernier at 237° 12', and then sight to station B. The limb of the theodolite will then have the same relative position as at the stations A and B. Then sight to E and D, and enter the directions as below.

Remove the instrument to E. To the direction CE=180 27', add 180°, and the sum will be 360° 27'. Then place the 0 of the vernier at 27', and direct the telescope to C. Or, the theodolite may be placed at E by adding 180° to the direction AE, as taken from A, or to the direction BE, as taken from B, and then directing the telescope to A or B.

By placing the instrument in a similar manner at every station, the line of the limb passing through 0 and 180o, continues parallel to the base AB, the o being constantly in the direction towards A. The instrument is thus placed at all the stations, and the following are the results of the measurements of the angles.

The measurements which have been made, enable us to calculate the lengths of the lines joining the several stations. For, commencing with the triangle AEB, we know all the angles and the base line AB; we can, therefore, find the sides EB, EA. We shall then know one side and all the angles of the triangle CEB, and by pursuing the calculation, the sides of all the triangles can be readily found.

Since the third angle of a triangle can always be found when two of the angles are known, it may seem unnecessary to measure all the angles. But when the three angles are measured and their sum found equal to 180°, the work is proved to be right, and this verification should never be omitted.

It is not probable that the sum of the three measured angles will be exactly equal to 180°. But they ought not to

times, and a mean of the measurements be taken, the errors of observation and of the instrument will be much diminished.

196. The method of determining points by a series of consecutive triangles, is called the method by triangulation. It may be extended to any number of triangles, and if the three angles of every triangle be measured, and the work carefully verified at each step, there is little danger of error. We have applied the method only in the survey of a harbour, but it may be used with equal advantage in all surveys in which long lines are to be determined, and is, indeed, the only one that can be relied on, where great accuracy is required.

Of the Manner of using the Compass.

197. The compass is often used in connection with the theodolite, and although a rude instrument, may yet be relied on for the shorter lines and smaller parts of a survey. The following is the manner of keeping the field notes.

Divide a paper into two equal parts, by two parallel lines near to each other, and consider each part as a separate leaf or page. Each leaf is divided into three spaces, and the middle one 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.

The stations, at which the compass is placed, are designated by o in the middle column, and the bearing of each course is entered directly above.

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

Enter this bearing at A. Then measure along the line 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,

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 62o E. We then measure the distances to m, n, p, and I, and enter them, together with the offsets, as in the notes.

198. 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.

199. In making the plan of the harbour, it might be found convenient to use the plain-table in connexion with the theodolite and compass. For example, we might place the plaintable at G, and having fixed stations at the principal points of the shore, between G and F, we would sight to each of them then remove the table to F, and do the same for that station we should thus determine the points between F and G, with reference to the line GF.

Of Plotting.

200. The lines of the triangles determined with the theodolite, can be plotted in the manner already explained. It would be better, however, to use the instrument which we are about to describe, and which is called

THE CIRCULAR PROTRACTOR.

201. This instrument consists of a brass circular limb (Pl. 2, Fig. 4), of about six inches in diameter, with a moveable index AB, having a vernier at one extremity A, and a milled screw at the other extremity B, with a concealed cog-wheel that works with the cogs of the limb, and thus moves the index AB about the centre of the protractor. At the centre of the protractor is a small circular glass plate, on which two lines are cut; the point of their intersection, is the exact centre of the instrument. The limb is generally divided to half degrees; the degrees are numbered from 0 to 360.

At the 0 point, and at the opposite extremity of the diameter passing through that point, are small lines on the inner edge of the limb; the two extremities of the diameter, perpendicular to this latter, are also designated in the same way.