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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.

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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 62° 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 theod. olite 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

TIIE 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 o 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 Two angular pieces of brass, each having a small and sharp steel pin at its extremity, are fastened to the index, and revolve freely around the lines ab and cd. The small screws, a, b, c, and d, move them in the directions of the lines ab, cd, for the purpose of bringing the steel pins exactly into the line which passes through theo of the index and the centre of the protractor.

To adjust them to their places, place the centre of the protractor over a marked point, and the o of the index to the o of the limb. Then mark the place of the index by the pins : after which, turn the index 180°, and see if the pins will mark the same points as before. If they do, the index is adjusted ; if they do not, correct the error with the screws a, b, c, and a

To lay off an angle with the Protractor. 202. Let its centre be placed over the angular point, and the diameter passing through 0 and 180', on the given line. Turn the screw that works the index, until the o of the vernier coincides with the division corresponding to the given angle; then let the angular brass pieces be turned down; the points dotted by the steel pins will show the direction of the required line.

If this line does not pass through the angular point, the pins are out of place, and must be adjusted.

First Method of Plotting.

203. Suppose it were required to make the plan of the harbour on a scale of 450 yards to an inch.

Divide the length of the base line AB, which we will suppose equal to 1140 yards, by 450, and the quotient 2.53 will express the length which is to represent the base line on the paper (Art. 33).

Draw an indefinite line AB, to represent the base, and having chosen any point, as A, for the first station, lay off 2.53 inches to B. The other extremity of the base line will thus be determined.

Then, place the circular protractor at A, and lay off the angle BAE, and then the angle EAG. Next, place the protractor at B, and lay off the angles ABE and EBC. the station E. Let the protractor be then placed at this point, and all the angles of station E, laid down.

The point G, where EG intersects AG, and the point C, where EC intersects BC, will then be found.

By placing the protractor at C and G, we can determine the points D and F, when the place, on the paper, of all the stations will be known.

To unite the work done with the compass, spread the compass-notes before you, and draw through A a line to represent the meridian. This line makes an angle of 120 with the course AE.

. Then, lay off from the scale the distances Ad, Ab, Aq, Ac, Ad, Ae, and at the several points erect perpendiculars to AE. Lay off on these perpendiculars the lengths of the offsets, and the curve traced through the points so determined, will be the margin of the lake.

At E, draw a parallel to the meridian through A, and lay down the course EH, which makes an angle of 50° with the meridian. Then, lay down the several distances to the offsets, and draw the offsets and lay off their lengths. Do the same for the course HI, and all the compass-work will be plotted.

Had there been work done with the plain-table, it could easily be united to that done with the theodolite.

Second Method of Plotting.

204. Place the centre of the protractor near the centre of the paper, and draw a line through the points 0 and 180°. This line will have the same position with the circular protractor that the base line AB had with the limb of the theodolite.

Lay off then from the o point an arc equal to the direction from A to. E, also an arc equal to the direction AG, and through the centre point, and the points so determined, draw lines. Lay off in succession, in a similar manner, the directions taken at all the stations; and through the centre point, and the points so determined, draw lines, and designate each by the letters of the direction to which it corresponds.

Now, since all the lines drawn on the paper have the same lines on the ground have with the limb of the theodolite, it follows that each direction will be parallel to its corresponding line upon the ground.

Hence, any line may be drawn parallel to that passing through 0 and 180°, to represent the base line AB. Having drawn such a line, and marked a point for the station A, lay off the length of the base, and the extremity will be the station B.

Through A and B, so determined, draw parallels respectively to the lines corresponding to the directions AE and BE, and the point of intersection will determine station E. Through B and E draw parallels to the lines which correspond to the directions BC, CE, and their point of intersection will determine station C. Through C and E draw lines parallel to the lines corresponding to the directions CE and ED, and the point of intersection will determine D. In a similar manner we may determine the stations F and G. Of surveying a harbour for the purpose of determining the depth

of water, &c. 205. When a harbour is surveyed for the second object, viz., for the purpose of ascertaining the channels, their depth and width, the positions of shoals, and the depth of water thereon, other means must be used, and other examinations made in addition to those already referred to.

Let buoys be anchored on the principal shoals and along the edges of the channel, and using any of the lines already determined as a base, let the angles subtended by lines drawn from its extremities, to the buoys respectively, be measured with the theodolite. Then, there will be known in each triangle the base and angles at the base, from which the dis. tances to the buoys are easily found ; and hence, their positions become known.

Having made the soundings, and ascertained the exact depth of the water at each of the buoys, several points of the harbour are established, at which the precise depth of the water is known; and by increasing the number of the buoys, the depth of the water can be found at as many points as may be deemed necessary.

206. If a person with a theodolite, or with any other in

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