The circumferentor-box may then be taken off.

Direct the sights to the object at the second station, and the degree cut by the opposite end of the index will be the bearing of that line from the north, and the same that the circumferentor would give.

After having measured the stationary distance, set up your instrument at the second station; unscrew it, and set either end of the index to the degree of the last line, and turning the whole about with that degree towards you, direct your sights to an object at the foregoing station, and screw the instrument fast; it will then be parallel to its former situation, and consequently north and south; direct then your sights to an object at the following station, and the degree cut by the opposite end of the index will be the bearing of that line.

In the like manner you may proceed through the whole.

If the brass circle be divided into four nineties, from 360 and 180, and the letters N, S, E, W be applied to them, the bearings may be obtained by putting down the letters the far or opposite end of the index lies between, and annexing thereto the degrees from the N or S, and this is the same as the quartered

compass.

If you keep the compass-box on, to see the mutual agreement of the two instruments: after having fixed the theodolite north and south, as before, turn the index about, the north end or flowerde-luce next your eye, and count the degree to the opposite or south end of the index, and this will correspond with the degree cut by the south end of the needle.

At the second or next station, unscrew the instrument and set the south of the index to the degree of the last station; turn the whole about, with the south of the index to you, and cut the object at the foregoing station; screw the instrument fast, and with the north of the index to you, cut the object at the next following station; the degree then cut by the south of the index will correspond with the degree cut by the south end of the needle, and so through the whole,

Some theodolites have a standing pair of sights fixed at 360 and 180, besides those on the moveable index; if you would use both, look through the standing sights with the 180 next you to an object at the foregoing station: screw the instrument fast, and direct the upper sights on the moveable index to the object at the following station, and the degree cut by the opposite end of the index will give you the quantity of the angle of the field.

Two pair of sights can be of no use in finding the angles from the meridian; and inasmuch as one pair is sufficient to

find the angles of the field, the second can be of no use: besides, they obstruct the free motion of the moveable index, and therefore are rather an incumbrance than of any real use.

Some will have it that they are useful with the others for setting off a right angle in taking an offset: and surely this is as easily performed by the one pair on the moveable index : thus, if you lay the index to 360 and 180, and cut the object either in the last or following station, screw the instrument fast and turn the index to 90 and 270, and then it will be at right angles with the line. So that the small sights, at those of the circle, can be of no additional use to the instrument, and therefore should be laid aside as useless.

This instrument may be used in windy and rainy weather, as well as in mountainous and hilly grounds; for it does not require a horizontal position to find the bearing or angle, as the needle doth, and therefore is preferred to any instrument that is governed by the needle.

THE SEMICIRCLE.

THIS instrument, as its name imports, is a half-circle, divided from its diameter into 180 degrees, and from thence again, that is, from 0 to 360 degrees. It is generally made of brass, and is from 8 to 18 inches diameter.

On the centre there is a moveable index with sights, on which is placed a circumferentor-box, as in the theodolite.

This instrument may be used as the theodolite in all respects, but with this difference; when you are to reckon the degree to that end of the index which is off the semicircle, you may find it at the other end, reckoning the degree from 180 forwards.

THE PLANE TABLE.*

A PLANE TABLE is an oblong of oak, or other wood, about 15 inches long and 12 broad. They are generally composed of three boards, which are easily taken asunder or put together for the convenience of carriage.

* This instrument is not much used by surveyors at present.

There is a box frame, with six joints in it, to take off and put on as occasion serves; it keeps the table together, and is likewise of use to keep down a sheet of paper which is put thereon.

The outside of the frame is divided into inches and tenths, which serve for ruling parallels or squares on the paper, or for shifting it, when occasion serves.

The inside of the frame is divided into 360 degrees, which, though unequal on it, yet are the degrees of a circle produced from its centre, or centre of the table, where there is a small hole.

The degrees are subdivided as small as their distance will admit; at every tenth degree are two numbers, one the number of degrees, the other its complement, to 360.

There is another centre-hole about one-fourth of the table's breadth from one edge, and is in the middle between the two ends. To this centre-hole on the other side of the frame, there are the divisions of a semicircle, or 180 degrees; and these again are subdivided into halves, or quarters, as the size of the instrument will admit.

That side of the frame on which the 360 degrees are, supplies the place of a theodolite, the other that of a semicircle.

There is a circumferentor-box of wood, with a paper chart at the bottom, applied to one side of the table by a dovetail joint fastened by a screw. This box (besides its rendering the plane table capable of answering the end of a circumferentor) is very useful for placing the instrument in the same position every remove.

There is a brass ruler or index, about two inches broad, with a sharp or fiducial edge, at each end of which is a sight; on the ruler are scales of equal parts, with and without diagonals, and a scale of chords; the whole is fixed on a ball and socket, and set on a three-legged staff.

To take the angles of a field by the table.

Having placed the instrument at the first station, turn it about till the north end of the needle be over the meridian, or flowerde-luce of the box, and there screw it fast. Assign any convenient point, to which apply the edge of the index, so as through the sights you may see the object in the last station, and by the edge of the index from the point draw a line. Again, turn about the index with its edge to the same point, and through the sights observe the object in the second station, and from the point, by the edge of the index, draw another line; so is the angle laid down; on that last line set off the distance to the second station, in chains and links: apply your instrument

to the second station, taking the angle as before; and after the like manner proceed till the whole is finished.

This method may be used in good weather, if the needle be well touched and play freely; but if it be in windy weather, or the needle out of order, it is better, after having taken the first angle as before, and having removed your instrument to the second station, and placed the needle over the meridian line as before, to lay the index on the last drawn line, and look backward through the sights; if you then see the object in the first station, the table is fixed right, and the needle is true; if not, turn the table about, the index lying on the last line, till through the sights you see the object in the first station: and then screw it fast, and keeping the edge of the index to the second station, direct your sights to the next; draw a line by the edge of the index, and lay off the next line; and proceed through the whole without using the needle, as you do with the theodolite. If the sheet of paper on the table be not large enough to contain the map of the ground you survey, you must put on a clean sheet, when the other is full; and this is called shifting of paper, and is thus performed.

PL. 6. fig. 8.

Let ABCD represent the sheet of paper on the plane table, upon which the plot E, F, G, H, I, K, L, M is to be drawn: let the first station be E; proceed as before, from thence to F and to G; then proceeding to H, you find there is not room on your paper for the line GH, however draw as much of the line GH as the paper can hold, or draw it to the paper's edge. Move your instrument back to the first station E, and proceed the contrary way to M and to L; but in going from thence to K, you again find your sheet will not hold it; however draw as much of the line LK on the sheet as it can hold.

Take that sheet off the table, first observing the distance oo of the lines GH and LK by the edge of the table; take off that sheet and mark it with No. 1, to signify it to be the first taken off. Having then put on another sheet, lay that distance oo on the contrary end of the table, and so proceed as before with the residue of the survey, from o to H, to K, and thence to o; so is your survey complete.

In the like manner you may proceed to take off and put on as many sheets as are convenient; and these may afterward be joined together with mouth glue, or fine white wafer, very thin.

1 If the index be fixed to the first centre, using the 360 side, it will then serve as a theodolite, and when to the second centre,

using the 180 side, it will serve as a semicircle; by either of which you may survey in rainy weather, when you cannot have paper on the table.

To measure Angles of Altitude by the Circumferentor, Theodolite, Semicircle, or Plane Table.

1. To take an angle of altitude by the circumferentor, let the glass lid be taken off, and let the instrument be turned on one side, with the stem of the ball into the notch of the socket, so that the circle may be perpendicular to the plane of the horizon; let the instrument be placed in this situation before the object, so that the top thereof may be seen through the sights; let a plummet be suspended from the centre-pin, and the object being then observed, the complement of the number of degrees comprehended between the thread of the plummet and that part of the instrument which is next your eye will give the angle of altitude required.

2. If an angle of altitude is to be taken by the theodolite, or semicircle, let a thread be run through a hole at the centre, and a plummet be suspended by it; turn the instrument on one side, by the help of the ball and notch in the socket for that purpose, so that the thread may cut 90, having 360 degrees next you; screw it fast in that position, and through the sights cut the top of the objects; and the degrees then cut by the end of the index next you are the degrees of elevation required. An angle of depression is taken the contrary way.

3. By the plane table an angle of altitude is taken in the like manner; by suspending a plummet from the centre thereof, having turned the table on one side, and fixed the index to the centre by a screw, so as to move freely, let the thread cut 90, look through the sights as before, and you have the angle of elevation, and on the contrary that of depression.

THE PROTRACTOR.

THE protractor is a semicircle annexed to a scale, and is made of brass, ivory, or horn; its diameter is generally about five or six inches.

The semicircle contains three concentric semicircles, at such distances from each other that the spaces between them may contain figures.