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Direct the sights to the object at the second sta. tion, 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 circumferentôt 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 index, will be the bearing of that line.

In like manner you may proceed through the whole.

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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 with 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 off-set : 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 an 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.




HIS 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 for, wards,



A PLANE TABLE is an oblong of oak, or

other wood, about 15 inches long, and 12 broad; they are generally composed of 3 boards, which are easily taken asunder, or put together, for the convenience of carriage.

There is a box frame, with 6 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

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 occa

sion 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 of the table's breadth from one edge, and is in the mid

dle 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

a paper chart at the bottom, applied to one side of the table by a dove-tail 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, of 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 flower-de-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 ob

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