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 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 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 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 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. S.

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 co 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 afterwards be joined together with mouth glue, or fine white wafer, very thin.

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.

The outward circle is numbered from the right to the left hand, with 10, 20, 30, &c. to 180 degrees; the middlemost the same way, from 180 to 360 degrees; and the innermost from the upper edge of the scale both ways, from 10, 20, 30, &c. to 90 degrees.

It is easy to conceive that the protractor, though a semicircle, may be made to supply the place of a whole circle; for if a line be drawn, and the centre-hole of the protractor be laid on any point in that line, the upper edge of the scale corresponding with that line, the divisions on the edge of the semicircle will run from 0 to 180, from right to left: again, if it be turned the other way, or downwards, keeping the centre-hole thereof on the aforesaid point in the line, then the divisions will run from 180 to 360, and so completes an entire circle with the former semicircle.

The use of the protractor is to lay off angles, and to delineate or draw a map or plan of any ground from the field notes; and is performed in the following manner.

To protract a field book, when the angles are taken from the meridian.

PL. 6. fig. 9.

On your paper rule lines parallel to each other, at an inch asunder (being most usual), or at any other convenient distance; on the left end of the parallels put N for north, and on the right S for south; put E at the top for east, and W at the bottom of your for west. paper

Then let the following field-book be that which is to be protracted, the bearings being taken from the meridian, whether by a

circumferentor, theodolite, or semicircle, and measured with a two-pole chain.

Pitch upon any convenient point on your paper for your first station, as at 1, on which lay the centre-hole of your protractor, with a protracting pin; then if the degrees be less than 180, turn the arc of your protractor downwards, or towards the west; but if more than 180, upwards, or towards the east.

Or if the right hand be made the north, and the left the south, the west will be then up, and the east down.

In this case, if the degree be less than 180, turn the arc of your protractor upwards, or towards the west; and if more, downwards, or towards the east.

By the foregoing field-book, the first bearing is 2831, turn the arc of your protractor upwards, keeping the pin in the centre-hole, move the protractor so that the parallel lines may cut opposite divisions, either on the ends of the scale, or on the degrees, and then it is parallel. This must be always first done, before you lay off your degrees.

Then by the edge of the semicircle, keeping the protractor steady, with the pin prick the first bearing 283, and from the centre-point, through that point or prick, draw a blank line with the pin, on which from a scale of equal parts, or from the scale's edge of the protractor, lay off the distance 55C. 20L. so is that station protracted.

At the end of the first station, or at 2, which is the beginning of the second, with the pin place the centre of the protractor, turning the arc up, because the bearing of the second station is more than 180, viz. 3483. Place your protractor parallel as before, and by the edge of the semicircle, with the pin prick at that degree,