2. Of the plane table. This instrument consists of a plain rectangular board, of any convenient size: the centre of which, when used, is fixed by means of screws to a three-legged stand, having a ball and socket, or other joint, at the top, by means of which, when the legs are fixed on the ground, the table is inclined in any direction *.

and the rest will be acres. These decimals are then multiplied by 4 for roods, and the decimals of these again by 40 for perches.

Exam. Suppose the length of a rectangular piece of ground be 792 links, and its breadth 385; to find the area in acres, roods, and perches.

Here we have, 792.385=3·0492=3ac Or 7·872p.

To the table belong various parts, as follow.

1. A frame of wood, made to fit round its edges, and to be taken off, for the convenience of putting a sheet of paper on the table. One side of this frame is usually divided into equal parts, for drawing lines across the table, parallel or perpendicular to the sides; and the other side of the frame is divided into 360 degrees, to a centre in the middle of the table; by means of which the table may be used as a theodolite, &c.

1. A magnetic needle and compass, either screwed into the side of the table, or fixed beneath its centre, to point out its directions, and to be a check on the sights.

3. An index, which is a brass two-foot scale, with either a small telescope, or open sights set perpendicularly on the ends. These sights and one edge of the index are in the same plane, and that is called the fiducial edge of the index.

To use this instrument, take a sheet of paper which will cover it, and wet it to make it expand; then spread it flat on the table, pressing down the frame on the edges, to stretch it and keep it fixed there; and when the paper is become dry, it will, by contracting again, stretch itself smooth and flat from any cramps and unevenness. On this paper is to be drawn the plan or form of the ground measured.

Thus, begin at any proper part of the ground, and make a point on a convenient part of the paper or table, to represent that place on the ground; then fix in that point one leg of the compasses, or a fine steel pin, and apply to it the fiducial edge of the index, moving it round till through the sights you perceive some remarkable object, as the corner of a field, &c.; and from the station point draw a line with the point of the compasses along the fiducial edge of the index, which is called setting or taking the object: then set another object or corner, and draw its line; do the same by another; and so on, till as many objects are taken as may be thought fit. Then measure from the station towards as many of the objects as may be necessary, but not more, taking the requisite offsets to corners or crooks in the edges, laying the measures down on their respective lines on the table. Then at any convenient place measured to, fix the table in the same position, and set the objects which appear from that place; and so on, as before. Thus continue till the work is finished, measuring such lines only as are necessary, and determining as many as may be by intersecting lines of direction drawn from different stations.

Of shifting the paper on the plain table.

When one paper is full, and there is occasion for more, draw a line in any manner through the farthest point of the last station line, to which the work can be conveniently laid down; then take the sheet off the table, and fix another on, drawing a line over it, in a part most convenient for the rest of the work; then fold or cut the old sheet by the line drawn on it, applying the edge to the line on the new sheet, and as they lie in that position, continue the last station line on the new paper, placing on it the rest of the measure, beginning at where the old sheet left off. And so on from sheet to sheet.

When the work is done, and you would fasten all the sheets together into one piece, or rough plan, the aforesaid lines are to be accurately joined together, in the same manner as when the lines were transferred from the old sheets to the new ones. But it is to be noted, that if the said joining lines, on the old and new sheets, have not the same inclination to the side of the table, the needle will not point to the original degree when the table is rectified; and if the needle be required to respect still the same degree of the compass, the easiest way of drawing the line in the same position, is to draw them both parallel to the same sides of the table, by means of the equal divisions marked on the other two sides.

3. Of the theodolite. The theodolite is a brass circular ring, divided into 360 degrees, etc. and having an index with sights, or a telescope, placed on the centre, about which the index is moveable; also a compass fixed to the centre, to point out courses and check the sights; the whole being fixed by the centre on a stand of a convenient height for use *.

4. Of the cross. The cross consists of two pair of sights set at right angles to each other, on a staff having a sharp point at the bottom, to fix in the ground+.

PROBLEM I.

To measure a line or distance.

To measure a line on the ground with the chain: Having provided a chain, with ten small arrows or rods, to fix one into the ground, as a mark, at the end of every chain; two persons take hold of the chain, one at each end of it; and

* In using this instrument, an exact account, or field-book, of all measures and things necessary to be remarked in the plan, must be kept, from which to make out the plan on returning home from the ground.

Begin at such part of the ground, and measure in such directions as are judged most convenient; taking angles or directions to objects, and measuring such distances as appear necessary under the same restrictions as in the use of the plain table. And it is safest to fix the theodolite in the original position at every station, by means of fore and back objects, and the compass, exactly as in using the plain table; registering the number of degrees cut off by the index when directed to each object; and, at any station, placing the index at the same degree as when the direction towards that station was taken from the last preceding one, to fix the theodolite there in the original position.

The best method of laying down the aforesaid lines of direction, is to describe a pretty large circle; then quarter it, and lay on it the several numbers of degrees cut off by the index in each direction, and drawing lines from the centre to all these marked points in the circle. Then, by means of a parallel ruler, draw from station to station, lines parallel to the aforesaid lines drawn from the centre to the respective points in the circumference.

corner;

The cross is very useful to measure small and crooked pieces of ground. The method is, to measure a base or chief line, usually in the longest direction of the piece, from corner to and while measuring it, finding the places where perpendiculars would fall on this line, from the several corners and bends in the boundary of the piece, with the cross, by fixing it, by trials, on such parts of the line, as that through one pair of the sights both ends of the line may appear, and through the other pair the corresponding bends or corners; and then measuring the lengths of the said perpendiculars.

Remarks. Besides the fore-mentioned instruments, which are most commonly used, there are some others; as,

The perambulator, used for measuring roads, and other great distances, level ground, and by the sides of rivers. It has a wheel of 8ft, or half a pole, in circumference, by the turning of which the machine goes forward; and the distance measured is pointed out by an index, which is moved round by clock-work.

Levels, with telescopic or other sights, are used to find the level between place and place, or how much one place is higher or lower than another. And in measuring any sloping or oblique line, either ascending or descending, a small pocket level is useful for showing how many links for each chain are to be deducted, to reduce the line to the horizontal length.

An offset-staff is a very useful instrument, for measuring the offsets and other short distances. It is 10 links in length, being divided and marked at each of the 10 links.

Ten small arrows, or rods of iron or wood, are used to mark the end of every chain length, in measuring lines. And sometimes pickets or staves with flags, are set up as marks or objects of direction.

Various scales are also used in protracting and measuring on the plan or paper; such as plane scales, line of chords, protractor, compasses, reducing scale, parallel and perpendicular rules, &c. Of plane scales, there should be several sizes, as a chain in 1 in, a chain in 2 of an inch, a chain in an inch, &c. And of these, the best for use are those that are laid on the very edges of the ivory scale, to mark off distances without compasses.

all the 10 arrows are taken by one of them, who goes foremost, and is called the leader; the other being called the follower, for distinction's sake.

A picket, or station-staff, being set up in the direction of the line to be measured, if there do not appear some marks naturally in that direction, they measure straight towards it, the leader fixing down an arrow at the end of every chain, which the follower always takes up, as he comes at it, till all the ten arrows are used. They are then all returned to the leader, to use over again. And thus the arrows are changed from the one to the other at every 10 chains' length, till the whole line is finished; then the number of changes of the arrows shows the number of tens, to which the follower adds the arrows he holds in his hand, and the number of links of another chain over to the mark or end of the line. So, if there have been 3 changes of the arrows, and the follower hold 6 arrows, and the end of the line cut off 45 links more, the whole length of the line is set down in links thus, 3645.

When the ground is not level, but either ascending or descending; at every chain's length, lay the offset-staff, or link-staff, down in the slope of the chain, on which lay the small pocket level, to show how many links or parts the slope line is longer than the true level one; then draw the chain forward so many links or parts, which reduces the line to the horizontal direction.

PROBLEM II.

To take angles and bearings.

Let B and C be two objects, or two pickets set up perpendicular; and let it be required to take their bearings, or the angles formed between them at any station.

1. With the plain table.

B

The table being covered with a paper, and fixed on its stand; place it at the station A, and fix a fine pin, or a foot of the compasses, in a proper point of the paper, to represent the place A close by the side of this pin lay the fiducial edge of the index, and turn it about, still touching the pin, till one object B can be seen through the sights: then by the fiducial edge of the index draw a line. In the same manner draw another line in the direction of the other object C; and it is done.

2. With the theodolite.

Direct the fixed sights along one of the lines, as AB, by turning the instrument about till the mark B is seen through these sights; and there screw the instrument fast. Then turn the moveable index round, till through its sights the other mark C is seen. Then the degrees cut by the index, on the graduated limb or ring of the instrument, show the quantity of the angle.

3. With the magnetic needle and compass.

Turn the instrument or compass so, that the north end of the needle point to the fleur-de-lis. Direct the sights to one mark as B, and note the degrees cut by the needle: direct the sights to the other mark C, and note again the degrees cut by the needle. Then, their sum or difference, as the case may be, will give the quantity of the angle BAC.

4. By measurement with the chain.

Measure one chain length, or any other length, along both directions, as to B and C. Then measure the distance BC, and it is done. This is easily trans

ferred to paper, by making a triangle ABC with these three lengths, and then measuring the angle A.

PROBLEM III.

To survey a triangular field ABC.

A

C

1. By the chain. Having set up marks at the corners, which is to be done in all cases where there are not marks naturally; measure with the chain from A to P, where a perpendicular would fall from the angle C, and set up a mark at P, noting down the distance AP. Then complete the distance AB, by measuring from P to B. Having set down this measure, return to P, and measure the perpendicular PC. And thus, having the base and perpendicular, the area from them is easily found. Or, having the place P of the perpendicular, the triangle is easily constructed.

P

B

Or, when practicable, measure all the three sides with the chain, and note them down. From which the content is easily found, or the figure is constructed.

Ex. Suppose AP = 794, AB = 1321, and PC = 826, to find the area.

2. By taking some of the angles. Measure two sides AB, AC, and the angle A between them. Or measure one side AB, and the two adjacent angles A and B. From either of these ways the figure is easily planned; then by measuring the perpendicular CP on the plan, and multiplying it by half AB, the content is found.

PROBLEM IV.

To measure a four-sided field. 1. By the chain. Measure along one of the diagonals, as AC; and either the two perpendiculars DE, BF, as in the last problem; or else the sides AB, BC, CD, DA. From either of these the figure may be planned and computed as before directed.

B

E F

A

D

Ex. The following measures were taken, AE = 214, AF 362, AC = 592, DE: =210, BF

306.

2. Otherwise, by the chain. Measure, on the longest side, the distances AP, AQ, AB; and the perpendiculars PC, QD. For example, AP= 110, AQ = 745, AB = 1110, and PC = 352, QD = 595.

D

୯

3. By taking some of the angles. Measure the diagonal A P

QB

AC (see the last fig. but one), and the angles CAB, CAD, ACB, ACD. Or measure the four sides, and any one of the angles, as BAD.

Thus AC 591, CAB=37°20′, ÇAD=41°15', ACB=72°25′, ACD=54°40'. Or thus: AB=486, BC=394, CD=410, DA=462, BAD=78° 35'.

PROBLEM V.

To survey any field by the chain only.

First method. Having set up marks at the corners, where necessary, of the proposed field ABCDEFG, walk over the ground, and consider how it can best be divided into triangles and trapeziums; and measure them separately, as in the last two problems. Thus, the following figure is divided into the two trapeziums

ABCG, GDEF, and the triangle GCD. Then, in the first trapezium, beginning at A, measure the diagonal AC, and the two perpendiculars Gm, Bn. Then the base GC, and the perpendicular Dq. Lastly, the diagonal DF, and the two perpendiculars pE, oG. All which measures write against the corresponding parts of a rough figure drawn to resemble the figure surveyed, or set them down in any other form you choose.

Thus: Am=135, An = 410, AC = 550; Cq = 152, CG = 440; Fo= 237, Fp=288, FD=520: mG = 130, nB = 180; qD = 230; oG= 120, pE = 80. Or thus Measure all the sides AB, BC, CD, DE, EF, FG, GA; and the diagonals AC, GD, GD, DF.

D

Second method. Many pieces of land may be very well surveyed, by measuring any base line, either within or without them, with the perpendiculars let fall on it from every corner. For they are by those means divided into several triangles and trapezoids, all whose parallel sides are perpendicular to the base line; and the sum of these triangles and trapeziums will be equal to the figure proposed if the base line fall within it; if not, the sum of the parts which are without, being taken from the sum of the whole which are both within and without, will leave the area of the figure proposed.

B

In pieces that are not very large, it will be sufficiently exact to find the points, in the base line, where the several perpendiculars will fall, by means of the cross, or even by judging by the eye only, and from thence measuring to the corners for the lengths of the perpendiculars. And it will be most convenient to draw the line so as that all the perpendiculars may fall within the figure.

Thus, in the annexed figure, beginning at A, and measuring along the line AG, the distances and perpendiculars on the right and left are as below.

Ab=315, Ac = 440, Ad= 585, Ae= 610, Aƒ= 990, AG = 1020, bB = 350, cC=70, dD = 320, eE = 50, ƒF = 470, 0.

PROBLEM VI.

To measure the offsets.

h

A C d

n

m

Let Ahiklmn be a crooked hedge, a brook, or other, irregular boundary. From A measure in a straight direction along the side of it to B. And in measuring along this line AB, observe when you are directly opposite any bends or corners of the boundary, as at c, d, e, ............; and from these measure the perpendicular offsets, ch, di, ...., with the offset-staff, if they are not very large, otherwise with the chain itself; and the work is done. The register, or fieldbook, may be as follows: