But some skilful surveyors now make use of a different method for the field book, namely beginning at the bottom of the page and writing upwards; by which they sketch a neat boundary on either hand, as they pass along; an example of which will be given further on, in the method of surveying a large estate.

In smaller surveys and measurement, a good way of setting down the work, is, to draw by the eye, on a piece of paper, a figure resembling that which is to be measured; and so writing the dimensions, as they are found, against the corresponding parts of the figure. And this method may be practised to a considerable extent, even in the larger surveys.

SECTION II.

THE PRACTICE OF SURVEYING.

This part contains the several works proper to be done in the field, or the ways of measuring by all the instruments, and in all situations.

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 stick 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 all the ten 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, til 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 ten 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 three changes of the arrows, and the follower hold six 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 on a declivity, ascending or descending; at every chain length, lay the offset staff, or link-staff down in the slope of the chain, upon 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 angle formed between them at any station A.

1. WITH THE PLAIN TABLE.

B

The table being covered with a paper, and fixed on its stand; plant it at the station A, and fix a fine pin, or a point of the compasses, in a proper point of the paper, to represent the point 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 very same manner draw another line in the direction of the other object C. And it is done.

2. WITH THE THEODOLITE, &c.

Direct the fixed sights along one of the lines, as AB, by turning the instru ment about till the mark B is seen through these sights; and there screw the instrument fast. Then turn the moveable index about, till through its sights you see the other mark C. Then the degrees cut by the index, upon 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 poit t to the flower-de-luce. Then direct the sights to one mark, as B, and note the degrees cut by the needle. Next 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 is, will give the quantity of the angle BAC.

4. BY MEASUREMENT WITH THE CHAIN, &c.

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

L L

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

PROBLEM III.

To measure the offsets.

Ahiklmn being a crooked hedge, or river, &c.: 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 opposite any bends or corners of the hedge, as at c, d, e, &c.; and from thence measure the perpendicular offsets ch, di, &c., with the offset-staff, if they are not very large, otherwise with the chain itself. And the work is done. The register, or field-book, may be as follows:

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.

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

2.-BY TAKING ONE OR More 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, you have the content.

Measure along either of the diagonals, as AC; and either the two perpendi culars DE, BF, as in the last problem; or else the sides AB, BC, CD, DA. From either of which the figure may be planned and computed as before directed.

Measure on the longest side, the distances AP, AQ, AB; and the perpendi culars PC, QD.

2.-BY TAKING ONE OR MORE OF THE ANGLES.

Measure the diagonal AC (see the last fig. but one), and the angles DAB, CAD, ACD. Or, measure the four sides, and any one of the angles as ABC.

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 in 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 to be surveyed, or set them down in any other form you choose.

Measure all the sides AB, BC, CD, DE, EF, FG, and GA; and the diagonals AC, CG, GD, DF

OTHERWISE

Many pieces of land may be very well surveyed, by measuring any base line, either within or without them, together with the perpendiculars let fall upon it from every corner of them. 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.

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

Plant the table at any angle, as C, from whence all the other angles, or marks set up, can be seen; turn the table about till the needle point to the flower deluce; and there screw it fast. Make a point for C

on the paper on the table, and lay the edge of the Index to C, turning it about C till through the sights you see the mark D; and by the edge of the index draw a dry or obscure line: then measure the distance CD, and lay that distance down on the line CD.