The first offset on the line 716 is (10+8), always on the left. This 8 is up to the bank bounding the lane, and 10 is the distance to its top. This 10 is repeated throughout, the average width having been taken. The other three lines have no offset to them.

·Offsets of Second Field.

The first line is 609, and the first offset is at 12 (still on the left), being (pond +20), or, 20 up to the edge of the pond: the second offset at 32, is (35+21), that is, 21 up to the pond, +35 across the pond, which, by the accompanying diagram, ends there; the distance 32 being taken, in order to shew that there was the end of the pond.

The next offset is at 40 (D+30), that is, 30 up to where the ditch of the field goes into the pond; at 50 there is an offset of 40 to first gate post; at 100 the offset is (D+27), that is, 27 to the brow of the ditch, which being beyond the boundary of the field, the width of that and the hedge is not required; the other offsets are regular to the distance

D

5.82, which has an offset of (6+4), that is, 4 up to the hedge, and 6 through the hedge, which is now within the field, to the brow of the ditch; the previous offset was (D+4), that is, 4 to the brow of the ditch (the hedge being then beyond the field), the ditch therefore changes at

this point, denoted in the diagram by

cross hedge; on the left, which the diagram

There is here also a

shows too.

In the next line, at 10, there is an offset, taken to the corner of the field, 90 links; and the relative position, of the sides, to the offset line, is expressed by the diagram in the notes, which should be in every case, as much as possible, a gound plan of the locality.

In line 690, at 50 links, the line touches the ditch, having 0 offset to it, the other offsets to this line are all regular.

To the two following lines, being check lines, there are no offsets.

COMPUTATION OF AREAS.

Divide the field into triangles, and find the area of each separately, by measuring the bases and perpendiculars off a scale of equal parts, and proceed according to the rules given in the chapter on mensuration (PROB. 1 & 7.)

Let, for example, the field ABCD be a trapezium, and let it be straight-sided, the area will

Now let the sides be irregular and take the diagram for a triangular field as an example (page 38), then AC multiplied by half the perpendicular let fall upon it from B, will give the area within the triangle ABC (which will be found to be

A. R. P.

2. 2. 27.), but the space included between that figure and

the irregular hedge, has still to be added to complete the area of the field.

Now to obtain this space, which is made up of as many trapeziums as are included within the several offsets taken upon the line as perpendiculars, find the areas of these trapeziums, by rule (page 26) in mensuration and add their sum to the area of the large triangle for the area of the whole field.

It will therefore stand thus:

EXAMPLE 2. Take for practice, the field notes of the fields Nos. 1 and 2, Plate No. 1, at pages (42 and 47), and calculate the areas, checking them by the second method.

When the offsets are taken at every chain's length, or at any equal distance, the whole area is equal to the sum of the offsets multiplied into the common distance between them, that is,

the area of ACB=d (bg+ch + dl + em + fn).

EXAMPLE 1. Let done chain, and bg, ch, &c., res

tively 10, 15, 17, 14, 9 links, what will be the area of the A. R. P. Answer 0. 0 10.

figure.

EXAMPLE 2. Given the several offsets 15, 25, 40, 10, 60, 30, 25, 8, 18, 9, 8, 4, 6, 0, taken at one chain's distance. Required the area.

A. R. P. Answer 0. 1. 0.

THE SECOND METHOD.

A common method in practice, in computing the areas of irregular-sided fields, is to have a piece of transparent horn-and by giving and taking, as it is termed—to draw a straight-sided polygon, equal to the given irregular one, and to divide this into triangles, then, by means of the compasses and scales, to measure the lengths of the new lines, and from these lengths, and the perpendiculars also measured off the scales, to calculate the area. This is the common method among the profession, and in good hands tolerably correct. I should, however, recommend young beginners to calculate their areas at first by both methods.

Thus,-Let ABCDE be the irregular outline of a hedge or ditch; by placing along it a straight-sided piece of transparent horn, the position of the line KL can be determined, such that the area KLGF shall be equal to the area of ABCDEGF; by making the pieces taken in at A and C, equivalent to the pieces given up at B and D.

The following examples of Field notes and plans are added for practice. The student had better plot them by the notes and compare them with the plans, and then calculate their areas.

EXAMPLES OF FIELD NOTES FOR
PRACTICE.

ALL PLOTTED TO A SCALE OF SIX CHAINS TO THE INCH.

Note. The student will remember that these are but Wood-blocks.