3000 and 1500 links of the Scots chain, and perpendicular diftance 1200 links.

3000

1500

2)4500

2250

1200

27.00000

Anf. 27 acres.

Ex. 2. Required the area of a field in the form of a trapozoid, its parallel fides being 1260 and 1500 links, and perpendicular breadth 1000 links of the English chain.

Anf. 13 ac. 3 ro. 8 poles. Ex. 3. How many acres are in a field in the form of a trapozoid, its parallel fides being 1000 and 1200 links, and perpen dicular breadth 650 links of the Scots chain?

Anf. 7 ac.ro. 24 falls.

PROBLEM V.

To measure off-fets. Fig. 2.

In actual furveying, it often happens that a field is bounded by a river, a crooked hedge, &c. in which cafe it will be neceflary to obferve the following directions:-Let A b c d e f represent a river or hedge. From A, in the direction of the river, measure the straight line AB. In doing of which, observe the bendings of the hedge; from thence measure the off-fets perpendicular upon the ftraight line AB, and note them down on the eye-draught, or record them in a field-book.

When the off-fets are fmall, measure them with an off-fet

ftaff

ftaff of 10 links; but when they are large, the chain is more expeditious.

Here the figure is divided into triangles and trapezoids. The most accurate method to find the area, is, to compute the area of each separately by the rule for their proper form, fum of these will be the area of the whole. Thus,

and the

Ag 300 gh 100 hi 50

ik 50 km 120

mB 130

bg 130ch+bg 290 ch+di 322 di+ch 262 178 2)3900 2)29000 2)16100 2)131002)21360

78,

1040

910

Agb 19500l

14500 8550

6550 10680

2)10140*

5070

Sometimes fuch a figure as that above is computed by finding a mean breadth, and reckoning the product of the mean breadth into the whole length of the ftation-line AB for the azea. Thus, add all the off-fet lines into one fum, and divide it

by their number, reckoning 1 for each time the irregular boundary meets the station-line, as at A and B; the quot gives the mean breadth, which, being multiplied into the length, produces the area.

However expeditious this method may be confidered, it is always false, except in the case when the off-fets are equi-diftant from each other, as may be seen from the following computation of the above figure.

To find the area of an irregular field. Fig. 3:

RULE.

Compute the areas of the figures into which the field is divi ded, whether triangles or trapeziums, &c. by the rules proper for the several figures; add the feveral results together, and the fum will give the content.

Let

When the irregularities of the boundaries of a field are numerous, it may not be improper to recommend a field-book, in which the several measures are to be recorded, to prevent confufion. But when the field is not very irregular, all the meafures may, with equal advantage, be marked upon an eyedraught of the field, each against the corresponding parts of the figure. And either of these methods may be practifed, whether the furvey be large or small.

There is no particular form for the field-book; every one rules and contrives as he judges most proper for himself; but, to avoid perplexity, the fimpleft form is the beft. The following is a fpecimen of a method generally practifed. It is divi ded into three columns; in the middle is marked the stations, bearing, and distances measured. On the right hand, the offfets are marked against their correfponding distances in the middle column, together with fuch other remarks as occur in measuring, such as houses, hedges, ponds, roads, &c. In the left hand column are marked the inlets against their corresponding distances in the middle column, and remarks, as above.

N. B. The inlets are perpendiculars dropt from fuch irregularities as fall within the ftation-line. The area of which is to be fubtracted from the general content of the field.

The measures of the preceding figure may be arranged in a field-book as follows:

THE