15220 the difference between the quantity proposed, and the quantity parted off by the guess-line, which being divided by 1058, we obtain 14.4 links, to be set off perpendicularly from m and n towards D and C. Hence EF is the true line of division; and the trapezium ABEF contains 2a. 2r. 24p.

As A is very nearly a right angle, measure, in the field, 230 + 14.4 = 244.4 links, from A to F; and upon any part of the line AB (towards B) as at e, erect the perpendicular er, which make 244.4 links; stake out the line

=

ErF, and the work will be completed.

Note. In order to prove the operation, find the area DCEF; then if it be equal to the difference between the area of ABCD and the quantity parted off, the work is undoubtedly right.

2. From any irregular field, whose dimensions are contained in the following notes, part off 2a. 3r. 20p. towards the line AE, by a fence made from the angle D to the side AB.

B

E

20648 the difference between the quantity proposed, and the quantity parted off by the guess-line, which being divided by 383, (half the guess-line,) gives 54 links to be set off from n towards A. Hence, DF is the true line of division; and the irregular figure AFDE contains 2a. 3r. 20p.

Now, by the scale, Ac 377 links. Measure therefore, in the field, 377 links from A to c; stake out the line DcF, and the work will be completed.

Note 1. The Rules given in this Problem, for parting-off land from irregular fields, are generally adopted by Practical Land-Surveyors; because they may be applied to any irregular figure whatever. Land, however, may sometimes be parted off more directly; for instance, the last example may be performed by finding the area of the irregular figure ADE, and subtracting it from the quantity to be parted off; then, if the difference be divided by half the line AD, the quotient will be the perpendicular of the triangle ADF; the side AB being nearly straight from A to F. Now, at the distance of this perpendicular, draw a line parallel to AD; and it will intersect AB in F, the point to which the division fence must be made.

2. It is not absolutely necessary to survey and plan the whole figure, in order to part a portion from it, as the guess-line and portion parted off may be measured in the field; but, in my opinion, the former, in general, is a more eligible method than the latter.

3. In order to divide a trapezium or an irregular polygon, among any number of persons, by fences made in a given direction, proceed thus: Part off the first person's share, then from the remainder of the figure, part off the second person's share; and thus continue, till the whole field be divided.

4. Those who desire to see a greater Variety of Examples in surveying single Fields, and to make themselves fully acquainted with the Methods of Laying out, Parting off, and Dividing Land; also of Dividing a Common, &c. of variable Value, among any Number of Proprietors, in the Proportion of their respective Interests, may consult my Treatise on Practical Land-Surveying, Seventh Edition, in which I flatter myself they will find these subjects satisfactorily treated.

PROBLEM XI.

To reduce statute-measure to customary, and vice versâ.

It has been before observed, that by custom the perch varies in different parts of England; and with it, consequently, varies the acre in proportion.

In Devonshire and part of Somersetshire, 15; in Cornwall, 18; in Lancashire, 21; and in Cheshire and Staffordshire, 24 feet in length, are accounted a customary perch.

GENERAL RULES.

I. To reduce statute-measure to customary, multiply the number of perches, statute-measure, by the square feet in a square perch, statute-measure; divide the product by the square feet in a square perch, customary measure, and the quotient will be the answer in square perches.

II. To reduce customary measure to statute, multiply the number of perches, customary measure, by the square feet in a square perch, customary measure; divide the product by the square feet in a square perch, statutemeasure, and the quotient will be the answer in square perches.

Note 1. It is scarcely necessary to remark that the length of any perch mul tiplied by itself will give the number of square feet, in a square perch of the same measure; hence we have 16.5 x 16.5=272.25, the statute perch; 15x15 225, the Devonshire and Somersetshire perch; 18x18-324, the Cornwall perch; 21 x 21= 441, the Lancashire perch; and 24 x 24 576, the Cheshire and Staffordshire perch. 2. When it is intended to find the area of an estate in customary measure only, It is generally thought most convenient to take the dimensions by a chain properly adapted for that purpose. The Devonshire and Somerset chain, is 60 feet; the Cornwall chain, 72 feet; the Lancashire chain, 84 feet; and the Cheshire and Staffordshire chain, is 96 feet in length. Each of these chains is divided into 100 equal links, in the same manner as the statute chain; consequently, the customary measure is found by the same Rules as the statute-measure.

3. It may also be observed, that 4840 square yards make one statute acre; 4000 make one Devonshire or Somersetshire acre; 5760 make one Cornwall acre; 7810 make one Lancashire acre; and 10240 square yards make one acre of the customary measure of Cheshire and Staffordshire. (See the Author's Land-Surveying. Parts II. III. and VI.)

EXAMPLES.

1. In 25a. 2r. 20p. statute, how many acres, &c. customary measure, of 15 feet to a perch?

2. In 31a. Or. 1p. customary measure, of 15 feet to a perch, how many acres, &c. statute-measure?

3. Reduce 56a. 3r. 36p. statute, to customary measure, Ans. 47a. 3r. 20p.

of 18 feet to a perch.

4. In 47a. 3r. 20p. customary measure, at 18 feet to a perch, how many acres, &c. statute-measure?

PROBLEM XII.

Ans. 56a. 3r. 36p.

To survey and plan Estates or Lordships.

Various methods are adopted by different surveyors, in taking the dimensions of Estates or Lordships; I shall, however, describe only four which I conceive to be the most accurate and practical.

METHOD I.

Having made yourself acquainted with the form of the estate, either by actual examination, or by the assistance of a previous plan, select two suitable places, at the greatest convenient distance from each other, as grand stations; and measure a principal base, or what is generally called a "main-line," from one to the other, noting every hedge, brook, or other remarkable object, as you cross or pass it; taking offsets likewise to the bends or corners of the hedges that are near you.

Next, fix upon some other suitable place, towards the outside of the estate, as a third grand station; to which,