When the dimensions are taken in feet and inches, the inches must be reduced to the decimal parts of a foot; and the area found from such dimensions, must be divided by 9, to bring it into square yards.

Whatever be the shape of the ground to be measured, it must be divided into such squares, rectangles, trapezoids, trapeziums, or triangles, as will give the true content of the whole; and if the sides be crooked, offsets must be taken as directed in Problem 6, Part III.

Narrow pieces of building-ground must be measured by Problem 7; and if they be very irregular, their areas may be correctly found by the method of equidistant ordinates described in Problem 9, Part III.

NOTE 1. As a measuring-tape is not so convenient in taking the dimensions of land as a chain, it is more eligible to use the latter when the land to be measured is extensive; the greatest care, however, must be used in order to obtain the dimensions correctly, which should be taken to a quarter of a link.

2. The chain must be completely stretched, and held at the bottom of the arrows, in measuring; and if it be an inch or two over long, an allowance must be made in the dimensions: thus, if a line of 650 links be measured by a chain that is 21 inches above 66 feet, we shall have 61 × 21 = 16 inches = 2 links nearly; hence the true length of the line will be 652 links.

3. The above method may also be adopted in measuring land, when it is found necessary to correct the dimensions taken by a chain that exceeds the proper length. (See the Description of the Chain, Part II.)

4. As 4840 square yards make 1 acre, 1210 square yards, 1 rood, and 30 square yards, 1 perch, we can easily reduce acres, roods, and perches to square yards, in the following manner: Multiply 4840 by the number of acres; 1210 by the number of roods; and 30.25 by the number of perches; then the sum of these three products will be the square yards required.

5. When the area is in square links, divide it by 20.6611, the number of square links in a square yard; and the quotient will be the area in square yards. (See the Table of Square Measures in Part III.)

6. Building-ground is generally sold in small parcels. Sometimes, however, it is sold by whole fields together, which are afterwards divided by the buyer, and retailed out in small lots.

EXAMPLES.

1. The length of a rectangular piece of building-ground is 65.8 yards, and its breadth 32.6 yards; what is its area in square yards, and its value at 5s. 9d. per square yard?

Yds.

65.8

32.6

3948

1316

1974

2145.08 Area.

S.

yds.

£. s.

d.

::

yd.
As 1 : 5.75

2145.08 : 616 14 21 the value.

2. The length of a rectangle measures 85.36, and its breadth 43.28 yards; what is its area in square yards, and its value at 6s. 3d. per square yard?

Ans. The area is 3694.3808 square yards; and the value of the land 1154£. 9s. 101d.

3. The parallel sides of a piece of ground in the form of a trapezoid, measure 84.63, and 72.78 yards, and the perpendicular distance between them 56.59 yards; what is its area in square yards?

Ans. 4453.91595 square yards.

4. The diagonal of a trapezium measures 236.5 feet, one of the perpendiculars 189.3 feet, and the other 127.9 feet; what is its area in square yards; and its value at 1£. 6s. 6d. per square yard?

Ans. The area is 4167.655 square yards; and the value of the ground 5522£. 2s. 101d.

5. The base of a triangle measures 369.9 feet, and the perpendicular 234.7 feet; what is its area in square yards, and its value at 2s. 6d. per square yard?

Ans. The area is 4823.085 square yards; and the value 602£. 17s. 8d.

6. The three sides of a triangle measure 362 feet 3 inches, 316 feet 6 inches, and 284 feet 9 inches respectively; what is its area in square yards?

Ans. By Note 4, Part IV., you will find the area to be 4810 square yards.

7. Draw a plan of an irregular piece of land, and find its area in square yards, from the following dimensions, taken in feet.

Answer.

Double areas.

359147.3 Offsets on the right.
676164.8 Ditto on the left.

2)1035312.1 Sum.

9)517656.05 Area in square feet.

57517.33 Ditto in square yards.

8. Required the plan of a piece of building-ground, and also its area in square yards, from the following equidistant ordinates, taken in feet.

9. Required the plan of a piece of ground, and likewise its area in square yards, from the following dimensions, taken in feet.

10. Required the plan of a portion of building-ground, and also its area in square yards, from the following dimensions, taken by Gunter's chain; likewise its value, supposing it to have been sold by auction, at 14s. 9d. per square yard.

NOTE. In calculating the area, the quarter-links must be treated as decimals.

Answer.

Double Areas.

1181895.00 Trapezium A B C D.

112881.25 Offsets on A B.

2)1294776.25 Sum.

647388.125 Area in square links.

By Note 5, we have 647388.125 ÷ 20.6611=31333.67, the area in square yards; then, as 1 yd.: 14.75s.::31333.67 yds.: 462171.6325s. =23108£. 11s. 74d., the value required.

Directions for Planning Building-ground, and Dividing it into convenient Lots for Sale.

Building-ground may be laid down by a plotting-scale, whether the dimensions be taken in yards or in feet, by calling each chain the scale, one yard, or one foot, as the case requires; and the intermediate divisions will evidently be tenths of a yard, or tenths of a foot.

upon

If the plot of ground be small, the scale made choice of should be pretty large, so as to make the ground, on the plan, appear to the best advantage; and exhibit every part distinctly.

After the plan has been drawn, the ground must be judiciously divided and laid out, by making streets at a proper distance from each other; and then subdivided into convenient parcels or lots for sale according to the situation of the place, and the size of the houses for which the ground is best adapted.

Main or principal streets should be much wider than it is necessary to make back or intermediate streets; and the size of house-steads adjoining main streets should exceed the size of those adjoining back

streets.

When it is practicable, all streets should be laid out in straight lines; and if possible, their intersections should be always at rightangles to each other; because straight streets are not only more beautiful than crooked ones, but also more commodious for business. Many of our old towns make a wretched appearance in consequence of the crookedness, narrowness, and irregularity of the streets.

Streets are laid out of very different breadths, from 15 to 90 or 100 feet; but when ground is of great value, the breadth of the streets becomes an object of serious consideration, whether the ground, occupied by them, be given by the seller, or purchased by the buyer of the adjoining lots.