Either the sextant or compass may be used for taking the angles, but if the ground is tolerably level, the former intrument will give them most correctly. The linear measurements should be performed with a chain and measuringtape, or, if these are not at hand, a rope may be used. Pacing is not suited to such an operation, and can only be admissible when other means cannot be employed.

A plan of any military work requires to be accompanied by profiles or cross vertical sections, showing the height and thickness of its parapets and ramparts, width and depth of the ditches, steepness of the slopes of the work, &c. But this part of the business belongs to levelling, and will be found in its proper place. [See Levelling.]

SECTION XVII.

MENSURATION OF PLANES-SURVEYING WITH THE CHAIN -METHOD OF CONDUCTING A SURVEY-PLOTTING THE SURVEY.

OUR civil surveyors rarely employ any instrument but the land-chain in surveys of limited extent, such as those of parishes, estates, &c.; and it must be admitted that the system is well adapted to the kind of work they are usually called upon to perform. Although military men in general may not often have occasion to employ the method of chainsurveying, yet a knowledge of it is very desirable, especially for engineer officers; and hence it is practised at the military colleges of Woolwich and Addiscombe.

Two measuring chains are in use among surveyors, viz.: one of 100, the other of 66, feet in length; both, however, being divided into 100 links; and therefore, while the link of the first measures 12 inches, that of the other is only 7.92 inches. The latter, called Gunter's chain, is very convenient for the computation of superficial measure, 10 square chains being equal to an acre; and as the chain is divided into 100 links, the content of a field or other enclosure given in chains and links, is converted into acres and decimals of an acre, by simply dividing by 10.

A few words on the mensuration of planes will here be of service.

MENSURATION OF PLANES.

The area of any plane figure is the measure of the space contained within its lines or bounds.

This area or content is estimated by the number of squares that may be contained in a figure; the length and breadth of those squares being an inch, a foot, a yard, an acre, or any other fixed quantity. And hence the area or content is said to be so many square inches, or square feet, or square yards, &c.

Thus, if the figure to be measured be the four-sided one, ABCD, which is termed a rectangle (its four angles being

right angles), and the little square, E, whose side is one inch, be the measuring unit proposed: then, whatever number of those little squares may be made to fit into the figure, so many square inches it is said to contain; which in the present case is 12.

TABLE OF SQUARE MEASURE.

144 Square Inches make 1 Square Foot. . Ft.

A pole, perch, and rod, are the same measure.

Now, the rule for finding the area of a rectangle is to multiply the length of the base by the height. In the figure above, this base is called 4 inches, and perpendicular 3 inches; and 3 x 4=12 square inches.

To find the area of any parallelogram, whether it be a square, a rectangle, a rhombus, or a rhomboid.

Multiply the length, stated in any linear measurement, as inches, links, feet, yards, &c., by the perpendicular height, and the product will be the area.

Example:-To find the area of a parallelogram, whose length is 12.25 feet, and breadth or height 8.5 feet.

12.25 length.

8.5 breadth.

6125

9800

104.125 area.

Gunter's chain being 4 poles, or 22 yards, or 66 feet, in length, divided into 100 links; each link is, therefore, of a yard, or of a foot, or 7.92 inches.

66

98. Land is estimated in acres, roods, and perches. An acre is equal to 10 square chains, or as much as 10 chains

in length, and 1 chain in breadth. Or, in yards, it is 220 × 22=4840 square yards. Or, in poles, it is 40 × 4 = 160 square poles. Or, in links, it is 1000 x 100 = 100,000 square links: these being all the same quantity.

Also, an acre is divided into 4 parts, called roods, and a rood into 40 parts, called perches, which are square polesor the square of a pole of 5 yards long-or the square of of a chain-or of 25 links, which is 625 square links. So that the divisions of land measure will be thus:

625 square links = 1 pole or perch.

40 perches . . . = 1 rood.

4 roods .... = 1 acre.

The lengths of lines, measured with a chain, are best set down in links as integers, and not in chains and decimals. Therefore, after the content is found, it will be in square links; then cut off five of the figures on the right hand for decimals, and the rest will be acres. These decimals are then multiplied by 4 for roods, cutting off five figures as before, and the decimals of these again by 40 for perches, when five figures are again to be cut off.

EXAMPLE.

Suppose the length of a rectangular piece of ground be 792 links, and its breadth 385; to find the area in acres, roods, and perches.