For the common occasions of levelling, set a pole upright in a spring, pond, &c. and mark how many feet and inches are above water; then set up another pole of equal length with the other, in the place to which the water is to come. Place the centre of a quadrant on the top of this last pole, the plummet hanging free; spy through the sights at the top of the pole in the water, and if the thread cuts any degree of the quadrant, the water may be conveyed by a pipe laid in the earth. If you cannot see from one extreme to the other, the operation may be repeated.

Levelling.—Table shewing the difference between the true and apparent level.

Dis-
tance.		Differ-
ence
of
level.		Dis-
tance.		Differ-
ence
of
level.		Dis-
tance.		Differ-
ence
of
level.		Dis-
tance.		Differ-
ence
of
level.
Yds.Inch.Yds.Inch.Mls.Ft.in.Mls.Ft.in.
1000.02610002.570¹⁄₄ 0 0¹⁄₂ 7 326
2000.10311003.110¹⁄₂ 0 2  8 426
3000.23112003.701³⁄₄ 0 4¹⁄₂ 9 539
4000.41113004.3441 0 8 10 664
5000.64314005.0382 2 8 11 803
6000.92515005.7843 6 0 12 952
7001.26016006.580410 7 131122
8001.64517007.425516 7 141301
9002.081 62311 15150
16175

This table will answer several useful purposes.

First.—To find the height of the apparent level above the true, at any distance.—If the given distance be contained in the table, the correction of level is found in the same line with it; but if the exact distance be not found in the table, then multiply the square of the distance in yards, by 2.57, and divide by 1,000,000, or cut off 6 places on the right for decimals; the rest are inches: or multiply the square of the distance in miles, by 66 feet 4 inches, and divide by 100.

Second.—To find the extent of the visible horizon, or how far can be seen from any given height, on a horizontal plane, at sea, &c.—The height of the observer’s eye above the horizon being known, the extent of his visible horizon is found in the column opposite, under the word Distances.

Third.—To find the distance of any object when it first comes in sight, its height being known.—For the distance of any object will be the extent of the visible horizon of the observer, added to the visible horizon of the point he observes. It is necessary in this case for the observer to know only the height of that part of the object which is kept from his view, by the curvilinear figure of the globe.—Knowing the distance of an object, its height may be found in the same manner.

If the height or distance exceed the limits in the table; then, first, if the distance be given, divide it by 2, 3, or 4, till the quotient comes within the distances in the table; then take out the height answering to the quotient, and multiply it by the square of the divisor for the height required. But when the height is given, divide it by one of these square numbers, 4, 9, 16, 25, &c. till the quotient come within the limits of the table, and multiply the quotient by the square root of the divisor.

Levelling staves, instruments used in levelling, that carry the marks to be observed, and at the same time measure the heights of those marks from the ground. These usually consist of two wooden square rulers, that slide over one another, and are divided into feet, inches, &c.

Levelling has two distinct applications in the art of war, in the one case it implies the reduction of an uneven surface to that of a plane, so that the works of a fortification may be of a correspondent height or figure throughout. The other is the art of conveying water from one place to another; in this process, it is found necessary to make an allowance between the true and apparent level, or in other words, for the figure of the earth, for the true level is not a straight line, but a curve which falls below the straight line about 8 inches in a mile, 4 times 8 in 2 miles, 9 times 8 in 3 miles, 16 times 8 in 4 miles, always increasing with the square of the distance.