B

A

Here AB one semidiameter of the earth, and the

That is, the distance of their centres is 60 226 of the earth's semidiameter's, or 30 diameters.

NOTE. Hence, and from the note to the last example, it appears, that the diameter of the earth is to that of the moon, as 10995 to 30, or as 11 to 3, or as 3 to nearly. Consequently, as 3: 7958 (the earth's diameter in miles): 2170 miles the moon's diameter.~ Likewise the surface of the earth is to that of the moon as (3X3 or) 13 to 1 nearly; or, the earth reflects upon the moon about 13 times as much light, as the moon does upon the earth. Moreover, the bulk of the earth is to that of the moon, as (3×33×33, or) 48 to I nearly.

MISCELLANEOUS

MISCELLANEOUS QUESTIONS.

A MAYPOLE, 50 feet 11 inches high, at a certain time will cast a shadow 98 feet 6 inches long; what then is the breadth of a river, which runs within 20 feet 6 inches of the foot of a steeple, 300 feet 8 inches high; the steeple, at the same time, throwing the extremity of its shadow 30 feet 9 inches beyond the stream?

Ans. 530 feet 5 inches,

2. Required the length of a shore, which being to strut 11 feet from the upright of a building, will support a jamb 23 feet 10 inches from the ground.

Ans. 26 feet 3 inches. 3

3. A line, 27 yards long, will exactly reach from the topof a fort to the opposite bank of a river, known to be 23 yards broad; what is the height of the wall?

Ans. 42 feet 5 inches.

4 Suppose the breadth of a well at the top to be 6 feet, and the angle, formed by its side and a visual diagonal line from the edge at the top to the opposite side at the bottom, 18° 30′; required the depth of the well.

Ans. 17.89 feet.

5. From the top of a tower 143 feet high, by the sea side, I observed, that the angle of depression of a ship's bottom, then at anchor, was 55°; what was its distance: from the bottom of the wall? Ans, 204'56 feet.

END OF HEIGHTS AND DISTANCES.

M

SURVEYING.

SURVEYING is that branch of MATHEMATICS, by which we measure, plan, compute, divide, and level

land.

INSTRUMENTS AND FIELD BOOK.

1. THE CHAIN.

LINES are measured with a chain, called Gunter's chain, four poles or rods in length.

The chain consists of 100 equal links, each link being of a yard, or of a

foot, or 792 inches long.

66

100

The length of lines, measured with a chain, are best set down in links, as integers, every chain in length being. 100 links; and not in chains and decimals.

2. THE PLANE TABLE.

This instrument consists of a plane rectangular board, of any convenient size, the centre of which, when used, is fixed by means of screws to a three-legged stand, hav

ing a ball and socket, or joint, at the top, by means of which, when the legs are fixed on the ground, the table is inclined in any direction.

To the table belong

1. A frame of wood, made to fit round its edges, and to be taken off, for the convenience of putting a sheet of paper upon the table. One side of this frame is usually divided into equal parts, for drawing lines across the táble, parallel or perpendicular to the sides; and the other side of the frame is divided into 360 degrees from a centre, which is in the middle of the table; by means of which the table is to be used as a theodolite, &c.

2. A needle and compass, screwed into the side of the table, to point out the directions, and to be a check upon the sights.

3. An index, which is a brass two foot scale, with either a small telescope, or open sights, erected perpendicu larly upon the ends. These sights, and one edge of the index, are in the same plane, and that edge is called the fiducial edge of the index.

When this instrument is to be used, take a sheet of paper, which will cover it, and wet it to make it expand; then spread it flat on the table, pressing down the frame. upon the edges, to stretch it and keep it fixed there; and when the paper is become dry, it will be smooth and even. On this paper is to be drawn the plan.

Then, begin at the part of the ground where you think it most expedient, and make a point on a convenient part of the paper or table, to represent that point of the ground; then fix in that point one leg of the compasses, or a fine steel pin, and apply to it the fiducial edge of the index, moving it round till through the sights you per ceive some remarkable object, as the corner of a field, &c.

and