SOLIDS.

563. To find the solid contents of a prism, or cylinder.

Multiply the area of one of its ends by its

1. A prism that is 4 inches wide and 3 inches thick, is 14 inches long. How many cubic inches in it?

2. A triangular prism whose sides are 16 inches in length and 2 inches wide, contains how many cubic inches?

564. A cylinder is a solid of uniform diameter, and whose ends are circles which are parallel to each other. 3. The length of a cylinder is 11 feet, and its diameter 15 inches. Find its contents.

4. Find the contents of a cylinder 3 feet long and 3 feet in diameter.

565. To find the surface of a sphere when its diameter is known.

Suggestion. - The area of a sphere equals the area of four circles having the same diameter as the sphere.

566. To find the solid contents of a sphere or globe. 1. Find the solid contents of a sphere whose diameter is 3 feet. Find its surface.

Suggestion.

- A sphere equals of a cylinder whose diameter and length each equals the diameter of the given sphere.

2. How many cubic inches in a ball of wood 8 inches.

in diameter.

Ans. 268.08+.

3. Find the cubic contents of a cylindrical tube that will just enclose a sphere whose diameter is 9 inches. Also, find the contents of the sphere.

567. To find the contents of a pyramid.

Suggestion.

A pyramid equals of a cylinder, or prism,

having the same base and altitude.

1. The base of a pyramid is side, its height being 21 inches.

a square 5 inches on a Find its contents? Ans. 175 cu. in.

2. Find the contents of a pyramid 10 inches high, with a triangular base 3 inches on a side.

3. Find the superficial contents of the above pyramid.

568. To determine the dimensions of a cistern which shall have a given capacity.

1. I wish to dig a cistern which shall have a uniform diameter of five feet, and shall hold 100 barrels. What must be its depth?

Area of base is (30) 2×3.1416—2827.44 sq. inches.

727650-2827,44-257.32 inches for the depth; or, 21.4 ft.

2. How many barrels will a cistern hold, if its diameter is 4 feet, and depth 9 feet?

MECHANICAL POWERS.

569. The Lever, the Wheel and Axle, the Screw, the Inclined Plane, and the Pulley, are known as the Five Mechanical Powers.

570. In the mechanical power known as the lever,

a. The fulcrum may be between the power and the weight. b. The weight may be between the power and the fulcrum. c. The power may be between the weight and the fulcrum.

GENERAL LAW.

The power is to the weight as the distance of the power from the fulcrum to the distance of the weight from the fulcrum.

1. In the lever of the first class, what power will raise a weight of 500 pounds at a distance of 21 feet, the length of the lever being 15 feet? Ans. 100.

2. In the lever of the second class, what weight situated 2 feet from the fulcrum can be raised by a power equal to 100 pounds, by using a lever 15 feet long? Ans. 600 lbs.

3. In the lever of the third class, what power will sustain a weight of 50 pounds at the other end of a lever 15 feet long, if the power is applied at a distance of 2 feet from the fulcrum? Ans. 300.

571. In the mechanical power known as the wheel and axle, the following principle applies:

GENERAL LAW.

The power is to the weight as the diameter of the wheel is to the diameter of the axle.

4. What weight can a man raise, if he apply a force equal to 100 pounds to a wheel 5 feet in diameter, the axle being 10 inches? Ans. 600 lbs.

5. With a wheel 3 feet in diameter, and axle 9 inches, what power will balance a weight 700 pounds? Ans. 175 lbs. 572. In the mechanical power known as the inclined plane the following principle applies:

GENERAL LAW.

The power is to the weight as the perpendicular height of the plane is to the length of the plane.

6. The length of a plane is 20 feet, and its perpendicular height 17 inches. What power will balance a weight of 1000 lbs. ?

7. On an inclined plane 16 feet long and 20 inches high, what weight will a force of 100 pounds sustain? 573. In the mechanical power known as the screw the following principle applies :

The power is to the weight as the distance between two consecutive threads of the screw to the distance traversed by the extremity of the lever in making one revolution.

8. The distance between the consecutive threads of a screw is one-fourth of an inch, and the length of a

lever 9 feet. What weight can be raised by a force of 75 pounds?

9. What force, with the above screw, sary to raise a weight of 1200 pounds?

will be neces

10. Find the length of lever necessary to raise 1000 pounds with the same screw, by applying a force of 150 pounds.

574. In the mechanical power known as the pulley the following principle applies:

GENERAL LAW.

The power is to the weight to be raised as one to twice the number of movable pulleys.

575. A single stationary pulley serves only the purpose of conveniently applying the power; it gives no other advantage.

576. With a single pulley, a weight at one end of the rope will just balance a force equal to the same number of pounds at the other end.

577. A single movable pulley doubles the effectiveness of the power.

NOTE. The consideration of this whole subject falls properly under Natural Philosophy. The further consideration of it in this place must necessarily be so meagre as to offer very little profit or pleasure.

In the instances given, the subject of friction, which is a material element when anything more than approximate accuracy is required, is usually left out of the calculation. Other elements, the direction in which the force acts, the nature of the system of pulleys considered, are all too complicated to be discussed here.

578. The following problems have been selected