foot from the fulcrum of a lever; required the power to raise the same when the length of the lever on the other side of the fulcrum is five feet?

CASE 2.-When the fulcrum is at one extremity of the lever and the power at the other.

RULE. As the distance between the power and the fulcrum is to the distance between the weight and the fulcrum, so is the effect to the power.

EXAMPLE 1.-Required the power necessary to raise 120 lbs., when the weight is placed six feet from the power, and two feet from the fulcrum? As 8:2: 120: 30 lbs., Ans.

EXAMPLE 2.-A beam, 20 feet in length, and supported at both ends, bears a weight of two tons at the distance of eight feet from one end; required the weight on each support?

RULE. As the radius of the wheel is to the radius of the axle, so is the effect to the power.

EXAMPLE.-A weight of 50 lbs. is exerted on the periphery of a wheel whose radius is 10 feet; re

quired the weight raised at the extremity of a cord wound round the axle, the radius being 20 inches. 50 lbs. x 10 feet x 12 inches

300 lbs., Ans.

RULE.-Divide the weight to be raised by twice the number of pulleys in the lower block; the quotient will give the power necessary to raise the weight.

EXAMPLE.-What power is required to raise 600 lbs., when the lower block contains six pulleys?

RULE. As the length of the plane is to its height, so is the weight to the power.

EXAMPLE.-Required the power necessary to raise 540 lbs. up an inclined plane, five feet long and two feet high.

As 5:2 540: 216 lbs., Ans.

WEDGE.

CASE 1.- When two bodies are forced from one another by means of a wedge, in a direction parallel to its back.

RULE. As the length of the wedge is to half its back or head, so is the resistance to the power.

EXAMPLE.-The breadth of the back or head of the wedge being three inches, and the length of either of its inclined sides 10 inches, required the power necessary to separate two substances with a force of 150 lbs.

As 10 13: 150: 22 lbs., Ans.

CASE 2.- When only one of the bodies is movable. RULE.-As the length of the weight is to its back or head, so is the resistance to the power. EXAMPLE. The breadth, length, and force, the same as in the last example.

As 103 150: 45 lbs., Ans.

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SCREW.

The screw is an inclined plane, and we may suppose it to be generated by wrapping a triangle, or an inclined plane, round the circumference of a cylinder. The base of the triangle is the circumference of the cylinder; its height, the distance between two consecutive cords or threads; and the hypothenuse forms the spiral cord or inclined plane.

RULE. To the square of the circumference of the screw, add the square of the distance between two threads, and extract the square root of sum. This will give the length of the inclined plane; its height is the distance between two consecutive cords or threads.

When a winch or lever is applied to turn the screw, the power of the screw is as the circle described by the handle of the winch, or lever, to the interval or distance between the spirals.

Velocity is gained at the expense of power by the lever and the wheel and axle.

LEVER.

CASE. When the weight to be raised is at one end of the lever, the fulcrum at the other, and the power is applied between them.

RULE. As the distance between the power and the fulcrum is to the length of the lever, so is the weight to the power.

EXAMPLE. The length of the lever being eight feet, and the weight at its extremity 60 lbs., required the power to be applied six feet from the fulcrum to raise it?

As 68: 60: 80 lbs., Ans.

N. B.-Any other example may be computed by reversing any of the foregoing operations.

FRICTION.

WE have considered the effects of the first movers of machinery, and we must now direct our attention to the subject of Friction, which, as we have

frequently noticed, tends to diminish these effects. On this subject it is not our intention to dwell long, as all the researches that have been hitherto made in this branch of mechanical science are not of such a nature as to furnish means of deducing satisfactory laws. The resistance arising from one surface rubbing against another is denominated friction; and it is the only force in nature which is perfectly inert—its tendency always being to destroy motion. Friction may thus be viewed as an obstruction to the power of man in the construction of machinery; but, like all the other forces in nature, it may, when properly understood, be turned to his advantage,-for friction is the chief cause of the stability of buildings or machinery, and without it animals could not exert their strength.

The friction of planed woods and polished metals, without grease, on one another, is about one-fourth of the pressure.

The friction does not increase on the increase of the rubbing surfaces.

The friction of metals is nearly constant.

The friction of woods seems to increase after they are some time in action.

The friction of a cylinder rolling down a plane, is inversely as the diameter of the cylinder.

The friction of wheels is as the diameter of the axle directly, and as the diameter of the wheel in