placed, to balance a weight of 1lb? A weight of 14 lb. I Of 2 lb.? Of 4 lb. ?

7. In a lever of the third kind, the distance from the fulcrum to the power is 5 feet, and from the fulcrum to the weight 8 feet: what power is necessary to sustain a weight or 40 lb. ?

8. In a lever of the third kind, the distance from the fulcrum to the weight is 12 feet, and to the power 8 feet: what power will be necessary to sustain a weight of 100 lb. ?

437. REMARKS.-In determining the equilibrium of the lever, we have not considered its weight. In levers of the first kind, the weight of the lever generally adds to the power, but in the second and third kinds, the weight goes to diminish the effect of the power.

In the previous examples, we have stated the circumstances under which the power will exactly sustain the weight. In order that the power may overcome the resistance, it must of course be somewhat increased. The lever is a very important mechanical power, being much used, and entering, indeed, into most other machines.

Of the Pulley.

438. THE PULLEY is a wheel, having a groove cut in its circumference, for the purpose of receiving a cord which passes over it. When motion is imparted to the cord, the pulley turns around its axis, which is generally supported by being attached to a beam above.

439. Pulleys are divided into two kinds, fixed pulleys and movable pulleys. When the pulley is fixed, it does not increase the power which is applied to raise the weight, but merely changes the direction in which it acts

440. A movable pulley gives a mechanical advantage. Thus, in the movable pulley, the hand which sustains the cask actually supports but onehalf of the weight of it; the other half is supported by the hook to which the other en of the cord is attached.

441. If we have several movable pulleys, the advantage gained is still greater, and a very heavy weight may be raised by a small power. A longer time, however, will be required, than with the single pulley. It is, indeed, a general principle in machines, that what is gained in power, is lost in time; and this is true for all machines. There is also an actual loss of power, viz., the resistance of the machine to motion, arising from the rubbing of the parts against each other, which is called the friction of the machine. This varies in the different machines, but must always be allowed for, in calculating the power necessary to do a given work. It would be wrong, however, to suppose that the loss was equivalent to the gain, and that no advantage is derived from the mechanical pcwers. We are unable to augment our strength, but by the aid of science we so divide the resistance, that by a continued exertion of power, we accomplish that

which it would be impossible to effect by a single effort.

If, in attaining this result, we sacrifice time, we cannot but see that it is most advantageously exchanged for power.

442. It is plain, that in the movable pulley, all the parts of the cord will be equally stretched; and hence, each cord ruu

ning from pulley to pulley, will bear an equal part of the weight; consequently,

Rule.-The power will always be equal to the weight divided by the number of cords which reach from pulley to pulley.

Examples.

1. In a single immovable pulley, what power will support a weight of 60 lb. ?

2. In a single movable pulley, what power will support a weight of 80 lb. ?

3. In two movable pulleys, with 4 cords (see last fig.), what power will support a weight of 100 lb.?

Rule. The power to the weight, as the radius of the axle, to the length of the crank, or radius of the wheel.

Examples.

1. What must be the length of a crank or radius of a wheel, in order that a power of 40 lb. may balance a weight of 600 lb. suspended from an axle of 6 inches radius ?

2. What must be the diameter of an axle, that a power of 100 lb., applied at the circumference of a wheel of 6 feet diameter, may balance 400 lb. ?

Inclined Plane

444. The inclined plane is nothing more than a slope or eclivity, which is used for the purpose of raising weights. It is not difficult to see that a weight can be forced up an inclined plane, more easily than it can be raised in a vertical line. But in this, as in the other machines, the advantage is obtained by a partial loss of power.

Thus, if a weight W, be supported on the inclined plane ABC, by a cord passing over a pulley at F, and the cord from

W

the pulley to the weight be parallel to the length of the plane AB, the power P will balance the weight W., when

P W height BC: length AB.

It is evident that the power ought to be less than the weight, since a part of the weight is supported by the plane: hence,

Rule. The power is to the weight, as the height of the plane is to its length.

Examples.

1. The length of a plane is 30 feet, and its height 6 feet: what power will be necessary to balance a weight of 200 lb. ?

2. The height of a plane is 10 feet, and the length 20 feet: what weight will a power of 50 lb. support?

3. The height of a plane is 15 feet, and length 45 feet: what power will sustain a weight of 180 lb. ?

The Wedge.

445. The wedge is composed of two inclined planes, united together along their bases, and form

ing a solid ACB. It is used to cleave masses of wood or stone. The resistance which it overcomes is the attraction of cohesion of the body which it is employed to separate The wedge acts, principally, by being struck with a hammer, or mallet, on

A

B

its head, and very little effect can be produced with it, by mere pressure.

All cutting instruments are constructed on the principle of the inclined plane or wedge. Such as have but one sloping edge, like the chisel, may be referred to the inclined plane; and such as have two, like the ax and the knife, to the wedge.

Rule.-Half the thickness of the head of the wedge, is to the length of one of its sides, as the power which acts against its head to the effect produced at its side.

Examples.

1. If the head of a wedge is 4 inches thick, and the length of one of its sides 12 inches, what will measure the effect of a force denoted by 96 pounds?

2. If the head of a wedge is 6 inches thick, the length of the side 27 inches, and the force applied measures 250 pounds, what will be the measure of the effect?

3. If the head of a wedge is 9 inches, and the length of the side 2 feet, what will be the effect of a blow denoted by 200 pounds?

4. If the head of a wedge is 10 inches, and the length of the side 30 inches, what will measure the effect of a blow denoted by 500?