ally adds to the power, but in the second and third kinds, the weight goes to diminish the effect of the power.

9. What has been stated in the previous examples? What is necessary that the machine may move?

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 all the other machines.

OF THE PULLEY.

10. What is a pulley?

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.

11. How many kinds of pulleys are there?

Pulleys are divided into two kinds, fixed pulleys and moveable pulleys.

12. Does a fixed pulley increase the power?

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.

13. Does a moveable pulley give any advantage in power?

A moveable pulley gives a mechanical advantage. Thus, in the moveable pulley, the hand which sustains the cask does not actually support but one half the weight of it; the other half is supported by the hook to which the other end of the cord is attached.

14. Will an advantage be gained by several moveable pulleys? What will be lost?

If we have several moveable 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 a 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.

15. Is there an actual loss of power? What does it arise from?

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 powers. 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.

16. In the moveable pulley, what proportion exists between the power and the weight?

It is plain that, in the moveable pulley, all the parts of the cord will be equally stretched, and hence, each cord running from pulley to pulley will bear an equal part of the weight; consequently, 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 immoveable pulley, what power will support a weight of 60 lbs.?

2. In a single moveable pulley, what power will support a weight of 80 lbs.?

3. In two moveable pulleys with 5 cords, (see last fig.,) what power will support a weight of 100 lbs.?

Ans. 20 lbs.

WHEEL AND AXLE.

17. Of what is the wheel and axle composed? How is the axle supported?

18. What is the proportion between the power and weight? In order to balance the weight, we must have, 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 lbs. may balance a weight of 600 lbs., suspended from an axle of 6 inches radius? Ans. 7 ft.

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

Ans. 1 ft.

INCLINED PLANE.

19. What is an inclined plane?

The inclined plane is nothing more than a slope or declivity, 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.

20. What proportion exists between the power and the weight, when they are in equilibrium ?

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

cord from the pulley to

A

W

B

P

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.

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 lbs. ? Ans. 40 lbs.

2. The height of a plane is 10 feet, and the length 20 feet what weight will a power of 50 lbs. support? Ans. 100 lbs.