increased in proportion to the thinness of the spindle or barrel, or by increasing the length of the winches or handspikes. It works by concentrating on a small space the power of a much wider circle, just as the large wheel on the rack concentrated its force in the smaller circle of the pinion.

S. But, if you think of it for a moment, the spokes or winches by which the windlass is moved are only the spokes of a wheel, so that the lever thus passes in a way you can at once understand into that form of mechanical power, which, though it is called the SECOND, is thus really only a variety of the first. If you join the different spokes by a rim, the different parts of which form a circle, you have a WHEEL at once.

ways.

The advantage of the wheel over the separate spokes or handspikes is, that it can always be turned round continuously by a force acting only on a small part of its circle. This may be done in two different For example, you all know how the man at the wheel steers the ship by turning round a wheel from which handles project at short distances from each other. Formerly the helm used to be turned by a windlass worked by a number of men, but the wheel now enables one man to do the same thing. This is one way of turning a wheel.

But, instead of projecting handles, a wheel may be worked by a rope passed over it, as in the wheel of a clock (Fig. 13). The cut represents what is called a racket wheel, from the catch (A) fixed on it, which prevents its

turning except in one direction. In that direction, however, the weight fixed to the rope passed over it keeps it steadily turning. You see this principle in the weight of a clock which hangs from a cord wound round a barrel in the works, and turns the whole of the wheels. In the cut, a small weight hung from the end (P) of a cord wound round the wheel (B) steadily pulls up a larger weight (W) wound in a contrary direction round an axle behind.

9. Levers owe much of their power to their not bending, but ropes and cords are valuable because they do bend. This property enables us to use them so that a force acting in any given direction may be made to balance an equal force in any other direction. If, for example, you pass

a rope, at one end of which hangs a heavy weight, through a ring, say in the ceiling, you raise the weight by pulling the rope through the ring, though you do not pull in the opposite direction to that in which the weight acts (Fig. 14). But it is clear that if, instead of a ring, however smooth, you used a wheel with a groove on its outer edge-that is, a pulley, instead of a ring-the friction would be much less, and your power consequently much greater.

10. Thus, again, you easily pass to the THIRD MECHANICAL POWER—that of the PULLEY. The PULLEY consists of a small wheel, called a sheaf, which turns on a pin or axis in a block, and has a cord or rope running in a groove on the outer edge of it. There are two kinds of pulleys, the movable and the fixed, both of which are represented in Fig. 15. The upper double pulley, which, as you see, is fixed by a hook to a beam, is a fixed pulley; the lower one is a movable pulley.

The rope by which a window-sash is raised is an illustration of the simplest use of the pulley, and so are the two buckets at the two ends of a well-rope running over a pulley, the one of which rises full as the other descends empty. The weights which lift the window pass over a pulley above the sash to be raised, and hang, unseen, behind the frame in which the sash runs. In order that they may raise the sash, and keep it raised, it is evident that they must, between them, be of equal weight with the sash itself. The pulley acts as a lever with equal arms, so that neither the window-sash nor the weights have any advantage, but balance each other at any height required. The cord, moreover, being free to move either up or down, must have an equal strain on it through its whole length.

But the pulley does not increase the power you exert in raising the window, it only changes the direction in which it acts; yet this is often a great advantage. Fixed pulleys, therefore, do not increase power.

11. With the movable pulley there is an apparent increase of power. If a rope fixed from a hook in a beam be passed over the under side of a movable pulley to which a weight is attached, and then passed over the upper side of a pulley fixed to the same beam as the hook, the downward part of the rope between the hook and the movable pulley, and the upward part from that pulley to the one fixed in the beam, must have an equal strain on them, and hence each part clearly sustains half the weight. But when a hand pulls the part of the rope hanging down from the pulley fixed to the beam, so as to raise the weight fixed to the movable pulley, it is also clear that the part of the rope pulled has the same strain put on it as the two other parts, and thus the hand pulls down its end with a force equal to only half the weight, and yet this half force raises the whole weight, so that it is really doubled.

The saving of power by the movable pulley, as in this case, lies in the fact that the hook in the beam, to which the rope is attached, bears half the weight.

Yet the doubling the power is only in appearance, for the hand must pull the rope two feet down to raise the weight one foot-that is, it must shorten both the downward and upward part

of the rope, to and from the movable pulley, a foot each, and to lift half a given weight two feet needs clearly no less force than to lift the whole weight one foot.

By combining pulleys skilfully the most surprising results are obtained in facilitating the raising of heavy weights. Take Figure 15 for an illustration. The power exerted at P is borne by the part of the cord between P and C, but as the tension or strain is everywhere equal, and there are four such parts of the cord between the four pulleys, it follows that a pull equal to 1 lb. at P would balance a weight of 4 lbs. at W. The power is concentrated or increased as many times as there are pulleys employed. An exertion equal to the lifting of 10 lbs. would thus with four pulleys raise a weight of 40 lbs., and if there were six, a force of 10 lbs. would raise 60 lbs.

From this you can easily see how combinations of pulleys might be made by which a child's strength could be easily able to raise a weight too heavy, without such help, for a man to move.

W

Fig. 15.

12. The FOURTH Mechanical Power is the INCLINED PLANE. (Fig. 16.) Every one knows how much easier it is to roll a heavy cask up a slope than to lift it perpendicularly to the same height at once. The greater ease in the case of the slope is an illustration of the benefit derived from the inclined plane as a mechanical power, for a slope and an inclined plane are different names for the same thing.

To explain the principles on which the advantage of the inclined plane rests in a simple way is not very easy, but a little thought will surmount any difficulty.

The line A C is called the length of the inclined plane, B C its height, and A B its base. If a heavy body (G) be placed on it, there will be a pressure through its centre of gravity G in the perpendicular direction G V. This line G V may now be made the diagonal or cross line of a parallelogram * G W V X, and hence if

B

Fig. 16.

G V represent the weight, and its direction, it may be resolved into the two forces represented by G W and G X, which show the magnitude and * See "Fifth Reader," Public School Series, p. 122.

direction of these forces. The force G X, as you see, is parallel to the inclined plane; the force G W is perpendicular to it. Hence the pressure G V through the centre of gravity is equal to these two other pressures GW and G X. But the pressure G W is not to be taken into account, for it is destroyed by the resistance the ground offers to it. The other pressure G X only acts so as to cause the body to run down the slope.

Now the short line G X bears the same proportion to the line V G as the height of the plane B C bears to its base A B, for these two lines in

The Tower of Belus, at Babylon, illustrating the inclined plane.

each are corresponding parts of an exactly similar triangle. G X is the height of one triangle, G V its base; just as C B and A B are the height and the base of another of the same geometrical shape.

To draw the body G up the inclined plane, therefore, it would be enough to use any pressure in the direction X G exceeding the pressure G X, and the friction of the plane surface.

า

13. The result of all this is that the resistance to be surmounted in bearing a weight up an inclined plane is as the length of a plane is to its height.

If A C be twice the length of C B, one hundredweight at P will sustain two hundredweights at G, and if A C be six times the length of C B, P will balance six times G. Hence if a horse had to drag a loaded cart up a road which rose one foot in ten, the cart would have a tendency to run back equal to one-tenth of the weight of the load, and, thus, if the load were a ton, the horse would need to drag with a force of 224 lbs., or onetenth of a ton more than would have been needed if the road had been level.

When mountains between which there is no pass have to be crossed by roads, the inclined plane is very often made use of, to make the ascent easy by winding round in a gradual rise, or ascending in slow zigzags, comparatively easy for travel. The tower of Belus at Babel is said to have been built with a winding path round it to aid the ascent to its lofty top, as in the background of the accompanying illustration. (Fig.17.)

14. The FIFTH MECHANICAL POWER, the WEDGE, is simply a movable inclined plane, or rather two inclined planes, placed base to base, so as to have the two slopes outwards.

In its simplest form the wedge is used for raising heavy bodies sufficiently to allow the use of levers, and to split timber, stones, &c. (Fig. 18.)

In countries like Canada the rails used everywhero for fences are split from the log by wedges. Ships are raised in the dry dock by driving wedges under them, and the oil is pressed from seeds by wedges driven between pieces of wood placed on each side of the seed bags.

Knives and all cutting-tools act on the principle of sharp wedges, and so does the plough, which forces itself through the soil by its wedge shape.

15. The SIXTH MECHANICAL POWER is the SCREW. It is another variety of the inclined plane. (Figs. 19, 20.) The moulds from which screws are made may be formed by wrapping an inclined plane of wire round a