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turning one of the wheels, the other moves round with it. If a large and small wheel are used together, the small wheel, having fewer teeth, will go round more often than the large. Thus, if a wheel with six teeth plays upon a wheel with sixty teeth, the former will move round ten times, while the latter moves round once. The cogs of wheels can be so arranged that a horizontal wheel will move a vertical one.

A crank is composed of two rods (one shorter than the other), joined together by a pivot or hinge, the shorter rod turning round a fixed centre. The shorter

rod is turned round the crank by pushing the longer rod backwards and forwards. A knife-grinder's wheel is turned by a crank, which is worked by the foot moving up and down.

The crank is of great use in machines, because by its help we can obtain one kind of motion from another.

In the steam-engine, the steam moves an iron rod up and down. The rod being connected with a wheel by means of a crank, turns it round, and thus from an upand-down motion we obtain a circular motion.

If, on the other hand, we have a wheel turning round, to which we attach by a crank the rod of a sucker of a pump, the sucker will be moved up and

down as the wheel turns round. Thus from a circular motion we obtain an up-and-down motion.

We must observe that though we can move weights by the mechanical powers, we can only do so slowly. A great block of stone raised by a lever is moved much more slowly than the hand which moves it. I can, by means of a moveable pulley, raise twice the weight which I can raise without it, but then I raise it twice as slowly. And so of the rest. It is commonly said, what you gain in power you lose in speed. But then in many works the speed is of no consequence compared with the power. For instance, we often see a great package, which ten men could not lift, drawn slowly to an upper warehouse-room by means of a crane.

One man does this easily, and if we look at him we see him turning a handle round very quickly. This moves a small toothed-wheel, and that a much greater one; so the package is raised; and although it moves slowly, that is of no consequence.

CHAPTER LXII.

THE THEORY OF GRAVITY.

ONE great use of machines is to help us to raise weights. Perhaps you have never thought much about the reason why things are heavy. Newton, a great philosopher, once observed an apple fall from a tree, and he set about asking himself why apples fall to the ground. This was not the only apple which Newton himself had seen fall, and apples had been falling ever since the creation; it was one of the commonest sights in the world; but when a very clever man began to think of the reason why it falls, he found out more and more about it; and by starting from this point, he at last arrived at the knowledge of the way in which the planets move round the sun.

I do not intend to say anything now about the motion of the heavenly bodies, but will only point out a few things which occur every day before our eyes. If you stand over a well and let a stone fall from your hand, it will move quickly to the bottom. If you throw a stone upwards, it will ascend every instant more slowly, until at last it ceases to ascend, and begins to descend. It will then come down through the air just as the stone went down to the bottom of the well. If you throw a stone at some mark at a distance, it will always at last come to the ground. If you try to lift a large stone lying on the earth, it will be difficult to do so; it will be just as if somebody were pulling against you.

We discover, then, that there is some power which is constantly drawing bodies to the ground. This is called the power of gravity, or of attraction-that is, the power of drawing to; and it always acts so as to draw the bodies to the ground in a vertical direction.

If we fasten a weight to a string, and hold the string in our hand, the string will hang down in a straight line; such a line is called vertical.

The plane to which this string is perpendicular is horizontal. The surface of standing water is horizontal.

The reason why arrows or bullets fall in different directions is, that the bow or gun sends them in one direction, and gravity pulls them in another; so they fly in some direction between the two, till they at last are pulled down to the earth.

All bodies of the same size are not of the same weight. This is because the particles are not so close in one body as in another. A ball of lead is much heavier than the same-sized ball of cork. But if we take two balls of lead, one of which is twice as large as the other, it will require twice as much force to hold the larger as it does to hold up the smaller ball.

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If we find a ball of wood of such a kind that it will just

balance two balls of cork of the same size as itself, then we shall find it will take exactly twice the force to hold up the wooden ball as it does to hold up one of the cork balls.

So the weight depends upon two things-(1) the size of the body, and (2) the closeness with which the particles are packed. This last is called its density.

The mass of a body depends upon its size and density together. The mass of the wooden ball just mentioned is twice as great as the mass of the cork ball: the size is the same, but the density is twice as great.

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The mass of the larger of the two leaden balls is twice as great as the mass of the smaller one. density is the same, but the size is twice as great.

It may at first sight appear that this force of attraction, or gravity, causes a great deal of trouble. We are constantly employed in raising weights, and find it often laborious work.

We shall soon see, however, that gravity is very useful to us.

What is it that enables us to build walls that will stand firm? We lay one course of bricks or stones upon another, always taking care that each course is quite horizontal on its surface and vertical at its side. This we discover by the use of the plumb-line. Then the force of gravity draws down the bricks upon each other, and the more bricks there are the more strongly they press. So the wall cannot easily be stirred, and the strong winds do it no hurt. The mortar would not hold the bricks together if it were not for their own weight; but cottages are sometimes built of blocks of stone without any mortar or cement at all, and the walls are kept quite firm by the weight of the stones.

A simple experiment will show you how gravity acts in this respect. Lay five or six books on each other upon a table. You will not easily draw a lower one out, because the upper ones press upon it, and you may

give a good push to the pile without disturbing it; but if you set the books up side by side, you can draw any one out with perfect ease.

Gravity, too, is of use even in moving weights; for if we press against the rope by which we draw them, we make our own weight help us. This is why we can pull down with more force than we can push upwards; and large stout horses are chosen for drays, not because these are always the strongest, but because they are the heaviest, and so, by pressing their weight forwards, they can move very heavy waggons.

CHAPTER LXIII.

FRICTION.

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If we try to pull a heavy body along a level road, shall not find it very easy to do so; and the rougher the road the harder our task will be. The same body which we could scarcely move upon the ground, can often be pushed along upon a frozen pond with the greatest ease. This is because the ice is so much smoother than the ground; and we soon discover that our difficulty in dragging a body upon level ground arises from the rubbing together of the two surfaces. This is called Friction, and is sometimes so great, that it is almost as troublesome to draw a body along the ground as it is to carry it in our arms.

In every machine there is a loss of power by friction, in consequence of the parts of the machine rubbing together.

The simplest case is that of the Inclined Plane. Travellers have often reason to complain of their trunks being rubbed, by the use of such a board as has been described in a former lesson. But if a cask is rolled by cords up the plane, the friction is avoided.

When a Lever rests upon a fulcrum, the friction

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