infinitely small straight lines, the moving body, owing to its inertia, always tends to follow the prolongation of the small straight line which it traverses. It tends then to retain its motion in a straight line, and to fly from the curve which it is compelled to describe. This action is called the centrifugal force, from two Latin words which signify to fly from the centre.

The production of centrifugal force in circular motion may be demonstrated by means of the apparatus represented in fig. 15. On a brass frame AB is stretched a stout brass wire, and on which are slid two ivory balls which can move freely along the wire: the balls being arranged as shown in the figure, the frame is rapidly rotated by means of the turning table. The balls, projected by the centrifugal force, glide along the wire; and strike the ends with the greater force, the greater the velocity of rotation.

29. Effects of centrifugal force. The centrifugal force is greater the greater the velocity, and the more marked the curvature of the line along which the movable body passes. Hence railways should be as straight as possible, for as the trains have a great velocity, when they move along a curve the centrifugal force is continually tending to throw them off, and the more so the sharper the

curve.

It is owing to centrifugal force that the wheels of a carriage moving along a muddy road throw off the mud that adheres to the rim.

In a circus, the horses and their riders always incline their bodies towards the centre, and the greater their speed the greater their inclination. The object of this is to allow their weight to counteract the influence of the centrifugal force, which would throw them off if they stood upright.

In sugar refineries centrifugal force is applied in removing syrup from crystallised sugar. The sugar is placed in a cylindrical vessel, whose sides are made of wire gauze, and which is put in rapid rotation. The centrifugal force scatters the coloured syrup through the meshes of the sieve, while, the solid crystals are left behind colourless and pure. The same principle is applied in drying clothes in large washing establishments. A wet mop made to turn quickly about its own handle as an axis throws the water off on all sides, and quickly dries itself.

A hoop trundled along the ground may move for a long time before falling, but if we attempt to keep it upright while in a state of rest, it at once falls. The reason of this is that, while in motion, if

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Flattening of the Earth at the Poles.

23

it inclines to one side, the inclination causes it to describe a curved line, whence arises a centrifugal force which opposes the fall of the hoop at any rate so long as it retains a sufficient velocity.

30. Flattening of the earth at the poles.-One of the most remarkable effects of centrifugal force is the flattening of the earth at the two poles. To explain this phenomenon we must premise that the earth, which is nearly spherical in form, rotates about an imaginary axis passing through its two poles, and that, in this rotation, all points on the surface have not the same velocity, for they do not describe the same paths. For at the equator they describe every twenty-four hours a circumference equal to that of the earth, while points taken at increasing distances from the equator gradually describe smaller and smaller circles to the poles where they have no motion. Hence owing to the diurnal rotation about the earth's axis, a centrifugal force is produced which is greatest at the equator, and gradually diminishes up to the poles where there is none at all. Hence, owing to this inequality in the intensity of the centrifugal force, there must arise an accumulation of matter about the equator, especially if, as geologists assume, the earth was originally in a state of fusion.

It has in fact been ascertained by direct measurement, that the radius of the earth at the poles is less than that at the equator by about the latter, or 131 miles. A similar flattening has been observed in other planets.

289

To demonstrate this bulging at the equator and flattening at the poles, use is made of the apparatus represented in fig. 16. It consists of an iron rod, which may be fixed upon the turning table, instead of the piece A B (fig. 15). At the bottom of the rod are fixed four thin elastic metal plates, which are joined at the top to a ring which can slide up and down the rod. The apparatus being then put in rapid rotation, the rings slide down the rod as represented in the figure to an extent depending on the rapidity of the rotation.

Fig. 16.

LEVERS.

31. Mechanics. Machines.-Mechanics is the science which treats of forces and of motion. Several forces being applied to the same body, it indicates the relation which must exist between them in order to produce equilibrium, or in order to produce a given effect.

Any apparatus which serves to transmit the action of a force is a machine; and any force which moves a machine is a motor. In cutting an apple with a knife, the hand is the motor, and the knife which transmits its action is a machine. A horse drawing a cart is a motor, and the cart which utilises the force of the horse in conveying loads is a machine. The watercourse which works a wheel, the wind which turns a mill, and the steam which moves a locomotive, are all motors; and the water-wheel, the wind-mill, and the locomotive are all machines.

Machines do not increase the force of a motor; but, by modifying its action, they render it capable of performing work which it alone could not do. For instance, by the aid of a lever, a man can raise burdens, which, without such help, would be impossible. We shall only describe here the lever, the simplest of all machines, and shall afterwards see its action in the case of balances.

32. Levers.-A lever is a rigid bar of wood or of metal moveable about a fixed point or edge called the fulcrum; and subject to the action of two forces which tend to move it in opposite directions. The force which acts as motor is called the power, and the other the resistance. Levers are divided into three classes, accord

reference to the fulcrum.

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Levers.

25

A lever of the first kind is one in which the fulcrum is between the power and the resistance. Fig. 17 represents one of this kind,

in which the hand is the power, the weight P the resistance, while C is the fulcrum.

B

Fig. 19.

and the fulcrum, as in fig. 18.

A lever of the third kind is one in which the power is applied between the resistance and the fulcrum as represented in fig. 19.

In these different kinds of levers, the distances from the fulcrum to the power and to the resistance are called the arms of the lever. In fig. 19, for instance, the arm of the power is the distance from C to B, and that from C to A is the arm of the resistance.

33. Effect of levers. Condition of equilibrium.-It may be shown that the effect produced by a force by means of a lever, increases with the length of the arm upon which it acts, that is, if the arm is twice, thrice, or four times as long, the useful effect is two, three, or four times as great. This is what led Archimedes to say, that, give him a fulcrum, and he would lift the world.

Since a force produces a greater effect the longer the arm of the lever, it follows that in order to produce equilibrium between the power and the resistance, acting at the same time on a lever, if the arms are equal, the two forces themselves must be equal, and that if the arms of the lever are unequal, the two forces must be inversely as the arms of the lever; thus, if the power is one-third that of the resistance, the arm of the power should be three times as long as that of the resistance.

In a lever of the third kind the power must be always greater than the resistance, for the distance of the resistance from the fulcrum (AC, fig. 19) is always greater than the distance BC from the power B to the fulcrum. In a lever of the second kind the power is always smaller than the resistance, for the arm BC is longer than the arm AC (fig. 18). These properties are expressed by saying that, in a lever of the third kind, there is a loss of power, and in one of the second kind a gain. In a lever of the first kind there may be either gain, or loss, or they may just balance each other, for the arm BC of the power (fig. 17) may be either greater, or less than, or equal to, the arm AC.

34. Various applications of levers.-Numerous applications

pump handle.

Fig. 20.

of the different kinds of levers are met with in articles of every-day use. The ordinary balance (fig. 34) is a lever of the first kind, as is also a

Scissors are another instance; each handle is a lever, the fulcrum of which is the pivot C, the power is the hand, and the resistance is the material to be cut (fig. 20).