alluded there is that of neutral or indifferent equilibrium, such as that of a sphere resting upon a horizontal plane.

Here, if a displacement occurs, the centre of gravity is neither raised nor lowered, but remains always at a height above the plane equal to the radius of the sphere, and in consequence the sphere will rest with indifference on any part of its surface, showing no tendency to prefer one point above another.

51. We have here an explanation of the principle of construction of those toys which, with the appearance of being top-heavy, are nevertheless so weighted beneath that the centre of gravity is raised, and not lowered, by displacement; the consequence is that when displaced they oscillate backwards and forwards until ultimately they regain the position from which they were moved. The following are a few examples in illustration of this subject :

Example I.—A cone is placed on its apex on a flat horizontal surface: will the equilibrium be stable or unstable? Answer.-Unstable.

Example II.—A uniformly heavy circular wooden disc has a piece of its substance taken out, and a piece of lead inserted instead. In what position will it rest on a flat

horizontal surface?

Answer.-It will rest so that the lead will be below the centre of the disc and in the vertical line joining it and the point on which the disc rests. For the centre of gravity of the whole heavy disc, including the lead, will in this case be as low as possible, and any displacement will tend to raise it, and will therefore be resisted by the action of gravity. Example III.-How will a man rising in a boat affect its stability?

Answer. It will make it more unstable, because it will raise the centre of gravity of the system, so that an oscillation would now be more ready to swamp the boat than if its centre of gravity were low.

Example IV.-In like manner a cart loaded with hay is more liable to be overturned, owing to irregularities in the road, than one loaded with lead, because in the former case

the centre of gravity of the system is high, and a comparatively small angular displacement, due to want of level in the road, may bring this centre of gravity into such a position that a line, drawn vertically downwards from it, shall pass without the wheels, in which case the system will topple over.

This 52. Let us now say a few words about the balance. important instrument consists of a lever, having equal arms on either side of a knife-edge upon which it rests (Fig. 18). From the extremities of these arms the scale-pans are suspended, and a pointer attached to the balance points vertically downwards when there are equal weights in the

FIG. 18.

two scale-pans; but should the left-hand weight predominate, the pointer will be deflected to the right, and vice versâ.

Let us begin by supposing that there is no weight in either scale-pan. The balance is so arranged that its centre of gravity is raised somewhat by displacement, so that, if displaced under these circumstances, it will come back to its original position.

If,

If the balance be very delicate, this force tending to bring it back is a very small one, so that a very small additional weight in one scale-pan will push the pointer aside a considerable distance before it is counteracted by this force. for instance, the one scale-pan be a milligramme heavier than the other, the pointer may be pushed aside one division before the force of restitution is sufficient to overcome the

additional pressure of the milligramme. If the additional weight be two milligrammes, the pointer will now be pushed aside two divisions, and so on. A sensitive balance enables us to ascertain with great exactness the weight of any body; for we have only to put the body to be weighed in the one scale-pan, and such a number

of standard weights in the other, as to cause the pointer to point vertically downwards, when we may be sure that we have ascertained the weight of the body with very great exactness; for were the one scale-pan the smallest degree heavier than the other, it would cause an appreciable deflection of the pointer either to the one side or the other.

FIG. 19.

53. The pendulum has been already alluded to (Art. 34) as a means of measuring the force of gravity by the rapidity of its oscillations. Thus we find that the same pendulum moves somewhat slower at the equator than near the pole, and hence we conclude that the force of gravity is slightly less at the equator than at the pole. at least, of the fact that, owing to the orange-like shape of the earth, a particle at the pole is really nearer the earth's centre than one at the equator. But the most frequent use of the pendulum is to regulate clocks, and the mode in which it is applied for this purpose is exhibited in Fig. 19, where B denotes the bob or heavy part of the pendulum. This pendulum in its oscillations moves backwards and forwards an escapement, C, terminated by two pallets which act upon the teeth of the escapement wheel, so that at each oscillation one tooth is allowed to escape, and thus the wheel moves

round one tooth at a time. If it were not for this connection of the escapement wheel with the pendulum, the effect of the weight, w, would be to make it move rapidly round until all the cord which is wrapped round its axis is uncoiled by the lowering of the weight. Thus the pendulum regulates the clock. The length of the seconds pendulum--that is to say, of the pendulum which vibrates from one of its extreme positions to the other once in a second-is very nearly one metre, and its time of oscillation is the same whether it makes small or very small swings. This property of the pendulum is called its isochronism, and was first discovered by Galileo, who noticed that a lamp swung by a chain in the cathedral of Pisa performed its oscillations in equal times without respect to their extent.

The time of oscillation of the pendulum will, however, be altered by altering its length. Thus, if it be four times as long, its time of oscillation will be doubled, if it be only one-fourth as long, its time of oscillation will be halved; if it be one-ninth as long, its time will be reduced to one-third, and so on, the time of oscillation varying as the square root of the length.

LESSON X.-FORCES EXHIBITED IN SOLIDS.

54. In the present chapter we propose to discuss molecular and atomic forces, as they are exhibited in the three states of matter-solid, liquid, and gaseous. Let us, in the first place, briefly describe the most prominent variety of these forces.

We have in the first place cohesion, adhesion, and chemical affinity, which are attractive forces; and in the next place we have those forces which resist any change of shape or volume in solids, and any change of volume in liquids and

gases.

Cohesion denotes the attraction which the various molecules of the same substance have for one another, and in virtue of which the various particles of solids and liquids keep together.

We may use the word adhesion to denote the attraction exerted between particles of two different bodies when placed in contact with one another. On the other hand, when particles of different bodies have such an attraction for each other as to rush together and form a substance of a different chemical nature, then we have the operation of chemical affinity.

Thus we should characterize that force which holds together the various particles of a piece of glass as the force of cohesion; but that force which causes a film of water to cling to a surface of glass we should denominate adhesion, while again that force which causes sulphuric acid and lime when brought together to unite in order to form sulphate of lime, we should term chemical affinity. Forces tending to alter the shape of a solid body may be applied to it in several different ways, each of which will be resisted by the body itself. Thus a thick metal wire, having one end fixed and a weight suspended from the other, will resist a force tending to twist the weight round; this is called resistance to torsion. Or, again, a thick rod of metal will resist any force tending to pull its particles apart; this is termed resistance to linear extension. And it will also resist any force tending to crush its particles together, and this is called resistance to linear compression.

Besides resisting deformation in these different ways, a solid bar, as for instance a bar of steel, will resist a force tending to bend it, thus exhibiting resistance to flexure.

Finally, it will resist any force tending to make its whole volume less, which we may term resistance to cubical compression.

We may exemplify this by a thick cylinder of indiarubber. A comparatively slight force will extend this cylinder or compress it in the direction of its length; but when the cylinder is extended it becomes attenuated as regards its thickness, and when it is compressed it bulges We cannot therefore well deduce the cubical compressibility of india-rubber from such experiments, or assert how far the substance will yield to a force which tends to

out.