differently coloured substances, and made to impinge on each other, then the parts which are brought into contact by the impact will be stained, and a spot will be produced on each of finite magnitude. This spot could not be produced if the balls retained their globular shape; and the spots are larger as the force of impact is greater. Thus the destruction and the communication of velocity is in all cases gradual; and the time employed will depend most materially on the nature of the substance.

We may then consider impact as a pressure of short duration; increasing from nothing to a finite magnitude, and then decreasing again to nothing: hence the third law of motion is true in cases of impact; consequently experiments made on the collision of bodies may be employed to establish the third law, as was done by Wren and Newton.

37. Sudden destruction of Velocity.-The effects produced by impact as compared with those produced by pressure appear so enormous, that they have sometimes been referred to different principles. But the whole difficulty vanishes when the element time is properly taken into the account. In impact there is a destruction of velocity, and the effect produced depends most materially on the time employed in its destruction. This may be illustrated by the familiar example of driving a nail. If the nail be struck by a soft body it can never be driven into any obstacle, whereas a very slight blow with a hard substance will fix it at once. The difference of these effects arises from the fact that the soft body being a yielding substance its velocity is being destroyed gradually during the yielding of the body, but the velocity of the hard body is destroyed in much less time since there is very small yielding of parts. Thus it may be laid down that the force requisite for the destruction of any velocity is greater, as the time occupied in its destruction is less; and it is this force which in the above instances drives in the nail. It appears then that the hardness of the surfaces between which the impact takes

place has a most material influence on the effect produced. When the surfaces are very hard there is scarce any yielding, the velocity must consequently be destroyed in a very small time. Thus the hardness of the surfaces must be considered as the real cause of the efficacy of impact; and it is so because of the almost instantaneous destruction of velocity which takes place when the surfaces are hard. Again, if we attempt to drive a nail into a yielding board, the same principle is illustrated in the small progress which is made; the yielding takes considerable time, hence the velocity which was suddenly destroyed in the hammer is destroyed gradually at the board, so that the effect produced towards making the nail enter is exceedingly small. The preceding remarks will fully explain the surprising effects produced by a constant small impact, when the striking surfaces are very hard, and when the parts are unyielding. The preceding explains also the great advantage with which impact may be used to overcome friction. The unyielding nature of the surfaces is the very circumstance which gives efficacy to the impact. Hence we see that wedges may be driven by impact which would scarce be pushed in by any conceivable pressure.

On the preceding principles we may explain the necessity of springs for carriages which are to travel at any rate. A carriage going along at the rate of ten miles an hour meets with an obstacle; if now the carriage is perfectly stiff, so that its whole weight has to be raised suddenly over this obstacle, the shock produced on the road and wheel by the sudden change in the direction of the motion is very great indeed; but when the mass of the load is sustained on springs, the only force exerted is that which will raise the wheels and bend the springs. If roads and wheels were perfectly smooth there would be no need of springs; but this being impossible they are as necessary for the preservation of the road as for the comfort of the passengers. For the shock produced by the rapid conversion of the direction of the motion of a mass of matter from a

horizontal to a vertical direction, is felt equally by the road and the carriages. These principles are of the greatest practical importance in railroads, where the velocity is great, and the surfaces are hard; and notwithstanding the degree of smoothness of the surfaces and the excellent springs with which all the carriages are furnished, the breakage of the rails and axle-trees from the above-mentioned cause is very great.

CHAP. V.

ON GRAVITY.

SECTION I.

GENERAL EFFECTS OF GRAVITY-LAWS OF FALLING BODIES - LAWS

AT SURFACE OF THE EARTH-CENTRE OF GRAVITY STABLE EQUI

LIBRIUM.

38. All bodies with which we are acquainted when left to themselves fall until they touch the earth, or some other body which can sustain them. This phenomenon, which takes place at the surface of the earth, at all known heights above, and depths below the surface, must be the consequence of some force residing somewhere. The natural inertness of matter, or its passive continuance in the state in which it exists, compels us to admit the existence of some force, and that peculiar force which produces these effects is termed gravity. Thus, gravity is the force which makes bodies fall to the earth; but this definition will convey to us a most inadequate idea of the power of this agent if we suppose it produces no other effects. It is to this that we owe many other phenomena and many other motions, to which different names have been applied. Thus, for example, the flowing of rivers, the ascent of light bodies in fluids, with many apparently contradictory phenomena, are but the effects of that same energy which we have called gravity. We may have some further idea of the way in which this force acts, by conceiving that all matter possesses the pro

perty of attracting all other matter; we have seen instances of this attraction exerted at insensible distances, but the attraction of gravitation acts at all sensible distances, however great.

39. Weight.-The first and principal effect of gravity is the pressure directed towards the earth which every body exerts upon those which are placed beneath it; this pressure is usually termed weight; if my hand supports a stone, the pressure which the stone exerts upon my hand is termed the weight of the stone; hence it is asserted, that all bodies are heavy, for all fall to the earth when left perfectly to themselves. This weight is the result of the mutual attraction of the earth and the stone; the earth attracts the stone, and the stone attracts the earth; each. moves towards the other (Art. 33): but, inasmuch as the motion of each is the less the greater the mass, we easily see that the motion of the earth to meet the stone, or any body which can be raised above its surface, is so indescribably small, that the motion of the stone only need occupy our attention. Hence, we never speak of the effect of the attraction of the stone upon the earth, but simply of the attraction of the earth upon the stone: but that we may have accurate conceptions on this point we must remember, that the weight of any body is really the effect of the attraction of the earth upon the body, increased by the effect of the attraction of the body upon the earth. Hence it follows, that the weight of a body is proportional to its mass; for the more particles there are in a given bulk, the greater must be this mutual attraction, that is, the weight of the body.

40. Direction of Gravity.—All bodies left to themselves fall to the surface of the earth, where all further progress is arrested, and the direction in which they fall, or in which gravity acts, may be observed by setting up straight rods, and watching when a body falls accurately along them. But this direction may be more readily ascertained by a plumb-line, that is, by any line hung up by one end, and