_Emily._ I do not quite understand that.

_Mrs. B._ Let us suppose that the instant after you have let a stone fall from a high tower, the force of gravity were annihilated; the body would nevertheless continue to move downwards, for it would have received a first impulse from gravity; and a body once put in motion will not stop unless it meets with some obstacle to impede its course; in this case its velocity would be uniform, for though there would be no obstacle to obstruct its descent, there would be no force to accelerate it.

_Emily._ That is very clear.

_Mrs. B._ Then you have only to add the power of gravity constantly acting on the stone during its descent, and it will not be difficult to understand that its motion will become accelerated, since the gravity which acts on the stone at the very first instant of its descent, will continue in force every instant, till it reaches the ground. Let us suppose that the impulse given by gravity to the stone during the first instant of its descent, be equal to one; the next instant we shall find that an additional impulse gives the stone an additional velocity, equal to one; so that the acc.u.mulated velocity is now equal to two; the following instant another impulse increases the velocity to three, and so on till the stone reaches the ground.

_Caroline._ Now I understand it; the effects of preceding impulses continue, whilst gravity constantly adds new ones, and thus the velocity is perpetually increased.

_Mrs. B._ Yes; it has been ascertained, both by experiment, and calculations which it would be too difficult for us to enter into, that heavy bodies near the surface of the earth, descending from a height by the force of gravity, fall sixteen feet the first second of time, three times that distance in the next, five times in the third second, seven times in the fourth, and so on, regularly increasing their velocities in the proportion of the odd numbers 1, 3, 5, 7, 9, &c. according to the number of seconds during which the body has been falling.

_Emily._ If you throw a stone perpendicularly upwards, is it not the same length of time in ascending, that it is in descending?

_Mrs. B._ Exactly; in ascending, the velocity is diminished by the force of gravity; in descending, it is accelerated by it.

_Caroline._ I should then imagine that it would fall, quicker than it rose?

_Mrs. B._ You must recollect that the force with which it is projected, must be taken into the account; and that this force is overcome and destroyed by gravity, before the body begins to fall.

_Caroline._ But the force of projection given to a stone in throwing it upwards, cannot always be equal to the force of gravity in bringing it down again; for the force of gravity is always the same, whilst the degree of impulse given to the stone is optional; I may throw it up gently, or with violence.

_Mrs. B._ If you throw it gently, it will not rise high; perhaps only sixteen feet, in which case it will fall in one second of time. Now it is proved by experiment, that an impulse requisite to project a body sixteen feet upwards, will make it ascend that height in one second; here then the times of the ascent and descent are equal. But supposing it be required to throw a stone twice that height, the force must be proportionally greater.

You see then, that the impulse of projection in throwing a body upwards, is always equal to the action of the force of gravity during its descent; and that whether the body rises to a greater or less distance, these two forces balance each other.

I must now explain to you what is meant by the _momentum_ of bodies. It is the force, or power, with which a body in motion, strikes against another body. The momentum of a body is the product of its _quant.i.ty of matter_, multiplied by its _quant.i.ty of motion_; in other words, its weight multiplied by its velocity.

_Caroline._ The quicker a body moves, the greater, no doubt, must be the force which it would strike against another body.

_Emily._ Therefore a light body may have a greater momentum than a heavier one, provided its velocity be sufficiently increased; for instance, the momentum of an arrow shot from a bow, must be greater than that of a stone thrown by the hand.

_Caroline._ We know also by experience, that the heavier a body is, the greater is its force; it is not therefore difficult to understand, that the whole power, or momentum of a body, must be composed of these two properties, its weight and its velocity: but I do not understand why they should be _multiplied_, the one by the other; I should have supposed that the quant.i.ty of matter, should have been _added_ to the quant.i.ty of motion?

_Mrs. B._ It is found by experiment, that if the weight of a body is represented by the number 3, and its velocity also by 3, its momentum will be represented by 9, not by 6, as would be the case, were these figures added, instead of being multiplied together.

_Emily._ I think that I now understand the reason of this; if the quant.i.ty of matter is increased three-fold, it must require three times the force to move it with the same velocity; and then if we wish to give it three times the velocity, it will again require three times the force to produce that effect, which is three times three, or nine; which number therefore, would represent the momentum.

_Caroline._ I am not quite sure that I fully comprehend what is intended, when weight, and velocity, are represented by numbers alone; I am so used to measure s.p.a.ce by yards and miles, and weight by pounds and ounces, that I still want to a.s.sociate them together in my mind.

_Mrs. B._ This difficulty will be of very short duration: you have only to be careful, that when you represent weights and velocities by numbers, the denominations or values of the weights and s.p.a.ces, must not be changed. Thus, if we estimate the weight of one body in ounces, the weight of others with which it is compared, must be estimated in ounces, and not in pounds; and in like manner, in comparing velocities, we must throughout, preserve the same standards both of s.p.a.ce and of time; as for instance, the number of feet in one second, or of miles in one hour.

_Caroline._ I now understand it perfectly, and think that I shall never forget a thing which you have rendered so clear.

_Mrs. B._ I recommend it to you to be very careful to remember the definition of the momentum of bodies, as it is one of the most important points in mechanics: you will find that it is from opposing velocity, to quant.i.ty of matter, that machines derive their powers.

The _reaction_ of bodies, is the next law of motion which I must explain to you. When a body in motion strikes against another body, it meets with resistance from it; the resistance of the body at rest will be equal to the blow struck by the body in motion; or to express myself in philosophical language, _action_ and _reaction_ will be equal, and in opposite directions.

_Caroline._ Do you mean to say, that the action of the body which strikes, is returned with equal force by the body which receives the blow?

_Mrs. B._ Exactly.

_Caroline._ But if a man strike another on the face with his fist, he surely does not receive as much pain by the reaction, as he inflicts by the blow?

_Mrs. B._ No; but this is simply owing to the knuckles, having much less feeling than the face.

Here are two ivory b.a.l.l.s suspended by threads, (plate 1. fig. 3.) draw one of them, A, a little on one side,--now let it go;--it strikes, you see, against the other ball B, and drives it off, to a distance equal to that through which the first ball fell; but the motion of A is stopped; because when it struck B, it received in return a blow equal to that it gave, and its motion was consequently destroyed.

_Emily._ I should have supposed, that the motion of the ball A was destroyed, because it had communicated all its motion to B.

_Mrs. B._ It is perfectly true, that when one body strikes against another, the quant.i.ty of motion communicated to the second body, is lost by the first; but this loss proceeds from the reaction of the body which is struck.

Here are six ivory b.a.l.l.s hanging in a row, (fig. 4.) draw the first out of the perpendicular, and let it fall against the second. You see none of the b.a.l.l.s except the last, appear to move, this flies off as far as the first ball fell; can you explain this?

_Caroline._ I believe so. When the first ball struck the second, it received a blow in return, which destroyed its motion; the second ball, though it did not appear to move, must have struck against the third; the reaction of which set it at rest; the action of the third ball must have been destroyed by the reaction of the fourth, and so on till motion was communicated to the last ball, which, not being reacted upon, flies off.

_Mrs. B._ Very well explained. Observe, that it is only when bodies are elastic, as these ivory b.a.l.l.s are, and when their ma.s.ses are equal, that the stroke returned is equal to the stroke given, and that the striking body loses all its motion. I will show you the difference with these two b.a.l.l.s of clay, (fig. 5.) which are not elastic; when you raise one of these, D, out of the perpendicular, and let it fall against the other, E, the reaction of the latter, on account of its not being elastic, is not sufficient to destroy the motion of the former; only part of the motion of D will be communicated to E, and the two b.a.l.l.s will move on together to _d_ and _e_, which is not so great a distance as that through which D fell.

Observe how useful reaction is in nature. Birds in flying strike the air with their wings, and it is the reaction of the air, which enables them to rise, or advance forwards; reaction being always in a contrary direction to action.

_Caroline._ I thought that birds might be lighter than the air, when their wings were expanded, and were by that means enabled to fly.

_Mrs. B._ When their wings are spread, this does not alter their weight, but they are better supported by the air, as they cover a greater extent of surface; yet they are still much too heavy to remain in that situation, without continually flapping their wings, as you may have noticed when birds hover over their nests: the force with which their wings strike against the air, must equal the weight of their bodies, in order that the reaction of the air, may be able to support that weight; the bird will then remain stationary. If the stroke of the wings is greater than is required merely to support the bird, the reaction of the air will make it rise; if it be less, it will gently descend; and you may have observed the lark, sometimes remaining with its wings extended, but motionless; in this state it drops quietly into its nest.

_Caroline._ This is indeed a beautiful effect of the law of reaction!

But if flying is merely a mechanical operation, Mrs. B., why should we not construct wings, adapted to the size of our bodies, fasten them to our shoulders, move them with our arms, and soar into the air?

_Mrs. B._ Such an experiment has been repeatedly attempted, but never with success; and it is now considered as totally impracticable. The muscular power of birds, is incomparably greater in proportion to their weight, than that of man; were we therefore furnished with wings sufficiently large to enable us to fly, we should not have strength to put them in motion.

In swimming, a similar action is produced on the water, to that on the air, in flying; in rowing, also, you strike the water with the oars, in a direction opposite to that in which the boat is required to move, and it is the reaction of the water on the oars which drives the boat along.

_Emily._ You said, that it was in elastic bodies only, that the whole motion of one body, would be communicated to another; pray what bodies are elastic, besides the air?

_Mrs. B._ In speaking of the air, I think we defined elasticity to be a property, by means of which bodies that are compressed, return to their former state. If I bend this cane, as soon as I leave it at liberty, it recovers its former position; if I press my finger upon your arm, as soon as I remove it, the flesh, by virtue of its elasticity, rises and destroys the impression I made. Of all bodies, the air is the most eminent for this property, and it has thence obtained the name of an elastic fluid. Hard bodies are in the next degree elastic; if two ivory, or hardened steel b.a.l.l.s are struck together, the parts at which they touch, will be flattened; but their elasticity will make them instantaneously resume their former shape.

_Caroline._ But when two ivory b.a.l.l.s strike against each other, as they constantly do on a billiard table, no mark or impression is made by the stroke.

_Mrs. B._ I beg your pardon; you cannot, it is true, perceive any mark, because their elasticity instantly destroys all trace of it.

Soft bodies, which easily retain impressions, such as clay, wax, tallow, b.u.t.ter, &c. have very little elasticity; but of all descriptions of bodies, liquids are the least elastic.

_Emily._ If sealing-wax were elastic, instead of retaining the impression of a seal, it would resume a smooth surface, as soon as the weight of the seal was removed. But pray what is it that produces the elasticity of bodies?

_Mrs. B._ There is great diversity of opinion upon that point, and I cannot pretend to decide which approaches nearest to the truth.

Elasticity implies susceptibility of compression, and the susceptibility of compression depends upon the porosity of bodies; for were there no pores or s.p.a.ces between the particles of matter of which a body is composed, it could not be compressed.

_Caroline._ That is to say, that if the particles of bodies were as close together as possible, they could not be squeezed closer.

_Emily._ Bodies then, whose particles are most distant from each other, must be most susceptible of compression, and consequently most elastic; and this you say is the case with air, which is perhaps the least dense of all bodies?