Part 4

14. (Pg. 28) What then will be the effect of increasing the surface of a body?

15. (Pg. 28) What could you do to a sheet of paper, to make it fall quickly, and why?

16. (Pg. 28) Inform me how a very dense body may be made to float in the air?

17. (Pg. 28) The air is a real body, why does it not fall to the ground?

18. (Pg. 29) The air is more dense near the surface of the earth, and decreases in density as you ascend, how is this accounted for, and to what is it compared?

19. (Pg. 29) What is it which causes the particles of air to recede from each other, and seems to destroy their mutual attraction?

20. (Pg. 29) Smoke and vapour ascend in the atmosphere, how can you reconcile this with gravitation?

21. (Pg. 30) How would you illustrate this by the floating of a piece of paper on water?

22. (Pg. 30) Does smoke rise to a great height in the air, and if not, what prevents its so doing?

23. (Pg. 30) What limits the height to which vapours rise?

24. (Pg. 30) Of what does smoke consist?

25. (Pg. 30) Air balloons are formed of heavy materials, how will you account for their rising in the air?

26. (Pg. 30) What influence does the air exert, on bodies less dense than itself, on those of equal, and on those of greater density?

27. (Pg. 31) If the air could be entirely removed, what influence would this have upon the falling of heavy and light bodies?

28. (Pg. 31) How could this be exemplified by means of the air pump?

CONVERSATION III.

ON THE LAWS OF MOTION.

OF MOTION. OF THE INERTIA OF BODIES. OF FORCE TO PRODUCE MOTION. DIRECTION OF MOTION. VELOCITY, ABSOLUTE AND RELATIVE. UNIFORM MOTION. RETARDED MOTION. ACCELERATED MOTION. VELOCITY OF FALLING BODIES. MOMENTUM. ACTION AND REACTION EQUAL. ELASTICITY OF BODIES. POROSITY OF BODIES. REFLECTED MOTION. ANGLES OF INCIDENCE AND REFLECTION.

MRS. B.

The science of mechanics is founded on the laws of motion; it will therefore be necessary to make you acquainted with these laws before we examine the mechanical powers. Tell me, Caroline, what do you understand by the word motion?

_Caroline._ I think I understand it perfectly, though I am at a loss to describe it. Motion is the act of moving about, of going from one place to another, it is the contrary of remaining at rest.

_Mrs. B._ Very well. Motion then consists in a change of place; a body is in motion whenever it is changing its situation with regard to a fixed point.

Now since we have observed that one of the general properties of bodies is inertia, that is, an entire passiveness, either with regard to motion or rest, it follows that a body cannot move without being put into motion; the power which puts a body into motion is called _force_; thus the stroke of the hammer is the force which drives the nail; the pulling of the horse that which draws the carriage, &c. Force then is the cause which produces motion.

_Emily._ And may we not say that gravity is the force which occasions the fall of bodies?

_Mrs. B._ Undoubtedly. I have given you the most familiar illustrations in order to render the explanation clear; but since you seek for more scientific examples, you may say that cohesion is the force which binds the particles of bodies together, and heat that which drives them asunder.

The motion of a body acted upon by a single force, is always in a straight line, and in the direction in which it received the impulse.

_Caroline._ That is very natural; for as the body is inert, and can move only because it is impelled, it will move only in the direction in which it is impelled. The degree of quickness with which it moves, must, I suppose, also depend upon the degree of force with which it is impelled.

_Mrs. B._ Yes; the rate at which a body moves, or the shortness of the time which it takes to move from one place to another, is called its velocity; and it is one of the laws of motion, that the velocity of the moving body is proportional to the force by which it is put in motion. We must distinguish between absolute and relative velocity.

The velocity of a body is called _absolute_, if we consider the motion of the body in space, without any reference to that of other bodies. When, for instance, a horse goes fifty miles in ten hours, his velocity is five miles an hour.

The velocity of a body is termed _relative_, when compared with that of another body which is itself in motion. For instance, if one man walks at the rate of a mile an hour, and another at the rate of two miles an hour, the relative velocity of the latter is double that of the former; but the absolute velocity of the one is one mile, and that of the other two miles an hour.

_Emily._ Let me see if I understand it--The relative velocity of a body is the degree of rapidity of its motion compared with that of another body; thus if one ship sail three times as far as another ship in the same space of time, the velocity of the former is equal to three times that of the latter.

_Mrs. B._ The general rule may be expressed thus: the velocity of a body is measured by the space over which it moves, divided by the time which it employs in that motion: thus if you travel one hundred miles in twenty hours, what is your velocity in each hour?

_Emily._ I must divide the space, which is one hundred miles, by the time, which is twenty hours, and the answer will be five miles an hour. Then, Mrs. B., may we not reverse this rule, and say that the time is equal to the space divided by the velocity; since the space, one hundred miles, divided by the velocity, five miles per hour, gives twenty hours for the time?

_Mrs. B._ Certainly; and we may say also that the space is equal to the velocity multiplied by the time. Can you tell me, Caroline, how many miles you will have travelled, if your velocity is three miles an hour, and you travel six hours?

_Caroline._ Eighteen miles; for the product of 3 multiplied by 6, is 18.

_Mrs. B._ I suppose that you understand what is meant by the terms _uniform_, _accelerated_ and _retarded_ motion.

_Emily._ I conceive uniform motion to be that of a body whose motion is regular, and at an equal rate throughout; for instance a horse that goes an equal number of miles every hour. But the hand of a watch is a much better example, as its motion is so regular as to indicate the time.

_Mrs. B._ You have a right idea of uniform motion; but it would be more correctly expressed by saying, that the motion of a body is uniform when it passes over equal spaces in equal times. Uniform motion is produced by a force having acted on a body once and having ceased to act; as, for instance, the stroke of a bat on a ball.

_Caroline._ But the motion of a ball is not uniform; its velocity gradually diminishes till it falls to the ground.

_Mrs. B._ Recollect that the ball is inert, and has no more power to stop, than to put itself in motion; if it falls, therefore, it must be stopped by some force superior to that by which it was projected, and which destroys its motion.

_Caroline._ And it is no doubt the force of gravity which counteracts and destroys that of projection; but if there were no such power as gravity, would the ball never stop?

_Mrs. B._ If neither gravity nor any other force, such as the resistance of the air, opposed its motion, the ball, or even a stone thrown by the hand, would proceed onwards in a right line, and with a uniform velocity for ever.

_Caroline._ You astonish me! I thought that it was impossible to produce perpetual motion?

_Mrs. B._ Perpetual motion cannot be produced by art, because gravity ultimately destroys all motion that human power can produce.

_Emily._ But independently of the force of gravity, I cannot conceive that the little motion I am capable of giving to a stone would put it in motion for ever.

_Mrs. B._ The quantity of motion you communicate to the stone would not influence its duration; if you threw it with little force it would move slowly, for its velocity you must remember, will be proportional to the force with which it is projected; but if there is nothing to obstruct its passage, it will continue to move with the same velocity, and in the same direction as when you first projected it.

_Caroline._ This appears to me quite incomprehensible; we do not meet with a single instance of it in nature.

_Mrs. B._ I beg your pardon. When you come to study the motion of the celestial bodies, you will find that _nature_ abounds with examples of perpetual motion; and that it conduces as much to the harmony of the system of the universe, as the prevalence of it on the surface of the earth, would to the destruction of all our comforts. The wisdom of Providence has therefore ordained insurmountable obstacles to perpetual motion here below; and though these obstacles often compel us to contend with great difficulties, yet these appear necessary to that order, regularity and repose, so essential to the preservation of all the various beings of which this world is composed.

Now can you tell me what is _retarded motion_?

_Caroline._ Retarded motion is that of a body which moves every moment slower and slower: thus when I am tired with walking fast, I slacken my pace; or when a stone is thrown upwards, its velocity is gradually diminished by the power of gravity.

_Mrs. B._ Retarded motion is produced by some force acting upon the body in a direction opposite to that which first put it in motion: you who are an animated being, endowed with power and will, may slacken your pace, or stop to rest when you are tired; but inert matter is incapable of any feeling of fatigue, can never slacken its pace, and never stop, unless retarded or arrested in its course by some opposing force; and as it is the laws of inert bodies of which mechanical philosophy treats, I prefer your illustration of the stone retarded in its ascent. Now Emily, it is your turn; what is _accelerated motion_?

_Emily._ Accelerated motion, I suppose, takes place when the velocity of a body is increased; if you had not objected to our giving such active bodies as ourselves as examples, I should say that my motion is accelerated if I change my pace from walking to running. I cannot think of any instance of accelerated motion in inanimate bodies; all motion of inert matter seems to be retarded by gravity.

_Mrs. B._ Not in all cases; for the power of gravitation sometimes produces accelerated motion; for instance, a stone falling from a height, moves with a regularly accelerated motion.

_Emily._ True; because the nearer it approaches the earth, the more it is attracted by it.

_Mrs. B._ You have mistaken the cause of its accelerated motion; for though it is true that the force of gravity increases as a body approaches the earth, the difference is so trifling at any small distance from its surface, as not to be perceptible.

Accelerated motion is produced when the force which put a body in motion, continues to act upon it during its motion, so that its velocity is continually increased. When a stone falls from a height, the impulse which it receives from gravitation in the first instant of its fall, would be sufficient to bring it to the ground with a uniform velocity: for, as we have observed, a body having been once acted upon by a force, will continue to move with a uniform velocity; but the stone is not acted upon by gravity merely at the first instant of its fall; this power continues to impel it during the whole time of its descent, and it is this continued impulse which accelerates its motion.

_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 accumulated 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 _quantity of matter_, multiplied by its _quantity 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 quantity of matter, should have been _added_ to the quantity 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 quantity 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 space by yards and miles, and weight by pounds and ounces, that I still want to associate 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 spaces, 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 space 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 quantity 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 balls 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 quantity 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 balls 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 balls 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 balls are, and when their masses 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 balls 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 balls 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?