Chapter IV: Introduction: General Properties of Bodies. Impenetrability. Extension (2)

_Mrs. B._ The diminution of the force of gravity, at so small a distance as that to which the atmosphere extends (compared with the size of the earth) is so inconsiderable as to be scarcely sensible; but the pressure of the upper parts of the atmosphere on those beneath, renders the air near the surface of the earth much more dense than in the upper regions. The pressure of the atmosphere has been compared to that of a pile of fleeces of wool, in which the lower fleeces are pressed together by the weight of those above; these lie light and loose, in proportion as they approach the uppermost fleece, which receives no external pressure, and is confined merely by the force of its own gravity.

_Emily._ I do not understand how it is that the air can be springy or elastic, as the particles of which it is composed must, according to the general law, attract each other; yet their elasticity, must arise from a tendency to recede from each other.

_Mrs. B._ Have you forgotten what I told you respecting the effects of heat, a fluid so subtile that it readily pervades all substances, and even in solid bodies, counteracts the attraction of cohesion? In air the quantity of heat interposed is so great, as to cause its particles actually to repel each other, and it is to this that we must ascribe its elasticity; this, however, does not prevent the earth from exerting its attraction upon the individual particles of which it consists.

_Caroline._ It has just occurred to me that there are some bodies which do not gravitate towards the earth. Smoke and steam, for instance, rise instead of falling.

_Mrs. B._ It is still gravity which produces their ascent; at least, were that power destroyed, these bodies would not rise.

_Caroline._ I shall be out of conceit with gravity, if it is so inconsistent in its operations.

_Mrs. B._ There is no difficulty in reconciling this apparent inconsistency of effect. The air near the earth is heavier than smoke, steam, or other vapours; it consequently not only supports these light bodies, but forces them to rise, till they reach a part of the atmosphere, the weight of which is not greater than their own, and then they remain stationary. Look at this bason of water; why does the piece of paper which I throw into it float on the surface?

_Emily._ Because, being lighter than the water, it is supported by it.

_Mrs. B._ And now that I pour more water into the bason, why does the paper rise?

_Emily._ The water being heavier than the paper, gets beneath it, and obliges it to rise.

_Mrs. B._ In a similar manner are smoke and vapour forced upwards by the air; but these bodies do not, like the paper, ascend to the surface of the fluid, because, as we observed before, the air being less dense, and consequently lighter as it is more distant from the earth, vapours rise only till they attain a region of air of their own density. Smoke, indeed ascends but a very little way; it consists of minute particles of fuel, carried up by a current of heated air, from the fire below: heat, you recollect, expands all bodies; it consequently rarefies air, and renders it lighter than the colder air of the atmosphere; the heated air from the fire carries up with it vapour and small particles of the combustible materials which are burning in the fire. When this current of hot air is cooled by mixing with the atmosphere, the minute particles of coal, or other combustible, fall; it is this which produces the small black flakes which render the air, and every thing in contact with it, in London, so dirty.

_Caroline._ You must, however, allow me to make one more objection to the universal gravity of bodies; which is the ascent of air balloons, the materials of which are undoubtedly heavier than air: how, therefore, can they be supported by it?

_Mrs. B._ I admit that the materials of which balloons are made are heavier than the air; but the air with which they are filled is an elastic fluid, of a different nature from atmospheric air, and considerably lighter; so that on the whole the balloon is lighter than the air which it displaces, and consequently will rise, on the same principle as smoke and vapour. Now, Emily, let me hear if you can explain how the gravity of bodies is modified by the effect of the air?

_Emily._ The air forces bodies which are lighter than itself to ascend; those that are of an equal weight will remain stationary in it; and those that are heavier will descend through it: but the air will have some effect on these last; for if they are not much heavier, they will with difficulty overcome the resistance they meet with in passing through it, they will be borne up by it, and their fall will be more or less retarded.

_Mrs. B._ Very well. Observe how slowly this light feather falls to the ground, while a heavier body, like this marble, overcomes the resistance which the air makes to its descent much more easily, and its fall is proportionally more rapid. I now throw a pebble into this tub of water; it does not reach the bottom near so soon as if there were no water in the tub, because it meets with resistance from the water. Suppose that we could empty the tub, not only of water, but of air also, the pebble would then fall quicker still, as it would in that case meet with no resistance at all to counteract its gravity.

Thus you see that it is not the different degrees of gravity, but the resistance of the air, which prevents bodies of different weight from falling with equal velocities; if the air did not bear up the feather, it would reach the ground as soon as the marble.

_Caroline._ I make no doubt that it is so; and yet I do not feel quite satisfied. I wish there was any place void of air, in which the experiment could be made.

_Mrs. B._ If that proof will satisfy your doubts, I can give it you. Here is a machine called an _air pump_, (fig. 2. pl. 1.) by means of which the air may be expelled from any close vessel which is placed over this opening, through which the air is pumped out. Glasses of various shapes, usually called receivers, are employed for this purpose. We shall now exhaust the air from this tall receiver which is placed over the opening, and we shall find that bodies within it, whatever their weight or size, will fall from the top to the bottom in the same space of time.

_Caroline._ Oh, I shall be delighted with this experiment; what a curious machine! how can you put the two bodies of different weight within the glass, without admitting the air?

_Mrs. B._ A guinea and a feather are already placed there for the purpose of the experiment: here is, you see, a contrivance to fasten them in the upper part of the glass; as soon as the air is pumped out, I shall turn this little screw, by which means the brass plates which support them will be removed, and the two bodies will fall.--Now I believe I have pretty well exhausted the air.

_Caroline._ Pray let me turn the screw.--I declare, they both reached the bottom at the same instant! Did you see, Emily, the feather appeared as heavy as the guinea?

_Emily._ Exactly; and fell just as quickly. How wonderful this is! what a number of entertaining experiments might be made with this machine!

_Mrs. B._ No doubt there are a great many; but we shall reserve them to elucidate the subjects to which they relate: if I had not explained to you why the guinea, and the feather fell with equal velocity, you would not have been so well pleased with the experiment.

_Emily._ I should have been as much surprised, but not so much interested; besides, experiments help to imprint on the memory the facts they are intended to illustrate; it will be better therefore for us to restrain our curiosity, and wait for other experiments in their proper places.

_Caroline._ Pray by what means is this receiver exhausted of its air?

_Mrs. B._ You must learn something of mechanics in order to understand the construction of a pump. At our next meeting, therefore, I shall endeavour to make you acquainted with the laws of motion, as an introduction to that subject.

Questions

1. (Pg. 22) What are those properties of bodies called, which are not common to all?

2. (Pg. 23) Why are they so called?

3. (Pg. 23) What is the cause of weight in bodies?

4. (Pg. 23) What is the reason that all bodies near to the surface of the earth, are drawn towards it?

5. (Pg. 24) If attraction is the cause of weight, could you suppose it possible for a body to possess the former and not the latter property?

6. (Pg. 24) When a stone falls to the ground, in which of the two bodies does the power of attraction exist?

7. (Pg. 24) If the attraction be mutual, why does not the earth approach the stone, as much as the stone approaches the earth?

8. (Pg. 24) If attraction be in proportion to the mass, why does not a hill, draw towards itself, a house placed near it?

9. (Pg. 25) How can the attraction of a mountain be rendered sensible?

10. (Pg. 25) Why cannot two lines which are perpendicular to the surface of the earth be parallel to each other?

11. (Pg. 26) Draw a small figure of the earth to exemplify this, as in fig. 1. plate 1.

12. (Pg. 27) If bodies were not resisted by the air, those which are light, would fall as quickly as those which are heavy, how can you account for this?

13. (Pg. 27) What then is the reason that a book, and a sheet of paper, let fall from the same height, will not reach the ground in the same time?

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?

_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 balls 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 balls 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, butter, &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 spaces 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?

_Mrs. B._ You will not in general find this rule hold good; for liquids have scarcely any elasticity, whilst hard bodies are eminent for this property, though the latter are certainly of much greater density than the former; elasticity implies, therefore, not only a susceptibility of compression, but depends upon the power possessed by the body, of resuming its former state after compression, in consequence of the peculiar arrangement of its particles.

_Caroline._ But surely there can be no pores in ivory and metals, Mrs. B.; how then can they be susceptible of compression?

_Mrs. B._ The pores of such bodies are invisible to the naked eye, but you must not thence conclude that they have none; it is, on the contrary, well ascertained that gold, one of the most dense of all bodies, is extremely porous; and that these pores are sufficiently large to admit water when strongly compressed, to pass through them. This was shown by a celebrated experiment made many years ago at Florence.

_Emily._ If water can pass through gold, there must certainly be pores or interstices which afford it a passage; and if gold is so porous, what must other bodies be, which are so much less dense than gold!

_Mrs. B._ The chief difference in this respect, is I believe, that the pores in some bodies are larger than in others; in cork, sponge and bread, they form considerable cavities; in wood and stone, when not polished, they are generally perceptible to the naked eye; whilst in ivory, metals, and all varnished and polished bodies, they cannot be discerned. To give you an idea of the extreme porosity of bodies, sir Isaac Newton conjectured that if the earth were so compressed as to be absolutely without pores, its dimensions might possibly not be more than a cubic inch.

_Caroline._ What an idea! Were we not indebted to sir Isaac Newton for the theory of attraction, I should be tempted to laugh at him for such a supposition. What insignificant little creatures we should be!

_Mrs. B._ If our consequence arose from the size of our bodies, we should indeed be but pigmies, but remember that the mind of Newton was not circumscribed by the dimensions of its envelope.

_Emily._ It is, however, fortunate that heat keeps the pores of matter open and distended, and prevents the attraction of cohesion from squeezing us into a nut-shell.

_Mrs. B._ Let us now return to the subject of reaction, on which we have some further observations to make. It is because reaction is in its direction opposite to action, that _reflected motion_ is produced. If you throw a ball against the wall, it rebounds; this return of the ball is owing to the reaction of the wall against which it struck, and is called _reflected motion_.

_Emily._ And I now understand why balls filled with air rebound better than those stuffed with bran or wool; air being most susceptible of compression and most elastic, the reaction is more complete.

_Caroline._ I have observed that when I throw a ball straight against the wall, it returns straight to my hand; but if I throw it obliquely upwards, it rebounds still higher, and I catch it when it falls.

_Mrs. B._ You should not say straight, but perpendicularly against the wall; for straight is a general term for lines in all directions which are neither curved nor bent, and is therefore equally applicable to oblique or perpendicular lines.

_Caroline._ I thought that perpendicularly meant either directly upwards or downwards?

_Mrs. B._ In those directions lines are perpendicular to the earth. A perpendicular line has always a reference to something towards which it is perpendicular; that is to say, that it inclines neither to the one side or the other, but makes an equal angle on every side. Do you understand what an angle is?

_Caroline._ Yes, I believe so: it is the space contained between two lines meeting in a point.

_Mrs. B._ Well then, let the line A B (plate 2. fig. 1.) represent the floor of the room, and the line C D that in which you throw a ball against it; the line C D, you will observe, forms two angles with the line A B, and those two angles are equal.

_Emily._ How can the angles be equal, while the lines which compose them are of unequal length?

_Mrs. B._ An angle is not measured by the length of the lines, but by their opening, or the space between them.

_Emily._ Yet the longer the lines are, the greater is the opening between them.

_Mrs. B._ Take a pair of compasses and draw a circle over these spaces, making the angular point the centre.

_Emily._ To what extent must I open the compasses?

_Mrs. B._ You may draw the circle what size you please, provided that it cuts the lines of the angles we are to measure. All circles, of whatever dimensions, are supposed to be divided into 360 equal parts, called degrees; the opening of an angle, being therefore a portion of a circle, must contain a certain number of degrees: the larger the angle the greater is the number of degrees, and two angles are said to be equal, when they contain an equal number of degrees.

_Emily._ Now I understand it. As the dimension of an angle depends upon the number of degrees contained between its lines, it is the opening, and not the length of its lines, which determines the size of the angle.

_Mrs. B._ Very well: now that you have a clear idea of the dimensions of angles, can you tell me how many degrees are contained in the two angles formed by one line falling perpendicularly on another, as in the figure I have just drawn?

_Emily._ You must allow me to put one foot of the compasses at the point of the angles, and draw a circle round them, and then I think I shall be able to answer your question: the two angles are together just equal to half a circle, they contain therefore 90 degrees each; 90 degrees being a quarter of 360.

_Mrs. B._ An angle of 90 degrees or one-fourth of a circle is called a right angle, and when one line is perpendicular to another, and distant from its ends, it forms, you see, (fig. 1.) a right angle on either side. Angles containing more than 90 degrees are called obtuse angles, (fig. 2.) and those containing less than 90 degrees are called acute angles, (fig. 3.)

_Caroline._ The angles of this square table are right angles, but those of the octagon table are obtuse angles; and the angles of sharp pointed instruments are acute angles.

_Mrs. B._ Very well. To return now to your observation, that if a ball is thrown obliquely against the wall, it will not rebound in the same direction; tell me, have you ever played at billiards?

_Caroline._ Yes, frequently; and I have observed that when I push the ball perpendicularly against the cushion, it returns in the same direction; but when I send it obliquely to the cushion, it rebounds obliquely, but on an opposite side; the ball in this latter case describes an angle, the point of which is at the cushion. I have observed too, that the more obliquely the ball is struck against the cushion, the more obliquely it rebounds on the opposite side, so that a billiard player can calculate with great accuracy in what direction it will return.

_Mrs. B._ Very well. This figure (fig. 4. plate 2.) represents a billiard table; now if you draw a line A B from the point where the ball A strikes perpendicular to the cushion, you will find that it will divide the angle which the ball describes into two parts, or two angles; the one will show the obliquity of the direction of the ball in its passage towards the cushion, the other its obliquity in its passage back from the cushion. The first is called _the angle of incidence_, the other _the angle of reflection_; and these angles are always equal, if the bodies are perfectly elastic.

_Caroline._ This then is the reason why, when I throw a ball obliquely against the wall, it rebounds in an opposite oblique direction, forming equal angles of incidence and of reflection.

_Mrs. B._ Certainly; and you will find that the more obliquely you throw the ball, the more obliquely it will rebound.

We must now conclude; but I shall have some further observations to make upon the laws of motion, at our next meeting.

Questions

1. (Pg. 32) On what is the science of mechanics founded?

2. (Pg. 32) In what does motion consist?

3. (Pg. 33) What is the consequence of inertia, on a body at rest?

4. (Pg. 33) What do we call that which produces motion?

5. (Pg. 33) Give some examples.

6. (Pg. 33) What may we say of gravity, of cohesion, and of heat, as forces?

7. (Pg. 33) How will a body move, if acted on by a single force?

8. (Pg. 33) What is the reason of this?

9. (Pg. 33) What do we intend by the term velocity, and to what is it proportional?

10. (Pg. 33) Velocity is divided into absolute and relative; what is meant by absolute velocity?

11. (Pg. 33) How is relative velocity distinguished?

12. (Pg. 34) How do we measure the velocity of a body?

13. (Pg. 34) The time?

14. (Pg. 34) The space?

15. (Pg. 34) What is uniform motion? and give an example.

16. (Pg. 34) How is uniform motion produced?

17. (Pg. 34) A ball struck by a bat gradually loses its motion; what causes produce this effect?

18. (Pg. 35) If gravity did not draw a projected body towards the earth, and the resistance of the air were removed, what would be the consequence?

19. (Pg. 35) In this case would not a great degree of force be required to produce a continued motion?

20. (Pg. 35) What is retarded motion?

21. (Pg. 35) Give some examples.

22. (Pg. 36) What is accelerated motion?

23. (Pg. 36) Give an example.

24. (Pg. 36) Explain the mode in which gravity operates in producing this effect.

25. (Pg. 37) What number of feet will a heavy body descend in the first second of its fall, and at what rate will its velocity increase?

26. (Pg. 37) What is the difference in the time of the ascent and descent, of a stone, or other body thrown upwards?

27. (Pg. 37) By what reasoning is it proved that there is no difference?

28. (Pg. 38) What is meant by the momentum of a body?

29. (Pg. 38) How do we ascertain the momentum?

30. (Pg. 38) How may a light body have a greater momentum than one which is heavier?

31. (Pg. 38) Why must we _multiply_ the weight and velocity together in order to find the momentum?

32. (Pg. 39) When we represent weight and velocity by numbers, what must we carefully observe?

33. (Pg. 39) Why is it particularly important, to understand the nature of momentum?

34. (Pg. 39) What is meant by reaction, and what is the rule respecting it?

35. (Pg. 39) How is this exemplified by the ivory balls represented in plate 1. fig. 3?

36. (Pg. 40) Explain the manner in which the six balls represented in fig. 4, illustrate this fact.

37. (Pg. 40) What must be the nature of bodies, in which the whole motion is communicated from one to the other?

38. (Pg. 40) What is the result if the balls are not elastic, and how is this explained by fig. 5?

39. (Pg. 40) How will reaction assist us in explaining the flight of a bird?

40. (Pg. 40) How must their wings operate in enabling them to remain stationary, to rise, and to descend?

41. (Pg. 41) Why cannot a man fly by the aid of wings?

42. (Pg. 41) How does reaction operate in enabling us to swim, or to row a boat?

43. (Pg. 41) What constitutes elasticity?

44. (Pg. 41) Give some examples.

45. (Pg. 41) What name is given to air, and for what reason?

46. (Pg. 41) What hard bodies are mentioned as elastic?

47. (Pg. 41) Do elastic bodies exhibit any indentation after a blow? and why not?

48. (Pg. 42) What do we conclude from elasticity respecting the contact of the particles of a body?

49. (Pg. 42) Are those bodies always the most elastic, which are the least dense?

50. (Pg. 42) Give examples to prove that this is not the case.

51. (Pg. 42) All bodies are believed to be porous, what is said on this subject respecting gold?

52. (Pg. 43) What conjecture was made by sir Isaac Newton, respecting the porosity of bodies in general?

53. (Pg. 43) If you throw an elastic body against a wall, it will rebound; what is this occasioned by, and what is this return motion called?

54. (Pg. 43) What do we mean by a perpendicular line?

55. (Pg. 43) What is an angle?

56. (Pg. 43) What is represented by fig. 1. plate 2?

57. (Pg. 44) Have the length of the lines which meet in a point, any thing to do with the measurement of an angle?

58. (Pg. 44) What use can we make of compasses in measuring an angle?

59. (Pg. 44) Into what number of parts do we suppose a whole circle divided, and what are these parts called?

60. (Pg. 44) When are two angles said to be equal?

61. (Pg. 44) Upon what does the dimension of an angle depend?

62. (Pg. 44) What number of degrees, and what portion of a circle is there in a right angle?

63. (Pg. 44) How must one line be situated on another to form two right angles? (fig. 1.)

64. (Pg. 44) Figure 2 represents an angle of more than 90 degrees, what is that called?

65. (Pg. 44) What are those of less than 90 degrees called as in fig. 3?

66. (Pg. 45) If you make an elastic ball strike a body at right angles, how will it return?

67. (Pg. 45) How if it strikes obliquely?

68. (Pg. 45) Explain by fig. 4 what is meant by the angles of incidence and of reflection.

CONVERSATION IV.

ON COMPOUND MOTION.

COMPOUND MOTION, THE RESULT OF TWO OPPOSITE FORCES. OF CURVILINEAR MOTION, THE RESULT OF TWO FORCES. CENTRE OF MOTION, THE POINT AT REST WHILE THE OTHER PARTS OF THE BODY MOVE ROUND IT. CENTRE OF MAGNITUDE, THE MIDDLE OF A BODY. CENTRIPETAL FORCE, THAT WHICH IMPELS A BODY TOWARDS A FIXED CENTRAL POINT. CENTRIFUGAL FORCE, THAT WHICH IMPELS A BODY TO FLY FROM THE CENTRE. FALL OF BODIES IN A PARABOLA. CENTRE OF GRAVITY, THE POINT ABOUT WHICH THE PARTS BALANCE EACH OTHER.

MRS. B.

I must now explain to you the nature of compound motion. Let us suppose a body to be struck by two equal forces in opposite directions, how will it move?

_Emily._ If the forces are equal, and their directions are in exact opposition to each other, I suppose the body would not move at all.

_Mrs. B._ You are perfectly right; but suppose the forces instead of acting upon the body in direct opposition to each other, were to move in lines forming an angle of ninety degrees, as the lines Y A, X A, (fig. 5. plate 2.) and were to strike the ball A, at the same instant; would it not move?