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.

r.e.t.a.r.dED 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 pa.s.siveness, 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 ill.u.s.trations 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 s.p.a.ce, 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 s.p.a.ce 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 s.p.a.ce 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 s.p.a.ce, 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 s.p.a.ce divided by the velocity; since the s.p.a.ce, 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 s.p.a.ce 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 _r.e.t.a.r.ded_ 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 pa.s.ses over equal s.p.a.ces 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 quant.i.ty 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 pa.s.sage, 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 _r.e.t.a.r.ded motion_?

_Caroline._ r.e.t.a.r.ded 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._ r.e.t.a.r.ded 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 r.e.t.a.r.ded 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 ill.u.s.tration of the stone r.e.t.a.r.ded 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 r.e.t.a.r.ded 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.