Illustrations of the Third Law.

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velocity, which is rapidly checked by the friction between the guncarriage and the ground. Were the cannon fired from a balloon, however, the reaction would be more marked.

The recoil of a light fowling-piece may hurt the shoulder, unless the piece be held close to it so as to form one mass with the body. A ship in chase, by firing her bow-guns retards her motion; by firing from her stern she quickens it.

A ship firing a broadside heels or inclines to the opposite side. A vessel of water suspended by a cord hangs perpendicularly; but if a hole be opened in one side the vessel will be pushed to the other side by the reaction of the jet, and will so remain while it flows. If the hole and jet be oblique, the vessel will constantly turn round in the direction opposite to the flow of the water.

A vessel of water placed upon a floating piece of plank, and allowed to throw out a jet, as in the last case, moves the plank in the opposite direction.

A steamboat may be driven by making the engine pump or squirt water from the stern, instead of making it, as usual, move paddlewheels. There is a great waste of power, however, in this mode of applying force, as will be explained under "Hydraulics."

The propelling force in rowing, in swimming, or in the motion of a steamer, is just equal and contrary to the force with which the water is pushed backwards.

The upward motion of a bird in flying is equal and opposite to the momentum with which its wings strike the air.

A sky-rocket, in like manner, ascends from the reaction of the force with which the exploding gas pushes against the air.

169. A bent spring, allowed to unbend between two masses, pushes both apart with equal force; only the greater the difference in the amounts of the masses, the greater will be the difference of velocity produced by this mutual action. If the one mass be very small compared with the other, the small one alone will seem to be repelled, and the other will appear merely to resist the motion.

Similar to this is the case of a person jumping up or throwing up a stone; his secret power of exerting force is like that of the bent spring, only of a more hidden and complex character: and the effort which projects either the stone or the person himself, throws the earth backwards, though imperceptibly.

So when a horse drags a boat on a canal, the force with which the boat moves is at the same instant communicated, through the frictional connection between the horse and the ground, to the

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Action and Reaction equal and opposite.

earth in a backward push of equal amount. If the horse were moving on ice, and the friction insufficient to connect the horse and the earth as one mass for the instant, then in attempting to pull a heavy boat the horse would move backwards himself faster than the boat would move forwards.

A man pushing against the ground with a stick may be considered to be compressing a spring between the earth and the end of his stick, which spring is therefore pushing him up as much as he pushes down; and if, at the time, he were balanced in the scale of a weighing beam, he would find that he weighed just as much less as he pressed down with his stick.

170. The truth of this law is well shown by the impact or concussion of elastic balls-as those made of ivory or glass.

When one billiard-ball strikes directly another ball of equal size it stops, and the second ball proceeds with the whole velocity which the first had the action which imparts the new motion being equal to the reaction which destroys the old. Although the transference of motion, in such a case, seems to be instantaneous, the change is really progressive, and as follows. The approaching ball, at a certain point of time, has just given half of its motion to the other equal ball, and if both were of soft clay, they would then proceed in contact with half the original velocity; but, as they are elastic, the touching parts at the moment supposed are compressed like a spring between the balls, and by then expanding and exerting force equally both ways, they double the velocity of the foremost ball, and destroy altogether the motion of the one behind.

If a billiard-ball be propelled against the nearest one of a row of similar balls in contact, it comes to rest as in the case last described, while the farthest ball of the row darts off with its velocity-the intermediate balls having each received and transmitted the motion in an instant, without appearing themselves to move.

171. If there be no external matter to react upon there can be no change in the state of a body's motion. A person suspended in mid-air would be quite powerless to move through space, because he would have no matter outside of himself to push against.

This may be well illustrated by a simple experiment represented in figure 16. Suspend two similar billiard-balls by two strings of the same length from a cord stretched tight across a room or

Illustrations of Action and Reaction.

87

-D

between two chairs. If now the ball, A, be made to swing along the direction of the cord, C D, it will keep on swinging, because it can give up none of its motion to B in that direction. If, however, it be made to move across the line of the cord, C D, it causes the cord to vibrate, and gradually sets B vibrating too. But A cannot cause B to move without itself losing an equal motion. Thus, while B swings wider and wider, A is slowly brought to dead rest; and the state of matters just begins to be reversed, B giving up its motion to A and gradually stopping, till the situation is precisely the same as at the beginning of the experiment; this alternation of motion would go on long enough, were it not that the friction of the air gradually exhausts the whole of the motion, and brings both to rest.

A
Fig. 16.

B

So, if both balls be suspended from the same point, and if one ball hang at rest while the other is made to circle round it, the first will, by the twisting of the thread, be gradually set in motion, while the second is brought for a moment to dead rest in the centre of the circle described by the first.

It is the same in whatever way the motion is communicated; whether it be by gravity, or by the momentum of visible matter, or by the more secret forms of magnetism and electricity, the law of action and reaction is invariable. For instance, we may substitute two straight magnets for the balls in last experiment, and place them so as to have their like ends-say the two north poles -towards each other. If then we leave B at rest, and make the other swing, so that its north end comes near the north end of B, the two will repel each other, and B will begin gradually to swing too; but A is at the same time gradually brought to rest by the reaction of B on it. When A is brought to a dead halt, B begins to give A motion again at the expense of its own, and so they will continue to take and give their motions until the resistance of the air brings both to rest.

ន

D

N

N

A

B

Fig. 17.

Again, if we turn one of the magnets round so that the unlike or attracting ends face each other, the force spent by the vibrating magnet, A, in pulling B towards it, is lost to A itself; so that, while B is made to vibrate, A comes gradually to rest as before.

Such are but a few of the illustrations that might be given to show that, in every case of mutual action between two bodies,

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The Doctrine of Energy.

whether it be one of attraction or of repulsion, there is a simultaneous equal and opposite action produced: or, in other words, that the sum of the momenta in any two bodies remains unaltered by any mutual action between them.

"THE PRINCIPLE OF ENERGY."

172. These three laws are subservient to one grand general principle which had not been conceived in the days of Newton, nor till long afterwards, a principle having for its fundamental axiom that the absolute creation and absolute destruction of force are alike impossible within the range of our experience. It is known as the law of Energy, and a clear conception of it is at the bottom of all knowledge of modern Physics.

Energy."

173. A man is said to have great bodily energy when he is capable of overcoming many obstacles, or of getting through a great amount of labour or work. His work is the measure of his energy, and the translation of it into a visible form.

The blacksmith who shoes two horses while his rival shoes only one is said to exert double the energy of the other.

If a man and a horse be employed separately to raise coals from a mine, the horse will raise perhaps ten times as many as the man in the same time; he is thus said to possess ten times the energy or work-power of a man.

Again, a steam-engine might raise ten times as many coals as the horse can do; and, though inanimate, may in respect of its work-power be compared with a horse or a man.

These terms-energy and work—are employed in like manner in speaking of the power of a moving body to overcome any resistance— such as that of the air, or of gravity, or of a magnet, or of a spring, &c. Only they are used with a more definite meaning, inasmuch as the actions of inanimate matter are susceptible of more exact comparison and measurement than those of living beings.

A man's energy or power of doing work will vary from day to day —even from hour to hour-according to the state of his body, and often in a manner which there is no accounting for, owing to the complexity of the animal machine.

On the other hand, the penetrating power of a 50-lb. cannon ball

Work-Its Measure.

89

projected with a given weight of a given kind of gunpowder may be calculated with exactness.

174. In mechanics, then, Energy is the power of effecting work; and Work is the overcoming of resistance of any sort.

A bullet that just pierces through 300 leaves of a book has been projected with triple the Energy of one that can pierce only 100 of these leaves; and if the former would reach 600 feet shot vertically up, the latter would reach only 200 feet.

The strength or energy of a man's arm is often measured by the extent to which he can overcome the clasticity of a spring either by a fair pull, or by a blow.

"The principle of the measure of Work."

175. For the precise estimate of the amount of Work-power in any moving mass, we must agree on some definable amount of esistance offered to some definite quantity of matter or mass; and we might select for this purpose any constant and reliable resistance.

On seeking for a standard of measure among the various resistances that have to be overcome, such as the resistance of the air, or of water, the friction of sliding bodies, cohesion, as in a steel spring, magnetism, electricity, gravity, we find that none of them is so simple, so constant, and so easy of employment as gravity.

The resistance of the air is variable, because its weight depends on its temperature, which is very far from constant. We might, if we chose, select the resistance of water to, say, a square foot of plate moving at a given rate as a standard of comparison for the measureing of Work; but practically this would be inconvenient. Again, the friction between rubbing surfaces depends so much on the variable condition of smoothness that this would be equally unsuitable as a standard of reference. Magnetism and electricity are qualities more or less transitory, and are on that ground unfit for our purpose. Lastly, the resistance offered by the elasticity of a spring, or of a piece of india-rubber, or of a column of air, is dependent on a minute molecular condition which we have no certain means of gauging, and is therefore unavailable as an absolute and ultimate representative of Work.

On the other hand, the resistance which the earth offers to the lifting of a given mass is invariable at the same spot on the globe, and is withal so convenient, that it is greatly preferable to any other standard.