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(40.) The quality of matter which is of all others the most important in mechanical investigations, is that which has been called Inertia.

Matter is incapable of spontaneous change. This is one of the earliest and most universal results of human observation: it is equivalent to stating that mere matter is deprived of life; for spontaneous action is the only test of the presence of the living principle. If we see a mass of matter undergo any change, we never seek for the cause of that change in the body itself; we look for some external cause producing it. This inability for voluntary change of state or qualities is a more general principle than inertia. At any given moment of time a body must be in one or other of two states, rest or motion. Inertia, or inactivity, signifies the total absence of power to change this state. A body endued with inertia cannot of itself, and independent of all external influence, commence to move from a state of rest; neither can it when moving arrest its progress and become quiescent.

(41.) The same property by which a body is unable by any power of its own to pass from a state of rest to one of motion, or vice versâ, also renders it incapable of increasing or diminishing any motion which it may have received from an external cause. If a body be moving in a certain direction at the rate of ten miles per hour, it cannot by any energy of its own change its rate of motion to eleven or nine miles an hour. This is a direct consequence of that manifestation of inertia which has just been explained. For the same power which would cause a body moving at ten miles an hour to increase its rate to eleven miles, would also cause the same body at rest to commence moving at the rate of one mile an hour; and the same power which would cause a body moving at the rate of ten miles an hour to move at the rate of nine miles in the hour, would cause the same body moving at the rate of one mile an hour to become quiescent. It therefore appears, that to increase or diminish the motion of a body is an effect of the same kind as to change the state of rest into that of motion, or vice versâ.

(42.) The effects and phenomena which hourly fall under our observation afford unnumbered examples of the inability of lifeless matter to put itself into motion, or to increase any motion which may have been communicated to it. But it does not happen that we have the same direct and frequent evidence of its inability to destroy or diminish any motion which it may have received. And hence it arises, that while no one will deny to matter the former effect of inertia, few will at first acknowledge the latter. Indeed, even so late as the time of Kepler, philosophers themselves held it as a maxim, that “matter is more inclined to rest than to motion;” we ought not, therefore, to be surprised if in the present day those who have not been conversant with physical science are slow to believe that a body once put in motion would continue for ever to move with the same velocity, if it were not stopped by some external cause.

Reason, assisted by observation, will, however, soon dispel this illusion. Experience shows us in various ways, that the same causes which destroy motion in one direction are capable of producing as much motion in the opposite direction. Thus, if a wheel, spinning on its axis with a certain velocity, be stopped by a hand seizing one of the spokes, the effort which accomplishes this is exactly the same as, had the wheel been previously at rest, would have put it in motion in the opposite direction with the same velocity. If a carriage drawn by horses be in motion, the same exertion of power in the horses is necessary to stop it, as would be necessary to back it, if it were at rest. Now, if this be admitted as a general principle, it must be evident that a body which can destroy or diminish its own motion must also be capable of putting itself into motion from a state of rest, or of increasing any motion which it has received. But this latter is contrary to all experience, and therefore we are compelled to admit that a body cannot diminish or destroy any motion which it has received.

Let us enquire why we are more disposed to admit the inability of matter to produce than to destroy motion in itself. We see most of those motions which take place around us on the surface of the earth subject to gradual decay, and if not renewed from time to time, at length cease. A stone rolled along the ground, a wheel revolving on its axis, the heaving of the deep after a storm, and all other motions produced in bodies by external causes, decay, when the exciting cause is suspended; and if that cause do not renew its action, they ultimately cease.

But is there no exciting cause, on the other hand, which thus gradually deprives those bodies of their motion?—and if that cause were removed, or its intensity diminished, would not the motion continue, or be more slowly retarded? When a stone is rolled along the ground, the inequalities of its shape as well as those of the ground are impediments, which retard and soon destroy its motion. Render the stone round, and the ground level, and the motion will be considerably prolonged. But still small asperities will remain on the stone, and on the surface over which it rolls: substitute for the stone a ball of highly-polished steel, moving on a highly-polished steel plane, truly level, and the motion will continue without sensible diminution for a very long period; but even here, and in every instance of motions produced by art, minute asperities must exist on the surfaces which move in contact with each other, which must resist, gradually diminish, and ultimately destroy the motion.

Independently of the obstructions to the continuation of motion arising from friction, there is another impediment to which all motions on the surface of the earth are liable—the resistance of the air. How much this may affect the continuation of motion appears by many familiar effects. On a calm day carry an open umbrella with its concave side presented in the direction in which you are moving, and a powerful resistance will be opposed to your progress, which will increase with every increase of the speed with which you move.

(43.) We are not, however, without direct experience to prove, that motions when unresisted will for ever continue. In the heavens we find an apparatus, which furnishes a sublime verification of this principle. There, removed from all casual obstructions and resistances, the vast bodies of the universe roll on in their appointed paths with unerring regularity, preserving without diminution all that motion which they received at their creation from the hand which launched them into space. This alone, unsupported by other reasons, would be sufficient to establish the quality of inertia; but viewed in connection with the other circumstances previously mentioned, no doubt can remain that this is an universal law of nature.

(44.) It has been proved, that inability to change the quantity of motion is a consequence of inertia. The inability to change the direction of motion is another consequence of this quality. The same cause which increases or diminishes motion, would also give motion to a body at rest; and therefore we infer that the same inability which prevents a body from moving itself, will also prevent it from increasing or diminishing any motion which it has received. In the same manner we can show, that any cause which changes the direction of motion would also give motion to a body at rest; and therefore if a body change the direction of its own motion, the same body might move itself from a state of rest; and therefore the power of changing the direction of any motion which it may have received is inconsistent with the quality of inertia.

(45.) If a body, moving from A, fig.3. to B, receive at Ba blow in the direction CBE, it will immediately change its direction to that of another line BD. The cause which produces this change of direction would have put the body in motion in the direction BE, had it been quiescent at B when it sustained the blow.

(46.) Again, suppose GH to be a hard plane surface; and let the body be supposed to be perfectly inelastic. When it strikes the surface at B, it will commence to move along it in the direction BH. This change of direction is produced by the resistance of the surface. If the body, instead of meeting the surface in the direction AB, had moved in the direction EB, perpendicular to it, all motion would have been destroyed, and the body reduced to a state of rest.

(47.) By the former example it appears that the deflecting cause would have put a quiescent body in motion, and by the latter it would have reduced a moving body to a state of rest. Hence the phenomenon of a change of direction is to be referred to the same class as the change from rest to motion, or from motion to rest. The quality of inertia is, therefore, inconsistent with any change in the direction of motion which does not arise from an external cause.

(48.) From all that has been here stated, we may infer generally, that an inanimate parcel of matter is incapable of changing its state of rest or motion; that, in whatever state it be, in that state it must for ever continue, unless disturbed by some external cause; that if it be in motion, that motion must always be uniform, or must proceed at the same rate, equal spaces being moved over in the same time: any increase of its rate must betray some impelling cause; any diminution must proceed from an impeding cause, and neither of these causes can exist in the body itself; that such motion must not only be constantly at the same uniform rate, but also must be always in the same direction, any deflection from one uniform direction necessarily arising from some external influence.

The language sometimes used to explain the property of inertia in popular works, is eminently calculated to mislead the student. The terms resistance and stubbornness to move are faulty in this respect. Inertia implies absolute passiveness, a perfect indifference to rest or motion. It implies as strongly the absence of all resistance to the reception of motion, as it does the absence of all power to move itself. The term vis inertiæ or force of inactivity, so frequently used even by authors pretending to scientific accuracy, is still more reprehensible. It is a contradiction in terms; the term inactivity implying the absence of all force.

(49.) Before we close this chapter, it may be advantageous to point out some practical and familiar examples of the general law of inertia. The student must, however, recollect, that the great object of science is generalisation, and that his mind is to be elevated to the contemplation of the laws of nature, and to receive a habit the very reverse of that which disposes us to enjoy the descent from generals to particulars. Instances, taken from the occurrences of ordinary life, may, however, be useful in verifying the general law, and in impressing it upon the memory; and for this reason, we shall occasionally in the present treatise refer to such examples; always, however, keeping them in subservience to the general principles of which they are manifestations, and on which the attention of the student should never cease to be fixed.

(50.) If a carriage, a horse, or a boat, moving with speed, be suddenly retarded or stopped, by any cause which does not at the same time affect passengers, riders, or any loose bodies which are carried, they will be precipitated in the direction of the motion; because by reason of their inertia, they persevere in the motion which they shared in common with that which transported them, and are not deprived of that motion by the same cause.

(51.) If a passenger leap from a carriage in rapid motion, he will fall in the direction in which the carriage is moving at the moment his feet meet the ground; because his body, on quitting the vehicle, retains, by its inertia, the motion which it had in common with it. When he reaches the ground, this motion is destroyed by the resistance of the ground to the feet, but is retained in the upper and heavier part of the body; so that the same effect is produced as if the feet had been tripped.

(52.) When a carriage is once put in motion with a determinate speed on a level road, the only force necessary to sustain the motion is that which is sufficient to overcome the friction of the road; but at starting a greater expenditure of force is necessary, inasmuch as not only the friction is to be overcome, but the force with which the vehicle is intended to move must be communicated to it. Hence we see that horses make a much greater exertion at starting than subsequently, when the carriage is in motion; and we may also infer the inexpediency of attempting to start at full speed, especially with heavy carriages.

(53.) Coursing owes all its interest to the instinctive consciousness of the nature of inertia which seems to govern the measures of the hare. The greyhound is a comparatively heavy body moving at the same or greater speed in pursuit. The hare doubles, that is, suddenly changes the direction of her course, and turns back at an oblique angle with the direction in which she had been running. The greyhound, unable to resist the tendency of its body to persevere in the rapid motion it had acquired, is urged forward many yards before it is able to check its speed and return to the pursuit. Meanwhile the hare is gaining ground in the other direction, so that the animals are at a very considerable distance asunder when the pursuit is recommenced. In this way a hare, though much less fleet than a greyhound, will often escape it.

In racing, the horses shoot far beyond the winning-post before their course can be arrested.