CHAPTER XI.The Laws of Motion.
We shall now make a few remarks on the general Laws of Motion by which all mechanicaleffects take place. Are we to consider these as instituted laws? and if so, can we point out any of the reasons which we may suppose to have led to the selection of those laws which really exist?
The observations formerly made concerning the inevitable narrowness and imperfection of our conclusions on such subjects, apply here, even more strongly than in the case of the law of gravitation. We can hardly conceive matter divested of these laws; and we cannot perceive or trace a millionth part of the effects which they produce. We cannot, therefore, expect to go far in pointing out the advantages of these laws such as they now obtain.
It would be easy to show that the fundamental laws of motion, in whatever form we state them, possess a very preeminent simplicity, compared with almost all others, which we might imagine as existing. This simplicity has indeed produced an effect on men’s minds which, though delusive, appears tobe very natural; several writers have treated these laws as self-evident, and necessarily flowing from the nature of our conceptions. We conceive that this is an erroneous view, and that these laws are known to us to be what they are, by experience only; that they might, so far as we can discern, have been any others. They appear therefore to be selected for their fitness to answer their purposes; and we may, perhaps, be able to point out some instances in which this fitness is apparent to us.
Newton, and many English philosophers, teach the existence ofthreeseparate fundamental laws of motion, while most of the eminent mathematicians of France reduce these totwo, the law of inertia and the law that force is proportioned to velocity. As an example of the views which we wish to illustrate, we may take the law of inertia, which is identical with Newton’s first Law of Motion. This law asserts, that a body at rest continues at rest, and that a body in motion goes on moving with its velocity and direction unchanged, except so far as it is acted on by extraneous forces.[24]
We conceive that this law, simple and universal as it is, cannot be shown to be necessarily true. It might be difficult to discuss this point in general terms with any clearness; but let us take the only example which we know of a motion absolutely uniform, in consequence of the absence of any force to accelerate or retard it;—this motion is the rotation of the earth on its axis.
1. It is scarcely possible that discussions on suchsubjects should not have a repulsive and scholastic aspect, and appear like disputes about words rather than things. For mechanical writers have exercised all their ingenuity so to circumscribe their notions and so to define their terms that these fundamental truths should be expressed in the simplest manner: the consequence of which has been, that they have been made to assume the appearance rather of identical assertions than of general facts of experience. But in order to avoid this inconvenience, as far as may be, let us take thefirst law of motionas exemplified in a particular case, the rotation of the earth. Of all the motions with which we are acquainted this is alone invariable. Each day, measured by the passages of the stars, is so precisely of the same length that, according to Laplace’s calculations, it is impossible that a difference of hundredth of a second of time should have obtained between the length of the day in the earliest ages and at the present time. Now why is this? How is this very remarkable uniformity preserved in this particular phenomenon, while all the other motions of the system are subject to inequalities? How is it that in the celestial machine no retardation takes place by the lapse of time, as would be the case in any machine which it would be possible for human powers to construct? The answer is, that in the earth’s revolution on her axis no cause operates to retard the speed, like the imperfection of materials, the friction of supports, the resistance of the ambient medium; impediments which cannot, in any human mechanism, however perfect, be completely annihilated. But here we are led to ask again, why should the speed continue the same when not affected by an extraneous cause? Why should it not languish and decay of itself by the mere lapse of time? That it might do so, involves no contradiction, for it was the common, though erroneous, belief of all mechanical speculators, to the time of Galileo. We can conceive velocity to diminish in proceeding from a certain point of time, as easily aswe can conceive force to diminish in proceeding from a certain point of space, which in attractive forces really occurs. But, it is sometimes said, themotion(that is the velocity)mustcontinue the same from one instant to another, for there is nothing to change it. This appears to be taking refuge in words. We may call the velocity, that is the speed of a body, its motion; but we cannot, by giving it this name, make it athingwhich has anyà prioriclaim to permanence, much less any self-evident constancy. Why must the speed of a body, left to itself, continue the same, any more than its temperature? Hot bodies grow cooler of themselves, why should not quick bodies go slower of themselves? Why must a body describe one thousand feet in the next second because it has described one thousand feet in the last? Nothing but experience, under proper circumstances, can inform us whether bodies, abstracting from external agency, do move according to such a rule. We find that they do so, we learn that all diminution of their speed which ever takes place, can be traced to external causes. Contrary to all that men had guessed, motion appears to be of itself endless and unwearied. In order to account for the unalterable permanence of the length of our day, all that is requisite is to show that there is no let or hindrance in the way of the earth’s rotation;—no resisting medium or alteration of size,—she “spinningsleeps” on her axle, as the poet expresses it, and may go on sleeping with the same regularity for ever, so far as the experimental properties of motion are concerned.
Such is the necessary consequence of the first law of motion; but the law itself has no necessary existence, so far as we can see. It was discovered only after various perplexities and false conjectures of speculators on mechanics. We have learnt that it is so, but we have not learnt, nor can any one undertake to teach us, that it must have been so. For aught we can tell, it is one among a thousand equallypossible laws, which might have regulated the motions of bodies.
2. But though we have thus no reason to consider this as the only possible law, we have good reason to consider it as the best, or at least as possessing all that we can conceive of advantage. It is thesimplestconceivable of such laws. If the velocity had been compelled to change with the time, there must have been a law of the change, and the kind and amount of this change must have been determined by its dependence on the time and other conditions. This, though quite supposable, would undoubtedly have been more complex than the present state of things. And though complexity does not appear to embarrass the operations of the laws of nature, and is admitted, without scruple, when there is reason for it, simplicity is the usual character of such laws, and appears to have been a ground of selection in the formation of the universe, as it is a mark of beauty to us in our contemplation of it.
But there is a still stronger apparent reason for the selection of this law of the preservation of motion. If the case had been otherwise, the universe must necessarily in the course of ages have been reduced to a state of rest, or at least to a state not sensibly differing from it. If the earth’s motion, round its axis, had slackened by a very small quantity, for instance, by a hundredth of a second in a revolution, and in this proportion continued, the day would have been already lengthened by six hours in the six thousand years which have elapsed since the history of the world began; and if we suppose a longer period to precede or to follow, the day might be increased to a month or to any length. All the adaptations which depend on the length of the day would consequently be deranged. But this would not be all; for the same law of motion is equally requisite for the preservation of the annual motion of the earth. If her motion were retarded by the establishment of any other law instead of the existing one,she would wheel nearer and nearer to the sun at every revolution, and at last reach the centre, like a falling hoop. The same would happen to the other planets; and the whole solar system would, in the course of a certain period, be gathered into a heap of matter without life or motion. In the present state of things on the other hand, the system, as we have already explained, is, by a combination of remarkable provisions, calculated for an almost indefinite existence, of undiminished fitness for its purposes.
There are, therefore, manifest reasons, why, of all laws which could occupy the place of the first law of motion, the one which now obtains is the only one consistent with the durability and uniformity of the system;—the one, therefore, which we may naturally conceive to be selected by a wise contriver. And as, along with this, it has appeared that we have no sort of right to attribute the establishment of this law to any thing but selection, we have here a striking evidence, to lead us to a perception of that Divine mind, by which means so simple are made to answer purposes so extensive and so beneficial.