Natural Philosophy

by Wilhelm Ostwald

43. Mechanics.

Recently many scientists have taken exception to the traditional division of mechanics into statics, or the science of equilibrium, and dynamics, or the science of motion, because it does not correspond to the essence of the thing, equilibrium being only the limit-case of motion. However, the classic presentations of this science are based on that division, so that it must express an essential difference. This difference we can clearly recognize through the application of the concept of energy to mechanics. We then learn that statics is the science of work, or the energy of position, and that dynamics is the science of living force, or of the energy of motion.

By work in the mechanical sense we mean the expenditure of force required for the locomotion of physical bodies. While a cube of lead is geometrically equal to a cube of glass, we experience a great difference between them when we lift them from the floor to a table. We call the cube of lead heavier than the glass cube, and we find it requires more work to raise the former than the latter. For psychologic reasons this judgment becomes especially clear when the work required to lift the lead cube marks the limit of our physical capacity.

Work depends not only upon the difference described above, but also upon the distance through which it is exerted. It increases in proportion as the distance increases. In mechanics work is proportional both to the distance and to that peculiar property which in the given example we call weight. But a more general concept has been formed for that property in the mechanical sense, called force, of which weight constitutes but a special instance. Whenever there is a resistance combined with a change of place we speak of a force, and the product of the force and the distance we call work.

The cause of this kind of concept formation is the following: There are a great number of different machines, all of them possessing the peculiarity that work can be put into them at a definite place and taken out at another place. Now, centuries of experience have shown that it is impossible to obtain more work from such mechanical machines than has been put into them. As a matter of fact, the work obtained is always less than the work put in, and the two approach equality as the machine approaches perfection. It is to such ideal machines, therefore, that the law of the conservation of work applies. This law states that, though a given quantity of work may be changed in the most manifold ways as to direction, force, etc., it is impossible to change its quantity.

The reason we can judge of this fact with such certainty is because for many centuries a number of the ablest mechanicians have sought for a solution of the problem of perpetual motion, that is, for the construction of a machine from which more work can be gotten than is put into it. All such attempts have failed. But the positive result secured from these apparently futile efforts is the law of the conservation of work. The greatness and importance of this result will become apparent in the further course of our study.

Here for the first time we meet with a law expressing the quantitative conservation of a thing, which may none the less undergo the most varied qualitative changes. With the knowledge of this fact we involuntarily combine the notion that it is the "same" thing that passes through all these transformations, and that it only changes its outward form without being changed in its essence. Such ideas, it is true, are widespread, but they have a very doubtful side to them, since they correspond to no distinct concept. If we want to call the quantitative magnitude of the product of the force and distance the "essence" of work, and the determination of the force and the distance according to magnitude and direction, which come under consideration for each special value, as its "form," then, of course, there is no objection to be made to mere nomenclature. But we must bear in mind that the difference obtaining here lies exclusively in the fact that the amount of work measured quantitatively remains unchanged, while its factors undergo simultaneous and opposite changes.

This discovery, that there is a magnitude which can be quantitatively determined, and which, as experience shows, remains unchanged, however much its factors may change, invariably results not only in a very simple and clear formulation of the corresponding natural law, but also corresponds to the general tendency of the human mind to work out conceptually "the permanent in change." If, in accordance with the word-sense, we denote everything which persists under changing conditions by the name of substance, we encounter in work the first substance of which we have attained knowledge in our scientific journeys. In the history of the evolution of human thought this substance has been preceded by others, especially by the weight and mass of ponderable bodies (which are also subject to a law of conservation), so that at present we are inclined to connect with the word substance a tacit secondary sense of ponderability. But this is a remnant of the still very widely spread mechanistic theory of the universe, which, though it has almost finished its rôle in physics, will presumably continue to persist for a long time to come in the popularly scientific consciousness in accordance with the laws of collective thought.

44. Kinetic Energy.

The law of the conservation of work is by no means true of all cases in which work is expended or converted, but, as has been said, only of ideal machines, that is, of such cases which do not exist in reality. But while in imperfect machines there is at least an approximation to this law, there are besides countless normal cases in which we cannot even speak of an approximation. When, for example, a stone falls to the ground from a certain height, a certain quantity of work is expended, which is equal to that by means of which the stone can be raised again to its original height. This quantity of work apparently disappears entirely when the stone remains lying on the ground. We shall discuss this case later. Or the falling of the stone can be so guided that it can lift itself again. This happens, for instance, when, by fastening the stone to a thread, it is forced to move in a curved path, or to perform pendular oscillations. In that case, it is true, the stone will fall to the lowest point which the thread permits, and so will there have lost its work without having done any other work in the meantime. But it has entered a condition by virtue of which it raises itself again, so that (as before, only in the ideal limit-case) it reaches its former height, and so has lost no work. For this moment, too, then, the law of the conservation of work obtains. But in the meantime new relations have arisen.