ACTION

, in Mechanics or Physics, a term used to denote, sometimes the effort which some body or power exerts against another body or power, and sometimes it denotes the effects resulting from such esfort.

The Cartesians resolve all physical action into metaphysical. Bodies, according to them, do not act on one another; the action comes all immediately from the Deity; the motions of bodies, which seem to be the cause, being only the occasions of it.

It is one of the laws of nature, that action and reaction are always equal, and contrary to each other in their directions.

Action is either instantaneous or continued; that is, either by collition or perc<*>ssion, or by pressure. These two sorts of action are heterogeneous quantities, and are not comparable, the smallest action by percussion exceeding the greatest action of pressure, as the smallest surface exceeds the longest line, or as the smallest solid exceeds the largest surface: thus, a man by a small blow with a hammer, will drive a wedge below the greatest ship on the stocks, or under any other weight; that is, the smallest percussion overcomes the pressure of the greatest weight. These actions then cannot be measured the one by the other, but each must have a measure of its own kind, like as solids must be measured by solids, and surfaces by surfaces: time being concerned in the one, but not in the other.

If a body be urged at the same time by equal and contrary actions, it will remain at rest. But if one of these actions be greater than its opposite, motion will ensue towards the part least urged.

The actions of bodies upon each other, in a space that is carried uniformly forward, are the same as if the space were at rest; and any powers or forces that act upon all bodies, so as to produce equal velocities in them in the same, or in parallel right lines, have no effect on their mutual actions, or relative motions. Thus the motion of bodies on board of a ship that is carried uniformly forward, are performed in the same manner as if the ship was at rest. And the motion of the earth about its axis has no effect on the actions of bodies and agents at its surface, except in so far as it is not uniform and rectilineal. In general, the actions of bodies upon each other, depend not on their absolute, but relative motion.

Quantity of Action, in Mechanics, a name given by M. de Maupertuis, in the Memoirs of the Academy of Sciences of Paris for 1744, and in those of Berlin for 1746, to the continual product of the mass of a body, by the space which it runs through, and by its celerity. He lays it down as a general law, that in the changes made in the state of a body, the quantity of action necessary to produce such change is the least possible. This principle he applies to the investigation of the laws of refraction, and even the laws of rest, as he calls them; that is, of the equilibrium or equipollency of pressures; and even to the modes of acting of the Supreme Being. In this way Maupertuis attempts to connect the metaphysics of sinal causes with the fundamental truths of mechanics; to shew the dependence of the collision of both elastic and hard bodies, upon one and the same law, which before had always been referred to separate laws; and to reduce the laws of motion, and those of equilibrium, to one and the same principle.

But this quantity of motion, of Maupertuis, which is defined to be the product of the mass, the space passed over, and the celerity, comes to the same thing as the mass multiplied by the square of the velocity, when the space passed over is equal to that by which the velocity is measured; and so the quantity of force will be proportional to the mass multiplied by the square of the velocity; since the space is measured by the velocity continued for a certain time.

In the same year that Maupertuis communicated the idea of his principle, professor Euler, in the supplement to his book, intitled Methodus inveniendi lineas curvas maximi vel minimi proprietate gaudentes, demonstrates, that in the trajectories which bodies describe by central forces, the velocity multiplied by what the foreign mathematicians call the element of the curve, always makes a minimum; which Maupertuis considered as an application of his principle to the motion of the planets.

It appears from Maupertuis's Memoir of 1744, that it was his reflections on the laws of refractions, that led him to the theorem above mentioned. The principle which Fermat, and after him Leibnitz, made use of, in accounting for the laws of refraction, is sufficiently known. Those mathematicians pretended, that a particle of light, in its passage from one point to another, through two mediums, in each of which it moves with a different velocity, must do it in the shortest time possible: and from this principle they have demonstrated geometrically, that the particle cannot go from the one point to the other in a right line; but being arrived at the surface that separates the two mediums, it must alter its direction in such a manner, that the sine of its incidence shall be to the sine of its refraction, as its velocity in the first medium is to its velocity in the second: whence they deduced the well known law of the constant ratio of those sines.

This explanation, though very ingenious, is liable to this pressing difficulty, namely, that the particle must approach towards the perpendicular, in that medium where its velocity is the least, and which consequently resists it the most: which seems contrary to all the mechanical explanations of the refraction of bodies, that have hitherto been advanced, and of the refraction of light in particular.

Sir Isaac Newton's way of accounting for it, is the most satisfactory of any that has hitherto been offered, and gives a clear reason for the constant ratio of the sines, by ascribing the refraction to the attractive force of the mediums; from which it follows, that the densest | mediums, whose attraction is the strongest, should cause the ray to approach the perpendicular; a fact confirmed by experiment. But the attraction of the medium could not caúse the ray to approach towards the perpendicular, without increasing its velocity; as may easily be demonstrated. Thus then, according to Newton, the refraction must be towards the perpendicular, when the velocity is increased: contrary to the law of Fermat and Leibnitz.

Maupertuis has attempted to reconcile Newton's explanation with metaphysical principles. Instead of supposing, as the aforesaid gentlemen do, that a particle of light proceeds from one point to another in the shortest time possible; he contends that a particle of light passes from one point to another in such a manner, that the quantity of action shall be the least possible. This quantity of action, says he, is a real expence, in which nature is always frugal. In virtue of this philosophical principle he discovers, that not only the sines are in a constant ratio, but also that they are in the inverse ratio of the velocities, according to Newton's explanation, and not in the direct ratio, as had been pretended by Fermat and Leibnitz.

It is remarkable that, of the many philosophers who have written on refraction, none should have fallen upon so simple a manner of reconciling metaphysics with mechanics; since no more is necessary to that, than making a small alteration in the ealculus founded upon Fermat's principle. Now according to that principle, the time, that is, the space divided by the velocity, should be a minimum; so that calling the space run through in the first medium S, with the velocity V, and the space run through in the second medium s, with the velocity v, we shall have minimum; that is to say, . Now it is easy to perceive, that the sines of incidence and refraction are to each other, as S^. to-s^.; whence it follows, that those sines are in the direct ratio of the velocities V, v; which is exactly what Fermat makes it to be. But in order to have those sines to be in the inverse ratio of the velocities, it is only supposing ; which gives a minimum: which is Maupertuis's principle.

In the Memoirs of the Academy of Berlin, above cited, may be seen all the other applications which Maupertuis has made of this principle. And whatever may be determined as to his metaphysical basis of it, as also to the idea he has annexed to the quantity of action, it will still hold good, that the product of the space by the velocity is a minimum in some of the most general laws of nature.