The third law of motion was enunciated by Newton as follows :— " Action and reaction are equal and opposite." Thus, if a body exerts a force upon another body B by contact, tension, thrust, attrac tion, repulsion, or otherwise ; then B exerts the very same force on A in the opposite direction. The principle thus laid clown belongs is much to statics as to dynamics, and is not therefore to be considered a special law of motion. It seems indeed to establish a relation between the statical and dynamical effects of a force—the action being repre sented by the pressure employed, the reaction by the motion produced. But how is this motion to be measured f Newton had decided that a body's motion should be measured by its momentum, and enunciated the third law on this supposition. But taking as we now do the velocity generated in a body to be the dynamical measure of the force,— that is, the reaction,—the third law of motion asserts that "the velocity generated in a body by the action of a force, whether impulsive or otherwise, is proportional to the force." Where the force continues to act during a finite interval of time, the body acquires an additional velocity in each succeeding instant— an evident consequence of the second law of motion. The velocity thus generated in a unit of time (as one second) is termed by some modern writers the "rate of acceleration." And this is all that is meant by the expression " accelerating force,"—namely, a force that, acting continually upon a body, produces in it a rate of acceleration. Thus the force of gravity is called an accelerating force, because the motion of a body, under its influence, becomes accelerated; the rate of acceleration being about 32/ feet per second. [ACCELERATED MOTION.] Let f and f' denote the rates of acceleration produced respectively by the action of two forces F and F'; then, by the third law of motion, f : f'=r : P'. Also, if t be the time during which these forces act, v and v' the respective velocities acquired at the end of time t. we have v=ft and e=1" t, hence v =P F'. If a body move under the action of gravitation, the rate of acceleration is g (=32/), hence if F act upon a body whose weight is w, we have the following very useful application of the third law of motion :— when v= velocity acquired in time t by the action of F.
The three laws of motion, then, may be thus enunciated : 1. A body, if acted upon by no external force, remains at rest ; or if in motion, continues to move uniformly in the same direction.
2. When any number of forces act upon a body in motion, each force produces the same effect in altering the magnitude and direction of the body's velocity, as if it acted singly on the body at rest.
3. The velocity generated in a unit of time by a force continually acting upon a body, is proportional to the force.
The reader will meet with some very clear conceptions of the three laws of motion in Dr. Young's ' Natural Philosophy,' edited by Pro fessor Kelland ; also in O'Brien's Natural Philosophy,' published by the Society for the Promotion of Christian Knowledge. He may
likewise refer to a paper by Dr. Whewell " On the Nature of the Truth of the Laws of Motion." (‘ Camb. Phil. Trans.' vol. v. part ii.) The mistakes into which philosophers fell upon the laws of motion are uninteresting except in the applications which were made of them ; and in the article MOTION OF THE Ennru will be found enough of these to give an idea of the difficulties which such fallacies placed in the way of sound knowledge. For an account. of Galileo's labours, see Gatiter, in Bioo. Div. For an account of the notions of Descartes ou the same subject, see VORTICES. The first distinct enunciation of these laws appears in the Principle of Newton.
Though all mechanical problems admit of solution upon the assumption of these laws, in conjunction with those which may be called the distinctive properties of the solid, fluid, and gaseous states, yet the purposes of mechanical inquiry are better served by certain general principles deduced from them, the proper conception of which can only be made by mathematicians, and are therefore referred to a purely mathematical alliC10—VIRTUZVELOCITIES. [PRESSURE, FORCE, INERTIA, CENTRIPETAL AND CENTRIFUGAL FORCES, ACCELERATED MOTION, VELOCITY, &C. ; MOVING FORCE. See particularly the article INERTIA, for the reason of the non-introduction of that word.] Among the many absurdities which have arisen out of a misappre hension of the laws of motion, is the attempt to discover what is called a perpetual motion, or a machine which of itself would never stop. The earth and planets are such machines in their rotations on their axes ; and we have seen that any particle of matter, unacted on by other matter, and once in motion, is a perpetual motion. If a wheel attached to an axle could be deprived of friction at the pivots, and enclosed in a air-tight and perfectly exhausted receiver, it would also, when onto in motion, he a perpetual motion. But as long as any friction or resistance, however small, is perpetually retard ing the motion, it is obvious that the velocity, if maintained, must be indebted to some external supply of moving power. To take the case of friction, which arises from the roughness of the supports, and which, independently of may be considered as a rapid succession of very small jolts, by which the roughnesses of the one surface strike upon those of the other, and communicate a portion of momentum to the frame. and finally to the earth : to SHADOW that a wheel as above described could go on for ever, with friction, would be to suppose that there could be action without reaction. In fact, a perpetual motion, such as is intended to be made by the speculators on the subject, is nothing less than a machine which will work for ever without new moving power ; it being not one bit less absurd to suppose that it would perpetually overcome friction and atmospheric resistance, than that it would continue to supply the impetus necessary to carry on the sawing of a plank or the weaving of lace.