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# Laws of Motion

## force, law, forces, body, third, change, system and derived

MOTION, LAWS OF, are the fundamental principles connecting force and motion in the physical universe; and are obviously to be derived from experiment alone, since intuitive reasoning cannot possibly give us any information as to what may or may not be a law of nature. Though these laws are derived from experiment, it cannot be said that we have any very direct experimental proofs of their truth—our most satisfactory verifica tions of them are derived from the exact accordance of the results of calculation with those of observation in the case of such gigantic combinations of mutually influencing bodies as that of the solar system; and it is by such proofs that they must be considered to have been finally established.

They seem first to have been given systematically and completely by Newton, at the opening of the Principia; but the first two were known to Galileo, and some of the many forms of a part of the third were known to Hooke, Huygliens, Wren, and others. We shall give them here in order, with a few brief comments, showing their necessity and their use.

First, then, we naturally inquire, what matter would do if left to itself; and, by con sidering cases in which less and less external force is applied to a body, we are led to the statement called the first law of motion: 1. Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by impressed forces to change that state.

This expresses simply the inertia of matter—i.e., a body cannot alter its state of rest or motion ; for any such alteration external force is required. Hence the definition of force (q.v.), as that which changes or tends to change a body's state of rest or motion.

Now, how does the change of state depend on the force which produces it? This is obviously a new question, to be resolved by experiment; and the answer is the second law of motion: 2. Change of motion is proportional to theimpressed force, and takes place in the direction of the straight line in which the force acts.

Newton's silence is as expressive as his speech. Nothing is here said about the pre vious motion of the body, or about the number of forces which may be at work simulta neously. Hence, a force produces its full effect in the form of change of motion, whether it act singularly, or be associated with others; and whatever, moreover, be the original motion of the body to which it is applied. Hence, there is no such thing as equilibrium of forces; every force produces motion—and what we call equilibrium is not the balancing of forces, but the balancing of their effects. Hence, the absurdity of found

the science of statics on any other basis than is to be derived from the second law of motion ; which, in fact, leads us at once (by the parallelogram of velocities, which is a purely geometrical conception) to the parallelogram of forces, and thence. with the help of the third law, to the whole subject of statics. The second law also supplies the means of measuring force and mass; and of solving any problem whatever concerning the motion of one particle.

But more is required before we can study the motion of a system of particles—as a rigid body, or a liquid, for instance; or a system of connected bodies. Here there are mutual actions and reactions of the nature of pressure or of transference of energy (see FoncE) between the parts—and these are regulated by the third law of motion: 3. lb every motion there is always an equal and contrary reaction: or, the mutual actions of any two bodies are always equal and oppositely directed in the same straight line.

Thus, the mutual pressure between two bodies has equal, but opposite, values for the two. The tension of a rope is the same throughout, and tends as much to pull back the horse at one end as to pull forward the canal-boat at the other. The earth exerts as much attractive force on the sun as the sun exerts on the earth—and the same law applies to the other attractive and repulsive forces, as those of electricity and magnetism.

But Newton goes much further than this; he shows, in fact, that action and reaction (subject to the third law) may consist in work done by a force, instead of the tnere force or pressure itself. From this form of the third law we derive at once the principle of virtual velocities (q.v.), which in its application to machines is familiar as " 1V7eat is gained in power is lost in speed." But we also derive the grand principle of the inde structibility of work or energy; at all events in the case of the ordinary mechanical forces— and this must be regarded as one of the grandest discoveries which science owes to New ton. It is true that he merely mentions it, and then abruptly passes tp another subject; yet we can hardly exaggerate the value of this singleremark. Experimenters, mainly Davy and Joule, have since shown that all the physical energies, as heat, light, electricity, etc., arc subject in their transformations to the third law of motion, and thus the system con structed by Newton for ordinary dynamical purposes, is now found to rule the most mysterious of the affections of matter. For a development of this, sec our article on FoncE.