Motion, LAWS OF. In developing the subject of Dynamics (q.v.) it is convenient to lay down in the form of postulates axioms or the fundamental principles on which the science is based. These axioms are generally referred to as the laws of motion. They rest ultimately, as do the axioms of geometry, upon our experience; and once the terms in which they are expressed are sufficiently understood, the laws themselves are admitted without further question. We owe to Newton what still remains the most serviceable, because the most concise and at the same time complete, expression of these dynamical axioms. Newton's predecessors, particularly Galileo, had already formulated some of the fundamental principles of abstract dynamics; but in the Three Laws of Motion, which form the basis of the Principia, we have for the first time all the necessary and sufficient principles laid down in a manner easy to understand and easy to apply. These three laws are given both under DYNAMICS and under FORCE, and need not be reproduced here.
Newton's method of presenting his definitions and axioms has been made the subject of much criticism. And doubtless a logician, confining his attention to the eight definitions of mass, momentum, inertia, force, acceleration, &c., and the three laws of motion, could easily discover faults of logical arrangement. Nevertheless, taking this preliminary section of the Principia, with its masterly scholia, as a whole, and bearing in mind that the aim is to establish a theory of dynamics that shall harmonise with the facts of experience, we shall find no difficulty in admitting the soundness of Newton's principles. There is absolutely no confusion of thought. The demands on our intellectual faith, whether explicitly stated or implicitly involved in other statements, are essentially rational. The treatment is luminous as it is profound. Attempts have been made to substitute a more logical procedure; but all such attempts lead to intricate phraseology and a corresponding intricacy of dynamic conception quite beyond the powers of apprehension of the tyro. And even when all is done it is doubtful if the strict canons of logic are quite satisfied. It may be safely said that, as an introduction to the study of dynamics, Newton's laws of motion, along with the definitions of the physical quantities involved, have not as yet been surpassed.
The train of thought running through Newton's method may be thus described. Everything dynamical that happens in nature consists of changes of position and motion of the parts of a material system. Fixing our attention on one body or particle in the system, we soon perceive by experience that its changes of motion or (more strictly) momentum relatively to the other parts of the system must depend on the mechanism connecting it with these parts. With this mechanism, how- ever, we do not at first explicitly concern ourselves. For it we substitute the conception of force, or its time-accumulation, impulse, which we regard as the external something causing the observed change in momentum and measured by that change. This force may be constant or variable in space, or it may depend on the velocity of the body. On these conceptions and definitions we base the simplest department of abstract dynamics—that known as the dynamics of a particle. Many of its theorems are found to be very approximately realised in the falling of bodies, in the flight of projectiles, in the motions of planets and comets round the sun. But before we can pass to the dynamics of material systems we must restore the bonds we severed when we introduced the idea of force acting on a single particle. This Newton completely effected by his third law, in which every force is recognised as being only the half of a whole, the other half being the equal but oppositely directed reaction. This means that whatever change of momentum may be observed to be taking place in one particle must be balanced by an equal and opposite change of momentum occurring elsewhere. Thus, the momentum of a material system as a whole can never change, however much its configuration may alter, in virtue of the mutual actions of its parts. And in this statement we may readily recognise the generalisation of the first law of motion—commonly called the Law of Inertia—in its application to any complex material system, dynamically isolated, and considered as a unity. Newton's very remarkable second interpretation of the third law, given at the end of the scholium attached, implicitly contains, as was first pointed out by Thomson and Tait, nearly the whole of the modern doctrine of energy. It is discussed under that heading. See also FORCE for the discussion of the Second Law.—For Motion in Plants, see IRRITABILITY, PLANTS, SENSITIVE PLANTS, SPORE; for animal locomotion, see FLYING, HORSE, &c.