67G MECHANICS STRICTLY speaking, the derivation of this word should have prevented the use of it as the designation of a pure science. It has been, however, employed for a long period in English speech in the identical sense that the French attach to Mecanique pure or the Germans to Reins Mechanik. These terms are all employed to denote what we should much prefer to call Abstract Dynamics, the pure science which (as the derivation implies) treats of the action of Force upon Matter, but which is, correctly, the Science of Matter and Motion, or of Matter and Energy. With the view of making clear from the outset the reason for the arrangement adopted in this article, we commence by stating in Newton s own words (accompanied by a paraphrase) the Axiomata, sive Leges Motus, which form the entire basis of our subject. These laws will at once indicate the order in which the subject may most logically be treated. We defer to the end of the article the more close consideration of the idea introduced by the word " force," as well as general remarks on " energy," &c. For the present we are content to regard force as denned for us by Newton s Laws. Newton s Laws of Motion. Newton s 1. Lex I. Corpus omne perseverare in statu suo qui- first law. escendi vel movendi uniformiter in directum, nisi quatenus illud a viribus impressis cogitur statum suum mutare. Every body continues in its state of rest, or of uniform motion in a straight line, except in so far as it is compelled by force to change that state. Second Lex- II. Mutationem motus proportionalem esse vi law. motrici impressse, et fieri secundum lineam rectam qua vis ilia imprimitur. Change of (quantity of) motion is proportional to force, and takes place in the straight line in which the force act-s. Third Lex III. Actioni contrariarn semper et aequalem esse law. reactionem ; sive corporum duorum actiones in se mutuo semper esse sequalea et in partes contrarias dirigi. To every action there is always an equal and contrary reaction ; or the mutual actions of any two bodies are always equal and oppositely directed. Scholium. 2. In 1863 Thomson and Tait (upon whose Treatise on Natural Philosophy much of what follows is based) called attention to the fact that, as regards Lex III., Newton gives in a scholium a second sense in which the words may be interpreted. In the first sense the action and reaction are mere forces, in the second they are the rates at lohich forces do iV jrk. Hence, and for another reason which will appear later, the word "activity" has been introduced as the English equivalent of the word actio in Newton s second sense. Here is the passage : Si testimetur agentis actio ex ejus vi et velocitate con- junctim ; et similiter resistentis reactio sestimetur con- junctiin ex ejus partium singularum velocitatibus et viribus resistendi ab earum attritione, cohsesione, pondere, et accelcratione oriundis ; erunfc actio et reactio, in omni instrumentorum usu, sibi invicem semper sequales. If the activity of an agent be measured by its amount and its velocity conjointly ; and if, similarly, the counter-activity of the resistance be measured by the velocities of its several parts and their several amounts conjointly, whether these arise from friction, molecular forces, iveight, or acceleration; . activity and counter-activity, in all combinations of machines, will be equal and opposite. This may be looked upon as a Fourth Law. But, in strict logic, the First Law is superfluous, because its con sequences are all implied (by negation) in the statement of the Second. (See 8 below.) Hence there are, virtually, only three laws, so far as Newton s system is concerned. 3. These laws are to be considered as deductions from Basis o observation and experiment, and in no sense as having an Newtoi a priori foundation. Their proof, so far as rigorous proof laws- is attainable in physical matters, is commonly looked on as being furnished in the most conclusive form by obser vational astronomy. The Nautical Almanac, published usually about four years in advance, contains the predicted places of the sun, moon, and principal planets from day to day, in some cases from hour to hour, throughout the year. The predictions are entirely based upon the laws of motion (along with the law of gravitation), and could not possibly be accurate unless these laws are true. So thoroughly satisfactory has hitherto been the coincidence between prediction and observation that, when a deviation occurs, no one dreams of a defect in the principles of the reasoning. On the contrary, such deviations are utilized for the purpose of correcting our knowledge of the " elements " of the orbits of the moon and planets, or our estimates of the masses of these bodies ; and, as in the brilliant investigations of Adams and Leverrier, they some times enable us to discover the existence and even assign the position of a planet never before seen. 4. It is not clear in what order, or by whom, these laws Newton were first discovered. Galileo was undoubtedly acquainted P*ede- with the first two ; and Huygens, Wren, Hooke, and ce others were acquainted with the Third Law in some of its many applications. But they were first systematized and, as we have seen, extended in a most important manner by Newton. Though they were sadly disfigured in Britain during the fifty years which elapsed after the revival of mathematics in the early part of this century, they have of late been restored to the form in which Newton gave them. This readoption of Newton s simple but comprehensive system has of itself aided in no small degree the recent rapid advance of science. One peculiarity of Newton s language must be noticed Anthro here, though very briefly, as we will return to the subject j* 01 T towards the end of the article. A force is said to " compel " a change of state in a body ; bodies are said mutually to " act " on one another, &c. Such language is, of course, in its literal acceptation, of an anthropomorphic character ; but, if one thinks of the habitual use even in scientific books of such expressions as " the sun rises," " the wind blows," &c., it cannot be construed into an assertion that force has real objective existence. Comments on the Laws of Motion. 5. Law I. First of all this law tells us what happens Defini te a piece of matter which is left to itself, i.e., not acted * ion of on by forces. It preserves its " state," whether of rest or lo of uniform motion in a straight line. This property (which, as we shall presently show, 7, is considerably extended by Newton himself) is commonly called the "inertia" of matter, in virtue of which it is incapable of Inertia, varying in any way its state of rest or motion. It may be the sport of forces for any length of time, but so soon as they cease to act it remains in the state in which it was left until they recommence their action on it. Hence, whenever we find the state of a piece of matter changing, we conclude that it is under the action of a force or force?. Thus, for the present, we have the definition of "force" as part of this First Law : Force is whatever changes the state of rest or uniform
motion of a body.