MOTION is change of place; there has been motion when a body, at one time, occupies a part of space different from that in which it was at a preceding time. The only additional necessary conception is continuity of change: every point which has moved from one point of space to another must have passed over every part of some line, straight or not straight, drawn from one point to the other.
Some of the ancients used the word in a more general sense, answer ing to change. Thus, according to them, creation, generation, corrup tion, increase, diminution, and change of place, are the six sorts of motion. We have here no further to do with this than to remind our readers, when they tree local motion spoken of in old writings, that this is the term by which simple change of place, to which the word motion is now restricted, is distinguished from the other changes which the same word then denoted. We still apply the word, as we do terms of magnitude (we that word) to changes of the moral system, as in speaking of the motions and emotions of the mind.
If there be anything which would need neither definition nor comment, it might be supposed to be simple motion, a thing never absent from one moment of the waking perceptions, nor even of the dream. Its existence was however denied, or is reported to have been denied, by various of the Greek sophists, though it is highly probable that some matter-of-fact historians have handed down as a deliberate opinion what was merely meant for an ingenious attack on one or another established school. According to Sextus Empiricus (i. § 17), Diodorus surnamed Cronus, a Carian, disproved the existence of motion as follows :—If matter moves, it is either in the place in which it is, or the place in which it is not ; but it cannot move in the place in which it is, and certainly not in the place in which it is net : consequently it cannot move at all To which the first named author replies, that by the same rule men never die, for if a man die, it must either be at a time when ho is alive, or at a time when he is not alive. A better answer would have been. that it is true of all material pheno mena that they happen either in the place in which the matter is, or in that iu which it is not, except only the change from that place in which the matter is and will not be, to that in which it is not but will be. The eyllogisio of Diodorus may be useful to remind us that motion implies both spaces and times, since the sophism excludes the latter from consideration. Zeno of Elea (not the Stoic) gavo the celebrated argument of Achilles and the Tortoise. [PRoonessioN.] If we consider merely motion, without any reference to the matter moved or the quantity of external force required to move it, we have, as we conceive, a subject of pure mathematics before us, though this has been contested. Newton however used considerations of motion without hesitation in his fluxion; and his successors have endeavoured to avoid them by circumlocutions, which, however consonant they may be to conventional ideas rigour, have never failed to introduce perplexity and obscurity to the beginner. It may be right to remind the student that the change of place introduced by Euclid (i., prop. 4 and other has not necessarily all the concomitants of the idea of 'motion ; geometry would not interfere to prevent the super position from being made without the notion of the triangle, whose place is changed, passing through the intervening parts of space. It
was the introduction of the idea of time which the parties who objected to the doctrine of fluxions repugned.
But if we consider matter' in motion, we must inquire into the external causes of motion, and the capabilities of matter with respect to motion ; this we shall do in the next article [MOTION, LAWS OF], confining ourselves in the present one to the first-mentioned branch of the subject.
Next to the idea of motion comes that of swiftness, rate of motion, or velocity (see also the latter word), suggested by observing different motions, or different changes of place in the same time. But here we must observe, that we are rather indebted to motion for our measure of time than to time for our measure of motion. If sentient beings, like ourselves, had lived in perpetual day, without any recurrence of periodical phenomena in nature, or any mechanical means of gene rating equable motion, we have no right to suppose that they would ever have learned to consider time as a measurable magnitude. They might admit that it might be more or less, as we do of industry, courage, or any other moral qualities [ leoNrrunE], but we cannot be more destitute of measures for those qualities, than they would be of means for measuring time. Since however we have obtained, though by means of equable motion, a distinct idea of successions of duration, equal in magnitude, we use this idea in the definition of motion, just as in geometry we consider the line before the surface, though we have no certainty that we ever should have a distinct notion of a line, if we had not formed lines by the intersection of surfaces. We say, though we have no certainty, but we do not forget that many philo sophers are of opinion that such ideas as those of time and of a line are fundamental notions, resulting from our rational organisation, and (if we do not mistake them) anterior to observation, or, at least, not derived from it. This question is here immaterial, as we suppose all parties ready to start with a definite notion of time. Considering the motion of a simple point, which describes a line, it is called uniform when the lengths described in successive equal times are equal, whatever each time may be. It is important to remember this, since different successive motions may be uniform in some respects and not in all. Thus successive revolutions may be performed in equal times, as to whole revolutions, but equal fractions of one revolu tion may not be performed in equal times. In uniform motion, an arbitrary unit of time is chosen, and the length described in that time is called the velocity, which is simply the Latin for quickness. If extreme verbal correctness were required, this length should be called, not the velocity or swiftness, but the measure of the velocity. For the length described in (say) one second is not the velocity or swiftness, but something by which we judge of it. The word velocity is an abstraction from the comparison of motions ; of two moving points, that one which described the greater length in a given time moved the quicker : and swiftness is the absolute substantive by which we express the existence of the obvious relation, just as magnitude is that by which we express the existence of the relation of greater and less.