The Continuity of Motion §55. Like the Indestructibility of Matter, the Continuity of Motion,or, more strictly, of that something which has Motion for one of its sensibleforms, is a truth on which depends the possibility of exact Science, andtherefore of a Philosophy which unifies the results of exact Science. Motions,visible and invisible, of masses and of molecules, form the larger half ofthe phenomena to be interpreted; and if such motions might either proceedfrom nothing or lapse into nothing, there could be no scientific interpretationof them.
This second fundamental truth, like the first, is not self-evident toprimitive men nor to the uncultured among ourselves. Contrariwise, to uninstructedminds the opposite seems self-evident. The facts that a stone thrown up soonloses its ascending motion, and that after the blow its fall gives to theEarth, it remains quiescent, apparently prove that the principle of activity(*) which the stone manifestedmay disappear absolutely. Accepting the dicta of unaided perception, allmen once believed, and most believe still, that motion can pass into nothing,and ordinarily does so pass. But the establishment of certain facts havingopposite implications, led to inquiries which have proved these appearancesto be illusive. The discovery that the celestial motions do not diminish,raised the suspicion that a moving body, when not interfered with, will goon for ever without change of velocity; and suggested the question whetherbodies which lose their motion, do not at the same time communicate as muchmotion to other bodies. It was a familiar fact that a stone would glide furtherover a smooth surface, as that of ice, presenting no small objects to whichit could part with its motion by collision, than over a surface strewn withsuch small objects; and that a stick hurled into the air would travel a fargreater distance than if hurled into a dense medium like water. Thus theprimitive notion that moving bodies have an inherent tendency to stop --a notion which the Greeks did not get rid of, and which lasted till the timeof Galileo -- began to give way. It was further shaken by such experimentsas those of Hooke, which proved that a top spins the longer in proportionas it is prevented from communicating motion to surrounding matter.
To explain here all disappearances of visible motions is out of the question.
It must suffice to state, generally, that the molar motion which disappearswhen a bell is struck by its clapper, re-appears in the bell's vibrationsand in the waves of air they produce; that when a moving mass is stoppedby coming against a mass that is immovable, the motion which does not showitself in sound shows itself in molecular motion; and that when bodies rubagainst one another, the motion lost by friction is gained in the motionof molecules. But one aspect of this general truth, as it is displayed inthe motions of masses, we must carefully contemplate; for, otherwise, thedoctrine of the Continuity of Motion will be misapprehended. §56. As expressed by Newton, the first law of motion is that "everybody must persevere in its state of rest, Or of uniform motion in a straightline, unless it be compelled to change that state by forces impressed uponit."
With this truth may be associated the truth that a body describing a circularorbit round a centre which detains it by a tractive force, moves in thatorbit with undiminished velocity.
The first of these abstract truths is never realized in the concrete,and the second of them is but approximately realized. Uniform motion in astraight line implies the absence of a resisting medium; and it further impliesthe absence of forces, gravitative or other exercised by neighbouring masses: conditions never fulfilled. So, too, the maintenance of a circular orbitby any celestial body, implies that there are no perturbing bodies, and thatthere is an exact adjustment between its velocity and the tractive forceof its primary: neither requirement ever being conformed to. In actual orbits,sensibly elliptical as they are, the velocity is sensibly variable. And alongwith great eccentricity there goes great variation.
With the case of these celestial bodies which, moving in eccentric orbits,display at one time little motion and at another much motion, may be associatedas partially analogous the case of the pendulum. With speed now increasingand now decreasing, the pendulum alternates between extremes at which motionceases.
How shall we so conceive these allied phenomena as to express rightlythe truth common to them? The first law of motion, nowhere literally fulfilled,is yet, in a sense, implied by these facts which seem at variance with it.
Though in a circular orbit the direction of the motion is continually beingchanged, yet the velocity remains unchanged. Though in an elliptical orbitthere is now acceleration and now retardation, yet the average speed is constantthrough successive revolutions. Though the pendulum comes to a momentaryrest at the end of each swing, and then begins a reverse motion, yet theoscillation, considered as a whole, is continuous: friction and atmosphericresistance being absent, this alternation of states would go on for ever.
What, then, do these cases show us in common? That which vision familiarizesus with in Motion, and that which has thus been made the dominant elementin our conception of Motion, is not the element of which we can allege continuity.
If we regard Motion simply as change of place, then the pendulum shows usboth that the rate of this change may vary from instant to instant, and that,ceasing at intervals, it may be afresh initiated.
