But if what we may call the translation-element in Motion is not continuous,what is continuous? If, like Galileo, we watch a swinging chandelier, andobserve, not the isochronism of its oscillations but the recurring reversalof direction, we are impressed with the fact that though, at the end of eachswing, the translation through space ceases, yet there is something whichdoes not cease; for the translation recommences in the opposite direction.
And on remembering that when a violent push was given to the chandelier itdescribed a larger arc, and was a longer time before the resistance of theair brought it to rest, we are shown that what continues to exist duringits alternating movements is some correlative of the muscular effort whichput it in motion. The truth forced on our attention is that translation throughspace is not itself an existence; and that hence the cessation of Motion,considered simply as translation, is not the cessation of an existence, butis the cessation of a certain sign of an existence.
Still there remains a difficulty If that element in the chandelier's motionof which alone we can allege continuity is the correlative of the musculareffort which moved, the chandelier, what becomes of this element at eitherextreme of the oscillation? Arrest the chandelier in the middle of its swing,and it gives a blow to the hand-exhibits some principle of activity suchas muscular effort can give. But touch it at either turning point and itdisplays no such principle of activity. This has disappeared just as muchas the translation through space has disappeared. How then, can it be allegedthat though the Motion through space is not continuous, the principle ofactivity implied by the Motion is continuous?
Unquestionably the facts show that the principle of activity continuesto exist under some form. When not perceptible it must be latent. How isit latent? A clue to the answer is gained on observing that though the chandelierwhen seized at the turning point of its swing, gives no impact in the directionof its late movement, it forthwith begins to pull in the opposite direction;and on observing, further, that its pull is great when the swing has beenmade extensive by a violent push. Hence the loss of visible activity at thehighest point of the upward motion, is accompanied by the production of aninvisible activity which generates the subsequent motion downwards. To conceivethis latent activity gained, as an existence equal to the perceptible activitylost, is not easy; but we may help ourselves so to conceive it by consideringcases of another class. §57. When one who pushes against a door that has stuck fast, producesby great effort no motion, but eventually by a little greater effort burststhe door open, swinging it back and tumbling headlong into the room, he hasevidence that the first muscular strain which did not produce transfer ofmatter through space, was yet equivalent to a certain amount of such transfer.
Again, when a railway-porter gradually stops a detached carriage by pullingat the buffer, he shows us that (supposing friction, etc., absent) the slowly-diminishedmotion of the carriage over a certain space, is the equivalent of the constantbackward strain put upon the carriage while it is traveling through thatspace. Carrying with us the conception thus reached, we will now considera case which makes it more definite.
When used as a plaything, a ball fastened to the end of an india-rubberstring yields a clear idea of the correlation between perceptible activityand latent activity. If, retaining one end of the string, a boy throws theball from him horizontally, its motion is resisted by the increasing strainon the string; and the string, stretched more and more as the ball recedes,presently brings it to rest. Where now exists the principle of activity whichthe moving ball displayed? It exists in the strained thread of india-rubber.
Under what form of changed molecular state it exists we need not ask. Itsuffices that the string is the seat of a tension generated by the motionof the ball, and equivalent to it. When the ball has been arrested the stretchedstring begins to generate in it an opposite motion, and continues to acceleratethat motion until the ball comes back to the point at which the stretchingof the string commenced -- a point at which, but for loss by atmosphericresistance and molecular redistribution, its velocity would be equal to theoriginal velocity. Here the truth that the principle of velocity, alternatingbetween visible and invisible modes, does not cease to exist when the translationthrough space ceases to exist, is readily comprehensible; and it becomeseasy to understand the corollary that at each point in the path of the ball,the quantity of its perceptible activity, plus the quantity which is latentin the stretched string, yields a constant sum.
