Aided by this illustration, we can vaguely conceive what happens betweenbodies connected, not by a stretched string, but by a traction exercisedby an invisible agency. It matters not to our general conception that theintensity of this traction varies in a different manner: decreasing as thesquare of the distance increases, but being practically constant for terrestrialdistances. Notwithstanding these differences there is a truth common to thetwo cases. The weight of something held in the hand shows that between onebody in space and another there exists a strain. This downward pull affectsthe hand as it might be affected by a stretched elastic string. Hence, whena body projected upwards and gradually retarded by gravity, finally stops,we must regard the principle of activity manifested as having become latentin the strain between it and the Earth -- a strain of which the quantityis to be conceived as the product of its intensity and the distance throughwhich it acts. Carrying a step further our illustration of the stretchedstring, will elucidate this. To simulate the action of gravity at terrestrialdistances, let us imagine that when the attached moving body has stretchedthe elastic string to its limit, say at the distance of ten feet (from whichpoint it is prevented from contracting back), a second like string couldinstantly be tied to the end of the first and to the body, which continuingits course stretched this second string, and so on with a succession of suchstrings, till the body was arrested. Then, obviously, the quantity of theprinciple of activity which the moving body possessed, but which has nowbecome latent in the stretched strings, is measured by the number of suchstrings over which the strain extends. Now though the tractive force of theEarth is not exercised in a like way -- though gravity, utterly unknown inits nature, is probably a resultant of actions pervading the ethereal medium;yet the above analogy suggests the belief that the principle of activityexhibited by a stone thrown up and presently arrested, has not ceased toexist, but has become so much imperceptible or latent activity in the mediumoccupying space; and that when the stone falls, this is re-transformed intoits equivalent of perceptible activity. If we conceive the process at all,we must conceive it thus: otherwise, we have to conceive that a power hasbeen changed into a space-relation, and this is inconceivable.
Here, then, is the solution of the difficulty The space-element of Motionis not in itself a thing. Change of position is not an existence, but themanifestation of an existence. This existence (supposing it not transferredby collision or friction) may cease to display itself as translation; butit can do so only by displaying itself as strain. And this principle of activitynow shown by translation, now by strain, and often by the two together, isalone that which in Motion we can call continuous. §58. What is this principle of activity? Vision gives us no ideaof it. If by a mirror we cast the image of an illuminated object on to adark wall, and then suddenly changing the attitude of the mirror make thereflected image pass from side to side, no thought arises that there is presentin the image a principle of activity. Before we can conceive the presenceof this, we must regard the visual impression as symbolizing something tangible.
Sight of a moving body suggests a principle of activity which would be appreciableby skin and muscles were the body laid hold of. This principle of activitywhich Motion shows us, is the objective sense of effort. By pushing and pullingwe get feelings which, generalized and abstracted, yield our ideas of resistanceand tension. Now displayed by changing position and now by unchanging strain,this principle of activity is ultimately conceived by us under the singleform of its equivalent muscular effort. So that the continuity of Motion,as well as the indestructibility of Matter, is really known to us in termsof Force. Here, however, the Force is of the kind known as Energy -- a wordapplied to the force, molar or molecular, possessed by matter in action,as distinguished from the passive force by which matter maintains its shapeand occupies space: a force which physicists appear to think needs no name. §59. And now we reach the truth to be here especially noted. Allproofs of the Continuity of Motion involve the postulate that the quantityof Energy is constant. Observe what results when we analyze the reasoningsby which the Continuity of Motion is shown.
