The “Phantom” Force¹

Abstract

III. WHILE very clearly establishing that it is to the force urging a body that the potential energy which the body has not, but can have, must properly be assigned, and calling it very appropriately the “energy of tension”,² a very apposite remark (which I do not remember to have met with before) is added by “X” in his concluding paragraphs. The body could not command this “force-work” in any position unless it had been pul into the proper position to command it; and the actual energy spent in putting it there is the “energy of tension” which, although forfeited to the force, it can reclaim. In this view it is not surprising that potential energy should have the same terms for its measurement as actual energy, since it is nothing but the actual energy which the body, or some agent operating upon it, has really lost; and if we pa s from permanent forces to those ephemeral ones which physical agents can produce on an already existing arrangement of bodies, then, according to the existing configuration of the bodies when the force is generated, and in proportion to the “potential”, or to the available statical energy developed, so is the work of the agent used to bestow this energy. In these cases of temporary “potentials” the actions are not actions at a distance, but through an intermediate medium, it may be strung with motion, and with permanent forces, which have absorbed the work applied to put the intervening medium, as it were, on the stretch, and to develop the ephemeral energy of tension. But we recognise this very clearly (as for instance in charging well-insulated electrical conductors) only in the rare cases of reversible arrangements. The fatigue and exhaustion which we soon feel when holding out at arm's length a heavy weight (although we do no work upon the weight) arise, for example (like that of a galvanic battery exciting an electro-magnet and supporting a heavy armature), from two causes, the first of which, the excitation of the magnet and armature, and the tightening of the muscles, or producing the requisite statical energy for the occasion, absorb but a small portion of the work. The main expenditure is “frittered away” (a most expressive description of the process, which I owe to Prof. Tait) in aimless and random paths as heat, by the wasteful process of electrical or muscular currents afterwards kept up to maintain the excitation.