University of Virginia Library

Chapter 6
The Persistence of Force*

§60. In the foregoing two chapters, manifestations of force of two fundamentally-different classes have been dealt with — the force by which matter demonstrates itself to us as existing, and the force by which it demonstrates itself to us as acting.

Body is distinguishable from space by its power of affecting our senses, and, in the last resort, by its opposition to our efforts. We can conceive of body only by joining in thought extension and resistance: take away resistance, and there remains only space. In what way this force which produces space-occupancy is conditioned we do not know. The mode of force which is revealed to us only by opposition to our own powers, may have for one of its factors the mode of force which reveals itself by the changes initiated in our consciousness. That the space a body occupies is in part determined by the degree of that activity of its molecules known as heat, is a familiar truth. Moreover, such molecular rearrangement as occurs when water is changed into ice, is shown to be accompanied by an evolution of force which may burst the containing vessel and give motion to the fragments. Nevertheless, the forms of our experience oblige us to distinguish between two modes of force; the one not a worker of change and the other a worker of change, actual or potential. The first of these — the space-occupying kind of force — has no specific name.

For the second kind of force, the specific name now accepted is "Energy." That which in the last chapter was spoken of as perceptible activity, is called by physicists, "actual energy;" and that which was there spoken of as latent activity, they call "potential energy." While including the mode of activity shown in molar motion, Energy includes also the several modes of activity into which molar motion is transformable — heat, light, etc. It is the common name for the power shown alike in the movements of masses and in the movements of molecules. To our perceptions this second kind of force differs from the first kind as being not intrinsic but extrinsic.

In aggregated matter as presented to sight and touch, this antithesis is, as above implied, much obscured. Especially in a compound substance, both the latent energy locked up in the chemically-combined molecules and the actual energy made perceptible to us as heat, complicate the manifestations of intrinsic force by the manifestations of extrinsic force. But the antithesis, here partially hidden, is clearly seen on reducing the data to their lowest terms — a unit of matter, or atom, and its motion. The force by which it exists is passive but independent; while the force by which it moves is active but dependent on its past and present relations to other atoms. These two cannot be identified in our thoughts. For as it is impossible to think of motion without something that moves, so it is impossible to think of energy without something possessing the energy.

While recognizing this fundamental distinction between that intrinsic force by which body manifests itself as occupying space, and that extrinsic force distinguished as energy, I here treat of them together as being alike persistent. And I thus treat of them together partly because, in our consciousness of them, there is the same essential element. The sense of effort is our subjective symbol for objective force in general, passive and active. Power of resisting that which we know as our own muscular strain, is the ultimate element in our idea of body as distinguished from space; and any motor energy which we give to body, or receive from it, is thought of as equal to a certain amount of muscular strain. The two consciousnesses differ essentially in this, that the feeling of effort common to them is in the last case joined with consciousness of change of position, but in the first case is not.*

There is, however, a further and more important reason for here dealing with the proposition that Force under each of these forms persists. We have to examine its warrant.

§61. A little more patience is asked. We must reconsider the reasoning by which the indestructibility of Matter and the continuity of Motion are established, that we may see how impossible it is to arrive by parallel reasoning at the Persistence of Force.

In all three cases the question is one of quantity. Does the Matter or Motion, or Force, ever diminish in quantity? Quantitative science implies measurement, and measurement implies a unit of measure. The units of measure from which all others of any exactness are derived, are units of linear extension. Our units of linear extension are the lengths of masses of matter or the spaces between marks made on the masses, and we assume these lengths, or these spaces between marks, to remain unchanged while the temperature is unchanged. From the standard-measure preserved at Westminster, are derived the measures for trigonometrical surveys, for geodesy, the measurement of terrestrial arcs, and the calculations of astronomical distances, dimensions, etc., and therefore for Astronomy at large. Were these units of length, original and derived, irregularly variable, there could be no celestial dynamics, nor any of that verification yielded by it of the constancy of the celestial masses and of their energies. Hence, persistence of the space-occupying species of force cannot be proved, for the reason that it is tacitly assumed in every experiment or observation by which it is proposed to prove it. The like holds of the force distinguished as energy. The endeavour to establish this by measurement, takes for granted both the persistence of the intrinsic force by which body manifests itself as existing, and the persistence of the extrinsic force by which body acts. For it is from these equal units of linear extension, through the medium of the equal-armed lever or scales, that we derive our equal units of weight, or gravitative force; and only by means of these can we make those quantitative comparisons by which the truths of exact science are reached. Throughout the investigations leading the chemist to the conclusion that of the carbon which has disappeared during combustion, no portion has been lost, what is his repeatedly-assigned proof? That afforded by the scales. In what terms is the verdict of the scales given? In grammes — in units of weight — in units of gravitative force. And what is the total content of the verdict? That as many units of gravitative force as the carbon exhibited at first, it exhibits still. The validity of the inference, then, depends entirely upon the constancy of the units of force. If the force with which the portion of metal called a gramme-weight tends towards the Earth, has varied, the inference that matter is indestructible is vicious. Everything turns on the truth of the assumption that the gravitation of the weights is persistent; and of this no proof is assigned, or can be assigned. In the reasonings of the astronomer there is a like implication, from which we may draw the like conclusion. No problem in celestial dynamics can be solved without the assumption of some unit of force. This unit need not be, like a pound or a ton, one of which we can take direct cognizance. It is requisite only that the mutual attraction which some two of the bodies concerned exercise at a given distance, shall be taken as one; so that the other attractions with which the problem deals, may be expressed in terms of this one. Such unit being assumed, the motions which the respective masses will generate in one another in a given time, are calculated; and compounding these with the motions they already have, their places at the end of that time are predicted. The prediction is verified by observation. From this, either of two inferences may be drawn. Assuming the masses to be unchanged, their energies may be proved undiminished; or assuming their energies undiminished, the masses may be proved unchanged. But the validity of one or other inference depends wholly on the truth of the assumption that the unit of force is unchanged. Let it be supposed that the gravitation of the two bodies towards each other at the given distance has varied, and the conclusions drawn are no longer true. Nor is it only in their concrete data that the reasonings of terrestrial and celestial physics assume the Persistence of Force. The equality of action and reaction is taken for granted from beginning to end of either argument; and to assert that action and reaction are equal and opposite, is to assert that Force persists. The implication is that there cannot be an isolated force, but that any force manifested implies an equal antecedent force from which it is derived, and against which it is a reaction.

We might indeed be certain, even in the absence of any such analysis as the foregoing, that there must exist some principle which, as being the basis of science, cannot be established by science. All reasoned-out conclusions whatever must rest on some postulate. As before shown (§23), we cannot go on merging derivative truths in those wider truths from which they are derived, without reaching at last a widest truth which can be merged in no other, or derived from no other. And the relation in which it stands to the truths of science in general, shows that this truth transcending demonstration is the Persistence of Force. To this an ultimate analysis brings us down, and on this a rational synthesis must build up.

§62. But now what is the force of which we predicate persistence? That which the word ordinarily stands for is the consciousness of muscular tension — the feeling of effort which we have either when putting something in motion or when resisting a pressure. This feeling, however, is but a symbol.

In §18 it was said that though, since action and reaction are equal and opposite, we are obliged to think of the downward pull of a weight as equal to the upward pull which supports it, and though the thought of equality suggests kinship of nature, yet, as we cannot ascribe feeling to the weight, we are obliged to admit that Force as it exists beyond consciousness has no likeness to force as we conceive it, though there is between them the kind of equivalence implied by simultaneous variation. The effort of one who throws a cricket ball is followed by the motion of the ball through space, and its momentum is re-transformed into muscular strain in one who catches it. What the force was when it existed in the flying cricket ball it is impossible to imagine: we have no terms of thought in which to represent it. And it is thus with all the transformations of energy taking place in the world around. Those illustrations given in §66, showing the changes of form which energy undergoes and the equivalence between so much of it in one form and so much in another, fail to enlighten us respecting the energy itself. It assumes under this or that set of conditions this or that shape, and the quantity of it is not altered during its transformations. For that interpretation of things which is alone possible for us this is all we require to know — that the force or energy manifested, now in one way now in another, persists or remains unchanged in amount. But when we ask what this energy is, there is no answer save that it is the noumenal cause implied by the phenomenal effect.

Hence the force of which we assert persistence is that Absolute Force we are obliged to postulate as the necessary correlate of the force we are conscious of. By the Persistence of Force, we really mean the persistence of some Cause which transcends our knowledge and conception. In asserting it we assert an Unconditioned Reality, without beginning or end.

Thus, quite unexpectedly, we come down once more to that ultimate truth in which, as we saw, Religion and Science coalesce — the continued existence of an Unknowable as the necessary correlative of the Knowable.

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