From terrestrial physics let us take the case of sound propagated to a great distance. Whenever we are directly conscious of the causation of sound (namely, when we produce it ourselves), its invariable antecedent is force. The immediate sequence of this force we know to be motion—first, of our own organs, and then of the body which we set vibrating. The vibrations so generated we can discern both through the fingers and through the ears; and that the sensations received by the ears are the equivalents of mechanical force communicated to the air, and by it impressed on surrounding objects, we have clear proof when objects are fractured: as windows by the report of a cannon; or a glass vessel by a powerful voice. On what, then, rests the reasoning when, as occasionally happens under favourable circumstances, men on board a vessel a hundred miles from shore, hear the ringing of church-bells on placing their ears in the focus of the main sail; and when it is inferred that atmospheric undulations have traversed this immense distance? Manifestly, the assertion that the motion of the clapper, transformed into the vibrations of the bell, and communicated to the surrounding air, has propagated itself thus far on all sides, diminishing in intensity as the mass of air moved became greater, is based solely upon a certain change produced in consciousness through the ears. The listeners are not conscious of motion; they are conscious of an impression produced on them—an impression which implies a force as its necessary correlative. With force they begin, and with force they end: the intermediate motion being simply inferred.       Again, where, as in celestial physics, the continuity of motion is quantitatively proved, the proof is not direct but inferential; and forces furnish the data for the inference. A particular planet can be identified only by its constant power to affect our visual organs in a special way—to impress upon the retina a group of forces standing in a particular correlation. Further, such planet has not been seen to move by the astronomical observer; but its motion is inferred from a comparison of its present position with the position it before occupied. If rigorously examined, this comparison proves to be a comparison between the different impressions produced on him by the different adjustments of the observing instruments. Going a step further back, it turns out that this difference is meaningless until shown to correspond with a certain calculated position which the planet must occupy, supposing that no motion has been lost. And if, finally, we examine the implied calculation, we find that it makes allowances for those accelerations and retardations which ellipticity of the orbit involves, as well as those variations of velocity caused by adjacent planets—we find, that is, that the motion is concluded to be indestructible not from the uniform velocity of the planet, but from the constant quantity of motion exhibited when allowance is made for the motion communicated to, or received from, other celestial bodies. And when we ask how this communicated motion is estimated, we discover that the estimate is based upon certain laws of force; which laws, one and all, embody the postulate that force cannot be destroyed. Without the axiom that action and re-action are equal and opposite, astronomy could not make its exact predictions; and we should lack the rigorous inductive proof they furnish that motion can never be lost, but can only be transferred.

Similarly with the à priori conclusion that Motion is continuous. That which defies suppression in thought, is really the force which the motion indicates. The unceasing change of position, considered by itself, may be mentally abolished without difficulty. We can readily imagine retardation and stoppage to result from the action of external bodies. But to imagine this, is not possible without an abstraction of the force implied by the motion. We are obliged to conceive this force as impressed in the shape of re-action on the bodies that cause the arrest. And the motion that is communicated to them, we are compelled to regard, not as directly communicated, but as a product of the communicated force. We can mentally diminish the velocity or space-element of motion, by diffusing the momentum or force-element over a larger mass of matter; but the quantity of this force-element, which we regard as the cause of the motion, is unchangeable in thought.

CHAPTER VIII.
THE PERSISTENCE OF FORCE.[[12]]

§ 72. Before taking a first step in the rational interpretation of Evolution, it is needful to recognize, not only the facts that Matter is indestructible and Motion continuous, but also the fact that Force persists. An attempt to assign the causes of Evolution, would manifestly be absurd, if that agency to which the metamorphosis in general and in detail is due, could either come into existence or cease to exist. The succession of phenomena would in such case be altogether arbitrary; and deductive science impossible.

Here, indeed, the necessity is even more imperative than in the two preceding cases. For the validity of the proofs given that Matter is indestructible and Motion continuous, really depends upon the validity of the proof that Force is persistent. An analysis of the reasoning demonstrated that in both cases, the à posteriori conclusion involves the assumption that unchanged quantities of Matter and Motion are proved by unchanged manifestations of Force; and in the à priori cognition we found this to be the essential constituent. Hence, that the quantity of Force remains always the same, is the fundamental cognition in the absence of which these derivative cognitions must disappear.

§ 73. But now on what grounds do we assert the persistence of Force? Inductively we can allege no evidence except such as is presented to us throughout the world of sensible phenomena. No force however, save that of which we are conscious during our own muscular efforts, is immediately known to us. All other force is mediately known through the changes we attribute to it. Since, then, we cannot infer the persistence of Force from our own sensation of it, which does not persist; we must infer it, if it is inferred at all, from the continuity of Motion, and the undiminished ability of Matter to produce certain effects. But to reason thus is manifestly to reason in a circle. It is absurd to allege the indestructibility of Matter, because we find experimentally that under whatever changes of form a given mass of matter exhibits the same gravitation, and then afterwards to argue that gravitation is constant because a given mass of matter exhibits always the same quantity of it. We cannot prove the continuity of Motion by assuming that Force is persistent, and then prove the persistence of Force by assuming that Motion is continuous.

The data of both objective and subjective science being involved in this question touching the nature of our cognition that Force is persistent, it will be desirable here to examine it more closely. At the risk of trying the reader’s patience, we must reconsider the reasoning through 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. From these, through the medium of the equal-armed lever or scales, we derive our equal units of weight, or gravitative force. And it is by means of these equal units of extension and equal units of weight, that 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, and that in any compound afterwards formed by the resulting carbonic acid the whole of the original carbon is present, what is his repeatedly assigned proof? That afforded by the scales. In what terms is the verdict of the scales given? In grains—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 quantity of matter is asserted to be the same, if the number of units of force it counter-balances is the same. 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 grain-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 physics 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, should 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 momenta which the respective masses will generate in each other in a given time, are calculated; and compounding these with the momenta 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 fixed, the motion may be proved to be undiminished; or assuming the motion to be undiminished, the masses may be proved to be fixed. 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. They equally assume it in the abstract principle with which they set out; and which they repeat in justification of every step. 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 is persistent. The allegation really amounts to this, that there cannot be an isolated force beginning and ending in nothing; but that any force manifested, implies an equal antecedent force from which it is derived, and against which it is a reaction. Further, that the force so originating cannot disappear without result; but must expend itself in some other manifestation of force, which, in being produced, becomes its reaction; and so on continually. Clearly then the persistence of Force is an ultimate truth of which no inductive proof is possible.

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 and 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 whoever contemplates the relation in which it stands to the truths of science in general, will see that this truth transcending demonstration is the persistence of Force.