University of Virginia Library

Chapter 7
The Persistence of Relation Among Forces

§63. The first deduction to be drawn from the ultimate universal truth that force persists, is that the relations among forces persist. Supposing a given manifestation of force, under a given form and given conditions, be either preceded by or succeeded by some other manifestation, it must, in all cases where the form and conditions are the same, be preceded by or succeeded by such other manifestation. Every antecedent mode of the Unknowable must have an invariable connexion, quantitative and qualitative, with that mode of the Unknowable which we call its consequent.

For to say otherwise is to deny the persistence of force. If in any two cases there is exact likeness not only between those conspicuous antecedents which we call the causes, but also between those accompanying antecedents which we call the conditions, we cannot affirm that the effects will differ, without affirming either that some force has come into existence or that some force has ceased to exist. If the co-operative forces in the one case are equal to those in the other, each to each, in distribution and amount; then it is impossible to conceive the product of their joint action in the one case as unlike that in the other; without conceiving one or more of the forces to have increased or diminished in quantity; and this is conceiving that force is not persistent.

To impress the truth thus enunciated under its most abstract form, some illustrations will be desirable.

§64. Let two bullets, equal in weights and shapes, be projected with equal energies; then, in equal times, equal distances must be travelled by them. The assertion that one of them will describe an assigned space sooner than the other, though their initial momenta were alike and they have been equally resisted (for if they are unequally resisted the antecedents differ) is an assertion that equal quantities of force have not done equal amounts of work; and this cannot be thought without thinking that some force has disappeared into nothing or arisen out of nothing. Assume, further that during its night one of them has been drawn by the Earth a certain number of inches out of its original line of movement; then the other, which has moved the same distance in the same time, must have fallen just as far towards the Earth. No other result can be imagined without imagining that equal attractions acting for equal times, have produced unequal effects; which involves the inconceivable proposition that some action has been created or annihilated. Again, one of the bullets having penetrated the target to a certain depth, penetration by the other bullet to a smaller depth, unless caused by greater local density in the target, cannot be mentally represented. Such a modification of the consequents without modification of the antecedents, is thinkable only through the impossible thought that something has become nothing or nothing has become something.

It is thus not with sequences only, but also with simultaneous changes and permanent co-existences. Given charges of powder alike in quantity and quality, fired from barrels of the same structure, and propelling bullets of equal weights, sizes, and forms, similarly rammed down; and it is a necessary inference that the concomitant actions which make up the explosion, will bear to one another like relations of quantity and quality in the two cases. The proportions among the different products of combustion will be equal. The several amounts of energy taken up in giving momentum to the bullet, heat to the gases, and sound on their escape, will preserve the same ratios. The quantities of light and smoke in the one case will be what they are in the other; and the two recoils will be alike. For no difference, of relation among these concurrent phenomena can be imagined as arising, without imagining it as arising by the creation or annihilation of energy.

That which holds between these two cases must hold among any number of cases; and that which here holds between comparatively simple antecedents and consequents, must hold however involved the antecedents become and however involved the consequents become.

§65. Thus Uniformity of Law, resolvable as we find it into the persistence of relations among forces, is a corollary from the persistence of force. The general conclusion that there exist constant connexions among phenomena, ordinarily regarded as an inductive conclusion only, is really a conclusion deducible from the ultimate datum of consciousness.

More than this may be said. Every apparent inductive proof of the uniformity of law itself takes for granted both the persistence of force and the persistence of relations among forces. For in the exact sciences, in which alone we may seek relations definite enough to prove uniformity, any alleged demonstration must depend on measurement; and as we have already seen, measurement, whether of matter or force, assumes that both are persistent in assuming that the measures have not varied. While at the same time every determination of the relations among them — in amount, proportion, direction, or what not — similarly implies measurement, the validity of which as before implies the persistence of force.

That uniformity of law thus follows inevitably from the persistence of force, will become more and more clear as we advance. The next chapter will indirectly supply abundant frustrations of it.

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