The Persistence of Relation Among Forces §63. The first deduction to be drawn from the ultimate universaltruth that force persists, is that the relations among forces persist. Supposinga 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 orsucceeded by such other manifestation. Every antecedent mode of the Unknowablemust have an invariable connexion, quantitative and qualitative, with thatmode of the Unknowable which we call its consequent.
For to say otherwise is to deny the persistence of force. If in any twocases there is exact likeness not only between those conspicuous antecedentswhich we call the causes, but also between those accompanying antecedentswhich we call the conditions, we cannot affirm that the effects will differ,without affirming either that some force has come into existence or thatsome force has ceased to exist. If the co-operative forces in the one caseare 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 theone case as unlike that in the other; without conceiving one or more of theforces to have increased or diminished in quantity; and this is conceivingthat force is not persistent.
To impress the truth thus enunciated under its most abstract form, someillustrations will be desirable. §64. Let two bullets, equal in weights and shapes, be projected withequal energies; then, in equal times, equal distances must be travelled bythem. The assertion that one of them will describe an assigned space soonerthan the other, though their initial momenta were alike and they have beenequally resisted (for if they are unequally resisted the antecedents differ)is an assertion that equal quantities of force have not done equal amountsof work; and this cannot be thought without thinking that some force hasdisappeared into nothing or arisen out of nothing. Assume, further that duringits night one of them has been drawn by the Earth a certain number of inchesout of its original line of movement; then the other, which has moved thesame distance in the same time, must have fallen just as far towards theEarth. No other result can be imagined without imagining that equal attractionsacting for equal times, have produced unequal effects; which involves theinconceivable 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 greaterlocal density in the target, cannot be mentally represented. Such a modificationof the consequents without modification of the antecedents, is thinkableonly through the impossible thought that something has become nothing ornothing has become something.
It is thus not with sequences only, but also with simultaneous changesand permanent co-existences. Given charges of powder alike in quantity andquality, fired from barrels of the same structure, and propelling bulletsof equal weights, sizes, and forms, similarly rammed down;*<* This waswritten while muzzle-loading was still usual.> and it is a necessaryinference that the concomitant actions which make up the explosion, willbear 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 inthe other; and the two recoils will be alike. For no difference, of relationamong these concurrent phenomena can be imagined as arising, without imaginingit as arising by the creation or annihilation of energy.
That which holds between these two cases must hold among any number ofcases; and that which here holds between comparatively ****** antecedentsand consequents, must hold however involved the antecedents become and howeverinvolved the consequents become. §65. Thus Uniformity of Law, resolvable as we find it into the persistenceof 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 conclusiondeducible from the ultimate datum of consciousness.
More than this may be said. Every apparent inductive proof of the uniformityof law itself takes for granted both the persistence of force and the persistenceof relations among forces. For in the exact sciences, in which alone we mayseek relations definite enough to prove uniformity, any alleged demonstrationmust depend on measurement; and as we have already seen, measurement, whetherof matter or force, assumes that both are persistent in assuming that themeasures have not varied. While at the same time every determination of therelations among them -- in amount, proportion, direction, or what not --similarly implies measurement, the validity of which as before implies thepersistence of force.
That uniformity of law thus follows inevitably from the persistence offorce, will become more and more clear as we advance. The next chapter willindirectly supply abundant frustrations of it.
