CHAPTER VII.

THE PERSISTENCE OF RELATIONS 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 most conspicuous antecedents which we distinguish as 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 cooperative 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 here enunciated under its most abstract form, some illustrations will be desirable.

8 64. Let two equal bullets be projected with equal forces; 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 flight, 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 altered shape of the bullet or 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 force 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 proportion, or no difference of relation, among these concurrent phenomena can be imagined as arising, without imagining such difference of proportion or relation as arising uncaused-as arising by the creation or annihilation of force.

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

§ 65. Thus what we call uniformity of law, resolvable as we find it into the persistence of relations among forces, is an immediate 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. Though, in saying this, we seem to be illegitimately inferring that what is true of the ego is also true of the non-ego; yet here this inference is legitimate. For that which we thus predicate as holding in common of ego and non-ego, is that which they have in common as being both existences. The assertion of an existence beyond consciousness, is itself an assertion that there is something beyond consciousness which persists; for persistence is nothing more than continued existence, and existence cannot be thought of as other than continued. And we cannot assert persistence of this something beyond con

sciousness, without asserting that the relations among its manifestations are persistent.

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 illustrations of it.

CHAPTER VIII.

THE TRANSFORMATION AND EQUIVALENCE OF FORCES.

eyes

66. WHEN, to the unaided senses, Science began to add supplementary senses in the shape of measuring instruments, men began to perceive various phenomena which and fingers could not distinguish. Of known forms of force, minuter manifestations became appreciable; and forms of force before unknown were rendered cognizable and measureable. Where forces had apparently ended in nothing, and had been carelessly supposed to have actually done so, instrumental observation proved that effects had in every instance been produced: the forces reappearing in new shapes. Hence there has at length arisen the inquiry whether the force displayed in each surrounding change, does not in the act of expenditure undergo metamorphosis into an equivalent amount of some other force or forces. And to this inquiry. experiment is giving an affirmative answer, which becomes daily more decisive. Meyer, Joule, Grove and Helmholtz are more than any others to be credited with the clear enunciation of this doctrine. Let us glance at the evidence on which it rests.

Motion, wherever we can directly trace its genesis, we find to pre-exist as some other mode of force. Our own voluntary acts have always certain sensations of muscular tension as their antecedents. When, as in letting fall a relaxed limb, we are conscious of a bodily movement requiring no effort, the explanation is that the effort was exerted in