From. this ample and general inductive reasoning, Boscovich would infer that the law of continuity is really universal ; and that, so far from conceding it in those cases where observation seems to contradict it, it -becomes us rather to search for some explana , ton by which they may be reconciled with the general law. To do otherwise, would be to contradict one of the fundamental principles of sound philosophy. For in the investigation of the general laws of nature, there is scarcely any other mode of- procedure than by induction: By its means, extension, figurability, mobility, impenetrability, have been always, even by the ancient philosophers, admitted as properties of matter ; and, in like manner, later philosophers have to these added inertia and general gravity. And although even in these, there appear to be some •bo dies which admit of a deviation from these general laws, yet a careful examination enables us to give a rational explanation of such cases, reconcileable with them ; and:therefore we consider such cases as no ways militating against the acknowledged principle. For example, because we see so many of the bodies that we have among. our hands resist others when we try to make them occupy the same -place, and rather giving way when the resistance is unequal, 'we admit the impenetrability of bodies ; nor does it prevent Us from doing so, that there are some which may insi - nuate themselves into other and even very hard bo dies, as oil into marble, light into glass and gems ; for this phenomenon can be easily reconciled-with im penetrability, by saying that these bodies penetrate through the pores and openings of the others.
Now the proofs by induction of the law of continu ity, are as abundant and as convincing as those for the impenetrability of matter. We sometimes 'make abrupt passages in our minds. Thus in physics, if we coriceive,the length of a day to be the interval from sunset to sunset, or from sunrise to sunset, we say, the preceding day differs'from the following by some seconds, where there -appears no intermediate day which differs less : but if we. take all the places on the same parallel, we find a series composed of days of all the intermediate lengths, the first of which was the preceding, and the last, the following. day above spoken of. In like manner, we say one oscil lation of the pendulum is shorter than the preceding, not observing, that if we were to subdivide the arcs, and compare corresponding parts, we would find , the change of velocity gradual throughout the whole course of the oscillation. The saltus, therefore, is not in nature, but in our minds. We are often apt to . confound a quick motion with an instantaneous one ; and to suppose something done in a moment, which, in fact, is done, in a continued, though very short space of time. Thus some will say, that a stone thrown from the hand, or water spouting from a vessel, acquires instantaneously a finite velocity. But in the. former case it is evident, that a finite velocity can by no means be produced in a moment. There must be some time, however little, for the mind to act upon the nerves and muscles, for the extension of the fibres and the like ; and if we would give any sensible velocity to the stone, the hand must be drawn back, and the stone held for some time, until by re turning it forwards, and perpetually accelerating it, we communicate to it the requisite velocity. In like
manner, the ball is not thrown out abruptly from the gun : for a certain space of time will be requisite ere the whole of the powder be inflamed, the air dilated, that by its elasticity the ball may be gradually acce lerated.
But however satisfactory this inductive reasoning may be, our author has adduced other arguments to spew, that a breach of the law of continuity is meta physically impossible. These arguments he derives from the very nature of continuity. . As was long ago observed by Aristotle, the limit which joins the precedent conditions with the consequent, must, in that respect, be common to both, and therefore indi Thus the superficies, which is the common boundary of two solids, is destitute of thickness ; the line separating the two parts of a continued sur face, has no breadth ; and a point separating the seg ments of a continued line, is altogether indivisible. Thus also in time, when an hour ends,' the next im mediately begins, the common boundary being an in divisible instant. Neither can two instants be chosen so contiguous, but that a finite portion of time must intervene between them, which is again divisible ad infinitum. Thus also in any variable quantity, since all variations are made in time, they all partake of its continuity ; and to every instant which may be as signed, a certain state of the variable quantity will correspond : As after the sixth hour we cannot have the 9th, without having previously the 7th and 8th ; so in motions, you cannot go from the distance 6 to the distance 9, without previously passing through the distances 7 and 8 ; for in that instant of passage, you would be both at the distance 6, and at the dis tance 9, which is evidently impossible. The same thing may be said of density, of heat and cold in the thermometer, and the weight of the air ; and, in fine, of all variable quantities.
But against this argument it may seem, that in vreation from nothing, or annihilation, the passage is made per saltum : Our author replies that it is not ; that, in cases, there is no passage from one state to another ; tbAt nonexistence is no state, but a. mere nothing, which, of course, has no properties or boun dary. Of a finite; real and existing series, there must be real and existing limits : But nothing has no limit ; and therefore, in creation, a body passes over no in termediate state. It begins to exist, and to have a state, and existence is not divisible. In passing from posi tive to negative quantities, have we not a saltus? In changing from attraction to repulsion, have we not a breach of continuity in .our very theory itself? To this we answer, that attractive forces dimini;h through all intermediate degrees down to nothing, through which, as a limit, they pass to repulsion. Nothing here, however, does not properly imply non existence, but is merely relative, and expresses the limit between two different variable states of exist ence, as the single parabola is the limit between the infinite variety of the ellipse and hyberbola.