For instance, let• two equal bodies be conceived" moving in the same direction ; A, which precedes, . with the velocity 6, and B following with the velo-. city. 12. After collision, it. is well known they both proceed with the velocity 9. Now if .each of the bodies retains it6 velocity until the very moment' of collision, it must follow, that at that very.instant, the one diminishes its velocity, while the other in creases, and each of them abruptly, per saltunz, viz.. A passing from 6.to 9, and B from 12 'to 9, without any. transit through the intermediate' degrees, 7 and Fl, 8-and' 1Q, 9; and 8,i, etc. Fur it would be ab surd to say; that during the contact any change • through the intermediate degrees ,can take place ; for the anterior, parts. of B; which is, by hypo thesis, moving faster, must, ,in the small portion of time which elapses between, the beginning of the con the acquisition of have s penetrated the posterior part of A, contrary to the acknowledged properties of matter. The change must, therefore, be abrupt ; and, consequently, in volve a breach Of the law of continuity, according to -which it is altogether impossible to pass from degree of magnitude to another, without also passing through all the intermediate degrees.
There are many who get rid of this difficulty, by denying altogether the existence of bodies perfectly hard, or incapable of compression, and by alleging .that the change of velocity takes place during the introcession or compression of the parts of the bodies, without any breach of the law of continuity.
But this argument is of no avail to those who, 'with Newton and Most of the ancient philosophers, suppose the first elements of matter to be altogether hard and solid, incapable of change of figure. •For, what are we to make of the .meeting of two atoms, ..or two monads, or by whatever other name we desig nate these primary particles of matter ? Maclaurin saw this difficulty, when.contemplating the collision of bodies, in his Account of Newton's Discoveries, book i. ch. 4.,,and finding that there was no way of preserving the law of continuity invio late in the case of actual contact, he allowed a breach of it in the collision of hard bodies. He had not the boldness to reject, as Boscovich has done, -impulsion and immediate contact altogether, and to insist -that a breach of the law • of continuity is altogether im possible.
The law of which we are now treating consists in this, that any variable quantity, whilst it passes from one magnitude to another, passes through all the in termediate magnitudes of the same kind ; by which it is to be understood, not that the different .magni
tudes are formed by certain small and momentary ac cessions, for that, as Maupertuis has objected, would be itself a breach of the law of continuity ; but that to every particular instant a particular state corre sponds, and that the increments or decrements are only formed during continued portiOns of time.
That this law. of continuity exists in nature, the majority of philosophers do admit. Boscovich con ceives that a breach of it is altogether impossible ; and has endeavoured to prove so, in several of -his wri tings, by the folloWing inductive reasoning.
The continuity is preserved in every kind of mo tion, since moving bodies •describe continued lines. The planets and comets perform their courses in con tinued lines ; their retrogradations arc gradual, and even when they appear stationary, there is always some little motion. The light of day comes in by the morning dawn, and departs by the evening twi light. The diameter of the sun, not suddenly', but by a continued motion, ascends above the horizon, or descends below it. Heavy bodies projected oblique ly perform, in like manner,• their motions in conti nued lines, viz. parabolas, if -we exclude the resist ance of the.air ; or, if we admit that, in curves-ap proaching the hyperbola. And, indeed, they must always have some little obliquity; it being infinitely improbable that any Of.them should be so projected, as to ascend and descend in a perpendicular line. Every other Motion depending on gravity, as well as on magnetism.or electricity, must necessarily follow the law of continuity. Gravity acts universally as the square of the distance ; and we evidently see that magnetism and other forces of that kind act much in the same way. In all these, therefore, and the mo tions dependent on them, the law of continuity is strictly observed, as wall in the lines described, as in the velocities acquired. Hence in natural motions there is nothing angular ; but the change of direction is always made gradually. And even in bodies them selves there are no exact angles ; for, however sharp the point or edge may appear in thorns and prickles, the beaks and talons of birds, or the like, the curva ture is always evident, at least through the. microscope. Thd same thing is also to be observed in the courses of rivers, the leaves of trees, the .twigs and branches, stones, and the like. In short, if we go through all nature, we find the continuity strictly, adhered to, if all things be rightly considered ; and it may be enough to challenge a single instance to'be produced • to the contrary, or where the continued connection is alto gether' undiscoverable.