752 



BOSCOVICH'S TftEORY. 



Natural 

 I'hiloso- 



JlllY. 



A hreach 

 ot it im- 

 puuible. 



I' above spoken of. In like manner, we say one oscil- 

 r >' ."' 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 

 shew, 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- 

 visible. 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 6tate 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 

 creation From nothing, or annihilation, the passage is 

 made per sallum : Our author replies that it is not ; 

 that, in these cases, there is no passage from one state 

 to another ; that 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 Boscnvich't 

 be real and existing limits : But nothing has no limit ; ,,,e< "7 " f 

 and therefore, in creation, a body passes over no in- p, at . llra ' 

 termediate state. It begins to exist, and to have a state, phv S ' 

 and existence is not divisible. In passing from posi- "' . 

 tive to negative quantities, have we not a saltits? In 

 changing from attraction to repulsion, have we no f a 

 breach of continuity in our very theory itself ? To 

 this we answer, that the attractive forces diminish 

 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. 



In this sense, too, rest is a real state of existence 

 so is no velocity, or perseverance in the same place, 

 no force or perseverance in retaining the previous ve- 

 locity ; and so of others. These differ greatly from 

 non-existence. When, in the solution of a problem, 

 we arrive at a quantity of the former description, the 

 determination is real, though of a peculiar kind. But 

 we arrive at an expression of the latter kind only, 

 where the problem is impossible. 



From what we have now said, we believe that the 

 general law of continuity is sufficiently manifest; and 

 it will be hardly necessary for us, as Boscovich has 

 done, to prove that, upon the same principles, the 

 change from one velocity to another never takes place 

 but by passing through all the intermediate veloci- 

 ties. For example, if there was an abrupt passage 

 from the velocity 6, arising from all the preceding 

 circumstances affecting the moving body, to the velo- 

 city 9, then, at the very instant of the passage, we 

 have a determination to two different velocities, 

 which, as already shown, would be absurd. 



It is therefore evident, that the whole velocity of a Deduction 

 body, can neither be created nor extinguished in a mo- of the law 

 ment : and consequently, in the collision of two bo- f force*, 

 dies, there must be a breach of the law of continuity, 

 if the contact takes place with any determinate dif- 

 ference of their velocities. Let us see what must 

 happen, if no such breach be admitted, since these 

 bodies cannot come into contact with the previous ve- 

 locities. The velocities must begin immediately to 

 change, either by the increase or diminution of one 

 or both. The cause of such a change as this, is called 

 a force; and there must consequently be some force 

 acting to produce this effect, even though the bodies 

 have not yet come into contact. 



To prevent the breach of continuity, it would be 

 sufficient that the forces should act only on one of 

 the bodies ; but from the principle of the equality 

 of action and reaction, for which there is abundant 

 evidence by induction, we must suppose, that this 

 force is mutual between them, increasing the velocity 

 of the one at the same rate as it diminishes that of 

 the other. This is, in fact, producing a sort of op- 

 posite velocities, by which, if the bodies were impres- 

 sed alone, they would be made to recede. The force 

 is therefore repulsive, and it becomes us to enquire 

 into the laws by which it is regulated. In the case 

 above mentioned, where A, moving with the velocity 

 6, is overtaken and hit by B, moving with the velocity 



