BOSCOVICH'S THEORY. 



751 



Boscovich's 

 theory of 

 Natural 

 Philoso- 

 phy. 



i j ~ 



Law of 

 continuity. 



What it is. 



Proofs of 

 its exist- 

 ence. 



By induc- 

 tion. 



penetrated the posterior part of A, contrary to the 

 acknowledger 1 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 one 

 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, wkilst 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 are 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 Boscovfch's 



the square of the distance ; and we evidently see that tn e r y of 



magnetism and other forces of that kind act much in f|r. t , ur '* 

 . o T 11 i \ c ii Philoso- 



the same way. In all these, therefore, and the mo- pnv- 



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. 

 The 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. 



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- 

 tion 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 lis 

 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 conceive the length of a day to be the interval 

 from sunset to sunset, or from sunrise to sunset, wc 

 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 



6 



