BOSCOVICH'S THEORY. 



753 



Boscovich' 

 theory of 

 Natural 



phy. 



Absolute 



contact 



impossible, 



Impenetra- 



jilitv. 



Gravity. 



Other 

 powers. 



12, it would be enough, that the repulsive power 

 which w; have now discovered, should be able to ex- 

 tinguish the 6 legrees of difference of velocity, and 

 the actual contact might take place at the very mo- 

 ; ment in which the velocities became equal. But 

 should B, following with 20 degrees of velocity, hit 

 A with 6, the difference or relative velocity is li ; 

 and though the repulsive power be equal to the 

 extinction of 6 degrees, there is still a difference of 8 

 at the time of contact : nay, there must be even a 

 greater difference than 8 degrees ; for the repulsive 

 power will have less time to act than in the former 

 case, and therefore, agreeably to constant experience, 

 it must produce a less effect than before. 



The contact of the two bodies would therefore 

 take place, although the difference of their velocities 

 be even greater than 8 degrees, and we should have 

 the same breach of continuity that we have already 

 demonstrated to be impossible. Nature therefore 

 will provide for this, as for the former case ; and at 

 a distance more minute, an additional force will take 

 away all the 14- degrees of difference even before the 

 contact takes place. But when we have come thus 

 far, it is evident that there can be no limits assign- 

 ed to the increase of the repulsive power, which 

 acts between the two bodies hindering their approach. 

 It must be equal to the extinction of any velocity, 

 however great. We must therefore admit, that the 

 repulsive forces, as the distances are diminished, in- 

 crease ad infinitum : that is, we must admit the ex- 

 istence of the asymptotic arc ED of the curve in 

 Fig. 1st, which exhibits the law of impenetrability, 

 and that the actual contact <rf bodies or particles is al- 

 . together impossible. 



This perhaps is not the only asymptotic arc in the 

 curve of forces : There may be others, or a succes- 

 sion of them a circumstance which opens a fertile 

 field of contemplation. But we proceed to those 

 branches of the curve for which we have undoubted 

 evidence. 



In the first place, the gravity of all bodies, which is 

 daily experienced, evinces, that the repulsive forces 

 which we discover in the smaller distances, is by no 

 means indefinitely extended ; but in the greater dis- 

 tances, giv*s place to a force of attraction : and the 

 laws of Kepler, in astronomy, so happily reduced by 

 Newton under the single law of general gravity, suffi- 

 ciently shew, that this attraction, if it does not ex- 

 tend ad iifif.itum, must, at least, pass as far as the 

 utmost limits of the planetary and cometary system. 

 The curve, expressing the law of forces, has there- 

 fore another arc STY, which, to all sense, is the same 

 with that hyperbola of the third order, of which the 

 ordinates are reciprocally in the duplicate ratio of the 

 distances or abscissa?. But it is evident that there 

 must be some place E, where this curve cuts the axis, 

 and in which the transition is made from attraction 

 to repulsion. 



The phenomena of vapour arising from water, and 

 of air produced from fixed substances, exhibit to us 

 two other limits of the same kind : For in these there 

 i? at firot no .epulsion, but rather an attraction and 

 coherence. Nevertheless their expansion and elastic 

 force are afterwards sufficient manifestations, that a 

 repulsive force exists among their particles. We have 



VOL. 111. l'AHT IV. 



therefore, first, a transition from the primary repul- Boscovich'', 

 sion to attraction ; then to repulsion again ; and last- '^eory ot 

 ly, to the general attraction of gravity. But indeed j> n iloo- 

 there appears to be many such limits and transitions^ p| lv . 

 for without them the numerous effervescences and 

 fermentations in which the particles approach and re- 

 cede so variously, and the phenomena especially of 

 soft bodies, are not otherwise to be explained. 



The whole form of the curve of forces being now 

 elicited, by direct reasoning, from the phenomena, it 

 remains to determine the constitution of the primary 

 elements of matter, as deduced from those forces ; and 

 this being done, the theory, as proposed in the be- 

 ginning of this account of it, may be legitimately ap- 

 plied to mechanical and physical science. 



Seeing that the repulsive force, in lessening the The first 

 distance, increases in infinitum, it is evident, that no elements of 

 particle of matter can be contiguous to, or in contact matter are 

 with, another. The first elements of matter must not ln con- 

 therefore be altogether simple, and composed of no ac ' 

 contiguous parts. They must be also inextended. 



We need not therefore be perplexed with the ques- are inex- 

 tions, whether any division of a real being can be car- tended; 

 ried ad infinitum? or, whether the number of distinct 

 and separable parts of matter be finite or infinite ? or 

 any of the numberless difficulties which arise from 

 the supposed continued extension of body, and which 

 philosophers have hitherto been so much puzzled to 

 explain : For if the first elements of matter are points * 

 altogether fnextended, indivisible, and separated by 

 some interval, the number in any given mass must ne- 

 cessarily be finite. The density of a body may be in- 

 definitely increased as well as diminished ; since the 

 distance between the particles may be indefinitely di- 

 minished ; but upon the supposition of solid and ex- 

 tended elements, there is an evident limit to the increase 

 of density, even when the particles come into contact. 



With the simplicity and inextension of the primary and homo- 

 particles, we should also admit their homogeneity, gencous. 

 The arch of the curve expressing impenetrability, 

 and the exterior arc exhibiting gravity, are always the 

 same; for all bodies are equally impenetrable, and 

 for their quantity of matter are equally heavy. It 

 is therefore exceedingly improbable, that there should 

 be any variety in the other parts of the curve 

 among different particles ; or that it should be dif- 

 ferent in different directions from the same particle. 

 Besides, such a variety is unnecessary, since it can, 

 as we shall soon see, be sufficiently provided for, 

 from the variety in the number and position of the 

 points composing the sensible particles of matter. 



The objections to this doctrine, which are urged 

 by the Leibnitzians, derived from the principle of 

 indiscerniblcs, and of the sufficient reason, (See 

 Leibnitz, ) Boscovich removes, by expressing his 

 conviction, that the infinite mind of the Divinity can 

 perceive the individuation of objects altogether simi- 

 lar ; and, with respect to the sufficient reason, he con- 

 tends for its falsity, as being founded on the princi- 

 ple of necessity, maintained by Leibnitz ; and as to 

 the argument from induction, derived from the won- 

 derful variety we find in nature, where not two leaves 

 in a forest are exactly the same, he says, all this va- 

 riety may be completely produced by the various ar- 

 rangement of the points of matter, seeing their num.- 



