750 



BOSCOVICH'S THEORY. 



ZtHC 



tUcory of 



Natural 

 Philoso- 

 phy. 



Plate 

 LXV. 

 (. I, 



wilferent 

 rom that 

 which ex- 

 presses 

 gravity. 



any whatever limits, though it will constantly ap- 

 proach nearer to the line AB, and come at length 

 within less than any assignable distance from it, yet 

 it will never meet it. On the other hand, the curve 

 the direction DE, constantly recedes from the 

 same right line, (nay, even all the other arcs to- 

 wards V, successively recede from it), and first ap- 

 proaching the axis CC, meets it somewhere in E, 

 cuts it, and departs off to a certain distance F ; from 

 whence it begins again to approach the axis, and 

 cuts it again in G ; and thus winds across the axis 

 CC for several times, until, at length, it ends in an- 

 other asymptotic branch T/?s V, which approaches 

 the axis so that the distances from it are apparent- 

 ly in the duplicate ratios of the corresponding dis- 

 tances from the centre A. 



It is hardly necessary to inform the scientific 

 reader, that if from any points of the axis, as a, b, d, 

 there be drawn perpendiculars a g, br, dh; any 

 segment of the axis, as A a, A b, A d, is called an 

 abscissa, and refers to the distance between the two 

 points of matter ; while the perpendicular a g, or b r, 

 or d h, is called the ordinate, and exhibits the mutual 

 force, repulsive or attractive, according as it lies on 

 the side of the axis towards D, or on the opposite 

 tide. 



Now, it is plain that in this form of the curve, 

 the ordinate ag increases beyond any limits what- 

 ever, if the abscissa A a is diminished equally be- 

 yond any given limits ; that if this abscissa be in- 

 creased as in A b, the ordinate is diminished as in 

 br ; and so continually, until it arrives at E, where 

 the ordinate vanishes. Then the abscissa being in- 

 creased to A d, the ordinate changes its direction 

 into d h ; and on the opposite side will increase, first 

 towards F, and then decrease by i I as far as G, 

 where it vanishes ; and again will change its direc- 

 tion into the former, as at m n, and so, after several 

 changes, the ordinates come to have a constant di- 

 rection, as in op, v s, sensibly decreasing in the in- 

 verse ratio of the squares of the abscissas Ao,Ab. 

 Wherefore it is manifest, that, by a curve of this 

 kind, these forces may be expressed ; first repulsive, 

 and in the smallest distances increasing indefinitely as 

 the distances are diminished ; lessening as these are 

 increased ; then vanishing ; then, with a change of 

 direction, passing off into attractive forces, which 

 also, in their turn, vanish ; and at length, after seve- 

 ral changes, they become, in distances sufficiently 

 great, attractive in the inverse duplicate ratio of the 

 distance. 



This curve, which Boscovich has exhibited in a 

 variety of his dissertations, differs considerably from 

 that expressing the Newtonian law of gravity. The 

 latter, which is a hyperbola of the third degree, lies 

 entirely on one side of the axis, and has two asymp- 

 totic branches ; the one of which, forming a part 

 also of Boscovich's curve, expresses the indefinite di- 

 minution of the force of gravity, while the distances 

 are increased ; the other, the indefinite enlargement 

 of that force, when the bodies are sufficiently near. 



According to Boscovich, however, this indefinite 

 enlargement of the force of gravity, is not only con- 

 trary to experiment, but even impossible. He occu- 

 pies a considerable part of the Dissertatio de Legibiu 



verium m Natura existentium in showing that there 

 cannot be attractive forces in the least distances* in- 

 creasing infinitely. For, in the first pjace, if these 

 forces act in small distances, they must augment the 

 velocity of approach until absolute contact. At 

 which instant this augmentation, where it has arri- 

 ved at a maximum state, will be at once destroyed. 



Secondly, should these forces thus acting in mi- 

 nute distances, increase in any inverse ratio of the 

 distance, the velocity increasing constantly until corr- 

 tact must be infinitely greater there than at any given 

 distance ; a supposition which Boscovich considers 

 as absurd, since an infinite velocity implies a finite 

 space passed over in an instant or point of time. For 

 these, and many other reasons unnecessary for us to 

 repeat, Boscovich has rejected the possibility of any 

 attractive force acting in the most minute distances, 

 let the law of action be what it may. But the whole 

 of these difficulties cease at once, were we to suppose 

 that a repulsive force, equal to the extinction of any 

 given velocity, should act in the like situations, since 

 that force must hinder entirely any mutual access or 

 concourse. - 



But it will in all probability be better for us to 

 follow our author, in the account he has given of 

 the way in which the essential parts of this theory 

 were originally suggested to him. 



In writing a dissertation De viribus vivis, or con- 

 cerning living forces, as they are called by the fol- 

 lowers of Leibnitz, and in which he derived all those 

 things commonly referred to the vires vivce, from the 

 sole velocity generated by the powers of gravity, 

 elasticity, &c, he began to enquire more carefully 

 into the velocity produced by impulsion ; where, since 

 the velocity is supposed to be acquired in a moment of 

 time, the force is said to be infinitely greater than 

 any pressure. And it occurred to him, that the laws 

 of percussions of that kind must be very different 

 from the other. But, upon more mature reflection, 

 it appeared, that this notion was inadmissible, since 

 nature every where employed the same mode of ac- 

 tion ; and that immediate impulse or percussion could 

 not exist without the production of a finite velocity 

 in an indivisible moment of time, without a cer- 

 tain saltus and breach of what is called the law of 

 continuity, a law which he conceived really to exist 

 in nature, and to be sufficiently demonstrable. 



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 its 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 saltum, viz. 

 A passing from 6 to 9, and B from 12 to 9, without 

 any transit through the intermediate degrees, 7 and 

 11, 8 and 10, 9\ and 8$, &c. For it wuld 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- 

 tact and the acquisition of the common velocity, have 



Boscovich's 

 theory of 

 Natural 

 Philoso- 

 phy- 



Discovery 

 of the 

 theory. 



Percussion. 



