The apparent complication of this, will be best removed, and a general idea of the whole system most readily obtained, by referring to Figure 1. Plate LXV. where the axis CAC' has, in the point A, a' perpendicular drawn to it ; on either side of which, there are two equal and similar branches of a citrve. One of these, DEFGHIKLMNOPQRSTV, has, in the first place, the asymptotic arc ED. That,is, if it were produced towards the parts BD, beyond any whatever- limits, though it' will-constantly proach nearer tb the line AB, and come at length within less than- any assignable distance from it, yet never meet it. On the other hand, the curve in 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 Tp 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 ag, br, dh; any segment of the axis, as A a, A 6, A d, is called an abscissa, and refers to the distance between the two points of matter ; while the perpendicular a g, orb 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 side.
Now, it is plain that in this form of the curve, the ordinate 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 r; and so continually, until it arrives at E, where thi ordinate vanishes. Then the abscissa being in to A d, the, ordinate changes its direction into d Is ;, and on the opposite side will increase, first towards F, and then decrease by i 1 as far as G, where it vanishes ; and again will change its direc tion •into the former, as at na n, and so, after several changes, the ordinates come to have a constant di rection, as in op, vs, sensibly decreasing in the in verse ratio of the squhres of the abscissas A o, A v. 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 great, attractive in the' inverse duplicate ratio of the distance.
This curve, which Boscovich has' in a' variety of his dissertations, differs considerably from that expressing the-Newtonian law of gravity: latter, which is a hypabola of the third degree, lies' entirely on one side of the axis, and has two asymp tbtic branches ; the one of which, forming a part also of Boscovich's curve, expresses the indefinite di mintition of the force ofgravity, while the distances are increased ; the other, the indefinite enlargement of that force, when the bodies'are sufficiently A'ccording,to Boscovich, however, this indefinite' enlargernentrof•the force•of gravity, is rot only con trary to experiment; but'eVen impossible.
pies- a considerable part' of the Disse'rtatio veriwn in Natura existentiunz in showing that there E cannot be attractive forces in the least distances, in- „il creasing infinitely. For, in the first place, if these 1. forces act in small distances, they must augment the r 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 coin 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 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 c the way in which the essential parts of this theory t 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 vivre, from 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 in nature, and to be sufficiently demonstrable.