760 



BOSCOVICH'S THEORY. 



Philoso- 

 phy- 



Plate 

 I.XV. 



Fig. 7. 



Fiif. 7. 



lioscovich's This theorem is general, and applies equally to 

 r y . the mutual action of three points hating any position, 

 whether in a right line or not. But its application 

 to unequal masses makes it much more general, and 

 will lead us to the equilibrium of the lever, centres 

 of oscillation, percussion, &c. 



If the three points do not lie in a straight line, 

 they will be in equilibrio only when the distances ex- 

 pressing the sides of the triangle correspond to li- 

 mits. Let AE, EB, BA, (Fig. 7.) be distances 

 constituting an assemblage of this 'kind; and let 

 AErrEB : let FEOH be an ellipse passing through 

 E, with A and B its foci. Let AN, Fig. 1., be 

 equal to the semitransyerse DOr=BE=AE, and let 

 DB be less than the breadth of the next arcs LN, 

 NP, Fig. 7. ; and the arcs NM, NO, Fig. 7., equal 

 and similar. It is plain, that if the point E were 

 moved to C, the attraction of A in CL, and repul- 

 sion of B in CM, would compose a force in CI along 

 the; tangent, which would return C to E ; since BC 

 would be as much shorter than at first as A was 

 longer ; and to these equal removals from the inter- 

 section, equal ordinates or forces will correspond. 



But should the point E be brought to O, the 

 forces of A and B will be equal and opposite, and 

 no motion will arise, unless the point be otherwise 

 somewhat removed from it, in which case it will re- 

 cede still farther, and pass with an accelerated mo- 

 tion toward^ E or H. The points E and H, there- 

 fore, are exactly similar to the limits of cohesion in 

 the original curve, Fig 1. ; the points F and O are 

 limits of non-cohesion. On the other hand, if the 

 distance BC was that of a limit of non-cohesion, the 

 less distance CB would produce an attraction CK ; 

 the greater AC, a repulsion ; and the resulting force 

 CG would make the point C pass to O. So that, 

 in that case, F and O would be limits of cohesion, 

 E and H of non-cohesion. 



The point C, if removed a little from the peri- 

 phery of the ellipse, will return towards it ; for the 

 increasing attractions when it passes without the 

 ellipse, and the increasing repulsion when within it, 

 will compose a force, in either case, tending towards 

 the periphery and the limits of cohesion. This as- 

 semblage of three points may even serve to give us 

 some idea of solidity, for if any thing should stop 

 the motion of the point B, Fig. 7., while the point 

 A is made to revolve round it, as from A to A' ; the 

 point E will, in like manner, pass from E to E', still 

 preserving the original form of the triangle. But 

 enough of the system of three points. 



The system of four or more points would afford us 

 a much greater variety, were we carefully to examine 

 them. We shall only observe, that if two points be 

 situated in the foci of an ellipse, and two others at 

 the vertices of the conjugate axis, they will form a 

 kind of square or rhombus ; and if on the four angles 

 of this square, there be conceived a series of points of 

 the same kind, to any height, some idea may be got of 

 the solid rod, in which, if the base be inclined, the 

 whole superstructure will immediately be moved to one 

 aide. And the celerity of conversion will depend partlv 

 on the magnitude of the connecting forces : for should 

 that be weak, the upper part of the structure will 

 move more slowly, and the rod will be bent like a 



Fig. 7. 



Of the sys- 

 tem of four 

 points. 



switch. And four points may be placed out of the Bu<covicKV 

 same plane, so that they will powerfully preserve t '; cor >' of 

 their position, even by the help of a single limit of phn^L. 

 distance sufficiently powerful : for the four points (,_, 

 may be arranged as a triangular p ; ramid, which will -y _ j 

 therefore constitute a kind of particle most tenacious 

 of its shape. Of four of these particles, disposed in 

 another pyramid, a particle of a second order may be 

 formed, less firm on account of the greater distance 

 of the primary particles composing it, whence the 

 action of external points upon it will be more un- 

 equal. In like manner, of these particles others may 

 be formed of a higher order, still less firm; and thus 

 at length we may arrive at those, which) being much 

 greater, are more moveable and variable, upon which 

 chemical operations depend, and of which the grosser 

 bodies are composed ; so that we" would arrive at the 

 same thing as Newton has proposed in his last optical 

 query respecting his primary and elementary par- 

 ticles, which compose other particles of various or- 

 ders. 



And here we would beg leave to object to Bos- Remark, 

 covich, that since he has admitted that all the par- 

 ticles of matter may be formed upon the supposition 

 only of one limit of distance, what good reason can 

 be given for supposing, as he has done, that there 

 are a succession of changes from attraction to repul- 

 sion, and vice versa, according to the change in the 

 distance of his primary points. Surely this is to con- 

 tradict one of the first rules of philosophising, and to 

 multiply causes without necessity. Would it not 

 have been infinitely preferable, to have proceeded at 

 once upon that supposition, for the existence of which 

 he appears to have brought forward such abundant 

 proof? In so doing, his theory would have appeared 

 abundantly more simple, and equally satisfactory. 

 We can see no use whatever for. that vague and Pro- 

 teus-like law of forces which he has just been esta- 

 blishing, unless it be to use a favourite phrase of his 

 own, to exhibit the injinitafjecunditas theories. How 

 different from, we had almost said how unsatisfac- 

 tory in comparison to, the beautiful law of Newton- 

 ian gravity, by which the infinite variety of physical 

 astronomy, the more generally it is applied, is the 

 more completely explained ! Compared to this, in- 

 deed, the theory of Boscovich is like the orbs, the 

 deferents, and the epicycles of our forefathers, which, 

 instead of explaining, only tended to multiply the 

 difficulties of our progress in science. But we defer 

 this, and some other remarks, until we have com- 

 pleted our account of the theory, and in the mean 

 time return to its application to mechanics, perhaps 

 the most valuable part of his work, and which is, in 

 reality, little dependent upon this peculiar law of 

 forces. 



In proceeding to the consideration of masses, the Of masses. 

 first subject which offers is, the numerous and import- 

 ant properties of the centre of gravity. These are 

 readily derived and demonstrated from our theory ; 

 but are of such importance, that we shall make them 

 the subject of a separate article. (See Centre of 

 Gravity.) In the mean time we shall only observe, 

 that our author has demonstrated generally, that in 

 every mass there must be some, and only one centre ; 

 he shows by what means it may be generally deter- 



