BOSCOVICH'S THEORY. 



O icovich'< 



Theory of 

 Natural 



riiiioso- 



phy. 



Plate 

 I.XV. 



Iig. 1. 



-Objections 

 answered. 



75G 



ever limits, and at last to coincide, which will be 

 done by making two M equal, and likewise two N 

 equal, then the curve sought will touch the arch of 

 the given curve there, and if three such points coin- 

 cide, it will osculate it ; nay, as many points as we 

 please may be made to meet together where we 

 please, and thus we may have osculations of what or- 

 der we please, and as near one another as we please, 

 the arch of the given curve approaching as we please, 

 and at whatever distances we please, to whatever 

 arches of whatever curves, and yet still preserving all 

 the six conditions required for expressing that law of 

 the repulsive and attractive forces. And whereas the 

 value of T can be varied in infinite manners, the same 

 may be done in an infinite number of ways, and there- 

 fore a simple curve, answering the given conditions, 

 may be found out in an infinite number of ways. Q. 

 JE. F. 



It would be very possible to divide this curve, 

 though single in itself, into two or more. Thus, if 

 any one should wish to consider general gravity as 

 accurately reciprocally as the squares of the distances, 

 he may describe on the attractive side the hyperbola 

 which expresses it, which, in fact will be a continua- 

 tion of the leg VTS, then to each of the ordiuates 

 og,hd, of the curve of forces, Fig. 1. he may add 

 the ordinates of this new hyperbola towards the parts 

 AB, beginning at the points g and h of the curve. 

 By which means a new curve will arise, coinciding to 

 sense with the axis, towards the parts V /;, but else- 

 where at a distance from it, and even winding about it, 

 if the vertices F, K, O, are more distant than the hy- 

 perbola is. In this way even many different forces may 

 be expressed, which, as in the resolution of forces, 

 may sometimes be found useful in more readily de- 

 monstrating the effects. And, in fact, it will be a 

 true resolution of forces : but, nevertheless, it is 

 merely the offspring of the mind. 



As we have mentioned the decrease of gravity to 

 be accurately in the reciprocal duplicate ratio of the 

 distance, which is generally admitted by the culti- 

 vators of mechanical astronomy, it may seem an ob- 

 jection against our theory, that it departs so widely 

 from that law. But, in the first place, the action of 

 the particles in the lesser distances does very much 

 differ from tliat law, seeing that vapours, which exert 

 such a great force of expansion, must have, in these 

 distances, a repulsion to each other, and not an at- 

 traction, and that even the attraction of cohesion is 

 vastly greater than that which should be produced 

 by general gravity ; and hence some of the disciples 

 of Newton have supposed a force corresponding to 



this formula r-f- , the former part of which is im- 

 x* x l r 



mensely less than the latter when .r is much greater 

 than the assumed unity, but is greater than it when 

 x is much less; so that in the greater distances the 

 force is very nearly inversely as the squares, and in 

 the less very nearly as the cubes of the distances. So' 

 that the duplicate ratio is not strictly adhered to-even 

 among the Newtonians. 



It has indeed been demonstrated by Newton, that 

 the line of apsides of the planets would have an im- 

 mense motion, if the ratio of forces were very distant 



Philoso- 

 phy- 



from being inversely as the squares of the distances. nocovicli' 

 But they have some motion, and it is not enougli to ' ihmr 7 of 

 say that this is owing to the disturbing force of the N 

 other planets, for this is not yet accurately demon- 

 strated; and indeed it is only after many attempts and 

 approximations, that a partial solution has been gi- 

 ven of the celebrated problem of three bodies, in 

 which there is sought the motion of three bodies act- 

 ing-on each other in the inverse duplicate ratio of the 

 distances. It may be guessed, therefore, how far 

 we yet are from having any demonstration of the strict 

 accuracy of this law of forces. 



To many the greatest difficulty in the theory ap- 

 pears to be the total rejection of immediate contact, 

 which, they think, is evidently shown by the testi- 

 mony of the senses ; a rod, they say, should be used 

 to him who denies contact. But it is admitted, that 

 bodies approach so near each other as to leave no sen- 

 sible distance between them ; and that the resistance 

 we experience is produced by the repulsive power, 

 which gives us the same sensation 36 actual contact 

 is supposed to do : the contact being physical, al- 

 though not mathematical. 



So much for the objections which may be made to 

 the proposed law of the forces. Let us next enquire 

 into those made to the constitution of the primary 

 elements, deduced from that law. 



In the first place, there are many who can by no Objections 

 means be persuaded to admit the existence of points to the ele- 

 altogether indivisible and inextended, alleging that men t- 

 they cannot possibly form any idea of them. Because 

 all the bodies cognisable by the senses are extended, 

 we are apt to look upon extension as essential to mat- 

 ter. But this error may be corrected by reflection ; 

 and the idea of an inextended point may be formed 

 by the help of geometry, and that very idea of con- 

 tinued extension, which is so familiar to our senses. 

 Thus the common section of two contiguous parts of 

 a plane surface is a mathematical line, destitute of 

 breadth, and the meeting of two such sections is an 

 indivisible point. 



We may here observe that Zeno among the an- 

 cients, and Leibnitz among the moderns, held that 

 the first elements of matter were simple and inextend- 

 ed ; but they were guilty of an inconsistency in main- 

 taining that these were contiguous to each other, and 

 thereby comparing a continued extension of indivisible 

 and inextended elements. 



There are some who say that if the elements of 

 matter are void of extension, they are in no respect 

 different from spirits. But the chief difference be- 

 tween body and spirit is, that the one is tangible and 

 incapable of thought or volition, the other may think, 

 and will, but does not affect the senses. For sensi- 

 bility does not consist in extension, but in impenetra- 

 bility, by which the fibres of the body are affected, 

 and the rays of light are reflected. 



But if substances capable of cogitation and volition 

 were endued with the same law of forces, would they 

 not produce to our senses the same effects as these 

 points ? We answer, that it is not our business to en- 

 quire whether 6uch a conjunction could take place 

 or not. 



Such a body would neither be matter nor spirit, 



