754 



BOSCOVICH'S THEORY. 



ttoscovicli's 

 theory of 

 Nmiral 

 l'liiloso- 

 phy. 



Objections 

 to the 

 theory 

 answered. 



ber is so great. This he illustrates, by supposing an 

 immense library of books in various languages, the 

 letters in which were formed by small round points, 

 placed so near each other, that the interval could only 

 be discovered by the help of the microscope. Now 

 should any person, ignorant of languages, and of this 

 kind of writing, begin diligently to examine this col- 

 lection, he would first find out of the vast multitude 

 of words, a certain number which occurred often in 

 some of the books, and in others never appeared ; 

 and collecting these together, he might form diction- 

 aries of the several languages. But U*pon further inves- 

 tigation, it would be found, that the whole of these 

 words were expressed by the help of only twenty-four 

 different letters ; and here he must stop, unless he 

 could procure farther assistance : But suppose him 

 provided with a microscope, he would at length dis- 

 cover, that by the variousarrangements of single points, 

 were formed the whole of the letters, words, langua- 

 ges, and books, on various subjects, that composed this 

 great collection. Just so, says Boscovich, Is it in 

 chemistry, where the farther we push our analysis, 

 the more nearly do we arrive at elements, simple and 

 homogeneous. And thus we have detailed the whole 

 of the proofs which Boscovich has given for his sys- 

 tem : but before going farther, it will not be impro- 

 per to follow him also in refuting some of the objec- 

 tions which have been, or may be, proposed against 

 its general reception. 



Against mutual attractive and repulsive forces, it 

 has been usual to object, that they are no better than 

 the occult qualities of the Peripatetics, and that they 

 induce action at a distance. The same objection has 

 been made to the Newtonian theory of gravity ; but 

 the answer is easy, we observe the effects, which are 

 sufficiently manifest. We must admit for them an 

 adequate cause. Whether that be the immediate act 

 of the Creator, or some mediate instrument which he 

 employs, we are unable to determine. With respect 

 to action at a distance, there is, at least, nothing more 

 occult in that, than in the production of motion by 

 immediate impulse. Newton has given a satisfacto- 

 ry explanation of the phenomena of light ; and has 

 reduced mechanical astronomy to rigid calculation, 

 without employing impulse ; and it is highly proba- 

 ble, that we may be equally successful in other de- 

 partments of nature. 



It has been objected, that the theory itself admit3 

 of a breach of continuity, in passing suddenly from 

 repulsion to attraction ; but this we have already 

 shown to take place, by passing through all the in- 

 termediate degrees, in the same manner as the change 

 is made from positive to negative quantities, by a con- 

 tinual subtraction. 



It may be objected, that the complication of the 

 curve, made up of many arches, repulsive and attrac- 

 tive, is no better than the old doctrine of the arbitra- 

 ry qualities and substantial forms. Boscovich an- 

 swers, that repulsion is but a negative attraction, as 

 may be illustrated by algebraic equations, and geo- 

 metric loci : and again, that, supposing us entirely 

 ignorant of the law of mutual forces, it is at first 

 much more likely, that the curve, which expresses it, 

 is of a high than of a low order ; that is, it is much 

 more likely that it frequently intersects the axis, or 

 lias frequent flexures, than otherwise; seeing that the 



higher orders of lines are eo much more numerous 

 than the lower.' But, independent of this conjecture, 

 the form of the curve has been derived by positive 

 argument from the phenomena ; and it is well known, 

 that there are many curves which, from their nature, 

 must form frequent flexures and intersections with 

 the axis. To our minds, the mutual congruity of 

 straight lines, upon which, by the way, the whole of 

 our geometry depends, makes them appear the sim- 

 plest of any, and others to be the more complicated, 

 only as they remove the more from the right line. 

 But all continued lines of uniform nature are equally 

 simple ; and a mind may be conceived, to which the 

 parabola, for instance, might appear as essentially 

 simple, as to us appears the straight line. But besides 

 this general reply to the objection before stated, Bos- 

 covich has shewed, in his Dissertation de Lege Viri- 

 WR, that this curve is uniform and regular, and may 

 be expressed by one general algebraic equation. 



For this purpose, six conditions are proposed, as 

 requisite to the complete expression of the law ef 

 forces. 1st, The curve must be regular and simple, 

 and not composed of an aggregate of different curves. 

 2d, It must cut the axis CAC' only in certain given 

 points, at equal distances on each side, as AE' AE, 

 AG' AG, AP AI, and so forth. 3d, To every ab- 

 sciss there must be a corresponding ordinate. 4th, 

 To equal abscisses on either side, equal ordinates 

 must correspond. 5th, The straight line AB must 

 be an asymptote to the curve on either side, and the 

 asymptotic area BAED must be infinite. 6th, 

 The arch, intercepted between any two intersections, 

 may be varied at pleasure, may recede to any dis- 

 tance from the axis, and may approach at pleasure 

 to an arch of any other curve, cutting, touching, or 

 osculating it, in any place, or in any way that may be 

 proposed. 



I. That these conditions may be fulfilled, he 

 finds an algebraic formula which contains his law, 

 calling the ordinate as usual y, and the abscissa 

 =.r, he takes xxz=z. Let all the values of AE, 

 AG, A I, &c. be taken with the negative sign, and 

 let the sum of the squares, of these values be called a ; 

 of the products of every two squares be called b ; of 

 every three c, and so on ; and let the product of 

 all of them be called f, and let the number of values 

 be called m. Now put 



Boj?ovich'i 

 theory of 

 Natural 

 Philoso- 

 phy. 



Analytical 

 deduction 

 of the 

 theory. 



-{az -\-bz +cz +, 



&c. +/=P. 



If we suppose P=0, it is clear that all the roots of 

 the equation will be real and positive, namely the 

 squares of the quantities AE, AG, AI, which are 

 the values of ~, and since x*=z, i= v / j, it is 

 plain that the values of x are as well AE, AG, AI, 

 positive, as AE', AG', AP negative. 



II. Next, let any given quantity be taken for z, 

 only that it may not have a common divisor with P ; 

 and z vanishing, it will also vanish ; and x being made 

 an infinitesm of the first order, it will also become an 

 infinitesm of the same, or a lower order, as any formu- 

 la z r +gz r ~ 1 +hz r ~ 2 , Sec. + A, which being put 

 Oj may have any number of imaginary, and any num- 

 ber of, and whatever real roots ; ( but none of them 

 = AE, AG, &c. either positive or negative ; ) if then 

 the whole be multiplied by z, let that be called Q. 



