VOL. XXVI.] PHILOSOPHICAL TRANSACTIONS. 41p, 



mena: this attraction in a given quantity of matter, at different distances, is 

 reciprocally proportional to the squares of these distances: from whence arises 

 that force we call gravity, by which all terrestrial bodies tend towards the earth 

 in a right line, and the weight of bodies is always proportional to the quantity 

 of maUer they contain ; from this attractive force Sir Isaac, in a very beautiful 

 manner, explained all the motions of the planets, and the phaenomena of comets, 

 and happily perfected physical astronomy. After repeated experiments, Mr. 

 Keill observed, that from this attractive force several phaenomena might be ac- 

 counted for. 



Theorem 4. — Besides that attractive force, by which both planets and comets 

 are retained in their orbits, there is also another power in matter, by which all 

 its particles mutually attract, and are mutually attracted, by each other; which 

 power decreases in a greater ratio, than the duplicate ratio of the increase of 

 the distances. This\theorem may be proved by several experiments: but it 

 does not yet so well appear by experiments, whether the ratio, by which this 

 power decreases, as the particles recede from each other, be in a triplicate, 

 quadruplicate, or any other ratio of the increase of the distances. 



Theorem 5. — If a body consist of particles, each of which has an attractive 

 force, decreasing in a triplicate, or more than triplicate, ratio of the distances, 

 the force by which a corpuscle is attracted by that body, in the points of con- 

 tact, or at an infinitely small distance, will be infinitely greater than if that 

 corpuscle were placed at a given distance from the said body. Vide Princip, 

 Newtoni. Prop. SO, Ql. 



Theorem 6. — From the same data, it follows, if that attractive force, at a 

 given distance, have a finite ratio to gravity, that in the points of contact, or 

 at an infinitely small distance, it will be infinitely greater than the force of 

 gravity. 



Theorem 7- — But if the attractive force of bodies in the points of contact 

 have a finite ratio to gravity, it is, at all assignable distances, infinitely less than 

 the force of gravity, and consequently vanishes. 



Theorem 8. — The attractive force, that each particle oi matter exerts, in the 

 point of contact, exceeds almost immensely the force of gravity; yet is not in- 

 finitely greater than it, and consequently, at a given distance, that attractive 

 force will vanish. Therefore, this power, which is superadded to matter, 

 diffuses itself only to very small distances; and at greater distances is none at 

 all : from whence the motions of the heavenly bodies (that are at great distances 

 from each other) are no wise disturbed by this attractive force, but move con- 

 tinually in the same manner, as if these bodies had no such force at all. 



3 H 2 



