c 



1820.] Mathematical Principles of Chemical Philosophy. 183 



Prop. 1. — The ultimate particles of ponderable matter being 

 spherical, and the centripetal force being reciprocally in the 

 duplicate ratio of the distance, the attraction of cohesion results 

 from the attraction of the portions of their surfaces which coin- 

 cide with each other in contact. 



Let A and B, fig. 6, be two ultimate particles of matter, of 

 which every point exerts a centripetal force which is as 



r^, c and d, the two indefinitely small portions of their 



-J^ Distance} 



surfaces which coincide with each other when in contact, the 

 force which c and (/ exert upon, or by which they tend to, each 



other is as —— ; let them be placed in contact; c d = .'. 



- — - = infinity i i. e. the force with which c and d attract each 



other when in contact is infinitely greater than when they are at 

 any finite distance however small. Hence if this force be finite 

 at any finite distance, it becomes infinite in contact ; but if finite 

 in contact, it vanishes at the least possible distance. 



Cor. 1. — If centripetal force vary reciprocally as any power or 

 root of the distance, the effect of cohesion will be produced; for 



since the force is as — - , when c d vanishes, the force with which 



erf"' ' 



c and d mutually attract each other becomes — = infinity; but 



if the force were supposed to be as c rf" in contact, the force with 

 which the parts c and d mutually attract each other = 0" = 0. 



Cor. 2. — Hence the particles of matter cannot be plane 

 figures of any sort, nor be terminated in any of their parts by 

 plane surfaces ; for since the attraction of one particle is finite 

 at a finite distance, consequently that of any finite part is finite ; 

 therefore the attraction of two such plane surfaces is infinite in 

 contact, which does not coincide with the observed phenomena. 



Prop. 2. — The attraction of cohesion between two particles of 

 matter is as the absolute force of attraction upon their surfaces 

 X the diameter, the spheres being equal; if unequal, it is as the 

 same x diameter of the smallest. 



By lemma 3, when the spheres are equal, the points of contact 

 are as their diameters ; when unequal, as the diameter of the 

 smallest ; and if the centripetal force vary, the force with which 

 they attract each other will vary in the same ratio. The force 

 of cohesion will be as the points of contact x absolute centri- 

 petal force. 



Prop. 3.— The same phenomena of cohesion will result of 

 whatever figures the particles of matter be assumed, provided 

 they be sucii as may be formed by the revolution of curves of 

 fliiite curvature, and which return into themselves upon their 

 axes. 



