1820.] Mathematical Principles of Chemical Philosophy. 181 



on examining the matter produced, a considerable part will be 

 found in a crystalline form lining the interior of the vessels in 

 which the experiment has been performed, and which will be 

 found to have a very considerable cohesive force. There is, 

 therefore, no impropriety in assuming that every particle of mat- 

 ter in nature attracts every other particle. 



Since it is found that the attraction of the planetaiy bodies 

 varies reciprocally in the duplicate ratio of the distance ; and it 

 is proved, Princip. lib. 1, prop. 71, that in order that this effect 

 may result, the attraction of each of the particles of which these 

 bodies are composed, must follow the same law ; and since none 

 of the researches that have been made into the various depart- 

 ments of physical astronomy indicate even the most minute 

 operation of any other centripetal force, 1 shall suppose the ulti- 

 mate atoms of ponderable matter to exert upon each other this 

 force only, and attempt to demonstrate its capability of produc- 

 ing all the primary phenomena of corpuscular attraction ; and 

 here we must suppose the particles of matter to have magnitude, 

 which is excessively minute ; and, therefore, to have figure, and 

 not to be, as some have imagined, mere physical points, which. 

 exert various forces upon each other. 



On the Attraction of Cohesion. 



Lemma 1. — If two spheres touch each ether, an indefinitely 

 small portion of the surface of each coincides with an equal one 

 of that of the other. 



Let A B C (PI. CVII), fig. 3, be a circle, .r ?/ a tangent at A, 

 draw the diameter A C, take D B perpendicular to x ?/, and 

 indefinitely near to A C ; join A B, B C ; then Princip. lemma 

 7, the arc A B coincides with the chord A B ; by similar trian- 



gles, AC:AB::AB:DB = — - , or since in the same circle, 



A C is constant, D B is as A B- ; let A D constantly diminish, 

 and D B, its deflexion from the ta*igent, will diminish in the 

 duphcate ratio of A B ; therefore, when A D is indefinitely near 

 coincidence with A C, D B will much more be indefinitely less 

 than the least possible finite quantity; or at the noint A, an 

 indefinitely minute portion of the circumference of the circle 

 will coincide with the tangent x ij : and if an equal circle be 

 drawn, touching the tangent xij, in A, but on the other side of 

 it, an equal portion of its circumference will coincide with it, 

 and, therefore, at A an indefinitely small portion of the circum- 

 ference of each circle coincides with an equal one of that of the 

 other. In the same manner it may be proved that the spherical 

 surfaces which are formed by the revolution of the circles upon 

 a straight line which joins their centers, and, therefore, passes 

 through the point of contact, coincide with each other at the 

 point of contact. 



It may, perhaps, be objected, that in spheres these points of 



