1822.] Mathematical Principles of Chemical Philosophy. 45^' 



thickness. The area K L : area G H :: A L^ : A H^ but force of 

 a particle at L : force of a particle at H :: A H^ : A L^ ; compound 

 these proportions, and the force of K L : force of G H :: A G : 

 A L. At A erect a perpendicular A N ; take L [ : FH :: force of 

 plate K L : that of G H ; and draw the hyperbola M I B, whose 

 ordinates LI, H F, D B will be as the force of attraction of the 

 sections at those distances ; therefore the area BI LD will repre- 

 sent the force of the frustum C K L D ; consequently the force 

 of the whole pyramid to a particle placed upon the vertex is infi- 

 nite, since the area B O M N A C is infinite. 



Take now two equal spheres of the same matter, A B C D, and 

 abed; let P be a corpuscle at a certain distance from ABCD, 

 p one in contact with abed; take two elementary cones passing 

 through the centres and equiangular, APE, ape; let A C = 

 C K of the former figure ; and in the same, let a p = G A ; then 

 the force with which P is attracted : force with which p is 

 attracted : area B I K C : area F M N A G :: a finite area : an 

 infinite one ; therefore the force with which a corpuscle is 

 attracted will be infinitely greater in contact than at the least 

 possible distance. Therefore if the attraction be finite in con- 

 tact, it vanishes when the corpuscle is removed to the least pos- 

 sible distance from contact ; but if at any distance it be finite, it 

 must be absolutely, and without any exception, infinite in con- 

 tact. By observation, the force of cohesion is finite ; but by 

 phenomena 2, 3, and 4, the attraction at a distance is finite ; 

 therefore if the force be inversely as the cube of the distance, it 

 must be mfinite, which is not the case. But such a force does 

 not exist. 



Let A B C, fl ^ c be two unequal spheres, having the same den- 

 sity, the force of attraction being inversely as the cube of the 

 distance ; let P and p be corpuscles similarly situated with 



