1823.] Mathematical Principles of Chemical Philosophy. 247 



and from A, let fall the perpendicular A E ; let the angle ADC 

 be that which the parallelogram has, when the particles are on 

 the point of separating from each other. When they have sepa- 

 rated, as a, b, c, d, "the angles are 60° and 120° respectively 

 (Prop. II.) ; \etfg be the distance to which they separate (the 

 liquid having the same temperature as the fusing solid) ; from b 

 let fall the perpendicular b e, which bisects gf and c d. 



The solid ABCD: solid ab cd::BC x AE 3 :dc x b e 2 , 

 or as A D x A E* : {A D + f g} x b e" ; but b e : b c in a 



constant ratio ; let b e = — ; that is = AJ)+fg i therefore, so- 



fl m 



lid A B C D : solid abcd.-.A'D x A E 8 : * A P w t /g *' . Now 



3 . A D* 



AD x A E- may have any value between A D s and — —^ — ; 

 while iM±£d! is always '^^^ which may be greater 



or less than the former according to the value of/g; therefore, 

 since these quantities admit of indefinite variation, some bodies 

 will expand, and others contract. Q. E. D. 



Prop. VI. 



Liquids will be attracted by solids. 



It has been proved (Prop. I), that beyond a certain distance, 

 the entire force exerted by the particles of a liquid is centripetal ; 

 at all distances the centripetal force of the particles of a solid 

 exceeds the repulsive ; therefore, the two will attract each 

 other. Q. E. D. 



Cor. 1. — If the mutual attraction of the particles of a liquid 

 exceeds their tendency to a solid, a small drop will retain nearly 

 a spherical figure upon the surface of that solid. 



Cor. 2.— If the mutual attraction of the particles of the liquid 

 be less than their attraction to the solid, the drop will spread 

 upon its surface. 



Cor. 3. — Hence in Cor. 1, a small mass of a solid specifically 

 heavier than a liquid may be made to float upon its surface. 



Cur. 4. — If two drops of a liquid, constituted as in Cor. 1, be 

 placed upon a horizontal polished surface, and very near toge- 

 ther, they will attract each other and unite. 



Cor. 5. — If two liquids be mixed, of which the similar parti- 

 cles attract each other more powerfully than the dissimilar, and 

 which differ in specific gravity, they wiil separate again. 



Prop. VII. 



If a porous solid be moistened with a liquid, the liquid will 

 cause expansion of the solid ; and if equal solids be taken, hav- 

 ing unequal pores, the entire expansive forces upon equal sur- 

 faces will be inversely as the diameters of the pores; the solid 

 being insoluble. 



