. Annals of Philosophy. 1823.] Mathematical Principles of Chemical Philosophy. 251 lines LD, SB, be produced infinitely; the area k BD lis as t4—;• D. Cor. 1 .—If the force of attraction be inversely as the square of the distance, the force is as —. Cor. 2.—The greater A K is taken, the nearer will this approximate to the truth. Cor. 3.—If at equal distances the forces of different particles be different, the areas B D K L at those distances will be as those forces. Cor. 4.—If the density of the medium vary, the area BDKL will be as that density. Co;-. 5.—If different particles be placed
. Annals of Philosophy. 1823.] Mathematical Principles of Chemical Philosophy. 251 lines LD, SB, be produced infinitely; the area k BD lis as t4—;• D. Cor. 1 .—If the force of attraction be inversely as the square of the distance, the force is as —. Cor. 2.—The greater A K is taken, the nearer will this approximate to the truth. Cor. 3.—If at equal distances the forces of different particles be different, the areas B D K L at those distances will be as those forces. Cor. 4.—If the density of the medium vary, the area BDKL will be as that density. Co;-. 5.—If different particles be placed in similarly constituted media of different densities, the areas B DK L at equal distances will be as their forces of attraction and the densities of the media. Prop. I. When a liquid has attained a certain temperature, its particles become mutually repulsive, and it becomes gaseous. Let Q R B be a par- ticle of matter, A its D centre; draw the right , L line A C; and at B draw the tangent B D. Describe the curve E M P, such, that its ordinates F H, MI, &c. may be propor- tional to the force of attraction at the dist- ances BH, B I, &c. In liquids, the force of repulsion exceeds that of attraction on the surface (Sect. 2, Prop. I). Take B D to represent the force of repulsion, and let the curve D S G O be such that its ordinates are as the forces of repulsion at the half distance of their abscissae. Within a certain distance of B, the curve DSGO will approach the axis more rapidly than E F M, and will, therefore, intersect it in some point F (Lemma 3, Sect. 2); therefore at H, the forces will balance each other. Beyond a certain distance, the curve DSGO will approach the axis less rapidly than D F M (Sect 3, Lemma), and will, therefore, intersect it in some other point G. Increase the heat, and the points H and K will conti- nually approach each other, until, at a certain temperature, they meet in some point I; draw the perpendicular I M, and the curve D
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