1823.] Mathematical Principles of Chemical Philosophy. 251 

 lines L D, SB, be produced infinitely ; the area k B D lis as 

 t4— ;• Q.E. 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 DS G O, i. e. at a higher temperature L M N is a tangent 

 to the curve E F M P at M ; hence between B and I the force 



