1823.] Mathematical Principles of Chemical Philosophy. 245 



the distance KG; for at G the ordinates of the two curves are 

 equal; therefore, the opposite forces are equal to each other: 

 also between G and K the force is repulsive ; beyond K, it is 

 centripetal ; therefore, the temperature being uniform, the dist- 

 ance between the particles can be only K G, and they are there 

 in equilibrio between two opposite forces ; therefore, they have 

 perfect freedom of motion round each other ; and a number of 

 such particles will constitute a liquid. Q. E. D. 



Cor.— Under atmospherical pressure, the distance K G will 

 be diminished, so that the excess of the force of repulsion above 

 that of attraction shall equal the pressure. 



Prop. II. 

 To find the order of arrangement of the particles of a liquid. 



Let there be a system of detached particles, B, C, A, F, Sec. ; 

 join their centres B C, C A, A B, &c. ; arrange them so that the 

 lines B C, C A, A E, Sec. which join the centres of contiguous 

 particles may form squares B A, C F, Sec. By the nature of the 

 figure, A is surrounded by the greatest possible number of par- 

 ticles under the given arrangement. Suppose the forces acting 

 between B and C, C and A, A and E, Sec. mutually to balance 

 each other, then A and B, C and E, See attract each other 

 (Prop. I.) ; and since AB is equal to CE, the arrangement of the 

 system may remain ; but if by any disturbing force, B be brought 

 nearer to A, since the distances B C, C A, Sec. must remain per- 

 manent, B will continually approach towards A ; E and C must 

 recede from each other, until their mutual attracting forces 

 balance their repulsion ; i. e. when B A is equal to C A, when 

 also C E is equal to 2 C A; consequently when the triangles 

 B C A, B E A, are equilateral. Similarly, since the position of 

 C is changed, the equilibrium of C D F A is destroyed, and the 

 particles D and F will assume the same order of arrangement; 

 and the same change must take place throughout the whole 

 system. Again : by the same reasoning, if B and A, C and E, 

 are in equilibrio, B and C, C and A, Sec. will be mutually repel- 

 lent; and finally, if disturbed, assume the same order. There- 

 fore, their arrangement a, b, c, d, Sec. becomes such that the 

 straight lines a 0,1 c, c a, Sec. joining their centres, form equila- 



