OF THE EQUILIBRIUM OF A SYSTEM. 17.5 



therefore the pressures are equal, and the bodies will 

 remain in equilibrium. If now the centre of inertia 

 ascended towards either weight, as A, the segment AC, 

 which determines the action of A, would be increased, 

 and BC lessened; therefore the weight of A would pre- 

 vail, and the centre would return to the vertical line. But, 

 supposing C above D, the rod and threads must change 

 places, and the same demonstration will hold good; and 

 since in this case the weights pull against each other, the 

 prevalence of A, if the centre of inertia descended 

 towards its place, would draw it still further from the 

 vertical line, and the equiUbrium would be lost. 



Now the magnitude of the ^ ^U.^ ^ 



distance of C above or below c 



D is of uo consequence to the ' C 



existence of the equilibrium; therefore when that dis- 

 tance vanishes, and the thread and rod are united into one 

 inflexible right line or lever, those points will coincide, and 

 there will still be an equilibrium ; which may properly be 

 termed neutral, since no change of the position of the 

 bodies will create a tendency either to return to their 

 places, or to proceed further from them. But the case 

 of an inflexible right line is perfectly out of the reach of 

 experiment, since the strength, necessary for the inflexi- 

 bility of a mathematical line, becomes infinite, and that, in 

 an infinitely small quantity of matter. 



Scholium. The demonstrations of the fundamental 

 property of the lever have been very various. Archimedes 

 himself has given us two. Huygens, Newton, Maclaurin, 

 Dr. Hamilton, and Mr. Vince, have elucidated the same 

 subject by different methods of considering it. The 

 demonstration of Archimedes, as improved by Mr. Vince, 



