OF THB EQUILIBRIUM OF A SYSTEM. l69 



velocity of 32 feet, which the preponderating weight alone 

 would have acquired. And when we compare the centri- 

 fugal forces of bodies revolving in the same time, at 

 different distances from the centre of motion, we find that 

 a greater quantity of matter compensates for a smaller 

 force ; so that two balls, connected by a wire, with liberty 

 to slide either way, will retain each other in their respective 

 situations, when their common centre of inertia coincides 

 with the centre of motion; the centrifugal force of each 

 particle of the one being as much greater than that of an 

 equal particle of the other, as its weight, or the number of 

 the particles, is smaller. 



302. Scholium 2, A.] The simplest case of the 

 equilibrium of several bodies is that of two material points 

 meeting each other with equal and directly contrary velo- 

 cities ; their mutual impenetrability must evidently annihi- 

 late their motion, and reduce them to a state of rest. 



[B.] Let us now suppose a number m of contiguous 

 material points, arranged in a right line, and moving in its 

 direction with the velocity m: and again another number 

 mf of contiguous points, disposed in the same line, and 

 moving with the velocity u in a contrary direction, so that 

 the two systems meet each other; there must exist a 

 relation between u and vf, such that the systems may both 

 remain at rest after the shock. 



[C] In order to determine this condition, we may 

 observe that the system m, moving with the velocity u, 

 would destroy the motion of a single point, moving with 

 the velocity mu, for every point in the system would 

 destroy, in this last point, a velocity equal to u, and conse- 

 quently the m points would destroy the whole velocity mu: 

 we may therefore substitute for this system a single point. 



