OF CENTRAL FORCES. 43 



could have no weight or gravity of itself; and conse- LECT. 

 quently, though it could have no tendency of itself to ^^^. 

 remove from that part of space, yet it might be very 

 easily moved by any other substance. 



10. As the centrifugal force of the light body B will 

 not allow the heavy body A to remain in the center of 

 motion, even though it be twenty-fonr times as heavy 

 as B ; let us now take the ball A, 

 which weighs six ounces, and con- 

 nect it by the wire C with the ball 

 B, which weighs only one ounce ; 

 and let the fork JB be fixed into 

 the center of the whirling-board : then hang the 

 balls upon the fork by the wire C in such a manner, 

 that they may exactly balance each other ; which will 

 be when the center of gravity between them, in the wire 

 at d, is supported by the fork. And this center of gra- 

 vity is as much nearer to the center of the ball A, than 

 to the center of the ball B, as A is heavier than JB, al- 

 lowing for the weight of the wire on each side of the 

 fork. This done, let the machine be put into motion 

 by the winch ; and the balls A and J3 will go round 

 their common center of gravity d, keeping their balance, 

 because either will not allow the other to fly off with 

 it. For, supposing the ball B to be only one ounce in 

 weight, and the ball A to be six ounces ; then, if the 

 wire C were equally heavy on each side of the fork, the 

 center of gravity d would be six times as far from the 

 center of the ball B as from that of the ball A, and con- 

 sequently B will revolve with a velocity six times as 

 great as A does ; which will give B six times as much 

 centrifugal force as any single ounce of A has: but 

 then, as B is only one ounce, and A six ounces, the whole 

 centrifugal force of A will exactly balance the whole 

 centrifugal force of B: and therefore, each body will de- 

 tain the other, so as to make it keep in its circle. This 

 shews that the sun and planets must all move round 

 the common center of gravity of the whole system, in 



