OF CENTRAL FORCES. 37 



the balls U and V will fly off towards 31 and N; and 

 will raise the weights in the towers at the same instant. v^v 

 This shews, that when bodies of equal quantities of mat- 

 ter revolve in equal circles with equal velocities, their 

 centrifugal forces are equal. 



5. Take away these equal balls, and instead of them, 

 put a ball of six ounces into the bearer M X, at a sixth 

 part of the distance w z from the center, and put a ball 

 of one ounce into the opposite bearer, at the whole dis- 

 tance xy, whieh is equal to 10 z from the center of the 

 bearer ; and fix the balls; at these distances on their 

 cords, by the screw nuts at top ; and then the ball U, 

 which is six times as heavy as the ball V, will be at 

 only a sixth part of the distance from its center of mo- 

 tion ; and consequently will revolve in a circle of only a 

 sixth part of the circumference of the circle in which V 

 revolves. Now, let any equal weights be put into the 

 towers, and the machine be turned by the winch ; which 

 (as the catgut string is on equal wheels below) will 

 cause the balls to revolve in equal times ; but V will 

 move six times as fast as U, because it revolves in a 

 circle of six times its radius ; and both the weights in 

 the towers will rise at once. This shews, that the cen- 

 trifugal forces of revolving bodies (or their tendencies 

 to fly off from the circles they describe) are in direct 

 proportion to their quantities of matter multiplied into 

 their respective velocities; or into their distances from 

 the centers of their respective circles. For, supposing 

 C7, which weighs six ounces, to be two inches from its 

 center of motion w, the weight multiplied by the dis- 

 tance is 12; and supposing V, which weighs only one 

 ounce, to be 12 inches distant from the center of mo- 

 tion i, the weight 1 ounce multiplied by the distance 12 

 inches is 12. And-as they revolve in equal times, their 

 velocities are as their distances from the center, namely, 

 as 1 to 6. 



