MOTION, MECHANICS, ETC. 165 



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

 the distance, w z, from the centre, and put a ball of one 

 ounce into the opposite bearer, at the whole distance, x y, 

 which is equal to w z, from the centre 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 Y, will be only a sixth part of the distance from 

 its centre of motion ; 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 shows that the centrifugal forces of re- 

 volving 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 centres of their respective circles. 

 For, suppose U, which weighs six ounces, to be two inches 

 from its centre of motion, w, the weight multiplied by the 

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

 ounce, to be 12 inches distant from the centre of motion, x, 

 the weight one ounce, multiplied by the distance, 12 inches, 

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

 are as their distances from the centre, namely, as 1 to 6. 



If these two balls be fixed at equal distances from their 

 respective centres of motion, they will move with equal 

 velocities ; and if the tower, 0, have six times as much 

 weight put into it, as the tower, P, has, the balls will raise 

 their weight exactly at the same moment. This shows that 

 the ball U, being six times as heavy as the ball V, has six 

 times as much centrifugal force, in describing an equal circle 

 with an equal velocity. 



6. A double velocity in the same circle is a balance to a 

 quadruple power of gravity. If bodies of equal weights re- 

 volve in equal circles with unequal velocities, their centri- 

 fugal forces are as the squares of the velocities. To prove 

 this law by an experiment, let two balls, U and V, of 

 equal weights, be fixed on their cords at equal distances 

 from their respective centres of motions, w and x ; and then 

 let the catgut string, E, be put round the wheel, K, whose 



