38 FERGUSON'S LECTURES. 



LECT. If these two balls be fixed at equal distances from 

 -v-^ their respective centers of motion, they will move with 

 equal velocities ; and if the tower has 6 times as much 

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

 raise their weight exactly at the same moment. This 

 shews that the ball U, being six times as heavy as the 

 ball V, has six times as much centrifugal force, in des- 

 cribing an equal circle with an equal velocity. 

 A double 6. If bodies of equal weights revolve in equal circles 

 unequal velocities, their centrifugal forces are as the 



circle, is a squares of the velocities. To prove this law by an expe- 

 a quadru- riment, let two balls U and V of equal weights be fixed 



pie power on jj )e j r corc } s a t equal distances from their respective 

 ui gravity. 



centers of motion w and x ; and then let the catgut 



string E be put round the wheel K (whose circumference 

 is only one half of the circumference of the wheel 

 H or G) and over the pulley s to keep it tight ; and 

 let four times as much weight be put into the tower P, as 

 in the tower O. Then turn the winch B, and the ball V 

 will revolve twice as fast as the ball U in a circle of the 

 same diameter, because they are equidistant from the 

 centers of the circles in which they revolve ; and 

 the weights in the towers will both rise at the same 

 instant, which shews that in a double velocity the 

 same circle will exactly balance a quadruple power of 

 attraction in the center of the circle. For the weights 

 in the towers may be considered as the attractive 

 forces in the centers, acting upon the revolving 

 ball ; which, moving in equal circles, is the same thing 

 as if they both moved in one and the same circle. 



7. If bodies of equal weights revolve in unequal cir- 



cles, in such a manner that the squares of the times of 

 their going round are as the cubes of their distances from 

 the centers of the circles they describe ; their centrifu- 

 gal forces are inversely as the squares of their distances 

 from those centers. For, the catgut string remaining 



