112 OF DEFLECTIVE FOKCES. 



equally loaded, one of them, which is made to revolve 

 with twice the velocity of the other, will raise four equal 

 weights at the same instant that the other raises a single 

 one, the velocities being gradually and slowly increased, by 

 turning the handle more and more rapidly, till the stages 

 fly off. 



261. Corollary 3. "242." If the times 

 are equal, the velocities being as the radii, 

 the forces are also as tlie radii ; and in general, 

 the forces are as the distances 'directly, and as 

 the squares of the times inversely : and the 

 squares of the times are directly as the dis- 

 tances, and inversely as the forces. 



The forces are as the distances directly, and as the 

 squares of the times inversely, because the velocities are 

 as the distances directly, and as the times inversely, and 

 their squares are as the squares of the distances divided 

 by those of the times, and dividing these quantities by the 

 distances (259) we have the distances divided by the 

 squares of the times, whence the other part of the pro- 

 position follows. 



Scholium. Thus if one of the stages of the whirling 

 table be placed at twice the distance of the other, it will 

 raise twice as great a weight, when the revolutions are 

 performed in the same time : and agam, the same weight 

 revolving in a double time, at the same distance, will have 

 its effect reduced to one fourth, but at a double distance 

 the effect will again be increased to half of its original 

 magnitude, while the time remains doubled. 



