OF DEFLECTIVE FORCES. 155 



tance from that line to the vertical height ; the other part 

 of the force being counteracted by the tension of the 

 thread ; and when the forces are as the distances, the times 

 must be equal. (261). 



Scholium. Thus, if a number of balls are fixed to 

 threads, or rather wires, connected to the same point of 

 an axis, which is made to revolve by means of the whirling 

 table, they will so arrange themselves, as to remain very 

 nearly in the same horizontal plane. 



292. Theorem. " 264.'' The time of a 

 revolution of a body, suspended by a thread, 

 is equal to the time occupied by a cycloidal 

 pendulum, of which the length is equal to the 

 height of the point of suspension above the 

 plane of revolution, in vibrating once forwards 

 and once backwards to the point at which its 

 motion began; and if the revolutions be 

 small, and the thread nearly vertical, they 

 will be very nearly isochronous, whatever be 

 their extent. 



For, supposing the distance to be equal to the height, 

 the centrifugal force will be equal to the force of gravity, 

 and while the body describes a distance equal to the 

 radius, another body, actuated by the same force, would 

 describe half that radius, (259) and the whole time of 

 revolution is, therefore, to this time, as the circumference 

 to the radius, and is consequently equal to the time of 

 four semivibrations of a cycloidal pendulum, of which the 

 length is equal to the given height (287). And since the 



