OF DEFLECTIVE FORCES. 



157 



section of KL, parallel to AB, and as much below it, as 

 DE was above it ; this vibration will terminate in a point 

 as far on one side of K as I is on the other : so thatrthe 

 extent of each vibration will be less than that of the pre- 

 ceding one, by twice the length of FE, until the whole 

 force is exhausted, the time of each complete vibration 

 remaining unaltered. 



294. Theorem. "A." (Nich. Journ. 1813.) 

 If the point of suspension (A) of a pendulum 

 ( AB) be made to vibrate in a regular manner, 

 that is, according to the law of cycloidal vibra- 

 tions, the pendulum itself may also vibrate 

 regularly in the same time, provided that the 

 extent of its vibrations (BC) be to that of 

 the vibrations of the point of suspension (AD) 

 as the length of the thread ( AE) supposed to 

 carry this point as a pendulum, is to the dif- 

 ference of the lengths of the two threads. 



In representing the vibrations, we may g 



disregard the curvature of the paths, 

 considering them as of evanescent ex- 

 tent, the forces being however still sup- 

 posed to depend on the inclination of the 

 threads, which must be exaggerated in 

 the figures employed. Let F be the in- 

 tersection of AB with the vertical line 

 EF; then, upon the conditions of the 

 theorem, BF will be equal to AE ; that 

 is, if BC : AD=AE : AEco AB, since b 



