163 



OF DEFLECTIVE FORCES. 



that, at the middle of a vibration, the point of 

 suspension (A) be so situated, as to cause a 

 propelling force equal to the actual resist- 

 ance, the extent of the vibrations being re- 

 duced, in the ratio of the whole excursion of 

 the point of suspension (BC) to its distance 

 from the middle, at the beginning of the mo- 

 tion of the pendulous body (DC) : and it will 

 ultimately acquire this mode of vibration, 

 whatever may have been its initial condition. 



Let FG be the supposed length of the thread carrying 

 the point of suspension, and draw FE passing through D 

 instead of B ; then if HC, = EG, be the extent of the vibra- 

 tion, it will be maintained according to the law of the 

 cycloidal pendulum. Draw the concentric circles BI, 

 DK, HL : then the initial force may be represented by 



HD, which determines 

 the greatest inclination of 

 the thread; and at any 

 subsequent part of the 

 vibration, if the point of 

 suspension be advanced 

 from D to M , the time 

 elapsed will be expressed 

 by the arc IN, DI and 

 MN being perpendicular 

 to AB, and taking HL 

 similar to IN, the per- 

 pendicular LP will show 

 the place of the pendulous 



