us 



OF DEFLECTIVE FORCES. 



by similar triangles BC : AD=:BF : BFoo 

 AB, it follows that AErzBF. Consequently 

 the inclination of the thread AB will always 

 be the same as if F were its fixed point of 

 suspension, and the body B will begin and 

 continue its vibrations like a simple pendu- 

 lum attached to that point, the true point 

 of suspension accompanying it with a pro- 

 portional velocity, so as to be always in the 

 right line passing through it and through F. 

 It is obvious, that when the thread supposed 

 to suspend the moveable point of suspension is the longer 

 of the two, the vibrations will be in the same direction ; 

 when the shorter, in contrary directions. 



Scholium 1. The truth of this proposition may 

 easily be illustrated, by holding any pendulous body in the 

 hand, and causing it to vibrate more or less rapidly, by 

 moving the hand regularly backwards or forwards, in a 

 longer or in a shorter time than that of the spontaneous 

 vibrations. 



Scholium. 2. The same mode of reasoning is appli- 

 cable to oscillations of any other kinds, which are governed 

 by forces proportional to the distances of the bodies 

 concerned, from a point of which the situation, either in a 

 quiescent space, or with respect to another moveable 

 point, varies according to the law of the cycloidal pendu- 

 lum, or may be expressed by the sines of arcs varying 

 with the time : such forces always producing periodical 

 variations, of which the extent is to that of the excursions 

 of the supposed point of suspension in the ratio of n to 

 w— 1, n being to 1 as the square of the time of the forced 

 to that of the time of the spontaneous vibration; and 



