148 OF DEFLECTIVE FORCfeS. 



Scholium. We may easily show, by an experiment 

 on a suspended ball, that its velocity is the same, when it 

 descends from the same height, whatever may be the form 

 of its path ; and this we prove by observing the height to 

 which it rises on the opposite side of the lowest point, 

 whether in the same curve, or in different ones. We may 

 alter the form of its path both in descending and in ascend- 

 ing, by placing pins at different points, so as to interfere with 

 the thread that supports the ball, and to form, in succes- 

 sion, temporary centres of motion ; and we shall find, in 



all cases, that the body 

 ascends to aheightequal 

 to that from which it has 

 I> descended, with a small 

 deduction on account of 

 friction. Thus, the same 

 ball, descending from equal heights at A, B, or C, by 

 different paths, will rise to the same height at D on the 

 opposite side of E, and the reverse. 



287. Theorem. " 259/' If a body be 

 suspended by a thread between two cycloi- 

 dal cheeks, it will describe an equal cycloid 

 by the evolution of the thread (208) ; and the 

 time of descent will be equal, in whatever part 

 of the curve the motion may begin, and will be 

 to the time of falling through one half of the 

 length of the thread, as half the circumference 

 of a circle is to its diameter : and the space 

 described in the cycloid will be always equal 



