OF DEFLECTIVE FORCES, 147 



for their squares are as the spaces directly and the forces 

 inversely (233). 



Scholium, This elegant proposition may be illus- 

 trated by an easy experiment : if we place two bodies at 

 different points of a circle, fixed in a vertical situation, 

 and suffer them to descend at the same instant along two 

 planes, which meet in the lowest point of the circle, they 

 will arrive there at the same time. 



286. Theorem. "258/' When a body is 

 retained in any curve by its attachment to 

 a thread, or descends along any perfectly 

 smooth surface of continued curvature, its 

 velocity is the same, at the same height, as if 

 it fell freely. 



Since the velocity is the same at A, whe- c 

 ther the body has descended an equal vertical 

 distance from B or from C, it will proceed ^ D 



in A D with the same velocity in both cases, provided that 

 no motion be lost in the change of its direction, and 

 therefore its velocity will be the same, after passing any 

 number of surfaces, as if it had fallen perpendicularly from 

 the same height.^ But where the curvature is continued, 

 no velocity is lost in the change of direction ; for let A B 

 be the thread, or its evolved portion, the body B, if no 

 longer actuated by gravity, would proceed in the 

 circular arc with uniform motion (263); conse-\ A 



quently no velocity is destroyed by the resistance 

 of the thread, nor by that of the surface BC, ^ 

 which can only act in the same direction, per- 

 pendicular to the direction of the moving body. 



L 2 



