ON CONFINED MOTION. 4$ 



great accuracy, when we consider the doctrine of" the cquihbrium of forces. 

 But the interference of friction will only allow us to observe, with respect to the 

 velocities, produced, that they nearly approach to those which the calculation 

 indicates. Thus if a plane be inclined one inch in 32, a ball will descend ou 

 it in two seconds, instead of 64 feet, somewhat less, than two feet. 



It may be deduced from the laws of acccleraiting forces, that when bodies 

 descend on any inclined planes, of equal heights, but of different inclinations, 

 the times of descent are as the lengths of the planes, and the final velocities 

 are equal. Thus a body will acquire a velocity of 32 feet in a second, after 

 having descended 16 feet, either in a vertical line ov in an oblique direction; 

 but tlie time of descent will be as much greater than a second, as the oblique 

 length of the path is greater than 16 feet. This may be sliown by experi- 

 ment, as nearly as the obstacles already mentioned will permit, the times be- 

 ing measured by a pendulum, or by a stop watch. (Plate H.. Fig. 21.) 



There is an elegant proposition, of a similar nature, which is still more capable 

 of experimental confirmation; that is, that the times of falling through all 

 chords drawn to the lowest point of a circle are equaL If two or more bodies 

 are placed at different points of a circle, and suffered to descend at the same 

 instant along as many planes, which meet in the lowest point of the circle, 

 they will arrive there at the same time. (Plate II. Fig. 32.) 



The velocity of a body, descending along a given surface, is the same as that 

 of a body falling freely through an equal height, not only Avhen the surface 

 is a plane, but also when it is a continued curve, in which the body is retain- 

 ed by its attachment to a thread, or is supported by any regular surface, sup- 

 posed to be free from friction. We may easily sliow, 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, by observing the height to 

 which it rises on the opposite side of the lowest point. We may alter the 

 fonn of the path in which it descends, 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 a height equal to that from which it descendetl, with a small de- 

 duction on account of friction, (Plate II. Fig. 23.) 



