MECHANICS. 127 



ther it fall freely, or descend on a plane any ho'w 

 inclined. 



199. The space through which a body will de- 

 scend OB an inclined plane, is to the space through 

 which it would fall freely in the same time, as 

 the sine of the inclination of the plane to the ra- 

 dius. 



The diameter of a circle perpendicular to the hori- 

 zon, and any chord terminating at either extremi- 

 ty of that diameter, are fallen through in the same 

 time. 



The velocities which bodies acquire by descending 

 along chords of the same circle, are as the lengths 

 of those chords. 



200. If a body descend over a series of inclined 

 planes, at each of the angular points, where it 

 passes from one plane to another, it loses a part of 

 the velocity it had acquired, proportional to the 

 versed sine of the inclination of the planes. 



If v be the velocity it has acquired when it comes to 

 any angle ?, v x vers. p is the velocity lost 



201. Any angle being given, it may be divided 

 into angles, so small, that the sum of the versed 

 sines of these angles shall be less than any given 

 magnitude. 



Hence 



