134 OUTLINES OF NATURAL PHILOSOPHY. 



r-.: ; : --' 



Heavy Bodies descending on a Cycloidal Surface* 



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212. If a circle DHE (fig. 12.) roll along a 

 line AB, until the point V in its circumference, 

 which touched the line AB in A, come to touch it 

 again in B, the curve AVB, generated by the 

 point V, is called a Cycloid. 



The line AB is called the Base ; DV, which bisects 

 AB at right angles, the Axis of the Cycloid ; and 

 the circle DHE, the Generating Circle. 



If AC and BC be two semicycloids, or semicycloidal 

 cheeks, each equal to the half of AVB, touching 

 AB in A and B, and touching one another in C ; 

 -and if there be fixed at C a pendulum P, hanging 

 by a thread PTC, equal in length to the semi- 

 cycloid, P in its vibrations will describe the cycloid 

 AVB. 



213. A pendulum being thus made to vibrate in 

 a cycloid, is at every moment of its descent acce- 

 lerated by a force proportional to the arch of the 

 cycloid, between it and the lowest point. 



.Hence the vibrations of this pendulum, whether great 

 or small, are all of the same duration* 



214. If 



