196 V. OSCILLATIONS AND CYCLIC MOTIONS. 



If #' is slightly different from zero, it will accordingly tend to 

 approach the value zero, so that the horizontal position is stable. 



A body moving according to the differential equation 221) is 

 called by Thomson and Tait 1 ) a quadrantal pendulum, since # changes 

 "according to the same law with reference to a quadrant on each 

 side of its position of equilibrium as the common pendulum with 

 reference to a half -circle on each side", or in other words, in the 

 ordinary pendulum the acceleration is proportional to the sine of 

 the angle of deviation from equilibrium, and in the quadrantal to 

 the sine of twice the angle. The small oscillation performed by the 



bar will be harmonic with the frequency ~- Here we have an ex- 

 cellent example of an apparent potential energy which is really kinetic. 



1) Thomson and Tait, Nat. Phil., 322. 



