NIPHER — SURFACES OF THE COMPOUND PENDULUM. 



647 



Equation (7), then, becomes the equation of a circle containing 

 the two points O and S, and tangent to VS at the point S. 



When S O is horizontal R' becomes j/, and when it is verti- 

 cal R'= CX). The position of the neutral circle, for various 

 values of 6, is shown in Fig. 2. For a pendulum of 39 inches, 

 vibrating 2 degs. on each side of the vertical, the radius of the 

 neutral circle, or the distance of the common center, varies be- 

 tween ziz 46 feet and dr OO . 



Within the pendulum the circle never departs materially from 

 the tangent SV, particles on the one side tending always to in- 

 crease, while those on the other side tend to diminish the actual 

 acceleration of the pendulum. 



In (8) the condition a = - — ; — - , or a = JR'= a', reduces the 

 4 sm ^ 



radius to zero. This gives the value of a at the center of the con- 



