F F. JWipher — Surfaces of the Compound Pendulum. 25 



S. The radius of any circle is 



V sin0\4sin0 / 



(8) 



If a=o, we have the condition that the motion of a particle is 

 unaffected by its connection with the system. The radius of 

 of this neutral circle is therefore 



R'=*A ( 9 ) 



sin o 



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

 the two points and S, and tangent to YS at the point S. 



When S is horizontal, B/ becomes \l and when it is ver- 

 tical B/= oo. The position of the neutral circle for various 

 values of d is shown in fig. 2. For a pendulum of 39 

 inches, vibrating 2° on each side of the vertical, the radius of 

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

 between ± 46 feet and ±<x> . 



"Within the pendulum, the circle never departs materially 

 from the tangent SV, particles on the one side tending always 



