VALUE OF ACCELERATION OF GRAVITY— MENDENHALL. 



Differentiating with respect to r: 



But if 



the period will be independent of /'. 

 which gives the condition — 



2TfT= 4 «f» *1 

 dr \_2g &gr _\ 



dT 



dr' 



W 



=0 



or 



2g 2;// 



R 2 = 3r 2 



[By noting the effect of putting r=0 this condition is seen to be that tor a minimum value of T]. 

 Introducing this relation above we find — 



Ip=MR s =3Mr» 



T=2^ 



Rx/3 



RV3 is evidently the length of the equivalent simple pendulum. 



It is also useful to know the radius of the equivalent "simple ring" pendulum— i. e., a 

 linear ring concentric with the real ring, and vibrating (by means of a massless support) around 

 the same point of suspension (P) with the same period. 



In this case: 



and: 



By hypothesis: 



or 



4 R 



'=&■ 



