VALUE OF ACCELERATION OF GRAVITY— MENDEXHALL. 11 



Irregularities in the outer radius must be determined in each case and their effect computed. 

 Irregularities in the inner radius are of no importance (except as they affect the amount of con- 

 tact on the knife edge) unless they result in making the inner surface conical, and hence forcing 

 the rine to swing out of its own plane. In this case if we consider a thin lamina of the ring, it 



will evidently he equivalent to its elliptical projection upon the vertical plane; and for small 

 values of a (tig. 7), since the external diameter is supposed uniform, all lamina^ will be equally 

 affected and it will suffice to consider a plane ring whose — 



external major axis (horizontal) =2R. 



external minor axis (vertical)=2R cos a. 



internal major axis (horizontal) = 2—-=. 



v 3 



internal minor axis (ve rtical) = 2— - cos a. 



v3 



If 

 I'=the moment of inertia of this equivalent elliptical ring: 



I =the moment of inertia of a corresponding circular ring about a normal axis through P 

 we find 



r n , a ., \ 



y = COS K ( o + o COS (( J 



and 



— vs-V i %l^ 



M 75' 



V 



1,2 , 

 o+o cos" a 



If. as a special case, t=15 mm. 



// ,.=0.001 mm. 

 Then cos (7 = 0.9999998 



