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MEMOIKS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 1. 



and the resulting error in T would be much less than 



1 



Even an error in /• two and 



1,000,000 

 one-half times as great, which could be easily detected, would produce a negligible error in T. 



Other special cases, such as abnormal density throughout a certain segment of the ring, 

 have been computed, but the results are of no particular assistance in discussing the experimental 

 data, and therefore need not be given here. 



4. THE AZIMUTH ERROR. 



Thei-e remains to consider onl}' the azimuth error — that is, an error in adjusting the plane of 

 the ring at right angles to the knife edge. (Rhoads.) 



Fig. 8. 



Consider a ring lamina of thickness dt (normal to its plane), and radii R and /'. To determine 

 its period of vibration around an inner circumferential axis making an angle n with its plane. 

 The moment of inertia of the lamina around a central axis will be: 



*V/7(R 4 -/- 4 ) (l+eos 2 «) = Ji„ 



The complete ring will be made up of a number of such laminae, which will not. however, be 

 symmetrically situated with respect to the axis of rotation. 



The moment of inertia of the complete ring about the central axis will be: 



Io = ^r(l+cos 2 «) (R*-y*) J 2 dt+'lrrp {W-r) sin 2 a j ' t'dt 

 = ^- fc (R a -^)r(2- S in s «)(R 2 +^)+| s in^]. 



