6 



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



Such a ring could be added to or taken from the perfect ring without altering the period; 

 hence any symmetrical system of tine lines or graduations could be made on the ring at the 

 distance /•' from the center without sensibly altering its period. 



The degree to which the period of a perfect ring is independent of /■ when the relation 

 R = v/jjy is nearly satisfied is shown by the following computed values of T for a constant R and 

 varying r. 



R= U.413 cm. 



ff=980. 



r= , 8 cm .31 

 T= I s . 00567 



I s . 005669+ 



8 cm .33 



I s . 005671- 



It is evident from this that it is a very easy matter to satisfy the relation R=v/3> with suf- 

 ficient accuracy. 



2. THE EFFECT OF FLAWS, OR SMALL IRREGULARITIES IN DENSITY, ON" THE PERIOD OF THE RING. 



[Rhoads.] 



Suppose a Haw of magnitude J/// located at the point /•,, 9 (fig. 3), and let this Haw produce 

 a change AT in the period T of the otherwise perfect ring. 



Then: 



(1) 



Fig. 3. 



T-f-JT = 2^ 



'An<r~ + Jinr'i 



\ g(mr-\-r t cos 6 Am) 



(2) 



Aw 



3rH — -n 

 m 



i Am, ... 



'/{'■+ /\ cos H) 



(3) 



= 2w/ 



gr(l+ 5 — cos 9) 



(4) 



-T 'uJ'i Am \~ T i n~\ 



- T M 1+ J-m7lfr- cos0 J 



