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



Ring EL— Maximum difference {T 6 —T i )=0.000875. 

 [Radius=14 om .42580; thickness=14""".21.] 



Final corrected period=l s .0030069. 



The first thing to be noticed is the much greater variation of T for different positions, in the 

 case of Ring II than Ring I; for Ring II the range being a .000275, and for Ring I, S .00005, 

 the latter being of the same order of magnitude as the accidental variations between individual 

 determinations at the same point. In both cases the variation with position is quite regular, a 

 minimum T on one side corresponding to a maximum at the opposite point, with intermediate 

 values between as would be expected; and it is very noticeable that the means of the periods 

 for diametrically opposite points agree almost as well for Ring II as for Ring I. The large vari- 

 ations for Ring II were quite unexpected, for its behavior in the course of construction had not 

 suggested that there was any great difference in the material at different points; and it would 

 seem probable that a difference in density which would produce the observed differences in 

 period would result in a difference in hardness or texture which the grinding wheel would be 

 sensitive to detect. The existence of actual flaws or crevices is unlikely, since the ring was 

 originally forged. Errors of figure which would produce these variations of period are: 



(1) Eccentricity of inner and outer circumferences. 



(2) Ellipticity. 



(3) Nonparallelism of faces. 



It is certain that neither (1) nor (2) i* present in sufficient magnitude to produce the observed 

 effects; (2) would have been detected by the direct measurements and (1) would have shown in 

 grinding. 



As before stated, the faces of Ring II were slightly out of parallel, the maximum difference in 

 thickness being less than 0""".OOl; whereas, it was shown above that a difference of 0""".01 would 

 produce. onh r about one-quarter of the maximum observed difference in period, and would be 

 equivalent to a regular change in density in which the maximum variation in density was one 



Ap 

 P ' 



one-thousandth of the mean density, i. e. 



=0.001. One is apparently forced to the conclu- 



Ap._ 



sion that Ring II is nonhomogeneous and that the ratio -- is, perhaps, 0.004. It should be 



added that the ring was examined with a flip coil and a ballistic galvanometer, but no magnet- 

 ization was detected. 



The calculation of the effect of a special case of nonuniform density (see p. 10 above) showed 

 that though the maximum difference of period for different positions might be considerable, the 

 mean period would differ by less than a tenth of this amount from the period of the correspond- 

 ing perfect ring; and also showed that (for the special case considered) the particular pair of 

 diametrically opposite periods (so to speak) which are equal to each other are, to a close approxi- 

 mation, equal to the period of a perfect ring. However, without knowing more about the real 



