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



5. Correction for the vibration of the support. — The correction for the vibration of the knife- 

 edge support was determined by the method of Schuman." For this purpose the two rings were 

 supported side by side on a steel knife edge, which took the place of the usual agate one. One 

 pendulum, the "driving" one [Ring I] was given a vibration of about the usual amplitude, the 

 other, the "driven," having been brought to rest with the greatest care; and the operation con- 

 sisted in measuring the gradually diminishing amplitude of the driving pendulum and the grad- 

 ually increasing amplitude of the driven one. The period of Ring I was first adjusted by means 

 of small attached weights to agreement with that of Ring II to within s . 00002, and it was so 

 arranged that one of the etched lines on Ring II, and a tine wire attached to Ring I, could be 

 simultaneously observed with a high power telescope, and the amplitude measured with a micro- 

 meter eyepiece. These amplitudes, measured at known intervals of time after the starting of 

 Ring I, were found, when plotted, to be linear functions of the time. According to Schuman, if: 



W x , S ir ] ,= amplitude of the driven pendulum at times t l and /.,. 

 $,, $ 2 = simultaneous amplitudes of the driving pendulum, 

 T= half-period of the pendulums. 

 ar=apparent lengthening of the driving pendulum on account of the 



we have 



vibrations of the case, 



R-1MII 



The values of Wand 4> were determined at an interval f. 2 — £ 1 =240 8 . by graphic interpolation 

 from the direct observations, and the following computed values of a obtained: 



cm. 



1. Top of pendulum case off. . . a= 0. 00063 



2. Top of pendulum case off. . . «= 0.00065 



3. Top of pendulum case on. . . a— 0. 00074 



4. Top of pendulum case on. . . a— 0. 000756 



To determine the corresponding change in period, we have, if— 



T = observed period 

 T' = corrected period 



T^27r^— l + g T a 



=T'+0.02«. 



Hence, using the mean value of a with "top on" it is found that: 



J r I\ = s . 0000150 



To determine the corresponding correction for Ring II, /?, we can write, according' to 

 Schumann, 



Q— a ' ;w n*'nlii g u 



miSiTi^i 



where ?//,,/// u = inasses of pendulums. 



.s 1 .v H = distances of center of gravity from point of 

 support. 

 Ti,Tn= periods. 

 e i,*n= constants which depend on the form of the 

 pendulums and the support. 



"Schumann, Zeits. f. Math, und Physik. 44 Jahrgang, pp. 124 to 126. 



