ON THE NfODTTLUS OF TORSIONAL RKHDITY OF METAL WIRES. 15 



coincidence is noted in the same way as the former one. Then, if the flashes are 

 " losing," after a time the 37th flash will have lost nearly a second and flash number 1 

 will l>e about to coincide. This coincidence is waited for and noted. In the same 

 way later on the 23rd gets a second behind and the 24th coincides. It is only 

 necessary to keep watching the flashes just when a coincidence is expected, and in 

 the intervals l>et\veen the coincidences the thermometers are read every few minutes. 

 In order to make sure that it has not l>een omitted to make a note of any 37th flash. 

 the time of the chronometer at which one of these flashes happens near the beginning 

 of the observation is noticed, and also again at the end. From the total time the 

 number can be checked 



After the observation of the period was finished, the candle was again placed 

 behind the slit and the amplitude of vibration again observed. When this became an 

 i-xadt number of divisions of the eye-piece scale the time of the chronometer was 

 noticed. From the times at the beginning and the end. and from the calculated 

 ]>eriod of vibration, the number of vibrations could be obtained, and hence the 

 logarithmic decrement of the swings calculated. 



The Effect of Damping on the Period of Vibration. 



I had anticipated having to correct the times of vibration on account of the 

 damping of the amplitude, but in nearly all cases the correction was too small to take 

 into account. If the equation of motion of the disc is 



+ K g + ,0 = o, 

 the period of damped vibration is given by 



where A. is the logarithmic decrement of the amplitude of vibration. 



Now if I is the moment of inertia of the vibrating system, and if /i is the rigidity 

 modulus. / the length, and a the radius of the wire, we have u 1 = nira*/2ll. 



"2ir 8 (ir 2 -f- X 2 ) II 



Hence r = ' " " = ' 



If now we correct T, the observed period, to T , the time of vibration the system 

 would have if there were no damping, 



n = 8ir*K/T W. 

 K<|iiating these two values of /*, 



77"' + \- 7T , rp 



'I'J ~ T i 01> 1 ~ 



A 



