ON THK Mobn.l'S <>K Tn|;sl< i\.\l. KICIDITY OF METAL WIRES. 



19 



a long gun-metal liar, which had teen cast at the same time as the ring. The 

 coefficient of expansion of this bar, as well as the coefficients of expansion of the 

 various wires, was determined in the manner described in Part IV. of this paper. 

 The results of the above observations of periods are given below : 



Mean of the periods with the ring on = 3'581456 seconds at 17'22 C. ; 17'00 C. 



Mean of the periods with the ring off = 2'915453 seconds at 17'25 C. ; 1677 C. 



The mean period with the ring on must now be corrected to the value it would 

 have if the temperatures had been the same as when the ring was off Correcting 

 therefore on account of the alteration of rigidity of the wire, and of the dimensions of 

 the wire and plate, we get the corrected time Q = 3'581454 seconds. 



Calling the period of the vibrator alone T, and I the moment of inertia of the ring, 

 we have 



M..M+I M IT* 



T J " < ' ~ Q 2 T 8 ' 



The value of I at 1677 C. was calculated from the known value at 13'90 C. and 

 the experimentally determined value of the coefficient of expansion. 



Hence M at 1677 C. = 19992'018 grm. cm. 2 



The values of M at the higher temperature were calculated in an exactly similar 

 manner, and the results obtained were 



From the first experiment, M = 20049*400 grm. cm. 4 at 99'06 C. 

 From the second experiment, M = 20049709 gnn. cm. 2 at 9878 C. 



From t-ach of these values. ;md that given above for 1677 C., the coefficient of 

 change of moment of inertia of the vibrator with temperature was found. The values 

 were '00003540 and '00003501 ; mean = -00003520; from which ft required in the 

 formula for correcting the periods is '00001760. 



i. _' 



