18 Dl;. F. MORTON ON THK KKKl-X'TS <>K CIIANC.KS ()K TEMPERATURE 



oscillations, and the other for their amplitude. The former \\.is ^viii-rally t<>< ( small 

 to take into account, and the latter was avoided by always dealing with the same 

 amplitude. 



The formula connecting the period of vibration with the rigidity and dimensions of 

 the wire, and the moment of inertia of the vibrator is T = 2 x/2lM.rr/na 4 , where M is 

 the moment of inertia of the vibrator and n the modulus of rigidity, a being the 

 radius and / the length of the wire. If now a is the coefficient of expansion of the 

 material of the wire, and /? that of the material of the vibrator, and if the wire is at 

 0, and the vibrator at <f>, we have 



T, = 2v/2irM (l 

 where n g is the rigidity modulus at 0. Hence 



T, = 2 A (1 + ft - fa0). 



In order, therefore, to correct the observed periods to the values they would have 

 if the wire and vibrator retained the dimensions they had at 0, they must -be multi- 

 plied by (1 /J( + fa0). In the experiments 15 C. was taken as the temperature 

 of comparison, and the observed times were corrected by multiplying by 



The value of $ and the various values of a for the different wires were determined 

 experimentally. The vibrator, as already stated, consisted of a gun-metal plate with 

 a steel rod through its centre, and the temperature coefficient of the moment of inertia 

 of this system was required. This was found in the following manner, a steel wire, 

 the temperature coefficient of the rigidity modulus of which had already been found, 

 being used to suspend the vibrator : The vibrations were timed at the ordinary 

 temperature and then the ring was lowered on to the vibrator and the period again 

 determined. The ring was next turned round about a vertical axis through an angle 

 of 60 and the period found again, then turned through a further 60, and so on, 

 taking six observations in all, the mean of which was taken as the period of vibration 

 of the vibrator + ring. The ring was lastly taken off the plate and the period ot 

 the vibrator again found, the mean of this and the first determination being taken as 

 the period of the vibrator alone. Each time the heating jacket was opened to move 

 the ring it had to be left for from one to two hours for the temperature to become 

 constant again. On the following day the temperature of the jacket was raised to 

 100, and two sets of observations with the ring on and off were taken. It had been 

 intended to take more, but the personal discomfort involved in removing the ring 

 from the plate whilst hot persuaded me to be content with two. The coefficient of 

 linear expansion of the material of the ring was assumed to be the same as that of 



