QUARTZ FIBRES AND ITS I KMI'KI; \TVRE COEFFICIENT. 



421 



in accommodating itself to a definite elastic state. It is only after the fibre has been 

 so treated that its modulus of rigidity assumes a steady value. This, over the range 

 of temperatures investigated, is a linear function of the temperature. 



It will be seen from the table that the effect of continued heating was sometimes 

 to increase the rigidity, and sometimes to diminish it. The alteration as time went on 

 was in all cases small, and the values of the modulus obtained by repeated heating to 

 any one temperature were much more constant than in the case of any of the metal 

 wires experimented on in a former research, with the exceptions of copper and of 

 steel. It will be observed that after the fibre had been allowed to rest for some 

 three weeks (from March 31st to April 20th) its rigidity had increased slightly, but 

 that on heating to 100 C. it re-accommodated itself back to the normal value. 



From the line drawn in Diagram I. the value of the modulus at C. was found by 

 exterpolation, and the temperature coefficient at was determined. The value found 

 was a = '0001146, where /* = n v (l + ctt), n a and >< t being the values of the modulus at 

 C. and t C. respectively. This fibre was No. 4 in the list of absolute values 

 already given. The value given in the list as the modulus of rigidity of this fibre at 

 15 C. was determined immediately after the fibre had taen brought to the state of 

 constant rigidity. 



Similar experiments were performed with three other fibres, and the general 

 behaviour of each was identical with that described above. The values of the 

 temperature coefficient obtained from these fibres were, however, considerably different, 

 as will be seen from the following table : 



Fibre 7 was unfortunately lost before its radius had been determined. The value 



w 



given above was calculated by assuming the value of the modulus of rigidity of the fibre. 

 The mean value of the temperature coefficient is a = -0001235, but the results of these 

 experiments show that this is far from being a constant value, and that its variation 

 in different fibres is greater than that of the modulus of rigidity itself. 



With fibres 4 and 6, at the end of the rigidity determinations, a series of 

 observations was taken to ascertain the manner in which the logarithmic decrement 

 and the torsional period varied with the amplitude of vibration, amplitudes up to 

 about 10 being used. It was found that both the logarithmic decrement and the 

 torsioiial period remained constant within these limits. In this respect quartz differs 



