402 On the Modulus of Torsional Rigidity of Quartz Mbres, etc. 



and 100 C. In every case the modulus of rigidity was found to increase 

 as a linear function of the temperature, but the values obtained for 

 the temperature coefficient of the modulus were considerably different. 

 The mean value was + 0-0001 235, but the experiments show that this 

 is far from constant in different specimens of quartz, its variations being 

 much greater than those of the modulus of rigidity itself. It was 

 found that the fibres became slightly more rigid as time went on, the 

 rate of increase of rigidity being greater at the higher temperatures. 

 This is probably due to a gradual annealing of the fibre, the annealing 

 consisting in an easing of the structure from contraction strains. 



In addition to the determination of the periods of torsional vibra- 

 tion, observations of the logarithmic decrements of the amplitudes of 

 the oscillations were taken at each temperature. Fibres were also 

 made to vibrate in an atmosphere of hydrogen, and the logarithmic 

 decrements were again observed. From the values thus found, and 

 the known ratio of the viscosities of air and hydrogen, a measure of 

 the internal friction of the fibre was obtained. It was found that the 

 internal friction of the fibres was very small, only about 2 '5 per cent, 

 of the observed logarithmic decrement at 15 C. being due to that 

 cause, arid that it remained roughly constant when the temperature of 

 the fibre was raised from 15 C. to 100 C. 



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 between 14' and 10 being used. 

 It was found that both the logarithmic decrement and the torsional 

 period remained constant within these limits. In this respect quartz 

 differs from metal wires, in which it was found that both the internal 

 friction and the period of torsional vibration increased with the 

 amplitude of oscillation. 



In the experiments between 20 C. and 1000 C. the fibres used were 

 .rather thick and were suspended inside a platinum tube which was 

 heated electrically, and which could be maintained at any desired 

 temperature. Observations were taken at intervals of about 50 C. , 

 and the temperature of the tube was obtained by means of a thermo- 

 junction of wires of platinum and rhodo-platinum. It was found that 

 the modulus of rigidity of the fibre increased with the temperature, at 

 first as a linear function of it, but as the temperature rose the rate of 

 increase gradually diminished, and a maximum rigidity was attained at 

 about 880 C. After passing this point the rigidity decreased very 

 rapidly with increase of temperature. 



The internal viscosity of the fibres increased with the temperature at 

 a rate which was at first small and constant, but after about 650 C. it 

 became much more rapid. At 1060 C. the internal friction of the fibres 

 was so great that the torsional vibrations were nearly dead-beat. 



