On the Modulus of Torsional Rigidity of Quartz Fibres, etc. 401 



" On the Modulus of Torsional Eigidity of Quartz Fibres and its 

 Temperature Coefficient." By FRANK HOTON, D.Sc., B.A., 

 St. John's College, Cambridge, late Mackinnon Student. 

 Communicated by Professor J. J. THOMSON, F.E.S. Eeceived 

 December 15, 1904, Eead January 26, 1905. 



[Abstract.] 



The author recently had the honour of reading to the Society the 

 results of some experiments in which a new method of timing by 



means of " coincidences " a method devised by Professor Poynting 



was applied to an investigation of the effects of changes of tempera- 

 ture on the modulus of torsional rigidity of metal wires. It seemed 

 desirable to repeat similar experiments with quartz fibres, seeing that 

 now they are almost universally employed as suspensions in torsion 

 instruments where accuracy is required. 



The fibres experimented on were prepared from different crystals of 

 quartz, and care was taken in their manufacture so as as to obtain them 

 free from air bubbles and of circular cross-section. The investigation 

 was divided into three parts : 



(1) The determination of the absolute value of the torsion modulus. 



(2) The variation of the modulus over a range of temperature from 

 15 C. to 100 C. 



(3) The variation of the modulus between 20 C. and 1000C. 



In the determination of the absolute value of the modulus, it is 

 necessary to find the radius of the fibres used. The method adopted for 

 this purpose consists of measuring the circumference of the fibre by 

 rolling a small length of it between two fine glass capillary tubes and 

 counting the number of revolutions it makes in travelling a distance 

 of 5 mm. With practice, this method was made to give very 

 good results ; a fibre of diameter 0*001 cm. being measured to O'Ol 

 per cent. 



The results of experiments on six fibres gave numbers for the 

 modulus of rigidity in very good agreement, showing that the rigidity 

 of quartz is practically constant, and does not vary in different speci- 

 mens as in the case of metal wires. The mean value obtained for the 

 modulus of rigidity at 15 C. was 



3-001 x 10 11 dynes per sq. cm. 



The results showed that this value is independent of the longitudinal 

 stress to which the fibres are subjected, so long as this is not greater 

 than that which they are usually required to bear when used as sus- 

 pensions in measuring instruments. 



In the second part of the research, observations were made on 

 several fibres at temperatures approximately 15 C., 35 C., 55 C., 75 C,, 



