QUARTZ FIBRES AND ITS TEMPERATURE COEFFICIENT. 411 



of the glass tube as it was being drawn up, but this could not well be managed after 



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the fibre had disappeared inside the jacket. The torsion head was next arranged so 

 that the mirror on the vibrator reflected an image of the slit, used in the timing 

 arrangements, into the observing telescope. The copper bottom was then screwed 

 on to the jacket, a lead washer being compressed between, so as to make an air-tight 

 joint. The glass jets for setting the vibrator in oscillation were next arranged in 

 position, and any final adjustment required in the position of the mirror was made 

 by means of the fine screw C which rotates the torsion head. A rapid stream of 

 water was then sent through the jacket, and the apparatus was allowed to rest until 

 a constant temperature had been attained. 



In determining the period of vibration the mean of some 10 or 15 observations wan 

 taken. The bottom of the jacket was then removed, the vibrator lowered outside, 

 and the small cylinder slipped off the rod and replaced with its axis perpendicular to 

 its first position, as shown in fig. 1. It was then raised again into the jacket, 

 adjusted into position, and allowed to rest until a constant temperature had been 

 established, when the torsional oscillations were timed as before. The vibrator was 

 then again lowered and the cylindrical part replaced in its first position, after which 

 the period was again observed. The mean of this and the first observation was 

 taken as the period corresponding to the moment of inertia of the vibrator with the 

 cylinder in the first position, and was used with the other observation to give the 

 modulus of rigidity. 



Corrections to the Observed Periods of Vibration. 



The value of the rigidity modulus to be determined was that corresponding to 

 15 C. It was therefore necessary to correct the observed periods to the values they 

 would have had if the temperature during the observations had been 15 C. The 

 periods were therefore first corrected for clock rate and then multiplied by the 

 factor 



in which ft is the coefficient of linear expansion of the material of the vibrator, a is 

 the coefficient of linear expansion of quartz, y is the temperature coefficient of the 

 modulus of rigidity of the fibre. 



Of these, /? was determined experimentally by measuring the coefficient of 

 expansion of the rod of brass from which the vibrator was afterwards made. This 

 was done with the measuring bench in the Physical Laboratory of the University of 

 Birmingham, for the use of which I am indebted to Professor POYNTING. The 

 instrument and method of experiment are described in the former paper. The mean 

 value found for the coefficient of expansion was '00001937. 



The correction on account of the expansion of the fibre is very small, owing to the 

 smallness of the coefficient of expansion of quartz. It was therefore not thought 



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