QUART/ FIBRES AND ITS TEMPERATURE COEFFICIENT. 427 



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. On passing this temperature, the rigidity decreased very rapidly with 

 increase of temperature. 



The logarithmic decrement of the torsional oscillations increased with the tempera- 

 ture at a rate which was at first constant, but after about 650 C. it l>ecame much 

 more rapid. In order to see what part of the observed logarithmic decrement was 

 due to the viscosity of the fibre, several fibres of about the same dimensions as those 

 used in these experiments, and carrying the same vibrator, were in turn suspended in 

 a large air-tight brass tube and made to vibrate first in air and then in hydrogen, the 

 logarithmic decrements of the torsional oscillations being observed in each gas. The 

 values of the logarithmic decrement due to the fibre were then obtained in the same 

 way as with the finer fibres. The values given differed very considerably even when 

 obtained from repeated olervations with the same fibre. This is no doubt largely 

 due to the smallness of the olerved logarithmic decrements. The results showed 

 that from to 5 per cent, of the observed logarithmic decrement in air at 17 C. was 

 due to the viscosity of the quartz fibre. In correcting the ol)served logarithmic 

 decrements in the experiment proper, 2 '5 per cent, of the observed logarithmic 

 decrement at 20 C. was taken as being due to the viscosity of the fibre, the 

 remaining 97 '5 per cent, being due to air-damping. This is, of course, only an 

 approximate value, but is, I think, good enough for the present purposes, for the 

 internal viscosity of quartz at the ordinary temperature of the laboratory is extremely 

 small in comparison with the value it has at high temperatures, and, consequently, a 

 difference of 50, or even 100, per cent, in the value at 20 C. would l>e hardly 

 noticeable in plotting a curve to represent the changes up to 1000 C. The 

 temperature of the air surrounding the vibrator was constant during the experiments, 

 and the logarithmic decrement due to air-damping was taken to have the same value 

 throughout the experiments. This would not be exactly the case, for the viscosity of 

 the air surrounding the part of the vibrating system the temperature of which is raised 

 would increase with the temperature. The effect of this increase would, however, 

 prolmbly be small in comparison with the whole damping effect due to the air, for 

 most of the damping of the torsional vibrations would doubtless be caused by the 

 metal cylinder (F, fig. 5), the temperature of which remains constant. It will also be 

 seen from the appended table that the logarithmic decrement due to air-damping 

 is itself a small fraction of the actual observed logarithmic decrement at high 

 temperatures. 



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