4 '-'I' 



DR. F. HORTON ON THE MODULUS OF TORSIONAL RIGIDITY OF 



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. 



The damping of the torsional oscillations observed in these experiments is, of course, 

 partly due to loss of energy from the vibrating system to the surrounding air, and 

 partly to the internal friction of the suspending fibre. In order, therefore, to obtain 

 a measure of the viscosity of quartz, it is necessary to find what proportion of the 

 observed logarithmic decrement is due to the friction of the air on the vibrating 

 system. For this purpose a fibre was suspended in the jacket and the logarithmic 

 decrement of the amplitudes of its torsional oscillations was observed. The apparatus 

 (which had previously been made air-tight by using an indiarubber bung instead of 

 the adjustable metal-head D, fig. 2) was then filled with hydrogen and the logarithmic 

 decrement again observed. The following table contains the results of experiments 

 with three fibres at 15 C. : 



The numbers in the column headed " Logarithmic decrement due to quartz fibre " 

 were calculated from the observed logarithmic decrements in air and in hydrogen, 

 using the values of the coefficient of viscosity of these gases given by O. E. MEYER.* 

 The vibrator used in these experiments was the one used in the rigidity experiments, 

 and the above results show that, when this vibrator is used at 15 C., only about 

 2 '5 per cent, of the observed damping is due to the viscosity of the suspending fibre, 

 and that this proportion is roughly constant for different fibres. 



From the table already given with the observed logarithmic decrements at different 

 temperatures it is seen that at 14'87 C. the logarithmic decrement was '01234. 

 Taking 2 '5 per cent, of this as being due to the viscosity of the quartz fibre, the 

 logarithmic decrement due to air-damping is '01203. The increase in this with rise 

 of temperature was calculated by means of the results of HOLMAN'S research on the 

 variation of the viscosity of air with temperature, t In the following table the mean 

 values of the observed logarithmic decrements at the different temperatures are 

 collected together. The value of the logarithmic decrement due to air-damping at 

 each temperature is given, and the difference between this and the observed 



* O. E. MEYER, 'Kinetic Theory of Gases,' p. 171. 



t S. W. HOLMAN, 'Phil. Mag.,' V., vol. 21, p. 199, 1886. 



