408 



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



limits. The mean value of the temperature coefficient of the modulus was +'000115, 

 but the agreement between the values obtained from different fibres was not 

 very good. 



The object in repeating these experiments was to apply, where possible, more 

 accurate methods for obtaining the data required in order to calculate the rigidity 

 modulus. In the experiments about to be described the points to which particular 

 attention was directed were the timing of the torsional oscillations of the fibres and 

 the determination of their radii. The experiments were divided into three parts : 



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



(2) The variation of the modulus over a range of temperatures from 15 C. 



to 100 C. 



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



PART I. THE DETERMINATION OF THK MODULUS OF TORSIONAL RIGIDITY. 



The fibres experimented on were prepared from different crystals of quartz by 

 means of the bow-and-arrow process originally used by BOYS.* Great care was 

 taken in their manufacture in order to obtain them free from air bubbles and of 



circular cross-section. A length of from 10 to 15 centims. of 

 a selected fibre was mounted as the suspension of a small 

 vibrator and enclosed in a double-walled jacket shown 

 diagrammatically in fig. 2. The vibrator, the total mass of 

 which was 27 grammes, is shown on a larger scale in 

 fig. 1. It consists of two parts; a brass rod, 1'5 millims. 

 in diameter and 8 centims. in length, and a small brass 

 cylinder about 11 millims. long by 5 '5 millims. in diameter. 

 This cylinder has two holes drilled through it, one along its 

 axis, and the other at right angles to the axis at the middle 

 of its length. These holes are of the same diameter as the 

 rod, and thus the cylinder can be fixed on the rod in the 

 two positions shown in fig. 1. In this way it is possible 

 to obtain, experimentally, the moment of inertia of the 

 vibrator without adding to its mass. This precaution seemed necessary in view of 

 the statement by BoYst that the rigidity of the fibres varies with the tension to 

 which they are subjected. A small plane mirror M fixed upon the rod serves as a 

 means of observing the torsional oscillations. The upper end of the vibrator rod is 

 pointed, and one half filed away in order that the fibres may be attached along the 

 axis. The upper end of the fibre is attached to a brass pin which can be clamped in 



First Second 



position. position. 



Fig. 1. The vibrator. 



* C. V. BOYS, 'Phil. Mag.,' V., vol. 23, p. 489, 1887. 

 t C. V. BOYS, ' Phil. Trans.,' A, vol. 186, p. 65, 1895. 



