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



It is difficult to see why the value of the modulus of rigidity obtained by BARNKTT 

 is so much lower than those found by the other observers. BARNETT states that the 

 fibres used by him were much thicker than those used by BOYS or THRELFALL, and 

 that it is probable that the rigidity of fine fibres, like the breaking weight per unit 

 area of cross-section, increases as the diameter decreases.* This, however, is not 

 borne out by the fact that some of the fibres used by THRELFALL were very nearly 

 of the same diameter as some of those used by BARNETT. BOYS and THRELFALL both 

 found considerable variations between the values of the rigidity modulus obtained 

 from different fibres. These observers used a high-power microscope to measure the 

 diameter of the fibres directly, and THRELFALL states that " it is impossible to be 

 sure of the thickness of threads of about "015 centim. diameter within less than 

 3 or 4 per cent, by a single measurement." It is therefore probable that the 

 discrepancies found were largely due to an inaccurate knowledge of the radius of the 

 fibres used ; indeed, it must have required great skill in experimenting, and patience 

 in taking many observations of the diameters, in order to obtain as good an 

 agreement as that given. 



Of the values of the temperature coefficient of the modulus between 15 C. and 

 100 C.,that given by THRELFALL was obtained from a single fibre. The value given 

 by BARNETT was the mean of the results of observations on several fibres. The 

 variation between the different values was considerable, but not so large as the 

 variation found in the present experiments. The fibres used by BARNETT were, 

 however, all prepared from one crystal of quartz, and the results obtained would 

 therefore be expected to be more uniform. 



BARNETT also made observations to determine if there was any change of rigidity 

 with time. Experiments extending over an interval of four months failed to detect 

 any alteration. The present experiments show that with more accurate timing of 

 the torsional oscillations, variations in the rigidity can be detected, and that, when a 

 fibre is allowed to rest at the ordinary temperature of the laboratory, its rigidity 

 increases slightly. The increase of rigidity with time is, however, not so marked in 

 the case of quartz as it was found to be with metal wires, and the reason for this 

 may possibly lie in the fact that the structure of fused quartz is amorphous, while 



* It is, of course, well known that the tensile strength of metal wires also increases as their diameter is 

 decreased. 



