1904.] on the Modulus of Torsional Rigidity of Wires. 



335 



The method of coincidences used in timing the torsional vibrations 

 consists in observing the reflections of a vertical flash occurring once 

 a second, in two mirrors, one of which is fixed in position, and the 

 other is attached to the vibrator and vibrates with it, swinging just 

 above the fixed mirror and being parallel to it when at rest. The 

 reflections are observed by means of a telescope, in the field of view 

 of which, in general, two flashes are seen, one always occurring in the 

 same position, and the other appearing in different parts of the field 

 according to the position of the moving mirror at the instant the flash 

 -occurs. If a second signal happens exactly when the two mirrors are 

 parallel, the two flashes coincide, and it is from these "coincidences" 

 that the time of vibration is obtained. The method of coincidences is 

 usually only applied to the comparison of two nearly equal times, but 

 it is shown in the paper to be equally applicable to any two periods 

 even if they are quite different. 



In order that the observed periods at different temperatures may be 

 comparable, it is necessary that they should be corrected for the 

 increased length and radius of the wire, and also for the expansion of 

 the vibrator at higher temperatures. For this purpose the coefficients 

 of expansion of the wires, and of a gunmetal bar cast at the same 

 time as the vibrator, were determined by means of the measuring bench 

 in the Physical Laboratory of the University of Birmingham, which 

 Professor Poynting kindly placed at my disposal. A description of 

 the instrument (which has not otherwise been described), and the 

 results of the experiments, are given in Part 4 of the paper. 



In addition to the determination of the periods of vibration, 

 observations of the logarithmic decrement of the amplitudes of the 

 oscillations were taken at each temperature, and thus the effect of 

 temperature on the internal viscosity of the wires was observed. At 

 the end of the rigidity determinations for each wire, a series of 

 observations was usually taken to ascertain the manner in which the 

 logarithmic decrement and the torsional period varied with the ampli- 

 tude of vibration, amplitudes up to about 10° being used. The main 

 observations for the rigidity determinations were all taken at the 

 constant average amplitude of 14'. 



The following is a summary of the principal results : — 



1. In all the materials examined, with the exception of pure copper 

 and of steel, the modulus of rigidity at one temperature is not 

 constant, but increases as time goes on. The rate of increase of 

 rigidity with time is greater the higher the temperature, and repeated 

 heatings to the same temperature gradually lessen the rate of altera- 

 tion with time at that temperature, but even in the course of months 

 of experimenting the increase of rigidity with time cannot be entirely 

 eliminated. 



2. The diminution of the modulus of rigidity per degree rise of 



