50 1>U. F. HOBTON ON THE EFFECTS OF CHANGES OF TEMPERATURE 



" if we start with a sufficiently low temperature the internal friction ot all annealed 

 metals is first temporarily decreased by rise of temperature and afterwards increased. 

 The temperature of minimum internal friction is for most annealed metals between 

 C. and 100 C." In the present research this effect was obtained in two cases only, 

 viz., for soft iron and for steel. There was, however, a slight decrease in the value 

 of the logarithmic decrement at the first rise of temperature in the case of platinum 

 and of commercial copper, but this was, I think, due to the " time effect " (a decrease 

 of internal viscosity with time) being greater than the increase due to the rise of 

 temperature. This time effect diminishes as time goes on and the decrease of 

 logarithmic decrement with increasing temperature did not occur again. TOMLINSON'S 

 other results are practically the same as those of STREINTZ, mentioned above. He, 

 too, states that the logarithmic decrement of the torsional oscillations is independent 

 of the amplitude of vibration, provided the deformations produced do not exceed a 

 certain limit, varying with the nature of the metal. This is contrary to the results 

 obtained in the experiments now described, in which it was found that the logarithmic 

 decrement increased as the amplitude was increased from 14' to ( J. In some cases 

 the rate of increase was greatest at the smallest amplitudes, and it may be that in 

 these cases, over larger amplitudes, the logarithmic decrement remains constant, but 

 this is not a general law. 



TOMLINSON also states that the logarithmic decrement of the amplitudes increases 

 with the period of vibration, on this point differing from STRETNTZ. In the present 

 research it was found that the period increases with the amplitude of vibration. If, 

 then, TOMLINSON is right, it would be expected that the logarithmic decrement would 

 also increase with the amplitude of vibration, and not, as he states, be independent 

 of it. 



PART IV. 

 THE DETERMINATION OP COEFFICIENTS OF LINEAR EXPANSION. 



The coefficients of expansion of the metal wires, and also of the gun-metal bar cast 

 at the same time as the ring used in determining the moment of inertia of the 

 vibrator, were determined by means of the measuring bench in the Physical 

 Laboratory of the University of Birmingham. This excellent instrument was 

 designed by Professor POYNTING, and he very kindly allowed me to work with it 

 during the Cambridge vacations. As no description of this measuring bench has yet 

 been published, I will describe it in detail, as well as giving the special arrangements 

 adopted for measuring the expansion of wires. 



A diagram of the apparatus is given in fig. 4. It consists of two microscopes held 

 rigidly in vertical positions by massive iron stands, which rest on a slate window-slab 

 and can l>c placed at any required distance apart. The microscopes project over a 



