24 MR. H. TOMLINSON ON THE INFLUENCE OF STRESS AND 



and the coefficients of increase of resistance were approximately '005 and '004 

 respectively. The value of J was assumed to be 42,000,000. 



The liability to error in the estimation of the number of vibrations executed by the 

 wire in a given time is comparatively small, and is certainly much smaller than that 

 arising from uncertainty as regards the emissivity. On the whole, then, it is only safe 

 to assume that, if the observed decrease of the longitudinal elasticity of the iron and 

 steel be entirely due to the rise of temperature caused by the current, this decrease 

 would be about '0003 per unit per degree Centigrade rise of temperature. Now, as 

 far as the author is aware, there have been no investigations of the effect of rise of 

 temperature on the longitudinal elasticity of iron and steel as determined by the 

 method of vibrations. The author has, however, by the method of static extension, 

 obtained for unannealed piano steel, and for soft iron, a decrease of longitudinal 

 elasticity per unit, resulting from a rise of 1 Centigrade, of between '0002 and "0003.* 

 Further, he has recently* obtained from experiments on torsionally vibrating iron wire 

 at various temperatures a decrease of torsional elasticity amounting to '0003 per unit 

 per degree Centigrade rise of temperature. Taking all these facts into consideration, 

 it seems probable that such effects as are produced by even powerful currents on the 

 longitudinal elasticity are solely to be ascribed to the heat generated by these currents. 



Discussion of WIEDEMANN'S Theory respecting the Internal Friction of Metals. 



It will be now advantageous to review very briefly some of the results recorded in 

 this and the author's two previous memoirs on the internal friction of metals, with the 

 object of ascertaining how far these results support WIEDEMANN'S ingenious theory 

 respecting the cause of the friction. According to WIEDEMANN, as the wire vibrates 

 torsionally in one direction or the opposite, so do the molecules rotate about their 

 axes in one direction or the opposite, and at each rotation are permanently deflected, 

 so that, if at the extremity of any one of the swings of the vibrator the latter could 

 be checked and afterwards quietly restored to its position of equilibrium without 

 allowing it to pass over to the other side, the molecules would be permanently 

 deflected. If, however, as in free torsional vibrations, the vibrator is allowed to pass 

 over the position of equilibrium, the molecules will be permanently twisted in the 

 opposite direction, and so on ; thus the loss of energy due to internal friction repre- 

 sents the work which has to be performed in order to twist the molecules from their 

 permanent positions on the one side to their permanent positions on the other. 

 WIEDKMANN founds his theory mainly on the results of his experiments on the torsion 

 experienced by wires as tested by the statical method. In these experiments he 

 finds that even the slightest torsional stress produces permanent torsion of the 

 wire, and also, as he assumes, permanent twist of the molecules. It will be as well 



* 'Phil. Trans.,' 1883 (vol. 174, Part I.), pp. 132-133. 



