Mi. V. .1. niyth. and Mr. J. S. Dunlop. 



" On the Effects of Changes of Temperature on the Elasticities m<l 

 Internal Viscosity of Metal Wires." By ANI>I:K\V GRAY, 

 LL.D., F.R.S., Professor of Natural Philosophy in tin 1 Uni- 

 versity of Glasgow, and VINCENT J. BLYTII, M.A.. and JAMES 

 S. DUNLOP, M.A., B.Sc., Houlds worth Research Students in 

 the University of Glasgow. Received May 24, Read June 

 21, 1900. 



At the outset the object of this investigation was to determine the 

 variation, produced by rise of temperature, in the rigidity-modulus 

 and in the Young's modulus of wires of different metals, but the obser- 

 vations made for this purpose yielded what seemed to us interesting 

 information as to the viscosity of the substances examined, and led to 

 an extension of the research. Heretofore but little attention seems 

 to have been paid to alteration of rigidity with temperature, though 

 several results, of apparently very different degrees of value, are 

 available for Young's modulus. The earliest of these are probably 

 those of Wertheim's experiments,* but on account of the smallness of 

 the quantities observed it is not possible to regard them as even nearly 

 correct. 



Experiments were made about 1870 by F. Kohlrausch and F. E. 

 Loomis.f After referring to the difficulties attending the method 

 adopted by Wertheim, they remark : " All these difficulties disappear, 

 however, and at the same time the most accurate method of observa- 

 tion is obtained, by employing for investigation the torsion elasticity, 

 whose choice is further to be recommended from the fact that torsion 

 is so generally employed in measurements. If a wire is loaded with a 

 weight and set in vibration about its vertical axis, the reciprocal value 

 of the square of the time of vibration affords a direct measure for the 

 coefficient of the torsion of the wire. Since observations of the period 

 of vibration are among the most accurate known in physics, the varia- 

 tions of elasticity may be thus determined with all the rigour de- 

 sirable." 



The authors seem here to indicate that the investigation of torsional 

 elasticity would yield information to be compared with that obtained 

 by Wertheim for Young's modulus, and this impression is confirmed 

 by the remark which occurs later, that the results obtained " show no 

 trace at all of the remarkable phenomenon of a maximum, alluded to 

 at the beginning of this article, which would seem to be indicated for 

 iron by the investigations of Wertheim." The Young's modulus is an 

 essentially composite one, involving both the rigidity-modulus and the 



* ' Annales de Chimie ct de Physique,' tome 12, 1844. 



t ' Pogg. Ann.,' bd. 141, 1870, or ' Amer. Jour. Sci.,' rol. 50, 1870. 



