1865.] Prof. Thomson on the Elasticity, fyc. t of Metals. 289 



IV. "On the Elasticity and Viscosity of Metals." By Prof. W. 

 THOMSON, LL.D., F.R.S., F.R.S.E. Received May 18, 1865. 



Among the experimental exercises performed by students in the phy- 

 sical laboratory of the University of Glasgow, observations on the elas- 

 ticity of metals have been continued during many years. Numerous ques- 

 tions of great interest, requiring more thorough and accurate investi- 

 gation, have been suggested by these observations ; and recently they 

 have brought to light some very unexpected properties of metallic wires. 

 The results stated in the present communication are, however, with one or 

 two exceptions, due to the careful experimenting of Mr. Donald Macfar- 

 lane, official assistant to the Professor of Natural Philosophy, whose in- 

 terested and skilful cooperation have been most valuable in almost every- 

 thing I have been able to attempt in the way of experimental investigation. 



The subject has naturally fallen into two divisions, Viscosity, and 

 Moduli of Elasticity. 



Viscosity. By induction from a great variety of observed phenomena, 

 we are compelled to conclude that no change of volume or of shape can 

 be produced in any kind of matter without dissipation of energy. Even 

 in dealing with the absolutely perfect elasticity of volume presented by 

 every fluid, and possibly by some solids, as for instance homogeneous 

 crystals, dissipation of energy is an inevitable result of every change of 

 volume, because of the accompanying change of temperature, and con- 

 sequent dissipation of heat by conduction or radiation. The same cause 

 gives rise necessarily to some degree of dissipation in connexion with 

 every change of shape of an elastic solid. But estimates founded on the 

 thermodynamic theory of elastic solids, which I have given elsewhere *, 

 have sufficed to prove that the loss of energy due to this cause is small in 

 comparison with the whole loss of energy which I have observed in many 

 cases of vibration. I have also found, by vibrating a spring alternately 

 in air of ordinary pressure, and in the exhausted receiver of an air-pump, 

 that there is an internal resistance to its motions immensely greater than 

 the resistance of the air. The same conclusion is to be drawn from the 

 observation made by Kupffer in his great work on the elasticity of metals, 

 that his vibrating springs subsided much more rapidly in their vibrations 

 than rigid pendulums supported on knife-edges. The subsidence of vi- 

 brations is probably more rapid in glass than in some of the most elastic 

 metals, as copper, iron, silver, aluminium f ; but it is much more rapid 

 than in glass, marvellously rapid indeed, in some metals (as for instance 

 zinc) , and in india rubber, and even in homogeneous jellies. 



* " On the Thermo-elastic Properties of Solids," Quarterly Journal of Mathematics, 

 April 1857. 



t We have no evidence that the precious metals are more elastic than copper, iron, 

 or brass. One of the new bronze pennies gives quite as clear a ring as a two-shilling 

 silver piece tested in the usual manner. 



J Torsional vibrations of a weight hung on a zinc wire subside so rapidly, that it 



