Page:Encyclopædia Britannica, Ninth Edition, v. 7.djvu/826

802 ELASTICITY virtue of which elastic force in the quiescent solid, and viscous resistance to change of shape in the non-quiescent fluid or solid, are produced. 30. Viscosity of Metals and Fatigue of their Elasticity. Experimental exercises performed by students in the physical laboratory of the university of Glasgow, during the session 1864-65, brought to lightsome very remarkable and interesting results, proving a loss of energy in elastic vibrators (sometimes as much as two or three per cent, of energy lost in the course of a single vibration in one direc tion) incomparably greater than anything that could be due to imperfections in their elasticity (section 1), and showing also a very remarkable fatigue of elasticity, according to which a wire which had been kept vibrating for several hours or days through a certain range came to rest much quicker when left to itself than when set in vibration after it had been at rest for several days and then immediately left to itself. Thus it was found that the rates of subsid ence of the vibrations of the several wires experimented on were generally much less rapid on the Monday mornings, when they had been at rest since the previous Friday, than on other days of the week, or than after several series of experiments had been made on a Monday. The following statement (sections 31-34) is extracted from a short article by W. Thomson, in the Proceedings of the Royal Society for May 18, 1865, containing some of the results of these observations. 31. " 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 accompany ing change of temperature, and consequent dissipation of heat by conduction or radiation. The same cause gives rise necessarily to some degree of dissipation in connection with every change of shape of an elastic solid. But estimates founded on the thermodynamic theory of elastic solids, which I have given elsewhere, 1 have sufficed to prove that the loss of energy due to this cause is small in comparison with the whole loss of energy 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 vibrations is probably more rapid in glass than in some of the most elastic metals, as copper, iron, silver, aluminium; 2 but it is much more rapid than in glass, marvellously rapid indeed, in some metals (as for instance zinc), 3 and in india-rubber, and even in homogeneous jellies. 32. " The frwtional resistance against change of shape must in every solid be infinitely small when the change of shape is made at an infinitely slow rate, since, if it were finite for an infinitely slow change of shape, there would be "On the Thermo-elastic Properties of Solids," Quarterly Journal of Mathematics, April, 1855. 3 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. 3 Torsional vibrations of a weight hung on a zinc wire subside so rapidly, that it has been found scarcely possible to count more than twenty of them in one case experimented on. infinite rigidity, which we may be sure 4 does not exist in nature. Hence there is in elastic solids a molecular friction which may be properly called viscosity of solids, because, as being an internal resistance to change of shape depending on the rapidity of the change, it must be classed with fluid molecular friction, which by general consent is called viscosity of fluids. But, at the same time, it ought to be remarked that the word viscosity, as used hitherto by the best writers, when solids or heterogeneous semi-solid semi fluid masses are referred to, has not been distinctly applied to molecular friction, especially not to the molecular friction of a highly elastic solid within its limits of high elasticity, but has rather been employed to designate a property of slow continual yielding through very great, or altogether unlimited, extent of change of shape, under the action of continued stress. It is. in this sense that Forbes, for instance, has used the word in stating that viscous theory of glacial motion, which he demonstrated by his grand observations on glaciers. As, however, he and many other writers after him have used the words plasticity and plastic, both with reference to homogeneous solids (such as wax or pitch even though also brittle, soft metals, drc.) and to heterogeneous semi-solid semi-fluid masses (as mud, moist earth, mortar, glacial ice, &c.), to designate the property common to all those cases of experiencing, under continued stress, either quite continued and unlimited change of shape, or gradually very great change at a diminishing (asymptotic) rate through infinite time, and as the use of the term plasticity implies no more than does viscosity any physical theory or explanation of the property, the word viscosity is without inconvenience left available for the definition I propose. 33. " To investigate the viscosity of metals, I have in the first place taken them in the form of round wires, and have chosen torsional vibrations, after the manner of Coulomb, for observation, as being much the easiest way to arrive at definite results. In every cas.e one end of the wire was attached to a rigid vibrator with sufficient firmness (thorough and smooth soldering I find to be always the best plan when the wire is thick enough) ; and the other to a fixed rigid body, from which the wire hangs, bearing the vibrator at its lower end. I arranged sets of observations to be made for the separate comparison of the following cases : (a) " The same wire with different vibrators of equal weights to give equal stretching-tractions but different moments of inertia (to test the relation between viscous resistances against motions with different velocities through the same range and under the same stress). (b) " The same wire with different vibrators of equal moments of inertia but unequal weights (to test the effect of different longitudinal tractions on the viscous resistance to torsion under circumstances similar in all other respects). (c) " The same wire and the same vibrator, but different initial ranges in successive experiments (to test an effect unexpectedly discovered, by which the subsidence of vibra tions from any amplitude takes place at very different rates according to the immediately previous molecular condition, whether of quiescence or of recurring changes of shape through a wider range). (d) " Two equal arid similar wires, with equal and similar vibrators, one of them kept as continually as possible in a state of vibration, from day to day ; the other kept at rest, except when vibrated in an experiment once a day (to test the effect of continued vibration on the viscosity of a metal). 34. " Results. (a) It was found that the loss of energy in 4 Those who believe in the existence of indivisible, infinitely strong

and infinitely rigid, very small bodies (finite hard atoms!) deny this.