BEHAVIOUR OF OVER-STRAINED MATERIALS 471 



effects, and the possible number of superpositions is not limited 

 to two. We may twist a wire first in one direction and then in 

 another, back again in the first, reverse again, and so on. We 

 shall thus superpose a large number of strains, the recovery 

 from which is in each case a function of the time, and we shall 

 find that the wire, when at length released, will commence to 

 recover from the final strain applied, then the next previous, and 

 so on, following in the reverse order, and in the opposite direc- 

 tion, all the series of strains. When this fact is borne in mind — 

 that the behaviour of a wire at any time depends to a greater 

 or less extent on all the deformations it has previously experi- 

 enced — it is surely not to be wondered at that some apparent 

 inconsistencies arise in experiments on elastic after-effects. It 

 is not enough that the wires under test should be of the same 

 material. Consistency of results cannot be expected unless, 

 also, they have exactly the same past history. It is evident, 

 too, what great care must be taken to ensure this being the case. 

 This behaviour of over-strained wires is, in many respects, 

 analogous to that of iron and steel under the action of mag- 

 netising forces. Elastic hysteresis is exhibited, and hysteresis 

 curves similar to those in the magnetic case have been obtained 

 by Cantone 1 in 1893 and 1898, and Weinhold in 1899. 



Yet another effect in connection w T ith the slow recovery after 

 strain has been noticed by Maxwell. 2 It has been shown that 

 a body, even when in a state of over-strain, retains certain 

 elastic properties. Hence it is possible for it to execute 

 vibrations. Suppose that a wire clamped at one end is caused 

 to execute small oscillations at the other end. If the amplitude 

 is not too large, the wire will continue to vibrate about the 

 unstrained position. The position of equilibrium is that un- 

 strained position. But if the wire is over-strained by turning 

 it through a large angle in either direction, then, although 

 vibrations may still persist, the point of equilibrium about 

 which they occur will no longer be the original unstrained 

 position. Neither will it be itself stationary, but will continue 

 to move slowly towards its initial position, gradually undoing 

 the effects of the over-strain. Maxwell has shown that this 

 recovery is more rapid when vibrations exist than when they 



1 M. Cantone, Rendic. R. Ace. Lined, 2, 1893 ; L. Weinhold, Zur Elastizitiit 

 der Metalle, Diss. (Leipzig), Chemnitz, 1899. 



2 J. C. Maxwell, Enc. Brit. vol. vi. p. 313. 



