698 Dr. C. V. Burton : Notes on 



constitution for the strain-figure (not of course its supposed 

 mode of formation) was thus explained * : — " Consider a 

 region, either infinite or having very distant boundaries, and 

 filled with a homogeneous isotropic elastic medium, whose 

 condition throughout is one of stable equilibrium for small 

 strains of any type. Let the medium now be strained, and 

 held in its strained condition by some compelling agency : 

 there will be a corresponding distribution of stress in the 

 medium, and, provided the strain has at no point too great a 

 value, the original condition will be completely regained after 

 the compelling agency has been removed. But suppose that, 

 instead, the medium is strained further and further from its 

 initial state, and suppose that the restoring stresses do not 

 always increase with the strain, but that beyond a certain 

 point in the process they begin to fall off in value, until at 

 last a point is reached at which the general tendency of the 

 stress is to further increase the strain. If the compelling 

 agency is now withdrawn, the medium will subside into a 

 new condition of stable equilibrium, involving stress and 

 strain at every point." It may not be superfluous to point 

 out that nothing in the nature of elastic hysteresis is here 

 contemplated, the stress being conceived as always determined 

 by the strain alone, independently of the manner in which the 

 strain may be changing. 



Though the possibility of ideally creating a strain-figure 

 by a process such as this is quite gratuitously assumed, it may 

 be remarked that the constitution so specified, if admissible 

 at all, ensures mobility. If this is not immediately evident, 

 imagine a strain-figure occupying a position A remote from 

 all disturbing influences, to be destroyed by the application 

 of an ideal forcive, so that the medium is allowed to revert 

 to its primitive unstrained state. Next suppose that a new 

 forcive is so applied that a like strain-figure is formed at a 

 new position B, which is only infinitesimally distant from the 

 old position A. The energy of the new distribution of strain 

 is precisely the same as that of the old, and since we suppose 

 that the medium exhibits no defect akin to imperfect elas- 

 ticity, it follows that the total work to be performed in the 

 two operations is zero. But in the new position B of the 

 strain-figure, the strain imposed upon any element of the me- 

 dium differs only infinitesimally from the strain of the same 

 element corresponding to the neighbouring position A. There- 

 fore to effect a transference of the strain-figure from A to B 

 it is only necessary for each strained element of the medium 

 to suffer a definite infinitesimal strain, the total expenditure 

 * Loc. cit. p. 192. 



