192 Dr. C. V. Burton on a Theory 



2. Fundamental Assumption. Strain-Figure. — 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 agency is now withdrawn, the medium will subside into a 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. The state of things thus impressed on the 

 medium is, according to my view, an atom or a constituent of 

 an atom ; it will hereafter be referred to as a " strain-figure, 33 

 and we may now proceed to examine its dynamical properties. 



3. Rigid Body Displacements. — A strain-figure, being of 

 itself in equilibrium, will remain in equilibrium if transferred 

 to some other portion of the medium, or if its orientation with 

 respect to the medium is changed (for originally the medium 

 was homogeneous and isotropic) ; we may therefore give to 

 the strain-figure any displacement of which a rigid body 

 would be capable, and the resulting condition of the medium 

 will be one of equilibrium ; there is no statical resistance to 

 such displacement, and no question of the medium giving way. 



4. Equations of Motion. — If a strain-figure is in motion 

 through the medium, certain conditions must be satisfied in 

 order that its degrees of freedom may not be more than those 

 of a rigid body ; in order, that is, that the strain-figure may 

 retain the same form as if it were at rest in the medium. For 

 suppose that disturbances of the same type as the strains in 

 the strain-figure are propagated through the medium with 

 velocity V; then obviously a necessary condition is that the 

 translational velocity of the strain-figure must be very small 

 compared with Y, the rotational motion being (in general) 

 subject to a similar restriction, which cannot be quite so simply 

 expressed. If V is (as I imagine) the velocity with which 

 gravitation is propagated, it is a quantity whose finiteness has 

 not yet been demonstrated, and compared with which all 

 known molar and molecular motions are extremely slow. 



