In the treatment of questions which relate to the equilibrium vibrations of elastic solids, it is usual to suppose the substance to start from a state without strain, and in general to consider only the case of small distortions, for which squares and products of the space-variations of displacement may be neglected. The mathematical solution depends, in the first instance, on the expression of the work done in distorting an element. This, as was first done by Green, is expressed in terms of six functions of the distortions termed strains.