"At the end of the year 1820 the fruit of all the ingenuity expended on elastic problems might be summed up as—an inadequate theory of flexure, an erroneous theory of torsion, an unproved theory of the vibrations of bars and plates, and the definition of Young's modulus. But such an estimate would give a very wrong impression of the value of the older researches. The recognition of the distinction between shear and extension was a preliminary to a general theory of strain; the recognition of forces across the elements of a section of a beam, producing a resultant, was a step towards a theory of stress; the use of differential equations for the deflexion of a bent beam and the vibrations of bare and plates, was a foreshadowing of the employment of differential equations of displacement; the Newtonian conception of the constitution of bodies, combined with Hooke's Law, offered means for the formation of such equations; and the generalization of the principle of in the Mécanique Analytique threw open a broad path to discovery in this as in every other branch of mathematical physics."