The changes which solids undergo under the action of external force, and their tendency to recover their natural forms, were studied by Hooke and Gravesande. The experimental fact that, for small changes of form, the extension of a rod or string is proportional to the tension to which it is exposed, is known as Hooke's law. The compression and extension of the fibres of a bent beam were noticed by James Bernoulli, in 1630, by Duhamel and others. The bending of beams was also studied by Coulomb and Robison, but Young appears to have been almost the first to apply the theory of elasticity to the statics of structures. In a letter to the Secretary of the Admiralty, written in 1811, in reply to an invitation to report on Mr. Steppings's improvements in naval architecture, Young claimed that he was the only person who had published "any attempts to improve the _theory_ of carpentry." It may be here mentioned that Young accepted the invitation of the Admiralty, and sent in a very exhaustive report, which their Lordships regarded as "too learned" to be of great practical value. Young's contributions to this subject will be chiefly remembered in connection with his "modulus of elasticity." This he originally defined as follows:-- "The modulus of the elasticity of any substance is a column of the same substance capable of producing a pressure on its base which is to the weight causing a certain degree of compression as the length of the substance is to the diminution of its length." It is not usual now to express Young's modulus of elasticity in terms of a length of the substance considered. As now usually defined, Young's modulus of elasticity is the force which would stretch a rod or string to double its natural length if Hooke's law were true for so great an extension.