"Hooke does not appear to have made any application of [his law] to the consideration of Galileo's problem. This application was made by Mariotte, who in 1680 enunciated the same law independently. He remarked that the resistance of a beam to flexure arises from the extension and contraction of its parts, some of its longitudinal filaments being extended, and others contracted. He assumed that half are extended, and half contracted. His theory led him to assign the position of the axis, required in the solution of Galileo's problem, at one-half the height of the section above the base."