Given a diffeomorphism of a two-dimensional manifold with a class of smoothness greater than one. Given a horseshoe of this diffeomorphism, R. Mane (1979) showed, based partially on a program introduced by R. Bowen (1973), that the Hausdorff dimension of this horseshoe depends smoothly on the diffeomorphism. We shall give a general discussion of Mane's aforementioned paper, and the techniques used therein.