  We show that the sum of the local cohomological dimension and the rectified
$\mathbb Q$-homological depth of a closed analytic subspace of a complex
manifold coincide with the dimension of the ambient manifold. The local
cohomological dimension is then calculated using the cohomology of the links of
the analytic space. In the algebraic case the first assertion is equivalent to
the coincidence of the rectified $\mathbb Q$-homological depth with the de Rham
depth studied by Ogus, and follows essentially from his work. As a corollary we
show that the local cohomological dimension of a quasi-projective variety is
determined by that of its general hyperplane section together with the link
cohomology at 0-dimensional strata of a complex analytic Whitney
stratification.
