  The volume density of a hyperbolic link is defined as the ratio of hyperbolic
volume to crossing number. We study its properties and a closely-related
invariant called the determinant density. It is known that the sets of volume
densities and determinant densities of links are dense in the interval
[0,v_{oct}]. We construct sequences of alternating knots whose volume and
determinant densities both converge to any x in [0,v_{oct}]. We also
investigate the distributions of volume and determinant densities for
hyperbolic rational links, and establish upper bounds and density results for
these invariants.
