The notion of the magnitude of a compact metric space was considered in
arXiv:0908.1582 with Tom Leinster, where the magnitude was calculated for line
segments, circles and Cantor sets. In this paper more evidence is presented for
a conjectured relationship with a geometric measure theoretic valuation.
Firstly, a heuristic is given for deriving this valuation by considering
'large' subspaces of Euclidean space and, secondly, numerical approximations to
the magnitude are calculated for squares, disks, cubes, annuli, tori and
Sierpinski gaskets. The valuation is seen to be very close to the magnitude for
the convex spaces considered and is seen to be 'asymptotically' close for some
other spaces.