  Magnitude is a measure of size defined for certain classes of metric spaces;
it arose from ideas in category theory. In particular, magnitude is defined for
compact subsets of Euclidean space and, in arXiv:1507.02502, Barcel\'o and
Carbery gave a procedure for calculating the magnitude of balls in odd
dimensional Euclidean spaces. In this paper their approach is modified in
various ways: this leads to an explicit determinantal formula for the magnitude
of odd balls and leads to the conjecturing of a simpler formula in terms of
Hankel determinants. This latter formula is proved using a rather different
approach in arXiv:1708.03227, but the current paper provides the reasoning that
lead to the formula being conjectured. Finally, an empirically-tested Hankel
determinant formula for the derivative of the magnitude is conjectured.
