  In brane world scenarios in which only gravity can propagate in the extra
dimensions, effects on the gravitational force may be experimentally testable
if there are two or three large extra dimensions. The strength of the force at
distances smaller than the compactification radius will be sensitive to the
volume of the extra dimensions, but the determination of the shape requires
knowing the gravitational potential at intermediate scales. We determine the
dependence of the potential vs. distance as a function of both the relative
size of the extra dimensions and the possible angle between the extra
dimensional unit vectors, and show that high precision measurements of the
gravitational force will allow the determination of the shape of the extra
dimensions.
