  The demagnetizing factor has an important effect on the physics of
ferromagnets. For cuboidal samples it depends on susceptibility and the
historic problem of determining this function continues to generate theoretical
and experimental challenges. To test a recent theory, we measure the magnetic
susceptibility of the Ising dipolar ferromagnet LiHoF$_4$, using samples of
varying aspect ratio, and we reconsider the demagnetizing transformation
necessary to obtain the intrinsic material susceptibility. Our experimental
results confirm that the microscopic details of the material significantly
affect the transformation, as predicted. In particular, we find that the
uniaxial Ising spins require a demagnetizing transformation that differs from
the one needed for Heisenberg spins and that use of the wrong demagnetizing
transformation would result in unacceptably large errors in the measured
physical properties of the system. Our results further shed light on the origin
of the mysterious `flat' susceptibility of ordered ferromagnets by
demonstrating that the intrinsic susceptibility of the ordered ferromagnetic
phase is infinite, regardless of sample shape.
