  In "Classical Electrodynamics" (Jackson) a theorem is proved on the average
of an electrostatic or magnetostatic field over a spherical volume. The proof
of the theorem is based on an expansion in spherical harmonics and it is useful
for deriving the singular behaviour of dipole fields. In this paper we give a
simple proof of this theorem, the key element being to use reciprocity. The
method also highlights the relation between the dipole singularity and the
depolarizing field of a sphere, which is thus also found very easily. In
addition this link enables us to extend the theorem to a more general
ellipsoidal volume. Unfortunately one can only prove the existence of the
depolarizing tensor in this way and one still needs another method for actually
calculating the tensor. Finally the theory is also extended to an anisotropic
background medium.
