  Two different formalisms for the homogenization of composite materials
containing oriented ellipsoidal particles of isotropic dielectric materials are
being named after Bruggeman. Numerical studies reveal clear differences between
the two formalisms which may be exacerbated: (i) if the component particles
become more aspherical, (ii) at mid-range values of the volume fractions, and
(iii) if the homogenized component material is dissipative. The correct
Bruggeman formalism uses the correct polarizability density dyadics of the
component particles, but the other formalism does not.
