  The Harman method for measuring the thermal conductivity of a sample using
the Peltier effect, may also be used to determine the dimensionless figure of
merit from just two electrical resistance measurements. We consider a modified
version of the Harman method where the current contacts are much smaller than
the contact faces of the sample. We calculate the voltage and temperature
distributions in a rectangular sample of a material having anisotropy in all of
its transport coefficients. The thermoelectric anisotropy has important
consequences in the form of thermoelectric eddy currents and the Bridgman
effect. We prove that in the limit of a very thin sample of arbitrary shape,
there exist van der Pauw formulae relating particular linear combinations of
the potential and temperature differences between points on the edges of the
sample. We show that the Harman figure of merit can be radically different from
the intrinsic figures of merit of the material, and can often be substantially
enhanced. By defining an effective figure of merit in terms of the rate of
entropy production, we show that the increase in the Harman figure of merit
does indicate an improvement in the thermoelectric performance of an
anisotropic sample having small current contacts. However, we also prove that
in the case of a material with tetragonal symmetry, the effective figure of
merit is always bounded from above by the largest intrinsic figure of merit of
the material.
