  Thermodynamic properties such as magnetic susceptibility and specific heat
have been computed for the Heisenberg Antiferromagnet with spatially
anisotropic exchange on the kagome lattice on clusters up to N=24 spins from
the full spectra obtained by exact diagonalization. This approach is shown to
provide a good represention of these thermodynamic properties above
temperatures of about $J_{\rm av}/5$ where $J_{\rm av}$ is an average of the
coupling constants. Comparison with experimental Volborthite data obtained by
Hiroi {\it {et al}} [J. Phys. Soc. Jpn. {\bf 70},3377 (2001)] shows that
Volborthite is best described by a model with nearly isotropic exchanges in
spite of the significant distortion of the kagom\'{e} lattice of magnetic sites
in this compound and suggests that additional interactions are present.
Comparison of the specific heat at low temperature raise the possibility that
the density of states at low energy in Volborthite might be much lower than in
the Heisenberg model. Magnetization curves under an applied field of the model
are also investigated. The M=1/3 plateau is found to subsist in the anisotropic
case and extend to lower field with increased anisotropy. For sufficient
anisotropy, this plateau would then be observable for a field reasonably
accessible to experiment. The absence of a plateau well below $\sim$ 70 Teslas
would further support a nearly isotropic model.
