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

Thermodynamic properties of the Spin-1/2 Heisenberg Antiferromagnet with Anisotropic Exchange on the Kagome Lattice: Comparison with Volborthite