Since effectively the local contact vortex velocity dependent part of
the Magnus force in a Josephson junction array is zero in the classica
l limit, we predict zero classical Hall effect. In the quantum limit b
ecause of the geometric phases due to the finite superfluid density at
superconductor grains, rich and complex Hall effect is found in this
quantum regime due to the Thouless-Kohmoto-Nightingale-den-Nijs effect
.