The measured orbital susceptibility of an array of 10 5isolated Ga-As squares of area L2 = 4.5 × 4.5 μm 2 has a paramagnetic contribution ≈ kFL = 100 times larger than the Landau susceptibility. With increasing magnetic field, this paramagnetic susceptibility decreases on a field scale of order H0 ≈ φ0/ L2, where φ0 = h/ e is the flux quantum. As the temperature is raised, this orbital paramagnetism decreases on the scale of 0.5 K ≈ Ec/2 where Ec = hvF/ L is the correlation energy. These experimental findings can be checked using Coulomb blockade spectroscopy. To this end, the thermodynamic relations between chemical potential and orbital currents are derived.