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The magnetic field geometry in the central regions of two dark clouds has been mapped by measuring the polarization at 2.2 μm of background stars and of stars embedded in the clouds. The observations were done with the Kyoto polarimeter on the Agematsu 1m IR telescope in December 1984 for Heiles Cloud 2 in the Taurus dark cloud complex, and on the UKIRT 3.8m in May and July 1985 for the ρ Ophiuchus dark cloud core. The main results are: