We present measurements of the magnetic field dependence of the penetration depth Lambda(H) for untwinned YBa_2Cu_3O_6.95 for temperatures from 1.2 to 70 K in dc fields up to 42 gauss and directions 0, 45 and 90 degrees with respect to the crystal b-axis. The experiment uses an ac susceptometer with fields applied parallel to the ab-plane of thin platelet samples. The resolution is about 0.15 Angstroms in zero dc field, degrading to 0.2 or 0.3 Angstroms at the higher fields. At low temperatures the field dependencies are essentially linear in H, ranging from 0.04 Angstroms/gauss for Delta-Lambda_a to 0.10 Angstroms/gauss for Delta-Lambda_b, values comparable to the T=0 Yip and Sauls prediction for a d-wave superconductor. However, the systematics versus temperature and orientation do not agree with the d-wave scenario probably due, in part, to residual sample problems.
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