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The torque on a superconducting sphere rotating in an arbitrary magnetic field is calculated. The result is expressed in terms of the coefficients of the expansion of the magnetic field in spherical harmonic functions, but in general a boundary‐value problem must be solved to obtain these coefficients. The boundary‐value problem is solved and the torque calculated for configurations pertinent to the gyroscope relativity experiment, a proposed satellite experiment which is to test various theories of gravitation. Typical numerical results for these torques are given and compared with the predicted relativistic effects.