The ability of humans to perceive the spatial orientation of an occluded arm was investigated. It was hypothesized that this ability is tied to the arm's inertial eigenvectors, invariant mechanical parameters corresponding to a limb's axes of rotational symmetry. By breaking the coincidence between the eigenvectors of the arm and its longitudinal axis, 3 experiments were directed at the possibility that the perceived orientation of an occluded arm would vary as a function of the eigenvectors. Overall, the angles in which the arm was positioned were affected by the direction in which the eigenvectors of the limb were oriented by small appended masses. Discussion focused on the importance of physical invariants for proprioception.