Single rigid cylindrical particles suspended in a fluid which is subjected to laminar shear execute rotations in spherical elliptical orbits in the manner predicted by Jeffery. It could not be established conclusively, however, whether a single undisturbed particle continues to rotate in a fixed orbit or drifts to preferred orbits. The variation in rotational velocity at various positions in the orbit may be expected to yield preferred orientations in various reference planes. Instantaneous particle orientations in the plane of shear, determined after shearing initially isotropic suspensions, yielded a steady-state distribution with a preferred orientation in the direction of flow after about 3000 particle rotations. The steady-state distribution of orbits was also determined and found to lie between those calculated from the assumptions made by Jeffery and Eisenschitz. The effects of two-body interactions upon the period of rotation and rotational orbit were studied. The results strongly suggest that the equilibrium distribution of orientations and of orbit constants is determined by the mechanics of particle interaction.