Abstract: In this paper. the disturbances ic a uniformly rotating ideal fluid with a spheremoving steadily along the axis of rotation are analysed by using linearization theory,the equations of disturbance pressure and disturbance stream function governing the stability of motion are derived based on the assumption that the flow is rotational symmetric. The equation of disturbance stream function is analysed with the method ofnormal modes, and the constraints on wave number and wave velocity of the nontrivial neutral disturbances are established and the exact expression of the neutral disturbances are obtained. The conclusion is drawn that there are three kinds of possible forms of neutral disturbances.