The theory of the stability of a gyroscope which has a right circular cylindrical cavity partially filled with liquid has been developed by Stewartson (reference 1), who has shown that instabilities occur at and near those filling-ratios for which the frequencies of free oscillations of the liquid filling coincide with the frequencies of precession and nutation of the empty gyroscope when the mass of liquid is small compared with the mass of the empty gyroscope. Then applied to the motion of a gyrostat, Stewartson's theory shows that there is an infinite number of filling-ratios at which instability is to be expected theoretically; but, in practice, it is to be expected that the effects of viscosity in the liquid filling will damp out all but the graver modes of oscillation, and one of the objects of the present experimental investigation was to determine how many of the instabilities could be detected. Stewartson's theory also predicts the range of filling-ratios for which the gyrostat should be unstable, and a second object of the experiments was to verify these predicted ranges.