The stability of a homogeneous cylinder is investigated by the method of small oscillations and normal modes. The normal modes with motions in the ( , ) directions are treated exactly, and the modes with motions in the ( , z) directions are treated by Chandrasekhar's variational principle In addition to the stable modes there are, as anticipated, convectively unstable solutions for each cylindrical harmonic. The varicose (sausage) instability does not exist as a separate mode but appears to enhance tbe instability of the convective modes Graphical and tabular material shows the characteristic frequencies and proper solutions of the axisymmetric modes for selected values of
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Jeremiah P. Ostriker (1964) studied this question.