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The stability of a stratified self-gravitating rotating medium is discussed. It is found that in all cases pressure effects stabilize short waves while long waves are stabilized by rotation. When | G/4²| is greater than a number between 1. 8 and 0. 7 (depending on the polytropic index) there is an intermediate range of unstable wave-lengths centred at several times the thickness of the sheet. These instabilities would lead to the break-up of the sheet into masses of definite size. This paper serves as an introduction to the following one on the stability of differentially rotating media and the formation of spiral arms.
Goldreich et al. (Sun,) studied this question.