Jeans' formula gives the condition that a gravitating mass of gas shall be stable to small fluctuations in the density. It was originally obtained for a static mass of uniform density, and the proof is questionable. In this paper the formula is derived by studying small perturbations of the density and velocity in an expanding Newtonian world-model. It turns out that, given a suitable interpretation of the quantities involved, the formula is valid in all cosmologies except the steady-state theory.
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W. B. Bonnor (1957) studied this question.