= Crossing-time cloud support mass
{title2=$M_{\rm cross}=\frac{4\pi}{3}(\frac{3\pi}{32})^{3/2}\frac{c_s^3}{G^{3/2}\rho^{1/2}}$}
Equate the <free-fall time of a uniform sphere> $\sqrt{3\pi/(32G\rho)}$ to a radius-based <sound-crossing time> $R/c_s$, then substitute $R$ in $M=4\pi\rho R^3/3$. This gives the displayed <mass>. It has the scaling of a <Jeans mass>, but its coefficient differs from the convention using a sphere of diameter equal to the <Jeans length>. Equality of these two times is an approximate support comparison, not the exact marginal mode of an infinite-medium <Jeans instability>.
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