= Vertical Jeans equation
{title2=$\partial_z(n\sigma_z^2)+R^{-1}\partial_R(Rn\overline{v_Rv_z})=-n\partial_z\Phi$}
For a steady axisymmetric <stellar population> with no mean vertical motion, the vertical <Jeans equation> balances the gradient of the vertical random-motion stress and the radial gradient of the tilted <velocity ellipsoid> against the vertical <Newtonian gravitational field>. Neglecting the mixed moment gives $\partial_z(n\sigma_z^2)=-n\partial_z\Phi$. A tracer density $n$ need not equal the density sourcing the <gravitational potential>.
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