Scale-free tracer virial ratio (${\Pi }_{\perp }/{\Pi }_{zz}=\int {\sin }^3\theta hd\theta /\int \sin \theta {\cos }^2\theta hd\theta$)

For $h=({\sin }^2\theta +q^{-2}{\cos }^2\theta {)}^{-\gamma /2}$, separation in spherical coordinates makes both stellar potential-energy tensor integrals contain $\int r^{3-\gamma }{\Phi }^{\prime }(r)dr$. Their ratio is the displayed positive finite angular expression. If the radial integrals diverge, identical spherical cutoffs give this same ratio of force moments, but there is no finite global pressure-energy ratio without further hypotheses. A finite-aperture tensor virial theorem retains its surface tensor.