We draw attention to the close relationship between the anisotropy parameter \beta ( r ) 
for stellar orbits in elliptical galaxies and the temperature T ( r ) of the hot interstellar gas .
For nearly spherical galaxies , the gas density \rho can be accurately determined from X-ray observations and the stellar luminosity density \ell _ { * } 
can be accurately found from the optical surface brightness .
The Jeans equation and hydrostatic equilibrium establish a connection between \beta ( r ) and T ( r ) 
that must be consistent with the observed stellar velocity dispersion .
Optical observations of the bright elliptical galaxy NGC 4472 indicate { { { { \beta ( r ) \mathrel { \mathchoice { \lower 2.5 pt \vbox { \halign { \cr } $ \displaystyle \hfil% < $ \cr$ \displaystyle \hfil \sim$ } } } { \lower 2.5 pt \vbox { \halign { \cr } $ \textstyle% \hfil < $ \cr$ \textstyle \hfil \sim$ } } } { \lower 2.5 pt \vbox { \halign { \cr } $ \scriptstyle% \hfil < $ \cr$ \scriptstyle \hfil \sim$ } } } { \lower 2.5 pt \vbox { \halign { \cr } $% \scriptscriptstyle \hfil < $ \cr$ \scriptscriptstyle \hfil \sim$ } } } } 0.35 within the effective radius .
However , the X-ray gas temperature profile T ( r ) for NGC 4472 requires significantly larger anisotropy , \beta \approx 0.6 - 0.7 , about twice as large as the optical value .
This strong preference for radial stellar orbits must be understood in terms of the formation history of massive elliptical galaxies .
Conversely , if the smaller , optically determined \beta ( r ) is indeed correct , we are led to the important conclusion that the temperature profile T ( r ) of the hot interstellar gas in NGC 4472 must differ from that indicated by X-ray observations , or that the hot gas is not in hydrostatic equilibrium .