  Stellar dynamics occupied Chandrasekhar's interest for a brief interlude
between his more prolonged studies of stellar structure and radiative transfer.
This paper traces the history of one of his ideas -- namely, that the shape of
the galactic potential controls the orientation of the stellar velocity
dispersion tensor. It has its roots in papers by Eddington (1915) and
Chandrasekhar (1939), and provoked a fascinating dispute between these two
great scientists -- less well-known than their famous controversy over the
white dwarf stars. In modern language, Eddington claimed that the integral
curves of the eigenvectors of the velocity dispersion tensor provide a
one-dimensional foliation into mutually orthogonal surfaces. Chandrasekhar
challenged this, and explicitly constructed a counter-example. In fact, the
work of neither of these great scientists was without flaws, though further
developments in stellar dynamics were to ultimately draw more on Eddington's
insight than Chandrasekhar's. We conclude with a description of modern attempts
to measure the orientation of the velocity dispersion tensor for populations in
the Milky Way Galaxy, a subject that is coming into its own with the dawning of
the Age of Precision Astrometry.
