  The formulation of a dynamical theory of General Relativity, including
matter, is viewed as a problem of coupling Einstein's theory of pure gravity,
formulated as an action principle, to an independently chosen and well defined
field theory of matter. It is well known that this is accomplished in a most
natural way when the matter theory is formulated as a relativistic, Lagrangian
field theory. Special matter models of this type have been available; here a
thermodynamical model that allows for general flows is used. A problem that is
of even older date, one that was pursued vigorously by leading scientists of
the 19'th century, is that of subjecting hydrodynamics and thermodynamics to an
Action Principle. A solution to this problem has been known for some time, but
only under the strong restriction to potential flows.
  A variational principle for general flows has now become available.
  The present paper lifts this theory to the relativistic context, Special
Relativity and General Relativity. The energy momentum tensor has a structure
that is more general than that postulated by Tolman, and different from
proposed generalizations; it appears to be well suited to represent rotational
flows in General Relativity. It incorporates a conserved mass current, the
relativistic analogue of the hydrodynamical equation of continuity.
