  The connection is established between two different action principles for
perfect fluids in the context of general relativity. For one of these actions,
$S$, the fluid four--velocity is expressed as a sum of products of scalar
fields and their gradients (the velocity--potential representation). For the
other action, ${\bar S}$, the fluid four--velocity is proportional to the
totally antisymmetric product of gradients of the fluid Lagrangian coordinates.
The relationship between $S$ and ${\bar S}$ is established by expressing $S$ in
Hamiltonian form and identifying certain canonical coordinates as ignorable.
Elimination of these coordinates and their conjugates yields the action ${\bar
S}$. The key step in the analysis is a point canonical transformation in which
all tensor fields on space are expressed in terms of the Lagrangian coordinate
system supplied by the fluid. The canonical transformation is of interest in
its own right. It can be applied to any physical system that includes a
material medium described by Lagrangian coordinates. The result is a
Hamiltonian description of the system in which the momentum constraint is
trivial.
