  For observers in curved spacetimes, elements of the dual space of the set of
linearized Poincar\'e transformations from an observer's tangent space to
itself can be naturally interpreted as local linear and angular momenta. We
present an operational procedure by which observers can measure such quantities
using only information about the spacetime curvature at their location. When
applied by observers near spacelike or null infinity in stationary, vacuum,
asymptotically flat spacetimes, there is a sense in which the procedure yields
the well-defined linear and angular momenta of the spacetime.
  We also describe a general method by which observers can transport local
linear and angular momenta from one point to another, which improves previous
prescriptions. This transport is not path independent in general, but becomes
path independent for the measured momenta in the same limiting regime. The
transport prescription is defined in terms of differential equations, but it
can also be interpreted as parallel transport in a particular direct-sum vector
bundle. Using the curvature of the connection on this bundle, we compute and
discuss the holonomy of the transport law. We anticipate that these measurement
and transport definitions may ultimately prove useful for clarifying the
physical interpretation of the Bondi-Metzner-Sachs charges of asymptotically
flat spacetimes.
