  Gravitational waves affect the observed direction of light from distant
sources. At telescopes, this change in direction appears as periodic variations
in the apparent positions of these sources on the sky; that is, as proper
motion. A wave of a given phase, traveling in a given direction, produces a
characteristic pattern of proper motions over the sky. Comparison of observed
proper motions with this pattern serves to test for the presence of
gravitational waves. A stochastic background of waves induces apparent proper
motions with specific statistical properties, and so, may also be sought. In
this paper we consider the effects of a cosmological background of
gravitational radiation on astrometric observations. We derive an equation for
the time delay measured by two antennae observing the same source in an
Einstein-de Sitter spacetime containing gravitational radiation. We also show
how to obtain similar expressions for curved Friedmann-Robertson-Walker
spacetimes.
