  In 1676 Olaus R{\o}mer presented the first observational evidence for a
finite light velocity $\cem$. He formed his estimate by attributing the
periodically varying discrepancy between the observed and expected occultation
times of the Galilean satellite Io by its planetary host Jupiter to the time it
takes light to cross Earth's orbital diameter. Given a stable celestial clock
that can be observed in gravitational waves the same principle can be used to
measure the propagation speed $\cgw$ of gravitational radiation. Space-based
"LISA"-like detectors will, and terrestrial LIGO-like detectors may, observe
such clocks and thus be capable of directly measuring the propagation velocity
of gravitational waves. In the case of space-based detectors the clocks will be
galactic close white dwarf binary systems; in the case of terrestrial
detectors, the most likely candidate clock is the periodic gravitational
radiation from a rapidly rotating non-axisymmetric neutron star. Here we
evaluate the accuracy that may be expected of such a R{\o}mer-type measurement
of $\cgw$ by foreseeable future space-based and terrestrial detectors. For
space-based, LISA-like detectors, periodic sources are plentiful: by the end of
the first year of scientific operations a LISA-like detector will have measured
$\cgw$ to better than a part in a thousand. Periodic sources may not be
accessible in terrestrial detectors available to us in the foreseeable future;
however, if such a source is detected then with a year of observations we could
measure $\cgw$ to better than a part in a million.
