As regards gravitational waves:
From Symon, Classical Mechanics, p. 581:
"Since the principle of relativity requires that gravitational effects cannot be
transmitted instantaneously from one mass to another but must propogate through
the intervening space, it is perhaps not surprising that the theory of
relativity predicts the existence of gravitational waves traveling with the
velocity c. Again the effects of such waves are expected to be very slight.
However, by 1969, experiments by J. Weber appeared to have detected such
waves.*"
* - it is now believed that Weber's results were in error.
"The Search for Gravity Waves" by P. C. W. Davies (Cambridge University Press,
Cambridge, 1980) is a concise summary of the properties of gravitational waves
and of experiments to attempt to detect them.
As a side note, for those who are really interested, I should point out that
some authors refer to gravitational waves as simply gravity waves, while
others reserve the latter term to refer to surface waves on water whose
restoring force is caused by gravity. These waves tend to be of much longer
wavelength than the smaller capillary waves.
You asked for it,
Lewis Taylor Goss