Do Gravitational Waves Travel at the Speed of Light?

Einstein's general relativity said nothing about the speed of gravitational waves - it was Eddington who discovered, in 1922, that some of them travel at the speed of light:

Arthur Eddington 1922: "The problem of the propagation of disturbances of the gravitational field was investigated by Einstein in 1916, and again in 1918. It has usually been inferred from his discussion that a change in the distribution of matter produces gravitational effects which are propagated with the speed of light; but I think that Einstein really left the question of the speed of propagation rather indefinite. His analysis shows how the co-ordinates must be chosen if it is desired to represent the gravitational potentials as propagated with the speed of light; but there is nothing to indicate that the speed of light appears in the problem, except as the result of this arbitrary choice. [...] Weyl has classified plane gravitational waves into three types, viz.: (1) longitudinal-longitudinal; (2)longitudinal-transverse; (3) transverse-transverse. The present investigation leads to the conclusion that transverse-transverse waves are propagated with the speed of light in all systems of co-ordinates. Waves of the first and second types have no fixed velocity - a result which rouses suspicion as to their objective existence." http://rspa.royalsocietypublishing.o...6/268.full.pdf

Was Eddington's discovery correct? Why do Einsteinians teach that "gravitational waves travel at the speed of light" is a prediction of Einstein's general relativity and don't mention the true discoverer - Eddington?

Pentcho Valev