More sophisticated experiments (specifically, experiments on the behaviour of light and experiments that dealt with fast moving particles) indicated that Galilean Relativity was approximately correct only for velocities much smaller than the speed of light.
What a conundrum !
Shall we throw out all the theories of Electro-magnetsim ? This is hard to do. If these theories seem to have no flaw in their derivation, are firmly based in
experiments, their predictions are verified by further experiments, and we all use our cell phones with impunity, then its hard to fault Maxwell's equations !
The problem must lie somewhere else ....
But where ?
Enter Special Relativity, which was first developed by Einstein (1905). This theory treats inertial reference frames in a way
that is compatible with all measurements so far. Later on, came General Relativity which is able to deal with non-inertial reference frames and also to provide a geometrical way of dealing with gravity.