Had to look that one up. The experiment was based on the belief in a so-called "luminiferious ether", the substance supposedly needed to transmit light, just as sound needs air/solids/fluids to get across.
The problem is that there is no such ether, and light itself is made of photons; it's the photons themselves that travel, without needing any supporting material. The starting point of the experiment was flawed anyway.
But in any case, what's your point?
That a nineteenth century experiment failed to prove the motion of the earth?
Ok. 19th century scientists would have failed to prove the exeitence of genes, germs, black holes, etc.
They were on the right track though by looking for things that can't be seen by the naked eye.
BTW, the theory of relativity has been confirmed by science.
And regarding the Morley experiment, see the second postulate of special relativity:
The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.
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