The famous experiment of Albert Abraham Michelson and Edward Williams Morley actually involved an interferometer - a device that measures how much out of phase two waves get when one travels a certain distance North and South while the other travels a different distance East and West. Since one of these signals may have to "swim upstream" and then downstream against the æther flowing past the Earth, it will lose a little ground overall relative to the one that just goes "across" and back, with the result that it gets out of phase by a wavelength or two. There is no need to know the exact phase difference, because one can simply rotate the interferometer and watch as one gets behind the other and then vice versa. When Michelson and Morley first used this ingenious device to measure the velocity of the Earth through the æther, they got an astonishing result: the Earth was at rest!
Did Michelson or Morley experience brief paranoid fantasies that the ergocentric doctrines of the Mediæval Church might have been right after all? Probably not, but we shall never know. Certainly they assumed they had made some mistake, since their result implied that the Earth was, at least at that moment, at rest with respect to the Universe-spanning luminiferous æther, and hence in some real sense at the centre of the Universe. However, repeating the measurement gave the same result.
Fortunately, they knew they had only to wait six months to try again, since at that time the Earth would be on the opposite side of the Sun, moving in the opposite direction relative to it (the Sun) at its orbital velocity, which should be easily detected by their apparatus. This they did, and obtained the same result. The Earth was still at rest relative to the æther.
Now everyone was in a bind. If they insisted in positing an æther to dispell the absurdities of propagation through a vacuum at a fixed velocity, then they had to adopt the embarrassing view that the æther actually chose the Earth, of all the heavenly bodies, to define its rest frame - and even followed it around in its accelerated orbital path! This was too much.