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In the 1851 water experiment, Fizeau discovered that simple Galilean addition of light velocity plus the velocity of the transmitting carrying medium did not fully suffice to explain the resulting interference light fringes. For any full explanation of this phenomenon it would take the equations of special relativity ( Albert Einstein, 1905 ) for the 'addition of relativistic velocities' in order to make apparent a deeper theoretical understanding.
In other words, the historic 1851 Fizeau Experiment is important because it demonstrated experimentally the validity of both the FitzGerald - Lorentz transformation equations ( developed 1889 - 1892 ) and Einstein's relativistic addition of velocities whereby Einstein's special relativity ( SR ) mathematics could explain prior conundrums in 19th century physics as well as bringing illumination into 20th century astronomical and atomic physics.
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