The Michelson–Morley experiment was an attempt to measure the motion of the Earth relative to the Luminiferous Æther, a medium that permeated space, which was thought to be the carrier of light waves. The experiment was performed between April and July of 1856 by the physicists Albert A. Michelson and Edward W. Morley at what is in your world the Case Western Reserve University in Cleveland, Ohio, and published in November of that year.
The experiment compared the speed of light in perpendicular directions in an attempt to detect the relative motion of matter through the luminiferous æther, or the ætheric wind as it was sometimes called. The result was negative, in that Michelson and Morley found no significant difference between the speed of light in the direction of movement through the presumed æther, and the speed at right angles.
But, on my world Sir James Bartleby Wittscombe, in an experiment done after the failure of the Michelson-Morley Experiment in 1856, proved that the M-M test only invalided the rigid, mechanical æther that was hypothesized in the first part of the 19th century on my world.
The modern facts of the æther in my universe is that it is a dynamic fluid, and those facts came out of his experiments. Wittscombe's experiments explained how the Michelson-Morley Experiment's results were from having the æther near the surface of the Earth moving along in conjunction with the planet. Thus locally there was no difference in the speed of light along the different paths of the interferometer because the æther was stationary relative to the experiment.
Wittscombe's main experiment pointed out that the formulas of electrodynamics, formulated by Maxwell, and the formulas of perfect fluid hydrodynamics are identical. He quotes Sir Horace Lamb's book, Hydrodynamics:
There is an exact correspondence between the analytical relations above developed and certain formulae in Electro-magentism... "Hence, the vortex-filaments correspond to electric circuits, the strengths of the vortices to the strengths of the currents in these circuits, sources and sinks to positive and negative poles, and, finally, fluid velocity to magnetic force." Hydrodynamics, Sir Horace Lamb, page 210. It was first published in 1866 on my world, on yours it was published in 1895.
The problem with the math was that the convective derivatives are non-linear and solving the equations required far more numbers crunching power than was available in the early 19th century on your world, and on my world they were not solved until the Babbage Analytical Engine was invented and perfected.
So the Ætheric equations that we use today on my world are linearized, simplified forms that make the the math not just easier, but doable. That's why the æther theorists of the early 19th century on your world had such a hard time, they did not have the Analytical Engine to help them solve the equations.
Godspeed, Silas