If you look at the folded light path used in the Michelson–Morley interferometer (figure 5), you'll see that the X and Y distances traveled on both paths add to

If you look at the folded light path used in the Michelson–Morley interferometer (figure 5), you'll see that the X and Y distances traveled on both paths add to the exact same value. Thus, it would be completely insensitive to changes in the speed of light in the X or Y directions, no matter how it were rotated.