Michelson and Morley’s experiment was designed to test whether or not the ether sweeps light along with it. It was set up as an interferometer using two light paths at right angles. Turning the device in the horizontal plane showed that no such effect could be detected. This is consistent with the behavior of light as discussed in this paper. However, if the interferometer were turned so that one path was vertical, given a long enough path length, a difference in the speed of light over the horizontal and vertical paths might be observed. A more sensitive arrangement would be to have the paths along the same axis with the interferometer in the middle. A possible arrangement is shown in Figure 1. The paths would be adjusted in the horizontal position and then the entire unit turned to the vertical position.

Figure 1
As is discussed elsewhere, this is due to the increase in the speed of light as it travels outward in a time gradient and the decrease in speed as it travels inward. This would be the case for the vertical axis relative to the surface of the earth. This has been observed in the Harvard Tower Experiment[1] in which the Mossbauer effect was used to detect the shift. The explanation of the result is somewhat different in relativity theory, in which the relativistic energy expression is used (which considers that the speed of light doesn't change), and this theory, which explains it as a change in the speed of the light. Energy considerations relative to this are briefly discussed in the section Implications – Light Energy.
[1] Harvard tower experiment: Ohanian, page IX-9. ,Kaufmann, Relativity and Cosmology p31 ,Pound & Rebka, Phys Rev Lett. 4, 337 (1960) ,Blatt, Modern Physics Ch3 ,Rohlf, Modern Physics, Section 19-4