O.k., I found how they are using the term "interpose" here...
http://hscnotes.weebly.com/uploads/1/2/0/4/12042261/space_-_notes_-_part_4.doc
“… they raced two light rays over two courses, one into the supposed aether wind and one across it, then swung the apparatus through 90 degrees to interpose the rays.”
Michelson and Morley were trying to detect an aether wind, and their apparatus was composed of two beams of light which had been split at 90 degrees from each other. They supposed that the direction of one beam might be heading perpendicular to the aether wind and one beam might heading parallel to it.
However, if they did measure a difference between the speed of the two light rays as they were hoping, it might be because their apparatus had some flaw in which one path of light was different from the other. In other words, recording a different speed might be because the path lengths that the two beams traveled were slightly different form each other. So what they did was rotate the apparatus 90 degrees so that they would be swapped with respect to which one was heading parallel to the aether wind and which one would be perpendicular to it.
Note: Having said all that (and I hope I got it right), I think what they actually did was rotate the apparatus gradually, and take measurements from all angles.