This article was taken from a website about the X-1 series of test aircraft. It alludes to previous research which dictated the use of a controllable horizontal stabilizer but it does not state who did the research.
"The Langley Memorial Aeronautical Laboratory, Hampton, Va., designed the instrumentation requirements for the craft, which included rate-of-turn recorders, pressure-distribution orifices on the wings and tail and pedal-force transmitters, as well as other data-gathering devices. From research acquired during earlier tests, the committee proposed installing a movable horizontal stabilizer. This element became crucial when Ship No. 1 reached Mach .94 and its elevators lost their effectiveness. So important was the all-movable horizontal stabilizer that virtually every transonic and supersonic aircraft since that time has had one".