The National Geographic link contains misinformation about the M.52/X-1. The following paras are nonsense, though being a UK publication it's expected the fallacious Eric Brown story would prevail,
While propulsion evidently wasn't a problem, stability at that speed was; with Miles ordered to share intel with the American company, some sources insist the Bell X-1 incorporated – at test stage – a baked-in element of the British M.52 design; the moving tailplane, designed to counteract a dangerous aerodynamic consequence of going supersonic. Without it, Yeager's record-breaking speed would have been impossible
Those on the X-1 program fully understood the aerodynamics involved, from the outset the aircraft was designed with a trimable tail plane with attached elevators, primary controls were all mechanical. Had the aircraft been fitted with an all flying tail as on the M.52 the pitching moments of the tailplane would have required powered controls, the X-1 was devoid of any power source, having only batteries to power the recorders and pressurised nitrogen for other services (trim motor, also used to pressurise fuel tanks, operate gear, flaps, and cockpit pressurisation).
Because in 1944 the British government agreed to share the secrets of Miles’ designs and work with the Americans: Brown recalled that Bell’s ‘engineers and designers had, on the insistence of the Ministry, had access to all the drawings, calculations and design data relating to the M.52.’ At the time Bell had already begun work on its own design and was wrestling with many of the same issues as Miles, including all-important pitch (the vertical inclination of the nose) control. Crucially they had not achieved the breakthrough with the all-moving tailplane. But by the time Yeager climbed into the cockpit on 14 October – after Bell's engineers had met with the Miles design team – they had.
The information provided to Dr. Millikan was rudimentary (have a copy), not even a scale drawing, he had to draw one from memory back in his hotel room.
Most of the theories concerning how much the Bell X-1 drew on the insights of the M.52 hinge around this tailplane. According to Rod Kirkby, Bell Aircraft decided to increase the power of the tailplane trimmer after talks with the Miles design team, on the off-chance it might be required. In test flights close to Mach 1 in the X-1 Yeager had found the aircraft's pitch almost impossible to control. Fitting an electric switch that controlled the tailplane incidence – Kirkby calls the addition a 'field fix' – solved the problem.
No field fix was involved of this nature occurred, the only field fix was adjustment of the rate of trim and addition of a more powerful trim motor, but that was a result of flight tests and not advice from Miles. No dialogue ever took place between Miles and Bell.
Just how much the Miles design informed the X-1 is not known – despite much rumour – but there is no doubt that without the all-moving tailplane Yeager wouldn’t have broken the sound barrier, or lived to tell the tale.
What Miles informed the US about is known exactly, the recipient of the information, was Doctor Clark B. Millikan, published a report which he forwarded to the United States Navy, of which I have a copy. The X-1 didn't have an all moving tailplane as on the M.52, it had a trimable tailplane with attached elevator, exactly the same as on your Boeing 737. Millikan thought the M.52 all moving tailplane interesting. He saw no reason for the US to pursue any further interest in the M.52. Sorry to be a wet blanket, but one is rather sick and tired of the fable, promoted in the main by Eric Brown, of how the M.52 benefited the X.1 program.