All observers measure the same speed of light,
no matter how any observer is moving.
The question is kind of awkward, though. It seems to say that
people were having a hard time accepting this postulate of relativity,
until Michelson and Morley came along and did their experiment, and
their results gave Relativity a boost.
Actually, Michelson and Morley did their famous experiment in 1887.
At the time, Einstein was only 8 years old, and Relativity was not even
a twinkle in his eye yet.