That the speed of light is variable, not constant, was proved by the Michelson-Morley experiment in 1887:
Wikipedia: "Emission theory, also called emitter theory or ballistic theory of light, was a competing theory for the special theory of relativity, explaining the results of the Michelson–Morley experiment of 1887. [...] The name most often associated with emission theory is Isaac Newton. In his corpuscular theory Newton visualized light "corpuscles" being thrown off from hot bodies at a nominal speed of c with respect to the emitting object, and obeying the usual laws of Newtonian mechanics, and we then expect light to be moving towards us with a speed that is offset by the speed of the distant emitter (c ± v)." https://en.wikipedia.org/wiki/Emission_theory
The analysis of the above information unavoidably leads to the following conclusion:
In 1887 the Michelson-Morley experiment UNEQUIVOCALLY confirmed the variable speed of light posited by Newton's emission theory of light and refuted the constant (independent of the speed of the light source) speed of light posited by the ether theory and later adopted by Einstein as his 1905 second postulate.
Banesh Hoffmann says essentially the same:
Banesh Hoffmann, Relativity and Its Roots, p.92: "Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether. If it was so obvious, though, why did he need to state it as a principle? Because, having taken from the idea of light waves in the ether the one aspect that he needed, he declared early in his paper, to quote his own words, that "the introduction of a 'luminiferous ether' will prove to be superfluous." https://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/dp/0486406768
Here is the short truth about the Michelson-Morley experiment:
John Norton: "The Michelson-Morley experiment is fully compatible with an emission theory of light that CONTRADICTS THE LIGHT POSTULATE." http://philsci-archive.pitt.edu/1743/2/Norton.pdf