The article starts with a general introduction to the problem in modern physics about the constancy of the speed of light for all frames of reference. In the “General Introduction”, besides presenting the used terms and definitions, the fundament of a real solution about all “unexpected” and “inexplicable” results of the experiments related to the measurement of the velocity of light in the time-spatial region “on the Earth surface” is given. The factual analysis of the “Michelson-Gale-Pearson” experiment shows that the equation that Michelson proves by means of this experiment (which, in the words of Michelson, is “deduced on the hypothesis of a fixed ether”), has actually been deduced on the basis of the classical mechanics and the Galilean relativity, which are indisputably valid and legitimate in our local time-spatial domain “on the Earth’s surface”. The speed of light in vacuum (in relation to the stationary space) depends on the intensity of the gravitational field. The speed of light in vacuum is constant in the time-spatial region “on the Earth’s surface” due to the uniform and constant intensity of the gravitational field in this region, which is determined (dominated) by the mass of the celestial body (the Earth). It is clear, however, that the experiment proves that the measured velocity of light in the frame of reference related to the Earth’s surface is different at different latitudes of the Earth surface and that in the “East-to-West” direction is higher, and in the direction “West-to-East” is lower than the speed of the light in vacuum. The difference is equal to the linear velocity of the Earth’s surface (the speed of motion of a point on the Earth’s surface in the stationary space for the respective latitude) where the northern and southern pipes are located. The question remains - why did not Michelson wish to make this conclusion... Probably because the experiment actually proves that the measured speed of light is not the same for all inertial frames of reference, which is the fundament of the special theory of relativity. That is why, probably, Michelson did not make this conclusion because at this time the special theory of relativity was already accepted as a true theory by contemporary physics and Michelson was awarded as Nobel laureate…. KEY WORDS: special theory of relativity; speed of light postulate; Michelson-Gale-Pearson experiment; speed of light invariance.