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 “Sagnac experiment” was carried out by the French physicist Georges Sagnac in 1913. The presented analysis is based on the classical mechanics and Galilean relativity, which are indisputably valid and legitimate in our local time-spatial region “on the surface of the Earth”. The experiment demonstrates that in relation to a moving system in the stationary space, the speed of the light differs depending on the speed and on the direction of movement of the system in the stationary space. However, the Sagnac experiment is considered as a paradox, because it demonstrates that the speed of light is not the same for all frames of reference – what is not convenient for modern physics, because the special theory of relativity is created on the basis of the claim that “the speed of light is the same for all frames of reference”. As further evidence of the authenticity of the presented analysis, the derivation of the equation which is often used in the rotation analyses is shown. Finally, we can underline that as early as 1913, the Sagnac experiment actually proved that “the speed of light is not the same in relation to all inertial frames of reference”. This was even before the publishing of the general theory of relativity. Is it not surprising that Einstein never commented on this experiment, although certainly knew about its existence… KEY WORDS: special theory of relativity; speed of light postulate; Sagnac experiment; æther; speed of light invariance.