In the article, the whole class of time and position transformations was derived. These transformations were derived based on the analysis of the Michelson-Morley experiment and its improved version, that is the Kennedy-Thorndike experiment. It is possible to derive a different kinematics of bodies based on each of these transformations. In this way, we demonstrated that the Special Theory of Relativity is not the only theory explaining the results of experiments with light. There is the whole continuum of the theories of kinematics of bodies which correctly explain the Michelson-Morley experiment and other experiments in which the velocity of light is measured. Based on the derived transformations, we derive the general formula for the velocity of light in vacuum measured in any inertial reference system. We explain why the Michelson-Morley and Kennedy-Thorndike experiments could not detect the ether. We present and discuss three examples of specific transformations. Finally, we explain the phenomenon of anisotropy of the cosmic microwave background radiation by means of the presented theory. The theory derived in this work is called the Special Theory of Ether – with any transverse contraction. The entire article contains only original research conducted by its authors. Keywords: Kinematics of bodies, Universal frame of reference, Transformation of time and position, One-way speed of light, Anisotropy of cosmic microwave background