Adialeiptometry means unceasing or continuous measurements. We have carried out continuous measurements with a stationary Michelson-Morley interferometer at our CIF laboratory in Bogota (Colombia) for almost two years from the end of 2003 to June 2005. The paper reports the results for year 2004, during which we identified large periodical fringe-shifts, after correcting for environmental variables. To provide a context for the new experimental results presented in this paper, we start by discussing the meaning of speed of light at the time of Einstein, and present next the evidence then available for its constancy. We argue that the evidence provided by the original MM experiment and its repetitions is not as strong as usually believed, thus justifying a new experiment that corrects for the main weaknesses uncovered. The observed periodical variations are consistent with the predicted curves using a constant speed of light in a preferred frame, that adds vectorially to the laboratory velocity using Galilean addition. The solar motion that explains our observations is similar to other modern estimates of solar velocity.