First edition. Offprint from an article published in the Bulletin astronomique . From the beginning of his article the author warns us: "Astronomers are preparing to renew and multiply the observations whose doubtful and hitherto uncontested results have nevertheless served as a fundamental basis for this sort of scientific religion which has become relativity". Esclangon re-examines the evidence then known (calculation of Mercury's perihelions, deviation of the Sun's rays, variations of lines), and exposes certain paradoxes (superluminal speed of a projected shadow).