Abstract: The method and apparatus are essentially characterized by the fact that the art (2, 201) is filled during a first phase with a gas under pressure from a source (10, 204), e.g. air, said air being cooled inside the part under test by means of an expansion nozzle (22, 79), and by a second phase in which variations in the pressure of the gas inside the part are observed by means of a pressure sensor (80, 214), and a processor unit (221) subsequently performs calculations based on the stabilization time for the pressure inside the part, the length of the measurement periods, the volume of the part, and the observed pressure variations.