In an apparatus for radiographic projection tomography, particularly mammography, an X-ray tube is mounted at the end of a swiveling arm, with a relative movement mechanism. The relative movement mechanism is such that it enables the tube to follow a path of a cycloid. Images or exposures taken only during the time when the tube, in its path, follows cusp points such that it is possible to keep a constant speed of movement of the arm while at the same time increasing the useful duration of an image. Vibration or oscillation effects inherent in the apparatus are compensated by the positioning, if necessary, of a counterweight.