The diameters of rod-shaped articles of the tobacco processing industry are ascertained while the articles are transported past a measuring station in the flutes of a drum-shaped conveyor moving along a range finder which measures the distance of each article of a series of articles from a reference point and transmits appropriate signals to an evaluating circuit wherein the diameters of successive articles are determined on the basis of comparison with a fixed reference distance of the bottoms of the flutes from the reference point. The beam of radiation which is emitted by the radiation source of the range finder is reflected by successive articles, and the intensity of reflected radiation is used to generate second signals which are processed into signals denoting a second diameter of each article. A third diameter of each article can be ascertained downstream of the range finder by an optoelectronic detector.