Cylindrical ionization chambers are used for the determination of absorbed dose in beams of heavy charged particles, where the effective point of measurement, Peff (the point in depth to which the measured dose refers), is a priori not known. A measurement of Peff for a Farmer-type chamber in a carbon ion beam is presented. It is based on a comparison of relative depth dose curves measured with a cylindrical chamber and a plane-parallel Markus chamber. Both measurements were compared against another high-precision relative depth dose measurement using large-area plane-parallel chambers. For Peff, a value of 72 +/- 7% of the inner radius of the chamber is obtained. The relative depth dose curve for the cylindrical chamber is calculated using an averaging of the depth dose values over the curved inner surface of the active volume while taking account of the different depths of points on the inner surface. Within the measurement uncertainty of 0.2 mm the measurements agree well with the calculated Bragg curve for the Farmer chamber. The result for Peff is in correspondence with the value suggested in a new code of practice by the IAEA for protons and ions, and somewhat less than that suggested by Palmans for protons. The measurements show that cylindrical chambers are in general well suited for depth dose measurements in fields of heavy charged particles if the correct Peff is used.