The subject of this study is the 'shift of the effective point of measurement', Delta z, well known as a method of correction compensating for the 'displacement effect' in photon and electron beam dosimetry. Radiochromic EBT 1 films have been used to measure the 'true' TPR curves of 6 and 15 MV photons and 6 and 9 MeV electrons in the solid water-equivalent material RW3. For the Roos and Markus chambers, the cylindrical 'PinPoint', 'Semiflex' and 'Rigid-Stem' chambers, the 2D-Array and the E-type silicon diode (all from PTW-Freiburg), the positions of the effective points of measurement have been determined by direct or indirect comparison between their TPR curves and those of the EBT 1 film. Both for the Roos and Markus chambers, we found Delta z = (0.4 +/- 0.1) mm, which confirms earlier experimental and Monte Carlo results, but means a shortcoming of the 'water-equivalent window thickness' formula. For the cylindrical chambers, the ratio Delta z/r was observed to increase with r, confirming a recent Monte Carlo prediction by Tessier (2010 E2-CN-182, Paper no 147, IDOS, Vienna) as well as the experimental observations by Johansson et al (1978 IAEA Symp. Proc. (Vienna) IAEA-SM-222/35 pp 243-70). According to a theoretical consideration, the shift of the effective point of measurement from the reference point of the detector is caused by a gradient of the fluence of the ionizing particles. As the experiments have shown, the value of Delta z depends on the construction of the detector, but remains invariant under changes of radiation quality and depth. Other disturbances, which do not belong to the class of 'gradient effects', are not corrected by shifting the effective point of measurement.