The distribution of scattered radiation was measured for transmission scans in positron emission tomography by adding the scattered radiation distributions in different projections from line source experiments. It is shown that in a 20 cm diameter water-filled phantom the scattered radiation effects contribute approximately one-third of the events centrally in the field of view. This may lead to systematic errors of the order of 15-25% in reconstructed images. A scheme for correction for scattered radiation effects in the transmission scans is described and tested in phantom experiments.