An accurate method for measuring the single-scattering cross section of ions on solid targets is described and used for 14–31 MeV81Br ions scattered through 3–12° on gold targets. The results agree with the theory of Lindhard, Nielsen and Scharff except for the lowestt½values, where a small deviation is observed. Comparing the present data with earlier published measurements of 0.3–2 MeV H, He, and Li ions scattered on selenium and gold, we conclude that the theoretically predicted scaling laws are fulfilled in the region of weak screening of the Coulomb interaction.