A new and efficient technique for measuring weak optical nonlinearities is reported. Like Z scan, its implementation is basic, both experimentally and theoretically, but leads to an improved sensitivity of λ/5.10⁴, which represents, to date, one of the highest observed enhancements. With this technique, which is based upon the use of a position sensitive detector, nonlinear properties are deduced by monitoring the barycentric position of a truncated pump-probe laser beam as the sample is moved along the optical axis. The technique is experimentally validated by measuring the pump-induced refractive index change and the underlying polarizability variation resulting from the excitation of the Cr(3+) ions in ruby.