Twisting of planar nematic layers is investigated for a finite strength of the surface anchoring by rotating the cell plate. The measurements of the director twisting are performed by measuring the rotation of polarization plane of light. Smooth and jump-wise changes of twisting variations were observed. The calculations similar to those in [1,2] performed for two different model anchoring potentials reveal that for thick samples the both potentials give almost the same results. For thin samples the calculation results for these potentials differ significantly. It is shown that the measurements allow the determination of the anchoring strength and may be used for the reconstruction of the shape of the actual surface anchoring potential.