The shear flow behaviour of the nematic liquid crystal 4-n-octyl-4'-cyano-biphenyl (8CB) was studied in a torsional shear flow apparatus. Experiments were performed near the smectic A-nematic phase transition, and they concentrated on the observation of the tumbling instability associated with a positive Leslie viscosity α3. From theoretical considerations presented here this instability is expected to occur for rather small director tilts when α3δ |α2|. Furthermore a functional dependence of the tumbling instability threshold on the parameter α3/|α2| is presented and evaluated experimentally for the nematic 8CB. Good agreement is found between these theoretical results from the Leslie-Ericksen continuum theory and the experimental measurements.