The19F N.M.R. spectrum of 1,2,2,2-tetrachloro-l,l-difluoroethane has been studied in the nematic liquid crystal ZLI1167 (Merck) upon rotation at the magic angle. The director of the liquid crystal is oriented perpendicular to the spinning axis when the angle between the rotation axis and the magnetic field is less than the magic angle and parallel when this angle is more than the magic angle. It is shown that exactly at the magic angle the spectrum corresponds to a frequency modulated powder pattern. This powder pattern leads to an understanding of the orientational behaviour of the director when a nematic is spun at the magic angle.