Abstract of the lecture: "The Theory of Nematic Semi-Liquids" Recently, I developed what I call the "Theory of Semi-Liquids", which are incompressible simple materials (in the sense of the "New Theory" of 1972) whose symmetry group is the full unimodular group. This lecture deals with the special case in which a part of the specification of a state is a term which can be interpreted to be the probability distribution of rod-like molecules, as described in Sect.1.3.1 of E.G. Virga's 1995 book on liquid crystals. The resulting theory then becomes a generalization of a frame-free version of the "Theory of incompressible anisotropic fluids" introduced by J.L.Ericksen in the early 1960s.