This is the first direct calculation of line tension at a curved edge of a solid. As an example, we consider an empty slit between two unconstrained coaxial cylinders with dispersion forces at nanoscale. The computational scheme includes the calculation of (a) the local stress tensor field inside the slit, (b) local thermodynamic surface tension as a function of the location on the slit walls, and (c) line tension at the circular rim as a function of the cylinder radius. The calculations have been made on the basis of the Irving-Kirkwood stress tensor of statistical mechanics.