The theory of the knotting of curves, except for a few elementary theorems due to Listing, was entirely neglected until Tait was led to a consideration of knots by Sir W. Thomson's (Lord Kelvin's) work on the Theory of Vortex Atoms. He attacked chiefly the problem of constructing knots with any number of crossings, and obtained a census of the knots of not more than ten crossings. Those knots which exhibit a special kind of symmetry—the amphicheiral knots—offer certain points of interest.