XXIII.—A Geometry associated with the Double Binary (2, 2) Form

The geometry associated with the double binary (2, 2) form has, previously, been exhaustively treated by Mr Kasner and Professor Turnbull by regarding the form as representing the twisted quartic: namely, the complete intersection of a sphere (more generally a quadric) and a quadric, and projectively as the bicircular quartic. A full list of references will be found in the paper of Professor Turnbull in the Proceedings of the Royal Society of Edinburgh, xliv (1924), 23–50. More recently Dr Vaidyanathaswami has investigated further properties of the cyclic, using a new canonical form for the (2, 2) curve.