The following paragraphs have been assembled in consequence of my reading Dr. Cundy’s note on 25-point geometry. Towards the end of it, apparently mindful of the adjunction of a “ line at infinity ” to the Euclidean plane, he adjoins a line to the 25-point plane and so obtains a geometry of 31 points. Here I reverse this procedure : I start with the 31-point geometry and thereafter assign to one of its 31 lines the rôle of the “ line at infinity ”. This seems more in the spirit of Cayley's dictum at the end of his Sixth Memoir on Quantics, that “ descriptive geometry is all geometry ” and metrical geometry only a part thereof.