If we join the angular points ABC of a triangle to any point O the locus of the centres of conies passing through A, B, C, O is a conic bisecting the six joins of the four points and passing through the intersections of OA, BC : OB, AC; and OC, AB. This conic is analogous to the nine-point circle, and at last meeting of the Society Mr Pinkerton showed that its centre lies on the line joining O to the centroid. In what follows an attempt is made still further to generalise this conception.