The area of the pedal triangle of a given triangle is easily shown by trilinear co-ordinates to bear to that of the original triangle the ratio R2 – S2: 4R2 where S is the distance of the point from the circumcentre of the triangle. A proof, by purely geometrical methods, of this theorem was read before the Society (Proceedings, Vol. III., pp. 78–79) by Mr Alison.