1. Let AP, BQ, CR be three lines through the vertices of the ΔABC which rotate with equal angular velocity ω, and which make equal angles with the opposite sides, the initial position being that of the three altitudes of ABC. Then the three circles AQR, BRP, CPQ, which meet in the well-known point O, will be shewn to form three coaxal systems; and among other things we shall shew that the locus of O is the circle on GH as diameter, G being the centroid and H the orthocentre.