In a recent paper, I showed how the properties of algebraic systems of circles in the (x, y) plane could be investigated by means of a representation in which to the circle x2 + y2 − 2px − 2qy + r = 0 there corresponds the point (p, q, r) in space of three dimensions. The plane of (x, y) may be considered to lie in the space (x, y, z), so that the centre of the mapped circle is the orthogonal projection of the representative point.