The object of the papers is to consider two modes of representing points and lines on a spherical surface by points and lines on a plane: one method being by orthogonal projection, and the other by stereographic projection. The authors consider that students of spherical trigonometry ought to be able to accurately draw any figure with which they may have to deal, using one or other of the above methods of projection. The following propositions indicate methods of solving the various problems which would arise in connection with such accurate drawing.

It may be useful to compare with the results proved above, the interesting and comparatively little known properties of the Stereographic Projection of the sphere so far as they affect its practical application to spherical triangles. This projection, in which we take a point S on the sphere as the vertex of projection, and the central plane parallel to the tangent plane at S as the plane of projection, has certain great practical advantages, as shown in (1) and (2) below; and obviates the difficulty of drawing an ellipse.