§ 1. It is proposed in this paper to describe some simple graphical constructions of theoretical or practical interest. They may be easily performed with ruler and compasses, though the stereographic and gnomonic nets will often save labour. To economize space the proofs of the constructions are left to the reader.

§ 2. First take the case of the gnomonie projection. Given the projections A, B, C, Q (fig. 1) of the poles of the faces (100), (010), (001) (111); find the projection of the pole of any other face (hkl).