PART I MANUSCRIPTS Systems of Rays. Part Third Two Letters to Augustus de Morgan(1858) Letter to Hart on Anharmonic Coordinates(1860 PART II. GEOMETRYOn SymIbe1 Geometry (1846-49)I Cambridge and Dublin Mathematical Journal, 1, 45-57, 137-154, 256-263 (1846);2,47-52,130-133,204-209(1847);3,68-84,220-225(1848); 4,84-89,105-118(1849)] On some new applications of Quaternions to Geometry (1849) British Association Report 1849, Part II,p. I On Polygons inscribed on a Surface of the Second Order(1850) British Association Report 1850, Part IL, p. 2.] Symbolical Extensions of Quaternions; and Geometrical Applications of Quaternions(1855) [Proceedings of the Royal Irish Academy 6, 250, 260, 311(1858).] VIIIXIXIII On a General Expression by Quaternions for Cones of the Third Order (1857) [Proceedings of the Royal Irish Academy 6, 506, 512(1858). On a certain harmonic property of the envelope of the chord connect-ing two corresponding points of the Hessian of a Cubic Cone(1857) [Proceedings of the Royal Irish Academy 6, 524(1858).] On some applications of Quaternions to Cones of the Third Degree (1857) [ British Association Report 1857, Part II, p. 3.] On Anharmonic Co-ordinates(1860 [Proceedings of the Royal Irish Academy 7, 286-289, 329, 350-354(1862).] 507 On Geometrical Nets in Space(1861) [Proceedings of the Royal Irish Academy 7, 532-582(1862). On Geometrical Nets in Space(1861) British Association Report 1861, Part II, p. 4.]