Author's offprint with holograph docketing by Hamilton at the top of the first page, "Recd., with other copies, at the house of the Royal Irish Academy, January 25th, 1862"; he has also amended the description beneath his name under the title, and made 6 small corrections in a very delicate hand to the text within. This paper on Geometrical Nets, read before the Royal Irish Academy in June of 1861, was Hamilton's last substantial mathematical contribution, following on the earlier study was published by Mobius in 1827. Hamilton describes a "quinary calculus" for specifying the location of points of three-dimensional Euclidean space relative to five given points in general position. The only listings of this paper in the RLG Union Catalog are two microform examples.