Hamilton published a short article entitled
On a New Method of investigating the relations of Surfaces to their Normals, with results respecting the Curvatures of Ellipsoids.which appeared in the Dublin University Review, volume 1 (1833), pp. 583-584.
This article is available in the following formats:
Hamilton outlines a method for applying the method of the characteristic function which formed the basis of his optical researches in order to prove results concerning the differential geometry of surfaces.
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D.R. Wilkins