William R. Hamilton gave a report On some Results of the View of a Characteristic Function in Optics at the meeting of the British Association for the Advancement of Science, held at Cambridge in 1833. In this report he described how his characteristic function could be used in the study of optical systems that are symmetric about an axis of rotation. He concludes the report with an account of his prediction of the phenomenon of conical refraction in biaxal crystals.
This report is available in the following formats:
At the same meeting of the British Association in 1833, Hamilton's colleague Humphrey Lloyd, Professor of Natural and Experimental Philosophy at Trinity College, Dublin, gave an account of the experimental verification of Hamilton's prediction of conical refraction in biaxal crystals.
The mathematical theory underlying Hamilton's prediction of conical refraction is described in more detail in the Third Supplement to an Essay on the Theory of Systems of Rays.
Robert Perceval Graves gave an account of the discovery of conical refraction in chapter XIII of the first volume of his Life of Sir William Rowan Hamilton (Hodges Figgis, Dublin, 1882).