The paper On a new Species of Imaginary Quantities connected with a theory of Quaternions is Hamilton's first paper on quaternions. It was read at the meeting of the Royal Irish Academy on November 13th, 1843, and is included in Vol. 2 of the Proceedings of the Royal Irish Academy.
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Hamilton described his discovery of quaternions in letters to one of his sons, Rev. A.H. Hamilton, and to Professor P.G. Tait.