THE year 1844 is memorable in the annals of mathematics on account of the first appearance on the printed page of Hamilton's “Quaternions” and Grassmann's “Ausdehnungslehre.” The former appeared in the July, October, and supplementary numbers of the Philosophical Magazine, after a previous communication to the Royal Irish Academy, November 13, 1843. This communication was indeed announced to the Council of the Academy four weeks earlier, on the very day of Hamilton's discovery of quaternions, as we learn from one of his letters. The author of the “Ausdehnungslehre,” although not unconscious of the value of his ideas, seems to have been in no haste to place himself on record, and published nothing until he was able to give the world the most characteristic and fundamental part of his system with considerable development in treatise of more than 300 pages, which appeared in August 1844.