The present publication is an essay that was sent in (December, 1887) to competefor the Smith's Prizes at Cambridge.To the onlooker it is always a mournful thing to see what he considers splendidabilities or opportunities wasted for lack of knowledge of some paltry commonplacetruth. Such is in the main my feeling when considering the neglect of thestudy of Quaternions by that wonderful corporation the University of Cambridge.To the alumnus she is apt to appear as the leader in all branches of Mathematics.To the outsider she appears rather as the leader in Applied Mathematics and as aready welcomer of other branches.
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