An Elementary Treatise on Quaternions (Classic Reprint)

PREFACE. TN the present edition this work has been very greatly en-larged; to the extent, in fact, of more than one-third. Had I not determined to keep the book iu moderate compass it might easily have been doubled in size. A good deal of re-arrangement also has been thought advisable, especially with reference to the elementary uses of q( )q~ and of V. Prominent among the additions is an entire Chapter, on the Analytical Aspect of Quaternions, which I owe bo the unsolicited kindness of Prof. Cayley. As will be seen by the reader of the former Preface (reprinted below) the point of view which I have, from the first, adopted presents Quaternions as a Calculus uniquely adapted to Euclidian space, and therefore specially useful in several of the most important branches of Physical Science. After giving the necessary geometrical and other preliminaries, I have endeavoured to de-velope it entirely from this point of view; and, though one can scarcely avoid meeting with elegant and often

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