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AUTHOR'S PREFACE. SINCE this Introduction to Vector Analysis and Quaternions was first published in 1896, the study of the subject has become much more general; and whereas some reviewers then regarded the analysis as a luxury, it is now recognized as a necessity for the exact student of physics or engineering. In America, Professor Hathaway has published a Primer of Quaternions (New York, 1896), and Dr. Wilson has amplified and extended Professor Gibbs' lectures on vector analysis into a text-book for the use of students of mathematics and physics (New York, 1901). In Great Britain, Professor Henrici and Mr. Turner have published a manual for students entitled Vectors and Rotors (London, 1903); Dr. Knott has prepared a new edition of Kelland and Tait's Introduction to Quaternions (London, 1904); and Professor Joly has realized Hamilton's idea of a Manual of Quaternions (London, 1905). In Germany Dr. Bucherer has published Elemente der Vektoranalysis (Leipzig, 1903) which has now reached a second edition. Also the writings of the great masters have been rendered more accessible. A new edition of Hamilton's classic, the. Elements of Quaternions, has been prepared by Professor Joly (London, 1899, 1901); Tait's Scientific Papers have been reprinted in collected form (Cambridge, 1898, 1900); and a complete edition of Grassmann's mathematical and physical works has been edited by Friedrich Engel with the assistance of several of the eminent mathematicians of Germany (Leipzig, 1894-). In the same interval many papers, pamphlets, and discussions have appeared. For those who desire information on the literature of the subject a Bibliography has been published by the Association for the promotion of the study of Quaternions and Allied Mathematics (Dublin, 1904). There is still much variety in the matter of notation, and the relation of Vector Analysis to Quaternions is still the subject of discussion (see Journal of the Deutsche Mathematiker-Vereinigung for 1904 and 1905).

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