ELEMENTS OF QUATERNIONS

object of the following treatise is to exhibit the elementary principles and notation of the Quaternion Calculus, so as to meet the wants of beginners in the class-room. The Elements and Lectures of Sir William Rowan Hamilton, while they may be said to contain the suggestion of all that will be done in the way of Quaternion research and application, are not, for this reason, as also on account of their diffuseness of style, suitable for the purposes of elementary instruction. Taits work on Quaternions is also, in its originality and conciseness, beyond the time and needs of the beginner. In addition to the above, the following works have been consulted Calcolo dei Quaternione. Bellavitis Modena, 1858. Exposition de la MetTiode des fiquipollences Traduit de 1 Italien de Giusto Bellavitis, par C.-A. Laisant Paris, 1874. Original memoir in the Memoirs of the Italian Society. 1854. Thorie lementaire des Quantites Complexes. J. Hoiiel Paris, 1874. Essai sur une Manure de Representer les Quantites Imaginaires dans les Construction G-eometriques. Par R. Argand Paris, 1806. Second edition, with preface. by J. Hoiiel Paris, 1874. Translated, with notes, from the French, by A. S. Hardy. Van Nostrands Science Series, No. 52 1881. Kurze Anleitunff zum Rechnen mit den Hamilton sclieri Quaternionen. J. Odstrcil Halle, 18T9. Applications Mecaniques du Qalcul des Quaternions. Laisant Paris, 1877. Introduction to Quaternions. Kelland and Tait Lon don, 1873. A free use has been made of the examples and exercises of the last work and, in Article 87, is given, by permis sion, the substance of a paper from Volume L, page 379, American Journal of Mathematics, illustrating admirably the simplicity and brevity of the Quaternion method. If this presentation of the principles shall afford the undergraduate student a glimpse of this elegant and pow erful instrument of analytical research, or lead him to follow their more extended application in the works above cited, the aim of this treatise