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AUTHOR'S PREFACE. THE author of the present volume feels some embarrassment in having already offered to the public a work upon the Theory of Determinants. The apparently general acceptability of this former work, which has now reached its third edition, doubtless led to his being invited by the editors of Higher Mathematics to prepare for them a chapter upon the same subject. This was done without the least thought of its publication as a separate volume. Now that its issue as such, along with the other chapters, is requested by both the publishers and the editors of Higher Mathematics, it is but just to the author that the above circumstances should be understood lest he be suspected of entertaining an unseemly desire to keep himself before the mathematical public by vain repetition. The limitations imposed have permitted the addition of only a few articles to the work as originally published; principally those treating of linear substitutions, quantics, invariance, covariance, and functional determinants. Determinants of special forms have not been considered, nor is there the least reference to the application of determinants to geometry. It is hoped, however, that the work may prove useful to the constantly increasing number of students who, while not wishing to specialize in mathematics, desire to obtain the comprehensive view of its methods and processes essential to the successful pursuit of the exact sciences in general.

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