The present volume is the first contribution towards the fulfilment of a promise made at the time of publication of my Treatise on Differential Equations. My desire has been to include every substantial contribution to the development of the particular subject herein dealt with; and the historical form, into which the treatment has been cast, has facilitated the indication of the continuous course of the development. All sources of information, which have been drawn upon, are quoted in their proper connection; a few investigations have been added, which I believe to be new ; and some examples have been made, in order to provide illustrations of various methods.

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