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Todhunter (I.) — continued. obtaining all the information which he will require on this branch of ''Mathematics. Each chapter is followed by a set of Examples: those'' which are entitled Miscellaneous Examples, together with a few in some of the other sets, may be advantageously reserved by the student for exercise ''after he has made some progress in the subject. In the Second Edition'' the hints for the solution of the Examples have been considerably increased.

The present work is constructed on the same plan as the treatise on ''Plane Trigonometry, to which it is intended as a sequel. In the account'' of Napier's Rules of Circular Parts, an explanation has been given of a method of proof devised by Napier, which seems to have been overlooked ''by most modern writers on the subject. Considerable labour has been'' bestowed on the text in order to render it comprehensive and accurate, and the Examples (selected chiefly from College Examination Papers) have ''all been carefully verified. “For educational purposes this work seems'' to be superior to any others on the subject.” —.

The author has here endeavoured to exhibit the subject in a simple manner for the benefit of beginners, and at the same time to include in one ''volume all that students usually require. In addition, therefore, to the'' propositions which have always appeared in such treatises, he has intro&shy;duced the methods of abridged notation, which are of more recent origin; these methods, which are of a less elementary character than the rest of the work, are placed in separate chapters, and may be omitted by the student at first.

The author has endeavoured in the present work to exhibit a compre&shy;hensive ''view of the Differential Calculus on the method of limits. In the'' more elementary portions he has entered into considerable detail in the explanations, with the hope that a reader who is without the assistance of a tutor may be enabled to acquire a competent acquaintance with the subject. ''The method adopted is that of Differential Coefficients. To the different''