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Boole — continued. This volume contains all that Professor Boole wrote for the purpose of enlarging his treatise on Differential Equations.

In this exposition of the Calculus of Finite Differences, particular attention has been paid to the connection of its methods with those of the Differential Calculus — a connection which in some instances involves far ''more than a merely formal analogy. The work is in some measure'' designed as a sequel to Professor Boole's Treatise on Differential Equa&shy;tions. “As an original book by one of the first mathematicians of the age, it is out of all comparison with the mere second-hand compilations which have hitherto been alone accessible to the student.” — .

Writers on Arithmetic at the present day feel the necessity of explaining the principles on which the rules of the subject are based, but few as yet feel the ''necessity of making these explanations strict and complete. If the science'' of Arithmetic is to be made an effective instrument in developing and strengthening the mental powers, it ought to be worked out rationally and conclusively; and in this work the author has endeavoured to reason out in a clear and accurate manner the leading propositions of the science, and ''to illustrate and apply those propositions in practice. In the practical'' part of the subject he has advanced somewhat beyond the majority of preceding writers; particularly in Division, in Greatest Common Measure, in Cube Root, in the Chapters on Decimal Money and the Metric System, and more especially in the application of Decimals to ''Percentages and cognate subjects. Copious examples, original and selected,'' ''are given. “This strikes us as a valuable Manual of Arithmetic of the'' ''Scientific kind. Indeed, this really appears to us the best we have seen”'' — . “This is an essentially practical book, providing very definite help to candidates for almost every kind of com&shy;petitive examination.” —.