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the second forms the remainder of the book. The first course may be read by any one who understands arithmetic, a little algebra, practical geometry, and the rules of mensuration; in many of the examples it is intended that a geometrical construction should take the place of calculation: instances of the use of construction are given in Examples 178, 216, &c. In this course the principles of the science are merely stated, their formal demonstration being reserved to the second course; in other words, the order most convenient for teaching and learning has been followed at some sacrifice of the systematic development of the subject. The second course presupposes that the reader is acquainted with Euclid, algebra, and trigonometry, as commonly taught in schools; a very few examples are inserted which require some acquaintance with co-ordinate geometry and the differential calculus; the reason for their insertion will generally be obvious from the context in which they occur. Frequent use has been made of simple geometrical limits; they will probably present but little difficulty to the reader: some remarks on the subject of limits will be found in the Appendix.

Very many examples require numerical answers; it is hoped that but few of the arithmetical operations will prove laborious to any one who possesses a proper facility in manipulating numbers, and it must be remembered that few things are more important to a learner in the earlier stages of his progress than that he should be continually referred to the numerical results that follow from the formulæ he investigates. Hints and explanations have

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* Most of these Examples are contained in Chap. IX. Part I. ; the others are distinguished by an asterisk.

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been freely given in connection with the more difficult examples, and it is hoped they will be found sufficient to enable the reader to complete the solutions, though many of them are important mechanical theorems, and some of them but rarely to be met with (e.g. Ex. 134, 149, 393, 429, 522, 553, 566, &c.).

A list is subjoined of the principal works referred to in drawing up the present Treatise; particular instances of obligation are acknowledged in the footnotes in the course of the work. A more explicit recognition of assistance is due to the Rev. H. Moseley, Canon of Bristol: about two hundred of the Examples were given by him to his classes at King's College, London, in the years 1840, 1, 2, 3; these he very kindly placed at the author's disposal, and also gave him permission to use freely his excellent treatise on the · Mechanical Principles of Engineering'—a permission of which great use has been made.

STAFF COLLEGE: Oct. 1870.

Works referred to.
M. Poisson, Traité de Mécanique.
M. PONCELET, Introduction à la Mécanique industrielle.
M. PONCELET, Traité de Mécanique appliquée aux Machines.
M. MORIN, Aide-Mémoire de Mécanique pratique.
M. Morin, Notions fondamentales de Mécanique pratique.
Dr. T. YOUNG, Lectures on Natural Philosophy.
Rev. W. WHEWELL, D.D., History of the Inductive Sciences.
Rev. H. MOSELEY, Mechanical Principles of Engineering.
Rev. R. Willis, Principles of Mechanism.
Dr. RANKINE, Applied Mechanics.
Sir W. THOMPSON and Mr. P. G. Tait, Natural Philosophy, Vol. I.

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