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THE work now presented to the public had its origin in a desire which I felt to draw up an Essay on the principles and applications of the mechanical sciences, for the use of the younger members of the Institution of Civil Engineers. The eminent individuals who are deservedly regarded as the main pillars of that useful Institution, stand in need of no such instructions as are in my power to impart : but it seemed expedient to prepare an Essay, comprised within moderate limits, which might furnish scientific instruction for the many young men of ardour and enterprise who have of late years devoted themselves to the interesting and important profession, of whose members that Institution is principally constituted. My first design was to compose a paper which might be read at one or two of the meetings of that Society; but, as often happens in such cases, the embryo thought has grown, during meditation, from an essay to a book and what was first meant to be a very compendious selection of principles and rules, has, in its execution, assumed the appearance of a systematic analysis of principles, theorems, rules, and tables.

Indeed, the circumstances in which the inhabitants of this country are now placed, with regard to the love and acquisition of knowledge, impelled me, almost unconsciously, to such an extension of my original plan, as sprung from a desire to contribute to the instruction of that numerous class, the practical mechanics of this country. Besides the early disadvantages under which many of them have laboured, there is another which results from the activity of their pursuits. Unable, therefore, to go through the details of an extensive systematic course, they must, for the most part, be satisfied with imperfect views of theories and principles, and take much upon trust: an evil, however, which the establishment of Societies, and the composition of treatises, with an express view to their benefit, will probably soon diminish.

LORD BROUGHAM, in his "Practical Observations upon the Education of the People," remarks that" a most essential service will be rendered

to the cause of knowledge, by him who shall devote his time to the composition of elementary treatises on the Mathematics, sufficiently clear, and yet sufficiently compendious, to exemplify the method of reasoning employed in that science, and to impart an accurate knowledge of the most useful fundamental propositions, with their application to practical purposes; and treatises upon Natural Philosophy, which may teach the great principles of physics, and their practical application, to readers who have but a general knowledge of mathematics, or who are even wholly ignorant of the science beyond the common rules of arithmetic." And again, "He who shall prepare a treatise simply and concisely unfolding the doctrines of Algebra, Geometry, and Mechanics, and adding examples calculated to strike the imagination of their connexion with other branches of knowledge, and with the arts of common life, may fairly claim a large share in that rich harvest of discovery and invention which must be reaped by the thousands of ingenious and active men, thus enabled to bend their faculties towards objects at once useful and sublime."

I do not attempt to persuade myself that the present volume will be thought adequately to supply the desiderata to which the passages advert; yet I could not but be gratified, after full two-thirds of it were written, to find that the views which guided me in its execution accorded so far with the judgment of an individual, distinguished as LORD BROUGHAM was, in early life, for the elegance and profundity of his mathematical researches.

With a view to the elementary instruction of those who have not previously studied mathematics, I have commenced with brief, but, I hope, perspicuous, treatises on Arithmetic and Algebra; a competent acquaintance with both of these being necessary to ensure that accuracy in computation which every practical man ought to attain, and that ready comprehension of scientific theorems and formulæ which becomes the key to the stores of higher knowledge. As no man sharpens his tool or his weapon, merely that it may be sharp, but that it may be the fitter for use; so no thoughtful man learns arithmetic and algebra for the mere sake of knowing those branches of science, but that he may employ them; and these being possessed as valuable pre-requisites, the course of an author is thereby facilitated: for then, while he endeavours to express even common matters so that the learned shall not be disgusted, he may so express the more abstract and difficult that the comparatively ignorant (and the mere knowledge of arithmetic and algebra is, in our times, comparative ignorance) may practically understand and apply them.

After the first 103'pages, the remaining matter is synoptical. The general topics of geometry, trigonometry, conic sections, curves, perspective, mensuration, statics, dynamics, hydrostatics, hydrodynamics, and pneumatics, are thus treated. The definitions and principles are exhibited in an orderly series; but investigations and demonstrations are only sparingly introduced. This portion of the work is akin in its nature to a syllabus of a Course of Lectures on the departments of science which it treats; with this difference, however, occasioned by the leading object of the publication, that popular illustrations are more frequently introduced, practical applications incessantly borne in mind, and such tables as seemed best calculated to save the labour of architects, mechanics, and civil engineers, inserted under their appropriate heads. Of these latter, several have been collected from former treatises, &c., but not a few have been either computed or contributed expressly for this Common-place Book. In a work like this, it would be absurd to pretend to originality. The plan, arrangement, and execution, are my own; but the materials have long been regarded, and rightly, as common property. It has been my aim to reduce them into the smallest possible space, consistently with my general object; but, wherever I have found the work in this respect prepared to my hands, I have transcribed it into the following pages, with the usual references to the sources from whence it was taken. They who are conversant with the best writers on subjects of mixed mathematics and natural philosophy, will know that Smeaton, Robison, Playfair, Young, Du Buat, Leslie, Hachette, Bland, Tredgold, &c. are authors who ought to be consulted, in the preparation of a volume like this. I hope it will appear that I have duly, yet, at the same time, honourably, availed myself of the advantages which they supply. I have, also, made such selections from my own earlier publications as were obviously suitable to my present purpose; but not so copiously, I trust, as to diminish the utility of those volumes, or to make me an unfair borrower even from myself.

Besides our junior Civil Engineers, and the numerous Practical Mechanics who are anxious to store their minds with scientific facts and principles; there are others to whom, I flatter myself, the following pages will be found useful. Teachers of mathematics and those departments of natural philosophy which are introduced into our more respectable seminaries, may probably find this volume to occupy a convenient intermediate station between the merely popular exhibitions of the truths of mechanics, hydrostatics, &c., and the larger

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