PREFACE.

IT has of late been a too prevailing opinion in this country, that

a man may become celebrated as a natural philosopher, and be very successful in the application of his knowledge to practical purposes, particularly in the construction of machinery, while he is completely unacquainted with the principles of mathematics. Among a variety of unpleasant consequences which have resulted from this erroneous opinion, may be reckoned, the rapid decline of the mathematical sciences in Britain, the dissemination of superficial and vague notions on physical topics, and the absolute necessity of having recourse to foreign publications for profound and extensive information on those subjects, which we should have supposed, had not experience convinced us to the contrary, Englishmen would have been proud to cultivate; since they were first placed upon an unshaken basis in the Principia of our own countryman, the illustrious Newton. It has been asserted by a competent judge, Dr. Robison, and it is mortifying to reflect that the assertion is true, "that while the continent has supplied us with most elaborate and useful treatises on various articles in physical astronomy, practical mechanics, hydraulics, and optics, there has not appeared in Britain half a dozen treatises worth consulting for the last forty years." We have, it is readily admitted, many popular works on mechanics, hydrostatics, &c. in which the principles are exhibited, and their application to the useful purposes in life illustrated by examples; but since their authors have scarcely ever aimed at demonstration, those who rest satisfied with the information they can gather from these treatises, can at best acquire but a kind of second-hand knowledge of unproved principles loosely floating in the mind; and must

generally hesitate in every case presenting a novel aspect, for want of that confidence in principles and results which the irresistible evidence accompanying the deductions of pure science alone can inspire. I would not be understood as intending to cast any censure upon the authors of familiar treatises on scientific subjects: I only wish it to be recollected that these are much fitter for children than for men; that they may be useful as introductory books for pupils, but of little or no immediate service in the active concerns of a more advanced state; and that, because they merely excite a thirst for knowledge which they cannot gratify. Nor would I wish to insinuate that there are not in our language some excellent works on the theory of mechanics; but I cannot help being apprehensive that most of these (chiefly on account of the small encouragement likely to be given them) are too confined in their object, and for that reason fail in being so beneficial to the public, as the talents of their authors might otherwise lead us naturally to expect.

For some years I have seen (or thought I have seen), and often regretted, that a forbidding distance and awkward jealousy seem to subsist between the theorists and the practical men engaged in the cultivation of mechanics in this country: and it is a desire to shorten this distance, and to eradicate this jealousy, that has been a principal stimulant in the execution of the following performance. I have by long habit, combined perhaps with early acquired prejudices, been much delighted with the investigations of theorists: but while I prize the deductions of sound theory as highly as any person, and rest as firmly upon them; yet am I desirous not to forget, that, as all general principles imply the exercise of abstraction, it would be highly injudicious not to regard them in their practical applications as approximations, the defects of which must be supplied, as indeed the principles themselves are deduced, from experience. Habits of abstraction and theorizing may be carried to excess; and crude experience without reflection will never be productive of essential good. But, as an eminent philosopher (for whose talents and virtues I entertain great respect) remarks, "Care should be taken to guard against both these extremes, and "to unite habits of abstraction with habits of business, in such

• Professor Dugald Stewart; Elements of the Philosophy of the Human Mind, p. 231, &c.

"manner as to enable men to consider things either in general or "in detail, as the occasion may require. Whichever of these "habits may happen to gain an undue ascendant over the mind, "it will necessarily produce a character limited in its powers, and "fitted only for particular exertions.-When theoretical knowledge " and practical skill are happily combined in the same person, the "intellectual power of man appears in its full perfection, and fits "him equally to conduct with a masterly hand the details of ordi"nary business, and to contend successfully with the untried diffi"culties of new and hazardous situations. In conducting the "former, mere experience may frequently be a sufficient guide: "but experience and speculation must be combined together to "prepare us for the latter."Expert men,' says Lord Bacon, ' can execute and judge of particulars, one by one; but the general ⚫ counsels, and the plots, and the marshalling of affairs, come best 'from those that are learned.'

Admitting the truth of these observations-and their truth I think cannot well be denied-it will thence follow, that theoretical and practical men will most effectually promote their mutual interests, not by affecting to despise each other, but by blending their efforts: and further, that an essential service will be done to mechanical science, by endeavouring to make all the scattered rays of light they have separately thrown upon this region of human knowledge converge to one point. In conformity with these ideas, I have undertaken a task, attended, I am aware, with so many difficulties, that even failure will not be disgraceful; while, on the other hand, success, if my labours should fortunately be crowned with it, will be doubly gratifying; as I shall then flatter myself with having contributed in some measure to the union of accurate theory and judicious practice, and thus, ultimately, to the promotion of arts and manufactures.

The Treatise of Mechanics I now presume to lay before the public is comprised in two large volumes, besides a volume of plates. Of these the first volume is devoted chiefly to the theory: the second is practical and descriptive. The theoretical part is divided into five books, and these are subdivided into chapters, as the nature of the several subjects seemed to require.

Book I. is appropriated to the subject of STATICS, and is subdi

vided into six chapters. It commences, as indeed do all the books, with definitions and preliminary remarks; which are succeeded by a statement and illustration of the Newtonian laws of motion and rest, which are assumed as fundamental principles to guide our subsequent enquiries. The nature of statical equilibrium, with the composition and resolution of forces, are then discussed; forces being considered, 1. as disposed in one plane, and concurring in the same point: 2. as directed to one point, but not confined to one plane: 3. as situated in one plane, but applied to different points of a body: 4. as not confined to one plane, and directed to various points of a body. This portion of the work occupies rather more space than has been commonly assigned to it in treatises of mechanics; but this circumstance will, I hope, be found to facilitate the application of the parallelogram of forces to the investigations which follow. The remaining chapters in this book treat of the centre of gravity, and the centrobaryc method; the simple machines, or, as they are usually called, the mechanical powers; the strength and stress of timber and other materials; and the equilibrium, tension, and pressure of cords, arches, and domes. The minuter topics connected with these general points of enquiry cannot well be specified here.

The second book relates to DYNAMICS. It comprehends six chapters; treating of, motion, uniform and variable; the descent and ascent of heavy bodies in vertical lines; the motion of projectiles, with observations on ricochet-firing; descents along inclined planes and curves; the vibrations of pendulums, and the curve of swiftest descent; central forces; the rotation of bodies about fixed axes, and in free space, with theorems relative to the centres of oscillation, gyration, percussion, spontaneous rotation, &c.; the physico-mathematical theory of percussion, nearly as first delivered in Don George Juan's Examen Maritimo; and the motion of machines, and their maximum effects; closing with some remarks that shew in what points of view machines ought to be considered by those who would labour beneficially for their improvement.

Book III. is devoted to the subject of HYDROSTATICS. It is divided into four chapters-on the pressure of non-elastic fluids; the determination of the specific gravities of solid and fluid bodies; the construction of hydrometers or areometers; the equilibrium,

stability, and oscillations of floating bodies, with a particular reference to ships and canal boats; and, on the phenomena of attraction in capillary tubes. This book contains an extensive, and, I trust, correct table of specific gravities.

In the fourth book I have given some of the most useful propositions and theorems relative to HYDRODYNAMICS. But as this is a very complex and intricate subject, in which the most elaborate theory can do but little, independent of numerous experiments, it seemed prudent, rather than to delude the student with a display of mathematical accuracy where it is so far from being attained, to curtail the theoretical part with a view to the introduction of some valuable experimental results. This book comprises, then, only four chapters. 1. On the discharge of fluids through apertures in the bottom and sides of vessels, and on spouting fluids: 2. an account of experiments made by different philosophers (as Bossut, Venturi, Eytelwein, Young, Vince, &c.) on the discharge of water through apertures and tubes; and the practical deductions from those experiments: 3. on the effect of water upon the motion of water-wheels: 4. an account of Mr. Smeaton's experiments on water-wheels, and some of those of M. Bossut.

The fifth book, which terminates the first volume, is on PNeuMATICS, and contains six chapters. The subjects stated and discussed in this book are, the equilibrium of elastic fluids; the measurement of altitudes with the barometer and thermometer; the motion of air when the equilibrium of pressure is removed; the theory of air-pumps, and pumps for raising water; the resistance of fluids to bodies moving in them; and results of experiments on the resistance of fluids.

The second volume of this work, which, as before mentioned, is chiefly practical, commences with an introduction occupying 84 pages, and comprising general remarks, rules, and directions, -on the construction and simplification of machinery; on rotatory, rectilinear, and reciprocating motions; on bevel-geer, and proportioning the number of teeth; on friction and the rigidity of cords, with the experiments of Vince, Coulomb, &c. and an example of the power of the capstan, allowing for friction and the stiffness of cords; on water and wind as movers of machinery, with Smeaton's rules relative to windmills; on the strength of fired gun-pow