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The object of this book is to provide, in moderate bulk, a collection of Rules and Tables relating to those parts of mathematical and mechanical science whose application most frequently occurs in the useful arts, and especially in engineering and practical mechanics. The use of algebraical symbols is avoided, except in those cases in which the rules cannot be clearly expressed without them.

The rules and tables of the First Part belong to Arithmetic and Mensuration. The tables of well-known quantities, such as squares, cubes, and logarithms, have been drawn from the most trustworthy sources, and their accuracy independently tested throughout; the circumferences and areas of circles may be relied on to the last figure. The table of trigonometrical functions consists of only a single page; but it is sufficient, nevertheless, for the solution of such problems in practical mechanics as involve the use of those functions; for purposes of Geodesy, the only proper trigonometrical tables are such as fill a large part of a bulky volume. The summary of the rules of trigonometry is complete. Great care has been bestowed on the arrangement and explanation of those important rules which relate to the measurement of the areas of surfaces, volumes of solid figures, and lengths of curves, and the finding of the centres of magnitude of all those classes of figures.

The Second Part relates to the Measures, commonly so called, of different nations, and contains tables and rules relating not only to measures of angles, time, length, surface, volume, weight, and value, but to those of quantities more or less complex, such as speed, heaviness, pressure, work, power, moment, absolute force, and heat. The values of the various units of measure mentioned are compared with the standards of the British legal system, and of the metrical system (whose use is now permitted in Britain); and those standards are compared with each other according to the best authorities--viz., the paper of Prof. Airy, Astronomer-Royal,

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“Standards of Measure," and that of Professor Miller on the “ Standard Pound.” (In the Second Edition, those comparisons were brought into conformity with the work of Captain Clarke, R.E., on “Standards of Length").

The Third Part relates to Engineering Geodesy, comprehending surveying, levelling, and the setting out of works. The rules which depend on the figure and dimensions of the earth, such as those for calculating the lengths of arcs of the meridian, and of arcs intersecting the meridian at different angles, are founded on the most probable determinations of the earth's dimensions. The rules for the setting out of works comprehend directions for ranging curves on lines of railway, and for easing the changes of curvature at the junctions of such curves with each other, and with straight lines. The Part concludes with a system of rules for the measurement of earthwork.

The Fourth Part relates to Distributed Forces and Mechanical Centres. It includes tables of heaviness and specific gravity, and of expansion by heat; and rules for finding centres of gravity, moments of weight and of inertia, centres of pressure, centres of percussion, and centres of buoyancy.

The Fifth Part relates to the Balance and Stability of Structures, including frames, chains, and arched ribs, retaining walls, piers and abutments, arches of masonry, and foundations of different kinds.

The Sixth Part relates to the Strength of Materials. It commences with a series of tables of the resistance of various kinds of materials to straining actions of different kinds; followed by rules for the computation of the strength of materials in the various forms in which they are used in structures and machines ; such as ties, pipes and cylinders, pillars, axles, beams, chains, and arches.

The Seventh Part relates to Machines in general ; giving in the first place rules for the comparison of the motions of different points in a machine, and for the designing of the more important parts of mechanism, such as wheels and their teeth, speed-cones, parallel motions, &c. These are followed by rules relating to the work of machines at uniform speed and at varying speed, to centrifugal force, the balancing of machinery, and the use of fly-wheels; and by directions how the rules of the sixth part are to be applied to the strength of machinery. In the course of this Part, rules are


given for the resistance of carriages on roads and railways, the tractive power of locomotives, and the ruling gradients of railways. The Part concludes with rules as to the power of horses and other animals, and of men, and a table of the quantity of labour required in various operations.

In the Eighth Part are given rules applicable to Hydraulic and Marine Engineering; such as those which determine the head required to produce a given discharge of water through a given channel or pipe; the discharge from a given outlet with a given head; the dimensions of the pipe or channel required to discharge water at a given rate with a given head; and the strength of waterpipes. Then follow rules for the designing of hydraulic prime movers; such as vertical water-wheels, overshot or undershot, and turbines; then rules applicable to windmills. Lastly, rules are given for the estimation of the resistance of water to the motion of ships; for the determination of the proper dimensions of propelling instruments of different kinds, jets, paddles, or screws, and of the engine-power required to drive them; and for calculating the quantity of sail which a given ship can safely carry ;-all founded on practical experience on the large scale.

The Ninth Part relates to Heat and the Steam Engine. It con. tains a system of rules and tables founded on the true principles of thermodynamics, and at the same time reduced to a degree of brevity and simplicity which it is believed has not hitherto been attained, for determining the relations between work done and heat expended in any actual or proposed steam engine. Those are followed by rules for fixing the leading dimensions of the principal parts of an engine required to do a given duty under given circumstances: for the heating power and the expenditure of fuel: for the efficiency and dimensions of furnaces and boilers; and for the proportioning of slide-valve gear, link-motions, and other fittings of steam engines. At the end of the text is a plate containing a pair of diagrams of the mechanical properties of steam, by the use of which much of the labour of calculation may be saved; and this is followed by a very full alphabetical index.

In this Third Edition various corrections, amendments, and additions have been made.

W. J. M. R.



In adding to the Sixth EDITION of this work, at the request of the Publishers, an Appendix comprising Rules, Tables, and Formulæ for the use of Electricians and Telegraph Engineers, I have to express my obligations to the authors of several standard works, and to all who have favoured me with original and valuable communications in reference to the different branches of the subject.

Especially my thanks are due to Sir William Thomson, F.R.S.; Professor Fleeming Jenkin, F.R.S. ; Professor Everett, F.R.S.; William Shuter, Esq., Manager of the Telegraph Construction and Maintenance Company; Messrs. Clark, Forde & Taylor, Consu ng Engineers; Dr. Muirhead; Messrs. Elliott Brothers; Mr. Thomas Gray, F.R.S.E. ; Mr. John Munro, Consulting Electrician ; Mr. Herbert Sullivan ; and Mr. W. Raitt, B.Sc.



GLASGOW, December, 1882.

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