ON MENSURATION AND MEASURING, WITH THE i · MENSURATION AND LEVELLING OF LAND FOR THE PURPOSES OF MODERN ENGINEERING. BY T. BAKER, C.E., of Differentials;" &c. &c. EIGHTH EDITION, ILLUSTRATED. LONDON: PATERNOSTER ROW. 1865. 183. G. 14 CONTENTS. PAGL. PRACTICAL GEOMETRY – Definitions Problems in Practical Geometry (40 Problems) . . . .. 4 Explanation of the Principal Mathematical Characters used in this Work 18 MENSURATION OF LINES—Table of Lineal Measure . . . . 19 Twelve Problems on the Mensuration of Lines, with Formulæ . .ibid. MENSURATION OF SURFACES—Table of Square Measure . . . 34 Sixteen Problems on the Mensuration of Surfaces, with Formulæ . ibid. Promiscuous Exercises . . . . . . . . . 52 MENSURATION OF SOLIDS—Definitions . . . . . . 52 Table of Solid Measure . . . . . . . . . 54 Twenty-one Problems on the Mensuration of Solids, Gauging, &c., with THE SLIDING, OR CARPENTERS' RULE-Seven Problems . TIMBER MEASURING—Three Problems .... ARTIFICERS' WORK-Bricklayers' Work. . Carpenters' and Joiners' Work , .. . . . . . 83 Slaters' and Tilers' Work . ie . . . . . . 86 Painters' Work-Glaziers' Work . Specific Gravity . . . . . . . . . . . 91 Offset Staff-Cross . . . . . . . . . . 93 Directions for Measuring Lines on the Ground . . . . . ibid. The common Drawing Compasses—Plotting Scales . . . 95 Planning Surveys—The Field Book . . . . . . . 96 To Survey with the Chain and Cross—Tables and five Problems, with . ibid. LEVELLING–Definition-Levelling Instruments . . . . . 115 The Y Level . . . . . . . . . . ibid. Levelling Staves (Gravatt's) . . . . . . . . . 118 Correction for Curvature . . . . . . . . .ibid. -- for Refraction, and Examples . . . . . . 119 To find the differences of Levels of several points on the Earth's surface 120 To draw a Sectional Line of several points in the Earth's surface, the Levels of which have been taken . . . . . . 121 Practical Level Book . . . . . . . . . . 123 Levels for the formation of a Section . . . . . . . 124 Level Book for plotting the Section . . . . . . . 125 THE METHOD OF LAYING OUT RAILWAY CURVES ON THE GROUND. . 127 PROB. I.—To lay out a Railway Curve by the common Method - Cases I. and II. . . . . . . . . . . . ibid. PROB. II.—To lay out a Railway Curve by Offsets from its Tangent.- Cases I. and II. . . . . . . . . . 129 CONTENTS OF RAILWAY CUTTINGS— Tables . . . . . . 130 PROB. I.– To find the Contents of Railway Cuttings from their Pepths 132 PROB.II.-To find the Contents of Railway Cuttings from Sectional Areas 133 General Rule for finding the Contents of Solids, with Examples . .135 TABLES, No. 1.-Areas of Segments of Circles . . . . . 137 - No. 2.-Offsets to Railway Curves . . . . . 138 umerous Li state. INTRODUCTION. It will at once be seen that condensation of the materials pro. duced by previous authors, and the introduction of a judicious selection of matter, adapted to the expanded intellect of the present age, are the proper requisites for a work on Mensuration. To this plan, the author trusts, from his long experience in engineering pursuits, that he has strictly adhered. In the first part, on PRACTICAL GEOMETRY, numerous examples are introduced, wherein the dimensions of certain parts are given to find the dimension of their corresponding parts, which has been rarely or never done by previous authors. This part is succeeded by a second part, on the MENSURATION OF LINES ; which is not added for the sake of novelty only, but because it seemed to be the natural order of a work of this kind. The third and fourth parts treat of the MENSURA TION OF SUPERFICES AND OF SOLIDS ; while in all the three last-named parts the rules are not only given in words at length, in the usual way, but the same rules are expressed by FORMULÆ, together with other formulæ depending thereon, by which the rules receive considerable extension. Some of the rules and examples are taken verbatim from Dr. Hutton's Mensuration ; for the author conceives that it would be disreputable to attempt, by terbal alterations in such rules, to give an air of originality to his work, as all other authors have done since Dr. H.'s time: the originality of this work consists in the new matter, everywhere added, to adapt it to the wants of modern times. Timber measure and Artificer's work, the latter with considerable modern improvements, are next introduced, with concise and practical methods of finding the surfaces and solidities of vaulted roofs, arches, domes, &c. Concise, and the author trusts, clear systems of Mensuration applied to land, i.e. surveying, levelling, laying out railway curves and finding the contents of railway cuttings, complete the work, and may serve as an introduction to other more extended treatises on Land and Engineering Surveying, adapted to modern practice. The demonstrations of all the rules and formula, in the four leading parts of the work, will be found in Dr. Hutton's |