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Articles 1 to 6. On setting out Tunnels

Notes 1 to 6 on excavating Tunnels

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Prob. I. To find the contents of railway cuttings when the surface lines

of the several sections are level.

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Table No. 1. Offsets to railway curves

No. 2. Correction of levels for parallax and refraction

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120, in formula for 4 (a+B) IV read 4 (am + Bo) IV.
120, first line in Note 1., for formulæ read formula.

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LAND SURVEYING is a branch of the mathematics, applied to practical purposes, and had its origin, it is said, in Egypt, more than 1000 years before the Christian era; where the annual inundations of the Nile, and the consequent large deposits of mud, destroyed the land marks of the different proprietors. It, therefore, became necessary to determine these land marks by measurement, or to lay out the proper quantities of land claimed by the several proprietors, irrespective of their land marks thus destroyed. Hence the origin of the science of geometry, so called from its being compounded of two Greek words, signifying "to measure the earth." This science, it is well known, is the foundation of the splendid system of mathematics, which has imparted to mankind a knowledge of the extent of the farthest visible universe, and of the laws by which ALMIGHTY POWER directs the celestial motions. But, notwithstanding the early origin of this science, in as far as it is applied to land surveying, it has received comparatively very little improvement almost up to the present time. The writers of extensive works on this subject being chiefly practical men, unacquainted with modern analysis, and some of them even ignorant of geometry, have successively produced works, which are little more than mere copies of those previously published, their examples being in all cases, simple and profuse without variety or elegance, the invariable result of such labours being a large volume, immeasurably behind the requirements of the subject as well as the science of modern times.

In the following work, I trust, it will be found that the author has avoided such profusion and want of variety in the subjects proposed, making, at the same time, the most important parts sufficiently clear to those students who have not had an opportunity of studying geometry and the higher branches of mathematics,—the demonstrations of all rules and formulæ not previously published, being given in notes, apart from the practical matter; while the demonstrations of all rules previously given in various works of geometry and analytical trigonometry, are omitted, to avoid increasing. the size of the work, which is divided into Two Parts, viz., Land and Engineering Surveying, and each part into six Chapters; on each of which it will be proper to make a few observations.

CHAPTERS I. and Il., on practical geometry and surveying by the chain and cross, are of two simple a character to admit of improvement, the author's object in these being condensation and clearness, with a sufficiency of examples to introduce the subject. CHAPTER III., on surveying with the chain only, contains several new Problems, among which may be named Problem IV., which furnishes an original and concise method of finding the width of a large river. Problem VII. gives three methods of surveying fields of from five to seven sides, with only five chain lines, with examples of the numerous lines adopted in old methods; and Problem IX. gives a method of surveying a small estate of six fields by either five or four chain lines, with the method of proving the positions of straight fences; which positions all previous authors have determined by the crossing of two chain lines, or by prolonging each straight fence to two chain lines; which methods constitute no check on wrong entries in the Field Book. This Chapter concludes with several specimens of laying out main lines of extensive surveys, which occurred in the author's practice, including the main lines recommended by the Tithe Commissioners.

In CHAPTER IV. are given engravings and descriptions of the most efficient drawing and surveying instruments, which are chiefly taken from Heather's Treatise on Mathematical Instruments, in the Rudimentary Series, the best work on this subject. In this Chapter Rodham's method of keeping the Field Book, invented about fifty years ago, is given with slight alteration, on a folding plate, and the plan of an estate, to which the field book refers.

CHAPTER V. contains several surveys chiefly by the Theodolite, including surveys for railways and other engineering purposes.

CHAPTER VI., on dividing and inclosing land, commons, &c., has been almost entirely remodelled by the author, several formulæ, never before published, being given, for the expeditious laying out and dividing land of uniform or variable value, the

demonstrations of which are given in the notes, or among the Formulæ in Part II. Chapter VI. This Chapter concludes Part I.; which, it will be seen treats exclusively on land surveying.

PART II. of this work, may with propriety be called modern, if we except Chapter 1. on levelling, which has been practised above a century, firstly for canals, and secondly for railways; however, no good treatise on this subject appeared till, that by Mr. Simms, whose plates and examples, being in the publisher's possession, were adopted by the author in this work, as well as some parts of Mr. Simms' ac-companying explanations of the subject. In this Chapter the author has also availed himself of Heather's Treatise on Mathematical Instruments for the plates of the levels, &c. and some parts of their descriptions.

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CHAPTER II. treats of the various methods required for laying out railway curves in the ground; these methods were invented by the author about twenty-seven years ago, were first published in the Gentleman's Diary, secondly in the Ninth Edition of Nesbits' Surveying, thirdly in the author's Railway Engineering, and now for the fourth time in this work. The author trusts that it will be found, that he has treated this subject in an improved and truly practical manner: the investigations of the additional formulæ here required are given in the notes, the others will be found in the author's V works above referred to, the geometrical constructions of compound and serpentine tl curves being here omitted, as being seldom used by practical men. See Remarks on the Invention of the Method of laying out Railway Curves, page 174. In CHAPTER III. the methods of setting out the widths of railway cuttings, on all varieties of sloping and undulating ground, are carried out chiefly by original formulæ, which are also given with their investigation, in the author's Railway Engineering. Mr. Simms also wrote on this subject, in his work on Levelling, but without giving any formula; these methods may therefore be considered as entirely new modelled. CHAPTER IV. is on tunnelling, on the setting out of which very little has been written by any author. The author has, he trusts, given clear and practical methods for this purpose, whether the tunnel be straight or curved, with copious notes, chiefly extracted from the Practical Railway Engineer, published by Mr. Weale in 4to., on thi the methods of excavating tunnels, &c.


CHAPTER V. is on the author's concise and original method of finding the contents of the earthwork of railways, almost entirely without calculation. This method was invented by the author about twelve years ago, although another author, the errors of bre whose methods approximate to 50 per cent. as their maximum, has the assurance to claim the same methods, (see remarks on this subject, page 198,) the errors of that author's method being further pointed out in this work, its falacy having been before fully established by rigid mathematical demonstration in the author's Railway Engineering. CHAPTER VI. contains a collection of problems and formulæ of utility in land and engineering surveying, the investigation of which are either given or referred to in dist other works, with a collection of unsolved problems original and select, for the exercise of students. At the end of this Chapter is given Pambour's Formula for the super-elevation of the exterior rail in railway curves.






The work concludes with an Appendix, in which are given the dimensions of the famous of tubular bridges, and several of the principal railway viaducts of various constructions, the which the late general extension of railways has called into existence in this kingdom. From the preceding analysis of the contents of this work, as well as from an inspection of its several details, and a comparison of these with the works of other authors, it will at once be seen that of the twelve Chapters of which this work is composed. three may be safely claimed by the author as having been originally drawn up by anot him, viz., Chapters II., III. and V. of Part II., while in all the other Chapters, excepting the first and second in Part I., considerable additions and improvements have also been made; and these in the compass of a smaller volume than those that treat only of land surveying. I trust, therefore, the intelligent reader will find that the ang author has placed this subject in the position it ought to occupy among the other 9 scientific works of the age.



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