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 SURVEYING and ENGINEERING SURVEYING, and each part into six chapters; on each of which it will be proper to make a Tew observations. CHAPTERS I. and II., On Practical Geometry and Surveying by the Chain and Cross, are of too 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. 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. 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. In this Chapter directions for town-surveys are rather prominently introduced. CHAPTER VI., on dividing and inclosing land, commons, &c., has been almost entirely remodelled, 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 I. on Levelling, which has been practised above a century, firstly for canals, and secondly for drainage, roads, and railways; however, no good treatise on this subject appeared till that by Mr. Simms, whose plates and examples, being in the publishers' possession, were adopted by the author in this work, as well as some parts of Mr. Simms' accompanying 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. CHAPTER II. treats of the various methods required for laying out railway curves in the ground; these methods were invented by the author about thirty years ago, and he trusts that it will be found that he has treated this subject in an improved and practical manner: the investigations of the additional formulæ here required are given in the notes. 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 formula, Mr. Simms also wrote on this subject, in his work on LEVELLING, but without giving any formulæ; these methods may therefore be considered as entirely newly 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 DEMPSEY'S PRACTICAL RAILWAY ENGINEER. CHAPTER V. is on the author's concise and original method of finding the contents of the earthwork of rail ways, almost entirely without calculation, which was invented by him many years ago. 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 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 FORMULÆ 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 tubular bridges, and several of the principal railway viaducts of various constructions, which the late general extension of railways has called into existence in this kingdom, and various useful addenda. 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, four may be safely claimed by the author as having been originally drawn up by him, viz., Chapters II., III., IV. and V. Part II., while in all the other Chapters, excepting I. and II. of Part I., consider. able additions and improvements have also been made. NOTE TO THE FIFTEENTH EDITION. Mr. Baker's Rudimentary Treatise on Land and Engineering Surveying, like his Treatise on Mensuration, has become a text-book in many of the principal schools in this country and in the colonies. The work in its present form has had the advantage of the careful revision of the late Professor Young, formerly of Belfast College, under whose direction several errors which had crept in were removed, and other improvements made. In issuing the present edition, opportunity has been taken to substitute the last three paragraphs now appearing on p. 221 for the paragraph with which, in previous editions, that page was concluded, and which was found to be erroneous in some particulars. 101 CONTENTS. Practical Geometry-Definitions Problems in Practical Geometry-Problems I. to IV. The Chain, Offset-staff, and Cross Directions for measuring lines on the ground To Survey with the Chain and Cross 32 LAND SURVEYING BY THE CHAIN ONLY. Prob. I. To erect a perpendicular with the chain Prob. II. and III. To measure lines obstructed by ponds, buildings, &c. Prob. IV. To find the width of a river, which is too wide to be reached across by the chain (a new method) Prob. V. Triangular Fields.—Methods of measuring and computing their areas.—Method of casting, &c. Prob. VII. Fields having more than four sides.-Several examples of expeditiously measuring fields of this kind.—Defects of old Prob. VIII. To survey woods, lakes, &c. Prob. IX. To survey a small estate, divided internally by straight The method of measuring hilly ground Che use of the Parallel Ruler in reducing crooked fences to straight 58 Surveying large Estates or Parishes - DRAWING AND SURVEYING INSTRUMENTS. Plotting extensive surveys from this Scale I ne Pantagraph, for copying maps EXTENSIVE SURVEYS OF VARIOUS KINDS, EITHER WITH OR WITHOUT THE Engineering and other Surveys by the Theodolite Prob. I. To survey woods, lakes, harbours, &c., by the Theodolite. Prob. II. To survey roads and rivers. Prob. III. To survey a part or the whole of a city or large town. Prob. IV. To determine the positions of several distant objects or To survey a district where obstructions occur, for a railway, &c. SECTION I. THE VARIOUS METHODS OF LAYING OUT ANY GIVEN QUANTITY OF LAND IN ANY PROPOSED REGULAR OR IRRE- GULAR FORM; AND OF SEPARATING ANY REQUIRED QUAN- TITY OF LAND FROM AN ENCLOSURE OR COMMON. Prob. I. To lay out a given quantity of land in the form of a Prob. II. To lay out a given quantity of land in the form of a rectangle, the length of which is given Prob. III. To lay out a given quantity of land in the form of a rectangle, the length of which shall have a given proportion to Prob. IV. To lay out a triangle, of a given area and a given base, one of the sides of which shall have a given position Prob. V. To lay out a trapezium of a given area, the positions and lengths of two of its adjoining sides being given, and also the |