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diff --git a/old/63834-0.txt b/old/63834-0.txt deleted file mode 100644 index 35568f9..0000000 --- a/old/63834-0.txt +++ /dev/null @@ -1,18078 +0,0 @@ -The Project Gutenberg EBook of Surveying and Levelling Instruments, by -William Ford Stanley - -This eBook is for the use of anyone anywhere in the United States and most -other parts of the world at no cost and with almost no restrictions -whatsoever. You may copy it, give it away or re-use it under the terms of -the Project Gutenberg License included with this eBook or online at -www.gutenberg.org. If you are not located in the United States, you'll have -to check the laws of the country where you are located before using this ebook. - -Title: Surveying and Levelling Instruments - Theoretically and practically described. - -Author: William Ford Stanley - -Contributor: H. T. Tallack - -Release Date: November 21, 2020 [EBook #63834] - -Language: English - -Character set encoding: UTF-8 - -*** START OF THIS PROJECT GUTENBERG EBOOK SURVEYING AND LEVELLING INSTRUMENTS *** - - - - -Produced by Chris Curnow, Ralph and the Online Distributed -Proofreading Team at https://www.pgdp.net (This file was -produced from images generously made available by The -Internet Archive) - - - - - - -Transcriber's Note: - - Punctuation has been standardised, and possible typographical errors - have been changed. - Archaic, variable and inconsistent spelling and hyphenation have been - preserved. - Bold text is surrounded by =equal signs= and italic text is surrounded - by _underscores_. - Footnotes appear at the end of their respective chapters. - - - - - SURVEYING AND LEVELLING - INSTRUMENTS - - - - - SURVEYING AND LEVELLING - INSTRUMENTS - - Theoretically and Practically Described. - - FOR CONSTRUCTION, QUALITIES, SELECTION, PRESERVATION, - ADJUSTMENTS, AND USES; WITH OTHER APPARATUS AND APPLIANCES - USED BY CIVIL ENGINEERS AND SURVEYORS IN THE FIELD. - - BY - - WILLIAM FORD STANLEY - - OPTICIAN, MANUFACTURER OF SURVEYING AND DRAWING INSTRUMENTS, - AUTHOR OF A TREATISE ON DRAWING INSTRUMENTS, - PROPERTIES AND MOTIONS OF FLUIDS, NEBULAR THEORY, ETC. - - _FOURTH EDITION_ - REVISED BY H. T. TALLACK. - - LONDON: E. & F. N. SPON, LTD., 57, HAYMARKET, S.W. - NEW YORK: 123, LIBERTY STREET - AND OF - W. F. STANLEY & CO., LIMITED - 286, HIGH HOLBORN, LONDON, W.C. - - 1914 - - - - -PREFACE TO FIRST EDITION. - - -Notes were taken for many years before the production of this work of -queries that came before the author for reply relative to functional -parts of surveying instruments. These bore most frequently reference -to optical and magnetic subjects, and to the qualities and action -of spirit level tubes, also occasionally to graduation and the -qualities of clamp and tangent motions. It was therefore thought that -it would be useful to give notes upon these subjects in detail as -far as possible in the early chapters. As the work proceeded it was -found that this plan saved much space in avoiding the necessity for -separate descriptions when parts of complex instruments were afterwards -described. - -To show the state of the art and render the work useful, it was -necessary that the structure of surveying instruments should be given -with sufficient detail to be worked out by the skilful manufacturer. -Beyond this it was thought to be most important that the professional -man, who must have limited experience of the qualities of workmanship, -should be supplied with as many simple tests as possible for assuring -the qualities of the instruments he might purchase or use, with details -also of their adjustments. This matter is therefore carried into detail -for one instrument at least of each class, as very little general -information is to be found on the subject in our literature. In fact, -large groups of instruments in extensive use, such as those used for -mining surveying, and subtense measuring instruments, have remained -heretofore nearly undescribed in our language. - -The technical principles followed in working out details in these pages -are given by illustrations of such parts of important instruments -as present any difficulty of observation from an exterior view of -the engraving of the entire instrument. The plans of construction -in general use are selected for illustration. Certain constructions -that are liable to failure are pointed out. Many recent improvements -in instruments are recognised and some are suggested, but no attempt -has been made to record the little differences of construction, often -meritorious, which give only a certain amount of style to the work of -each country and of each individual. Upon this point it must occur that -the work done in any workshop must vary from other work according to -the skill and judgment of the master. It is intended, therefore, that -distinctly typical instruments only should be described, in a manner -that details may be worked out therefrom. To make this matter as clear -as possible, with few exceptions these pages were written with the -instruments described upon my table, and the illustrations, when not -taken directly from the instruments, were taken from workshop drawings -to a reduced scale. - -In practice it is found that instruments performing similar functions -may be very much varied in construction, bearing reference frequently -to the conditions under which they are to be used. The same may be -said of the functional parts of instruments. We may also observe that -English instruments differ in detail from foreign ones, and upon this -point there is no doubt much may be learned by comparison of some -details of English with foreign work, although our own is admitted -to rank high. Comparisons are therefore freely made in the following -pages, and suggestions offered after study abroad of foreign work, and -careful inspection of nearly the whole literature upon the subject, -in which it is very observable that some modern continental books, -treating upon parts of the subject, are much in advance of our own. - -The surveying instruments described in these pages are nearly -limited to those used in the field. Instruments for plan drawing and -calculation of areas, which the surveyor uses in the office, have been -described in the author's work on Drawing Instruments (now in Seventh -Edition), to which this is intended to be the complement of the subject. - -To render the work as complete as possible, it was thought necessary -to give briefly the manner of using many instruments in practical -surveying. This part of the subject, from the author's very limited -experience in the field, is largely taken from inspection of the best -works on surveying. The author, however, is very pleased to acknowledge -the kindness of many professional friends for assistance on this and -many other points, and for historical notes. For the description of -the 36-inch theodolite, given in Chapter VII. (now X.), the author is -indebted to the late Col. A. Strange, F.R.S., who gave every detail of -his design and discussed many points. The author is also indebted to -Mr. Thomas Cushing, F.R.A.S., Inspector of Scientific Instruments for -India, who has given information and his opinions upon many subjects -from his large practical experience. Also to Prof. George Fuller, C.E., -who has kindly read proofs, examined formulæ, and made some technical -points clearer. Also to Mr. W. N. Bakewell, M.Inst.C.E.; Major-General -A. De Lisle, R.E.; Right Hon. Lord Rayleigh, F.R.S., for assistance on -several technical points. - -In this First Edition, entirely from manuscript, there will no doubt -be errors and omissions; therefore the author will feel obliged by the -receipt of any notes that he may make use of for future corrections, -should another Edition be demanded. - - W. F. S. - - GREAT TURNSTILE, 1890. - - - - -PREFACE TO THIRD EDITION. - - -The note at the end of the First Edition of this work referred to -on the preceding page has brought the author many letters from -professional men, who have kindly taken interest in the work by -offering suggestions which are now incorporated as far as practical in -this Edition, and for which thanks are tendered. - -One important improvement of late years in the construction of -surveying instruments is due to the greater perfection of modern -machinery, and the adoption of special machines to shape out many -parts of the work from the solid which were formerly screwed together -in many pieces, which made the instruments heavier and also liable to -become loose in parts by jars, so as to cause the necessity of frequent -readjustments. - -Another important improvement in modern surveying instruments is in -their lightness, due to the discovery of permanent aluminium alloys, by -which many parts of instruments that are shaped out in the solid may be -reduced to one-third the weight of the gun-metal castings formerly used -entirely for these parts. - -In the present Edition, which represents forty-seven years of -experience of the author's life devoted to the details of the subject, -it is hoped that some permanent improvements in surveying instruments -may be shown, and that many new designs now first described, founded -upon this experience, may merit trial. - -The author is pleased to acknowledge the zealous aid his working -manager and at present co-director, Mr. H. T. Tallack, has given in -perfecting this work to bring it to its present state. - - W. F. S. - - GREAT TURNSTILE, 1901. - - - - -PREFACE TO FOURTH EDITION. - - -Since the publication of the Third Edition of this work, the author -has been taken from us, and it has fallen to my lot to revise it and -bring it up to the present time. This work I have approached with -the greatest diffidence, having to follow one who had such profound -knowledge of the subject, and I have earnestly endeavoured, as closely -as possible, to act as I think he would have done had he been alive, -and having enjoyed over twenty years of the happiest and closest -business relations with him--actively co-operating in bringing many of -the instruments to their present state, I venture to hope that I have -to some extent carried out what his wishes would have been. - -I have carefully read over and corrected the whole work, and the -additions to it are only in the nature of bringing it up to date. - - H. T. TALLACK. - - 286, HIGH HOLBORN, - - _June, 1914._ - - - - -CONTENTS. - - - CHAPTER I. - PAGE - - INTRODUCTION:--Historical Sketch--Classification of the Subject-- - Purposes and Qualities of Instruments--Workmanship--Metals-- - Aluminium--Framing--Tools--Axes of Instruments--Soldering-- - Finishing--Bronzing--Lacquering--Graduating--Engraving--Style-- - Glass-Work--Woodwork--Lubrication--Preservation of Instruments-- - Packing 1 - - - CHAPTER II. - - THE TELESCOPE AS A PART OF A SURVEYING INSTRUMENT:--General - Description--Qualities--Optical Principles--Refraction - of Glass--Limit of Refraction--Reflection--Prisms--Lenses, - Convex and Concave--Aberration--Formation of Images--Dispersion-- - Achromatism--Curvature of Lenses--Telescopes--Eye-pieces--Powers-- - Dynameter--Construction of the Telescope--Diaphragm--Webs--Lines-- - Points--Parallax--Examination and Adjustment 24 - - - CHAPTER III. - - THE MAGNETIC COMPASS AS A PART OF A SURVEYING INSTRUMENT OR - SEPARATELY:--Broad and Edge-bar Needles--Manufacture of the - Needle--Magnetisation--Suspension--Dip and Adjustment--Lifting-- - Inclination--Declination--Variation--Correction--Compass-Boxes-- - Description of Compasses--Ring Compasses--Trough Compasses-- - Prismatic Compasses--Stand--Surveying with Compass--Pocket - Compasses 59 - - - CHAPTER IV. - - LEVELS:--Methods of Ascertaining--Level Tubes--Manufacture-- - Curvature--Sensitiveness--Testing--Reading--Circular Levels-- - Surveyors' Levels--Y-Levels--Parallel Plates--Adjustments of - Y-Levels--Suggested Improvements--Dumpy Levels--Tripod Stands-- - Adjustment of Dumpy--Collimator--Improvements in Dumpy Levels-- - Tribrach Head--Diaphragms--Cushing's Levels--Cooke's Levels--Cheap - Forms of Level--Hand Levels--Reflecting Levels--Water Levels 85 - - - CHAPTER V. - - LEVELLING STAVES:--Construction--Various Readings Discussed-- - Sopwith's--Field's--Strange's--Stanley's New Metrical--Simple - Construction--Mining Staff--Papering Levelling Staves-- - Preservation--Packing Pads--Staff Plate--Staff Level--Practice of - Levelling--Index of Bubble--Lamp--Curvature Corrections--Station - Pegs--Refinement of Levelling--Levelling Books 148 - - - CHAPTER VI. - - DIVISION OF THE CIRCLE AND METHODS EMPLOYED IN TAKING ANGLES:-- - Dividing Engine--Surfaces for Graduation--Vernier--Various - Sections--Reading Microscopes--Shades--Micrometers--Clamp and - Tangent Motions--of Limbs--of Axes--Use and Wear--Difference of - Hypotenuse and Base 175 - - - CHAPTER VII. - - THEODOLITES:--Constructive Details of 5-inch and 6-inch Transits-- - Special Additional Parts--Old Form with Four Screws--Improved - Form--Additional Parts--Plummets--Striding Level--Lamp-- - Adjustments over a Point--Solar Attachment--Photographic - Attachment 214 - - - CHAPTER VIII. - - SPECIALTIES IN MODERN FORMS OF TRANSIT:--Theodolites for General - Surveying--Railway Work--Exploring 246 - - - CHAPTER IX. - - PLAIN THEODOLITES IN WHICH THE TRANSIT PRINCIPLE IS NOT - EMPLOYED:--The Plain Theodolite--Improved Construction--Everest's - Simple--Adjustments and Examination of Theodolites 267 - - - CHAPTER X. - - LARGE THEODOLITES USED ONLY FOR GEODETIC SURVEYS:--Stanley's - 10- and 12-inch--14-inch Altazimuth--Col. Strange's 36-inch - Theodolite 293 - - - CHAPTER XI. - - MINING SURVEY INSTRUMENTS:--Circumferentors--Plain Miner's Dial-- - Sights--Tripod Stand--Adjustments--Henderson's Dial--Lean's - Dial--Adjustments--Hedley's Dials--Additional Telescope--Improved - Hedley--Tribrach and Ball Adjustment--Reflectors--Continental - Forms--_Théodolite Souterrain_--Tripod Tables--Stanley's Mining - Theodolite--Pastorelli's and Hoffmann's Adjustable Tripod Heads-- - Mining Transit Theodolites--Stanley's Prismatic Mining Compass-- - Hanging Dial--Hanging Clinometer--Semi-circumferentor--Mining - Lamps 307 - - - CHAPTER XII. - - INSTRUMENTS TO MEASURE SUBTENSE OR TANGENTIAL ANGLES TO ASCERTAIN - DISTANCES:--Historical Notes of the Method--Principles Involved-- - Stadia Measurements, Direct and by the Ordinary Telescope-- - Corrections for Refraction of the Object Glass--Stanley's Subtense - Diaphragm--Anallatic Telescope of Porro--Tacheometers--Stadia-- - Omnimeter--Field book--Bakewell's Subtense Arrangement 355 - - - CHAPTER XIII. - - INSTRUMENTS CONSTRUCTED ESPECIALLY FOR FACILITY OF TAKING - INCLINATIONS:--Inclinometer Theodolite--Gradiometer--Clinometers: - Abney's--Troughton's--De Lisle's--Stanley's--Barker's--Burnier's-- - Watkin's--Clinometer Sights--Rule Clinometer--Road Tracer 389 - - - CHAPTER XIV. - - INSTRUMENTS OF REFLECTION:--Octant or Quadrant--Reflecting - Circle--Sextant--Principle--Parallax--Construction--Examination-- - Adjustment--Artificial Horizon--Sounding Sextant--Box-Sextant-- - Supplementary Arc--Improvements upon this--Optical Square--Optical - Cross--Apomecometer 422 - - - CHAPTER XV. - - GRAPHIC SURVEYING INSTRUMENTS AND APPLIANCES CONNECTED - THEREWITH:--Plane Tables--Alidades--Telescopic Arrangements-- - Subtense Measurements--Various Devices for Holding the Paper-- - Continuous Papers--Adjustment of Tripod Heads--Method - of Using--Edgeworth's Stadiometer--Sketching Protractor--Sketching - Case--Camera Lucida, etc. 472 - - - CHAPTER XVI. - - INSTRUMENTS FOR MEASURING LAND AND CIVIL WORKS DIRECTLY:--Chains-- - Various Tellers--Standard Chains--Arrows--Drop Arrows--Vice for - Adjusting Chain--Caink's Rule for Inclines--Steel Bands--Wire Land - Measures--Linen Tapes--Offset Rods--Pine Standard Rods--Rods with - Iron Core--Beam Compass Rods--Coincidence Measurements-- - Compensated Rods--Base Line Apparatus--Coast Survey Lines-- - Perambulator--Pedometer--Passometer--Sounding Chains--Sounding - Lines--Telemeters--Hand Rods--Rules 490 - - - CHAPTER XVII. - - STATIONS OF OBSERVATION:--Pickets--False Picket--Permanent - Stations--Referring Object--Heliotrope--Heliostat--Heliograph - Signalling--Morse Alphabet--Night Lights--Oil Lanterns--Magnesium - Light 533 - - - CHAPTER XVIII. - - MEASUREMENT OF ALTITUDES BY DIFFERENCES OF ATMOSPHERIC PRESSURE:-- - Historical Note--Mercurial Barometer--Construction--Operation-- - Aneroid Barometer--Construction--Various Improvements--Hypsometer 548 - - - CHAPTER XIX. - - MISCELLANEOUS SURVEYORS' AND ENGINEERS' INSTRUMENTS, APPLIANCES, - AND ACCESSORIES:--Cross Staff--Mechanics' Levels--Boning Rods-- - Footner's Railway Gauge--Girth Strap for Timber Measurement--Girth - Tapes--Timber Marker--Slashing Knife--Bill-Hook--Reconnoitring - Glass--Telescope--Sun Spectacles--Whistles--Pioneer Tools--Sketch - Block Book--Camera--Geological Tools--Wealemefna--Opisometer-- - Boucher's Calculator--Slide Rules--Fuller's Calculator--Engineers' - Pocket-Books--Chronometer--Outfits 573 - - - INDEX 601 - - - - -SURVEYING INSTRUMENTS. - - - - -CHAPTER I. - - HISTORICAL SKETCH--CLASSIFICATION OF THE SUBJECT--PURPOSES AND - QUALITIES OF INSTRUMENTS--WORKMANSHIP--METALS--ALUMINIUM--FRAMING-- - TOOLS--AXES OF INSTRUMENTS--SOLDERING--FINISHING--BRONZING-- - LACQUERING--GRADUATING--ENGRAVING--STYLE--GLASS-WORK--WOODWORK-- - LUBRICATION--PRESERVATION OF INSTRUMENTS--PACKING. - - -1.--=Historical Sketch.=--Although the aim of this work is to show the -state of the art it is intended to represent at the present period, a -large amount of literature, ancient and modern, has been consulted for -its production, principally with the object that the authorship, as far -as possible, should be given of the instruments described which have -come into general use. Many of these instruments have been brought to -their present state of perfection by small consecutive improvements -upon older forms. Therefore, it is hoped, a brief historical sketch of -the literature of the subject may be thought to form a fit introduction. - -2.--Land surveying was possibly first practised in Egypt, where -landmarks were liable to be washed away or displaced by the overflow -of the Nile. That it was also used otherwise is shown in that there is -extant in Turin a papyrus giving the plan of a gold mine of about 1400 -B.C. The earliest surveying instrument of which we have record is the -_diopter_ of Hero of Alexandria, about 130 B.C. This instrument appears -to have been a wooden cross, with sights to take right angles. In the -_astrolabe_ of Hipparchus, we have a divided quadrant of a circle -sighted from the centre. In Tycho Brahé's _Astronomica Instaurata -Mechanica_, 1598, we have descriptions and engravings of the astrolabe -of Hipparchus, Ptolemy, Alhazen, and of his own instruments. These all -embrace the principle of the quadrant, but the sighting of the star -or object with the instrument by movable parts is effected in various -ways. These instruments were made at first only for astronomical -observations; but they appear to have been applied, at a very early -date, with slight modifications, to topographical surveying. - -3.--In Thomas Digges' _Pantometrie_, 1571, we have several instruments -described for surveying purposes:--The geometrical quadrant is an arc -of 90°, with sights to the 90° radius, and a plummet from the radiant -angle to read degrees of elevation. The geometrical square, sighted -upon one edge, with an alidade centred from the corner from which the -90° radiate to take horizontal angles. In another instrument the two -instruments described above are combined. The theodolitus--the origin -of the theodolite, a word probably derived from _theodicæa_, taken -in the sense of perfection, as being the most perfect instrument. It -consists of a complete circle divided and figured to 360°, mounted upon -a stand, with a sighted alidade moving upon its centre and reading -across the circle into opposite divisions. An artificial horizon is -also described for ascertaining altitudes by reflection. - -4.--In 1624, Edmund Gunter, to whom science is indebted for the -invention of the slide rule, sector, and chain of 100 links, published -a work giving descriptions of the cross-staff, his improved form of -quadrant, with improvements on some other instruments. In 1686 we have -the first treatise on mine surveying, the _Geometria Subterranea_ of -Nicolaus Voigtel, published in Leipzig, in which we have the _hanging -compass_, still much in use on the Continent, described. Beyond this, -few improvements are recorded upon surveying instruments in the -seventeenth century. - -5.--Near the commencement of the eighteenth century we have a somewhat -important work, published in Paris, written by Nicolaus Bion, -_Constructions des Instruments de Mathematique_, 1718. This treatise -was translated into English by Edm. Stone, who made many additions to -it in 1723. It formed an important work in its day, and is excellently -illustrated. In this we find an account of the circumferenters, -plane tables, magnetic compasses, and other instruments then in use. -The next important work treating upon the subject is _Gardiner's -Practical Surveyor_, 1737. In this we have the theodolite much -improved and brought to nearly its present form by Jonathan Sisson, -but it was not, however, perfected until the introduction of the -achromatic telescope by John Dollond, about 1760. Gardiner gives also -a careful consideration of the best instruments employed generally -in the practice of surveying. Nothing from this time appears except -transcriptions and incidental descriptions of instruments in works on -surveying, until the publication of Geo. Adams's important _Geometrical -and Graphical Essays, Containing a Description of Mathematical -Instruments_, in 1791. In this work we have an able discussion of the -best surveying instruments then in use. It was much extended in later -editions by the descriptions of the great improvements made in the -construction of instruments by Jesse Ramsden, as also by the invention -of the box-sextant by Wm. Jones. The last edition carries the subject -well up to date at the beginning of the last century (1803). - -6.--In the last century no original work appeared on the subject till -F. W. Simms's treatise on _Mathematical Instruments_, 1834. This -small work is limited to descriptions of popular instruments for -land surveying and levelling. It was probably called hurriedly into -existence to supply a want at the commencement of the railway mania. -Another small popular work, by the late J. F. Heather, 1849, appeared -in _Weale's Rudimentary Series_. This was almost entirely compiled, old -and even then obsolete engravings being used. No work in the English -language, from an early date in the last century, is found to treat -the subject comprehensively, or to bring it nearly up to date with -the advanced work of our best opticians of the period at which it was -published. - -7.--In Germany we have recent works of an altogether higher order in -_Die Instrumente und Werkzeuge der hoheren und niederen Messkunst, -sowie der geometrichen Zeichnenkunst; ihre Theorie, Construction, -Gebrauch und Prufung_, by C. F. Schneitler, 1848; and a work upon -the larger instruments, _Die geometrischen Instrumente_, by Dr. -G. C. Hunäus, 1864. These works are original, and enter ably into -constructive details. The authors, however, do and mention, and were -possibly unacquainted with, many excellent instruments in the hands -of the British surveyor. As regards reflecting instruments, which -derive their first principles from Hadley's sextant, there is no work -in which these are treated so ably as that of the Italian, Captain G. -B. Magnaghi, in _Gli Strumenti a Reflessione per Misurare Angoli_, -1875. The consideration of these instruments is, however, in this work -more in reference to astronomical and nautical observations than to -surveying. - -8.--The important class of subtense instruments, the use of which was -first proposed by our countryman, James Watt, in 1771, and brought out -by Wm. Green in 1778, since reinvented in Italy by J. Porro, 1823, of -which we have a description in his work, _La Tachéomètre, ou l'Art -de lever les Plans et de faire les Nivellements_, 1858, is now in -extensive use on the Continent, and to some extent in America. Their -use is becoming more general in this country but they are not nearly -so well known as they should be. One of the first was Edgecombe's -little-used stadiometer, of which we have descriptions, without any -recognition of the optical correction always required to render this -instrument practical; and some descriptions of Eckhold's omnimeter, -given generally with an illustration of an early abandoned form of the -instrument. More recently we have the subject of subtense instruments -ably discussed in a paper by B. H. Brough, C.E., on "Tacheometry," as -it is termed, read before the Inst. C.E.s, 1887. - -9.--=Classification.=--The surveying instruments necessary to be -employed on any particular survey will depend, in a great measure, upon -the nature of the work to be performed. Thus, if it is for a simple -plan of an estate, the surveyor requires to ascertain the positions of -buildings and important objects, the internal divisions of the land, -and the surrounding boundaries of the estate, placing all parts in -their true horizontal positions and bearings in relation to the points -of the compass. If it is for a topographical survey of great extent, he -requires these matters in less detail, but, in addition to the above, -means of finding the true latitudes and longitudes, and the relative -altitudes of the parts of his work. If for a railway, a canal, or -water-works, he requires to ascertain, besides the general horizontal -plan, especially the altitudes of all parts of his work very exactly. -If it is for coast survey, he requires, besides the bearings, the exact -relative trigonometrical positions of all parts of the coast-line, as -also the relative soundings on the sea front. If for a mining survey, -he requires to ascertain, besides the horizontal plan, sections showing -the position and depths of strata, faults, veins, etc.; and, as the -work is principally underground, it is necessary that he should be able -to take his observations by artificial light. It becomes, therefore, -clear that special instruments can be adapted, more or less perfectly, -to these various kinds of work without that amount of complication and -of weight which would be required in any single instrument constructed -to perform many of the above-named functions. - -10.--Taking the subject in a general way, the instrumental aid of the -greatest importance in the work a surveyor has to perform is such as -will provide measurements of distances and of angles by which he may -be enabled to make a horizontal plan or map of the ground he surveys -to a measurable scale. The method employed to secure this object is -by taking linear measurements in certain lines to fixed positions, -or _stations_, as they are termed, and by taking angles in relation -thereto from such stations to prominent points of view, which may be -either natural or artificial objects. To obtain this end, he requires -means of measuring such lines, and some instrument that will take -angles of position in the horizontal plane, or, as it is termed, in -_azimuth_. - -11.--The instruments used in practice for measuring the complete circle -in angles of azimuth are the various kinds of theodolites, including -transits, omnimeters, tacheometers, circumferenters, also mining-dials -of various kinds, prismatic compasses, and plane-tables. Instruments -limited to measuring angles upon the plane, within a segment of -a circle, are sextants, box-sextants, and semi-circumferenters. -Instruments adapted to take certain fixed angles only are the optical -square (90°), the cross-staff (90° and 45°), the apomecometer (45° -only). The theodolite being a universal instrument, is used for taking -angles in altitude as well as in plane. The sextant is also adapted -to this. Circumferenters and mining dials are generally constructed -to measure altitudes less exactly than the theodolite. In extensive -surveys of countries a constant check is required by taking the -latitude and longitude, for which a good transit instrument is required -to take observations of celestial bodies, and a reliable chronometer. - -12.--Practically for taking altitudes for railway, canal, road, and -drainage survey, a telescopic level is used, either with or without -a magnetic compass. For topographical work and measurements of great -altitudes in extensive surveys, the theodolite, aneroid or mercurial -barometer, or boiling-point thermometer is used. In important surveys -of mountainous countries, all of these instruments are used, the one -as a check upon the other. For taking merely angles of inclination -of surface, angles of embankment or cutting, and dip of strata, a -clinometer of some kind is used. Some general details of construction -will be considered in this chapter before proceeding with the details -of the instruments mentioned above, and some particulars also which it -would be difficult to introduce hereafter. - -13.--=Qualities of Work.=--The qualities that instruments should -possess will be separately discussed, with the description of each -special instrument. It may be stated generally that much of the quality -of surveying instruments depends upon the perfection of the tools used -in their manufacture, but very much also depends upon the character of -the man who produces them--not only upon his intellect, but whether his -chief object is the perfection of his work, or the amount of profit he -can obtain from it. It is generally known in all branches, as a rule, -that the cheaper kinds of work, from the less care required in details, -secure the greatest profits. In the author's and some other optical -works, a completely fitted engineer's shop is employed to keep tools -in perfect order, make special tools, and produce the heavier class of -work, for which the engineer is better adapted than the mathematical -framer. It is also advantageous at all times to have at least one -skilled engineer, who is styled _the engineer_, in a workshop where as -many as fifty men are employed. - -14.--=Metals.=--The alloys generally used in the construction -of surveying instruments are brass, gun-metal, bell-metal, and -occasionally electrum or German silver, silver, aluminium, gold, and -platinum. These are required to possess certain qualities, and, where -the magnetic needle is used, to be perfectly pure or free from iron. -The certainty of copper alloys being quite free from iron is one of the -great troubles with which the manufacturer of magnetic instruments has -to contend when obtaining his castings from the ordinary commercial -founder. This has led the author, and some others in his line of -business, to cast their own metals as the only means of getting them -pure. Where the metal is had from the commercial founder, every part -of the casting should be carefully brought within the influence of a -delicately-suspended magnetic needle. If the slightest attraction be -found in any part of the casting it should be rejected. - -15.--=Aluminium=, from its much lower price of production than -formerly, and from its extreme lightness and freedom from tendency -to oxidation, except when exposed to sea air, as the presence of -common salt appears to completely decompose the surface, is now -recognised as a metal which may be used for the manufacture of parts -of surveying instruments. This metal, in its pure state, is too soft -and malleable to be used advantageously for many parts of these -instruments. It, however, appears to alloy with many metals, some of -which increase its hardness and stiffness without making its specific -weight more than one-third that of gun-metal, and without greater -liability to oxidation. The following alloys are now offered in -commerce:--Aluminium-nickel, al-chromium, al-tungsten, al-titanium. -These possess many distinct qualities, and may be found, under -judicious handling, useful for many parts of these instruments. There -is, however, from the fineness of grain of aluminium, even in its -alloys, a tendency to fret in surfaces exposed to friction. This can -be avoided in many cases by lining such parts with a suitable metal -without materially changing the general lightness of the instrument. -The author has devoted much time to forming and testing aluminium -alloys, particularly with nickel, but there is no doubt there is still -much to be learned of the alloys of this beautiful metal, as it is -still, comparatively, so new to manufacturers. The author has found -many difficulties to be overcome in obtaining fine solid castings, and, -as far as his experience goes, there are only very imperfect solders -offered for it in commerce. It therefore remains advisable to work up -all parts in the solid in this metal as far as possible, and where -there is risk of exposure to salt air to confine the aluminium alloys -to such parts of the instrument as may not be seriously injured by -surface oxidation. On the whole this metal is only recommended where -lightness is of more importance than durability. - -16.--The general object to be obtained in the distribution of metals -to the various parts of an instrument is to get good wearing surface -with solidity, and an even balance of the moving parts with moderate -lightness. In practice, such parts as can be thoroughly hammered, -drawn, or rolled in a cold state will form stiff, elastic, and -durable parts in brass. For the composition of this metal the author -uses copper ·69, zinc ·30, tin ·01. The tin is used in place of the -lead of the ordinary founder, and produces thereby a stiffer alloy. -For such parts as require stiffness, where sufficient hammering is -impossible, or the metal is in considerable mass, gun-metal should be -used. The author has found the best practical mixture for this--pure -copper ·88, tin ·12. For centres requiring great rigidity, as those -of the theodolite, level, or sextant, bell-metal is used by all the -best makers. This should be of such composition that it cannot be -permanently bent without immediate fracture. It should possess about -the hardness and stiffness of untempered steel. The best alloy the -author has found for the bell-metal for these instruments is copper -·83, tin ·17. If very small castings are made with this alloy they are -somewhat brittle, probably from the rapid cooling of the surface in the -mould, therefore, for small castings, a safer alloy is copper ·85, tin -·15. - -17.--In making all the above alloys, for the best results the metals -are assumed to be commercially pure. The introduction of a little -uncertain scrap, which the ordinary founder is so fond of using to make -his metal run down, will often foul a pot of metal. In all cases of -copper alloys the copper should be entirely melted before the addition -of the zinc or tin, after which it should be thoroughly stirred with -a charred stick or earthenware rod, and then be cast in small ingots, -to be re-melted and cast a second or, even better, a third time before -melting for the final castings. - -18.--=Workmanship.=--It would be quite impossible, within the limits -of this work, to give such particulars of the workmanship in surveying -instruments as to enable a person to manufacture them without practical -knowledge of the manipulation of the various branches of the art, -but it is thought that a general sketch of the various operations -entailed, which vary somewhat in different workshops, may be useful. -Some of these particulars may be also useful to the surveyor, not only -as general knowledge of the instruments he uses, but in some cases of -accidents and emergencies, and for the sake of keeping his instruments -in order when he is far away from the manufacturing optician. - -19.--=Framing Work.=--The ordinary turning and filing of metals, -and some knowledge of the workmanship of the business, are assumed -to be understood by those who may use this book for special -constructive details. The tools in a mathematical or philosophical -instrument-maker's workshop, where high-class work is done, nearly -resemble in every way those of a good engineer's shop, except that -on an average the tools are much lighter, and run at a higher -speed. Where the works are extensive, steam-power, a gas engine, or -electric-motors are used. In small shops the foot lathe is the only -important tool. There is a great advantage in using power for good -work, as the oscillation of the tool, which is always caused by the -action of the foot, produces what is termed a chatter upon the work. -For turning brass and silver, a high speed is desirable with a lathe of -sufficient rigidity to give no sensible vibration. A surface cut speed -of about 250 feet per minute should be aimed at. For turning gun-metal, -German silver, and mild wrought-iron, about 100 feet per minute is -required. For turning bell-metal and cast-steel, a very slow speed is -required--about 16 feet per minute. The lathe should therefore possess -means of ensuring these differences by back gear, overhead motions or -otherwise. - -20.--=Tools.=--The lathe of the most suitable construction for -surveying instruments has the upper surfaces of the bed, one side of -Λ section, and the other flat--not both flat as in many engineers' -lathes. This ensures the certainty that rests and other tools can -be firmly clamped down without possibility of lateral shake. The -slide-rest should have a broad base and be provided with direct -perpendicular and rotatory motions, with means of clamping the motive -parts not in immediate use, as smooth cuts can only be obtained on -copper alloys by perfect rigidity of all parts of the tools. The lathe -should also possess a bed-screw and overhead motions suitable for -applying flying cutters and milling-tools in every desired direction -upon the piece of work when it is once chucked in the lathe. _A -universal shaping machine_ and a milling machine generally replace -the planing machine of the engineer. These tools are sufficient for -producing the flat surfaces for all ordinary work. Even when power is -generally used, small hand planing and shaping machines, worked with a -lever, are very useful for working up single pieces and small parts. A -circular saw and a good grindstone are also indispensable. With good -rigid tools, well applied, very little work is left for the rough or -bastard file; on many instruments none whatever--only a little fine -scraping, superfine filing and stoning being required. - -21.--The greatest technical skill required in the manufacture of -surveying instruments is in the principal axes of these instruments, -particularly in theodolites, tacheometers, sextants, and some kinds -of mining dials, wherein a class of work is demanded which must be -performed by a skilful, experienced, and careful workman. The axis of -these instruments, as already mentioned, should be formed of a casting -of good bell-metal. This axis must be turned upon its own centres, -which should be drilled up sufficiently to keep a steady bearing, so -that the truth of the work is quite independent of any fault there -may be in the lathe. The turning must be performed with a point-tool, -the upper angle of which should be about 60°. This should be kept -constantly sharp, and be allowed to take only the finest possible cut -at a slow speed. The slide-rest should be set to the exact angle of -the taper of the axis. The socket, if it is not very stout, should be -placed in a massive metal box and embedded in plaster of Paris, which -must be allowed to set perfectly hard before use. The socket is turned -out, if possible, or otherwise it is roughed out with a hard steel -fluted cutter, and finally cut up by another fluted cutter which has -been carefully ground to the correct cone intended for the finished -axis. The axis is chambered back in its central part, so that it may -fit the socket for about from half to three quarters of an inch, only -at its extreme ends. After turning and boring as correctly as possible, -the axis and socket are ground together with soft oil-stone dust to -true form. After this, the surface is turned, or scraped entirely off, -with a sharp tool, and the axis is again fitted by rubbing contact -only. It is most important to be sure that no grit remains embedded -in the metal from the grinding, as this will be sure to work out and -abrade the axis afterwards. - -22.--The same care as is necessary to be bestowed upon the centres -of instruments, is required for tangent motion screws when these act -directly without counter springs. These should be made, if possible, of -hard drawn wire. They should be turned on their own centres, the cut -of the tool being extremely light to avoid flexure, all screws of over -1/8-inch diameter should be cut direct in a light screw-cutting lathe, -although it is advantageous to run a pair of dies lightly over them -afterwards to make the thread smooth, and ensure a perfect fit in the -nut. - -23.--=Soldering.=--Besides the tubes of instruments, all parts which -are difficult or impossible to be formed advantageously in a single -casting, are _hard soldered_ or brazed together where this will render -the part of the instrument more rigid than by screw attachment. The -pins of all screws should be made of drawn metal, to which the part to -form the milled head may be a casting. Hard soldering in this country -is now generally performed with one of Fletcher's gas blow-pipes, -the parts of the instrument, if large, being embedded in a pan of -charcoal. The author uses a pair of gas blow-pipes, taking the blast -of a centrifugal blower driven by an electric motor. These blow-pipes -are placed opposite to each other, so that the pieces being soldered -together are entirely surrounded by the flames projected from both -sides. The flames of the gas blow-pipe may, with this apparatus, be -reduced to mere points for small pieces. The solder employed for -ordinary work is fine spelter with a flux of ground borax. The most -convenient method of using this is to put about a quarter of a pound of -spelter and an ounce of ground borax in a saucer, and add sufficient -water to cover it. The borax and spelter may then be taken up together -with a small spoon and placed directly upon the clean part of the metal -which is to be soldered. With deep or difficult joints it is well to -soak the whole of the pieces an hour or so in a saturated solution of -borax before commencing the soldering. - -For soldering very small pieces, or for soldering steel to brass, -silver solder is better than spelter; it appears to bite the steel more -firmly and it runs at a lower heat. - -24.--=Soft Soldering=, or what is termed in the trade _sweating_, -should be resorted to as seldom as possible. It is necessary in making -attachments to drawn tubes, as the heat of hard soldering would destroy -the rigidity of the tube, due to the drawing processes. In this case, -where soft solder is employed, the tube should be, if possible, -surrounded by a band of solid metal, which forms a part of the -attachment, or the attached part should be well secured with screws, -tapped dry, before the soldering is commenced. Soft soldering on brass -is generally very deceptive; the solder may form a glaze round the -joint with no attachment within. Many surveyors will recognise this who -may have had one of the slop-made soldered-up levels fall to pieces in -their work by a simple jar accidentally given to the instrument. - -25.--=Finishing= mathematical work: the surface as it leaves the -superfine file is brought up by cutting it down to a mat with Water of -Ayr stone, and finally clearing with soft grey slate-stone. - -26.--=Polishing.=--Where brightness is desirable, particularly for -steel work, wash-emery and French polishing paper are used. Heads of -screws and small turned parts are better finished off by a clean cut or -with the burnisher on the lathe. - -27.--=Optical Black.=--The interior parts of telescopes are painted -over with a dull black paint, the object of which is to cut off the -reflection of extraneous light entering the object-glass obliquely. -Optical black is made by finely grinding drop-black in turps or spirits -upon a stone with a muller, this is afterwards strained through fine -muslin; if it is ground in turps a little good gold-size is added; if -in spirit, a little spirit varnish. The black should be tested. It -should appear quite dull, and yet be sufficiently firm to bear the -finger rubbing upon it without soiling. For eye-pieces, the dull black -generally employed is due to oxidation obtained by burning off an acid -solution of cuprous-nitrate in a gas flame. - -28.--=Bronzing.=--For the protection of finished metal work in -surveying instruments the surface is generally _bronzed_, as it is -termed, leaving bright only such parts as are required to be easily -seen, such as milled-heads, heads of screws, etc. The dark gray of the -bronze is also much more pleasant to the eye than a bright surface, -particularly when out in the sunlight, so that bright instruments have -gone nearly out of use. The bronzing is effected by the application -of a liquid that will corrode the metal and, at the same time, -leave a dark pulverent deposit upon it. There are a great number of -bronzes to be had, but that which the author has found to be the -most permanent and safest from after corrosion is platinic-chloride, -dissolved in sufficient water. This bronze is well known, but is -not used so frequently as it should be from its great expense. The -bronzes which are to be particularly avoided are those containing -mercuric-dichloride. These are very cheap, and they give a fine dark -surface; but they are certain to rot the brass and produce a pitted -or spotted appearance after the instrument has been much exposed. The -bronze, whatever kind is used, is put on with a brush upon the surface -of the metal, which must be quite clean to receive it. After the -colour is well brought up by passing the brush over the work several -times, the work is then thoroughly gone over with a hard brush and -fine black lead until every trace of free corrosive liquid is removed, -as far as possible, from the surface, and the work is left quite dry -in all parts. Some makers put a thin coat of asphaltum, dissolved in -turpentine, over this, which produces a light black surface. Some, -to save trouble and expense, simply paint the instrument with black -varnish without bronzing. This looks very smart at first, but the black -is very liable to chip off in use and make the instrument unsightly. - -29.--=Lacquering.=--All parts of instruments intended to be left -bright, as well as all properly bronzed parts, are separately -covered with a thin coating of _lacquer_, the application of which -is technically termed _varnishing_. The metal is raised to an equal -temperature of about 200° Fahr., and the varnish is applied with a -fine, flat camel-hair brush. The process requires considerable skill, -so that only a few workmen do it to perfection. Special varnishes are -made for the philosophical and mathematical instrument trades, all of -which have a base of fine shellac, dissolved in absolute alcohol. - -30.--=Engraving= of figures, words, etc., where there is much -repetition, is best done by the engraving machine--general work by the -ordinary skilled engraver. - -The method employed for the graduation of instruments will be -considered further on in the discussion of instruments reading with a -vernier scale. - -31.--=Style.=--This must, of course, depend upon the taste of the -manufacturer. In modern machinery, and in scientific instruments, there -is a strong tendency to avoid all useless mouldings or ornaments, and -to finish all parts of the work uniformly with clean smooth cuts. In -surveying instruments which have to be handled, it is desirable to -avoid angles as much as possible, both by form and by rounding off -all corners neatly, so as to produce a general feeling of smoothness -over the whole instrument; useless metal, as, for instance, in milled -heads of screws, should be hollowed away to avoid weight, and this -object should be observed in the general distribution of metal, never -neglecting at the same time to insure the firmness of the instrument. -Parts shaped out of the solid may be made much lighter than when -screwed together in separate pieces and are of greater rigidity, and -admit of better style. The leading makers all have a style of their -own, some more graceful than others; most of the smaller makers make -bad copies of these designs. - -32.--=Glass-Work.=--The most important technical work, except perhaps -the graduation in surveying instruments, is found in the optical parts, -of which only a brief description can be given. The glass used for -the lenses, particularly for the achromatics, is that manufactured by -Messrs. Chance Bros., of Birmingham, or by M. Mantois, of Paris, both -of which firms use the process discovered by Guinard, of Solothurn, -in Switzerland, which was afterwards much improved by Geo. Bontemps. -This glass is nearly white and transparent, of uniform density, and -free from veins and striæ. It is also perfectly annealed, which is -important. The following kinds of glass are usually employed for the -object-glasses of surveying instruments:-- - - +------------+---------+-----------------------------------+ - | | | | - | | | Index of Spectrum Lines. | - | |Density. +--------+--------+--------+--------+ - | | | | | | | - | | | C | D | F | G | - +------------+---------+--------+--------+--------+--------+ - | Hard Crown | 2·485 | 1·5146 | 1·5172 | 1·5232 | 1·5280 | - | Dense Flint| 3·660 | 1·6175 | 1·6224 | 1·6348 | 1·6453 | - +------------+---------+--------+--------+--------+--------+ - -These particulars are given by the glass-makers who supply the glass. -For cheapness the optical crown-glass is often replaced by common -plate-glass. A specially clear and hard glass is made by Shott, of -Jena, but early specimens of this glass did not appear to stand -climatic influences. This defect is now remedied, and the glass is very -pure in body, but not free from air-bubbles. - -33.--Two _pairs_ of tools are used for glass-grinding for every curve. -These possess two spherical surfaces, one of each pair resembling a -shallow basin, and the other, of the same diameter, fitting into this. -After turning the tools they are ground together, and are afterwards -kept in order by constant regrinding together. These tools may be of -cast-iron or brass. The working surface of the tool is, of course, of -the reverse curvature to that of the glass to be ground in it. When -the glass is ground by hand, each tool possesses a screwed socket by -which it can be screwed to a stump or post, fixed in the ground, or to -a short knob-handle to be used as the upper tool by hand. For working a -glass, or several glasses, it or they are cemented upon a hand tool or -holder, which is of less curvature than the working tool. The working -is performed by rubbing in a straight alternately with a circular -direction, with a certain stroke difficult to describe, at the same -time walking round the post to reverse all positions. The grinding is -continued over the spherical tool until the surface of the glass is -brought up to its curvature, being supplied at first with coarse emery, -60-hole, which is kept in a very moist state, and afterwards with finer -emery, 100-hole, and then by eight or ten still finer grades, carefully -washing off between the processes, and reserving the mud most carefully -for wash-emery, which is used in completing the grinding. Where -machinery is employed, hand motions are imitated as nearly as possible -by the motion of the tools, particularly for the forming processes. - -34.--_The wash-emery_ is formed of particles which are held suspended -for a minute or so when the mud is stirred in a large vessel of water. -This water is drawn off for final settlement to form the wash. The -final grinding with the wash is continued until the emery appears jet -black on the surface of the glass, which has then a semi-polished, -almost metallic, lustre. - -35.--_Polishing._--This is performed in various ways, generally moist -cloth is placed over the tool. The better way is to cover the polishing -tool with patches of hard pitch, which are made to take the form of the -hand tool by having the fellow tool to that used in working pressed -upon the surface while the pitch is still warm, using a sheet of moist -tissue-paper to prevent adhesion. The polishing is effected in the same -manner as the grinding, but with peroxide of tin (putty powder), or -rouge. - -36.--The great difference in the value of achromatic lenses depends -upon the truth of the curvature due to the accuracy of the tools and -the continuity of the grinding processes until a perfect surface is -produced before polishing, so that a given lens may have treble the -labour bestowed upon it to one of inferior quality in the grinding -only. Beyond this its ultimate perfection will depend much upon the -polish. - -37.--It may be well here to note how this may be observed. A good test -is to throw the shadow of a thin object, as that of a piece of wire -upon the surface obliquely. This should show clear edges when the lens -is changed to all positions for reflection. The test of polish is -really only the test of brightness of the surface of the glass, which -may be distinguished in many ways that will readily suggest themselves. -The importance of the perfect grinding is that to which attention is -desired to be drawn. - -38.--_Centring--Figuring and Testing._--After the above described -processes, the glass is centred by grinding off the edges until its -axis is exactly central with the periphery, so that it can be mounted -in its cell. It is then tested for figure. The technical difficulties -of figuring are too great to be discussed briefly in this treatise; -much of this work is performed by the skilled workman in the manner he -works his tool and applies his grinding and polishing material, every -stroke giving a slightly different figure. Some method, however, may be -given of _testing_, which will be useful in estimating the quality of a -lens, irrespective of its manufacture. To test the objective it may be -mounted in its telescope and focussed upon a star, or more practically -in workshops, upon the reflection of the sun as this is seen in the -mercury of a small bulb of a thermometer placed conveniently on a -black background at as great a distance as it is clearly visible in -the telescope--a common distance is 20 feet. The telescope is made to -traverse the sighted object so as to cross the field of view. If the -focus under this test remains constant, so that the image of the sun -in the mercury bulb appears sharp and without colour, the objective is -fairly corrected. Further information on this subject may be gained -from a very important paper read by Sir Howard Grubb, the eminent -optician, before the Royal Institution.[1] - -39.--=The Woodwork of the Stands= of instruments made in this country -is generally of straight-grained Honduras mahogany. For occasional work -the mahogany is better if seasoned for three or four years in boards -which are cut to thicknesses increasing by quarter inches, so that -about the thickness of the finished work in one dimension may be used. -Where a number of stands of constant dimensions, as for ordinary -theodolites and levels, is required, it is better to cut the mahogany a -little over finishing size directly from the fresh log, and then allow -it to season three or four years. In this manner any natural warp of -the wood takes place before it is worked up, which causes it to stand -well afterwards. - -40.--=Lubrication of Instruments.=--For the lubrication of all screws, -good watch oil should be used. Where this cannot be obtained, salad oil -filled up in its bottle with fresh-cut shavings of lead will produce -a perfect oil free from acidity. For working centres and collars, a -grease is better--that extracted from pork fat, by leaving it in the -sunshine, answers very well, but what the author has found best for the -purpose is pure vaseline. This keeps its greasiness, and appears to be -perfectly non-corrosive. For the collars of tangent screws, a mixture -of tallow, wax, and soap is employed. This mixture does not fret out -to cause a bite upon the surfaces. As the instrument-maker leaves the -working centres of instruments they will generally perfectly maintain -their lubrication for four or five years, and it is not well to disturb -them; so that this note may be considered only for the restoration of -old instruments to order, or for cleaning them up generally, which is -nevertheless best done by skilful hands. - -41.--=Preservation of Instruments.=--Instruments that have by any -accident become splashed, or dirty by exposure to rain and dust -or otherwise, may be washed with damp wash-leather. If a piece of -soft, dry leather be afterwards moistened with a little linseed-oil, -and this rubbed over the instrument when it is quite dry, it will -restore the original brightness, and tend to preserve it. For wiping -object-glasses some prefer a piece of clean old linen, others an old -silk handkerchief; either will answer if kept quite clean. If the -glasses are only dusty, the application of a soft camel hair brush is -all that is necessary, and this is quite safe from carrying grit. If -glasses are stained by slight corrosion, this can be partially removed -by clean spirit. In replacing glasses, it is important to observe that -the notch marks, if any, on the edges of the glass agree, and that the -double-convex lens is placed outwards in the telescope. - -42.--=Packing of Instruments.=--This is really a very important matter -seldom estimated at its proper value. An instrument should lie or -stand in its case in such a manner that its most solid parts only -take the bearing surfaces, and thus perfectly secure it. When this is -effected there should be no possibility of an exceptional jar on any -delicate part from the jolting of the conveyance of the instrument. -Great care should be taken to note how the parts of the instrument were -originally arranged by the packer, and this arrangement should always -be followed in replacing the instrument in its case to its position, -into which it should fall with perfect ease. Instruments are frequently -strained by being placed wrongly in their cases. Even with all these -precautions, the wood of the case may shrink or warp to a certain -extent, particularly in tropical climates, so that the instrument may -be exposed to external pressure from closing the case or otherwise, -so as to injure it or to spoil its adjustment. In such cases it is -better to examine the packing occasionally, and, if the case does not -easily and perfectly close, there is a risk that the instrument is -being strained. If this is the case, assuming the instrument to be in -its correct position, the bearing surfaces should be lowered with the -penknife or other tool, so that it is just free, but not to shake. -The author was the first to place a piece of cork under each bearing -surface. This gives a certain amount of elasticity, with sufficient -rigidity for support, to preserve the instruments from injurious jar, -and it may afterwards be cut away more easily with the penknife than -wood. - -43.--With complicated instruments there are always a number of loose -pieces which are used occasionally upon or with the instrument. These, -for compactness of packing, are often placed one above the other, and -are liable to get astray. It is very desirable that complete parts -should be arranged, as far as possible, to go into their cases in -any state of adjustment,--this is, however, not always possible. As -a rule, before putting an instrument or any portions of it by, all -movable parts, such as the telescope, eyepieces, etc., should be closed -in their closest form. Parallel plates should be left square to the -instrument, with the screws loose. Generally the packer leaves little -liberty. Instruments are often packed so that they will go into their -cases only just in one state of adjustment, and in one position of -the movable parts. In this case, great care must be taken at first in -examining the position in which the instrument and its parts arrive -from the maker. The late M. Gavard, of Paris, who was celebrated for -his delicate pentagraphic instruments, and to whom the writer owes many -useful hints, put initial letters on the parts of his instruments, and -placed printed labels on the parts of the cases where these should go. -Mr. Hennessey, First Assistant in the great Trigonometrical Survey of -India, gives some excellent notes upon the subject of packing in his -_Topographical Instructions_ for the use of the Survey Department. -He recommends upon opening a case that a sketch should be made of -the contents as they lie, and all possible particulars should be -recorded; but his most useful hint is, always to replace an instrument -gently, and in no case to use force if the instrument will not fall -into its place. Unless the packings have been damaged in some way, -the instrument will go easily into its case, and if it does not, it -shows that some part is not in its proper position, and this must be -carefully looked into to avoid injury. - -44.--=Leather Over Cases.=--For an instrument for use in the field it -is better to have a solid leather case over the ordinary mahogany one. -This acts as a kind of buffer, and takes off the jar of an accidental -blow upon the case, which might otherwise injure the instrument. It -also protects the mahogany case from the warping effect of direct -sunshine and rain, and closes the meeting-joint to keep out the dust. - -Solid leather cases are also general for all light instruments, -rendering a stiff case of wood or pasteboard unnecessary. These admit -most perfectly of straps being placed conveniently to adapt them to the -person for carrying. - -=Waterproof Covers.=--In very rainy climates a waterproof cover for -a delicate instrument is desirable. This can be thrown over the -instrument instantly in case of a sudden storm, and the instrument left -ready for continuing the work when it clears up. - -FOOTNOTE: - -[1] _Proc. Royal Institution_, vol. xi. p. 413. - - - - -CHAPTER II. - - THE TELESCOPE AS A PART OF A SURVEYING INSTRUMENT--GENERAL - DESCRIPTION--QUALITIES--OPTICAL PRINCIPLES--REFRACTION OF - GLASS--LIMIT OF REFRACTION--REFLECTION--PRISMS--LENSES, - CONVEX AND CONCAVE--ABERRATION--FORMATION OF IMAGES--DISPERSION-- - ACHROMATISM--CURVATURE OF LENSES--TELESCOPES--EYE-PIECES--POWERS-- - DYNAMETER--CONSTRUCTION OF THE TELESCOPE, DIAPHRAGM--WEBS--LINES-- - POINTS--PARALLAX--EXAMINATION AND ADJUSTMENT. - - -45.--=General Description of the Telescope.=--This instrument forms -part of the theodolite, level, some kinds of miner's dials, sextants, -plane tables, and other surveying instruments. For this purpose it is -made of similar construction to that of the refracting telescope used -for astronomical purposes. The great object desirable in the telescope, -when used as a part of a surveying instrument, is that it shall assist -vision in obtaining the true direction, or pointing to the position of -an object in such a manner that it can be employed to ascertain the -angular position of two or more objects in relation to the position of -the centre of the instrument upon which it is fixed; also to obtain -relative altitude to this centre in relation to a distant station by -the reading of a divided measure or staff placed thereon. - -46.--The qualities desirable in a surveying telescope are, that -sufficient rays of light may be collected from the object observed -for it to be clearly seen as a whole, and in some cases that -sufficient magnifying power should be available, in order that -details or divisions painted upon a staff may be sharply defined. The -amount of light received by the eye which is effective in producing -distinct vision is in proportion to the extent of active surface of -the object-glass converging the light rays. The magnifying power is -regulated by the sum of the convexities of the lenses of the eye-piece -upon principles to be explained. The surveying telescope is required to -possess only a very limited field of view, but very great focal range, -so that objects may be seen at any distance. - -By the necessary optical arrangement of the telescope, which will be -further described, the object observed is generally _inverted_. This -inversion of the _image_ as it appears, at first presents a little -difficulty to the learner, but in practice this soon becomes so -familiar as not to be even recognised mentally. - -47.--=Optical Principles involved in the Telescope.=--To commence with -the optical construction of the telescope, that this may be thoroughly -understood, it is necessary to give brief details of some first -principles upon which it is constructed, assuming that optics have not -been made a special subject of study. - -48.--=Refraction of Glass.=--The properties of a lens depend entirely -upon the fact that a ray of light passing from air obliquely into -the surface of a dense transparent medium (in this case of glass) -and equally from the glass into air is bent, or, as it is termed, -_refracted_, to a certain angle at the surface of contact of the air -and glass. The ray of light entering the glass is termed the _incident -ray_, that proceeding from it the _emergent ray_. - -49.--There is no known medium, glass or other, which refracts a ray -of white light at one uniform angle. The white ray is universally -separated upon refraction, or _dispersed_, as it is termed, into rays -of all colours of the rainbow. In considering refraction, therefore, -in its simplest aspect we are compelled to take the refraction of one -uniform ray which is distinguished by one colour, that forms a part -of the white ray, as for instance the red, yellow, green, or blue, -that is, a _monochromatic_ ray, as it is termed, which gives a sharp -refraction of its own coloured light only in its ray. Incandescent soda -produces monochromatic rays, but in practice an intense flame behind -a bright-coloured glass will answer the same purpose, as the coloured -glass may be arranged to absorb all, or nearly all, parts of the white -ray, except that of its own colour. - -50.--Every transparent medium has a special quality of refraction. -Therefore, different kinds of glass refract in different degrees -within certain limited angles which will be hereafter considered. The -refraction is uniformly in the _plane containing the incident ray, -and the perpendicular to the surface separating the two media_. Every -medium refracts monochromatic light equally according to the following -law for any angle of refraction:-- - -_Whatever the obliquity of the incident ray may be, when it passes from -a rarer to a denser medium the ratio which the sine of the angle of -incidence bears to the sine of the angle of refraction is constant for -any two transparent media._ - -51.--The natural law by which the power of refraction of any medium -may be shown, and consequently the magnifying power of a lens in the -ratio of its curvative through this refraction may be exemplified, is -illustrated by the diagram on the following page (Fig. 1). - -_PP′_, a line perpendicular to the surface of the plane of the medium -(glass) with air above it, a ray of light would pass directly _P_ to -_P′_ through the glass surface _SS′_ without refraction, and so for -all perpendicular incidences or emergences. By this perpendicular line -_PP′_, termed the _normal_, all refractions are measured. The incident -ray _I_ to _C_ is refracted to _R_. Then if we call the angle _ICP_ -_I_, and the angle _RCP′_ _R_, it is found by experiment that the -perpendicular from _I_ on _PP′_ (or sin _I_) bears a certain proportion -to the perpendicular from _R_ on _PP′_ (or sin _R_) according to the -density of the glass. This proportion is generally expressed by the -formula--sin _I_ = µ sin _R_. Another incident ray _I′_ to _C_ would be -refracted to _R′_, and using similar notation to the above we have sin -_I′_ = µ sin _R′_, and from this it follows that (sin _I_)/(sin _R_) = -(sin _I′_)/(sin _R′_) = µ, which is called the _index of refraction_. -Thus, if in a certain glass the sine of I measure 3 equal parts on any -scale of length, and the sine _R_ 2 parts on the same scale, the _index -of refraction_ of this glass would be 3 divided by 2 or 1·5. - -[Illustration: Fig. 1.--_Diagram of Refraction and Reflection._] - -If the above process be reversed, and the ray of light _R_ be refracted -on passing _from_ the glass to the air, it will be projected to _I_ in -the emergent ray, and follow the same law as that given above. - -52.--=Limit of Refraction--Reflection.=--The sines to the angles _ICP_ -and _I′CP′_ being constantly greater in proportion to the obliquity -in the case of glass we are considering by 1/3 than the sine of the -angles _RCP′_ and _R′CP′_ of the rays of incidence thrown upward -upon the surface _SS′_, it will be seen that at a certain angle or -that in which the sine is 2/3 the radius, namely, 41° 48′ 37″, the -equation given above makes sin _I_ = 1 its maximum value; therefore, -at any angle of incidence greater than this, the sine of refraction -to continue in proportion would exceed the radius--an impossibility. -The refraction, if possible, would carry the ray into the substance -of the glass. This is therefore called the _critical angle_ or _angle -of total reflection_. At this point we may consider what must happen. -By our rule, refraction must cease at the angle refraction becomes -impossible by increase of sine, and as light cannot be extinguished in -a transparent medium it must be _reflected_. Thus the ray _r_ cannot -be refracted in the proportion according to the rule given for sine -_I_ to sine _R_, as this would exceed the greatest sine, that is _SC_ -the radius, this ray will therefore be _reflected_ at the surface -from the point _C_, and pass in the direction _r′_. This property of -refraction, continuing, as it were, into reflection, is made use of in -many instruments. - -53.--It may be worthy of repeating, as it is a mistake occasionally -made by persons designing instruments for special purposes (as -telemeters), that the refractions are not equal for varying angles of -incidence, but only, as before stated, in the ratio of the sines. Thus -there is no refraction _P_ to _P′_ a certain refraction I to R, and a -greater refraction _I′_ to _R′_, the refraction constantly increasing -with the angle of incidence. - -54.--_The Reflection of Light_ follows a very simple law, viz.:--_The -angle of reflection of a ray of light from a reflecting surface is -equal and opposite to the angle of incidence upon it._ Thus, in Fig. -2, let a ray of light _IA_ fall upon the reflecting surface _SS′_ at -30° of inclination to this surface, then this ray will be reflected -from _A_ to _R_ at the angle _RAS′_, which is also 30°. If an object be -at _O_, and the eye at _I_, then the object will appear as though it -were at _O′_, as the eye only recognises the object in the direction -from which it actually receives the light. The apparent angle _S′AO′_ -is equal to _IAS_, so that the point of a mirror from which an object -reflected is received is in direct line between the eye and the -apparent object. This observation will be found useful in placing -mirrors. - -[Illustration: Fig. 2.--_Diagram reflections from a plane._] - -[Illustration: Fig. 3.--_Reflection from a prism._] - -55.--_Prismatic Reflection._ The same law as given above applies to -internal reflection from glass. Let Fig. 3 represent the section of a -prism _ff′_, two plain surfaces of glass at right angles to each other, -and the third side making an angle of 45° with each of the other two. -The ray _i_ will therefore pass perpendicularly through the plane _f_ -without refraction to meet the plane 45° and the angle of reflection, -being equal to the angle of incidence, will leave this plane at 45°, -and reach _r_. The angle of glass here given of 45° being greater than -41° 49′, its extreme angle of refraction, the internal reflection will -be therefore perfect. - -56.--_Prismatic Reflection_, as this is termed, is largely used in -optics in preference, where practicable, to open reflecting surfaces, -from the certainty of keeping the reflecting surface clean; as dirt -exterior to the reflecting surface of the prism does not affect the -internal reflection in any degree. - -57.--The reflection is shown for clearness from the plane (Fig. 2) as -it actually occurs, or as it is measurable, independent of theory. -In optics it is found much more convenient to take the reflection in -relation to an imaginary line drawn perpendicular to the plane. In -Fig. 4 _NA_ is termed the normal. Taking the angles as before as 30° to -the plane, the optical expression of this would be 60° to the normal, -and the reflection of the incident ray _IA_ to _R_ would be in the -angle _IAR_ 60° + 60° = 120°, the amount the incident ray is deflected -from its former course. This principle is important to be understood -in the construction of the sextant and other reflecting instruments. -In reflection the ray is found to follow the shortest path,--that is, -the path _I_ to _R_ by reflection is shorter in the lines _IAR_, placed -at equal angles to the normal, than it would be by any other possible -path. As, for instance, it is shorter than _IaR_, shown by dotted lines. - -[Illustration: Fig. 4.--_Measurement of angle of reflection in optics._] - -[Illustration: Fig. 5.--_Diagram illustrating the principle of the -lens._] - -58.--_Passage of a Ray of Light through a Prism or a Lens--Convex -Refraction._ If we comprehend the law of refraction exemplified above, -art. 51, the path of a monochromatic ray through a prism or a lens is -easily determined, taking into consideration the refraction index of -the glass. In Fig. 5 let _a″a‴_ be the base of an equilateral prism, -which base may also represent the axis of a lens linear or parallel -with the direction from the centre of the eye to _O_. Now, if a ray -of light pass from a small luminous object at _O_ in the path _a′_ to -the prism, we may assume all other parts of the prism covered, and -the refraction of the glass be such that the ray will pass through -it from this position in a horizontal direction, or that parallel to -the assumed axis _a″a‴_, then the same ray will pass through the -prism to equal distance from the centre of the prism,--that is, to the -position of the eye shown by the ray continuing in the path _a_, the -angles to or from the prism being equal; so that if we cover up all -parts of this prism except a line parallel with its base joining the -ends of the lines _aa′_, where it is shown passing through the prism, -any ray of light from _O_, under the conditions given, will appear as -a spot of light on the plane parallel to the base of the prism; or if -we place our eye at the position shown, we shall see the image of the -light _O_. If we take a prism of the same kind of glass, but of less -angle, whose base is _b″b‴_, the refraction would then be less (that -is in the ratio of the sines), that is if the ray pass through the -prism at less distance from the base, so that the ray _Ob′_ would pass -through horizontally as before, and emerge from the prism in the path -_b_, also with equally less refraction, so that the ray would reach the -eye at the same point as the more refracted ray. In like manner, if the -prism were of still less angle with base _c″c‴_ and pass through the -prism at a lower position, the refraction would be proportionally less, -and therefore reach the eye at the same point. - -59.--If we take the half lens shown in section in the figure, this may -be considered to touch the surface of the prisms described tangentially -in the lines _a″a‴_, _b″b‴_, and _c″c‴_, where the angles -of contact of _O_, _a_, _b_, or _c_ upon the prism would be equal -to those upon the lens for an infinitely small extent of surface. -Therefore, if we make the lens of such form that a ray of light may -pass from any single point upon the line of its axis, and be refracted -by every point of the surface of the lens to a single point or focus -on the opposite side of the axis, such form would be a perfect lens. -For simplicity of demonstration the refractions given above are made -parallel with the axis of the lens. This parallelism could only occur -with the object and the eye at equal distance from the centre of -the lens, and with this distance also proportional to the amount of -refraction of the glass used in the construction. If the rays were all -parallel to each other upon incidence they would still be bent in the -same ratio (to the sines of the angles of contact and departure), and -this would bring the focus nearer to the glass; but it is evident the -same principles would hold. - -60.--As regards the action of the eye in this matter, it can only -recognise the direction from which it receives the light, and not the -processes the rays may have undergone before reaching it. Therefore the -ray proceeding from _O_ in the path _b′_, passing through the lens or -prism and emerging in the path _b_, is recognised by the eye as the ray -_b_ only. So that the point of light _O_ appears visually as proceeding -from the direction _bs_, and this convergence or expansion of the point -_O_, with its coincidence from the opposite side of the lens, produces -the effect of magnification of the object represented by _O_. - -61.--=Concave Refraction.=--In Fig. 6 a convex lens is shown in which -the parallel rays _L_ are drawn to a focus at _F_ upon the principles -just demonstrated. If the lens were made _concave_, as shown in section -Fig. 7, by the same principles of refraction, it is evident that the -rays would _diverge_, as the refraction bends the ray uniformly towards -the thickest section of the glass. If two lenses are brought together, -one with convex face, and one of the same radius of curvature, but -with concave face, the rays in passing through would not be refracted. -In this case the lens would be said to be _corrected_. A convex lens -has a _focus_ where the rays converge. A concave lens is said to have -a _negative focus_ equal to the focus of the convex lens, that will -correct it, or make it equal, as regards refraction, to plane parallel -glass. - -[Illustration: Fig. 6.--_Diagram convex lens._] - -[Illustration: Fig. 7.--_Diagram concave lens._] - -62.--_Spherical Aberration._--If the surfaces of convex lenses are -truly spherical, it is found, by an analysis too complex to be -described in this work, that the rays which pass through at different -distances from the axis converge to slightly different points of -distance. This subject was at one time seriously discussed for the -proper formation of objectives for telescopes; but at present it is -entirely neglected by the optician, as it is found practically to be -as difficult to make a lens truly spherical as one of the convergent -or divergent form required under the special conditions present. The -spherical form, as it is approximately produced from the grinding with -spherical tools, being always nearly correct, the correct forms of -object-glasses are made by _figuring_, which has been already referred -to, art. 38. In eye-pieces the spherical aberration would cause some -confusion were the glasses not adjusted in such a manner as largely to -prevent this. - -63.--_The Formation of Images by Refraction from a Convex Lens._--If -we take any double convex lens, as that shown in section Fig. 6, we -find, if it is held towards the sun at a certain distance from a solid -surface, we form a burning-glass,--that is, we produce an _image_ of -the sun where his rays of light and heat are refracted by the whole -of the surfaces of the glass. The distance from the centre of the -lens to the point of greatest light is called the _solar focus_ of -the lens,--that is, the point at which it concentrates or converges -parallel rays, and forms the image of the sun. With parallel rays -from the sun, the distance of focus is less than if these rays were -divergent in any degree. Consequently the _solar focus_ is less than -that subtended by any object on the earth. - -[Illustration: Fig. 8.--_Diagram of the convergence of rays of light._] - -64.--In the diagram, Fig. 8, a candle-flame at _acb_ forms its focus -at _a‴c‴b‴_, where all rays converge to form an image in the -following manner:--Every point of the candle throws its light upon -every point of the surface of the lens, and, therefore, throws the -image of each point to its focal position behind the lens, according to -the direction of its refractions; so that, if we take all the separate -points of light thrown from the candle, we then have a perfect image of -it formed by an infinite number of separate focal points, and as the -rays by their direction necessarily cross over the axis the image is in -an _inverted position_. - -65.--The whole of these lines would form a confusion if shown in a -diagram. We may, therefore, take for illustration the exterior of a -cone of rays proceeding from three points only. Thus the _clear_ lines -_aa′_ and _aa″_ from the point of the flame would refract to the lower -part of the image _a‴_. The _dotted_ lines _bb′_ would proceed to the -upper part of the image, as shown by the continuation of the _dotted_ -lines to _b‴_, whereas the central _dash_ lines _c′c″_ would form -their images in the centre following the dash lines to _c‴_, and -thus, from the number of luminous points, the whole image of the -candle would be produced at the foci _b‴c‴a‴_ in an inverted -position. - -66.--_Dispersion of Light._--The conditions stated above for refraction -of monochromatic light would not answer for perfect vision, which is -only possible in clear white light. It therefore becomes necessary in -practice to correct the quality of _dispersion_ which light suffers -in refraction through any dense medium. The evidence of dispersion by -glass may be shown by a prism, as in the following diagram:-- - -[Illustration: Fig. 9.--_Diagram showing chromatism of light by the -prism._] - -67.--In Fig. 9 let _P_ represent the section of a prism of glass, -covered except at the narrow opening _a_. Let a strong light, as shown, -be covered, except from a narrow slit, then the ray from the light, -refracted from _a_ towards _a′_ in the prism, will be dispersed or -split up at _a_ into the colours of the rainbow, shading from blue, -green, and yellow, to red, within the prism. Upon emergent refraction -at _a′_ this dispersion will increase so that an image of the slot near -the light, if thrown on a plane proceeding from the base of the prism -to the right, will be represented at _BGR_ by a prismatic or _chromatic -spectrum_, as it is termed, shading off from blue to green, yellow, red. - -68.--_Achromatism of the Prism in the same Quality of Glass._--Taking -the prism, Fig. 10, _C_ as before, and applying a second exactly -similar prism _C′_ reversed upon the face of the first--then at every -part of the process of dispersion from a point of white light under -diffraction into the first prism, will by equal diffraction, in passing -through the second prism, be brought _to a point_, where it will issue -a white ray at the point _a″_, as it entered at the point _a_; or, -practically, the emergent ray will be achromatised. This principle -must be followed in the manufacture of achromatic lenses, although -under various indices of refraction and dispersion from differences -in qualities of glasses. It is made use of in the achromatism of -eye-pieces, and in combinations, and assures the achromatism of -parallel glasses used for sextants under different angles of incidence. - -[Illustration: Fig. 10.--_Diagram perfect achromatism._] - -69.--=The Achromatic Lens.=--The achromatism of a pair of lenses by -which a large amount of refraction of pure white light is obtained, -depends upon differences in the qualities of glasses which are due to -their density and chemical composition, so that in one glass a less -amount of dispersion is produced at an angle which gives an equal -amount of refraction than in another. The combinations of glasses in -use are crown and flint, as already described, art. 32, the crown being -a light glass of soda and silica, the flint being a heavier glass -containing silica, potash, and lead. In a certain kind of flint glass -used for optical purposes, for a prism giving only slightly greater -refraction than one of crown glass, the dispersion is about double. -Therefore, we may combine a pair of glasses so as to obtain a desired -amount of refraction from the combination if we make the crown glass -refract something over double the amount we require for the perfected -lens or prism, and diminish this quantity by the reverse refraction of -the flint glass, thereby correcting the dispersion, as may be shown by -the diagram on this page. - -70.--In fig. 11 let _C_ be a prism of crown glass giving over double -the amount of refraction to a prism of flint glass _F_, but only of -total dispersion equal to the thicker crown glass. The compound white -ray of light _a_ will then be dispersed upon refraction at the meeting -faces of the two prisms, a certain quantity represented by the cone of -rays shown, and again converge at _a′_, an equal quantity on emergence -from the exterior surface of the flint prism, so as to issue again -a white ray, of which this system of prisms has refracted, but not -dispersed, the light. - -[Illustration: Fig. 11.--_Showing principles of achromatism._] - -71.--That the same principles given above for the prism will hold in -the achromatic compound lens, is already demonstrated by the comparison -of lenses and prisms shown in Fig. 5; but for the sake of clearness it -may be again shown diagrammatically in Fig. 12 for an actual objective, -wherein the parallel rays _ab_, proceeding from a distant object or -star, are shown refracted to _a′b′_, and coming to a focus at _F_, -although dispersed at the meeting surfaces of the two glasses, as shown -diagrammatically, by the internal cone of rays. - -[Illustration: Fig. 12.--_Showing achromatic objective._] - -72.--Practically, the matter is not quite so simple as it would appear -to be theoretically, by the above-described conditions, as we actually -find the spectrum of a prism of flint glass of equal dispersion to one -of crown glass does not give exactly similar extent of separate colours -within its spectrum, the medium ray of the spectrum in the flint glass -being nearer the blue than in the crown. Thus, this compound lens does -not perfectly correct by inversion as it does in the perfect case -discussed, and shown in Fig. 10. For this reason better definition is -found by slight displacement and slight difference of total extent of -dispersion of one of the spectra in coincidence on the _meeting planes_ -between the lenses, leaving in all cases a certain amount of residual -colour, blue or red, uncorrected, by making the glass _under-_ or -_over-corrected_, as it is termed, which does not, however, seriously -impair distinct vision. It is quite possible that, by some future -improvements in the chemical constitution of the glass, this defect may -be remedied. English glass-workers prefer to _over-correct_, German and -French glasses are more often _under-corrected_. - -73.--The measurements of refraction and dispersion being both in one -direction, may be taken together within certain angular limits in one -term in the construction of a lens as _the ratio of dispersive powers_, -the indices being certain dark lines which are observed uniformly in -the spectrum of the sun projected from a narrow slit. These lines or -bands in the sun's spectrum are known to be due to metallic vapours -which are present in his atmosphere, and can therefore be reproduced by -the deflagration of like metals on a small scale. To certain of these -lines letters of the alphabet have been applied. Of these letters, a -pair of lines due to sodium vapour marked _D_, and three lines due to -hydrogen, marked _C_, _F_ and _G_, are commonly taken for reference of -dispersion. Achromatism is generally considered duly corrected when the -lines _C_ and _G_ are united. The middle of the spectrum between these -lines is about _E_; and chromatic dispersion of optical flint and crown -may be taken to be fairly corrected if the spectra are coincident in -colour at this line. - -74.--_Curvatures in the Achromatic Lens._--A large amount of -mathematical power has been expended upon this matter, but the -perplexity of the subject is due to small differences of the material; -and the impossibility of working absolutely true spherical curves has -rendered this work of little practical value to the optician, who still -resorts to the formulæ of Dollond and Tully. Those who care to follow -the subject beyond the scope of this work will find numerous papers in -the _Phil. Trans._, and in the works of Herschel, Barlow, Coddington, -Robinson, and Stokes, wherein what is known theoretically of the -subject is fully investigated and discussed. - -75.--For all small achromatics, such as are employed in surveying -instruments with Chance's hard crown and dense flint, the following -approximate formula is commonly employed, expressed in terms of the -radius of the curved surface into _f_, the total focus of the finished -objective, for first working before trial:-- - - 1st.--Outside surface, _f_/2 convex, } - } crown. - 2nd.--Inside " _f_/3 " } - - 3rd.--Outside " _f_/3 concave, } - } flint. - 4th.--Inside " 4_f_ convex, } - -76.--By different makers the surfaces are changed as far as reversing -the curvature of the front glass, and indeed very good glasses are made -with the 1st, 2nd and 3rd = (_f_/2·5). In all cases true convergence -of the white ray is only obtained by correction of the outer and inner -surfaces, or by _figuring_, as it is technically termed, in which -the curvature is not only made greater or less, but its character is -altered generally in the direction from circular to elliptical section. -The qualities of the object-glass cannot be over-estimated by the -practical surveyor. A heavy instrument with inferior object-glass may -be carried about for years, whereas a lighter instrument with good -object-glass would perform better work. Excellent information upon this -subject was given in a lecture before the Royal Institution by the -eminent optician, Sir Howard Grubb, of Dublin. - -77.--_Optical Arrangements of the Telescope._--The earliest form -of telescope is that of Kepler, Fig. 13. In this the rays from the -object-glass cross in front of the eyeglass; consequently, the image -is inverted. This form is at present little used except in combination -with a separate eye-piece. - -[Illustration: Fig. 13.--_Kepler's telescope._] - -[Illustration: Fig. 14.--_Galileo's telescope._] - -78.--_Galileo's Telescope_, Fig. 14.--In this the eye-piece is a -concave glass. This glass is placed inside the focal distance, so that -the rays from the object-glass are bent to less convergence, that they -may enter the pupil of the eye in a direction possible to reach the -retina. The image in this telescope is maintained erect. This principle -is used entirely for field and opera glasses, also for sextants and -some other instruments where it is desirable to keep the image erect, -and small power is required, sufficient only to obtain more distinct -vision. The lines _aa′_ in Figs. 13, 14 are termed the axis of the -telescope. - -79.--_Optical Arrangement of the Huygenian Telescope._--In surveying -instruments, where angles and directions are not taken by coincidence -of direct and reflected images, it is necessary that the direction of -the axis of the telescope should be clearly indicated. In this case the -focus of a distant object--that is, its exact image--is projected upon -a plane termed the _diaphragm_, Fig. 15, _SS′_ upon which a visible -object or index is placed, the position of which is picked up by a -secondary telescopic arrangement, or _eye-piece_ as it is technically -termed. - -[Illustration: Fig. 15.--_Diagram of arrangement of lenses._] - -80.--The arrangement of lenses in a surveying telescope is shown in the -illustration above, where _OG_ is the _object-glass_ or _objective_, -_E_ the _eye-glass_, _F_ the _field-glass_. The two lenses _E_ and -_F_, in their mountings, form the _eye-piece_ _EP_. The dotted line -_a_ is the _axis_ of the telescope, _SS′_ is the _focal plane_ of the -object-glass, where a metal disc is placed with an opening in its -centre--this is termed the diaphragm or technically, the _index-stop_. -Across the opening in the disc, spider's webs or other fine visible -objects are placed, to be described further on. - -81.--Both the object-glass and the eye-piece are fitted in sliding -tubes, which will be described presently, in such a manner that -they may be made to approach or recede from the focal plane _SS′_. -The nearest distance of the object-glass to this plane is the solar -focus, or the distance at which a sharp image of the sun or a star -placed in the axial line would be formed. The greatest distance of the -object-glass from the focal-plane in most instruments is such that a -clear image will be given on this plane _SS′_ of an object placed at -about twenty feet from it. - -82.--=The Ramsden Eye-piece=, the optical arrangement of which is shown -in Fig. 16, is also known as a positive eye-piece. It consists of two -plano-convex lenses, the convex surfaces of which are turned towards -each other. They are separated by a distance equal to two-thirds the -focal length of either glass, and placed so that the diaphragm is -one-fourth this focal length from the field-glass. - -83.--This eye-piece is considered not to be quite so achromatic as -another form known as the Huygenian eye-piece, but its spherical -aberration is less than any other, and it gives what is necessary in -all measuring instruments--a flat field of view, requiring no change -of position to see the centre and border of the field with equal -distinctness. - -[Illustration: Fig. 16.--_Ramsden eye-piece._] - -84.--_The Field of View_ should be as bright as possible. To ensure -this, the field of the object-glass which is taken by the eye-piece -at the position of the front of the eye should not be larger than the -pupil. If the whole field of light enter the eye as it should do, the -brightness will then vary directly as the square of the diameter of the -object-glass, and inversely as the square of the magnifying power. The -directions of the rays are shown by dotted lines as _aa_ and _a′a′_ for -the Ramsden eye-piece in Fig. 16. This eye-piece is sometimes called an -_inverting eye-piece_. It is not really so: the object-glass _inverts_ -its image and the eye-piece picks up the image in its inverted -position. Two or three eye-pieces of this kind, of different magnifying -powers, are sometimes supplied with one surveying instrument. The same -form of eye-piece, being also a simple microscope, is used to read the -divisions on the divided circles of theodolites, sextants, and other -instruments, and for such purposes it is often desirable to ascertain -its focal length. - -85.--_The Focal Length_ of the positive or Ramsden eye-piece is found -by dividing the product of the focal lengths of the two lenses by their -sum, diminished by the distance between them. Thus, if the focal length -of each of the lenses be 1·5 inches, the distance between them 1 inch:-- - - (1·5 × 1·5)/(3 - 1) = 1·125 inches. - -86.--_The Magnifying Power of the Telescope._--The focal length of -the objective divided by that of the eye-piece gives the power of the -telescope. Thus, a 14-inch telescope with the above eye-piece would -have a power, - - 14/1·125 = 12·444, or 12½ nearly, - -a very general lower power eye-piece with telescopes of this focus. - -[Illustration: Fig. 17.--_Dynameter._] - -87.--=Dynameter.=--The magnifying power of a telescope may be -ascertained, without any knowledge of the focus of the glasses used in -its construction, by the use of a dynameter. This instrument, Fig. 17, -consists of a compound microscope in which a finely divided transparent -scale is placed in the mutual focus of its object-glass and of the -eye-piece at _a_. The divisions of the scale may be ·01, ·02, or ·001 -inches apart, adjusted so that a disc ·1 inch diameter at the exterior -focus of the eye-piece may read a given quantity upon the scale. To use -this apparatus, the flanged face is placed in front of the eye-piece -of the telescope, previously set at solar focus. The telescope throws a -circular image of its object-glass through the eye-piece, where it is -picked up by the object-glass of the dynameter and brought to focus on -the scale _a_, where it appears as a circular disc of light. If this -image be measured by the scale, and the diameter of the object-glass be -divided by this measure, the quotient will be the magnifying power of -the telescope. There are several other forms of dynameter. - -88.--=The Erecting Eye-piece=, sometimes supplied with theodolites and -occasionally with other instruments, is the ordinary one of the common -telescope, Fig. 18. The glasses are so arranged that the image brought -to the focus of the telescope inverted is again erected, so that -objects appear in their natural position. The complete eye-piece is -of the same optical arrangement as that of a compound microscope. The -arrangement of lenses is shown in the engraving on next page. - -[Illustration: Fig. 18.--_Optical arrangement of erecting eye-piece._] - -89.--_A object lens, B amplifying lens, C field lens, D eye lens._ -Stops are placed at _d_ and _d′_ to cut out extreme rays. The image -is formed by the objective at _O_, and the light passes in the -direction shown by fine lines, being thrown from side to side of the -lenses. The ray is achromatised proportionally to its dispersion by -the separate lenses, upon principles discussed art. 68 and shown Fig. -10, as independently of the small amount of opacity of the lenses, -extreme rays are cut off, so that central portions only are used. This -eye-piece suffers loss of light at each of the four lenses; therefore, -a telescope with it, for equally distinct vision to that obtained -by using the Ramsden eye-piece previously described, would require a -larger objective. - -This eye-piece is rarely used now, excepting with American instruments -in which they are almost universal, as the very slight advantage of -seeing the image erect is far outweighed by the loss of light it -entails. The American manufacturers place them inside the telescope -instead of outside, thus the telescopes look much the same as our -ordinary ones, but the focal length of the object-glass is shortened by -the length of the eye-piece, and as this takes up from three to four -inches, a telescope which would appear to be say 10 inches solar focus -is, in reality, only six or seven inches and consequently only about -two-thirds the power. - -[Illustration: Fig. 19.--_Diagonal eye-piece, full size; S G -sun-glass._] - -It is astonishing that the Americans, who are usually so quick in -adopting the most practical appliances, are so slow in seeing the -advantage gained by the use of the now almost universal inverting -eye-piece. - -90.--=The Diagonal Eye-piece=, Fig. 19, is used upon transit -instruments, theodolites, and occasionally upon mining-dials. It -permits the telescope to be used by the observer looking at right -angles to its axis. Thus, by the natural direction of the eye, stars or -the sun may be observed to near the zenith, or the direction of a line -cut by two lights at the bottom of a shaft may be observed from above -by the telescope of a theodolite having a hollow centre on its ordinary -stand, to check the magnetic bearing of the needle below ground, if -this is assumed to be subject to local disturbance. The socket of this -eye-piece screws upon the telescope and has a free inner tube for -rotation, so that the 90° to the axis of the telescope may be placed -at any angle to the axis of its cylindrical circumference; as, for -instance, instead of being used vertically or for zenith stars, it may -be used horizontally, where precipitous ground would not permit direct -axial vision through the telescope. The reflecting arrangement of this -eye-piece may be adapted either to the Ramsden or the _erecting_ form. -In either case the reflector is placed in the central portion of the -eye-piece. In surveying instruments the reflector is generally a piece -of polished speculum metal for portable instruments, but a prism of -glass for larger fixed instruments. The general arrangement is shown in -the section of a diagonal Ramsden eye-piece on page 42, full size. _A_ -object lens, _D_ eye lens, adjustable for distance from the reflector -_R_, _S_ outer casing which permits adjustment for focusing, _SG_ sun -glass, the diaphragm being in front of _A_. - -91.--When a rectangular prism is used for the reflector, it is worked -with one plane 45°, as previously discussed, art. 55, Fig. 3. In place -of one or both the 90° faces these surfaces are sometimes worked convex -so as to form a magnifier, dispensing with one of the convex lenses -of the eye-piece. A long diagonal eye-piece is necessary, where stars -towards the zenith are to be observed, to prevent interference of the -limb of a theodolite with the face of the observer. - -92.--=Reflecting Eye-piece= is used to observe small stars, as for -instance the circumpolar stars in the southern hemisphere, by -illuminating the front of the webs or lines. A strong light thrown down -the telescope from a reflector to illuminate the webs would tend to dim -the effect of blackness of the sky and render these stars indistinct. -In the eye-piece, Fig. 20, a piece of plain parallel glass is placed -at an angle of 45° to the axis. This permits the webs to be clearly -observed through the glass at the same time that it throws light from -a lamp placed at a distance from the glazed aperture _L_ by reflection -of the surface of _R_ sufficient for front illumination. The amount of -light required is regulated by the distance of the lamp from _L_. This -eye-piece is made to fit into the diagonal eye-piece casing, as _S_ -Fig. 19, _E_ Fig. 20 being the position of the eye, _F_ field-lens. - -[Illustration: Fig. 20.--_Reflector in eye-piece to illuminate the -front of diaphragm._] - -93.--=Sun-glass.=--Sextants and theodolites are supplied with a very -dark glass or a combination of dark glasses fixed in a rim to form an -eye-piece front, which screws or fits on in front of any eye-piece, to -take observations of the sun for longitude or bearing, Fig. 19, _SG_. -It needs no description, but is necessary to be mentioned to complete -the _optical_ arrangements of a telescope, as it is sometimes used for -surveying purposes. - -94.--=The Body of a Telescope= that forms part of a surveying -instrument is constructed of a pair of _triblet_ drawn tubes, Fig. 21, -_TT′ T′_. These tubes should be truly cylindrical and straight, so as -to fit smoothly together, the one within the other, and slide in and -out quite freely but without any play. The inner tube should be as long -as practicable, so as to remain steady when racked out to the full -extent required to focus near objects. The object-end _R_ is generally -enlarged so as to take the cell in which the objective _O_ is placed, -without cutting off any part of the light, or entailing the weight of -larger tubes than is necessary to make use of the full field of the -objective. The objective is generally held in its cell by an internally -fitting screwed ring with milled edge, so that the glasses may be taken -out and separated to be cleaned, and be easily replaced. Two notches or -grooves are commonly made in the edges of the glasses, each of which is -deep enough to take a small brass pin which is soldered to the inside -of the cell. The second notch indicates relative position, so as to -secure the glasses being replaced properly. In all cases the double -convex crown glass is placed outwards from the telescope. A glass of -large size should have a loose ring within the cell to act as a spring -to save distortion of the objective from expansion or contraction of -the metal; but this is not necessary in small surveying instruments. -In some common telescopes the object-glass is burnished into its cell, -in which case the glasses of the objective cannot be separated for -cleaning. - -[Illustration: Fig. 21.--_Body of surveying telescope._] - -[Illustration: Fig. 22.--_Section Fig. 21, A to B._] - -95.--=Stops.=--Within the inner tube two or more thin metal rings, -termed technically _stops_ _SS_ and _S′S′_, are placed to cut off any -extraneous light that may enter the telescope obliquely, and which, -if not stopped off, would produce a fogginess over the whole field of -view. It is important that these stops should not cut out any part -of the full aperture of the object-glass if it be a good one. In the -manufacture of the telescope this is easily seen by looking in at the -eye-piece of the unglazed telescope to see if the stops clear the -objective cell. In the finished glazed telescope another method will be -discussed further on. - -96.--The inner or the outer tube of the body of the telescope slides -towards or from the objective for focussing by means of a _rack_ _R″_ -and _pinion_ _P_. The rack is soldered to the inner tube, and the -pinion fitted in a _cock-piece_, as shown Fig. 22 _C_, on the outer -tube. The pinion is moved by a large milled head _M_. This fitting -should be made with care. The pinion should be very free, so that it -does not lift the body at any tooth, and at the same time there should -be no shake on the gearing. It needs considerable practice to rack a -telescope properly. - -97.--The outward part of the object end of the telescope is generally -turned to fit the interior of a separate short tube, shown at _R_, -which is placed over it. The outer end is closed by a ring to the size -of the aperture of the objective. This is termed a _ray-shade_ or -sometimes a _dew-cap_. The ray-shade is extended when the telescope -is directed to such an angle that the sun's rays would fall upon -any part of the objective, and thereby cause internal reflections. -A swivel shutter, Fig. 21, _R′_, is placed upon the outward end of -the ray-shade, which, when closed, as shown in the cut, forms a cap -to the telescope. The eye-piece _EP_ before described, art. 82, Fig. -16, is placed in a tube constructed upon the end of the telescope, in -which it slides freely, to focus upon the diaphragm to be presently -described. The telescope is mounted sometimes solidly upon a transverse -axis, or it is mounted in turned bearings, or it has two collars placed -round it which are turned quite equal and true, and are mounted on Y's -to be hereafter described. - -98.--_Mechanical Adjustment of the Eye-piece._--In some large -instruments the eye-pieces are racked for adjustment in the same manner -as the object-glass already described. A better plan is to have an -inner tube to the socket tube cut with a screw into this, and provided -with a milled edge, so that the eye-piece may be screwed gently to -focus upon the webs of the diaphragm. - -[Illustration: Fig. 23.--_Elevation of diaphragm._] - -[Illustration: Fig. 24.--_Section of diaphragm._] - -99.--=The Diaphragm of the Telescope= is so constructed as to permit -the displacement of spiders' webs or other fine objects in any -direction at right angles to the axis of the telescope, or in the -vertical only in the dumpy level, to be described, the object in all -cases being to adjust the crossing of the webs, lines, or points to -the axis of the telescope. It will be convenient here to discuss a -general form of diaphragm applicable to theodolites, mining-dials, and -plane-tables only, which gives movement in two directions at right -angles to each other. - -100.--The diaphragm, Fig. 23, is formed of a stout disc of brass having -a centre hole of about ·30 inch diameter. Upon the side which is placed -next the eye-piece the hole is brought to a thin edge by an internal -bevel or _countersink_, which leaves the hole much larger at its off -surface, Fig. 24 _P_. The disc is held in its place and adjusted by -four capstan-headed screws, termed _collimating screws_, two of which -are shown in section as _CC′_, the screws being tapped into the rim of -the diaphragm frame _P_. The screws are placed through a stout collar. -The theodolite diaphragm has generally three spiders' webs or lines -crossed in the manner shown in the centre of Fig. 23. The eye-piece is -screwed into the thick plate, Fig. 24, _TT′_, and adjusts to the focus -of the webs. - -[Illustration: Fig. 25.--_Webs wound off for use._] - -101.--=Webs.=--It is a somewhat delicate process to web a diaphragm, -but it is necessary that every surveyor abroad, out of the reach of -an optician, should understand the method if his instrument were -originally webbed. The webs are taken from a small or young garden -spider. The best are taken when the spider has first commenced -spinning. To wind off the web a fork is bent up out of a piece of thin -brass wire. A long hairpin will answer for this purpose very well, or -even a fork formed of a thin branching twig of a shrub; but if this -last be used it should be thoroughly dry, or the webs will be broken or -be baggy by its warping in drying. - -102.--The web in connection with the spider is first attached to one -prong of the fork by looping or by any sticky matter, if the web be not -sufficiently sticky naturally. The spider is then suspended from the -fork and jerked down a foot or so, and the web is wound off as shown in -Fig. 25. The last length of web being attached by gum. A dozen or so of -the forks may be taken from the same spider before she is exhausted. -The webs are then gummed or varnished to the sides of the fork, and are -ready for use at any future time. They are best preserved if placed -in an air-tight box, which may have slots in an internal fitting to -hold them. The small amount of spring given by the fork keeps the webs -always taut. Where a living spider cannot be found, the open ties of -an old web may be taken; but in this case, after the web is wound -on the fork, it should be carefully washed by immersing it in clean -water, and, if necessary, brushing it gently under water with a light -camel-hair brush, examining it occasionally with a magnifier to see -that it is sufficiently clean and free from knots for its purpose. - -103.--_To Fix the Webs_, lines are drawn on the diaphragm, into which -the webs are to fall. It is then varnished over the divided side with -Canada balsam, laudanum, or other quick-drying, sticky varnish--at a -pinch, sealing-wax dissolved in strong whisky will answer. The outer, -or the unused web upon the fork, is lowered carefully over one of the -most nearly vertical lines, and lightly pressed down to assure its -perfect adhesion to the varnish. It is then either broken off or cut -loose. The second nearly vertical line is then webbed in the same -manner, and the horizontal line finally, being sure that this last cuts -the intersection of the others. The diaphragm should then be put in a -warm place to be allowed to thoroughly set without disturbance before -it is fitted in the telescope. - -104.--=Platinum Wires= are sometimes used in place of webs. These -wires are made by drawing a piece of fine platinum wire, which has -been previously soldered into a silver tube, to the greatest fineness -possible with the draw-plate, and afterwards dissolving the silver -off the platinum by nitric acid. The platinum wire is thus produced -of less than ·001 inch diameter. For a time these wires were very -popular, and it was thought that they would supersede the use of webs, -but they do not appear entirely to answer expectation. The platinum -drawn in this manner appears to lose some part of its elasticity. It is -not easily attached, that is, it is liable to shift from its fixing, -possibly from its contraction and expansion with change of temperature, -not being of the same metal as the diaphragm. It also oxidises a little -or becomes in some way corroded in use out of doors. It appears to -answer better for astronomical telescopes, but the finest platinum wire -obtainable is not so fine as a spider's web. - -105.--=Lines Ruled upon Glass.=--A glass diaphragm is frequently used -in a surveying instrument to replace the webs. Lines are ruled upon the -glass in similar positions to the webs already described. They appear -quite sharp in the eye-piece, and are more permanent than webs. Glass -is also convenient for permitting space lines to be ruled for subtense -measurements, a subject to be considered further on. The objections -that have been found to glass are that it obstructs a little light, -and is subject to dewing. The dewing is particularly annoying when -temperature is lowering quickly, as a diaphragm may become bedewed many -times in a few hours. In all cases where a glass diaphragm is used it -should be placed in a ground metal fitting, so that it may be taken -out in a minute to clean and be replaced with perfect certainty of its -adjustment. It is a very convenient practice where webs are used to -have a spare glass diaphragm to replace them should they become broken. -This may be constructed by means of a ground metal fitting to be put in -a webbed instrument in perfect adjustment in cases where it might be -impossible to find a new web. - -106.--=Points.=--The author for a large number of instruments employs -very fine points in place of webs, which he highly recommends. These -are fixed for support upon the margin of the diaphragm, and projected -therefrom into the field of view. The points are formed of a special -alloy, 75 platinum, 25 iridium, which has the hardness of steel, and is -perfectly non-corrosive in air or moisture. They are made sufficiently -stiff to be dusted with a camel-hair brush, supplied in the instrument -case, without the slightest fear of disturbance of position in the -instrument. They form a perfectly permanent index of sufficient -stability to last in perfect adjustment as long as the instrument lasts -in wear. One objection is that a point gives less field of observation -for levelling than a line, but this does not hold if there is tangent -adjustment to the instrument to bring the point up to its reading -position. The value of the reading from these points will be discussed -further on. - -107.--=Position of the Diaphragm in the Telescope.=--If the objective -be accurately centred, and its mounting true, the intersections of -the webs, lines, or points should come exactly in the axis of the -telescope; but it would never do to accept this without critical -examination. Therefore the webs may be placed approximately in the -centre, and adjusted true to the axis of the objective and the -telescope by what is technically termed _collimation_. The first point, -however, to be studied in this adjustment is to get the eye-piece and -the objective accurately in focus with the webs. The same description -of focussing which answers for collimation will answer also for -ordinary use of the telescope. - -108.--_Adjustment of the Eye-piece to the Webs_ is effected by pushing -in or drawing out the eye-piece in its tube with a slight screwing -motion until the webs, lines, or points appear quite distinctly. To -prevent confusion from the sighting of objects, it is better to take -off the ray-shade, to point the telescope to the distance in opposition -to the direction of the sun, and to keep the telescope rack fully -extended, so that it is quite out of focus. When the light is not very -bright a sheet of notepaper or an envelope may be placed obliquely in -front of the object-glass to obtain a soft reflection from the sky. -This method is always employed by some observers. - -109.--_Adjustment to Focus of the Objective._--_Parallax._--The -eye-piece remaining in focus, the telescope is racked out until the -object desired to be brought into view, either for the collimation or -for ordinary reading, is sighted. After this the milled head is moved -as slowly as possible until what is thought to be the exact focus is -obtained. The certainty of exact focus is not easily obtained by direct -observation, but it may be obtained by what is termed _observation -for parallax_, which must be taken in all cases when adjustment is -required for collimation. Thus, having obtained the nearest possible -adjustment by sighting a small object or a division upon the staff, -bring the object to read exactly in a line above the horizontal web -in the centre of the stop or the corner against a vertical web. If -now the eye be moved up and down as far as the range of the eye-piece -will permit vision of the centre of the webs, and the object sighted -appears fixed at the same position to the webs, the focus is perfect. -If, in moving the eye, the object sighted appears to follow its motion -about the intersection of webs, the focus of the telescope lies beyond -the webs; the objective must therefore be moved slightly nearer the -webs by turning the milled head very gently. If, on the other hand, -the object sighted moves in the opposite direction to the eye about -the intersection of the webs, the focus of the telescope is towards -the eye-piece, and the telescope requires slightly racking outwards by -moving the milled head in the reverse direction. After a few trials the -object and webs appear stationary, however obliquely observed. - -110.--=Collimation= is the adjustment of the crossing of the webs -of the diaphragm to the axis of the telescope and its object-glass. -This is effected by adjustment of the opposite collimating screws, -Fig. 24, _CC′_, in two directions at right angles to each other. -Where the telescope is placed in Y's or collars, this adjustment is -made by placing the webs or lines in focus of the eye-piece and the -object-glass of the telescope in focus upon a small distant object. -Then if the telescope is rotated in all directions, and the small -distant object cuts the crossing of the webs in all positions, it is -said to be truly _collimated_. It is necessary to discuss the structure -of various instruments to show the methods of collimating in special -cases; therefore this subject will be again brought forward. - -111.--_The Qualities of a Telescope_ of a surveying instrument are best -ascertained by its performance. The general method is to place a staff -at the full range, 10 to 15 chains, and to see if the ·01 foot in fine -bright weather is read clearly and sharply. This outdoor observation is -not always possible, particularly in large towns, but it may very well -be supplanted by reading at a short distance. The author made for the -late Colonel Strange, F.R.S., whose knowledge of scientific instruments -was of the highest order, a test-card for the Lambeth Observatory, to -be placed at 25 feet from the instrument. This card had on one part -fine lines ruled ·01 inch apart. A 14-inch telescope was considered -sufficiently good if these lines could be clearly separated at this -distance by the telescope when it was in correct focus. The dial of -a watch, or an ivory scale, answers very well as a test object, as -sharpness of outline is the point to be ascertained. - -112.--A more refined technical method than that described above, which -also tests the general accuracy of the optical arrangement of the -telescope, is to fix a small disc of white writing-paper, say 1/8 inch -diameter, cut out with the point of a pair of compasses with sharp -outline, on a black surface of a board, paper, or cloth. If this be -placed as before, 30 feet or more distant in a good light, and be -correctly focussed in the telescope, a sharp image of it should be -obtained. This focal position of the telescope may be temporarily -marked upon the inner tube with a fine soft black-lead pencil. If now -the object-glass be racked outwards or inwards from this line, say -for about a twelfth of an inch, and the image appears to be surrounded -with a uniform haze, the objective may be considered to be correctly -formed, or to be free from spherical aberration, as it is termed, and -the combination to be correctly centred. If the haze appears more -on one side than the other the centring is defective. If the object -remains fairly sharp when out of exact focus the curves of the lens are -defective, as the shorter the range of focus the more perfect is the -correction from spherical aberration. - -113.--If the curves are not sufficiently correct to bring the image -from all parts of the objective to a focus, such incorrect parts are -useless, and a good glass of smaller size would be better. The fault -is generally found in the marginal portion of the objective, which -requires the greatest skill of the glass-worker. Therefore, a very -good test to find whether the whole of the aperture of the objective -is in effective use is to cut out a piece of card of the size of this -aperture and to cut a second piece out of the centre of this, of half -the diameter, so as to form a disc and a ring. If the objective be now -covered by the ring and accurately focussed upon a test object, and -this be then removed and replaced by the disc fixed over the centre of -the objective, and the focus remains equally sharp, the curves may be -said to be, practically, correctly worked. - -114.--As the central part of an objective is more easily brought -to correct curvature than the marginal parts it is not uncommon in -inferior instruments to make the aperture of the central stop of the -telescope cut off the margin of the objective. This renders it only -equal to a smaller glass. - -115.--Whether the full aperture of a telescope is used may be -discovered by employing a second eye-piece--outside the regular -eye-piece that is placed in the telescope--to pick up the image of -the object glass formed through the eye-piece which is placed against -the telescope in the manner of using a dynameter, art. 87. With the -ordinary surveyor's level, two eye-pieces are commonly sold; one of -these may be placed in the telescope and the other used to pick up -the image of the object-glass. With a theodolite one eye-piece may be -placed in the telescope, and one of the readers used to magnify the -divisions of the limb may be used to pick up the image. The best manner -of proceeding is to fix with water or thin gum two or three small -pieces of paper, say 1/20, 1/10, and 1/7 inch square, close against -the edge of the cell upon the face of the objective. Then focus the -telescope on an object at some distance, say a chain or two. Now use -the second eye-piece in front of the one in the telescope, and an image -of the object-glass will be seen; and if the aperture is fully open all -the pieces of paper in their places will be clearly distinguishable. -If one or other piece is invisible, the margin of the glass is cut -off to this extent. If the objects in front of the telescope tend to -confuse, a piece of white paper may be placed obliquely to reflect the -light of the sky into the telescope, which will at the same time fully -illuminate the objective. - -The discussion of the principle of the anallatic telescope, used only -with the tacheometer, is deferred to another chapter, wherein subtense -instruments are described. - - - - -CHAPTER III. - - THE MAGNETIC COMPASS AS A PART OF A SURVEYING INSTRUMENT - OR SEPARATELY--BROAD AND EDGE-BAR NEEDLES--MANUFACTURE - OF THE NEEDLE--MAGNETISATION--SUSPENSION--DIP AND ADJUSTMENT-- - LIFTING--INCLINATION--DECLINATION--VARIATION--CORRECTION-- - COMPASS-BOXES--DESCRIPTION OF COMPASSES--RING COMPASSES--TROUGH - COMPASSES--PRISMATIC COMPASSES--STAND--SURVEYING WITH COMPASS--POCKET - COMPASSES. - - -116.--=The Magnetic Needle=, which forms part of a great many surveying -instruments, is made of the form adapted to the special purposes of -the instrument in which it is placed. There are two prevailing forms -commonly in use--one in which the needle is made pointed at one or both -ends to read directly upon a divided circle fixed upon the instrument, -and the other form in which it is made to carry and to direct a divided -circle by its magnetic force. - -[Illustration: Fig. 26.--_Broad needle._] - -[Illustration: Fig. 27.--_Edge-bar needle_.] - -The magnetism which gives directive force to the needle has been found -by experiment to reside in every separate part of the magnet, that is, -it is assumed to be a _molecular_ force. Therefore, it would not appear -to be very important, within certain limits, of what form the magnetic -needle is made, and this is found by experiment to be to a large extent -true. The only important conditions appear to be that the needle shall -be of such form that the inducing magnet, to be described, arts. -120-123, which is used for magnetising may be brought into contact upon -every part of its surface, and that the molecular continuity of the -parts should mutually support the general directive influence of the -magnetism longitudinally in parallel lines. - -117.--Magnetic needles are generally made in the form of flat bars, -which are balanced upon a standing point falling into a cup which forms -the centre. When the greatest section of the bar is placed horizontally -it is termed a _broad needle_, as shown Fig. 26. This may be made of -the lozenge form shown, or be parallel throughout. When the greatest -section is placed vertically it is termed an _edge-bar_ needle, as -shown Fig. 27. The north pointing end of the broad needle is commonly -tempered dark blue, or has a deep cut across it, if the needle is -left open. This is not necessary if it carries a ring. The edge-bar -is generally used where it is required to read into a fixed circle of -division, in which case its ends are brought to fine knife-edges. - -118.--From the difficulty of reading a sharp point in bright metal -against the black line of a divided circle, the author occasionally -makes one point of the needle with a fine cut, sawn vertically for a -short distance from its end, so as to form a kind of _split_ which is -afterwards closed, so that it presents the appearance of a fine black -line of the same character as the divisions into which it reads. With -this, as shown Fig. 28, the reading is found to be much more easy. -The point is also more readily adjusted by grinding, as the end of -the needle being broad, less care is necessary to avoid reducing it -so much that it may leave the interior of the circle short where it -reads into the divisions. This form of needle is not adapted to mining -instruments, which have often to be read in an oblique direction. - -[Illustration: Fig. 28.--_Author's plan of needle reading._] - -119.--_In the Manufacture of the Needle_ it should be made of the -finest cutler's cast steel, or, better still, of steel containing 3 -per cent. of tungsten. If not left in a parallel strip as it is drawn -or rolled, it should be brought as nearly to its form as possible -by forging at a low heat. The steel should not be over-heated for -hardening. It should be hardened in cold water or oil, and be tempered -afterwards down to a very pale straw-colour--in fact, the temper colour -should only just appear. Long needles may have the temper sufficiently -lowered at the centre to set them approximately straight during the -tempering; but the temper should not be lowered even in the centre -below a pale blue, _spring temper_. After tempering, the setting and -working up to balance is best done by grinding, and for the final -adjustment, by stoning with Water-of-Ayr stone. - -120.--_Magnetisation of the Needle_ may be performed in many ways by -means of a permanent magnet or an electro-magnet, or electrically -by means of a solenoid. When the magnetism is induced from another -magnet it is only important that the properly hardened needle should -be regularly and equally magnetised over its surface by pressure upon -it of the proper poles of the inducing magnet--that is, that the north -pole of the magnet should induce magnetism in the southern half of the -needle only; and the south pole in the northern half only. - -121.--_Method of Magnetisation by Single-touch._--This method is more -generally applied to touching up needles than magnetising them at -first. The northern pole of a strong permanent magnet is stroked down -the southern end of the needle from its centre to its end three times -on one side of the needle. The needle is then turned round, and the -northern end is stroked down in like manner with the southern pole. The -needle is then turned over, and the process is repeated on the other -side. This may be done a second time and the edges of the needle be -stroked down also. - -122.--_Method with both Poles._--In this process the needle is held -down firmly with pegs on a board, and a strong horse-shoe magnet with -rather close poles is laid on the bare needle without its cap, in a -manner that both terminals press upon it. It is then drawn backwards -and forwards from end to end of the needle several times, lifting the -magnet finally from about the centre. The process is then repeated on -the opposite side of the needle and its edges. - -[Illustration: Fig. 29.--_Divided-touch magnetisation._] - -123.--_Method of Divided-touch_ is a somewhat quicker process, which -does not entail removing the cap, the general plan of which is shown -in the engraving below. The poles of the magnets, or one of them, is -marked. Two good straight bar magnets are used. The needle is fixed -down on a board and the poles of the two magnets are laid upon it at an -angle of about 30°, applying one north or marked pole, and one south -or unmarked pole. The magnets are then drawn apart in a horizontal -direction along the needle, with constant pressure upon it, so as to -reach the opposite ends of the needle simultaneously, and then again -pressed back to the centre. After this operation is performed three or -four times on one side of the needle, it is turned over and the process -is repeated on the other side, being careful as before to use the same -ends of the magnets upon the same ends of the needle. The operation may -be repeated several times to be sure of saturation of the needle. It is -better to lift the magnets off at the termination of the operation at -the centre of the needle. - -124.--It is found that the needle is magnetised a little more quickly -if it is laid upon a strong magnetised bar during magnetising, or upon -the ends of two bars, as shown in the engraving, Fig. 29, or on the two -ends of a wide horse-shoe magnet. - -125.--Needles are now more generally magnetised electrically by placing -them in a solenoid or coil of stout insulated copper wire through which -a strong direct current is passing from a dynamo or powerful battery. -This method is employed in the best shops. The touch system above -described is convenient for the profession for remagnetising a needle -when weak, as a horse-shoe magnet at small cost may be kept for the -purpose. It is generally used in small shops, as being at all times -ready to hand, less expensive, and sufficient to ensure saturation if -it is skilfully done. - -126.--With every care in the manufacture of the needle there remains -a little difference in the qualities of needles which are apparently -otherwise identical. Little local differences in the quality of the -steel, slight over-crystallisation from over-heating in hardening or -unequal tempering, or unequal magnetising, are liable to form weak -parts, or even what are termed _consequent points_. These are points -in which the magnet possesses a reversal of its general longitudinal -polarity. This can be made quite evident by experiment, as it is -possible to make a needle not only with poles at each end, but with -intermediate poles which are easily detected by sifting iron filings -over it. The filings are found to adhere strongly at other local -points than those near the ends, where a good magnet is alone strongly -attractive. - -127.--_Mounting of the Needle._--The needle for a surveying instrument -has a female centre upon which it is suspended. The centre, termed -technically _cap_, is generally formed of a hard precious stone, agate, -chrysolite, ruby or sapphire, the latter being best, simply from the -high polish it attains in grinding out with diamond dust. Rubies and -sapphires are like minerals, except in the colour, which varies very -much; the _off-colour_ stones, which are of small value for jewellery, -are used for scientific purposes. The cap is mounted in a brass or -aluminium cell made as light as possible for sufficient stability. - -The needle is supported upon a hardened steel point, upon which it is -perfectly balanced. The base of the point is tempered down to a low -degree in order to admit a certain amount of bending to counteract the -slight warping which generally occurs in the hardening. - -128.--_Correction of Errors._--The needle, after it is mounted, -although in balance may not have the steel placed symmetrically about -its axis through slight curvature, unequal thickness about the cap, -or otherwise, so that the magnetic direction is not perfectly linear -between the points and the centre. If the points and centre are not -magnetically linear, the correction for declination, which will be -presently considered, cannot be made accurately. On this account it is -better for the manufacturer to mount the needle on a slate bed with -two sliding heads that may be brought up to the points of the needle. -The heads have upon their upper surfaces lines drawn perfectly linear -with the centre point of suspension of the needle, and a few lateral -divisions to these lines for determining errors. On this bed the needle -is placed upon the centre point to be examined how nearly its reading -points are true with the axis. The error being recorded, the needle -is demagnetised, and remagnetised end for end, and again examined. -Corrections are then made by grinding or stoning from observations of -bisections of the points cut in the separate readings, until the needle -is made symmetrical and invariable, whichever end is magnetised for the -north or south. - -[Illustration: Fig. 30.--_Section of mounted needle._] - -129.--_Lifting the Needle._--The needle of a surveying instrument -should never be supported upon its centre except for the time it is in -use for observation, as a fine steel point against a hard stone must, -by any jar in conveyance from place to place, receive a certain amount -of abrasion that will make it duller. For this reason a lift for the -needle is always provided in scientific instruments. In the engraving, -Fig. 30, an edge-bar needle is shown in section with its lift. The lift -is made in the form of a bent lever, whose fulcrum is upon the bottom -of the box. On the left-hand side of the broken line at _B_ the needle -is shown lifted. On the right-hand side _A_ the needle is shown at its -position for use, floating just slightly above the divided circle _D_. -The pressure of the milled-head screw _C_ depresses the bent lever -or lift on the bottom of the box and thereby raises the point under -the centre of the needle. This point has a hollow cone formed upon it -which fits over the standing-point to keep the lift in position. The -cone fits externally into the cap to lift the needle vertically. The -screw _C_ should always be clamped down when the needle is out of use. -In place of the screw a wedge shaped sliding piece is sometimes fixed -inside the compass-box, which is moved by a stud projecting through -the outer case. Another plan of raising the lift is by a cam, or -what is technically termed a _kidney-piece_, applied to the exterior -part of the lift. Either of these plans answer, but the screw first -described, being the gentler motion, jars the needle least. A screw is -occasionally used longitudinally to the needle connected with a cam -lift, the object in all cases being to lift the cap entirely clear of -the standing-point. - -130.--=The Inclination or Dip of the Needle= is the position a needle -balanced level upon a free centre _before_ magnetisation takes in -the vertical plane _after_ magnetisation. This inclination or dip -varies in different parts of the globe, and at different times. At the -present time at Greenwich (Jan., 1914) the angle is 66° 50′ from the -horizontal. It is uniformly nearly _nil_ at the equator, and increases -until over one of the magnetic poles, where it becomes vertical. There -are two magnetic poles in the northern hemisphere active in directing -the needle, one in Siberia, but the most active is about Melville -Island; also two in the southern hemisphere, which are supposed to be -nearly together, but the exact positions of which are not ascertained. -As we require only the horizontal component in surveying and not -the dip, it is necessary to balance the needle in opposition to the -direction of the dip until it keeps in a horizontal position. This may -be done by making the needle lighter on the dip side--that is, the -northern in this hemisphere. But the plan adopted in all scientific -instruments is to place a rider over the needle, as shown Fig. 30 under -_B_. This clips the needle sufficiently to hold it firmly to its place, -and yet is loose enough to be moved by the fingers to balance. The -rider has to be shifted when the instrument is taken into a country -where the dip is different from its position at home. When a needle is -taken abroad without any rider, it may be balanced by means of a little -sealing-wax placed upon its uptending end. - -131.--To get at the needle for suppression of dip when it is placed -in the compass-box, it is necessary to raise the spring ring, which -is placed over the glass to keep it down, by inserting the point of a -pocket-knife between the ring and the glass, moving the knife entirely -round it and using a little twist upon it if necessary until the ring -is free. This must be done gently or the glass will break. The needle -is then adjusted to read correctly to the plane of the divided circle -and is replaced in its box. The glass is then replaced and the spring -ring is pressed down by passing the finger firmly round it until it is -tight upon the glass. Sometimes a little extra pressure by a hard body -is needed, but this must be done with care or the glass will be broken. - -132.--=The Declination of the Needle=, that is, its variation in -pointing in a true northernly and southernly direction, is necessary -to be known and considered by the surveyor where the needle is used, -both in relation to the locality and to the time, as this declination -not only varies in different countries but also from year to year. For -instance, this year (Jan., 1914) it points 15° 12′ West at Greenwich. -The following chart, Fig. 31, gives the declination variation for 1914. -The whole system of declination lines is now moving westward at the -rate of about seven minutes per annum, but the rate varies slightly and -from year to year. The declination lines, independently of correction, -which will be presently considered, may not be exactly represented by -the symmetrically curved lines shown in the figure. There are small -local deflections from the theoretical curves here given, which are -permanent and need local consideration when using the needle for -obtaining very correct bearing. These have been ably considered by -Professor Rücker and Dr. Thorp, but the subject is too complicated to -be entered upon here, except for this note of observation.[2] - -133.--For new countries, where the needle often becomes most important -from the impossibility of tying up lines by direct observation through -forests and other obstructions, reference must be had to magnetic -charts which give systems of lines easily worked through by symmetry, -even for unexplored countries. At present the declination is west in -Europe and in Africa; east in Asia and the greater part of North and -South America. - -[Illustration: Fig. 31.--_Magnetic and Greenwich time chart for Great -Britain, 1914._] - -134.--=The Magnetic Variation of Declination in Time=, becomes -important in reference to old plans in which the magnetic north of the -period has been plotted for the true north very much to the pecuniary -advantage of the legal profession when engaged upon actions with -regard to disputed boundaries. The following table gives an idea of the -variation in declination for Greenwich approximately for a few dates:-- - - Year 1580, Dec. 11° 36′ E. | Year 1860, Dec. 20° 40′ W. - " 1663, " 0° | " 1870, " 20° 19′ W. - " 1700, " 8° 20′ W. | " 1880, " 18° 58′ W. - " 1818, " 25° 41′ W. | " 1890, " 17° 9′ W. - " 1850, " 19° 31′ W. | " 1900, " 16° 30′ W. - -It will be seen by the above table that the needle pointed due north in -1663, that it attained its greatest western declination in 1818, and -that it is now losing its westerly declination at the rate of about 7′ -annually. - -135.--=Annual Variation.=--The declination is subject also to a small -annual variation which is greatest about spring time, diminishes -towards the summer solstice, and increases again during the following -nine months. It varies at different periods, and seldom exceeds 16′ of -arc. - -136.--=Declination Correction= to true north may be made for the -compass by observation in this hemisphere of the pole star, which -is practically due north in January at 6 p.m., February at 4 a.m., -March at 2 a.m., April at midnight, May at 10 p.m., August at 4 a.m., -September at 2 a.m., October at midnight, November at 10 p.m., December -at 8 p.m. Most surveying instruments, except the transit theodolite, -are not made convenient for this observation. More generally -observations of the position of the sun may be made where a sun-glass -is provided to the telescope of the theodolite, Fig. 19, _SG_, page 45, -with the aid of a chronometer or a good watch. For this observation -we may remember that the sun is true south at twelve o'clock on the -16th April, 15th June, 1st September, and 25th December. The following -table may be useful for some intermediate times to show how much the -chronometer (mean time) is faster or slower than the sun's southing -approximately at noon:-- - - Jan. 1 subtract 4 min. | July 15 subtract 6 min. - " 16 " 10 " | " 30 " 6 " - " 31 " 14 " | Aug. 14 " 4 " - Feb. 15 " 14 " | Sept. 13 add 4 " - Mar. 2 " 12 " | " 28 " 9 " - " 17 " 8 " | Oct. 13 " 14 " - April 1 " 4 " | " 28 " 16 " - May 1 add 3 " | Nov. 12 " 16 " - " 16 " 4 " | " 27 " 12 " - " 31 " 3 " | Dec. 12 " 6 " - June 30 subtract 3 " | " 31 subtract 3 " - -137.--As variation in time of southing is from fourteen minutes fast -to sixteen slow, or a difference of thirty minutes, correction becomes -important, as the sun passes over 7½° in this period. In these -observations the diaphragm lines, webs, or points must bisect the sun's -disc. This is done more exactly by taking the mean positions of the -sun's eastern and western limbs or its semi-diameter, which is given -for every day of the year in the _Nautical Almanac_. - -138.--=The Compass-box.=--The needle, as it is generally mounted for -the theodolite, mining-dial, and many other instruments, reads into -a divided circle of 360°. The circle is raised up from the bottom of -the compass-box to the height of the top of the needle, as shown in -section Fig. 30, _D_, and is generally silver-plated. The bottom of -the compass-box is sometimes divided with a _compass-rose_ giving the -points N. E. S. W. The E. and W. in some cases are reversed from their -natural directive positions from the centre of the box, so as to read -the letter indicating the point nearest to the division instead of that -opposite to it. In modern surveying instruments, however, no regard -is paid to the points of the compass, north being 0°, east 90°, south -180°, west 270°. - -139.--In the manufacture of the compass-box very great care should be -taken that the metal is quite free from iron, and that no iron comes -near it. On this point the maker cannot be too guarded. The author has -in several instances found the compass-box of perfectly free metal; but -a single foul screw made of commercial brass wire, being used to fix -the ring or the rose plate, has by its influence entirely destroyed the -value of the compass. - -140.--In the construction of the compass-box the author has found the -most certain method of getting the divisions correct with the centre is -to make the division directly from the standing-point of the compass, -and not to try to get this point correct to the divisions afterwards. -The standing-point may be fixed directly to the box by screwing, or -be attached to a brass plate before fixing. It is adjusted to the -compass-box by bending until the needle turns freely, but at the same -time nearly touches the circle. The needle is then removed and the -circle is divided with the point as its centre. Where the divisions -read to the point of the needle, or to a line upon it without a -magnifier, the divisions of the circle may be made directly upon the -lathe by a lever to the slide-rest if the lathe has a well-divided -headstock. When the divisions are magnified and require great accuracy, -or where a floating ring is used upon the needle, the circle should be -divided upon the dividing engine, which will be described further on, -the centre used being still the point or pivot on the bottom of the -case, from which the divisions are to be made radially. - -141.--=Preservation of the Magnetism in Needles.=--It is most important -that the magnetism of the needle, particularly in mining-dials where -so much depends upon it, should be preserved to near saturation in -order to secure certain direction in opposition to the friction of -the centre, necessarily always present. This is often much neglected -from carelessness, or want of knowledge of the principles of magnetic -action. In the first place we know that a bar of soft iron, possessing -no evident magnetism, if it be placed in the magnetic meridian with -proper dip, will after a time manifest strong magnetic properties. -Thus, such a bar in London placed due north and south, with a dip of -67° to the north, becomes a weak magnet. From this we may also infer, -and this experiment shows, that a needle placed in this position will -not lose its magnetism. But what is most important to observe is that -if the needle is placed in a _contrary direction_, as, for instance, -with its northern end towards the south, it is in constant opposition -to the influences of terrestrial magnetism, and will certainly become -weaker. Therefore, although it is necessary to lift the needle when -carrying the instrument, which must necessarily place its poles in -all directions, it is not at all necessary that the needle should be -lifted when the instrument is put by out of use. Indeed, magnetism is -_materially preserved_ by releasing the lift to let the needle take -its true bearing. This does not at all injure the standing-point, as -there is no movement upon it to cause wear. Of course if the needle is -at first magnetised beyond its permanent condition it will lose this -surplus magnetism, but the residual magnetism in this position will -remain nearly constant. - -142.--A valuable precaution for a needle in constant wear is -occasionally, say twice a year, or much oftener if it is used in a -dusty mine, to take it out of its box and wipe out the cap with the -point of a small sable brush. The standing-point may at the same time -be sharpened if necessary by gently rubbing it all round with a slip of -oiled Arkansas stone at its former pointing angle. The sharpness of a -needle is easily ascertained by sliding the thumb-nail over the point -at an angle of about 30° to it. If the point sticks and holds the nail, -it is sharp; if it glides upon it, it is dull. The author has often had -compasses of various kinds sent to him for remagnetisation whose only -fault has been dulness of centre. - -143.--=Ring Compasses.=--In modern theodolites, levels and prismatic -compasses, the magnetic needle carries a light divided circle, -which is now generally made of aluminium on account of the extreme -lightness of this metal. A broad needle is used of about ¼ inch in -width and 1/18 inch in thickness. There is considerable difficulty -in mounting the circle to get it truly concentric and correct for -bearing, therefore ring compasses are often found to be inaccurate. -The author has followed two methods of construction, either of which -answers fairly well:--The one is to leave a bar across the compass when -cutting out the compass ring from a plate of aluminium. In this case, -when the outer edge of the ring is chucked in the lathe to be turned, a -centre hole is also made in the cross-bar which exactly fits over the -cap of the needle, so that the adjustment for centre is practically -secured, and attention is only necessary to get the adjustment correct -for bearing--that is, the 0° at true magnetic north to the axis of -the needle. Another method, which was suggested to the author by the -late Mr. Thos. Cushing of the India Office, answers perfectly, and -only entails a little extra trouble in setting for dividing. This -is to permanently mount the ring on the needle without any means of -after-adjustment, and to divide the circle from a point placed in the -axis of the dividing engine, upon which the ruby centre is placed, -being of course particular that the zero line 0° cuts the magnetic axis -true north in the graduation. - -144.--=Mariners' Compasses=, and an inexpensive class of prismatic -compasses, are made with a paper disc in place of the ring above -described answering the same purposes. The paper disc is generally -made in two thicknesses with a thin sheet of talc placed between them. -Mariners' compasses have frequently the divisions painted directly -upon talc for transparency by lighting from beneath, also for general -lightness combined with stiffness. - -145.--The reading of mariners' compasses, and the compasses on levels -where the needle carries a divided ring, is taken from a line drawn -vertically up the inside of the box or a pointer. This _lead_ line in -the mariners' compass gives the direction of the head of the vessel; a -pointer in the level compass gives a direction in line with the axis of -the telescope. In high-class theodolites, a microscope is used by the -author reading to a spider's web in the diaphragm. - -146.--=Trough Compass=, sometimes termed a _long compass_. Where an -instrument possesses a double vertical axis and a divided circle, as -the theodolite, the division of the circle may take the place of the -divided ring of the compass and save the repetition of the graduation, -at the same time the needle may often be made longer, as the bulk of -the compass-box is proportionately less. In fact in all cases where the -magnetic north only is required the trough compass is to be preferred. -The ordinary construction of this compass is in the form of a narrow -box, Fig. 32, _A_ representing a plan, and _B_ a parallel section taken -through it horizontally. About 10° are graduated on each side of the -meridian line, _aa_ being adjusting screws to bring the scale true with -the needle. - -[Illustration: Fig. 32.--_Trough compass for attachment to an -instrument._] - -147.--=Magnification of Reading.=--With the trough compass it is very -common to have some form of microscope for reading the needle more -exactly. This may be done by a Ramsden eye-piece being placed directly -over the needle, as is common in some German instruments. A much -more convenient plan for certain instruments is to read the needle -longitudinally. This is generally done by means of a transparent scale -being placed across the end of the needle which is divided upon glass -or horn. This may read to either the near or distant point of the -needle. A very good form of needle reading is found in some French -instruments. This is shown Fig. 33, where the compass is shown entirely -enclosed in a tube _C_ which protects it from dust. The needle _N_ has -a vertical point fixed upon its end at _P_ which reads pretty closely -to a scale of 10° divided upon glass at _G_ by the eye-piece _E_. It -has a lifter _L_ pressed up by a milled-head screw _M_. Fig. 34 shows -the graduated glass. This compass is attached beneath the limb of a -theodolite, or in any other convenient position upon an instrument. -The author has placed a compass constructed upon this principle in -a telescope, in such a manner that the needle may be read with the -eye-piece, so as to cut a line with a distant object coincident with -the line cut by the principal telescope of the instrument at 0° of its -graduation. This plan will be more fully explained with tacheometers, -Chapter XII. - -[Illustration: Fig. 33.--_Needle with reader._] - -[Illustration: Fig. 34.--_Scale at G._] - -148.--=The Prismatic Compass=, shown Fig. 35, was invented by Charles -August Schmalcalder in 1812. It is the most convenient portable -instrument for reading magnetic bearings. Angles may be taken with -great rapidity within about 15′ of arc by holding the instrument in -the hand, or perhaps within 5′ if the instrument is of 4 to 6 inches -diameter and placed on a stand. It is a most valuable instrument for -filling in close details, such as may occur among buildings, trees, -etc., after the principal points have been laid down from observations -taken with the theodolite. The principles of the reflection of a prism -were discussed, art. 55, Fig. 3, p. 29. - -[Illustration: Fig. 35.--_Ordinary prismatic compass._] - -[Illustration: Fig. 36.--_Section of the same, but with mirror._] - -149.--_Prismatic Compasses_ are made from 2½ to 6 inches in -diameter. The compass needle is sometimes made to carry a card -dial for the 2½-inch size; for larger sizes the ring is now made -uniformly of aluminium. The reading of the compass ring is effected by -means of a glass prism, Fig. 36, _P_, which is cut to 45° upon one face -and 90° for the two others, one 90° face being worked convex, so as to -give magnifying power simultaneously with reflection of the ring at -right angles, so that the reading of the compass appears to stand erect -before the user of the instrument, and to be considerably magnified. -As the reading is made on the side of the ring nearest the observer, -the figures on the ring are engraved right to left. The prism is placed -in a box, with a vertical sight slit _SS_ over it, which cuts a line -with the centre of the top of the prism. The box with its prism moves -upwards or downwards in a sliding fitting _SL_ by means of a _thumb -nail_ stud, which adjusts the prism until it is in exact focus with -the divisions on the ring. The back of the prism-box has a hinge _H_, -so that this box may be closed down to the level of the compass-box -to render it portable when out of use. On the opposite side of the -compass-box to that upon which the prism is placed a long vertical -window _SV_ is attached, having a central hair placed so as to cut a -direct line from the slit _SS_ in the prism-box across the axis of the -needle. This window-piece is jointed to turn down upon the face of the -compass-box and simultaneously to lift the compass needle off its -centre by a part of it pressing the outer end of the lifting lever _L_. -To prevent too great a continuity of the oscillation of the compass -needle and the ring, through unsteadiness of the hand in holding it, a -pin is placed at _S_, through the compass-box under the window, which -carries a light spring _B_ that just touches the ring lightly when the -pin is pressed in, and thereby brings the compass ring to rest, or -fixes it for reading with some degree of certainty. An open ring under -the prism-box is sometimes used for placing a piece of ribbon through -it, to attach it to some part of the person to save dropping the -compass accidentally when it is used in the hand. When the instrument -is out of use a metal cover is provided to protect the glass. The -instrument is uniformly carried in a leather case with strap to pass -over the shoulder. As these instruments are often carried by military -surveyors, they are better made of a stiff aluminium alloy, which makes -the instrument less than half its ordinary weight. - -150.--=Additional Parts= commonly provided with the prismatic compass -are a mirror and sunshades, shown only in section Fig. 36. The mirror -_M_ is carried in a frame attached with a sliding piece to the -window, upon which it can be placed either upwards or downwards. It -is jointed with a hinge so as to be set at any angle. By reflection -from the mirror, bearings in azimuth are taken much above or below the -horizontal plane. Sun-glasses are also provided in front of the prism, -which are used for taking the sun's place either with or without the -mirror, a single sun-glass being also used very comfortably for working -towards the sun at all times. The sun-glasses, which are simply small, -dark-coloured glass circles in frames, are not shown in the engraving. - -151.--=To Prepare to take Observations with the Prismatic Compass.= -After the window and prism are opened out, the prism is adjusted -to read the divided ring sharply when the compass is about level, -by raising or lowering the prism _P_ by pressure of the thumb and -forefinger of the right hand upon the stud placed upon the prism slide -fitting, shown below _SL_, until the divisions appear clear. - -152.--=In Using the Prismatic Compass=, the compass-box is held with -the thumb of the right hand under the prism at _SL_ and the forefinger -upon the stud _S_. The object which it is desired to observe is sighted -through the slit _SS_, cutting the left-hand side of the hair in the -window _SV_, while the division which comes opposite the reading point -at its edge by the reflection from the prism is noted. The ring when -free oscillates for a time, but is easily brought to rest for reading -by gently pressing the pin _S_ upon which the forefinger is placed. - -153.--Where objects are observed for taking their bearings above the -horizontal plane, the length of the window will be sufficient to -take in a vertical angle of 20° to 30°; but for such altitudes it is -necessary to take very great care that the compass is held level, -to get magnetic angles even approximately true. Below the horizon, -angles can be obtained with somewhat greater certainty by means of -reflections from the mirror. Altogether, except for taking nearly -horizontal angles, or for very close work in filling in after the -theodolite, it is much better to have the prismatic compass mounted -upon a tripod stand. With a stand, where the angle in azimuth is much -above or below the horizontal plane, it is better to have a small glass -level, described further on, art. 181, to place across the compass -when setting it up. If the compass ring is very carefully balanced -across 90° to 270° two bright wire points may be placed inside the -compass-box, level with the compass ring, which will answer for the -cross levelling. - -154.--=Stands.=--The author has made a very simple and inexpensive -tripod stand for the prismatic compass, the head of which consists of -a ball and socket only, clamped by a large milled-head screw. An axis -through the ball permits horizontal adjustment, shown in section, Fig. -37. - -[Illustration: Fig. 37.--_Improved prismatic compass stand._] - -[Illustration: Fig. 38.--_Hutchinson's prismatic compass._] - -155.--=Hutchinson's Prismatic Compass=, Fig. 38, is now very generally -used by military men. In this compass the metal cover is fixed on the -top of the compass-box, and a glazed opening is placed in the cover, -occupying about one-eighth of its area, near the prism. This opening -gives sufficient light to the compass card to permit it to be easily -read, and the loose cover is dispensed with; besides which, the cover -being fixed, this, as well as the whole instrument, may be made much -lighter, while retaining equal rigidity for wear. This compass is not -fitted with shade and mirror arrangements as before described. Size, -2½ inches diameter, ¾ inch in thickness; weight, only 8½ oz. in -brass; 3¼ oz. in aluminium. - -156.--=Captain Burnier's Military Compass.=--This portable compass is -more generally used on the Continent than other forms. It is generally -combined with a clinometer, therefore the illustration is deferred, -_seq._ with clinometers. The compass ring is set up vertical to the -plane of the needle, and is read by an index point by means of a -cylindrical lens. It has a pair of sights formed of a slit near the -eye-piece, and a hair in the window as in the prismatic. When this -instrument is held horizontally, at about a foot distance from the eye, -the sight line and the index line read distinctly into the graduations -of the ring. A lifter is provided to raise the compass off its -centre, as with the prismatic compass, and a spring clutch to prevent -continuity of oscillation. It is adapted to be set up on a plain rod -stand, the socket fitting to which is held in the hand when it is used -as a hand instrument. - -[Illustration: Fig. 39.--_Sketching protractor for use with prismatic -compass._] - -157.--=Surveying with the Compass only.=--In modern practice very -little surveying is performed with the compass, except for sketch or -exploring maps and filling in details, wherein the prismatic compass is -useful. The magnetic needle was formerly much used for surface work, -and depended upon almost entirely for underground work; but this has -been found practically in many cases unsafe, from the uncertainty of -magnetic variations, local and other, in the district surveyed. Mining -compasses, or _dials_, as they are termed, are now in modern practice -made with means of taking angles with the compass, and independently -of it. This subject will therefore be deferred to a future chapter on -mining instruments. - -158.--=In Plotting Military Sketch Surveys= from angles taken with -the prismatic compass, the paper employed is ruled lightly all over -with parallel lines an inch or less apart. The angles taken with the -prismatic compass from 0° to 360° (northern zero) are set off with -an ivory military protractor, which has lines to correspond with -latitudinal lines drawn over its face at 90° to its base, so that the -protractor may be placed transverse to any line drawn on the paper with -its centre in any position. Particulars of this method are given in -every detail in Major Jackson's _Course of Military Surveying_, and in -my work on Drawing Instruments. The military protractor is shown Fig. -39. - -159.--For making a sketch plan with the prismatic compass, a very -convenient way is to use the tee-square, the upper edge of the blade -of which represents magnetic east to west, the upper end of the board -magnetic north and the lower end south, according to the reading of -the compass. The bearings taken from any starting-point are set off -on the plot by a semicircular protractor with its base resting along -the tee-square. The northern angles are raised with the square at the -left-hand side of the board and the southern with it at the right. The -distances from the station for all bearings are measured and set off by -scale. - -160.--It is indifferent how many stations are taken by the prismatic -compass. The measurements in any direction may continue all round an -estate, and will be found fairly correct if carefully made, as the -small personal errors in reading the prismatic, which may be _plus or -minus_, tend to correct each other on the whole, and to tie up the -lines. - -161.--The rolling parallel rule may replace the tee-square, if it is -thought desirable to place the plan in a direction other than that -erect to magnetic north with the paper, or that it is inconvenient to -use the tee-square. In this case a few parallel lines may be at first -drawn correctly across the paper, at about equal distances, with a -sharp pencil E. to W. for references to reset the parallel rule at any -position desired. - -[Illustration: Figs. 40, 41, 42, 43.--_Pocket magnetic compasses._] - -162.--=Pocket Magnetic Compasses.=--The subject of compasses will -scarcely be complete without mention of the small pocket compasses -which are so useful and universal. Several well-known forms are shown -in the next illustration. The square form shown first, Fig. 40, will -be found the most useful for very rough sketching. The edges may be -sighted for the direction of roads, etc., or the box may be placed -against a wall for taking the magnetic direction of a building. In like -manner also the compass-box may be laid on a drawing and lines drawn -along by the edges of the box to the magnetic directions taken. This in -most cases is sufficiently accurate for architectural work, in which -the exact direction is not generally thought to be important. Fig. 41 -is a French form of compass with step reading level with the upper -surface of the needle. Fig. 42 is an old English form with enamelled -dial, with lifter under the bow of the handle. Fig. 43 is the same make -in a hunter case. In this the lifter rises upon the case being closed. - -[Illustration: Fig. 44.--_Trough form "Egyptian compass."_] - -163.--The author has made a small pocket magnetic compass, which is -represented in the illustration above. The needle is placed in a long -box. It reads at its point into a single line when the needle is -exactly parallel with the sides of the box. The lid turns up endwise. -The needle is lifted by closing the box. - -[Illustration: Fig. 45.--_The author's under slide for setting off -variation._] - -164.--In a form of compass similar to the above, the author has added a -thin slide to the under side of the box, by means of which the magnetic -variation may be adjusted, as shown Fig. 45. This slide moves out just -the amount of magnetic variation, the stud _S_ being made concentric -for this adjustment. If the slide box be made of ivory a few useful -scales may be divided upon it. The compass slips into a light leather -case, and is the most portable for its length of needle of any compass -made. The edges of the box are used as directing lines, as above -described for the square form. The illustrations show a compass made -for Great Britain, but a similar instrument is also made universal. -In this case the box is a little wider, with the centre of the slide -in the middle, so that the magnetic variation can be set off west or -east. A rider also on the needle enables it to be balanced in southern -latitudes. - -[Illustration: Fig. 46.--_Barker's luminous compass._] - -165.--=Barker's Luminous Compass=, with floating dial of -mother-of-pearl, one-half of this being engraved with black figures -and the other half painted black with the figures left white, permits -magnetic direction to be observed in the dusk and by moonlight. These -compasses, Fig. 46, are much used by travellers. Mr. Francis Barker has -also designed a compass in which the needle carries a bar coated with -luminous paint. - -FOOTNOTE: - -[2] See _Phil. Trans._ 1896, vol. 188, Map. 9. - - - - -CHAPTER IV. - - LEVELS--METHODS OF ASCERTAINING--LEVEL TUBES--MANUFACTURE--CURVATURE-- - SENSITIVENESS-TESTING--READING--CIRCULAR LEVELS--SURVEYORS' LEVELS-- - Y-LEVEL--PARALLEL PLATES--ADJUSTMENTS OF Y-LEVELS--SUGGESTED - IMPROVEMENTS--DUMPY LEVEL--TRIPOD STANDS--ADJUSTMENT OF DUMPY-- - COLLIMATOR--IMPROVEMENTS IN DUMPY LEVEL--TRIBRACH HEAD--DIAPHRAGMS-- - CUSHING'S LEVEL--COOKE'S LEVEL--CHEAP FORMS OF LEVEL--HAND LEVELS-- - TELESCOPIC LEVEL--REFLECTING LEVELS--WATER LEVELS. - - -166.--=A Level Plane= is understood technically to be a plane truly -tangential to the theoretical spheroidal surface of the earth, as -represented by any spot upon the mean surface of the ocean or of still -water free from local attraction. The importance of having the means of -constructing efficient instruments that can be conveniently employed to -obtain the correct relative altitudes of points or stations upon the -earth's surface, in relation to such a plane or _datum_, can scarcely -be overrated. Such instruments are not only used for topographical -surveys of countries, but also in designing and carrying out public -works adapted to the local conditions of natural inclination of the -land surface, for railways, drainage, irrigation, canals, water-works, -and other constructions. - -167.--The force constantly at our command to enable us to ascertain -relative altitudes and to form mentally or graphically local level -lines on the earth, is that of _gravity_; and it is only a question -in any case how the action of this force shall be employed. There are -four principles which we may accept as data for employing gravity, each -depending upon a natural phenomenon:--(1) The open upper surface of a -liquid unaffected by currents of air, or the influence of solid objects -in close proximity causing capillary action, or local attraction of -solid masses, represents a level plane. (2) The line of a plummet -unaffected by currents or lateral attractions forms a vertical line -to which the level plane is everywhere at right angles. (3) The -atmospheric pressure, from the approximated equality of its density due -to its weight in proportion to its height over limited areas, gives -pressure according to its gravity--therefore altitude or difference -of level relatively to lesser pressure compared with a lower datum. -This pressure is measurable with a barometer or other form of pressure -gauge. (4) The resistance to ebullition in a liquid is inversely -proportional to the weight or pressure of the aërial fluid resting -upon its surface. This is measurable by the temperature at which -liquids boil under varying atmospheric pressures. Various instrumental -refinements have been discovered to render these natural phenomena -available in practical use for ascertaining difference of height. The -first and most exact method employed for this purpose, by means of the -liquid plane, will be considered in this chapter. The other methods -will be deferred to later pages. - -168.--In taking the level of a liquid surface contained in a vessel, -we have, as just stated, to keep this surface free from the disturbing -influence of air currents, and to surround the surface with equal -conditions of capillary attraction, or to make these conditions equal -in the direction in which we desire to ascertain our level. This is -found practically to be best performed by means of a sealed glass tube, -in which the liquid will by gravitation naturally occupy the lower -place, and any air or lighter fluid contained therein the space above -this. - -[Illustration: Fig. 47.--_Level tube (bubble)._] - -169.--=Level Tubes=, _or Bubble Tubes_, as they are technically -termed, are used as a part of nearly all important surveying -instruments. One of these is represented Fig. 47. The glass for the -construction of these tubes is drawn at the glass-houses in lengths of -about 6 feet, and may be ordered of any desired size and substance. The -tubes are drawn of as nearly straight and equal bore as possible. They -are, nevertheless, found to be, when examined after annealing, curved -more or less in various directions at different parts of their lengths. -They are found also generally to be slightly tapering from end to end -and of slightly unequal substance. In the manufacture of level tubes -parts of the tube are selected with approximately regular longitudinal -curvature, and these parts are cut off into the required lengths by a -triangular file dipped in spirits of turpentine, to be ready for the -future operations of grinding, sealing, and dividing. After the tube -is cut off and carefully examined to get its most concave internal -surface upwards, this is then marked by a _test mark_, with the flat of -a file, near one end for future work and reference. The grinding of the -inside of the glass tube to true curvature is performed by passing it -over a brass mandrel or _core_, which is employed to grind the glass by -means of fine emery. The _core_ is turned slightly barrel-form to the -longitudinal curvature intended for the upper surface of the finished -tube. It is made of full three-quarters the diameter of the interior -of the tube, and a little longer than the entire tube. This core is -attached by its ends to two stiff but flexible wires of brass, about 8 -B.W.G. for a tube of ·7 inch diameter, and these wires are held firmly -by their ends in two vices, so that the core is slung, as it were, -to permit a certain amount of flexibility under the pressure of the -hand used in grinding. Some good makers do not use a mandrel core, -but only a strip of brass on the mandrel, extending about 60° of the -circumference. In this case the strip has to be corrected for curvature -during the grinding, which plan is sometimes preferred for certainty. -The grinding of a tube cannot be commenced with coarse emery, such as -is used in the grinding of lenses, as the cut of a coarse emery will -quickly split the tube. After the glaze is removed there is not so -much risk, so that a little time may be saved by passing a current of -hydrofluoric acid gas through the tube; but more careful testing is -required afterwards, as the cut of the grinding tool is not so evident -at sight when the glazed surface is removed. - -170.--The operation of grinding is very much the same as that described -for lenses, p. 17. The surface is required to be traversed in every -direction longitudinally and transversely, which is effected as far -as possible by a twist of the hand alternately to the right and left. -The tube should also be frequently taken off and turned end for end. -Slight variations of curvature are readily made by differences of -pressure of the hand on parts of the tube; and a little _coaxing_ is -allowed to get the centre of the tube _quick_ where the tube is to be -used for levelling only, and not for measuring small angles, so that -in this case the finished tube is slightly parabolical. The finishing -touch is produced with wash-emery. The inside should be left smooth but -not polished, as the slight roughness of a fine ground surface assists -the capillary action by causing better adhesion of the spirit, and -gives a quicker run to the bubble. Where the tubes are required of a -given radius they are tested frequently, during the grinding, upon the -_bubble trier_, by placing two corks in the ends of the tube, which is -nearly filled first with water for rough trial, and then with spirit -for final correction. - -171.--=The Bubble Trier= is a bar or bed 12 to 20 inches long, with -two extended feet ending in points at one end, and a micrometer screw -at the other, the point of which is a resting foot, thereby forming -a tripod. This stands on a cast-iron or slate surface plate. The -micrometer screw has a fine thread, and a large head with divisions -upon it to read seconds of arc. The tube is supported on the bar by two -Y's, which are adjustable for distance apart, according to the length -of the tubes to be tried. - -172.--_The Sensitiveness of a Level Tube_, the upper curvature and -ground surface being equal, depends very much upon the capillary -action due to its internal diameter, the larger tube, from the freedom -of restraint by capillarity, being the more active. As regards the -ultimate settling to gravitation equilibrium, perhaps there is no -difference, but small tubes are sluggish and take time to work. The -following are about the usual dimensions of the interior of sensitive -tubes--8 inches × 1 inch diameter, 7 inches × ·9, 6 inches × ·8, 5 -inches × ·7, 4 inches × ·6, 3 inches × ·5, 2½ inches × ·45, 2 inches -× ·4, 1½ inches × ·35, 1 inch × ·3. The larger the volume the -greater the expansion of liquid with heat; the longer the tube the less -torsion it is liable to suffer from sealing, so that if possible, as -expansion is a serious defect, it would be better to have short tubes, -if these could be sealed without disturbance of curvature. Much shorter -tubes are used in America than in Great Britain. - -173.--_The Curvature of a Level Tube_ is worked to radius according to -the delicacy of the work to be performed with it afterwards. The radii -of curvature of different level tubes used for scientific purposes -vary from about 30 feet to 1000 feet or more. The radius of any curve -may be conveniently measured by the relation of its versed sine to -its chord of arc, the chord being the length of the tube. If this is -first calculated out, a piece of shellac may be attached by melting it -down upon the centre of the edge of a parallel glass straight-edge, to -represent by its thickness the versed sine. The spot of shellac may be -brought to the exact height required from the straight-edge by filing -and stoning, at the same time taking its protuberance by a calliper -gauge provided with vernier or micrometer to read ·001 inch. The versed -sine of a given radius is formed for a given chord-- - - _versed sine_ = _rad_ - √(_rad_^2 - (½ _cho_)^2). - -174.--The general instruction, however, given to the maker is the -distance of run of the bubble that is required to give seconds or -minutes of arc; and perhaps this is after all the best test for -accuracy of the tube which, like all other articles in glass submitted -to the process of grinding, is subject to a certain amount of local -error. By this method the local error is discovered by testing with -the bubble trier. When the run is given, the radius of the curve of -the tube may be found if desired by the use of a common multiplier, as -follows, very approximately-- - - _Arc equal to radius expressed in minutes, 3437·74677._ - _ " " " seconds, 206264·80625._ - -The run of a good sensitive tube is frequently made 1/30 inch to the -second, here (omitting decimals)-- - - arc sec (206264·8) × 1/30 inch = 573 feet radius nearly. - -For scientific purposes a millimetre run per second is commonly used, -then-- - - arc sec (206264·8) × ·001 metre = 206·264 metres radius - or 680 feet nearly. - -For an ordinary 12-inch dumpy level the tube is divided into minutes at -about 1/10 inch apart, radius 28 to 30 feet; for a sensitive 14-inch -Y-level of good construction the same divisions may represent five -seconds, radius of bubble tube about 170 feet. - -175.--_The Divisions upon Ordinary Level Tubes_ are made after the tube -is finished, but with the highly sensitive ones the divisions are made -first. The run is taken from ten to thirty divisions on each side -of the centre of the tube, where it is lightly marked with a marking -diamond. These spaces are then equally subdivided and etched in with -hydrofluoric acid or marked with a hard steel edge dipped in turps. If -further refinement be required, the errors of run in relation to the -divisions are tabulated from the testing of the tube with the bubble -trier. A less careful method is employed by some makers of leaving the -level tube undivided and fixing an independent metal or ivory scale -over it. - -176.--Level tubes are generally filled with pure alcohol for ordinary -purposes; for trade purposes with methylic alcohol, which is much -cheaper. For very delicate tubes sulphuric ether or chloroform is -used. The sensitiveness of the bubble depends very greatly upon the -mobility of the liquid with which it is filled, and to the quality -of adhesion of the liquid to the glass. The relative mobility of the -above-mentioned liquids is found by delicate tests with the bubble -trier for small distances under the microscope at a temperature of 60° -Fahr. Taking water as 100:--we find commercial methylic alcohol 22, -absolute alcohol 13, sulphuric ether 5, chloroform 3,--that is, for -equal small runs taken in 15 seconds of time. All bubbles appear to be -more or less affected by temperature, particularly where the spirit is -not nearly absolute. In the higher temperatures the bubbles are more -active. The objection to chloroform, where it is likely to be subject -to great changes of temperature, and where there is no provision made -for regulating the size of the bubble--the means of doing which will be -presently discussed--is that its expansion from heat is so great that -it is very liable to burst its tube. It can therefore only be used with -ordinary sealed tubes where these are small and strong. Sulphuric ether -has the same fault, but in a lesser degree. - -177.--The sealing of ground tubes requires the skill of a very -experienced glass-blower, and is a technical matter on which no written -instructions would be of value under any conditions. A little strain -is unavoidably put upon the tube in sealing with the blow-pipe, so that -the curvature to which it is worked is more or less disturbed. For this -reason level tubes which are required to be of the highest degree of -accuracy are sometimes left as they are ground, and closed at the ends -by small discs of glass grooved to the end surfaces. These are fixed -on with glue, and when the glue is set are bound over with silk and -finally varnished; but this plan is much too delicate for instruments -for use in the field. - -[Illustration: Fig. 48.--_Colonel Strange's level tube._] - -178.--=Colonel Strange's Level Tube.=--These tubes, Fig. 48, are blown -with an outward bead at each end of the tube, two outwardly screwed -collars, _F_, being first placed over the tube before the blowing. -The tube is then ground to curvature. A plug, _S_, is formed for each -end of the tube from a plano-convex lens, ground to a bevel on the -plano side, and also ground into the end of the tube as a stopper. A -cap, _C_, is screwed over the end upon the collar. The springiness of -the cap keeps the stopper always tight. As there is no blow-pipe used -after the grinding, the tube remains constant as it is ground, or it -can be adjusted by grinding to any desired sensitiveness. This cap, -for security, is better covered with silk tied over it, and afterwards -well varnished. In this class of tube there is always a little risk of -evaporation. The system is not adapted to instruments to be used in the -open air. - -179.--=Chambered Level Tubes.=--As the run of a bubble varies -slightly with its size, for exact purposes and extreme climates it -is very desirable to be able to adjust the size of the bubble to the -surrounding temperature, so that it shall be kept at about equal -dimensions for all measurements made with it. This becomes particularly -important where chloroform is used, from the expansion being very -great. A general way of doing this is to have a stopper ground into one -end of the tube, which is itself a small bottle, on the under side of -which a hole is ground, so that by turning the tube over and raising it -more or less, any amount of the highly rarefied air it contains may be -taken to form the bubble that may be desired. The stopper is fixed with -thin glue. The general construction is shown below, Fig. 49. Of course -where such a tube is used there must be means of tipping and turning -the instrument in which it is fixed over, or the bubble itself must -have separate fixings. The portability of a surveyor's level admits -readily of the necessary tipping; with theodolite levels at right -angles to each other upon the vernier plate it would be impossible. - -[Illustration: Fig. 49.--_Bubble with supplemental air-chamber._] - -[Illustration: Fig. 50.--_Colonel Scott's patent protected bubble._] - -180.--=Extra Strong Level Tubes.=--Colonel Scott's very ingenious -device of enclosing a level tube within another tube of thoroughly -annealed glass will be found valuable in all cases where the tube is -much exposed, or where it is difficult afterwards to procure a new -tube in the case of accident. These tubes are at present only made -by the author for Scott's telescopic gun-sights, which are nearly -like small theodolites. The level tube, Fig. 50, is made as stout as -possible to be soundly sealed after filling. It is then enclosed in -an annealed tube, _CC′_, of about ·08 to ·12 inch in thickness, the -interspace between the two tubes being filled with Canada balsam. It is -then plugged with elastic marine glue, _KK′_ and cemented over _PP′_. -The annealed tube is of great strength, so that the complete naked tube -thus formed will bear dropping on the ground, and also when attached to -a large gun will bear the violent vibration of firing without injury. - -[Illustration: Fig. 51.--_Artificial horizon level._] - -181.--=The Level Tube may form a Complete Instrument in itself.=--In -this case the lower surface is ground to a flat plane to rest on any -plane surface. This level is generally contained in a small pocket -case, and is most convenient for adjusting instruments to level. It is -commonly used with the black glass artificial horizon, to be described. - -182.--=Mounting Tubes.=--Level tubes when applied to instruments are -generally mounted in brass covering tubes. Small level tubes under -2½ inches are conveniently mounted in such tubes with a fixing -of slaked plaster of Paris inserted at each end of the brass tube. -Larger level tubes should be bound round with thin paper pasted round -the ends, which is allowed to get quite dry, to be afterwards fitted -to the brass tube with a file. Fitted in this manner the tubes admit -of adjustment to the difference of expansion of the metal and glass -by change of temperature without distortion. There is no objection, -however, to thoroughly fixing one end of the tube with plaster if -the other be left free, and this is perhaps advisable for portable -instruments. - -It is convenient in mounting level tubes to place white glazed paper -under the bubble to reflect the light that passes through it to ensure -better observation. - -183.--=In Fixing Undivided Level Tubes=, or replacing them in -instruments, it is important to observe that the side with the _test -mark_, which is a small ground facet, should be placed on the _top_. - -184.--_In the Use of Level Tubes_ generally, it is not well to have -them of greater sensitiveness than the general construction of the -instrument upon which they are placed permits. Thus the centre of a -surveyor's level that may be under constant strain from the unavoidable -inequality of the pressure of parallel plate screws, will appear never -to reverse properly if it has a very sensitive bubble, the cause of the -irregularity being entirely due to the distortion from the strain on -the vertical axis of the instrument. The same irregularity occurs in a -lesser degree with the Y's of a theodolite, where these and the collars -become corroded by exposure. The optician often gets an undue amount of -credit for perfecting such instruments when he has merely replaced the -sensitive bubble by a dull one--that is by doing what is really in this -case the best for the instrument. - -185.--When an instrument that depends entirely upon the level for -its possible working is to be used abroad, an extra tube should be -taken, as the level tube is very generally more exposed and is more -delicate than any other part of the instrument. The tube may not only -be accidentally fractured with a slight bow, but even the heat of the -sun's rays will sometimes burst it. - -186.--=Reading the Bubble.=--The exact position of the capillary -concave surface of the spirit in the tube is liable to deceive the -observer by the difference of refraction and reflection it gives, -whether the light is towards the right or left hand. To avoid this -cause of error it is better, in sunlight, to hold a piece of white -paper at a short distance over the end of the bubble during the -observation taken of its terminal reading into the divided scale on -the tube. It is also important to note that the observer should stand -at right angles to the tube to see the position exactly where the -upper capillary line of the spirit cuts, as the tube itself refracts -the light unequally. It is not at all difficult to read the bubble if -the observer stand over it; but generally, as it is mounted upon an -instrument, it is at the height of the eye. In this position the hollow -surface round the bubble, caused by the adhesion of the liquid to the -sides of the glass tube, reflects the light in a manner that the hollow -may be taken for the end of the bubble, and a false reading made. It -is better if possible to take the convenient side reading first, and -afterwards get a glance at the upper surface reading for certainty. -In some cases this may be much assisted by the employment of a small -mirror of about the size of a spectacle eye, which is carried open in -the pocket, or, as the author has made it, it may close in a horn case -with a pocket lens, as in the Fig. 52 shown below. _C_ sheath, _M_ -mirror, _L_ lens. - -[Illustration: Fig. 52.--_Pocket lens and mirror._] - -187.--=Circular Levels= have been made tentatively for a long period. -They consist of a worked concave lens fitted into a brass cell with -indiarubber seating, the glass being secured by burnishing over a -bezel. This construction answers very well when new, but the spirit -the level contains is certain to evaporate slowly under every possible -care. Mr. J. J. Hicks has patented a hermetically sealed circular -level, in which he has succeeded in working the upper surface of -the glass to curvature. These levels, of course, are not subject -to evaporation, and are very useful and portable for approximate -levelling--as for plane tables, cameras, etc. - -[Illustration: Fig. 53.--_Hicks' patent circular level._] - -188.--=Surveyors' Levels=, of which there are many forms, consist -essentially of a telescope with a diaphragm at the mutual foci of the -objective and the eye-piece, the axis of the telescope being placed in -a direction truly parallel with the crown of a sensitive level tube. -The telescope with its level is mounted upon metal frame-work, carried -up from a vertical axis upon which the telescope rests. The vertical -axis is adjustable in relation to the axis of the telescope, so that -they may be brought perfectly perpendicular, the one to the other. The -whole instrument is also adjustable to a position of verticality of -its central axis, and the horizontality of the telescope in relation -to the surface of the earth in what is termed the _setting-up_ of -the instrument; so that when it is set up in this position levels -may be taken from it in any horizontal direction from one point of -observation, by rotation of the telescope about the vertical axis. -Having these essential objects in view in the construction of the -level, the form of the instrument may be varied as to details according -to the mechanical skill and taste of the maker and the special demands -of the civil engineer. - -189.--In the design of a surveyor's level very important considerations -are:--That the metal should be so distributed that every part is as -light as possible, consistently with sufficient solidity to take a -moderate amount of accidental rough usage, and ensure freedom from -vibration; that the whole structure should be in equilibrium about its -vertical axis when the telescope is extended at mean range, that is, -at about the focus of three chains--this is a quality often neglected; -that there should be sufficient light in the telescope, and that it -should possess a firm and durable stand. Every form of level should -embrace these qualities. - -190.--_The Oldest Form of Surveyor's Level_ is that termed the Y-level, -so named from the telescope being supported in Y-formed bearings. -This instrument was originally invented by Jonathan Sisson, a leading -instrument maker of the 18th century. It was much improved and brought -nearly to its present state of perfection by Ramsden, to whom practical -opticians owe so much for many advancements of their science, and to -his liberal publication thereof. This instrument is now very little -used in Great Britain; but it still maintains its original position, -to a certain extent, on the Continent and in America. In the eyes of -the optician it is still the most perfect level, possessing all the -instrumental refinements of adjustment he can desire. The reasons for -its partial abandonment by the profession will be discussed further on. - -191.--=The Y-Level= in a modern form is represented in the engraving -below, Fig. 54. The Y's are shown at _YY″_ edgewise. They are -supported by standards _SR_ upon the limb _L_. The telescope is -surrounded by two collars which are soldered upon it at positions -exactly corresponding with the Y's. The collars are turned perfectly -cylindrical and parallel on the surface with the axis of the telescope, -and ground in a gauge-plate to exact size so that the telescope may be -turned end for end in the Y's without altering the linear direction -of its axis in reversing it. The telescope is held from shifting -longitudinally in its Y's by a pair of flanges placed on the inside of -the collar pieces. - -[Illustration: Fig. 54.--_Surveyor's Y-level._] - -192.--The Y's are erected upon the limb, to which they are each fixed -firmly by a clamping nut _R_ at one end, and a milled head clamp at -_M_. The telescope is held down by strap pieces, each of which has a -joint at one end and a loose pin at the other, _PP_. The pin is secured -from dropping when out of use by a piece of cord attached to a part of -the instrument and to a loop through its head. At the top of the inner -side of the strap-piece under _YY″_ a piece of cork is inserted in a -cave. The cork by its elasticity keeps an equal but light pressure upon -the collar of the telescope. It will be seen that by the above plan of -holding the telescope, it is so far free that it may be revolved on its -axis, by which perfect adjustment of the diaphragm to the axis of the -instrument may be made in any direction. - -[Illustration: Fig. 55.--_Section of parallel plate and vertical -axis--arrangement of Y and other levels._] - -193.--=Parallel Plates= as a mode of adjustment of the vertical axis -will be first described, as they present the oldest form of setting -up adjustment. The vertical axis of the Y-level was formerly carried -tapering downwards, and the upper parallel plate was placed at about -the centre of the socket. Under this construction the socket was more -liable to strain from the use of the parallel plate screws. It is more -general now to construct the axis as represented in the illustration -above, Fig. 55, for Y and other levels with parallel plates. This -construction also renders the instrument more portable, as the parallel -plates and axis may be detached and lie closer in the case; the plan -is nevertheless open to many risks, which will be referred to in -discussing a three-screw arrangement. The general construction is shown -in the figure, of which the left-hand side is a half-section. _A_ is -a screw by which the parallel plates are attached to the limb of the -instrument; _M_ a large _milled head_, by means of which the screw -can be brought up firmly to its collar; _SS′_ the _socket_ which is -ground to fit the cone _C_; _C_ forms a part of the _upper parallel -plate_ _UP_; _B_ a _ball pin_ which screws firmly into _C_; _LP_ _lower -parallel plate_, part of which forms the ball socket, so that the whole -instrument rocks about the ball _B_ as a centre, by the action of the -parallel plate screws _PS_; _B′_ female screw for fixing this part, -which is called altogether the _parallel plates_, to the tripod head. A -clamping screw is sometimes placed upon the axis for slow motion. The -parallel plate screws are _tapped_, that is, have female threads cut -into the upper plate _UP_, and their points press the lower parallel -plate _LP_ at certain points, there being a _stop-piece_ placed round -the point of one screw to prevent rotation. The pressure upon the -screws can be increased as desired by means of the milled heads, and -the instrument made rigid in proportion; but it is very undesirable -that the pressure should be greater than that just necessary to support -the instrument firmly, as it is easy by the power of the screws to -disturb the figure of the axis and thereby derange it. - -The diaphragm of the telescope of the Y-level is generally webbed with -plain cross webs. The diaphragm and webs were described arts. 99 to 106. - -194.--_The Setting-up of the Y-Level_ is necessary to be understood -before the instrument can be adjusted. The same description which -answers for the setting up for adjustment will also answer for -the setting-up of the instrument in the field for actual work. In -this description it will be convenient, therefore, to consider the -instrument as being in this case _in adjustment_ as it leaves the hand -of the maker. The after adjustments will be presently taken as from the -original state of the instrument, as the maker has to do them in the -first instance. Practically, the civil engineer has only to make slight -differential adjustments at any time, as an instrument, by the solidity -of its construction, will retain the general adjustment nearly, upon -which further adjustments take more the nature of final corrections, -which become necessary only from accidental causes. - -195.--_Setting-up of the Y or other Level with Parallel Plates._--The -tripod stand is opened out so that the legs stand, if on level ground, -inclined towards the centre of the instrument at an angle of about 70° -to the horizon. The toes of the legs are each separately pressed into -the ground sufficiently to make the instrument stand quite firmly. The -instrument is then taken from its case and screwed down tightly upon -the tripod head. - -196.--_The Eye-piece is Adjusted_, art. 108, by sliding it gently in -and out until the webs can be seen most distinctly. On a bright day a -white pocket-handkerchief may with advantage be thrown singly over the -object-glass to prevent any confusion from objects in the field of view -during the focussing of the eye-piece. For the setting-up adjustment of -the telescope, it is brought in position to lie directly over one pair -of parallel plate screws, Fig. 55, _PS_, _SP_. - -[Illustration: Fig. 56.--_Diagram plan of parallel plate screw milled -heads._] - -197.--The milled heads only of these screws are represented in plan -in the diagram Fig. 56, _aa′_ being the opposite pair over which the -telescope will be assumed to be at first placed. The level tube is now -brought to adjustment by bringing the bubble to the centre of its run -by means of the parallel plate screws _aa′_, by taking the milled heads -of these screws, one between the ball of the thumb and forefinger of -each hand, and rolling them simultaneously the one in one direction and -the other in the reverse. This action tips the axis of the telescope in -one direction or the other. Thus by the screws being rolled inwards, as -shown by the direction of the arrows in the diagram, the left-hand side -of the instrument would be raised. If turned the reverse way, the right -hand end would be raised. The opposite end, from that to which the -bubble runs, always requires to be raised. Where the ground is rather -soft, adjustment when nearly correct may be made partially by pressing -down one or other of the legs; in this case the telescope should be -placed parallel with the toe of the leg which is pressed down and the -axis of the instrument. - -198.--When the level tube is adjusted over the screws _aa′_ it is then -placed over _bb′_ and adjusted in a similar manner, returning again to -the position _aa′_ for final adjustment. When the level is in perfect -adjustment the bubble should stand in the centre of its run in making a -complete circuit of the horizon by rotation of the instrument upon its -vertical axis. - -199.--In and during the setting-up adjustment it is most important that -the screws should not be made tight enough to cause, by their pressure -upon the parallel plates, distortion of the vertical axis. Should this -occur, the instrument will not level in all positions by the same -setting. The action of the screws also, from the great elasticity of -the metal, should distribute the pressure about equally between the -_opposite pairs aa′ and bb′_. The difficulty of accomplishing this -with certainty makes another form of adjustment, with three screws -only, preferable for setting-up, which will be considered further on. -Where the instrument is set up for use, if the adjustment of the bubble -be fairly correct to the centre of its run, the reading of the staff -may be sighted and the telescope brought to true focus upon it by -moving its milled head until the divisions of the staff are as sharp -as possible, and then moving the eye upwards and downwards to be sure -there is no error of parallax, art. 109. After this the final adjusting -of the bubble should be made, noting particularly that there are the -same number of divisions in its run on each side from the centre if it -is a divided bubble. - -200.--_Adjustment of the Axis of the Telescope_ in true parallel -direction with the periphery of its supporting collars in its Y's. -This is performed entirely with the four capstan-headed screws which -adjust the diaphragm, one of which is shown, Fig. 54, _C_. Having -the adjustment of the eye-piece in focus for the webs in the manner -described, arts. 108, 109, the object-glass focussed upon a distant -distinct small object or mark, and without parallax, the instrument -which carries the telescope is then exactly adjusted to make the -intersection of the webs cut the mark. The telescope is now turned -half round on its axis, so that the lower part becomes the upper, and -observation is again made of the distant small object or mark. If the -same intersection of the webs falls on the same point of the object, -the collimation adjustment is perfect. If it does not do so, the upper -capstan-headed screw at _C_, or the under opposite one, is loosened by -means of the small pin provided with the instrument, and the opposite -screw tightened until the webs are brought over a point situated -half-way between the points cut by the first and second observation. -The telescope is again directed to the point first observed, and the -adjustment checked to see if it has been done correctly, that is, if -the level reverses, cutting the same point, or whether it requires -further adjustment by the same process as before. The other web of -the diaphragm, at right angles to the first, is adjusted in a similar -manner, but with the other pair of capstan-headed screws. - -201.--It is sometimes inconvenient to adjust out of doors: this may be -performed very well indoors. By daylight a small cross may be made with -ink on a sheet of white writing-paper for the sighting object, which -should be placed at as great a distance as convenient, say 20 or 30 -feet. By night a pin-hole may be made through a piece of paper and a -candle or a lamp be placed behind it. - -202.--_Adjustment of Vertical Axis._--For this the eye-piece is first -brought to focus on the webs. The telescope is then placed directly -over one pair of parallel plate screws opposite each other, and the -instrument is levelled. The Y's are then opened out; and the telescope -is directed so that the intersection of the webs cuts or covers any -distinct small mark upon a distant object, or preferably upon the -centre reading of a foot line upon a levelling staff. There is no -objection to adjusting slightly to this by the parallel plate screws, -as this adjustment is independent of the level of the instrument. The -telescope is then taken out of its Y's and is turned end for end and -replaced. The telescope is now turned half a revolution on its vertical -axis, and the webs are again brought to read on the staff, if one is -used. If they now fall upon the same spot or foot line, the vertical -axis is perfectly perpendicular to the axis of the telescope in this -direction. If the webs do not fall upon the first reading or point, the -amount of difference of reading is recorded and this space is bisected; -so that now, if the telescope be adjusted by the milled head _M_, at -its bearings upon the limb upon which it is supported, for the webs -to cut the bisection, the axis will be perfectly perpendicular in the -direction of its bearing socket. The same process must now be repeated -with the telescope placed at right angles to its first position, -that is by bringing it over the other pair of parallel plate screws -which were not used at first. There is at all times a certain amount -of disturbance of the instrument due to handling it; it is therefore -necessary to repeat the whole of the above process until the instrument -reverses in any direction, but this final adjustment is better deferred -until the adjustment of the level tube, to be next described, has been -made. - -203.--_Adjustment of the Level Tube._--The telescope is placed as -before over an opposite pair of parallel plate screws, and these are -adjusted until the bubble is in the centre of its run. The telescope -is then turned half a revolution, so that it is placed over the same -pair of screws in the reverse direction, and the displacement from the -bubble from the centre is now noted. The capstan-headed bubble screws -at the end of the level _B_ are then adjusted to one-fourth of the -difference observed, and the parallel plate screws are adjusted for -the other fourth, so that by these two adjustments the difference of -the run in the two positions is bisected. The same process is repeated -over the second opposite pair of parallel plate screws. If this be -very carefully done with a correctly divided bubble, the Y's of the -telescope may be opened out and the telescope be reversed end for end -in its Y's, and the bubble remain true. But it is quite as well to go -over all the adjustments a second time, as before recommended. - -204.--If the level is to be adjusted by night, this can be done very -correctly by a fine cross drawn on paper placed on a wall, with -a candle or gas burner shining brightly on it at twenty feet or -so distance from the instrument. For this adjustment by night the -instrument must be well constructed, as the tubes require drawing out -to their full extent for focussing near objects. If the tubes are not -quite straight, the object-glass suffers considerable displacement in -the drawing out, or technically _droops_, which is a very common fault -in badly-made instruments. - -205.--Where webs are used for the reading, they are liable to become -baggy or dirty, art. 101, and very frequently to break; nothing can, -therefore, be more useful than to be able to re-web a stop in the -evening, with command of the easy and certain means of readjustment -described, when far from the optician's aid. - -206.--As the Y-level is so perfect in its arrangement for adjustments, -and so nearly meets the optician's ideal, it will be well to inquire -what are the objections made to its use by the majority of British -surveyors. The first and most important is that it possesses so -_many loose parts_, to which the practical man honestly objects. The -author was, many years ago, when Y-levels were more popular, trying -to persuade a cautious practical surveyor who appeared to be very -anxious for the certainty of his work, and who was going abroad, to -take a Y-level instead of a dumpy one he was selecting, when he had -his arguments stopped by the following question:--"Suppose you were -surveying in a tropical country, thousands of miles and an ocean voyage -from civilisation, where your native porter objected to carry much -weight, and your instrument case had to be left at a back station--when -your umbrella was all the burden you felt you could support. In this -case, suppose your porter, whom you had lost sight of for a short -time, arrived with your level, minus the telescope--lost by becoming -loose, perhaps from having been played with while he was resting--how -would you praise the Y-level?" This gentleman assured me that _he_ -did not, and that this was a true account of his experience with the -last Y-level he possessed. Other objections, besides loose parts, are -that Y's and collars do not remain as perfect as when they leave the -optician--that they are liable to wear by friction of constant movement -in being carried about upon the points in contact between them, and -thereby form facets; that the collars become corroded by exposure, and -that they have open spaces that collect sand from flying dust which -fixes itself into the collars and Y's, so that this arrangement loses -the perfection the optician claims for it. Further, that the cross -bubble, which is uniformly placed on the dumpy level, effects a great -saving of time over swinging the telescope backwards and forwards -with every movement of the adjusting screws. Another feature is that -in the dumpy level, to be described, the vertical and horizontal webs -of the diaphragm cannot be disturbed from their position by rotation -of the telescope after the level is once set up; and this verticality -indicates conveniently at once whether the staff is held vertically, -which is otherwise a great difficulty with the ordinary form of Y-level -reading. - -207.--=Improved Y-Level.=--The above-described defects the author has -tried to remedy by a modification of the Y arrangement, by forming -the Y's with much broader bearings, and instead of the old loose -pins screw fastenings are fitted, which firmly lock the telescope in -position with the webs vertical. This, so far, obviates the danger -from loose parts, as by this arrangement the telescope also becomes -practically firmly fixed. In adjustment the collars are opened out, and -in closing press a stud into the telescope by which it takes a given -position. This enables a cross bubble, shown on Fig. 57, to be also -placed on the telescope for approximate adjustment, which saves the -frequent disturbance of the telescope by making cross adjustments. The -diaphragm of this Y-level is exactly the same as that of the dumpy, to -be described art. 210. From the limb downwards the author uses the same -construction as he now employs on his improved dumpy level. This will -be described with that instrument further on, art 231, _seq._ Also the -setting-up adjustment with it, which is different from that already -described where parallel plates are employed. - -[Illustration: Fig. 57.--_Improved Y-level._] - -208.--Perhaps, upon the whole, the conditions which formerly rendered -the Y-level undoubtedly the best practical level have so much changed -that the more solid construction of the dumpy may entirely supersede -it, as it seems likely to do in modern practice, and the optician -will lose his ideal. Some reasons for this may be stated, but whether -sufficient is a question. The manufacture of object-glasses of good -figure and proper centring was formerly understood by a few scientific -opticians, who were principally engaged upon astronomical telescopes, -so that, with the exception of those made by Troughton and Simms, -no very good and accurately centred lenses were used in surveying -instruments. With bad centring alone, in ordinary telescopes, the -webs in collimating were drifted aside, and needed the Y system of -adjustment to make the telescope workable for levelling. In the -modern good object-glass, of which there are now several makers, the -centring is so nearly perfect that the webs in adjustment fall in the -centre of the diaphragm when it is placed true to the cylindrical -axis of the telescope. If the webs are placed as suggested without -further adjustment, no very serious interference is caused by want -of collimation of the axis. With this fact in view, the instrument -maker needs leave little space for adjustment of the webs for centre -displacement to become a source of error to persons not used to -adjustments. - -209.--Further, with a well-centred object-glass, as it leaves the hands -of the scientific optician, and a solidly constructed adjustment to -collimation being provided for in the making of a level, true working -may be done even if there is a small error in the collimation. The -late William Gravatt, C.E., was of opinion that firm construction, -compact form, and plenty of light in the telescope were more important -than easy facilities of adjustment. There is no doubt he found the -less open adjustments the better in the hands of the imperfectly -trained assistants who were pressed into service during the railway -mania of 1848. At any rate, at this period we have his invention of -the "Gravatt," or, as it was afterwards termed, the "Dumpy" level, -which has remained with us with slight modifications in its mechanical -parts and with increasing popularity until the present time. The late -Mr. Troughton, recognising the same facts, also made a level in which -there was no adjustment to the supports of the telescope after it -left the hands of the maker. In his level he also left no adjustment -to the bubble tube, which no doubt would prevent tampering, but which -could scarcely be called an improvement; as this tube is liable at all -times to be broken, therefore to need replacing with another tube, -which cannot be made quite similar, and therefore needs easy means of -adjustment for a surveyor to replace it when abroad. This level has -gone out of use, but it is mentioned here, as the old engraving of it -remains in some of our _modern_ text-books. - -[Illustration: _Fig. 59.--Dumpy level._] - -210.--=The Dumpy Level.=--One of the most important structural -improvements made by the late William Gravatt in his dumpy level, was -the addition of a cross bubble, shown end-view in Fig. 59 at _CB_. -This improvement over the old form of Y-level permitted the setting-up -of the instrument to be completed approximately, without turning the -level a quarter revolution backwards and forwards several times during -the operation, as was necessary in the setting-up of the Y-level. The -compact form, lightness, and large field of view in the telescope -otherwise commended it to civil engineers, when Gravatt had pointed out -the possibility of sufficient practical adjustment without resorting -to the cumbrous proportions of the Y-level as it was then made. Modern -experience has shown that the dumpy form of telescope could very well -be applied to the Y construction, and this has been done, as shown in -the preceding pages; but at the time the dumpy was invented by Gravatt, -the Y-levels were very commonly made 20 inches or more in length of -telescope, and were altogether very flimsy affairs. Gravatt's 12-inch -level was found to be quite equal in power and of less than half the -bulk and weight. A 12-inch dumpy should read the ·01 foot on a Sopwith -staff, which is described in the next chapter, at 5 chains with a -webbed or glass diaphragm, Fig. 61; with a more open reading than -Sopwith's staff a greater distance than this. A 14-inch dumpy should -read the ·01 foot at 10 chains. - -211.--=The Dumpy Level= of modern form is represented in the engraving, -Fig. 59. It consists of a telescope, fully described art. 94, which -carries a ray shade _RS_ at the object-glass end, to work in the -field to eastward or westward facing a low sun. The eye-piece _EP_ is -adjustable to the webs in the telescope by pressure in or out. Two -straps or bands are accurately fitted and soldered round the tube of -the telescope; one of these carries a hinge joint, and the other a pair -of locking nuts to support the level tube _GG_, and at the same time -permit its adjustment. The level casing tube has two three-quarter -bands, which slide upon it, pointed at one end _GG_: these adjust to -the length of the bubble for changes by temperature. The lower part -of each strap-piece is left a solid block of metal, to give very firm -support to the telescope as it rests upon the limb _L_ beneath. The -limb may be either a casting with a socket screw only in its centre, -or a compass box may be formed in the centre and the socket screw be -placed under this, as it is shown in the figure at _S_. The attachment -of the telescope support to the limb is made by three screws, two of -which draw the limb down, and one in the centre presses it upwards, as -shown in the section Fig. 60--_CC′_ telescope, _TT′_ drawing screws, -_P_ pressing screw. - -[Illustration: Fig. 60.--_Attachment of telescope block to limbs._] - -212.--It will be seen that by this means firm adjustment may be made -either by raising or lowering one end of the telescope, as also by -a lateral rocking motion should the web or bubble not be quite to -position. This plan is certainly moderately solid, and little fault -can be found with it, except that a little torsion may be put on the -telescope by unequal screwing, and that it appears slovenly in leaving -an open gap between the limb and block; therefore the author prefers -in his own form of level, which will be presently described, that the -block be solidly fitted down upon the limb, as is shown in the section -Fig. 60, and the telescope be placed permanently exactly parallel with -it. If the vertical axis be once fixed truly perpendicular to the axis -of the telescope as solidly as possible there is very little risk of a -bell-metal centre of ¾ inch or so diameter being bent; therefore all -parts may be closely fitted between the axis and the telescope. Some -makers, instead of screwing down at both ends of the limb, make one end -a rocking centre and adjust only by screw at the other end. This plan -lacks a little of the stability looked for in the dumpy system. The -general construction of the vertical axis is the same as that of the -Y-level already described. The parallel plates, tripod head, and tripod -are also the same, art. 193, Fig. 55. - -213.--As the telescope of the dumpy level does not possess any simple -means of determining the accuracy of the fitting of its sliding tube, -it is a very important point in these levels that this fitting should -be good, so that the object-glass does not droop when extended. For -this reason the inner sliding tube of the telescope should be as long -as possible, and its adjustment by the rack sufficient to bring an -object in focus at 15 to 20 feet distance. This point is sometimes -neglected. The author was once amused by a young surveyor bringing him -an invention, which was to fix two points by the side of the telescope -_to enable him to read at short distances_. It was seen on examination -of his own level that his telescope, a badly-fitted one, would not read -at half a chain, hence the ingenuity of his invention. In some cheaply -made levels the solid ring fitting to the telescope, above described, -which connects the limb firmly with the bubble tube, is replaced by -blocks soldered on the telescope with soft solder: the method is very -unsound from risk of imperfect soldering. The blocks are very liable to -become loosened by a jar. - -214.--The diaphragm of the dumpy level is generally webbed with two -vertical webs and one horizontal. In use the image of the staff is -brought between the vertical webs, which indicate whether it is held -upright. The upper margin of the portion of the horizontal web between -the two vertical ones is the index of level to which all readings are -made, either for adjustment or for reading the levelling staff in the -field. The somewhat loose and slovenly four-screw adjustment for a -level diaphragm used in rough work with capstan-head screws, shown -Fig. 23, p. 50, which is necessary for the adjustment of the telescope -in Y's, has been abandoned for many years in the better-constructed -dumpy levels by all good makers, and the more solid construction, shown -below, Fig. 61, used in the place thereof. In this plan there is no -lateral adjustment: the diaphragm is carried as a frame in a dovetail -slide, and is adjustable by vertical screws only. The figure shows the -face of diaphragm:--_BB′_ slide pieces, _A_ slide moved by capstan-head -screws. - -[Illustration: Fig. 61.--_Diaphragm of dumpy level with webbed stop._] - -[Illustration: Fig. 62.--_Same, with stadia webs._] - -215.--=Subtense or Stadia Webs.=--It is very advisable in all levels to -have two extra webs, or lines cut on glass, placed one on each side of -the central horizontal web or line, fixed at such a distance apart that -the image of 10 feet of the staff when placed at 10 chains distance may -exactly cut the inner space between the lines. These webs or lines may -be used as a means of measuring distances often more exactly than can -be performed with the chain if the surface of the land is irregular; -or, in any case, they form a good check upon chain measurement. If the -webs or lines are separated so as to subtend an arc whose chord is 10 -feet at 10 chains, it is easily seen that 1 foot of the staff will -represent this chord at 1 chain, and that each ·01 of the foot on the -staff will represent 1 link in distance. A diaphragm webbed or lined -in the manner described is shown in Fig. 62. There is some difficulty -in placing webs in exact position, and allowance should be made for the -optical conditions by the addition of a plus factor. This important -subject will be fully discussed hereafter in Chapter XII. - -[Illustration: Fig. 63.--_Tripod._] - -[Illustration: Fig. 64.--_Section of one turn-up leg of the same._] - -[Illustration: Fig. 65.--_Section of tripod._] - -216.--=Tripods, or Stands.=--This matter was deferred when -describing the Y-level. The same form of tripod is used for both -Y-level and dumpy. In this country the tripod is generally made of -straight-grained, well-seasoned Honduras mahogany, which stands better -than any other wood. When the tripod is folded up for carrying or for -putting by it forms a cylindrical pole which is bellied out at about -one-third its length from the top, and diminishes downwards and upwards -from this point. For a 14-inch Y-level or dumpy the dimensions of the -tripod are about 3½ inches at its greatest diameter when closed, -tapering off to 2½ inches at both the top and the bottom ends. For -a 12-inch level the section is somewhat less. Each leg of the tripod -takes an equal section of the cylinder, the inner angle meeting in -the axis being at an angle of 120°, as shown in section Fig. 65. -_Shovel-pieces_ are shown in Fig. 59 _AA′_ (p. 110), attached to the -top of each leg by four screws passing from the brass to the wood. -There should be also two screws from a brass plate inside the leg to -the shovel-piece, making connection brass to brass: this is important, -as fixings from the brass to the wood only become loose and shaky by -shrinkage. The shovel-piece is formed into a strong tenon at its upper -end, through which a bolt passes connecting the _book-pieces_ together. -The book-pieces are plates cut to an angle of 120°, so as to fall -true on the tenons of the shovel-pieces. Where hand-work is used for -making the tripod head, the book-pieces are attached by three screws; -where machinery is used, the head is made in the shaping machine out -of a solid casting, which is much better. The tripod head carries a -screw about 1½ inches diameter with coarse thread, which fits into -a socket on the lower parallel plate of the level, whether Y or dumpy. -There should always be a plain piece, technically a _lead_, above the -screw. This holds the instrument steady before it is screwed down, -and also leads the screw directly to its corresponding thread, thus -saving risk of crossing the thread. A common defect in tripod heads is -the thinness of the tenon, so that the leg, if twisted, is felt to be -rickety. This tenon is better made wide, as shown in the staff head in -Fig. 70A, _seq_. - -217.--There is a little difference of opinion as to the form of the -woodwork of the tripod for 14-inch levels, some preferring an open -framed stand in place of the solid form shown in section Fig. 65. These -open framed stands are not so compact to carry, and, as the author -thinks, unnecessary for levels of 12 inches and under where the tripod -head is solidly made. They are well adapted for larger levels and for -theodolites, therefore the description of a framed tripod will be -deferred to the discussion of these instruments further on. - -A few engineers prefer yellow pine for the tripods instead of mahogany: -this is much lighter for its relative stiffness, but it is rather soft -for the fixing to the shovel-pieces, and therefore scarcely so reliable -as mahogany for durability. Where lightness is important the author -employs cedar, which is as light as pine but harder. - -218.--The lower points of the legs, technically _toes_, are pointed to -an angle of about 60°, and are shod on the insides with steel plates -to bite the surface upon which the tripod stands when the legs are -extended for use. Two brass rings slip over and bind the legs together -when the tripod is out of use. - -219.--Many years ago the author introduced the plan of having one of -the legs to turn up at about 1 foot distance from the toe. This is -shown Fig. 63 at _A_, and in detail section Fig. 64. The joint is made -perfectly firm by a winged screw at _S_, which screws from a boss cast -on the hinge _J_ to a solid metal shoe _P_. When the leg is turned -up, the screw fixes it in the female screw _S_. This plan is very -convenient for use in mountainous districts, as it enables the level -to be set up fairly well without an uncomfortable angle to any of the -legs, or risk of the instrument toppling over. This plan is now nearly -superseded by a ball joint as a part of the setting-up adjustment. - -The tripod head shown under the level of Fig. 59 is by no means the -best, but it is the easiest made therefore, it is the general trade -form in use, both for the level and theodolite. Some very superior -forms will be discussed further on in description of the instruments to -which they are attached. - -220.--=The adjustments of the Dumpy Level.=--As this instrument does -not possess the means of revolving the telescope upon its axis as with -the Y-level, the adjustments are somewhat more complicated, and are -performed in an entirely different manner when they are to be made by -the civil engineer. The differences are not so great in the hands of -the optician, as he generally possesses a movable pair of Y's upon -which he can adjust the telescope conveniently for collimation within -his own works, by supporting the telescope tube in Y's at a position -exterior to the bands which surround it. The tools for this adjustment -the author has occasionally supplied upon demand with the dumpy level. -But what is necessary here will be to give the mode of adjustment which -the civil engineer can accomplish at any time without supplementary -apparatus. - -The bubble is handier to work with when adjusted to reverse in the -centre of its run, but it does not really matter, as equally accurate -work can be done with it in any other position. Should the bubble -not reverse in the centre of its run, adjust the instrument by the -levelling screws until it reverses in some position. Say you start with -bubble in the centre, and on reversing, it runs towards the eye end -of the telescope six divisions, then alter the levelling screws until -it is only half this, or three divisions towards the eye end, then, -if properly levelled, the telescope will make an entire revolution -with the bubble in that position, which will prove that the axis is -vertical. The bubble can now be adjusted by the opposing nuts at the -one end by means of the tommy pin (provided in the case) until it is -in the centre of its run, and it will then reverse in that position -instead of three divisions towards the eye end. - -221.--_Adjustment to Collimation._--Upon a fairly level piece of ground -the staff plate, fully described further on, is trodden well down on -the ground, and the level is set up at say 3 chains from this, in -which position the staff is read as a back sight. Now in the opposite -direction in the same line, at 3 chains distance from the level, a -second staff plate, or in defect of this if the surface be not firm, a -stake or a boulder, is driven firmly down in the earth, and the staff -is placed upon this erect and face to the instrument as a foresight. -The instrument is turned half round and the second station is read. -These readings of the staves taken will be truly level with each other, -if the axis of the instrument has been set up quite vertically, so that -the bubble has kept its centre in all positions. This is true although -the axis may have been out of collimation. This arrangement is shown -in Fig. 66, _L_ the first position of the level taking sights at equal -distance from _S_ and _S′_. Let the level be now removed to _L′_: if -correct it should cut the staves _SS′_ at equal distances above or -below the first readings at _aa′_, which are at equal distances from -_bb′_ readings from _L′_, therefore level and parallel with the first -reading. - -[Illustration: Fig. 66.--_Adjustment of dumpy level._] - -222.--In the dumpy level, as it leaves the hands of any respectable -maker, the subsequent adjustments required can never be great, unless -the level has suffered a serious fall so as to bend the limb. The -rewebbing the stop, if carefully done, would require only a slight -readjustment; but it may be convenient to give an exact method for -extreme cases, which may be given in detail for clearness, and at the -same time we may also consider the influence of the curvature of the -earth. - -223.--_Original Adjustment of the Dumpy Level to Collimation with -consideration of the Curvature of the Earth._--Suppose the readings -of the two levelling staves at 10 chains apart, taken with the level -placed at intermediate distance as before, read 7·50 and 4·50, and that -we now place the level linearly at 1 chain outside the first reading -and it reads the near staff 6·50 and the distant staff 5·50, by the -inclination of the ground, this would be a + and a - reading; but we -require both readings of one sign, and as the distant staff reading is -much too high, it is clear we require - readings for correction. The -correction will be of the difference of reading in proportion to the -distances, calling the lower reading minus-- - - 7·50 - 6·50 = -1, 4·50 + 5·50 = +1, difference = 2. - -That is -2′, as our readings are - and as the -2′ is in 10 chains, -at 1 chain the distance of - the near staff = -·2, and 11 chains the -distant staff = -2·2. The correction will therefore be for the near -staff 1 chain distant 6·50 - ·2 = 6·30, and for the distant staff at -11 chains 5·50 - 2·2 = 3·30 = -1·2 below each of the first readings. -If the telescope be now collimated to the near staff reading 6·30, by -adjusting the screws immediately under it for distance between the -limb and the telescope, and the bubble be readjusted to the telescope -without moving the instrument or touching the parallel plate screws, -the adjustment will be perfect, less the small error due to the earth's -curvature in 1 chain. If the telescope be adjusted to the distant staff -3·30, curvature of the earth will be corrected by the level for 11 -chains, which is 0·0106 foot or ·01 nearly, the smallest reading we -have on the staff. - -224.--It was claimed by the late William Gravatt for his method of -adjustment,[3] which was equivalent to that given above, but more -complicated and with three staves, that the fixed correction for -curvature at 10 chains would be uniform in the working of the level -_pro ratâ_ for all distances. There is some difference of opinion -on this subject: at any rate, a 10 chain correction would only be -applicable to very approximately level ground where average 10-chain -stations could be taken. - -225.--Where space is not at command and curvature correction is not -desired, adjustments of the level may be made with care at 1 chain -distance on each side of the setting-up of the level with one staff -only, which can be moved from one stake to the other, and with the -final setting-up of the instrument at 1 chain distance from these -stakes as before, art. 221. For this the staff only requires moving -twice, if the collimation adjustment is to the last reading only -calculated out as above. This close system has a certain amount of -merit, that by reading from one staff only for both stations it is -more accurate, as any inequality between the divisions of two separate -staves is avoided. - -[Illustration: Fig. 67.--_Collimator for adjustments to horizontality -of the telescope._] - -226.--=Collimator.=--Optical manufacturers in populous districts, and -some observatories, as that of the India Store Department at Lambeth, -adjust by means of the collimator by the exact method due to the late -eminent German mathematician, Carl F. Gauss, which is hence termed -the _method of Gauss_. The collimator consists of any good telescope -permanently adjusted to solar focus, with a webbed diaphragm placed in -the focus, where it may be illuminated by a lamp or by the reflection -of daylight, and provided with means of bringing the telescope to a -level position. As the collimator is generally constructed, it consists -of an 18-inch telescope, Fig. 67, of the same description as that used -for a Y-level, described art. 94, in which the telescope is surrounded -by accurately turned collars formed to rest in Y's. The Y's are -supported upon a heavy cast-iron stand, of somewhat triangular form, -of nearly the length of the telescope, about 6 inches wide at one end -and 2 inches at the other. The stand has two feet extended to the full -width at the wider end, and one foot at the narrower end under the -telescope. Each foot has an adjusting screw. The complete collimator -is supported, at about the height of the telescope of the level on its -stand, on a very solid pier of stone or brickwork in cement capped with -a stout slate slab. The telescope is brought to perfect collimation as -with the Y-level, already described art. 200, and the level is fixed -true with the axis of the telescope, when the collimation is perfect. - -227.--A lamp or gas flame is placed at a short distance from the -eye-piece end of the telescope, so as to illuminate the webs that they -may be distinctly seen when looking into the objective end of the -telescope. In bright daylight, if there is a skylight over, a reflector -will answer the same purpose. At the Lambeth Observatory a fine -needle-point hole is used instead of webs. - -228.--The instrument to be adjusted may be placed at any convenient -distance from the collimator. For adjustment of a level, where the -collimator is already in adjustment, the level is raised upon its stand -until the axis of the telescope sensibly coincides with the axis of -the collimator; then if the telescope of the level to be adjusted be -focussed into the objective end of the collimator, the illuminated webs -will be clearly seen; and if these webs be brought by adjustment of -the level exactly to coincide with its own webs, the collimation lines -of the two instruments are exactly parallel. In this adjustment it is -only necessary to be sure that the vertical axis of the level is truly -vertical, so that the bubble reverses without displacement, in which -case the whole instrument must then be in perfect adjustment. - -229.--It would be very difficult to use this method of adjustment if -it were necessary that the axes of the level and collimator should -_exactly_ coincide. It is only necessary that they should nearly -coincide, on account of the imperfection of object-glasses, which -rarely work so well near the edge as towards the centre; otherwise any -directly parallel position in front of the object-glass would answer, -as the next diagram will show. Let _O_, Fig. 68 be the object-glass of -the collimator, whose solar focus is at _F_. Then the rays _PP_, and -all other parallel rays falling on the object-glass, will be brought -to a focus at _F_; and reciprocally all rays departing from _F_ in -passing through this object-glass will leave in parallel lines _PP_. -Let _O′_ be the object-glass of a telescope to be collimated, _F′_ its -solar focus. Then all rays from _P_ to _P_ departing from _F_ that fall -within the parallel space _P′P′_ will be brought to focus at _F′_. When -the image at _F_ is illuminated by a lamp _L_, the webs or other index -will be clearly seen by the eye-piece at _F′_ when the two telescopes -are exactly parallel with each other. In this position the webs of the -level are adjusted to make this coincidence. It is easily seen that by -this method we eliminate all errors of atmospheric refraction, and are -quite independent of the state of the atmosphere for obtaining distinct -vision for adjustment. - -[Illustration: Fig. 68.--_Diagram of collimation by two telescopes._] - -230.--When two levels are at command, one a Y-level, or even a dumpy -in perfect adjustment, the one may be used as a collimator to the -other by setting them up at a distance within their focal range on a -firm basement floor. A candle or a lamp will give sufficient light to -illuminate the webs of the instrument, which is used as a collimator, -being certain, of course, that this instrument is first placed in level -adjustment and set at _solar focus_, and that the instrument used as a -collimator has a good object-glass. - -[Illustration: Fig. 69.] - -[Illustration: Fig. 70.--_Stanley's model 14-inch dumpy level._] - -[Illustration: Fig. 70A.--_Tripod._] - -231.--=Improved Dumpy Level.=--The writer has made some improvements in -the dumpy level, which have so far met with very general approbation -from the profession, Fig. 70. These improvements are directed to -ensure much greater sensitiveness in the longer bubble, therefore -greater accuracy in the work performed by it; more solidity of -construction without increase of weight; and permanence of reading -index, with some additional matters. In these improvements the -mounting of the longer level tube, instead of being placed in a stiff -joint at one end, or between rigid clamping nuts at both ends, has a -barrel-fitting at one end which is ground into a parallel hole. This -plan admits of circular self-adjustment to the bubble tube, which -the clamping of the nuts can never twist or strain during vertical -displacement; and the joint can be made perfectly sound with certainty, -which saves the risk of accident to the bubble from expansion by heat -and some other conditions. A more recent form of cross level, Fig. -69, shown in perspective near the ray-shade in the engraving Fig. 70 -has been designed by the author, in which the level casing is bored -entirely out of the solid. It is supported upon the side of one -telescope strap by three stout pins, the centre one fitting its hole, -and the two outer ones are loosely held by cross screws to permit a -small amount of adjustment, which is all that is necessary. By this -construction the level fixings are made in five pieces only, including -screws, instead of thirteen as usual, at the same time making the level -more portable and solid for hard wear. The telescope straps are fitted -at their stumps solidly down upon the limb, as shown Fig. 60, p. 112. -Adjusting screws are placed under this as in the dumpy level described, -but the pressure screw is not employed except in case of accident far -away from an optician, when it is found to be there ready for use. The -limb is framed out into two edge bars: this gives greater vertical -sectional strength and resistance to torsion without increase of weight -in the instrument. Where a compass is used, this is included in the -frame of the limb, as shown in the engraving. The compass is read -with a prism, this being much more convenient and exact than looking -down upon the divided circle, the instrument being necessarily placed -for use at nearly the height of the eye. The compass ring is made of -aluminium. - -232.--The further improvement, which the author considers of the -greatest moment, is that the vertical axis is fixed directly and firmly -upon the limb, and not through a loose screw fitting for separation -at this point as in the ordinary dumpy. This is shown to be important -in that, with the dumpy, where a loose screw is employed, any little -difference of screwing down upon the axis when the instrument is set -up causes so much derangement of a sensitive bubble in relation to the -vertical axis, that the optician is bound to use a rather dull bubble -with the ordinary dumpy. Further, a particle of grit or the slightest -bruise on the collar in replacing the instrument in its case throws -it out of adjustment at this important point. The objection to the -author's plan is that it makes the case for the instrument somewhat -larger; but the advantage of certainty of permanent adjustment appears -to him very far to counterbalance this objection where accuracy is -aimed at. - -233.--=Tribrach.=--The setting-up adjustment of the instrument is upon -tribrach limbs with three screws only. These screws can never strain -the vertical axis, which in this instrument is somewhat deeper and -more firmly made than that of the dumpy. In the old form of tribrach -the points of the screws were held down by a spring plate placed above -them. This plate, in carrying the instrument upon its stand over the -shoulder, which is the most comfortable way if the stations are not far -apart, was very liable to strain sufficiently for the screws to get -loose. The author patented a much more solid method, by which the old -spring plate is entirely dispensed with. In this plan each screw has a -ball at the lower end, which is inserted in a tubular fitting formed -in a solid tribrach, made of exact dimensions to take it. The tube is -open on the upper side, as shown in longitudinal section _H_, Fig. 71. -Many years' experience and the fact that numbers of makers have copied -this form since the expiration of the patent, shows this plan to be -perfectly successful. The general construction of the lower part of -this level may be seen from inspection: _L_ limb, fitted with compass; -_C_ axis, in one casting with the limb; _S_ sprang, carrying the socket -and supporting the instrument. _PH_ shows the ball head arrangements to -the screws. A central screw in this part detaches the tripod. One point -is shown at _P_, of which there are three, to support the level upon a -wall or rock in cases where the tripod cannot be used--a most important -advantage in town levelling. The tripod head is made much more firmly -than that of the ordinary construction, by extending two wing fittings -from the top of the shovel-plates as wide apart as possible, instead -of the narrow tenon fitting before described. The shovel-plates are -screwed to the staff by means of a stout nut-plate inside the tripod -_F_. Those who have experienced how much defective levelling is due -to a shaky tripod head will appreciate this precaution. The general -arrangement is also shown in Fig. 70A. - -[Illustration: Fig. 71.--_Details of Stanley's dumpy level: half -elevation to left, half section to right._] - -234.--As the tribrach system of adjustment is of somewhat recent -adoption to ordinary surveying instruments in this country, it strikes -the stranger to it as being more difficult in use. It is really the -most simple and expeditious system as is clearly explained by the -foregoing diagrams, Figs. 72, 73 of the plan of a level, omitting its -lower parts. - -[Illustration: Figs. 72 and 73.--_Tribrach adjustment._] - -235.--The bubble of the level is placed parallel with two of the screws -of the tribrach, that is as _B_ and _C_, Fig. 72, and is adjusted to -the centre of its run. It is then placed at right angles to the first -position, so that the screw _A_ comes directly under the bubble, to be -adjusted by this screw only until it again comes in the centre of its -run. Fig. 73 shows this second position with the screw _A_ underneath. -The level should after this read all round true, but it is well to try -it round parallel with the different pairs of screws in all positions -to give small adjustment if required. Where there is a cross bubble -the level may remain for adjustment in its first position, but it is -well to try it all round, as the long bubble is made uniformly the more -sensitive. - -[Illustration: Fig. 74.--_Ray shade._] - -236.--=The Ray Shade= to the telescope used in the above-described -level has two narrow slits opposite each other at 180°. A zero line -is carried from one slit to a line on the ray shade fitting when the -slits are quite horizontal. Sights through the slits at zero enable an -approximate cross-level to be taken. The edge of the tube of the ray -shade is divided 30° on each side of the zero line to 2°, so as to take -approximate lateral inclines of the surface of the land in levelling. -This useful plan of cross-sighting was originally proposed by Gravatt. - -[Illustration: Fig. 75.--_Stanley's platino-iridium point level stop._] - -237.--The most important variation from the telescope of the dumpy -level described is in the diaphragm, where webs or lines of any kind -are entirely done away with, and are replaced by a special form of -index. This is represented in Fig. 75. The movable part carrying the -opening of the diaphragm is placed in a sliding fitting, as previously -described, art. 214, for the dumpy level. The index which replaces the -web is a finely-pointed needle formed of platino-iridium (platinum ·75, -iridium ·25). This alloy has about the hardness of spring-tempered -steel, and is, as far as known, perfectly non-corrosive in air or -moisture. A pair of vertical points indicate the position for holding -the staff. It will be found by experiment that the point reading is -much more exact than with the web, as irradiation due to edge reading -of the web is entirely avoided, and also the covering of the object -as it would be intersected by the web due to the angle its thickness -subtends upon the staff, which is very palpable at 10 chains distance. -The iridium point is sufficiently strong to be kept perfectly clean -by touching it occasionally with the point of a camel-hair brush if -it appear dusty. With care this point will last in adjustment for as -long a period as the level itself remains in use. Upon first impression -the point may not appear so fine as a web, but practically it is more -exact, as the previous exaggerated images will show--Fig. 76 is the -image of a division of the staff partially covered by a web _WW′_; -Fig. 77 that of a magnified image of the point _P_ brought towards a -division for reading. It will be readily observed that the fractional -part of the 1/100 foot block, which the point _P_ cuts, is much more -easily estimated than that in which the web _WW′_ covers a part of a -similar block. - -[Illustration: - - Fig. 76. Fig. 77. - -_Difference of reading with a web and a point, shown much magnified._] - -238.--In early levels of improved construction, as shown Fig. 70, a -difficulty was experienced in practice in bringing the index point -exactly up to the edge of the line as it is shown in Fig. 77 at _P_. -This difficulty has been obviated in recent highest class instruments -by making a tangent screw adjustment to the axis as shown under the -level in Fig. 78. There was a great objection to the old form of -tangent adjustment by clamping on the axis, as this was found to -disturb the centre. In the plan shown in the illustration the clamp is -left free by jointing to the axis until it grips one of the arms of the -tribrach upon a vertical surface; in this way it cannot disturb the -axis. The level, Fig. 78, is shown mounted on a framed stand, which -is preferred by the Indian Government, and is generally necessary for -rigidity for large instruments of over fourteen inches. This will be -described further on with theodolites, art. 447, on framed stands. - -[Illustration: Fig. 78.--_Stanley's improved dumpy._] - -239.--=Stadia Points.=--The author commonly makes the points, Fig. 75, -_VV′_ stadia points, by making the distance of the extreme ends of -these subtend an angle, equal to 10 feet of the levelling staff at ten -chains distance, or 1 foot of the levelling staff at 100 feet distance -(+ a constant to be discussed Chapter XII.), by which measurements -of the distance of the staff can by taken or checked by observation -through the telescope only. - -[Illustration: Fig. 79.--_Stanley's quick setting-up level._] - -240.--=Quick setting-up Tribrach.=--One objection has to be made to the -tribrach over the four-screw system of adjustment, that the four-screw -admits of greater inclination to the tripod, which is important in -hilly countries. To remedy this defect the author designed a ball -arrangement to the axis, which permits the level to be set 15° to -the inclination of the tripod independently of the screw adjustment, -so that the level, when the tripod is set at its best angle, may be -brought immediately to nearly its final position. The arrangement is -shown in the engraving Fig. 79. The axis carries a cup formed in the -metal casting, which can be clamped down upon a ball-shaped recess -formed upon the tribrach by means of a winged nut placed under it, -the wings of which project between the tribrach screws. A very slight -pressure is sufficient to firmly clamp the ball. This form of level is -now very popular with civil engineers. With a point diaphragm and a -tangent screw to the axis, not shown in the engraving, it is, in the -author's opinion, the best practical level he has been able to design. - -[Illustration: Fig. 80.--_Stanley's Engineer's level._] - -Since the last edition was written the reviser of this work introduced, -in conjunction with Mr. Stanley, his new solid bodied engineer's level, -which has practically revolutionized the form of dumpy level and has -proved such a success that more of this form are now made than all -other forms put together. In this level, Fig. 80, the centre, body of -telescope, object end and bubble fitting are all combined in one piece -of gun-metal, so that although of vastly greater strength and rigidity -it does not weigh as much as the old form of tubular body with its -collar and stage. This does away with many separate pieces which are -usually soldered and screwed together. It thus forms the strongest -and most compact level yet made, and with ordinary care it will last -in perfect adjustment a lifetime. The pinion for focussing is fitted -to the side of the cast body, instead of to a tube, thus greatly -increasing its firmness. Its form is equally adapted to the four-screw -levelling if desired, as shown on next page, Fig. 81, in which it will -be seen the four-screw levelling is of much improved form, giving -greater strength and far more wearing and bearing surface to the -levelling screws. - -[Illustration: Fig. 81.--_Stanley's Engineer's level._] - -The reviser has also patented a new form of spherical joint, which -has met with equal favour. This improvement consists of a section of -a ball (screwed to fit the stand head) fitted within the lower plate -and a simple means of clamping it in any position, which, when released -allows of sufficient rocking movement in any direction to compensate -for any uneven setting up of the stand. It does not add to the height -of the instrument, may be instantly set nearly level, and less than -half a turn of the levelling screws will bring the instrument into true -position. It is shown fitted to the new engineer's level at Fig. 82 -below, but is equally applicable to any other form of instrument. - -[Illustration: Fig. 82.--_Stanley's Engineer's level fitted with quick -setting spherical lower plate._] - -As ninety per cent. of the orders now for levels are for the form shown -at Fig. 82, the reviser ventures to think that this must be favoured -by the profession as the best practical instrument yet made. - -A further improvement has been made by making the diaphragms -interchangeable, so that any form of diaphragm that is preferred may -be instantly fitted without disturbing the adjustment, and when lines -on glass are used it may be removed for cleaning, and replaced without -interfering with the adjustment. - -The diaphragms illustrated below, Fig. 83, are usual forms, and it is -recommended that when webs are preferred a glass one should be carried -as a spare in case of accidents. - -[Illustration: Fig. 83. - - E - _Stadia points for - clamp and - tangent levels._ - - F - _Stadia points - for ordinary - levels._ - - G - _Stadia glass - diaphragm._ - - H - _Webs._ - - J - _Stadia - webs._] - -241.--The further discussion of the subject of high-class levels -becomes somewhat difficult. Leaving out of consideration the levels -sold by the trading optician, who deals in the commercial article -but sometimes superadds a little fad, every genuine manufacturer -has his pet plans of carrying out details, some of which may be -very meritorious, but which could scarcely be described without a -fuller discussion than our space permits. There is also, no doubt, -a great number of mistakes that have been made in the construction -of surveyor's levels. The direction in which the scientific optician -generally fixes his attention is to give the advantages of the Y-level -in the dumpy form, assuming the civil engineer holds a certain amount -of prejudice against the use of the Y, for which, in its old form at -least, the writer must admit that he was fully justified. Whether -the professional man, nevertheless, will ever depart from the solid -construction of the dumpy remains an open question. - -[Illustration: Fig. 84.--_Cushing's 12-inch improved level._] - -242.--=Cushing's Level.=--The level illustrated above, Fig. 84, by the -late Mr. Thos. Cushing, F.R.A.S., Inspector of Scientific Instruments -for India, would under any circumstances claim attention, from this -gentleman's well-known high technical scientific attainments. It has -also the merit of being in practical use in India at the present -time.[4] The principal improvement in this instrument over the dumpy -form, which it otherwise represents, is in the construction of the -telescope, which is said to possess all the necessary adjustments of -the Y-level. The telescope is firmly fixed in collars soldered to the -tube, as in the dumpy. The tube at each end is formed into a stout -socket collar. These socket collars are exactly alike, and are ground -to fit either the objective or the eye-piece end of the telescope, so -that these parts may be reversed, the one for the other. This -reversing is nearly equivalent to turning the telescope end for end -in the Y-level. The end also rotates in its fitting, which is nearly -equivalent to rotating the telescope half a revolution in the Y-level. -The reversible ends of the telescope are held in their ground fittings -by studs and slides (_bayonet notches_). It is easily seen that by this -plan adjustments may be made of collimation and of fixing the line of -collimation perpendicular to the vertical axis, as with the Y-level, -if the object-glass be originally correctly centred. The stop is of -the slide form described for the dumpy, Fig. 61, and a glass diaphragm -is used. One important arrangement is also made in this part of the -instrument--which is necessary, as glasses become frequently bedewed -in the telescope--viz., that the eye-piece end may be removed from its -ground fitting and the glass cleaned and replaced without disturbing -the adjustment in any injurious degree. The general construction of -the instrument can be seen from the illustration. The supports of -the telescope have a rocking axis at one end, and are adjusted by -capstan-headed nuts at the other. The adjustable support for setting up -the instrument is upon Everest's tribrach system for theodolites, to -be described further on, in Chapter IX. The tripod head has also wider -bearing than is general, which is attained by extending the book-plates -into the form of a socket fitting. The illustration given is of a -12-inch level; in the 14-inch an open framed stand is used in place of -the solid tripod, as in Fig. 78, which will be described further on, -for theodolites. The level is a decidedly good one; but the author has -experienced with it some slight defects when compared with his own Y -form. The ground collars are a little inclined to bite, particularly if -the instrument has been laid by for some time, so that in reversing for -adjustment there is great risk of disturbing the instrument. The glass -index, although permanent, has the same defect as the web--of covering -the image of the staff reading. It also obstructs a little light, and -is subject to dew, which the point system avoids. The weight of the -instrument is increased by the collar fittings. - -243.--=Cooke's Level.=--An instrument somewhat equivalent to the above -has been patented by Messrs. T. Cooke & Sons. In this, instead of the -objective and eye-piece ends of the telescope only being reversible in -the collar fittings, as in Mr. Cushing's level, the entire telescope -reverses end for end in an extra outer tube, which is fitted between -the collars. This tube also permits the rotation of the whole optical -parts about the axis of the telescope for adjustment for collimation, -although in a manner more frictional, and therefore more likely to -disturb the instrument than in the simple Y adjustment. In this -instrument, again, it is easily seen that it is the perfection of the -Y-level, without its outward appearance, that is aimed at, and to gain -this the weight is increased by extra fittings and double tubes, which -are liable to become fixed by a slight dent upon the outer tube. Taken -altogether it is not quite so convenient or so simple as the best -constructed Y-level; but if it gives the adjustments the optician holds -to be most important, in a disguised form it may be acceptable to the -civil engineer. We may in this manner, perhaps, from the optician's -point of view, count it a certain gain in the same direction as Mr. -Cushing's level just described; but if we may accept the late Mr. Wm. -Gravatt's ideas, already mentioned, the complication is unnecessary. - -244.--A few other structural variations of details may be mentioned, as -these are constantly cropping up as new inventions. The bubble tube is -sometimes placed upon the stage instead of being upon the telescope. -This is thought to protect it. It is not, however, so easy to read it -in this position. The compass is sometimes made a loose part--when -it is not required on the work its weight is saved. Various forms of -locking screws are made to the supports of the telescope; these are -only necessary to correct imperfect work. The axis collar is sometimes -extended to a limb bearing. This is common in French instruments; it -makes the movement stiffer, and is quite unnecessary unless the axis is -made too short. A well-known German firm recently brought out a level -with internal focussing, by means of an auxiliary lens mounted in a -tube inside the telescope, moved by a rack and pinion, but any internal -lens is a source of trouble, as it cannot be got at to be cleaned, -and in hot, damp climates it becomes bedewed. The device is very old, -having been patented in America many years ago and discarded. - -245.--=Supplementary Parts to Levels.=--As a rule, supplementary -parts fixed to the instrument, beyond the magnetic compass sometimes -required, are very objectionable if the object of the level is to -be levelling, as these additional parts inevitably increase the -weight which has constantly to be borne in carrying the instrument. -Supplementary parts have been carried, in various schemes, to the -extent of combining the entire level with the theodolite, at the same -time nearly combining the united weights of the two instruments. As a -rule, professional men rarely care for complex combinations; and even -after a limited popularity is granted to extra parts not absolutely -required, these are generally finally abandoned. Mention of two such -parts, therefore, only will be made, as these owe their introduction to -the late William Gravatt, and are found applied to many levels in use, -or at least contained in the case with the instrument. - -246.--_Bubble Reflector._--This was formerly placed upon all dumpy -levels. It consists of a small mirror about 2 inches by 5/8 inch fixed -in a frame that is jointed at its lower end to a short piece of tube -partly cut away so as to form only a little over a semi-cylinder. This -tubular part just clips firmly upon the brass casing tube of the spirit -level. The reflector, when placed vertically on the level tube, can be -adjusted by its joint, so that the run of the bubble may be observed -by reflection in looking above the eye-piece to see that it is in -adjustment at the time of taking an observation. Its use was thought -to be a precaution in levelling, particularly on marshy ground. The -observation of the bubble is less exact than by a side reading, and -cannot be relied on. - -[Illustration: Fig. 85.--_Compact cheap form of dumpy level._] - -247.--_Sight Vanes._--Two sight vanes are placed above the telescope, -either as loose fittings or to hinge down upon the level tube. One vane -has a vertical narrow slit and cross hair; the other has a window with -a vertical horse-hair placed in its centre. This arrangement gives -sight of distant landmarks in line with the direction of the telescope, -upwards or downwards, beyond its field of view. A slider, fixed upon -the window sight, reads at its upper edge into divisions cut on the -vane, by means of which an approximate rate of forward inclination of -the land may be taken. This sighting arrangement adds about half a -pound weight to the instrument. It was useful with object-glasses of -small field of view, but is useless with good modern glasses of wide -angle. - -248.--=Lower-class Levels.=--A level is often required by an architect -or a contractor for works of limited area, where it is quite -unnecessary to go to the expense of a civil engineer's level of refined -manufacture. In such cases the level may only be used occasionally -and under favourable circumstances, so that extreme solidity is not -demanded, neither is distant view in the telescope required. The level -generally made for such work is a simple dumpy, without cross bubble, -compass, or any extra fittings, and with one eye-piece only. - -249.--The instrument Fig. 85 illustrates the author's newest design for -a simple level. It has a light form of tripod. The legs clamp directly -between angle plates--these are not quite so portable or so neat as -cylindrical legs, but they are easily made, very firm, and will bear -considerable wear and keep in order. A still cheaper form is made with -smaller telescope and turned legs for the tripod. - -[Illustration: Fig. 86.--_Contractor's or builder's level._] - -250.--The illustration Fig. 86 represents the cheapest form of level -with a tripod stand that has been constructed, which contains the -important factor of a telescope. The telescope has a sliding fitting, -which is moved by a knob outside, this being made more quickly than -a rack and pinion fitting. The level tube is solidly supported in -collars. The adjustment is in one direction only, so that the bubble -must be set and examined at the time of reading the staff. The -instrument is supported on a _sprang_, jointed at one end and held by -a milled-headed screw at the other. Any shakiness of the thread of -screw there may be is taken up by a stiff German silver spring between -the sprang and the limb. It is sometimes made with a ball and socket -joint for first adjustment, but this renders it nearly as costly as a -superior level. The tripod head is of simple construction. The legs are -oak or ash, and are clamped on the head by bolts. This simple tripod -is fairly firm in use. The level is good enough for ordinary building -works, laying short drains, etc., within limited areas. It is much more -accurate than any form of open sighted level without telescope. Sir -George Leach has recently made a modification of this old form of level -by placing a pendulum to rock the axis to cross level position, which -is a refinement, although rather a costly one. - -[Illustration: Fig. 87.--_Sighted reflecting pocket level._] - -251.--=Sighted Pocket Level.=--This consists of a tube, which is -generally drawn of square section. A pin-hole sight is made in the -closed end of the tube, Fig. 87, at _E_. The field end of the tube is -left open. The sight is taken by looking through the centre of the -pin-hole across the edge of the reflector _R_. A level with a small -bubble is placed or inserted in the top of the tube at _B_. The metal -casing of this is cut away on the upper and under sides to render the -bubble visible from the interior of the tube by means of the reflector -_R_, which occupies one half vertical section of the interior of the -tube. This is placed at 45° to the axis. The reflector is fixed upon an -inner tube so that it may be withdrawn to be cleaned. When the level -is set horizontally, a distant object in the direct sight line is seen -through half the tube, and simultaneously the reflection of the bubble -in the other half appears. A line engraved upon _R_ indicates when the -bubble is central, and when these coincide the distant object and the -eye are level. The instrument is about 4 inches long, and weighs about -8 oz. in its case. - -[Illustration: Fig. 88.--_Pocket telescopic level._] - -252.--=Pocket Telescopic Level.=--In the above-described pocket level, -where it is made short, the average middle-aged man will not have -sufficient accommodation of vision to be able to see the bubble and -the screen sharply defined simultaneously with the distant object to -which the level is to be taken. In Captain Barrie's[5] level these -objections are avoided by making the reflector and bubble form part of -a telescope, Fig. 88. An achromatic glass of short focus is used, and -the eye-piece is of long focus so as to bring the bubble to focus in -the centre of the mirror, which is made of curved form to decrease the -apparent size of the bubble. The image of the bubble does not give by -bisection a very definite index. The author has found that this level -may be much improved by placing a point in the telescope at the mutual -foci of the object-glass, eye-piece and the bubble. The appearance -of the mirror and point is shown at _B_. The point is shown by a -dot at _P_. The curved mirror _R_. The dotted line shows the path -of reflection from the bubble. This level will work with very fair -accuracy as a hand instrument. Size, about 4½ inches by ¾ inch. -Weight in case, about 8 oz. - -[Illustration: Fig. 89.--_Reflecting level._] - -[Illustration: Fig. 90.--_The same construction in protecting case._] - -253.--=Reflecting Level.=--This simple level, Fig. 89, the invention -of Colonel Burel, is one of the most portable. When it is used with a -fair amount of care it will give good approximate results. It consists -of a piece of parallel glass, which has half the surface silvered to -form a reflector. It is suspended in such a manner that the glass hangs -vertically by gravitation. The position of the mirror to the plain -glass may be that shown in the engraving, or horizontally if preferred. -The mirror, Fig. 89, is inserted in a solid metal frame suspended from -a gimbal, which permits it to hang perfectly free to the action of -gravitation. The centres of suspension are made with slightly-rounded -knife-edges. A ring at the upper part of the instrument is placed over -the thumb or finger to support the instrument when in use. A stout pin -passes through a prolongation of the lower part of the frame, screwed -or otherwise, which permits adjustment by filing to bring the mirror -when it is suspended exactly into a vertical plane. The instrument, -fitted into a neat case, weighs from 5 oz. to 9 oz. - -254.--_In using the Reflecting Level_, it is held upon the thumb at -about arm's length, and adjusted by raising or lowering the arm until -the reflection of the pupil of the eye seen in the mirror is exactly -bisected by the line cut by the mirror against the clear glass. The -distant object seen in front, that cuts this sight line and the image -of the pupil of the eye, will then be in true level position with the -eye of the observer, provided the air is still, so that the mirror is -not deflected from verticality. From the natural unsteadiness of the -hand there is some little difficulty of getting this level quite free -from oscillation. This may be obviated, or nearly so, by clutching a -picket or staff with the hand and suspending the level from the thumb -projected out for the purpose, or by resting the hand against a tree or -other firm support. Capt. A. H. East, R.A., has suggested to the author -a very capital device which he employs for hand instruments. This is to -place the handle of a stick (or umbrella) in the waistcoat pocket, to -clutch the body of the stick with the hand which holds the instrument, -and to steady it with the other hand. In this manner the two arms and -the stick form a tripod of surprising steadiness. - -255.--=Reflecting Level in Case.=--In windy weather much greater -exactness may be secured by placing the pendulous level, just -described, in a tubular case, Fig. 90. The case is made of double -tubes, so that the aperture cut on one side may by a half turn of -the outer tube close and protect the instrument when out of use. The -transparent side of the inner case is sometimes closed by thin glass -tube of its own internal diameter. It is much better if made with two -vertical sides glazed with parallel glass. When this form of instrument -is used, it may be, if required, made to fit on the top of a light -staff. The eye is then brought with much greater certainty to the -point of bisection on the edge of the mirror, and much greater accuracy -is thus attained in levelling with it. - -256.--=Water Levels.=--The antique form of level, composed of two vials -fixed on the ends of a tube and partly filled with water, by which a -level is sighted in looking over the surface of the water, is still -used to a limited extent in rural districts on the Continent; but the -spirit level in some simple form is fast superseding it. The same -principle of level, but with long tube, has been found convenient for -the surveyor in measuring through close buildings, Fig. 91. - -[Illustration: Fig. 91.--_Tubular water level with open vials._] - -[Illustration: Fig. 92.--_Browne's standard water level._] - -257.--=Browne's Water Level=[6] is found to be a convenient instrument -for levelling in close towns. It consists of a pair of glass tubes -of about 2 feet in length, placed in a casing tube for protection. -The casing tube is divided into inches and parts, or the scale is a -detached piece of painted wood, or any rod or rule. A cock at the -bottom admits the water to flow to level in the pair of tubes, one of -which is shown, Fig. 92. There is a handle at the top which unscrews to -fill the level, and a small air cock. It is easily seen that the water -finds its level, and the difference of reading of the two standards is -the difference of level of the surfaces upon which they are placed. By -closing the cocks the level is made portable. In this position it does -not matter how high the centre of the pipe is placed--for instance, -in crossing over a wall--as the water will still find its level when -the cocks are released by syphoning the water from the one side or the -other. It is a very convenient and exact level for laying drain pipes -in open weather, and for making foundations for heavy machinery, etc., -but of course it will not stand frost. - -Platelayers' levels and mechanics' levels generally are deferred to -consider with useful hand tools and apparatus employed by surveyors in -the final chapter. - -FOOTNOTES: - -[3] See Simms' _Mathematical Instruments_, p. 3. - -[4] See pamphlet on _A New Form of Levelling Instrument_, by Thos. -Cushing, F.R.A.S., 1879. - -[5] Patent No. 69, Wm. Barrie, 1856. - -[6] Patent No. 6742, John Browne, June, 1834. - - - - -CHAPTER V. - - LEVELLING STAVES--CONSTRUCTION--VARIOUS READINGS DISCUSSED-- - SOPWITH'S--FIELD'S--STRANGE'S--STANLEY'S NEW--METRICAL--SIMPLE - CONSTRUCTION MINING STAFF--PAPERED LEVELLING STAFF-- - PRESERVATION--PACKING PADS--STAFF PLATE--STAFF LEVEL--PRACTICE - OF LEVELLING--INDEX OF BUBBLE--LAMP--CURVATURE CORRECTIONS--STATION - PEGS--REFINEMENT OF LEVELLING--LEVELLING BOOKS--INK BOTTLE, ETC. - - -258.--=Levelling Staves.=--Since great improvements have been made -in the telescopes used as part of all modern surveyors' levels, -particularly by increasing their light-receiving capacity, all systems -of vanes which were formerly made to be seen distinctly at a distance -have disappeared from use by British surveyors; it is now found that -the plain reading of a divided staff can be taken by means of the -telescope at a sufficient distance from the observer for all practical -purposes. In this country one construction of staff is now generally -adopted; and the only variations that are made in this are found -occasionally in the readings. The construction of the level staff in -common use is that invented by the late Thomas Sopwith,[7] called -the _telescopic staff_, the face view of which is shown Fig. 96. -For ordinary open field work this is made 14, 16, or 18 feet in its -extended length; but generally, except for levelling on mountainous -land, the 14 feet is used. This staff when closed is about the same -length as the tripod, 5 _feet_ 4 _inches_, and may be conveniently -stowed away under the seat of a railway carriage. Sopwith's staff, as -it was formerly made, consisted of two square parallel tubes and one -inner solid parallel slide. Made in this manner it was liable to be -rather shaky when extended, besides which it frequently got jammed in -the telescopic boxes if put away damp from rain: this tended at first -to limit its use. It is now usual to make the boxes slightly conical, -that is, diminished towards the upper part, so that they are rigid when -opened out but are very free when closed, which quite remedies the -defects just mentioned. - -[Illustration: Figs. 93, 94.--_Section of Sopwith's staff._] - -259.--The ordinary construction of Sopwith's staff and the best mode of -manufacture is shown, with the joints grooved together, in section Fig. -93. The outer tube or case _A_, which in the 14-feet staff is 5 feet in -length, is made of mahogany 5/16 inch thick, the front being ¼ inch. -The outer dimensions of the section are 3-1/8 inches by 2 inches. The -second tube _B_ is 5 feet 1 inch long, of outer dimensions 2-3/8 inches -by 1¼ inches. The inner slide _C_ is solid, 5 feet 2 inches long, -1¾ inches by ¾ inch. All the slides are sunk on the face about -1/16 inch to prevent the divisions being rubbed by exposure in sliding -together. The slides have each a brass shoe and cap. They are held when -extended by a spring catch, the detail of which is shown in Fig. 94, -section _y_ to _z_ of Fig. 93--S spring of T form screwed firmly to the -edges of the box. The catch is made at _A_ over the edge of the brass -cap _A′_. The spring should be of very hard rolled brass. It is well -to have one or two brass bands round the body of the outer casing to -secure this as far as possible from being split by accident. - -260.--The most important consideration in the manufacture is that the -telescopic work should fit well, and that the boxes should be glued up -quite square and out of winding. The boxes should, after the glue is -quite set, be screwed with brass screws at distances of about 6 inches -apart, to secure the joints which may afterwards in use be exposed to -long-continued rain. The fittings should be carefully made, so that -when the staff is extended there should be no shakiness sufficient to -cause serious vibration when it is used in windy weather. The interior -of the slides when finished should be thoroughly oiled with raw linseed -oil, and the outer surfaces be well soaked in shellac dissolved in -spirit, and then French polished over this. The brass work should be -well lacquered. - -[Illustration: Fig. 95.--_Section of semi-cylindrical staff._] - -261.--=Semi-circular Staff.=--This is another kind of telescopic staff, -with Sopwith sliding arrangement, which possesses a certain merit, but -is more expensive to make. It is semi-cylindrical, the cylindrical part -being made without any joint. This is shown in the section Fig. 95. -The general dimensions of the face of the staff are the same as those -given for the Sopwith staff. This staff is a little stiffer, but there -is more risk of its not standing true. As in the union of four pieces -of wood in the square form, previously described, the tendency of one -piece to warp in a certain direction is resisted by the other pieces; -but in this cylindrical form there is no such resistance, so that it -is found that these staves when exposed to wet are much more liable to -become warped and fixed in their slides. There is also more difficulty -in getting the conical form fairly accurate in the working. One -particular merit, when a pair of staves of this kind is used, is that -the two go together and form a cylinder, which is a very compact form, -but perhaps a little more difficult to carry, owing to the tendency of -a cylinder to roll off the shoulder. - -[Illustration: Fig. 96.--_Sopwith pattern staff._] - -[Illustration: Fig. 97.--_Field's pattern._] - -[Illustration: Fig. 98.--_Stanley's old pattern._] - -262.--What was originally considered as the defect of the Sopwith -staff, besides its shakiness, as it was first made, was the diminished -width of reading of the upper length, this being only 1¼ inches -wide. This caused for a long period other forms of staves, which -maintained the same width of reading surface quite to the top, to be -preferred by many. This fault has been partly remedied by the author -in making the feet readings of the upper staff by dots, instead of the -narrow figures, which were very difficult to read. In other respects -the light and portable form of the Sopwith staff has ensured its -general use. - -[Illustration: Fig. 99.--_Sopwith's staff._] - -[Illustration: Fig. 100.--_Rogers Field's staff._] - -[Illustration: Fig. 101.--_Col. Strange's staff._] - -263.--The original form of reading designed by Sopwith is still much -more in use than any other. It is similar in pattern to Fig. 96, shown -in detail for 1 foot Fig. 99. The dots at the end of the lines shown -in the figure were introduced by the author to render this staff more -distinct than when lines only are used, as in the ordinary pattern. - -264.--Sopwith's pattern is sometimes printed on paper for pasting on -the staff, and in this manner the staff comes out much cheaper than -by drawing the readings in solid paint. Paint, however, is strongly -recommended, not only because it wears much better and keeps cleaner, -but that the painting and varnishing add very much to the durability of -the staff, exposed as it must necessarily be to rainy weather; further, -the paper, however well it is fixed at first, is liable to creep away -from the edges of the staff, and leave a space into which rain enters -very freely by capillary attraction; but it does not again freely -evaporate, so that it rots the staff and makes the paper reading after -a time mouldy. It is, nevertheless, convenient to take a set of first -length papers if a surveyor is going abroad, as from accidents--grazing -by carrying the staff with the tripod of the level, etc.--the first -length of surface is very liable to become too much injured and effaced -for fair reading. A description of fixing the paper will be given -further on. - -265.--_For Reading the Sopwith Staff_, the foot readings are taken from -the tops of the red figures. The ·1 foot figures are in black, and -are all odd numbers, 1, 3, 5, 7, 9. These read also from the top. The -height of the figure is exactly ·1 foot, so that the bottom of each -figure reads the lower even number--thus the bottom of 3 reads 2, of 5 -reads 4, of 7 reads 6, and of 9 reads 8. The 6 and 9 foot figures if -made alike, from effect of telescopic inversion, may cause error. The -author has for many years made the head of the 9 a solid black block to -avoid this. - -266.--=Various Readings.=--A very large number of surveyors design -their own staff readings. This was formerly very much the fashion, -consequently a great number of patterns come before the manufacturer. -The author for about twelve years kept a copy of what he considered -the most meritorious of these patterns, both for future reference and -to judge of their comparative merits. This was discontinued, as it was -found that the number of designs became a little perplexing, and they -were rather dangerous to show to a customer, who often selected from -its appearance a pattern which proved afterwards unsatisfactory in use. - -267.--_Rogers Field's and Colonel Strange's Readings._--The author -made some experiments to obtain a clear staff, readable beyond the -ordinary range of staves with a 14-inch level; but much more complete -experiments were made with the author's set of patterns by Mr. Rogers -Field, C.E., whose ingenuity is well known. This gentleman finally -designed a staff which in the author's opinion is still one of the -best, but it has not generally pleased the profession: this is -illustrated, Figs. 97, 100. The author has tried it at all distances: -at 20 chains he has found a reading of ·01 foot could be taken -approximately with a good 14-inch level with his point index-stop -level, Fig. 75. The late Colonel Strange made a series of experiments -with the author's patterns placed at 10 and 20 chains distance. He -also had for these experiments one of Mr. Rogers Field's staves. He -arrived at the conclusion, for distant reading particularly, that the -black markings on all the twenty staff patterns he had were excessively -heavy, so that the lightest and most open readings were the clearest. -This led him to design a staff, a part of which is shown in Fig. 101, -which has been since generally used on the great India survey. This -staff somewhat resembles the English ordnance pattern. The fault found -with these patterns is that they do not read the ·01 foot, which is -necessary for close reading in hilly districts, otherwise they may -be read very clearly at a distance of 20 chains, where the Sopwith -becomes a blur. We may take it that the surveyor, if he be a fairly -good draughtsman, would subdivide the ·05 block to the ·01 foot; but -it is argued that his assistant, who might be a fair leveller, might -not. Another objection is that the reading is on one side and is not -cut through by the horizontal web, so that a white margin can be seen -in the telescope on both sides of the vertical webs, between which -it is most pleasant and exact that the reading should be taken. This -objection does not, however, hold for the point reading, Fig. 75. -Colonel Strange's pattern has not been very generally accepted by civil -engineers. The author tried to meet the matter by making the block ·05 -foot, but so subdivided as to indicate ·01 foot. This has frequently -been preferred to his dotted Sopwith. - -[Illustration: Fig. 102.--_Details of Stanley staff; A bottom length, B -middle, C top with dot figures._] - -268.--The author designed another staff especially for his point index. -This is shown above, Fig. 102. It has had a very fair popularity, -being good both for distant and near sighting. In this staff for the -close figures 11, 12, 13, on a 14-feet staff, which are with great -difficulty distinguishable at a distance, the author employs dots only -as before mentioned--one dot for the 11, two for the 12, and three -for the 13, as shown _C_ for the 12 and 13 in the right-hand figure. -It must be remembered that a good clear staff is a great desideratum, -as it means less size, weight, and cost in the level necessary to be -used with it for equal exactness. A clear staff with a 14-inch level -is quite equal to a complex misty one with a 16-inch level, with the -advantage of saving expense in the purchase, and about 2 lbs. in the -weight of the level to be carried in work. - -269.--Our space will not permit the discussion of the various staff -readings that have been designed, many of which are, in the author's -opinion, superior to the Sopwith; but some variations are necessary -occasionally for personal reasons. Some surveyors, from imperfect -colour vision perhaps, strongly object to the red foot figure as being -indistinct at a distance, hence in many patterns a clear black figure -is employed. Some get confused with the number of equal lines of ·01 -foot in the Sopwith, what is sometimes termed _Sopwith's ladder_. In -this case these lines may be made unequal in different ways: several -patterns have this peculiarity. Some persons cannot get over the -inverted figure as seen in the telescope. In this case it would be -much better, perhaps, to read with an erecting eye-piece to the level; -but practically the manufacturer has to invert the figures. Other less -important variations are common. - -270.--=Metrical Staves.=--These are in this country generally made 14 -feet, to keep the length the same as the tripod. The most approved -patterns are shown Figs. 103 and 103A. In using the metre pattern at -short distances often a complete metre cannot be taken in the field of -view, so that there is a little difficulty in being certain to what -metre interspace the subdivisions belong. To avoid this the author -places a dot or dots after the decimetre figures that follow the -metre--one dot for 1 metre, two dots for 2 metres, three dots for 3 -metres. Thus 1·4 metre reads ·4; 2·4 metre reads :4. The dots need -only be very small, as they are not required except for very close -readings, that is, within about 30 metres: at 40 metres distance one -complete metre comes into the ordinary telescopic field. - -[Illustration: - - Fig. 103.--_Metres and Half Centimetres._ Fig. 103A.--_Centimetres._ - Stanley's metre levelling staves.] - -271.--=Feet and Inches Staff.=--For building works, drainage, and some -other cases, the staff is divided into feet and inches, and subdivided -again into eighths or tenths of inches. This is most convenient when -the work has to be carried out with 5 or 10 feet rods and the 2-feet -rule. The intermediate inches between the feet are better marked 3, -6, 9 only than fully figured. For rough usage the author has made a -solid 10-feet pine staff, well painted. This has a strong hinge in -the centre, and is kept stiff when open by a strong open hook. It -closes face to face in two parts, which keeps the face clean. This is -important for dock and drainage works, where the staff holder's hands -in many cases necessarily get dirty by climbing; otherwise it bears -much more rough usage than the telescopic staff, and is much cheaper to -make. Fig. 104. - -[Illustration: Fig. 104.--_Stanley's rough levelling staff._] - -272.--=Mining Staves.=--For levelling in mines, large sewers, and other -cases were there is no height for the ordinary staff, the Sopwith staff -is made in its closed form commonly 2 feet 3 inches and 3 feet 3 inches -only in length, to open out respectively 5 feet and 8 feet, or in some -few instances even shorter than these dimensions. The mine staff is in -every way, except its length, similar to the ordinary Sopwith, art. 259. - -[Illustration: Fig. 105.--_Stanley's patented mine staff._] - -273.--=Stanley's Portable Staff.=--The writer has made a portable staff -in lengths of 18 inches, somewhat like a French folding rule. It may be -formed of three, four, five, or six lengths, opening out respectively 4 -feet 6 inches, 6 feet, 7 feet 6 inches, and 9 feet. The separate pieces -are flat boards, slightly sunk on the face to prevent the divisions -being scratched in opening and closing, but left solid at the joint -ends. The boards are attached together with a kind of rivet at each -joint. A strong spring at the end of each piece with a catch and notch -keeps the length opened or closed with sufficient rigidity.[8] The -entire length of the staff when closed in 20½ inches. The same kind -of staff forms a very useful builder's or drainage staff, divided in -this case in feet and inches; and it is conveniently portable for -carrying abroad. Fig. 105--_E_ shows back view, _F_ front view, _G_ -cross section, _A_ longitudinal section. The holding springs are shown -at _BB′B″_. - -274.--A portable mine staff designed by Mr. G. J. Jee,[9] is said -to be a useful staff for colliery work. It is constructed in three -lengths, sliding one into the other. The bottom length of three feet -is graduated in the ordinary way. The top of this length has a band -attached to it, painted to continue the lower division of the staff -upwards. The other end of the band passes over a roller attached to the -top division of the staff. The roller contains a spring which keeps a -constant tension on the band. By extending the lengths of the staff and -clamping them, the staff may be lengthened out any distance to 9 feet. -The weight of the staff is 5 lbs. - -275--=Papering or Repapering a Sopwith Staff.=--The staff, if new, -is painted with three coats of rather flat, thin white-lead paint on -the face, and left to season till the paint is quite hard. It is then -washed thoroughly with a sponge dipped in stout, until this adheres -without beading, and is again left to dry. For repapering an old staff, -this is soaked with hot water in which there is some washing soda, and -rubbed until the old paper is brought off. After the staff is in either -of the states described above, it has to be made warm and coated with -one or two coats of size. The size may be made of a piece of glue left -in water for a night, and then melted in a jam-pot placed in a saucepan -of water over a slow fire. When the staff is sized and dry, if -ordinary papers be used, it has to be divided carefully into foot -lengths, which are marked with a set square in pencil across the face -of the staff. The foot lengths may be set off accurately from an -engine-divided chain scale, or by beam compasses. The papers, which -are printed short, are then pasted over, preferably with paste made of -starch with boiling water, but not afterwards boiled. As the lengths -of paper are pasted they are laid aside, pasted side upon pasted side, -to thoroughly absorb the paste for a few minutes, the time varying -according to the increased length required above that of the original -printed paper. While still wet, the upper paper of the two is lifted up -and cut with scissors, at the same time fitting to the boundary lines. -This wet cutting ensures the paste being equally distributed quite up -to the edges. The foot length of pasted paper is then laid by setting -the upper edge exact to the upper foot line, and gradually bringing -the paper down from this by dabbing with a clean cloth or straight -hat-brush. If the paper does not reach the foot mark when laid, it is -again lifted, and a little more pressure used in laying it the second -time, which will lengthen it out as required. Other lengths are laid in -the same manner. The skilled workman requires no lap to the joins of -the papers, but brings them up edge to edge; with the amateur a lap of -1/8 inch is advisable. - -To avoid the trouble of marking off and stretching each foot, the -author has introduced jointless levelling staff papers, so that the -entire length of each section may be put on in one piece. These are of -special paper, and it is only necessary to paste the face of the staff -well and smoothly, and lay the paper unpasted down in position upon it. - -After the papers are thoroughly dry they require two coats of thin -isinglass size, and then a coat or two of varnish. Paper varnish can be -bought; but in defect a varnish may be made of Canada balsam dissolved -in oil of turpentine. This should be laid on with a flat bristle brush -(varnish brush), and set in a warm room to dry for a day or two. - -276.--=Preservation of the Levelling Staff in Use.=--Where two staves -are used they may be placed face to face for carrying, and be strapped -together, and will take little harm with moderate care. Where one only -is used it is generally strapped to the tripod. A strip of wood is -sometimes used to protect the face of the staff. - -[Illustration: Fig. 106.--_Pad for holding a staff and tripod._] - -277.--For carrying the staff with the tripod, a convenient plan is to -have two pads formed of stout ox-hide butt, each pierced with two slots -near their ends at the exact distance apart of the width of the staff, -Fig. 106. The strap of calf leather is passed from one slot round the -staff into the other slot, and then passed round the tripod and pulled -up tightly and buckled. The pad of course protects the front of the -staff from grazing by the friction of the tripod against it. - -There is a certain amount of risk, under any circumstances, of the -cylindrical tripod pressing against the front of the staff and -splitting it. To avoid this the author has lately made the pads with a -mahogany bridge piece, so that the pressure is distributed, coming upon -the edges of the front where the staff is strongest to resist it. This -is shown, Fig. 107. - -278.--For the entire protection of the staff a leather-bound sailcloth -case is very generally used. This may be divided into two compartments -for the staff and the tripod, with pads between. The whole case has a -neat appearance, and forms a protection from slight bruises and dirt, -either in travelling or when set up in an office corner for future use. - -[Illustration: Fig. 107.--_Improved pad for staff and tripod._] - -279--=Repairing Figures and Divisions.=--Surveyors going abroad -will find it very convenient to have a few tubes of artist's oil -colours--white, black, and vermilion, with one or two sable brushes -to touch up any divisions or figures upon the staves that have become -accidentally injured or worn off by friction. A tube of medium is also -useful, which will cause the colour to dry quickly and leave it bright. -The tubes of colour will keep any number of years if the caps are -carefully replaced. The brushes after use should be well washed with -soap and hot water, rubbing the soap in quite thickly till they are -quite clean, and then well rinsed before putting them by. - -[Illustration: Fig. 108.--_Iron triangle to support a staff._] - -280.--=Iron Triangle.=--For use of the staff in the field, particularly -in open grass or moist lands, a triangular plate of iron, as -represented Fig. 108, is very useful. This is trodden down firmly by -the staff holder before he places the staff upon it. In use it gives a -certain base to turn the staff upon from fore to back sight. It is very -inexpensive. - -281.--=Staff Level.=--This is a small circular level, shown at -Fig. 109, the upper surface of which is formed of a glass worked -slightly concave and fixed into a short cylindrical box. The glass is -hermetically sealed after being nearly filled with spirit. The circular -level is mounted on a plate with a dovetail fitting which fits in a -slot in the holding plate attached to the back of the staff. In use the -staff holder has to observe when the bubble under the concave glass is -in its centre. A very little practice is required to hold the staff -vertically by means of this little contrivance, which only weighs, -about 2 oz. - -[Illustration: Fig. 109.--_Staff level, ½ scale._] - -[Illustration: Fig. 110.--_Staff-holder, 1/10 scale._] - -282.--=Staff-holder.=--This implement, shown Fig. 110, striding a -staff, is very generally used in Germany and other parts of the -Continent. The staff is sunk into one side of a hardwood block. The -block is turned at one end to form a handle. A second similar handle -is cut with a strong screw and screwed into the end of the block. This -screw handle by turning brings up a following piece, shown inside -next the staff, which is covered with leather. When it is screwed up, -the staff may be held firmly by the handles only, without the risk of -the fingers coming in front. With this accessory it is also held more -easily and truly vertical. It is a comfort in use in cold weather. - -283.--=Practice of Levelling with the Staff.=--This subject can be -followed here only so far as to exemplify the uses of the instruments -and of accessories connected with such instruments. For practical -levelling we have the standard original works of Simms, Ainsley, and -others, with many modern works.[10] - -284.--_For Holding the Staff_, Mr. Holloway, in the work referred -to in the last note, gives instructions in such concise form that -they may be quoted with advantage. He says:--"I generally enter into -confidential chat with my staff holder, in which I explain to him the -vast importance of his duties, _i.e._, I endeavour to make him a man of -importance in his way, and I never fail to get those duties properly -performed. My instructions to him are seven in number:-- - - "1. Draw out the slides of the staff, and be sure the - joints are properly locked. Draw out one length - only unless signalled to do otherwise. - - "2. When the staff is once on a point never move it - unless signalled to do so. - - "3. Examine the staff regularly before setting it down - to see that no dirt is sticking to the bottom of it. - - "4. Always stand erect behind the staff, so that the - figures face the level. - - "5. Do not let any part of the hand come before the - face of the staff. - - "6. In no case put a downward pressure on the staff. - - "7. If the grass be long, mossy, or spongy, tread - it down, so that the staff shall have a firm - footing--select a firm spot if the selection is - left to yourself."[11] - -285.--The manner of setting up a level has been already described in -the previous chapter. The leveller generally follows a definite track -which he has previously arranged and marked out on a map. The distances -apart for placing the staves or staff are measured by the chain, or -by the subtense system to be fully described hereafter. Where the -levelling is very important, as for canal work, topographical survey, -etc., wooden pegs are driven down at the measured stations where the -staff is to be placed from which the levels are to be taken. A general -rule followed, as far as practicable, for starting is to select an -easily recognised, permanent, solid station for first placing of the -staff--a mile-stone, large boulder, or other solid object answers: a -datum line is generally assumed to be at a certain depth below this, -to which all levels are referred. From this station, if the ground be -fairly level, 5 chains is the ordinary advanced position where the -level is set up and the first staff reading taken. The level is set up -at the measured distance from the staff, which is indicated by a mark -left by the chainman. - -[Illustration: Fig. 111.--_Level height tape._] - -286.--Occasionally in town surveys the height of the level has to be -taken. For this a small steel spring pocket tape is used to take the -height of the axis of the telescope, Fig. 111. The tape may be adjusted -by taking a piece off the first end, and allowing for the width of the -tape case, so that by placing the ring of the tape upon the hook under -the instrument and bringing the case just to the ground, the height of -the axis of the telescope above the ground may be read off at the point -where the tape leaves its case. - -287.--_The Reading of the Staff._--The first position, which is -afterwards termed the _back reading_, is taken at a distance behind the -first forward position of the level. This is recorded exactly as it -appears in the telescope, the height of the telescope being also noted -in the levelling book, to be described. Thus in Fig. 112, _S_ the first -staff; _L_ the first station for taking levels. The fore reading _L_ to -_S′_ reads to a higher part of the staff _S′_; _L′_ next level station -back sight. _L′S′_ reads high on the staff _S′_; fore sight _L′S″_ -reads low; back sight _L″S″_ again low, following the contour; fore -sight _L″S‴_ low; thus giving data in the levelling book from which -the contour can be plotted from the datum line, which is taken low to -make all readings plus. - -[Illustration: Fig. 112.--_Practice of levelling._] - -288.--The staff reading, as already described, is divided into feet, -with two places of decimals. The safest method of taking this reading -is to take the second decimal place first and then record it, then -the first decimal, and finally the foot. In this manner no effort of -memory is required, and the staff being sighted three times assures the -certainty of the reading. The telescope should not be touched during -the operation, so that the reading in this manner is only a cautious -transfer. - -289.--If two staves are used on fairly level ground, the second staff -is now advanced 5 chains from the level to a measured station, the -staff holder here sighting the line through the level to the back -staff, and firmly treading down the staff plate if the land is soft -or grass, or otherwise requires it, or an iron triangle is used. When -time is given to hold the staff vertically by means of the staff level, -the reading is taken in this position by the leveller as before, and -this is recorded in the levelling book. The level is now moved forward -10 chains, that is, 5 chains ahead of the forward staff. The staff is -carefully turned half round without pressure upon its standing place -or plate to face the level as now placed, in which position it is then -read off by the level as the back sight, the back staff now being moved -5 chains forward of the level, and so on alternately staff and level -until the distance required to be levelled is completed, if there is no -obstruction which causes another method of procedure to be adopted. A -similar plan is pursued with a single staff; but care has to be taken -in securing the right line of march, which will be by placing the staff -in a sight line through the level with a fixed landmark instead of the -back staff mentioned. - -290.--The equal back and fore sights as far as practicable are insisted -upon by all levellers, as by this means any inaccuracy in the level, if -the run of the bubble is kept constantly true, is thereby compensated; -but it is not always convenient, and when it is not the accuracy of the -work must depend largely upon the qualities of the level. It is not -necessary or convenient at all times to take the back and fore sight -in a line--obstructions of woods, rivers, etc., may occur. In these -cases very often what is quite equivalent may be done by taking equal -angular back and fore sights from the apex of an equilateral triangle -thus:--Say an obstruction occurs for the chain by a pond or wood, but -that both points to which the levels are to be taken are visible at -some lateral position. Levels may be taken from this place, and if the -intermediate point of distance is equal from both stations there will -be no instrumental error. Thus, suppose the direct level line east -(90°), and that the two stations can be seen and the staves read at -150° and 210°; here, evidently, this is equivalent to a direct back and -fore sight, the right angle to the level course being 180°--the one -station is 150° = 180° - 30°, and the other 210° = 180° + 30°. If these -equal angles can be even approximated with a fairly good level the -error will be small. In this manner intermediate and extended points -may often be conveniently taken by previous arrangement with a good -staff holder. It is in this angular levelling that the greatest use of -the compass is found to give the angles, to make entries of the work in -the levelling book. - -291.--In levelling hilly ground great loss of time would sometimes be -incurred from taking equal back and fore sights; the best plan in this -case is to make as much use as possible of the length of the staff in -use. It is in hilly districts only that a staff longer than 14 feet -is advantageous. With any staff in descending a hill only 5 feet of -the staff can be used for the back sight, that is, a part of it equal -to the height of the level, and sometimes 4 feet or less if there is -grass, brambles, or other obstruction. Whereas for the foresight all -the staff upwards of the height of the level, that is, about 9 feet in -a 14-feet staff, can be used with certainty. The distance of setting -up of the levels and staves must in this case entirely depend upon the -length of the staff and other conditions present. - -292.--For near reading of the staff on sharp inclines, reading to -two places of decimals is not near enough, as errors may accumulate -rapidly. It is in such cases that a fully divided staff is best. The -divisions upon a near staff appear in the telescope much magnified; and -three places of decimals may easily be taken by anyone used to reading -a chain scale, particularly if a point diaphragm be used. Through -valleys the level may be often checked at some point from hill to hill -by a back sight: the contour must nevertheless be followed for the -section. It is in these shorter unequal ranges and in distant sights -that accuracy in the level is demanded; and it becomes interesting to -know how nearly this may be depended upon for such readings. - -293.--As already mentioned, a sensitive 14-inch level of Y -construction, or a dumpy in perfect adjustment supported on the -tribrach system, will work with a level tube divided to read 5 seconds -in divisions 1/20 inch apart. There will be a little personal error -in reading the bubble from difference of reflection, according to -the direction of the light from the two ends of the bubble, as before -discussed; but the bubble may be assumed to be read within less than -half a division, that is, within 2½ seconds--say 2 seconds. A -distinct staff may be read with a good glass within ·1 foot at one -mile. A second of arc subtends ·025598 of a foot = approximately ·3 -inch at a mile distance. Therefore a back reading at this distance can -be taken within an inch or so of allowance for instrumental errors. -A reading taken in this way at a mile distance would require a plus -allowance for curvature of the earth of 8 inches, minus say 1 inch for -refraction = 7 inches. From these data we can get a fair check level -for hilly ground, possibly more accurate than by contour levelling for -a distant station, even if we allow double the probable error, say ·1 -foot for error of reading the staff at a mile distance. - -[Illustration: Fig. 113.--_Calder stove used as a lamp._] - -294.--=Lamp.=--At heights between hills in wide valleys check levels -may be taken from five to ten miles very well with a good 14-inch -level in still clear weather in dark nights by the use of an oil lamp. -Coincident points above datum being selected, the lamp is set upon -the ground, or at a measured height at a calculated point, or raised -or lowered to lantern signals, allowance being made for curvature and -refraction. The wide band of light is read very easily by shifting the -observer's position and raising or lowering his tripod. The "Calder" -lamp stove answers very well as a lamp. It has a wick about 3½ -inches wide, and by means of a masked chimney may be made to present a -clear white line of light of 1 inch in depth, Fig. 113. - -The heliostat is sometimes used for check levelling in sunlight. This -will be described further on with the theodolite. - -295.--=Curvature Corrections of the earth and of Refraction= to be -made use of occasionally for check levelling. The rule for finding -curvature is "_That the difference between true and apparent level is -equal to the square of the distance between two places or stations -in miles--divided by the earth's mean diameter, 7916 miles_"; -consequently, by this rule the correction is always proportional to -the squares of the distances. By proportioning the excesses of height -to the squares of the distances, we may obtain a curvature table for -corrections. This is, however, always in excess of the true curvature -by the refraction caused by the increase of density of the air towards -the earth's surface, which bends the visual ray. The curvature of the -earth may be corrected for refraction one-fifth to one-sixth,[12] which -varies according to the atmospheric pressure. - -296.--The following table, which takes curvature minus refraction, -will be found useful to have at hand: it may be written out and pasted -inside the lid of the level case:-- - -_Table of Differences of Apparent and True Level for Distances in -Chains._ - - Distances in Curvature minus Distances in Curvature minus - Chains. Refraction in Chains. Refraction in - Dec. Ft. Dec. Ft. - - 1 ·000089 14 ·0175 - 2 ·000358 17 ·0258 - 3 ·000804 20 ·0357 - 4 ·001435 22 ·05 - 5 ·002233 24 ·06 - 6 ·003216 26 ·07 - 7 ·00437 28 ·08 - 8 ·0057 30 ·09 - 9 ·0072 40 ·14 - 10 ·089 60 ·31 - 11 ·011 80 ·56 - -Where great precision in levelling is required, as for important -trigonometrical surveys, many precautions are required to be taken -which would be quite superfluous, for instance, in railway work. Thus -much greater exactness and freedom from personal error is secured by -having two levellers to go over the same ground simultaneously. Errors -by two persons in the same part of the track are very unlikely to -occur, and by comparing books every part may be checked. - -297.--=Pegs.=--Where the work is to be entirely pegged for chain -measurements, the pegs may be made of natural sticks sawn off and -pointed up with a bill hook. If they are sawn from timber they are -generally made about 9 inches long and sawn to a point, the head -being full 2 inches by 2 inches. Where great precision is required a -cast-brass or iron nail is driven into the head after the peg itself is -driven down. This is used to turn the staff upon, Fig. 114. _A_ the peg -shown with a nail in its head, 1/8 size. _B_ nail about full size. - -[Illustration: Fig. 114.--_A, staff pegs of sawn timber, 1/8 scale; B, -nail, full size._] - -298.--It is considered a precaution with an ordinary level to mark -one leg of the tripod and always place this in the same position to -the staff. Thus, if the marked leg is placed to the forward staff at -first, it is put at the next station backward to the back staff. This -corrects any general error from defective work in the instrument and -want of adjustment; and if the staves are placed at equal stations -any instrumental defect whatever, to act cumulatively upon a distant -station, is then prevented, as this principle produces an alternate -plus and minus error. - -299.--Differences of true level have been found between working -southward towards the sun from working northward from it, which are -caused by the expansion of the instrument and bubble tube upon the side -heated by his rays. These matters of higher refinement may be followed -in some of our best works on levelling. Most excellent instructions in -this matter will be found in the appendix of _A Manual of Surveying for -India_,[13] in a paper by Colonel J. T. Walker, R.E., F.R.S., etc., of -the great Trigonometrical Survey of India, wherein levels have been -carried across from ocean to ocean for over 1500 miles of land surface. - -300.--=Levelling Books= which record the levels as they are taken are -considerably varied in form, much influenced, no doubt, by the method -pursued by the civil engineer for the execution of his work. The -illustration, Fig. 115, shows the most general forms, but there are -many others. - -301.--Entries are very generally made in levelling books in black lead. -Faber's artists' pencils, which require no cutting, are very generally -used, No. 2 being black and moderately hard. It is very convenient to -carry a small file for sharpening the lead frequently. In the author's -surveyor's knife, described further on, a file forms one of the blades. - -302.--Where it is desirable to make the original levelling book -readings permanent for reference or otherwise, they are very commonly -written in ink, Morrell's registration ink being very generally used, -or the author's drawing ink answers; this being permanent is not liable -to corrode the pen, nor permit the writing to be effaced in any degree -by moisture. - -[Illustration: Fig. 115.--_Specimens of levelling books, 1/3 scale._ - -_Ordinary Level Book_ with columns for No., Back Sight, Intermediate, -Rise, Fall, Reduced Level, Distance, Remarks. - -_Collimation Level Book, with columns for Back Sight, Intermediate, -Fore Sight, Height of Collimation, Reduced Level, Distance, Remarks._ - -_Railway Engineers' Level Book_, ruled for Back, Intermediate, Fore -Sight, Rise, Fall, Distance, Reduced Level, Formation Levels, Cutting, -Embankment, Remarks. - -_Tacheometer Survey Book, ruled as above illustration._ - -_Traverse Survey Book, ruled as above illustration._] - -303.--_The Ink Bottle_ mostly used is that known as the excise bottle. -This is of a smooth, oval form, covered with black leather, with a tab -and buttonhole to hang upon a button of the coat, Fig. 116. One of the -numerous fountain pens is now generally used instead of the bottle -described. - -[Illustration: Fig. 116.--_Excise ink bottle._] - -FOOTNOTES: - -[7] _Brit. Assoc. Report_, 1838, p. 154. - -[8] Patent No. 12590, 1889. - -[9] _Colliery Guardian_, vol. xxxviii. p. 576, 1879. - -[10] _A Treatise of the Principles and Practice of Levelling_, by -F. W. Simms, 1842; _A Treatise on Land Surveying_, by John Ainsley, -revised by William Galbraith, 1849. Quite modern works--_Aid to Survey -Practice_, L. D'A. Jackson, Crosby Lockwood, 1910; _On Levelling and -its General Application_, by Thomas Holloway, Spon, 1887; revised 1914. - -[11] _Levelling_, p. 49. - -[12] Deschanel's Natural Philosophy, by Prof. Everett, p. 1018, 1876. - -[13] _A Manual of Surveying for India_, by Colonel H. L. Thuillier, -C.S.I., F.R.S., etc., and Lieutenant-Colonel R. Smith. Thacker, -Calcutta, 1875. (Now out of print). - - - - -CHAPTER VI. - - DIVISION OF THE CIRCLE AND METHODS EMPLOYED IN TAKING ANGLES--DIVIDING - ENGINE--SURFACES FOR GRADUATION--VERNIER--VARIOUS SECTIONS--READING - MICROSCOPES--SHADES--MICROMETERS--CLAMP AND TANGENT MOTIONS--OF - LIMBS--OF AXES--USE AND WEAR--DIFFERENCE OF HYPOTENUSE AND BASE. - - -304.--=Division of the Circle.=--_Sexagesimal Division._--All true -surveying instruments depend, as their special function, upon taking -the direction, or angular position, of surrounding objects or definite -parts of the surface of the earth from positions which are at first -accurately measured or ascertained. The instruments required for such -work must possess an accurately divided circle or arc, with means of -subdividing the visible divisions of this to greater closeness than -any possible method of drawing lines simply would permit. The lines -upon the circle in general practice in Great Britain are divided into -degrees, which are subdivided to 30, 20, 10, or 5 minutes, according -to the size of the instrument, and arranged for further subdivisions -by means of a vernier into minutes or 30, 20, or 10 seconds of arc. -Upon large circles, say of 10 and 12 inches diameter, and with modern -5, 6, and 8 inch diameters, angular displacements in the direction of -the telescope are ultimately read off with a microscope by means of a -screw with divided head, termed a _micrometer_, placed tangentially to -the divided circle; or by a series of lines placed at equal distances -apart in front of an eye-piece or within a microscope; but in the -ordinary portable instruments, or those that a surveyor can personally -carry about the country, the ultimate subdivisions of the circle are -still generally made by a vernier scale only, which will presently be -described, although the smaller modern micrometer reading instruments -are slowly but surely coming into favour for all high class work. - -305.--_Centesimal Division._--Ten to fifteen years ago on the Continent -generally, and in America occasionally, the division of the circle into -400-grades and ½-grades, and the subdivision of these decimally to -centigrades, appeared to be coming more and more into use, particularly -with the more extended use of the tacheometer. Under this system it -will be seen that the right angle subtends 100 grades. This division, -with its centesimal parts, was found to blend conveniently with -logarithmetical calculation and to permit the free use of the slide -rule with great saving of time over ordinary calculation, but it is now -very little used. - -The decimal division of the ordinary degree of 90 to the quadrant -greatly facilitates the calculation compared with what is necessary -with the sexagesimal division into minutes and seconds, and the reading -of the verniers is much simpler and less liable to errors; moreover, -the mental conversion of the sexagesimal division into decimals of the -same degrees is much simpler than the conversion into the centesimal -degrees of 100 to the quadrant. - -306.--=Dividing Engine.=--This important tool is used for cutting the -graduations on all surveying instruments. If possible a position should -be secured for it on a ground floor at a mile or more distance from -any railway, and at a good distance from roads upon which there is -heavy traffic, as small vibrations are sufficient to cause unpleasant -working and some error in the division of large instruments. For very -accurate work some makers divide at night for the sake of stillness. -The principles of construction of this machine, as at present in -general use, were invented by Jesse Ramsden, of which an account was -printed by the Board of Longitude in 1777. Refinements of detail have -been added to the invention, and the steady action of steam or electric -power has been applied in place of the foot, but otherwise the machine -remains practically the same. Therefore a brief description of this -machine as originally invented will be sufficient for the purposes of -this work, which is not intended to fully describe the tools used in -the manufacture of instruments. - -307.--_Ramsden's Engine_ consists of a circular brass surface plate, -made generally of 36 inches diameter. This plate is supported from -below upon a hollow vertical axis, which moves in an adjustable collar -placed at its upper end and in a conical point or pivot at its base. -The pivot rests in a cup of oil and supports the weight of the plate -and axis, so that this part rotates with little friction. The outer -edge of the surface plate is cut with 2160 teeth or threads, into which -an endless or tangent screw works, so that the plate can be revolved -any desired quantity by means of the screw. Six turns of the _tangent_ -screw moves the plate 1°. The head of the tangent screw is divided -as a micrometer into 60 parts; therefore the movement of one of the -divisions of this head revolves the plate 10″ of an arc. A ratchet -wheel of 60 teeth is attached to the tangent screw, and so arranged -that by reciprocating motion applied to a rack which works into it the -circle can be advanced any multiple of 10″. Motion is given to the -tangent screw by a catgut over a pulley worked by the foot. The work is -centred and clamped down upon the surface plate. While the divisions -are being cut this surface plate remains for the time quite stationary. - -308.--The dividing knife is attached to a swinging frame having a -reciprocating motion. The forward extent of its swing is regulated by a -detent wheel with teeth of varied heights, which, as they are brought -by the mechanism consecutively forward, stop the knife at a definite -position; so that the cuts upon the circle--technically the limb--are -regulated for lengths to represent 10 degrees, 5 degrees, degrees and -parts. In the use of this dividing machine the divider who worked it -had alternately to press his foot upon a treadle and then pull a cord -attached to the dividing knife frame. These motions are now performed -by self-acting mechanism. For full particulars and details of the -dividing engine see Troughton's Memoir, _Phil. Trans._, 1809: _Memoirs -of the Royal Astronomical Soc._, vol. v. p. 325; vol. viii. p. 141; -vol. ix. pp. 17 and 35. For various plans that have been tried see -_Holtzapffel's Turning and Mechanical Manipulation_, pp. 651-955. - -309.--_The Material_ upon which the _limb_ or circle of an instrument -is divided is almost uniformly of silver, except for mining survey -instruments, which need a very strong cut. Silver being dense and -of extremely fine crystallisation, or _grain_, as it is technically -termed, bears a uniform smooth cut with sharp outline. Occasionally -circles or arcs are divided on platinum, certainly the best metal, -as it keeps constantly clean; but it is expensive. The verniers are -then made either of this metal or of gold. The silver of the circle, -when this metal is employed, is rolled down from a surfaced cast plate -of about ·25 inch in thickness to about ·045 inch, by means of which -it becomes uniformly dense and fine grained. In all cases possible, -that is, upon all flat internal surfaces, the silver is placed in an -undercut groove and planished down to fill the groove without any other -fixing being necessary. This plan of insertion is employed for all -vertical circles--the horizontal circle of Everest's theodolite, limbs -of sextants, box sextants, etc. In Fig. 117 the silver is shown at -_A_, in the section to which it is drawn by a plate after it is cut in -slips. It is shown placed in its groove _B_ ready for planishing down. -By this method certainty of dense surface is obtained for the future -division. - -310.--Upon bevelled edges and outer surfaces the rolled silver is -planished to form, and then soldered to the metal of the part of the -instrument to be divided. The surface, after being made as dense as -possible by planishing or otherwise is turned to form and stoned to -surface ready for the dividing knife. - -[Illustration: Fig. 117.--_Insertion of silver in circle._] - -311.--=Graduating.=--The object aimed at by the skilful divider is to -obtain as deep a sharp-edged cut as possible, which shall be at the -same time as fine as it can be read clearly by the microscope with -which it is to be used. This matter is most important to the possessor -of the instrument afterwards for use, as in the atmosphere the silver -soon forms an oxide and a sulphuret upon its surface which has to -be cleaned off; and at every cleaning a portion of the silver is -necessarily removed, so that in old or badly divided instruments the -divisions become dull or lost from this reason. - -[Illustration: Fig. 118.--_Piece of charcoal._] - -312.--After the instrument is divided it is engraved with figures and -stoned off with fine blue-stone, and finally finished with willow or -pearwood charcoal, which has just sufficient cut in it to leave a hard -edge to the division lines. - -313.--It may be useful to the surveyor, far from aid of the optician, -to know that divisions on silver which are much oxidised may be brought -up to sharp lines by the use of a piece of fine-grained charcoal, -sharpened by a clean file to a chisel point. This should be frequently -dipped in water, and rubbed lightly with the flat of its end surface, -Fig. 118, keeping the motion of the hand in the direction of the -circumference of the circle. The piece of charcoal before being used -should be first tried upon a piece of plain, smooth metal--an old coin -which is worn smooth will do--to see that it is not _scratchy_. No -kind of polishing powder should in any case be used for cleaning limbs -or verniers, as _this_ is sure to rub down the edges of the cuts and -thereby ruin the divisions of the instrument. - -314.--It must be understood that the above directions are not intended -for the ordinary cleaning of the circle for an instrument in general -use, as such would be injurious to it. In the ordinary daily use of -the circle, if it is not in any case touched by the hand, and is kept -carefully brushed with a large, soft camel-hair brush when taken from -the case, and the same when returned to it, it will keep a long time in -an excellent state. If the circle is slightly tarnished, this tarnish -may be removed by a piece of quite clean wash leather; but the brush is -always the safest if sufficient. If the vernier gets _grubby_ against -the circle, a piece of clean thin writing-paper may be passed between -these parts, which will clear out any dirt or grit there may be between -sufficiently. - -315.--=The Vernier Reading Index.=--This is one of the most important -inventions ever applied to instruments of precision for measuring -upon the circumference of the circle. It was invented or brought into -practical use by Pierre Vernier, a native of Ornans, near Besançon, in -Burgundy. The first publication of the invention appears in a pamphlet -published in Brussels in 1631, _Construction, Usage, et Proprietes -du Quadrant Nouveau de Mathematique_. This invention was possibly -foreshadowed, as it is mentioned by Cristopher Clavius in his _Opera -Mathematica_, 1612, vol. ii. p. 5, and vol. iii. p. 10; but he did not -propose to attach it permanently to read into an arc, that is, to place -it in its practical form. - -316.--The value of the vernier as a means of reading small quantities -depends upon the fact that the _eye_ cannot separate lines, drawn at -equal distance apart, of above a certain degree of closeness, there -being a point for all vision where such lines appear to mix with -the ground upon which they are drawn and form a tint; therefore, an -index reading into such close lines would be, unless under extreme -magnification, most indefinite; whereas the eye can see a single -separate line clearly and detect any break in it. The vernier for -reading subdivisions depends upon the functions of the eye having power -to detect any break in an otherwise straight line, so that a line that -appears without a break may be taken as the index of reading from -among others that appear broken or separated. It is found in practice -that a line as fine as it can be clearly seen will appear broken in -its continuity with another equally fine line, if at the meeting the -rectilinear displacement is as much as ·25 to ·2 part of the width of -the line. It therefore follows that we may read closer by displacement -of parts of a single line than by any possible series of lines that -can be drawn in spaces apart upon a surface; so that if we can arrange -lines in such a manner that they open out or separate into distinct -lines to admit of this principle, we obtain the full value of the -unbroken single line reading, and this is the principal aim of the -vernier. - -317.--On the same principle that we can find the straight or most -direct line of a series of lines to take as our index, we can also -estimate the amount of the displacement of our selected line, if this -does not read perfectly straight from the vernier division to the -circle division. This small difference is detected in practice by many -experienced surveyors, so that a vernier reading nominally to minutes -only is recorded _n_′ + 15″, 30″ or 45″, that is to 15″. There is -no doubt that this will be approximate, but it may be much nearer than -the even minutes, say to the 30″ on a 5-inch, or the 15″ on a 6-inch -sharply divided circle. - -[Illustration: Fig. 119.--_Origin of vernier scale._] - -318.--_The Vernier Scale_, as employed by Vernier, was divided to -read minutes upon a circle or limb divided to half degrees, by taking -thirty-one divisions of the scale and dividing these in thirty equal -parts for a separate scale to read against it. This plan is now termed -an _inverse reading_, the reading being the reverse to the direction -of that of the arc. In modern practice the vernier to read minutes is -divided to the length of 29 half degrees, and this length is subdivided -into thirty equal parts: consequently, where the vernier and scale -are placed edge to edge or reading to reading, every division of the -vernier _advances_ consecutively on the scale one-thirtieth of the half -degree, that is = 1′ of arc on the scale divided to half degrees. In -the above diagram, Fig. 119 represents the scale and vernier at the -position from which the description is taken, wherein the vernier is -shown to cover 29 half degrees or 14° 30′, and this length is divided -into thirty parts. The consecutive advance of the vernier on the scale -is shown + 1′ for each half degree. In this position of the vernier, -or at a similar position in relation to any other half degree of the -circle the arrow placed at the zero of the vernier reads direct into -the degree or half degree, so that this reading must be _n_° or _n_° -30′ at any equivalent position in relation to any line on the limb. - -[Illustration: Fig. 120.--_Vernier scale, reading 23° 12′._] - -319.--In Fig. 120 the arrow upon the vernier scale is shown reading -at a position beyond 23°, which we then know must be 23° _n′_. Now, -if we look along the vernier, the lines of this and the scale appear -coincident at the twelfth division of the vernier; consequently, the -_n′_ is 12′, and the reading is altogether 23° 12′. - -320.--Learning the reading of the vernier is very similar to that of -the clock, wherein a child at first gets confused by the difference of -value of the minute hand and the hour hand. In the case of the vernier -we have only to get clearly in our minds that the degree reading and -the vernier reading are quite distinct processes, in which the vernier -reads _minutes_ only, and this _by coincidence of lines only_, and that -it has nothing to do with degrees, which are indicated by the arrow -_only_. The arrow may be assumed to be placed on the vernier scale to -save an unnecessary line of division; but this practically might just -as well be placed quite outside of it, as it has nothing whatever to do -with the vernier reading. - -[Illustration: Fig. 121.--_Vernier scale, reading, 23° 47′._] - -321.--It is important to make this matter of reading the vernier clear; -therefore in Fig. 121 the index arrow and vernier are shown reading -past a half degree. At this position the arrow reads 23·30 on the limb -+ the vernier, or 23° 30′ + _n′_ of the vernier reading. We find the -coincident line of the vernier with the limb is at 17, therefore the -reading is 23° 30′ + 17′ or 23° 47′. - -322.--The principle of the vernier, upon which it takes its reading -from the coincidence of lines, as just stated, points out that -the figuring of values of points of coincidence may be varied at -discretion, and the zero index may be in any convenient position. The -above described is the common reading to the theodolite and many other -instruments. In mining dials and some other instruments the zero is -placed in the centre. We may, for example, take a central reading with -a vernier reading to 3′, wherein the circle being divided into degrees; -the vernier is then, necessarily, in the direct method, divided into -twenty divisions (20 × 3 = 60) which correspond with nineteen degree -marks of the circle. With a central reading the vernier in this case is -figured 30, 45, 0, 15, 30. This is rather a simple reading, as the zero -to which an arrow is attached gives the true bearing, and it is readily -seen to which degree it refers. - -[Illustration: Fig. 122.--_Vernier reading centrally to 3′._] - -[Illustration: Fig. 123.] - -In Fig. 122 the 45 of the vernier is coincident with a line of the -limb, this must, therefore be 45′; and as the index arrow is past 44°, -it is 44° 45′. If the vernier had read the division next past the 45, -the division being to 3′, this reading would have been 44° + 45′ + 3′ = -44° 48′. The same principles may be applied to any subdivision. Circles -are commonly divided by the vernier in various ways to give readings -from 5′ to 5″. - -Theodolites reading to 30 seconds are usually divided degrees and -thirds of degrees on the circle and minutes and halves on the vernier, -as illustrated (Fig. 123), the reading in this case being 153 degrees -40 minutes on the circle and 8 minutes 30 seconds on the vernier, -giving a total reading of 153° 48′ 30″. - -A 20 second reading usually has divisions of 20 minutes on the circles -and these are subdivided into minutes and thirds by means of the -vernier. - -[Illustration: Fig. 124.] - -Fig. 124 is an illustration of this, showing a reading of 28 degrees 40 -minutes on the circle and 12 minutes 20 seconds on the vernier, giving -a total of 28° 52′ 20″. - -A 10 second reading is designed in the same manner as the above, but -each division of the circle is 10 minutes instead of 20 minutes, with -minutes and sixths on the vernier. Fig. 125 is an illustration of this, -showing a reading of 7° 16′ 30″. - -[Illustration: Fig. 125.] - -323.--_For Centesimal Division_ the vernier to read minutes is -generally divided 50 into 49 for the half grades, for small circles 4 -inches to 5 inches. For larger circles, 6 inches to 8 inches, verniers -are cut 25 to 24. The circle is then divided to ·25. Where there is -space for five divisions to the grade, ·20, the third decimal place, -may be estimated or read exactly to ·005 by a vernier 40 to 39, or -more closely if desired by a micrometer, to be described presently. - -[Illustration: Figs. 126, 127.--_Sections of scales and vernier for -circular readings._] - -[Illustration: Figs. 128, 129.--_Sections of scales and vernier for -circular readings._] - -324.--=Surfaces of Limb and Vernier.=--To get a perfect reading of -a vernier the scale and vernier should be brought into contact upon -a plane. This, for many reasons, is impossible in a great number of -cases upon an instrument, from the conditions of its construction, -convenience of vision, and in some cases for want of means of ensuring -durability of the edges which work together. Therefore verniers and -scales are more commonly constructed upon the methods shown in section -Figs. 126, 127, where _VV_ are verniers, _LL_ limbs. The plan shown -in section Fig. 128 gives a nice reading on a new instrument; but the -part of the edge not covered by the vernier is open to accident, or if -nearly covered by a part of the instrument, open to the introduction -of gritty dust, which wears the meeting line open, and thereby causes -loss of edge to edge reading. Fig. 129 shows a section we find on some -French instruments. This plan was introduced by the late Colonel A. -Strange for the section of the limb reading of theodolites for India, -but it was found in practice awkward to use upon this instrument, as it -required unpleasant stooping to read it. It is, nevertheless, one of -the best permanent vernier readings, as the division remains constant -under the amount of wear occasioned by the sliding of the vernier upon -its circle. - -325.--With the reading planes shown in section Fig. 126 we require -great care to bring the eye, whether open or through the microscope, -directly radial with the centre of the circle at the line into which -the vernier cuts. If we read the line in the slightest degree one-sided -it is quite possible to make a difference of a minute on a 5-inch or -6-inch circle. This is the section of the general reading plane of -theodolites, where, from the necessary height of the telescope, the -limb has to be placed much lower than the eye. With this section the -circle comes fairly square to a comfortable position for reading. It -will be noticed that there is a slight lap shown to the vernier over -the limb at _a_, Fig. 126, which is always found in new instruments of -this section. It gives an allowance for wear between the vernier and -the limb caused by the fretting of the metals together, as also by the -intrusion of grit, which is always present in instruments used in the -open air. The lap should not be great, and it should be nearly equal -along the edge of the vernier, although it is a difficult matter for -the maker to get it perfectly so. - -Fig. 127 is a section of the reading planes common to sextants and -parts of many instruments. This plan requires the same care to obtain a -truly perpendicular reading to the division as that described above for -Fig. 126. - -326.--In the very best of work there is at all times a certain amount -of error, both between the divisions themselves, and in the place of -the axis in relation to the centre of the divided circle, and of the -position of the vernier in relation to both these. It therefore becomes -necessary, where exactness is required, to place at least two verniers -to read opposite sides of the circle. These bisect every reading -through the axis of the instrument, and detect very small errors in -the work, as well as personal errors of the observer, of which the -mean reading of the minutes or seconds only may be taken and used for -correction to mean position. Where very great precision is aimed at, -three or even five verniers are sometimes placed round the circle, -and the mean reading is taken of the small differences in minutes or -seconds, after calculation for correction, to find the direct position -of the axis of the telescope required for the record of the observation. - -327.--=Reading Microscope.=--The microscope usual for reading the -vernier is either a simple plano-convex lens of short focus or a -Ramsden eye-piece of the kind described for observing lines on -the diaphragm of a telescope, art. 82. Frequently the microscope, -technically called the _reader_, is made of a compound form, sometimes -with a diagonal prism or mirror. It is uniformly mounted in such a -manner that it may move concentrically to the divided circle into which -it reads. In English instruments it is placed normal to the surface of -the vernier, so that following its curvature it may read opposite any -line upon it. In French instruments the reader is frequently placed -obliquely, so as to look along the line of the limb into that of the -vernier, which is said to be advantageous in certain lights. - -328.--In theodolites for reading the horizontal circle, the reader is -sometimes mounted to slide in an undercut groove near the circumference -of the limb to follow its curvature. This motion is not pleasant; it -is better in this and all cases of vernier reading, if possible, to -mount the reader on frame-work proceeding directly from and moving -upon the axis. Where it is practicable, it is much better to have two -readers where there are two verniers, and in all cases to have one -to each vernier, than to shift one reader about after the instrument -is placed in position, which is liable to disturb it. With opposite -readers mounted on a pair of arms formed of one piece of metal, where -these bisect the circle working through its axis, by the setting of -one reader truly normal to the coincident division of the vernier the -opposite reader will be set also; so that this does not only save time, -but the instrument need not be touched for reading the second vernier. -The same principle should be applied to any greater number than two -verniers as nearly as it may be practical. - -329.--Instruments that have to be packed in cases for conveyance should -always have readers removable from the instrument, with proper fittings -in the case provided for them, or they should be hinged to turn up to -a secure position, the latter being a more expensive but a much better -way. It is better also, if possible, to remove the light frame with -the reader if this does not turn up, so that it cannot be injured in -replacing the instrument in its case. - -[Illustration: Fig. 130.--_Reader fixed normal to surface._] - -[Illustration: Fig. 131.--_Jointed reader to set to any angle._] - -330.--Fig. 130 shows a good rigid form of reader for an oblique -plane of division:--_V_ vernier, _L_ limb. This reader is placed on -an arm radial from the centre of the instrument, more generally in -pair with an opposite reader. The connection with the arm is commonly -made for portability with a dovetail slide fitting to the reader, -sprung by a saw-cut down it to ensure constant contact after wear, -as shown in section Fig. 132; _N_ arm of reader, _O_ fitting to arm. -The better form is shown in Fig. 131. In this the arm is jointed, -so that the reader out of use is turned up into the central part of -the instrument. This plan admits of adjustment of the reader for -reflection of light from the division, or for reading _down the lines_ -if preferred. The magnifying power of either of these microscopes is -generally two to three diameters. The adjustment of the glasses should -be such as will produce a flat field (Ramsden's principle, p. 41), so -that several divisions of the vernier and limb may be read sharply when -it is in focus, although the central division only is taken for the -reading. - -[Illustration: Fig. 132.--_Section of movable arm fitting to reader._] - -331.--=Surface Reflection to Reader.=--In reading with the microscope -the silver surface, from its brightness in certain lights, gives -unpleasant reflections which render the reading difficult. In practice -the hand or a piece of white paper is used to shade the open vernier in -such cases. In large instruments a piece of ground glass is fixed in a -frame over the vernier, which throws a soft light, producing the effect -of a dead surface upon the silver, or the light is reflected from a -cardboard or ivory surface. Fig. 133 shows a common form of microscope -for reading a vertical circle, by which the light is reflected from a -white surface surrounding the field-glass end of the reader. - -[Illustration: Fig. 133.--_Reflecting surface reader._] - -332.--=Shades for Vernier.=--It is very general on the Continent to -place the divided reading of the circle and its vernier on a plane -perpendicular to the axis, Fig. 128, and to place the reader at a fixed -angle for down-the-line reading, the object-glass of the reader being -constructed to focus parallel rays. In this way the division of the -circle is followed into its vernier or _vice versa_. In this case the -silver may be shaded by ground glass, which gives a soft, pleasant -reading in most lights. The general arrangement is shown, Fig. 134; _L_ -limb, _V_ vernier, _S_ shade of ground glass, _M_ reader. Objection -is made to glass shades by civil engineers as being too delicate and -liable to fracture, with risk of the particles of glass getting into -the working parts of the instrument. To obviate this the author has -made the shade of a piece of thin horn or transparent ivory, which -appears to answer very well and to save this risk. - -[Illustration: Fig. 134.--_Oblique reading microscope with shade, -French plan._] - -333.--For ordinary instruments with no provision for shading, a piece -of transparent horn about 2¼ inches by 1¼ inches may be carried -in the waistcoat pocket, and will be found a great comfort if held -over the vernier when the lines appear glary, or the horn may be -placed in a pocket frame with the case containing reflector for bubble -reading, Fig. 52. In large theodolites, used for geodetic surveys, the -object-glass of the micrometer microscope is sometimes surrounded by -a thin belt of turned ivory. This throws a very soft light upon the -divisions. - -334.--=Micrometer Microscope=, _for Reading Subdivisions_.--Where -more exact reading is required than is possible with the vernier, as -in the case of the reading of circles 10 inches or more to seconds, a -micrometrical microscope is employed, which gives means of measuring -the distance from line to line of the division upon the limb by the -displacement of a web, point, or line moved by a fine screw with a -divided head. - -The great demand of late years for reducing the size and increasing -the accuracy of theodolites has induced the highest class makers -to introduce micrometer reading instruments of six, five, and even -four-inch circles, and their accuracy is far greater than is possible -with any instrument of the same size that reads by verniers. Of course -the workmanship in these instruments has to be of a higher order, -and the reviser estimates the accuracy of the micrometer through -magnification and the necessary refined workmanship to be at least four -times as great as the vernier reading, with the advantage that the -micrometer is much more certain and easier to read. - -335.--The construction of the reading micrometer as originally designed -by Troughton has not been materially modified in those in general use. -Certain refinements have been introduced for astronomical work: these -are sometimes expensive and often cumbersome, so that they need not be -considered in relation to surveying instruments. - -336.--In all cases where micrometers are used, the structure of the -framework of the instrument which carries them should be made extremely -rigid, as very minute deflections or vibrations render the reading -to seconds of arc impossible. The number of micrometers applied to a -circle is generally 2, 3, or 5. - -337.--If a circle is to be read by micrometers, the vernier is -generally dispensed with. The circle is usually divided to read in -5′. The first approximate reading used to be taken by a single index -line with the aid of the ordinary reader, Fig. 130. From the index -line the degrees or minutes were taken to the last 5′ line indicated. -Since the introduction of high-class engraving machinery the figuring -is made at each degree and is clearly read in the microscope, so that -the index reader is unnecessary. This engraving is quite a nice piece -of work, as to figure from 0 to 360 means nearly a thousand figures, -and on a 5-inch circle these have to be less than 1/100th of an inch -high. Only the highest class makers are able to do this work. When a -microscope is adjusted to one line it should be observed that all the -other microscopes upon the same circle should also read exactly to a -line that should be true from microscope to microscope to the arc they -subtend between each other. - -[Illustration: Fig. 135.--_Side elevation of Troughton's micrometer._] - -[Illustration: Fig. 136.--_Section of micrometer._] - -[Illustration: Fig. 137.--_Micrometer slide._] - -338.--=The Micrometer=, as it is now technically termed to include the -whole piece of apparatus, is a compound microscope consisting of three -lenses, with measuring apparatus at the mutual foci of the field-glass -and of the two lenses which form the eye-piece. The field-glass, -which is placed nearest the divided arc, is generally an achromatic -microscopic lens of an inch or more in focus. The eye-piece is of the -Ramsden form, Fig. 16. By the construction of the compound microscopic -arrangement the eye of the observer may be placed at any convenient -distance from the limb, and any desired magnification may be obtained -to assure micrometric nicety of measurement. The engravings represent -the micrometer, Fig. 135 in side elevation, Fig. 136 longitudinal -section, and Fig. 137 the micrometrical slide, which is shown partly -in section for demonstration in all the figures; _a_ the micrometer, -_q_ microscope body tube. This has a male screw outside at _b′_, upon -which there are two collars _dd′_ with capstan heads. These collars -hold the microscope upon the reading frame _b_ at any required distance -from the limb to secure proper focal adjustment. _g_ objective tube. -This screws into the body tube and permits adjustment of the objective -to the division of the limb and the micrometer index web by the milled -head _s_. This tube has a locking nut _i_ to secure it from after -movement when it is once properly adjusted. _h_ an achromatic object -glass of half an inch or over in focus. _e_ the casing that receives -the eye-piece which screws into the outer plate of the micrometer. -_f_ the eye-piece, generally made about one inch long. This slides by -friction in its cell to produce distinct vision of the spider lines in -the micrometer. - -339.--The micrometer frame, Fig. 137, _a_ has a fixed scale or _comb_, -with five or more points or teeth formed upon it, and a movable sliding -frame, upon which a spider web or webs are inserted and cemented in -finely engraved lines to form an index, brought as nearly as possible -to the mutual focal plane of the object-glass and the eye-piece. The -index web frame has a fine screw of about a hundred threads to the inch -tapped into it. The micrometer screw, divided drum, and milled head are -now generally constructed as shown in Fig. 137. Two springs press upon -the index frame and the outer frame, and thus keep the drum up to its -collar. The drum _r_ is divided upon its edge into sixty equal parts, -to read seconds of arc generally to a single line index. The screw is -moved by the milled head beyond the drum, so that the divided surface -of the drum need not be touched. - -340.--The portion of the arc measured being generally 5′, the distance -of it, as it appears at the magnified image of the arc at the position -of the index of the micrometer, is made to correspond with five turns -of the micrometer screw, the head of which divides each turn into 60. -By this means the 5′ is divided into 300, that is, to single seconds, -and by approximation of the interspaces on the micrometer head, as -far as the reading is concerned, to fractions of a second. The fixed -scale, or _comb_, as it is termed, is commonly placed in the focus of -the eye-piece with five webs upon it, fixed to agree with five turns -of the screw or a rack with points at the bottom. These webs or rack -divide the 5′ of arc in minutes, and indicate the number of revolutions -of the screw, as shown by the displacement of its index line. A pair of -lines or webs are commonly placed in modern instruments at 1′ part, to -ensure certainty of reading by the mean of two observations. - -341.--The magnitude of 5′ of arc depends necessarily upon the radius -of the divided circle; therefore the microscope of the micrometer has -to be made to suit the division it is required to subdivide--that -is, using the same micrometer, the smaller the circle the higher the -magnifying power is required to be to take register by the same screw. -Within a wide range the micrometer is perfectly adjustable, to ensure -exactness upon this point, by varying the distance of the object-glass -from the limb, for which purpose the microscope is made adjustable by -the pair of screws _dd′_ which clamp it to its standard as already -mentioned. The principle of this adjustment is easily seen, for if -we place the object lens at a distance equal to its solar focus from -the limb, the image will emerge in parallel lines; but as we cause -it to recede from the limb, the image may be brought to any position -within the tube greater than the solar focus of the objective of the -microscope. The image is therefore brought to a position where it may -be picked up conveniently by the eye-piece. In this manner we have only -to make the adjustment of the object-glass from the limb such as the -space of any pair of divisions of the limb may be magnified up equal to -the displacement of five turns of the screw for seconds measurement. - -342.--The two points where the divisions and their images are situated -are termed the _conjugate foci_ of the lens, and the magnifying power -is proportional to these distances; thus, if we call the distance -of the object, that is the limb, from the object lens _f_, and the -distance of the focal plane of its image within the tube _F_, the image -will exceed that of the object in the ratio of _Ff_, or _F_/_f_ will -represent the magnified image. By this method it will be seen that the -expression _F_/_f_ will have an increased value, if we either increase -_F_ or diminish _f_, which we have to consider in the construction of -the microscope to bring it to the conditions under which it will adjust -to bring the micrometer screw exactly to its required reading. - -[Illustration: Fig. 138.--_Grubb's plan of securing micrometer screw._] - -343.--It is very general in instruments at the present time to tap the -micrometer screw directly into the micrometer frame, and to make the -drum and milled head a part of the screw. In this case a very soft -motion may be given to the screw by dividing its nut longitudinally and -bringing the parts together with a certain amount of spring. Sir Howard -Grubb, of Dublin, has placed a spring ball fitting, as shown Fig. 138 -at _EE′_, over the screw upon his astronomical instruments, which gives -a very soft motion to the screw. These refinements are very important, -as it is not desirable that any undue pressure should be put upon a -delicate instrument which under all conditions must be made rigid -enough to resist it, and the greater the pressure required to bring the -instrument to bearing the stronger it must be made. - -[Illustration: Fig. 139.--_Stanley's micrometer slide._] - -344.--=Stanley's Micrometer.=--The author has made an arrangement in -which the screw has a long, double tubular sliding stem, Fig. 139. The -inner stem which carries the milled head has a groove cut down it, -into which a stud from the inside of its covering tube slides. This -arrangement permits the milled head to be pressed inwards or outwards -in turning it without any pressure coming upon the micrometer greater -than the friction upon the sliding tube, and that of a weak spring -which keeps the stem nearly extended in its tube. A simple Hook's joint -_H_ is formed at the head of the screw, so that no part of the weight -of the hand comes upon the screw. A tubular guard-piece _T_ prevents -the milled head hanging down too far when out of use. When the screw -is used it is lifted to about the centre of the guard tube. With -this arrangement, as no practical weight or pressure comes upon the -micrometer from handling it, the supporting frame-work may be made much -lighter than is necessary with any other form of micrometer. - -345.--The author prefers to form the micrometer scale and the index -of fine lines engraved upon parallel worked glass for surveying -instruments. This avoids the risk of breaking webs, and, what is much -more important, he finds that with engraved lines on glass he is able -to bring the scale and index exactly and permanently into the plane -of mutual foci of the object-glass and eye-piece by placing the lines -upon the same faces of glass, thus avoiding the great difficulty of -focussing to guess-work of an intermediate position between two sets of -webs at different distances. - -The strip of glass _A_ is fixed by a clamp and two screws to the side -of the micrometer box. The slip _B_ is ground and polished to fit _A_. -_B_ is carried by the micrometer frame _F_, which holds it in a clamp -by two screws. A spring, not shown, presses _B_ against _A_, so that -any displacement of the micrometer lines may be made by the milled -head. The lines upon _A_ are adjusted to the position of the circle -they are intended to read at exactly 5′ or other quantity. - -For the smaller instruments which will be much more frequently used by -the surveyor a simpler form of reading is used, and as the reviser is -convinced that in future this form of reading will gradually replace -the vernier for all high-class work, a full description of this very -simple reading is here given. The reviser is confident, after many -years of practice for the most accurate form of index, that a point -certainly stands first, a pair of webs or lines on glass, between which -the division is seen, second; and a single web or line on glass placed -over the division, third. The comb mentioned in art. 339 is done away -with, and one revolution of the micrometer screw made to carry the -index over one division of the limb. For clearness the engravings show -only a 10″ reading; for a 5″ reading the divisions on the limb are -to 5′ instead of 10′, and the micrometer head is divided and figured -accordingly. - -[Illustration: Fig. 140.--_Stanley's micrometer reading._] - -Fig. 140 shows at _C_ a portion of the theodolite circle as seen -through the micrometer microscope. _P_ is the movable pointer, _M_ the -micrometer head, and _I_ the index or reading line. - -To use the micrometer the first steps are to carefully focus the -pointer _P_ by means of the eye-piece until it appears clear and -perfectly sharp, and set the reflector at the bottom of the microscope -so that it reflects sufficient light to illuminate the divisions on -the circle. Then, by turning the micrometer head _M_, set the pointer -_P_ to the centre of its travel, so that it covers the _V_ cut in the -bottom of the slide, and leave the _0_ of the micrometer head exactly -opposite the index line _I_. Now proceed in the same manner with the -other microscope. After setting the microscopes as described above, -lightly clamp the lower clamp screw of the instrument and release -the upper one. Now revolve the upper part of the theodolite until 360 -degrees on the circle appears exactly under the pointer of one of the -microscopes. The other will then be pointing to 180 degrees, and the -instrument is set ready for measuring the first angle. - -[Illustration: Fig. 141.] - -We will presume now that a bearing has been taken by the telescope -and it is required to read the angle, and that on inspection of the -micrometer it is seen to be in the position illustrated at Fig. 141, -viz., between 227 and 228 degrees. Now as the degree is subdivided into -6 parts, each of these subdivisions must represent 10 minutes of arc, -therefore the pointer is situate between 227° 30′ and 227° 40′. It is -now necessary to measure exactly the distance of the pointer from the -division 227° 30′, which is done in the following manner, by means of -the micrometer head _M_. - -[Illustration: Fig. 142.] - -This micrometer head is so constructed that one complete revolution of -it causes the pointer to exactly travel over the space of one division -on the circle. - -The head itself is divided into 10 primary parts, which indicate single -minutes, and these are subdivided into 6 parts of 10 seconds each, -therefore in order to measure the exact position of the pointer in Fig. -141 it is only necessary to turn the head _M_ until the pointer is -exactly over the previous division of the circle (as shown in Fig. 142) -and read the distance on the micrometer head _M_. In this case the head -has been turned through six main divisions of 1 minute = 6 minutes and -two subdivisions of 10 seconds = 20 seconds, giving a total reading of -6′ 20″, this, added to the circle reading of 227° 30′, gives 227° 36′ -20″, which is the correct reading of the angle. - -It will be seen that this method is very much simpler and a great deal -more accurate than any form of vernier reading, and also that its -greater accuracy permits the use of smaller instruments. Thus a 5-inch -micrometer reading theodolite is more accurate than a 6-inch one with -verniers. - -Six-inch micrometer theodolites are usually divided to read to 5 -seconds of arc. The method of reading is the same as described above, -but in this case the circle is divided to spaces of 5 minutes each and -the micrometer head to 5 main divisions of 1 minute, each of these -having 12 subdivisions of 5 seconds, which it is possible to again -subdivide by estimation and so measure angles to 2½ seconds. - -Another feature in favour of micrometer reading instruments is the -ease with which they can be adjusted. With verniers, should they get -out of adjustment through damage, the instrument must be returned to -a maker; with micrometers, if through rough usage or accident, it is -found that after bringing the pointers to the centre of their _V_'s and -setting the micrometer heads to _0_ they are not exactly opposite one -another (180 degrees apart), then their setting has become disturbed -and must be readjusted in the following manner:--First bring the _V_ -of one micrometer to the 360° on the circle, then see if the _V_ of -the opposite micrometer is exactly at 180°, if not this can be easily -set to it by means of the small adjusting screw which will be found at -the left end of the micrometer box, that is, the opposite end to the -divided head. Having examined the _V_'s and adjusted them if necessary, -the next step is to set the pointers _P_ exactly to 360° and 180° -respectively, in which position the divided heads should both read -_0_; if they do not do so reset them as follows: Take a screw-driver -and slacken the small screw which is in the centre of the divided -head; this will free the divided rim so that it can be turned without -shifting the position of the pointer. Turn the divided rims until they -read exactly _0_ at the index line and retighten the screws. This -completes the adjustment. - -[Illustration: Fig. 143, 144.--_Sections of clamp and tangent in two -directions._] - -346.--=Clamp and Tangent Adjustment.=--The vernier reading to the -circle, when this was adjusted by the hand, was scarcely practicable -at nearly its full value until the discovery of the _clamp and tangent -screw motion_ was made. This useful invention is due to Helvetius, -the celebrated astronomer of Danzig (about 1650). By this mechanical -arrangement the circle or arc is left quite free to move about its axis -until the clamp is screwed down, which then fixes it firmly. The fixing -arrangement of the clamp is attached to a solid part of the instrument, -but is so constructed that when it is clamped it may yet be moved -without unclamping, in relation to the fixed part of the instrument, -by the tangent screw which, as its name indicates, is placed in a -direction tangential to the circle or arc. This arrangement may take -many forms in detail, two of which, the most general and especially -adapted to surveying instruments, will be described. - -[Illustration: Fig. 145.--_Elevation and part section of clamp and -tangent._] - -347.--The above illustrations, Figs. 143, 144, represent a clamp and -tangent motion in two sections at right angles to each other. This form -is common to vertical circles and arcs generally, of a theodolite, -arc of sextant, circles upon some mining-dials, protractors, and many -other instruments. Fig. 145 is partly a front elevation of the same, -but with part of the clamp screw _A_ cut off. The stem of the tangent -screw is shown in section at _E_. In all the figures _L_ is the limb -of the circle or arc. This has a groove at its under side at _G_, into -which a fillet of the clamping piece _C_ is inserted to make the clamp -slide freely about the periphery of the circle when the clamping screw -_A_ is loose. A spring is sometimes inserted to open the clamp between -the sliding piece _K_ and the clamp _C_. _FF_, Figs. 143, 144 is the -tangent nut to _E_. This nut is sawn down and has a cross screw to keep -sufficient tightness to prevent loss of time, and yet to allow the -tangent screw to work pleasantly at the same time that it holds the -circle and vernier quite dead to the position to which it is adjusted -by the screw. The tangent nut _F_ has to move to the direction -horizontal to the plane of the tangent screw; therefore it has an axis -vertical to the plane of the clamp. This is shown at _K_. The axis is -held down firmly by a nut and a washer fitted with a square hole, to -prevent the nut unscrewing. The tangent screw has a collar fitting or -shank at the tangent boss _B_, which is turned down from the full-sized -metal of the screw. The fellow collar on the outer side of the boss is -formed by the shank of the milled head of the tangent screw _D_. The -hole through the milled head is made square, so that it can be adjusted -up to the boss without risk of after unscrewing by friction by the -screw _E_. This is tightened up by means of a screw-driver applied at -_E_. The boss _B_ has a vertical axis _N_, similar to the tangent nut, -and is attached to a solid part of the instrument by the washer and nut -shown at _0_. - -348.--The above construction is solid and good, and will bear -considerable wear; but there is a little delicacy of touch required to -adjust the collars to the boss and to give pleasant tightness to the -screw; a better plan is to dispense with the split in the tangent nut -and the inner collar turned on the tangent screw, and place a spiral -spring over the tangent screw which follows the adjustment, or in -some cases a long bow spring may be conveniently used in place of the -spiral. These plans answer very well: one of them will be presently -described for axis clamping. In place of the groove at _G_ the clamp -is sometimes constructed to move on an arm direct from the axis of the -circle. This is on the average a pleasanter motion, but in complex -instruments it would often interfere with the motion of other necessary -parts. - -349.--=Axis Clamp and Tangent.=--This is generally used to bring the -horizontal axis of an instrument to bearing, and is made independent of -the circle and vernier. The ordinary form, which is very effective when -properly constructed, is shown Fig. 146. This form is used for clamping -the vertical axis of a theodolite, mining-dial, Y-level, and some -other instruments. The clamp _C_ surrounds the axis as a collar, from -which two _lugs_ in the same casting are projected at _a_. These are -brought tight upon the outer axis socket _B_ by means of the screw _W_, -which has a _wing-nut_ head to give good purchase. In the construction -of this form of clamp the collar should be fitted and ground to its -bearings with the lug in the solid, and the cut at _a_ be sawn through -afterwards. - -[Illustration: Fig. 146.--_Clamp and tangent to a vertical axis._] - -350.--The tangent screw adjustment is shown at _T_, moved by the milled -head _M_, the boss _E_ being fixed to the instrument. This part of the -arrangement is just the same as that described above for a vernier -tangent. Objection has sometimes been made to this form of clamp, that -it tends to become weak after a time from the constant clamping and -releasing, which causes loss of elasticity in the metal. When this -occurs it is no doubt due to the metal of the clamp not being good -gun-metal; or, if brass, not thoroughly pressed or hammered before the -piece is made up. A plan, in not uncommon use in Germany, of avoiding -this supposed source of weakness is to bring up a _tumbling piece_ -direct on the axis by a screw. This is shown in Fig 147, screw _W_; -tumbling piece _A_. This produces a direct clamp upon the axis socket -_B′_. The clamp ring _CC′_ is made loose on its socket. - -351.--In practice it is found impossible to clamp the axis of a -theodolite without disturbing the centre more or less. In some -experiments the author made he found the direct or tumbling piece clamp -Fig. 147, although it holds firmly, disturbs the centre much more than -the clasping clamp Fig. 146. Therefore when the former is used the -clamp should be upon a strong flange. This increases weight, and it can -scarcely be so well for a portable instrument. In all cases, in the -construction of the instrument, clamps should be fitted and screwed -down before the centre is ground and finished. This ensures the centre -being made correct in its clamped position, in which it will afterwards -be used. - -[Illustration: Fig. 147.--_Clamp and tangent to vertical axis, German -plan--Hunäus._] - -The arrangement Fig. 147 shows also a spring S falling upon a stud -at _E_, fixed upon a part of the instrument upon which it acts as a -fulcrum. The spring should be of hard rolled German silver. In this -case the tangent screw needs no split or other adjustment to make it -tight, as all loss of time is taken up by the spring.[14] The plan is -found practically to answer fairly; but unless this is very carefully -made there is a want of solidity in the movement which a well-fitted, -direct-acting tangent screw possesses. - -352.--The French generally in all their superior instruments clamp upon -a flange carried out from the lower rim of the socket, with the screw -placed longitudinally to the axis. When this plan is very carefully -carried out, so that the clamping has neither tendency to raise or -lower the socket-piece, it is no doubt very good. In large instruments, -where weight is no object and the flange may be made large, it is -certainly the best plan. In such cases the clamp may be released as -a free fitting to prevent the possibility of strain. Fig. 148 shows -the French plan attached to a tribrach: _S_ socket, _F_ flange, _C_ -clamping screw, _T_ tangent screw. The tangent in this arrangement acts -against a spiral spring contained in a tube _A_, which gives a very -steady motion to the instrument. - -[Illustration: Fig. 148.--_French axis clamp and tangent._] - -353.--Some particulars of the care required in the manufacture of the -tangent screw were given, art. 22. The test for the equality of this -screw, which is important when it moves a vernier, is to loosen its -clamp and to see whether it works equally, firmly, and smoothly at -all parts when it is turned down from end to end. The test for its -straightness is to screw down the clamp, then to notice any little -mark on the milled head of the tangent screw, or make a slight mark -upon it, and to place this mark uppermost, and then to take a reading -with the vernier, then to turn the milled head a quarter turn and take -another reading, and again another quarter, and so on consecutively. -By comparing the rates of reading of the vernier at the quarter turns, -if we find these equal the screw is straight. A little allowance is -necessary for imperfect work. If the work is very bad at some quarter -turns there will be an advance at the opposite quarter of nearly double -the proper mean quantity. - -354.--=For Testing and Adjusting the Fitting of the Tangent -Screw.=--The clamp should be tightened down and the ball _B_, Fig. 144, -held tightly between the thumb and forefinger; then, by using a gentle -reciprocating motion in the direction of the tangent just sufficient -to move the circle, if there is any looseness in the screw or the ball -fitting _B_ it will be felt as a jar, or technically, a slight _loss -of time_. If this be in the ball _B_ it can be taken up by the screw -_E_ at its end. If it be in the screw it can be taken up by the cross -clamp screw. If it be in neither of these, it may be in one or both -of the axes _N_ and _K_. In this last case it will need refitting. It -appears a somewhat simpler test with a theodolite to lightly press -the telescope on one side of the eye-piece and take a reading of the -vernier, and then to press the other side and again take a reading. -This, possibly, indicates loss of time in the clamp and tangent if -there is found any difference in these readings; but this would not -be with any certainty, as the fault might be in some other part of -the instrument. It, nevertheless, is a simple plan to test the whole -instrument, including the clamp and tangent, although this does not -localise any defect there may be in any special part of it. - -355.--=Use and Wear of the Clamp.=--The common fault of a novice when -he commences to use an instrument is that he applies too much violence -to all clamping parts. Thus we find the lower parallel plate of an -instrument soon becomes deeply indented, and the clamp of the tangent -screw often strained, or its screw worn loose by extreme clamping. -The best rule to avoid this with a clamp is to make a personal test -of how little force is required to produce sufficient hold for the -action of the tangent screw, and when this is found out to try to clamp -_only slightly in excess of this_. A novice scarcely recognises the -power of a screw. It is, perhaps, a fault of some makers of giving -much too large heads to clamp screws which to a certain extent permits -this overstraining from clamping. In discussing this matter with a -scientific civil engineer upon an instrument which had been very -much strained, to which small clamping screw heads were suggested, -this gentleman replied that he looked to the optician to "supply -instruments, not _brains_," and made the user responsible; but, really, -a young surveyor is generally so intent on the object of his work that -he cannot consider the mechanical details of his instrument, to which -his attention possibly has never been properly directed; so that there -is a policy in cutting off possibility of injury to the instrument -where this can be conveniently done. - -356.--_Use and Wear of the Tangent Screw._--Seeing that the axis of -an instrument is quite free to the extent of the loss of time on the -tangent screw which holds it, and that this freedom, by any slight -touch of the telescope, may cause a difference of reading--in some -cases of several minutes of arc--it becomes important to observe that -the tangent screw is in good order. This matter considered at its full -value, we may wonder, perhaps, what kind of work may have been done -with the tangent screw loose and worn down in its central part, as we -find it in many old instruments sent for repair. A great amount of the -common defects we find in worn tangent screws might have been prevented -by using certain precautions; and even the much-worn tangent screws -would sometimes go on fairly by a different method of use from that to -which they have evidently been submitted. The wear of a tangent screw -is due principally to the fact that this screw is necessarily oiled -to make it work freely, and that the oiled part being exposed to dust, -this dust attaches itself and works into the thread with the oil so as -to cut both the screw and the nut. Precaution is necessary that this -should be obviated as far as possible. One precaution may be taken, -that when the screw is oiled, say once in three months, the parts -outside the nut should be cleaned off quite dry with a few strands of -thread. The oil left in the nut, if the screw has been turned through -it, will be quite sufficient to lubricate the screw. Another better -precaution is to use only one part of the screw for a period, say one -month. The screw may be divided mentally into three parts--_near part, -middle part_, and _end part_. If one part only be used for a period, -and the vernier be set in using the instrument so that not more than -about 1° of motion is required of the screw, no grit can be carried far -into the centre of the nut; and if the precaution of cleaning the screw -with thread be taken every time the instrument is returned to its case -after a day's work, the screw being left at about the same place on the -screw and nut, it will keep true with little wear. When another part -of the screw is taken into use, this part should be first cleaned with -thread and then oiled with watch oil, after which the former position -of the nut should be cleaned quite dry with thread. Treated in this -manner a tangent screw will last, in constant wear, for ten years or -so, keeping in fairly good order. Where a spring is used to take up -loss of time there is less risk, and the only precaution necessary is -to be sure the spring continues to act properly. There is generally, -however, a little more wear with a spring than with a free thread. - -357.--If the instrument be not touched after the tangent is set, and -there is no wind to cause vibration, the instrument will read correctly -although the tangent may be out of order. But after the adjustment -by the tangent screw, which may cause a disturbance, it is always -necessary to set the microscope to the vernier. This is one important -reason why the microscope should move as softly as possible, and that -it is advisable to centre it upon the axis. Where any doubt of the -quality of the tangent exists, the telescope should be reobserved for -verification of its position after reading, which is also undoubtedly -the safest in all cases. - -358.--Some contrivances have been applied to tangent screws to prevent -wear from dust, and also to take up the nut after wear. A very good -plan, common in American instruments, is to insert the end part of -the screw beyond the nut in a closed tube. This entirely prevents -dust from resting on this part; and if the precaution be taken to -clean the exposed part of the screw after use it is very effective -for preservation. This plan the author has combined with a spring -arrangement, which appears to render it very safe from loss of time -and much wear. This arrangement is, however, a little expensive to -make, therefore can only be applied to high-class instruments. Fig. -149, _C_ nut, through which tangent screw passes; _B_ tangent boss, A -milled-head, _H_ covering tube to the point of the screw, _GG′_ _EE′_ -pair of telescopic tubes which cover the screw. A German silver or -platinum spring works inside these tubes, keeping a constant separating -pressure between _C_ and _B_ to take up any loss of time in the screw. - -[Illustration: Fig. 149.--_Protected tangent screw with helical -spring._] - -359--=Free Tangent Screw.=--There is always a risk of a tangent screw -of any fixed kind producing a certain amount of strain upon the -instrument, therefore, where practicable, it should be made free. The -illustration, Fig. 150, shows the form of free tangent the author now -applies to many instruments. The centre stud is clamped to the lower -part of the instrument by the screw shown in dotted lines. To the left -hand a piston containing a spiral spring carries a pressing-rod against -which the screw to the right hand works. - -[Illustration: Fig. 150.--_Free tangent adjustment._] - -360.--=Loss of Time by Wear= of the nut is variously taken up when no -spring is used. One plan was shown of splitting it up. A plan common in -Germany is to make the nut in two pieces, which are brought up by two -screws. This is a very effective plan. The author has found a tumbling -piece arrangement also effective. Fig. 151, _S_ section of tangent -screw, _T_ tumbling piece moved by the adjusting screw, shown above, -for wear of the tangent screw. This adjusting screw _A_ should be -tapped tight without oil, and put together dry to prevent its receding -by pressure. - -[Illustration: Fig. 151.--_Tumbling piece adjustment for wear of -tangent screw._] - -361.--=Hypotenuse and Base.=--Other trigonometrical values besides -the division of the circle into equal parts are occasionally placed -on instruments for special purposes. The most common of these is the -scale of difference of hypotenuse and base, which is generally placed -upon the back of the vertical arc of a theodolite and upon some dials -and clinometers. The division for this purpose is generally done by -hand. The scale gives a percentage difference for certain angles. Thus -when used with chain measurement, it gives the number of links of the -chain to be deducted per chain of 100 links for the inclination of land -that the theodolite or other instrument indicates in following the -surface contour. - -362.--=A Horizontal Scale of Tangents= was placed upon the surveying -theodolites by Ramsden. This was divided upon a scale carried by the -vernier plate, which read to the zero line (0°) of the limb. It is -found in practice more accurate to take the tangent to any curve from a -scale of tangents, as, for instance, that in Molesworth's pocket-book, -and set this off upon the limb by means of the vernier. - -363.--=Gradient Scale.=--Civil engineers engaged on railway work -occasionally have a scale of gradients upon the back of the vertical -arc 1 to 100, 150, 200, etc. These are better read from the circle with -vernier from a table of gradient arcs. - -FOOTNOTES: - -[14] The illustration is taken from _Die geometrischen Instrumente_, -Dr. G. Chr. K. Hunäus. Hanover, 1864. - - - - -CHAPTER VII. - - THEODOLITES--CONSTRUCTIVE DETAILS OF 5-INCH AND 6-INCH TRANSITS-- - SPECIAL ADDITIONAL PARTS--PLUMMETS WITH SCREW ADJUSTMENTS OF - IMPROVED FORM--STRIDING LEVEL--LAMP--ADJUSTMENT OF AXIS OVER A - POINT--SOLAR ATTACHMENT--PHOTOGRAPHIC ATTACHMENT. - - -364.--=The Theodolite= is the most perfect instrument for measuring -both horizontal and vertical angles by the aid of a telescope and -graduated circles. For the purpose of surveying, the theodolite is -mostly employed to take a system of triangles upon the horizontal plane -of the surface of the land, and of objects at any position in which -they may be placed. When altitude angles are taken separately these -are generally applied to give corrections to chain or other actual -measurements upon the surface by calculation of the difference of -hypotenuse and base. - -365.--The theodolite in all its essential features, as differentiated -from sighted compasses for taking angles, mentioned by Digges,[15] was -the invention of Jonathan Sisson, a celebrated mathematical instrument -maker of the beginning of the 18th century.[16] Great improvements -were afterwards made in this instrument by Ramsden, who brought it up -nearly to its modern efficiency by the introduction of the transit -principle.[17] Later improvements in portable instruments consist -in the application of the _transit_ principle to the telescope, -which was formerly applied to astronomical and the larger geodetic -instruments only. Other improvements have been made more recently in -constructive details. - -366.--Theodolites were commonly made of two distinct types, which -were originally distinguished as _plain_ theodolites and _transit_ -theodolites. In the plain theodolite the telescope moves through an -arc of about 45° upwards or downwards from the horizontal plane, but -very few of these are now made compared with the number of transit -theodolites in which the telescope may take a complete revolution upon -its horizontal axis, so that a back and fore sight may be taken by a -half revolution. This difference of construction entails a difference -in the manner of mounting the telescope to correct its adjustments. In -the transit the accuracy of centring and reading is easily discovered -by taking a back and fore sight at a distance as equivalent to an arc -of 180°, which may be read on any part of the limb by transitting the -telescope, wherein the correspondence of this arc to the reading of -the limb to right and left hands will detect error. With the plain -theodolite the equivalent method of examination is effected by placing -the telescope in Y's, as previously discussed for the Y-level, and -turning it end for end on its bearings, a process liable to disturb -the direction of the telescope unless special care be taken. In the -following description of the details of construction of a theodolite it -will be convenient to take the transit form of instrument, as this is -more comprehensive, the original pattern being selected, as this may -be constructed with the limited amount of tools generally found in a -surveying instrument workshop. - -[Illustration: Fig. 152.--_5-inch transit theodolite (old form)._] - -367.--The size of a theodolite is fixed technically by the diameter of -the line of division upon the horizontal circle. A 5-inch or 6-inch -theodolite is the largest size that may be carried comfortably in a -single case; and no great advantage is gained by having an instrument -beyond this size if the work is that of the ordinary surveyor on town -and county surveys. The verniers of 4- and 5-inch instruments read -sharply to single minutes of arc, which is as nearly as can be plotted -with any degree of certainty with an ordinary protractor reading -by vernier also to minutes only; 6-inch instruments read to 30 but -generally to 20 seconds. Occasionally 4-inch theodolites are selected -for lightness at a sacrifice of capability and of distinct and exact -reading. The following table gives the average weight of the transit -theodolite illustrated on the last page:-- - - Instrument. Case. Overcase. Tripod. - - 4-inch Transit. 11 lbs. 8 lbs. 4 lbs. 8 lbs. - 5-inch " 13½ " 9 " 5 " 9 " - 6-inch " 19 " 10 " 6 " 11 " - 8-inch " 36 " 20 " 10 " 18 " - - If with lamp extra about ¾ lb. If with striding level extra - about ¾ lb. - -It will be seen that the 5-inch instrument of this class with cases -and tripod, say altogether 36 lbs., is really of quite as much weight -as a fairly strong man can carry through a hard day's work. The 5-inch -instrument is therefore becoming more and more popular with practical -civil engineers, and its performance, if of good modern work, is quite -equal to the 6-inch of less than half a century ago. - -368.--By giving a description in detail of a transit theodolite, the -general principles of a great number of other instruments, particularly -those of larger dimensions, will be included, except for certain -details that the specialities of the particular instruments demand. -The most convenient plan to follow in this description will be to take -the structure of a 6-inch transit theodolite of common construction, -as it is built up from its base, piece by piece, according to the rule -of ordinary structure; where more modern theodolites vary mostly from -this is in having many parts shaped out of the solid, which are screwed -together in the form illustrated. - -369.--_The Tripod Stand_ of a theodolite of 6 inches and under is -generally made identical with that of a level, a common form being that -described for a dumpy, art. 216. The arrangement of one turn-up leg, -as shown Fig. 63, is very advantageous for the theodolite if it is to -be used on mountainous or even very hilly ground. For instruments -exceeding 6 inches a framed stand, which will be described further on, -is better. Some makers use a framed stand for a 6-inch instrument. The -rigidity of the stand ought to be quite equal to that of the work in -the theodolite, or a little in excess, and when this is attained it is -sufficient. Where the stands of theodolites so often fail is from the -defective construction of the tripod head, not at all from deficiency -of timber in the tripod itself; and overloading this, in adding weight -without attention to scientific construction, is worse than useless. - -370.--In the following description of the transit theodolite the -parallel plate setting-up arrangement is taken, as this is at the -present time (1914) still in use in this country and in America. There -is nevertheless great probability that it will not long continue -to be so, as year by year the tribrach system, described art. 233, -for levels is coming more forward, both for levels and theodolites. -This tribrach system the author holds to be much more scientific, -and when thoroughly understood, more simple and expeditious to work -with. It is also to be recommended, as there is no possible risk of -strain upon the general work of the instrument, nor risk of error -from distortion of the vertical axis from strain in setting it up to -adjustment. A constructive drawing of a common transit theodolite with -parallel plates is shown Fig. 153, of which the following is a detailed -description. - -[Illustration: Fig. 153.--_6-inch transit theodolite--back view, with -sections._] - -371.--_The Lower Parallel Plate N._--This has a large boss-piece taken -up from its central part, which forms a dome of a hollow globular -section, technically termed the _socket_, shown at _X_. In the interior -of the lower part _N_ a coarse female screw is cut, of about fourteen -threads to the inch, which is used to attach the instrument to its -tripod. - -372.--_The Upper Parallel Plate_ is constructed as a flange from a -solid _boss L_. This piece is generally made in gun-metal of a form -as solid as possible, to resist the straining action of the parallel -plate screws. The boss is prolonged downwards by a _stem-piece_, upon -the lowest part of which a _ball collar_ of globular section is firmly -screwed. The screw is turned by means of two opposite holes, into which -a powerful forked screw-driver is inserted, until it is jambed up too -tightly against its shoulder to ever become loose by the ordinary use -of the instrument. The ball collar fits into the socket carried up -from the lower parallel plate. The whole of this globular arrangement -is termed the _ball and socket_. The boss _L_ of the upper parallel -plate, with its stem, has a hollow conical hole through its axis, into -which the _body-piece_, to be described, fits accurately. Upon its -outer upper part an inset collar is formed which acts as a guide to the -clamp _K_. At the outer edge of the parallel plate _M′_ four vertical, -conical holes are made, which take _socket-pieces_, which are tapped as -_nuts_ to the parallel plate screws _M_. These socket-pieces are jambed -into their holes tight home to their shoulders. The socket-pieces are -made separate, both to give a greater length of female screws than the -thickness of the plates, and that they may be easily restored at any -time if worn loose in the threads by the action of the plate screws. - -373.--_The Parallel Plate Screws._--One in elevation is shown at _M_, -with its point dotted, and one in section at _M′_. The four parallel -plate screws are in opposite pairs, placed exactly at right angles -to each other in a line passing through the vertical axis of the -instrument. These are made of gun-metal about 3/8 inch in diameter, -with a deep thread of about thirty-two to the inch. They require -cutting on a nice steady screw-cutting lathe. The lower points of the -screws are slightly domed, sufficiently only for the amount of rocking -they have to take, so as to impress the lower parallel plate as little -as possible. The milled heads _M_ are placed between the parallel -plates, not above, as previously described for levels. There being -a constant strain upon these screws in use and by intrusion of grit -from flying dust they soon become worn. After wear the threads may -be recut deeper, and new socket-pieces fitted to the upper parallel -plate. To prevent wear the upper parts of these screws are sometimes -encased in tubes--a plan very generally adopted in America. At the -foot of one of the parallel plate screws a _stay-piece_ is fixed to -the lower parallel plate, which forms a kind of ring round the screw. -This prevents the parallel plates from shifting upon the axis at the -ball and socket. The parallel plate screws should be without any shake -or what is technically termed _loss of time_. They should move firmly -but softly. They should _support_ the instrument against the ball and -socket upon which the whole rocks to position by their aid, but not be -screwed down too tightly, as this has a tendency to disturb the axis -of the instrument however solidly it may be made. Makers often have -instruments in their hands for repairs in which the parallel plate -screws have been deeply indented into the lower parallel plate, with -the centre of the instrument permanently strained more or less. - -374.--_The Body-piece._--The only outward part seen in elevation of -this is shown at _T_: it is shown in section _T′_. This piece carries -the _limb_ of the instrument _SS′_ by a centred collar to which it is -attached by screws. About the centre of the body-piece an inset collar -is formed to take the clamp _KK_ which bites upon it. The lower outer -part of the body-piece forms a conical fitting in the boss of the -upper parallel plate _L_. The interior is a hollow conical axis. The -body-piece is generally made of hard gun-metal. The greatest possible -care is required in its manufacture, art. 21. The interior and exterior -should be perfectly concentric at every part. Much of the value of the -instrument depends upon the perfection of the work in this piece. - -375.--_Axis Collar Clamp K_ has been already described, art. 349, and -is illustrated in Fig. 146, which is taken from a theodolite, so that -only specialities in relation to the instrument Fig. 153 need be noted. -This clamp surrounds the body-piece and clamps it by means of the screw -_K_ shown on the left hand. The clamp is connected with the upper -parallel plate through the _tangent screw_, the head of which is shown -at _P_, so that when the screw _K_ is tightened the parts _L_ and _T_ -are fixed together, except that a slow motion can be given to these -parts by the tangent screw _P_. By this clamp and tangent arrangement -the whole of the upper part of the instrument is rendered free to -revolve, to bring the instrument to bearing when the clamp is loosened, -the final adjustment being secured after clamping by the tangent screw. -It is this part of the instrument which is used after setting it up -to bring the magnetic needle true to magnetic north, or otherwise to -direct the telescope to any established distant mark, object, or star -that may be fixed for the zero or other index point of the horizontal -circle, to which all readings from its position are referred. - -376.--_The Central Vertical Axis_ is shown only in half section at -_Z_. This is made uniformly of bell-metal, in the form of a truncated -cone, extending from the horizontal circle plate S to the interior -of the socket _N_. Its fitting surfaces are at the two ends of the -cone, extending about half an inch, the central part being chambered -back. At the upper part a _pin-piece_ centres the _vernier plate_, to -which it is attached by a wide collar with three or four screws. A -square shoulder rests with weight only just sufficient to support the -instrument upon the body-piece. This part has to be so adjusted that -the axis perfectly fits and yet moves freely. A square-hole collar -and screw are fixed on the lower end of the axis, just to touch the -socket of the body-piece, so as to secure the axis in its position when -the instrument is lifted. An eye or a hook is fixed into the screw -at the lower end to take the cord of the plummet used for fixing the -instrument over a definite point on the ground. This is not shown in -the engraving. - -377.--The axis of an ordinary theodolite is made the weakest part. It -is generally considered in the trade right for it to be so, as in case -of accident no other part of the vertical axis system is likely to be -deranged; and this is the easiest part to replace, being, as it were, -independent of other fittings. Whether this should be taken _cum grano -salis_ is a question; at any rate with the axis weak it is not policy -to load the upper part of the instrument with metal--which in places -at least, is generally made ten times as strong as the axis--when the -instrument has to be carried about by a person over his shoulder. Some -suggestions will be made on this point hereafter. - -378.--_The Horizontal or Lower Plate or Limb._--Sometimes the whole -of the piece _SS′_ is termed the _limb_, but more generally this word -is applied to the divided part only. This plate is of brass, and is -attached to the body-piece by screws. The outer rim, which is somewhat -triangular section, is undercut upon the inner side of its lower -surface to support the _clamp-piece_, the outer edge being turned to a -fillet to take the clamp which is rebated to fit it. The upper surface -of the rim, or the limb proper, is turned to the frustum of a cone of -about 45°. This part is covered with silver, which is beaten out to the -conical form and soldered down upon it, and afterwards turned to true -form. The dividing has been discussed in the last chapter. - -The 6-inch instrument is generally divided to 20′, but sometimes to -30′, and the vernier reads to 20″ or 30″. The figuring is from 0 to -360, right to left, taken facing the instrument. - -379.--_The Vernier Plate_ is shown in section under _P′_. The vernier -from which it is named is shown at _VV′_, Fig. 155. The vernier plate -is carried from the central axis and forms the foundation for all the -superstructure. The upper and lower plates are left very free where -they are brought together, the verniers being generally sprung down -just to gently touch the limb. The vernier surface is let down some -distance into its plate for protection. The reading of the vernier has -been discussed in the last chapter. - -380.--It may be particularly noted, as already stated, that the -central axis and the body-piece are attached to the vernier and -horizontal plates by _screws_. This plan might strike one as being -unsound: it is not really so, the reason for this construction being -that these axes are, or should be, of bell-metal, and that this metal -being very hard and brittle it would not be so easily worked, or so -serviceable as brass for the limb and vernier plate, neither would -there be means of correcting errors which generally occur both in the -workmanship and in the dividing of this delicate part. The adjustment -for fixing the limb and vernier plate, technically called _centring_, -in particular requires considerable technical skill. It is generally -performed by the divider, who is a specially intelligent artisan. In -the author's improved theodolite, to be described further on, the axis -is in one casting with the standard; but in this case the construction -is different, the axis being made larger and the whole body being in a -special gun-metal which approaches bell-metal in hardness. - -381.--The vernier plate carries the ball nut of the tangent screw, -shown at Fig. 153_J_. The general arrangement may be seen by the -section, but is more fully described art. 347. One thing is important -in this screw, viz., that it should range without strain quite parallel -with the plates, so as not to give the slightest tendency to elevate or -depress the edge upon which it is placed during motion in any part of -its thread. The clamp is sometimes placed between the plates. - -382.--_The Compass-box._--The general construction of this is shown, -Fig. 155, W. In the transit theodolite it is fixed firmly by screws -to the vernier plate and is made to form a steadying piece to the -_A-frames C′ C″_ which support the upper part of the instrument. For -this purpose the compass-box is made as a solid casting in brass, -which is much stiffened by the raised step which forms the divided -circle. Four solid lugs in the same casting project from the rim of -the compass, and form stiffening pieces between the lower parts -of the A-frames; these are secured to the lugs by four screws, one -of which is shown, Fig. 153, at _a_. The lug screws hold the whole -superstructure together quite independently of the vernier plate, to -which it is afterwards firmly fixed. The compass needle is lifted by -means of a milled head, just inside one of the standards, _not shown_. -For a general description of the compass-box see art. 138. The vernier -plate carries two or more verniers. The verniers are read by a pair of -microscopes, Fig. 155 _MM′_ placed one on each end of a radial arm _N_ -having its axis of motion upon a large collar of the vertical axis. By -this plan, when one microscope is set to read by the coincidence of -lines upon one of the verniers, the other microscope on the other arm -or arms will be set also in like position over the other vernier or -verniers. - -[Illustration: Fig. 154.--_Vertical circle with clipping arm of transit -theodolite._] - -The verniers are adjusted ready for reading when the telescope is -accurately directed upon any object of which it is desired to ascertain -the angular position in relation to magnetic north, or a definite -object. The vernier plate also carries a spirit level at _O_, Fig. 153, -which is adjustable by a pair of capstan-headed screws. - -[Illustration: Fig. 155.--_Cross section of the upper part of a transit -theodolite._] - -383.--_The Standards or A-Frames_, shown _C′ C″_ Fig. 155, are solid -castings in brass of about 7 inches in height. They are set up upon -the vernier plate, to which they are attached by four stout screws, -as also by cross screws to the compass as stated. This renders -the superstructure of the transit as firm as may be in a built-up -construction. Upon the front of one of the standards a spirit level, -Figs. 153, 155, _I_, is placed adjustable by two capstan screws. This -level, and one shown Fig. 153 at _0_ on the vernier plate are used -entirely in setting up the instrument; and being placed at right angles -to each other, are a means of making the vernier plate quite level. -Upon the inside of each of the standards, at about 2 inches from the -vernier plate, a _clip-piece_, Figs. 154, 155, _P_ is secured by two -screws. This takes the clipping screws, Fig. 154 _HH′_ to be described. -At the top of the standards two V's are formed, upon which the transit -axis rests. One of these is cut out of the solid casting. The other -as shown in half section Fig. 155 _c_ is formed as a parallel sliding -piece with the V at the top placed in a vertical slot formed in the -standard. This sliding piece has a screwed stem continued from its -lower surface that passes through a vertical hole at the top of the -A-frame, which is formed here as a cross-piece. Upon the screw two -capstan nuts are placed, one on each side of the cross-piece, Fig. 155 -_xx′_; these permit the adjustment of this in height so as to get the -transit axis _perfectly horizontal_ when the vertical axis is perfectly -perpendicular to the horizon. The sliding piece is covered by plates -back and front to render it firm in its position. The transit axis in -practice is adjusted with a striding level which will be described -presently. - -With the author's theodolites from 6 inches downwards the old-fashioned -adjustment to one upright for levelling the horizontal axis has been -dispensed with for many years, and is only fitted if specially ordered, -as it has been found to be a frequent source of error. Long experience -has proved beyond doubt that the fewer adjustments there are, and the -more parts that can be fashioned from the solid metal correctly, the -longer will the instrument keep in adjustment. Should there ever be any -wear on either of the V's a few strokes with a piece of very fine emery -paper upon the opposite one will put it right in half the time that it -could be corrected with the old-fashioned adjustable V, and no amount -of vibration can alter it as with the adjusting screws. - -An axis _cover cap bb′_ is placed on the top of each standard. The cap -is screwed down at one end with a cut screw and collar. The screw is -used for adjustment to gentle pressure on the axis. The second screw -is a milled head _EE′_. Under this screw the cap is slotted out to one -side, and turns on the cut screw as an axis to open the cap without -removing its milled-head screw, so that the telescope can be lifted out -to turn its face to the opposite side of the instrument. In the under -side of the centre of the cap a cell is bored out, into which a small -cork is fitted, which produces, when the cap is clamped down, a soft -elastic pressure on the axis. - -384.--_The Transit Axis_ which supports the telescope rests at its ends -upon two trunnions, Figs. 154, 155 _AA′_, technically called _pivots_, -in the V's of the standards already described. The pivots are turned -as true as possible, and afterwards ground to exactly equal size in -a collar, so that they may be reversed end for end in their bearings -without changing the linear direction of the transit axis, except by -the little difference of pressure that one end of the axis imposes by -the weight of the vertical circle and its attachments being eccentric. -In larger instruments this difference of weight is counterbalanced, -as shown in dotted lines at _p_, Fig. 155. The centre of the transit -axis is formed into a _collar e_ of about 1¼ inches in width, which -exactly fits the outer tube of the telescope, and to which it is fixed -with soft solder. The collar is directly connected with and supports a -_flange f_. Upon this flange the vertical circle _FF_ is fixed by three -or four screws. - -385.--In front of the vertical circle a flanged collar-piece carries -the _vertical vernier frame VV′_, Fig. 154, centred upon it. The -vernier frame is attached by three screws to the _clipping arm_ to -be described, and in front of this the vertical microscope arms are -centred. These carry two readers _U_, Fig. 155, exactly similar to -those which read upon the horizontal circle, and they are similarly -centred, so that by setting one, the other is set at exactly 180° from -it. In front of the centre of the microscope arms on the transit axis, -an _axis collar-piece j_ is attached by three screws cut directly -into the axis. This collar and one at the other end of the axis _A′_, -turned out of the solid, are nicely fitted to the opening between the -standards to prevent lateral displacement of the axis. - -386.--_The Clips._--The clipping arm, which is centred on the transit -axis and attached to the verniers, is shown Fig. 154 _BB′B′_. It is -fitted to move freely on its axis at _A_, so as to permit unrestrained -motion of the telescope. A milled-head clamping screw with clamp, -Fig. 155, _K_, and the same partly cut away to show the slot in which -it works, are shown at K′ Fig. 154. This is used to fix the verniers -stationary on the circle, except for the adjustment by the tangent -screw _G′_, which has its collar attached to the clipping arm, and -its ball nut attached to the clamp at _D_ when using the telescope -for levelling. This clamp and tangent sets the vernier to zero on the -circle. It is also used in setting the telescope before angles of -altitude or depression can be measured. The clipping screws _HH′_ are -used to bring the principal bubble _B_, Fig. 153, on the top of the -telescope to the centre of its run after the verniers have been brought -to zero by means of the clamp and tangent screws. The clipping screws -hold the clips, Fig. 155, _P_ or _P′_ to the one standard or the other. -The whole of the vertical adjustment is exactly equivalent to that -already described for the horizontal motion, except that it is placed -in the vertical plane. - -387.--_The Vertical Circle_, Figs. 154, 155, _F_ is carried by four -arms from a central boss attached firmly by screws to the transit -axis. It is grooved at the edge to take the _clamp-piece_. The silver -is inlaid in this circle in the manner shown Fig. 117. The vernier is -read upon the circle on the plan shown Fig. 127. The circle is divided -generally to half degrees or 20′, and is figured 0 to the horizontal -with 90° upwards and downwards. The zero lines are made directly -coincident with the optical axis of the telescope when it is level. The -vernier reads to half minutes or 20″, in either direction, the rising -arc above the level datum being considered as plus, the falling arc as -minus. - -388.--On the outer edge of the circle or at the back a scale of -difference of hypotenuse and base reads to a line on a fiducial -edge upon a part of the clip _BB′_, Fig. 154, at _N_. This scale is -calculated for decimal quantities, and gives the percentage number of -links, feet, or metres to be deducted from the chain measurements upon -the ground line to give the horizontal distance corresponding to the -angle of inclination at which the telescope is set for observation. - -389.--_The Telescope_, Fig. 153, _DD′_ has been described art. 94. Its -general construction is also shown in partial sections in the figure. -Its body tube passes through the transit axis in which it is soldered. - -390.--_The Principal Level Tube_ is generally mounted on the telescope -upon two stiff screws which rise from plates attached to the telescope -body by pairs of screws. Each level screw has a pair of capstan nuts. -The level is mounted in a brass tube with stop-pieces at the ends, each -of which carries a _tenon_ with a hole in its centre through which the -level screw passes to be clamped top and bottom by the capstan nuts. -These nuts give adjustment to the level, so that the centre of its -inner upper surface may be placed parallel with the optical axis of the -telescope. - -[Illustration: Fig. 156.--_Stanley's new model of 4-screw transit -theodolite._] - -391.--Until 1898 the author was unwilling to attempt to remodel the -old form of transit theodolite, believing the 4-screw adjustment would -soon become a method of the past, but as a small demand continued -from the Colonies and United States for this form of instrument he -felt bound to make it of more solid construction to bring it somewhat -up to date. The illustration shown, Fig. 156, is of an instrument, -following in construction the transit theodolite already described in -many details, the marked exception being that the standards are in one -casting with the compass-box and axis, these being entirely shaped out -in the solid metal. The upper parallel plate is of special design, -being far stronger, yet lighter, and gives a much longer bearing to -the levelling screws. The lower parallel plate is also shaped with -three feet so that the instrument may be set up without its stand when -required. It has also modern spring tangent adjustments with covered -screws. The limb is covered, and the readers are jointed across the -axis to turn up without separation. It has a floating aluminium compass -read by a microscope, so that the instrument, except in the four-screw -arrangement for setting up, embraces many modern improvements -formerly applied only to special high-class theodolites. The improved -construction permits greater rigidity with fifteen per cent. less -weight. - -[Illustration: Fig. 157.--_The plummet._] - -[Illustration: Fig. 158.--_Gurley's plummet._] - -[Illustration: Fig. 159.--_Loop._] - -[Illustration: Fig. 160.--_Ring plummet, Shortt's Patent._] - -Of later years, however, the demand for four-screw levelling -instruments has been maintained, especially from Canada, owing to -the influence of the American school of teaching, and in consequence -all the author's improved theodolites are fitted with either three- -or four-screw levelling, whichever is desired. It is a strange fact, -however, that with all the American makers, although they list all -their ordinary instruments with four-screw levelling, their refined -ones, which they term "precision" instruments, will be found with -three-screw levelling. - -392.--=Detached parts of a Theodolite.=--_The Plummet_ supplied with -the theodolite is made to hang from a hook under the centre of the -axis of the instrument, the cord, which is of soft silk, being looped -or knotted to hold in the hook. The lower end of the plummet is brought -to a point which, when in use, falls directly under the vertical centre -of the instrument upon the surface of the ground. In Fig. 157 the screw -and plummet are shown detached. The cord _C_ is attached to the plummet -by passing it through a hole in the milled-head screw _S_ at the top -of the plummet, and by making a knot _K_ in the cord. Fig. 160 shows -an ingenious ring plummet recently invented and patented by Mr. W. H. -Shortt, A.M. I.C.E. The chief object was the production of a plumb -bob whose plumbing point should be situated at, or very close to, the -centre of oscillation in order that the position of the point might be -unaffected by oscillation of the bob itself, apart from any swing which -it might have about the point of suspension of the string. A further -object was to shape the bob so that a person holding the string, or -standing close to it when attached to an instrument and looking down -at the bob, should be able to see readily the exact position of the -plumbing point. - -These objects have been attained by making the bob in the form of a -ring, so that the centre of oscillation which lies in the centre of the -ring can itself be used as the plumbing point, since it can be readily -seen and indicated by the extremities of pointers projecting towards -the centre from the inside of the ring. - -A great advantage of this bob is that when plumbing on to a flat -surface it does not fall over when lowered, but may be allowed to -actually lie on the surface while the position of the point is being -marked. Also it can best be steadied by lowering into contact with the -ground and raising again. - -The plumbing pointers are largely protected from injury when the bob -is in use, and when not in use the suspension string can be wound -diametrically across the bob, in recesses provided for the purpose, -thus completely protecting the points. - -393.--_The Loop._--It is somewhat difficult in the ordinary way to -adjust the plummet to the station mark on the ground or on a peg. The -cord is sometimes placed in an ivory runner fixed to the top of the -cord, Fig. 159. This gives friction on the cord and permits extension -and contraction of the loop for adjustment. Where the plummet has to be -suspended from the instrument as well as from a hook inside the stand, -which is sometimes convenient, it is better to have the runner cut out -on one side. This permits easy change and it is just as firm. - -394.--Messrs. Gurley Bros. of Troy, N.Y., have a good plan for -shortening the plummet line. This is effected by making a reel in the -plummet, which is wound by a milled head at the top of it, Fig. 158. - -395.--_Screw-drivers, Tommy Pins, etc._--A screw-driver and a tommy -pin, the last to turn the capstan heads, are placed in the case with -the theodolite. Two screw-drivers with proper handles are better, -as there are small and large screws. A camel-hair brush to dust the -instrument, a piece of wash-leather, a little vaseline, and a small -bottle of good watch oil are also very useful. These little refinements -are generally kept out to keep down the price of the instrument. - -396.--=Additional Parts, and Variations in Theodolites.=--_Illuminated -Axis._--4, 5 and 6-inch transits sometimes, and larger instruments -always, have the transit axis bored on one side through to the interior -of the telescope, as shown on Fig. 155. Through the hole a small pencil -of light is sent by a lamp _l_ with a plano-convex lens front, to a -lens placed in the end of the axis. This, by a slight adjustment of -the lamp on its stand, focusses the light upon a small mirror placed -within the telescope, which reflects its rays to the diaphragm. The -lamp gives a faint light only sufficient to distinguish the webs for -night and underground observations. The mirror is about 1/10 inch in -diameter, and is generally mounted upon a milled head screw tapped -into the trunnion band of the telescope _m_. The point of the screw -is extended as a thin stem into the axis of the telescope, where the -mirror is held by it. This arrangement permits the mirror, which is -generally made of silver, but is much better of platino-iridium, to -be removed for cleaning. The lamp is mounted upon a wooden stand _w_ -carried upon a slide _n_ or upon two brass pins direct to the A-frame. -The wood is employed in this case to cut off conduction of heat to the -near standard from the lamp as much as possible to prevent disturbance -of the axis from expansion by heating. The stand may be removed when -the lamp is not required and placed in the case. In large theodolites a -pair of lamps are used, that the transverse axis may not be heated more -on one side than on the other. - -397.--_The Lamp_, which is found so convenient for bringing a star or -distant light to read with the webs, becomes difficult to use when -the object is very faint, as the light thrown into the telescope by -the lamp takes off the effect of blackness of the night sky or that -of total darkness. This becomes important in taking observations of -small stars, as for instance, the circumpolar stars of the southern -hemisphere. In some theodolites, made first for the Sydney Government, -the author placed a very small lamp to throw light upon the face of the -webs only, making these appear as light lines on a black ground. The -reflecting eye-piece, Fig. 20, will be found to answer very well, and -this is a simple, inexpensive contrivance. Any amount of illumination -desired may be thrown on the front of the diaphragm, according to the -distance at which the light is held from the eye-piece: generally a -very faint light only is required. - -398.--The author has illuminated the webs front and back by means of -a very small (one-quarter candle power) incandescent lamp, which is -charged by a portable battery, or a secondary battery where a dynamo -is at hand for charging it, and for countries where these cannot be -renewed or where the extremes of temperature are too great for their -use, he has devised a small hand dynamo for generating the current and -a rheostat for controlling the power of the lamp, so that resistance -may be employed to reduce the light to the faintest possible glimmer. - -The electric lamp is far superior to the old oil lamp and safe to -use in gaseous mines; it is far cleaner, does not give out a tithe -of the heat, and may be removed from its socket and used in the hand -for reading the verniers in a bad light. All the author's modern -instruments that are required with illuminated axis are now fitted with -electric lamps. - -[Illustration: Fig. 161.--_Trough needle for transit theodolite._] - -399.--_A Trough or Long Compass, used in place of Circular Compass._--A -long compass, Fig. 32, p. 74, is often applied to a theodolite, either -upon the top of the telescope, or more generally and conveniently -for reading under the limb. In this last case the trough needle is a -separate piece, which is only attached to the limb of the theodolite -by means of _loop slides_ or _bayonet fittings_ under the limb, when -required to take a bearing. The engraving Fig. 161 shows the long -compass with bayonet fittings. There are four slots, two of which are -shown _SS′_, which fit in under the heads of round-headed, shouldered -screws. The author has somewhat modified this pattern recently by -making it slide into grooves. - -The trough needle is generally made 5 or 6 inches long, and reads into -a short scale of about 10° at each end. The divisions are best placed -upon sliding fittings, so that they may be adjusted by four screws from -the outside of the box--screws shown _AA′_. This enables the needle -to be adjusted to its own axis, and also to the 0° reading of the -horizontal limb of the theodolite. A slide lift to the needle is shown -at _L_. When the same form of compass is used upon large instruments a -reader is placed at each end of the needle. - -[Illustration: Figs. 162, 163, 164.--_Striding level._] - -400.--_Striding Level._--For the adjustment of the transverse axis of -a theodolite a very sensitive spirit level is used. This is mounted -upon a _bed_, which may be formed of brass tubing, from the two ends -of which adjustable legs descend, the ends of which are _forked_, the -hollows of the forks forming V bearing surfaces. The V's rest upon -the pivot of the axis. By reversing the striding level on the pivots -the transverse axis of the telescope, or transit axis, can be readily -adjusted truly perpendicular to the vertical axis. In the construction -of the striding level, shown in detail in Fig. 162, the two striding -standards _SS_ are carried down from the ends of the casing tube B of -the spirit level. These are adjustable: one, Fig. 164, by raising or -lowering the end of the level tube by the capstan screws _CC′_, and the -other, Fig. 163, by a lateral adjustment of the capstan screws _PP′_ -that act upon the stud _S_, which is fixed upon an arm centred upon the -axis of the tube. This connection is shown by dotted lines. By these -two motions the standards are brought to perfect parallelism with each -other for their bearing surfaces and adjustment of the crown of the -bubble tube. - -[Illustration: Fig. 165.--_Wallis' shifting centre for theodolites._] - -401.--_Adjustment of the Axis for Setting it up over_ _a -Point._--Every surveyor experiences an amount of difficulty in getting -the plummet to fall from the axis of the instrument exactly over a -point upon the ground, or a mark upon a rock, or still more so upon a -point in street paving in a town, which is necessary for exact work. -It is easily set near the point, that is, within half an inch or so, -by pressing or shifting the legs; but the difficulty increases as the -exact point is approached, so that the setting has generally to be -left at a certain state of approximation. There are a great number of -schemes in use for moving the axis by adjustment of the instrument the -small quantity required, without disturbing the legs of the tripod -when they are firmly set down nearly correct to position. One of these -would no doubt be generally applied to the theodolite, except for -the reason that every means yet devised adds to its weight, and also -to the expense of the instrument. A moderately simple plan, which is -especially adapted to the parallel plate adjustment, is to make the -lower flange of the theodolite, upon which it stands when set down -off its tripod, somewhat larger and thinner. This flange, instead of -being screwed directly down upon the tripod head, is placed between -two ring plates, which are clamped together when the theodolite is set -in position. The large hole in the centre of the ring permits movement -of the lower plate of about 1 inch. Fig. 165 is an arrangement of -this kind by Mr. J. Wallis. This is made entirely independent of the -theodolite, and may be used or not as required. _I_ is a screw that -corresponds with the head of the tripod which takes the theodolite; -_T_ similar female screw to take the tripod head when the shifting -centre is used; _CC′_ a box formed by screwing two tray-pieces firmly -together; _S_ clamping flange; _HH′_ clamp screwed into the top of box -_C_. This has two handles by which the screw is moved to clamp when -the instrument is in position. The weight of this additional part is -about 3 lbs. The arrangement is particularly adapted to parallel plate -adjustments. - -402.--In an American plan of a transit by Messrs. Heller & Brightly, -the flange is lifted by the parallel plate screws, which tighten it at -the same time.[18] Messrs. Troughton & Simms have a plan of shifting -the axis by means of a pair of eccentric plates, which carry the -instrument in two directions nearly at right angles to each other. By -this arrangement an amount of leverage is secured which produces an -easier motion than that of shifting the weight of the instrument on the -plans mentioned above. The author's schemes will be described as a part -of his new theodolites a few pages on. - -403.--_Stadia Webs or Lines_ used for taking subtense angles by the -telescope for measuring distances, which are frequently applied to -theodolites, will be fully described, Chapter XII., in treating of -subtense instruments generally. - -404.--_Solar Attachment to a Theodolite._--This appliance is an -adaptation to the theodolite of the solar compass of W. A. Burt, of -Michigan, which was made to replace the magnetic compass in determining -a true meridian, or north and south line, by observation of the sun -only. It was brought into general use in the surveys of the United -States public lands. The solar compass consists mainly of three arcs of -circles by which the latitude of a place, the declination of the sun, -and the hour of the day can be set off. In the solar attachment to the -theodolite the latitude arc is found unnecessary, as this is formed by -the vertical arc of the theodolite; therefore the hour and declination -arcs need only be described. - -[Illustration: Fig. 166.--_Burt's solar attachment to a theodolite._] - -405.--_The Hour Circle_, Fig. 166, _H_ is fixed upon the centre of -the telescope upon a socket axis _S_, which is placed perpendicularly -to the optical axis and to the transverse axes or pivots of the -theodolite. This circle is divided to read five minutes of time, and -is figured I to XII twice, or I to XXIV, the index being a fine line -carried down on a plate from the lower arm of the _declination arc_, -which is fixed to the socket _S_. The hour circle, when set to any -reading, may be clamped to this position by means of the milled head -placed over the socket _M_. - -406.--_The Declination Arc_ is of 5 inches radius, divided to read on -the same plane with a vernier _V_ to single minutes of arc. The vernier -arm is fixed by a clamp at _C_, which carries tangent adjustment _T_. -At the back of the vernier arm two spur-pieces are carried out directly -from it, _L_ and _I_. These are blocks of metal about 1½ by 1¼ by -¼ inches, which carry each a lens of a focus _L_ to _I_, and a silver -plate to be presently described, upon which the sun's image is received -in one direction or the other. - -[Illustration: Fig. 167.--_Image plate of solar attachment._] - -407.--_The Image Plate_, Fig. 167, is marked with two sets of lines -intersecting each other at right angles. The lines _bb_ are termed -_hour lines_, the lines _cc_ _equatorial lines_; these lines having -reference respectively to the hour of the day and the position of the -sun in relation to the equator. The intervals between the lines _bb_ -and _cc_ are just sufficient to include the circular image of the sun -formed by the solar lens on the opposite end of the vernier arm. The -axes of the solar lenses and corresponding image plates are placed -parallel with each other, and with the direction of the vernier arm. -Below the lower line c three other lines are cut at 5 minutes apart. -These are useful for making allowance for refraction. The following -description for the use of the instrument is partly extracted from -Messrs. Gurley's manual. - -408.--When the instrument is made perfectly horizontal, the equatorial -lines and the opposite lenses being accurately adjusted to each other -by a previous operation, the sun's position in the heavens with -reference to the horizon will be defined with precision. Suppose the -observation to be made at the time of one of the equinoxes; the arm _R_ -set at zero on the declination arc _V_; and the polar axis is placed -exactly parallel to the axis of the earth. Then the motion of the arm -_R_, if revolved on the polar axis around the hour circle _H_, will -exactly correspond with the motion of the sun in the heavens on the -given day and at the place of observation; so that if the sun's image -be brought between the lines _cc_ on the image plate in the morning it -will continue in the same position, passing neither above nor below the -lines as the arm is made to revolve in following the motion of the sun -about the earth. - -409.--In the morning as the sun rises from the horizon, the arm _R_ -will be in a position nearly at right angles to that shown in the -illustration, the lens being turned towards the sun and the silver -plate, on which his image is thrown, directly opposite. As the sun -ascends, the arm must be moved around, until when he has reached the -meridian, the graduated side of the declination arc will indicate XII -on the hour circle; and the arm _R_, the declination arc _V_, and the -latitude arc, that is the vertical arc of the theodolite, will be in -the same plane. - -As the sun declines from the meridian the arm R must be moved in the -same direction, until at sunset its position will be the exact reverse -of that it occupied in the morning. - -410.--_Allowance for Declination._--Let us now suppose the observation -made when the sun has passed the equinoctial point, and when his -position is affected by declination. Then, by referring to the -_Nautical Almanac_ and setting off on the arc his declination for the -given day and hour, we are still able to determine his position with -the same certainty as if he remained on the equator. - -When the sun's declination is south, that is, from the 22nd of -September to the 20th of March in each year, the arc _R_ is turned -towards the plates of the instrument in the opposite position to that -shown in the engraving, using the solar lens at _I_, with the silver -plate opposite at _L_. - -The remainder of the year the arc is turned from the plates, and the -lens at _L_ and plates at _I_ are employed in the position shown in the -figure. - -411.--When the solar compass is accurately adjusted and its plates made -perfectly horizontal, the latitudes of the place and the declination -of the sun for the given day and hour being also set off on their -respective arcs, _the image of the sun cannot be brought between the -equatorial lines until the polar axis is placed in the plane of the -meridian of the place, or in a position parallel to the axis of the -earth_. The slightest deviation from this position will cause the image -to pass above or below the lines and thus discover the error. - -412.--We thus, from the position of the sun in the solar system, obtain -a certain direction absolutely unchangeable from which to run our lines -and measure the horizontal angles required. - -The transit theodolite will, without the solar compass, perform the -same functions; but by means of this instrument the calculation for -position is much more simple. - -413.--=Photographic Apparatus in Connection with the Theodolite.=--The -application of photographic apparatus as an accessory to surveying -instruments has been tried tentatively for many years. A practical -introduction to the subject was first given by M. Laussedat in a paper -published in the _Comptes Rendus de l'Academie des Sciences_, 1859. The -subject has since been well studied by many writers, and is written -up extensively by Dr. E. Deville, LL.D., Surveyor-General of Canada, -in a work entitled _Photographic Surveying_, published in Ottawa, to -which we must refer the reader for full discussion of the subject. In -England, Mr. J. Bridges Lee has invented a very suitable camera in -which a negative glass photograph of 4½ × 3½ inches is taken, -with an axis line from the shadow of a hair permanently photographed -coincident with the axis to the telescope as it appears to view. At -the same time degrees and subdivisions are taken on the photograph to -right and left of the axial line. The edge of the magnetic circle is -also photographed upon the plate, indicating clearly the bearing of -the station taken by the axis line. The whole of these operations are -performed at once in a perfect manner. - -414.--Mr. J. Bridges Lee's photo-theodolite was made in excellent -workmanship by Messrs. Troughton & Simms. The inventor has published -a paper on the subject, to be had of the Society of Engineers, -Westminster. - -[Illustration: Fig. 168.--_Light camera upon the telescope of a -theodolite._] - -At the present time a camera is very commonly taken by a civil engineer -for prospecting in new countries,--a convenient form of this will be -discussed at nearly the end of this work--but it is not generally held -that photography will ever offer a means of expeditious surveying, -except possibly in very mountainous countries where the necessary -stations for observation become difficult of approach and of clear -definition. The objections to the more general adoption of photography -are, otherwise, that the processes are in degree tedious, and require -special skill in manipulation, and that the apparatus is heavy and -expensive with sensitive glass plates for use with it. - -415.--There are many cases, no doubt, where a photograph would be -valuable for the exact definition of a station. To meet this case -the author has made a small light camera, shown Fig. 168, giving -photographs 2 × 2 inches only, with axis line from shadow of a -point. The camera to be placed when required upon the telescope of a -theodolite for special cases. He has lately used his patent slide for -this camera that carries films which will be further described at the -end of this work. The films are unbreakable, and remain sensitive many -years if kept dry. The weight of this camera with its double slides and -100 films is about 1 lb. There is ample room for it in the ordinary -theodolite case. - -FOOTNOTES: - -[15] Digges's _Pantometria_, see p. 2. - -[16] Gardiner's _Practical Surveying_, p. 59, 1737. - -[17] Adam's _Geometrical Essays_, pp. 217-229, 1803. - -[18] _Civil Engineers' Pocket-Book_, by J. C. Trautwine, C.E. - - - - -CHAPTER VIII. - - SPECIALITIES IN MODERN AND IMPROVED FORMS OF TRANSIT THEODOLITES FOR - SURVEYING--RAILWAY WORK--EXPLORING. - - -416.--The description given in the last chapter of a 6-inch transit -theodolite gives all particulars of the original Old English form, -which in a general way comprises the constructive principles of all -others. When we consider modern instruments the details are found to -vary greatly, but most particularly in the direction of uniting in -solid castings many parts that may be shaped out by machinery in a -manner impossible by hand-work, which avoids the instability of the -work being screwed together in many pieces, and makes it at the same -time lighter, more rigid, and less liable to jar out of adjustment. -This direction of construction is also followed in the best modern -work on the Continent and in America. It would extend this work beyond -convenient limits to offer details of the wide variations employed in -practice, but as the author has made this subject a life study, and has -embraced, modified, and endeavoured to improve this class of work in -all its details, freely adopting any improvement he has observed, his -own instruments will represent largely his present ideas of the best -forms, with the economy of having engravings for illustration to hand. -Transit theodolites of portable form will be considered here, leaving -larger stationary instruments to another chapter. - -[Illustration: Fig. 169.--_Stanley's patent new model theodolite._] - -417.--=New Model Transit Theodolite.=--In this instrument the -principles of construction are the same as in the ordinary transit -theodolite fully described in the last chapter, but the distribution -of materials and details are very different. The general arrangement -of a 5-inch instrument is shown in Fig. 169. One important difference, -as before mentioned, is that the work is not built up so much in -separate castings and pieces as is usual, but every possible casting is -shaped out of the solid to the finished form. The vertical axis is of -nearly the same construction as the ordinary transit, except that the -central axis is about double as strong, being of once and a half the -ordinary diameter. It is made in one casting with the upper framework. -The vernier plate is formed of thin hard hammered gun-metal, which -is screwed upon the axis. This plate has not in this construction to -support the superstructure as in an ordinary theodolite, but has only -to hold the two axis bubbles, which are thereby brought distinctly -in view, and the clamp and tangent motion, which is also placed -conveniently for use upon this upper plate, in a position where there -is less risk of accident than when it is placed upon the outer edge of -the limb. - -418.--_The Readers_ to the horizontal limb are jointed to turn up -against the standards and adjust for reflection, as shown Fig. 131. In -this manner the readers do not need detachment to place the instrument -in its case. - -[Illustration: Fig. 170.--_Section of standards of new model -theodolite._] - -419.--_The Central Axis_ and the standards are made in one casting -in hard gun-metal. The standards are of light cylindrical and ribbed -section. This construction, although of only about one-half the -weight of the A-frame arrangement with its attachments, described in -the last chapter, was found upon testing to have more than double -the rigidity in resisting deflection, with perfect certainty of -avoiding the accidental occurrence of imperfect fitting of parts, or -of screws jarring loose, Fig. 170. The making of the vertical axis -and the standards in one piece was in a certain sense an experiment. -It has been found in practice of many years now to give much greater -resistance to all ordinary strains and jars, and ensure the instrument -keeping in order and adjustment when jolted by carrying over the -shoulder, just as the same principle acts in the dumpy level; but at -the same time, in cases of violent accident, such as the fall of the -instrument from a height, it renders repairs somewhat more expensive, -as this entire part might have to be reinstated instead of the axis -only, the axis of the theodolite being generally made very weak that it -may go first, often indeed with a slight jar. Many details are the same -as the transit theodolite before described, adopting what is thought to -be the soundest principle in all cases. - -420.--_The Compass-box_ in this instrument is attached under the limb. -It is of the trough form shown Fig. 32, page 74. The magnetic north -is set to zero. The tribrach is of the form described for levels, -illustrated Figs. 72 and 73, p. 128. - -421.--The weights of transit theodolites of this construction are about - - 6-inch in gun metal 14 lbs., aluminium, 8 lbs. - 5-inch " 11 " " 6 " - 4-inch " 7¾ " " 4½ " - -This pattern embodies all the essential features of a thoroughly -reliable and convenient instrument for all-round general surveying. -It has no unnecessary elaborations and is a strong, light and compact -instrument suitable for continuous hard wear. It has fewer pieces than -any other design and is packed in its case complete in one piece ready -to screw upon its stand upon being taken out of its case. - -[Illustration: Fig. 171.--_Stanley's simple sliding stage for tribrach -theodolite._] - -422.--The author has devised a special arrangement for displacement of -axis for this theodolite, which does not interfere with its valuable -quality of standing the tribrach on a wall or flat surface, Fig. 171. -In this scheme the arms of the tribrach are slightly elevated by the -foot screws. A flange is formed on the top of the head with a leading -tube through it to the upper surface of the lower tribrach plate; upon -this tube an upper flange is screwed, so that the plate comes between -the two flanges, where it may be fixed by means of rotation of the -flange by a thumb-piece. The engraving shows the arrangement with the -axis displaced to its extreme point, about ¾ of an inch from the -centre. - -[Illustration: Fig. 172.--_Stanley's 4-screw sliding stage._] - -[Illustration: Fig. 173.--_Stanley's solid round form tripod with -sliding head._] - -[Illustration: Fig. 174.--_Stanley's telescopic tripod with sliding -head._] - -A somewhat similar arrangement is made for four-screw levelling -instruments shown on page 250 at Fig. 172, but in this the sliding -motion is fixed to position by the action of the levelling screws. It -is sometimes preferred to have the sliding adjustment upon the tripod -head instead of upon the instrument, and in some cases for getting a -greater range of movement, on both, and for this purpose the reviser -has designed the two tripods shown at Figs. 173 and 174, the former -being of the round solid pattern, and the latter having adjustable -sliding legs. A somewhat similar arrangement is made for a sliding head -to a framed tripod as shown below, Fig. 175. - -[Illustration: Fig. 175.--_Stanley's framed stand with sliding head._] - -423.--=Improved Transit with Adjustable Axis.=--This instrument, Fig. -176, in general, resembles that last described, except that it has -a larger telescope and it is mounted on a sliding stage with screw -adjustments, which is particularly described below. It is frequently -provided with a tacheometrical eye-piece for giving horizontal -distances by subtense taken on the incline, which will be described in -Chapter XII. - -[Illustration: Fig. 176.--_Stanley's patent new model theodolite, with -mechanical stage._] - -424.--_The Mechanical Tribrach Stage._--This important addition to the -theodolite above described permits exact adjustment over a station. The -upper plate of the tribrach with the movable stage is shown in Fig. -177. A dovetail slide is fitted upon the base of the stage adjustable -for wear by a slip-piece with two screws at the narrow part. The slide -is adjusted to position in the direction of its dovetail fitting by -a large milled screw so as to move the whole instrument above it for -centring in this direction. An upper slide acting in the same manner, -with dovetail fitting pieces at sides moves for an equal distance for -centring transverse to the lower slide by a milled head. This gives the -same kind of motion of displacement that we have in the slide rest of -a lathe or the mechanical stage of a microscope, except that in this -case we have a kind of three-point bearing surface. The motion given -to the screws permits the perfect adjustment of the theodolite over a -point on the ground corresponding with the suspended plummet, after -the instrument is set up to nearly its true position by movement of -the tripod legs. The range of motion is from ¾ to 1 inch, a quantity -quite sufficient for final adjustment, but which does not materially -affect the equilibrium of the instrument upon its rigid tripod, as it -has in this case a broad solid base even in the extreme positions of -the slide. - -[Illustration: Fig. 177.--_Stanley's patent tribrach mechanical stage._] - -This movement being _above_ the levelling screws, the adjustment of the -instrument for level is not affected by its use, as in the case of all -sliding arrangements _below_ the levelling screws. Suitable means are -provided for taking up any wear that might occur in the slides. - -425.--The above stage is supported upon three foot screws, the female -fittings being specially long to give plenty of bearing surface to -prevent wear; they are sawn down on one side so that they spring -lightly upon the screws, and are provided with cross capstan screws for -tightening up when necessary. This plan gives the screw about ¾ inch -of thread, and permits adjustment for comfortable movement and for wear -without any risk of shakiness. The screw in larger instruments of this -class has a cap to exclude dust. The foot of the screw has a ball which -rests in a slotted tube before described, Fig. 71, p. 127. - -426.--This theodolite with mechanical stage is generally fitted with -illuminated axis for tunnel work, art. 383. The lamp is not shown in -the illustration. - -The weights of this make of theodolite are about - - 6-inch in gun-metal 18¾ lbs., aluminium 10 lbs. - 5-inch " 13¾ " " 7½ " - 4-inch " 9½ " " 4½ " - -427.--=8-inch Transit Theodolite.=--For ordinary surveying the smaller -instruments are sufficient. For opening a survey in new countries the -8-inch instrument, Fig. 178, or a larger one, is generally used for -the superior triangulation, particularly for observations at night of -distant lights when greater light-grasping power is demanded of the -telescope. The larger circle gives a more exact reading of the limb, -which is generally divided to read clearly to ten seconds of arc, and -by estimation sufficiently near to obtain five seconds reading very -approximately with the verniers. When instruments exceed 8-inches, the -reading is by means of microscopes, the application of which will be -described further on. - -[Illustration: Fig. 178.--_8-inch transit theodolite._] - -428.--The 8-inch transit illustrated is of the author's model. It is -in general structure similar to the 6-inch just described, except in -certain specialities. The instrument does not clamp upon the vertical -circle, but a similar circle is provided upon the opposite side of -the axis. This answers two purposes, it balances the pressure upon -the pivots and obviates disturbance of the division by the clamp. -The principal bubble is supported upon the vernier frame, as special -exactness is not required for the instrument to be used as a level. -The base support is upon the Everest tribrach system, which will -be described in the next chapter. A long compass is shown, but a -telescopic compass is sometimes used. The instrument is shown with an -axis-lamp and diagonal eye-piece for star observation. - -[Illustration: Fig. 179.--_Stanley's quick-setting transit theodolite._] - -429.--The vertical axis of this instrument is sometimes pierced for a -look-down telescope to sight its vertical position on the ground to the -centre of a peg. This will be described with geodetic instruments in -the next chapter. It is an expensive refinement, seldom necessary, as -the axis with plummet may easily be brought within the tenth of an inch. - -Theodolites of eight inches and over are uniformly packed in two -cases. The lower part is packed in a case by itself, the upper parts -connected with the vertical circle and all the accessories, eye-piece, -plummet, etc., forming the contents of another case, each part being -sufficient for one man to carry without the tripod. The weight of the -entire instrument is 29½ lbs. - -430--=Quick-setting Theodolites.=--The demand for instruments with -quick-setting arrangements has greatly increased of late years. They -save a great deal of time in setting up, and also save wear of the -levelling screws, as the instrument may be instantly set nearly level -by its means, so that less than half a turn of the levelling screws -will bring it to true level. An ordinary transit is shown Fig. 179, -fitted with a similar arrangement to that described art. 240, p. 132. - -[Illustration: Fig. 180.--_Railway theodolite._] - -431.--=Railway Theodolite.=--There are objections made to the transit -theodolite by some civil engineers that it is a large and heavy -instrument, only to be accepted for its perfect convenience over -lighter forms. To meet this objection the author has made a special -transit theodolite, Fig. 180, which is sufficient for railway work and -general surveying upon moderately level country. The transit principle -is conserved by balancing the telescope on its axis to permit it to -transit over the eye-end only. The vertical arc is omitted as being -unnecessary for railway work. The instrument is constructed especially -low and of great rigidity and solidity, with light weight. The compass -is of the trough kind. The limb is covered for protection. It is -extremely portable. Weight of 4-inch, 7¼ lbs.; 5-inch, 9½ lbs.; -6-inch, 12¾ lbs. Being constructed for rough, hard wear and local -use it is not made in aluminium. - -432.--For tunnelling underground railways the mining theodolite -described further on will be found the most valuable for railway -engineers. - -433.--=Mountain Transit Theodolite.=--This instrument, Fig. 181, is -designed for geographical exploration, and making sketch surveys. It -embraces the transit principle for the convenience of taking zenith -stars. It is made in 3-inch and 4-inch sizes. It has two verniers to -the horizontal limb reading to minutes, and a single vernier to the -vertical circle. It has been made by the author in aluminium alloy -only, the total weight being 2¼ lbs. for the 3-inch and 3½ lbs. -for the 4-inch. The eye-piece reads direct or diagonally. It has -clamp and tangent adjustment to both circles, and a trough compass. -The tripod slides up to half length, each leg being adjustable to fix -to any length within the range of the slide to accommodate it to the -surface of inclined rocks. - -434.--_A Mountain Theodolite_ is a term applied to any very small or -light theodolite. These are generally made to order, very frequently to -a reduced model of a larger theodolite, 3 inches being a common size. -The telescope is occasionally placed upon the side of the horizontal -axis to transit. Theodolites of this class generally weigh much more -than the above-described instrument, a common weight being 5 to 7 lbs. - -[Illustration: Fig. 181.--_Stanley's mountain transit theodolite._] - -435.--=Improved Solar Attachment.=--The reviser's improved solar -attachment admits of a full vertical circle being employed; it also has -a clamp and tangent to the hour circle and declination arc and quick -acting clamp and fine adjustment to the solar arm. An instrument so -fitted is shown on p. 260, Fig. 182. - -[Illustration: Fig. 182.--_Stanley's solar attachment._] - -436.--=Micrometer Reading Theodolites.=--The favor with which the -smaller micrometer reading theodolites have been received and the ever -increasing demand for them owing to their much greater accuracy has -induced the reviser to introduce a whole range of these instruments. In -many cases where greater accuracy is required for horizontal than for -vertical angles, the micrometers are only fitted to the horizontal -circle and the vertical circle has verniers as usual. A useful -instrument for general surveying without any unnecessary elaboration is -shown below at Fig. 183. - -[Illustration: Fig. 183.--_Stanley's micrometer transit theodolite._] - -The 6-inch instrument reads to 5 seconds of arc on the horizontal and -to 10 seconds of arc on the vertical circle, and the 5-inch instrument -to 10 seconds of arc on the horizontal and to 20 seconds of arc on the -vertical circle. - -A full micrometer reading instrument is shown at Fig. 184, the 6-inch -reading to 5 seconds of arc on both circles and the 5-inch reading to -10 seconds of arc on both circles. - -[Illustration: Fig. 184.--_Stanley's full micrometer transit -theodolite._] - -A specially light form of micrometer reading transit (Fig. 185) has -recently been designed by the reviser which has met with much favour. -It has a 4½-inch horizontal circle reading by micrometers to 20 -seconds of arc which may be approximately read by mental subdivision to -5 seconds, and a 4-inch vertical circle reading by verniers to single -minutes. It is also made micrometer reading to 20 seconds of arc to -both circles. The compass is of circular form reading by microscope to -¼-degrees, which may easily be estimated to a third of this. - -[Illustration: Fig. 185.--_Stanley's light micrometer transit._] - -An example of a more refined micrometer transit is shown at Fig. 186. -This instrument was designed by Dr. E. Deville, LL.D., Surveyor-General -of Canada, and is arranged for latitude determination by Talcott's -System, and general geodetic work. - -[Illustration: Fig. 186.--_Dr. Deville's transit._] - -It has a 6-inch horizontal circle reading by micrometers to 5 seconds -of arc, and a 4-inch vertical circle reading by vernier to 1 minute, -with zenith spirit level graduated to 2 seconds of arc, detachable and -interchangeable with a small level for ordinary use. The telescope is -14 inches solar focus with large object glass so that observations -may be taken of stars up to the sixth magnitude; it has a revolving -micrometer diaphragm and electric illumination to micrometers, to -diaphragm both front and back, and to zenith spirit level, it has also -a rheostat for regulating the amount of light, and a dynamo generator -for supplying the current. - -[Illustration: Fig. 187.--_Stanley's patent universal transit -theodolite._] - -The universal transit designed by the reviser is shown at Fig. 187. - -This is an 8-inch instrument, reading by micrometers on both circles to -2 seconds of arc, and is fitted with all the necessary arrangements for -universal work. - -A description of the larger geodetic instruments is given in a -subsequent chapter. - - - - -CHAPTER IX. - - PLAIN THEODOLITES IN WHICH THE TRANSIT PRINCIPLE IS NOT - EMPLOYED--THE PLAIN THEODOLITE--IMPROVED CONSTRUCTION--EVEREST'S-- - SIMPLE--ADJUSTMENTS AND EXAMINATION OF THEODOLITES. - - -437.--The plain theodolite is of nearly its original form as invented -by Sisson. It still retains a limited popularity, which is principally -due to its portability, being of less bulk and weight than the transit -of equal diameter of circle. If we consider the railway theodolite -described in the last chapter as a simple form of transit, this must -be considered as an exception with regard to the bulk and weight, not -being greater than that of the plain theodolite. - -438.--=The Plain Theodolite.=--For the general description we may -follow that given in Chapter VII. for the 6-inch transit for all parts -of the instrument below the vernier plate, and for the compass-box -above this plate. The construction of the instrument varies from -the transit in having a half vertical circle only, with a single -vernier, and in the differences in the arrangement of the fittings -connected with the telescope. A single microscope is generally used on -the horizontal circle, and this passes in a groove from one vernier -to another, instead of having two microscopes on arms jointed upon -the vertical axis, as in the better construction of transits before -described. - -The standards or A-frames in the ordinary plain theodolite are attached -to the vernier plate, but not generally to the compass-box. The -pivots of the transverse axis, which are made exactly equal in size, -rest on coupled bearings on the tops of the standards, which are in -construction made together, and therefore exactly alike. The transverse -axis is not adjustable, as in the transit theodolite previously -described; the standards have therefore to be adjusted to height in -the manufacture by filing, with the application of a special striding -level, until the transverse axis is brought permanently perpendicular -to the vertical axis. - -[Illustration: Fig. 188.--_5-inch plain theodolite._] - -439.--The vertical arc is fitted over the transverse axis; that is -constructed with a turned flange to which the arc is firmly screwed. -The arc is divided to 30′ and reads with a vernier to minutes. The -vernier is fixed directly to the vernier plate, and reads generally -with a microscope jointed on the transverse axis, but sometimes with -a loose magnifier for economy. Divisions for difference of hypotenuse -and base are occasionally divided on the back of the arc. The vertical -arc has a clamp and tangent placed at the back, therefore this cannot -be shown in the engraving. Along the bar above the vertical arc a -stout plate is attached by screws. From this a pair of Y's with clips -and eye-pins, as described for the Y-level, art. 192, supports the -telescope. - -The telescope is of the same construction as that described for -Y-levels, with turned collars. The diaphragm is cross-webbed. For -economy a simple cap is generally put to the telescope instead of the -better plan of a ray shade. The principal level is fixed to collars -fitted round the telescope, to which are attached one slot-piece -for lateral adjustment of the level, and one screw-piece for linear -adjustment by means of two capstan nuts. The level is placed under the -telescope for compactness. - -440.--The parts of the plain theodolite below the standards are the -same as those already described for the transit theodolite, except that -the vernier plate carries one level only at right angles to that of the -telescope. The telescope is therefore set to zero by the vertical arc, -and the two levels are then used as the pair upon the vernier plate -of the transit. The means provided for the adjustment are the same as -those of the Y-level, but the Y's are adjusted firmly by the maker by -fitting them down upon the Y-plate in the manufacture. - -441.--The plain theodolite, except where price is the first -consideration, appears to be going gradually out of use, being -superseded by the transit. It has had a long day since its first -conception by Sisson about 1730. For 4-inch and 5-inch instruments -the makers still find a small demand. The 6-inch is rarely enquired -for. The plain theodolite cannot compete with the transit for perfect -utility, but it holds the merit of less weight and of greater -portability. The weights of the three sizes in general use are as -follows:-- - -_Weights of Plain Theodolites._ - - Instrument. Case. Outer Case. Tripod. - - 4-inch 7 lbs. 7½ lbs. 3½ lbs. 8 lbs. - 5-inch 11 " 8½ " 4 " 9 " - 6-inch 17 " 10 " 5 " 11 " - -Very light 3-inch and 4-inch plain theodolites of from 5 lbs. to 7 lbs. -complete are made occasionally for travellers. - -[Illustration: Fig. 189.--_Stanley's new model plain theodolite._] - -442.--The author has recently modified the plain theodolite, Fig. -189, for which there still remains a small demand in the Colonies, -by making the construction much more solid by shaping the work out of -single castings in gun-metal for parts formerly screwed together in -many pieces, which formerly was necessarily arranged to permit facility -of construction by hand-work. There are also in the new instrument -some improvements made in detail. The limb dividing is covered for -protection. The readers are joined through the vertical axis and are -hinged to turn up. The compass has an aluminium ring with a microscope -which permits it to be read at a convenient height and much more -accurately. The tangent screws are covered to exclude dust, and some -other improved details. - -[Illustration: Fig. 190.--_Everest's theodolite._] - -443.--=Everest's Theodolite=, Fig. 190, designed by the late Sir -George Everest, and used for details of the great trigonometrical -survey of India, is built up very much upon a well-known common French -model. In service in India it has proved an excellent instrument. The -horizontal circle or limb of this instrument consists of a single -plate, upon which the silver is inlaid flat upon the surface, upon the -plan shown, Fig. 128. In place of the ordinary vernier plate three -arms are extended from the central axis, which carry each a vernier at -its end, reading to a fiducial edge, Fig. 127, p. 186. The verniers -trisect the circle, and are marked _A_, _B_, and _C_. A fourth arm, -proceeding from the same relative position of the centre as the arms of -the vernier, carries a clamp and tangent which is similarly constructed -to that of the ordinary theodolite described. The instrument has also -an under clamp and tangent for setting the telescope to bearing, or for -repeating, as in the ordinary theodolite. - -444.--The horizontal axis carries the telescope in a cylindrical -fitting as in the transit theodolite, terminating in two pivots which -are set to permanent position as in the plain theodolite. The pivots -rest in bearings upon short standards carried out from the centre -upon a flat horizontal bar to which a spirit level is attached for -adjustment of the pivots to horizontality. Vertical angles are read off -upon two arcs which have a horizontal axis as their centre attached to -the telescope, so as to move with it in the vertical plane, with clamp -and tangent adjustment. An index, upon the same centre carries two -verniers and has a spirit level attached to it. The verniers are read -by a pair of microscopes. Upon the upper side of the telescope a trough -needle is placed. - -445.--This instrument has been used in military surveys by the Royal -Engineers. The objections that civil engineers have made to Everest's -theodolite are that the working parts are made very open, so that the -wet and dust intrude; further it lacks the general convenience of the -transit principle, which is necessary for astronomical observations. -The tripod is sometimes made of the ordinary solid section, art. 216; -but for India, where carrying labour is cheap, a heavy framed stand is -used, which is special, as follows:-- - -[Illustration: Fig. 191.--_Everest's locking plate tribrach._] - -446.--_Everest's Tribrach._--The upper part of the engraving, Fig. -191, shows this tribrach that supports the upper part of the instrument -directly upon its vertical axis. The three arms of the tribrach carry -each a milled-headed adjusting screw, the nut of which is formed in -the arm. The arm is sawn up to admit of adjustment, that the milled -head may turn softly but without any shake. The lower points of the -milled-headed screws, technically _feet_, fall into V-grooves in the -head of the tripod. The V's are not shown in the engraving. Above the -upper surface of the tripod head, a thin, three-armed plate of metal, -termed the _locking plate_, is centred upon the hollow axis of the -head, so that it will move laterally. The locking plate has a _hole -and slot_ at the end of each of its arms, the holes of which admit -the toes of the feet of the tribrach into the V-grooves formed in the -head of the tripod. The locking plate when moved laterally locks all -the toes in at once, so that the instrument is secured by this means -to a certain degree from accident. This locking plate has commonly a -milled-headed screw clamp which fixes it in its locked position. The -head of this screw is under the tripod head, and consequently cannot be -shown in the engraving. It is a defect of this locking plate that the -screws, unless they fall perfectly in the V-grooves have a tendency to -_ride_. To avoid this the author has for many years made the ball feet -fall upon a plain surface, being at the same time held in their places -by a slotted plate which fits over the neck of the balls. This plan, -which is not shown in the engraving, is now adopted by other makers. -The author uses also his patent tribrach sometimes on this instrument. - -[Illustration: Fig. 192.--_Stanley's Everest theodolite._] - -447.--_The Framed Tripod_ of Sir Geo. Everest's design is made of -straight-grained mahogany, each leg being formed of two _side-pieces_, -with one or two cross-pieces. The engraving, Fig. 191, shows the head -of a tripod of this construction. The side-pieces are spliced together -at the lower ends, where they form a rather obtuse point, which is -shod with a gun-metal shoe. The upper ends of the side-pieces carry -_strap plates_ that receive a bolt which holds them firmly by means of -winged nuts to the tripod head. The legs can be detached after use and -the tripod head be placed in the case with the instrument in a packing -provided for it. Some modification of this form of tripod is generally -used for all large field instruments. The author's improved Everest -theodolite is shown at Fig. 192. - -[Illustration: Fig. 193.--_Simple theodolite._] - -448.--=Simple Theodolite.=--The plain theodolite being of the cheapest -construction may be stripped of its superior functions, which are used -for testing its adjustments, and be made into a simple angle measurer -for laying out or plotting small parcels of ground, small estates in -building ground, local sewage, gas and water works, and many other -cases of small surveys, for which purpose it will be found sufficient, -with a saving of about half the cost of a perfect theodolite. The -instrument shown above, Fig. 193, was designed by the author to meet -the above cases. In this instrument there is no vertical arc. The -telescope has a socket axis carried upon a single standard. The axis -cannot be seen in the figure from interference of the telescope placed -in front of it. The telescope is arranged to be fixed in a level -position by means of the loose pin being pressed in a pair of holes. It -may then be used as a level by means of the spirit level shown on the -vernier plate. The horizontal circle is divided to read with a single -vernier to 3′ of arc by means of a hand magnifier which is placed in -the case with the instrument. There are internal and external axes, -each provided with clamp and tangent motions to the horizontal circle, -as with the plain theodolite. It is supported on a tribrach, the legs -of which are upon the plan, art. 249. - -If it be made with two verniers and divided upon silver it becomes -a useful light instrument for filling in details of superior -triangulation. Weight, about 4¾ lbs. - -449.--=Examination and Adjustment of the Theodolite.=--The description -given of a transit theodolite, arts. 369 to 389, will show that -this instrument is provided with means of adjustment in every -requisite direction. Larger transit instruments possess the same -means of adjustment, but in some parts these have greater refinement. -Plain theodolites have the like methods, except in the case of the -transverse axis, which is adjusted once for all by the maker. It will -be necessary, therefore, to limit our space to a discussion of the -examination and adjustments of the transit theodolite only, of which -we have given a full description, arts. 369 to 389, noting only where -variations occur from partial differences between this and others. - -450.--A theodolite as it comes from a respectable maker is usually -carefully adjusted in all its parts. If it has travelled a long journey -it is, however, well for an experienced surveyor to put it through its -various adjustments. The corrections, if any are required, will be -generally very small, and these in all probability will be of the same -kind as will occur in the use of the instrument and in the accidental -conditions to which it may be subjected during conveyance from place to -place upon a survey; therefore it is well to be familiar with them. - -When a new instrument is received from the maker, it is necessary to -observe attentively the manner of its packing as it lies in its case. -It is well at first to lift the parts a few times gently out of the -case and replace them, so that this may be done at any future time -with certainty and without any risk of strain upon the instrument, -remembering always that an instrument in conveyance is much more liable -to be thrown out of adjustment by carelessly replacing it in its case -than from its ordinary use, art. 42. - -451.--For examination or adjustment of the theodolite the tripod -stand should be at first firmly fixed with legs extended to an angle -of about 70° to the ground, which should be solid and hard. As the -telescope has to be brought to the height of the observer's eye, it -is well to mention his stature in ordering an instrument. The tripods -that are made for tall men are often awkward and unsteady if the legs -are extended to bring the telescope down to the height of a short -person. They may always be cut down and refinished by the maker. When -the tripod is set up the toes should be each separately pressed down, -so that future slips are impossible. This being done the instrument -is taken from its case and grasped firmly by the body part under the -horizontal circle, and placed on the tripod at once, then screwed -firmly but not too tightly down upon its bearing surface. With a -6-inch transit theodolite the upper part is sometimes detached and -packed separately in its case. Where this is so, after the body part -is fixed on the tripod, the cleats on the top of the standards must -be opened out, and the upper part of the instrument, lifted by its -telescope, be slowly lowered into its bearings, being particular at the -same time that the clips under the telescope embrace their stay-piece -on the standard. The cleats must then be closed over the pivots. The -instrument being set up to position, all levels may be adjusted to the -centres of their runs, and every part clamped sufficiently to make the -instrument firm, but in no case using violence to produce a strain -in any part. The clamps or other fittings are afterwards separately -released as they are required for examination or adjustment of the -parts to which they relate. - -452.--_Examination for Coincidence of Exterior and Interior Vertical -Axes._--The theodolite being set up solidly, and all clamps fixed as -above described, unclamp the lower or exterior axis clamp and set -the vernier plate levels parallel with opposite pairs of parallel -plate screws if the instrument adjusts on the parallel plate system, -art. 193, or one level parallel with one pair of foot screws if it -is made on the tribrach system, art. 234. Now adjust both levels. -Turn the instrument half round (180°) and observe if the levels keep -the centres of their runs. If they do so they are in adjustment to -the exterior axis. If found imperfect, the adjustment by the capstan -heads of the levels is set, by means of the _tommy_ or pin which is -provided in the instrument case, for half the error as it appears by -the bubble, the other half being given by readjustment of the parallel -plate or tribrach screws. In these adjustments it is necessary to be -particular _always_ to observe the bubbles after the hands have left -the instrument, _not during the adjustment_, which produces strain upon -the instrument. Now clamp the lower clamp and note if this clamping has -disturbed the levels. If the levels are very sensitive it will do so in -a slight degree, but the disturbance should be very small if the clamp -is perfect. Now unclamp the vernier plate and note again if this clamp -disturbs the levels: this should also affect them very little. Now -observe the levels if they stand exactly as they did when the exterior -axis was unclamped at their present position, and also at right angles -to this. If they remain as before the axes are truly concentric. If -they do not, there is no remedy except at the hands of the maker. The -vertical axis to which the above examination applies is considered -the most important part of the instrument, and the work should be -thoroughly well done; nevertheless, if the levels are very sensitive, -which they seldom are, such minute faults may be detected, that a small -allowance may be made for imperfection of work, and the instrument -still be considered a sound one. In the use of the instrument it is -always well, after the circle is set either by the magnetic compass or -by sighting a distant point for direction, to clamp the lower clamp and -readjust the levels to the vernier plate. In this way the axis that -will afterwards be used for triangulation will be vertical, and small -errors due to want of coincidence of axes be eliminated. - -453.--_Examination of the Azimuthal Level._--This level, which is -placed over the telescope, being made of superior sensitiveness to the -vernier plate levels, is much more accurate for adjusting the vertical -axis, but much slower in operation for testing. The verniers of the -vertical circle should be accurately set to zero, in which position the -run of the bubble should exactly agree with those on the vernier plate -when placed parallel with them in any direction, but this level may -also be considered by itself. Assuming the circle and verniers correct, -or otherwise, it may be reversed over the axis by half turns in all -positions over the parallel plate or tribrach screws, and adjusted by -the capstan heads half the error, as before described, for the vernier -plate levels. - -454.--_Examination of the Divisions and Centring._--The vernier plate -being unclamped, the verniers, if two, should be brought approximately -to 0° (360°) and 180°, and then the plate be lightly clamped. The -microscopes or readers are then to be set truly radial with the zero -reading of the verniers, and the tangent screw adjusted to make one of -the readings, say the 360°, exact. The opposite reading, 180°, is then -carefully examined, and the error discovered, if any, is due to the -imperfection of centring, assuming the dividing perfect. At this point -it is well to record the amount of difference. The same examination -is then repeated with the 90° and 270°. In a properly centred and -accurately divided 5-inch or 6-inch theodolite this difference will not -amount to more than 1′ error, in larger instruments proportionately -less. Owing to the difficulties at all times of reading the circle -correctly from difference of direction of light, and what is termed -personal error, it is well to entirely repeat this examination, turning -the instrument half round. It is also well to repeat the examination -at what are termed the _half points_, 45°, 235°, and 135°, 315°. This -will sometimes detect the error of centring, if there be any, in its -true direction. The purpose of the two verniers is to discover this -error. In practice the two readings are always taken, and the mean is -considered as the true reading. Where there are a greater number of -verniers exactly the same principle is followed, but the mean of three -or more readings is taken, which of course assures great accuracy. - -Examination of the telescope has been discussed arts. 107 to 115. - -455.--_Testing an Instrument for its Stability._--The stability of an -instrument will depend principally upon the quality of the workmanship; -but the same test will also indicate, at any time, whether the -instrument has been submitted to sufficient wear to need the repair -of the optician. For this examination the eye-piece of the telescope -requires to be focussed against a piece of white paper held obliquely -in front of the object-glass so as to throw a soft white light into -the telescope. After the eye-piece is focussed, any distant point may -be taken for a sighting object upon which to direct the telescope. -This point should be focussed by the telescope so that its image falls -centrally upon the intersection of the webs. The eye should then be -shifted up and down or sideways within the range of clear vision of the -webs in the eye-piece to ascertain that there is no parallax, that is, -that the adjustments of the eye-piece and the telescope are in true -focus upon the webs. This preliminary arrangement being made, which -will serve in future examination for other adjustments, all parts of -the instrument should be examined to see that the clamps are firmly -clamped. The object to be used as an index or sighting point should be -brought by the clamp and tangent motions exactly upon the intersection -of the webs as they appear in the telescope, when the following -examinations are to be made. - -456.--_Tripod Head Examination._--The telescope being sighted upon an -index point, and all clamps screwed down and the tripod firmly fixed on -the ground, take the tripod head of the theodolite in both hands and -give it a twist of about a pound pull in one direction; then examine -the telescope to see if the index point is displaced in the telescope. -If it still stands correct give a like twist in the opposite direction -and again examine the telescope. If it stands these opposite firm -twists retaining its position the stand is good and in good order. If -it does not, assuming good construction of stand, the remedy may be -found in tightening up all its screws; but if its construction is bad -it will not, even after this tightening, keep in order. There is no -doubt that more inaccurate triangulation is caused by defective tripods -than from any other cause whatever. A perfect instrument is useless on -a bad tripod. - -457.--_General Examination of Fixed Parts._--The stand being found -good by the above process, the general fittings of the instrument may -be examined, after clamping all parts and directing the telescope to a -distant point, by taking a quill pen by its root or pipe and pressing -its feathered end upon one side of the eye-piece of the telescope -sufficiently to bend the quill, and afterwards examining the telescope -to see that the webs are not displaced from the index point. This may -be done first to the right hand and then to the left. If the webs -still cut the same object it is clear that the whole of the centres, -fittings, clamps, and tangent screws of the horizontal circle are -correct. If any displacement be discovered, the amount of difference -between the right and left handed twists will be the total error due -to imperfection of work or wear as the case may be. In exactly the -same manner, but by pressing the eye-piece upwards and downwards, the -transit axis and its fittings may be examined. If the instrument be -not generally sound enough to bear the above tests, other critical -adjustments become necessary. For the correction of faults that may be -included in the above operations, the parts of the instrument must be -separately examined. - -458.--_Examination of the Transit Axis._--The best means of adjusting -this axis in a theodolite is by a _striding level_, art. 400. When -this is not provided with the instrument, and it is often omitted for -economy, the axis is generally better to be left as it is adjusted in -this particular, by the maker. To adjust the transit axis the vernier -plate bubbles are set exactly true by reversing angles of observation. -The cleats are opened and the striding level is mounted above the -instrument resting upon the pivots. The telescope is placed exactly -over an opposite pair of parallel plate screws, or parallel with -two screws if the base adjustment be on the tribrach principle. The -striding level is then carefully observed and reversed on the pivots. -If there be any difference in the run of the level bubble the transit -axis is adjusted by raising or lowering the movable V on which one -pivot rests by turning the capstan nuts until it is quite correct, if -the instrument has this old-fashioned arrangement, or if not, by a few -strokes of fine emery paper upon the V which is higher. This adjustment -is almost superfluous, as the axis is generally set right at first, -and is not subject to change, especially if solid without an adjustable -V. - -459.--For larger theodolites of 12 inches and over, the transit axis -is much better adjusted by means of an artificial horizon, which will -be described further on. By the use of this instrument in the northern -hemisphere the pole star is first observed directly by the telescope, -and then by its reflection from the horizontal surface of clean mercury -placed on the ground at 12 feet or so from the instrument. If the star -and its reflection cut the webs equally in directing the telescope by -movement of its transit axis only from the one to the other, this axis -must be truly horizontal. If the vernier plate be then turned a quarter -of a revolution and the exterior axis a quarter of a revolution, the -telescope transitted and observation be repeated, the verticality -of the principal axis may be adjusted with perfect certainty. The -principal axis should be moved one-eighth of a revolution all round and -the bubble examined at every position to assure perfect adjustment. -With the plain theodolite, Everest's and some others, the transverse -axis is fixed to position by the maker, therefore cannot be adjusted. - -460.--_Examination and Adjustment of Webs, Lines on Glass, or -Points._--The ordinary manner of webbing the diaphragm of a theodolite -was shown Fig. 23. Horizontal angles are taken by the upper -intersection of the diagonal webs or lines. A single web is placed -horizontally for taking vertical angles: it is necessary that this -should be nearly true. When the theodolite has its axis vertical, as -shown by the vernier plate bubbles being in the centre of their runs, -if one end of the horizontal web or line be set to cut a small distant -object by sight in the telescope, the same object should keep on the -web while the tangent screw of horizontal circle is moved a distance -sufficient to traverse it, the hand being always taken from the screw -while the observation is made. If it does not do so, the collimating -screws should be lightly tapped with the back of a penknife in the -direction to set it right. These screws have a slot in the body of the -telescope, under the loose covering plate, sufficient to permit of this -small adjustment. - -461.--_Adjustment of the Telescope to Vertical Collimation._--The -eye-piece is first focussed as before against a piece of white paper -held obliquely in front of the object-glass until the webs are -sharply seen. The axis of the telescope is then examined for vertical -collimation error. The method of doing this has been already described -for a telescope placed in Y's, as it is in the Y-level, and the plain -theodolite, art. 200. The only difference with the transit theodolite -is that instead of turning the instrument in its Y's, the telescope -is _transitted_, as it is termed, over on the transverse axis exactly -half a revolution, or 180° as seen by the vernier reading; and the -horizontal circle is moved also half a revolution, so that the -telescope points again on the same distant point which is used for an -object. If the webs or lines still cut the same point or small object, -they are in vertical collimation, or truly in the optical axis of the -telescope, as regards the vertical direction which this adjustment is -intended to secure, presuming the circle has been correctly divided and -centred and the verniers accurately set. If the webs or lines do not -cut the same point, half the error is corrected by the top and bottom -collimating screws near the eye-piece. This process is repeated until -it is exact, being particular to observe, as before mentioned, that -there is no parallax. This adjustment cannot be made with the plain -theodolite; but the zero of altitude may be examined on both sides of -the arc. - -For the transit theodolite, adjustment by means of a collimator, art. -229, is much more convenient and exact, as lateral and vertical errors -in the position of the webs can be detected in one operation. When a -Y-level is at hand, this may be used as a collimator if it is first set -to solar focus. - -462.--_Examination for Perpendicularity of Transit Axis and -Telescope._--The whole of the lower part of the instrument retaining -its position with all clamps firm, open the cleats upon the top of the -standards so as to release the transit axis. Now release one of the -clip screws and gently lift the upper part of the instrument out of -its bearings. Turn the telescope the reverse way upwards, which will -be in this case bubble downwards. Release the clamp and turn the clips -to the reverse position of the telescope, and reverse the position of -the pivots in their bearings. If the telescope be now directed to the -same point as before, and the webs still fall upon it, the telescope -adjustment is at right angles to the transit axis. - -463.--_Examination of the Magnetic Needle._--If the needle be placed -in a circular box, as shown in the engraving, Fig. 30, it admits of -no adjustment. If it is placed in a trough, Fig. 161, it admits of -adjustment generally by lateral screws to a portion of its division. -If the needle is used for a survey, it is set to the zero of the -horizontal circle by clamping the vernier plate and bringing the -northern vernier to zero, then releasing the exterior axis and bringing -the needle by the motion of the lower tangent screw to the zero of -its circle. The corrections of the needle for giving true north have -been discussed, art. 132. It is difficult to read an ordinary edge-bar -needle correctly, it is also difficult to mount it perfectly true. It -may be read at both ends, and if the 0° and 180° points cut the line -fairly it is considered correct; if not, the mean of the difference may -be taken. In some instruments a microscope is mounted over the needle -point that the needle may be adjusted to a web; but British surveyors -seldom feel confident of surveys by the magnet, and for triangulation -generally prefer to employ a certain number of distant fixed points, -the bearings of which are at first as accurately ascertained as -possible, for referring objects, rather than to refer frequently to the -magnet. When the needle is out of use it should always remain lifted -off its centre. When the instrument is put by for a long period it is -better to place it in a vertical position and free the needle, so that -it rests in the magnetic meridian, in order to preserve its magnetism -as much as possible. - -464--=Use of the Theodolite.=--In setting up a theodolite, place the -tripod nearly over the position in which it is to be used. This is -frequently the socket hole formed in the earth by the removal of a -ranging pole or _picket_, to be described Chapter XVII. Then, after -it is set up, suspend the plummet from the hook, which will be found -inside the head of the tripod. If the ground be solid and level, then -by shifting the toes of the tripod slightly, and firmly pressing them -down one by one, the centre of the plummet may be brought easily within -about ·25 of an inch of its true position. The theodolite is then -placed on its tripod, observing that the telescope is in a position -easy to be used. The centre of the picket-hole, when this is used for -a station, is generally taken by guess-work, which is considered near -enough. It may be taken with a little more refinement by placing, in -the same hole, a short false picket of nine inches or so in length, -but of the same diameter as the ordinary picket, the top of which is -cut off smooth and polished, and has lines sawn across its centre -inlaid with ebony, described in Chapter XVII. The false picket is -carried about with the theodolite. With Everest's and many other forms -of theodolites the hook is fixed under the axis of the instrument. In -this case it is usual to set the theodolite before adjusting it to the -station, as there is no separate hook to the tripod, which also occurs -with all framed stands. - -465.--Where there is no hook to the tripod an excellent plan is to have -a false centre, which may be a piece of turned wood with a hole through -it, to fix on the top of the tripod head. The plummet cord adjusts -through the hole. This false centre is also convenient where the axis -adjusts to position by a mechanical stage. Fig, 194 shows a false -centre formed of a piece of ivory with two slots to permit the cord to -loop over and yet hang centrally. - -466.--It may be observed that if the tripod be set up out of level, -which it must necessarily be in many cases, the hook, if attached -to the stand and following its inclination, will not hold the cord -at a truly vertical position to the axis. Surveyors commonly allow -a little for this inclination. It is much more accurate to have the -cord suspended directly from the axis of the instrument when it is -constructed to admit this. Then if a false centre be used the plummet -should be suspended a second time from the axis hook. With the kind -of runner shown in the figure this need take little time, as it is -instantly detached and replaced. - -[Illustration: Fig. 194.--_False centre for a tripod head._] - -467.--After the tripod is fixed with the theodolite upon it, the -readers are set to exact focus. The horizontal circle is then brought -to zero by the vernier plate clamp and tangent, and the compass brought -to magnetic north, if all angles are taken in reference to this as -a check, by means of the lower clamp and tangent. The vernier plate -clamp is then released. The eye-piece is correctly focussed upon the -webs, lines or points against the northern sky, or upon a piece of -white paper held obliquely if this is preferred. The telescope is -then ready to be directed towards a picket or other station mark to -be observed, and set correctly to focus this, after which the eye -is moved to the right and left, to the extent of clear vision in the -eye-piece, to see that the object appears to remain fixed upon the -intersection of the upper V of the webs, or does not _dance_, as it is -sometimes termed. The observation, if of a picket, should be taken as -near the ground as possible, as it may not be set quite upright. If -the telescope is directed to objects where the sun's rays would enter -it, the ray shade should be pulled out sufficiently to quite shield -the object-glass. The initial reading to be recorded is always taken -on the _face_ of the instrument, in which position the upper tangent -screw is always on the right-hand side. When the observation is clear -and satisfactory, it is recorded in the field-book. If the sight lines -taken are to be measured by the chain, the amount of inclination is -taken by the vertical circle reading to the top of the picket if this -is the 6-feet ordinary length, or to a marked band if this is longer. -The inclination may be taken exactly to angle by vernier, or roughly -by scale of difference of hypotenuse and base if this is engraved on -the vertical circle, or by both of these--the one as a check upon -the other. It is common to take the upper inclination as a plus (+) -and the lower as a minus (-). Inclination observation is recorded at -the same time as the horizontal position. Other observations of the -various positions or pickets are taken in a similar manner at the same -time. When a stadia or tacheometrical diaphragm is used the angle is -recorded and the stadia reads the distance. It is thought well when -the theodolite is in position to take as many exact observations as -possible in all directions of intended stations. It is also convenient -to take a number of observations, which from the circumstances present -may be inexact, such for instance as the angles subtended by trees, -gates, rough buildings, or even sometimes the corners of fields, as -from such observations these objects may be placed nearly enough for -ordinary plotting by the angles they subtend from this and another -station upon the plan. In any case they form a check to positions if -taken with pickets afterwards more definitely. These may be marked in -the field-book _inx._ for _inexact_. - -468.--=Field Book.=--This book is generally made 8 inches by 4 inches, -covered with red leather, with elastic closing band and sheath for -pencil, as an ordinary pocket-book. It contains about 100 pages of good -stout writing-paper. Two lines are ruled in red ink, ¾ inch apart, -vertically down the centre of each page. The column between the lines -is used for distances measured by the direct chain line at which hedges -are crossed, stations, offsets, or other measurements are taken. In the -right and left columns observations are made of objects desirable to be -recorded or triangulated. - -469.--For superior triangulation, definite and prominent fixed objects -are taken at as great distances as possible, so as to include the -details of measured triangles within a superior triangle. A church -steeple, for instance, is a favourite sighting object. This cannot, -however, generally be made, a station for future triangulation unless -a scaffold is built up around it. Generally the most convenient method -on fairly level ground, if the survey is large, is to have an ordinary -scaffold pole, 20 feet or so in length, carefully straightened by a -village carpenter with a stretched chalk line and then painted white. -This may be squared at the end and fixed vertically in a socket formed -of crossed boards to a depth of about 3 feet in the ground, with long -crossing tail pieces rammed firmly with the soil to keep it steady. -When this is used for a triangulating station, the pole is taken -out of its socket and its exact position is centred for placing the -theodolite. Flags are sometimes used to indicate stations: their defect -is that the wind may blow them from or to the observer and thus render -them invisible. Other methods will be found in practical works on -surveying. This subject will also be reconsidered in Chapter XVII. - -[Illustration: Fig. 195.--_Diagram bisection of circle._] - -470.--_Elimination of Instrumental Errors during -Triangulation--Changing Face._--It is generally advised to _change -face_ with the theodolite after angles are taken in the ordinary way, -that is, to take first the initial angles reading from the _face_ -vernier with the tangent screw on the right hand, and then to take the -same angles with the back vernier, the telescope being transitted. -This, of course gives a reading on a different part of the circle and -corrects the error of position of the vernier, or centring, in the -following manner:--In Fig. 195 let a be zero (360°), the reading of -the face vernier. Let the opposite reading (180°) be at _a′_. Suppose -at 180° on the left-hand side of the instrument the 180° reads at -_b_, then observe by the telescope an object that cuts this reading, -or place a picket to do so. Change face; then the same arc will come -to _c_, and the telescope must traverse _cb_ to come to the first -direction. The instrumental error is half _bc_, which bisected in _a′_ -gives 180° exactly. The same principle of repetition with changed face -may be made an any part of the circle, and the mean will be the correct -reading. - -471.--_Repeating Angles._--This is performed by taking all parts of -the circle for reading a given angle, so that errors of division -and centring of the instrument are eliminated. The process is as -follows:--Take the angular positions of two objects in azimuth, -commencing with the zero of the horizontal circle, say the two objects -subtend from the centre of the instrument 36° 10′; then turning the -telescope back from its advanced position at 36° 10′ by releasing the -lower or axis clamp, we may bring the first reading to the original -zero position. Now clamp the lower clamp and release the vernier plate -clamp and take again a forward reading. If this reads 36° 10′ + 36° 10′ -= 72° 20′, the circle and centring appear so far correct; but it will -probably read 72° 21′, and the corrected reading would be the mean 36° -10′ 30″. If we continue this system round in ten pairs of readings -the whole circle will be embraced, then the mean of the sum of the -minutes divided by the number of pairs of observations will give the -true reading of the minutes. By taking the readings of two opposite -verniers separately, the circle would be encompassed by five readings. -This plan is followed in all important triangulations where the work -is submitted to calculation. Such refinement is scarcely necessary for -direct plotting with the protractor. - -472.--It may be observed that if the horizontal circle is placed with -its zero constantly to magnetic north--not necessarily for taking -angles in reference to this--that the same part of the circle will -always be used in the same direction; so that the sum of errors of the -whole circle must necessarily tend to tie, even if the division is to -a certain degree imperfect, provided also that the protractor used in -plotting is also kept in one direction. This plan has otherwise no -inconvenience, as any arc or angle may be taken by the difference of -the circle reading in any position in which it may happen to fall. -This does not mean that it is advisable to survey above ground by -the needle--it is quite otherwise. It is best to have some distinct, -sharply defined object to which all angles are referred, and therefore -called a _referring object_, as the general index. The magnetic bearing -need only be the initial position of the horizontal circle of the -instrument. - -473.--With larger, what are termed geodetic instruments, to be -described in the next chapter, constructive errors are not permissible; -but these instruments are observed under altogether different -conditions, which are suitable to the precision demanded. A large -theodolite is generally fixed upon solid rock, or masonry with good -foundation, or upon a very firm solid framed stand, and is protected -from wind, sun and rain. Where it is necessary on level ground to -elevate the instrument for more extensive view, a proper structure is -built, in which the theodolite is isolated from the outer walls or -enclosure carrying the stage upon which the observer works, so that -no vibration or deflection of this, caused by the wind or the weight -of the body, affects the instrument. Under such conditions angles are -read on various points of the circle by micrometer microscopes so as -to obtain a sufficient number of means, that personal and instrumental -errors may be reduced to a minimum. - - - - -CHAPTER X. - - LARGE THEODOLITES USED ONLY FOR GEODETIC SURVEYS--STANLEY'S 10- AND - 12-INCH--14-INCH ALTAZIMUTH--COLONEL STRANGE'S 36-INCH THEODOLITE. - - -474.--Large theodolites employed upon geodetic surveys. Where the -complete survey of a country has to be made, a system of large -triangles is formed over the country from convenient positions which -are naturally or artificially elevated so as to obtain distant views -with the telescope. These triangles are correctly measured by angles -subtended from a very carefully measured base or bases set out upon -approximately level planes, which are generally of a mile or more in -length. Where measurements are derived from such bases by constant -intersection of angular positions extended therefrom to large triangles -or other polygons, it becomes important that the theodolite employed -should measure such angles with great accuracy. In this case the -vernier reading does not possess sufficient refinement, and the -divisions representing the degrees have to be magnified to appear wider -apart, so that they can be more finely subdivided for the reading to be -taken by means of a micrometer microscope capable of subdividing the -divisions made upon the instrument even to single seconds of arc. The -theodolites used for the superior triangulation of Great Britain were -Ramsden's 36-inch and 18-inch, which, although constructed in the last -century, remain excellent instruments. - -475.--The construction of large theodolites is varied very -considerably according to the conditions present in the country to -be surveyed. This subject if carried into detail would extend much -beyond the intended limits of this work. This chapter will therefore be -limited to the description of a 10- or 12-inch instrument, and to two -historical instruments which have been used successfully for geodetic -work. - -[Illustration: Fig. 196.--_Stanley's 10-inch transit theodolite._] - -476.--=10- or 12-inch Theodolite.=--These instruments approach the -limit in size of portability for movable stations in triangulation. The -illustration, Fig. 196, is of the author's latest 10-inch model, the -patterns of which were made for a theodolite with vernier readings to -be used for the construction of a spiral tunnel through the Andes, now -completed. The object in its construction was to obtain great rigidity -with moderate weight. To this end the gun-metal of which it is made -is shaped out from castings as comprehensive in unity of parts as -possible. It has a framed mahogany stand (not shown) which is braced in -every way and provided with a very rigid head. In general construction -of the instrument illustrated it has a mechanical sliding stage and an -extra powerful clamp and tangent arrangement for the lower limb, the -adjusting screws being all covered to exclude dust. The circles are -divided to 5 minutes, and are read by micrometers to single seconds -of arc. Two vertical arcs are used, the second one carrying the clamp -and tangent arrangements, which also serves to balance the trunnion. -The 10-inch instrument carries a 16-inch telescope with 2-inch -object-glass, and the 12-inch instrument an 18-inch telescope with -2-1/8-inch object-glass. The tangent screws all act against springs to -avoid loss of time. - -[Illustration: Fig. 197.--_14-inch altazimuth theodolite._] - -477.--=14-inch Theodolite.=--For this description a modern instrument -is taken which Colonel A. R. Clark selected for illustration in his -excellent article on Geodesy in the ninth edition of the _Encyclopædia -Britannica_, to the publishers of which the author is indebted for the -illustration, Fig. 197. The instrument is a combination of a transit -theodolite with special arrangements as an altazimuth instrument -with fixed base, one side of the vertical circle being divided to -place the zero in a direction coincident with the polar axis. The -construction as a simple fixed transit theodolite for support upon a -pedestal in stone wherein the axis remains permanent for a principal -geodetic station, and therefore requires only a single setting to -bring it to true north and south for zero, renders change of position -of horizontal limb unnecessary for a permanent station. For this the -instrument is well adapted, and will be discussed here. The telescope -is of 18 inches focus, with 2 inches clear object-glass. The axis -pivots are of hard steel: one is perforated for illumination by a -lamp. The vertical circle is placed almost directly upon the side of -the telescope, and the tangent arm on the opposite side is of nearly -equal weight, so that there is no counterbalance necessary. There are -three Ramsden eye-pieces giving powers of 17, 35, and 54, and one -diagonal eye-piece. A level is attached inside the standard, divided -to read 10″ of arc: this has cemented ends, art. 177, and is enclosed -in an outer tube for protection. Two other exactly similar levels are -attached to the exterior axis of the instrument. The circle is divided -to 5′ of arc and reads by two micrometer microscopes to single seconds. -The vertical axis of the instrument is of steel. It is placed with -the apex of the cone upwards, and terminates on a triangular spring -with three adjusting screws by which any portion of the weight of the -upper part of the instrument can be relieved from the axis, so that the -whole instrument moves quite freely. The horizontal circle reads with -three micrometer microscopes on the upper circle to single seconds. -Originally the light was thrown down on the divisions by three ivory -cones placed over the fronts of the microscopes, as shown in the -illustration; but these have been changed in the present instrument for -concave swivelled reflectors, which may be set to any angle convenient -to throw sufficient light upon the circle. The microscopes are -supported from the body of the instrument upon hollow conical arms upon -the same excellent plan originally used by Ramsden. The microscopes -have adjustments in three directions, so as to bring them exactly into -place for trisection of the horizontal circle. The clamp and tangent -motion is placed directly upon the divided circle, and has adjustments -to secure freedom from strain; but this is not perfect--it is perhaps -the worst feature in the instrument, some modification of the plan -shown, Fig. 196, being much better for large instruments. - -The whole instrument is mounted on a tribrach frame, which is adapted -to stand upon a portable table or upon masonry. The screws have lateral -adjustment to prevent loss of time by wear. - -478.--It is a common custom with this class of instrument to make the -axes of hard steel. This plan is no doubt very satisfactory as it -leaves the optician's hands, but the author very much prefers good hard -bell-metal. When he saw the above described instrument at Southampton, -there was quite sufficient evidence of rust on the pivots to destroy -all perfection of centring, and this could scarcely have occurred -with bell-metal. Of course the brittleness of bell-metal would be -objectionable where the instrument might be subjected to severe jar -in carriage from place to place; but the author has obviated this by -a plan he would strongly recommend for general adoption--of having -the axis of good gun-metal, and to silver-solder a ring of bell-metal -thereon where the fitting surfaces occur. If the gun-metal is pure -it will bear the average reliable strain of hardened steel, which in -hardening and tempering is not with certainty always free from flaws; -and the average wear of pure bell-metal is perhaps quite as good as -steel. - -479.--=36-inch Theodolite=, Fig. 198, was designed by the late Colonel -A. Strange and constructed by Messrs. Troughton & Simms for the Great -Trigonometrical Survey of India. It is probably the most complete -and perfect theodolite ever constructed. The leading characteristics -of this important instrument only will be given. It has a horizontal -circle 36 inches diameter, and a vertical circle 24 inches diameter. -The telescope has a focal length of 36 inches: the aperture of the -object-glass is 3·25 inches. - -[Illustration: Fig. 198.--_36-inch theodolite--Great Indian Survey. -From a photograph._] - -480.--_The Stand_ has three massive mahogany legs _AA_ braced together -with horizontal and oblique wrought-iron bars _B_. Each leg is divided -vertically, and contains a long, gun-metal, square-threaded screw _C_ -which is made to rotate by means of a worm-wheel and endless screw -worked by a winch handle _D_, and capable of being firmly clamped -after adjustment at points about 15 inches apart _E_. The upper ends -of these screws are conical, and fit into three inverted radial grooves -formed in the lower side of a cast-iron circle or table, which is thus -supported by the three screws without being attached to them, and is -therefore free to accommodate itself to expansional changes without -restraint. The upper surface of the cast-iron circle is turned flat and -true to receive the tribrach of the instrument. The three screws _F_ -which pass through the side of this circle are intended to adjust the -centre of the instrument over the station mark. A lever _G_ also passes -through the side of the circle and actuates three rollers, which, when -in action, support the greater part of the weight of the instrument, -and so enables the horizontal zero to be set without difficulty. As -the instrument weighs over 400 lbs., it will be seen that some such -arrangement is absolutely necessary to enable it to be moved on the -cast-iron circle. When the correct position has been obtained, the -lever is thrown out of action, and the instrument remains immovably -seated upon its circular frame. - -481.--_The Foot Screws_ are tapped through the ends of the tribrach -arms in the usual way, but have a range of motion not exceeding 1/10 -inch. This range may appear small, but is really much more than is -required, as the upper surface of the cast-iron circle can be levelled -by the long screws in the mahogany legs before the instrument is placed -on it, so that not more than about 1/100 inch of motion is required. -The foot screws do not rest directly on the cast-iron circle, but on -the extremities of an intermediate three-armed plate, securely bolted -to the centre of the instrument, the distance between the tribrach -and the plate being about 1/10 inch. The object of this arrangement -is to obviate the disturbance of level and azimuth which arises from -clamping foot screws of the ordinary construction after adjustment, -as well as that due to looseness of the foot screws in the tribrach -arms. The arms of the spring plate, being of considerable width, have -great horizontal rigidity, but being comparatively thin are easily bent -vertically. The outer ends of the arms rest on the cast-iron circle or -stand; the foot screws pass through the tribrach arms, but not through -the spring arms. It is evident therefore that when the foot screw is -turned inwards with the screwing motion, the solid end of the tribrach -will be raised and the slit between the two arms widened; but since the -end of the screw does not rest on the stand, but on an intermediate -arm, which is actually a portion of the tribrach itself, it is clear -that if a lateral pressure be applied to the tribrach no motion will be -caused thereby, however loose the screw may be, so long as the pressure -is less than the lateral rigidity of the intermediate arm. The lateral -pressure caused by turning the instrument in azimuth when taking -observations is greatly within this limit. This plan is perfectly -successful, but it is only available where a moderate range of vertical -movement is needed. In the present instance, as the cast-iron ring -or stand on which the instrument is supported is always first made -practically level, the vertical range of the foot screws need not be -more than a small fraction of an inch. Another point with regard to the -foot screws is their delicacy and certainty of action. This is attained -by applying to them a clamp and tangent screw arrangement _H_ very -similar in principle to that sometimes applied to circles. Although -the foot screws themselves are rather coarse, having only about eight -threads to the inch, the arrangement is such that one entire revolution -of the slow motion tangent screw alters the level only about one second -of arc. Hence the foot screws in this instrument, though coarse and -strong enough to bear great weight are probably for the first time made -in keeping, in point of refinement, with its most delicate parts. - -482.--_The Horizontal Circles._--The inner or working circle is 36 -inches in diameter. It is very finely divided on silver to 5 minutes, -and is read by five equidistant micrometer microscopes to tenths of -a second of arc. It is fixed at the centre to the tribrach, but -everywhere else is perfectly free. The outer or _guard circle_ consists -of a second horizontal circle exterior to and concentric with the inner -circle. There is a space of about 1/10 inch all round between the two -circles, and the upper plane of the outer circle stands about the -same quantity above that of the inner or principal circle. The guard -circle is supported by radii of its own, quite independent of those of -the inner circle. This circle has several functions. It protects the -working circle from accidental injury; it helps to distribute changes -of temperature uniformly over the circumference of the working circle; -it receives the clamp and tangent screw, leaving the working circle -absolutely free from contact at all times; and it bears a strongly-cut -set of divisions, more visible to the naked eye than those of the -working circle, which are exceedingly fine, and therefore would be -inconvenient for setting the instrument approximately in azimuth. - -483.--_The Horizontal Tangent Screws._--It will be seen at _II′_ that -there are two clamps and two tangent screws to the horizontal circle. -It is necessary to have both, on account of the large size of the -circle. In use, of course, they are not both used at the same time. -In the present position of the instrument the clamp and tangent screw -on the left-hand side of the illustration would be employed; but on -reversing the telescope this clamp would be released and the one on -the opposite side made use of. It is necessary with this, as with -smaller instruments, to avoid loss of motion in the tangent screws. -Many methods have been employed to obviate this loss of motion, but -while they are suitable to small instruments they are not so effective -with large ones, such as that under consideration. The plan adopted in -this case is that known as the _divided nut_ principle. The block into -which the tangent screw is tapped is divided transversely and the two -halves are forced asunder, and therefore act against the contrary sides -of the screw threads by four internal spiral springs. The tension of -these springs is necessarily constant, and therefore not subject to -the disturbance and slow recovery of elastic force unavoidable in an -external spring. Means are supplied for regulating the tension of the -four springs, which must be a little in excess of the force necessary -to move the revolving mass, without taking the parts to pieces. - -484.--_The Vertical Axis_ is a truncated cone of steel with its base -downwards. It is about 6·5 inches high and 3·3 inches and 2 inches in -diameter at the base and summit respectively, the flange being about -4·5 inches in diameter and constructed on the isolated principle. The -vertical axis socket and the five horizontal microscopic arms are cast -in one piece of aluminium bronze, the elliptical table carrying the -telescope supports being bolted to the central boss in which the socket -of the vertical axis is formed. The vertical axis and the elliptical -table are both perforated in the centre so as to allow of a look-down -telescope being employed in adjusting the instrument accurately over -the station mark. - -485.--_The Telescope_ is furnished with two separate eye-ends, carrying -respectively a vertical and a horizontal parallel wire micrometer _J_. -It is also supplied with both bright and dark field illumination, the -latter being employed when faint stars are observed. The vertical -circle _K_ is divided on silver similar to the horizontal circle, and -is read by two opposite micrometer microscopes when the instrument -is used for terrestrial work: but when required for astronomical -purposes four micrometers can be used, and they can be shifted to any -part of the circle on which they are clamped. In the illustration the -four micrometers are shown in position. The two rods or handles seen -parallel with the telescope at _LL′_ are attached to the middle of the -transit axis where the telescope passes through it, and are intended to -raise or depress the telescope without touching it by hand. These rods -are also used for carrying adjustable counterpoises, the instrument -being so balanced in every part that the equipoise is as nearly -perfect as practicable through any diametrical section of the vertical -axis. - -486.--_The Spirit Levels_, both horizontal _M_ and vertical _N_, are -very delicate. They are constructed so that the divisions on their -scales represent as nearly as possible one second of arc. The scales -are divided to twenty per inch. The glass bubble tubes are mounted -on V bearings, and are kept in position by light springs in such a -manner that they are free to adapt themselves to changes of temperature -with perfect freedom. They are also enclosed in external cylindrical -glass covers to protect them from sudden changes of temperature. The -arrangements for adjusting the levels are such as to obviate strains -without risk of shake, and to ensure delicacy of action. - -487.--_The Five Micrometer Microscopes O_ for reading the horizontal -circle are carried by the same number of equidistant radial arms -branching from the central boss which carries the whole of the -instrument above the horizontal circles. These micrometers are made on -Robinson's principle, Fig. 199, that is, with a short bow spring _S_ -having a central nut tapped through it to keep the tension between the -bearing of the micrometer screw on the end of the outer box and the -slide which carries the webs constant with whatever part of the screw -may be in use. The radial arms each carry a vertical socket which is -bored out cylindrically to receive the microscope. These sockets are -slotted vertically, and have three clamping screws at the side to -hold the microscopes firmly in position when they are once adjusted. -The two webs in these micrometers are placed parallel to one another, -and at such a distance apart that when in proper adjustment they are -a trifle wider apart than the width of one line on the circle, as -shown in Fig. 200. The micrometer heads are divided into sixty parts, -and the whole is arranged so that in practice ten revolutions of the -micrometer screw traverse the webs over ten minutes of arc or two -divisions on the circle. Each division therefore on the micrometer -head represents one second of arc; and as the divisions are clearly cut -on silver and about one-tenth of an inch apart, there is no difficulty -in reading to the tenth of a second, which, on a circle of 36 inches in -diameter, is equal to the ·00000872 of an inch, or the three-thousandth -part of one division of the circle; this, as before stated, is equal -to five minutes of arc, or the ·02616 of an inch. The illumination -of the microscopes, or rather of the divisions of the circle, is a -most important matter. When such exact measures are to be taken it -is effected by means of perforated silver reflectors attached to the -micrometer arms and mounted quite independently of the micrometers -themselves. The axis of each reflector coincides with the axis of -its microscope. All the reflectors have both vertical and horizontal -movements, and are therefore readily adjustable to the best position -for securing effective illumination under the varying conditions in -which the instrument may be employed. - -[Illustration: Fig. 199.--_Robinson's micrometer._] - -[Illustration: Fig. 200.--_Webs of micrometer._] - -488.--_Relieving Apparatus._--It will be readily understood that the -moving parts of so large an instrument must necessarily be very heavy. -In this case the telescope, vertical circle, pillars, elliptical table, -horizontal micrometer arms, and vertical axis socket weigh nearly 300 -lbs. It would of course be impossible to take horizontal angles with so -much friction on the flange of the vertical axis as this weight would -produce, hence the necessity for some form of relieving apparatus. That -employed in this case is a system of forty spiral springs, each of a -definite length, which when adjusted support about 6·25 lbs. The spiral -springs are mounted on a flat ring in two circles with projecting pins -to keep them in position. The upper ends of the springs support a -steel ring with a circular groove on its upper surface, between which -and a corresponding groove in the outer part of the vertical axis -socket three equidistant, nearly frictionless steel rollers run; so -that by this means about 250 lbs. weight is taken off the flange of -the vertical axis, the remaining weight being sufficient to allow of -the instrument moving with the necessary freedom, and at the same time -giving all the stability requisite for accurate levelling. - - - - -CHAPTER XI. - - MINING SURVEY INSTRUMENTS--CIRCUMFERENTORS--PLAIN MINER'S - DIAL--SIGHTS--TRIPOD STAND--ADJUSTMENTS--HENDERSON'S DIAL--LEAN'S - DIAL--ADJUSTMENTS--HEDLEY'S DIAL--ADDITIONAL TELESCOPE--IMPROVED - HEDLEY TRIBRACH AND BALL ADJUSTMENT--REFLECTORS--CONTINENTAL - FORMS--THEODOLITE SOUTERRAIN--TRIPOD TABLES--STANLEY'S MINING - THEODOLITE--PASTORELLI'S AND HOFFMANN'S ADJUSTABLE TRIPOD HEADS-- - MINING TRANSIT THEODOLITES--STANLEY'S PRISMATIC MINING COMPASS-- - HANGING DIAL--HANGING CLINOMETER--SEMI-CIRCUMFERENTOR--MINING LAMPS. - - -489.--=Miner's Circumferentor.=--In the original form of theodolite, -as it was at first designed by Digges, open sights took the place of -the telescope. The sights in this case were extended on arms. The -compass-box, afterwards added, was placed over the axis and made as -free from obstruction as possible, so that the needle, upon which -general surveying formerly depended, could be read correctly by -placing the eye vertically to the plane of the horizontal circle of -division against which the needle read. After the introduction of -the telescope to the theodolite this old form of instrument took the -general designation of the _circumferentor_; and subsequently, being -best adapted to underground surveying, it became, with some slight -alterations, the _miner's dial_. - -490.--Upon this original circumferentor improvements have been made in -the various mining dials we possess, in all of which the large open -compass is still preserved. This prominence of the compass does not -indicate that the modern scientific mining engineer has any desire to -depend upon it for taking horizontal angles, but that in close and -tortuous workings it provides the nearest and often the only possible -means of taking angles having regard to the extreme difficulties of -observation of any kind. Where workings are open and fairly plane -the telescope and circle with vernier reading can be used, so that -at the present time the better instruments possess the means also of -taking observations of angular direction by vernier reading. Several -other very important factors specialize mining from ordinary surveying -instruments, which may be stated as follows:--1. That there shall be -means of shortening the tripod for work in strata of small depth. 2. -That the instrument shall be low and compact in itself, that the head -of the surveyor may be placed above it if possible, even in shallow -workings. 3. That great extent of adjustment of the compass-box to -horizontality shall be given in the fittings of the instrument, on -account of the difficulty of extending the legs at all times for tripod -adjustment and from the extreme inclination of the floor of the working -in some cases. 4. That it is desirable in mining survey instruments -that the telescope, if there is one, shall take sights at all angles -upon the surface of the earth in the locality in which the instrument -is used, as also about a vertical position, so as to be able to sight -lines from the top to the bottom of the shaft, or _vice versa_, to -set off angles in the same azimuth as those taken at the surface by -direction of stretched wires or otherwise. This last contrivance will -also give the means of sighting a perfectly vertical point beneath the -centre of the instrument placed at the top of the shaft, to make a -concurrent station below during ventilation, when the plummet would be -disturbed. The devices by which these various requirements have been -met more or less perfectly will go far to explain the specialities of -construction found in mining surveying instruments, which will now be -described, commencing with the oldest and most simple specialised form -upon which improvements have been made in many directions. - -491.--=Plain Miner's Dial.=--The original simple form of specialized -miner's dial is shown in Fig. 201. It consists of a compass, divided to -single degrees, read by a finely pointed edge-bar needle mounted on a -jewelled cap. The needle has a sliding rider placed upon it, art. 130, -so that it may be carefully balanced to horizontality in any locality -in which it is used. The divided compass is raised on a step, and the -upper surface of the needle is made to be quite level with the division -when the compass is horizontal. In erecting the instrument with the -needle correctly balanced, the compass may therefore be brought to -horizontality by the coincidence of the upper surface of the needle -with the plane of the divisions, without the necessity of having spirit -levels. - -[Illustration: Fig. 201.--_Mining dial._] - -[Illustration: Fig. 202.--_Cover to the same._] - -[Illustration: Fig. 203.--_Sight._] - -[Illustration: Fig. 204.--_Section of ball and socket joint._] - -492.--The compass-box is extended in one meridian, north to south, by -strong arms that carry a pair of sights hinged to turn down to the -surface of the cover for portability. The compass-box and arms together -are termed the _limb_. The limb of the instrument is mounted upon a -_ball and socket joint_ to be described. The socket is slotted down on -one side to permit the limb to be turned to a vertical position. In -this position the level shown on the front of the instrument is used -for levelling by means of the sights: this level is not, however, put -on all plain dials. - -493.--The cover of the compass-box, Fig. 202, is fixed on the box to a -given position by a stud and slot. It has an arc divided upon its outer -surface, which is centred from a small hole placed near the outer edge. -A line from the centre of the hole to the zero of the arc is made -perpendicular to the central indices of the sights. A piece of silk or -a horse-hair carrying a small plummet is fixed to hang from the hole. -By this means when the limb is turned down in the slot of the socket -and the silk or hair stretched by the plummet to permit it to hang in -front of the arc, it will then cut the divisions, and thus form a -reading index to the arc, giving thereby approximately the vertical -angle at which the sights are set to degrees. - -494.--The instrument is mounted on a simple jointed tripod to be -described. It will be seen by the above description that this -instrument is cheaply made, and is not designed for very exact work. -It is now giving way for more exact instruments, but it forms the -groundwork on which mining survey instruments are most generally -constructed. The height of this dial with sights erect is 11 inches; -weight, 6 lbs. Some of the separate parts above enumerated, which are -common to many other forms of mining instruments, will now be more -particularly described. - -495.--_Sights_, one of which is shown separately, Fig. 203, are common -to mining instruments. They are constructed essentially in two parts, -technically termed the _slit_ and the _window_. The _slit_ _A_ is a -narrow parallel cut made through the metal upon the inner surface -of the sight, which is turned towards the centre of the instrument. -The thickness of the metal is hollowed away on the outer side which -comes next the eye, so as to present a thin edge only for the sighting -slit, as shown in section at _A′_. In some instruments the slit is -formed of two thin plates fixed to the sight by screws in slots, which -render it adjustable both to width and position; this is the better -way if machinery be not used for cutting the slit. The _window_ _B_ -is an oblong opening, across which a hair wire or a thin plate placed -edgewise is fixed in line with the slit. The hair or wire is laid in a -deeply engraved line, so that it is in the same plane as the centre of -the slit. The ends of the hair are held firmly by drawing them through -small holes and fixing them therein by means of dry, conical, pinewood -pins pressed tightly in the holes. When a thin plate is used edgewise, -this is soft-soldered into the top and bottom of the window. In the -pair of sights the window of one sight is placed at the lower position -and the slit in the upper. In the fellow sight the positions of these -parts are reversed, the observation being always taken from the slit -through the window. The duplication of parts in each sight permits it -to be used in either direction. - -496.--_In the use of the Sight_ the point or object to be observed from -the slit should appear to be bisected by the hair in the window at the -same time that it appears to the eye to stand in the centre of the -slit. For this reason it is not necessary that the slit should be very -narrow. It is generally more comfortable to take the sight with the eye -at the distance of 10 to 12 inches in front of the slit to obtain clear -vision of it. In this case if it be made too narrow it shuts out the -field of view. - -497.--It is not quite certain that the old slit and window is the -best form. Many mining engineers prefer a pair of equal slits, one of -which replaces a window. In this case, instead of the wire covering -the object sighted in the use of the instrument, the object is made to -appear in the centre of the forward sight slit. In this construction -the sight apertures are made much narrower so that they do not cover -too much of the field of view. Excellent work is done with this open -form of sight, and its construction is much more solid than that of -having loose hairs. - -498.--_Universal Sight_, termed technically _hole and cross sight_, -consists of a small hole _C′_, Fig. 203, on the inner side of one sight -that is hollowed away on the outer side which comes next the eye, so -as to present a thin edge of the hole only. The fellow sight _C_ has a -hair cross placed centrally in a circular window. This is of occasional -use for sighting angles approximately in altitude and horizon -simultaneously; but the cross occupies so much of the sight space that -observation with it cannot be depended upon. - -499.--_Ball and Socket Joint._--This is shown in elevation Fig. 201 at -_F_, and in section Fig. 204 _F, D_. It is one of the oldest forms -of adjustment, and is common to many dials. When the clamping screw -_G_ is released the ball is free in its socket _F_ to move about its -centre, to the extent of the opening at the top of the socket, in -any direction. A _plug_ _E_, which really forms the lower half of -the socket, is screwed into the part _F′_ at the lower part of what -is technically called the _socket-piece_. The plug is turned upwards -by its screws so as to tighten the ball by means of a tangent screw -_G_ which works in a rack thread cut in a part of the circumference -of the plug, thus forming a _screw and cross screw_, which, as the -construction indicates, clamps the ball with great rigidity. There are -several other ball and socket arrangements; these will be discussed in -describing the special instruments to which they are affixed. The only -objection to this form is that it elevates the dial very much more than -others. - -500.--_The Tripod Stand of an Ordinary Miner's Dial._--The upper part -is shown in Fig. 205. This form of tripod is common to many dials. The -legs are made about 1¼ inches in diameter. The heads of the legs -are fitted directly without brasswork between the _book-plates_ _A_, -to which they are held by cross screws or bolts which form the joint -on which the legs move for extension. Unless the head be worked out of -the solid, the book-pieces are screwed to a plate that carries a male -plug centre to which the dial is fixed by a milled-headed screw shown -at Fig. 201 _L_. The plug is grooved at the position of the point of -the screw so as to permit rotation of the instrument when the screw -is slightly released. This tripod head remains permanently fixed to -the legs. Each leg is jointed to part in its centre by unscrewing, -to present when disjointed a metal point to hold the surface of the -ground, to form a short stand. The usual height of the full tripod -legs is 5 feet; the upper part only 2 feet 6 inches. The usual form of -joint is shown in detail in section Fig. 205. _C_ the male screw, which -is fitted to the woodwork by a socket and cross pinned to it. This -piece has a point at its lower end. _D_ the socket-piece is screwed -over the point to extend the leg when the tripod is required of full -length. The woodwork of this lower piece has a conical metal point to -bite the ground when it is set up in use. Occasionally for close work -shorter legs are provided, or the legs are jointed in three parts. In -the common dial shown, the legs are left exposed when out of use; with -superior instruments they are packed in a deal case that protects the -socket fitting to which the instrument is attached. Another much better -form of tripod will be discussed further on with the instrument to -which it is attached. - -[Illustration: Fig. 205.--_Jointed tripod legs of a miner's dial._] - -501.--_Examination and Adjustment of the Plain Miner's Dial._--The -tripod should be first set up to full length and each length separately -twisted to right and left to see that its socket fittings are good and -free from shakiness. The legs should each be separately pressed in and -out at its centre to see that the screws clamp the parts firmly and -are free from shakiness. The instrument should then be set up and its -socket fitting be felt to see that it is free from shake, and also be -turned round to see that it moves freely. The ball fitting should be -clamped and its rigidity be tested by fair pressure on the two ends -of the limb separately. The sights should be examined to see that -they are quite linear with hair and slit. The compass-box should be -levelled by the coincidence of the upper surface of the needle with the -plane of the division, and be reversed in every direction by turning -the compass-box, the reading being observed with the N. point of the -needle at N. E. W. S. to see that it bisects the graduation by angles -180° apart. The compass-box being level, the sights should be ranged -with an external object at a distance--a plumb-line is best--a piece -of string suspending a stone answers--to see that they are vertical, -and that they cut the same line with the position of the sights changed -fore to back. If the sights are coincident, but do not range with the -plumb-line, the needle is out of balance, and this may be corrected by -shifting the rider. - -502.--=Henderson's Dial.=--This is an improvement upon an old form -of circumferentor,[19] in which four sights are centred in opposite -pairs so as to revolve about the vertical axis, so that one pair of -sights may take any angle to the other pair. In Mr. J. Henderson's -dial the improvement consists in making the compass larger, the needle -being made to read by a vernier placed upon one end to 3′ of arc. Mr. -Henderson prefers plain slit sights instead of slit and window sights, -as before stated, which avoids the accidental derangement of the -horse-hair.[20] The instrument combines some of the parts of Lean's -dial, to be next described. Illustration of this instrument is given in -Mr. B. H. Brough's _Mine Surveying_. - -503.--=Lean's Dial.=--The inventor of this instrument was Mr. Joel -Lean, a Cornish mine manager, who was well known at the end of the 18th -century for his important improvements in mining apparatus. This dial -is still popular in Cornwall and other mineral districts. In general -construction the sights and limb on which they are mounted are the same -as in the plain dial just described, art. 491. The legs are also -the same--other parts are additional or modified. In the engraving, -Fig. 206, the sights and vertical arc with its telescope are shown -mounted together on the limb. This is done to show the relative -position of these parts: they could not in practice be used -simultaneously upon the instrument. They are separately attached to -the limb by the same pair of milled headed screws. As a general rule -the telescopic arrangement, which will be described further on, is -used above ground and the sight arrangement below. The details of -construction are as follows:-- - -[Illustration: Fig. 206.--_Mining circumferentor or Lean's dial._] - -504.--_The Tripod_--of the mining circumferentor, in common with -many other forms of dial, has the legs fitted directly between -_book-pieces_, which are fixed to the lower parallel plate, as shown -Fig. 206, thus dispensing with the separate tripod head, common to -levels and theodolites. Otherwise the parallel plates are similar to -those described for levels and theodolites, art. 193, and are used in -the same manner. The upper parallel plate in this dial carries the male -axis, which fits into a socket attached below the centre of the limb in -the manner just described for plain dial. The tripod stand, with its -parallel plates attached, is generally packed in a pinewood case when -out of use. The reason for attaching the legs directly to the lower -parallel plate instead of having a tripod head is that it saves the -extra elevation of the instrument by the depth of one screw fitting. -At the same time it must be observed that it exposes the axis to the -air by separating the instrument at this part when it is put by, which -renders the axis difficult to be kept lubricated and in smooth working -order. On the Continent and in America it is general to detach the legs -only, on a plan shown, Fig. 85, p. 140. This keeps the axis attached, -and is probably the better plan, although it may be found a little more -troublesome to erect the instrument. - -[Illustration: Fig. 207.--_Section of compass-box and axis of Lean's -dial._] - -505.--_Revolving Compass_ forms a part of Lean's dial and many other -dials. It is shown in section Fig. 207. As the axis is constructed in -this instrument, the socket-piece _A_ is ground to fit the male axis -_S_, and at the same time it is shouldered to fit the surface of the -parallel plate _T_ to prevent excess of friction on the axis fitting, -so that it may move easily to set the needle to magnetic north of the -compass-box if desired. The socket-piece is attached to the compass-box -through a collar. The compass has a step _D_ which is divided to -degrees on its inner edge to read to the point of the needle, and -similarly to degrees on its outer edge to read with a vernier scale, -shown _D_ to 3′. The vernier is set off on each side of the zero line -in ten divisions, which are figured 30, 45, 0, 15, 30, art 322, p. 184. -The upper surface of the needle is made level with the upper surface -of the step. The bottom plate of the compass-box is divided to 10°: -in some difficult positions in the use of the instrument this last is -the only reading that can be sighted. The compass-box, which carries -the vernier _B_, is fixed centrally on the arm plate. The arm plate is -centred upon a step fitting between the compass and the socket-piece, -so that it carries the whole superstructure of the instrument around -the compass, its relative position being read by the vernier. The -edge of the compass plate is formed into a toothed wheel, as shown -in section in the figure on the right-hand side, into which a small -wheel or pinion _R_ is fixed in a box upon the arm plate that works by -means of a large milled-head screw _P_. By means of this milled head -the instrument may be rotated about the compass, so that the line of -division on the compass step reading into the vernier performs the -functions of the horizontal limb of a theodolite. In this manner angles -may be taken by means of the vernier, quite irrespective of the reading -of the needle. When the compass is set to the zero of the vernier at -north (360°) it may be fixed in this position by means of a pin fitting -in opposite holes to the arm plate and bottom plate of the compass, -_not shown_; and when thus fixed the needle only is used as in the -plain dial. Between the collar-piece _C_ and the socket-piece _A_ a -wedge-shaped lift raises the needle off its centre by pressing in a -slide shown at _L_. - -506.--_The Vertical Arc_ is erected upon the limb as close as possible -to the compass-box, so as to leave room for a level to be placed -between the seatings of the arc and sights. The axis of this arc -is a simple hinge joint, brought down nearly to the surface of the -cover which protects the glass of the compass-box: this is done to -keep the instrument as low down as possible. The telescope, which is -of the same kind as that used for the theodolite, traverses the arc -tangentially, permitting it to be adjusted for reading the arc by its -vernier by means of a clamp and tangent motion at any position. The -arc is divided on one side into degrees, and reads by the vernier to -3′ in the same manner as the horizontal circle. On the opposite side -it is divided with a percentage scale of difference of hypotenuse and -base which reads to an index line. A spirit level is placed under the -telescope, in line with its axis, to which it is adjustable by means -of capstan-headed screws. The telescope when fixed is placed just -sufficiently above the arc to permit it to be brought to a vertical -position at 90°, or a degree or two over this, with the full aperture -of the object-glass beyond the extreme edge of the horizontal circle. -By this construction a bearing may be taken of any object upon the -surface from the top of a shaft, and a line may be sighted to the -bottom of the shaft in exact azimuth with this without changing the -horizontal adjustment of the instrument. In the same manner, if the -vertical axis be perfectly adjusted by the level on the vernier plate, -the telescope at 90° + _n_ will indicate a perfect vertical to the -station of the instrument above, the + _n_ being the allowance to be -made for the eccentricity of the telescope, provided the collimation -is perfect. If this is not perfect, the vertical may still be taken -accurately by means of three observations taken from equal division of -the entire horizontal circle, say at 360°, 120° and 240°. - -507.--It will be noticed that the vernier to the compass circle -comes directly under the vertical arc, therefore it can only be read -obliquely when this arc is mounted: with open sights the vernier can be -read directly. This is a defect in this instrument, as the vernier is -mostly required for exact work when the telescope is used. - -508.--Lean's dial possesses the qualities 1 and 4, pointed out in art. -490 as important to dials; in 4 the power of setting the telescope to -the vertical with great facility being the most important. This quality -has kept the dial a favourite with many mining engineers in mineral -districts for many years. Otherwise for general work the compass is -most inconveniently obstructed by the arc above it, and the instrument, -although, of course, of less height than the theodolite, some of the -functions of which it performs indifferently, is too high to be used -in shallow workings. The height of a 5-inch Lean's dial to the central -apex of the telescope is 9½ inches; to the top of the sights placed -in a level position, 8 inches; weight of instrument only, 6½ lbs. -The 6-inch instrument is about 1 inch higher, and weighs 1 lb. more. - -509.--A number of variations have been made in Lean's dial; but none -that the author is aware of has proved successful. In an instrument -of this class, designed by Mr. J. Whitelaw,[21] the vertical arc is -brought down to the compass-box by placing pivots on each side of the -box after the manner of Hedley's dial, to be next described. This -lowers the instrument about an inch, and is an improvement; but this is -effected at the expense of placing a striding bar across the compass -box, which is a great impediment to the clear sighting of the compass. - -Messrs. Newton & Son have made the telescope to detach from the arc of -Lean's dial to be placed directly upon the limb. In this way they claim -for it that it combines a miner's dial and dumpy level. The -arrangement appears to the author to make the instrument top heavy as a -dial, and to give too little power for a good level, added to which it -costs about the same as the two separate instruments of equal quality. -Of course any telescopic dial may be used as a level by clamping it at -zero. Practical surveyors generally object to compound instruments that -entail many loose pieces. These were a fashion in the middle of the -nineteenth century. - -510.--_Examination of Lean's Dial._--As regards the stand, sights -and parallel plates, particulars have been given upon the plain dial -just described. The revolving compass should be turned round by the -milled head _P_, Fig. 207, of the pinion wheel _R_ to see that the -compass-box revolves steadily at all points without disturbance of the -needle. It may also be particularly observed that the needle does not -oscillate at any part of the circle, to be sure that the compass-box is -quite free from iron. The vernier should be examined at four opposite -positions of the needle to see that the needle is truly centred and is -in accord with the vernier. The lifter should be tried to see that it -lowers the needle gently on the centre, and that it holds the needle -firm off the centre. The telescope should be set up and directed to -an object, and all parts of the instrument clamped and the needle -observed. The telescope should then be detached and the sights set up, -to see that they range fairly with the telescope. If they do not do so -the difference should be noted and treated as a constant in any case -of change from telescope to sights on the same survey. The difference -ought to be very small, otherwise the instrument should be returned to -the maker. - -511.--_The Adjustment of Lean's Dial_ is the same as that of the plain -theodolite, so far as this can be carried out; but generally the -adjustment is depended upon as it leaves the manufacturer. For the -general use of this and other dials some notes will be made further -on, but as regards vertical position and the taking of azimuth angles, -for which this dial is specially adapted, notes may be made here. - -512.--_To set a line in Azimuth with one taken above Ground._--This is -necessary where there is local attraction to the needle below, or there -is a suspicion of this, so that the needle cannot be depended upon -with certainty. The instrument is placed on staging over the pit and a -vertical is taken to its centre either by the means briefly discussed -art. 506 by the instrument, or by suspending a plummet, a ball, or a -bullet from the centre of the instrument by a thread and burning the -thread when the ball is free from vibration. The ball is allowed to -fall upon a smooth horizontal surface formed of earth or otherwise, -in which it makes a dent which will be vertical to the axis of the -instrument if the ball has not been deflected by ventilation currents. -Two lights, as distant as possible to be seen to range in line with -the dent, are placed at the bottom of the pit. The lights, if thought -desirable, may range north and south with the needle; but in whatever -direction this may be set the correct azimuth of this may be taken by -cutting them by the webs of the nearly vertical telescope of the dial; -and this azimuth may be correctly set out on the surface by a pole or -other station mark, or its true direction by a pair of these, one on -each side of the pit's mouth, the second station mark being set out -after a shift of the horizontal vernier exactly 180° on the circle. A -straight-edged flooring board painted white may be made to cut the line -from light to light, which is more definite for bearing than the lights -themselves. - -513.--=Hedley's Dial=, the invention of John Hedley, H.M. Inspector of -Mines, in 1850, has now become the most popular form of miner's dial, -modified, however, from its original form in various ways. The peculiar -feature of this form of dial is that the sights move upon a framework -centred upon a horizontal axis, so that they may by a rocking motion -take horizontal angles within a wide azimuth without obstruction to the -sight of the compass. - -[Illustration: Fig. 208.--_Hedley's dial._] - -514.--For consideration of the general features of Hedley's dial, the -tripod and the ball and socket are the same as that described for -the plain dial; but the socket is not cut down on one side to change -the position of the axis, as the compass-box in this instrument is -required to be kept uniformly level. The general appearance is shown -Fig. 208. For districts in which the working strata are fairly level, -parallel plates are put to this instrument in place of the ball and -socket joint. The compass-box revolves, as that described for Lean's -dial; but it is more general in this instrument to have a clamp and -tangent motion, as in a theodolite, than the rack and pinion motion. -Two levels for setting the compass horizontal are sunk into the plate -of the compass-dial low enough to miss the edge-bar needle. The step of -the compass is divided into degrees and the plate of the dial to 10°. -The vernier, which is placed on the opposite side of the box to the -vertical arc, reads to 3′, as described for Lean's dial. - -515.--_The Rocking Centre_ forms the peculiar feature of Hedley's dial. -From opposite points of the under side of the compass two pivots are -projected. These are set perpendicular to the vertical axis, which is -placed above the ball and socket. The pivots are placed central with -the vernier and in line with E. to W. of the compass when this is set -to _zero_ (360°). The pivots form the axes of a stout ring--_rocking -ring_--which surrounds the compass-box, with space sufficient to clear -it when the ring is rocked about its axis. The ring has two extended -arms which carry sights as shown. These turn down upon the compass-box -when out of use. One of the pivots is prolonged for about ¾ inch -beyond the outer circumference of the ring. The prolongation is made -generally of triangular section. This forms a fitting to the vertical -arc, which is attached by a milled-headed screw when required, the arc -being an encumbrance when this dial is used for making horizontal plans -only. - -516.--_The Vertical Arc_, with its index arm, forms a separate piece. -The arm is centred upon the arc with a ground fitting, which is -retained in its position by a collar fixed with three screws. The -arm-piece forms the axis, through the centre of which a triangular -hole is made to fit the triangular prolongation of the pivot, so that -the index arm remains fixed, and the arc moves with the rocking ring, -to which it is held by a pair of dowels. The arc is divided into -degrees on the outer edge of its surface, and a scale of difference -of hypotenuse and base upon its inner edge. The graduations read to a -single index line upon a fiducial edge carried down from an opening in -the index arm. - -Hedley's dial can be locked by a pin, which is attached to the under -side of the compass-box, so as to work by the compass only. The ring -can also be locked level with the compass by a sling _latch-piece_ so -as to convert it into a plain dial. - -517.--The great merit of Hedley's dial is that the rocking centre -permits a greater range of open sighting than any other; and the -instrument is very low, permitting its use in shallow workings. -Further, that it is a very strong instrument to resist accidents, and -is very portable. The height of a 6-inch Hedley's dial above the tripod -head, in a level position, is 9 inches to the top of the sights. Weight -of instrument, 7 to 10 lbs. - -[Illustration: Fig. 209.--_Hedley's dial with ball clamp._] - -518.--In the author's simple dial, Fig. 209, which is of a modern -form, the ball is clamped by a capping-piece over it moved to clamp by -two stout pins. This form gives a little less height and still holds -the dial firmly. The horizontal axis moves rather stiffly, so that no -clamp to the arc is required. It is a very cheap form of dial, but -substantially made. It answers for a small mine survey. - -519.--There have been many variations made and proposed for Hedley's -dial. Mr. Casartelli, of Manchester, places the arc over the centre of -the compass-box.[22] This plan is intended to make the rocking centre -firm; but the arc interferes a little both with the sights and the -view of the compass box. Messrs. Davis and Son connect wheel-work with -the arc, so as to magnify the scale of motion. Other less important -variations in Hedley's dial are common. - -520.--_Examination and Adjustment of Hedley's Dial._--The general -examination of the stand and of such parts of the instrument as -correspond with Lean's dial is the same as just given. The rocking ring -should be lifted and pressed down at each end alternately to see that -there is _no loss of time_ on the axis. The arc should be examined in -like manner. The dial should be set up in front of a plumbed line to -see that its sights range properly when the instrument is set level -by its bubbles. A point should be observed, say through the hole and -cross webs at the top of the sight; and with this point kept in view -the rocking ring should be moved upwards or downwards so that the -point traverses the plumb-line to the extent of the rocking motion. If -it does not do so, possibly the transverse level in the plate of the -compass-box may be adjusted to make it do so; but in this adjustment it -must be particularly observed that the balance of the needle remains -so that it still reads the graduation with its upper edge, and that -the sights traverse the same plumb-line when turned about, as it is -possible to set the level right with one pair of sights and throw other -parts out. There are no simple means of adjustment provided, so that if -the instrument is not accurate it should be returned to the maker for -correction. - -521.--=Improvement in Hedley's Dial=, _by Addition of -Telescope_.--Surface work being generally performed with the -theodolite, surveying with open sights following this cannot be -effected with sufficient accuracy; therefore there becomes a necessity -for the use of the telescope, which was first placed on this instrument -by the author at the suggestion of Mr. W. Preece, C.E. In mines, also, -although sights present often the only possible means of directing -angular positions in cramped and tortuous workings, on the other hand, -better work can very often be done and the telescope be conveniently -used. Under these conditions, this addition forms an important -improvement in the instrument, to be at hand to apply when desired. -The telescope of this instrument detaches exactly as with Lean's dial, -but the sights are made with an angle piece, so as to extend them to -a distance of about 12 inches apart for sighting. Fig. 211 is of one -cranked sight. The instrument illustrated Fig. 210 has parallel plates, -art. 193, p. 99, suitable for fairly level workings. A ball and socket -joint is sometimes fitted to this instrument in place of these. - -[Illustration: Fig. 210.--_Hedley's dial with telescope._] - -[Illustration: Fig. 211.--_Bracket sight._] - -522.--_The Telescope_ is placed on Y's, and is of exactly the same -form as that described for a plain theodolite. The Y's in this -instrument offer a great convenience for reversing the telescope for -back sights in range when the vertical axis is fixed. The level under -the telescope is sufficiently good to convert this instrument into a -level for drainage, etc., when the rocking ring is locked with the -compass. _Its examination and adjustment_ are the same as those last -given, except for the telescope, which is the same in all particulars -as that of a 5-inch plain theodolite. - -[Illustration: Fig. 212.--_Improved miner's dial._] - -523.--=Improved Miner's Dial.=--The illustration given, Fig. 212, is of -the form of dial introduced by the author, a part of the arrangement -only being of his own design. The telescope with Y supports is the same -as that just described, and the sights, _not shown_, are cranked in -the same manner as shown Fig. 211. The horizontal circle, instead of -being in the interior of the box, is placed on the exterior rim, and -reads with two verniers--not for correction, but for convenience of -reading in different positions. The compass is divided upon the upper -surface of the step to degrees, and in the same manner on the interior -cylindrical surface of the step. This last often permits the compass to -be read in a close working when the upper surface could not either be -lighted or sighted. This plan was used on old circumferentors.[23] The -plane of the compass is divided to 10° as usual. The compass adjusts -by clamp and tangent motion. The axis of the instrument is supported -upon a ball and socket arrangement designed by the author for roughly -bringing the compass to level, and a parallel plate adjustment for -final setting. The ball is fixed by clamping a pair of plates together -by a thumb-screw. Each plate is hollowed in the centre to hold nearly -half the ball. When fixed, the instrument is found to be very rigid. - -524.--A plan of clamping designed by the author to meet the conditions -of the tribrach system of adjustment of equal rigidity to that above -described, is shown in elevation, Fig. 213 _B_. In this the upper half -of the socket is screwed down outside the lower half socket by means -of three projecting handle pins. This is a somewhat neater arrangement -than that shown in Fig. 212. Either of the above-described ball -arrangements elevate the instrument, and are better omitted for close -working if there is a special adjustment in the tripod attached to the -instrument, as that to be described presently, which will be found -sufficient in most cases. The height of the instrument from the tripod -is about 6½ inches; weight, 11 lbs. for both parallel plate and -tribrach adjustments. - -525.--_Adjustable Tripod for Dials._--The author's improved form of -tripod is adjustable to all heights between 30 inches and 57 inches, -Figs. 213, 214. Each leg is formed of two stiff bars of mahogany, shown -in detail, Fig. 214 G of section, about 1¼ inches by 5/8 inch, and -a third bar or leg _G′_ of about 1¼ inches square, which slides -between the other two. The sliding surfaces are grooved and tongued -together in V grooves in the solid. Two strap-pieces of brass _SS′_ are -fixed near the ends of the bars. One of these _S′_ is firmly soldered -to a boss-piece that takes a thumb-screw, which has quite sufficient -power to hold the leg _G′_ firmly at any position of extension. It is a -rigid stand, which may leave the tripod head nearly vertical upon any -inclination of the floor surface. - -[Illustration: Fig. 213.--_The author's adjustable ball joint and -socket tribrach stand._] - -[Illustration: Fig. 214.--_Adjustment to leg of tripod._] - -526.--=Hedley's Dials, with Pastorelli's and Hoffmann's Ball -Arrangements.=--By either of these arrangements the ball and socket is -brought down close into the parallel plate adjustment so that the dial -is of less total height. Hoffmann's is now becoming the most popular -system, as practice has shown it to be the most perfect for mining -survey. By either of these arrangements the ball and socket is clamped -by the same screws that bring the instrument to final position. In -Pastorelli's arrangement[24] the socket is drawn down upon the ball by -the adjusting screws. In Hoffmann's[25] the ball is pressed up into -the socket, which is the exact mechanical equivalent. When the screws -are lightly clamped the ball can be moved with moderate force, or even -quite loosely by careful adjustment; and in either case, when the ball -is once set, care must be taken to keep pressure constantly upon it -during the final adjustment by the screws. The general arrangements -are shown in two Figs. 215, 216, which are taken from the drawings of -the respective patents. In Fig. 215, _va_, the axis of the instrument -terminates in a ball _e_ which works in a cup _f_. The axis has also -a portion of a ball of greater radius _b_ concentric with the lower -ball _e_. The upper parallel plate _d_ is cupped over this ball. When -the parallel plate is moderately free on _b_, the axis _va_ may be -set to any angle within the range of the central opening of _d_; and -as the friction upon _bd_ is greater than that upon _fe_, the axis -moves by the adjustment of the parallel plate screws _aa_. In Fig. -216 the action is precisely the same, except that the pressure is -upwards instead of downwards. In Fig. 215 there are springs _s_ under -the parallel plate screw heads to keep contact when the screws are -loosened. In Fig. 216 the spring is a plate under the screws _s_, the -action being the same in both cases. - -[Illustration: Fig. 215.--_Pastorelli's ball and socket adjustment._] - -[Illustration: Fig. 216.--_Hoffmann's ball and socket adjustment._] - -527.--Some objections have been made to this class of arrangement, over -the simpler one of clamping the ball independently and then adjusting -by the screws, as being more complex. On the other hand this compound -arrangement has the merit in underground instruments of being lower and -more compact, which is very important. The author has somewhat modified -the arrangements of Hoffmann's head, as shown in the engraving on next -page, to render it still more compact for mining instruments. - -[Illustration: Fig. 217.--_Improved Hedley's dial, mounted on -Hoffmann's head._] - -528.--In Fig. 217 an improved Hedley's dial is mounted upon an improved -form of Hoffmann's head. The whole arrangement is very compact, rigid, -and rapid in action. The height of this dial is 9½ inches; the -weight 8 lbs. for a 6-inch instrument, in aluminium 5 lbs. - -[Illustration: Fig. 218.--_Improved Hedley, with cradle ring._] - -529.--=Hedley's Dial with Cranked Rocking Centre.=--One defect of the -Hedley's dial, which in certain cases makes Lean's preferred, is that -with the rocking ring the sights cannot be brought vertical for looking -up or down a shaft. The author has devised a means of getting over this -difficulty by making the ring of cradle form, thus throwing the bearing -surfaces to sufficient height to cause the ring, when the arc is raised -to about 90°, to fall under the compass-box and its adjustments, Fig. -218. This dial presents possibly the greatest refinements of the Hedley -principle at the time of its patent, No. 9134, 1898. Since this date -the reviser has introduced a few further refinements as illustrated at -Fig. 219. - -[Illustration: Fig. 219.--_Stanley's improved dial._] - -This instrument has tribrach levelling with quick-setting spherical -lower plate, a sliding tribrach for centring over any desired spot, -and full clamp and tangent motions to both horizontal centres. The -dividing is upon silver on a 6-inch covered limb reading by two -verniers to single minutes, folding sights interchangeable with -telescope Y's, and this dial may be used upon any staging without its -stand. The somewhat peculiar shape of the cranked rocking ring is -necessitated by the movement of the sliding tribrach, which it has to -clear in all positions for reading vertical sights. - -530.--=Accessories Common to Hedley's Dials= are a vertical reflector -and a diaphragm illuminator. - -_Reflecting Cap._--One of the disadvantages of Hedley's dials over -Lean's was pointed out to be the impossibility of vertical sight where -the two last described dials are not used. Some years ago the author -devised a plan of obtaining this vertical sight by reflection by means -of a reflecting cap, Fig. 220, placed over the end of the telescope. -The cap is formed of a tube which fits the outer surface of the object -end of the telescope. This is prolonged sufficiently to lock it by a -dowel in correct position against revolution when the points that are -used for index in the diaphragm of the telescope are vertical. The tube -is cut in two and hinged to turn up, as shown in two positions _H_ -and _H′_. When turned up it leaves the tube open for direct vision. A -reflector _R_ is placed in the cap, and there is an opening below it -equal to the full aperture of the telescope. It is easy to see that -by this means a pair of lights or a line may be sighted up or down a -shaft, and the azimuth of its direction be reflected to follow a line -by slightly rocking the telescope upon its pivots. This may be done, -however, with more refinement if there is a clamp and tangent motion to -the vertical arc, which is placed only on first-class instruments. - -[Illustration: Fig. 220.--_Reflecting cap to miner's dial._] - -531.--_Illumination of the Diaphragm_ for observing the webs or a -point, may be conveniently effected underground by employing a conical -ring reflector in front of the object-glass. The aperture through the -cone leaves the field of the object-glass nearly free, as it is only -necessary that the cone should project in front of this for a very -small distance. This reflector is placed over the object end of the -telescope when it is required, just the same as the ray shade. The -vertical reflector, Fig. 220, goes on the same fitting. The reflector -Fig. 221 _R_ may be made of silver or platinum. A light placed anywhere -opposite this, and perpendicular to the axis of the telescope will -throw sufficient light to show the webs or point. Sometimes a simple, -plain mirror placed on an arm bent over to the centre of the front of -the object glass, in which the mirror stands at 45° to the axis, is -used; but this plan is not so good as that shown Fig. 221, as the light -has to be brought to face the mirror quite perpendicular to the axis of -the telescope, and this process is frequently difficult to accomplish -underground. - -[Illustration: Fig. 221.--_Conical reflector to illuminate axis of -telescope._] - -532.--=Continental Forms of Miner's Dials.=--On the Continent generally -sights have been abandoned for miner's dials. The telescopes are -usually of short form, with large object-glass and wide field of view. -The telescope is generally placed eccentrically, which permits the -instrument to be made of very low form. There is a certain amount of -disadvantage in the eccentricity of the telescope, as angles cannot be -taken direct from the centre of the instrument but this is compensated -for in the plotting by making each station a small circle equal to the -amount of the eccentricity of the instrument to scale, and setting -off angles tangentially to this, which may be done with a little more -trouble than that of plotting the angle from a point. - -533.--=French Miner's Compasses.=--Fig. 222 shows the simpler form of -this instrument. The needle is open and quite free from obstruction. -The telescope is centred about level with the compass-box. The -vertical axis has clamp and tangent adjustment. The transverse axis is -set entirely by hand as with the plain dial. The instrument is set up -level by its tribrach adjustment. The height with 5-inch needle in a -level position, without tripod head, is about 5 inches; weight about -11 lbs. without the tripod table. The extremely squat form of the -instrument permits its use in very close workings, with a short tripod, -if the workings are fairly level. It is used also as a cheap form of -surface surveying instrument, consequently it is not generally very -carefully made. As a good instrument of the class it cannot compete -with that to be next described. - -[Illustration: Fig. 222.--_French form of miner's dial._] - -534.--It will be seen by Fig. 222 that the instrument has no direct -connection with its stand or tripod. This is general with all French -and German instruments, even with theodolites and surveying levels, it -being the rule that the top of the tripod should form a kind of table -upon which the instrument is set up. The table is almost uniformly made -of wood, and is somewhat bulky and clumsy in construction, therefore -not very well adapted to mining surveying, particularly in wet mines. -Neither is the tribrach system of adjustment, unless it is supplemented -by some form of ball and socket arrangement, or with adjustable stand. -This subject will be further discussed in the description of superior -instruments presently. - -[Illustration: Fig. 223.--_French miner's transit survey instrument._] - -535.--=Miner's Transit Instrument.=--This is the _théodolite souterrain_ -of the French, and is of a construction very general throughout the -Continent--Fig. 223. The compass is placed clearly in view. The -vertical axis has a clamp and tangent motion to bring the compass to -exact bearing if desired, or to permit surveying with the compass only. -The axis has also a clamp and tangent screw to the exterior divided -circle, which reads with two verniers. The telescope is placed on the -side of the instrument, and has clamp and tangent motions to read -the vertical circle which the vernier traverses in transit. All the -divisions are made strong to be read clearly by lamp-light, either to -1′ or 3′ by the vernier, as desired. A second level is generally placed -on some part of this instrument at right angles to the one shown. The -instrument is balanced by a counterpoise weight to keep its vertical -axis in equilibrium. The height of an instrument with 5-inch needle -is about 6¼ inches; the weight without the tripod table is about -14 lbs. The tripod table is constructed in various ways by different -makers. - -536.--The value of the transit principle applied to mining instruments, -for taking back and fore sights for hanging lines in undulating strata, -by simply turning the telescope over on its axis, cannot be overrated -for exact work such as the telescope alone can perform. Further, with -this construction the inclination and difference of hypotenuse and -base for correction of the chain measurements may be taken. But it -is important in the use of this instrument to observe the side upon -which the telescope is situated at the time of observation, _right_ or -_left_. For this a column should be placed in the field-book. As a rule -fore sights are taken with the telescope _left_; back sights with the -telescope _right_, remembering that in plotting all angles are taken -eccentrically from the axis of the instrument, that is, tangential -to a small circle which represents the eccentricity of the telescope -according to the scale used in plotting. - -537.--_The Tripod Table_ of a superior class of Continental -instruments, whether this is used for surface or mining surveying, is -usually made with some form of adjustment to bring the upper surface -approximately level before setting up the instrument. In this case the -table is made a combination of wood and metal; and the only difference -between mine and surface tables is that in the former case there is a -jointed arrangement for shortening the legs, but not in the latter. The -table surface for superior work is generally adjusted to approximate -level either by a ball and socket joint or by a pair of knee joints -placed at right angles to each other, with clamps to hold it firmly -when adjusted. Radial V-grooves are commonly made for the points of the -tribrach, and a hole is sometimes made in the centre of the table for -suspending a plummet from the axis of the instrument. There are many -forms of tripod table in use, a modified form of one of which in metal -will be described further on in the chapter on plane tables. There are -certain merits in this table arrangement over connective stands, as the -table is convenient to set up fairly level, and the instrument need not -be exposed until the operation is complete. On the other hand there is -more risk of upsetting and injuring the instrument by accident when -loosely placed on the table. There are, however, schemes more or less -complicated to prevent this, as by a screw fixed in the tripod head -acting against a spring which draws the instrument constantly down when -attached, and other contrivances, none of which is perhaps equal in -simplicity to Everest's arrangement for the tribrach, Fig. 191, p. 273, -on this particular point. - -[Illustration: Fig. 224.--_Stanley's improved mining survey transit._] - -[Illustration: Fig. 225.--_Stand for the same._] - -538.--=Improved Mining Survey Transit.=--The author has modified the -form of instrument last illustrated, retaining the general principles. -In Fig. 224 the compass is made larger and reads in the inside of the -step as well as upon the surface, which is the only way in many cases -that it can be read in a close working. The reading of the horizontal -circle is placed nearly vertical, so that it may be seen clearly when -the instrument is near the roof of the mine. The vertical circle is -made smaller than the horizontal, as this circle, as a rule, is of -less importance, and it can generally be read more exactly from its -convenient position. The arrangement also permits greater freedom for -the use of the tribrach. The telescope is made with a much larger -object-glass than is usual, to take a wide field of view; therefore it -forms a good level. - -[Illustration: Fig. 226.--_Stanley's miner's dial sight._] - -539.--Two pairs of sights are placed upon the telescope, either for -roughly sighting an object or station, or to be used in difficult -positions. These are made on a new principle, shown Fig. 226. The -sights are placed in two windows, each of which is formed of a needle -point of platino-iridium. In sighting, the points are brought over each -other, the distant lamp or object appearing between them. A sharp point -gives much clearer definition than a hair, as it subtends of itself no -angle to the axis of the eye. _ab_ represent the pair of sights, _c_ as -they appear superimposed. This instrument is very conveniently fitted -with subtense points in the telescope, by which distances may be taken -with the author's staff, Fig. 105, p. 158, without actual measurement, -for the particulars of which see next chapter. The subtense points -are arranged to measure the staff either vertically or horizontally. -As a rule it will be found with this instrument better to take rough -positions first with the points, and afterwards by the telescope. The -instrument cannot be recommended universally for underground surveying, -but it is valuable under certain conditions in close strata. Its height -is 6 inches and weight 13 lbs. - -Fig. 225 is an ordinary tripod, like that used with a level. This is -preferred by many mining engineers as being firmer than any jointed -arrangement, and is sufficient for working in a seam of fairly equal -thickness. The legs vary from 9 inches to the full height, 5 feet 4 -inches. An ordinary set of three tripods would be 1 foot 6 inches, 3 -feet 6 inches, and 5 feet 4 inches. - -[Illustration: Fig. 227.--_Stanley's underground theodolite._] - -540.--=Mining Theodolite.=--This theodolite is of the most convenient -form for underground railways, Fig. 227. The telescope transits on -its axis to be brought to a vertical position. The vertical axis is -pierced so that about 10° of angle may read below the vertical most -conveniently by means of a diagonal eye-piece. The centre is supported -upon a sliding fitting so that it may be displaced about 1¼ inches -about the centre of the tripod and be clamped to its position. The -horizontal axis is pierced to permit the diaphragm to be illuminated -by a lamp. The tripod stand is fitted with sliding legs, if it is to -be used for mine survey, to adjust for irregularity of surface of -the ground and for low workings. The form of the instrument is very -compact, rigid, and portable. - -[Illustration: Fig. 228.--_Stanley's prismatic mining compass._] - -541--=Prismatic Mining Survey Compass.=--This arrangement is designed -by the author for very close workings. The entire depth of the -instrument being only 4 inches, any reading may be taken from one point -of view simultaneously with the observation. The 5-inch compass, Fig. -228, has a floating ring divided to half degrees, and the reading of -this is reflected through a prism so that it appears directly under -the fore sight, to be seen at the same time. The prism has a slight -magnifying power, so that by estimation a bearing may be easily taken -to ¼ degree or nearer. The principle of the compass is described art. -148, the prism art. 55; but in this case the prism is raised and has -a second lens under it, so that it forms a kind of prismatic Ramsden -eye-piece. This elevation of the prism permits sighting under a certain -amount of downward inclination, regulated by the height of the prism -and the length of the back sight, as well as the upward inclination -which is common to the use of prismatic compasses. The most important -feature in this compass is the mode of lighting, which is effected by -means of a large prism, Fig. 229 _R_, placed under the compass-box in -a square tube, and a small movable lamp to throw light into it, Fig. -228 _L_. The floating ring, Fig. 229 _C_, is made of celluloid, quite -transparent, so that the divisions upon it are clearly read through the -small window in the cover of the compass-box. The fore sight _W_ is -jointed in two folds _jj_, so that it extends the distance of sights -to about 10 inches apart in use, and yet folds away closely to the -compass for portability when out of use. On the near sight a cut is -made transversely to the slit. A second similar cut on the fore sight -is made level with this to take levels roughly. About 20° are set off -on each side of the cut on the fore sight, so that angles of altitude -may be approximately taken--although the instrument is not well adapted -to this. Two levels set at right angles to each other, to be used in -setting up the instrument, are fixed under the compass-box. Weight of -instrument, 4¼ lbs. without the tripod stand. - -[Illustration: Fig. 229.--_Section of prismatic mining compass._] - -542.--=Hanging Compass.=--A very general method of underground -surveying in mineral districts upon the Continent is by means of the -_hanging compass_; this instrument is therefore generally found in -catalogues of surveying instruments in France, Germany, and Italy. -The original hanging compass was invented by Balthasar Rössler about -1660.[26] It appears to the author to be a valuable instrument for -surveying in tortuous mineral veins where sighting is difficult. The -measuring line upon which it is used is either a hempen or copper -cord or a chain. The compass is hung upon the cord or chain, which -may be stretched to any point out of sight, and the compass will then -indicate the bearing of the line. In Germany two instruments are used -simultaneously--the hanging compass for taking the bearing, and a -clinometer, composed of a light brass semicircle graduated to degrees, -with a small plummet for taking the inclination. - -[Illustration: Fig. 230.--_Stanley's hanging dial._] - -543.--=Hanging Dial.=--Fig. 230 represents a modification of the -hanging compass designed by the author, by which inclination may be -taken simultaneously with bearing, if the dial can be suspended near -the centre of the line or chain where the catenary curve is parallel -with its points of support. - -544.--In the construction of the instrument a circle of brass about 6 -inches diameter, ½ inch wide, and 1/8 inch thick, has two arms -extended to 12 inches at the upper part, on the end of each of which a -hook is formed for hanging the instrument upon a cord or chain. Upon -the lower part of the circle a _fork-piece_, with a bearing clipping -the circle, is attached by two screws. The fork-piece is constructed -to support two axes concentric to the vertical circle, in which the -compass-box is suspended much above its centre of gravity, so that it -falls by its own weight in use to a level position. Upon the edge of -the compass-box an index is brought up nearly to the interior surface -of the vertical circle, which reads into graduations upon this circle -into degrees and half degrees. - -[Illustration: Fig. 231.--_Hanging clinometer._] - -545.--=A Light Hanging Clinometer=, Fig. 231, shows the kind that is -used in Germany, of 5 inches diameter, graduated to degrees, made -of thin brass. It is packed in the case with the hanging compass, -described art. 542. The ends of the semicircle are formed into hooks -for hanging on the line. The plummet has a horse-hair line, which cuts -the degrees. The clinometer may be used only when the hanging dial Fig. -230 cannot be suspended near the centre of the line, in which case -this light semicircle will cause less deflection of the line, and give -the inclination approximately. For further details of the use of the -hanging compass the reader is referred to Mr. B. H. Brough's admirable -work on _Mine Surveying_. - -[Illustration: Fig. 232.--_French semi-circumferentor._] - -[Illustration: Fig. 233.--_Tripod head._] - -546.--=Semi-circumferentor.=--This simple instrument can scarcely be -enumerated with mining surveying instruments, as it is much more used -for surface work; but being of the class of circumferentors to which -miners' instruments generally belong, this is the most convenient place -for its description. It has very general use on the Continent. Its -construction is very simple, Fig. 232. It is supported on a ball and -socket joint. The socket is formed in two pieces, which are clamped -together to hold the ball by a winged-headed screw. One pair of sights -is mounted upon the extreme ends of lugs upon the limb. The limb is -divided to half degrees. When the ball is loosely clamped the fixed -pair of sights may be adjusted to cut any desired object. A second -pair of sights is jointed upon an axis to move centrally between the -first pair. These are made shorter to pass within the first pair to -any angle around the arc, except the small angles with which the -sights themselves interfere when they are superimposed. The movable -sights carry verniers to read on the limb to 2′. There is a small -compass attached to the limb. As a cheap instrument for taking angles -approximately it is very useful, particularly for workmen employed -in carrying out work from drawings plotted from a survey by a better -instrument. The weight of the instrument with 6-inch circle is about 2 -lbs.; height above tripod, 7 inches. - -547.--The tripod of this instrument is made of wood. The head is shown -Fig. 233. The legs are simply extensions of the upper parts, which are -shown attached with bolts. The point of each leg has a steel shoe to -prevent it slipping in use. The head is turned to a cone, which fits -into the socket-piece of the instrument and permits it to be rotated -with moderate friction. The head is made of triangular section that -the legs may be clamped firmly to it. When used for underground work a -separate set of short legs is provided, which attach to the head by the -same bolts. - -548.--=Lighting Underground.=--The old underground station, formed of -a lighted candle or lamp, is not now considered good in practice where -surface land is exactly defined by boundaries held by legal clauses and -rights. The system of underground surveying now very generally followed -is that first recommended by Mr. Thomas Baker, C.E., and afterwards -fully developed by Mr. H. Mackworth,[27] by which a station taken for -angular directions is formed by the position of the centre of a tripod. -For this system three tripods are provided for each instrument, with -head adjustment complete. These tripods are made in such a manner that -the instrument can be placed on any one of them in a level position. -Two lamps are provided, the flame of either of which will take the -position of the vertical axis of the instrument when the lamp is placed -upon the tripod formerly occupied by it. It is easily seen that by this -system fore and back sights or angular positions can be extended with -all the accuracy that the uniformity of the flame of the lamp will -permit. - -549.--=Mining Survey Lamp.=--The author constructed this lamp from an -idea given to him by Mr. Geo. Kilgour, C.E., Fig. 234. It is somewhat -different from the ordinary form. Its accuracy does not depend upon the -regularity of the flame. A vertical axis is formed under the lamp, -which is made to the same fitting on which the mining survey instrument -is placed. The lamp is placed entirely eccentric to the vertical axis -in such a manner that a vertical line formed by a wire upon its face -may stand central and linear with the axis. A cross line is also placed -at the same height above the tripod head as the centre of the axis of -the telescope or cross sight. By this means, although the lamp throws -its light broadly in one direction only, the cross is a perfectly -defined object, easily picked up and brought to exact bearing in the -instrument when placed upon another tripod. In converting this lamp -from a fore to a back sight it has simply to be turned half round -on its axis, which is done without any displacement of the relative -position of the cross in vertical or horizontal directions. Where this -lamp is required in mines liable to fire-damp, it is made on the safety -principle of the Davy lamp. - -[Illustration: Fig. 234.--_Mining survey lamp._] - -Electricity has been applied to lamps for surveying. This plan has -been found successful where a secondary battery is used that can be -charged by a dynamo upon or in the mine, or with some of the modern dry -batteries. - -[Illustration: Fig. 235.--_Stanley's complete mining outfit._] - -550.--=Mining Targets.=--The three tripod system has been much -improved by the introduction of accurate targets made specially for -the instrument used, and interchangeable with the instrument on -either stand. The reviser has designed several forms of these. They -are generally used with a mining theodolite for high-class mine -surveying, and the lower part is similar to the lower part of the -theodolite they are used with. Instead of a horizontal circle, they -simply support a plate carrying cross levels, and a pillar carried up -to bring the target level with the optical centre of the telescope of -the theodolite; this part is made to fit the outer centre of the lower -part into which it is held by a special clamp. The theodolite is made -with a double outer vertical centre, and this is held to the lower part -similarly clamped, so that the theodolite and targets all lift out of -their centres and interchange with each other. A complete mining set -of this description is shown at Fig. 235. This forms a very complete -mining outfit. It consists of a highest-class tacheometer with quick -setting spherical lower plate, mechanical centring stage, auxiliary -top and side telescope, illuminated axis, striding level, also two -targets with quick setting spherical lower plates, mechanical stages, -cross levels, and swivelled sighting crosses. All three are made with -lift-out centres, which are interchangeable, and all have base plates -permitting their use on any staging or fixing without their stands. The -targets are sometimes made to hold candles instead of the swivelled -cross, and sometimes with plain steel points only. - -The auxiliary telescope is the special form designed by Mr. Dunbar -Scott, and it embraces all the advantages and eliminates all the -disadvantages of all other types. - -The particular feature is its interchangeability with top or side -positions, and the means provided to ensure perfect adjustment with -the minimum of trouble, thus forming a mining transit which will -perform with exactness all the complex functions in mine surveying and -requiring no correction for eccentricity. - -The auxiliary telescope is provided with a centre that may be screwed -to the threaded extension of either the transverse axis or the vertical -pillars of the main telescope. In either position it is clamped firmly -and ranged quickly into alignment with the main telescope by two -opposing screws. The diaphragm of the auxiliary telescope has one web -only, so placed that it is vertical when on the top and horizontal when -at the side. - -[Illustration: Fig. 236.--_Stanley's Dunbar Scott auxiliary._] - -The observation of steep horizontal angles is made only with the -auxiliary on top, and of precipitous vertical angles with the auxiliary -on the side. A counterpoise is provided, which exactly balances the -auxiliary, so that there is no strain upon the instrument. - -For vertical sighting it is also most useful and accurate, as by -transferring the lines of both positions of auxiliary two lines are -transferred down a shaft, at right angles to each other, which, if -produced, will intersect each other exactly under the centre of the -instrument, and no allowance or calculation whatever has to be made to -ascertain the centre. - -The whole attachment adds very little to the weight, the greater part -being of aluminium, and it is packed separately in the case so as not -to interfere in any way with the instrument when not in use. - -In Fig. 235 the auxiliary telescope is shown at top; Fig. 236 shows it -attached at the side. - -551.--=Pocket Instruments.=--A very light pocket instrument has been -designed by Mr. D. W. Brunton, which will be found useful; he terms -it a pocket mine transit, but of course it has nothing to do with a -transit. It is designed for roughly taking horizontal and vertical -angles, and answers the purpose of a prismatic compass, clinometer and -Abney level, and is very portable, made in aluminium, and weighing only -8 oz. It is shown at Fig. 237. - -[Illustration: Fig. 237.--_Pocket mine transit._] - -The cover is provided on its inside with a mirror, and this acts as a -back sight; it is opened out to an angle which reflects the fore sight, -and the object sighted and the reading of the needle is then taken. It -is necessary to hold the instrument firmly against the body and see -that it is level sideways by placing the spirit level across the box -and bringing the bubble to the centre of its run, while any turning -movement should be made by turning the body from the hips. For vertical -sighting the fore sight is used as the back sight, and the mirror in -the lid moved to reflect the bubble, the back sight being formed by -the hole in the mirror seen at the bottom of the centre line, the -clinometer bubble is then moved till the air bell is seen in the centre -of its run and the vernier reading taken. - -552.--=Dip Compass.=--This consists of a magnetic needle suspended -between centres so as to move readily in a vertical plane, and is -shown at Fig. 238. When in use the ring is held in the hand and the -compass-box by its own weight takes a vertical position; it must then -be held in the plane of the meridian. In this position the needle when -unaffected by the attraction of iron assumes a horizontal position. -When brought over any mass of magnetic iron ore it dips, and thus -detects the presence of such ore with certainty. - -[Illustration: Fig. 238.--_Dip compass._] - -If held in a horizontal position it serves as an ordinary pocket -compass and thus indicates the magnetic meridian in the plane of which -it should be held when used to ascertain dip. - -FOOTNOTES: - -[19] Plate xiv., fig. 5. _Geometrical Essays_, Geo. Adams, 1803. - -[20] _Proc. Min. Inst._, Cornwall, 1883, vol. i. p. 317. - -[21] Patent No. 1592, April 1878. - -[22] Patent No. 1857, J. L Casartelli, May, 1874. - -[23] Illustrated plate xv. Fig. 1., _Geometrical Essays_, John Adams, -1803. - -[24] Pastorelli's patent, No. 2714, 1863. - -[25] Hoffmann's patent, No. 2084, 1878. - -[26] _Geometria Subterranea_, Voitel, 1686. - -[27] _Subterranean Surveying_, Thos. Fenwick, Lockwood. - - - - -CHAPTER XII. - - INSTRUMENTS TO MEASURE SUBTENSE OR TANGENTIAL ANGLES TO ASCERTAIN - DISTANCES--HISTORICAL NOTES OF THE METHOD--PRINCIPLES INVOLVED-- - STADIUM MEASUREMENT, DIRECT AND BY THE ORDINARY TELESCOPE--CORRECTIONS - FOR REFRACTION OF THE OBJECT-GLASS--STANLEY'S SUBTENSE DIAPHRAGM-- - ANALLATIC TELESCOPE OF PORRO--TACHEOMETERS--STADIUM--FIELD-BOOK-- - OMNIMETER AND ITS FIELD-BOOK--BAKEWELL's SUBTENSE ARRANGEMENT. - - -553.--=Direct Subtense Measurement of Distances=, _by an Instrument_, -depends upon our powers of measuring the image of a distant staff or -stadium, or the divisions marked thereon as they appear at the focus -of the telescope. If the stadium is placed at right angles to the -direction of one of two sight lines which subtend a given angle, the -number of units divided upon the stadium cut by these lines will be -proportional to units of length of base or cotangent for a constant -focus of the telescope; so that if we can measure at a fixed angle the -number of equal units of measurement of a stadium correctly, we can -obtain its exact distance; and whether this method is more or less -exact than chain measurement will depend entirely upon the perfection -with which either of these operations may be practically performed. - -554.--_The Origin of the Invention of Subtense Surveying_ was thought -to be due to Wm. Green, an optician of Great Moulton Street, London, -who was awarded a premium for its invention by the Society of Arts -in 1778. He published a pamphlet giving a description of his method -in 1778.[28] This subject he pressed upon the notice of professional -men at the time, and his method has continued in use in this country -ever since. His refracting telescope, which alone has remained in use, -formed part of the theodolite. A micrometer was placed in the focus -of the eye-piece of the telescope, which revolved a quarter turn in -its axis to read angles vertically or horizontally. He constructed his -micrometer with lines fixed at a given distance apart, and by a second -method with the lines adjustable. For this adjustment a fine line -was ruled upon one side of two pieces of glass. The ruled sides were -placed face to face, so as to be at the same focus. One of the lines -was adjustable by a micrometer screw. His staff was 20 links in length -by 4 inches in width, divided decimally into 1000. His description of -the manner of using his instrument will give a general idea of working -the others which have been derived from it--tacheometers, omnimeters, -etc.--and this is worthy of note, as the invention, though generally -attributed to him, was not his:-- - -555.--"To find the contents of a field with either of the instruments -described, let the telescope be placed so that the observer may see -all its angles from his station. If near the centre of the field -the better. The person who carries the scale (_staff_) is to go all -round the field, stopping at every angle, and to place the scale at -right angles to the axis of the telescope (_passing_) from corner to -corner (from right to left if required) with the help of a signal -by the observer. After the distances all round the field are taken -(_by measurement of the image of the micrometer_) and all the angles -included betwixt them, with the theodolite, plot it out in the usual -manner, _e.g._, with a nonius protractor. Describe a circle, and on -this circle set off all the angles from the centre through each point -upon the circumference. Set off the length of every line by a scale -of equal parts. These points will give the limits of the field, which -may be laid out in trapeziums, triangles, etc., and measured from the -same scale of equal parts. The surveyor will comprehend how easily the -contents of the field are found by trigonometrical calculation, since -by this method there are two sides and one included angle given. - -"The common method of measuring with the chain, besides the -inaccuracies to which it is liable, does only give the length of the -surface of the ground between two objects, and therefore not its proper -distance, unless the surface be straight and no object to hinder its -being measured from one end to the other. How often this is practicable -I leave to the consideration of those who are most accustomed to -measure lines, and doubt not that upon the whole they will find -the telescope method has besides ease, accuracy, and universality, -necessity itself to recommend it." - -He points out the utility of the system for levelling, as "both -distance and inclination may be taken at the same time." He finds by -experiment that the accuracy of the method exceeds that which he could -reasonably expect by calculations deduced from theory, by several -circumstances in its favour being inseparable from it. - -"The observer's station is the centre of circle whose radius is the -distance required, which is obtained by measuring the length, that is, -the tangent or subtense, of the small arcs whose limits are defined -by viewing their image in the focus of a telescope between two points -there placed, and moving them up and down until they appear to touch -the very extremities of said limits exactly. The manner of seeing is -natural and by practice will become habitual, and therefore continually -approach nearer to perfection. - -"Thus may any surveyor in less than two hours take all the dimensions -of an irregular polygon necessary for obtaining its area, if it be as -much as 80 or 100 acres and limited by twenty or thirty unequal sides." - -Green points out that if the subtense angle is taken horizontally, -atmospheric refraction error is eliminated. He proposes to use both -reflecting and refracting telescopes. With the reflector he possibly -obtained accurate results, but with the refracting telescope he does -not appear to have recognised a constant correction which is necessary -and important. - -It has since been found that in 1778 the Danish Academy of Sciences -awarded a prize to G. F. Brander for a similar device, which he had -applied to his plane-table, six years before. Its real discoverer was -James Watt, who used it in 1771 for measuring distances in the surveys -for the Tarbert and Crinan Canals. In James Patrick Muirhead's _Life of -James Watt_, he gives a statement by Watt himself that he constructed -his instrument in 1770 and showed it to Smeaton in 1772. - -556.--=Subtense Instruments=, as that originally made by Green, are -of some form of theodolite, the telescopes of which are constructed -to measure either the angle subtended by the chord of a small arc -or the tangent of the same. For convenience the tangent is more -generally taken upon a graduated stadium or staff, which is erected for -measurement perpendicularly to the horizon, the principle of which is -shown in the following scheme:-- - -[Illustration: Fig. 239.--_Diagram of tangential angle measurement._] - -Let _AC_, Fig. 239, be a horizontal line; _BC_ a stadium set up -vertically. Then if the angle _BAC_ and the height _BC_ are known, -the distance of _AC_ can be easily calculated. For any intermediate -distance between _A_ and _C_ a vertical will be in length proportional -to this distance. Let _de_ be at one-third the distance from _A_; then -the line _de_ will be one-third the length of _BC_. If we divide _BC_ -into three parts and place the stadium at _fg_ two-thirds the distance -from _A_, the angle _dAe_ given by an instrument subtending a fixed -angle will cut the staff at the second division, equal to two thirds -the staff, which demonstrates the principle of all tacheometers, Cleps, -etc. - -If the tangent be made a constant equal to the length of the stadium -_BC_, and this stadium be placed at another position, say _de_ or _fg_; -then the angle subtended by its entire length will vary in a manner -that can only be estimated by trigonometrical calculation. - -In case of reading two distant marks on the stadium only for the -subtense, the single central web of the telescope being directed first -to one and then to the other of these webs, the distance is calculated -as follows:-- - -Given the tangent _BC_ and the angle _BAC_, required the distance _AC_. -Let the angle _BAC_ be represented by _D_; then-- - - _CA_ / (_CB_) = cotan _D_, or _CA_ = _CB_ × cotan _D_. - -Reducing by logarithms, we have-- - - log _CA_ = log _CB_ + _L_ cotan _D_ - 10. - -For example, make _CB_ 14 feet, and the angle _D_ 2° 45′ 50″, thus:-- - - log _CB_ = 1·146128 - _L_ cotan _D_ - 10 = 1·316265 - ---------- - log _CA_ = 2·462393, or _CA_ = 290 feet. - -The above gives the principles followed with instruments of the -theodolite class simply; but arrangements are made in omnimeters and -similar instruments to read the tangent directly and determine the -height _CB_ in equal parts, so that observation of the heights _BC_ -gives rectangular co-ordinates and thus saves reduction from degrees of -arc. - -In practice the staff or stadium is made of the greatest length -convenient for portability. With a telescopic staff, 14 or 16 feet is -commonly used. If a unit tangent be not employed, the foot is divided -into 100 parts, each of which parts, with the tacheometer, represents 1 -foot of the base, and the whole staff 1400 or 1600 feet. The ordinary -Sopwith staff, art. 263, answers the purpose, but art. 268 better. - -557.--_Measuring Distances by the Ordinary Telescope by Measurement -of its Focal Image._--When we apply a refracting telescope to measure -a subtense angle by webs fixed in the diaphragm, vision is not direct -as in the scheme Fig. 239, but subject to bending caused by the -refractive quality of the lens, art. 58, the telescopic focus varying -with the distance from the staff. Thus with a 12-inch telescope there -will be a difference of about ·25 inch in the focus, whether the staff -is held at 50 or 500 links from the telescope; and this difference -of focus is equal to a difference of base or cotangent between the -points _A_ and _C_ in the last figure, so that these distances do not -remain proportional to the fixed unit of the tangent or stadium. It is -important to go carefully into this subject of the use of subtense webs -in the ordinary telescope, as the necessary correction does not appear -to have been recognised by English writers on instruments, and no doubt -this is the principal reason that subtense measurement has not been -more practised in this country. - -558.--At the commencement of the last century, Riechenbach, a Bavarian -engineer, pointed out a method still in use on the Continent. The -author is indebted to the kindness of Lord Rayleigh for the following -demonstration of Riechenbach's formula:-- - -[Illustration: Fig. 240.--_Subtense diagram._] - -Let Fig. 240 _AB_ = _s_, _ab_ = _i_, _OA_ = _d_, _Ob_ = _r_. _O_ is the -optical centre of the object-glass; _ab_ a pair of webs at variable -distance _r_ from _O_ according to telescopic focus; _f_ focus for -parallel rays. Then by similar triangles _s_/_d_ = _i_/_r_ or _d_ = -_rs_/_i_, _r_ is found by optical laws to vary in the proportion of -1/_r_ + 1/_d_ = 1/_f_. We may therefore eliminate the variable _r_ by -substituting its value _r_ = _fd_/(_d_ - _f_), by which we find _d_ = -_sf_/_i_ + _f_, which gives the true correction; and the distance from -the axis of the instrument will be _d_ = _sf_/_i_ + _f_ + _c_ where -_c_ is the constant distance of the object-glass from the axis of the -instrument. It is usual to place the vertical axis of a theodolite -central between the object-glass and the diaphragm at solar focus, so -that the constant _c_ becomes _f_/2. - -It is seen that _sf_/_i_ represents the direct subtense, whereas the -refraction, which is a constant, gives f and the position of the -object-glass _f_/2. Riechenbach's formula being true for parallel rays -is evidently also true for any subtense with refraction for the staff -at any distance. We may therefore adopt a plus constant of 1½_f_, -which added to the apparent subtense is found to produce no error. Thus -with a telescope of 1 foot solar focus, and using the decimal system -of notation, as before mentioned, if a stadium or distinct scale be -placed at 301½ feet distance from the centre of the instrument, -and the webs or points of the diaphragm be adjusted to read 3 feet = -300 divisions, every subtense may afterwards be taken as number of -divisions read + 1½ feet for distance in feet. If the subtense is -to be taken in links or metres the dividing of the stadium will be to -these measures, but the constant remains the same 1½ feet always. - -559.--When the line of sight is inclined from the horizon and the -stadium is held erect--a convenient method commonly followed upon the -Continent--the reading becomes in excess of the true reading, in the -ratio of the cosine of the angle of the stadium, represented by a line -tangent to the sight-line subtended to the foot of the stadium, as -shown in the following diagram. - -[Illustration: Fig. 241.--_Diagram of vertical stadium on an incline._] - -Thus, Fig. 241, let the portion cut by the lines _AB_, _S′_ be the -reading of the stadium; then - - _S′_(cos _a_) = _S_. - -The inclined distance is then equal to - - (_f_/_i_)_S′_(cos _a_) + _f_ + _c_ - -and the horizontal projection of that distance or - - _a_ = ((_f_/_i_)_S′_(cos _a_) + _f_ + _c_)cos _a_; - -or as _f_ + _c_ is small and the angle generally small also, _f_ + _c_ -may be taken equal to (_f_ + _c_) cos _a_. Then - - _a_=(_f_/i)_S′_ cos^2 _a_ + _f_ + _c_. - -[Illustration: Fig. 242.--_Stanley's patent subtense diaphragm._] - -560.--=The Subtense-diaphragm= of the author, Fig. 242, forms the -eye-piece of a theodolite. It has movable indices which are separated -according to a scale formed by calculation upon the data of the above -formulæ. By this, distances may be taken in the horizontal plane for -land of any inclination without after calculation. This result is -obtained by observing the angle of inclination upwards or downwards -on the theodolite and setting the micrometer to this angle before -reading the subtense distance. The reading is taken by points which -are arranged to measure the subtense 1 to 100, so that the ordinary -Sopwith staff may be used. The diaphragm at zero appears as an ordinary -subtense-diaphragm. It may be observed that this diaphragm may be used -as a good check, as distances may be taken over any irregularities of -intervening incline and give the true base for the entire distance. - -561.--If the mean contour distance is required from station to station, -this may be taken directly by subtense from the staff-reading held at -right angles to the axis of the telescope. The means of doing this, -devised by the author, is to place a _sight director_ of a special form -upon the side of the staff, Fig. 243. This small piece of apparatus -is shown attached to the staff. It consists of a small telescope -three inches long attached at right angles to the staff by means of a -dovetail slide fitting when in use as shown. The staff-holder sights -the tacheometer through the short telescope, which can only be seen to -appear therein by moving the staff until it is approximately at right -angles to the direction of the tacheometer. - -[Illustration: Fig. 243.--_Sight director for stadium._] - -562.--=The Anallatic Telescope.=--In this telescope the focus is -constant, and consequently the tangential measurements indicated by -the numerical qualities subtended by a constant angle are directly -proportional to the base, so that there is no constant to be added. The -invention of this instrument and its modern application to subtense -measurement was due to Professor J. Porro, of Milan, who put it to -practical test in 1823,[29] in an instrument termed a tacheometer. The -telescope will be best understood by the following details:-- - -The object-glass _O_, Fig. 244, is made of a focus that falls well -in front of the axis of the instrument _CC′_, so that the rays cross -before falling upon the anallatic lens _A_, the optical arrangement -being such that if the rays fell direct without any refraction -they would reach the axis and subtend angles therefrom inversely -proportional to the distance of the stadium. The object-glass and -anallatic lens are of the same focus, so that the rays after crossing -from equal refraction may emerge parallel in the space _A_ to _M_. -The stop at _S_ and at the axis _CC′_ cuts off eccentric rays that -would otherwise give internal reflections from the telescope tube. -The eye-piece, represented by _MF_, may be made to pick up the image -of the stadium in front of it upon an ordinary webbed diaphragm or -upon ruled glass. The diaphragm webs are fixed, or the glass surface -engraved with three or five horizontal lines and one vertical. The -outer horizontal lines are used generally as the subtense lines, and -the central line for levelling and taking altitudes. The vertical line -is used for triangulating on the surface of the ground. - -[Illustration: Fig. 244.--_Diagram of anallatic telescope._] - -563.--There is an adjustment made by sliding tubes to bring the -object-glass and anallatic lens within mutual focus to ensure the -parallelism of the emergent rays and to adjust magnification. This is -commonly effected by means of a rack and pinion, moved by a separate -key kept in the instrument case, but which should not be touched after -the instrument is once adjusted by the maker, except in the case of -accident. It is much better made without this rack adjustment and -permanently fixed by the maker, as if it has the adjustment it is -likely to be tampered with and thus defeat its object. The eye-piece -adjusts to distance from the object-glass in the ordinary manner of the -surveying telescope--by rack and pinion. - -564.--The eye-piece of the anallatic telescope is generally made -of much higher power than those ordinarily employed for levels and -theodolites--25 to 30 diameters is usual. Where a diaphragm is used the -subtense lines are commonly placed on a slip of glass in two or three -sets, so that greater magnitude of image may be taken for objects at -distances of from 2 to 7 chains with the 14-feet staff, or that the -staff may be read at greater distances than 14 chains. This series of -lines is distinguished as 50, 100, and 200, Figs. 245, 246 and 247; so -that with this as great a distance as 28 chains with a 14-feet staff -may be estimated, but this is beyond the safe power of the instrument. -The intermediate line, as shown Fig. 220, is valuable in all cases for -levelling. The advantage of the increased power of the eye-piece is -more than neutralized by the loss of light. - -[Illustration: Figs. 245, 246, 247.--_Subtense lines ruled on glass._] - -[Illustration: Fig. 248.--_Adjustable point diaphragm with stadia -points._] - -565.--While many civil engineers are satisfied with a single percentage -pair of subtense lines the author much prefers using the point system, -arts. 237 to 239. In this case the diaphragm, as made by the author, -possesses two systems of adjustment; that shown Fig. 248 at a for the -single point for altitudes, and the pair of points separated by the -spring _ss_ for subtense angles. These points adjust by separate screws -top and bottom with a milled-headed key _f_. The two verticals are -fixed permanently. These points are all made of platino-iridium, which -possesses the hardness and elasticity of spring steel, and is at the -same time, as far as is known, perfectly non-corrosive. In case of any -light dust or moisture resting upon the points, it is perfectly safe to -brush them lightly with a soft camel-hair brush to clean them. Where -the 200 factor is required, a mean may be taken of two observations -above and below the central point. Where 50 is required, the vertical -points may be adjusted to this. - -566.--In adjusting the lines, webs, or points to a given subtense, the -anallatic lens may be moved to give more or less angular displacement -or magnification of the image. Greater accuracy is obtainable when the -staff is held normal to the line of sight instead of vertical. If the -staff be held incorrectly in the inclined position at great angles of -elevation or depression, the resulting error is very much smaller than -in the case of an equal variation of the staff from the true vertical -position. When adjustment is made upon a distant stadium at small -angles of elevation or depression, the subtense of the small arc will -vary so little from a tangent to one of its radii that the one or other -may be taken without sensible error. The plan originally proposed by -Green of placing a sight tube through the stadium at right angles to -its face, as a means of keeping it in the chord of the arc, is as good -as any other, but is more cumbersome than that described art. 561. If -the vertical stadium be preferred, this may be set up by the small -level, Fig. 109, p. 163. - -567.--It is well to note that with the anallatic telescope the stadium -must not be so near that the rays from the object-glass _do not -cross_ in front of the anallatic lens or the subtense will appear -much increased, so that there is a fixed nearness at which this form -of telescope can be used, say 50 feet. For this reason engineers -generally prefer an ordinary telescope, making use of the addition of -a constant. The author also prefers the plain telescope, as being more -correct according to his experiments where the constant is correctly -allowed. There are many advantages in the use of a plain open telescope -instead of the anallatic telescope for tacheometers, among them the -following may be mentioned. More light reaches the eye because there -are fewer lenses; there is no intermediate lens requiring adjustment -and which becomes dirty and bedewed and is inaccessible for cleaning, -and for the same dimensions of the telescope greater power can be -obtained. A larger telescope and of higher power is of great advantage -in subtense measurement, but the full advantage is not obtained in -the anallatic telescope. The idea which appears to be still common -that an ordinary open telescope will not give accurate results at -all distances by means of stadia readings, plus the distance of the -anterior principal focus of the object-glass from the axis of the -instrument, is entirely erroneous. When a staff is held at any distance -in front of the object-glass of an open telescope, an inverted image -of the staff is formed at the conjugate focus which subtends an angle -at the corresponding nodal point of the lens, equal to that subtended -by the staff at the other nodal point. If a diaphragm with two stadia -points or webs be placed at this conjugate focus the ratio _i_/_f′_ = -the ratio _l_/_D_; where _i_ is the space between the stadia points, -_l_ the height on the staff which these points appear to intercept -when viewed through the eye-piece accurately focussed on them, _D_ the -distance of the staff from the object-glass, and _f′_ the distance -of the diaphragm from the object-glass. Now in this equation _i_ is -a fixed space, _l_ is the observed height on the staff, and both f′ -and D are variables, of which it is desired to find the value of D. -From the laws of optics it is also known that 1/_f′_ + 1/_D_ = 1/_F_ -where _F_ is the principal focal length of the lens. Therefore _f′_ -= _FD_/(_D_ - _F_) for all values of _D_. Substituting this value -of _f′_ in equation (1) we get _i_ × (_D_ - _F_)/_FD_ = l/_D_; and -multiplying both sides by _D_, _i_ × (_D_ - _F_)/_F_ = _l_. ∴ _D_ - -_F_ = (_F_/_i_)_l_ and _D_ = (_F_/_i_)_l_ + _F_ which is true for -all distances. But this distance is measured from the object-glass, -and the distance _S_ required by the surveyor is that from the axis -of the instrument, and it is therefore necessary to add that of the -object-glass from the axis _d_. ∴ _S_ = _D_ + _d_ = (_F_/_i_)_l_ + _F_ -+ _d_, and _F_ + _d_ is the constant of the instrument = _c_. ∴ _S_ = -(_F_/_i_)_l_ + _c_. - -When the range is greater than that at which the divisions of an -ordinary levelling staff can be clearly read with the stadia points, -target stadia rods or targets fixed to a levelling staff are used. -It is usual to use plain targets fixed with their centre lines at -exactly 10 or 20 feet apart or other convenient distance, and the -angle subtended by these is measured by a micrometer diaphragm. The -reviser, in conjunction with Mr. C. W. Scott, B.A.I., A.M.I.C.E., has -designed a micrometer diaphragm which has been proved to give very -accurate results. It is made to revolve, so that either horizontal or -vertical stadia rods may be measured, and it is fitted with fine fixed -platino-iridium points, which are much more satisfactory than webs or -lines engraved on glass. These are fixed on one side of the diaphragm, -two each 1/200 part of the principal focal length of the object-glass -above and below the axial point. On the other side of the diaphragm -is a movable point which can be traversed over the fixed points by a -micrometer screw, every complete turn of which moves the point over -a distance equal to 1/1000th of the principal focal distance and the -head of the micrometer being divided into 100 parts, it reads to the -one hundred-thousandth part of the same; while a small star-wheel -records the number of complete revolutions, five of which cover the -space between any two of the fixed points. In using this micrometer -with say a 10-foot target, let the lower target cross-bar be clamped to -the level staff at 2 feet, and the upper target cross-bar at 12 feet. -Direct the axial point to the centre between the targets at 7 feet and -read the angle, then bring the nearest fixed point to the top or bottom -mark by means of the tangent screw, and bring the micrometer point -to the other mark by the micrometer screw. The micrometer reading is -the reading on the divided head plus the hundredths indicated on the -star-wheel plus 500 for each included complete space between the fixed -points. See whether the micrometer reads up or down, and set the fixed -point to the lower or upper mark on target accordingly. To obtain the -distance from the axis of instrument, divide 100,000, multiplied by the -length of the target by the micrometer reading, and add the constant of -the instrument _S_ = 100,000_l_/_x_ + _c_ where _x_ is the micrometer -reading, and _l_ the length of the target. The tacheometer which the -author has lately made has a plain open telescope, but this is of the -same size as that used upon the Porro system, and consequently it gives -much more light and better definition. - -568.--=Tacheometers= consist essentially of any form of theodolite that -is provided with means for reading distances by its telescope. Stadia -work is simply another name for tacheometry, which is derived from the -Greek _tacheos_ (quickly), and _metreo_ (I measure), and signifies the -art of measuring rapidly. The graduation of the arcs and circles of -these instruments is sometimes made upon the centesimal system, the -circle reading 400 grades, which are subdivided to half grades to read -with the vernier or micrometer to centigrade minutes of ·01 grade. -The centesimal system facilitates calculation, and permits a free -use of a logarithmic slide rule of a special kind. In France, where -working with this system at one time became more general, we have very -complete centesimal trigonometrical tables adapted to the tacheometer -published in stereotype,[30] but it has not gained favour, and very few -instruments are now so divided. A compromise which has found a certain -amount of favour is the decimal division of the ordinary degree of 90 -to the quadrant; this greatly facilitates the calculation compared -with what is necessary with the sexagesimal division into minutes -and seconds and the reading of the verniers is much simpler and less -liable to errors. Moreover, the mental conversion of the sexagesimal -division into decimals of the same degree is much simpler than the -conversion into the centesimal degree of 100 to the quadrant. Any -instrument divided sexagesimally can be converted by simply changing -the vernier if the divisions on the limb are degrees or half degrees. -The theodolite, Fig. 169, the author made specially for a tacheometer. -Any theodolite may be converted into a tacheometer by fitting it with -a subtense diaphragm. A modern tacheometer should be a high-class -theodolite in which every possible refinement is included. - -569.--The tacheometer, although manufactured for many years for export, -has been very little used in this country. The instrument to be -described, shown Fig. 249, is the author's latest pattern. It is made -with sexagesimal division or ingrades, to read by the verniers to 20″ -or to centigrade minutes. The telescope is of much larger and of higher -power than that of the ordinary theodolite. For a 6-inch instrument the -telescope is of 11 inches focus, with an object-glass of 1¾ inches -aperture. The eye-pieces are of the Ramsden form of powers 18 and 25. -The points in the diaphragm are set to cut 100 divisions of the stadium -at 100 units + constant of the measurement intended to be taken, links, -feet, or metres. This precludes distant measures, say of over 15 -chains, where a 16-feet stadium is used, but they are made adjustable -so that they may be set, if desired, for any other subtense, although -this is not recommended. It is doubtful whether the subtense method -can be considered as reliable at a distance of over 1500 links; or at -any rate we must assume that much greater accuracy can be obtained -by dividing distances greater than this into two by an intermediate -station for observation, independently of the additional convenience of -having the staff-holder within easy distance of communication. - -[Illustration: Fig. 249.--_Stanley's 6-inch tacheometer._] - -570.--Where points are not used in the diaphragm or where lines are -preferred, these may be divided upon glass in fine lines as Fig. 246; -or spider webs may be used, but these are more difficult to set exact -for stadia. - -571.--=Stadium.=--Any accurate levelling staff will answer for the -stadium, but the ordinary Sopwith, Fig. 99, is slightly confusing. A -more open reading is generally recommended--that shown Fig. 102, p. -155, which the author designed for the purpose, answers perfectly. It -is better to read the stadium low, as there is less vibration; but it -is not often possible or at any time advisable to read it from the -bottom--1 foot up is generally most convenient. Readings are taken and -recorded of each subtense web, or point, separately, and the difference -of reading subtracted for the subtense of tangent. With a point -diaphragm for taking the subtense angle a fair certainty of accuracy -of measurement of distance within ·002 may be assured, which is much -nearer than can be attained by average chaining, taking six times the -labour. - -572.--_The General System of Working the Tacheometer_, with sufficient -detail for practice, would take too much of our limited space to be -given here. We now have several good works published in Great Britain, -in addition to the able paper by Mr. Brough before mentioned, such -as _The Tacheometer: Its Theory and Practice_, by Mr. Neil Kennedy; -_Surveying_, by Whitelaw; _Aid to Survey Practice_, by L. D'A. -Jackson, &c. There is a small work published in New York giving some -details.[31] There are complete works in French, Italian, German, and -Spanish. In French, _Leves de Plans a la Stadia_, by M. J. Moinot, -engineer to the Paris, Lyons, and Mediterranean Railway, gives very -complete instructions for all conditions of country, upon surveys which -he has personally carried into practice with this instrument. - -There are several tacheometers made upon the Continent, of more -complicated forms than those herein described, but they do not produce -better work. - -573.--=Field-books= for the tacheometer are ruled in various ways in -columns, which vary in number in different books from twelve to twenty. -The French generally have fourteen columns, giving the number of the -station, time, heights of line of collimation above point levelled, -numbers of points selected, horizontal and vertical angles observed, -reading of subtense webs and their differences, height of staff by -reading central web, and columns for calculations and remarks; most -English forms are more simple. - -[Illustration: Fig. 249_a_.] - -574.--A convenient protractor in which the equivalent of surface -reading is taken from a scale upon its lower part directed from the -centre of the protractor is here shown. - -[Illustration: Fig. 250.--_Perspective view of 5-inch omnimeter._] - -575.--=The Omnimeter= is one of the class of instruments in which the -tangent to a radius proceeding direct from the axis of the telescope -is represented by the stadium made of constant length, the subtense -angle varying with the distance. The omnimeter is the invention of -Chas. A. C. Eckhold, a German engineer, described in the provisional -British patent[32] as "a person living in Alexandria." The instrument -as originally devised consisted of a kind of theodolite to which the -subtense tangential system was added as an entirely separate part. -The important part of the provisional specification shows that the -principle of the invention consists in the use of two sights to the -instrument, one a telescope to sight the object, and the other a -powerful compound microscope to read divisions upon a tangential scale. -The telescope and microscope are firmly united together in parallel -position with their axes exactly crossing the transverse axis of the -theodolite, so as to move together through the same angle by the motion -of the telescope in traversing the azimuth. A delicate level is placed -upon the telescope, and when the bubble is in the centre of its run -the scale is truly at right angles to the axis of the microscope. The -scale in the early instruments stood vertically at the extreme edge -of the instrument in a position lateral to the object-glass of the -telescope. It was finely divided to millimetres, and read the intervals -of the divisions by means of a micrometer screw with a vernier. - -[Illustration: Fig. 251.--_Details of omnimeter, showing section of -microscope and scale._] - -576.--With the instrument as originally constructed, it was found that -the delicate scale, protruding vertically to the extreme edge of the -instrument, was very liable to injury unless supported by heavy metal -work, which rendered the instrument cumbersome. A great improvement -was made in this instrument, which brought it to its modern form, by -placing the tangent scale in a horizontal position, where it could -be firmly fixed upon the vernier plate as shown Fig. 251 _S_, and -reading the scale by means of a reflecting prism _P_ in the eye-piece -of the microscope. In this improved instrument, as the microscope and -telescope are still united on one axis so that they move at equal -angles to each other, it is clearly indifferent whether the scale be -placed vertically or horizontally, provided it is placed truly at right -angles to the microscope when the axis of the telescope is horizontal. -The scale, which is 4 inches long, is placed in a sliding fitting to -adjust longitudinally to its position by means of a micrometer screw. -In the English instrument the scale is divided into 100 parts for -calculation. The divisions are subdivided by shorter lines, making the -actual division 200. The micrometer screw has 50 threads to the inch, -and moves over one of the divisions of the scale only. The micrometer -head is divided into 100, numbered at the tens; a vernier placed -against the head subdivides each of these divisions into 5, making the -total micrometer 500 for one complete revolution. The total division -of the 4-inch scale therefore becomes: 200 (divisions of scale) × 500 -(micrometer) = 100,000 in 4 inches. The scale is placed centrally to -the instrument, so that when the telescope is level the microscope is -vertical, and reads 50,000 when in perfect adjustment. - -[Illustration: Fig. 252.--_Details of prismatic eye-piece._] - -577.--The general appearance of the instrument resembles the transit -theodolite, already described art. 368, in every way except for the -addition of the microscope and scale, shown in perspective in Fig. -250. The details of construction of the microscopic apparatus may be -followed in Fig. 251. _T_ telescope with sensitive level _B_ mounted -upon it; _R_ body of microscope connected solidly upon the same axis -as the telescope, shown in half section. The eye-piece is placed at -right angles to the microscope and telescope, and reads through the -reflection of a prism _P_ to the face of the instrument. The details -of the eye-piece are shown in section Fig. 252. The tangential scale -is shown in section Fig. 251 _S_ with the micrometer with edge reading -vernier at _M_. The compass of the instrument _C_ is of the trough -form, and placed on the opposite side to the level to be used after -transitting the telescope from the position in which it is shown in the -figure. The axis of the connected telescope and microscope is exactly 6 -inches above the surface of the tangential scale _S_. - -[Illustration: Fig. 253.--_Omnimeter webs; a telescope, b microscope._] - -578.--The telescope diaphragm is generally webbed with one horizontal -and two vertical webs, Fig. 253 _a_, the altitude reading being -taken from the top of the horizontal web, and the horizontal angular -position from the centre of the interval between the vertical webs. -The microscope diaphragm _b_ has two horizontal webs, and reads from the -centre of the interval, which is judged by the eye. Observed in this -manner, there is no error due to covering angle subtended by the webs -themselves. The most exact reading is obtained with a fine point. - -579.--_Reading of the Tangent Scale._--As the micrometer divides half -a principal division into 500, the complete _figured_ divisions are -therefore divided into 1000. This is done for the sake of decimal -notation. In reading it is only necessary to observe that the shorter -or half division is 500, which must be added to the micrometer reading -when it is past this division; as for instance 65½ reading is -65,500, and say the micrometer reads 234 past this, the reading is then -clearly 65,500 + 234 = 65,734, just as before described for reading -half degrees with the vernier. - -580.--_Value of the Scale taken in Rectangular Coordinates._--The -radius from the transverse axis of the telescope to the tangent surface -of the scale is exactly 6 inches. The scale is 4 inches divided into -100,000 parts, as it is read with the aid of the micrometer and -vernier. The radius therefore in terms of the scale would be at 6 to -4, that is 150,000. By this we see that the divisions of the scale -by the angle subtended give tangents, the value of each division of -which is the reciprocal of this on 150,000 of the radius or base to -any unit we may select. If we make the unit 1 foot, then one division -represented by a unit of change of position of the vernier reading, -and consequently of equal angular change in the direction of the -axis of the telescope, would give a tangent of 1 foot upon a stadium -placed at 150,000 feet distance. If the stadium were made 10 feet, as -is usual, the same angular magnitude would be traversed in ten times -this distance, or over 280 miles, making the value of the units of the -vernier 1,500,000. This will give a general idea of the delicacy of the -instrument so far as constructive principles are concerned, and not its -performance. - -581.--_The Stadium_ is marked off in a number of feet, links, or -metres, according to the unit taken for measurement of the surface -of the land. The English stadium is generally formed of a 14-feet -levelling staff, with the surface painted with a ground of plain -white. At 10 feet apart two black bands about 2 inches wide are -painted in, leaving in the centre of each band a clear white line of -about one-tenth of an inch in width. These white lines are carefully -set to 10-feet standard centre to centre. But a better plan is to -have two equilateral triangles painted, with their apices meeting to -the centre. An intermediate 5-feet line is drawn in black, which is -found convenient for near measurements, to avoid too great angular -displacement of the telescope. When the measurement is in chains, 15 -links or 20 links may be taken for the distance of the lines apart to -give the tangent. For metre measurement 3 metres are commonly taken for -the stadium division. These are in each case subdivided. The lowest -stadium reading should be 1 foot at least from the ground to avoid -grass and other obstructions. - -[Illustration: Fig. 254.--_Ruling of omnimeter field-book._] - -582.--_Field-book._--The field-book as shown above, Fig. 254, was -recommended by the inventor. - -583.--_Mode of Operating with the Omnimeter._--Carefully set the -instrument up at its station in perfect adjustment as a theodolite, -noting the departure point upon the scale reading through the -microscope. Place the stadium in a vertical position at the point to -which measurements are required. Direct the telescope so that the -horizontal web cuts the upper line of the stadium, and lightly clamp -it. Now read the microscope and record the reading as observed in -the field-book. Unclamp the telescope and take the reading of the -lower point of the staff and record this. Record the bearing of the -instrument on the horizontal circle as with a theodolite. - -584.--_To Determine the Horizontal Distance in Feet._--Divide the -constant radius of 1,500,000 given before by the difference of the two -readings of the stadium mark, which are 10 feet apart. For example:-- - - First reading of scale 67,500, micrometer 235 = 67,735 - Second " 64,000, " 450 = 64,450 - Difference 3,285; - -then 1,500,000/3285 = 456·6 feet distance. - -The process is somewhat simplified by logarithms, as we have only the -log. of the difference to subtract from the constant, the 1,500,000 -mantissa of which is 1,760,913. Thus-- - - log. 1,500,000 6·1760913 - log. 3,285,000 3·5165354 - --------- - 2·6595559 = 456·6 feet. - -585.--_To Determine Horizontal Distance in Chains_ the stadium should -be marked as just described for feet, but at 20 links distance from -line to line. Then the radius 150,000 × 20 gives 3,000,000. Taking for -example, readings as before with difference of 3285 we have-- - -3,000,000/3285 = 913·2, or 9 chains 13·2 links distance. - -_To Determine Horizontal Distance in Metres_, the stadium is divided -to 4 metres. Then radius 150,000 × 4 = 600,000. Taking, for example, -difference of reading as before 3285 then - -600,000/3285 = 182·64 metres. - -586.--_Levelling--Taking Altitudes._--To take the elevation of the -staff above the level of the instrument, subtract the reading of the -scale, when the axis of the telescope is level, from the lower reading -of the staff on the scale, and divide by the distance difference, as -found by the method discussed before, then multiply this by 10 feet. -Thus taking the lower reading as before 64,450 and the constant for the -level position of the instrument, say 50,010, we then have-- - - Lower reading 64,450 - Level " 50,010 - ------ - Difference 14,440 - -then 14,440/3285 × 10 = 43·96 feet nearly. The heights, in relation to -the position of the instrument, are _positive_ or _negative_ according -as the scale readings are greater or less than the constant level -reading or departure point. - -587.--_Work of the Omnimeter._--The perfection of the principles of -the omnimeter would lead anyone to infer that work might be done with -it of the highest degree of accuracy. The testimony of the greatest -authorities show by comparison that it is unable to compete in this -respect with the best made tacheometers. A large number of these -instruments are employed in India. Colonel Laughton reports upon -it--"It has been found to give very accurate heights of buildings, -etc., also to be wonderfully accurate when used as a levelling -instrument; _but it is not so accurate for measuring distances over_ 600 -_feet_, and even at this distance the error sometimes amounts to as much -as 1 _foot_. It is recommended as admirably adapted for city surveys -and traversing, also in hilly and jungly countries, and for railway and -similar purposes."[33] - -588.--Wherein the instrument fails to give exact results is no doubt in -the difficulty of its manipulation. For taking two readings, which are -necessary for every operation in distance, the instrument has -necessarily to be set twice, the hand being placed upon the micrometer -for the second observation while the attention is upon the sighting of -the telescope; and even when the readings are taken by the telescope, -the microscope has to be separately adjusted to read the micrometer -scale. In the repetition of these processes it is almost impossible -to avoid some slight disturbance of centre by pressure. In distant -readings atmospheric changes giving difference of refraction occur -quickly, so that there is more risk of error from two separate -observations than if the observations of the subtense webs are -taken simultaneously, as with the tacheometer. Further, any defect -in workmanship or wear tells seriously against the readings of the -instrument. Its advantages are theoretically that a wide angle is -subtended by the stadium with the omnimeter in short distances which -must be in every way an advantage. Further, since the early general -use of the omnimeter, the tacheometer has been greatly improved, -particularly in providing it with a larger and better object-glass so -as to obtain greater field of view, that fairly near stations may be -taken with it that were formerly only possible of reading with the -omnimeter. The manufacture of omnimeters is now very limited; the -subject is only retained in this edition because there are still some -hundreds of these instruments in use. - -589.--_Improvement in the Omnimeter._--One improvement in this -instrument by Mr. W. N. Bakewell, M.Inst.C.E., consists in turning -the body of the microscope to a right angle at the position of the -transverse axis of the omnimeter, and placing a reflecting prism at the -angle. By this means the eye-pieces of the telescope and the microscope -are brought side by side, greatly facilitating the joint readings. A -second improvement is in making the scale 1,000,000 instead of 150,000, -which much facilitates calculation, but it is doubtful if these -improvements will stay the declining popularity of the omnimeter. - -[Illustration: Fig. 255.--_Bakewell's tangential arrangement to a -theodolite._] - -590.--=Bakewell's Tangential Arrangement= _to a Theodolite for -Measuring Distances_.--This arrangement, which gives the distances by -direct reading without calculation, was devised by Mr. W. N. Bakewell -to extend the power of an ordinary 6-inch transit theodolite fitted -with subtense webs. The observations are made on marks at 3 feet and -13 feet on an ordinary Sopwith staff--a 10-feet base, as is usual with -the omnimeter. Any other base may be used if the distances registered -are proportionally altered, or the scale may be divided to suit. It -was first applied by the author to a theodolite that had been in good -service, without the necessity of making any structural alterations in -the instrument.[34] The measuring apparatus consists of a tangent screw -impinging upon a radial plane, with micrometer and vernier. The details -will be readily comprehended from the engraving, Fig. 255, and the -following full description. - -591.--The transverse axis of a theodolite, upon the opposite side of -the telescope to that upon which the vertical arc is fixed, is turned -down to a cylindrical surface true with the pivots. A collar _A_, -which fits the cylindrical surface, is slit up on one side to enable -it to be clamped firmly to any position of the axis by a clamping -screw _B_. The collar is connected in the same gun-metal casting with -the radial arm _C_ that terminates at _T_ in a plane, which is made -truly radial with the transverse axis of the telescope. This radial -arm _C_ has a long German-silver spring _S_ at the opposite side to -the radial plane, which keeps it up firmly in contact with the point -of the micrometer screw. A screw is cut on the drum of the micrometer -_D_; on the spiral the scale of distances is engraved; and readings are -taken from a line on the index _I_ which slides on the bar _E_. The -scale being one of reciprocals the divisions are at unequal distances, -so a vernier cannot be used; consequently at long ranges where the -divisions are close, the subdivisions must be estimated. Where this is -too rough a method, resort must be had to calculation. The outer end -of the drum _D_ is divided into 200, and reads by vernier _V_ carried -by the arm _E_ in 5 or thousandths of a revolution. The micrometer -screw has twenty-five threads to an inch, and the radius of the arm -_C_ is 4 inches. One complete revolution of the screw is one-hundredth -of the radius, and using a base of 10 the radius factor is 1000 × -100 × 10 or 1,000,000; consequently Barlow's or any other table of -reciprocals can be used, and the distances obtained, by inspection -with comparatively little labour. This additional part has not range -sufficient for altitudes, being available for about 2 degrees only. -The distance may be taken as a subtense or small tangential angle at a -radius which, with the azimuthal angle taken by the vertical arc of the -theodolite, will give altitude by its sine and horizontal distance by -its cosine in the usual manner. The principle is that of the omnimeter, -and it possesses the same objection for perfect performance, that the -theodolite has to be handled twice for the two observations necessary. - -592.--=The Gradienter Screw.=--This is no doubt a simplified copy of -Bakewell's tangential arrangement and is shown at Fig. 256. - -[Illustration: Fig. 256.--_Gradienter screw._] - -It is a micrometer screw fitted to a tangent arm, which can be clamped -to the trunnion of telescope when the latter is in any position. - -The screw is cut of a value that causes the web of the telescope to -move 50/100 of a foot at 100 feet distance for each revolution, and the -head of the screw is divided into 50 parts, consequently each division -upon the head represents a movement of the cross web of the telescope -of 1/100 of a foot upon a scale placed at 100 feet distance. The scale -on the arm over the gradienter screw indicates the number of complete -revolutions of the head, therefore, if the screw be revolved two whole -revolutions the two divisions covered on this scale indicate 50/100 × 2 -= 1 foot to the 100 feet. - -_To establish any grade with this screw._--Set the gradienter head to -zero, then level the telescope and clamp the gradienter arm. Suppose -grade required be 1·75. Turn the gradienter head through three whole -revolutions, which will equal 150, then go on turning through 25 of the -divisions on the head and the total movement will be 1·75, the required -grade. - -_For Measuring Distance._--First with a staff for moderate distances. -Any space on the staff covered by two complete revolutions of head -is 1/100th part of distance, thus, if the difference between the two -readings be 3·475 feet the staff is distant 347·5 feet. - -_Second Method._--For long distances with any rod of known length, such -as a 20-foot stadia rod. Send out a man with the rod which he holds -vertical at place to be measured. Then measure its length with the -gradienter screw; say it takes 2 revolutions and 45 divisions over, -thus 2 revolutions = 100 and 45 extra divisions = 145. Then-- - - 20·00 feet/1·45 × 100 = 1379·3 feet. - -Another instance.--Suppose the man at a distance has no stadia rod. -He simply holds up any stick, say a walking stick. Measure this in -telescope. Say it subtends 1 revolution and 28 divisions. This = 78. -When your man comes in with the stick, measure its length. Say it was -3·25 feet. Then-- - - 3·25 feet/0·78 × 100 = 416·6 feet. - -The above illustrations are for readings taken approximately level. -If there be much elevation or depression the angle must be read and -the difference of hypo and base calculated and the stadia rod or staff -must be inclined so that its face is at right angles to the line of -sight from telescope. This can be done by the rod man inclining the -staff or rod until the shortest reading is given if a staff be used, or -the longest measurement is recorded by the gradienter screw head if a -stadia rod be used. It is better in this case to have the staff fitted -with a director (see art. 561), so that the person holding the staff -may sight into the telescope of the instrument, thus ensuring the staff -being exactly at right angles to the line of sight. - -No constant should be added with either this, Bakewell's, or omnimeter -measurements, as the angles are taken from the centre of the -instrument. This gradienter screw has the same fault as mentioned for -the two foregoing, viz., that all readings are taken by two movements -of the instrument. - -FOOTNOTES: - -[28] _Description and use of an Improved Reflecting and Refracting -Telescope and Scales for Surveying_, by William Green, 1778. - -[29] _La Tachéomètre, ou l'Art de Lever les Plans et de Faire les -Nivellements_, Paris, 1858. - -[30] _Tables Trigonométriques Centésimales_, by J. L. Sanguet, Paris. - -[31] _Manual of the Theory and Practice of Topographical Surveying by -Means of the Transit and Stadia_, by J. B. Johnson. New York. - -[32] Patent, prov., No. 1859, June, 1868; patent No. 3759, Dec., 1868. - -[33] _Report on Omnimeter_, by Major G. A. Laughton, Superintendent, -Bombay Revenue Survey. - -[34] _Proc. Inst. C.E._, vol. xcii. part ii. p. 248, 1887-1888. - - - - -CHAPTER XIII. - - INSTRUMENTS CONSTRUCTED ESPECIALLY FOR OFFERING FACILITY OF TAKING - INCLINES--INCLINOMETER--THEODOLITE--GRADIOMETER--CLINOMETERS--ABNEY'S, - TROUGHTON'S, DE LISLE'S, STANLEY'S, BARKER'S, BURNIER'S, WATKINS'-- - CLINOMETER SIGHTS--RULE CLINOMETERS--ROAD TRACER. - - -Certain instruments are constructed specially with the object of taking -inclines, where this is the predominant work to be performed with them. -They form an important branch of surveying instruments, and for their -special kind of work present many time-saving capabilities. - -593.--=Lister's Inclinometer Theodolite.=[35]--This instrument is the -invention of Mr. James Lister, C.E. It was originally designed to set -out upon the surface of land the widths of slopes or batters by pegs, -as required in the execution of railway, canal, and other earth works. -In general construction it resembles a theodolite as before described, -arts. 370 to 391, with the addition of an extra vertical axis to the -telescope piercing the horizontal axis at right angles, Fig. 257. In -this construction the telescope upon the horizontal axis can be set -by the vertical supplementary axis to any inclination, so that if the -vertical axis be set to the slope of a railway cutting, any number of -points or pegs may be set out continuously with the same setting by -direct observation through the telescope across any irregularity or -inclination of the land surface. In this operation an immense amount of -labour is saved over the ordinary system of pegging by calculation with -the aid of a theodolite, where each peg requires a separate setting of -the instrument. When the inclinometer theodolite is used for surveying -purposes, the telescope is fixed by a spring catch which places it -firmly true to the reading of the ordinary vertical arc. - -[Illustration: Fig. 257.--_Lister's inclinometer theodolite._] - -The instrument is also fitted with a mechanical device for repeating -the tangential angles when operating on curves, which obviates the -necessity of reading them on the horizontal arc, thus facilitating the -work. This will be referred to in the following explanation of the -manipulation of the instrument as the "angle repeater." - -The main difference between the method of taking cross sections by -the level and by the inclinometer theodolite is in substituting -inclined bases for horizontal ones, which will be clearly understood by -reference to the following diagrams, which illustrate somewhat extreme -surface inclination. - -[Illustration: Fig. 258.] - -[Illustration: Fig. 259.] - -Fig. 258 shows the levelling method and Fig. 259 the method by the -inclinometer theodolite. In the first it will be seen that each section -requires to be taken singly with repeated changes in the position of -the instrument at each section, involving numerous readings on the -staff, booking, and reduction of the levels for changes only. Also -the sectional measurements require to be taken in short horizontal -lengths with the plumbing of the end of the tape at each length. By the -inclinometer method this unnecessary labour is avoided, there being no -changes in the position of the instrument, as from one setting a series -of sections may be taken on either side of it. There is no reduction -of levels, and the sectional measurements are taken on the surface to -which the base line is always approximately parallel. - -The saving of labour is even more marked in the setting out of slope -pegs than in the taking of cross sections, for in addition to the -transference of level from the centre pegs to the outcrop of the slope -several approximate calculations have to be made before the exact -position of the slope peg can be found, while by using the inclinometer -theodolite it is only necessary to put in normal slope pegs at -intervals of a quarter of a mile, or at such distances apart that a -ranging rod may be seen from one point to the other, and by setting up -the instrument at each alternate peg, or at half mile intervals, the -whole of the intermediate pegs for a quarter of a mile on each side of -it can be "boned" as simply as ranging a straight line, the telescope -being inclined to, and revolving in the plane of the slope. In this -manner as much work may be done in a few hours as will take a week with -the levelling method, and this without the slightest physical or mental -strain to the operator. - -594.--_Explanation of the Method of Operating with the Inclinometer -Theodolite._--For setting out a centre line of railway, etc., and -putting in level pegs the instrument may be used as an ordinary -theodolite, or even as a level, and the work performed in the usual -manner. It may also be used as a level when setting out the normal -slope pegs on slightly inclined ground surfaces, but when the -inclination is considerable it may be used in a special manner with -advantage as hereinafter explained. - -595.--_To take Cross Sections when the Line is Straight._--It is -unnecessary to explain the use of the instrument when the ground -surface is comparatively level, so as to require no change in position -and resetting of the instrument, it being obvious that in this case -it may be used simply as a level with advantage; but when the surface -is inclined in the direction of the centre, and also at a right angle -thereto in the direction of the section lines, the method of procedure -is as follows:-- - -Assuming that it is desired to take a series of 15 sections (and this -is within the limit of the number that can be taken from one setting of -the instrument), set up the inclinometer, preferably over the centre -peg of the series, in such a position that the two front legs of the -tripod stand across the centre line, and the back leg (which has a -distinguishing mark) rests upon the centre line. Set the lower limb of -the tribrach stand upon which the instrument is supported to a level -condition in its lateral direction by manipulating the back leg, and at -the same time observing the bubble on the stand. This will enable the -instrument to be subsequently tilted to a certain extent in a perfectly -vertical position. Clamp the horizontal arc to zero and direct the -telescope to the centre line. Clamp the lower limb and bring the arc -round to an angle of 90°. The vertical arc is now at right angles to -the centre line and parallel with the section lines. Now release the -telescope from the vertical arc and turn it again on the centre line, -and by working the back adjusting of the instrument (or in case of -necessity manipulating the back leg) tilt the instrument until the -cross web of the telescope is elevated to a short distance above the -seventh or most distant peg of the sections, or site of the first -section to be taken. Now tilt the vertical arc until the cross web -assumes a position parallel to the general inclination of the ground -surface laterally. Clamp the arc to this inclination and note the angle -thereon, for this will be the angle of the inclined base from which the -whole of the sections will be taken and subsequently plotted. - -Commencing at the seventh peg at this side of the instrument, the -sections may now be taken consecutively to the seventh peg on the other -side by taking readings on a level staff held in an inclined position -at a right angle to the cross web or base, as shown in Fig. 259, and -oscillated that the lowest reading may be taken. A reading must be -taken on the centre peg at each section to establish the height of the -base above the peg. The base may be raised or lowered at any section, -or part of a section, to meet any excessive elevation or depression -of the ground surface which might prevent the staff being read, but a -separate reading on the centre peg at each variation of the base must -be taken, thus:--Fig. 260. - -[Illustration: Fig. 260.] - -The bases being parallel the angle of inclination remains the same. -The tilting of the instrument produces a variation in the angle of the -vertical arc, but this is only to such an infinitesimal extent that -unless the tilt be excessive it may be disregarded. The correction, -however, may be simply made after the instrument has been adjusted for -any operation by ascertaining or simply noting approximately the angle -of the tilt, and setting off this angle on the horizontal arc towards -the tangent line, thus varying the chord or base line to this extent, -or it may be found by referring to a table of natural sines, etc., -and multiplying the cosine of the angle of the tilt by the tangent of -the vertical arc angle, the result being the tangent of the corrected -angle, thus:--if the angle of the tilt be 10°, and the vertical arc -angle 25°--Referring to tables, cosine 10° = ·98481, tangent 25° = -·46631. ·46631 × ·98481 = ·45924 = tangent 24° 40′, the corrected angle -making a variation of 20′. - -596.--_To take Cross Sections when the Line is on a Curve._--This -operation is similar to that explained above for taking cross sections -when the line is straight, except that being on a curve a variation -of the tangential angle must be made at each peg or section. As this -is performed mechanically by a single movement of the angle repeater -and no reading of the angle is required, the work is just as readily -performed. To more clearly elucidate the method, we will take a case in -point and assume that the number of sections to be taken is 15 and that -the radius of the curve is 50 chains, which the accompanying diagram -illustrates. - -Diagram (Fig. 261) showing the adjustment of the instrument for taking -sections on curves and the variation of the tangential angles for each -section. - -[Illustration: Fig. 261. - -If the centre pegs be taken as slope pegs, the diagram applies to -illustrate the setting out of half widths.] - -Having set up the instrument at A, Fig. 261, over the centre peg of the -series in the manner before described, ascertain the tangential angle -for the first chain of the curve by dividing the constant, 1719, by -the radius of the curve in chains, which gives the angle in minutes or -1719 ÷ 50 = 34′ 24″, and set the angle repeater to give a movement of -double this angle or 1° 8′ 48″, ready for application at each change -of section. - -Set the horizontal arc to the tangential angle for the seventh peg -from the instrument at which the first section has to be taken, or -34′ 24″ × 7 = 4° 0′ 48″, and direct the telescope to the peg. Zero -is now on the chord line AD, which is parallel to the tangent at the -seventh peg, and at an angle of 8° 1′ 36″, from the tangent line AB, -which divided by 7 gives the variation of the tangential angle at -each section, or 1° 8′ 48″, to which the angle repeater has been -set. Release the horizontal arc and bring it round to an angle of 90° -from zero, and the vertical arc will be at a right angle to the line -A D and parallel with the section line at the seventh peg. Release -the telescope from the arc and turn it at right angles thereto in the -direction of the zero line AD. Now, by working the back adjusting -screw of the tribrach, tilt the instrument until the cross web comes -somewhat above the seventh centre peg, then tilt the vertical arc until -the cross web is parallel with the lateral inclination of the ground -surface. Clamp the arc and note the angle thereon to determine the -inclination of the base to plot the sections from, and the instrument -is then in adjustment for taking the first section at the seventh peg -in the manner already described, being careful that the lateral bubble -on the instrument is in a perfectly level condition. To take the second -section at the sixth peg, one movement of the angle repeater must be -made and the lateral bubble adjusted, which operation must be repeated -for every succeeding section. - -The movement of the angle repeater brings the vertical arc parallel -to the section line at each peg, and the adjustment of the bubble -maintains the angle of the inclined base uniform throughout. - -When the sections are all taken on this side of the instrument, the -telescope is turned to the other side and the operation continued until -the whole fifteen are completed. - -From the above detailed description it may be thought that the -adjustment of the instrument for the operation is somewhat complicated, -but in practice it is not so. After the first experience and the method -is understood, it is only a matter of two or three minutes, and once in -position the sections may be taken as rapidly as on level ground, and -the saving of labour is practically the same as in taking sections when -the line is straight. - -597.--_To set out Half Widths or Slope Pegs when the Line is -straight._--In commencing this operation it is necessary in the first -instance to set out two or more half widths, according to the length -of the cutting or embankment. These may be a quarter of a mile apart, -or so far as a ranging rod may be clearly seen from one point to the -other. The pegs put in at these points act as normals from which to -"bone" or range in all intermediate pegs by sight simply, without -further recourse to levelling measurement or calculation. If the ground -surface be comparatively flat, these normals may be put in in the usual -way by using the instrument as a level, but if the surface is much -inclined and the slope deep, a simpler method may be adopted, which -will be hereafter explained. - -[Illustration: Fig. 262.] - -Assuming that the normals have been put in, set up the instrument at -any intermediate peg in such a position that the telescope when set -to the angle of the slope shall line with the top of the peg, as per -sketch, Fig. 262. Then release the telescope from the vertical arc and -direct it to one or other of the nearest normals, adjusting the cross -web to cut the top of the peg by turning the instrument on its axis. -Clamp in this position and the telescope will revolve in the plane of -the slope, and any point on the intermediate surface intersected by -the cross web is the outcrop of the slope and the position of the peg. -When all the pegs on the one side of the instrument are put in, turn -the telescope to the other side to cut the next normal and proceed in -the same manner. When all the pegs have been put in for this half mile -distance, the instrument may be moved to the next half mile normal -and the operation repeated, until the whole cutting or embankment is -completed, the last normal point being in all cases the formation width -at the ends. - -In speaking of half-mile distances we are assuming the most favourable -conditions of surface and application of the method, but in practice -where the surface is undulating the positions of the normals should be -at the most elevated points from which a considerable range of sight -may be obtained. - -In fixing the points for the slope pegs, a rod should be held in an -inclined position and be brought to line exactly with the cross web of -the telescope, the pegs should then be driven level with the ground -surface where the foot of the rod has rested. - -598.--_To set out Slope Pegs when the Line is on a Curve._--The -operation is similar to that described above, except as explained for -taking cross sections on a curve. A variation of the tangential angle -must be made for each peg, and if the centre peg shown on the diagram -accompanying that explanation be taken as one of the slope pegs, it -will also serve the purpose of illustrating the present one, and a -brief recapitulation of the manipulation of the instrument to bring it -into adjustment for the operation is all that will be required. - -The normal slope pegs having been set out and the instrument set up -at an intermediate one, as before explained, instead of directing the -telescope in the first instance to intersect one of the next normals, -set the angle repeater to double the tangential angle for the first -chain in the curve, and the horizontal arc to the tangential angle for -the distance in chains that the normal is from the instrument. Then -turn the telescope to cut the normal peg and clamp the lower limb. Now -bring the horizontal arc round to an angle of 90° from zero and clamp. -Release the telescope from the vertical arc and turn it at a right -angle thereto in the direction of the zero line AD, and by working -the back adjusting screw tilt the instrument until the cross web cuts -the normal peg again. Adjust the lateral bubble on the instrument to a -level condition and it is in adjustment for the operation. - -To put in the first peg from the normal, make one movement of the angle -repeater and adjust the bubble. To put in the second one, make another -movement of the repeater and adjust the bubble, and so on until the -whole is completed. It will thus be seen that by a simple mechanical -operation a vast amount of work can be done in an incredibly short -space of time as compared with the levelling method, and that with -little or no effort on the part of the operator. - -599.--_Alternative method of setting out the Normal Pegs._--Let the -diagram, Fig. 263, represent the section of a cutting at the point -opposite which the normal has to be set out, when the section depth may -be assumed to be 16 feet, the formation width 30 feet, and the slope -1½ to 1, or at an inclination of 56° 18′. The distance _bc_ for a -1½ to 1 slope is one-third the formation width, or 10 feet. The data -required for the operation is the distance _ad_ from the centre peg -to the plane of the slope, which is found by multiplying _ac_ by the -natural sine of the slope angle 56° 18′, thus: 26 × ·831 = 21·60 feet. - -The operation when the line is straight is to set up the instrument -at a centre peg some distance away from the normal in the manner -previously described, _viz._, with the front legs set across the centre -line, the back leg on the centre line, and the bubble on the tribrach -set level before adjusting the instrument, which manipulation produces -a perfectly vertical tilt. - -After adjustment, set the horizontal arc to zero and direct the -telescope to the centre line, clamp the lower limb, set the vertical -arc to the angle of the slope, and bring the horizontal arc round to -an angle of 90°, or a right angle to the centre line. Liberate the -telescope and direct it again to the centre line, and by working the -back adjusting screw tilt the instrument until the cross web intersects -the top of the centre peg at the normal. The telescope will now revolve -in the line _ag_ parallel with the plane of the slope and at a distance -of 21·60 feet from it. Therefore any point on the surface in the line -of the slope where 21·60 can be read on the staff is the outcrop of the -slope and the position of the peg. - -In this example, when the required reading is higher than the ordinary -staff, lower the tilt and take an intermediate reading, as at _f_ in -the diagram, Fig. 263, which may read, say, 12·00, when the required -reading on the peg will be reduced to 9·60. - -[Illustration: Fig. 263.] - -In setting out normals on a curve by this method the only difference -in the operation to that above described is that instead of in the -first instance clamping the instrument with zero on the centre line, -it must be clamped with zero on the chord line, _i.e._, at double the -tangential angle for the distance the instrument is from the peg, as -before explained in detail for operations on curves. - -By this method two normals may be set out at least 20 chains apart from -one setting of the instrument, or several slope pegs may be set out in -like manner, which under certain contingent difficulties of ground -surface is an advantage of considerable importance. - -In this connection there is also an alternative method of putting -in the slope pegs after the normals have been set out, which, under -certain conditions, may be employed with advantage. - -Instead of setting up the instrument at the back of the normal with -the telescope set to line with the plane of the slope, and to range -the pegs in by means of a rod or staff held at the inclination of the -slope, as before described, it may be set up in any position in the -line of slope where a reading can be taken on the peg, as at _a_ on the -sketch (Fig. 264), and at the point read, as at _b_, a disc should be -clamped to the staff, as this can be much more clearly seen than the -staff graduations when sighting long distances. The staff should then -be transferred to the next normal and held on the peg. If the telescope -be now turned in this direction and the cross web adjusted to cut the -disc, any point on the intermediate surface where the disc can be -intersected is the outcrop of the slope and position of the slope peg. - -[Illustration: Fig. 264.] - -It is necessary to observe in the setting out of slope pegs that when -there is a change of gradient the operation must cease, but if the -point where this occurs be made the position of a normal the operation -may be proceeded with, if the instrument be set up at this point. - -600.--_To set out Slope Pegs on both sides of the Line simultaneously -without moving the Instrument from the Centre Line._--CONDITIONS. -Single Line. (_ab_) Formation 15 feet. (_cd_) Depth of cutting 14 feet. -Slope 1 to 1. - -The point _e_, Fig. 265, is the extension of the slope lines to cut the -centre line, and its depths below formation for 1 to 1 slope is half -the formation width, or 7′ 6″. - -[Illustration: Fig. 265.] - -OPERATION.--The instrument being set over a centre peg with the -telescope at the slope angle, turn the telescope to any other peg -and adjust the cross web to line therewith (on line _c f_). Take the -section depth _cd_ (14 feet), to which add _de_ (7′ 6″) = 21′ 6″. -This multiplied by ·707, the natural sine of the slope angle (45°) will -give the distance from the axis of the instrument to the slope line, -thus: 21·50 × ·707 = 15·20 feet, and the point on the surface at _g_ -where 15·20 can be read on the staff is the position of the slope peg. -This is similar to that described in the last paragraph, _but_ if the -telescope be now changed to the angle of the slope on the other side -of the line _ch_, the peg _i_ is instantly found by the same reading -(15·20). - -601.--_The Use of the Inclinometer in Mining._--A lode having been -discovered, it is required to mark out on the ground the general line -of the outcrop. Hitherto the method employed has been to find the -strike and drift of the lode and to level and survey the surrounding -country and plot on a contour plan. Lines parallel to the strike and -spaced according to the trigonometrically calculated bases are ruled -in. The points of intersection of the contour line with that of the -parallel line to the strike of the same height above datum will be a -point of outcrop. The bearings of these points are read, and their -distances scaled from the plan, the theodolite is then taken to the -field, and the points found are marked out on the ground. This entails -a considerable amount of labour and careful work both in the field -and office, and then only points at intervals are obtained and not a -continuous line. - -The inclinometer, having an adjustable axis at right angles to the -horizontal, enables the line of sight to be made to revolve in any -plane. If at the spot where the lode has been discovered the instrument -be set up in line with the strike, and the movable axis adjusted to -the angle of dip, it is evident the line of sight lies wholly in that -plane, and a continuous line of outcrop may be pegged out on a flat -or undulating country, which can be produced to any length required -by taking the instrument to a fresh station. This feature of the -instrument is equally, if not more, important than its use for rapidly -pegging out railway slopes. - -602.--=The Gradiometer.=--This instrument, while performing all the -duties of a first-class level, is designed also for taking vertical -inclines at small fixed angles for railways, drainage works, steep -incline levelling, etc., etc., and also telemetrical readings up to -great distances. - -In general construction, as regards telescope, stand, etc., it -resembles a level, and when set at zero is equal in every way to one of -the best, with the additional advantage that it may be used for rapid -work without the trouble of setting up by the levelling screws, as the -telescope may be levelled at any sight by means of the gradienter drum -milled head. The gradiometric arrangement is effected by the telescope -being mounted in trunnions, one pair being adjusted vertically; the -amount of elevation or depression is indicated by a drum carrying an -open extended scale graduated to read rise or fall, from 1 in 12 to 1 -in 1,200, which may be conveniently and distinctly read without the use -of a vernier. - -The additional parts do not increase the bulk of the case and add very -little to the weight. - -[Illustration: Fig. 266.--_Stanley's gradiometer._] - -By its use a great saving of work is effected. For instance, for a town -drainage in which it is desired to work out an inclination, say the -levels indicate a fall of 10 feet between the extreme points: if the -line the drainage is intended to take be measured, however angular or -zigzag it may be, and the length of that line be divided by the amount -of fall, this will give the gradient; say the line of streets measures -5,000 feet, this, divided by 10 feet, gives a gradient of 1 foot in -500. Therefore if the drum be set to that proportion, all the pipes may -be laid directly without further setting. The gradients for any railway -may be instantly found by merely turning the drum until the telescope -sights, up or down the incline to be measured, a reading on the staff -equal to the height of the instrument, and taking the reading of the -drum at the position of the indicator. - -For levelling steep inclines it also saves a great number of settings -up, as, instead of levelling for, say every 14 feet rise or fall, the -gradient of the total distance can be taken and also the distance -measured by stadia reading, when the incline is not too great for -taking one reading with telescope level, or by gradient reading when -this cannot be done, and by adding the staff reading to the distance -divided by the gradient, and deducting the height of the instrument the -difference of level can at once be ascertained. - -Example: Sighting a staff at a gradient which falls conveniently -upon it, say 1 in 35 and this reads 8·7 feet. Distance measured, as -explained later, say 735 feet, then 735/35 = 21 feet + 8·7 feet = 29·7 -feet; deduct the height of instrument, say 4·9 feet, difference of -level 24·8 feet. - -For measuring long distances beyond the range of the stadia lines or -points in the diaphragm, or for measuring distance on inclines, the -gradiometer will also be found very useful, as by taking the difference -of any two suitable gradients, the base distance is given without -calculation for difference of hypo and base. - -If the gradient be not very steep or below the height of the staff, -the simplest method is to sight the staff with the telescope level and -take the staff reading; say this is 12·45 feet, then set the gradient -drum to 1 in 100 and again take the staff reading and, say this is 4·30 -feet, the difference between these readings = 8·15 feet. Strike out the -decimal point which multiplies it by 100 and we have the base distance -815 feet. - -For shorter distances a larger base upon the staff may be taken, thus -giving greater accuracy; for instance, if the gradient drum after -taking the level reading be set to 1 in 50 and the resulting difference -divided by 2, any error in taking exact readings is reduced by one -half, or 1 in 33-1/3 and divide difference by 3; or 1 in 25 and divide -difference by 4: or 1 in 20 and divide difference by 5, etc. Any error -of reading would be reduced by one third, one fourth, one fifth, etc. - -The difference of readings obtained by either of the following two -gradients will also give base measurement without any calculation -whatever: 100 and 50 | 63-2/3 and 40 | 60 and 37½ | 50 and 33-1/3 | -33-1/3 and 25 | 25 and 20 | 20 and 16-2/3 | 12½ and 11-1/9 | 11-1/9 -and 10. - - Example: Suppose the top of staff is below level altogether, - turn the drum until the top of staff is sighted in the telescope; - say the gradient of this is 27½ go on turning until gradient 25 - is indicated and take the staff reading; say this is 12·75, then - move the drum until gradient 20 is indicated and take the - staff reading: suppose this to be 3·40, then 12·75 - - 3·40 - ------ - = 9·35 - -Omit the decimal point and the measurement reads 935 feet, which is the -horizontal distance. The two most suitable gradients would of course be -used according to the position. - -Distances may be set out with equal facility with the gradiometer -by the subtense method, by working out a subtense suitable for the -distance. This is easily done by dividing the distance required by any -two numbers having a difference of the required subtense, the result -being two gradients, which, when worked with, will give that subtense -at the required distance. - - Example: If the distance required to be set out be 650 feet, - a suitable size for an object to be plainly visible at this distance - would be 10 feet. Then take as divisors two numbers - having a difference of 10, say 10 and 20. - 650 ÷ 10 = 65 - 650 ÷ 20 = 32½ - -These two gradients will give a subtense of 10 feet at a distance -of 650 feet, and all that is necessary is to send a man out in the -required direction with a 10-feet rod (preferably having ⊤ ends, thus -⊢ ⊣, for long distances, to facilitate distinct reading), and signal -him to move farther off, or nearer until the length of the rod, held -vertically, is exactly covered by the movement of the telescope caused -by revolving the drum between gradients 65 and 32½. - -[Illustration: Fig. 267.--_Stanley's gradioplane._] - -It is always preferable to make the subtense as large as possible, as -the larger it is the more accurate the result will be. All distances -set out by this method are base distances, no matter what the -difference of level may be, and such figures for divisors should be -used as give the gradients below 100. Gradients between 12 and 65 are -the best and quickest to work with, and with care more accurate results -are obtained than with chaining. - -Thus, at one time, a distance may be set out or measured, the -difference of level taken, and also the gradient ascertained, and the -drum can instantly be set to zero and all ordinary levelling operations -continued. - -If preferred the gradient drum can be divided to percentage gradients -·001 to 8 instead of ordinary gradients 1 in 12 to 1 in 1,200. - -603.--=Gradioplane.=--This is a new instrument, specially designed -by the reviser for very accurate underground surveying, such as is -required for large sewage work or water works, long tunnels, or any -work requiring a very rigid and accurate instrument, with a very -powerful telescope for measuring all horizontal and small vertical -angles. - -The horizontal circle is 6 inches diameter, and reads by two verniers -to 20 seconds of arc, or it is fitted with micrometer microscopes -reading to five seconds of arc if desired. - -In the former case it carries a floating bevelled aluminium ring -compass divided to ¼ degrees, reading by microscope, and in the -latter a long trough compass. - -Vertical angles are measured by a very accurate form of gradiometer -screw carrying a drum with open extended scale in exactly the same -manner as the foregoing instrument, and the remarks regarding that and -its working apply equally to this instrument. The telescope, which is -14 inches long and carries a 1¾ inch object glass is so mounted that -it will revolve in the plane of any inclination set by the gradiometer -drum, and is provided with a locking arrangement for fixing it -absolutely true for fore or back sight, and it carries a long sensitive -spirit bubble to enable it to be used as a most accurate level and -for rapid levelling; this may instantly be set level by the drum at -any sight without troubling to level the instrument. The diaphragm is -fitted for subtense measurements. - -A further refinement is fitted to the telescope when desired, by -which any grade may be instantly divided into any desired number of -parts; this is effected by means of a horizontal circle fitted to the -stage under the telescope, which is read by a vernier attached to the -telescope. This circle is divided from 0 when the telescope is fixed at -zero round each way to 90 degrees into 100 parts, the vernier divided -to read 100ths or 10ths of each division. It will be seen that when the -telescope is in line with the gradient drum, that is at zero, it will -be raised or depressed to whatever grade is indicated upon the drum, -and is then capable of being revolved 180 degrees for taking a back -sight, when it sights the opposite grade to that which it does when at -zero. When it has revolved 90 degrees only the telescope becomes level -at any grade, and therefore at any position it is set between zero and -90 degrees it sights a part of that grade; supposing the telescope -at zero is set by the gradienter drum at 1 = 1,000 then by revolving -the telescope from that to level, it passes over 100 parts of that -grade, each of which may be subdivided by the vernier to 100 parts -again, consequently 100 × 100 × 1,000 which equals 1 in 10,000,000 -or any desired number of 10,000,000ths may be readily set by means -of the clamp and tangent fitted to the telescope, or if the grade be -set by the gradient drum to 1 = 100 then 100 × 100 × 100 equals 1 in -1,000,000, or any other grade which is set by the gradient drum may, -with equal ease, be divided by 10,000 or any other proportion that the -horizontal circle vernier may be divided to give. - -A sliding lower plate is provided for accurately centring the -instrument, the levelling screws are adjustable for wear, and the -tribrach is fitted with quick-setting spherical joint. - -This instrument will also be found of great utility in mining work, -to mark out the general line of the outcrop when a lode has been -discovered. This, by the ordinary method, entails a considerable amount -of labour and careful work both in the field and office, and then only -points at intervals are obtained, not a continuous line. With this -instrument the line of sight may be made to revolve in any plane, so -that if it be set up in line with the strike at the spot where the -lode has been discovered and the gradient drum adjusted to the angle -of dip, it is evident that the line of sight will be wholly in that -plane, and a continuous line of outcrop may be pegged out on a flat or -undulating country and can be produced to any length required by taking -the instrument to a fresh station. - -[Illustration: Fig. 268.--_Stanley's gradioplane._] - -The above illustration, Fig. 268, shows the gradioplane fitted with a -horizontal circle to the telescope for subdividing the grades of the -gradienter drum, and when thus fitted forms the most exact instrument -for setting out or ascertaining gradients that has been devised. - -604.--=Abney's Clinometer.=--This very popular little instrument, the -invention of Captain Abney, Fig. 269, embraces the same form of sighted -level with reflector as that shown in section, Fig. 87, p. 142, but -the level instead of being fixed in line with the tube is placed above -it upon an axis which forms the centre of a divided arc. The axis with -the bubble is turned to any angle by means of a light milled-edged -wheel placed in front of the arc. It carries an index which reads -on the arc the angular position of the level to the centre of the -instrument by a vernier to 10′. There is also a scale placed upon the -arc giving gradients from 1 in 1 to 1 in 10. As the bubble of the level -in its course passes the centre over the axis its reflection is made -to become coincident with the sight line through the tube only when it -is quite level. Therefore whatever the inclination of the tube, the -bubble may be brought level by turning the milled head until it appears -centrally in the sight axis of the tube, and the angle at which this -occurs can be clearly read afterwards upon the arc. The size of the -instrument in its case is 5 by 2½ by 1½ inches; weight, 8 oz. - -[Illustration: Fig. 269.--_Abney's clinometer._] - -[Illustration: Fig. 270.--_Troughton's clinometer._] - -605.--=Troughton's Abney's Clinometer.=--In the Troughton form, Fig. -270, the arc is toothed, and it is moved by a pinion similar to the -movement of the box sextant, so that the bubble moves slowly in -relation to the motion of the fingers when adjusting. The arc is read -by a single index line instead of by a vernier. - -606.--=Telescopic Hand Clinometer.=--The author has recently added a -telescope to the Abney form of clinometer, as shown Fig. 271. The arc -is moved by rack and pinion and reads by a vernier to single minutes, -therefore good reading within one minute of arc may be made with it. -Captain East, R.E., suggested a mode of steadying the instrument for -observation which appears to answer admirably for hand observation. He -puts the hook-end of his walking-stick into his waistcoat pocket and -clutches a part of the stick by his right hand at the height of his -eye. Then holding the instrument in his right hand supported by the -stick it is kept quite steady for observation. - -[Illustration: Fig. 271.--_Telescopic Abney clinometer._] - -607.--=De Lisle's Reflecting Clinometer.=--There have been several -arrangements made for converting the Burel level, Fig. 89, into -a clinometer; that devised by General A. De Lisle, R.E., with -modifications by Colonel Bell and Mr. Alfred Cooke, as represented in -Fig. 272, is the most popular. In this a heavy arc is constructed upon -the lower part of the instrument. This is jointed upon a vertical axis -at _C_ so that it may be revolved to bring the mass of the arc either -forward or backward, to take inclines upwards or downwards, or to rest -at an intermediate position to make the instrument flat and portable -in its case, it takes the position shown in the figure. The arc has a -stiff centre axis with a radial bar, the edge of which forms the index. -A sliding weight is placed on the radial bar, which is sufficiently -heavy when at its greatest extension to exactly counterbalance the -weight of the arc in a horizontal position and to make the mirror quite -vertical. In this position it forms a simple Burel level. A set of -graduations are made upon the arc, which are numbered 1 to 50 to 1 to -1. The radial bar index set to one of these numbers gives the amount of -inclination that will result from the coincidence of the reflection of -the centre of the pupil of the eye cutting the object to be observed. -The length of this instrument is about 6 inches; its weight about 10 oz. - -[Illustration: Fig. 272.--_De Lisle's reflecting clinometer._] - -608.--=Prismatic Clinometer.=--This instrument was originally devised -by the author about 1860. The form of the instrument, Fig. 273, is that -of a prismatic compass, art. 155. A similar metal or card and talc dial -to that of the prismatic is used, but this is centred upon a transverse -axis which is pointed at the ends to fit into hollow centres. This -card is weighted on one side, so that when the sights are in a truly -horizontal position the prism will show the zero of the card cutting -the sight line. If the instrument be inclined upwards or downwards, -the degrees of elevation or depression will be indicated by the card -retaining its pendulous position. This is a very convenient instrument -for use with the box sextant, and as it is only of about half an inch -in thickness, and of the same diameter, it will pack conveniently in -the case with that instrument--weight, 8 oz. - -[Illustration: Fig. 273.--_Stanley's prismatic clinometer._] - -[Illustration: Fig. 274.--_Barker's clinometer._] - -_In Using this Form of Clinometer_ the prism is raised or lowered -in its sliding fitting until the divisions of the card are sharply -defined. Then in looking over the edge of the prism through the slot -above it, the hair in the window of the back sight will appear to cut -the divisions of the card; and the object seen in the distance, in -front of the hair to which the instrument is directed, will appear -coincident with the number of degrees of inclination indicated by the -card. - -This clinometer is sometimes fitted upon a prismatic compass, so that -inclines may be read by the same prism and sight arrangement. This is, -however, done more neatly by the arrangement next described, if the -instrument is intended to be used with the prismatic compass only, and -is not wanted separately for use with the chain. - -609.--=Barker's Combined Prismatic Compass and Clinometer=,[36] Fig. -274.--The prismatic compass of this arrangement is that of Hutchison's -form, art. 155. The clinometer is of the same kind as that just -described, but this, instead of being a separate part of the instrument -capable of detachment, remains permanent. To effect this arrangement -the clinometer card is mounted over the compass card on a pin axis -instead of centres. A part of the clinometer card is cut away so as -to permit the compass card to be read beneath. This cut-away part -is held by a stop to a position out of the field of the prism when -the instrument is to be used as a prismatic compass. When the stop -is released and the instrument is held with its face vertical, the -pendulous clinometer card comes into view, and cuts by its reading -through the prism the sight line, as before described for the prismatic -clinometer. The prism is focussed to the upper or lower dial by a long, -sliding fitting. It is used as the instrument last described. - -[Illustration: Fig. 275.--_Continental form of clinometer (Burnier)._] - -[Illustration: Fig. 276.--_Section of the same._] - -610.--=Continental Form of Clinometer.=--Hand clinometers on the -Continent are generally made on Captain Burnier's plan, Fig. 275, -which was explained for the prismatic compass, art. 156. Indeed this -instrument is more generally combined with the prismatic compass. The -graduation is set up on a plated ring vertical to the plane of the -swing of a pendulum, shown in section Fig. 276. The reading index is a -hair which is read on the graduation by means of a cylindrical lens, -_B_, when this is brought coincident with the sights _D′W′_ as described -for Burnier's compass. When the clinometer and compass are combined -the vertical rims stand opposite to each other, _AC_. A lifter, Fig. -275, _L_, is provided to take the working parts out of bearing, and a -stop _S′_ to prevent oscillation. The illustrations show the combined -instrument: _B_ cylindrical lens reading the drums; _A_ clinometer; _C_ -compass; _DD′_ fore sight; _WW′_ windows, both of which fold down on -the top of the instrument. - -[Illustration: Fig. 277.--_Major Watkins clinometer._] - -611.--Major Watkins' Clinometer.[37]--The vertical plane of division -is adopted, as in that of Captain Burnier, but the reading, instead of -being taken on the exterior of the ring by a magnifier, which entails -a projection, is placed on its interior. This reading is magnified -by a concave reflector, shown Fig. 277 at _R_, which reads to a line -on a slip of ivory placed just beside the eye-hole _E_ shown in the -engraving. The pendulum is stopped by a pin, upon which it springs when -the box is rotated vertically to prevent wear when out of use. There -is much less work in making this instrument than Burnier's, and the -round form is more portable. The only point on which it does not bear -comparison is in that the concave mirror represents a uniform distance -sight which makes the reading indistinct to persons of weak sight, -whereas Burnier's admits of adjustment by placing the instrument nearer -to or further from the eye, the cylindrical lens being made large to -admit of this form of adjustment. This instrument could be improved by -the mirror being made adjustable. Weight, 6 oz. - -[Illustration: Fig. 278.--_Compass with clinometer sight._] - -612.--=Clinometer Sights.=--A clinometer sight is often attached to -a light pocket compass, as shown Fig. 278 at the upper part of the -engraving, consisting of a pin hole and hair cross. This, used in the -manner shown by the position of the eye in the engraving, can only be -made to take sight inclines by another person reading the pendulum -index, which marks the inclination in the degrees to which the compass -is divided. This portable pocket instrument is, however, useful in -other ways. Standing face to the instrument it will measure inclines -directly very fairly by looking over the top edge and bringing this to -the visual rate of inclination at which the pendulum index can be read -in front view. Geologists commonly use it in this way to take the dip -of strata. It can also be used by putting it on or against any inclined -surface. The case is generally gilt or nickel plated, and is about 2 -inches diameter, and the instrument weighs about 3 oz. - -[Illustration: Fig. 279.--_Rule form clinometer._] - -613.--=Rule Form Clinometer.=--This is made in the form of a stout -12-inch, one-fold boxwood rule, Fig. 279. It is much used by civil -engineers as a working tool, and intended to be applied directly to -an inclined surface, either placed on a straight-edge or otherwise, -generally to take the inclination of earth work. It may be placed upon -a picket laid upon the ground to take natural slope. When used in this -manner the lower surface is placed on the straight-edge or picket, and -the rule is slowly opened until the bubble in the level in the upper -limb becomes central. The arc of the head joint will then indicate -the inclination. It may be used in another way: the lower limb may be -set level on the dumpy level compass or on any flat plane, and the -inclination may be sighted through the pin-hole and cross-hair sights -shown at the ends of the upper part of the instrument. Its size is -6¾ by 1¾ by ½ inches; weight 9 oz. There are several varieties -of this instrument. - -[Illustration: Fig. 280.--_Road tracer._] - -614.--=The Road Tracer= is a balanced clinometer much used by natives -in India and China for road making, Fig. 280. It consists of a -pendulum, supported upon a stand that carries a sighted tube which -indicates the level of the ground when the weight is carried in the -axis of suspension. The weight is adjustable to a scale by a screw. The -scales read inclines, by displacement of the weight, up and down in -percentages or gradients, to which it may be divided. - -[Illustration: Fig. 281.--_Bellamy's road tracer._] - -This instrument has been improved by Mr. C. V. Bellamy, M.I.C.E., -M.I.M.E., F.G.S., &c., Director of Public Works, Lagos, West Africa, -a civil engineer who has had great experience in the colonies, and it -will be found much more accurate, less liable to get out of order and -far more convenient to use than the old forms. It is shown at Fig. 281. - -The chief feature of this pattern lies in the adoption of the arc of a -circle instead of a straight scale, and a pendulum weight actuated by -a rack and pinion in place of the screw and sliding weight. This admits -of greater nicety in the divisions and allows a stronger and lighter -construction. - -The sighting tube is provided with reversible sliding shutters, so -that back readings may be taken without unclamping the instrument or -altering the vernier or index. A powerful clamp is provided for locking -at any desired grade. - -A recent further improvement by Mr. Bellamy has been made by making -this instrument in a form to give readings in degrees of arc as well as -in gradients. Fig. 282. - -[Illustration: Fig. 282.--_Bellamy's improved road tracer._] - -FOOTNOTES: - -[35] Lister's Patent, No. 2375, 1864. - -[36] Francis Barker's patent, No. 1926, 1881. - -[37] British patent, No. 217, 1884. - - - - -CHAPTER XIV. - - INSTRUMENTS OF REFLECTION--OCTANT OR QUADRANT--REFLECTING - CIRCLE--SEXTANT--PRINCIPLE--PARALLAX--CONSTRUCTION--EXAMINATION-- - ADJUSTMENT--ARTIFICIAL HORIZON--SOUNDING SEXTANT--BOX SEXTANT-- - SUPPLEMENTARY ARC--IMPROVEMENTS UPON THIS--OPTICAL SQUARE--OPTICAL - CROSS--APOMECOMETER. - - -615.--=The Octant or Quadrant= measures angles within 90° by an arc of -45°. This instrument is generally termed an _octant_ on the Continent -from the space of the divisions; a quadrant by English-speaking races, -from the extent of angles it takes. The idea of bringing the reflection -of an object from a mirror in line with the direct sight line from -another object, to measure the angle at the position of the observer -subtended by the two objects, was originally proposed and worked out -in a manner by Hooke,[38] and also by Newton.[39] Newton's invention -was the more simple and important. This was communicated to Dr. Halley, -then Astronomer Royal, but it was left unpublished until after his -death, when it was found in Newton's own handwriting among Dr. Halley's -papers. - -Newton employed two mirrors to obtain the reflection of an object -placed at any angle of less than 90° to the axis of the telescope or -sight tube, to throw an image directly through the tube. One of these -mirrors was placed at an angle of 45° to the axis of the telescope and -covered half its field aperture, so that a direct image of an object -could be received by the eye from the open uncovered part of the -telescope at the same time as the reflected image of another object -from the mirror. The second mirror was placed so as to throw its -reflection into the mirror on the end of the telescope without giving -any obstruction to the open aperture. This side mirror was fixed with -the centre of its plane over the axis of a movable arm which read upon -an arc the amount of its angular displacement to 90°. The mirrors were -so arranged that their faces should be parallel to each other when the -movable arm was placed at the zero of the arc. The graduation of the -arc was of double the closeness of the ordinary arc reading, so that -the angular positions of the two mirrors in relation to each other was -indicated according to the following law:-- - -_That the angle between two reflections in the same plane is equal to -twice the inclination of the reflecting surfaces to each other._ - -616.--=Hadley's Quadrant.=--In Newton's quadrant the arc was brought -most inconveniently in front of the face. By Hadley's arrangement the -telescope or sight line is brought in a direction about parallel with -the chord of the arc, producing the very convenient form of instrument -now in use. This instrument was exhibited at the Royal Society, -13th May, 1731.[40] It was tried experimentally by the Astronomer -Royal, August, 1732, in a yacht excursion, when readings were taken -satisfactorily within a minute of arc.[41] It afterwards came into -general use. - -The quadrant was at first held to be sufficient for measuring the sun's -altitude for obtaining latitude, but Hadley, as early as 1731, saw the -advantage of extending the arc so as to be able to observe the -opposite horizon if the direct one was obscured. It was also found -that measuring the moon's angular distance from a star beyond 90° -was serviceable in determining longitude. He therefore proposed by a -duplicate system of reflections to extend the arc by what is termed -a _back sight_ to 220°. The means he suggested, which were commonly -carried out in instruments of the period, were found to be too -complicated for practice.[42] In the meantime the construction of these -instruments, originally framed of a combination of wood, ivory, and -metal, was much improved by making the frame entirely of metal. There -were also great improvements made in the optical parts, by which the -arc of 90° was extended. In 1757 Captain Campbell had an instrument -constructed of metal of 60° of arc which therefore read to 120°. This -instrument, with details of improvement, principally by Ramsden,[43] -became the modern sextant. - -617.--=Reflecting Circle.=--As soon as the success of the sextant was -assured there appeared to be a general desire to complete the circle -by reflections, many inventors thinking this would possess great -advantages over the arc of 120°, and we find therefore no lack of -inventions to this end, even by eminent men. _Reflecting circles_, as -they are termed, that were of sufficient merit to come into limited -use, were designed by Mayer, 1770; Borda, 1787; Mendoza, 1801; Hassler, -1824; Fayrer, 1830. Troughton's circle of about this period was no -doubt the best instrument of the class.[44] We have also meritorious -reflecting circles by Pistor and Martins, and by Amici.[45] Although -these instruments were used at sea to a limited extent, particularly on -foreign ships, they were also used on land, where indeed they were more -manageable. As no further reference to these reflecting circles will -be given, anyone interested in the matter may refer to the books -mentioned in the notes, where very full particulars of their structure -are given. It was felt necessary to mention the subject here, as the -same ideas are constantly cropping up as assumed advantages where -previous experience is forgotten. Reflecting instruments at sea are -tedious to use when the angle to be taken exceeds that taken in by -the eye without movement of the whole body. On land, when the angle -exceeds 120°, a theodolite is better; but supplementary angles may be -taken with the sextant conveniently on land, where the portability of -the instrument is of great consideration. This will be again brought -forward in discussing box sextants with supplementary arc. - -618.--=The Sextant=, of the invention of which some particulars have -just been given, is only used as a surveying instrument for the -exploration of new countries, for which employment--it may be used with -or without a tripod or stand--it is found to be a most convenient, -light, and portable instrument for the traveller for ascertaining -longitude, latitude, and time with the aid only of an artificial -horizon. Triangulation may also be taken with it of terrestrial -objects, even for the complete circle, by repetitions from station to -station in angles within 120°. The same principles which are followed -in the construction of the nautical sextant are followed also in the -manufacture of two modified forms of this sextant which are used for -surveying only, the _sounding sextant_ and the _box sextant_. As the -nautical sextant is most open to observation of its parts it will be -more convenient to discuss the construction and general arrangements of -this instrument first. - -619.--_Optical Arrangements of the Sextant._--Newton in the description -of his instrument placed the mirrors parallel to each other, that -is, to zero of the arc, in his illustration for the demonstration of -the principle. In this position he showed that the direction of the -reflected ray is coincident with the direct ray entering the eye from -the same object or star. This scheme the author has generally found the -clearest for illustrating the principle to persons not well acquainted -with optics, there being some difficulty in explaining the law just -given, art. 615, from a more complicated scheme. - -[Illustration: Fig. 283.--_Reflection in direct line from two plain -mirrors._] - -620.--_If two mirrors be placed with their faces parallel to each other -in such a manner that a ray of light may continue after two reflections -from them, the ray will continue its path parallel in its direction to -its incidence upon the first mirror._ - -Let _MM′_, Fig. 283, be two mirrors placed with their faces opposite -and parallel to each other. Let the incident ray _IM_ fall on the -mirror _M_ whose normal is _a_. Then, as the angles of incidence and -reflection are equal, art. 54, it will be reflected at equal and -opposite angle to the normal to _M′_. Let the normal of _M′_ be _a′_. -Then again, the incident line _MM′_ will be reflected at equal angles -to the normal to _D′_, that is, as shown by the diagram, it will -continue parallel with the incident ray and in such a position that an -object at _P_ would appear to the eye, placed at _D′_, as though it -were at _P′_ in the direct line of sight. - -621.--_Parallax._--It will be seen by the figure that the point _P_ -does not appear to the eye at _D′_ in its true position but at _P′_ -therefore with the mirrors _MM′_ quite parallel, the points _P_ and -_P′_ appear coincident, and would read as one point with the index of -the sextant set at zero, that is, at the position when the mirrors -are parallel to each other; whereas the points _P_ and _P′_ really -subtend a small angle if direct lines be drawn from them to _D′_. It is -therefore clear that the angle read by coincident reflection and direct -or, as it is sometimes called, visual image is less than the true angle -at about the position shown. This difference is called the _error -of parallax_. When the object is distant this error is immeasurably -small. The parallax error varies proportionately to the distance of -the mirrors apart and with their angular position. If the mirrors are -in such an angular position that the rays proceeding from an object -impinging upon the centre of the first mirror would, if continued, -reach the eye, there would be no error of parallax. This occurs in the -nautical sextant at about 60°, and the parallax error increases on -either side of this point. - -622.--In the practice of surveying this small error is neglected. -When the box sextant is used the mirrors are placed at a very small -distance apart, and the parallax error therefore is extremely small -even for near objects. Where two objects are to be triangulated, the -one near and the other distant, the parallax error is much decreased or -eliminated by taking the near object by direct vision, and the distant -object by reflection. In this case, if the near object be towards -the right hand, the sextant must be used in an inverted position. If -the two objects be both near, a distant object may be sighted in the -direction of one of them for the reflected image. - -623.--It is readily seen that if the parallelism of the glasses shown -in the figure be disturbed, say by a change in the relative angular -position of _M′_ so that the planes _M_ and _M′_ continued to subtend -an angle to each other, then the normal of _M′_ must also be changed in -direction equal to this; but the ray _MM′_ remaining constant, as there -is no movement of _M_, this ray will therefore be displaced in its -reflection from _M′_ an amount equal to the angle of incidence on _M′_ -from its normal, plus the angle of reflection from the opposite side -of the normal, that is, to double the amount of angular change of the -position of the mirror or of its normal, which is the same thing. The -sextant therefore reads, by change of position of one of its mirrors, -half the angle of reflection upon its arc; and to make it read to the -angular value of its reflection the divisions on the arc are made twice -as close, that is, half degrees are made to read as degrees. This will -be better explained by the following scheme.-- - -[Illustration: Fig. 284.--_Principles of reflection of the sextant._] - -624.--The above scheme, Fig. 284, is taken from Captain Magnaghi's -admirable work before mentioned, which gives a very clear geometrical -demonstration of the value of angular positions in compound reflection. -A ray of light _SR_ directed to a plane mirror _R_ is reflected -therefrom to a plane mirror _R′_, following a plane of reflection -perpendicular to the intersection of the two mirrors. The direction -_R′T_ of the ray reflected by the second mirror falls into the same -plane of reflection, and makes with the direction _SA_ of the incident -ray an angle double that which is comprised between the two mirrors. - -The two planes of reflection _SAB_ and _ABT_ unite in one because they -both contain the line _AB_ and the normal _BP_ to the mirror _R′_. - -In prolonging the normals of the mirrors to their point of intersection -_P_ we find that-- - - _BTS_ = _BAS_ - _ABT_; - but as ½ _BAS_ - ½ _ABT_ = _BPA_ = _BDA_, - therefore _BTS_ = 2 _BDA_. - -625.--The mirrors being placed in the position shown in the figure, if -we look through a telescope whose visual axis is placed in the line -_ET_, with its objective to the mirror _R′_, we see in the centre of -the field of view the image of the object _S_ reflected consecutively -by the mirrors _R_ and _R′_. We also see in the telescope whether the -mirror _R′_ is only a certain height above the plane of reflection, so -as to permit half of the object-glass to receive the rays coming from -the point _E_ situated in the prolongation of the line _TB_, also the -image of _E_ which is necessarily coincident with that of _S_, because -the rays by which each image is formed enter the telescope in the same -direction _BT_. Therefore when the images of the two objects _E_ and -_S_ appear superimposed or coincident in the middle of the field of -view, we have an index given that the mirrors form an angle with each -other which is half that which is made at the point _T_ from the same -objects, and when one is known the other is easily deduced. - -626.--=Nautical Sextant.=--The ordinary construction of this -instrument, Fig. 285, consists of a cast gun-metal frame, forming -approximately in outline a segment of a circular disc _AA″_ including -within its extreme radii about 155°. - -[Illustration: Fig. 285.--_Nautical or astronomical sextant._] - -627.--_The Limb G_, which is made only about 1/12 inch in thickness, -has generally a face of about ¾ inch in width, which is inlaid with -silver or platinum, as Fig. 127, p. 186, to take the graduation to -about 140°. The limb is stiffened by a deep, thin rib about ½ inch -wide, supported by a corner hollow. The exterior radial arms and -interspace framing, Fig. 285 _MM_, which vary very much in design -according to the taste of the maker, is made generally of about 1/14 of -an inch in width upon the face of the bars, with a depth of 3/8 inch. -This arrangement of the bars placed edgewise gives great stiffness -to the surface of the arc with little weight. A handle _L_, made -generally of ebony, is supported on two standards or _brace-pieces_ -_N_, which are carried off to about 2 inches from the back of the frame -to hold the handle parallel with the face. The handle has sometimes -a hole bushed through it with metal, to support the sextant upon a -corresponding pin forming part of a stand or tripod when the instrument -is used for taking observations on land. Three feet are placed at the -corners of the frame of the sextant, one shown at _Q_, to support it -conveniently on a table to take the reading of an observation just made. - -628.--At the centre of the arc a female axis of about 1½ inches in -depth _E_ is attached by three screws to the frame perpendicular to -the plane of graduation. This carries the male axis, which centres the -vernier on the vernier arm _M_. The axis is covered by a protecting -tube which forms one of the three feet upon which the instrument rests -when laid down. The vernier arm is made of gun-metal of about 1/16 inch -in thickness and from 1 inch diminishing to ¾ inch in width. This is -stiffened by a light rib on its upper side. - -629.--_The Vernier V_ reads upon an 8-inch sextant, that is, one of -eight inches radius, to 10″, the graduations being to 20′ and the -vernier taking 120 divisions. A description of the vernier reading was -given, art. 318. The vernier falls upon the arc on the plan shown Fig. -127, p. 186. It is clamped near to position by the milled-headed screw -_H_, and is adjusted by the tangent _I_. A magnifier _J_ is placed on a -jointed sling-piece _K_ which traverses the vernier. This is sometimes -provided with a ground glass shade to dull the silver for reading. The -sling-piece moves the magnifier opposite to any division of the vernier. - -630.--Over the axis of the vernier arm a large, oblong mirror, termed -the _index glass_, _A_, is fixed with its face in a plane cutting the -centre of the axis. _The index glass_ is placed with its longest sides -approximately in line with the vernier arm. This mirror is placed in a -metal tray and is sometimes made adjustable by three screws; but it is -better fixed by the maker by screwing the flange-piece, which forms one -end of the tray, hard down. The index glass moves with the index arm -and gives the first reflection of sun, moon, or star which falls thence -upon the _horizon glass B_. - -631.--_The Horizon Glass B_ is placed upon a spur-piece formed in -the same casting as the frame. This glass, which is worked perfectly -parallel, has the lower half of its surface next the frame silvered. -The silver is cut to a sharp line against the plain part. The horizon -glass placed in its metal tray has adjustments given to it by means of -capstan-headed screws in a manner that will be presently described. - -632.--_The Telescope_ screws into a ring fitted at _R_, which stands -upon a bar erect from near the edge of the frame. The female screw -by which the telescope is held is formed of two rings which adjust -for the amount and direction of separation, so that the telescope may -be directed coincident with the horizon glass. The bar or standard -supports the ring fitting and is made of either square or triangular -section, fitted accurately in a deep socket fitting, in which it slides -to raise or lower the ring by means of a milled-headed screw placed on -the end of the bar. This permits adjustment only sufficient to bring -the axis of the telescope opposite the line of division between the -plain and silvered parts of the horizon glass. - -633.--_Four Circular Shades_, carried in square frames fitted with -dark bluish-grey glasses, are jointed to the frame at _C_. These have -nib-pieces at the upper corners, so that one or more of the shades may -be turned up at a time by the finger-nail to intercept any surplus -amount of light from a luminous body reflected from the index-glass; -or the whole of the shades may be turned up when observation is made -of the mid-day sun. Three other similar shades, but placed in circular -frames are fixed at _D_, which hinge over and back, to be thrown in or -out of interception, and are used to subdue the light from the horizon -if required. - -634.--_The Telescopes_ used as a part of the sextant are generally -two in number. One for _direct vision_ is a short tube of about 3 -inches in length, focussing at about 4 inches. The optical arrangement -is the same as that of an opera glass, consisting of an achromatic -object-glass of about 4 inches focus and a concave eye-glass of about 2 -inches negative focus, Fig. 14. The second telescope is about 7 inches -to 8 inches in length. This has two Huygenian eye-pieces, which have -each a wired diaphragm at the mutual focus of the eye-piece and the -object-glass. One of these has two fine wires placed parallel for use -in adjusting the telescope, and the other has two pairs of crossed -wires to indicate the centre of the field of view. There is also a -plain pin-hole sight provided for open vision. - -635.--_The Case_ in which the instrument is packed is generally made -of well-seasoned mahogany, dovetailed together at its corners. The -fittings are made to put the instrument back in its case as it was -last used within a wide range. A tommy-pin for adjustments and a hand -magnifier are supplied with the instrument. The case is generally -French polished inside as well as out to prevent absorption of moisture -from sea air. - -636.--_Manufacture and Examination of the Nautical Sextant._--Besides -the general good work that this instrument demands, the important -points to be observed are, that the glasses should be of hard crown -glass worked perfectly parallel from face to face; they should also be -well polished. These observations apply to both the reflecting glasses -and the shades. The silvering of the mirror should be protected with -a good coating of copal varnish. The mirrors should be held by three -points only, and be quite free from strain. The upper of the three -points should detach, so as to be able to remove the glass at any time -for resilvering. The axis should be fitted with all the care necessary -for a theodolite, and be placed truly central to the arc. The extremity -of the vernier arm when free of its clamp should traverse the arc at -equal distance from its face and move with very light friction. The -extreme lines of the vernier should cut equal divisions all along the -arc 0° to 140°, observations being taken particularly at both ends and -in the centre of the arc. The vernier should lie flat on the limb from -end to end of the arc. The standard or stem-piece for elevating the -telescope should move upwards and downwards stiffly but equally by the -motion of its milled-headed screw. The division lines of the limb and -vernier should be cut fine but very deep: they should be cut on the -dividing engine from the axis of the sextant to ensure true centring of -the arc, and not as in the usual plan of having the axis adjusted to -the divisions. - -[Illustration: Fig. 286.--_Section of axis and index glass of sextant._] - -[Illustration: Fig. 287.--_Section of limb and clamp and tangent._] - -637.--_Axis._--This is the most important part of the instrument, -and requires the greatest care in construction. Fig. 286 represents -this to a scale half size. _a_ the axis, made of hard gun-metal, has a -collar by which it is attached to the index arm. The axis is ground and -burnished carefully into _S_ the socket-piece, which is fitted into the -frame and held down by three screws. At the end of the socket there is -a collar-piece _B_ attached upon an angular or tight conical fitting by -the screw _D_, which prevents the axis rising out of its socket. The -axis is covered by a cap _L_ which protects it from injury, and this -at the same time forms a leg to the instrument as before mentioned. -The index glass _I_ is mounted in a tray _T_ shown in section. There -are two points of contact at the lower part of the back of this glass, -formed by pins, and one point of adjustment pressing against the clip -_G_ by a spring _C_ in front, acting _contra_ to a screw at the back -_E_, which adjusts only a small distance to bring the index glass to -perpendicularity. The flange-piece _F_ is adjusted in the manufacture -so as to leave very small separate adjusting to the index glass -necessary. - -638.--_Section of the Limb and Clamp and Tangent._--The general -arrangement is shown in Fig. 287. _M_ arms of the frame; _J_ section of -the limb; _C_ clamp attached to the tangent _N_ for clamp and tangent -motion, described art. 346; _O_ milled head to clamp; _N_ milled head -to tangent. The vernier is shown at _V_, reading through an opening on -the face of the index arm _P_. The rib to stiffen this arm is shown at -_R_. - -[Illustration: Fig. 288.--_Vertical section of horizon glass._] - -[Illustration: Fig. 289.--_Plan of section A to B._] - -639.--_The Adjustment Arrangement of the Horizon Glass._--This most -important adjustment is constructed in various ways. The plan now -generally thought to be the best is for the maker to fix the horizon -glass frame firmly in its true position perfectly perpendicular to -the surface of the frame, and to allow a small amount of adjustment -to the glass only. A convenient plan of doing this is shown in the -vertical section full size in Fig. 288. The frame _FF_ is made in one -casting, which has its base collar firmly fixed to the frame of the -sextant. Fig. 289 is a cross section _A_ to _B_. _H_ the horizon glass -is held upon its face by three points, one of which is shown at _L_, -which is placed in the centre of the top. The lower front points are -the exterior corners of a plate which is cut away between. This plate -is held by the screw _G_. The screw _G_ forms a kind of hinge which, -together with the elasticity of the plate, gives a slight pressure -directing the glass hard upon the points of the screws _J_ and _Q_. -The screw _J_ resists this pressure lightly and permits adjustment of -the horizon glass _H_ to angular position in relation to the plane of -the index glass to a small extent, by means of a pin placed in the -capstan head _J_. The perpendicular position of the horizon glass, _H_, -is secured by slight adjustment of the capstan head _K_, which moves -against a spring _L_ in the vertical centre of the top of _H_. This -piece, with screw and spring, is attached to the horizon glass frame -_FF′_ by the screw M, so that it may be easily removed to replace or -resilver the glass. The silver on the glass is cut to a sharp line at -about the point _H_ with a razor. - -640.--_Testing the Parallelism of the Surfaces of the Glasses._--The -best method is to firmly fix a telescope provided with webbed or -pointed index diaphragm so that the webs or points cut a distant, -sharply defined object, or its edge only, quite clearly. If the glass -to be tested be now placed in four directions agreeing with its four -sides in front of the object-glass of the telescope, and it is worked -perfectly parallel, and is free from striæ, the distant object will -not appear to be displaced by its presence in the slightest degree at -any position. If the glass be not mounted and is quite square, should -there be any very small error, the thickest or thinnest edge should be -placed towards the frame; but in this case only a very small error is -permissible. The coloured glasses require the same test as the white -ones. Where the parallel glass to be tested is small, the object-glass -of the telescope may be covered by a paper cap, with a small hole only -left through its centre, sufficient to take the glass. - -641.--The glasses, when fixed in the sextant, may be examined for -parallelism approximately by setting them end up singly to the sun, -with the sextant set at an angle that the direct and reflected -images of the sun's limb appear just to touch, the eye-piece of the -telescope being constantly covered by the sun-glass. If there be a -want of parallelism, the image will be disturbed. One reason that -the telescopic plan first proposed is better to be followed in the -construction of the instrument, is that the telescope is fixed and that -there is no indistinctness from unavoidable motion of the body, such as -occurs when the sextant is held in the hand. - -642.--_The Quality of the Surfaces of the Glasses_ may be examined, -both for flatness and brightness and for equality of density, by -holding them so that the reflected image of a straight body, as for -instance a stretched thin string placed at a distance, may be observed -by reflection in glancing over the surfaces with the eye nearly -parallel with its plane. If the glass be imperfect the image that -reaches the eye will appear to be wavy. If the reflection appear misty, -this is generally due to want of parallelism of the glass; but this -mode of observation is altogether somewhat technical and difficult to -attain without skill. - -643.--_To Silver the Index or Horizon Glass with Mercury._--Clean the -glass thoroughly by boiling it in water containing an alkali (potash -or soda), and then polish it off with whiting and water, using a clean -piece of old linen or perfectly clean wash-leather. Do not touch the -surface with the fingers. Take a piece of clean tin-foil freshly opened -from the roll and cut out a piece slightly larger than the glass to -be silvered. Lay this upon a smooth pad--an old leather book-cover -answers. Place a single drop of clean mercury about the size of an -ordinary shot upon the tin-foil and rub this gently over the surface -until it is entirely silvered. Now pour very gently sufficient mercury -upon the foil till the surface appears to be flooded. Take a sharply -cut straight-edge formed of stiff writing-paper, and draw this over -the surface of the mercury to clear it. Take a slip of clean smooth -writing-paper very little wider than the foil and of about one and a -half times its length: spring the paper to a slight curve and place -one part of it over the silvered foil so that when it springs open it -will cover it and exclude the air from the surface. Now give the glass -a final polish and lay it upon the paper over the foil. Hold the glass -down with slight pressure with the left hand, and slowly and steadily -draw out the slip of paper in the linear direction of the surface of -the glass with the right hand. This will take out the air between the -foil and the glass, so as to bring the mercury in contact and leave a -perfect mirror. It must now be set aside with the glass turned face -downwards in an inclined position, so that the surplus mercury may -drain off from the foil. Small slips of foil should be put at its lower -edge, which, by their attraction for the mercury, will accelerate the -draining. The mirror should not be touched after setting it up to drain -for twelve hours at least, after which the surplus foil may be trimmed -off. After another thirty hours or more it may have any varnish or -other protection applied to the back of the silver. - -644.--Where instruments are taken abroad mercury silvering may become -spotted, so that a small store of mercury and tin-foil should be taken -out with the sextant for resilvering. But it should be particularly -observed that the mercury should never be placed in the same case with -the instrument, as the smallest particle, if it touch the frame, will -eat into the brass and destroy its strength. Sealing-wax dissolved in -spirit answers for a varnish at the back of the foil fairly well after -resilvering if proper varnish be not at hand. It is advisable before -attempting to silver a sextant mirror to practise on a few slips of -ordinary glass in order to get into the way of doing it. In modern -practice base silver is deposited, and no mercury is used, but the -process requires special skill. - -645.--_Adjustment of the Index Glass._--Hold the sextant clamped to -about 60° in a horizontal position with the index glass near the eye. -Look nearly along the plane of the glass in such a manner as to be able -to see one part of the plane of the arc by direct vision, and another -part by reflection of it at the same time. If the direct view and the -reflected join in one line, and the arc appears as the continuity of -a single plane, the index glass is perpendicular to the plane of the -sextant. If this be not the case it can be adjusted by turning the set -screw placed at the back of its upper centre, Fig. 286 _E_, very gently. - -646.--_Adjustment of the Horizon Glass to Perpendicularity._--Place the -vernier at zero. Hold the plane of the sextant parallel to the horizon -and observe if the image of the horizon seen by reflection at the edge -of the silver line coincides exactly with the image received directly -through the plain part of the glass. If it does so the horizon glass -is perpendicular to the plane of the instrument, that is, assuming the -index glass is also perpendicular. In this adjustment it is well to -rock the plane of the instrument say 20°, to see that the horizon is -cut as a clear line about its horizontal position for this amount of -angle. If the mirror be not perpendicular adjust gently by the single -screw at the top of the horizon glass frame. If the horizon be not -water, the sharp outline of any distinct distant object will answer, or -a piece of fine string placed at a distance and stretched straight. - -647.--_Adjustment for Index._--This is the adjustment for parallelism -of the two mirrors at the zero of the arc. The sextant is clamped at -zero as before: the arc of the instrument is turned in a vertical -position and the horizon again observed. If this appears to cut a clear -line through the plain glass and the mirror there is no index error, -and the planes of the glasses are truly parallel to each other in this -position. If the line is not continuous adjust gently by the lower -screw, Fig. 288, at _G_. - -648.--_Adjustment of the Horizon Glass by the Sun._--This is a better -adjustment than that given above, except that it introduces any error -that may be due to the imperfection of the shades; and it is more -difficult particularly for the first approximate adjustment. Arrange -the telescope and shades so that a clear outline of the sun's limb -may be observed without distressing the eye. Place the vernier at -zero. Observe the sun, which will be most conveniently sighted at -about 40° elevation, first with the plane of the frame vertical, and -then horizontally perpendicular to this. If the sun presents a round -disc in both these positions the sextant is in adjustment. If in the -vertical position there appears to be a small notch at top and bottom -of the sun's limb, the glass is not perpendicular to the plane of the -instrument, and this requires adjustment by the screw at Fig. 288 _K_. -If notches appear at the sides of the limb when it is held horizontally -there is an index error, which may be adjusted at _G_ if it be small. - -649.--_Index Error after Adjustment Allowance._--The limb of the -sextant is graduated 5° beyond the zero position when the glasses are -parallel to each other. This is called the _arc of excess_. The vernier -is also divided three lines beyond its zero position, which is marked -by an arrow. These extra divisions are placed on the instrument for -correcting the index error by measurement of the angle subtended by the -diameter of the sun's disc alternately on one side and the other of -the zero line, in which observations, if the two readings agree, the -sextant must be in perfect adjustment; when they do not agree half the -error may be adjusted by the horizon glass. The same observations may -also be made with a bright star by setting the index alternately on -one and the other side of zero. When the sun is used the reflected and -direct images are brought together, so that the two suns that appear -in the instrument just touch limb to limb, first upon direct reading -and then upon the arc of excess. When the division is adjusted very -nearly, any small error, plus or minus, may be allowed as a constant -for all readings. In observations of the sun care should be taken that -the eye is protected, both by the sun-glass cover to the telescope and -by sufficient use of the shades. - -650.--_Adjustment of the Telescope to Set its Axis Parallel to the -Plane of the Sextant._--In fixing up the instrument after manufacture, -the ring standard which carries the telescope is set at a measured -distance from the plane of the frame, so that the centre of the ring -coincides with the height of the silver line cut on the horizon -glass. This is necessarily a primary adjustment. For final adjustment -the long, inverting telescope is screwed home in the ring, and the -eye-piece which has two parallel wires across its diaphragm placed -in it. The telescope is brought to focus on any distant object, the -eye-piece being turned at the same time to bring the wires parallel -with the face of the instrument. Two objects are taken subtending an -angle of 90° or over,--as the sun and moon, or the moon and a bright -star,--and the index is moved so as to bring the objects, say the limbs -of sun and moon, in contact with the wire nearest to the sextant, and -fixed there. Then by changing the position of the instrument a little, -the images are made to appear upon the wire furthest from the sextant. -If the limbs of the sun and moon still remain in exact contact as they -appeared before, the axis of the telescope is truly adjusted. If the -limbs of the two objects appear to separate at the wire furthest from -the sextant, the ring-adjusting screw furthest must be loosened a very -little and the screw nearest the sextant tightened the same amount. If -the reverse, and the images appear to overlap, adjust in the reverse -direction. By repeating this operation a few times the contact will -appear to be the same at both wires, and the axis of the telescope will -be in collimation, that is parallel with the plane of the instrument. -After the telescope is truly adjusted it may be raised or lowered a -little to make the reflected and direct images appear equally clear. - -651.--_Final Examination of the Sextant._--It will be readily seen that -an instrument, although correct in theory but depending upon perfection -of workmanship in centring, division, surface and parallelism of -glasses, and also in its adjustments, can scarcely be brought to -perfection. The errors generally increase from the zero point, where -adjustments are possible, and are greatest at 140°. In the ordinary -commercial sextant of the dealers the errors of centring alone are -commonly 3 minutes to 5 minutes, with like errors in other parts. It is -therefore better, where the sextant has to be absolutely relied upon, -to subject it to actual trial. The zero point can be readily fixed by -rules already given; besides this the meridian altitude of several -bright stars subtending angles of about 30°, 60°, 90°, and 120° should -be measured either from a clear horizon or from a mercury artificial -horizon, to be described presently, for angles under 60°, and the -errors plus or minus tabulated. The data for the meridian altitudes of -certain stars upon any night may be taken from the _Nautical Almanac_, -which will require correction for the latitude and longitude of the -observer. This subject is too complicated to be entered upon in detail -here. At the present time the National Physical Laboratory undertakes -the examination of sextants for a moderate fee. This is effected by -means of fixed collimators, art. 229. For angles distributed over the -arc the parallax error is eliminated by placing the collimators in -pairs. The N.P.L. certificate may now be had with good instruments when -purchased. It may be noted that an originally well-made instrument -retains its qualities for all time, the wear of such instruments being -inappreciable. - -652.--_To Use the Sextant_ the right foot should be placed nearly 2 -feet in advance of the left and directed at right angles to it. In -this position the body is firm. The instrument is supported by the -right hand, the elbow being brought down firmly upon the body. The -clamp screw first and then the tangent screw are moved by the thumb -and finger of the left hand. Some practice is required to make a -steady observation. To bring two objects into apparent juxtaposition, -methods of observation for terrestrial objects will be reconsidered -in discussing the box sextant further on. As regards celestial -observations reference should be made to works on practical astronomy, -as the subject would take too much space to be entered upon here. The -whole subject, with many refinements of correction of parallax, etc., -which fall beyond the limits of practical surveying with the sextant, -is ably discussed in Chauvenet's _Spherical and Practical Astronomy_. - -653.--=Artificial Horizon.=--For ascertaining the latitude of a place -from the observation of a celestial body by means of a sextant, it is -necessary to have some means of estimating the position of the horizon. -A method of doing this, originally proposed by the elder George Adams, -optician, 1748,[46] was to float a parallel disc of glass upon a basin -of mercury, and to receive the reflected image of a star from the -mercury by the sextant simultaneously with its direct image. The angle -then given by the reading of the arc is double the angle at which -the true horizon is placed relatively at the same time. This idea, -carried out in a practical form in an instrument henceforth called the -_artificial horizon_[47] is due to Wm. Jones, a well-known optician at -the end of the 18th and beginning of the last centuries, who arranged -convenient means of making the instrument portable, and to keep the -mercury from disturbance of the air by covering it with a glass roof. -The form of artificial horizon that he invented has been in common use -ever since. He also invented another simpler form, which was that of -taking the reflection from a piece of silvered, or of black, glass. -The performance of the artificial horizon depends in any case entirely -upon means of obtaining a reflection from a perfectly horizontal -surface. - -[Illustration: Fig. 290.--_Diagram of artificial horizon._] - -654.--_Theory of the Artificial Horizon._--A ray _M′_ Fig. 290, from a -luminous body, at infinite distance will have its image reflected from -a level reflecting surface _SS′_ at an angle equal and opposite to the -incident ray, the angles _M′AS_ and _EAS′_ being equal. Let _E_ be -the place of the eye or the sextant: this will receive a ray from the -same distant body in direction _ME_, which is sensibly parallel with -_M′A_. The angle _MEA_ being double the angle of incidence _M′AS_, the -half of this angle will therefore produce the horizontal line -_EH_ at the height of the observer's eye if the plane of reflection -_SS′_ be level. Therefore if we take half this angle _MEA_ as it -appears in the sextant, it will give an angular position of the object -in relation to the horizon at the height of the eye, or be tangential -to the surface of the earth. If _M′AS_ be 30°, the angle _AEM_ will -be 60°, showing the elevation of object half this or 30°. The sextant -takes 120° with certainty; therefore 60° will be the limit of meridian -altitude the artificial horizon will measure. - -[Illustration: Fig. 291.--_Artificial horizon of black glass._] - -655.--=Artificial Horizon in Black Glass.=--This instrument is the most -portable, packing in a close pocket case. It is made of both circular -and square form in plan. Fig. 291 is the Admiralty pattern. The black -glass should have a truly plane surface. It is fixed over a brass -tray by being floated on plaster of Paris to avoid strain. A light rim -of brass is screwed down over the glass to keep it in position. There -are three adjusting screws _AA′A″_. It is adjusted to level by a -loose level tube ground on its under face _P_. The level tube shown in -detail Fig. 51, p. 94, is placed on the surface lineally with the two -screws, Fig. 291 _AA′_, and afterwards at a right angle to its first -position with one end of the tube towards _A″_. It is finally tested -by traversing at the position shown in the Fig. 291, and at right -angles to this direction. There is a great risk of getting a strain on -the glass in fixing it in its frame. The author therefore prefers the -circular form that leaves the glass quite free except at its fixings -at three equidistant points only. In this kind of artificial horizon -there is only one surface of glass to be worked true; therefore, there -is perhaps less risk of error on this account than in other forms. On -the other hand the mercury presents a more perfectly level plane. The -circular artificial horizons are commonly made 3¼ inches diameter; -weight, ¾ lb.; the oblong, Fig. 291, 4 inches by 3 inches; weight 2 -lbs. - -[Illustration: Fig. 292.--_Artificial horizon, mercury._] - -[Illustration: Fig. 293.--_Mercury bottle to the same._] - -656.--=Artificial Horizon of Mercury=, Fig. 292. This instrument -consists of an oblong tray of about 6 inches by 3 inches by ¾ inch in -depth made of wrought iron. It is covered by a roof with two sloping -sides at about 45° to the plane. The sides of the roof are glazed with -worked parallel glass fixed by screws at three points. The mercury when -out of use is contained in an iron screw-stoppered bottle, Fig. 293. -It is poured into the open tray for use, and the tray is afterwards -covered by the roof to prevent currents of air disturbing the level of -the surface. After use the mercury is poured back into the bottle from -the corner of the tray. It should be particularly observed that it is -perfectly drained, as any free particles in the case in which all parts -of the instrument are packed would be certain to attack the roof, which -is made of brass and simply varnished. The instrument is packed in a -mahogany case, size 7½ inches by 6 inches by 5 inches; weight, with -1 lb. of mercury, about 4¾ lbs. - -657.--_The Bottle_, Fig. 293, is made of cast iron. It has a screwed -plug stopper with a leather collar and a covering cap with a small -hole through its apex. To pour out the mercury the cap and stopper are -unscrewed, the plug is taken away, and the cover is screwed on again. -The mercury then issues from the small hole in the cap. To return the -mercury the cap is reversed and screwed upon the bottle. It then forms -a funnel. The tray has a covered corner at which there is a small -hole. This permits the mercury to be poured into the funnel without -splashing. Both plug and cap are then screwed down firmly, and the -bottle is placed in a secure fitting in the case. - -[Illustration: Fig. 294.--_Captain George's artificial horizon._] - -658.--=Captain George's Artificial Horizon=,[48] Fig. 294. This is a -great improvement on that last described. The instrument being made -entirely of iron there is no risk of getting it injured by escape of -the mercury. It is also much more portable and convenient. Two chambers -_E_ and _M_ are connected together by a tube through a stem-piece in -which there is a strong iron cock at _a_. The chamber E is cored out -and form a bottle into which about 1 lb. of mercury is introduced by -removing a screwed stopper at _B_. The chamber _M_ is an open tray with -a cover formed of a piece of parallel glass placed in an iron rim which -screws down upon it. A milled-headed screw at _C_ forms an air plug. -The cock moves very stiffly by the leverage given by a tommy-pin, shown -_a′_, which is inserted in the hole at _a_. The chamber _E_ is slightly -elevated to cause the mercury to flow from it to _M_, the cock being -turned on at the same time and the air screw _C_ released a little. By -the same arrangement, _M_ being raised, the mercury flows back into the -bottle for storage. - -659.--_For Using this Artificial Horizon_, when the mercury is poured -out in the tray _M_, it is levelled by the three screws _AA′A″_ so -that it covers the bottom of the tray and presents a clear, level -surface. A separate disc of parallel glass, which fits the tray _M_ -very loosely, is provided with the instrument. This floats on the -surface of the mercury and keeps it quite still, even when the covering -glass is removed. This arrangement is useful also in case of an -accident to either of the glass covers. The disc is kept when out of -use in a soft leather bag which fits in the tray _M_. This artificial -horizon is generally carried in a solid leather case with sling to go -over the shoulder. Its weight complete is about 4½ lbs.; size, 9½ -inches by 4 inches by 1½ inches. The surface of mercury is a circle -of 3 inches diameter. - -660.--=Improved Captain George's Artificial Horizon.=--Mr. S. A. -Ionides, C.E., has devised an improved form of the foregoing instrument -shown at Fig. 295. - -[Illustration: Fig. 295.--_Ionides's artificial horizon._] - -In this the container is formed beneath the horizon box with a plug tap -fitted in the thickness of metal between the two; this form makes the -whole much lighter and less than half the size of the usual Captain -George's pattern. - -661.--_In Using the Artificial Horizon with the Sextant_ it is -generally placed on the ground at such a distance in front of the -observer that he can conveniently see the required reflection of -the star or sun, the observer moving about until the reflection is -obtained. This is a tedious process and requires some practice. It is -much more easily effected if the sextant be mounted on a tripod or -other stand. When a stand is used it has generally a universal joint, -so as to be able to take surface angles also from the fixed position. -When the altitude of objects on the earth is taken, the observation -requires reduction for refraction, which becomes an important factor, -although this is variable with atmospheric conditions; but upon the -whole it always tends to make the object appear higher than it really -is. Commonly one-seventh of curvature is used as an approximate -correction. For solar and stellar refraction, works on astronomy should -be consulted. - -The index error of the sextant is corrected before refraction, when the -natural horizon is employed. When the artificial horizon is used the -index error is allowed before taking its half as a single measure. The -artificial horizon is used also with the theodolite. It forms the most -perfect means of adjusting the transverse axis by taking an observation -of the pole star with the telescope, first directly and then by its -reflection from the artificial horizon. If the images cut the centre of -the webs in the two positions by the movement of the transverse axis -only from the one to the other, this axis is proved perfectly level. - -662.--Various schemes for obtaining the horizon by some system of -levelling apparatus attached to the sextant have been devised, none -of which are very practical, as they all depend upon a pendulum or a -gravitation surface of a liquid or a gyroscope, and are all unstable as -hand instruments. There have been numerous patents taken out with this -object from that of Winter (1760) downwards, which anyone interested -in the subject may consult.[49] The matter is mentioned here as the -recurrence of the idea appears to be frequent. - -[Illustration: Fig. 296.--_Sounding sextant._] - -663.--=The Sounding Sextant.=--This instrument is used for coast -surveys. Angles are taken with it of objects, buoys, etc., from the -land and also from a boat on the water for such objects or for others -upon land. It is constructed upon the same principle as the ordinary -nautical sextant; but as it is to be used as an all-day working -instrument, and not for a few diurnal observations only, it is made -much more solid, and its optical parts take a more extended field of -view. The graduation is also stronger, such precision of reading only -being required as may afterwards be plotted on a chart. This instrument -is shown in perspective, Fig. 296. The index glass is large--about -2¼ inches by 1¼ inches. This is secured on all sides by a -firm rim to the tray in which the glass is held at three points. -The adjustment of the index glass is left under control, as it may -occasionally be necessary to remove it from effects of spray upon and -about it. The horizon glass is made about 1½ inches in width and -¾ inch in depth. This is entirely enclosed in a tray, the whole -surface being a mirror without any plane part to the glass as with -the ordinary sextant, so that it is entirely protected by the metal. -By this arrangement the eye receives the direct ray from the object -immediately before it, and the reflected ray from an object whose -angular position is desired to be taken with it: but these images do -not come exactly into contact, as the narrow frame interposes. It is, -however, sufficiently near for terrestrial observations. The adjustment -of the horizon glass to the perpendicular of the plane of the arc -is the same as that shown in detail for the box sextant further on. -The adjustment of the horizon glass to the index is by a stiff arm -extended from the sole-plate projected into a loose opening, where -it is held firmly by two opposing capstan-headed screws, as before -described. The arc of the sextant is of 6 inches radius, graduated upon -silver to 20′, and reading by the vernier to single minutes only by the -microscope. The clamp and tangent are the same as those described for -the nautical sextant. The frame is straight braced. The telescope has -a wide field, with achromatic object-glass of 4½ inches focus, the -clear aperture being 1-1/8 inches. The supporting ring of the telescope -has no rising stem or collimating adjustment, but is solidly fixed in -its true position by the maker. The ring carries a plain disc pin-hole -sight, which takes the place of the telescope for near observations. -The instrument in use is held in the hand by a firm oblong handle. -The instrument rests, if required for reading, upon three legs as the -ordinary sextant. Its weight is about 2¾ lbs., or when packed in its -case, 5 lbs. Its examination and adjustment are of the same kind as -those just described for the nautical sextant. - -664.--=Box Sextant.=--This very neat and portable instrument was -invented by the late William Jones.[50] It is used for taking angles -within 120° upon the surface of the land to within a single minute -of arc. It has become deservedly popular with British surveyors as a -land surveying instrument, and is equally so as a military one. It is -the same in principle as the nautical sextant already described, but -it possesses the great merit--as a surveying instrument constantly in -hand--that all its glasses and delicate parts are securely protected -from accidental injury by being covered; whereas the nautical sextant, -made for one or two diurnal observations only, has all these parts -exposed. And it is not only that all parts are protected when the -instrument is in use, but they are all doubly protected by the covering -box when carried about out of use; so that it is found that a well-made -box sextant set originally in perfect adjustment will retain this -adjustment in average use for very many years. The author has seen an -instrument twenty years in use still in perfect adjustment. The box -which covers the instrument out of use forms also a most convenient -handle or support for it when in use by attaching it in a reversed -position underneath, as it appears in Fig. 297. This attachment is made -either by a screw cut entirely round the body of the instrument, or, -what is much better, by a bayonet fitting, for the reason that large -screws of this description are liable to _cross thread_. The general -description of the outer parts is as follows:-- - -[Illustration: Fig. 297.--_Perspective view of the box sextant ready -for use._] - -665.--_C_ a covering box which inverts from the position shown in the -figure and covers the instrument. This has a diameter of 3 inches and -a depth of 1½ inches. _B_ box containing the optical and moving -parts of the sextant. _A_ axis of index glass. This axis also carries -a toothed segment fixed close under the front of the box, by which -both the index glass and index are moved by means of a pinion to be -described. The index carries a vernier divided into 30, which reads -into the arc to single minutes; the arc is divided to half degrees -on silver. The magnifier is centred by a swivel hinge joint over the -axis, so as to permit it to be brought to focus upon the arc at any -position. This magnifier is held down on the front of the box when out -of use by a nib catch at a position of about 80° of the arc. _O_ a -milled head, the axis of which carries a pinion which works into the -segment above described under the index glass. The pinion is about 1 to -9 of the segment, so that the index traverses the arc of 60° (reading -120°) by one-and-a-half turns. This gives a conveniently slow motion to -the index glass, and enables this sextant, if it be well made, to be -set rapidly with great precision. _S_ two nibs, part of two levers for -putting the shades in or out of action. - -666.--In the closed form of sextant the shades block the reflecting -position between the index and the horizon glass. For surface surveying -they have therefore to be opened out, through an opening closed by a -slide shutter which moves by a stud in a slot on the under side. The -shades consist of one green and one dense red glass which must be -worked parallel, as before described for the nautical sextant. These -are used for taking altitudes of the sun, for adjustments only. - -667.--_The Key K_ is a milled head which screws out, and carries -a watch-key pipe at the end of its stem by which adjustments may -be made from three square-headed screws fitting its pipe, two of -which are close to _b_, the axis of the horizon glass. These adjust -perpendicularly to the plane of the arc. One screw at a adjusts the -parallelism of the index and horizon glasses when the index is at zero. - -668.--_The Telescope_ is achromatic, with draw tube for focussing. -It magnifies about 2½ diameters. It has a concave eye-glass, and -therefore gives an erect image, Fig. 14. A sun-glass _E_ screws over -the eye-glass when it is required for sun observations. The telescope -is attached to the sextant by means of a crank-piece upon the telescope -which is fixed by the mill-headed screw _T′_ and two steady pins. -The crank-piece screws in reverse position upon the telescope for -portability before putting it by in its case. - -669.--By some makers the telescope is made to slide into the body of -the sextant and thus become quite portable. This plan is a very neat -one, but it requires care to see that the shades do not interfere -before it is put by. The weight of the entire sextant with its solid -leather case is about 18 oz. only. For close work the telescope is not -generally used. A sliding shutter pierced with a small hole covers the -telescope opening into the sextant, which is used as a sight hole. - -[Illustration: Fig. 298.--_Box sextant under the face._] - -670.--_The Interior or Optical and Mechanical part of the Sextant_ is -shown Fig. 298. _I_ index glass, fixed over the toothed segment on -the same axis. The pinion is shown working into the segment moved by -the milled head _O_ of Fig. 297 on the face of the sextant. Fig. 298: -horizon glass, cut by _ED_, adjusts to the vertical by screws _CC′_, -which have square fittings on the face of the instrument, shown Figs. -299 and 300 full size. The differential adjustment between horizon and -index glasses is made by a screw with a square fitting at _P_. This -adjustment acts by screwing against a helical spring, shown at _Q_. The -reflected rays enter by a wide window in the side of the box, Fig. 298 -_d_, the direct rays by a small window _f_. The path of a ray is shown -by fine lines from _R_ to _E_, for the positions in which the index -and horizon glasses are placed. The pin-hole opposite which the eye is -placed is shown white. _S_ shades with their axis are shown cut off, -to prevent confusion of other parts. They are simply round discs of -parallel glass on arms which rise from the back of the face by pressure -of the nibs at _S_. - -[Illustration: Fig. 299.--_Plan of horizon glass._] - -[Illustration: Fig. 300.--_Section of the same._] - -671.--_The Construction of the Box Sextant_ may be fairly inferred -from inspection of the engravings. The face-plate is made of a casing -in brass 1/8 inch thick, which should be well hammered to harden and -stiffen it. The axis, which has a wide collar, is fitted into a hole -in the plate, first by turning it as exactly as possible, and then by -burnishing it in by friction, the hole being broached slightly conical -with a D-broach. The careful fitting of the axis is an important part. -The horizon glass frame, Fig. 300, is held down by a central screw -which fits tightly both in its fore hole and thread. The flange of the -tray _F_ is cut to an angle on its under side to permit adjusting to -verticality by rocking over this angle, by tightening and loosening -the adjusting screws _cc′_ which protrude in square heads to the face -of the instrument. The horizon glass, _H_, which is half silvered, is -fixed in a tray-piece which has two narrow fillets turned to the face -of the glass, and a spring-piece at the back brought up by a screw -_a_. This glass is entirely open at its unsilvered part. The toothed -segment should be cut upon its own axis, and although fitted to the -pinion without any looseness, it should not press the index axis. The -silver is inlaid in the arc on the plan shown Fig. 127. The vernier is -soldered closely on the index and should read down to a fine clean edge. - -672.--_Examination of the Box Sextant._--The glasses should be cleanly -silvered, with a sharp, clear cut between the silver and the clear -glass of the horizon glass. The pinion should move softly and equally -in causing the index arm to traverse the arc. If the pinion be moved -in little jerks backwards and forwards there should be no shake, but -the index should follow every slight motion. The magnifier rising joint -should move rather stiffer than the traversing joint, so that the focus -is not changed by traversing across the arc. The magnifier should have -about 1 inch or less focus, and should stand square to the plane of the -sextant when in focus. The graduation should be deep and fine, and the -vernier should read 30 = 29 at the two ends and the centre of the arc. -If there be a small excess or defect of vernier to arc, this should be -noted and allowed for, either at the time of reading or as an index -error. The sliding fittings of the pin-hole sight, shades, and under -shutter should move firmly but not stiffly. The telescope should fit -without shake. The covering box should fit well in both positions of -cover or hand-hold. - -673.--_Adjustment._--The box sextant is best adjusted by the sun upon -the plan described art. 648. The adjusting screws, as already stated, -are moved by the key, which unscrews from the face of the sextant, Fig. -297 _K_. The adjustment is made permanently by the maker, except only -that of the horizon glass, which is at the command of the user. The -adjustment to perpendicularity of face is made by the two screws upon -the face near _b_; adjustment to zero of arc by the screw at the side -_a_. In defect of appearance of the sun, the sextant may be adjusted -to any clear, sharp line, as that of a stretched piece of twine, -for perpendicularity of plane, and to any object of clear outline -sufficiently distant, say at half a mile, to avoid error of parallax -for index zero, art. 621. - -674.--_Use of the Box Sextant._--The sextant has its under shutter -opened by pressing the stud attached over in its slot. The nibs of the -shade levers, Fig. 297 _S_, are then raised and the shades depressed. -The cover is then screwed, or slid on if it fixes with bayonet notches, -upon the under side of the sextant to form the hand-hold. The pin-hole -sight is pressed over for use if not already in its position, unless -it be intended to use the telescope. The box sextant is held in the -left hand, with the right-hand thumb and forefinger constantly holding -the milled head, and turning this so as to bring the two objects, of -which it is desired to obtain the angular position, from the observer, -exactly in apparent juxtaposition, the one over the other. In turning -the milled head it is better to let all the other fingers of the right -hand clutch and steady the instrument. To take angles objects should be -observed that cut sharp, erect outlines, as buildings, posts, trees, -etc., if possible. In open country it is necessary to use pickets, to -be described further on. With pickets the reflected image of the upper -half of one picket should form a continuous outline with the direct -image of the lower half of the other picket in the eye, so that the -pair of pickets appear as one. Where an angle greater than 120° is -required an intermediate picket is set up, and angles taken to the -right and left of this are added together. - -675.--It must always be remembered that the sextant takes angular -positions _actually_, whereas plans are made in _azimuthal_ angles. -There are some not very satisfactory means of approximate correction -for this, for which books on surveying may be consulted; but altogether -the sextant is not very useful for taking angles for plans on other -than fairly level ground, wherein it has proved a most valuable and -sufficiently exact instrument. Where ground is undulatory fairly good -work may be done with it by taking stations for exterior triangles -at equal heights on the hillsides, as ascertained by a hand level or -clinometer to be described, or sometimes from hilltop to hilltop where -these are of fairly equal heights. For sketch plans of very hilly or -mountainous districts the prismatic compass, art. 148, is better, as -this gives, although with less precision than the sextant, its angles -in azimuth. - -[Illustration: Fig. 301.--_Interior construction of box sextant with -supplementary arc._] - -676.--=Box Sextant with Supplementary Arc.=--This sextant is preferred -by many because of its more extended use. It is complete as an ordinary -sextant for angles up to 120°; but if it be thought desirable to extend -the angles to 220°--by a single observation this may be done. The -ordinary arrangement of the box sextant just described is left intact -and forms the upper part of the instrument. This arrangement, as in the -box sextant, is attached entirely to the face or arc plate, the only -difference being that the index glass is made of less depth. For the -supplementary arc arrangement a mirror is fixed upon the lower or _sole -plate_ exactly under the position of the index glass. This mirror is -termed the _supplementary index glass_. The position of the face of the -index glass is at right angles to the face of the ordinary index glass -when the index is at zero. The arrangement of glasses is shown Fig. -301: _MM′_ index glasses. The supplementary angle is read through a -separate pin-hole sight which is placed at about 90° from the pin-hole -sight of the proper sextant and a little lower down on the rim. The -arc of this sextant reads in the ordinary manner, left to right, to an -inner circle of figures for angles from 0° to 130°. The supplementary -arc reads by the same vernier, and is figured in the same manner at -the tens; but it reads into an outer circle of figures which progress -in the _reverse direction_, that is, right to left. The readings of the -supplementary arc are from 90° to 220°, so that for a certain range, -that is, for angles from 90° to 130°, these may be taken either by -direct arc or by supplementary arc. The supplementary angle is taken by -means of the coincident images of _two reflections_, one from the index -glass and one from the supplementary index glass, and not by one direct -and one reflected image as in the sextant proper. - -[Illustration: Figs. 302, 303.--_Diagram of supplementary arc sextant._] - -677.--_Theory of Supplementary Angles to the Sextant._--For the -measurement of these angles we have to consider direct reflections -only of two reflecting planes placed one above the other nearly in -contact, so that the images projected from both planes may reach -the eye superimposed. Let Fig. 302 _II′_ be the surface of a mirror -(_index glass_) which is movable to any angle in relation to the face -of the mirror _SS′_ (_supplementary index_). For demonstration of the -principle these mirrors are shown in this diagram at 90° to each other; -therefore coincident reflections will be at 90° + 90° = 180°. Let the -lines _FC_ and _BC_ form a right line (180°); _F_ fore sight and -_B_ back sight. An object at _F_ would be reflected from the mirror -_II′_ to the eye at _E_, the angles _FCI_ and _ECI′_ being equal. -Another object at _B_ reflected from the face of the mirror _SS′_ would -also reach the eye at _E_, the angles _BCS′_ and _ECS′_ being -equal. And as the angles _FCI_ and _BCI′_ are equal in crossing a -right line, the line _FCB_ must be also a right line (180°) which is -indicated by the angle of coincidence of the two reflections to _E_. -The positions of the reflections are shown as angular measurements upon -the graduated arc. - -678.--In Fig. 303 let _SS′_ remain as before, angle _BCE_ will remain -as shown in both figures. Move the index glass from the position _II′_ -of Fig. 302 to the position _JJ′_ of Fig. 303, so that after this -movement the eye at _E_ would receive the image of an object at a new -position _F′_ as reflected from the mirror _JJ′_, _F′CJ_ and _ECJ′_ -being equal. In this process, as the reflector _JJ′_ in the angle _ICJ_ -would have moved half the angle _JCF_, the record of this movement -upon the index, which moves with _JJ′_, is at the same time double the -true angular difference, as with the sextant proper fully described, -the graduations being in both cases the same _pro ratâ_. The increase -of angle is taken supplementary to the angle given by the first -reflection, by addition to this angle in a direction right to left from -the right line of the former sight _EC_; consequently this increase is -read backward on the sextant, that is, right to left, and is indicated -by the outer line of numerals. - -679.--_Manufacture._--The general structure of this instrument is -nearly the same as the ordinary box sextant, except the parts just -referred to. The supplementary index glass is an ordinary mirror -similar to the index glass but of only ¼ inch in depth: it is mounted -in the same way. Its adjustments are similar to the horizon glass in -kind, but there are no exterior screws, this glass being permanently -fixed by the maker. Opposite the supplementary index glass a wide -window is cut through the rim of the case near the sole plate to take -sight of the object at angles exceeding 120°, so that in this sextant -two large windows are cut out opposite to each other. The diameter of -this sextant is 3 inches; the exterior depth about 1-5/8 inches, that -is, 1/8 inch deeper than the ordinary box sextant. It weighs about 20 -oz. It is carried in a solid leather case with strap to pass over the -shoulder. - -680.--_Examination and Adjustment._--Examination will be nearly the -same as for the common box sextant. The most important point is -that the readings taken within both arcs should be alike, assuming, -which is necessary, that the part comprising the sextant proper is -perfectly adjusted. Thus there is a 90° on both direct and reverse -arcs. The 90° may be measured by any pair of objects on the direct -arc, and afterwards compared by shifting the index to the 90°, on the -supplementary arc. If no object be found at 90°, then 95° 30′ or any -other quantity may be compared. It is also well to compare readings -at or about 120° on both arcs. The 90° and 120° fall in the same -position in the reading, and this checks any error in either. If the -adjustment be not fairly perfect, the instrument should be returned to -the maker. Indeed, this sextant would be better without any external -means of adjustment, leaving these to be made by the optician in such -a permanent form that they will not be liable to change. It is, as the -plain box sextant, exceptionally protected from accident. - -681.--_In using this instrument_ the arc up to 120° is taken exactly as -with the plain box sextant. Beyond 120° the sextant is shifted to take -sight through the supplementary pin-hole, being particular to observe -that the pinion is now turned the _reverse way to increase the angle_, -and that the vernier reads for the supplementary arc right to left. -It is in this reversing, if not carefully performed, that a little -difficulty is experienced in using this instrument. - -682.--=Box Sextant, with Continuous Arc to 240°.=--This instrument is -an improvement by the author upon one originally designed by Mr. W. -Franklin. The reading is taken continuously from the same sight-hole -and by the same arc, and in a direct manner without any reversal for -part of the arc. This sextant reads with certainty to 240°. - -683.--In the construction of this sextant there are two horizon glasses -superimposed one above the other and crossing each other, with faces -which are adjustable for perpendicularity at an angle of 120°. The -horizon glass is divided top from bottom by a clear band cut through -it, as in the old form of back-sight nautical sextants. One of the wide -glasses reflects into the upper, and the other into the lower mirror of -the horizon glass. The pin-hole sight or the telescope is placed in the -same position as in the plain box sextant described. The horizon glass -is fixed and both the index mirrors adjust to angular positions, or one -index glass only and the horizon glass is adjusted, this arrangement -being optional. The arc is graduated as the plain box sextant, but -it reads with two rows of figures from 0° to 120°, and from 120° to -240°, the 0° of the under line being under 120° of the upper. When the -arc is set to zero the index glasses are in such a position that the -direct vision and the reflection as seen in the upper mirror of the -horizon glass are coincident for direct images, as at the zero of the -plain sextant, but at this point the lower mirror of the horizon glass -reflects to the eye an object at 120°. When the index is moved forward -the angles continue onward, reflected from both glasses, so that the -upper reads on 10°, 20°, 30°, etc., whereas the lower read 130°, 140°, -150°, etc.; so that if the objects desired to be triangulated are -under 120° the coincidence is seen in the upper mirror, and if over -this in the lower, the great distance of 120° apart of the angles -preventing the risk of accidentally taking the one for the other. In -the compact form of a box sextant this instrument embraces the uses -of the ordinary reflecting circle of double the diameter, due to the -entire circle graduation; and the range is sufficient, as beyond 240° -the head materially interferes with observation. The size and weight -of the instrument are generally but little over that of the plain box -sextant. The adjustments are made permanently by the maker. The use -of this instrument is fully inferred from the description given. The -construction is shown in Fig. 304, _E_ place of the eye with direct ray -through the horizon glass _H_ to _O_. The index glass _I_ is that of -the ordinary sextant, shown by dotted lines, throwing the image of an -object at _P_ to the upper horizon glass and thence to the eye at _E_. -_B_ is the fixed supplementary glass with its surface at 60° to the -lower horizon glass at _A_. The sight lines from an object at _Q_ are -reflected from _B_ to _A_ and thence to _E_. A spring arrangement shown -_SS_ with a milled head underneath permits the lower glass _A_ to be -drawn down to convert the instrument into a simple box sextant. - -[Illustration: Fig. 304.--_Stanley's continuous arc box sextant._] - -[Illustration: Fig. 305.--_Section of supplementary horizon -arrangement._] - -684.--_Details of Spring Arrangement_ to the supplementary horizon -glass are shown in Fig. 305 full size in section. The springs _SS_ in -Fig. 304 and _S_ Fig. 305 form two points of support to the horizon -glass, the silvered face of which is shown at _A_. A third point of -contact is near _D_, placed in the centre of the end of the supporting -plate for the horizon glass. When the screw _R_, which is placed in -a loose fitting, is released, the springs bring the supporting plate -tight up to _D_ and hold the horizon glass firmly in an elevated -position. When the screw _R_ is tightened it brings this glass down. -The horizon glass is adjusted over a rocking centre by the screws -_CC′_. A screw and collar b prevent the loss of the screw _R_. By -this arrangement the horizon glass is brought in or out of the field -of view, in order to use the supplementary arc or for leaving it as a -plain sextant. - -[Illustration: Fig. 306.--_Stanley's portable surveying sextant._] - -685.--=Open Surveying Sextants=, similar to nautical sextants but -generally smaller and of stronger construction, preceded the box -sextant, and are still used to a limited extent upon the Continent, -particularly with some form of supplementary arc, or arrangement to -produce a large part of the reflecting circle. These forms are also -occasionally revived by the opticians of our own country. The reason -of this is easily seen. To the optician who lives in a town, moves on -a level surface, and has comfortably warm hands, even in the winter, -to hold and move the separate parts of an instrument, the open sextant -appears the most perfect, as he can get at every part of it easily to -clean and adjust. The surveyor takes another view of the subject. He -is exposed in the open country to all weathers and all difficulties -of movement over the land; therefore that form of instrument which is -best protected and least liable to injury by a fall will be sure to be -popular with him. It is upon these conditions the box sextant of some -form is generally preferred. - -A handy form of portable surveying sextant has been devised by the -author and is shown at Fig. 306. - -The arc is of 4 inches radius and is divided on silver to read 20″, is -complete with shades and telescope and packs into a case 7 × 6 × 2½ -inches. - -[Illustration: Fig. 307.--_Optical square._] - -[Illustration: Fig. 308.--_Double optical square._] - -686.--=Optical Square.=--This extremely handy little instrument is -invaluable for taking offsets in chaining for any irregularity or -obliquity to the right line in the boundaries of fields, hedgerows, -fences, streams, etc., giving as it does instantly at sight a right -angle to any object that may be sighted on either hand. The instrument -is optically constructed exactly as a box sextant; but the glasses are -fixed with their faces permanently at the angle of 45° to each other, -by which means the reflection of 90° is truly given on principles -fully discussed at the commencement of this chapter. This instrument -being made very small, that is, 2 inches or less in diameter, it is -found most convenient for manipulation to place the adjustments to -the larger glass, that is, the index glass. The horizon glass, Fig. -307, _h_ is therefore fixed firmly, like the index glass of the box -sextant, by two screws to the sole plate. The index glass _i_ is held -and adjusted in exactly the same manner as the horizon glass of the box -sextant, as shown in detail, Figs. 299, 300, the only difference being -that the frame which holds the glass is made of the entire height. The -rim of the case of the optical square is formed of a short length, -3/8 inch to 5/8 inch, of a pair of telescope tubes which slide easily -together. One of these is attached to the sole plate and the other to -the cover, so that at first they close together as a box and lid. All -the openings required for sight, as Fig. 307 at _Q_ for horizon sight, -_o_ for index sight, and _e_ for pin-hole or eye sight, are cut through -the two tubes. - -[Illustration: Fig. 309.--_Optical square._] - -687.--The inner case is cut in the plane of some part of the -circumference of the instrument from a pin-hole into a bayonet notch, -made with a horizontal slot for the two cases to revolve upon each -other upon a pin, sufficiently to close and open the sight holes. -This plan secures the instrument from any intrusion of dust when it -is closed and out of use. An adjusting key is placed in the case, -held by a tube or stud at the position _k_. The weight of the entire -instrument is about 4 oz. if of ordinary make; but smaller ones are -made in German-silver or silver, 1¼ inches diameter, 3/8 inch thick, -weighing under 2 oz. These latter are very convenient for the waistcoat -pocket, and are equally as exact as the larger instruments. Fig. 309 -shows the general outward appearance of the optical square. - -688.--_Examination and Adjustment of the Optical Square._--Place two -pickets in an open space at a distance apart, the further the better. -Range an intermediate short picket in right line with these or the -top of a stake the height of the eye, or what is better still, if at -hand, the top of a tripod stand. Place the optical square over the -intermediate station or tripod. Place another picket, which we will -distinguish as the 90° _picket_, at a distance, and make this appear in -the optical square coincident by reflection with the direct sight of -one of the pickets in the right line from our station. Turn the optical -square right over on its place, and looking in the opposite direction -take a sight at the other right line picket and observe the 90° picket. -If this still appears coincident with the direct line in reflection -the optical square is in perfect adjustment. If it does not appear so, -half the difference must be adjusted by means of the key taken from the -interior of the case and placed on the square at _k_, Fig. 307, and -this observation repeated until the 90° is correct. - -689.--_In Using the Optical Square_ it is customary to walk along the -chain line at about the desired position for taking an offset, looking -by direct vision through the plain part of the horizon glass _h_ at a -fore sight object until the required object is sighted by reflection at -right angles to this, where it appears by coincidence of image with the -fore sight. The heel of the forward foot in stepping indicates fairly -the vertical position of the optical square; but some surveyors prefer -the use of a drop arrow to fix the point. The offset is then chained in -the line. - -690.--=Double Optical Square.=--This instrument is exactly what its -title indicates, that is two optical squares, the one placed exactly -over the other, the one reflecting to the right hand and the other to -the left. A simpler name, however, would be an _optical cross_. This -arrangement of reflectors greatly extends it use. First, as regards the -90°, this need not depend in any way upon the position of the observer, -as two objects may be observed, one to the right and one to the left, -to appear to cut the direct forward line of sight, and therefore to cut -the base line at the exact position of the instrument at right angles -to it. Secondly, an intermediate station can be found in direct line -between any two points, as the 90° + 90° forms this line. - -691.--The arrangement of the optical part of the instrument is shown -Fig. 308. The two index glasses _CD_ are fixed at equal angles to -the direct line of sight _EO_. The two horizon glasses _AB_ are -superimposed with the interval of a small space, 1/16 inch, between -them. The horizon glasses are each separately adjusted so that their -reflecting planes are respectively 45° to the index glass from which -they receive the reflections. The diameter of the instrument as usually -made is about 2¼ inches; its depth 7/8 inch. The weight is about -9 oz. It is generally carried in a light, solid leather, sling case. -Total weight with instrument, 12 oz. - -692.--_Examination and Adjustment of the Double Optical Square._--1. -Place the instrument, as already described for the optical square, at -a station intermediate between two pickets. Examine the right angles, -first looking towards one picket and then towards the other from the -same position, as with the optical square, turning it over for this -examination. 2. Turn the instrument half round and examine it this way -also by turning it over again in like manner. Adjust either horizon -glass if required. 3. Now take the position for the eye of the former -90° and see whether the extreme pickets appear in true position by the -exact coincidence of their images at 180°. 4. Do this again, facing -the opposite way and turning the instrument half round. If the extreme -pickets still range in line from the central station the adjustment -is perfect. If they do not do so half the error must be corrected by -returning to the first and second adjustments to find out between -which pair of mirrors it lies. For this adjustment the instrument is -much better to be placed upon the top of a tripod, as the position -of the axis should remain fixed after turning it over or changing the -direction of the instrument. It is only from severe accident that the -maker's adjustment will be disturbed. - -693.--=Apomecometer.=--This little instrument, the invention of Mr. -R. C. Millar, is intended to measure the height of buildings, trees, -etc., by measuring the distance from the vertical upon the surface of -the ground. It performs one of the functions of the box sextant in the -same manner as the optical square, that is, to measure a single angle -by reflection. The angle measured is 45°, consequently by measuring a -space upon level ground up to a vertical, the vertical will be known, -this being equal to the horizontal. Of course this will always be -approximate, as the ground will seldom be truly level; but by taking -a position, even on an incline, as nearly as possible level with the -object, a very fair estimate may be made. Horizontal distances may be -measured in the same manner from a perpendicular to any line. - -694.--The instrument is constructed in exactly the same manner as -the optical square just described as regards its mirrors and its -adjustments, but the faces of the mirrors are fixed at the angle of -22° 30′, so as to give a reflection of 45°, upon principles fully -discussed. In Fig. 310, _A_ is the index glass, _B_ the horizon glass, -_E_ the pin-hole sight. There is a window opposite the index glass, -and one behind the horizon glass, each sufficient to take in a wide -field of view at about 45° and in the direct line _E_ to _H_. These -windows close by rotation of the casing of the box, which is made as -the optical square. When closed the instrument is dust-tight and may be -carried in the waistcoat pocket loose, or in a light snap leather case. -Its size is 1¼ inches diameter, 3/8 inch in thickness, weight 2 oz. -in German silver. - -695.--_The Use of the Apomecometer._--To measure the altitude of a -building the open side nearest level is selected, and a station for -observation is taken which is at a distance thought to be approximate -to the height. The instrument is held edgewise with the pin-hole sight -to the eye, and the reflection of a point of the building about level -with the eye is observed by direct vision through the instrument. At -the same time there will appear a reflection of the summit of the -building. If we now walk backwards or forwards, as the case demands, -keeping sight of a level object, as for instance in Fig. 311 the plinth -of a building, then at a certain point the summit of the building -will appear by coincident reflection. The height of the object will -be the same as the distance plus the height of the observer's eye. -This distance may be measured on the ground, or if a rough estimate is -sufficient it may be stepped, the principle of which is shown by Fig. -310 in the line _OH_, being equal to _FH_. If a part of an object is -required to be measured such part may be taken on the horizontal plane, -as for instance the height of the figure in Fig. 311, by _ab_ being = -_ed_, as the base _ab_ can easily be measured. An approximate may be -found by dropping a small pebble at _a_ and at _b_ and then measuring -the distance apart of these pebbles. - -[Illustration: Fig. 310.--_Optical details of the apomecometer._] - -[Illustration: Fig. 311.--_Scheme for measuring heights._] - -696.--The distance of an inaccessible object may be measured, as for -instance a buoy at sea, by measuring in any straight line double -the distance and taking equal angles thereto by the apomecometer -on any direct line. An approximate idea may be formed by walking -over measuring points. As for instance, _b_ being a buoy at sea, -Fig. 312, walk from _e_, at which a walking-stick may be set up, -towards an object _o_. At _E_ the buoy and object _o_ will appear to -be coincident. Then drop a stone or make a mark directly under the -instrument. Walk on till beyond _E′_ and turn to face _e_. Now in -returning, the buoy and the object e will appear coincident at _E′_. -The distance _EE′_ is double that of the intermediate _a_ to _b_. - -[Illustration: Fig. 312.--_Scheme for measuring distances._] - -FOOTNOTES: - -[38] _Posthumous Works_, p. 502; also _Animadversions to the_ Machina -Cælestis _of Helvetius_, p. 49. - -[39] _Phil. Trans._, vol. xlii. p. 155. - -[40] _Phil. Trans._, vol. xxxvii. p. 147. - -[41] _Ibid._ p. 340. - -[42] See Nicholson's _Navigator's Assistant_. - -[43] Pearson's Practical Astronomy, p. 537. - -[44] _Ibid._ p. 577. - -[45] _Gli Strumenti a Reflessione per Mesurare Angoli_, by G. B. -Magnaghi, 1875. - -[46] _Description of a New Quadrant_, by George Adams, 1748. - -[47] Adams' _Geometrical Essays_, edited by William Jones, 1803. - -[48] Prov. Patent No. 2624; Christopher George, 1868. - -[49] See British patents--Winter, 1760, No. 752; Ould, 1791, No. 1842; -Nugent, 1794, No. 1980; Wright, 1796, No. 2081; Cook, 1796, No. 2087; -Roxby, 1822, No. 4695; Glover, 1839, No. 8256; Lane, 1857, No. 1669; -Rahill, 1860, No. 1845, etc. - -[50] Adams' _Geometrical Essays_, p. 264, 1803. - - - - -CHAPTER XV. - - GRAPHIC SURVEYING INSTRUMENTS AND APPLIANCES CONNECTED - THEREWITH--PLANE TABLES--ALIDADES--TELESCOPIC ARRANGEMENTS--SUBTENSE - MEASUREMENTS--VARIOUS DEVICES FOR HOLDING THE PAPER--CONTINUOUS - PAPERS--ADJUSTMENT OF TRIPOD HEADS--METHOD OF USING--EDGEWORTH'S - STADIOMETER--SKETCHING PROTRACTOR--SKETCHING CASE--CAMERA LUCIDA, ETC. - - -697.--=Plane Tables.=--These instruments have been used for filling -in the greater number of topographical surveys in all countries. They -possess the merit that any intelligent, untrained person can be readily -brought to comprehend their manipulation in the work to be performed, -as angles of position of objects are taken directly by drawing lines -pointing to them from a point upon a sheet of paper stretched upon a -table. In new countries natural objects without very marked outline are -conveniently defined for position. The objection to this method, from -a point of view of the practical surveyor, is that the work which can -be done with equal facility in a comfortable office from the field-book -is with this instrument performed in the open air, under risk of rain, -dust, and other atmospheric discomforts affecting both the person and -the material on which he works. But for countries where the climate -can be depended upon, the facility with which surveyors with little -experience can map details for filling in superior triangulations made -with the theodolite, its use has gained much favour. Natives can -be easily taught to use it, and the check on their work through the -previous triangulation is perfect. The subject of plane tables will in -these pages be considered only in its general aspect, with the examples -of a few good instruments, referring the reader who cares to follow -the subject further to an excellent paper by Mr. J. Pierce, Jun., read -before the Institute of Civil Engineers, February, 1888.[51] - -698.--_The Plane Table_ in its simplest form consists of a small -drawing-board mounted upon a firm tripod stand, and is shown at Fig. -313. - -[Illustration: Fig. 313.--_Simple plane table._] - -A rule termed an _alidade_, with sights placed at its ends, gives -the direction of any object from a given point on the sheet of paper -stretched upon the table, to which a fine line is drawn by an HH pencil -to point the direction. The alidade sometimes carries a trough compass -fixed upon it, but this is generally a separate instrument which is -placed against its _fiducial_ or ruling edge to give a magnetic north -to south line, to which all other lines are assumed to take angular -direction. A loose spirit level is also provided, by means of which -the board may be set level by shifting the legs of the tripod. - -699.--=Plane Table with Telescope.=--Where greater refinement of -observation is required than is possible with sights, a telescope is -mounted on the alidade, which moves in the vertical plane upon an axis, -so that it may be directed in a linear direction with the fiducial edge -of the rule to any point in azimuth. The telescope sometimes carries a -level, so that the table may be set level by means of the alidade. - -[Illustration: Fig. 314.--_Plane table._] - -[Illustration: Fig. 315.--_Tripod stand._] - -700.--A class of plane table which meets all necessary refinement -for ordinary filling in of field work is shown in the illustration, -Fig. 314. This nearly resembles those made by the author for filling -in details of the great trigonometrical survey of India. The drawing -surface of this table consists of a loose panel which stretches the -sheet of paper by pressing it into its frame, where it is afterwards -held by a pair of ledges which fit at their ends into long slots. The -panel of the board, shown in detail Fig. 316, is mounted upon a firmly -braced tripod stand. The head of the tripod stand, shown Fig. 315, is -secured to the board with a central screw (not shown) which permits the -board to be set in any direction, it being the rule that the edge _W_ -should always take a north to south direction. Three screws _sss_ at -the corners of the triangular head can be raised or lowered by milled -heads from the under side. These screws permit about 15° of adjustment -to the table without any unsteadiness, as the centre screw clamps it -finally hard down upon them when all adjustments are made. A small -trough form of magnetic compass a is placed upon the rule to strike -the magnetic north to south line, to which all angles are referred in -transposing the work of the plane table. The diaphragm of the telescope -is provided with a platino-iridium point fixed vertically at the -mutual focus of the object-glass and the eye-piece. A pair of points -to subtend an angle to measure a staff for distance, Fig. 319, is a -convenient addition. - -[Illustration: Fig. 316.--_Panel board of plane table._] - -701.--_The Telescopic Arrangement_ of the alidade is varied in -different countries. In some cases it is placed near to one end, which -is perhaps better than in the centre of the rule, as it is more easily -read. In the modern French military alidade a prismatic eye-piece is -used, so that observation is made by looking directly down upon the -eye-piece of the telescope. In the Prussian alidade adjustment is made -to the standard of the telescope so as to bring the horizontal axis -upon which it moves level, that the telescope may move in azimuth, -however irregular or uneven the surface of the paper on the board may -be. This is necessary for any great degree of refinement in the plane -table, as the surface of a piece of wood upon which the paper is -stretched will be almost certain to warp if exposed to all weathers, -and this, added to the small width of the alidade, can scarcely retain -the axis in exact horizontality, placed as it is high above the -surface of the table. Some plane tables made by the author for General -Robinson for Indian service were of papier-maché to remedy the defect -of warping, but even this material warps upon exposure. Plane tables -have been made in Germany of metal and of glass, but in this case the -weight is a great objection. The author has found surfaced slate very -good, but it has the same objection of too much weight for a portable -instrument. - -[Illustration: Fig. 317.--_Stanley's plane table._] - -[Illustration: Fig. 318.--_Alidade to plane table._] - -702.--_Lateral Adjustment to the Alidade._--The author's plan of -obtaining this is to increase the practical width of the rule by giving -it an extended point of support on one side so as to set the telescope -in azimuth. For this construction the telescope is mounted upon a -plate with an arm extending outwards upon the back of the rule. This -has a milled-headed screw placed at the near extremity of the arm. The -screw is inserted in a deep bush for wear; this attachment is shown in -section Fig. 318. The adjusting screw _A′_ has a collar fixed upon its -point which is centred upon a tight screw tapped into the milled head. -This collar, as it does not turn with the milled head, does not abrade -the surface of the paper by contact with it. A small cross level _B_ -is put upon the arm between the milled head and the standard of the -telescope. The under side of the rule is cut away or placed obliquely -to the surface, so that it bears on the outer ruling edge only. The -milled-headed screw being at its normal position and the table level, -less than half a turn one way or the other will bring the small cross -bubble to its centre in a few seconds for any average irregularity of -the surface of the table, and by this means cause the telescope to move -correctly in azimuth. - -[Illustration: Fig. 319.--_Subtense points._] - -703.--_The Telescope Arranged for Subtense Measurements._--Where a -stadium, art. 556, is to be used for estimating distances from station -to station, when an ordinary telescope is used, the author places two -platino-iridium points vertically from top and bottom of the diaphragm, -and adjusts these by a screw until a subtense angle upon the stadium of -1 foot cuts the point at a distance of 100 feet, or according to the -measurements to which the land is taken. In this case it is necessary -to have an altitude arc to the telescope, as shown upon the alidade in -Fig. 317. This has a degree scale reading by vernier to about 3 minutes. - -704.--_Various Devices for Fixing the paper on the Surface of the -Table_ have been made. Many prefer simply pinning it with drawing -pins on a quite plain pinewood surface. In this case the table is -better slightly sunk round the edges with a rabbet of the depth of the -thickness of the head of the pin, so that the alidade may rest firmly -even over the pin heads. The French plane tables have very generally -rollers at each end of the table, upon which a long slip of paper is -rolled, sufficient for twelve or more stations. The rollers for small -tables are made of brass tube about 5/8 inch in diameter. They commonly -move with a turn-key which is inserted in a square fitting in the end -of the roller. The rollers keep the paper tight by means of ratchet -wheels and spring pawls at their ends. This plan is very convenient -for topographical work, as for instance a river may be followed from -station to station right down its course and appear on a single slip, -its bearing being indicated by the compass north line. Fig. 320 shows -the manner in which the author has made this plane table. - -[Illustration: Fig. 320.--_Plane table with rollers._] - -[Illustration: Fig. 321.--_Gurley's plane table adjustment._] - -705.--_Adjustment of the Plane Table._--There are a great many devices -for this. Mr. Pierce, in the admirable paper already mentioned, gives -illustrations of the different plans. Some of these have all the -complication of the adjustment of the stage of a theodolite, and one -has superadded to this a slide-rest motion. These things of course -are necessary if the field work is made to take the place of finished -office work. One general feature of plane table tripods is some means -of adjustment of the table to uneven ground, when the tripod-head -cannot be brought nearly level. Gurley's plane table adjustment is -perhaps the simplest of any of these devices, and appears to the author -to be as good as any other. Fig. 321, _D_ the table top; _A_ a ball -fitting turned inside and out, and attached firmly to the table top; -_C_ a socket fixed firmly in the head of the tripod; _B_ a bolt with -globular head fitting the interior of _A_, and carried through the -head to a winged nut which clamps it firmly. A spring is placed to act -against the winged nut, so that when this is slightly loosened the ball -fitting A may move between _B_ and _C_ with moderate firmness when the -table is being set to an angle. - -[Illustration: Fig. 322.--_Stanley's high-class plane table._] - -To meet all conditions the revisor has designed a high-class plane -table shown at Fig. 322. This has a ball and socket rough levelling -arrangement and parallel screws for fine levelling, circular motion to -table with clamp and tangent, spring rollers for taking any length of -paper and instantly clamping it, alidade with extra powerful telescope -with vertical circle divided on silver reading by two verniers to -minutes with clamp and tangent motion, cross levels, diagonal scale, -and adjustment for setting telescope to revolve in vertical plane, -circular compass with cross levels and plumbing bar. The board is -generally made 30″ × 24″. The telescope is stadia reading and is made -with long sensitive bubble mounted upon it or upon the verniers if -preferred as shown at Fig. 323. - -[Illustration: Fig. 323.--_Stanley's high-class alidade with bubble on -verniers._] - -706.--_Method of Using the Plane Table._--The table is first set and -levelled up at a commanding position to observe the extent of country -it is intended to plot from observation from a single station. Let -Fig. 324 1 be the first station for plotting the enclosure _abcdef_. -Draw lines by the alidade pointing to these angles represented by the -letters from a point near 1. Set up a picket or stadium at the station -2 where it is intended that the plane table shall next be set up, and -draw the line 1 2 distinctly on the paper. Measure the line 1 2 either -by its subtense on the stadium or by direct chain measurement, and -plot this from station 1 on the paper according to the scale to be -worked to in making the plan. On removing the table set up a picket or -distinct land mark vertical with the position of station 1 occupied on -the paper. Move the table to station 2 at the measured distance and set -the direction of the board by means of the alidade so that the line -2 1 cuts the picket left at station 1. Now draw lines from station 2 -to all the points _abcde_, cutting the former lines as represented by -dotted lines in the figure, and the intersections of these lines will -give the true positions of _abcde_, according to the scale selected for -the base 1 2, and these may be tied up to represent the boundaries, as -shown on the plane table 2. It will be readily seen that the line 1 2 -represents a bearing in azimuth; so that if the edge of the table be -set, say truly N. to S., in both positions the line on the paper 1 2 -will agree in both these positions of the table; but the check by the -alidade of this line is valuable to save risk of error. - -[Illustration: Fig. 324.--_Diagram of plane table work._] - -707.--Where an extent of land is to be surveyed by the plane table, -longitudinal bands of a mile or so in width are taken. Where the roller -plane table with continuous paper, Fig. 320, is used, the forward -points of observation are lined in and the backward ones simply tied -up, being certain by observations written in pencil upon the paper that -identical objects are tied up from the positions of both stations. -Where an object cannot be seen from both stations its position may be -indicated by the stadium from a single bearing, or it may possibly be -tied up from a further advanced station. - -708.--=Edgeworth's Stadiometer.=[52]--The general construction of -this instrument is given in the inventor's specification of patent, -from which the engraving, Fig. 325 is taken. The vernier plate of -an ordinary theodolite is extended to a plate of about 10 inches -in diameter. This is adjusted to level by means of parallel plate -screws. The plate or plane table is divided on its edge ¼°. The part -representing the limb of a theodolite is carried out from its axis -by two arms only: upon these the standards _RR_ of the telescope are -mounted. These standards leave a striding space near the plate, into -which any scale S of equal parts with a zero centre is introduced, -which is intended to be used for the plotting, the striding space being -so arranged that the fiducial edge of the scale shall pass exactly over -the axis of the instrument. The standards unite in the same casting to -form the horizontal axis bearing of the telescope. This axis permits -the telescope to move in azimuth. The telescope carries a vertical -arc divided to degrees, also a scale of centesimal differences of -hypotenuse and base, with the ordinary clamp and tangent adjustment of -a theodolite. It is also fitted with a level above it which is used in -setting up the instrument. Stadia webs are placed in the diaphragm and -are made adjustable to subtend upon the stadium a percentage of arc -agreeing with the unit to which the land is measured. The inventor does -not appear to have known the optical error of the system proposed for -measuring distance, art. 558. Neither does this appear to have been -recognised by others writing upon the instrument, who have generally -followed the late J. F. Heather's description.[53] - -[Illustration: Fig. 325.--_Edgeworth's stadiometer._] - -709.--_To Use Edgeworth's Stadiometer._--After it is set up, a circular -disc of paper of about an inch less diameter than the table is -held down upon it by four spring clips. The telescope is directed -consecutively from object to object, the positions of which it is -desired to take. It is clamped by the screw below the plate during the -observation. The stadium is placed against the object and the distance -taken by the subtense of the webs in the diaphragm, which may be exact -if a constant be added after proper adjustment, art. 558. If the -stadium be above or below the horizontal plane it is inclined by means -of a sight-hole through it, as originally proposed by Green, so that -the subtense is equal under all conditions. The horizontal distance -is taken by the difference of hypotenuse and base, as shown on the -vertical arc, so that the record of a complete observation appears for -calculation as-- - - _stadium reading_ + _constant_ - _altitude correction_. - -This distance is at once set off from the centre of the instrument by -the scale on a line drawn upon the disc of paper, and observations are -written against the line. In making a number of observations from one -station two or more discs of paper may be employed to save confusion -of lines and interference of descriptions. These papers are separately -used in plotting as protractors by pricking holes through the stations -defined in the field from the centre of the disc which represents the -station of observation. - -710.--=The Sandhurst Protractor=, Fig. 326, is a military protractor -adapted especially for topographical delineation, which is commonly -used with the plane table. It is different from many instruments of -its kind in having only useful matter upon it. It is made of boxwood, -upon which the protractor is cut, and has also one scale of 6 inches -to a mile in yards, at the lower edge, the tens of which are carried -across to make parallels of 90° in the manner of an ordinary military -protractor. Over the back of the protractor is a scale which gives -a standard for shading slopes of land upon topographical maps, Fig. -327, from 2° to 35°, also lines for contour shades. A small plummet, -the cord of which is passed through a hole in the centre, from which -the degrees are protracted, is supplied with the instrument. When the -protractor is held up, degrees downwards, the cord of the plummet will -pass over the degrees and indicate the angle at which it is held. By -looking over the edge the angle of inclination of the land may be taken -directly, as with a clinometer, or by looking along the edge by a -second person reading the plummet the angles of altitude may be taken -more exactly. - -[Illustration: Fig. 326.--_Sandhurst Sketching clinometer protractor._] - -[Illustration: Fig. 327.--_Example of scale of shades for slopes._] - -711.--=Military Sketching Board.=--This sketching board, Fig. 328, -the invention of Mr. Graham F. Hodgson, will be found a very great -improvement upon the old pattern boards. It is designed to meet the -requirements of military and other officers not conversant with the -higher branches of surveying, and it will also be found of great use -to surveyors, explorers, and other travellers. - -It consists of a mahogany board revolving on a circular metal plate -attached to a handle held in the operator's left hand. - -Mounted on the metal plate is a compass, which is visible through a -glass plate flush with the face of the board and the tracing paper or -cloth on which the map is made; the paper being stretched tightly over -the board by means of rollers. - -A magnetic north line is drawn on the paper over the centre of the -compass. The operator invariably has his board in its relatively -correct position by always keeping the magnetic north line immediately -over the top of and aligned with the compass needle when his sights are -taken. - -[Illustration: Fig. 328. Top view. Under view.] - -The sights are taken by means of an alidade moving along a slotted bar, -which itself slides along a bar fixed at the side of the board. - -The object aimed at is sighted in a mirror attached to the end of the -alidade and aligned with a point at its other end, and the alidade is -clamped into position by a thumb-screw on the slotted bar. - -The advantages of this instrument are many and will only be fully -realised when it is in practical use. No backsights are necessary. -Sights can be taken with one hand. The operator is always in a -comfortable position and the object aimed at is always immediately in -front of him. The alidade remains in position by means of the clamp -screw along the ray drawn till the object sighted at is reached and the -distance known, which is merely marked off by means of the scale on the -alidade. It is invaluable when sketching rivers from launches or canoes -when backsights are often impossible. It is light and portable, being -easily carried slung over the shoulder in a canvas case. - -712.--The method of using is simple and ensures a great degree of -accuracy with a minimum amount of time and trouble:-- - -(1) The tracing cloth is first fixed by means of the rollers over -the board. (2) A magnetic north line is then ruled across the paper -and passing immediately over the centre of the compass visible under -the paper. (3) The operator then, holding the board by the handle -underneath, proceeds to make his map and first brings the magnetic -north line immediately over the top of and aligned with the compass -needle. (4) He then from some point, marked as his starting point -on the paper, proceeds to take sights to any objects he may wish to -delineate on his map. These sights are taken by means of the alidade -fixed above the board. The sighting rule is pushed along a slotted -bar, which itself slides along a bar at the edge of a board until the -edge of the alidade is against the starting point and is sighted on -the object aimed at. The object is sighted in a small mirror fixed -at the end of the alidade and aligned with the point at its other -end. The alidade is then clamped into position with the thumb-screw -on the slotted bar and the operator draws his ray corresponding with -the direction of the object aimed at. The distance is then marked off -on the scale on the alidade. (5) When the operator moves to the next -station no back-sight is necessary. He at once puts the board into its -relative correct position by merely revolving it until the magnetic -north line is again lying over the top of and aligned with the compass -needle and he then proceeds to take all necessary sights at that -station. - -[Illustration: Fig. 329.--_Cavalry sketching case._] - -713.--=Cavalry Sketching Case.=--This forms a very convenient exploring -sketching board, permitting sketches to be made on horseback while en -route. The pattern shown in Fig. 329 is that of Captain W. Vernier. It -consists of a small board 9¼ inches by 7½ inches, at two sides -of which there are small rollers to hold paper 7 inches wide and from -3 feet to 6 feet in length, according to its thickness. Two stout -indiarubber bands, which hold a small straight-edge to scale in any -position on the paper with sufficient firmness to be able to draw a -line against it, are passed over the board. A small compass on one side -of the board indicates direction. After one sketch is made, a new part -of the paper is rolled forward. - -714.--=Camera Lucida--Optical Compass.=--In new countries where -landmarks are not clear a sketch of the general aspect of the country -will make the points of triangulation more clear. Where the plane table -is not used these sketches may be made with accuracy as to positions -by the use of the photograph camera, the camera lucida, or points of -observation may be taken in correct bearing by the optical compasses. -These latter instruments are described in the author's _Treatise on -Drawing Instruments_, seventh edition. - -FOOTNOTES: - -[51] _Proc. Inst. Civil Engineers_, vol. xciii. part iii. paper No. -2308. See also _Military Surveying in the Field_, by Major The Hon. M. -G. Talbot, Prof.; _Papers Royal Engineers_, vol. xiv. p. 25. - -[52] Patent No. 1202, D. R. Edgeworth, April 1866. - -[53] Heather's _Surveying Instruments_, 1870, p. 85. - - - - -CHAPTER XVI. - - INSTRUMENTS FOR MEASURING LAND AND CIVIL WORKS - DIRECTLY--CHAINS--VARIOUS TELLERS--STANDARD CHAINS--ARROWS--DROP - ARROW--VICE FOR ADJUSTING CHAIN--CAINK'S RULE FOR INCLINES--STEEL - BANDS--WIRE LAND MEASURES--COMPENSATION SYSTEMS--LINEN TAPES--OFFSET - RODS--PINE STANDARD RODS--RODS WITH IRON CORE--BEAM COMPASS RODS-- - COINCIDENT MEASUREMENTS--COMPENSATED RODS--BASE LINE APPARATUS--COAST - SURVEY LINES--PERAMBULATOR--PEDOMETER--PASSOMETER--SOUNDING CHAINS-- - SOUNDING LINES--TELEMETERS--HAND RODS--RULES. - - -715.--_The Instruments Generally Employed for Measuring Land_ are -chains, steel bands, and tapes. Where roads are roughly measured, -pedometers are commonly used. Where very exact measurements are -required, rods have been used. Rough approximate measurements are -obtained by stepping, with the use of the passometer to count the steps. - -716.--=Land Chains.=--Although these are made in many qualities -the forms vary very little. They are too well known to need much -description. In the British Isles and some of our colonies the chain -of 100 links, equal to 66 feet, the invention of Edmund Gunter about -1620, is generally used, 10 square chains (100,000 square links) giving -the statute acre, presenting a decimal system of measurement much in -advance of any other at the present time. The best land chains are -made of steel, which is afterwards hardened and tempered to spring -temper, in the process of which the surface is burnt off with asphalt -varnish in order to produce a covering to resist the rusting effects of -moisture. Steel chains are made _light_ and _strong_. The light chain, -of No. 12 Birmingham wire gauge, weighs under 5 lbs. The strong chain, -of No. 8 B.W.G., weighs about 12 lbs. A light chain of 50 links, of -weight under 3 lbs., is sometimes used with the complete chain of 100 -links for taking offsets. - -[Illustration: Fig. 330.--_Land chain and arrows._] - -All the best chains, whether of steel or iron, are made with long links -formed by turning up the ends of a length of wire. Three small oval -links are placed between each pair of long links. These three interval -links are found to cause the chain to kink less than when only two are -used. Each oval link is sawn through at the meeting line, which is -brought up on one flat side of the oval in bending it from the wire. -The saw-cut forms the point of adjustment. The small link is afterwards -re-sawn and closed to shorten it, or forced open to lengthen it. There -are generally four swivels in the length of the chain, two of which -are at the handles: these prevent the chain from becoming twisted in -turning the handles over in use. A swivel is shown Fig. 331 at S. Iron -chains are sometimes galvanized to prevent rust. This process, however, -makes the chain much more brittle, and cannot be recommended. It may be -noted that all link chains lengthen with use. - -717.--=Tellers= are small pieces of brass suspended to the chain -by a spare link placed at every ten links. They divide the chain -decimally from either end equally. Proceeding from one end of the chain -the tellers read 10, 20, 30, 40, 50, and the other end they read by -subtraction from the complete chain: 100 - 10 = 90, 100 - 20 = 80, -100 - 30 = 70, and 100 - 40 = 60. Fig. 331 shows detached pieces of -chain with value of the tellers figured under. _S_ inserted swivel. -The 50 teller shows the link attachment. _A_ shows the position at -which the arrow or other mark is placed to commence or finish the chain -measurement, the handle being included in the first link. These tellers -are liable to catch and get dragged off in chaining. When this chain -is used abroad, or far from home, it is well to have an extra set of -tellers to repair losses. - -[Illustration: Fig. 331.--_Gunter's land chains._] - -718.--_Inserted Tellers._--This form of teller is preferred by many, -Fig. 332. It is much less liable to get dragged off, but it is not -considered quite so distinct, and it is a little liable to get clogged -with grass and weeds. - -[Illustration: Fig. 332.--_Inserted tellers._] - -719.--The author's design for inserted tellers is shown Fig. 333. -These are perhaps quite as distinct as the last. The holes in wet -weather fill up with mud and the surfaces keep bright, so that they -remain very readable. There is much less drag, and the chain therefore -wears longer. - -[Illustration: Fig. 333.--_Stanley's inserted tellers._] - -720.--=Feet Chains= are usually made 100 feet, more rarely 50 feet. -They are generally made in foot lengths, but sometimes for flexibility -are preferred in 6-inch lengths. They are commonly made of No. 8 B.W.G. -steel or iron. The weight of 50 feet is 6 lbs.; 100 feet, 11 lbs. If -made of light steel, No. 12 B.W.G., the 100 feet weighs 6 lbs. - -721.--=Mining Chains= used in mineral districts are made generally 10 -fathoms, or 60 feet, 6-inch links counted off by tellers in fathoms. -They are made entirely of brass. The weight is about the same in -brass as steel--No. 8 B.W.G., 9 lbs. Occasionally they are made extra -strong, No. 7 B.W.G.; weight 12 lbs. In coal mines Gunter's chains are -generally used. - -722.--=Metre Chains= are made 20 or 25 metres long. They are marked -with tellers at every two metres with a plain ring at the metre. -The tellers are generally of the inserted kind, Fig. 332. In taking -measurements the sign of the teller is doubled: thus the ordinary 1 or -10 is counted 2 metres; the 2, 4, and so on. 20-metre chains in light -steel, No. 12 B.W.G., weigh 4½ lbs.; strong, in No. 8 B.W.G., 9 lbs. -25-metre, light, 6 lbs.; strong, 11 lbs. - -A land chain is generally secured for carrying by a leather strap with -a buckle. Occasionally it is carried in a sailcloth bag with a strap -over the shoulder. - -723.--=Standard Chains.=--These are of the same form as the ordinary -steel chain, but all the links are hard soldered after being adjusted -link by link. They are not intended to be used for regular chaining, -except it be for laying down rough base lines. Their special employment -is to test chains, or to set out with two pegs on a straight piece of -ground a standard length or station where the common chains in use may -be tested daily. A standard chain is commonly enclosed in a box with a -lock to prevent its accidental use for an ordinary chain. - -724.--=Arrows.=--These are sometimes called _pins_. Ten form a set. -They are shown with the chain in Fig. 330, and are commonly made -of the same wire as the chain--No. 8 B.W.G. They are much better -made one gauge stouter (equal to about 1/7 inch), and preferably of -hardened steel than of iron. The common length is 15 inches. Where -heath, stubble, or woodlands prevail 18-inch are better for use, and -in some exceptional cases even 2-feet are very convenient. Surveyors -going to new countries are recommended to take the longer arrows as -well as those supplied with the chain. It is common either to tie a -short length of scarlet webbing upon each ring of the arrow or to sew -a piece of red flannel or bunting upon it to find it easily in long -grass. Arrows are sometimes carried in a quiver with a strap over the -shoulder, Fig. 334, which leaves the hands of the fore chainman free to -remove obstructions where they occur. - -725.--=Drop Arrow=, Fig. 335. Where ground is very hilly it is common -to roughly level the chain by holding the lower position shoulder -high, either by guess work or by using any kind of rough hand level -or clinometer to ascertain this. The arrow is then dropped, and the -point, held at first lightly in the ground, is pressed hard down or -another arrow supplanted for it. The chain in this case is used in odd -multiples of links as they occur, of which record is taken separately -at each station. In going downhill a drop arrow answers very well. In -going uphill a plummet to the last arrow is better. Some use the drop -arrow as a plummet, carrying for this purpose in the pocket a piece -of fine whipcord, with a bent hook tied to one end, to be used when -required. - -[Illustration: Fig. 334.--_Quiver with arrows._] - -[Illustration: Fig. 335.--_Drop arrow._] - -726.--_Examination and Adjustment of Chains._--Respectable makers -send out chains tested to within half of one of the small links of -standard, that is, within a quarter of an inch; but in use this error -may increase either by the bending of the long links of the chain, when -it becomes shorter, or in the more general case of friction from wear -and from strain, by which it becomes longer. In London, standards are -fixed upon the pavement in Trafalgar Square and at the Guildhall. These -standards are also fixed at many municipal town halls. Surveyors very -commonly lay down a standard on the pavement, or by pegs on a level -gravel path. Where a peg is used it should be driven home nearly to the -surface. It should if possible be made of a piece of heart of oak 12 -inches long and about 2½ inches square. The standard length, which -may be set off by a standard chain or new steel tape, should be from a -saw-cut across the centre of one peg to a similar cut on the other. It -is well also to have the centre space (50 links) indicated by a smaller -peg. - -727.--_The Chain to be Adjusted_ should be first examined and its long -links set straight by means of a hammer on a flat, hard stone or anvil, -after which the error will be, if it has been much used, that it is -too long. It should be then laid in direct line on the standard just -described, and stretched lightly with a pull of about 7 lbs., and then -left to rest. Assuming it too long, the centre of the chain should be -observed to ascertain which half is of the greater length, then short -links should be taken out at distributed distances, if more than one be -required, by twisting the link open in a vice, and opening and closing -another link to restore the chain. - -[Illustration: Fig. 336.--_Stanley's vice for adjusting and repairing -land chains._] - -728.--=Chain Vice.=--The links of steel chains can seldom be twisted -open without breaking, and broken links cannot be restored by steel -links. Iron links answer, but they are very stiff to twist open. -Generally it will be found best for professional men to repair the -chain with spare _brass links_. These wear very well. Where a smith is -near with his vice and a light hammer the links are readily opened. It -often occurs in open districts and abroad that no smith's shop is to be -found. To meet these cases the author has constructed a special vice, -as shown Fig. 336. This vice is let into a piece of hard wood--an old -oak post answers admirably. In stone districts it is perhaps better to -let it into a stone and fix it by pouring hot lead round it. The part -_B_ is used for an anvil for straightening the links. The vice _V_ -holds the link edgewise very firmly by bringing up the slide _J_ by -means of the screw _S_. The link may then be knocked open by the pane -end of a light hammer. The link is closed again in the same manner. If -the vice be left out of doors the screw should be well greased and the -whole covered with a leaden cover. The weight of the vice is about 6 -lbs. It is made of cast iron with chilled face, or the jaws are faced -with steel. - -729.--_Opening and Closing the Chain for Use._--The chain is most -readily unfolded by taking the two handles in the hand and walking -away from it as it lies on the ground. It is most convenient to place -it about 45°, and half a chain length from the first station, each -chainman taking a handle and moving to his position. The only danger in -undoing a chain is from two chainmen taking one handle each and walking -in opposite directions, in which case, if there happens to form a kink, -the opposite movement of the two men will probably stretch or break the -chain. In closing the chain it is taken by the middle links and folded -up two links at a time till the handles are reached. If the links be -placed consecutively in position round the axis formed by the first -links, it may be folded up very compactly in a twisted form ready for -the strap, by which it is carried, to be passed round it. - -730.--_Chaining_ is performed by two chainmen, termed the _leader and -follower_. The follower, having pressed a stake into the ground for a -starting point, then places the centre of the outside of the handle of -the chain against it. The leader takes ten arrows in his right hand -and one handle of the chain in his left, and walks directly towards a -point which is to be the termination of the measurement, stopping at -nearly the length of the chain, examining the chain to see that it is -straight. He then places an arrow lightly outside the centre of his -handle. The follower looks over this arrow to the distant station to -see whether it is in direct line. If it be not so, he waves his right -or left hand once, twice, or thrice for 1, 2, or 3 inches for movement -to right or left. The follower picks up the arrows consecutively as -left by the leader, and when he has the ten, 10 chains have been -measured, which is then recorded in the field-book, or earlier than -the ten if a shorter distance or object completes the measurement. It -is most important to observe that if an arrow be taken for the first -station, _the follower having ten counts nine only for the first ten_. -To prevent accident it is therefore safer to start from a stake or -other landmark, _not one of the arrows_. Some surveyors advise eleven -arrows. If eleven be used, one should be distinctly marked from the -rest so as never to be counted. This may be done by omitting the red -webbing tie, or using a green tie for the odd arrow. The French always -make the drop arrow the eleventh arrow, which is never counted in -direct chaining. - -[Illustration: Fig. 337.--_Caink's rule for correcting inclines._] - -731.--=Caink's Rule= for correcting inclines in chaining is the -invention of Mr. Thos. Caink, C.E., of Malvern, Fig. 337. It is made -four-fold, each fold being one link. The link is divided decimally -along the inside of the rule. On the outer edge of the rule there is -a scale marked degrees, a part of which is subdivided where the scale -is open to read closer, that is, to 20 or 30 minutes. These degree -divisions, which read up to 16° on one side of the rule, indicate the -space from the end of the rule to be allowed in addition for the same -degrees of inclination of the land up to 4 links of measurement. On the -opposite side of the rule the inclination scale is carried from 16° -to 22° 10′. For these higher numbers the length of the rule is first -set off, and then plus such part of the rule as is indicated by the -position marked upon it of the required number of degrees. - -732.--_To Use Caink's Rule._--The follower has a clinometer of one of -the kinds shown, Figs. 260 or 264. He notes at starting the position -upon the face or body of the leader that corresponds with the height of -his own eye. He takes the inclination of the land to this point of the -leader's body while he is standing upright at one end of the chain and -the leader standing at the other, noting the number of degrees shown by -the clinometer. He then places the rule in the direction of the chain, -with the number of degrees indicated, in front of the arrow, and moves -the handle of the chain to this position. For the sake of verification, -if he has a second arrow he may place it in the new position, which -gives the true allowance. In either case the leader moves the chain -forward by the amount required and places his arrow ready to continue -the work. By this method it is seen that there is no after calculation -or separate record necessary for undulating land, but the true -horizontal position is given correctly at each chain measured. The same -form of rule is made for feet and metres. - -733.--In mountainous countries the eight links of the rule is -insufficient allowance for common inclinations. Such countries are -measured much more accurately by some system of subtense measurement, -for which see Chapter XII.; but where a small piece of sudden steep -inclination occurs half a chain may be taken, and the number of degrees -indicated upon the rule be doubled, so that the full rule, instead of -taking 22° only, will take 44°. - -734.--=Steel Bands= for measuring, termed _steel band chains_, are made -in various forms in this country, and sold by nearly all opticians. -They are much lighter than chains of equal strength, and are made of -standard length. They are also lighter to use, being smooth and without -any projection. On the other hand the reading is less distinct than -with the chain, and they need more careful usage in chaining. They also -require oiling before being put by. From the thinness of the metal they -are altogether more delicate and less durable than the chains for hard -wear; but it is thought by many to be a compensation that they are -always of true length. - -[Illustration: Figs. 338, 339, 340.--_Steel bands and tapes._] - -[Illustration: Fig. 341.--_One link of steel band._] - -735.--The bands commonly used for land measuring are made 3/8, ½, -5/8, and ¾ inch wide, of Nos. 26 and 24 B.W.G. in thickness, -respectively. The chain is divided into links by a small stud riveted -through the centre of two small washers, a large stud being placed at -the fives and an oval plate held by two rivets at the tens, which are -numerically indicated in plain engraved figures, as shown in detail, -Fig. 341 _b_, or perforated with holes indicating the number of tens. -These band chains are made in links, feet, metres, or to any foreign -measure to order, and of any length corresponding with land chains. -Weights, approximately--100 feet: ¾ inch, 7 lbs.; 5/8 inch, 4¾ -lbs.; ½ inch, 4 lbs. 100 links: ¾ inch, 4¾ lbs.; 5/8 inch, 2¾ lbs.; -½ inch, 2¼ lbs. 20 metres: ¾ inch, 5 lbs.; 5/8 inch, 4 lbs. - -736.--Steel band measures are also made with divisions throughout, -etched upon them with acid in such a manner that the divisions and -figures stand in relief up to the original surface, whereas the new -surface, which is etched back to form the ground, appears dull. The -brightness of the figures and divisions on the dull ground makes them -easily read. These bands are divided into links, feet and inches, -metres and decimeters, or closer quantities either on one or both sides -of the band as required. With the etched band there is perhaps a little -risk of weak places from over-etching, although these bands are most -carefully made, but perhaps this is not greater than in the inserted -stud band, where weak places are necessarily caused by the loss of -width at the points where the holes are made for the studs, wherein -moisture hides after use in damp weather. - -737.--The steel bands have handles the same as a land chain. They -are wound upon a steel cross, Fig. 340. They are commonly placed in -a wind-up case similar to that of an ordinary measuring tape, but in -steel, provision being made that one of the pair of handles may be -secured about the position of the axis of the tape for winding it up. -In Fig. 338 the axis is made very large, so that the handle may be -pressed in from an opening in one side of it. The newest idea is to -cut a slit in one side of the plate up to the centre, as shown, Fig. -339. In this case the handle and band are put in from the side, so that -the axis is no larger than is necessary to take the handle. A strap is -placed on the side of the case for holding it. This is shown cut off to -admit sight of the handle. - -738.--The French make the handle generally T-shaped and hollow in -the cross part, which renders it very light and perhaps less cramping -to hold. The arrows are very commonly held by loops to the cross on -which the band is wound. This general arrangement is very portable and -convenient to carry; it is shown Fig. 342. - -739.--=Wire Land Measures.=--Where long open stretches of new country -are to be measured, it is common to employ a steel wire chain, of 5 -chains or of 500 feet in length, fitted with a pair of strong cross -handles only. - -[Illustration: Fig. 342.--_French land measure._] - -[Illustration: Figs. 343, 344.--_Marchant's 500-feet band._] - -740.--The author has made many chains of 500 links; in Fig. 344 a part -of one is shown full size. This _band_, as we may term it, is wound -upon a reel in an iron case, Fig. 343. A spring brake is placed at the -position _A_, which holds the reel and prevents the band from springing -out into loose hoops when it is run out. The 50 and 100 links are -indicated by short lengths of brass tube placed over the band--single -at the 50 links, but numerically indicated by number of bands as 2, 3, -and 4 chains. In Fig. 344 a 50 and a 300 links are shown; weight, 3½ -lbs. This flat, narrow, steel band chain was unknown until introduced -to the notice of the profession in the first edition, 1890. It is now -in very general use, and lengths may be had from stock of 2, 3, 4, or -5 chains, or 200, 300, or 400 feet wound upon a steel cross. - -[Illustration: Fig. 345.--_Richmond's tension handle._] - -741.--=Richmond's Tension Handle.=--Various devices have been employed -for giving equal tension to chains and bands to ensure equality of -measurements. Salter's spring balance has been very commonly used -attached to one handle of the chain to give a uniform pull, say of -15 lbs. This appears to answer very well. Mr. Richmond, surveyor, of -Sydney, has devised a very simple plan for tension of light bands, -which, being lighter and attached, is much more convenient than -Salter's balance. This is shown Fig. 345. The band passes through a -fitting in the centre of the handle, and a spiral spring is fixed to -this and the band at a short distance along it. By pulling the handle -a given tension can be applied, which is shown by the mark it reaches -towards the end of the band. This is adjusted to standard length, and -a small notch is placed in the centre of the end, from which a plummet -may be suspended if necessary.[54] - -The engraving is of a slightly modified form by the author, in which a -thin tubular cap covers the free end of the band to save this exposed -part from accidents. - -[Illustration: Fig. 346.--_Copper case thermometer for suspending to a -band chain._] - -742.--=Chain and Band Thermometer.=--Where very great accuracy of chain -or band measurement is aimed at, temperature is taken to allow for -expansion of the metal. A thin plain glass thermometer of the -_clinical_ form is the most sensitive of any. This is carried in a -wooden pull-off case lined with indiarubber. When it is used it is -placed upon the ground by the side of the chain. The delicacy of the -clinical form of thermometer is often objected to by the practical -surveyor, hence there are several other forms with boxwood and ivory -scales. These are not very satisfactory, as the boxwood and ivory -retain the heat of the body, from being carried in the pocket, for a -long time after exposure. The author has enclosed the clinical form of -thermometer in a copper case with open face, Fig. 346. The copper being -a good conductor of heat, this is very sensitive to the temperature -of the air. Two turn-down hooks are placed at the ends of the tube to -suspend it on the band. The thermometer stem has two indiarubber caps, -so that it will bear dropping on grass. It is contained in the same -form of pull-off case as the clinical. - -[Illustration: Fig. 347.--_Littlejohn's temperature handle._] - -743.--The coefficient of expansion for steel between 32° and 212° Fahr. -is about ·000012, which is less than ·01 inch per degree per chain. -Temperature corrections can therefore be recognised only upon very -exact work, appreciable only when long bands of the Marchant type, -lately described, of from 5 chains to 10 chains in length are used. - -744.--Mr. Littlejohn has patented an adjustable handle for temperature. -This is divided for allowance for the 100-feet or other band for -every degree Fahr. or centigrade. Fig. 347. The handle is set to the -temperature as it changes during the day. It offers, perhaps, the -highest refinement in ordinary land measurements. - -[Illustration: Fig. 348.--_Stanley's repairing sleeve._] - -745.--=Repairing Sleeve for Steel Bands.=--The reviser has patented a -sleeve which will be found useful, as by its use a broken band can be -immediately and permanently repaired in the field without the use of -tools. They are made to fit all sized bands, but it is necessary that -the correct sized sleeve should be used. One of these sleeves is shown -attached to a band at Fig. 348. - -In order to effect a repair it is merely necessary to clean the broken -ends of the band, and insert them into the sleeve, then hold a lighted -match under it until the soldering material is melted, when the repair -is completed. - -The central hole in the sleeve is to enable the user to see when the -broken ends are in contact, and the other two are to indicate when the -soldering material is melted, which takes place when it either bubbles -up in or runs away from these holes. - -[Illustration: Fig. 349.--_Linen Tape._] - -[Illustration: Fig. 350.--_Small steel pocket tape._] - -746.--=Linen Tapes.=--This most useful implement, Fig. 349, is one -of the most unsatisfactory measures the trader and user has to do -with. It consists, as is well known, of a tape oiled, painted, and -varnished, which is rolled up in a leather case when out of use. When -the weather is moist it shrinks, and when dry it expands. If it be too -heavily painted it becomes brittle and rotten; if it be lightly painted -it remains more flexible, but is more affected by moisture. A good -tape bears very well a stretching force of 7 lbs. to 14 lbs., but if -strained over this it is permanently stretched. There is no plan known -to the author by which these defects can be remedied. Numerous attempts -have been made--often valueless or worse--some, although popular, mere -claptraps, such as the insertion of wire. The best tapes for strength -and permanency are made entirely of green, hand-made, unbleached flax. -The tape is said to come from Holland to this country. These are at -first oiled with a drying oil (boiled linseed oil), and when seasoned -for a month or so, painted once or twice with white lead colour--not -too thickly. The printing is more permanent if done in oil; but the -tape is somewhat more flexible if the figures are stencilled in Indian -ink and the whole afterwards thinly varnished over with copal varnish. -The great secret for preserving the tape is to use it very carefully -and only in fine weather. In wet weather for taking offsets a light -steel 50-link chain is quite as convenient as the tape, and safer. - -Tapes are divided into links, feet and inches, metres, and all measures -as required. A decimal yard is commonly placed on tapes for measuring -earth work. For use with the chain a 66-feet tape is usually employed, -but many think a 33-feet better, using the chain for dimensions above -this. For measuring buildings, 50-feet or 100-feet tapes subdivided to -inches are employed. - -747.--=Steel Tapes.=--Thin steel tapes, 3/8, ½, and 5/8 inch wide -are in very extensive use. They are more accurate and more costly than -linen tapes, but less flexible and less durable. Where dimensions -are important they should always be used for short measurements. In -all cases it is advisable for a surveyor to keep a steel tape for -examination of the lengths of linen tapes in use. They are made to all -the measurements of linen tapes. - -748.--=Pocket Steel Tapes= 6 feet to 12 feet, Fig. 350, are used more -generally by mechanical engineers. These tapes, which are very light, -are held open by a catch, and closed by a spring. - -[Illustration: Fig. 351.--_Jointed offset rod, top and centre._] - -749.--=Offset Rods= are generally made 10 links long, either in one -piece or jointed in the centre with a bayonet joint. They are about -1-1/8 inches in diameter, diminishing towards the top to 7/8 inch, and -made either of yellow pine or ash. A hook is commonly put at the top, -Fig. 351, which takes the handle of a chain to draw it through a hedge -or other obstruction. The author's plan of making this is shown at _H_. -The lower end of the offset is shod with a steel or wrought iron socket -point, so that it may be set up in the ground and used if required as -a picket. Bands are painted alternately black and white at every link. -Square or flat rods are occasionally used for the same purpose, but -they are not generally so convenient. - -_The offset is Used_ in the manner of an ordinary rule to take -rectangular short measurements from the chain as it lies upon the -ground, commonly in order to obtain the contour of irregular outlines. - -750.--=Measurement by Rods= has become less general than formerly, -from the greater accuracy of Konstat or Invar steel tapes, by which -practically correct base lines may be laid down. For geodetic works -requiring the greatest accuracy the bases have been laid with rods of -various forms. These rods will be briefly described. It is only in the -construction of iron bridges, roofs, etc., that rods are at present -generally employed in the work of the civil engineer. - -751.--=Pine Standard Rods=, made of straight-grained pinewood seasoned -five or six years and then well soaked in linseed oil, make good -standard rods. The ordinary length in use is 10 feet by 1¾ inches -square. If the rod be used for butt measurement the ends are tipped -with gun-metal in which a turned steel stud is hard-soldered. The stud -is afterwards ground to true face in a lathe, and left of standard -length at 60° Fahrenheit (15·5 centigrade), Fig. 352. A disc of brass -1 inch diameter is inlaid at every foot for 5 feet from one end of the -rod, with a line at the true foot. These rods, after the work upon them -is finished, are lightly French polished to keep them clean and to -prevent the effects of moisture. The effect of temperature upon deal -was found by Roy to be about the same as upon glass--·0000085, average -of total length per degree centigrade, which is about three-fourths -that of iron. - -[Illustration: Fig. 352.--_One end of a pinewood butt rod._] - -[Illustration: Fig. 353.--_S--Block square._] - -752.--Where butt rods are used for continuous measurement, it is -necessary that they be brought very carefully together. In base line -measurement three or four are used, but for metal work or masonry two -10-feet only are generally employed. It is necessary that the rods -should lie upon a straight surface or be supported in a straight line. -In bringing them together, a piece of indiarubber 1/8 inch or so in -thickness temporarily placed at one end will prevent any palpable -disturbance of the percussion if the fixed rod be well weighted. One -5-feet more fully divided butt rod is very commonly supplied with a -pair of 10-feet rods for supplemental measurement. - -753.--=Angle-piece.=--A solid angle-piece with two planes at right -angles is very convenient for use with butt rods to give means of -scribing the true length down to a surface, Fig. 353 S. - -754.--=Butt Rods with Iron Core.=--Where rods are to be used for -preparing iron work it is better to have an iron core through the -rod, that may expand and contract with the metal on which they are -used. The rods that the author has designed for this purpose are made -out of a length of seasoned pine 2¼ inches square, sawn down and -turned cut sides outwards to prevent warping. A 10-feet length of iron -steam tube about ½ inch diameter is painted several times and then -bound round with paper soaked in paraffin. This is placed in a pair of -meeting grooves, as shown in section Fig. 355. The two pine flitches -are cross-tongued together and glued up with the inserted tube between -them. The tube has a turned steel cap placed over each end, Fig. 354, -and this is ground in a lathe to true standard at the temperature -of 60° Fahr. A steel pin is placed through the centre of the rod to -indicate 5 feet. The finished size of the rods is 2 inches square. - -The author has made these rods in sets, consisting of two 10-feet and -one 5-feet packed together with an angle-piece, Fig. 353 S, in a deal -case. - -755.--_The 5-feet Rule_ is of steel, ¾ inch by ¼ inch, inlaid in a -piece of dry pine, altogether of only half the thickness of the rods, -so that it stands the correct height for central butt measurement, -Fig. 356. The rule is divided into feet and inches, with one foot to -eighths. A centigrade thermometer is placed in one of the rods to -indicate the prevailing temperature, and a small piece of scale showing -amount to be allowed in 10 feet per degree centigrade for temperature -above or below 15·5° centigrade is engraved upon the thermometer scale. -The coefficient for the expansion of wrought iron is given by Lord -Kelvin as ·000019 mean per degree centigrade. - -[Illustration: Figs. 354, 355, 356.--_Butt rods with iron core._] - -Where a long length is laid down for a base line or other purpose, it -is better to take the thermometer reading at each measurement and defer -correction to the completion of the work; the temperature errors may -then be added together as a total, and the space allowance may become a -measurable quantity. For example, say ten 10-feet lengths give by these -united centigrade degrees, plus and minus, shown at separate readings -+ 167°, and that the standard of the rods is true at 15·5°. Then 167 - -(10 × 15·5) = + 12° per foot total allowance, that is, 12° × 10 feet × -·000019 = ·0228 feet or ·2736 inches to be added. In measuring iron of -course no correction has to be made. - -756.--_Beam Compass Measurements_ are occasionally preferred for -iron work. In this case the beam is moved from centre punch mark to -mark along a surface by the beam producing a scratch for the forward -position in which to place the punch mark. Rods of pine are commonly -employed. Figs. 357, 358 will sufficiently illustrate the instruments. - -[Illustration: Fig. 357.--_Beam compasses._] - -[Illustration: Fig. 358.--_Standard scale._] - -[Illustration: Fig. 359.--_Coincidence rods._] - -757.--=The Method of Coincidence= in measurements by rods has often -been applied to measurement of base lines. The plan consists in -allowing one rod, or a lighter continuous part of it, to pass the -other rod, so that a line cut to standard on one rod may be read into -one on the other. The best plan to do this is to have a scale fixed -along the face of one rod near its end, as shown Fig. 359, and to have -an extension from the other end of the second rod to pass alongside -this scale, so that two lines may be brought into coincidence. The -rod _B_ has a fixed scale _b_ placed on top of it at one end. The rod -_A_ has a scale protruding from it. This scale may be jointed with a -good ground joint at _J_ for portability. The rods are laid lightly -together, and any final adjustment is given by light taps with a small -hammer or mallet upon one or the other side of the stud _P_ until exact -coincidence of the lines shown at _b_ is brought about. This tapping -operation appears a rather rough process, but practically it is very -exact. - -[Illustration: Fig. 360.--_Bessel compensated rod._] - -758.--=Compensated Rods.=--The plan used by Bessel for the measurement -of a base upon the shores of the Baltic in 1836 is looked upon as a -model of the most perfect work of its kind. The rods were composed of -two bars of iron having surfaces accurately planed, with a similar bar -of zinc placed between them. The bars were laid one on the other, but -not in contact, the surfaces being kept apart by glass plates, upon -which they could slide with little friction. The linear expansion of -zinc per degree centigrade is about ·0000292 (Fizeau); that of iron -much less than half this--about ·0000119 (Thomson). The bars are -attached to each other in such a way that the expansion of the zinc may -act in the opposite direction to the expansion of the iron. The form -followed for the construction is shown in Fig. 360 where _II′_ are the -iron bars, _Z_ zinc. The length of the zinc required for compensation -between the junctions is found in the equation-- - - (_S_ + _Z_)(0000119) - _Z_(0000292) = _0_, - -_S_ being the total length of the standard rod in feet, and _Z_ the -length of zinc in feet required for compensation. This plan is that -adopted for the compensation of pendulums. For the verification of -a rod it may also be made to form the rod of a pendulum, by which -temperature expansion and contraction upon the system will be clearly -indicated by difference of time rate in the change of temperature -during night and day. This test becomes important where great precision -is aimed at, as the expansion in metals varies according to their -purity and state. The standard lines in rods made upon this model are -placed upon small inserted discs of platinum placed near the ends, -which are read by microscopes in coincidence upon a pair of rods. - -759.--=Colby Compensated Rods=, the invention of Major-General T. F. -Colby, who was for twenty-seven years superintendent of the Ordnance -Survey, upon which these rods were used. Each rod is composed of one -rod of iron and one of brass, which are so arranged in pairs that the -difference of expansion of these metals shall act to diminish the -amount of entire expansion at the points measured, a quantity equal to -its increase by temperature, in a manner to be described. - -_The Rods_ are each made 10 feet 1·5 inches long, 5 inches broad, and -1·5 inches deep. Fig. 362 _i_ is a side elevation of one rod, Fig. 363 -_ib_ plan of iron and brass rods, Fig. 365 _ib_ perspective view. By -this it will be seen that the rods are placed edgewise. The distance -apart is 1·125 inches. They are supported in the middle upon rollers, -Fig. 362 _F_. They are firmly fixed together at their centres by -transverse steel cylinders, Fig. 363 _RR′_ 1·5 inches diameter, each -rod being left free to expand or contract from the neutral central -point independently of the other. The neutral point is formed of a -T-piece _E_, Fig. 363, fixed firmly on the bottom of the box _bx_. At -the extremity, and at right angles to each of these bars, is a flat -steel tongue, Figs. 364, 365 _A_, 6·2 inches long, 1·1 inches broad, -and 0·25 inch thick, which projects 3·25 inches from the side of the -iron bar _i_. The tongue _A_ is jointed by double conical pivots at -_f_ and _f′_, which form axes perpendicular to the surface of the -tongue, allowing it to be inclined to slightly different angles to the -direction of the bars according to the expansion or contraction the -system experiences by heat. The pivots are 0·5 inch diameter, and are -placed at 2·3 inches from the end of the tongue next the brass bar. -On the tongue at _P_, flush with its upper surface, a small stud of -platinum is inserted, upon which a small dot is struck to form the -point of standard measurement. - -[Illustration: _Colby Compensated Measuring Rods._ - -Fig. 361.--_End of rod mounted with microscopes, trestles and ground -plate._] - -The bars are placed in strong wooden boxes, to the bottoms of which -are fixed the plates that hold the brass rollers upon which the bars -are supported, Fig. 362 _F_, and the central stay _E_ mentioned before -prevents any displacement of the bars when the rods are held by the -rollers _RR′_. To protect the tongue _A_, which projects beyond the -boxes, there is a special covering nozzle having a hole and cover over -the dot. A level is placed on one of the bars, which is seen through a -window in the lid of the box. At the ends of the box plates are fixed -for supporting the tripod of the double compensated microscope, Fig. -361 _D_, employed to observe the standard points of one pair of rods -brought by adjustment to true position _MM′_. A pair of sight vanes -which shut down are placed on the ends of the box for setting the rods -approximately in line. - -[Illustration: _Colby Compensated Measuring Rods._ - -Fig. 362.--_Side elevation of point of support of rod._ - -Fig. 363.--_Side elevation of centre, with section of box bx._ - -Fig. 364.--_Plan of rods and compensating arm._ - -Fig. 365.--_Perspective view of the same._] - -_Two Rigid Tripod Stands_ Fig. 361 _S_ are used to each of the rods -placed under the rollers Fig. 362 _F_ upon which the bars are supported -in the box. The tripods carry a universal slide-rest by which the rod -may be adjusted to position both in horizontal and vertical planes -Fig. 361 _A_. Six rods were used for the Ordnance Survey at one time, -and were designated by the letters A B C D E F. The weight of each rod -complete with microscopes in its case is 136 lbs. - -_Compensated Microscopes._--The compound microscopes, Fig. 361 _MM′_, -used with the Colby apparatus form a complete separate instrument, -consisting of two microscopes placed parallel to each other and -united together for reading the rods when they are brought with their -standard points the distance apart that separates the axes of the two -microscopes. In the intermediate space between the two microscopes, -and parallel with them, a telescope _T_ is fixed on the same piece -of apparatus, with adjustment for reading a point on the ground _G_ -perpendicular to the measuring rod. The microscopes are held apart -by two bars of brass and iron 7 inches long, 0·5 inch broad, and -0·375 inch thick, which are placed at 2·5 inches apart and secured -with the telescope, which forms the fixed centre, by collars to the -bodies of the microscopes. The difference of expansion of the iron -and brass maintains the separation of the microscopes at their foci -at one distance with every change of temperature of the air. The -object-glasses are of 2 inches focus. The microscopes are brought to -adjustment and bearing by levelling on a tribrach whose base is fixed -firmly to one of the rod cases, and by lateral adjusting screws. -Special microscopes are used with each of the six rods of the Colby -apparatus, and are distinguished by the letters M N O P Q R S. The -weight of each compound microscope is 5 lbs. Very full particulars of -the Colby apparatus with engravings of all parts, are given in "The -Ordnance Survey Account of the Measurement of the Lough Foyle Base." - -In measuring a base line a piece of nearly level land is selected, and -the rods are supported upon the trestles or tripod stands at about 3 -feet from the ground. The heights of the upper surfaces of the tripods -are ranged by a theodolite or level for all intermediate points between -the two ends of the line. Generally twelve trestles are employed with -these rods, which are fixed firmly to the ground at every station by -legs well rammed in, Fig. 361 _HH′_. The cases containing the rods, or -the rods themselves, are made sufficiently strong to be supported upon -two points only without serious deflection. - -The Colby system of measurement of base lines varied in detail has been -employed by nearly all the nations of Europe and in America. - -760.--=Modern Base-line Apparatus.=--The introduction of "Konstat" -steel (highest grade Invar) tapes and wires has revolutionised the -method of measuring base lines. These tapes offer a means which is -far superior to anything obtained by measuring bars, because they -combine the advantages of great length and simplicity of working, -with more precision than the shorter laboratory standards, providing -that suitable apparatus is used in applying them to their work. Base -lines may now be rapidly measured with long "Konstat" steel tapes so -that much longer lines are laid down than was formerly the practice -when measured with bars, with the result that any errors that may be -introduced do not affect the ultimate expansion so much owing to the -greater length of the base. - -The coefficient of expansion of "Konstat" steel is under ·0000005 per -degree Fahrenheit, so that provided accurate means of suspending the -tape and reading it and transferring the readings to a plate properly -let in the ground are used, we have a most exact and rapid method for -this important work. - -The tapes are usually 100 feet or 30 metres long, but 300 feet or 100 -metres are often used. The tapes are a few feet longer than these -measurements, so that the rings are well clear of the reading lines. A -silk cord is attached to these rings and passes over the end suspension -supports, one of which is shown at Fig. 366. These are made with two -steel bars rigidly mounted on two tripods; upon the bars a sliding -carriage is mounted carrying a pulley running on ball bearings with a -vertical motion for final adjustment of the tape for height. A weight -is attached to the other end of the silk cord to give the same tension -as that under which the tape was divided. - -[Illustration: Fig. 366.--_One of the two end supports of the band, -showing tension weight, with cord running over the ball-bearing -pulley._] - -To prevent catenery light intermediate stands, as shown at _B_ Fig. -367, are used at about every ten feet; these have a rising cross piece -with guides which are adjustable for height and sideways to support -the tape in perfect alignment. Having the tape properly suspended the -reading instruments, _C_ Fig. 367, are placed in position at either -end. These are mounted on rigid-framed stands and provided with -levelling screws, cross levels, transverse screw motions and movement -in azimuth, with clamp and tangent motions and aligning telescopes. A -powerful microscope is rigidly fixed over a little table over which the -tape passes and reads its division with great exactness, coincidence -with the division being made by the traversing screw. By the side of -the reading microscope, and in exact collimation with it, a plumbing -telescope is rigidly fixed, and this sights down to a transferring -apparatus, _D_ Fig. 367, which is over the plate let into the ground. - -[Illustration: Fig. 367.--_Two reading and plumbing instruments, C, -C; transferring instrument, D; and one of the adjustable intermediate -supports, B._] - -The transferring apparatus is a spring centre punch rigidly mounted -truly vertical on a supporting plate having transverse motions, -cross levels and levelling screws. The top of the centre punch has -a small platinum disc let in a recess, and upon this disc very fine -cross lines are marked. This apparatus is placed on the ground over -whatever has been let in to receive the mark, it is then levelled and -the cross lines upon the punch top brought by means of the transverse -motion screws exactly to coincide with the spider web of the plumbing -telescope, and in this position the centre punch is lightly struck -with a mallet which marks the plate let in the ground in the exact -position of the centre of the cross lines at its top, so that if now -the transferring apparatus be removed the cross webs of the plumbing -telescope would cut the dot marked in the plate by the centre punch. -This method is far more exact than any hanging plumb-bob, as even if -they are screened to prevent swinging very few hang with the point -perfectly true. In laying down a base line No. 1 reading and plumbing -instrument is set up and levelled over the starting end block, -which is usually of hard stone or granite set on a firm foundation, -with a copper plate let in its top about the centre, the line having -been previously set out with a theodolite, and the intermediate -stations being roughly measured with an ordinary steel tape. At each -intermediate station or length of Konstat tape used a teak post is -driven into the ground and a zinc plate screwed upon its top; the -other end block is similar to the starting one. The Konstat tape is -now mounted between the end suspension supports, one being outside the -starting end block and the other outside the first teak post which has -been put in for the first length. No. 2 reading and plumbing instrument -is set up over this post, and No. 1 and No. 2 are aligned upon each -other by their aligning telescopes, and the Konstat tape adjusted over -the little tables under the microscope of each; the intermediate stands -are then put in and adjusted for height to prevent catenery, and the -guide pieces are brought up to the tape on either side and clamped to -prevent side deflection by wind. The tape being properly suspended it -can be easily moved with the fingers lengthways, as it is suspended at -either end by silk cords over ball-bearing pulleys. It is brought in -position with its starting end division somewhere under the microscope -of No. 1 reading apparatus, and the microscope is then brought into -exact coincidence by the traversing screws. The transferring apparatus -is put on the granite block with the centre punch in the field of view -of the plumbing telescope and then levelled; the cross lines in the -top of the centre punch are then brought to exactly coincide with the -plumbing telescope webs by the transverse motion of the transferring -apparatus, the centre punch is struck and the mark thus made in the -copper plate has a line engraved through it. The transferring apparatus -is then removed to the position under No. 2 reading and plumbing -apparatus. No. 2 microscope is made to coincide with the end division -on the Konstat tape by its traversing screws, the centre punch of -transferring apparatus, brought by its traversing screws to coincide -with the webs of the plumbing telescope and struck, marks the first -section. No. 1 reading and plumbing apparatus is then transferred to -the next post, No. 2 remaining over the first section post, the first -end suspension stand is transferred outside No. 2 post and the tape -mounted between as before, the traversing motion of No. 2 reading -apparatus must not be touched, but the end division of the tape brought -to coincide with its microscope web by shifting lengthways. No. 1 -microscope at the further end is adjusted to coincide by its traversing -screws and the transferring apparatus as before, and so on until the -entire length is measured, the last centre punch mark on the copper -plate let in the further end block or stone having a line engraved -through it. - -A few 1-100th of an inch divisions, or 1-10ths of a millimetre, are -divided on either side of one end division of the Konstat tape so -that any allowance for expansion or contraction may be made under the -microscope at the time, but with Konstat tapes this is very small -indeed. With fairly level ground any slight differences of level can be -allowed for in setting up the stands, so that the tape remains level; -if the difference is too great for this the difference of hypo and base -must be calculated. Thermometers are used, generally one suspended on -the tape at each end. - -761.--=Perambulator.=--A very ancient instrument, described by -Vitruvius as being among the effects of the Emperor Commodus; it was -used by hand, or attached to a carriage to measure distances. The -instrument is at present used as formerly for measuring roads. Upon -pavements and asphalt roads it measures accurately, where by reason of -traffic it is sometimes a difficult or very slow process to use the -chain. The plan of manufacture is varied considerably. The author makes -the felloe of the wheel in segments of well-seasoned mahogany in two -rings, Fig. 368. These are rivetted together from side to side in such -a manner that the grain of the wood is crossed as much as possible to -prevent lateral warping. The tyre, which is 6 feet in circumference, -is made of hard rolled brass 1 inch by ¼ inch thick. The spokes are -light steel tubes covered with brass tube, and screwed into a brass -hub. The axle of the wheel is placed in a steel fork which is formed -by screwing, by means of a winged nut, two bars of about 18 by 1½ -by 3/8 inches upon a boss formed at the end of the steel stem of the -turned wood handle. Made in this manner the handle may be easily -detached and placed flatwise upon the wheel, so that the whole may be -packed in a square deal case of moderate dimensions for transport. - -[Illustration: Fig. 368.--_Perambulator._] - -[Illustration: Fig. 369.--_Details of registering box._] - -[Illustration: Fig. 370.--_Section._] - -_The Registering Part of the Instrument_, Figs. 369, 370. The axle is -protruded through the fork on the left-hand side, and thence through -the registering box supporting one of its ends. The other end of the -box is supported by a stud which fits into the side of the fork. The -axle in the part contained within the box is cut into a screw, Fig. -370 _S_, of about sixteen threads to the inch. The screw works in the -edges of a pair of discs _R_, placed one upon the other upon the same -axis; these are cut on their edges with teeth to form worm wheels in -which the screw upon the axis of the wheel works. The upper disc has -110 teeth. This therefore moves one revolution by 110 turns of the -wheel. It is divided into 110 divisions at its circumference, but is -figured 20 yards to 220 yards or 1 furlong, so that each division -represents 2 yards, corresponding with the circumference of the wheel, -Fig. 369 _O_. The divisions are read by a point attached to the side of -the box shown at the top of the figure. Single yards are shown by the -intermediate position of the pointer between the divisions, but single -feet may very well be estimated approximately. The lower disc is cut -with 111 teeth. The ratio 110 to 111 gives a differential displacement -of one tooth only after 110 revolutions of the wheel, or of 220 yards -traverse. The two discs take, therefore, by revolution over the surface -220 × 110 = 24,200 yards or 13·5 miles before they return to the same -relative position as at starting. This is, therefore, the space this -perambulator will traverse without resetting. To enable the lower -disc to be read the upper disc is cut away for half the interior -circumference of its circle. A part of the upper disc is formed into a -point, to read direct from the centre into divisions on the lower disc, -in furlongs up to 13½ miles. - -_The Measuring Box_ is covered with glass for protection. The box can -be taken off by removal of the milled-headed screw at any time to set -it back to zero, but in practice it is often found more convenient to -spin the wheel round to zero or an even mile of the outer circle, and -record differences of reading, if this can be done in the distance -within the record of 13 miles of the lower disc. The screw and axis, -which are of hard steel, should be occasionally oiled with watch oil to -keep the perambulator in good working order. - -762.--The reviser has designed a light form of perambulator on the -bicycle wheel principle. It is shown at Fig. 371, and is very light -and portable. The rim of the wheel is of gun-metal and is usually made -two yards in circumference. It is fitted with a counter which denotes -two yards to every revolution, and the distance is given in number of -yards only. The handle is detachable from the fork for packing, and -the whole is contained in a light pine case. The wheel is also made two -metres and ten links in circumference. - -[Illustration: Fig. 371.] - -763.--=Pedometer.=--Used for roughly ascertaining distances passed over -in walking. This ingenious instrument was the invention of William -Payne in 1831 (patent No. 6078). It is the size of an ordinary watch, -and has a similar face; but between the figures, which indicate miles 1 -to 12, there are four divisions only, to indicate quarter miles. The -pedometer is slung up by a loop, Fig. 371, _H_ fixed upon the handle, -which in use is passed over the edge of the waistcoat pocket so as to -keep the instrument in an approximately vertical position. - -[Illustration: Fig. 372.--_Construction of pedometer._] - -[Illustration: Fig. 373.--_Face of passometer._] - -764.--_The Registering Apparatus_ consists of a pendulum, Fig. 372, -_P_ placed horizontally by being supported by a delicate spring _L_ to -its highest position, where it rests against a stud. The action of the -pendulum is caused by its following the motion of the body in stepping, -until stopped by the foot reaching the ground, when the momentum -attained by the pendulum carries it from its upper position of rest -where it is sprung against the stop to its lower free position, where -it is stopped by a screwed adjustable stud _S_, shown under it. The -axis of the pendulum is free upon the axis of the ratchet wheel _R_. -When the pendulum falls, a fine spring, fixed to its upper surface, -drops its end into the teeth of the ratchet, moving over two or three -teeth, which are held against retrograde motion by the spring pawl _D_. -When the pendulum rises, the ratchet is moved forward the number of -teeth that the spring at first slipped over. The ratchet is connected -with a pair of geared wheels, _not shown_, the axis of the second of -which forms the axis of the hand. In this manner each oscillation of -the pendulum is communicated to the index hand. The ratchet is made -with extremely fine teeth, so that by adjustment of the screw stud _S_ -a greater or less number of these teeth may be taken by one beat of -the pendulum, and thus the mileage rate may be adjusted approximately -to the step. This is done, however, very imperfectly, as the variation -of the average steps of men amounts to one or two inches, and the -difference from the number of teeth taken will scarcely indicate less -than three inches in the step. - -765.--=Passometer.=--This instrument was originally invented by the -author as an improvement upon the pedometer (1868). The instrument, -Fig. 373, is not intended to indicate miles or any distance, it -simply counts the number of steps taken. The action is just the same -as the pedometer, but the ratchet teeth are larger and less liable to -miss a tooth, as it is made to take one tooth only at a single step. -The dial arrangement is entirely changed. The steps are numerically -indicated by a separate hand which reads into the graduations up to -50 steps upon a small dial. Each revolution of the small hand reads -through gearing one division of the central hand, which moves over the -complete circumference of the dial, reading up to 25,000 steps. This -is the extent of indication. It is necessary in continuation beyond -25,000 steps to take a record of progression per 25,000 where a greater -distance is required to be measured. - -766.--The average step may be estimated perhaps within 1 or 2 per cent. -by training in walking several miles steadily, counting the steps, -always remembering that we take shorter steps uphill and when we are -tired. But the mean step of the individual under all the different -circumstances is the only rule that can be followed. - -[Illustration: Fig. 374.--_Sounding chain._] - -767.--=Sounding Chains= used for coast surveys are generally made of -iron, but sometimes of brass. They are usually made of 10 fathoms -entire length. The links are 1 inch, and the feet are indicated by -tellers. The form of teller designed by the author is shown in Fig. -374 for the 3. A leaden weight, similar to that shown Fig. 375, is -used upon the end of the chain--of 28 lbs., for ordinary coast work, -or heavier if there are strong currents. The chain is contained in a -strong wooden box. - -[Illustration: Fig. 375.--_Sounding line and weight._] - -A very elaborate apparatus with steel wire line has been made for -deep-sea sounding by Lord Kelvin and others; but this subject is beyond -the province of the present work. - -768.--=Sounding Lines=, used for survey of shallow coasts and harbours, -are made of water-laid line of fine green hemp, about ¾ inch -circumference, Fig. 375. White tapes are inserted as tellers at every -foot, and red tapes at every fathom. 3 to 6 fathoms are the ordinary -lengths employed. If the water is shallow the fathoms are easily -counted, but if thought necessary knots may be tied to indicate the -number of fathoms on the red tellers. The weight is about 7 lbs. for -50 feet line, about 15 lbs. for 100 feet. The under side of the weight -is commonly recessed to take tallow when it is desired to bring up a -specimen of the bottom, if this is loose sand or mud. - -769.--=Coast Survey Lines.=--For surveying distances, from point to -point of soundings along a coast, lines of fine copper wire rope -marked with tellers at 50 and 100 feet are commonly used. The line -is generally allowed to rest on the bottom of shallow water, and is -floated up by means of attached corks in deep water. It is usually -laid and picked up by means of a reel fixed at the stern of the -surveying boat. The lengths of line used vary from 1000 to 5000 feet. - -770.--=Telemeters.=--These scarcely enter within the practical limits -of surveying instruments, but as several attempts have been made to -introduce their use it is necessary to mention them. The general -attempt has been to measure a great distance, 1000 feet or more, by -means of the angles subtended from the ends of a short base to a -distant point. This base in the telemeter of Piazzi Smyth is 60 inches; -Colonel Clarke, 72 inches; Otto Struve, 73·5 inches; and Adie, 36 -inches. The angles are usually taken upon the principle of the sextant -by coincidence of image. Very much greater success has been attained -recently by Messrs. Barr and Stroud by means of their range-finder -of 54 inches base. The author, as far as his information reaches, is -assured that no instrument of the class is satisfactory for surveying -purposes. Further, the subject is one to which he has devoted some -study, and designed two telemeters.[55] One of these appeared to -him for a time satisfactory within certain limits. The base in this -instrument was 50 feet, formed of a fine pianoforte wire stretched -between two observing telescopes, the tension of the wire directing the -one telescope to a right angle, and the other telescope to an arc which -read either degrees and minutes or absolute distances in the eye-piece -to the direction in which the telescope was pointed. In first trials -this instrument was found fairly satisfactory; but subsequently in -windy weather the deflection of the wire rendered the action of a pair -of instruments quite unreliable. - -There are some instruments, as Colonel Gautier's telemeter used in the -French army, which depend upon combined reflectors placed normally at -15° to 45°, as in the apomecometer, art. 693, but with a tangent screw -to give a small motion of displacement to one mirror which reads on -a scale of calculated distances to angle from a certain base measured -between two stations of observation. A very similar instrument, -invented by Labez, has one reflector only at 45°. These instruments may -be useful for measuring approximate distances for range in the army, -but can scarcely rank as surveying instruments, the box sextant, art. -664, being in every way a superior telemeter for the purpose when a -measured base can be fixed and well-known trigonometrical calculation -used. - -771.--The simplest and best telemeter for surveying purposes is the -subtense telescope, and all good, up-to-date surveying instruments -have their telescopes so fitted, but for those who do not carry an -instrument with a telescope the reviser has designed a small subtense -telemeter, Fig. 376, which consists of a small telescope fitted with -subtense points, and mounted in a collar which has vertical and -horizontal motions and a centre socket to fit a Jacob's staff. The -stadia is set to read 1 in 100. The telescope has rack and pinion -focussing and may be revolved in its socket so that the stadia rod -may be read held either horizontally or vertically. It is packed in a -leather holster case, and a four-fold 10-feet spring-pointed stadia rod -is supplied with it divided into feet, tenths, and hundredths. - -[Illustration: Fig. 376.] - -772.--=Hand Rods=, although used more generally by building surveyors, -are extremely useful also to the civil engineer and land surveyor -for town work among buildings and in mines. They are made 5 feet in -length, less generally 10 feet. The 5-feet are made of single blades -of lancewood or of two jointed to fold. The 10-feet are always jointed -and made much stouter than the 5-feet. The 5-feet are generally sold in -pairs. - -[Illustration: Fig. 377.--_Ordinary 5-feet jointed rods--plan and -section of joint._] - -773.--=Ordinary 5-feet Rods= are divided to every 3 inches, with feet -only stamped with numbers, as shown Fig. 377. Where the rod is jointed -the best form of folding joint is shown in the figure in section and -plan. The spring S is sunk into the face of the rod at the joint on -one side, and springs into a groove (_housing_) in the other side so -as to lock the joint when it is either open or closed. The most useful -dimension for the rod is 1 inch by 1/6 inch. Rods are nearly always -made of lancewood, but they are preferred dyed black for neatness by -many surveyors. A pair of rods is usually carried in a cowhide case. -They are also often carried in the stem of a walking-stick hollowed out -for the purpose. The rod or rods in this case are made much lighter, -generally ½ inch by 1/8 inch for a pair of rods, or 7/16 inch by 7/32 -inch for a single rod. The single rod is to be preferred in this case -for its extra strength. - -774.--=Fully Divided Rods.=--The author has made rods for many years -divided to single inches. These measure from both ends--one end direct -as Fig. 378 and the other end reversed by turning the rod over as Fig. -379. By this plan the rod gives direct measurement in feet, inches, -and parts from either end, and the division is always placed outwards -against the work, so that measures may be taken from either end by -turning the rod over sideways, without turning it end for end. - -[Illustration: Figs. 378, 379.--_Stanley's surveyors' rods._] - -775.--Connecting Link for Rods, which weighs only 1 oz. and may be -carried loose in the pocket, is often found convenient for measuring -heights, as it permits the ends of a pair of rods to be brought -together, Fig. 380. By this means the arm will raise the rods about 7 -feet, and with 10 feet, the height of the pair of 5-feet rods, this -will make 17 feet of measurement. When the 10-feet is set against a -wall, its height, if 20 or 30 feet, may be guessed very approximately -by standing at a distance from it. - -[Illustration: Fig. 380.--_Connecting link for rods._] - -[Illustration: Fig. 381.--_Slip jointed rod._] - -776.--=Slip Jointed Rod.=--This form is less general, but it is a very -convenient form of rod. The jointing is effected by two loops which are -fixed to the centre end of one part of the rod in such a manner that -the other part may slide through the loops. When the rod is extended -to 5 feet there is a stop which prevents further extension, and a -spring to keep it at this exact position, Fig. 381. The outside of the -rod is divided into feet and inches. The inside is divided so that -any addition to the half rod, produced by extending it; may give the -measurement from end to end of the rod at this position, thus:--The -half rod being 2 feet 7 inches closed, if the loose side be drawn out -19 inches the rod from end to end will be 4 feet 2 inches, which will -be indicated by the division and figuring inside the rod. This is very -convenient for measuring openings such as doorways or passages. - -777.--=Brace-piece.=--A 10-feet rod is sometimes made with a -brace-piece, which folds up inside the rod. This brace-piece is jointed -to fix both half rods to 90° when it is desirable to use the rod as a -square. - -[Illustration: Fig. 382.--_Civil engineer's rule._] - -778.--=Civil Engineer's Rule= is made fourfold in both boxwood and -ivory, Fig. 382. The most convenient size is 1 inch wide. Some of the -profession prefer them narrow for lightness--¾ inch; and some wide -for strength--1¼ inches. This rule is generally well made, with -German-silver joints and outside joint-plates. The divisions placed -on the rule outside are inches in eighths and tenths; the inside, the -ordinary architects' scales, 1/8, ¼, ½, 1, and four chain scales, -20, 30, 40, and 50. A 10 is got by halving the 20; 60, by doubling the -30. A protractor reading to 5° is divided on the head. With silver -joints and in fine ivory this rule is often made a presentation -instrument. - -FOOTNOTES: - -[54] _The Surveyor_, vol. ii. No. 5. Sydney, Nov. 1889. - -[55] Patent No. 2142, May, 1880. - - - - -CHAPTER XVII. - - STATIONS OF OBSERVATION--PICKETS--FALSE PICKET--PERMANENT STATIONS-- - REFERRING OBJECT--HELIOTROPE--HELIOSTAT--HELIOGRAPH--SIGNALLING-- - MORSE ALPHABET--NIGHT LIGHTS--OIL LANTERNS--MAGNESIUM LIGHT. - - -779.--=Stations of Observation= vary materially according to the -extent of the survey and its purpose. For geodetic works stations -are raised at great expense, often in masonry or solid woodwork. For -ordinary local or civil surveys the stations are commonly formed of -single poles set up vertically, which vary in dimensions according to -the extent of survey and the difficulties which may be encountered by -various obstructions to direct visions by woods, lakes, marshes, etc. -The apparatus that may be useful in the work of the civil engineer in -ordinary practice will only be considered here. - -[Illustration: Fig. 383.--_Ranging pole or picket._] - -780.--=Pickets or Ranging Poles=, Fig. 383, as the name indicates, are -used for ranging a direct line through a district, either by a series -of poles sighted from one to the other or by being placed in position -convenient for triangulating by the theodolite where the country is -open, or free from many buildings, trees, or other convenient landmarks. - -781.--The picket (Fr. _piquet_) is a straight, slightly tapering pole -shod with wrought iron or steel. It is generally made of about 1-1/8 -inches diameter, and is painted in alternate feet red and white with -an enamel paint that will not soil the hands or take dirt from them. -The shoes should be made with strap-pieces, so that the picket, which -is generally made of yellow pine for lightness, should not be liable -to break off at the shoe in use. Fig. 381 represents the lower part of -a picket as made by the author: _B_ black, _W_ white, _R_ red. It is -usual to have six pickets at least out in use with a theodolite in open -country. - -[Illustration: Fig. 384.--_False picket._] - -[Illustration: Fig. 385.--_Spur-shod picket._] - -782.--False Picket.--For the placing of a picket it is usual to clear -the sod with a small spade where possible, so as to suspend the plummet -from the theodolite into the hole made by the picket to triangulate -from its position. In marshy lands and under many conditions this is -not easily done. It will generally be found more expeditious to carry -about one of the author's false pickets, to place directly in the hole -from which the picket is removed, which saves the trouble of removing -the grass. This is shown in Fig. 384. It consists of a wooden peg, upon -the top of which a cross is sawn to represent the axis. This cross is -filled in with a veneer of ebony, and the whole is polished over to -keep it clean. It will be readily seen that any picket accidentally -broken will make a false picket. In setting up the theodolite over it -the plummet is brought to verticality with the centre of the cross. -In moving the false picket the original one is easily replaced, if -required, in the same position for continuing the work. - -783.--=Spur-shod Picket.=--Much stouter poles than may readily be -pressed in by hand, as for instance, of 2 inches diameter, may be -driven into the ground by having a spur or cross-bar of steel, about -7 inches long and about 3/8 inch diameter, placed through the pole, -say at 1 foot distance from the point, a form which is much used on -the Continent. This picket may be jerked down for a certain distance -by pressure of the foot on each side, and then jerked home to the -ground by standing upon it, to make a 10-feet or 12-feet pole stand -sufficiently rigid for temporary work, Fig. 385. - -[Illustration: Fig. 386.--_Socket for station pole._] - -784.--=Permanent Stations= are commonly constructed upon hilltops or -other commanding positions. A very general way is to set up a long -pole of fir or other wood at command, from 10 to 20 feet in height, -according to the circumstances. Occasionally it is desirable to -remove the pole and place the theodolite centrally over its vertical -position. A very good way to do this is to have a slightly tapered -wooden socket, Fig. 386 _S_, constructed of stout boards, say 1½ -inches thick, made into a hollow square with a cross of boards, _WWWW_ -fixed to it. The socket is placed in a hole dug out entirely below the -ground, and is rammed in and fixed as an ordinary gate post. The pole -_P_ is squared at the end to fit the tapered socket up to shoulders -which are formed by leaving the other part of the pole round. The -socket for a 15-feet pole should be 18 inches deep; for a 20-feet -one, 2 feet deep. Where these poles are properly prepared they may be -jointed together in two or more parts for portability. Bunting flags, -red and white, about 18 inches by 9 inches, may be fixed at the tops -of the poles. In fixing the socket the pole should be erected in it to -be able to keep it constantly vertical during the ramming. A plummet -suspended at arm's length, at a distance from the pole in two positions -at about right angles to each other from the centre of the pole, will -provide a means of keeping it erect during the fixing of its socket. -The socket hole, upon lifting the pole out, forms the centre for -erecting the theodolite over its position. - -785.--=Referring Object.=--It is desirable that all arcs taken by -the theodolite from an important station should contain one point in -common, for which the best defined object to be found at a distance -may be selected. Colonel Clark, of the Ordnance Survey, recommends as -a referring object two rectangular plates of metal placed with their -edges parallel to each other in the vertical plane, at such a distance -apart that the light of the sky seen through the opening appears as -a vertical line of about 10″ in width. The best distance for this -object is from 1 mile to 2 miles. Two pieces of board, fixed a small -distance apart by ledges screwed thereon, answer the same purpose. The -description fully conveys the method without illustration. - -_Stations Visible at Great Distances_ are formed by means of reflection -of the sun's rays or by artificial light. - -[Illustration: Fig. 387.--_Stanley's heliotrope._] - -786.--=Heliotrope=, or _heliostat_ as it is sometimes called, may be -any form of mirror to throw the sun's ray in a constant direction or -to a distant station at a time of day fixed for making observation. -The instrument is uniformly constructed with a small glass mirror -having a plane surface. The angle of divergence of the extreme rays -in the reflection is the same as that subtended by the sun's diameter -at the position of the mirror, that is, of about 32 minutes of arc. -This divergence is sufficient to render the reflector visible at a -great distance. The plan upon which the author has constructed this -instrument is shown in Fig. 387. It consists of a reflector _M_ formed -of a plain glass mirror of about 5 or 6 inches in diameter, placed in -a metal tray. The mirror is centred vertically upon an axis to which -a worm wheel _B_ is attached upon one side that works into a tangent -screw which is moved by a milled head so as to place the mirror at -any angle to the horizon. The mirror and its vertical adjustment just -described are carried by a fork which is erected from the base board -of the instrument upon a socket joint which permits the mirror to be -turned about. Upon the lower part of the fork above its socket another -worm wheel is constructed centrally to the axis. This works into a -tangent screw attached by fittings to the base board. The tangent -screw has a long shank leading to a milled head _A_. By means of the -milled heads the mirror may be set to any position, so as to throw the -reflection of the sun in any required forward direction. A small hole -is cut through the silver in the centre of the mirror to sight the -position to which the sun's reflection is directed. - -787.--_The Base Board_ is of ¾ inch mahogany about 20 inches by 10 -inches, and is supported upon a very firm tripod stand, like that -described for a plane table, art. 700. At one end of the board a -sighting screen of mahogany, 10 inches by 10 inches and ¾ inch thick, -is hinged, so as to be held erect by means of a stay bar _E_. In the -centre of the screen an opening is turned out 3½ inches diameter, -and a frame-piece of half circle only is placed over this. The frame -piece is grooved out at the back so as to hold discs, shown _abc_ in -the figure. - -788.--_The Discs abc_, are of thin brass and have openings -respectively ¼, ¾, and 1½ inches wide, so as to reduce the width -of the line of light which appears through them when the reflection of -the sun is thrown from the back. These have each a fine wire stretched -across them to indicate the centre. A fourth disc, not shown, has a -double cross of wires to indicate the centre only. - -789.--_To Pack the Instrument_, the screen is turned down the index -frame, falling into the opening _F_; the mirror with its fork is lifted -out and secured to the surface of the base board by buttons; and the -whole apparatus is put in a pine case. Its weight without tripod stand -is 8 lbs. - -790.--_To Use the Heliotrope_, the station on which the sun's light is -to be thrown is sighted by looking through the small hole in the centre -of the mirror, and adjusting the base board until the station appears -in the centre space of the disc opening. The mirror is then turned -towards the sun by means of the milled heads until its image, reflected -upon the back of the screen, appears central with one of the discs -which is intended to be used. All parts of the stand and fittings being -made quite firm, the attendant moves the milled heads, as required, to -follow the apparent motion of the sun, at intervals of five minutes -or less. It must be observed that the centre of the slit in the disc -represents the station visible to the observer. This point must -therefore be plumbed to the station point in setting up the instrument. -A part of the screen at _P_ is cut away to admit of the suspension of a -plummet. - -791.--The heliotrope was much used in India for the great -trigonometrical survey. Colonel H. Thuillier states from experiment -that "A heliotrope of 9 inches diameter answers for 90 to 100 miles. -For nearer distances it is much too bright to be observed through -a telescope, and the light must be diminished in the following -proportion. For distances of 2 or 3 miles (the usual distance of a -referring mark) an aperture of 0·25 of an inch will answer, and for -longer distances about 0·1 of an inch of aperture per mile of distance -will suffice, viz., an inch for 10 miles, 2 inches for 20 miles, and so -on, provided always the apparatus is carefully adjusted and the man who -works is alert and skilful."[56] - -Practically the discs here described will give all the variation -required. In less favoured climates than India more opacity will be -found in the atmosphere, and larger apertures required than those just -stated. - -_Signalling with the Heliotrope._--A thin wooden bat _D_ is moved over -and off the outside front of the open disc aperture, following the rule -of Morse signals, which will be presently described for the heliograph. - -792.--=Heliostat.=--Is a smaller instrument than the heliotrope, in -which the mirror or mirrors are moved by clockwork, so as to keep -the sun's reflection in a uniform direction throughout the day. This -instrument is delicate and not generally well adapted to field work. - -[Illustration: Fig. 388.--_Heliograph._] - -793.--=Heliograph.=--This instrument is the invention of Sir H. C. -Mance,[57] since improved by Major Macgregor, Colonel Bonham, and -others. It is used for a military signalling apparatus, but it is also -employed, on account of its portability in place of the heliotrope -for surveying, where great precision by limiting the area of light -reflection is not required. The construction of the instrument is shown -in Fig. 388. _B_ is the back of a plain circular mirror of 5 inches -diameter, supported upon pivots on a fork frame _J_, the lower part -of which forms a socket. The socket is furnished with a thumb-screw -to secure the mirror and its frame when placed upon a cone projecting -from the apparatus connected with the base plate formed on the top of -the tripod head. The cone is erected upon a disc or wheel cut at its -edge in teeth and centred upon the axis of the tripod head. The wheel -is revolved by means of a pinion connected with a milled head _A_ -which moves the mirror and the entire apparatus above in horizontal -revolution. - -794.--_The Sighting Arm L_ is attached to a collar fitting projected -from the tripod head. This may be fixed in any horizontal direction -by means of the tangent clamping screw _C_. The arm _L_ has a -supplementary extension by the piece _Sj_, which is jointed at the -position of these letters and also by a socket fitting into the arm. -The termination of the extension is a sighting point _I_ formed of a -thin blade of metal. The arm and its fittings permit the sighting point -I to be set in any direction or elevation to follow the inclination of -the land. - -795.--_The Sighting Vane_ is a piece of white metal upon which there is -placed a black dot termed the _sighting spot_. A small circle, about -1/5 inch diameter, is left unsilvered in the centre of the mirror, -which does not reflect the sun's rays. It therefore causes a small disc -of shadow in the centre of the reflection of the mirror, termed the -_shadow spot_. The shadow spot is made to appear upon the sighting spot -when the instrument is adjusted to throw the sun's image upon a distant -station. - -796.--_The Supplementary Mirror M_ is similar to that already -described, centred also on pivots and placed in a forked frame. This -is mounted on a cone _S′_ which fits into a socket at _S_, when the -extension arm _J_ is removed. This mirror is intended to receive the -image of the sun when placed towards the back of the pointing of the -instrument to throw the sun's image from the mirror _M_ to _B_, to -signal by double reflection, when the sun is at a forward angle to -the distant station. The coincidence of reflection is taken with this -mirror by the reflection of a piece of paper pasted on its centre of -the same form as the index _I_. - -797.--_Telegraphing Apparatus_, called technically _flashing_ -apparatus. This consists of a rod _R_ hinged to the top of the mirror -at its upper end and also to a lever which forms a Morse key at the -lower end. The rod is formed of a screw of about half its length, -which passes into a female screw tube so as to shorten or lengthen it -as required to direct the reflection of the sun's rays by turning the -milled head above _R_, which forms a part of the tube. The Morse key is -hinged at _J_ to the stem of the instrument, and is kept up to a fixed -stop by means of a spring _P_ extended by an arm from the stem of the -instrument, so that pressure upon the disc _F_ moves the key down to -its stop _P_, and also tilts the mirror to throw its reflection off the -observing station during the pressure. The flashing described by the -jar of its action is liable to displace the mirrors. The use of the -bat, shown at Fig. 387 _D_, is more certain for signalling words. - -798.--_The Tripod of the Heliograph TT′T″_ consists of three circular -mahogany legs 1-1/8 inches in diameter and about 4 feet 9 inches long. -The legs are capped with sockets carrying collar-pieces which are -attached to the tenon-pieces of the head. The head forms a box for -the revolving apparatus and remains attached to it when the mirror -apparatus and arm are removed. The tripod head is protected when out of -use by a leather cap attached by a strap to one of the legs. The weight -of the tripod is 6 lbs. In fixing the tripod for use it should have the -legs extended nearly 60°, and the toes should be firmly pressed into -the ground. At windy stations it is well to dig holes and sink the -toes, or to have a heavy stone suspended under the centre of the head. - -799.--_The Case for the Heliograph_ is made of solid leather, with -separate divisions for mirrors, arm, and sight. A spare mirror is -sometimes packed in the same case that the instrument may not be made -useless by accidental breakage. A strap is provided with the case to go -over the shoulder. The instrument weighs 5 lbs. complete in its case. -Great care should be taken to observe the arrangement and position of -the parts of the instrument before taking it from its case, as it is -always packed closely. - -800.--_To use the Heliograph with a Single Mirror._--In this case the -reflection is direct. The instrument is approximately directed by -looking through the mirror from behind, moving the arm _L_ and the -sight _I_ to cut the distant station, and then clamping the screw _C_. -After this is done the exact position is found by placing the head -nearly in _front_ of the mirror, with the back to the distant station -with which it is intended to communicate. Then to adjust the mirror, if -required, and move the eye until the distant station appears reflected -in the exact centre of the mirror. After this, without moving the -head, finally to adjust the sight vane _I_ until the reflection of -the sighting spot is brought exactly in line with the centre of the -mirror and appears reflected upon the image of the distant station. -The sighting spot is then in direct line between the distant station -and the centre of the mirror, in whatever direction or inclination the -mirror may be afterwards placed to reflect the sun's image. Care should -be taken not to disturb the stand nor arm in future movements of the -mirror. - -801.--_To Adjust the Mirror_, stand behind the instrument and adjust -the vertical screw _R_ and the horizontal pinion A until the black -spot, as it appears on the mirror from the reflection of the hole -through it, is seen upon the centre of the point of the sight vane -surrounded by a ring of bright reflection from the silvered surface of -the mirror. The distant station will then receive the reflection, which -must afterwards be kept constantly upon it by gently moving the screw -_R_ and pinion _A_, following the apparent path of the sun. - -802.--_To Use the Heliograph with Two Mirrors_, which is necessary when -the sun is shining towards the distant station and its image can only -be projected by double reflection, the second mirror is placed upon the -end of the arm in the socket _S_. This has a white paper vane cemented -upon it, as shown at _M_. The mirror _B_ is placed roughly facing the -sun. The mirror M is turned towards the distant station upon which -it is intended to direct the rays, being careful at the same time to -observe that the two mirrors do not intercept each other's rays. Now -from the back of the mirror M we look into the mirror _B_, moving the -head until the centres of the two mirrors appear in a line with the -eye. Then without moving the head, adjust the direction and inclination -of _M_ until the reflection of the distant station appears in the -centres of the mirrors. Now clamp the mirror _M_ in this position, from -which it must not be moved so long as it is required to keep the same -station in communication. - -To keep the reflection following the sun a position is taken at the -back of the mirror _B_, and this mirror is worked as before described, -when it is used singly, by the milled heads, only that in the present -case the paper vane _M_ takes the place of the metal vane _I_. - -803.--_Telegraphing by the Heliograph._--The communication is made by -the alternate pressure and release of the Morse key _F_, each pressure -throwing the reflected image of the sun off the observing station. The -Morse alphabet, which is universally used, consists of rapid touches -represented by dots, and pressures of at least four times the time -of a touch represented by dashes. The following arrangement forms the -alphabet:-- - - A ·- | N -· - B -··· | O --- - C -·-· | P ·--· - D -·· | Q --·- - E · | R ·-· - F ··-· | S ··· - G --· | T - - H ···· | U ··- - I ·· | V ···- - J ·--- | W ·-- - K -·- | X -··- - L ·-·· | Y -·-- - M -- | Z --·· - -The time between the words is double that of a dash. Many other signs -are commonly used for figures, etc., for which the reader may consult -_The Manual of Instructions in Army Signalling_. The same system is -used for signalling by flags; and by stopping off light of lamps -this system is most valuable for the surveyor in new countries for -information of forward ground and other matters. - -804.--=Lights for Observations by Night.=--Under many conditions an -observation of a distant station may be much more conveniently and -accurately taken at night by observation of a luminous object of -limited area. For this purpose the arc light, lime light, blue signal -light and others have been employed. For the civil engineer where -regular stations are not erected, as with geodetic work, oil lights or -the burning of magnesium ribbon are the most convenient. - -805.--=Oil Lanterns.=--In the great trigonometrical survey of India -large reverberatory lamps were used, which were furnished with Argand -burners with circular wicks about 2 inches in diameter. The back arc -of rays was reflected by a parabolic reflector 12 inches in diameter -and 4·9 inches in depth. The lamp was enclosed in a strong box with -a plate-glass face 12 inches in diameter, with apertures to admit -sufficient air and chimney to carry off fumes. The box was constructed -to form a packing case for conveyance of the apparatus.[58] - -806.--The oil lantern which will be found most convenient for the civil -engineer will be one of the same form of construction as the bull's-eye -lantern, but much larger--6 inches square is a good size. This may be -made to go on the same tripod as the heliograph, and will take its -place for signalling by night, or telegraphing by the Morse signals -by the hand or bat shown Fig. 387, _D_. A 6-inch bull's-eye lamp with -treble wick may be seen well in clear weather 5 miles to 10 miles off. -A railway signalman's hand lamp forms a very good signal, or even an -ordinary 4-inch bull's-eye is very useful in working over new countries. - -807.--=Magnesium.=--The intense light given by burning ribbon -magnesium, and the extreme lightness in weight of this material, -render it of especial value for night signalling. Magnesium ribbon is -now sold at a very low price (about two shillings per oz.), and 1 oz. -will give a continuous intense light, visible at 30 miles, for over an -hour, whereas for a night signal arranged to be given at a stated time, -fifteen minutes is amply sufficient for a single observation. Great -difficulty is often found in lighting magnesium ribbon when this is -slightly oxidized from exposure to air. The best method is to employ -the flame of a portable spirit lamp, made for the purpose. Under any -condition the burning ribbon should be shaded from wind. A common plan -is to hang a straight slip of ribbon from the centre of a tripod which -can be readily shaded by a pocket handkerchief. Where expense is not -the object to be considered, lamps may be had for burning the wire. -Tin cases are made for soldering up and storing the ribbon in for use -abroad. - -FOOTNOTES: - -[56] _Manual of Surveying for India_, p. 478, 1875. - -[57] Patent No. 3390, October 1874. - -[58] For full description and plate, see Everest's _Measurement of the -Meridional Arc of India_, Introd. p. cxv. - - - - -CHAPTER XVIII. - - MEASUREMENT OF ALTITUDES BY DIFFERENCES OF ATMOSPHERIC PRESSURE-- - HISTORICAL NOTE--MERCURIAL BAROMETER--CONSTRUCTION--OPERATION--ANEROID - BAROMETER--CONSTRUCTION--VARIOUS IMPROVEMENTS--HYPSOMETER. - - -808.--_Historical Note._--The observation that the atmosphere decreases -in density with increase of height is due to Alhazen the Saracen, -about a.d. 1000. By this he explains that a ray of light entering -the atmosphere obliquely follows a curvilinear path, bending towards -the denser strata, that is concave towards the earth. He showed that -a body will receive difference of pressure in a rare and a dense -atmosphere, and calculated that the height of the atmosphere to its -final attenuation would be from his data nearly 58½ miles. The -practical instruments that have been devised for measuring altitudes, -by the differences of pressure due to the weight of superincumbent -atmosphere are the barometer, the aneroid, and the hypsometer. The -barometer was invented by Torricelli about the year 1640. Its principle -was demonstrated and first applied to altitude measurement by Pascal in -1647. The aneroid barometer was suggested by Conti in 1798, and said to -be devised as a practical instrument by Vidie in 1808. The hypsometer -or boiling-point thermometer, which depends for its boiling temperature -upon the pressure of the atmosphere above the liquid which surrounds -it, was suggested by Fahrenheit in 1724, experimented with by de Luc -in 1772, and brought to its present practical form by Regnault about -1840. At the present time the aneroid is almost exclusively used by -the civil engineer, as this instrument when made with great care is -sufficiently reliable, more portable, and not so delicate in use as -the others. So that it is only when very great precision is desired, -or when the one instrument is used as a check upon the other, that the -mercurial barometer, or the hypsometer, or both are now employed. At -the same time it must be understood that the aneroid barometer scale -is in a certain degree arbitrary, as the divisions at best are only -made up from a certain number of points taken from observations of the -mercurial barometer placed simultaneously with the aneroid under an -air pump, and therefore its errors comprise those of the particular -mercurial barometer with which it is compared, and those due to the -difficulties of the comparison, and of making subdivision afterwards in -the same relative proportion, by copying to the scale of the aneroid. - -809.--=The Mercurial Barometer.=--The principle of the barometer is -generally understood. If a glass tube, closed at one end, 33 inches -long, say of ¼ inch or over in bore, be filled brimful of mercury and -the point of the forefinger be firmly pressed on the surface of the -mercury, the tube may be inverted without the admission of air. If the -covered end of the tube be now plunged into a basin of mercury and the -finger slowly withdrawn from under the tube beneath the surface of the -mercury, the latter will sink in the tube to about 30 inches above the -surface of that in the basin--that is, if the experiment be performed -at about the sea level. The empty space in what now becomes the top of -the tube is termed a _Torricellian vacuum_. - -810.--In removing the pressure of the atmosphere from its surface in -the tube, which in the above experiment produces the barometer, the -pressure of the atmosphere then falls only upon the exposed surface -of the mercury in the _basin_, or what is technically termed the -_cistern_. This pressure is equal per area, according to hydrostatic -laws, to the upper surface area of any equal column of mercury that the -barometer may contain. Therefore the weight of the column of mercury -in the tube, if cylindrical, above the surface of that in the cistern, -is the same as that of a column of air of equal size reaching upwards -to the full height of the atmosphere. In fact the one exactly balances -the other, and it is by the difference of the weight or quantity of air -above the barometer _per area_ of bearing surface that it is possible -to ascertain the altitude of its position by means of the height of -mercury in the tube, after proper allowance is made for sudden changes -of conditions of the atmosphere itself from time to time, capillary -attraction of the tube, temperature, etc. - -811.--The mean height of the barometrical column in Great Britain, at -sea level at the temperature of 32° Fahr., is about 29·95 ins. A cubic -inch of mercury at this temperature weighs 0·48967 lbs. Therefore - - 29·95 × 0·48967 = 14·66 lbs. - -gives the mean pressure of the atmosphere on each square inch of -surface of the earth in this latitude. Nearer the tropics the pressure -is greater, near the poles less. It can be shown that as the heights -ascended by the barometer increase in arithmetical progression, the -pressure upon the mercury diminishes in geometrical progression. - -812.--=Mountain Barometer.=--The barometer used for measuring -altitudes, to which the above term has been applied, is now made only -upon Fortin's plan, in which the bottom of the cistern wherein the -glass tube is plunged is made of fine, close-grained leather, the best -for the purpose being a stout kid. The pores of the leather must be -sufficiently fine not to admit of the escape of the mercury, and yet at -the same time sufficiently soft and pliable to transmit the exterior -pressure of the air. Fortin's construction permits the cistern to -be closed entirely secure from leakage of the mercury, in whatever -position the barometer may be placed. The closing is effected by means -of an adjusting screw, Fig. 390 _F_, which by its pressure decreases -the capacity of the cistern and forces the mercury up the tube, or -adjusts it to a given height, so that the scale of the barometer may -be read correctly from a given point _X_ placed within the cistern. To -prevent injury to the tube the adjusting screw is made of a length just -sufficient to force the mercury to fill it, so that when it is closed -home there is no jar or percussion of the mercury in carrying the -barometer. The details of the mountain barometer may be best followed -by the illustrations. - -813.--_The Glass Tube_ is made of mild flint glass thoroughly annealed -and sufficiently stout to resist all the strain and percussion that -may occur with fair usage. One end of the tube is slowly sealed by the -blow-pipe, so that the closed end may be as strong as the other parts. - -814.--_Mercury--Filling the Barometer Tube._--The mercury of commerce -is generally impure, and it contains occluded air. For standard -and mountain barometers the mercury should be distilled in an iron -apparatus, at just its boiling heat, leaving about one-sixth of the -mercury in the still. The tube, which should be perfectly clean, is -left about 12 inches too long for the barometer. It is charged with -clean mercury for about 36 inches in height. It is then boiled in -a special circular charcoal stove, in the centre of which there is -a vertical iron tube of 2 inches diameter. The barometer tube is -introduced from the bottom of the stove, to heat about 4 inches of -the top of the mercury only. The tube remains in this position till -the mercury boils. It is then elevated for another 4 inches and again -brought to boiling point, and so on until the end of the tube is -reached. Under this process the air and some impurities rise to the -surface of the mercury, and the tube is considered to be properly -boiled. The end of the tube is then cut off to its proper length and -inserted in the cistern, in which there is left sufficient clean -mercury to complete the barometer. - -815.--The lower part of the barometer tube, after it is filled, is -attached to a thin boxwood socket of about an inch in depth by means of -hot thin glue. The socket piece is afterwards bound over with sewing -silk, which is again covered with glue, and is finally varnished so as -to form an elastic, secure fitting upon the glass. The socket-piece is -secured to a wide boxwood collar, Fig. 390, _D_. Upon the under side of -the collar an ivory gauge peg _X_ is inserted, which forms the index -point for reading the surface of the mercury in the cistern upon the -Fortin principle. - -816.--_The Cistern._--The glass sighting tube, Fig. 390 _H_, of the -cistern, through which the mercury and gauge point _X_ are visible, -is made about 1½ inches long and from 1 inch to 1½ inches -internal diameter, the glass being 1/8 inch to 1/5 inch in thickness, -ground square at its ends. The upper end of the glass fits upon the -boxwood collar _D_, with the interval of an indiarubber band to make -the fitting air-tight. The lower end of the glass tube fits upon the -boxwood collar _I_, with an interval of a turned leather collar. The -boxwood collar prolonged forms the lower part of the cistern. This -has a second boxwood collar screwed upon it, to which the leather bag -_E_ is attached by silk and glue. A stout leather capping plug is -glued upon the lower end of the bag, upon which the boxwood cap of the -adjusting screw _F_ presses for adjustment of the mercury, or to close -the tube. - -[Illustration: Fig. 389.--_Mountain barometer erected for use._] - -[Illustration: Fig. 390.--_Section through the cistern._] - -[Illustration: Fig. 391.--_Vernier reading, showing gauge point S._] - -[Illustration: Fig. 392.--_Sling case for carrying._] - -817.--_The Cistern Casing_, which is of brass, consists of upper and -lower collar pieces, Fig. 390 _AA′_ and _BB′_, and their attachments. -The upper collar is fixed to the casing tube of the barometer. In the -inside of this collar a leather washer is placed, which comes above the -boxwood collar on the glass tube _D_ and makes soft contact between -these parts. The lower collar has been partly described with the -cistern. This has a brass tube _E_ screwed upon it, covering the bag -and lower part of the plug of the cistern. The lower closed end of the -covering tube is formed into a nut for the adjusting screw _F_ placed -in the axis of the tube. There are four bolts or screws _GG′_ which -bring the two collars of the cistern casing towards each other, support -the lower part of this casing, and produce a pressure between the -boxwood collar on the barometer tube and the top of the glass sighting -tube with the intervening rubber collar, so that the mercury at this -point is secured. - -818.--_The Stem, or Barometer Casing Tube_, is made of brass, about ¾ -inch diameter. This has a slot, of about ¼ inch in width, down two -concentrically opposite sides, from near the top of the tube downwards -for about 20 inches. The tube is graduated along one open edge next -the slot in inches and tenths, these being again subdivided to -twentieths, and figured to read from 13 inches to 32 inches of mercury, -as shown in detail for the upper part in Fig. 391. The same space is -divided into centimetres and millimetres if metrical measure be used. -Within the outer tube an inner tube of about 12 inches in length fits -telescopically to move with a soft smooth motion. This inner tube -carries one vernier at top and one at bottom, Fig. 389, _rr′_. The top -vernier, shown Fig. 391, is placed above a slot in this tube which -corresponds with the outer tube, so that the level of the mercury can -be seen below the top vernier-piece at _S_. The verniers are divided -into 50, so that, reading into the 20, they give reading 50 × 20, or -1000 to the inch. The inner tube carries a rack about 11 inches long, -which moves by a pinion fixed upon a _cock-piece_, Fig. 389 _m_, on -the outer tube in the same manner as before described for telescope -racking, art. 96. Two _stay-pieces_ placed over the outer tube hold -the slots firmly at an equal opening. A ring is placed at the head of -the barometer to suspend it in a room, to be used, if required, as an -ordinary meteorological barometer, as shown at the top of Fig. 391. - -819.--_Mounting of the Barometer._--The barometer is mounted upon a -tripod formed of three light tubes with steel points, as shown Fig. -389. These screw into a collar which is packed in the cap of the -leather case. The collar has two opposite screws that screw into a -second collar, which is also held by two opposite points at right -angles to the first. The points of the screws form axes in the manner -of a Hook's joint, permitting the barometer to take a vertical position -by the superior gravity of its cistern and lower parts. - -820.--_The Thermometer_, shown at Fig. 389 _t_, has its bulb brought -as nearly as possible into contact with the glass tube enclosed in the -casing tube. It is commonly divided with both centigrade and Fahrenheit -scales. Correct observation of the thermometer is necessary to be made -with every observation of the barometer, as the specific gravity of the -mercury, and consequently the height of the column, depend partly upon -this for its correct determination. - -821.--_The Packing Case_, Fig. 392, is made of solid leather lined -with thick felt to fit the barometer. The legs are placed in packings -outside the case. In packing for carriage the screw of the cistern is -turned nearly home, leaving only sufficient space for any probable -expansion of the mercury from increase of temperature. The barometer -should always be carried in an inverted position, as this precludes the -possibility of air getting into it, and even tends to exclude, by the -jarring motion of carrying, any air that may have accidentally become -occluded. A strap is attached to the case for holding it over the -shoulder. - -822.--_Reading the Barometer._--It will be observed that the mercury -against the sides of the tube presents an upward curved appearance, due -to the resistance of the glass to perfect contact, and the cohesion -of the mercury in what is termed capillary action. This _beading_, -as it is termed, varies according to whether the mercury is rising -or falling. It is always necessary before taking an observation to -raise the mercury, by turning the screw _F_, until its surface just -touches the peg _X_, to make observations uniform. The reading is -taken by slowly lowering the index-piece by means of the milled screw -until light is just excluded between the fore and back index surfaces, -as shown Fig. 391 at _S_, at the highest point of the surface of the -mercury. The inches, tenths, and half-tenths (·05) are read on the -scale, and the thousandths on the vernier. Thus, suppose the scale -reads 26·45 and the vernier 25 = 25 thousandths, the reading will be-- - - 26·45 - ·025 - ------ - 26·475 - -For altitude the upper and lower stations are taken, and the difference -subtracted for difference of barometrical scale. - -823.--_Difference in Altitude in feet taken from Barometrical -Inches._--Complete barometrical tables for this comparison will be -found in Molesworth's and other pocket-books in use by all engineers. -It is therefore unnecessary to occupy our space with them. A very -approximate rule may be given, which was proposed by Mr. R. Strachan in -the _Meteorological Magazine_, as follows:-- - -"Read the barometer to the nearest hundredth of an inch; subtract the -upper reading from the lower, leaving out the decimal point; and then -multiply the difference by 9, which gives the elevation in feet. Thus:-- - - Lower station 29·25 inches - Upper " 28·02 " - ------ - 123 - 9 - ------ - Elevation 1107 feet." - -824.--_Capillarity._--For meteorological observations a quantity -must be added to the reading equal to the resistance of the tube in -capillary action to the rise of the mercury. This is greater in an -unboiled tube than in one in which the mercury is boiled. For altitude -measurements with a single barometer, or by two barometers with equal -tubes, it may be neglected, as it will be equal in all parts of the -tube. Where two barometers of different bores are used, the following -table gives the correction:-- - -_Correction of Capillarity to be Added to the Reading._ - - Diameter of Tube in Inches ·6 ·55 ·5 ·45 ·4 ·35 ·3 ·25 ·2 - Unboiled Tube, Inches ·004 ·005 ·007 ·01 ·014 ·02 ·025 ·04 ·059 - Boiled " " ·002 ·003 ·004 ·005 ·007 ·01 ·013 ·02 ·029 - -825.--_Temperature Correction._--As the mercury increases in -temperature it becomes specifically lighter, therefore rises higher in -the tube under equal atmospheric pressure. The temperature is indicated -by the thermometer, shown at Fig. 389 _t_. The expansion of mercury -for 1° Fahr. is 0·000101; but the brass tube also expands 0·0000104, -and it is the difference between the two expansions that we require, -the mercury expanding about 7·15 more than the brass. If we subtract -from the reading ·00014 of the observed altitude for every degree of -Fahrenheit above 32°, the correction will be practically very near. -Thus for a single reading--thermometer, 52° Fahr.; barometer, 30 inches - - -(52 - 32) × 30 × ·00014 = ·084, - -making the true reading 30 - ·084 = 29·916 inches at 32° Fahr. - -Tables for correction without any calculation will be found in -Molesworth's and other pocket-books. - -826.--_Gravity Correction._--The force of gravity decreases as we -ascend to a higher level in proportion to the square of the distance -from the centre of the earth. It follows that the force of gravity as -we ascend at the equator diminishes at a less rapid rate than at the -poles. Its amount is always small--on an average it may be taken at -about 0·001 inch of mercury per 400 feet of ascent. - -_Time._--Humboldt discovered that the barometer varied within the -tropics at different hours of the day. This has also been found to -be general to some extent in all countries, depending upon many -conditions. It is only important for consideration of altitude -measurements, that it is advisable if possible to take the upper -and lower stations simultaneously by a pair of barometers for exact -determination of altitude. - -827.--=Aneroid Barometer.=--The first introduction of this instrument -into England was by Pierre Armand, le Comte de Fontainmareau.[59] -This instrument consisted of a vacuum chamber as its prime mover. The -chamber was made a flat cylindrical box, with its upper surface of thin -metal, with corrugations covering its surface in concentric rings. -The chamber was filled with a number of spiral springs which resisted -the pressure of air, to prevent the collapsing of the corrugated -surface when the chamber was exhausted, and so placed the surface in -equilibrium with the pressure it received from the atmosphere. The -movements under various pressures were multiplied by gear work and -levers so as to make a small movement of the corrugated surface evident -in the extent of motion of an index hand reading upon a dial. - -[Illustration: Fig. 393.--_Stanley's civil engineer's aneroid._] - -The aneroid practically in its present form was devised by Lucien Vidie -from 1848 to 1862.[60] In this instrument the vacuum chamber, which is -a thin, flat, circular box, is corrugated equally on both sides, so as -to obtain double area of active surface under atmospheric pressure to -that of the older form. The chamber has its surfaces drawn apart by an -exterior spring, the point of communication or tension being placed at -the centre of its corrugated sides only. - -[Illustration: Fig. 394.--_Perspective view of the interior of an -aneroid._] - -828.--The construction of this aneroid is shown in Fig. 394, which -is of a 4½-inch instrument, aneroids made for surveying being of -two sizes, 3 inches and 4½ inches. _A_ is a solid plate of metal -1/8 inch in thickness, termed the base plate; _B_ the vacuum chamber, -circularly corrugated on both sides, made of thin, hard-rolled German -silver containing a large percentage of nickel. - -829.--An axis is projected from the lower side of the chamber, of about -1/5 inch diameter. This is tapped with a screw and screwed firmly -down into the base plate with a counternut. On the upper side of the -vacuum chamber the axis is projected upwards to receive the tension -of a strong, very flexible spring _D_ above it, to be described. A -bridge-piece _EE_ of steel of strong section strides over the vacuum -chamber. This piece has a stout arm-piece projecting from it towards -_A_, which is secured to the base plate by a screw that is left open -to a hole indicated near _A_ through the outer case of the instrument, -by means of which the bridge-piece can be rocked so as to produce more -or less tension of the spring _D_ upon the vacuum chamber for final -adjustment. The bridge-piece has two points of rigid support in right -line, which form a primary--adjusted when the instrument is made--of -the spring _contra_ to the pull of the vacuum chamber. The _main spring -D_ is made of fine thin steel, carefully tempered, as broad as the -chamber. This spring is constructed so that by its elasticity it may -have sensitive movement under the pull of 10 lbs. to 15 lbs. per inch -of active surface of the vacuum chamber. It is upon the perfection of -this spring as much as upon the construction of the vacuum chamber -that the sensitiveness of the instrument depends. The upper axis of -the vacuum chamber is secured by a cross cotter pin _C_ which gives an -exact point of resistance and yet secures flexibility of the spring -at the junction. This cotter pin is placed in the centre of the three -points of support of the bridge-piece _EE_. A _lever arm G_ is fixed -to the main spring _D_ upon a stout plate of metal which is in direct -connection with the point of tension of the vacuum chamber. It is the -small movement of this lever arm (about ·01 inch at the chamber) that -gives motion to the indicating apparatus. The lever moves a cranked arm -on the axis _HK_, which communicates through the axis to a second -cranked arm placed at right angles to the first _I_. This pulls a -chain _Q_ attached to the arm _J_. The chain is wound round a small -drum fixed upon the axis which carries the hand near _R_. The drum -keeps the hand in one direction _contra_ to the pull of the chain by -a hair spring _R_ which is just sufficient to overcome the friction -of the axis of the hand _F_. The hand and drum and their fixings are -carried by the plate _M_, which is a light piece of brass projected -from a stiff standard fixed from the base plate _K_. The compound lever -apparatus described moves the point of the hand about five hundred -times the amount of movement over the first fulcrum of the lever at the -chamber. - -830.--_Compensation for Temperature._--This is a somewhat difficult -matter, which is generally brought about by several modifications -of parts. Some ordinary aneroids will move upwards about 1/10 inch -of mercury by a rise of temperature of 8° centigrade only. This is -caused principally by the increase of temperature softening the spring -to render it less rigid, and the softening of the vacuum chamber to -render it more flexible or sensitive to atmospheric pressure. Some -little difference is also caused by the unequal relative expansion of -the lever, arms, spring, and chain, these parts being of steel and -brass. Compensation can be made in the lever arm _G_ by making this -curved and of two unequally expansive metals, as zinc and steel, so -that the curvature increases with increase of temperature and the -lever shortens. Compensation can also be partially made by making the -base plate in two metals--iron and brass--so as to press the standards -fixed through the two metals nearer or further apart with temperature -changes. But the whole subject is too technical to be entered upon in -our limited space, as it depends so much upon the construction of the -instrument, which is modified in various ways by different makers in -order to effect this correction. - -831.--_Dial and Hand._--From the delicacy of the structure of the -aneroid it becomes evident that no two instruments can be made to -exactly the same rate of movement; therefore each instrument has to -be separately graduated when it is intended to measure altitudes with -it exactly. However close or open the scale may be, it becomes closer -as greater altitudes are ascended, the density of the atmosphere as a -gaseous fluid decreasing in geometrical progression as the altitude -increases in arithmetical progression. From this we can understand -that a vernier to the index hand can only read approximately, although -it will act fairly well at a certain point of the scale. The best and -possibly only correct method of dividing the scale is to put at first a -false scale to the instrument, and to read this scale by the index hand -with a microscope under an air-pump, compared at every half-inch of -height of the column of the mercury by the gauge attached to the pump. -When this is carefully done, a zero point is taken of the position of -the index hand at the atmospheric pressure at the time, as indicated -on the false scale. The proper scale, as it appears upon the dial, is -divided from the position of the readings of the false scale, the two -scales being superimposed upon a special dividing machine. The dial is -afterwards figured and finished. - -832.--The ordinary method of reading the aneroid is to let the index -point read over the divisions. The author devised a plan, which he has -used for many years, of fixing a small plate of aluminium upon the -point of the hand, level with the scale, which is raised on a step to -read it upon its inside edge, to a fine line on the aluminium. By this -means error of parallax in reading is entirely avoided. The author also -places an adjustable magnifier to move over the index for reading. -This last improvement is now followed by other makers. A pointer also -revolves with the outer rim to show the last reading before ascent or -descent. - -Instruments made with care in the points just indicated must -necessarily become expensive. Where the aneroid is to be used as -a weather glass, or even as a travelling companion to judge of -approximate heights in climbing mountains, such care is not needed, -and the instrument may be produced very cheaply of useful quality. On -the other hand, where precision is required, a delicately made aneroid -will indicate a movement of 3 feet or less in raising or depressing, -when holding the instrument horizontally in the hand and giving a light -tap on the glass with the finger-nail before reading, so as to put all -motive parts in equilibrium. - -833.--_The Altitude Scale_ is generally placed near the periphery of -the dial; it is the all-important part to the surveyor. This scale is -usually set out from a mean of atmospheric pressure at sea level, taken -from Sir George B. Airy's tables, which give the extreme pressure of 31 -inches barometric pressure for zero at sea level. With this pressure -altitudes are taken at intervals according to the indices tested under -the air-pump, and the intermediate divisions are graduated to scale. -These index points are shown in the table below for a few points:-- - -_Table of Altitude with Barometrical Scale._ - - Height Barometer in Height Barometer in - in Feet. Inches. in Feet. Inches. - - 0 31 6000 24·875 - 250 30·717 7000 23·979 - 500 30·436 8000 23·125 - 750 30·159 9000 22·282 - 1000 29·883 10,000 21·479 - 1500 29·340 11,000 20·706 - 2000 28·807 12,000 19·959 - 2500 28·283 13,000 19·236 - 3000 27·769 14,000 18·535 - 4000 26·769 15,000 17·853 - 5000 25·804 - -It may be generally observed that the more open the scale the less -altitude can be obtained by a single revolution of the hand; therefore -the more points can be taken per 1000 feet. Thus, with an altitude -barometer reading to 3000 feet, readings can be pointed in construction -at every 250 feet; with one of 6000 feet, at every 500 feet; and over -this at every 1000 feet. - -834.--_Movable Altitude Scale._--In this the altitude scale revolves so -as to be able to set it at zero for ascending from any point. As the -barometrical scale diminishes, it is necessarily inaccurate, and cannot -therefore be used upon a surveying aneroid; but the plan is pleasant -for approximate measurements for amusement in making ascents. It is -only mentioned here for the reason that the inaccuracy of the movable -scale is not always recognised. - -835.--_Adjustment of the Aneroid._--There is a screw at the back of -every aneroid somewhere under the point _A_, Fig. 394, by means of -which an aneroid may be brought to the reading of a mercurial barometer -at the position the mercury may be read. Where a good instrument has -been set by the maker to a standard barometer, it is not wise to -alter it frequently if it keeps in good working order for altitude -measurements without being again set by a standard. On the other hand, -however well the aneroid may have been made it works gradually to a -slight change, caused by the smooth wearing of parts in action. It is -well to have an aneroid, after one or two years' wear, cleaned and -adjusted by the maker. It will then, if a good instrument, work well -for many years. - -836.--_Directions for Measuring Altitudes._--Turn the outer rim of the -instrument until the index carried thereby reads to the same point -as the index hand. Raise the magnifier until the reading comes into -sharp focus. Hold the instrument as nearly horizontal as possible, -and tap the case lightly with the thumb-nail two or three times, so -as to overcome any slight friction of its mechanism. This places the -action of the works in equilibrium. Write down the observation as it -now reads in the pocket-book, taking thousands from the right hand -(large figures), hundreds from the right hand (small figures), tens -from the lines to the left of this, and units from observation of the -position of the index line in the space between the last and the next -line. Say this observation reads 2465. Whether we ascend or descend, -the instrument acts similarly. We will now presume we ascend to the -height we require to ascertain, and take a second reading, 1945; the -difference between these numbers, 2465 - 1945 = 520 feet, is the -number of feet ascent. It is necessary, where exact measurement is -required, to take the reverse reading, as the atmospheric pressure -may have changed. We now descend, taking the last observation, 1945, -and find the reading at the first position 2463 instead of 2465, -that is 2 difference, which proves that the atmospheric pressure has -decreased. If we take half this difference = 1 and correct the first -deduction, 520 - 1 = 519 will give us the correct measurement, subject -only in this instance to the irregular possible fall of atmospheric -pressure, which will not in many instances, if the times of observation -have been nearly equal, be a quantity worthy of consideration. It is -not necessary to make any correction for the height of the observer -in positions above ground, as the instrument must be placed at a -uniform distance from the eye to obtain the reading. In mines it will -frequently be necessary to measure the heights from the ground at which -the observation is made. - -837.--_Various Improvements in the Aneroid._--It is uncertain whether -any great internal improvements have been made in this instrument, -except by Vidie, at various times. Many attempts have been made to -increase the length of scale to obtain more open reading. These -attempts have all been in the direction of increasing the difference -of space between the fulcra of the levers or by additional gearwork, -producing thereby a greater multiplication of the small unit of -displacement of the axis of the vacuum chamber beyond the normal × -500, which is already great. The multiplication has been taken up -to × 2000 or more. This increases the difficulty of manufacture and -certainty of permanent action. Many of these plans were tried by Vidie -and abandoned. A plan of Vidie's[61] of giving the hand three or four -revolutions, and to register this upon a spiral scale upon the dial, -also by counting on a second dial the number of revolutions, has been -repeated with slight variation by E. T. Loseby in 1860[62] and by Major -Watkin later. Vidie's plan of drawing back the hand to read the spiral -has been modified also by Major Watkin in a manner which may be a -little less frictional.[63] - -[Illustration: Fig. 395.--_Watkin's extended scale surveying aneroid._] - -838.--=Watkin's Extended Scale Aneroid.=--This instrument is shown -at Fig. 395, and has a very extended reading, consisting of _three -complete_ circles, in place of the usual single scale, with a hand or -pointer sufficiently long to extend across them all. In order to show -clearly which circle of scales should be read there is an indicator -attached to the movement of the instrument which causes a series of -figures (I., II., III., corresponding with the three circles) to be -exhibited through an aperture in the dial. For instance, when the -instrument is in its normal state the hand will point to the first or -outer circle, and the figure I. will appear and remain in the aperture -until the barometer falls to 27·8, where the break takes place in the -circle, as will be seen in the illustration. The hand then takes up -the reading on the second circle (where the break appears at 27·8) and -figure II. replaces figure I. in the aperture, remaining there until -the barometer falls to 25, when the reading is transferred to the third -circle, and figure III. appears in the aperture. - -[Illustration: Fig. 396.--_Face._] - -[Illustration: Fig. 397.--_Back._] - -839.--=Watkin's New Patent Mountain Aneroid Barometer.=--This -instrument, of which both a front and back view is shown above at Figs. -396 and 397, is the invention of Colonel H. S. Watkin. The special -feature is that it can be put in or out of action as required, and -when out of action is impervious to the influence of variations in -atmospheric pressure. This relieves the strain on the mechanism of -the aneroid, as it is only put into action when a reading is required. -The lower portion of the vacuum-box instead of being a fixture (as -is the case with ordinary instruments) is allowed to rise, which is -effected by attaching to the lower portion of the vacuum box a screw -arrangement actuated by a fly nut on the outside of the case. Under -ordinary conditions this screw is released, and the vacuum-box put out -of strain. When a reading is required, the fly nut is screwed up as far -as it will go, thus bringing the instrument into the normal condition -in which it was graduated. - -It has an aluminium case for lightness, is made in two sizes (3 inch -and 4½ inch), and has a sling leather case. - -These plans are again on their trial. It is the author's opinion on -the subject, knowing the delicacy and skill shown in Vidie's work, -that little improvement is likely to be obtained by magnification of -the small motion of the vacuum chamber by mechanical means, which -must necessarily be by a process both delicate and highly frictional. -Attempts, he thinks, may otherwise be successfully made in the -magnification of the small motion of the hand in a frictionless manner -by optical means to obtain clearer definition. - -840.--An improvement was made in the aneroid in one direction by the -late Thomas Cooke[64] by replacing the chain by a thin gold band upon, -and leading from, the drum. This obviated the small difference of rate -of displacement due to separate jointed links as they leave the tangent -of the drum. It is said, however, to cause a little springiness at -this point, where it should be very dead, which somewhat minimises the -improvement; so that it has not been very generally adopted. - -841.--=Bourdon's Aneroid=, invented by C. Bourdon in 1849.[65] The -motor of this instrument consists of a flat, oval tube bent into a -circular form. This tube opens to greater and lesser curvature by -difference of external pressure upon it. The small motion given at one -free end of the tube is multiplied up by gearwork. This instrument -is found to act most delicately as a steam gauge; but experience has -shown that it is not so sensitive or durable for indicating atmospheric -pressure as the vacuum-chamber aneroid last described. - -842.--=Hypsometer=, _or Boiling-point Thermometer_.--That water or -any other liquid boils at a certain temperature, according to the -amount of atmospheric pressure surrounding it, is easily observed by -placing a cup of boiling hot water under the receiver of an air-pump. -At first the surface will remain still, but as the pressure of the air -is pumped off it may be made to boil time after time until it arrives -at a low temperature. The temperature at which the water boils as the -air is rarified may be easily followed by observation of a thermometer -immersed in the cup of water; and at the same time, if a barometer be -placed in connection with the receiver it will indicate the pressure, -from which the scale of differences may be practically made. For the -civil engineer this instrument, accompanied by the aneroid, is in every -way superior to the mountain barometer, which must necessarily have a -three-feet tube, as the hypsometer is much lighter, more portable, and -less liable to injury, and perhaps, from the uncertainty of keeping a -pure vacuum in the barometer, safer as a means of observation. - -[Illustration: Fig. 398.--_Hypsometer, or boiling point thermometer._] - -[Illustration: Fig. 399.--_Case for hypsometer._] - -843.--The modern form of instrument is shown in Fig. 398. The boiler -shown immediately over the lamp is filled about half full of rain water -by lifting off its covering tube _C_. The covering tube has a smaller -tube, about 3 inches long and ½ inch diameter leading upwards from -it, through which the thermometer bulb is passed into the boiler. This -tube is covered by the _jacket J_, formed of four telescopic tubes -that are extended, as shown in the figure, for use, but which close -up quite compactly when the instrument is put in its case. The upper -drawer of the jacket tube is about ¾ inch diameter, so that the tube -enclosing it passes over the leading tube when the apparatus is closed. -The lamp, which is filled with pure spirit, draws out from the bottom -of the outer casing _O_. It carries a wick holder with screw cap, and -this again has a covering cap to secure the spirit perfectly when the -instrument is carried about. The inner casing _A_ is perforated with -holes to admit air at the level of the body of the lamp. When the lamp -is lighted and complete for use it is placed vertically in its outer -case _O_, which is jointed in two parts and perforated by large holes -surrounding it top and bottom: the bottom holes are covered with wire -gauze. By this arrangement the flame is not seriously disturbed by -wind or rain. - -844.--_The Thermometer_, upon which the action of the instrument -depends, has a stout stem about 6 inches long and ¼ inch diameter, -with a very fine, flat, oval bore about ·01 inch wide and not much -over ·005 inch in thickness. The stem is divided very openly for about -25° below 100° centigrade, each degree being subdivided into 10, below -212° if Fahrenheit scale be used, with each degree divided into 5. The -divisions are filled in with lamp-black, and the stem is backed with -white enamel to give clear reading. The thermometer _T_ when in use is -surrounded by a vulcanized indiarubber collar _I_ which slips over its -stem to adjust it to position in the boiler tube as shown. - -In placing the thermometer in its jacket, it is important to hold it -erect to be sure it passes into the leading tube from the boiler, -as there is generally just room for it to catch by the side of this -tube, where if it were pressed down it would break the bulb. When -the thermometer is out of use the rubber collar is removed, and the -thermometer is placed in a tubular metal case which is lined with -indiarubber tubing, so that no jar can injure it. - -The whole apparatus when closed is carried in a solid leather case, -which contains divisions for the separate parts of the apparatus, and a -strap for passing over the shoulder for carrying it. Fig. 399 shows the -general form of case. - -845.--_Use of the Hypsometer._--Saussure calculated, from data of his -ascents of Swiss mountains, that the temperature of boiling water -decreased 1° centigrade for every 978·5 feet of ascent, where the -mean temperature of the atmosphere was estimated at 0° centigrade, or -freezing point. If the temperature of the surrounding atmosphere be -taken as 5·5° centigrade, the ascent per degree of that scale is 1000 -feet. This becomes, therefore, the most convenient data to calculate -from, allowing 3·9 feet per 1000 per degree centigrade for temperature -above or below 5·5° centigrade at any two stations of observation, -of which the difference of level is required. Thus:--If at the first -station the temperature of air be 15·6 centigrade, the boiling point -95·5° centigrade; second station temperature of air 14·1° centigrade, -boiling point 94·2° centigrade, the barometrical pressure of the lower -station being taken as a constant, or referred to the aneroid for -correction; then 15·6° - 5·5° = (9·1) (3·9) = 29·2 + dif. 95·5 - 94·2 = -(1·3) (1000) = 1329·2 - dif. external temperature (15·6 - 14·1) (3·9°) -= 1323·4 difference of level in feet. - -Sometimes the thermometer is divided to Fahrenheit degrees, subdivided -into 5 to read by interspace and line to ·1° F. This may be changed to -centigrade for use of the above formula by taking 32° F. lower than the -reading and multiplying by 5/9. Thus-- - - 60° Fahr. = 5/9 (60 - 32) = 15·55° centigrade. - -The calculation proposed by Lefroy is, however, simpler for Fahrenheit -scale. To allow for diminution of boiling temperature, with height -from 212°, with barometer at 30 inches, take 511 feet of altitude for -the first degree and add 2 feet for each succeeding degree. Thus, -taking height of first station = h corrected for 212° Fahr., 30 inches -barometer, remembering decrease of barometrical pressure acts the same -as increase of height. Then-- - - 211° boil point _h_ + 511 feet. - - 210° " _h_ + 511 + 513 = _h_ + 1024 feet. - - 209° " _h_ + 511 + 513 + 515 = _h_ + 1539 feet. - -FOOTNOTES: - -[59] British patent, No. 10157, April, 1844. - -[60] British patents--No. 13332, November, 1850; and No. 682, March, -1862. - -[61] Patent, No. 13332, May, 1850. - -[62] Patent No. 3454, December, 1862. - -[63] Patent No. 3425, March, 1886. - -[64] Patent No. 2714, October, 1865. - -[65] Patent No. 12889, December, 1849. - - - - -CHAPTER XIX. - - MISCELLANEOUS SURVEYORS' AND ENGINEERS' INSTRUMENTS, APPLIANCES, - AND ACCESSORIES--CROSS STAFF--MECHANICS' LEVELS AND CLINOMETERS-- - BONING RODS--FOOTNER'S RAILWAY GAUGE--GIRTH STRAP FOR TIMBER - MEASUREMENT--GIRTH TAPES--TIMBER MARKER--SLASHING KNIFE--BILL-HOOK-- - RECONNOITRING GLASS--TELESCOPE--SUN SPECTACLES--WHISTLES--PIONEER - TOOLS--SKETCH BLOCK BOOK--CAMERA--GEOLOGICAL TOOLS--WEALEMEFNA-- - OPISOMETER--BOUCHER'S CALCULATOR--SLIDE RULES--FULLER'S CALCULATOR-- - ENGINEERS' POCKET BOOKS--CHRONOMETER--OUTFITS. - - -846.--=Cross Staff.=--Those of Tycho Brahé and of Gunter were very -elaborate affairs, consisting of a pair of notched cross-bars sliding -on a divided rod which gave directions to form any angle in a quadrant -from the eye by sliding the bars further from or nearer to it. The -surveying cross staff, after better instruments were invented to take -angles, became a cross at right angles, sawn upon a disc of wood and -supported upon a staff which was pressed into the ground. This was used -by looking along the saw cuts to take offsets to the chain, and for -setting out buildings. The fixed cross-head was much improved by making -it a cross of metal with turned-up ends, down the centre of which -vertical saw cuts were made at right angles, Fig. 400. This, in the -author's opinion, is still the best form. - -847.--Cylindrical heads superseded the open cross-head. The modern -instrument in use is the French form, Fig. 401, which is made of -octagon brass tube. This is cut with alternate sight slit and opposite -window, with vertical hair on each of four rectangular sides of the -octagon. On the other four sides there are plain slits subtending -45° to those first mentioned. The octagon tube is mounted upon a -socket-piece which fits upon a conical pointed staff. The defect -of this cross-head is the closeness of the slits, due to the small -diameter of the tube, which renders the direction given for sighting -uncertain. - -[Illustration: Fig. 400.--_Open cross-head._] - -[Illustration: Fig. 401.--_French form._] - -[Illustration: Fig. 402.--_Adjustable cross staff head._] - -848.--=Adjustable Cross Staff Head.=--The cross staff head is sometimes -made cylindrical, in two parts, Fig. 402. The upper part is centred -upon the lower so that the upper series of sights move to any angle in -relation to the lower. In this construction a wheel is cut about the -axis of the upper part, which works into a pinion in the lower part, -so that the upper part may be revolved horizontally by it. The meeting -planes of the two cylinders are divided, the lower into degrees and the -upper with a vernier. The vernier is almost an unnecessary refinement, -as the sighting distance from slit to hair is only about three inches, -and no very great exactness can be obtained in the sighting. This -instrument has commonly a magnetic compass upon the upper surface. -It is about as expensive as the semi-circumferenter, shown Fig. 232, -p. 347, and very inferior to that instrument owing to the extreme -closeness of the sights. Its use is obvious. - -Many of the following articles, briefly described, may be beyond the -direct province of this work; but the utility of these implements for -completing the equipment of a surveyor or engineer for special work it -is hoped will be sufficient apology for their introduction. The subject -can scarcely be treated except in a desultory manner. - -849.--=Mechanics' Levels.=--In crowded Eastern cities, in levelling -through close passages, in many cases the surveyor has to resort to -mechanical levelling to carry his levels through. Mechanics' levels are -too well known to need much description. The ordinary good kinds are -made from 6 inches to 18 inches long, generally of rosewood, as this -wood is very hard and stands well. They have a brass plate at the top, -and tips of the same metal at the base. The illustration, Fig. 403, is -of a 12-inch level. The level tube, which is of blown glass, is fixed -in plaster of Paris, and the upper plate screwed down over it. - -[Illustration: Figs. 403, 404.--_Mechanics' Levels._] - -850.--=The Author's Hand Level= is shown Fig. 404--12 inch. This is -made of a casting either of iron or brass. The level tube is ground to -curvature and is somewhat superior to the ordinary run of this class of -work. The level tube is fitted with ball socket at one end and stiff -spring fitting at the other, which is adjustable, so that the tube may -be easily replaced if broken. - -These levels are commonly fixed upon a stout fir straight-edge of about -5 feet to 10 feet in length by the lugs at the ends. The level is taken -by blockings upon the ground. Corrections of error, both in level and -straight-edge, may be made for any considerable distance by reversing -the forward and backward position of the level with its straight-edge -alternately. - -851.--=Square Level--Circular Level.=--Fig. 405 represents a very -useful class of level for setting up some instrument stands, plane -tables, etc., in which a pair of level tubes are placed at right -angles to each other. It is generally made very small--1½ inches -square only. A circular level, the upper surface of which is formed -of a worked concave glass, was lately very popular, and is still used -to a small extent. As the spirit cannot be hermetically sealed in, it -evaporates, and this level soon fails. Mr. J. J. Hicks has taken out a -patent for a hermetically sealed circular level, described p. 96, which -appears to answer very well. - -[Illustration: Fig. 405.--_Square level._] - -[Illustration: Fig. 406.--_Surface level and clinometer._] - -852.--=Incline Level.=--For laying railway rails and drainage works -the bubble is frequently made adjustable by the tube in which it is -contained being hinged at one end and fitted in slides to rise with a -screw at the other end, as shown Fig. 406. A scale of percentage of -inclination _S_ is commonly divided upon the adjustable end. The tube -is raised or lowered by the key _A_, which is removed after setting -and cannot be tampered with. - -[Illustration: Fig. 407.--_Stanley's sight for mechanics' levels._] - -[Illustration: Fig. 408.--_Section._] - -853.--=Sighted Levels.=--A mechanic's level is commonly made with a -hole longitudinally through it of about ½ inch diameter, closed at -one end, except a small hole of 1/30 inch or so, and a cross upon a -piece of glass at the other end. This plan permits a sight to be taken -through it which gives an approximate level. Occasionally the same form -of sight as that described is hinged on the top surface at each end of -the level. The author has found a better plan of sighting to be given -by a pair of sights placed on a centre upon the ends of the level to -turn up when required for use, as shown Fig. 408, _P S_ one of the -pair of points. This, when turned up, shoulders on the stop-piece _A -B_. The stop-piece is made of sufficient thickness to admit the point -in the hole near _B_ for protection when it is folded away out of use. -The section of the level, as shown by the end view _D_, is the same -as that of the level, Fig. 404. Very fair accuracy may be obtained by -making these sights appear coincident upon a distant staff or rod. - -[Illustration: Fig. 409.--_Boning-rod._] - -[Illustration: Fig. 410.--_Boning-rod with standard._] - -854.--=Boning-Rods=, Fig. 409. These are very commonly employed with -mechanics' levels. They are made somewhat like a stout T-square of 3 -feet to 4 feet in length, about 3 inches in width, and ¾ inch in -thickness both of the stem and head. They are at first placed at a -distance apart, 9 or 10 feet, and a straight-edge of this length is -laid from one to the other, upon which the mounted level is afterwards -placed, the boning-rod being tapped down in the ground till the bubble -is in the centre of its run. A third boning-rod is then placed at -the same distance as the first pair, and the straight-edge with the -level upon it is reversed end for end. This, if the work be fairly -down, leaves the two outer boning-rods level, however imperfect the -straight-edge and level may be, if the run of the bubble be taken -correctly. By removing the central boning-rod from the outer pair -of rods, levels may be continued by sighting over them, or _boning -forward_ as it is termed. On the Continent boning-rods are commonly -fixed by driving a separate standard into the ground, which has a pair -of brass slings by its side to hold the rod, Fig. 410. This is a -much neater plan than that in common use of blocking the rod up with -stones. Boning-rods are also sometimes used conveniently with a proper -surveying level, from the tops of water-pipes, etc. - -[Illustration: Fig. 411.--_Footner's railway gauge and clinometer._] - -855.--=Railway Gauge=, combining level and clinometer. This high-class -gauge, Fig. 411, is the invention of Mr. H. Footner, C.E., late of the -London and North-Western Railway. It is formed of a bar of Spanish -mahogany neatly shaped. The end fittings are of steel. The gauging -part is formed of two turn-up steel flap-pieces with back stops. A -spirit level is sunk in the end fitting, shown in the figure towards -the left hand. The clinometer is formed by a gun-metal pin of ½ inch -in diameter; 9 inches long. This slides perpendicularly in a spring -fitting sufficiently stiff to support the gauge, and is made to fall -on the centre of the rail. The pin is divided into inches and eighths. -When it is out of use it slides up the end of the gauge and leaves the -whole instrument smooth and portable to carry open or go into a leather -case. Its use is implied. - -856.--=Timber Girth Strap.=--The direction for removal and estimate of -the value of timber often falls into the hands of the surveyor. The -height of standing timber may be taken by a long rod, or a pair united -by a link, art. 775, or by the apomecometer, art. 693. The girth is -most conveniently taken by a leather girth strap, of which there are -various patterns: but that illustrated below, Fig. 412, is perhaps the -most popular form. This strap is made of two straps of bullock's hide 1 -inch wide, thinned down to about 1/8 inch in thickness; the two pieces -are stitched together to make it 12 feet to 14 feet long. The strap is -divided by lines into inches, but figured in units at every 4 inches -= single inches of quarter-girth. The figures and lines are stamped. -A brass weight, shown at one end of the strap, is thrown by the strap -with a swing round the standing tree, and encompasses it in a second of -time. The weight is caught by the hand and the strap brought up to it -to read the quarter-girth. The _quarter-girth_ gives roughly the equal -sides of a square; as, for instance if a quarter-girth reads 10, the -size of the tree is 10 × 10 = 100 inches, or 8·4 cubic foot-inches per -foot run. - -[Illustration: Fig. 412.--_Leather girth strap with throwing reel._] - -Some surveyors prefer a hook instead of a weight, as being more -convenient to measure close timber. This is shown Fig. 413. The hook is -stuck into the bark and the tree is girthed by walking round until the -hook is met. - -[Illustration: Fig. 413.--_Leather girth strap with clutch hook._] - -857.--=Girth Tapes=, similar to measuring tapes, Fig. 349, p. 506, are -occasionally used, but these are more convenient for felled timber. -Tapes for the purpose are made from ¾ inch to 1 inch wide, and 6, 12, -and 24 feet long. They have the ordinary feet and inches on one side -and quarter-girths on the other. - -It is customary to allow 1 or 1½ inches, and sometimes more for -bark, according to the species of tree and the custom of the country. - -858.--=Marking off Timber.=--For this a special tool with a gouge -point, Fig. 414, and strong buck-horn handle, termed a _timber-marker_, -is used for standing timber intended to be felled. The contents of the -tree are sometimes marked with the marker upon it if for sale, good -bark allowance being made in cases of difficulty of extraction from the -forest, etc. A plain knife is usually put with the marker, which is -useful as a food knife. - -[Illustration: Fig. 414.--_Timber marker, nearly full size._] - -859.--The author makes a very small, neat surveyor's knife, with -marker, for the waistcoat pocket, Fig. 415, which combines--_M_ tree -marker (small); _S_ screw-driver for small screws of instruments; _P_ -tommy-pin for turning capstan heads; _F_ file for sharpening lead of -pencil, when this is used for the field-book; and _E_ _R_ two penknife -blades. The knife is similar to the author's architect's knife, which -is well known. The tree marker is not strong enough for constant work. - -[Illustration: Fig. 415.--_Surveyor's pocket knife._] - -860.--=Slashing Knife--Bill-Hook--Axe.=--In new countries where sight -way has to be obtained for the survey through forests and jungles, one -or more of the tools illustrated next is most valuable as a part of -the surveyor's equipment. The slashing knife, Fig. 416, which is over -a yard long, wielded by a strong man will remove light brushwood very -quickly. Where the wood is close and of larger growth the bill-hook, -Fig. 417, is better; and with thickset timber the axe becomes -necessary. The well-known Canadian axe is found to be the best. - -[Illustration: Fig. 416.--_Slashing knife._] - -[Illustration: Fig. 417.--_Bill-hook._] - -861.--_Hedging Gloves--Iron Hooks for Climbing Trees._--For clearing -land to avoid spines hedging gloves are generally used; these are made -of soft horse-hide, and although pliable resist thorns to a great -extent. Clutch hooks are also very convenient to climb trees, to look -forward for the easiest direction for sight way. - -862.--=Rods for Measuring Standing Timber.=--These are generally made -25 feet long, jointed in 5 feet lengths, similar to a fishing rod, but -much stiffer. The rod is set by the side of a tree to be measured and -observed from a distance where the first breech cuts its length. - -[Illustration: Fig. 418.--_Reconnoitring glass, India pattern._] - -863.--=Reconnoitring Glass.=--At present it is customary to use a -binocular field-glass in preference to a telescope. The telescope -gives greater penetration from its higher power; the field-glass is -preferred for its wider field of view. The field-glass the author has -supplied to the Indian Government has neutral-tint glasses centred on -the eye-pieces to take off the glare when looking towards the sun, -Fig. 418. These have also hinge joints between the pair of bodies, -which permit adjustment of distance of centres to the distance of the -eyes. The object-glass should be 1¾ inches, not over this. Where a -telescope is used, the 30-inch--the original, not the present--India -military telescope is to be recommended, Fig. 419. This is portable, -has a sling case and a good 2-inch object glass. For lightness, -aluminium bodies are preferred by many for both field-glasses and -telescopes; at present the price of this metal is very low, so that it -is probable it may become in a short time general for the purpose. - -[Illustration: Fig. 419.--_Army telescope._] - -864.--=Prism Binoculars.=--These will be found a great improvement on -the old form of field-glasses, as owing to the optical arrangement a -high power is obtained combined with a larger field of view and good -illumination. Fig. 420 shows the most modern form with all refinements; -hinged body, central focussing and separate focussing to suit each -eye. It has a very compact and strong body, and the size magnifying 8 -diameters or about 64 times weighs only 13 ozs. - -[Illustration: Fig. 420.--_Stanley's prism binocular._] - -865.--=Dome Spectacles--Bogles.=--Spectacles of neutral tint are most -comfortable for general wear in sunny or snowy countries. The dome or -globular form is generally preferred. Where there is hot dust gauze -sides are to be preferred. There is a very cheap form with gauze sides, -which holds on the head by an elastic band, termed _bogles_. These are -rather hot to the face, and the band after a time becomes sticky. The -spectacle form is much better. The glasses are made in various shades -to choice: some very dark or even black, the latter being made for -viewing and tending arc lights. - -866.--=Whistles= made very powerful are much used in exploring abroad -to bring the party together, and for signalling generally by sound, -using the Morse signals, art. 803. - -867.--=Pioneers' Tools.=--A small set of these is often very useful -to the surveyor in new forest countries. The common set consists of a -claw-hammer, wood-chisel, stone-chisel, pincers, screw-driver, gimlet, -and brad-awl. The leather case is 8 by 4 by 2½ inches; it weighs -1¾ lbs. with strap. This may be supplemented by a small American -saw, cutting both edges, about 20 inches long, and the axe previously -described, with a few pounds of wire nails. The tools serve for marking -trees or rocks, erecting signals, temporary covers, etc. - -868.--=Sketch Block Book--Pocket Book.=--In reconnoitring no better -information can be given of a track than forward sketches from -commanding station to station. Sketch books about 7 inches by 5 inches -are generally found sufficient. The drawing-paper should be thin, and -the pocket large enough to contain all the separate sheets as they -are taken off by the penknife after completion from the block. The -sketches may be made with pencil, or a fine fountain pen; or if the -surveyor be a colourist a light box of moist colours and a water bottle -will often leave pleasing sketches as reminiscences. Pocket-books with -section lines to 1/8 inch or 1/10 inch scale are sometimes used to give -approximate plans to scale of buildings, etc., where required, as well -as the ordinary field-book record. - -869.--=Camera.=--Recently the camera has been much used for -reconnoitring. These are now made very light and portable to take ¼ -plate or 3 × 3 inch films, either on rollers or in separate films. - -870.--=Cement Testers= are made in various manners, generally to test -the cohesion of the cement as a homogeneous hard body. Mr. Mann's -cement tester, Fig. 421, goes on another principle--it tests the -adhesion of the cement to stone, which appears to the author to be its -most important function; it is always hard enough. - -[Illustration: Fig. 421.--_Mann's cement tester._] - -871.--=Watson's Improved Vicat Needle= is a most refined and accurate -instrument for determining the time taken by cement in setting. The -cement is placed in the circular container shown in the illustration, -and the weighted needle is lowered into it by means of the handle -at the top. The depth of penetration is shown in millimetres on the -divided arc. - -[Illustration: Fig. 422.--_Watson's vicat needle._] - -872.--=Geological Tools.=--_Acid-bottle--Blow-pipe--Touch-stone._-- -Where countries are prospected for railways it often becomes important -to examine the rocks, both to detect the softer rocks for cutting and -to find limestone suitable for mortar. A geological hammer, weight -about 2 lbs. to 3 lbs., is the ordinary tool. This, with a chisel -and sailcloth bag with strap, is all the necessary appliance. In -searching for limestone a small bottle of sulphuric acid sewn up in -a leather case is useful. A dipper is blown on the stopper of the -bottle, and a single drop of acid will detect limestone by the bubble -of froth it produces. Where minerals are to be examined, a small -blow-pipe apparatus is necessary. This should be accompanied by a book -of instructions. Where the surveyor has not been trained to use the -blow-pipe, one with constant blast should be employed. For examination -for precious metals a touch-stone and two-acid bottle--sulphuric and -nitric--for silver and gold, are useful. The metal is merely rubbed on -the stone and the acid applied. If the metal is base the acid removes -it from the surface of the stone. If precious it removes other matter -and leaves it visible. - -873.--=Wealemefna--Opisometer.=--The wealemefna is a very neat form -of space runner invented by Mr. E. R. Morris, which is found a very -convenient instrument for measuring distances on maps in prospecting. -It is very small and light, and may be, if desired, attached to the -watch-chain. It gives distances run over in inches and eighths, to be -afterwards calculated to the scale of the map, Fig. 423. The opisometer -for the same purpose, Fig. 424, is formed of a spur wheel at the end of -an ivory handle running upon a screw. This instrument gives measurement -by reversing its run upon the scale of the map. - -[Illustration: Fig. 423.--_Wealemefna._] - -[Illustration: Fig. 424.--_Opisometer._] - -874.--Boucher Calculator, the invention of M. Alex. E. M. Boucher, -engineer, of Paris.[66] This is one of the most convenient pocket -calculators that a civil engineer can desire, being only of the size -of an ordinary watch. The instrument was formerly made in France for -this country in a very slovenly manner. It is now made in London by the -author, of sound work and accurate centring, Fig. 425. It has face back -and front. The front one, which is shown in the illustration, carries -logarithmic scales of sines, numbers and square roots, and is made to -revolve by turning the milled head placed under the handle, as the -winder of a keyless watch. The back dial, which is fixed and does not -revolve, has upon it a scale of equal parts giving the decimal parts -of logarithms, and a logarithmic scale of cube roots. There are three -index hands, one fixed on the side of the case over the front dial, -as shown in Fig. 425, and one on each end of the central axis made -to revolve simultaneously over the back and front dials by means of -the milled head at the side of the case. Any operation involving -multiplication, division, proportion, powers or roots can be performed -approximately with great rapidity by the aid of this calculator, and it -is practically as simple to use as an ordinary slide rule, as will be -seen from the following explanation of its use:-- - -[Illustration: Fig. 425.--_Boucher's calculator._] - -[Illustration: Fig. 426.--_Stanley-Boucher calculator._] - -Multiplication, using the second circle of divisions from the outside -of the front dial:--Bring the first factor under the fixed index, set -the movable index to 1, then bring the second factor under the movable -index, and the product will be found under the fixed index. - -Division is performed on the same scale as follows:--Bring the dividend -under the fixed index, set the movable index to the divisor, then bring -1 to the movable index, and the quotient will be found under the fixed -index. - -For proportion the second circle is also used:--Set the first factor -under the fixed index and set the movable index to the second one, then -the proportionate equivalent of any number brought under the former -will be found at the movable index. - -Square roots, using the same scale:--Bring the number under either of -the indices, and the square root will be found upon one of the two -inner circles of the same dial. - -Cube root:--In this case it is necessary to first bring the 1 on the -front dial under the fixed index, then set the movable index to the -number, and the cube root will be found on one of the inner circles of -the back or fixed dial. - -To use the trigonometrical dial:--Bring the needle of this dial over -the angle of which the sine or tangent is required, and read upon the -other dial (indicated by the needle) the natural trigonometrical line -upon the inner circle, or its logarithm upon the outer circle. - -The book of instructions supplied with the instruments, written by -Professor George Fuller, C.E., for the author, gives all directions for -working and also gauge points from which calculations are made as with -the slide rule. - -875.--In reduction of factors of a calculation collectively Boucher's -calculator may take more than one turn or less than unity. The author -has added a central index to record the number of turns. This is said -to be of great value for the perfection of the instrument, Fig. 426. - -876.--=Slide Rules=, of which there are great varieties, are of too -complex a nature to discuss, except very briefly, in our limited -space, particularly as general descriptions have been often given. The -ordinary logarithmical scales of Gunter (1619), known as _Gunter's -lines_, are placed upon most slide rules. The arithmetical lines are -lettered _A_, _B_, _C_, _D_, and _E_. _A_ and _B_ are alike: these are -technically termed _double radius log. lines_. They are used for all -processes of multiplication and division. _C_ and _D_ are also alike -and are termed _single radius log. lines_. They are used together for -ordinary multiplication and division, and in conjunction with A and -B scales for squares and square roots. The _E_ line, not originally -a Gunter's line, but found early in the century on several rules, is -termed a _triple radius log. line_. The numbers of the divisions on -this line are the cubes of the numbers of the corresponding divisions -of the _D_ line, with which it generally works. All these lines work -reciprocally together, performing the most complex calculations by -simply setting them to numbers or gauge points of which given solutions -are required, as for instance, the first four lines in combination -give answers to such questions as:--To divide by a number two numbers -multiplied together, one of which is squared; to divide the product -of two numbers by the square of a third number, etc., each of which -calculations is performed at a single setting. By inversion of the -slide _A_ to _C_ the reciprocal of a given number is found, also the -mean proportional between two numbers, the fourth term is inverse -proportion, etc. Trigonometrical calculations are performed by the -lines of sines, tangents, etc. Instructions are to be found in the -books supplied with the rules, and as a part of many works. Among the -most complete books may be mentioned "The Slide Rule," by R. G. Blaine, -M.E., and "The Slide Rule," by Chas. N. Pickworth. These both contain -very full information on the subject. - -877.--_The Slide Rules_ in most general use are A. Nestler's and A. -W. Faber's. Both these well-known firms make a very complete series, -applicable to a great variety of technical calculations. - -878.--The reviser has recently completed from the designs of the author -an entirely automatic dividing engine for these rules, which is the -only one in existence. - -A great number of slide rules are made for special purposes only: some -of these are very useful to the civil engineer. - -879.--_Hudson's Slide Rules_ give strength of shafts, beams, and -girders; pump duty; and computation of horse-power in engines. - -880.--_Honeysett's Hydraulic Slide Rule_ gives discharge of water from -channels and pipes of different forms and inclinations. - -881.--_Tacheometrical Slide Rules_ with scale of sine^2 and sine × -cos. for calculating the horizontal equivalents and vertical heights -from tacheometrical observations. These are made either for use with -instruments divided sexagesimally to 360° or centesimally to 400. - -882.--_Sheppard's Slide Rule_ has duodecimal lines, double reading, for -squaring and cubing timber. - -883.--_Young's Slide Rule_ is designed for squaring and valuing timber -simultaneously, which operations it performs in a very expeditious -manner. - -884.--Essex's Slide Rule is the best for calculating the rates of -velocity and discharge from sewers, water mains, channels, and culverts -of different forms, as it works with all formulæ. - -885.--=The Slide Rule of Prof. Geo. Fuller, C.E.=, Fig. 427, presents -perhaps the highest present refinement of this class of rules, capable -of greatly facilitating the numerous arithmetical calculations of the -civil engineer. Its range is greater than most calculating machines, -and besides the operations of multiplication and division, squaring and -cubing, results requiring the reciprocals, powers, roots, or logarithms -of numbers can be quickly and easily worked out by its use. - -[Illustration: Fig. 427.--_Professor Fuller's calculating slide scale._] - -The rule consists of an outer cylinder that can be moved up or down, -and turned round upon the cylindrical axis which is held by the handle. -Upon the outer cylinder a single spiral, logarithmical scale is -continued from end to end, the total length of which makes the scale -500 inches long. This is graduated into 7250 divisions. One index is -fixed to the handle. A second index is attached to the inner tube -blocked out by a flange to read upon any part of the scale; so that -altogether there are three tubes which work together telescopically, -by means of which the indices may be set to any position on the -graduated cylinder. Stops are placed so that the indices may be brought -to zero. By these means, the indices being set to any of the gauge -points, the logarithmical scale, moving by itself, will maintain -the same proportion for any numbers. In this rule a single log. -radius is repeated by coincidence of indices, so that its scale of -divisions, 41 feet 8 inches long, if compared with an ordinary double -radius slide rule, becomes equal to a slide rule of 83 feet 4 inches -long. The ordinary 12-inch slide rule has about 80 divisions to each -radius, so that it is easily seen how much more exact quantities may -be brought out with a rule of 7250 divisions. It is a most valuable -rule for calculations for the tacheometer. Copious tables of gauge -points for civil engineers are printed upon the central tube, which is -supplemented by a book of instructions. The value of this rule has been -much extended by scales to facilitate subtense calculations, by Mr. W. -N. Bakewell, C.E., in the "Fuller-Bakewell" slide rule. - -[Illustration: Fig. 428.--_Improved Fuller's slide rule._] - -An additional improvement, as shown at Fig. 428, has now been effected -in these instruments by adapting the case to support the rule when in -use, thus overcoming the objection of being always obliged to hold it -in the hand. - -The use of Professor Fuller's rule is, however, confined to -arithmetical computations. The numerical solution of formulæ comprising -trigonometrical functions can only be performed by extracting, with -considerable loss of time, the values of these functions from a -book of tables. To do so requires a certain effort of mind with its -consequent risk of mistakes. This limitation has restricted its use -in a considerable body of calculations, such, for example, as in -the computation of the co-ordinates of surveys from the lengths and -bearings of their lines, a method of plotting which is very largely -used by land surveyors at present; in astronomical computations; in -civil and mechanical engineering, etc.; the use of logarithms being -preferred on the score of speed, although the degree of accuracy -attained with Professor Fuller's rule is amply sufficient in the large -majority of cases. - -[Illustration: Fig. 429.--_Barnard's co-ordinate spiral slide rule._] - -886.--=The Co-ordinate Spiral Slide Rule= has been designed to meet -these requirements by Mr. H. O. Barnard, A.C.H., F.R.A.S., etc., -Superintendent of Trigonometrical Surveys, Ceylon, Fig. 429. Like -Professor Fuller's rule, upon which it is an improvement, it enables -the user to perform with speed and accuracy arithmetical computations -involving multiplication, division, proportion, continuous fractions, -powers, roots, and logarithms; but in addition, the natural and -logarithmic values of trigonometrical functions of any angle can -be determined by inspection with the same accuracy as in numerical -computation, while the products, quotients, etc., of these functions, -by lengths or numbers, integral or fractional, are obtained with equal -ease, rapidity and precision. The scope of its operations will be -gathered from the examples which are given to illustrate its use in the -instructions supplied with the rule. - -[Illustration: Fig. 430.--_Thacher's slide rule._] - -Although the co-ordinate spiral rule, as all varieties of slide rules, -is based primarily upon the theory of logarithms, a knowledge of that -theory is by no means essential to its practical use. - -887.--=Thacher's Slide Rule.=--Fig. 430. This contains a shorter scale -than Professor Fuller's, and the system is not quite so simple. Full -printed instructions are given in the book supplied by the inventor, -Mr. Edwin Thacher, of Pittsburg, U.S.A., or of the author, who is his -agent for this country. The original divisions of this rule were made -by the author. The scale is manufactured in the United States. There -appears to be found some difficulty in its construction to keep the -scales to true length and get them to exact position. - -888.--=Pocket Sets of Chain Scales.=--These are made 3, 4, 5, and 6 -inch. Three of 6 inch form the ordinary set. The chain scales, if three -only, are 10, 20, 30, 40, 50, and 60; if six they generally contain -the same scales with feet equal to the links. An extra scale with -the ordnance or other scale of the country is found also useful for -measuring from maps or plans. Some civil engineers prefer the pocket -scales made wide with quite square ends, to be used as offsets or for -sketching. These scales are generally made in ivory and placed in a -light morocco or Russia leather case. The numbers of divisions of the -scales should be stamped on the ends to prevent the wrong scale being -drawn from the case. - -[Illustration: Fig. 431.--_Biram's anemometer._] - -[Illustration: Fig. 432.--_Lowne's anemometer._] - -889.--=Anemometers= are used by mining engineers for testing the -ventilation of mines. The original and best known form is that of -Biram, Fig. 431. This instrument is held in any current of air, and the -velocity of the current is registered by the motion of oblique fans, -by means of ordinary decimal gearwork on five dials giving feet and -multiples by 10. Lowne's anemometer, with the author's improvements, -Fig. 432, is of similar principles of construction, but it is arranged -in portable form to go in a pocket case. Another well-known form of -anemometer is built upon the same principle, but of cubical form. It -is customary to take the velocity of the current for one minute by a -watch, there being a detent provided in most instruments to start and -stop the motion of the hands upon the dials. - -890.--=Books of Tables and Formulæ.=--Few British Surveyors are -without Molesworth's pocket-book. This contains all the useful -tables and notes of reference valuable to the civil engineer in his -ordinary work--weight, 5 ozs. Many pocket-books have been written on -the same plan. Hurst's pocket-book contains all matters of reference -for the town surveyor among buildings. Trautwine's _Civil Engineer's -Pocket-book_ (American) is the most complete, but it is of double the -weight of the Molesworth. Spon's _Engineers' Tables for the Waistcoat -Pocket_--weight, little over ½ oz.--is a very useful little book. Of -_Traverse Tables_ both Gurden's and Boileau's are comprehensive and -reliable. There are several pocket-books of _Curve Tables_, those of -Cutler & Edge, Beazeley, and Kennedy & Hackwood being perhaps in the -most general use. - -891.--=Technical Books--Ordnance Maps= are published on special -districts and subjects which are often relative to the country or the -special conditions of work abroad and at home for minerals, etc. It is -very useful to possess such of these as may be required, and the note -is only made here as a reminder. - -892.--=Sling Case for Drawings.=--The most convenient method of -carrying maps or drawings for public works in execution is to have a -solid leather case similar to a telescope case. This is best if made -with the cap or lid of the same length as the body: it can then be -drawn out any distance according to the length of the rolled drawing. -If thought more convenient, and the map or drawings are heavy, a strap -may be added to pass over the shoulder, Fig. 433. - -893.--=Chronometer.=--This may be any form of watch with compensated -escapement. At present the prices run high for this class of work; but -from the simplicity and moderate certainty of compensation it does -not appear that this should be necessary for the production of a fair -working instrument useful for the surveyor in new countries to check -his longitude. Where a good chronometer is used it is better to keep it -to Greenwich time without alteration. If there is a gaining or losing -rate this will most probably remain constant in equal times, so that -corrections may be made _pro ratâ_ for all observations until a check -can be taken with certainty when arriving at a town which possesses -an observatory. The quality of a chronometer is fully ascertained by -having a certificate from one of our observatories, that of Kew being -the most popular. - -[Illustration: Fig. 433.--_Sling case for drawings._] - -894.--=Chronograph.=--For the observation of stars in transit for the -purpose of taking longitude, a dead-stop watch or chronograph is most -useful. This can now be had in combination with an otherwise fair going -watch at a very moderate price. - -895.--=Outfit of a Surveyor for Work in a New Country.=--The ordinary -items of strong, dust-coloured woollen clothing, good boots, saddle, -firearms, etc., do not come within the province of this work. The -instruments he will require will depend partly upon the nature of the -country and the kind of work to be done. If for prospecting only, light -instruments are commonly selected--the sextant, or box sextant with -glass artificial horizon, good pocket chronometer, _telescope_, aneroid -barometer, prismatic compass, and clinometer. If a general survey is -to be made, the first instrument of importance is the theodolite, the -4 or 5-inch being the most usual. With this, pickets, land chain and -arrows, a steel tape for testing, and a linen tape. If for survey in -mineral districts, a good mining-dial is required, with all accessories -of chains, etc. If for railway work, a 5-inch theodolite, a good -level, staves, pickets, clinometer, and prismatic compass. In all -cases, field-books, drawing instruments, supply of paper, drawing -boards, squares, parallel rule, pencils, Indian ink, colours, stencil -plates, and other articles for office use, of which the established -optician or trader will give full information from his experience, or -general reference may be taken from any complete catalogue of such -instruments. - -FOOTNOTE: - -[66] Patent, No. 4310, November, 1876. - - - - -INDEX - - Abney's clinometer, 411 - - Achromatism explained, 35 - - Adjustable axis, of plane table, 479 - of theodolite, 237 - - Adjustable tripod, 329 - - Alidades for plane tables, 473 - - Alloys used for surveying instruments, 7 - - Altazimuth theodolite, 295 - - Altitudes, measurements of, 550 - - Aluminium alloys, 8 - - Anallatic telescope, 364 - - Anemometers, 596 - - Aneroid barometers, Vidie's, 558 - Bourdon's, 568 - - Apomecometer, 469 - - Arrows, for chain, 494 - - Artificial horizons, 443 - - Atmospheric pressure, measurements of, 550 - - Axes, workmanship in, 11 - - - Bakewell's tangential index, 384 - - Ball and socket adjustments: Hoffmann's, Pastorelli's, 330 - - Bands, steel, for measuring land, 449 - - Barker's clinometer, 415 - - Barometer, aneroid, 558 - mountain, 550 - mercurial, 549 - - Base line apparatus, 517 - - Beam compass measurements, 510 - - Bellamy's road tracer, 420 - - Bill-hook, 582 - - Binoculars, prism, 584 - - Black, optical, 14 - - Boiling-point thermometer, hypsometer, 569 - - Boning rods, 578 - - Books, levelling, 173 - - Boucher's calculator, 587 - improved, 590 - - Box sextant, 451 - with continuous arc, 461 - with supplementary arc, 458 - - Bronzing instruments, 14 - - Brunton mine transit, 353 - - Bubble trier, 88 - - Burel's reflecting level, 144 - - Burnier's clinometer, 416 - - - Caink's rule for correcting inclines, 498 - - Calculators: Barnard's, 594 - Boucher's, 587 - Fuller's, 592 - Thacher's, 595 - - Camera, 243, 585 - - Cases, for carrying maps, 597 - leather, for instruments, 23 - - Cavalry sketching case, 488 - - Cement tester, Mann's, 585 - - Centesimal division, 185 - - Chain scales, pocket sets, 596 - - Chain vice, 496 - - Chaining, 497 - - Chains, land, various, 490 - - Chains, sounding, 526 - - Chronometer and chronograph, 598 - - Circumferentor, 307 - - Clamp and tangent motions, various, 202 - - Classification of instruments, 5 - - Clinometer compasses, 418 - hanging, 344 - - Clinometers, various, 411 - - Coast survey lines, 527 - - Coincidence rods, 511 - - Collimation, 55 - - Collimator, 121 - - Compass, surveying with, 80 - - Compasses: magnetic, bar, 59 - Barker's, 84 - Burnier's, 80 - hanging, 344 - Hutchinson's, 79 - luminous, 84 - mariners', 73 - prismatic, 75 - pocket, 82 - ring, 72 - trough, 74, 83 - - Compensated rods, 512 - - Connecting link, to extend hand rods, 531 - - Convex and concave lenses, 32 - - Cooke's level, 138 - - Co-ordinate slide rule, 594 - - Cross-staff heads, 573 - - Curvature, correction for, 170 - - Cushing's level, 136 - - - De Lisle's reflecting clinometer, 413 - - Declination of needles, 67 - - Deville's theodolite, 263 - - Diagonal eye-piece, 45 - - Dials, mining, 309 - - Diaphragm of telescope, 50, 114, 135 - - Dip compass, 354 - - Dip of needles, 66 - - Dispersion of light, 35 - - Dividing engine, 176 - - Division of the circle, 175 - - Double optical square, 467 - - Drop arrow, 494 - - Dumpy level, 110 - improved, 123 - - Dynameter, 43 - - - Edgeworth's stadiometer, 482 - - Engineer's level, 133 - - Engraving, note on, 16 - - Everest's theodolite, 271 - tripod, 273 - - Excise ink bottle, 174 - - Eye-pieces: Ramsden, 41 - erecting, 44 - diagonal, 45 - reflecting, 46 - - - Field-books, 289, 374, 380 - - Field-glasses, 582 - - Finishing of surveying instruments, 14 - - Formation of images in a telescope, 33 - - French forms of miners' dials, 336 - - Fuller's rule, 592 - - - Geological tools, 587 - - George's artificial horizon, 446 - - Girth straps, tapes, etc., 579 - - Glass diaphragm, 53 - - Glass, working, 16 - refraction of, 25 - - Gradient scale, 213 - - Gradienter Screw, 386 - - Gradiometer, 404 - - Gradioplane, 409 - - Graduation, 179 - - Green, William, Subtense instruments, 355 - - - Hadley's quadrant, 423 - - Hanging mining compass, 344 - - Hedley's dial, 322 - improved, 326, 329, 333 - - Heliograph, 540 - - Heliostat and heliotrope, 537 - - Henderson's miners' dial, 315 - - Hick's patent level, 96 - - Historical sketch of surveying instruments, 1 - - Hoffmann's ball and socket head, 330 - - Horizontal scale of tangents, 213 - - Hypotenuse and base, 212 - - Hypsometer, 569 - - - Illumination of axis of telescope, 234 - - Inclinometer: Lister's, 389 - - - Lacquering work, 15 - - Lamp, magnesium, 545 - for levelling, 169 - mining, 348 - theodolite, 235 - - Land chains, 490 - vice for adjusting, 496 - - Lanterns, oil, 545 - - Lean's miners' dial, 315 - - Leather cases, 23 - - Lenses, 33 - achromatic, 36 - - Level: for levelling staff, 163 - mechanics', 575 - with inclines, 576 - - Levels: surveyors', 97 - Cooke's, 138 - Cushing's, 136 - dumpy, 110 - same improved, 123 - engineers', 133 - reflecting, 144 - pocket, 142 - simple construction of, 141 - supplementary parts to, 139 - water, 146 - Y-form, 98 - same improved, 107 - - Level tubes, 86 - circular, 96, 576 - curvature of, 87 - divisions upon, 90 - readers for, 95 - Scott's, 93 - sensitiveness of, 89 - Strange's, 92 - with air cell, 93 - - Level tube trier, 88 - - Levelling: books, 172 - staves, telescopic, 148 - semicircular, 150 - mining, 158 - papering of, 159 - preservation of, 161 - various patterns of, 151 - holder for, 163 - pads for, 161 - pegs for, 171 - practice of, 163 - - Light for night observations, 169, 545 - - Light, refraction of, 27 - - Line, sounding, 527 - - Lubrication of joints, etc., 20 - - Luminous compass, 84 - - - Magnesium lamp, 546 - - Magnetic compasses, 59 - correction of, 64 - declination of, 67 - inclination of, 66 - trough, 74 - variation of, 68 - various forms, 82 - - Magnetic needles, 59 - lifting, 65 - mounting, 64 - - Magnetic needles, various, 59 - - Magnetism, 59 - preservation of, 71 - - Magnifying power of telescope, 43 - - Measuring rods, 530 - - Mechanics' levels, 575 - - Mercurial barometer, 549 - - Metals employed in surveying instruments, 7 - - Micrometer microscopes: various, 192 - Stanley's, 197 - - Micrometer theodolites, 259 - - Military sketching board, 485 - cavalry, 488 - - Miners' circumferentor, 307 - - Miners' compasses: French, 336 - hanging, 344 - Stanley's prismatic, 343 - - Miners' dials: various, 309 - hanging, 344 - Hedley's, 322 - Henderson's, 315 - Lean's, 315 - improvements in Hedley's dial, 326, 329, 333 - - Mining, survey lamp, 348 - targets, 349 - theodolite, 342 - - Morse signaling, 544 - - Mountain barometer, 550 - theodolite, 258 - - - Nautical sextant, 429 - - Needles, magnetic, 59 - - Night signalling stations, 545 - - - Octant or quadrant, 422 - - Offset rods, 507 - - Omnimeter, 374 - - Opisometer, 587 - - Optical black, 14 - - Optical principles of telescope, 25 - - Optical square, 465 - - Outfits for surveyors abroad, 598 - - - Packing of instruments, 21 - - Parallax, in eye-piece, 55 - - Parallel plates, to level, 99 - to theodolite, 219 - - Passometer, 525 - - Pastorelli's ball and socket head, 330 - - Pedometer, 524 - - Perambulator, 521 - - Permanent stations, 535 - - Pickets or ranging poles, 533 - - Pine measuring rods, 508 - - Pioneer tools, 585 - - Photographic camera, 243, 585 - - Plain theodolite, 215, 267 - - Plane tables, 472 - - Platinum-iridium points, 53, 129, 135 - - Plummets, 232 - - Pocket-books, 534, 596 - - Pocket levels, 96 - sighted, 142, 525 - - Pocket magnetic compasses, 83 - - Point diaphragm, 53, 129, 135 - - Polishing work, 14 - - Preservation of instruments, 20 - - Prismatic clinometers, 414 - - Prismatic compasses, 75 - Hutchinson's, 79 - stands, 78 - - Prismatic mining survey compass, 343 - - Prisms as reflectors, 29 - - Protectors for the eyes, 584 - - Protractors, sketching, 82, 374, 485 - - - Quadrant, 422 - - Qualities of work, 7 - of a telescope, 56 - - Quick-setting surveyor's level, 132 - - Quick-setting theodolites, 257 - - Quiver for arrows, 494 - - - Railway gauge, 579 - theodolite, 258 - - Ramsden eye-piece, 41 - - Ranging poles, 533 - - Ray shade, 129 - - Reader for level tube, 95 - - Reading microscopes, 188 - - Reconnoitring glass and telescope, 582 - - Reflecting cap to telescope, 334 - - Reflecting circle, 424 - - Reflecting clinometers, 413 - - Reflecting levels, 144 - - Reflection of glass, 25 - - Reflector in eye-piece, 46 - - Refraction of light, 25 - - Repairing sleeves for steel bands, 505 - - Revolving compass to dial, 318 - - Richmond's tension handle, for steel band, 503 - - Road tracer, 420 - - Rods: coincidence, 511 - compensated, 512 - hand, 530 - standard, 508 - - Rule, civil engineer's, 532 - - Rule for correcting inclined measurement, 498 - - Rule form clinometer, 418 - - - Semi-circumferentor, 346 - - Sextants, 425 - box, 451 - with supplementary arc, 461 - continuous arc, 458 - sounding, 449 - surveying (open), 464 - - Sight director to stadium, 364 - - Sighted pocket level, 142 - - Silvering sextant glasses, 437 - - Sketch books, etc., 585 - - Sketching board, military, 485 - - Slashing knife, 582 - - Slide rules, various, 590 - - Sliding stage to theodolite, 249 - - Socket for station pole, 535 - - Solar attachment to theodolite, 239, 259 - - Soldering, 13 - - Sounding chain, 526 lines, 527 - - Sounding sextant, 449 - - Spectacles for protecting the eyes, 584 - - Spherical aberration, 33 - - Spur shod picket, 535 - - Stadia points, 131 - webs, 114 - - Stadium for tacheometer, 155, 373 - - Stadiometer, 482 - - Standard rods, 508 - - Stands of instruments, 19 - - Stations for observation, 533 - - Staves, levelling, 149 - - Steel bands and tapes, 499, 507 - - Striding level, 237 - - Style of work, 16 - - Subtense, instruments, 355 - diaphragm, 114, 363 - - Supplementary arc to box sextant, 461 - - Sun glass to telescope, etc., 47 - - - Tacheometers: general description, 370 - Stanley's, etc., 371 - - Tacheometers: stadium for, 155, 373 - field book, 374 - - Tangent motions, 202 - - Tapes, linen, etc., 505 - - Targets, mining, 349 - - Telemeters, 528 - - Telescope: general description of, 24 - Kepler's, Galileo's, 40 - body of, 47 - - Telescope: optical arrangements, 47 - optical principles, 25 - qualities, 56 - reconnoitring, 582 - - Telescopic pocket level, 143 - - Tension handles for steel bands, 503 - - Theodolites, 214 - adjustment, 276 - adjustable axis, 237, 248 - Deville's, 263 - Everest's, 271 - micrometer, 259 - mountain, 258 - plain, 265, 267 - railway, 258 - simple construction, 275 - solar attachment to, 239 - Souterrain 348 - Stanley's, 247 - transit, 215, 231, 247 - 14-inch, 295 - 36-inch Colonel Strange's, 298 - Universal, 265 - - Thermometer for steel band, 503 - boiling point, 569 - - Timber girth strap, 579 - marking knife, 581 - rods, 582 - - Tools used in manufacture of instruments, 11 - - Triangle for levelling staff, 162 - - Tribrach adjustments, 126 - Everest's, 272 - with mechanical stage, 251 - - Tripods, 114, 217, 322 - framed, 250 - miners', 313 - - Tripods, jointed, for mining instruments, 313 - - Trough compass, 74, 83, 236 - - - Vernier scale readings, 180 - - Vicat needle, 586 - - Vice for adjusting land chain, 496 - - - Water levels, 146 - - Waterproof covers, 23 - - Watkin's aneroid, 567 - - Watkin's clinometer, 417 - - Wealemefna, 587 - - Webs, collecting and mounting, 51 - - Whistles, 585 - - - Y-levels, 98 - improved construction, 107 - - - - -[Illustration: WIRE UP YOUR OWN HOUSE - -Have Electric LIGHT HEAT POWER] - - This Book - - WIRING HOUSES--SCHNEIDER - - Shows you in detail how to install electric wires. 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