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+Project Gutenberg (https://www.gutenberg.org) public repository for
+eBook #63834 (https://www.gutenberg.org/ebooks/63834)
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-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
-
-
-
-
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-<pre>
-
-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)
-
-
-
-
-
-
-</pre>
-
-<div class="transnote">
-
-<h2 class="bold">Transcriber's Note:</h2>
-
-<p>Punctuation has been standardised, and possible typographical errors have been changed.</p>
-
-<p>Archaic, variable and inconsistent spelling and hyphenation have
-been preserved.</p>
-
-</div>
-
-<div class="chapter">
-<hr class="chap" />
-<p class="xxxlarge center padding3">SURVEYING AND LEVELLING</p>
-<p class="xxxlarge center padding08">INSTRUMENTS</p>
-</div>
-
-<div class="chapter">
-<hr class="chap" />
-<h1>SURVEYING AND LEVELLING<br />
-INSTRUMENTS<br />
-<br />
-<span class="medium font-weight-normal">Theoretically and Practically Described.</span></h1>
-<p class="p2 medium center line-height200">FOR CONSTRUCTION, QUALITIES, SELECTION, PRESERVATION,
-ADJUSTMENTS, AND USES; WITH OTHER APPARATUS AND APPLIANCES
-USED BY CIVIL ENGINEERS AND SURVEYORS IN THE FIELD.</p>
-<p class="p6 small center">BY</p>
-<p class="xlarge p2 center margin-top1">WILLIAM FORD STANLEY</p>
-<p class="p1 small center line-height180">OPTICIAN, MANUFACTURER OF SURVEYING AND DRAWING INSTRUMENTS,</p>
-<p class="small center line-height180 margin0-6">AUTHOR OF A TREATISE ON DRAWING INSTRUMENTS,
-PROPERTIES AND MOTIONS OF FLUIDS, NEBULAR THEORY, ETC.</p>
-<p class=" center margin-top5"><i>FOURTH EDITION</i></p>
-<p class=" center margin-top05"><span class="smcap">Revised by</span> H. T. TALLACK.</p>
-<p class="large center margin-top4">LONDON: E. &amp; F. N. SPON, LTD., 57, HAYMARKET, S.W.</p>
-<p class=" center">NEW YORK: 123, LIBERTY STREET</p>
-<p class="small center margin05-0-02-0">AND OF</p>
-<p class=" center">W. F. STANLEY &amp; CO., LIMITED</p>
-<p class=" center">286, <span class="smcap">High Holborn, London, W.C.</span></p>
-<p class="p1  center">1914</p>
-</div>
-
-<div class="chapter">
-<hr class="chap" />
-<h2>PREFACE TO FIRST EDITION.</h2>
-<hr class="r12" />
-</div>
-<p class="padding-top1 text-indent0"><span class="smcap">Notes</span> 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.</p>
-<p>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<span class="pagenum"><a name="Page_iv" id="Page_iv">[iv]</a></span>
-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.</p>
-<p>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.</p>
-<p>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<span class="pagenum"><a name="Page_v" id="Page_v">[v]</a></span>
-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.</p>
-<p>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.</p>
-<p>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<span class="pagenum"><a name="Page_vi" id="Page_vi">[vi]</a></span>
-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.</p>
-<p>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.</p>
-<p class="text-align-right margin-right2">W. F. S.</p>
-<p class="smcap">Great Turnstile, 1890.</p>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_vii" id="Page_vii">[vii]</a></span></p>
-<h2>PREFACE TO THIRD EDITION.</h2>
-<hr class="r12" />
-</div>
-<p class="padding-top1 text-indent0"><span class="smcap">The</span> 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.</p>
-<p>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.</p>
-<p>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.</p>
-<p>In the present Edition, which represents forty-seven years
-of experience of the author's life devoted to the details of the<span class="pagenum"><a name="Page_viii" id="Page_viii">[viii]</a></span>
-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.</p>
-<p>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.</p>
-<p class="text-align-right margin-right2">W. F. S.</p>
-<p class="smcap">Great Turnstile, 1901.</p>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_ix" id="Page_ix">[ix]</a></span></p>
-<h2>PREFACE TO FOURTH EDITION.</h2>
-<hr class="r12" />
-</div>
-<p class="padding-top1 text-indent0"><span class="smcap">Since</span> 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&mdash;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.</p>
-<p>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.</p>
-<p class="smcap text-align-right margin-right2">H. T. Tallack.</p>
-<p class="smcap">286, High Holborn,</p>
-<p class="margin-left5"><i>June, 1914.</i></p>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_x" id="Page_x">[x]</a><br /><a name="Page_xi" id="Page_xi">[xi]</a></span></p>
-<h2 class="margin-top3 font-size150">CONTENTS.</h2>
-<hr class="r12" />
-</div>
-<div class="center margin-top2">
-<table summary="">
-    <tr>
-      <td class="tdc">CHAPTER I.</td>
-    </tr>
-    <tr>
-      <td></td>
-      <td class="tdr small">PAGE</td>
-    </tr>
-    <tr>
-      <td class="toc2"><span class="smcap">Introduction</span>:&mdash;Historical
-      Sketch&mdash;Classification of the Subject&mdash;Purposes and Qualities of
-      Instruments&mdash;Workmanship&mdash;Metals&mdash;Aluminium&mdash;Framing&mdash;Tools&mdash;Axes of
-      Instruments&mdash;Soldering&mdash;Finishing&mdash;Bronzing&mdash;Lacquering&mdash;Graduating
-      &mdash;Engraving&mdash;Style&mdash;Glass-Work&mdash;Woodwork&mdash;Lubrication&mdash;Preservation
-      of Instruments&mdash;Packing</td>
-      <td class="tdrb"><a href="#Page_1">1</a></td>
-    </tr>
-    <tr>
-      <td class="tdca">CHAPTER II.</td>
-    </tr>
-    <tr>
-      <td class="toc2"><span class="smcap">The Telescope as a Part of a Surveying
-      Instrument</span>:&mdash;General Description&mdash;Qualities&mdash;Optical
-      Principles&mdash;Refraction of Glass&mdash;Limit of
-      Refraction&mdash;Reflection&mdash;Prisms&mdash;Lenses, Convex and Concave&mdash;Aberration&mdash;Formation of
-      Images&mdash;Dispersion&mdash;Achromatism&mdash;Curvature of
-      Lenses&mdash;Telescopes&mdash;Eye-pieces&mdash;Powers&mdash;Dynameter&mdash;Construction of the
-      Telescope&mdash;Diaphragm&mdash;Webs&mdash;Lines&mdash;Points&mdash;Parallax&mdash;Examination and Adjustment</td>
-      <td class="tdrb"><a href="#Page_24">24</a></td>
-    </tr>
-    <tr>
-      <td class="tdca">CHAPTER III.</td>
-    </tr>
-    <tr>
-      <td class="toc2"><span class="smcap">The Magnetic Compass as a Part of a Surveying
-      Instrument or Separately</span>:&mdash;Broad and Edge-bar
-      Needles&mdash;Manufacture of the Needle&mdash;Magnetisation&mdash;Suspension&mdash;Dip and
-      Adjustment&mdash;Lifting&mdash;Inclination&mdash;Declination&mdash;Variation&mdash;Correction&mdash;
-      Compass-Boxes&mdash;Description of Compasses&mdash;Ring Compasses&mdash;Trough Compasses&mdash;Prismatic
-      Compasses&mdash;Stand&mdash;Surveying with Compass&mdash;Pocket Compasses</td>
-      <td class="tdrb"><a href="#Page_59">59</a></td>
-    </tr>
-    <tr>
-      <td class="tdr"><span class="pagenum"><a name="Page_xii" id="Page_xii">[xii]</a></span></td>
-    </tr>
-    <tr>
-      <td class="tdca">CHAPTER IV.</td>
-    </tr>
-    <tr>
-      <td class="toc2"><span class="smcap">Levels</span>:&mdash;Methods of
-      Ascertaining&mdash;Level
-      Tubes&mdash;Manufacture&mdash;Curvature&mdash;Sensitiveness&mdash;Testing&mdash;Reading&mdash;Circular
-      Levels&mdash;Surveyors' Levels&mdash;Y-Levels&mdash;Parallel Plates&mdash;Adjustments
-      of Y-Levels&mdash;Suggested Improvements&mdash;Dumpy
-      Levels&mdash;Tripod Stands&mdash;Adjustment of
-      Dumpy&mdash;Collimator&mdash;Improvements in Dumpy Levels&mdash;Tribrach Head&mdash;Diaphragms&mdash;Cushing's
-      Levels&mdash;Cooke's Levels&mdash;Cheap Forms of Level&mdash;Hand
-      Levels&mdash;Reflecting Levels&mdash;Water Levels</td>
-      <td class="tdrb"><a href="#Page_85">85</a></td>
-    </tr>
-    <tr>
-      <td class="tdca">CHAPTER V.</td>
-    </tr>
-    <tr>
-      <td class="toc2"><span class="smcap">Levelling
-      Staves</span>:&mdash;Construction&mdash;Various Readings
-      Discussed&mdash;Sopwith's&mdash;Field's&mdash;Strange's&mdash;Stanley's New Metrical&mdash;
-      Simple Construction&mdash;Mining Staff&mdash;Papering Levelling
-      Staves&mdash;Preservation&mdash;Packing Pads&mdash;Staff Plate&mdash;Staff Level&mdash;
-      Practice of Levelling&mdash;Index of Bubble&mdash;Lamp&mdash;Curvature
-      Corrections&mdash;Station Pegs&mdash;Refinement of Levelling&mdash;Levelling Books</td>
-      <td class="tdrb"><a href="#Page_148">148</a></td>
-    </tr>
-    <tr>
-      <td class="tdca">CHAPTER VI.</td>
-    </tr>
-    <tr>
-      <td class="toc2"><span class="smcap">Division of the Circle and Methods Employed in
-      Taking Angles</span>:&mdash;Dividing Engine&mdash;Surfaces for
-      Graduation&mdash;Vernier&mdash;Various Sections&mdash;Reading
-      Microscopes&mdash;Shades&mdash;Micrometers&mdash;Clamp and Tangent Motions&mdash;of Limbs&mdash;
-      of Axes&mdash;Use and Wear&mdash;Difference of Hypotenuse and Base</td>
-      <td class="tdrb"><a href="#Page_175">175</a></td>
-    </tr>
-    <tr>
-      <td class="tdca">CHAPTER VII.</td>
-    </tr>
-    <tr>
-      <td class="toc2"><span class="smcap">Theodolites</span>:&mdash;Constructive Details
-      of 5-inch and 6-inch Transits&mdash;Special Additional Parts&mdash;Old Form with Four
-      Screws&mdash;Improved Form&mdash;Additional Parts&mdash;Plummets&mdash;Striding
-      Level&mdash;Lamp&mdash;Adjustments over a Point&mdash;Solar Attachment&mdash;Photographic Attachment</td>
-      <td class="tdrb"><a href="#Page_214">214</a></td>
-    </tr>
-    <tr>
-      <td class="tdca">CHAPTER VIII.</td>
-    </tr>
-    <tr>
-      <td class="toc2"><span class="smcap">Specialties in Modern Forms of
-      Transit</span>:&mdash;Theodolites for General Surveying&mdash;Railway Work&mdash;Exploring</td>
-      <td class="tdrb"><a href="#Page_246">246</a></td>
-    </tr>
-    <tr>
-      <td class="tdc"><span class="pagenum"><a name="Page_xiii" id=
-      "Page_xiii">[xiii]</a></span></td>
-    </tr>
-    <tr>
-      <td class="tdca">CHAPTER IX.</td>
-    </tr>
-    <tr>
-      <td class="toc2"><span class="smcap">Plain Theodolites in which the Transit
-      Principle is not Employed</span>:&mdash;The Plain Theodolite&mdash;Improved
-      Construction&mdash;Everest's Simple&mdash;Adjustments and Examination of Theodolites</td>
-      <td class="tdrb"><a href="#Page_267">267</a></td>
-    </tr>
-    <tr>
-      <td class="tdca">CHAPTER X.</td>
-    </tr>
-    <tr>
-      <td class="toc2"><span class="smcap">Large Theodolites used only for Geodetic
-      Surveys</span>:&mdash;Stanley's 10- and 12-inch&mdash;14-inch Altazimuth&mdash;Col. Strange's 36-inch Theodolite</td>
-      <td class="tdrb"><a href="#Page_293">293</a></td>
-    </tr>
-    <tr>
-      <td class="tdca">CHAPTER XI.</td>
-    </tr>
-    <tr>
-      <td class="toc2"><span class="smcap">Mining Survey
-      Instruments</span>:&mdash;Circumferentors&mdash;Plain Miner's Dial&mdash;Sights&mdash;Tripod
-      Stand&mdash;Adjustments&mdash;Henderson's Dial&mdash;Lean's Dial&mdash;Adjustments&mdash;
-      Hedley's Dials&mdash;Additional Telescope&mdash;Improved Hedley&mdash;Tribrach and Ball
-      Adjustment&mdash;Reflectors&mdash;Continental Forms&mdash;<i>Th&eacute;odolite Souterrain</i>&mdash;
-      Tripod Tables&mdash;Stanley's Mining Theodolite&mdash;Pastorelli's
-      and Hoffmann's Adjustable Tripod Heads&mdash;Mining Transit Theodolites&mdash;Stanley's Prismatic Mining
-      Compass&mdash;Hanging Dial&mdash;Hanging
-      Clinometer&mdash;Semi-circumferentor&mdash;Mining Lamps</td>
-      <td class="tdrb"><a href="#Page_307">307</a></td>
-    </tr>
-    <tr>
-      <td class="tdca">CHAPTER XII.</td>
-    </tr>
-    <tr>
-      <td class="toc2"><span class="smcap">Instruments to Measure Subtense or Tangential
-      Angles to Ascertain Distances</span>:&mdash;Historical Notes of the
-      Method&mdash;Principles Involved&mdash;Stadia Measurements, Direct and by the Ordinary Telescope&mdash;Corrections for Refraction of the
-      Object Glass&mdash;Stanley's Subtense Diaphragm&mdash;Anallatic Telescope
-      of Porro&mdash;Tacheometers&mdash;Stadia&mdash;Omnimeter&mdash;Field
-      book&mdash;Bakewell's Subtense Arrangement</td>
-      <td class="tdrb"><a href="#Page_355">355</a></td>
-    </tr>
-    <tr>
-      <td class="tdca">CHAPTER XIII.</td>
-    </tr>
-    <tr>
-      <td class="toc2"><span class="smcap">Instruments Constructed Especially for
-      Facility of Taking Inclinations</span>:&mdash;Inclinometer
-      Theodolite&mdash;Gradiometer&mdash;Clinometers: Abney's&mdash;Troughton's&mdash;De
-      Lisle's&mdash;Stanley's&mdash;Barker's&mdash;Burnier's&mdash;Watkin's&mdash;Clinometer Sights&mdash;Rule Clinometer&mdash;Road Tracer</td>
-      <td class="tdrb"><a href="#Page_389">389</a></td>
-    </tr>
-    <tr>
-      <td class="tdc"><span class="pagenum"><a name="Page_xiv" id=
-      "Page_xiv">[xiv]</a></span></td>
-    </tr>
-    <tr>
-      <td class="tdca">CHAPTER XIV.</td>
-    </tr>
-    <tr>
-      <td class="toc2"><span class="smcap">Instruments of Reflection</span>:&mdash;Octant
-      or Quadrant&mdash;Reflecting Circle&mdash;Sextant&mdash;Principle&mdash;Parallax&mdash;
-      Construction&mdash;Examination&mdash;Adjustment&mdash;Artificial Horizon&mdash;Sounding
-      Sextant&mdash;Box-Sextant&mdash;Supplementary Arc&mdash;Improvements upon
-      this&mdash;Optical Square&mdash;Optical Cross&mdash;Apomecometer</td>
-      <td class="tdrb"><a href="#Page_422">422</a></td>
-    </tr>
-    <tr>
-      <td class="tdca">CHAPTER XV.</td>
-    </tr>
-    <tr>
-      <td class="toc2"><span class="smcap">Graphic Surveying Instruments and Appliances
-      Connected therewith</span>:&mdash;Plane Tables&mdash;Alidades&mdash;Telescopic
-      Arrangements&mdash;Subtense Measurements&mdash;Various Devices for Holding the Paper&mdash;Continuous Papers&mdash;Adjustment of Tripod
-      Heads&mdash;Method of Using&mdash;Edgeworth's Stadiometer&mdash;Sketching
-      Protractor&mdash;Sketching Case&mdash;Camera Lucida, etc.</td>
-      <td class="tdrb"><a href="#Page_472">472</a></td>
-    </tr>
-    <tr>
-      <td class="tdca">CHAPTER XVI.</td>
-    </tr>
-    <tr>
-      <td class="toc2"><span class="smcap">Instruments for Measuring Land and Civil
-      Works Directly</span>:&mdash;Chains&mdash;Various Tellers&mdash;Standard
-      Chains&mdash;Arrows&mdash;Drop Arrows&mdash;Vice for Adjusting Chain&mdash;Caink's Rule for Inclines&mdash;Steel Bands&mdash;Wire Land
-      Measures&mdash;Linen Tapes&mdash;Offset Rods&mdash;Pine Standard Rods&mdash;Rods with
-      Iron Core&mdash;Beam Compass Rods&mdash;Coincidence
-      Measurements&mdash;Compensated Rods&mdash;Base Line Apparatus&mdash;Coast Survey
-      Lines&mdash;Perambulator&mdash;Pedometer&mdash;Passometer&mdash;Sounding Chains&mdash;Sounding Lines&mdash;Telemeters&mdash;Hand Rods&mdash;Rules</td>
-      <td class="tdrb"><a href="#Page_490">490</a></td>
-    </tr>
-    <tr>
-      <td class="tdca">CHAPTER XVII.</td>
-    </tr>
-    <tr>
-      <td class="toc2"><span class="smcap">Stations of
-      Observation</span>:&mdash;Pickets&mdash;False Picket&mdash;Permanent Stations&mdash;Referring
-      Object&mdash;Heliotrope&mdash;Heliostat&mdash;Heliograph Signalling&mdash;Morse Alphabet&mdash;Night Lights&mdash;Oil
-      Lanterns&mdash;Magnesium Light</td>
-      <td class="tdrb"><a href="#Page_533">533</a></td>
-    </tr>
-    <tr>
-      <td class="tdca">CHAPTER XVIII.</td>
-    </tr>
-    <tr>
-      <td class="toc2"><span class="smcap">Measurement of Altitudes by Differences of
-      Atmospheric Pressure</span>:&mdash;Historical Note&mdash;Mercurial
-      Barometer&mdash;Construction&mdash;Operation&mdash;Aneroid Barometer&mdash;Construction&mdash;Various Improvements&mdash;Hypsometer</td>
-      <td class="tdrb"><a href="#Page_548">548</a></td>
-    </tr>
-    <tr>
-      <td class="tdc"><span class="pagenum"><a name="Page_xv" id=
-      "Page_xv">[xv]</a></span></td>
-    </tr>
-    <tr>
-      <td class="tdca">CHAPTER XIX.</td>
-    </tr>
-    <tr>
-      <td class="toc2"><span class="smcap">Miscellaneous Surveyors' and Engineers'
-      Instruments, Appliances, and Accessories</span>:&mdash;Cross
-      Staff&mdash;Mechanics' Levels&mdash;Boning Rods&mdash;Footner's Railway Gauge&mdash;Girth
-      Strap for Timber Measurement&mdash;Girth Tapes&mdash;Timber
-      Marker&mdash;Slashing Knife&mdash;Bill-Hook&mdash;Reconnoitring
-      Glass&mdash;Telescope&mdash;Sun Spectacles&mdash;Whistles&mdash;Pioneer Tools&mdash;Sketch
-      Block Book&mdash;Camera&mdash;Geological
-      Tools&mdash;Wealemefna&mdash;Opisometer&mdash;Boucher's Calculator&mdash;Slide Rules&mdash;Fuller's
-      Calculator&mdash;Engineers' Pocket-Books&mdash;Chronometer&mdash;Outfits</td>
-      <td class="tdrb"><a href="#Page_573">573</a></td>
-    </tr>
-    <tr>
-      <td class="tdl padding-top05 padding-bottom2"><span class="smcap">Index</span></td>
-      <td class="tdr"><a href="#Page_601">601</a></td>
-    </tr>
-  </table></div>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_xvi" id="Page_xvi">[xvi]</a><br /><a name="Page_1" id="Page_1">[1]</a></span></p>
-<p class="xxlarge center padding-top1 padding-bottom06">SURVEYING INSTRUMENTS.</p>
-<div class="fig-center">
-  <img src="images/i_hr.png" width="57" height="8" alt="" />
-</div>
-</div>
-
-<div class="chapter">
-<h2>CHAPTER I.</h2>
-</div>
-<p class="ch">HISTORICAL SKETCH&mdash;CLASSIFICATION OF THE SUBJECT&mdash;PURPOSES
-AND QUALITIES OF INSTRUMENTS&mdash;WORKMANSHIP&mdash;METALS&mdash;ALUMINIUM&mdash;FRAMING&mdash;TOOLS&mdash;AXES
-OF INSTRUMENTS&mdash;SOLDERING&mdash;FINISHING&mdash;BRONZING&mdash;LACQUERING&mdash;GRADUATING&mdash;ENGRAVING&mdash;STYLE&mdash;GLASS-WORK&mdash;WOODWORK&mdash;LUBRICATION&mdash;PRESERVATION
-OF INSTRUMENTS&mdash;PACKING.</p>
-<p>1.&mdash;<span class="large bold">Historical Sketch.</span>&mdash;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.</p>
-<p>2.&mdash;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<span class="pagenum"><a name="Page_2" id="Page_2">[2]</a></span>
-plan of a gold mine of about 1400 <span class="smcap">B.C.</span> The earliest surveying
-instrument of which we have record is the <i>diopter</i> of
-Hero of Alexandria, about 130 <span class="smcap">B.C.</span> This instrument appears
-to have been a wooden cross, with sights to take right
-angles. In the <i>astrolabe</i> of Hipparchus, we have a divided
-quadrant of a circle sighted from the centre. In Tycho
-Brahé's <i>Astronomica Instaurata Mechanica</i>, 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.</p>
-<p>3.&mdash;In Thomas Digges' <i>Pantometrie</i>, 1571, we have
-several instruments described for surveying purposes:&mdash;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&mdash;the origin of the theodolite, a word probably
-derived from <i>theodicæa</i>, 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.</p>
-<p>4.&mdash;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<span class="pagenum"><a name="Page_3" id="Page_3">[3]</a></span>
-on mine surveying, the <i>Geometria Subterranea</i> of Nicolaus
-Voigtel, published in Leipzig, in which we have the <i>hanging
-compass</i>, still much in use on the Continent, described. Beyond
-this, few improvements are recorded upon surveying
-instruments in the seventeenth century.</p>
-<p>5.&mdash;Near the commencement of the eighteenth century
-we have a somewhat important work, published in Paris,
-written by Nicolaus Bion, <i>Constructions des Instruments de
-Mathematique</i>, 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 <i>Gardiner's Practical Surveyor</i>, 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 <i>Geometrical and Graphical Essays,
-Containing a Description of Mathematical Instruments</i>, 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).</p>
-<p>6.&mdash;In the last century no original work appeared on
-the subject till F. W. Simms's treatise on <i>Mathematical
-Instruments</i>, 1834. This small work is limited to descriptions<span class="pagenum"><a name="Page_4" id="Page_4">[4]</a></span>
-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
-<i>Weale's Rudimentary Series</i>. 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.</p>
-<p>7.&mdash;In Germany we have recent works of an altogether
-higher order in <i>Die Instrumente und Werkzeuge der hoheren
-und niederen Messkunst, sowie der geometrichen Zeichnenkunst;
-ihre Theorie, Construction, Gebrauch und Prufung</i>, by C. F.
-Schneitler, 1848; and a work upon the larger instruments,
-<i>Die geometrischen Instrumente</i>, 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 <i>Gli Strumenti a
-Reflessione per Misurare Angoli</i>, 1875. The consideration of
-these instruments is, however, in this work more in reference
-to astronomical and nautical observations than to surveying.</p>
-<p>8.&mdash;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, <i>La Tachéomètre, ou l'Art de lever les
-Plans et de faire les Nivellements</i>, 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<span class="pagenum"><a name="Page_5" id="Page_5">[5]</a></span>
-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.</p>
-<p>9.&mdash;<span class="large bold">Classification.</span>&mdash;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.</p>
-<p><span class="pagenum"><a name="Page_6" id="Page_6">[6]</a></span></p>
-<p>10.&mdash;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 <i>stations</i>,
-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 <i>azimuth</i>.</p>
-<p>11.&mdash;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.</p>
-<p>12.&mdash;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<span class="pagenum"><a name="Page_7" id="Page_7">[7]</a></span>
-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.</p>
-<p>13.&mdash;<span class="large bold">Qualities of Work.</span>&mdash;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&mdash;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 <i>the engineer</i>,
-in a workshop where as many as fifty men are employed.</p>
-<p>14.&mdash;<span class="large bold">Metals.</span>&mdash;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<span class="pagenum"><a name="Page_8" id="Page_8">[8]</a></span>
-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.</p>
-<p>15.&mdash;<span class="large bold">Aluminium</span>, 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:&mdash;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<span class="pagenum"><a name="Page_9" id="Page_9">[9]</a></span>
-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.</p>
-<p>16.&mdash;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&mdash;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.</p>
-<p>17.&mdash;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<span class="pagenum"><a name="Page_10" id="Page_10">[10]</a></span>
-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.</p>
-<p>18.&mdash;<span class="large bold">Workmanship.</span>&mdash;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.</p>
-<p>19.&mdash;<span class="large bold">Framing Work.</span>&mdash;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,<span class="pagenum"><a name="Page_11" id="Page_11">[11]</a></span>
-and mild wrought-iron, about 100 feet per minute is required.
-For turning bell-metal and cast-steel, a very slow speed is
-required&mdash;about 16 feet per minute. The lathe should therefore
-possess means of ensuring these differences by back gear,
-overhead motions or otherwise.</p>
-<p>20.&mdash;<span class="large bold">Tools.</span>&mdash;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&mdash;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. <i>A
-universal shaping machine</i> 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&mdash;only a
-little fine scraping, superfine filing and stoning being required.</p>
-<p id="Art_21">21.&mdash;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<span class="pagenum"><a name="Page_12" id="Page_12">[12]</a></span>
-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.</p>
-<p id="Art_22">22.&mdash;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.</p>
-<p><span class="pagenum"><a name="Page_13" id="Page_13">[13]</a></span></p>
-<p>23.&mdash;<span class="large bold">Soldering.</span>&mdash;Besides the tubes of instruments, all
-parts which are difficult or impossible to be formed advantageously
-in a single casting, are <i>hard soldered</i> 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.</p>
-<p>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.</p>
-<p>24.&mdash;<span class="large bold">Soft Soldering</span>, or what is termed in the trade
-<i>sweating</i>, 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<span class="pagenum"><a name="Page_14" id="Page_14">[14]</a></span>
-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.</p>
-<p>25.&mdash;<span class="large bold">Finishing</span> 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.</p>
-<p>26.&mdash;<span class="large bold">Polishing.</span>&mdash;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.</p>
-<p>27.&mdash;<span class="large bold">Optical Black.</span>&mdash;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.</p>
-<p>28.&mdash;<span class="large bold">Bronzing.</span>&mdash;For the protection of finished metal
-work in surveying instruments the surface is generally <i>bronzed</i>,
-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.<span class="pagenum"><a name="Page_15" id="Page_15">[15]</a></span>
-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.</p>
-<p>29.&mdash;<span class="large bold">Lacquering.</span>&mdash;All parts of instruments intended to
-be left bright, as well as all properly bronzed parts, are
-separately covered with a thin coating of <i>lacquer</i>, the application
-of which is technically termed <i>varnishing</i>. 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.</p>
-<p><span class="pagenum"><a name="Page_16" id="Page_16">[16]</a></span></p>
-<p>30.&mdash;<span class="large bold">Engraving</span> of figures, words, etc., where there is
-much repetition, is best done by the engraving machine&mdash;general
-work by the ordinary skilled engraver.</p>
-<p>The method employed for the graduation of instruments
-will be considered further on in the discussion of instruments
-reading with a vernier scale.</p>
-<p>31.&mdash;<span class="large bold">Style.</span>&mdash;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.</p>
-<p id="Art_32">32.&mdash;<span class="large bold">Glass-Work.</span>&mdash;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<span class="pagenum"><a name="Page_17" id="Page_17">[17]</a></span>
-kinds of glass are usually employed for the object-glasses of
-surveying instruments:&mdash;</p>
-<div class="m5 padding-top1 padding-bottom2">
-<table summary="" class="border border-collapse" width="90%">
-  <tr>
-    <th></th>
-    <th rowspan="2" class="td01">Density.</th>
-    <th colspan="4" class="td01a">Index of Spectrum Lines.</th>
-  </tr>
-  <tr>
-    <td></td>
-    <td class="td01a">C</td>
-    <td class="td01a">D</td>
-    <td class="td01a">F</td>
-    <td class="td01a">G</td>
-  </tr>
-  <tr>
-    <td class="td01ca">Hard Crown</td>
-    <td class="td01ca">2·485</td>
-    <td class="td01ca">1·5146</td>
-    <td class="td01ca">1·5172</td>
-    <td class="td01ca">1·5232</td>
-    <td class="td01ca">1·5280</td>
-  </tr>
-  <tr>
-    <td class="td01c">Dense Flint</td>
-    <td class="td01c">3·660</td>
-    <td class="td01c">1·6175</td>
-    <td class="td01c">1·6224</td>
-    <td class="td01c">1·6348</td>
-    <td class="td01c">1·6453</td>
-  </tr>
-</table>
-</div>
-<p>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.</p>
-<p>33.&mdash;Two <i>pairs</i> 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.<span class="pagenum"><a name="Page_18" id="Page_18">[18]</a></span>
-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.</p>
-<p>34.&mdash;<i>The wash-emery</i> 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.</p>
-<p>35.&mdash;<i>Polishing.</i>&mdash;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.</p>
-<p>36.&mdash;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.</p>
-<p>37.&mdash;It may be well here to note how this may be observed.
-A good test is to throw the shadow of a thin object,<span class="pagenum"><a name="Page_19" id="Page_19">[19]</a></span>
-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.</p>
-<p>38.&mdash;<i>Centring&mdash;Figuring and Testing.</i>&mdash;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 <i>testing</i>, 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&mdash;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.<a name="FNanchor_1_1" id="FNanchor_1_1"></a><a href="#Footnote_1_1" class="fnanchor">[1]</a></p>
-<p>39.&mdash;<span class="large bold">The Woodwork of the Stands</span> of instruments
-made in this country is generally of straight-grained Honduras
-mahogany. For occasional work the mahogany is better if
-<span class="pagenum"><a name="Page_20" id="Page_20">[20]</a></span>
-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.</p>
-<p>40.&mdash;<span class="large bold">Lubrication of Instruments.</span>&mdash;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&mdash;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.</p>
-<p>41.&mdash;<span class="large bold">Preservation of Instruments.</span>&mdash;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<span class="pagenum"><a name="Page_21" id="Page_21">[21]</a></span>
-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.</p>
-<p id="Art_42">42.&mdash;<span class="large bold">Packing of Instruments.</span>&mdash;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<span class="pagenum"><a name="Page_22" id="Page_22">[22]</a></span>
-may afterwards be cut away more easily with the penknife
-than wood.</p>
-<p>43.&mdash;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,&mdash;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 <i>Topographical
-Instructions</i> 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.</p>
-<p><span class="pagenum"><a name="Page_23" id="Page_23">[23]</a></span></p>
-<p>44.&mdash;<span class="large bold">Leather Over Cases.</span>&mdash;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.</p>
-<p>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.</p>
-<p><span class="large bold">Waterproof Covers.</span>&mdash;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.</p>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_24" id="Page_24">[24]</a></span></p>
-<h2>CHAPTER II.</h2>
-</div>
-<p class="ch">THE TELESCOPE AS A PART OF A SURVEYING INSTRUMENT&mdash;GENERAL
-DESCRIPTION&mdash;QUALITIES&mdash;OPTICAL PRINCIPLES&mdash;REFRACTION
-OF GLASS&mdash;LIMIT OF REFRACTION&mdash;REFLECTION&mdash;PRISMS&mdash;LENSES,
-CONVEX AND CONCAVE&mdash;ABERRATION&mdash;FORMATION
-OF IMAGES&mdash;DISPERSION&mdash;ACHROMATISM&mdash;CURVATURE
-OF LENSES&mdash;TELESCOPES&mdash;EYE-PIECES&mdash;POWERS&mdash;DYNAMETER&mdash;CONSTRUCTION
-OF THE TELESCOPE,
-DIAPHRAGM&mdash;WEBS&mdash;LINES&mdash;POINTS&mdash;PARALLAX&mdash;EXAMINATION
-AND ADJUSTMENT.</p>
-<p>45.&mdash;<span class="large bold">General Description of the Telescope.</span>&mdash;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.</p>
-<p>46.&mdash;The qualities desirable in a surveying telescope are,
-that sufficient rays of light may be collected from the object<span class="pagenum"><a name="Page_25" id="Page_25">[25]</a></span>
-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.</p>
-<p>By the necessary optical arrangement of the telescope,
-which will be further described, the object observed is
-generally <i>inverted</i>. This inversion of the <i>image</i> 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.</p>
-<p>47.&mdash;<span class="large bold">Optical Principles involved in the Telescope.</span>&mdash;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.</p>
-<p>48.&mdash;<span class="large bold">Refraction of Glass.</span>&mdash;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, <i>refracted</i>, to a certain angle at the
-surface of contact of the air and glass. The ray of light
-entering the glass is termed the <i>incident ray</i>, that proceeding
-from it the <i>emergent ray</i>.</p>
-<p>49.&mdash;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,<span class="pagenum"><a name="Page_26" id="Page_26">[26]</a></span>
-or <i>dispersed</i>, 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 <i>monochromatic</i> 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.</p>
-<p>50.&mdash;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
-<i>plane containing the incident ray, and the perpendicular to
-the surface separating the two media</i>. Every medium refracts
-monochromatic light equally according to the following law
-for any angle of refraction:&mdash;</p>
-<p><i>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.</i></p>
-<p>51.&mdash;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).</p>
-<p><i>PP′</i>, a line perpendicular to the surface of the plane
-of the medium (glass) with air above it, a ray of light would
-pass directly <i>P</i> to <i>P′</i> through the glass surface <i>SS′</i> without
-refraction, and so for all perpendicular incidences or emergences.
-By this perpendicular line <i>PP′</i>, termed the <i>normal</i>,
-all refractions are measured. The incident ray <i>I</i> to <i>C</i> is<span class="pagenum"><a name="Page_27" id="Page_27">[27]</a></span>
-refracted to <i>R</i>. Then if we call the angle <i>ICP</i> <i>I</i>, and the
-angle <i>RCP′</i> <i>R</i>, it is found by experiment that the perpendicular
-from <i>I</i> on <i>PP′</i> (or sin <i>I</i>) bears a certain proportion
-to the perpendicular from <i>R</i> on <i>PP′</i> (or sin <i>R</i>) according
-to the density of the glass. This proportion is generally
-expressed by the formula&mdash;sin <i>I</i> = µ sin <i>R</i>. Another incident
-ray <i>I′</i> to <i>C</i> would be refracted to <i>R′</i>, and using similar
-notation to the above we have sin <i>I′</i> = µ sin <i>R′</i>, and from
-this it follows that (sin <i>I</i>)/(sin <i>R</i>) = (sin <i>I′</i>)/(sin <i>R′</i>) = µ,
-which is called the <i>index of refraction</i>. Thus, if in a certain glass
-the sine of I measure 3 equal parts on any scale of length, and the
-sine <i>R</i> 2 parts on the same scale, the <i>index of refraction</i> of this
-glass would be 3 divided by 2 or 1·5.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i027">
-  <img class="w100" src="images/i_027.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 1.&mdash;<i>Diagram of Refraction and Reflection.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_027a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>If the above process be reversed, and the ray of light <i>R</i>
-be refracted on passing <i>from</i> the glass to the air, it will be
-projected to <i>I</i> in the emergent ray, and follow the same law
-as that given above.</p>
-<p>52.&mdash;<span class="large bold">Limit of Refraction&mdash;Reflection.</span>&mdash;The sines to
-the angles <i>ICP</i> and <i>I′CP′</i> 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 <i>RCP′</i> and <i>R′CP′</i> of the<span class="pagenum"><a name="Page_28" id="Page_28">[28]</a></span>
-rays of incidence thrown upward upon the surface <i>SS′</i>, 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>I</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&mdash;an impossibility.
-The refraction, if possible, would carry the ray into the
-substance of the glass. This is therefore called the <i>critical
-angle</i> or <i>angle of total reflection</i>. 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 <i>reflected</i>. Thus the ray <i>r</i> cannot be refracted in the
-proportion according to the rule given for sine <i>I</i> to sine <i>R</i>, as
-this would exceed the greatest sine, that is <i>SC</i> the radius, this
-ray will therefore be <i>reflected</i> at the surface from the point <i>C</i>,
-and pass in the direction <i>r′</i>. This property of refraction,
-continuing, as it were, into reflection, is made use of in
-many instruments.</p>
-<p>53.&mdash;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 <i>P</i> to <i>P′</i> a
-certain refraction I to R, and a greater refraction <i>I′</i> to <i>R′</i>, the
-refraction constantly increasing with the angle of incidence.</p>
-<p>54.&mdash;<i>The Reflection of Light</i> follows a very simple law,
-viz.:&mdash;<i>The angle of reflection of a ray of light from a reflecting
-surface is equal and opposite to the angle of incidence upon it.</i>
-Thus, in Fig. 2, let a ray of light <i>IA</i> fall upon the reflecting
-surface <i>SS′</i> at 30° of inclination to this surface, then this
-ray will be reflected from <i>A</i> to <i>R</i> at the angle <i>RAS′</i>, which
-is also 30°. If an object be at <i>O</i>, and the eye at <i>I</i>, then the
-object will appear as though it were at <i>O′</i>, as the eye only
-recognises the object in the direction from which it actually<span class="pagenum"><a name="Page_29" id="Page_29">[29]</a></span>
-receives the light. The apparent angle <i>S′AO′</i> is equal to
-<i>IAS</i>, 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i029">
-  <img class="w100" src="images/i_029.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 2.&mdash;<i>Diagram reflections from a plane.</i></p>
-    <p class="caption float-right">Fig. 3.&mdash;<i>Reflection from a prism.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_029a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p id="Art_55">55.&mdash;<i>Prismatic Reflection.</i> The same law as given above
-applies to internal reflection from glass. Let Fig. 3 represent
-the section of a prism <i>ff′</i>, 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>i</i> will therefore pass
-perpendicularly through the plane <i>f</i> 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 <i>r</i>.
-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.</p>
-<p>56.&mdash;<i>Prismatic Reflection</i>, 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.</p>
-<p>57.&mdash;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<span class="pagenum"><a name="Page_30" id="Page_30">[30]</a></span>
-perpendicular to the plane. In Fig. 4 <i>NA</i> 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 <i>IA</i> to <i>R</i> would be in the angle
-<i>IAR</i> 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,&mdash;that is, the path <i>I</i> to <i>R</i> by reflection
-is shorter in the lines <i>IAR</i>, placed at equal angles to the
-normal, than it would be by any other possible path. As,
-for instance, it is shorter than <i>IaR</i>, shown by dotted
-lines.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe25" id="i030">
-  <img class="w100" src="images/i_030.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 4.&mdash;<i>Measurement of angle of reflection in optics.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_030a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i030b">
-  <img class="w100" src="images/i_030b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 5.&mdash;<i>Diagram illustrating the principle of the lens.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_030ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p id="Art_58">58.&mdash;<i>Passage of a Ray of Light through a Prism or a
-Lens&mdash;Convex Refraction.</i> 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 <i>a″a‴</i> be the base of an equilateral prism, which<span class="pagenum"><a name="Page_31" id="Page_31">[31]</a></span>
-base may also represent the axis of a lens linear or parallel
-with the direction from the centre of the eye to <i>O</i>. Now, if
-a ray of light pass from a small luminous object at <i>O</i> in the
-path <i>a′</i> 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 <i>a″a‴</i>, then
-the same ray will pass through the prism to equal distance
-from the centre of the prism,&mdash;that is, to the position of the
-eye shown by the ray continuing in the path <i>a</i>, 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 <i>aa′</i>, where it is shown passing through the
-prism, any ray of light from <i>O</i>, 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 <i>O</i>. If we take a prism of
-the same kind of glass, but of less angle, whose base is <i>b″b‴</i>,
-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 <i>Ob′</i> would pass through
-horizontally as before, and emerge from the prism in the
-path <i>b</i>, 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
-<i>c″c‴</i> and pass through the prism at a lower position, the
-refraction would be proportionally less, and therefore reach
-the eye at the same point.</p>
-<p>59.&mdash;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 <i>a″a‴</i>, <i>b″b‴</i>, and
-<i>c″c‴</i>, where the angles of contact of <i>O</i>, <i>a</i>, <i>b</i>, or <i>c</i> 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<span class="pagenum"><a name="Page_32" id="Page_32">[32]</a></span>
-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.</p>
-<p>60.&mdash;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 <i>O</i> in
-the path <i>b′</i>, passing through the lens or prism and emerging
-in the path <i>b</i>, is recognised by the eye as the ray <i>b</i> only. So
-that the point of light <i>O</i> appears visually as proceeding from
-the direction <i>bs</i>, and this convergence or expansion of the
-point <i>O</i>, with its coincidence from the opposite side of the
-lens, produces the effect of magnification of the object
-represented by <i>O</i>.</p>
-<p>61.&mdash;<span class="large bold">Concave Refraction.</span>&mdash;In Fig. 6 a convex lens
-is shown in which the parallel rays <i>L</i> are drawn to a focus
-at <i>F</i> upon the principles just demonstrated. If the lens
-were made <i>concave</i>, as shown in section Fig. 7, by the same
-principles of refraction, it is evident that the rays would
-<i>diverge</i>, 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 <i>corrected</i>. A convex lens has a <i>focus</i> where the<span class="pagenum"><a name="Page_33" id="Page_33">[33]</a></span>
-rays converge. A concave lens is said to have a <i>negative
-focus</i> equal to the focus of the convex lens, that will correct
-it, or make it equal, as regards refraction, to plane parallel
-glass.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i033">
-  <img class="w100" src="images/i_033.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 6.&mdash;<i>Diagram convex lens.</i></p>
-    <p class="caption float-right">Fig. 7.&mdash;<i>Diagram concave lens.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_033a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>62.&mdash;<i>Spherical Aberration.</i>&mdash;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 <i>figuring</i>, 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.</p>
-<p>63.&mdash;<i>The Formation of Images by Refraction from a
-Convex Lens.</i>&mdash;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,&mdash;that
-is, we produce an <i>image</i> 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 <i>solar focus</i> of the<span class="pagenum"><a name="Page_34" id="Page_34">[34]</a></span>
-lens,&mdash;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 <i>solar
-focus</i> is less than that subtended by any object on the
-earth.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i034">
-  <img class="w100" src="images/i_034.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 8.&mdash;<i>Diagram of the convergence of rays of light.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_034a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>64.&mdash;In the diagram, Fig. 8, a candle-flame at <i>acb</i> forms
-its focus at <i>a‴c‴b‴</i>, where all rays converge to form an
-image in the following manner:&mdash;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 <i>inverted position</i>.</p>
-<p>65.&mdash;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 <i>clear</i> lines <i>aa′</i> and <i>aa″</i> from the point of the
-flame would refract to the lower part of the image <i>a‴</i>. The
-<i>dotted</i> lines <i>bb′</i> would proceed to the upper part of the image,
-as shown by the continuation of the <i>dotted</i> lines to <i>b‴</i>, whereas
-the central <i>dash</i> lines <i>c′c″</i> would form their images in the
-centre following the dash lines to <i>c‴</i>, and thus, from the
-number of luminous points, the whole image of the candle<span class="pagenum"><a name="Page_35" id="Page_35">[35]</a></span>
-would be produced at the foci <i>b‴c‴a‴</i> in an inverted
-position.</p>
-<p>66.&mdash;<i>Dispersion of Light.</i>&mdash;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 <i>dispersion</i> 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:&mdash;</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i035">
-  <img class="w100" src="images/i_035.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 9.&mdash;<i>Diagram showing chromatism of light by the prism.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_035a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>67.&mdash;In Fig. 9 let <i>P</i> represent the section of a prism of
-glass, covered except at the narrow opening <i>a</i>. Let a strong
-light, as shown, be covered, except from a narrow slit, then
-the ray from the light, refracted from <i>a</i> towards <i>a′</i> in the
-prism, will be dispersed or split up at <i>a</i> into the colours of the
-rainbow, shading from blue, green, and yellow, to red, within
-the prism. Upon emergent refraction at <i>a′</i> 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 <i>BGR</i> by a prismatic or
-<i>chromatic spectrum</i>, as it is termed, shading off from blue to
-green, yellow, red.</p>
-<p id="Art_68">68.&mdash;<i>Achromatism of the Prism in the same Quality of
-Glass.</i>&mdash;Taking the prism, Fig. 10, <i>C</i> as before, and applying
-a second exactly similar prism <i>C′</i> reversed upon the face of
-the first&mdash;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 <i>to a point</i>, where it will issue a white ray at the<span class="pagenum"><a name="Page_36" id="Page_36">[36]</a></span>
-point <i>a″</i>, as it entered at the point <i>a</i>; 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i036">
-  <img class="w100" src="images/i_036.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 10.&mdash;<i>Diagram perfect achromatism.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_036a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>69.&mdash;<span class="large bold">The Achromatic Lens.</span>&mdash;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, <a href="#Art_32">art.
-32</a>, 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.</p>
-<p>70.&mdash;In fig. 11 let <i>C</i> be a prism of crown glass giving over<span class="pagenum"><a name="Page_37" id="Page_37">[37]</a></span>
-double the amount of refraction to a prism of flint glass <i>F</i>,
-but only of total dispersion equal to the thicker crown glass.
-The compound white ray of light <i>a</i> 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 <i>a′</i>, 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i037a">
-  <img class="w100" src="images/i_037a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 11.&mdash;<i>Showing principles of achromatism.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_037aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>71.&mdash;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 <a href="#i030b">Fig. 5</a>; but for the sake of clearness it may be again shown
-diagrammatically in Fig. 12 for an actual objective, wherein the
-parallel rays <i>ab</i>, proceeding from a distant object or star, are
-shown refracted to <i>a′b′</i>, and coming to a focus at <i>F</i>, although
-dispersed at the meeting surfaces of the two glasses, as shown
-diagrammatically, by the internal cone of rays.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i037b">
-  <img class="w100" src="images/i_037b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 12.&mdash;<i>Showing achromatic objective.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_037ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>72.&mdash;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<span class="pagenum"><a name="Page_38" id="Page_38">[38]</a></span>
-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 <a href="#i036">Fig. 10</a>. 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 <i>meeting planes</i> between the lenses, leaving in all
-cases a certain amount of residual colour, blue or red, uncorrected,
-by making the glass <i>under-</i> or <i>over-corrected</i>, 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 <i>over-correct</i>,
-German and French glasses are more often <i>under-corrected</i>.</p>
-<p>73.&mdash;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 <i>the
-ratio of dispersive powers</i>, 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 <i>D</i>,
-and three lines due to hydrogen, marked <i>C</i>, <i>F</i> and <i>G</i>, are
-commonly taken for reference of dispersion. Achromatism is
-generally considered duly corrected when the lines <i>C</i> and <i>G</i>
-are united. The middle of the spectrum between these lines
-is about <i>E</i>; 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.</p>
-<p>74.&mdash;<i>Curvatures in the Achromatic Lens.</i>&mdash;A large amount<span class="pagenum"><a name="Page_39" id="Page_39">[39]</a></span>
-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 <i>Phil. Trans.</i>, and in the works of Herschel, Barlow,
-Coddington, Robinson, and Stokes, wherein what is known
-theoretically of the subject is fully investigated and discussed.</p>
-<p>75.&mdash;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 <i>f</i>, the total focus of the finished objective, for first
-working before trial:&mdash;</p>
-
-<div class="padding-top1 padding-bottom05">
-<div class="m25" style="display: inline-block; vertical-align: middle; width: 40%; border-right: 1px solid black;">
-<p class="noindent center padding-right1">
-1st.—Outside surface,
-<span class="division padding-top0 padding-bottom05">
-  <span class="numerator"><i>f</i></span>
-  <span class="denominator">2</span>
-</span>
-convex,
-</p>
-<p class="noindent center padding-right1">
-2nd.—Inside &nbsp;&nbsp;&nbsp;&nbsp;"&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-<span class="division padding-top0 padding-bottom05">
-  <span class="numerator"><i>f</i></span>
-  <span class="denominator">3</span>
-</span>
-convex,
-</p>
-</div>
-<p style="display: inline-block; margin-left: -10em;">crown.</p>
-</div>
-
-<div class="padding-top05 padding-bottom1">
-<div class="m25" style="display: inline-block; vertical-align: middle; width: 40%; border-right: 1px solid black;">
-<p class="noindent center padding-right1">
-3rd.—Outside &nbsp;&nbsp;&nbsp;&nbsp;"&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-<span class="division padding-top0 padding-bottom05">
-  <span class="numerator"><i>f</i></span>
-  <span class="denominator">3</span>
-</span>
-concave,
-</p>
-<p class="noindent center padding-right1">
-4th.—Inside &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-<span class="padding-top0 padding-bottom05">4<i>f</i></span>
-convex,
-</p>
-</div>
-<p style="display: inline-block; margin-left: -10em;">flint.</p>
-</div>
-
-
-<p>76.&mdash;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 = (<i>f</i>/2·5). In
-all cases true convergence of the white ray is only obtained by
-correction of the outer and inner surfaces, or by <i>figuring</i>, 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<span class="pagenum"><a name="Page_40" id="Page_40">[40]</a></span>
-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.</p>
-<p>77.&mdash;<i>Optical Arrangements of the Telescope.</i>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i040">
-  <img class="w100" src="images/i_040.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 13.&mdash;<i>Kepler's telescope.</i></p>
-    <p class="caption float-right">Fig. 14.&mdash;<i>Galileo's telescope.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_040a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p class="clear">78.&mdash;<i>Galileo's Telescope</i>, Fig. 14.&mdash;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 <i>aa′</i> in Figs. 13, 14 are termed the axis of
-the telescope.</p>
-<p>79.&mdash;<i>Optical Arrangement of the Huygenian Telescope.</i>&mdash;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&mdash;that is, its exact image&mdash;is projected upon a plane
-termed the <i>diaphragm</i>, Fig. 15, <i>SS′</i> upon which a visible<span class="pagenum"><a name="Page_41" id="Page_41">[41]</a></span>
-object or index is placed, the position of which is picked up
-by a secondary telescopic arrangement, or <i>eye-piece</i> as it is
-technically termed.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i041">
-  <img class="w100" src="images/i_041.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 15.&mdash;<i>Diagram of arrangement of lenses.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_041a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>80.&mdash;The arrangement of lenses in a surveying telescope
-is shown in the illustration above, where <i>OG</i> is the <i>object-glass</i>
-or <i>objective</i>, <i>E</i> the <i>eye-glass</i>, <i>F</i> the <i>field-glass</i>. The two lenses
-<i>E</i> and <i>F</i>, in their mountings, form the <i>eye-piece</i> <i>EP</i>. The
-dotted line <i>a</i> is the <i>axis</i> of the telescope, <i>SS′</i> is the <i>focal plane</i>
-of the object-glass, where a metal disc is placed with an
-opening in its centre&mdash;this is termed the diaphragm or technically,
-the <i>index-stop</i>. Across the opening in the disc, spider's
-webs or other fine visible objects are placed, to be described
-further on.</p>
-<p>81.&mdash;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 <i>SS′</i>. 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 <i>SS′</i> of an object placed at about
-twenty feet from it.</p>
-<p id="Art_82">82.&mdash;<span class="large bold">The Ramsden Eye-piece</span>, 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<span class="pagenum"><a name="Page_42" id="Page_42">[42]</a></span>
-of either glass, and placed so that the diaphragm is one-fourth
-this focal length from the field-glass.</p>
-<p>83.&mdash;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&mdash;a
-flat field of view, requiring no change of position to see the
-centre and border of the field with equal distinctness.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i042">
-  <img class="w100" src="images/i_042.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 16.&mdash;<i>Ramsden eye-piece.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_042a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>84.&mdash;<i>The Field of View</i> 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 <i>aa</i>
-and <i>a′a′</i> for the Ramsden eye-piece in Fig. 16. This
-eye-piece is sometimes called an <i>inverting eye-piece</i>. It is not
-really so: the object-glass <i>inverts</i> 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.</p>
-<p><span class="pagenum"><a name="Page_43" id="Page_43">[43]</a></span></p>
-<p>85.&mdash;<i>The Focal Length</i> 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:&mdash;</p>
-
-<div class="m25">
-<p class="noindent center padding-right1">
-<span class="division padding-bottom05">
-  <span class="numerator">1·5 <span class="large">×</span> 1·5</span>
-  <span class="denominator">3 - 1</span>
-</span>
-= 1·125 inches.</p>
-</div>
-
-<p>86.&mdash;<i>The Magnifying Power of the Telescope.</i>&mdash;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,</p>
-
-<div class="m20">
-<p class="noindent center padding-right1">
-<span class="division padding-top0 padding-bottom05">
-  <span class="numerator">14</span>
-  <span class="denominator">1·125</span>
-</span>
-= 12·444, or 12&frac12; nearly,</p>
-</div>
-
-<p class="noindent">a very general lower power eye-piece with telescopes of
-this focus.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i043">
-  <img class="w100" src="images/i_043.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 17.&mdash;<i>Dynameter.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_043a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p id="Art_87">87.&mdash;<span class="large bold">Dynameter.</span>&mdash;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 <i>a</i>.
-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<span class="pagenum"><a name="Page_44" id="Page_44">[44]</a></span>
-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 <i>a</i>, 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.</p>
-<p>88.&mdash;<span class="large bold">The Erecting Eye-piece</span>, 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i044">
-  <img class="w100" src="images/i_044.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 18.&mdash;<i>Optical arrangement of erecting eye-piece.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_044a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>89.&mdash;<i>A object lens, B amplifying lens, C field lens, D eye
-lens.</i> Stops are placed at <i>d</i> and <i>d′</i> to cut out extreme rays.
-The image is formed by the objective at <i>O</i>, 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 <a href="#Art_68">art. 68</a> and shown <a href="#i036">Fig. 10</a>, 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<span class="pagenum"><a name="Page_45" id="Page_45">[45]</a></span>
-telescope with it, for equally distinct vision to that obtained
-by using the Ramsden eye-piece previously described, would
-require a larger objective.</p>
-<p>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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i045">
-  <img class="w100" src="images/i_045.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 19.&mdash;<i>Diagonal eye-piece, full size; S G sun-glass.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_045a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-<p>90.&mdash;<span class="large bold">The Diagonal Eye-piece</span>, Fig. 19, is used upon
-transit instruments, theodolites, and occasionally upon mining-dials.
-It permits the telescope to be used by the observer<span class="pagenum"><a name="Page_46" id="Page_46">[46]</a></span>
-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 <i>erecting</i> 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. <i>A</i> object lens, <i>D</i> eye lens, adjustable for
-distance from the reflector <i>R</i>, <i>S</i> outer casing which permits
-adjustment for focusing, <i>SG</i> sun glass, the diaphragm being
-in front of <i>A</i>.</p>
-<p>91.&mdash;When a rectangular prism is used for the reflector, it
-is worked with one plane 45°, as previously discussed, <a href="#i029">art. 55,
-Fig. 3</a>. 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.</p>
-<p>92.&mdash;<span class="large bold">Reflecting Eye-piece</span> is used to observe small stars,
-as for instance the circumpolar stars in the southern hemisphere,<span class="pagenum"><a name="Page_47" id="Page_47">[47]</a></span>
-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 <i>L</i> by reflection
-of the surface of <i>R</i> sufficient for front illumination. The
-amount of light required is regulated by the distance of the
-lamp from <i>L</i>. This eye-piece is made to fit into the diagonal
-eye-piece casing, as <i>S</i> <a href="#i045">Fig. 19</a>, <i>E</i> Fig. 20 being the position of
-the eye, <i>F</i> field-lens.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i047">
-  <img class="w100" src="images/i_047.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 20.&mdash;<i>Reflector in eye-piece to illuminate the front of diaphragm.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_047a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>93.&mdash;<span class="large bold">Sun-glass.</span>&mdash;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, <a href="#i045">Fig. 19</a>, <i>SG</i>. It needs no description,
-but is necessary to be mentioned to complete the <i>optical</i>
-arrangements of a telescope, as it is sometimes used for
-surveying purposes.</p>
-<p id="Art_94">94.&mdash;<span class="large bold">The Body of a Telescope</span> that forms part of a
-surveying instrument is constructed of a pair of <i>triblet</i> drawn
-tubes, Fig. 21, <i>TT′ T′</i>. These tubes should be truly cylindrical
-and straight, so as to fit smoothly together, the one<span class="pagenum"><a name="Page_48" id="Page_48">[48]</a></span>
-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 <i>R</i> is generally enlarged
-so as to take the cell in which the objective <i>O</i> 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<span class="pagenum"><a name="Page_49" id="Page_49">[49]</a></span>
-case the glasses of the objective cannot be separated for
-cleaning.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i048a">
-  <img class="w100" src="images/i_048a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 21.&mdash;<i>Body of surveying telescope.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_048aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe28_125" id="i048b">
-  <img class="w100" src="images/i_048b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 22.&mdash;<i>Section Fig. 21, A to B.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_048ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>95.&mdash;<span class="large bold">Stops.</span>&mdash;Within the inner tube two or more thin
-metal rings, termed technically <i>stops</i> <i>SS</i> and <i>S′S′</i>, 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.</p>
-<p id="Art_96">96.&mdash;The inner or the outer tube of the body of the telescope
-slides towards or from the objective for focussing by
-means of a <i>rack</i> <i>R″</i> and <i>pinion</i> <i>P</i>. The rack is soldered to the
-inner tube, and the pinion fitted in a <i>cock-piece</i>, as shown Fig.
-22 <i>C</i>, on the outer tube. The pinion is moved by a large
-milled head <i>M</i>. 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.</p>
-<p>97.&mdash;The outward part of the object end of the telescope
-is generally turned to fit the interior of a separate short tube,
-shown at <i>R</i>, 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 <i>ray-shade</i> or sometimes a <i>dew-cap</i>. 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,
-<i>R′</i>, 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 <i>EP</i> before described, <a href="#Art_82">art. 82</a>, Fig. 16, is placed
-in a tube constructed upon the end of the telescope, in which<span class="pagenum"><a name="Page_50" id="Page_50">[50]</a></span>
-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.</p>
-<p>98.&mdash;<i>Mechanical Adjustment of the Eye-piece.</i>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i050">
-  <img class="w100" src="images/i_050.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 23.&mdash;<i>Elevation of diaphragm.</i></p>
-    <p class="caption float-right">Fig. 24.&mdash;<i>Section of diaphragm.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_050a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p id="Art_99" class="clear">99.&mdash;<span class="large bold">The Diaphragm of the Telescope</span> 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.</p>
-<p><span class="pagenum"><a name="Page_51" id="Page_51">[51]</a></span></p>
-<p>100.&mdash;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 <i>countersink</i>,
-which leaves the hole much larger at its off surface, Fig. 24 <i>P</i>.
-The disc is held in its place and adjusted by four capstan-headed
-screws, termed <i>collimating screws</i>, two of which are
-shown in section as <i>CC′</i>, the screws being tapped into
-the rim of the diaphragm frame <i>P</i>. 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, <i>TT′</i>, and adjusts to the focus of the webs.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i051">
-  <img class="w100" src="images/i_051.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 25.&mdash;<i>Webs wound off for use.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_051a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>101.&mdash;<span class="large bold">Webs.</span>&mdash;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.</p>
-<p>102.&mdash;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<span class="pagenum"><a name="Page_52" id="Page_52">[52]</a></span>
-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.</p>
-<p>103.&mdash;<i>To Fix the Webs</i>, 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&mdash;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.</p>
-<p>104.&mdash;<span class="large bold">Platinum Wires</span> 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.<span class="pagenum"><a name="Page_53" id="Page_53">[53]</a></span>
-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.</p>
-<p>105.&mdash;<span class="large bold">Lines Ruled upon Glass.</span>&mdash;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.</p>
-<p>106.&mdash;<span class="large bold">Points.</span>&mdash;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<span class="pagenum"><a name="Page_54" id="Page_54">[54]</a></span>
-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.</p>
-<p id="Art_107">107.&mdash;<span class="large bold">Position of the Diaphragm in the Telescope.</span>&mdash;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 <i>collimation</i>. 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.</p>
-<p id="Art_108">108.&mdash;<i>Adjustment of the Eye-piece to the Webs</i> 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<span class="pagenum"><a name="Page_55" id="Page_55">[55]</a></span>
-front of the object-glass to obtain a soft reflection from the sky.
-This method is always employed by some observers.</p>
-<p id="Art_109">109.&mdash;<i>Adjustment to Focus of the Objective.</i>&mdash;<i>Parallax.</i>&mdash;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 <i>observation for parallax</i>,
-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.</p>
-<p>110.&mdash;<span class="large bold">Collimation</span> 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, <a href="#i050">Fig. 24</a>, <i>CC′</i>, in two directions at right
-angles to each other. Where the telescope is placed in Y's or<span class="pagenum"><a name="Page_56" id="Page_56">[56]</a></span>
-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
-<i>collimated</i>. 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.</p>
-<p>111.&mdash;<i>The Qualities of a Telescope</i> 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.</p>
-<p>112.&mdash;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<span class="pagenum"><a name="Page_57" id="Page_57">[57]</a></span>
-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.</p>
-<p>113.&mdash;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.</p>
-<p>114.&mdash;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.</p>
-<p>115.&mdash;Whether the full aperture of a telescope is used may
-be discovered by employing a second eye-piece&mdash;outside the
-regular eye-piece that is placed in the telescope&mdash;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, <a href="#Art_87">art. 87</a>. With the ordinary surveyor's level, two<span class="pagenum"><a name="Page_58" id="Page_58">[58]</a></span>
-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.</p>
-<p>The discussion of the principle of the anallatic telescope,
-used only with the tacheometer, is deferred to another chapter,
-wherein subtense instruments are described.</p>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_59" id="Page_59">[59]</a></span></p>
-<h2>CHAPTER III.</h2>
-</div>
-<p class="ch">THE MAGNETIC COMPASS AS A PART OF A SURVEYING INSTRUMENT
-OR SEPARATELY&mdash;BROAD AND EDGE-BAR NEEDLES&mdash;MANUFACTURE
-OF THE NEEDLE&mdash;MAGNETISATION&mdash;SUSPENSION&mdash;DIP
-AND ADJUSTMENT&mdash;LIFTING&mdash;INCLINATION&mdash;DECLINATION&mdash;VARIATION&mdash;CORRECTION&mdash;COMPASS-BOXES&mdash;DESCRIPTION
-OF COMPASSES&mdash;RING COMPASSES&mdash;TROUGH
-COMPASSES&mdash;PRISMATIC COMPASSES&mdash;STAND&mdash;SURVEYING
-WITH COMPASS&mdash;POCKET COMPASSES.</p>
-<p>116.&mdash;<span class="large bold">The Magnetic Needle</span>, 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&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i059a">
-  <img class="w100" src="images/i_059a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 26.&mdash;<i>Broad needle.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_059aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i059b">
-  <img class="w100" src="images/i_059b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 27.&mdash;<i>Edge-bar needle.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_059ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>The magnetism which gives directive force to the needle
-has been found by experiment to reside in every separate part<span class="pagenum"><a name="Page_60" id="Page_60">[60]</a></span>
-of the magnet, that is, it is assumed to be a <i>molecular</i> 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&ndash;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.</p>
-<p>117.&mdash;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 <i>broad needle</i>, 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 <i>edge-bar</i> 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.</p>
-<p>118.&mdash;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 <i>split</i> 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<span class="pagenum"><a name="Page_61" id="Page_61">[61]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i061">
-  <img class="w100" src="images/i_061.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 28.&mdash;<i>Author's plan of needle reading.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_061a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>119.&mdash;<i>In the Manufacture of the Needle</i> 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&mdash;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, <i>spring temper</i>. 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.</p>
-<p>120.&mdash;<i>Magnetisation of the Needle</i> 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&mdash;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.</p>
-<p><span class="pagenum"><a name="Page_62" id="Page_62">[62]</a></span></p>
-<p>121.&mdash;<i>Method of Magnetisation by Single-touch.</i>&mdash;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.</p>
-<p>122.&mdash;<i>Method with both Poles.</i>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i062">
-  <img class="w100" src="images/i_062.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 29.&mdash;<i>Divided-touch magnetisation.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_062a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>123.&mdash;<i>Method of Divided-touch</i> 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<span class="pagenum"><a name="Page_63" id="Page_63">[63]</a></span>
-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.</p>
-<p>124.&mdash;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.</p>
-<p>125.&mdash;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.</p>
-<p>126.&mdash;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
-<i>consequent points</i>. 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<span class="pagenum"><a name="Page_64" id="Page_64">[64]</a></span>
-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.</p>
-<p>127.&mdash;<i>Mounting of the Needle.</i>&mdash;The needle for a surveying
-instrument has a female centre upon which it is suspended.
-The centre, termed technically <i>cap</i>, 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 <i>off-colour</i> 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.</p>
-<p>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.</p>
-<p>128.&mdash;<i>Correction of Errors.</i>&mdash;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<span class="pagenum"><a name="Page_65" id="Page_65">[65]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i065">
-  <img class="w100" src="images/i_065.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 30.&mdash;<i>Section of mounted needle.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_065a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>129.&mdash;<i>Lifting the Needle.</i>&mdash;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 <i>B</i> the needle is shown lifted. On the right-hand side
-<i>A</i> the needle is shown at its position for use, floating just
-slightly above the divided circle <i>D</i>. The pressure of the
-milled-head screw <i>C</i> 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 <i>C</i> 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<span class="pagenum"><a name="Page_66" id="Page_66">[66]</a></span>
-what is technically termed a <i>kidney-piece</i>, 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.</p>
-<p id="Art_130">130.&mdash;<span class="large bold">The Inclination or Dip of the Needle</span> is the
-position a needle balanced level upon a free centre <i>before</i> magnetisation
-takes in the vertical plane <i>after</i> 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 <i>nil</i> 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&mdash;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 <i>B</i>. 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.</p>
-<p>131.&mdash;To get at the needle for suppression of dip when it
-is placed in the compass-box, it is necessary to raise the spring<span class="pagenum"><a name="Page_67" id="Page_67">[67]</a></span>
-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.</p>
-<p id="Art_132">132.&mdash;<span class="large bold">The Declination of the Needle</span>, 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.<a name="FNanchor_2_2" id="FNanchor_2_2"></a><a href="#Footnote_2_2" class="fnanchor">[2]</a></p>
-<p>133.&mdash;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,
-<span class="pagenum"><a name="Page_68" id="Page_68">[68]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i068">
-  <img class="w100" src="images/i_068.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 31.&mdash;<i>Magnetic and Greenwich time chart for Great Britain, 1914.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_068a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>134.&mdash;<span class="large bold">The Magnetic Variation of Declination in
-Time</span>, 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<span class="pagenum"><a name="Page_69" id="Page_69">[69]</a></span>
-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:&mdash;</p>
-<div class="m5 padding-top1 padding-bottom1">
-<table summary="" width="90%" class="border-collapse">
-  <tr>
-    <td class="tdc">Year</td>
-    <td class="tdc">1580,</td>
-    <td class="tdc">Dec.</td>
-    <td class="tdc">11° 36′ E.</td>
-    <td class="tdcbl">Year</td>
-    <td class="tdc">1860,</td>
-    <td class="tdc">Dec.</td>
-    <td class="tdc">20° 40′ W.</td>
-  </tr>
-  <tr>
-    <td class="tdc">"</td>
-    <td class="tdc">1663,</td>
-    <td class="tdc">"</td>
-    <td class="tdc">0</td>
-    <td class="tdcbl">"</td>
-    <td class="tdc">1870,</td>
-    <td class="tdc">"</td>
-    <td class="tdc">20° 19′ W.</td>
-  </tr>
-  <tr>
-    <td class="tdc">"</td>
-    <td class="tdc">1700,</td>
-    <td class="tdc">"</td>
-    <td class="tdc">8° 20′ W.</td>
-    <td class="tdcbl">"</td>
-    <td class="tdc">1880,</td>
-    <td class="tdc">"</td>
-    <td class="tdc">18° 58′ W.</td>
-  </tr>
-  <tr>
-    <td class="tdc">"</td>
-    <td class="tdc">1818,</td>
-    <td class="tdc">"</td>
-    <td class="tdc">25° 41′ W.</td>
-    <td class="tdcbl">"</td>
-    <td class="tdc">1890,</td>
-    <td class="tdc">"</td>
-    <td class="tdc">17°&nbsp; 9′ W.</td>
-  </tr>
-  <tr>
-    <td class="tdc">"</td>
-    <td class="tdc">1850,</td>
-    <td class="tdc">"</td>
-    <td class="tdc">19° 31′ W.</td>
-    <td class="tdcbl">"</td>
-    <td class="tdc">1900,</td>
-    <td class="tdc">"</td>
-    <td class="tdc">16° 30′ W.</td>
-  </tr>
-</table>
-</div>
-<p>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.</p>
-<p>135.&mdash;<span class="large bold">Annual Variation.</span>&mdash;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.</p>
-<p>136.&mdash;<span class="large bold">Declination Correction</span> 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, <a href="#i045">Fig. 19</a>, <i>SG</i>, 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<span class="pagenum"><a name="Page_70" id="Page_70">[70]</a></span>
-(mean time) is faster or slower than the sun's southing
-approximately at noon:&mdash;</p>
-<div class="m5 padding-top1 padding-bottom1 font-size09">
-<table summary="" width="90%" class="border-collapse">
-  <tr>
-    <td class="tdc">Jan.</td>
-    <td class="tdc">1</td>
-    <td class="tdc">subtract</td>
-    <td class="tdc">4</td>
-    <td class="tdc">min.</td>
-    <td class="tdcbl">July</td>
-    <td class="tdc">15</td>
-    <td class="tdc">subtract</td>
-    <td class="tdc">6</td>
-    <td class="tdc">min.</td>
-  </tr>
-  <tr>
-    <td class="tdc">"</td>
-    <td class="tdc">16</td>
-    <td class="tdc">"</td>
-    <td class="tdc">10</td>
-    <td class="tdc">"</td>
-    <td class="tdcbl">"</td>
-    <td class="tdc">30</td>
-    <td class="tdc">"</td>
-    <td class="tdc">6</td>
-    <td class="tdc">"</td>
-  </tr>
-  <tr>
-    <td class="tdc">"</td>
-    <td class="tdc">31</td>
-    <td class="tdc">"</td>
-    <td class="tdc">14</td>
-    <td class="tdc">"</td>
-    <td class="tdcbl">Aug.</td>
-    <td class="tdc">14</td>
-    <td class="tdc">"</td>
-    <td class="tdc">4</td>
-    <td class="tdc">"</td>
-  </tr>
-  <tr>
-    <td class="tdc">Feb.</td>
-    <td class="tdc">15</td>
-    <td class="tdc">"</td>
-    <td class="tdc">14</td>
-    <td class="tdc">"</td>
-    <td class="tdcbl">Sept.</td>
-    <td class="tdc">13</td>
-    <td class="tdc">add</td>
-    <td class="tdc">4</td>
-    <td class="tdc">"</td>
-  </tr>
-  <tr>
-    <td class="tdc">Mar.</td>
-    <td class="tdc">2</td>
-    <td class="tdc">"</td>
-    <td class="tdc">12</td>
-    <td class="tdc">"</td>
-    <td class="tdcbl">"</td>
-    <td class="tdc">28</td>
-    <td class="tdc">"</td>
-    <td class="tdc">9</td>
-    <td class="tdc">"</td>
-  </tr>
-  <tr>
-    <td class="tdc">"</td>
-    <td class="tdc">17</td>
-    <td class="tdc">"</td>
-    <td class="tdc">8</td>
-    <td class="tdc">"</td>
-    <td class="tdcbl">Oct.</td>
-    <td class="tdc">13</td>
-    <td class="tdc">"</td>
-    <td class="tdc">14</td>
-    <td class="tdc">"</td>
-  </tr>
-  <tr>
-    <td class="tdc">April</td>
-    <td class="tdc">1</td>
-    <td class="tdc">"</td>
-    <td class="tdc">4</td>
-    <td class="tdc">"</td>
-    <td class="tdcbl">"</td>
-    <td class="tdc">28</td>
-    <td class="tdc">"</td>
-    <td class="tdc">16</td>
-    <td class="tdc">"</td>
-  </tr>
-  <tr>
-    <td class="tdc">May</td>
-    <td class="tdc">1</td>
-    <td class="tdc">add</td>
-    <td class="tdc">3</td>
-    <td class="tdc">"</td>
-    <td class="tdcbl">Nov.</td>
-    <td class="tdc">12</td>
-    <td class="tdc">"</td>
-    <td class="tdc">16</td>
-    <td class="tdc">"</td>
-  </tr>
-  <tr>
-    <td class="tdc">"</td>
-    <td class="tdc">16</td>
-    <td class="tdc">"</td>
-    <td class="tdc">4</td>
-    <td class="tdc">"</td>
-    <td class="tdcbl">"</td>
-    <td class="tdc">27</td>
-    <td class="tdc">"</td>
-    <td class="tdc">12</td>
-    <td class="tdc">"</td>
-  </tr>
-  <tr>
-    <td class="tdc">"</td>
-    <td class="tdc">31</td>
-    <td class="tdc">"</td>
-    <td class="tdc">3</td>
-    <td class="tdc">"</td>
-    <td class="tdcbl">Dec.</td>
-    <td class="tdc">12</td>
-    <td class="tdc">"</td>
-    <td class="tdc">6</td>
-    <td class="tdc">"</td>
-  </tr>
-  <tr>
-    <td class="tdc">June</td>
-    <td class="tdc">30</td>
-    <td class="tdc">subtract</td>
-    <td class="tdc">3</td>
-    <td class="tdc">"</td>
-    <td class="tdcbl">"</td>
-    <td class="tdc">31</td>
-    <td class="tdc">subtract</td>
-    <td class="tdc">3</td>
-    <td class="tdc">"</td>
-  </tr>
-</table>
-</div>
-<p>137.&mdash;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 7&frac12;° 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 <i>Nautical Almanac</i>.</p>
-<p id="Art_138">138.&mdash;<span class="large bold">The Compass-box.</span>&mdash;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 <a href="#i065">Fig. 30</a>, <i>D</i>,
-and is generally silver-plated. The bottom of the compass-box
-is sometimes divided with a <i>compass-rose</i> 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°.</p>
-<p>139.&mdash;In the manufacture of the compass-box very great<span class="pagenum"><a name="Page_71" id="Page_71">[71]</a></span>
-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.</p>
-<p>140.&mdash;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.</p>
-<p>141.&mdash;<span class="large bold">Preservation of the Magnetism in Needles.</span>&mdash;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<span class="pagenum"><a name="Page_72" id="Page_72">[72]</a></span>
-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 <i>contrary direction</i>, 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 <i>materially preserved</i>
-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.</p>
-<p>142.&mdash;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.</p>
-<p>143.&mdash;<span class="large bold">Ring Compasses.</span>&mdash;In modern theodolites, levels
-and prismatic compasses, the magnetic needle carries a light<span class="pagenum"><a name="Page_73" id="Page_73">[73]</a></span>
-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 &frac14; 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:&mdash;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&mdash;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.</p>
-<p>144.&mdash;<span class="large bold">Mariners' Compasses</span>, 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.</p>
-<p>145.&mdash;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<span class="pagenum"><a name="Page_74" id="Page_74">[74]</a></span>
-pointer. This <i>lead</i> 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.</p>
-<p>146.&mdash;<span class="large bold">Trough Compass</span>, sometimes termed a <i>long
-compass</i>. 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, <i>A</i> representing a plan, and <i>B</i> a parallel section
-taken through it horizontally. About 10° are graduated on
-each side of the meridian line, <i>aa</i> being adjusting screws to
-bring the scale true with the needle.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i074">
-  <img class="w100" src="images/i_074.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 32.&mdash;<i>Trough compass for attachment to an instrument.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_074a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>147.&mdash;<span class="large bold">Magnification of Reading.</span>&mdash;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<span class="pagenum"><a name="Page_75" id="Page_75">[75]</a></span>
-needle reading is found in some French instruments. This is
-shown Fig. 33, where the compass is shown entirely enclosed
-in a tube <i>C</i> which protects it from dust. The needle <i>N</i> has a
-vertical point fixed upon its end at <i>P</i> which reads pretty closely
-to a scale of 10° divided upon glass at <i>G</i> by the eye-piece <i>E</i>.
-It has a lifter <i>L</i> pressed up by a milled-head screw <i>M</i>. 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i075">
-  <img class="w100" src="images/i_075.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 33.&mdash;<i>Needle with reader.</i></p>
-    <p class="caption float-right">Fig. 34.&mdash;<i>Scale at G.</i></p>
-    <p class="caption center ebhide"><a href="images/i_075a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p id="Art_148" class="clear">148.&mdash;<span class="large bold">The Prismatic Compass</span>, 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, <a href="#i029">art. 55, Fig. 3, p. 29.</a></p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i076">
-  <img class="w100" src="images/i_076.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 35.&mdash;<i>Ordinary prismatic compass.</i></p>
-    <p class="caption float-right">Fig. 36.&mdash;<i>Section of the same, but with mirror.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_076a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>149.&mdash;<i>Prismatic Compasses</i> are made from 2&frac12; to 6 inches
-in diameter. The compass needle is sometimes made to<span class="pagenum"><a name="Page_76" id="Page_76">[76]</a></span>
-carry a card dial for the 2&frac12;-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, <i>P</i>, 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 <i>SS</i>
-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 <i>SL</i> by means of a <i>thumb nail</i> 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 <i>H</i>, 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 <i>SV</i> is attached, having a central hair
-placed so as to cut a direct line from the slit <i>SS</i> 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<span class="pagenum"><a name="Page_77" id="Page_77">[77]</a></span>
-simultaneously to lift the compass needle off its centre by a
-part of it pressing the outer end of the lifting lever <i>L</i>. 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 <i>S</i>, through the compass-box
-under the window, which carries a light spring <i>B</i> 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.</p>
-<p>150.&mdash;<span class="large bold">Additional Parts</span> commonly provided with the
-prismatic compass are a mirror and sunshades, shown only in
-section Fig. 36. The mirror <i>M</i> 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.</p>
-<p>151.&mdash;<span class="large bold">To Prepare to take Observations with the
-Prismatic Compass.</span> After the window and prism are opened
-out, the prism is adjusted to read the divided ring sharply when<span class="pagenum"><a name="Page_78" id="Page_78">[78]</a></span>
-the compass is about level, by raising or lowering the prism <i>P</i>
-by pressure of the thumb and forefinger of the right hand upon
-the stud placed upon the prism slide fitting, shown below <i>SL</i>,
-until the divisions appear clear.</p>
-<p>152.&mdash;<span class="large bold">In Using the Prismatic Compass</span>, the compass-box
-is held with the thumb of the right hand under the prism
-at <i>SL</i> and the forefinger upon the stud <i>S</i>. The object which
-it is desired to observe is sighted through the slit <i>SS</i>, cutting
-the left-hand side of the hair in the window <i>SV</i>, 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 <i>S</i> upon which the forefinger is
-placed.</p>
-<p>153.&mdash;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.</p>
-<p>154.&mdash;<span class="large bold">Stands.</span>&mdash;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<span class="pagenum"><a name="Page_79" id="Page_79">[79]</a></span>
-milled-head screw. An axis through the ball permits horizontal
-adjustment, shown in section, Fig. 37.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe24_375" id="i079a">
-  <img class="w100" src="images/i_079a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 37.&mdash;<i>Improved prismatic compass stand.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_079aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i079b">
-  <img class="w100" src="images/i_079b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 38.&mdash;<i>Hutchinson's prismatic compass.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_079ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p id="Art_155">155.&mdash;<span class="large bold">Hutchinson's Prismatic Compass</span>, 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<span class="pagenum"><a name="Page_80" id="Page_80">[80]</a></span>
-before described. Size, 2&frac12; inches diameter, &frac34; inch in thickness;
-weight, only 8&frac12; oz. in brass; 3&frac14; oz. in aluminium.</p>
-<p id="Art_156">156.&mdash;<span class="large bold">Captain Burnier's Military Compass.</span>&mdash;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, <i>seq.</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i080">
-  <img class="w100" src="images/i_080.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 39.&mdash;<i>Sketching protractor for use with prismatic compass.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_080a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>157.&mdash;<span class="large bold">Surveying with the Compass only.</span>&mdash;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<span class="pagenum"><a name="Page_81" id="Page_81">[81]</a></span>
-district surveyed. Mining compasses, or <i>dials</i>, 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.</p>
-<p>158.&mdash;<span class="large bold">In Plotting Military Sketch Surveys</span> 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 <i>Course of Military Surveying</i>,
-and in my work on Drawing Instruments. The military
-protractor is shown Fig. 39.</p>
-<p>159.&mdash;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.</p>
-<p>160.&mdash;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 <i>plus or minus</i>, tend to correct each other
-on the whole, and to tie up the lines.</p>
-<p>161.&mdash;The rolling parallel rule may replace the tee-square,<span class="pagenum"><a name="Page_82" id="Page_82">[82]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i082">
-  <img class="w100" src="images/i_082.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Figs. 40, 41, 42, 43.&mdash;<i>Pocket magnetic compasses.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_082a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>162.&mdash;<span class="large bold">Pocket Magnetic Compasses.</span>&mdash;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.</p>
-<p><span class="pagenum"><a name="Page_83" id="Page_83">[83]</a></span></p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i083a">
-  <img class="w100" src="images/i_083a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 44.&mdash;<i>Trough form "Egyptian compass."</i></p>
-    <p class="caption ebhide clear"><a href="images/i_083aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>163.&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i083b">
-  <img class="w100" src="images/i_083b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 45.&mdash;<i>The author's under slide for setting off variation.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_083ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>164.&mdash;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 <i>S</i> 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<span class="pagenum"><a name="Page_84" id="Page_84">[84]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe23_75" id="i084">
-  <img class="w100" src="images/i_084.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 46.&mdash;<i>Barker's luminous compass.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_084a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>165.&mdash;<span class="large bold">Barker's Luminous Compass</span>, 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.</p>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_85" id="Page_85">[85]</a></span></p>
-<h2>CHAPTER IV.</h2>
-</div>
-<p class="ch">LEVELS&mdash;METHODS OF ASCERTAINING&mdash;LEVEL TUBES&mdash;MANUFACTURE&mdash;CURVATURE&mdash;SENSITIVENESS-TESTING&mdash;READING&mdash;CIRCULAR
-LEVELS&mdash;SURVEYORS' LEVELS&mdash;Y-LEVEL&mdash;PARALLEL
-PLATES&mdash;ADJUSTMENTS OF Y-LEVELS&mdash;SUGGESTED IMPROVEMENTS&mdash;DUMPY
-LEVEL&mdash;TRIPOD STANDS&mdash;ADJUSTMENT OF
-DUMPY&mdash;COLLIMATOR&mdash;IMPROVEMENTS IN DUMPY LEVEL&mdash;TRIBRACH
-HEAD&mdash;DIAPHRAGMS&mdash;CUSHING'S LEVEL&mdash;COOKE'S
-LEVEL&mdash;CHEAP FORMS OF LEVEL&mdash;HAND LEVELS&mdash;TELESCOPIC
-LEVEL&mdash;REFLECTING LEVELS&mdash;WATER LEVELS.</p>
-<p>166.&mdash;<span class="large bold">A Level Plane</span> 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 <i>datum</i>, 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.</p>
-<p>167.&mdash;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 <i>gravity</i>; and<span class="pagenum"><a name="Page_86" id="Page_86">[86]</a></span>
-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:&mdash;(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&mdash;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.</p>
-<p>168.&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i087">
-  <img class="w100" src="images/i_087.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 47.&mdash;<i>Level tube (bubble).</i></p>
-    <p class="caption ebhide clear"><a href="images/i_087a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>169.&mdash;<span class="large bold">Level Tubes</span>, <i>or Bubble Tubes</i>, as they are<span class="pagenum"><a name="Page_87" id="Page_87">[87]</a></span>
-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 <i>test mark</i>, 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 <i>core</i>, which is employed to
-grind the glass by means of fine emery. The <i>core</i> 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<span class="pagenum"><a name="Page_88" id="Page_88">[88]</a></span>
-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.</p>
-<p>170.&mdash;The operation of grinding is very much the same as
-that described for lenses, <a href="#Page_17">p. 17</a>. 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 <i>coaxing</i> is allowed to
-get the centre of the tube <i>quick</i> 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 <i>bubble trier</i>,
-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.</p>
-<p>171.&mdash;<span class="large bold">The Bubble Trier</span> is a bar or bed 12 to 20
-inches long, with two extended feet ending in points at one<span class="pagenum"><a name="Page_89" id="Page_89">[89]</a></span>
-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.</p>
-<p>172.&mdash;<i>The Sensitiveness of a Level Tube</i>, 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&mdash;8
-inches × 1 inch diameter, 7 inches × ·9, 6 inches × ·8,
-5 inches × ·7, 4 inches × ·6, 3 inches × ·5, 2&frac12; inches ×
-·45, 2 inches × ·4, 1&frac12; 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.</p>
-<p>173.&mdash;<i>The Curvature of a Level Tube</i> 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<span class="pagenum"><a name="Page_90" id="Page_90">[90]</a></span>
-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&mdash;</p>
-<p class="center padding1">
-<i>versed sine</i> = <i>rad</i> - √(<i>rad</i><sup>2</sup> - (&frac12; <i>cho</i>)<sup>2</sup>).<br />
-</p>
-<p>174.&mdash;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&mdash;</p>
-
-<div class="padding1">
-    <p class="center"><i>Arc equal to radius expressed in minutes, 3437·74677.</i></p>
-    <p class="center padding-left3"><i>" &nbsp; &nbsp; &nbsp;  &nbsp; &nbsp; " &nbsp; &nbsp;  &nbsp; &nbsp;  &nbsp; &nbsp; " &nbsp; &nbsp;  &nbsp; &nbsp;  &nbsp; seconds, 206264·80625.</i></p>
-</div>
-
-<p>The run of a good sensitive tube is frequently made 1/30 inch
-to the second, here (omitting decimals)&mdash;</p>
-<p class="center padding1">
-arc sec (206264·8) × 1/30 inch = 573 feet radius nearly.
-</p>
-<p>For scientific purposes a millimetre run per second is commonly
-used, then&mdash;</p>
-<p class="center padding1">
-arc sec (206264·8) × ·001 metre = 206·264 metres radius
-or 680 feet nearly.
-</p>
-<p>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.</p>
-<p>175.&mdash;<i>The Divisions upon Ordinary Level Tubes</i> are
-made after the tube is finished, but with the highly sensitive
-ones the divisions are made first. The run is taken from<span class="pagenum"><a name="Page_91" id="Page_91">[91]</a></span>
-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.</p>
-<p>176.&mdash;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:&mdash;we find commercial methylic
-alcohol 22, absolute alcohol 13, sulphuric ether 5, chloroform
-3,&mdash;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&mdash;the means of doing
-which will be presently discussed&mdash;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.</p>
-<p>177.&mdash;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<span class="pagenum"><a name="Page_92" id="Page_92">[92]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i092">
-  <img class="w100" src="images/i_092.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 48.&mdash;<i>Colonel Strange's level tube.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_092a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>178.&mdash;<span class="large bold">Colonel Strange's Level Tube.</span>&mdash;These tubes,
-Fig. 48, are blown with an outward bead at each end of the
-tube, two outwardly screwed collars, <i>F</i>, being first placed over
-the tube before the blowing. The tube is then ground to
-curvature. A plug, <i>S</i>, 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, <i>C</i>, 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.</p>
-<p>179.&mdash;<span class="large bold">Chambered Level Tubes.</span>&mdash;As the run of a
-bubble varies slightly with its size, for exact purposes and<span class="pagenum"><a name="Page_93" id="Page_93">[93]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i093a">
-  <img class="w100" src="images/i_093a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 49.&mdash;<i>Bubble with supplemental air-chamber.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_093aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i093b">
-  <img class="w100" src="images/i_093b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 50.&mdash;<i>Colonel Scott's patent protected bubble.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_093ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>180.&mdash;<span class="large bold">Extra Strong Level Tubes.</span>&mdash;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<span class="pagenum"><a name="Page_94" id="Page_94">[94]</a></span>
-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, <i>CC′</i>, 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, <i>KK′</i> and cemented over
-<i>PP′</i>. 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i094">
-  <img class="w100" src="images/i_094.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 51.&mdash;<i>Artificial horizon level.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_094a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>181.&mdash;<span class="large bold">The Level Tube may form a Complete Instrument
-in itself.</span>&mdash;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.</p>
-<p>182.&mdash;<span class="large bold">Mounting Tubes.</span>&mdash;Level tubes when applied to
-instruments are generally mounted in brass covering tubes.
-Small level tubes under 2&frac12; 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<span class="pagenum"><a name="Page_95" id="Page_95">[95]</a></span>
-tube with plaster if the other be left free, and this is perhaps
-advisable for portable instruments.</p>
-<p>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.</p>
-<p>183.&mdash;<span class="large bold">In Fixing Undivided Level Tubes</span>, or replacing
-them in instruments, it is important to observe that the side
-with the <i>test mark</i>, which is a small ground facet, should be
-placed on the <i>top</i>.</p>
-<p>184.&mdash;<i>In the Use of Level Tubes</i> 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&mdash;that is by doing what is really in this case the best for
-the instrument.</p>
-<p>185.&mdash;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.</p>
-<p>186.&mdash;<span class="large bold">Reading the Bubble.</span>&mdash;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.<span class="pagenum"><a name="Page_96" id="Page_96">[96]</a></span>
-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. <i>C</i> sheath,
-<i>M</i> mirror, <i>L</i> lens.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i096">
-  <img class="w100" src="images/i_096.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 52.&mdash;<i>Pocket lens and mirror.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_096a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p id="Art_187">187.&mdash;<span class="large bold">Circular Levels</span> 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<span class="pagenum"><a name="Page_97" id="Page_97">[97]</a></span>
-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&mdash;as for plane tables, cameras, etc.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe35" id="i097">
-  <img class="w100" src="images/i_097.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 53.&mdash;<i>Hicks' patent circular level.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_097.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>188.&mdash;<span class="large bold">Surveyors' Levels</span>, 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 <i>setting-up</i> 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.</p>
-<p><span class="pagenum"><a name="Page_98" id="Page_98">[98]</a></span></p>
-<p>189.&mdash;In the design of a surveyor's level very important
-considerations are:&mdash;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&mdash;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.</p>
-<p>190.&mdash;<i>The Oldest Form of Surveyor's Level</i> 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.</p>
-<p>191.&mdash;<span class="large bold">The Y-Level</span> in a modern form is represented in
-the engraving below, Fig. 54. The Y's are shown at <i>YY″</i>
-edgewise. They are supported by standards <i>SR</i> upon the
-limb <i>L</i>. 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<span class="pagenum"><a name="Page_99" id="Page_99">[99]</a></span>
-longitudinally in its Y's by a pair of flanges placed on the
-inside of the collar pieces.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i099">
-  <img class="w100" src="images/i_099.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 54.&mdash;<i>Surveyor's Y-level.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_099a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>192.&mdash;The Y's are erected upon the limb, to which they
-are each fixed firmly by a clamping nut <i>R</i> at one end, and a
-milled head clamp at <i>M</i>. The telescope is held down by
-strap pieces, each of which has a joint at one end and a loose
-pin at the other, <i>PP</i>. 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 <i>YY″</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i100">
-  <img class="w100" src="images/i_100.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 55.&mdash;<i>Section of parallel plate and vertical axis&mdash;arrangement
-of Y and other levels.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_100a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p id="Art_193">193.&mdash;<span class="large bold">Parallel Plates</span> 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<span class="pagenum"><a name="Page_100" id="Page_100">[100]</a></span>
-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. <i>A</i> is a screw by which the parallel plates
-are attached to the limb of the instrument; <i>M</i> a large <i>milled
-head</i>, by means of which the screw can be brought up firmly
-to its collar; <i>SS′</i> the <i>socket</i> which is ground to fit the cone
-<i>C</i>; <i>C</i> forms a part of the <i>upper parallel plate</i> <i>UP</i>; <i>B</i> a
-<i>ball pin</i> which screws firmly into <i>C</i>; <i>LP</i> <i>lower parallel
-plate</i>, part of which forms the ball socket, so that the
-whole instrument rocks about the ball <i>B</i> as a centre, by
-the action of the parallel plate screws <i>PS</i>; <i>B′</i> female screw
-for fixing this part, which is called altogether the <i>parallel
-plates</i>, to the tripod head. A clamping screw is sometimes
-placed upon the axis for slow motion. The parallel plate
-screws are <i>tapped</i>, that is, have female threads cut into the<span class="pagenum"><a name="Page_101" id="Page_101">[101]</a></span>
-upper plate <i>UP</i>, and their points press the lower parallel
-plate <i>LP</i> at certain points, there being a <i>stop-piece</i> 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.</p>
-<p>The diaphragm of the telescope of the Y-level is generally
-webbed with plain cross webs. The diaphragm and webs were
-described <a href="#Art_99">arts. 99 to 106</a>.</p>
-<p>194.&mdash;<i>The Setting-up of the Y-Level</i> 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 <i>in adjustment</i> 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.</p>
-<p>195.&mdash;<i>Setting-up of the Y or other Level with Parallel
-Plates.</i>&mdash;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.</p>
-<p><span class="pagenum"><a name="Page_102" id="Page_102">[102]</a></span></p>
-<p>196.&mdash;<i>The Eye-piece is Adjusted</i>, <a href="#Art_108">art. 108</a>, 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, <i>PS</i>, <i>SP</i>.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i102">
-  <img class="w100" src="images/i_102.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 56.&mdash;<i>Diagram plan of parallel plate screw milled heads.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_102a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>197.&mdash;The milled heads only of these screws are represented
-in plan in the diagram Fig. 56, <i>aa′</i> 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 <i>aa′</i>, 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<span class="pagenum"><a name="Page_103" id="Page_103">[103]</a></span>
-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.</p>
-<p>198.&mdash;When the level tube is adjusted over the screws
-<i>aa′</i> it is then placed over <i>bb′</i> and adjusted in a similar
-manner, returning again to the position <i>aa′</i> 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.</p>
-<p>199.&mdash;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 <i>opposite pairs
-aa′ and bb′</i>. 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, <a href="#Art_109">art. 109</a>. 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.</p>
-<p id="Art_200">200.&mdash;<i>Adjustment of the Axis of the Telescope</i> in true
-parallel direction with the periphery of its supporting collars
-in its Y's. This is performed entirely with the four capstan-<span class="pagenum"><a name="Page_104" id="Page_104">[104]</a></span>headed
-screws which adjust the diaphragm, one of which is
-shown, <a href="#i099">Fig. 54</a>, <i>C</i>. Having the adjustment of the eye-piece
-in focus for the webs in the manner described, <a href="#Art_108">arts. 108, 109</a>,
-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 <i>C</i>, 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.</p>
-<p>201.&mdash;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.</p>
-<p>202.&mdash;<i>Adjustment of Vertical Axis.</i>&mdash;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<span class="pagenum"><a name="Page_105" id="Page_105">[105]</a></span>
-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 <i>M</i>, 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.</p>
-<p>203.&mdash;<i>Adjustment of the Level Tube.</i>&mdash;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 <i>B</i> are then adjusted to one-fourth of the difference
-observed, and the parallel plate screws are adjusted for the<span class="pagenum"><a name="Page_106" id="Page_106">[106]</a></span>
-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.</p>
-<p>204.&mdash;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 <i>droops</i>, which is a very common fault in
-badly-made instruments.</p>
-<p>205.&mdash;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.</p>
-<p>206.&mdash;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 <i>many loose parts</i>, 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:&mdash;<span class="pagenum"><a name="Page_107" id="Page_107">[107]</a></span>"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&mdash;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&mdash;lost
-by becoming loose, perhaps from having been
-played with while he was resting&mdash;how would you praise
-the Y-level?" This gentleman assured me that <i>he</i> 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&mdash;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.</p>
-<p>207.&mdash;<span class="large bold">Improved Y-Level.</span>&mdash;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<span class="pagenum"><a name="Page_108" id="Page_108">[108]</a></span>
-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, <i>seq.</i> Also the setting-up adjustment with
-it, which is different from that already described where parallel
-plates are employed.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i108">
-  <img class="w100" src="images/i_108.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 57.&mdash;<i>Improved Y-level.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_108a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>208.&mdash;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<span class="pagenum"><a name="Page_109" id="Page_109">[109]</a></span>
-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.</p>
-<p>209.&mdash;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<span class="pagenum"><a name="Page_110" id="Page_110">[110]</a></span>
-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 <i>modern</i> text-books.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i110">
-  <img class="w100" src="images/i_110.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 59.&mdash;<i>Dumpy level.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_110a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>210.&mdash;<span class="large bold">The Dumpy Level.</span>&mdash;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 <i>CB</i>. This improvement over
-the old form of Y-level permitted the setting-up of the instrument
-to be completed approximately, without turning the level<span class="pagenum"><a name="Page_111" id="Page_111">[111]</a></span>
-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.</p>
-<p>211.&mdash;<span class="large bold">The Dumpy Level</span> of modern form is represented
-in the engraving, Fig. 59. It consists of a telescope, fully described
-art. 94, which carries a ray shade <i>RS</i> at the object-glass
-end, to work in the field to eastward or westward facing
-a low sun. The eye-piece <i>EP</i> 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 <i>GG</i>, 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 <i>GG</i>: 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 <i>L</i> beneath. The limb may be either a<span class="pagenum"><a name="Page_112" id="Page_112">[112]</a></span>
-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 <i>S</i>. 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&mdash;<i>CC′</i>
-telescope, <i>TT′</i> drawing screws, <i>P</i> pressing screw.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i112">
-  <img class="w100" src="images/i_112.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 60.&mdash;<i>Attachment of telescope block to limbs.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_112a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>212.&mdash;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 &frac34; inch
-or so diameter being bent; therefore all parts may be closely<span class="pagenum"><a name="Page_113" id="Page_113">[113]</a></span>
-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, <a href="#i100">art.
-193, Fig. 55</a>.</p>
-<p>213.&mdash;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 <i>to enable him to read at short distances</i>.
-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.</p>
-<p id="Art_214">214.&mdash;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<span class="pagenum"><a name="Page_114" id="Page_114">[114]</a></span>
-for a level diaphragm used in rough work with capstan-head
-screws, shown <a href="#i050">Fig. 23, p. 50</a>, 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:&mdash;<i>BB′</i> slide pieces, <i>A</i> slide
-moved by capstan-head screws.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i114">
-  <img class="w100" src="images/i_114.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 61.&mdash;<i>Diaphragm of dumpy level with webbed stop.</i></p>
-    <p class="caption float-right">Fig. 62.&mdash;<i>Same, with stadia webs.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_114a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>215.&mdash;<span class="large bold">Subtense or Stadia Webs.</span>&mdash;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<span class="pagenum"><a name="Page_115" id="Page_115">[115]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i115">
-  <img class="w100" src="images/i_115.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 63.&mdash;<i>Tripod.</i></p>
-    <p class="caption float-right">Fig. 64.&mdash;<i>Section of one turn-up leg of the same.</i></p>
-    <p class="caption float-right">Fig. 65.&mdash;<i>Section of tripod.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_115a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p id="Art_216">216.&mdash;<span class="large bold">Tripods, or Stands.</span>&mdash;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 3&frac12; inches at its greatest diameter
-when closed, tapering off to 2&frac12; 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. <i>Shovel-pieces</i> are shown<span class="pagenum"><a name="Page_116" id="Page_116">[116]</a></span>
-in <a href="#i110">Fig. 59</a> <i>AA′</i> (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 <i>book-pieces</i> 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 1&frac12;
-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 <i>lead</i>,
-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 <a href="#i124b">Fig.
-70<span class="smcap">A</span></a>, <i>seq</i>.</p>
-<p>217.&mdash;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.</p>
-<p>A few engineers prefer yellow pine for the tripods instead
-of mahogany: this is much lighter for its relative stiffness, but<span class="pagenum"><a name="Page_117" id="Page_117">[117]</a></span>
-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.</p>
-<p>218.&mdash;The lower points of the legs, technically <i>toes</i>, 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.</p>
-<p>219.&mdash;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 <i>A</i>, and in detail
-section Fig. 64. The joint is made perfectly firm by a winged
-screw at <i>S</i>, which screws from a boss cast on the hinge <i>J</i> to a
-solid metal shoe <i>P</i>. When the leg is turned up, the screw
-fixes it in the female screw <i>S</i>. 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.</p>
-<p>The tripod head shown under the level of <a href="#i110">Fig. 59</a> 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.</p>
-<p>220.&mdash;<span class="large bold">The adjustments of the Dumpy Level.</span>&mdash;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<span class="pagenum"><a name="Page_118" id="Page_118">[118]</a></span>
-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.</p>
-<p>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.</p>
-<p>221.&mdash;<i>Adjustment to Collimation.</i>&mdash;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.<span class="pagenum"><a name="Page_119" id="Page_119">[119]</a></span>
-This is true although the axis may have been out of collimation.
-This arrangement is shown in Fig. 66, <i>L</i> the first position
-of the level taking sights at equal distance from <i>S</i> and <i>S′</i>.
-Let the level be now removed to <i>L′</i>: if correct it should cut
-the staves <i>SS′</i> at equal distances above or below the first
-readings at <i>aa′</i>, which are at equal distances from <i>bb′</i> readings
-from <i>L′</i>, therefore level and parallel with the first reading.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i119">
-  <img class="w100" src="images/i_119.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 66.&mdash;<i>Adjustment of dumpy level.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_119a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>222.&mdash;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.</p>
-<p>223.&mdash;<i>Original Adjustment of the Dumpy Level to Collimation
-with consideration of the Curvature of the Earth.</i>&mdash;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<span class="pagenum"><a name="Page_120" id="Page_120">[120]</a></span>
-reading in proportion to the distances, calling the lower
-reading minus&mdash;</p>
-<p class="center padding1">
-7·50 - 6·50 = -1, 4·50 + 5·50 = +1, difference = 2.
-</p>
-<p>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.</p>
-<p>224.&mdash;It was claimed by the late William Gravatt for
-his method of adjustment,<a name="FNanchor_3_3" id="FNanchor_3_3"></a><a href="#Footnote_3_3" class="fnanchor">[3]</a> 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 <i>pro ratâ</i> 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.</p>
-<p>225.&mdash;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,
-<span class="pagenum"><a name="Page_121" id="Page_121">[121]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i121">
-  <img class="w100" src="images/i_121.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 67.&mdash;<i>Collimator for adjustments to horizontality of the telescope.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_121a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>226.&mdash;<span class="large bold">Collimator.</span>&mdash;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 <i>method of
-Gauss</i>. 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 <a href="#Art_94">art. 94</a>, 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<span class="pagenum"><a name="Page_122" id="Page_122">[122]</a></span>
-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 <a href="#Art_200">art. 200</a>, and
-the level is fixed true with the axis of the telescope, when the
-collimation is perfect.</p>
-<p>227.&mdash;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.</p>
-<p>228.&mdash;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.</p>
-<p id="Art_229">229.&mdash;It would be very difficult to use this method of
-adjustment if it were necessary that the axes of the level and
-collimator should <i>exactly</i> 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<span class="pagenum"><a name="Page_123" id="Page_123">[123]</a></span>
-will show. Let <i>O</i>, Fig. 68 be the object-glass of the collimator,
-whose solar focus is at <i>F</i>. Then the rays <i>PP</i>, and all
-other parallel rays falling on the object-glass, will be brought
-to a focus at <i>F</i>; and reciprocally all rays departing from <i>F</i> in
-passing through this object-glass will leave in parallel lines
-<i>PP</i>. Let <i>O′</i> be the object-glass of a telescope to be collimated,
-<i>F′</i> its solar focus. Then all rays from <i>P</i> to <i>P</i> departing
-from <i>F</i> that fall within the parallel space <i>P′P′</i> will be
-brought to focus at <i>F′</i>. When the image at <i>F</i> is illuminated
-by a lamp <i>L</i>, the webs or other index will be clearly seen by
-the eye-piece at <i>F′</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i123">
-  <img class="w100" src="images/i_123.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 68.&mdash;<i>Diagram of collimation by two telescopes.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_123a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>230.&mdash;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 <i>solar focus</i>, and that the instrument used as a
-collimator has a good object-glass.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i124a">
-  <img class="w100" src="images/i_124a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 69.</p>
-    <p class="caption ebhide clear"><a href="images/i_124aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<div class="figcenter padding1" id="Fig_70">
-<div class="figcenter illowe37_5" id="i124b">
-  <img class="w100" src="images/i_124b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 70.&mdash;<i>Stanley's model 14-inch dumpy level.</i></p>
-    <p class="caption float-right">Fig. 70A.&mdash;<i>Tripod.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_124ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>231.&mdash;<span class="large bold">Improved Dumpy Level.</span>&mdash;The writer has made
-some improvements in the dumpy level, which have so far met
-with very general approbation from the profession, Fig. 70.<span class="pagenum"><a name="Page_124" id="Page_124">[124]</a></span>
-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<span class="pagenum"><a name="Page_125" id="Page_125">[125]</a></span>
-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 <a href="#i112">Fig. 60, p. 112</a>. 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.</p>
-<p>232.&mdash;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<span class="pagenum"><a name="Page_126" id="Page_126">[126]</a></span>
-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.</p>
-<p id="Art_233">233.&mdash;<span class="large bold">Tribrach.</span>&mdash;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 <i>H</i>, 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: <i>L</i> limb, fitted with
-compass; <i>C</i> axis, in one casting with the limb; <i>S</i> sprang,
-carrying the socket and supporting the instrument. <i>PH</i>
-shows the ball head arrangements to the screws. A central
-screw in this part detaches the tripod. One point is shown<span class="pagenum"><a name="Page_127" id="Page_127">[127]</a></span>
-at <i>P</i>, of which there are three, to support the level upon a wall
-or rock in cases where the tripod cannot be used&mdash;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 <i>F</i>. 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 <a href="#i124b">Fig. 70A</a>.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i127">
-  <img class="w100" src="images/i_127.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 71.&mdash;<i>Details of Stanley's dumpy level: half elevation to left, half section to right.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_127a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p id="Art_234">234.&mdash;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.</p>
-<p><span class="pagenum"><a name="Page_128" id="Page_128">[128]</a></span></p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i128">
-  <img class="w100" src="images/i_128.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Figs. 72 and 73.&mdash;<i>Tribrach adjustment.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_128a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>235.&mdash;The bubble of the level is placed parallel with two
-of the screws of the tribrach, that is as <i>B</i> and <i>C</i>, 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 <i>A</i> 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 <i>A</i> 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.</p>
-<p><span class="pagenum"><a name="Page_129" id="Page_129">[129]</a></span></p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i129a">
-  <img class="w100" src="images/i_129a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 74.&mdash;<i>Ray shade.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_129aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>236.&mdash;<span class="large bold">The Ray Shade</span> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe23_4375" id="i129b">
-  <img class="w100" src="images/i_129b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 75.&mdash;<i>Stanley's platino-iridium point level stop.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_129ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p id="Art_237">237.&mdash;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<span class="pagenum"><a name="Page_130" id="Page_130">[130]</a></span>
-placed in a sliding fitting, as previously described, <a href="#Art_214">art. 214</a>, 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&mdash;Fig. 76 is the image of a
-division of the staff partially covered by a web <i>WW′</i>; Fig. 77
-that of a magnified image of the point <i>P</i> brought towards a
-division for reading. It will be readily observed that the
-fractional part of the 1/100 foot block, which the point <i>P</i> cuts,
-is much more easily estimated than that in which the web
-<i>WW′</i> covers a part of a similar block.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i130">
-  <img class="w100" src="images/i_130.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 76.</p>
-    <p class="caption float-right">Fig. 77.</p>
-    <p class="caption"><i>Difference of reading with a web and a point, shown much magnified..</i></p>
-    <p class="caption ebhide clear"><a href="images/i_130a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>238.&mdash;In early levels of improved construction, as shown
-<a href="#i124b">Fig. 70</a>, a difficulty was experienced in practice in bringing<span class="pagenum"><a name="Page_131" id="Page_131">[131]</a></span>
-the index point exactly up to the edge of the line as it is shown
-in Fig. 77 at <i>P</i>. 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i131">
-  <img class="w100" src="images/i_131.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 78.&mdash;<i>Stanley's improved dumpy.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_131a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>239.&mdash;<span class="large bold">Stadia Points.</span>&mdash;The author commonly makes the
-points, Fig. 75, <i>VV′</i> 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<span class="pagenum"><a name="Page_132" id="Page_132">[132]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i132">
-  <img class="w100" src="images/i_132.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 79.&mdash;<i>Stanley's quick setting-up level.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_132a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p id="Art_240">240.&mdash;<span class="large bold">Quick setting-up Tribrach.</span>&mdash;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.</p>
-<p><span class="pagenum"><a name="Page_133" id="Page_133">[133]</a></span></p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i133">
-  <img class="w100" src="images/i_133.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 80.&mdash;<i>Stanley's Engineer's level.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_133a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i134a">
-  <img class="w100" src="images/i_134a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 81.&mdash;<i>Stanley's Engineer's level.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_134aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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)<span class="pagenum"><a name="Page_134" id="Page_134">[134]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i134b">
-  <img class="w100" src="images/i_134b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 82.&mdash;<i>Stanley's Engineer's level fitted with quick setting spherical
-lower plate.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_134ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>As ninety per cent. of the orders now for levels are for
-the form shown at Fig. 82, the reviser ventures to think that<span class="pagenum"><a name="Page_135" id="Page_135">[135]</a></span>
-this must be favoured by the profession as the best practical
-instrument yet made.</p>
-<p>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.</p>
-<p>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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i135">
-  <img class="w100" src="images/i_135.png"  alt="" />
-</div>
-<div class="caption2">
-  <p class="caption2">E Stadia points for clamp and tangent levels.</p>
-  <p class="caption2">F Stadia points for ordinary levels.</p>
-  <p class="caption2">G Stadia glass diaphragm.</p>
-  <p class="caption2">H Webs.</p>
-  <p class="caption2">J Stadia webs.</p>
-  <p class="caption2">Fig. 83.</p>
-  <p class="caption ebhide clear"><a href="images/i_135a.png" rel="nofollow">Larger image</a></p>
-</div>
-</div>
-
-<p>241.&mdash;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<span class="pagenum"><a name="Page_136" id="Page_136">[136]</a></span>
-was fully justified. Whether the professional man, nevertheless,
-will ever depart from the solid construction of the
-dumpy remains an open question.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i136">
-  <img class="w100" src="images/i_136.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 84.&mdash;<i>Cushing's 12-inch improved level.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_136a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>242.&mdash;<span class="large bold">Cushing's Level.</span>&mdash;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.<a name="FNanchor_4_4" id="FNanchor_4_4"></a><a href="#Footnote_4_4" class="fnanchor">[4]</a> 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
-<span class="pagenum"><a name="Page_137" id="Page_137">[137]</a></span>
-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 (<i>bayonet notches</i>). 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, <a href="#i114">Fig. 61</a>, and a glass diaphragm is
-used. One important arrangement is also made in this part
-of the instrument&mdash;which is necessary, as glasses become
-frequently bedewed in the telescope&mdash;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 <a href="#i131">Fig. 78</a>, 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&mdash;of covering the image of the staff reading. It also<span class="pagenum"><a name="Page_138" id="Page_138">[138]</a></span>
-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.</p>
-<p>243.&mdash;<span class="large bold">Cooke's Level.</span>&mdash;An instrument somewhat equivalent
-to the above has been patented by Messrs. T. Cooke &amp; 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.</p>
-<p>244.&mdash;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&mdash;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<span class="pagenum"><a name="Page_139" id="Page_139">[139]</a></span>
-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.</p>
-<p>245.&mdash;<span class="large bold">Supplementary Parts to Levels.</span>&mdash;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.</p>
-<p>246.&mdash;<i>Bubble Reflector.</i>&mdash;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<span class="pagenum"><a name="Page_140" id="Page_140">[140]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i140">
-  <img class="w100" src="images/i_140.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 85.&mdash;<i>Compact cheap form of dumpy level.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_140a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>247.&mdash;<i>Sight Vanes.</i>&mdash;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.</p>
-<p><span class="pagenum"><a name="Page_141" id="Page_141">[141]</a></span></p>
-<p>248.&mdash;<span class="large bold">Lower-class Levels.</span>&mdash;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.</p>
-<p id="Art_249">249.&mdash;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&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i141">
-  <img class="w100" src="images/i_141.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 86.&mdash;<i>Contractor's or builder's level.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_141a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>250.&mdash;The illustration Fig. 86 represents the cheapest
-form of level with a tripod stand that has been constructed,<span class="pagenum"><a name="Page_142" id="Page_142">[142]</a></span>
-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 <i>sprang</i>, 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i142">
-  <img class="w100" src="images/i_142.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 87.&mdash;<i>Sighted reflecting pocket level.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_142a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>251.&mdash;<span class="large bold">Sighted Pocket Level.</span>&mdash;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 <i>E</i>. 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 <i>R</i>. A level with a small bubble is placed<span class="pagenum"><a name="Page_143" id="Page_143">[143]</a></span>
-or inserted in the top of the tube at <i>B</i>. 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 <i>R</i>, 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 <i>R</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i143">
-  <img class="w100" src="images/i_143.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 88.&mdash;<i>Pocket telescopic level.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_143a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>252.&mdash;<span class="large bold">Pocket Telescopic Level.</span>&mdash;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<a name="FNanchor_5_5" id="FNanchor_5_5"></a><a href="#Footnote_5_5" class="fnanchor">[5]</a> 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
-<span class="pagenum"><a name="Page_144" id="Page_144">[144]</a></span>
-object-glass, eye-piece and the bubble. The appearance of
-the mirror and point is shown at <i>B</i>. The point is shown by
-a dot at <i>P</i>. The curved mirror <i>R</i>. 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 4&frac12;
-inches by &frac34; inch. Weight in case, about 8 oz.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i144">
-  <img class="w100" src="images/i_144.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 89.&mdash;<i>Reflecting level.</i></p>
-    <p class="caption float-right">Fig. 90.&mdash;<i>The same construction in protecting case.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_144a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>253.&mdash;<span class="large bold">Reflecting Level.</span>&mdash;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<span class="pagenum"><a name="Page_145" id="Page_145">[145]</a></span>
-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.</p>
-<p>254.&mdash;<i>In using the Reflecting Level</i>, 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.</p>
-<p>255.&mdash;<span class="large bold">Reflecting Level in Case.</span>&mdash;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<span class="pagenum"><a name="Page_146" id="Page_146">[146]</a></span>
-greater certainty to the point of bisection on the edge of the
-mirror, and much greater accuracy is thus attained in levelling
-with it.</p>
-<p>256.&mdash;<span class="large bold">Water Levels.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i146">
-  <img class="w100" src="images/i_146.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 91.&mdash;<i>Tubular water level with open vials.</i></p>
-    <p class="caption float-right">Fig. 92.&mdash;<i>Browne's standard water level.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_146a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>257.&mdash;<span class="large bold">Browne's Water Level</span><a name="FNanchor_6_6" id="FNanchor_6_6"></a><a href="#Footnote_6_6" class="fnanchor">[6]</a> 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
-<span class="pagenum"><a name="Page_147" id="Page_147">[147]</a></span>
-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&mdash;for instance, in
-crossing over a wall&mdash;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.</p>
-<p>Platelayers' levels and mechanics' levels generally are
-deferred to consider with useful hand tools and apparatus employed
-by surveyors in the final chapter.</p>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_148" id="Page_148">[148]</a></span></p>
-<h2>CHAPTER V.</h2>
-</div>
-<p class="ch">LEVELLING STAVES&mdash;CONSTRUCTION&mdash;VARIOUS READINGS
-DISCUSSED&mdash;SOPWITH'S&mdash;FIELD'S&mdash;STRANGE'S&mdash;STANLEY'S
-NEW&mdash;METRICAL&mdash;SIMPLE CONSTRUCTION MINING STAFF&mdash;PAPERED
-LEVELLING STAFF&mdash;PRESERVATION&mdash;PACKING
-PADS&mdash;STAFF PLATE&mdash;STAFF LEVEL&mdash;PRACTICE OF LEVELLING&mdash;INDEX
-OF BUBBLE&mdash;LAMP&mdash;CURVATURE CORRECTIONS&mdash;STATION
-PEGS&mdash;REFINEMENT OF LEVELLING&mdash;LEVELLING
-BOOKS&mdash;INK BOTTLE, ETC.</p>
-<p>258.&mdash;<span class="large bold">Levelling Staves.</span>&mdash;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,<a name="FNanchor_7_7" id="FNanchor_7_7"></a><a href="#Footnote_7_7" class="fnanchor">[7]</a> called the <i>telescopic staff</i>, 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,
-<span class="pagenum"><a name="Page_149" id="Page_149">[149]</a></span>
-5 <i>feet</i> 4 <i>inches</i>, 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i149">
-  <img class="w100" src="images/i_149.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Figs. 93, 94.&mdash;<i>Section of Sopwith's staff.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_149a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p id="Art_259">259.&mdash;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 <i>A</i>, which in the 14-feet staff is 5 feet in length, is made
-of mahogany 5/16 inch thick, the front being &frac14; inch. The outer
-dimensions of the section are 3-1/8 inches by 2 inches. The
-second tube <i>B</i> is 5 feet 1 inch long, of outer dimensions 2-3/8
-inches by 1&frac14; inches. The inner slide <i>C</i> is solid, 5 feet
-2 inches long, 1&frac34; inches by &frac34; 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<span class="pagenum"><a name="Page_150" id="Page_150">[150]</a></span>
-a spring catch, the detail of which is shown in Fig. 94, section
-<i>y</i> to <i>z</i> of Fig. 93&mdash;S spring of T form screwed firmly to the
-edges of the box. The catch is made at <i>A</i> over the edge of
-the brass cap <i>A′</i>. 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.</p>
-<p>260.&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i150">
-  <img class="w100" src="images/i_150.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 95.&mdash;<i>Section of semi-cylindrical staff.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_150a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>261.&mdash;<span class="large bold">Semi-circular Staff.</span>&mdash;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<span class="pagenum"><a name="Page_151" id="Page_151">[151]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i151">
-  <img class="w100" src="images/i_151.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 96.&mdash;<i>Sopwith pattern staff.</i></p>
-    <p class="caption float-right">Fig. 97.&mdash;<i>Field's pattern.</i></p>
-    <p class="caption">Fig. 98.&mdash;<i>Stanley's old pattern.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_151a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>262.&mdash;What was originally considered as the defect of the<span class="pagenum"><a name="Page_152" id="Page_152">[152]</a></span>
-Sopwith staff, besides its shakiness, as it was first made, was
-the diminished width of reading of the upper length, this
-being only 1&frac14; 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i152">
-  <img class="w100" src="images/i_152.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 99.&mdash;<i>Sopwith's staff.</i></p>
-    <p class="caption float-right">Fig. 100.&mdash;<i>Rogers Field's staff.</i></p>
-    <p class="caption">Fig. 101.&mdash;<i>Col. Strange's staff.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_152a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>263.&mdash;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<span class="pagenum"><a name="Page_153" id="Page_153">[153]</a></span>
-introduced by the author to render this staff more distinct
-than when lines only are used, as in the ordinary pattern.</p>
-<p>264.&mdash;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&mdash;grazing by
-carrying the staff with the tripod of the level, etc.&mdash;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.</p>
-<p>265.&mdash;<i>For Reading the Sopwith Staff</i>, 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&mdash;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.</p>
-<p>266.&mdash;<span class="large bold">Various Readings.</span>&mdash;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<span class="pagenum"><a name="Page_154" id="Page_154">[154]</a></span>
-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.</p>
-<p>267.&mdash;<i>Rogers Field's and Colonel Strange's Readings.</i>&mdash;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, <a href="#i129b">Fig. 75</a>. 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<span class="pagenum"><a name="Page_155" id="Page_155">[155]</a></span>
-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, <a href="#i129b">Fig. 75</a>. 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i155">
-  <img class="w100" src="images/i_155.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 102.&mdash;<i>Details of Stanley staff; A bottom length, B middle,
-C top with dot figures.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_155a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>268.&mdash;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<span class="pagenum"><a name="Page_156" id="Page_156">[156]</a></span>
-a 14-feet staff, which are with great difficulty distinguishable
-at a distance, the author employs dots only as before mentioned&mdash;one
-dot for the 11, two for the 12, and three for the 13, as
-shown <i>C</i> 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.</p>
-<p>269.&mdash;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 <i>Sopwith's ladder</i>. 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.</p>
-<p>270.&mdash;<span class="large bold">Metrical Staves.</span>&mdash;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&mdash;one
-dot for 1 metre, two dots for 2 metres, three dots for 3 metres.<span class="pagenum"><a name="Page_157" id="Page_157">[157]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i157">
-  <img class="w100" src="images/i_157.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 103.&mdash;<i>Metres and Half Centimetres.</i></p>
-    <p class="caption float-right">Fig. 103A.&mdash;<i>Centimetres.</i></p>
-    <p class="caption"><i>Stanley's metre levelling staves.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_157a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>271.&mdash;<span class="large bold">Feet and Inches Staff.</span>&mdash;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.<span class="pagenum"><a name="Page_158" id="Page_158">[158]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i158a">
-  <img class="w100" src="images/i_158a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 104.&mdash;<i>Stanley's rough levelling staff.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_158aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>272.&mdash;<span class="large bold">Mining Staves.</span>&mdash;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, <a href="#Art_259">art. 259</a>.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i158b">
-  <img class="w100" src="images/i_158b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 105.&mdash;<i>Stanley's patented mine staff.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_158ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>273.&mdash;<span class="large bold">Stanley's Portable Staff.</span>&mdash;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<span class="pagenum"><a name="Page_159" id="Page_159">[159]</a></span>
-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.<a name="FNanchor_8_8" id="FNanchor_8_8"></a><a href="#Footnote_8_8" class="fnanchor">[8]</a> The entire length of the staff when
-closed in 20&frac12; 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&mdash;<i>E</i> shows back view, <i>F</i> front view, <i>G</i>
-cross section, <i>A</i> longitudinal section. The holding springs are
-shown at <i>BB′B″</i>.</p>
-<p>274.&mdash;A portable mine staff designed by Mr. G. J. Jee,<a name="FNanchor_9_9" id="FNanchor_9_9"></a><a href="#Footnote_9_9" class="fnanchor">[9]</a>
-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.</p>
-<p>275&mdash;<span class="large bold">Papering or Repapering a Sopwith Staff.</span>&mdash;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
-<span class="pagenum"><a name="Page_160" id="Page_160">[160]</a></span>
-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.</p>
-<p>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.</p>
-<p>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<span class="pagenum"><a name="Page_161" id="Page_161">[161]</a></span>
-be laid on with a flat bristle brush (varnish brush), and set in
-a warm room to dry for a day or two.</p>
-<p>276.&mdash;<span class="large bold">Preservation of the Levelling Staff in Use.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i161">
-  <img class="w100" src="images/i_161.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 106.&mdash;<i>Pad for holding a staff and tripod.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_161a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>277.&mdash;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.</p>
-<p>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.</p>
-<p>278.&mdash;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.</p>
-<p><span class="pagenum"><a name="Page_162" id="Page_162">[162]</a></span></p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe36_375" id="i162a">
-  <img class="w100" src="images/i_162a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 107.&mdash;<i>Improved pad for staff and tripod.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_162aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>279&mdash;<span class="large bold">Repairing Figures and Divisions.</span>&mdash;Surveyors
-going abroad will find it very convenient to have a few tubes of
-artist's oil colours&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i162b">
-  <img class="w100" src="images/i_162b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 108.&mdash;<i>Iron triangle to support a staff.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_162ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>280.&mdash;<span class="large bold">Iron Triangle.</span>&mdash;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.</p>
-<p><span class="pagenum"><a name="Page_163" id="Page_163">[163]</a></span></p>
-<p>281.&mdash;<span class="large bold">Staff Level.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i163">
-  <img class="w100" src="images/i_163.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 109.&mdash;<i>Staff level, &frac12; scale.</i></p>
-    <p class="caption float-right">Fig. 110.&mdash;<i>Staff-holder, 1/10 scale.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_163a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>282.&mdash;<span class="large bold">Staff-holder.</span>&mdash;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.</p>
-<p>283.&mdash;<span class="large bold">Practice of Levelling with the Staff.</span>&mdash;This
-subject can be followed here only so far as to exemplify the
-uses of the instruments and of accessories connected with such<span class="pagenum"><a name="Page_164" id="Page_164">[164]</a></span>
-instruments. For practical levelling we have the standard
-original works of Simms, Ainsley, and others, with many
-modern works.<a name="FNanchor_10_10" id="FNanchor_10_10"></a><a href="#Footnote_10_10" class="fnanchor">[10]</a></p>
-<p>284.&mdash;<i>For Holding the Staff</i>, 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:&mdash;"I
-generally enter into confidential chat with my staff holder,
-in which I explain to him the vast importance of his duties,
-<i>i.e.</i>, 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:&mdash;</p>
-<p class="px" style="padding-top: .5em;">"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.</p>
-<p class="px">"2. When the staff is once on a point never move it
-unless signalled to do so.</p>
-<p class="px">"3. Examine the staff regularly before setting it down
-to see that no dirt is sticking to the bottom of it.</p>
-<p class="px">"4. Always stand erect behind the staff, so that the
-figures face the level.</p>
-<p class="px">"5. Do not let any part of the hand come before the
-face of the staff.</p>
-<p class="px">"6. In no case put a downward pressure on the staff.</p>
-<p class="px" style="padding-bottom: .5em;">"7. If the grass be long, mossy, or spongy, tread
-it down, so that the staff shall have a firm
-footing&mdash;select a firm spot if the selection is
-left to yourself."<a name="FNanchor_11_11" id="FNanchor_11_11"></a><a href="#Footnote_11_11" class="fnanchor">[11]</a></p>
-
-<p>285.&mdash;The manner of setting up a level has been already
-described in the previous chapter. The leveller generally
-<span class="pagenum"><a name="Page_165" id="Page_165">[165]</a></span>
-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&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i165">
-  <img class="w100" src="images/i_165.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 111.&mdash;<i>Level height tape.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_165a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>286.&mdash;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.</p>
-<p>287.&mdash;<i>The Reading of the Staff.</i>&mdash;The first position, which
-is afterwards termed the <i>back reading</i>, 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<span class="pagenum"><a name="Page_166" id="Page_166">[166]</a></span>
-of the telescope being also noted in the levelling book, to be
-described. Thus in Fig. 112, <i>S</i> the first staff; <i>L</i> the first
-station for taking levels. The fore reading <i>L</i> to <i>S′</i> reads to a
-higher part of the staff <i>S′</i>; <i>L′</i> next level station back sight.
-<i>L′S′</i> reads high on the staff <i>S′</i>; fore sight <i>L′S″</i> reads low;
-back sight <i>L″S″</i> again low, following the contour; fore sight
-<i>L″S‴</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i166">
-  <img class="w100" src="images/i_166.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 112.&mdash;<i>Practice of levelling.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_166a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>288.&mdash;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.</p>
-<p>289.&mdash;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<span class="pagenum"><a name="Page_167" id="Page_167">[167]</a></span>
-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.</p>
-<p>290.&mdash;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&mdash;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:&mdash;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°&mdash;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<span class="pagenum"><a name="Page_168" id="Page_168">[168]</a></span>
-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.</p>
-<p>291.&mdash;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.</p>
-<p>292.&mdash;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.</p>
-<p>293.&mdash;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,<span class="pagenum"><a name="Page_169" id="Page_169">[169]</a></span>
-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 2&frac12; seconds&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i169">
-  <img class="w100" src="images/i_169.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 113.&mdash;<i>Calder stove used as a lamp.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_169a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>294.&mdash;<span class="large bold">Lamp.</span>&mdash;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<span class="pagenum"><a name="Page_170" id="Page_170">[170]</a></span>
-lamp. It has a wick about 3&frac12; 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.</p>
-<p>The heliostat is sometimes used for check levelling in
-sunlight. This will be described further on with the theodolite.</p>
-<p>295.&mdash;<span class="large bold">Curvature Corrections of the earth and of
-Refraction</span> to be made use of occasionally for check levelling.
-The rule for finding curvature is "<i>That the difference
-between true and apparent level is equal to the square of the
-distance between two places or stations in miles&mdash;divided by
-the earth's mean diameter, 7916 miles</i>"; 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,<a name="FNanchor_12_12" id="FNanchor_12_12"></a><a href="#Footnote_12_12" class="fnanchor">[12]</a> which varies according to the
-atmospheric pressure.</p>
-<p>296.&mdash;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:&mdash;</p>
-<div class="m10" style="padding: 1em 0;">
-<table summary="" style="border: 1px solid black; border-collapse: collapse;" >
-<caption style="padding-bottom: .5em;"><i>Table of Differences of Apparent and True Level for Distances in Chains.</i></caption>
-  <tr>
-    <th class="td01" style="padding: .25em .5em;">Distances in Chains.</th>
-    <th class="td01" style="padding: 0em 1em; border-right: 2px solid black;">Curvature minus<br />Refraction in Dec. Ft.</th>
-    <th class="td01" style="padding: 0em 1em;">Distances in Chains.</th>
-    <th class="td01" style="padding: 0em 1em;">Curvature minus<br />Refraction in Dec. Ft.</th>
-  </tr>
-  <tr>
-    <td class="td01">1</td>
-    <td class="td01 br2">·000089</td>
-    <td class="td01">14</td>
-    <td class="td01">·0175</td>
-  </tr>
-  <tr>
-    <td class="td02">2</td>
-    <td class="td02 br2">·000358</td>
-    <td class="td02">17</td>
-    <td class="td02">·0258</td>
-  </tr>
-  <tr>
-    <td class="td02">3</td>
-    <td class="td02 br2">·000804</td>
-    <td class="td02">20</td>
-    <td class="td02">·0357</td>
-  </tr>
-  <tr>
-    <td class="td02">4</td>
-    <td class="td02 br2">·001435</td>
-    <td class="td02">22</td>
-    <td class="td02">·05</td>
-  </tr>
-  <tr>
-    <td class="td02">5</td>
-    <td class="td02 br2">·002233</td>
-    <td class="td02">24</td>
-    <td class="td02">·06</td>
-  </tr>
-  <tr>
-    <td class="td02">6</td>
-    <td class="td02 br2">·003216</td>
-    <td class="td02">26</td>
-    <td class="td02">·07</td>
-  </tr>
-  <tr>
-    <td class="td02">7</td>
-    <td class="td02 br2">·00437</td>
-    <td class="td02">28</td>
-    <td class="td02">·08</td>
-  </tr>
-  <tr>
-    <td class="td02">8</td>
-    <td class="td02 br2">·0057</td>
-    <td class="td02">30</td>
-    <td class="td02">·09</td>
-  </tr>
-  <tr>
-    <td class="td02">9</td>
-    <td class="td02 br2">·0072</td>
-    <td class="td02">40</td>
-    <td class="td02">·14</td>
-  </tr>
-  <tr>
-    <td class="td02">10</td>
-    <td class="td02 br2">·089</td>
-    <td class="td02">60</td>
-    <td class="td02">·31</td>
-  </tr>
-  <tr>
-    <td class="td02" style="border-bottom: 1px solid black;">11</td>
-    <td class="td02" style="border-bottom: 1px solid black; border-right: 2px solid black;">·011</td>
-    <td class="td02" style="border-bottom: 1px solid black;">80</td>
-    <td class="td02" style="border-bottom: 1px solid black;">·56</td>
-  </tr>
-</table>
-</div>
-<p><span class="pagenum"><a name="Page_171" id="Page_171">[171]</a></span></p>
-<p>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.</p>
-<p>297.&mdash;<span class="large bold">Pegs.</span>&mdash;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. <i>A</i> the
-peg shown with a nail in its head, 1/8 size. <i>B</i> nail about full
-size.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i171">
-  <img class="w100" src="images/i_171.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 114.&mdash;<i>A, staff pegs of sawn timber, 1/8 scale; B, nail, full size.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_171a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>298.&mdash;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<span class="pagenum"><a name="Page_172" id="Page_172">[172]</a></span>
-then prevented, as this principle produces an alternate plus
-and minus error.</p>
-<p>299.&mdash;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 <i>A Manual of Surveying for India</i>,<a name="FNanchor_13_13" id="FNanchor_13_13"></a><a href="#Footnote_13_13" class="fnanchor">[13]</a> 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.</p>
-<p>300.&mdash;<span class="large bold">Levelling Books</span> 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.</p>
-<p>301.&mdash;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.</p>
-<p>302.&mdash;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.</p>
-<p><span class="pagenum"><a name="Page_173" id="Page_173">[173]</a></span></p>
-
-<p class="noindent center pt1">Fig. 115.&mdash;<i>Specimens of levelling books, 1/3 scale.</i></p>
-
-<div class="figcenter">
-<div class="figcenter illowe37_5" id="i173a">
-  <img class="w100" src="images/i_173a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption"><i>Ordinary Level Book</i> with columns for No., Back Sight, Intermediate, Rise, Fall,
-Reduced Level, Distance, Remarks.</p>
-    <p class="caption ebhide clear"><a href="images/i_173aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<div class="figcenter">
-<div class="figcenter illowe37_5" id="i173b">
-  <img class="w100" src="images/i_173b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption"><i>Collimation Level Book</i>, with columns for Back Sight, Intermediate, Fore Sight,
-Height of Collimation, Reduced Level, Distance, Remarks.</p>
-    <p class="caption ebhide clear"><a href="images/i_173ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<div class="figcenter">
-
-<div class="figcenter illowe37_5" id="i173c">
-  <img class="w100" src="images/i_173c.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption"><i>Railway Engineers' Level Book</i>, ruled for Back, Intermediate, Fore Sight, Rise,
-Fall, Distance, Reduced Level, Formation Levels, Cutting, Embankment,
-Remarks.</p>
-    <p class="caption ebhide clear"><a href="images/i_173ca.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<div class="figcenter">
-
-<div class="figcenter illowe37_5" id="i173d">
-  <img class="w100" src="images/i_173d.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption"><i>Tacheometer Survey Book</i>, ruled as above illustration.</p>
-    <p class="caption ebhide clear"><a href="images/i_173da.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<div class="figcenter" style="padding-bottom: 1em;">
-
-<div class="figcenter illowe37_5" id="i173e">
-  <img class="w100" src="images/i_173e.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption"><i>Traverse Survey  Book</i>, ruled as above illustration.</p>
-    <p class="caption ebhide clear"><a href="images/i_173ea.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>303.&mdash;<i>The Ink Bottle</i> mostly used is that known as the
-<span class="pagenum"><a name="Page_174" id="Page_174">[174]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe11_6875" id="i174">
-  <img class="w100" src="images/i_174.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 116.&mdash;<i>Excise ink bottle.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_174a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_175" id="Page_175">[175]</a></span></p>
-<h2>CHAPTER VI.</h2>
-</div>
-<p class="ch">DIVISION OF THE CIRCLE AND METHODS EMPLOYED IN TAKING
-ANGLES&mdash;DIVIDING ENGINE&mdash;SURFACES FOR GRADUATION&mdash;VERNIER&mdash;VARIOUS
-SECTIONS&mdash;READING MICROSCOPES&mdash;SHADES&mdash;MICROMETERS&mdash;CLAMP
-AND TANGENT MOTIONS&mdash;OF
-LIMBS&mdash;OF AXES&mdash;USE AND WEAR&mdash;DIFFERENCE OF
-HYPOTENUSE AND BASE.</p>
-<p>304.&mdash;<span class="large bold">Division of the Circle.</span>&mdash;<i>Sexagesimal Division.</i>&mdash;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 <i>micrometer</i>, placed
-tangentially to the divided circle; or by a series of lines
-placed at equal distances apart in front of an eye-piece or<span class="pagenum"><a name="Page_176" id="Page_176">[176]</a></span>
-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.</p>
-<p>305.&mdash;<i>Centesimal Division.</i>&mdash;Ten to fifteen years ago on
-the Continent generally, and in America occasionally, the
-division of the circle into 400-grades and &frac12;-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.</p>
-<p>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.</p>
-<p>306.&mdash;<span class="large bold">Dividing Engine.</span>&mdash;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<span class="pagenum"><a name="Page_177" id="Page_177">[177]</a></span>
-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.</p>
-<p>307.&mdash;<i>Ramsden's Engine</i> 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 <i>tangent</i> 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.</p>
-<p>308.&mdash;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<span class="pagenum"><a name="Page_178" id="Page_178">[178]</a></span>
-that the cuts upon the circle&mdash;technically the limb&mdash;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, <i>Phil. Trans.</i>, 1809: <i>Memoirs of the
-Royal Astronomical Soc.</i>, vol. v. p. 325; vol. viii. p. 141;
-vol. ix. pp. 17 and 35. For various plans that have been
-tried see <i>Holtzapffel's Turning and Mechanical Manipulation</i>,
-pp. 651&ndash;955.</p>
-<p>309.&mdash;<i>The Material</i> upon which the <i>limb</i> 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
-<i>grain</i>, 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&mdash;the
-horizontal circle of Everest's theodolite, limbs of sextants,
-box sextants, etc. In Fig. 117 the silver is shown at <i>A</i>,
-in the section to which it is drawn by a plate after it is
-cut in slips. It is shown placed in its groove <i>B</i> ready for
-planishing down. By this method certainty of dense surface
-is obtained for the future division.</p>
-<p>310.&mdash;Upon bevelled edges and outer surfaces the rolled<span class="pagenum"><a name="Page_179" id="Page_179">[179]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe36_9375" id="i179">
-  <img class="w100" src="images/i_179.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 117.&mdash;<i>Insertion of silver in circle.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_179a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>311.&mdash;<span class="large bold">Graduating.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i179b">
-  <img class="w100" src="images/i_179b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 118.&mdash;<i>Piece of charcoal.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_179ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>312.&mdash;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.</p>
-<p>313.&mdash;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<span class="pagenum"><a name="Page_180" id="Page_180">[180]</a></span>
-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&mdash;an old coin which is worn smooth will do&mdash;to see
-that it is not <i>scratchy</i>. No kind of polishing powder should
-in any case be used for cleaning limbs or verniers, as <i>this</i> is
-sure to rub down the edges of the cuts and thereby ruin the
-divisions of the instrument.</p>
-<p>314.&mdash;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 <i>grubby</i> 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.</p>
-<p>315.&mdash;<span class="large bold">The Vernier Reading Index.</span>&mdash;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, <i>Construction, Usage, et Proprietes du
-Quadrant Nouveau de Mathematique</i>. This invention was
-possibly foreshadowed, as it is mentioned by Cristopher Clavius
-in his <i>Opera Mathematica</i>, 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.</p>
-<p>316.&mdash;The value of the vernier as a means of reading<span class="pagenum"><a name="Page_181" id="Page_181">[181]</a></span>
-small quantities depends upon the fact that the <i>eye</i> 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.</p>
-<p>317.&mdash;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
-<i>n</i>′ + 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i182a">
-  <img class="w100" src="images/i_182a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 119.&mdash;<i>Origin of vernier scale.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_182aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p id="Art_318">318.&mdash;<i>The Vernier Scale</i>, as employed by Vernier, was<span class="pagenum"><a name="Page_182" id="Page_182">[182]</a></span>
-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 <i>inverse reading</i>,
-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 <i>advances</i> 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<span class="pagenum"><a name="Page_183" id="Page_183">[183]</a></span>
-this reading must be <i>n</i>° or <i>n</i>° 30′ at any equivalent position in
-relation to any line on the limb.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i182b">
-  <img class="w100" src="images/i_182b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 120.&mdash;<i>Vernier scale, reading 23° 12′.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_182ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>319.&mdash;In Fig. 120 the arrow upon the vernier scale is
-shown reading at a position beyond 23°, which we then know
-must be 23° <i>n′</i>. 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 <i>n′</i> is 12′, and the reading is
-altogether 23° 12′.</p>
-<p>320.&mdash;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 <i>minutes</i>
-only, and this <i>by coincidence of lines only</i>, and that it has
-nothing to do with degrees, which are indicated by the arrow
-<i>only</i>. 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i183">
-  <img class="w100" src="images/i_183.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 121.&mdash;<i>Vernier scale, reading, 23° 47′.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_183a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>321.&mdash;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′ + <i>n′</i>
-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′.</p>
-<p>322.&mdash;The principle of the vernier, upon which it takes<span class="pagenum"><a name="Page_184" id="Page_184">[184]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i184a">
-  <img class="w100" src="images/i_184a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 122.&mdash;<i>Vernier reading centrally to 3′.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_184aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i184b">
-  <img class="w100" src="images/i_184b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 123.</p>
-    <p class="caption ebhide clear"><a href="images/i_184ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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″.</p>
-<p><span class="pagenum"><a name="Page_185" id="Page_185">[185]</a></span></p>
-<p>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″.</p>
-<p>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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i185a">
-  <img class="w100" src="images/i_185a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 124.</p>
-    <p class="caption ebhide clear"><a href="images/i_185aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p class="noindent">28 degrees 40 minutes on the circle and 12 minutes 20
-seconds on the vernier, giving a total of 28° 52′ 20″.</p>
-<p>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″.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i185b">
-  <img class="w100" src="images/i_185b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 125.</p>
-    <p class="caption ebhide clear"><a href="images/i_185ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>323.&mdash;<i>For Centesimal Division</i> 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<span class="pagenum"><a name="Page_186" id="Page_186">[186]</a></span>
-to ·005 by a vernier 40 to 39, or more closely if desired by a
-micrometer, to be described presently.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i186a">
-  <img class="w100" src="images/i_186a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Figs. 126, 127.&mdash;<i>Sections of scales and vernier for circular readings.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_186aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<div class="figcenter padding1" id="Fig_128">
-
-<div class="figcenter illowe37_5" id="i186b">
-  <img class="w100" src="images/i_186b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Figs. 128, 129.&mdash;<i>Sections of scales and vernier for circular readings.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_186ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>324.&mdash;<span class="large bold">Surfaces of Limb and Vernier.</span>&mdash;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 <i>VV</i> are verniers, <i>LL</i> 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<span class="pagenum"><a name="Page_187" id="Page_187">[187]</a></span>
-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.</p>
-<p>325.&mdash;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 <i>a</i>, 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.</p>
-<p>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.</p>
-<p>326.&mdash;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<span class="pagenum"><a name="Page_188" id="Page_188">[188]</a></span>
-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.</p>
-<p>327.&mdash;<span class="large bold">Reading Microscope.</span>&mdash;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, <a href="#Art_82">art. 82</a>.
-Frequently the microscope, technically called the <i>reader</i>, 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.</p>
-<p>328.&mdash;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<span class="pagenum"><a name="Page_189" id="Page_189">[189]</a></span>
-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.</p>
-<p>329.&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i189">
-  <img class="w100" src="images/i_189.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 130.&mdash;<i>Reader fixed normal to surface.</i></p>
-    <p class="caption float-right">Fig. 131.&mdash;<i>Jointed reader to set to any angle.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_189a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>330.&mdash;Fig. 130 shows a good rigid form of reader for an
-oblique plane of division:&mdash;<i>V</i> vernier, <i>L</i> 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; <i>N</i> arm of reader, <i>O</i> 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<span class="pagenum"><a name="Page_190" id="Page_190">[190]</a></span>
-instrument. This plan admits of adjustment of the reader for
-reflection of light from the division, or for reading <i>down the
-lines</i> 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, <a href="#Art_82">p. 41</a>), 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe19_3125" id="i190a">
-  <img class="w100" src="images/i_190a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 132.&mdash;<i>Section of movable arm fitting to reader.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_190aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>331.&mdash;<span class="large bold">Surface Reflection to Reader.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe29_625" id="i190b">
-  <img class="w100" src="images/i_190b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 133.&mdash;<i>Reflecting surface reader.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_190ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p><span class="pagenum"><a name="Page_191" id="Page_191">[191]</a></span></p>
-<p>332.&mdash;<span class="large bold">Shades for Vernier.</span>&mdash;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, <a href="#i186b">Fig. 128</a>, 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 <i>vice versa</i>. 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; <i>L</i> limb,
-<i>V</i> vernier, <i>S</i> shade of ground glass, <i>M</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i191">
-  <img class="w100" src="images/i_191.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 134.&mdash;<i>Oblique reading microscope with shade, French plan.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_191a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>333.&mdash;For ordinary instruments with no provision for
-shading, a piece of transparent horn about 2&frac14; inches by
-1&frac14; 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, <a href="#i096">Fig. 52</a>.
-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.</p>
-<p><span class="pagenum"><a name="Page_192" id="Page_192">[192]</a></span></p>
-<p>334.&mdash;<span class="large bold">Micrometer Microscope</span>, <i>for Reading Subdivisions</i>.&mdash;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.</p>
-<p>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.</p>
-<p>335.&mdash;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.</p>
-<p>336.&mdash;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.</p>
-<p>337.&mdash;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,<span class="pagenum"><a name="Page_193" id="Page_193">[193]</a></span>
-<a href="#i189">Fig. 130</a>. 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i193a">
-  <img class="w100" src="images/i_193a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 135.&mdash;<i>Side elevation of Troughton's micrometer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_193aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i193b">
-  <img class="w100" src="images/i_193b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 136.&mdash;<i>Section of micrometer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_193ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p><span class="pagenum"><a name="Page_194" id="Page_194">[194]</a></span></p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i194">
-  <img class="w100" src="images/i_194.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 137.&mdash;<i>Micrometer slide.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_194a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>338.&mdash;<span class="large bold">The Micrometer</span>, 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, <a href="#i042">Fig. 16</a>. 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; <i>a</i> the
-micrometer, <i>q</i> microscope body tube. This has a male screw
-outside at <i>b′</i>, upon which there are two collars <i>dd′</i> with capstan
-heads. These collars hold the microscope upon the
-reading frame <i>b</i> at any required distance from the limb to
-secure proper focal adjustment. <i>g</i> 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 <i>s</i>. This tube has a locking nut <i>i</i>
-to secure it from after movement when it is once properly
-adjusted. <i>h</i> an achromatic object glass of half an inch or<span class="pagenum"><a name="Page_195" id="Page_195">[195]</a></span>
-over in focus. <i>e</i> the casing that receives the eye-piece which
-screws into the outer plate of the micrometer. <i>f</i> 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.</p>
-<p>339.&mdash;The micrometer frame, Fig. 137, <i>a</i> has a fixed scale
-or <i>comb</i>, 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 <i>r</i> 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.</p>
-<p>340.&mdash;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 <i>comb</i>, 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<span class="pagenum"><a name="Page_196" id="Page_196">[196]</a></span>
-1′ part, to ensure certainty of reading by the mean of two
-observations.</p>
-<p>341.&mdash;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&mdash;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 <i>dd′</i> 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.</p>
-<p>342.&mdash;The two points where the divisions and their images
-are situated are termed the <i>conjugate foci</i> 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 <i>f</i>, and the distance of the focal plane of its image
-within the tube <i>F</i>, the image will exceed that of the object in
-the ratio of <i>Ff</i>, or <i>F</i>/<i>f</i> will represent the magnified image. By
-this method it will be seen that the expression <i>F</i>/<i>f</i> will have
-an increased value, if we either increase <i>F</i> or diminish <i>f</i>, which<span class="pagenum"><a name="Page_197" id="Page_197">[197]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i197a">
-  <img class="w100" src="images/i_197a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 138.&mdash;<i>Grubb's plan of securing micrometer screw.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_197aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>343.&mdash;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 <i>EE′</i>,
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i197b">
-  <img class="w100" src="images/i_197b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 139.&mdash;<i>Stanley's micrometer slide.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_197ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>344.&mdash;<span class="large bold">Stanley's Micrometer.</span>&mdash;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<span class="pagenum"><a name="Page_198" id="Page_198">[198]</a></span>
-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 <i>H</i> 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 <i>T</i> 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.</p>
-<p>345.&mdash;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.</p>
-<p>The strip of glass <i>A</i> is fixed by a clamp and two screws to
-the side of the micrometer box. The slip <i>B</i> is ground and
-polished to fit <i>A</i>. <i>B</i> is carried by the micrometer frame <i>F</i>,
-which holds it in a clamp by two screws. A spring, not shown,
-presses <i>B</i> against <i>A</i>, so that any displacement of the micrometer
-lines may be made by the milled head. The lines upon
-<i>A</i> are adjusted to the position of the circle they are intended
-to read at exactly 5′ or other quantity.</p>
-<p>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<span class="pagenum"><a name="Page_199" id="Page_199">[199]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i199">
-  <img class="w100" src="images/i_199.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 140.&mdash;<i>Stanley's micrometer reading.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_199a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>Fig. 140 shows at <i>C</i> a portion of the theodolite circle as
-seen through the micrometer microscope. <i>P</i> is the movable
-pointer, <i>M</i> the micrometer head, and <i>I</i> the index or reading
-line.</p>
-<p>To use the micrometer the first steps are to carefully focus
-the pointer <i>P</i> 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 <i>M</i>, set the pointer <i>P</i> to the centre of its travel, so that
-it covers the <i>V</i> cut in the bottom of the slide, and leave the
-<i>0</i> of the micrometer head exactly opposite the index line <i>I</i>.
-Now proceed in the same manner with the other microscope.
-After setting the microscopes as described above, lightly clamp<span class="pagenum"><a name="Page_200" id="Page_200">[200]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i200a">
-  <img class="w100" src="images/i_200a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 141.</p>
-    <p class="caption ebhide clear"><a href="images/i_200aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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 <i>M</i>.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i200b">
-  <img class="w100" src="images/i_200b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 142.</p>
-    <p class="caption ebhide clear"><a href="images/i_200ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-<p><span class="pagenum"><a name="Page_201" id="Page_201">[201]</a></span></p>
-<p>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 <i>M</i> 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 <i>M</i>. 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.</p>
-<p>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.</p>
-<p>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 2&frac12; seconds.</p>
-<p>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 <i>V</i>'s and setting the micrometer
-heads to <i>0</i> they are not exactly opposite one another
-(180 degrees apart), then their setting has become disturbed
-and must be readjusted in the following manner:&mdash;First bring
-the <i>V</i> of one micrometer to the 360° on the circle, then see if
-the <i>V</i> of the opposite micrometer is exactly at 180°, if not<span class="pagenum"><a name="Page_202" id="Page_202">[202]</a></span>
-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 <i>V</i>'s and adjusted them if necessary, the next
-step is to set the pointers <i>P</i> exactly to 360° and 180° respectively,
-in which position the divided heads should both read <i>0</i>;
-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 <i>0</i> at the index line and
-retighten the screws. This completes the adjustment.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i202">
-  <img class="w100" src="images/i_202.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 143, 144.&mdash;<i>Sections of clamp and tangent in two directions.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_202a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p id="Art_346">346.&mdash;<span class="large bold">Clamp and Tangent Adjustment.</span>&mdash;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 <i>clamp and tangent screw motion</i> 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<span class="pagenum"><a name="Page_203" id="Page_203">[203]</a></span>
-in detail, two of which, the most general and especially
-adapted to surveying instruments, will be described.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe29_4375" id="i203">
-  <img class="w100" src="images/i_203.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 145.&mdash;<i>Elevation and part section of clamp and tangent.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_203a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>347.&mdash;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 <i>A</i> cut off. The stem of the tangent screw is
-shown in section at <i>E</i>. In all the figures <i>L</i> is the limb of the
-circle or arc. This has a groove at its under side at <i>G</i>, into
-which a fillet of the clamping piece <i>C</i> is inserted to make the
-clamp slide freely about the periphery of the circle when the
-clamping screw <i>A</i> is loose. A spring is sometimes inserted to
-open the clamp between the sliding piece <i>K</i> and the clamp <i>C</i>.
-<i>FF</i>, Figs. 143, 144 is the tangent nut to <i>E</i>. 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 <i>F</i> has to move to the direction<span class="pagenum"><a name="Page_204" id="Page_204">[204]</a></span>
-horizontal to the plane of the tangent screw; therefore it has
-an axis vertical to the plane of the clamp. This is shown at
-<i>K</i>. 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 <i>B</i>, 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 <i>D</i>. 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 <i>E</i>. This is tightened up by means of a
-screw-driver applied at <i>E</i>. The boss <i>B</i> has a vertical axis <i>N</i>,
-similar to the tangent nut, and is attached to a solid part of
-the instrument by the washer and nut shown at <i>0</i>.</p>
-<p>348.&mdash;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 <i>G</i> 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.</p>
-<p id="Art_349">349.&mdash;<span class="large bold">Axis Clamp and Tangent.</span>&mdash;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 <i>C</i> surrounds the axis as a<span class="pagenum"><a name="Page_205" id="Page_205">[205]</a></span>
-collar, from which two <i>lugs</i> in the same casting are projected
-at <i>a</i>. These are brought tight upon the outer axis socket <i>B</i> by
-means of the screw <i>W</i>, which has a <i>wing-nut</i> 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 <i>a</i> be sawn through afterwards.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i205">
-  <img class="w100" src="images/i_205.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 146.&mdash;<i>Clamp and tangent to a vertical axis.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_205a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>350.&mdash;The tangent screw adjustment is shown at <i>T</i>, moved
-by the milled head <i>M</i>, the boss <i>E</i> 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 <i>tumbling piece</i> direct on the
-axis by a screw. This is shown in Fig 147, screw <i>W</i>;
-tumbling piece <i>A</i>. This produces a direct clamp upon the<span class="pagenum"><a name="Page_206" id="Page_206">[206]</a></span>
-axis socket <i>B′</i>. The clamp ring <i>CC′</i> is made loose on its
-socket.</p>
-<p>351.&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i206">
-  <img class="w100" src="images/i_206.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 147.&mdash;<i>Clamp and tangent to vertical axis, German plan&mdash;Hunäus.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_206a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>The arrangement Fig. 147 shows also a spring S falling
-upon a stud at <i>E</i>, 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.<a name="FNanchor_14_14" id="FNanchor_14_14"></a><a href="#Footnote_14_14" class="fnanchor">[14]</a> The plan is found practically
-<span class="pagenum"><a name="Page_207" id="Page_207">[207]</a></span>
-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.</p>
-<p>352.&mdash;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: <i>S</i>
-socket, <i>F</i> flange, <i>C</i> clamping screw, <i>T</i> tangent screw. The
-tangent in this arrangement acts against a spiral spring contained
-in a tube <i>A</i>, which gives a very steady motion to the
-instrument.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i207">
-  <img class="w100" src="images/i_207.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 148.&mdash;<i>French axis clamp and tangent.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_207a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>353.&mdash;Some particulars of the care required in the manufacture
-of the tangent screw were given, <a href="#Art_22">art. 22</a>. 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<span class="pagenum"><a name="Page_208" id="Page_208">[208]</a></span>
-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.</p>
-<p>354.&mdash;<span class="large bold">For Testing and Adjusting the Fitting of
-the Tangent Screw.</span>&mdash;The clamp should be tightened
-down and the ball <i>B</i>, <a href="#i202">Fig. 144</a>, 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 <i>B</i> it will
-be felt as a jar, or technically, a slight <i>loss of time</i>. If this be
-in the ball <i>B</i> it can be taken up by the screw <i>E</i> 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 <i>N</i> and <i>K</i>. 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.</p>
-<p>355.&mdash;<span class="large bold">Use and Wear of the Clamp.</span>&mdash;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<span class="pagenum"><a name="Page_209" id="Page_209">[209]</a></span>
-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 <i>only slightly in excess of this</i>. 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 <i>brains</i>," 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.</p>
-<p>356.&mdash;<i>Use and Wear of the Tangent Screw.</i>&mdash;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&mdash;in some cases of several minutes of arc&mdash;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<span class="pagenum"><a name="Page_210" id="Page_210">[210]</a></span>
-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&mdash;<i>near part, middle part</i>, and <i>end part</i>. 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.</p>
-<p>357.&mdash;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<span class="pagenum"><a name="Page_211" id="Page_211">[211]</a></span>
-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.</p>
-<p>358.&mdash;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, <i>C</i> nut, through which tangent
-screw passes; <i>B</i> tangent boss, A milled-head, <i>H</i> covering tube
-to the point of the screw, <i>GG′</i> <i>EE′</i> pair of telescopic tubes
-which cover the screw. A German silver or platinum spring
-works inside these tubes, keeping a constant separating pressure
-between <i>C</i> and <i>B</i> to take up any loss of time in the screw.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i211">
-  <img class="w100" src="images/i_211.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 149.&mdash;<i>Protected tangent screw with helical spring.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_211a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>359&mdash;<span class="large bold">Free Tangent Screw.</span>&mdash;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<span class="pagenum"><a name="Page_212" id="Page_212">[212]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i212a">
-  <img class="w100" src="images/i_212a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 150.&mdash;<i>Free tangent adjustment.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_212aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>360.&mdash;<span class="large bold">Loss of Time by Wear</span> 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, <i>S</i> section of tangent screw,
-<i>T</i> tumbling piece moved by the adjusting screw, shown above,
-for wear of the tangent screw. This adjusting screw <i>A</i> should
-be tapped tight without oil, and put together dry to prevent its
-receding by pressure.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe12_875" id="i212b">
-  <img class="w100" src="images/i_212b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 151.&mdash;<i>Tumbling piece adjustment for wear of tangent screw.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_212ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>361.&mdash;<span class="large bold">Hypotenuse and Base.</span>&mdash;Other trigonometrical
-values besides the division of the circle into equal parts are occasionally
-placed on instruments for special purposes. The most<span class="pagenum"><a name="Page_213" id="Page_213">[213]</a></span>
-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.</p>
-<p>362.&mdash;<span class="large bold">A Horizontal Scale of Tangents</span> 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.</p>
-<p>363.&mdash;<span class="large bold">Gradient Scale.</span>&mdash;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.</p>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_214" id="Page_214">[214]</a></span></p>
-<h2>CHAPTER VII.</h2>
-</div>
-<p class="ch">THEODOLITES&mdash;CONSTRUCTIVE DETAILS OF 5-INCH AND 6-INCH
-TRANSITS&mdash;SPECIAL ADDITIONAL PARTS&mdash;PLUMMETS WITH
-SCREW ADJUSTMENTS OF IMPROVED FORM&mdash;STRIDING LEVEL&mdash;LAMP&mdash;ADJUSTMENT
-OF AXIS OVER A POINT&mdash;SOLAR
-ATTACHMENT&mdash;PHOTOGRAPHIC ATTACHMENT.</p>
-<p>364.&mdash;<span class="large bold">The Theodolite</span> 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.</p>
-<p>365.&mdash;The theodolite in all its essential features, as
-differentiated from sighted compasses for taking angles, mentioned
-by Digges,<a name="FNanchor_15_15" id="FNanchor_15_15"></a><a href="#Footnote_15_15" class="fnanchor">[15]</a> was the invention of Jonathan Sisson, a
-celebrated mathematical instrument maker of the beginning
-of the 18th century.<a name="FNanchor_16_16" id="FNanchor_16_16"></a><a href="#Footnote_16_16" class="fnanchor">[16]</a> 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.<a name="FNanchor_17_17" id="FNanchor_17_17"></a><a href="#Footnote_17_17" class="fnanchor">[17]</a> Later improvements in portable instruments consist
-<span class="pagenum"><a name="Page_215" id="Page_215">[215]</a></span>
-in the application of the <i>transit</i> 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.</p>
-<p>366.&mdash;Theodolites were commonly made of two distinct
-types, which were originally distinguished as <i>plain</i> theodolites
-and <i>transit</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe22_125" id="i216">
-  <img class="w100" src="images/i_216.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 152.&mdash;<i>5-inch transit theodolite (old form).</i></p>
-    <p class="caption ebhide clear"><a href="images/i_216a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>367.&mdash;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<span class="pagenum"><a name="Page_216" id="Page_216">[216]</a></span>
-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<span class="pagenum"><a name="Page_217" id="Page_217">[217]</a></span>
-the average weight of the transit theodolite illustrated on the
-last page:&mdash;</p>
-<div class="m5" style="padding: .5em 0;">
-<table summary="" width="100%" style="border: 1px solid black; border-collapse: collapse;" class="med90">
-  <tr>
-    <th class="tdc" colspan="2" style="padding: 1.5em; border: 1px solid black;"></th>
-    <th class="tdc" colspan="2" style="border-top: 1px solid black; border-bottom: 1px solid black;">Instrument.</th>
-    <th class="tdc" colspan="2" style="border: 1px solid black;">Case.</th>
-    <th class="tdc" colspan="2" style="border-top: 1px solid black; border-bottom: 1px solid black;">Overcase.</th>
-    <th class="tdc" colspan="2" style="border: 1px solid black;">Tripod.</th>
-  </tr>
-  <tr>
-    <td class="td01b pt1">4-inch</td>
-    <td class="tdc pt1">Transit.</td>
-    <td class="tdrbl pt1">11</td>
-    <td class="tdc pt1">lbs.</td>
-    <td class="tdrbl pt1">8</td>
-    <td class="tdc pt1">lbs.</td>
-    <td class="tdrbl pt1">4</td>
-    <td class="tdc pt1">lbs.</td>
-    <td class="tdrbl pt1">8</td>
-    <td class="tdc pt1">lbs.</td>
-  </tr>
-  <tr>
-    <td class="tdrbl">5-inch</td>
-    <td class="tdc">"</td>
-    <td class="tdrbl">13&frac12;</td>
-    <td class="tdc">"</td>
-    <td class="tdrbl">9</td>
-    <td class="tdc">"</td>
-    <td class="tdrbl">5</td>
-    <td class="tdc">"</td>
-    <td class="tdrbl">9</td>
-    <td class="tdc">"</td>
-  </tr>
-  <tr>
-    <td class="tdrbl">6-inch</td>
-    <td class="tdc">"</td>
-    <td class="tdrbl">19</td>
-    <td class="tdc">"</td>
-    <td class="tdrbl">10</td>
-    <td class="tdc">"</td>
-    <td class="tdrbl">6</td>
-    <td class="tdc">"</td>
-    <td class="tdrbl">11</td>
-    <td class="tdc">"</td>
-  </tr>
-  <tr>
-    <td class="tdr pb1">8-inch</td>
-    <td class="tdc pb1">"</td>
-    <td class="tdrbl pb1">36</td>
-    <td class="tdc pb1">"</td>
-    <td class="tdrbl pb1">20</td>
-    <td class="tdc pb1">"</td>
-    <td class="tdrbl pb1">10</td>
-    <td class="tdc pb1">"</td>
-    <td class="tdrbl pb1">18</td>
-    <td class="tdc pb1">"</td>
-  </tr>
-</table>
-<p class="med90 center">If with lamp extra about &frac34; lb. &nbsp;&nbsp;If with striding level extra about &frac34; lb.</p>
-</div>
-
-<p class="noindent">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.</p>
-<p id="Art_368">368.&mdash;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.</p>
-<p id="Art_369">369.&mdash;<i>The Tripod Stand</i> 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, <a href="#Art_216">art. 216</a>.
-The arrangement of one turn-up leg, as shown <a href="#i115">Fig. 63</a>, is
-very advantageous for the theodolite if it is to be used on
-<span class="pagenum"><a name="Page_218" id="Page_218">[218]</a><br /><a name="Page_219" id="Page_219">[219]</a></span>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.</p>
-<p id="Art_370">370.&mdash;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 <a href="#Art_233">art. 233</a>, 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe23_1875" id="i218">
-  <img class="w100" src="images/i_218.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 153.&mdash;<i>6-inch transit theodolite&mdash;back view, with sections.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_218a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>371.&mdash;<i>The Lower Parallel Plate N.</i>&mdash;This has a large
-boss-piece taken up from its central part, which forms a dome of
-a hollow globular section, technically termed the <i>socket</i>, shown
-at <i>X</i>. In the interior of the lower part <i>N</i> a coarse female
-screw is cut, of about fourteen threads to the inch, which is
-used to attach the instrument to its tripod.</p>
-<p>372.&mdash;<i>The Upper Parallel Plate</i> is constructed as a flange
-from a solid <i>boss L</i>. 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<span class="pagenum"><a name="Page_220" id="Page_220">[220]</a></span>
-downwards by a <i>stem-piece</i>, upon the lowest part of which a
-<i>ball collar</i> 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 <i>ball and socket</i>. The boss <i>L</i> of the
-upper parallel plate, with its stem, has a hollow conical hole
-through its axis, into which the <i>body-piece</i>, to be described, fits
-accurately. Upon its outer upper part an inset collar is formed
-which acts as a guide to the clamp <i>K</i>. At the outer edge
-of the parallel plate <i>M′</i> four vertical, conical holes are made,
-which take <i>socket-pieces</i>, which are tapped as <i>nuts</i> to the
-parallel plate screws <i>M</i>. 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.</p>
-<p>373.&mdash;<i>The Parallel Plate Screws.</i>&mdash;One in elevation is
-shown at <i>M</i>, with its point dotted, and one in section at <i>M′</i>.
-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 <i>M</i> 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<span class="pagenum"><a name="Page_221" id="Page_221">[221]</a></span>
-fitted to the upper parallel plate. To prevent wear
-the upper parts of these screws are sometimes encased in tubes&mdash;a
-plan very generally adopted in America. At the foot of
-one of the parallel plate screws a <i>stay-piece</i> 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 <i>loss of time</i>.
-They should move firmly but softly. They should <i>support</i>
-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.</p>
-<p>374.&mdash;<i>The Body-piece.</i>&mdash;The only outward part seen in
-elevation of this is shown at <i>T</i>: it is shown in section <i>T′</i>.
-This piece carries the <i>limb</i> of the instrument <i>SS′</i> 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 <i>KK</i> which bites upon it. The lower outer part of
-the body-piece forms a conical fitting in the boss of the upper
-parallel plate <i>L</i>. 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, <a href="#Art_21">art. 21</a>. 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.</p>
-<p>375.&mdash;<i>Axis Collar Clamp K</i> has been already described,
-<a href="#Art_349">art. 349</a>, and is illustrated in <a href="#i205">Fig. 146</a>, which is taken from
-a theodolite, so that only specialities in relation to the instrument
-<a href="#i218">Fig. 153</a> need be noted. This clamp surrounds the
-body-piece and clamps it by means of the screw <i>K</i> shown on<span class="pagenum"><a name="Page_222" id="Page_222">[222]</a></span>
-the left hand. The clamp is connected with the upper parallel
-plate through the <i>tangent screw</i>, the head of which is shown
-at <i>P</i>, so that when the screw <i>K</i> is tightened the parts <i>L</i> and <i>T</i>
-are fixed together, except that a slow motion can be given to
-these parts by the tangent screw <i>P</i>. 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.</p>
-<p>376.&mdash;<i>The Central Vertical Axis</i> is shown only in half
-section at <i>Z</i>. 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 <i>N</i>. 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 <i>pin-piece</i> centres the <i>vernier plate</i>, 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.</p>
-<p>377.&mdash;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<span class="pagenum"><a name="Page_223" id="Page_223">[223]</a></span>
-part to replace, being, as it were, independent of other fittings.
-Whether this should be taken <i>cum grano salis</i> is a question;
-at any rate with the axis weak it is not policy to load the upper
-part of the instrument with metal&mdash;which in places at least, is
-generally made ten times as strong as the axis&mdash;when the
-instrument has to be carried about by a person over his
-shoulder. Some suggestions will be made on this point
-hereafter.</p>
-<p>378.&mdash;<i>The Horizontal or Lower Plate or Limb.</i>&mdash;Sometimes
-the whole of the piece <i>SS′</i> is termed the <i>limb</i>,
-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 <i>clamp-piece</i>, 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.</p>
-<p>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.</p>
-<p>379.&mdash;<i>The Vernier Plate</i> is shown in section under <i>P′</i>.
-The vernier from which it is named is shown at <i>VV′</i>, <a href="#i226">Fig. 155</a>.
-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.</p>
-<p>380.&mdash;It may be particularly noted, as already stated,<span class="pagenum"><a name="Page_224" id="Page_224">[224]</a></span>
-that the central axis and the body-piece are attached
-to the vernier and horizontal plates by <i>screws</i>. 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 <i>centring</i>, 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.</p>
-<p>381.&mdash;The vernier plate carries the ball nut of the tangent
-screw, shown at <a href="#i218">Fig. 153</a><i>J</i>. 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.</p>
-<p>382.&mdash;<i>The Compass-box.</i>&mdash;The general construction of
-this is shown, <a href="#i226">Fig. 155</a>, 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 <i>A-frames C′ C″</i> 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<span class="pagenum"><a name="Page_225" id="Page_225">[225]</a></span>
-parts of the A-frames; these are secured to the lugs by four
-screws, one of which is shown, <a href="#i218">Fig. 153</a>, at <i>a</i>. 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, <i>not shown</i>. For a general description
-of the compass-box see <a href="#Art_138">art. 138</a>. The vernier plate
-carries two or more verniers. The verniers are read by a pair
-of microscopes, Fig. 155 <i>MM′</i> placed one on each end of a
-radial arm <i>N</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe29_25" id="i225">
-  <img class="w100" src="images/i_225.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 154.&mdash;<i>Vertical circle with clipping arm of transit theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_225a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>The verniers are adjusted ready for reading when the<span class="pagenum"><a name="Page_226" id="Page_226">[226]</a></span>
-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 <i>O</i>, <a href="#i218">Fig. 153</a>, which is adjustable by a pair of
-capstan-headed screws.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe34_3125" id="i226">
-  <img class="w100" src="images/i_226.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 155.&mdash;<i>Cross section of the upper part of a transit theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_226a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p id="Art_383">383.&mdash;<i>The Standards or A-Frames</i>, shown <i>C′ C″</i> 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<span class="pagenum"><a name="Page_227" id="Page_227">[227]</a></span>
-the front of one of the standards a spirit level, Figs. <a href="#i218">153</a>, 155,
-<i>I</i>, is placed adjustable by two capstan screws. This level,
-and one shown <a href="#i218">Fig. 153</a> at <i>0</i> 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 <i>clip-piece</i>, Figs.
-154, 155, <i>P</i> is secured by two screws. This takes the
-clipping screws, Fig. 154 <i>HH′</i> 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 <i>c</i> 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 <i>xx′</i>; these permit the
-adjustment of this in height so as to get the transit axis <i>perfectly
-horizontal</i> 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.</p>
-<p>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<span class="pagenum"><a name="Page_228" id="Page_228">[228]</a></span>
-adjustable V, and no amount of vibration can alter it as with
-the adjusting screws.</p>
-<p>An axis <i>cover cap bb′</i> 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 <i>EE′</i>.
-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.</p>
-<p>384.&mdash;<i>The Transit Axis</i> which supports the telescope
-rests at its ends upon two trunnions, Figs. <a href="#i225">154</a>, <a href="#i226">155</a> <i>AA′</i>,
-technically called <i>pivots</i>, 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 <i>p</i>, <a href="#i226">Fig. 155</a>.
-The centre of the transit axis is formed into a <i>collar e</i> of about
-1&frac14; 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 <i>flange f</i>. Upon this
-flange the vertical circle <i>FF</i> is fixed by three or four screws.</p>
-<p>385.&mdash;In front of the vertical circle a flanged collar-piece
-carries the <i>vertical vernier frame VV′</i>, <a href="#i225">Fig. 154</a>, centred
-upon it. The vernier frame is attached by three screws to the
-<i>clipping arm</i> to be described, and in front of this the
-vertical microscope arms are centred. These carry two<span class="pagenum"><a name="Page_229" id="Page_229">[229]</a></span>
-readers <i>U</i>, <a href="#i226">Fig. 155</a>, 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 <i>axis collar-piece j</i> is attached by three screws cut directly
-into the axis. This collar and one at the other end of the
-axis <i>A′</i>, turned out of the solid, are nicely fitted to the opening
-between the standards to prevent lateral displacement of
-the axis.</p>
-<p>386.&mdash;<i>The Clips.</i>&mdash;The clipping arm, which is centred
-on the transit axis and attached to the verniers, is shown
-<a href="#i225">Fig. 154</a> <i>BB′B′</i>. It is fitted to move freely on its axis at <i>A</i>,
-so as to permit unrestrained motion of the telescope. A milled-head
-clamping screw with clamp, <a href="#i226">Fig. 155</a>, <i>K</i>, and the same
-partly cut away to show the slot in which it works, are shown
-at K′ <a href="#i225">Fig. 154</a>. This is used to fix the verniers stationary on
-the circle, except for the adjustment by the tangent screw <i>G′</i>,
-which has its collar attached to the clipping arm, and its ball
-nut attached to the clamp at <i>D</i> 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 <i>HH′</i> are used to bring the principal bubble <i>B</i>,
-<a href="#i218">Fig. 153</a>, 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,
-<a href="#i226">Fig. 155</a>, <i>P</i> or <i>P′</i> 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.</p>
-<p>387.&mdash;<i>The Vertical Circle</i>, Figs. <a href="#i225">154</a>, <a href="#i226">155</a>, <i>F</i> 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 <i>clamp-piece</i>.
-The silver is inlaid in this circle in the manner shown
-<a href="#i179">Fig. 117</a>. The vernier is read upon the circle on the plan<span class="pagenum"><a name="Page_230" id="Page_230">[230]</a></span>
-shown <a href="#i186a">Fig. 127</a>. 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.</p>
-<p>388.&mdash;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 <i>BB′</i>, <a href="#i225">Fig. 154</a>,
-at <i>N</i>. 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.</p>
-<p>389.&mdash;<i>The Telescope</i>, <a href="#i218">Fig. 153</a>, <i>DD′</i> has been described
-<a href="#Art_94">art. 94</a>. 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.</p>
-<p>390.&mdash;<i>The Principal Level Tube</i> 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 <i>tenon</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe19_25" id="i231">
-  <img class="w100" src="images/i_231.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 156.&mdash;<i>Stanley's new model of 4-screw transit theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_231a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>391.&mdash;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<span class="pagenum"><a name="Page_231" id="Page_231">[231]</a></span>
-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<span class="pagenum"><a name="Page_232" id="Page_232">[232]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i232">
-  <img class="w100" src="images/i_232.png"  alt="" />
-</div>
-  <div class="caption2">
-    <p class="caption2">Fig. 157.&mdash;<i>The plummet.</i></p>
-    <p class="caption2">Fig. 158.&mdash;<i>Gurley's plummet.</i></p>
-    <p class="caption2">Fig. 159.&mdash;<i>Loop.</i></p>
-    <p class="caption2">Fig. 160.&mdash;<i>Ring plummet, Shortt's Patent.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_232a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-<p>392.&mdash;<span class="large bold">Detached parts of a Theodolite.</span>&mdash;<i>The Plummet</i>
-supplied with the theodolite is made to hang from a hook under<span class="pagenum"><a name="Page_233" id="Page_233">[233]</a></span>
-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 <i>C</i> is attached to the
-plummet by passing it through a hole in the milled-head screw
-<i>S</i> at the top of the plummet, and by making a knot <i>K</i> 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.</p>
-<p>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.</p>
-<p>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.</p>
-<p>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.</p>
-<p><span class="pagenum"><a name="Page_234" id="Page_234">[234]</a></span></p>
-<p>393.&mdash;<i>The Loop.</i>&mdash;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, <a href="#i232">Fig. 159</a>. 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.</p>
-<p>394.&mdash;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, <a href="#i232">Fig. 158</a>.</p>
-<p>395.&mdash;<i>Screw-drivers, Tommy Pins, etc.</i>&mdash;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.</p>
-<p>396.&mdash;<span class="large bold">Additional Parts, and Variations in Theodolites.</span>&mdash;<i>Illuminated
-Axis.</i>&mdash;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 <a href="#i226">Fig. 155</a>. Through the hole a small pencil of light
-is sent by a lamp <i>l</i> 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<span class="pagenum"><a name="Page_235" id="Page_235">[235]</a></span>
-band of the telescope <i>m</i>. 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 <i>w</i> carried upon a slide <i>n</i> 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.</p>
-<p>397.&mdash;<i>The Lamp</i>, 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, <a href="#i047">Fig. 20</a>, 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.</p>
-<p>398.&mdash;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<span class="pagenum"><a name="Page_236" id="Page_236">[236]</a></span>
-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.</p>
-<p>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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i236">
-  <img class="w100" src="images/i_236.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 161.&mdash;<i>Trough needle for transit theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_236a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>399.&mdash;<i>A Trough or Long Compass, used in place of
-Circular Compass.</i>&mdash;A long compass, <a href="#i074">Fig. 32</a>, 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 <i>loop slides</i> or <i>bayonet fittings</i> 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 <i>SS′</i>, 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.</p>
-<p>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&mdash;screws
-shown <i>AA′</i>. This enables the needle to be adjusted
-to its own axis, and also to the 0° reading of the horizontal<span class="pagenum"><a name="Page_237" id="Page_237">[237]</a></span>
-limb of the theodolite. A slide lift to the needle is shown
-at <i>L</i>. When the same form of compass is used upon large
-instruments a reader is placed at each end of the needle.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i237">
-  <img class="w100" src="images/i_237.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Figs. 162, 163, 164.&mdash;<i>Striding level.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_237a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p id="Art_400">400.&mdash;<i>Striding Level.</i>&mdash;For the adjustment of the transverse
-axis of a theodolite a very sensitive spirit level is used.
-This is mounted upon a <i>bed</i>, which may be formed of brass
-tubing, from the two ends of which adjustable legs descend,
-the ends of which are <i>forked</i>, 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 <i>SS</i> 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 <i>CC′</i>, and the other, Fig. 163, by a lateral adjustment
-of the capstan screws <i>PP′</i> that act upon the stud <i>S</i>, 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i238">
-  <img class="w100" src="images/i_238.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 165.&mdash;<i>Wallis' shifting centre for theodolites.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_238a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>401.&mdash;<i>Adjustment of the Axis for Setting it up over</i><span class="pagenum"><a name="Page_238" id="Page_238">[238]</a></span>
-<i>a Point.</i>&mdash;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>I</i> is a screw that corresponds with the head<span class="pagenum"><a name="Page_239" id="Page_239">[239]</a></span>
-of the tripod which takes the theodolite; <i>T</i> similar female
-screw to take the tripod head when the shifting centre is used;
-<i>CC′</i> a box formed by screwing two tray-pieces firmly together;
-<i>S</i> clamping flange; <i>HH′</i> clamp screwed into the top
-of box <i>C</i>. 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.</p>
-<p>402.&mdash;In an American plan of a transit by Messrs.
-Heller &amp; Brightly, the flange is lifted by the parallel plate
-screws, which tighten it at the same time.<a name="FNanchor_18_18" id="FNanchor_18_18"></a><a href="#Footnote_18_18" class="fnanchor">[18]</a> Messrs.
-Troughton &amp; 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.</p>
-<p>403.&mdash;<i>Stadia Webs or Lines</i> 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.</p>
-<p>404.&mdash;<i>Solar Attachment to a Theodolite.</i>&mdash;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
-<span class="pagenum"><a name="Page_240" id="Page_240">[240]</a></span>
-theodolite; therefore the hour and declination arcs need only
-be described.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe35_9375" id="i240">
-  <img class="w100" src="images/i_240.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 166.&mdash;<i>Burt's solar attachment to a theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_240a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>405.&mdash;<i>The Hour Circle</i>, Fig. 166, <i>H</i> is fixed upon the
-centre of the telescope upon a socket axis <i>S</i>, 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 <i>declination arc</i>, which is fixed to the socket <i>S</i>.
-The hour circle, when set to any reading, may be clamped to
-this position by means of the milled head placed over the
-socket <i>M</i>.</p>
-<p>406.&mdash;<i>The Declination Arc</i> is of 5 inches radius, divided<span class="pagenum"><a name="Page_241" id="Page_241">[241]</a></span>
-to read on the same plane with a vernier <i>V</i> to single minutes
-of arc. The vernier arm is fixed by a clamp at <i>C</i>, which
-carries tangent adjustment <i>T</i>. At the back of the vernier
-arm two spur-pieces are carried out directly from it, <i>L</i> and <i>I</i>.
-These are blocks of metal about 1&frac12; by 1&frac14; by &frac14; inches, which
-carry each a lens of a focus <i>L</i> to <i>I</i>, and a silver plate to be
-presently described, upon which the sun's image is received in
-one direction or the other.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe26_375" id="i241">
-  <img class="w100" src="images/i_241.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 167.&mdash;<i>Image plate of solar attachment.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_241a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>407.&mdash;<i>The Image Plate</i>, Fig. 167, is marked with two
-sets of lines intersecting each other at right angles. The lines
-<i>bb</i> are termed <i>hour lines</i>, the lines <i>cc</i> <i>equatorial lines</i>; 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 <i>bb</i> and <i>cc</i> 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.</p>
-<p>408.&mdash;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 <i>R</i> set at zero on the
-declination arc <i>V</i>; and the polar axis is placed exactly parallel<span class="pagenum"><a name="Page_242" id="Page_242">[242]</a></span>
-to the axis of the earth. Then the motion of the arm <i>R</i>, if
-revolved on the polar axis around the hour circle <i>H</i>, 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 <i>cc</i> 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.</p>
-<p>409.&mdash;In the morning as the sun rises from the horizon, the
-arm <i>R</i> 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 <i>R</i>,
-the declination arc <i>V</i>, and the latitude arc, that is the vertical
-arc of the theodolite, will be in the same plane.</p>
-<p>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.</p>
-<p>410.&mdash;<i>Allowance for Declination.</i>&mdash;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 <i>Nautical Almanac</i> 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.</p>
-<p>When the sun's declination is south, that is, from the
-22nd of September to the 20th of March in each year, the
-arc <i>R</i> is turned towards the plates of the instrument in
-the opposite position to that shown in the engraving, using
-the solar lens at <i>I</i>, with the silver plate opposite at <i>L</i>.</p>
-<p>The remainder of the year the arc is turned from the
-plates, and the lens at <i>L</i> and plates at <i>I</i> are employed in the
-position shown in the figure.</p>
-<p><span class="pagenum"><a name="Page_243" id="Page_243">[243]</a></span></p>
-<p>411.&mdash;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, <i>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</i>. The slightest deviation from
-this position will cause the image to pass above or below the
-lines and thus discover the error.</p>
-<p>412.&mdash;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.</p>
-<p>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.</p>
-<p>413.&mdash;<span class="large bold">Photographic Apparatus in Connection with
-the Theodolite.</span>&mdash;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
-<i>Comptes Rendus de l'Academie des Sciences</i>, 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 <i>Photographic Surveying</i>, 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
-4&frac12; × 3&frac12; 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.<span class="pagenum"><a name="Page_244" id="Page_244">[244]</a></span>
-The whole of these operations are performed at once in
-a perfect manner.</p>
-<p>414.&mdash;Mr. J. Bridges Lee's photo-theodolite was made in
-excellent workmanship by Messrs. Troughton &amp; Simms. The
-inventor has published a paper on the subject, to be had of the
-Society of Engineers, Westminster.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe30_375" id="i244">
-  <img class="w100" src="images/i_244.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 168.&mdash;<i>Light camera upon the telescope of a theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_244a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>At the present time a camera is very commonly taken by a
-civil engineer for prospecting in new countries,&mdash;a convenient
-form of this will be discussed at nearly the end of this work&mdash;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.</p>
-<p><span class="pagenum"><a name="Page_245" id="Page_245">[245]</a></span></p>
-<p>415.&mdash;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.</p>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_246" id="Page_246">[246]</a></span></p>
-<h2>CHAPTER VIII.</h2>
-</div>
-<p class="ch">SPECIALITIES IN MODERN AND IMPROVED FORMS OF TRANSIT
-THEODOLITES FOR SURVEYING&mdash;RAILWAY WORK&mdash;EXPLORING.</p>
-<p>416.&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe20_4375" id="i247">
-  <img class="w100" src="images/i_247.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 169.&mdash;<i>Stanley's patent new model theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_247a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>417.&mdash;<span class="large bold">New Model Transit Theodolite.</span>&mdash;In this<span class="pagenum"><a name="Page_247" id="Page_247">[247]</a></span>
-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<span class="pagenum"><a name="Page_248" id="Page_248">[248]</a></span>
-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.</p>
-<p>418.&mdash;<i>The Readers</i> to the horizontal limb are jointed to
-turn up against the standards and adjust for reflection, as
-shown <a href="#i189">Fig. 131</a>. In this manner the readers do not need
-detachment to place the instrument in its case.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i248">
-  <img class="w100" src="images/i_248.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 170.&mdash;<i>Section of standards of new model theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_248a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>419.&mdash;<i>The Central Axis</i> 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<span class="pagenum"><a name="Page_249" id="Page_249">[249]</a></span>
-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.</p>
-<p>420.&mdash;<i>The Compass-box</i> in this instrument is attached
-under the limb. It is of the trough form shown <a href="#i074">Fig. 32</a>,
-page 74. The magnetic north is set to zero. The tribrach is
-of the form described for levels, illustrated <a href="#i128">Figs. 72 and 73</a>,
-p. 128.</p>
-<p>421.&mdash;The weights of transit theodolites of this construction
-are about</p>
-
-<div class="m10">
-<table summary="">
-  <tr>
-    <td class="tdc">6-inch</td>
-    <td class="tdc">in gun metal</td>
-    <td class="tdc">14</td>
-    <td class="tdc">lbs.,</td>
-    <td class="tdc">aluminium,</td>
-    <td class="tdc">8</td>
-    <td class="tdc">lbs.</td>
-  </tr>
-  <tr>
-    <td class="tdc">5-inch</td>
-    <td class="tdc">"</td>
-    <td class="tdc">11</td>
-    <td class="tdc">"</td>
-    <td class="tdc">"</td>
-    <td class="tdc">6</td>
-    <td class="tdc">"</td>
-  </tr>
-  <tr>
-    <td class="tdc">4-inch</td>
-    <td class="tdc">"</td>
-    <td class="tdc">7&frac34;</td>
-    <td class="tdc">"</td>
-    <td class="tdc">"</td>
-    <td class="tdc">4&frac12;</td>
-    <td class="tdc">"</td>
-  </tr>
-</table>
-</div>
-
-<p>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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i249">
-  <img class="w100" src="images/i_249.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 171.&mdash;<i>Stanley's simple sliding stage for tribrach theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_249a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>422.&mdash;The author has devised a special arrangement for
-displacement of axis for this theodolite, which does not interfere<span class="pagenum"><a name="Page_250" id="Page_250">[250]</a></span>
-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 &frac34; of an inch from the centre.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i250">
-  <img class="w100" src="images/i_250.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 172.&mdash;<i>Stanley's 4-screw sliding stage.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_250a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i250b">
-  <img class="w100" src="images/i_250b.png"  alt="" />
-</div>
-  <div class="caption">
-     <p class="caption float-left">Fig. 173.&mdash;<i>Stanley's solid round form
-tripod with sliding head.</i></p>
-     <p class="caption float-right">Fig. 174.&mdash;<i>Stanley's telescopic tripod
-with sliding head.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_250ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-<p>A somewhat similar arrangement is made for four-screw<span class="pagenum"><a name="Page_251" id="Page_251">[251]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i251">
-  <img class="w100" src="images/i_251.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 175.&mdash;<i>Stanley's framed stand with sliding head.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_251a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>423.&mdash;<span class="large bold">Improved Transit with Adjustable Axis.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe20" id="i252">
-  <img class="w100" src="images/i_252.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 176.&mdash;<i>Stanley's patent new model theodolite, with mechanical stage.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_252a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>424.&mdash;<i>The Mechanical Tribrach Stage.</i>&mdash;This important
-addition to the theodolite above described permits exact
-adjustment over a station. The upper plate of the tribrach<span class="pagenum"><a name="Page_252" id="Page_252">[252]</a></span>
-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<span class="pagenum"><a name="Page_253" id="Page_253">[253]</a></span>
-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 &frac34; 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i253">
-  <img class="w100" src="images/i_253.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 177.&mdash;<i>Stanley's patent tribrach mechanical stage.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_253a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>This movement being <i>above</i> the levelling screws, the
-adjustment of the instrument for level is not affected by its
-use, as in the case of all sliding arrangements <i>below</i> the
-levelling screws. Suitable means are provided for taking up
-any wear that might occur in the slides.</p>
-<p>425.&mdash;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<span class="pagenum"><a name="Page_254" id="Page_254">[254]</a></span>
-necessary. This plan gives the screw about &frac34; 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, <a href="#i127">Fig. 71</a>, p. 127.</p>
-<p>426.&mdash;This theodolite with mechanical stage is generally
-fitted with illuminated axis for tunnel work, <a href="#Art_383">art. 383</a>. The
-lamp is not shown in the illustration.</p>
-<p>The weights of this make of theodolite are about</p>
-
-<div class="m10">
-<table summary="">
-  <tr>
-    <td class="tdc">6-inch</td>
-    <td class="tdc">in gun-metal</td>
-    <td class="tdc">18&frac34;</td>
-    <td class="tdc">lbs.,</td>
-    <td class="tdc">aluminium</td>
-    <td class="tdc">10</td>
-    <td class="tdc">lbs.</td>
-  </tr>
-  <tr>
-    <td class="tdc">5-inch</td>
-    <td class="tdc">"</td>
-    <td class="tdc">13&frac34;</td>
-    <td class="tdc">"</td>
-    <td class="tdc">"</td>
-    <td class="tdc">7&frac12;</td>
-    <td class="tdc">"</td>
-  </tr>
-  <tr>
-    <td class="tdc">4-inch</td>
-    <td class="tdc">"</td>
-    <td class="tdc">9&frac12;</td>
-    <td class="tdc">"</td>
-    <td class="tdc">"</td>
-    <td class="tdc">4&frac12;</td>
-    <td class="tdc">"</td>
-  </tr>
-</table>
-</div>
-<p>427.&mdash;<span class="large bold">8-inch Transit Theodolite.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe21_4375" id="i255">
-  <img class="w100" src="images/i_255.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 178.&mdash;<i>8-inch transit theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_255a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>428.&mdash;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
-<span class="pagenum"><a name="Page_255" id="Page_255">[255]</a><br /><a name="Page_256" id="Page_256">[256]</a></span>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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe23_25" id="i256">
-  <img class="w100" src="images/i_256.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 179.&mdash;<i>Stanley's quick-setting transit theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_256a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>429.&mdash;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.</p>
-<p>Theodolites of eight inches and over are uniformly packed<span class="pagenum"><a name="Page_257" id="Page_257">[257]</a></span>
-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 29&frac12; lbs.</p>
-<p>430&mdash;<span class="large bold">Quick-setting Theodolites.</span>&mdash;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 <a href="#Art_240">art. 240</a>, p. 132.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe24_1875" id="i257">
-  <img class="w100" src="images/i_257.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 180.&mdash;<i>Railway theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_257a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p><span class="pagenum"><a name="Page_258" id="Page_258">[258]</a></span></p>
-<p>431.&mdash;<span class="large bold">Railway Theodolite.</span>&mdash;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, 7&frac14; lbs.; 5-inch, 9&frac12; lbs.; 6-inch,
-12&frac34; lbs. Being constructed for rough, hard wear and local
-use it is not made in aluminium.</p>
-<p>432.&mdash;For tunnelling underground railways the mining
-theodolite described further on will be found the most valuable
-for railway engineers.</p>
-<p>433.&mdash;<span class="large bold">Mountain Transit Theodolite.</span>&mdash;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 2&frac14; lbs. for the 3-inch and 3&frac12; 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.</p>
-<p>434.&mdash;<i>A Mountain Theodolite</i> 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,<span class="pagenum"><a name="Page_259" id="Page_259">[259]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe22_1875" id="i259">
-  <img class="w100" src="images/i_259.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 181.&mdash;<i>Stanley's mountain transit theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_259a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>435.&mdash;<span class="large bold">Improved Solar Attachment.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe31_1875" id="i260">
-  <img class="w100" src="images/i_260.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 182.&mdash;<i>Stanley's solar attachment.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_260a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>436.&mdash;<span class="large bold">Micrometer Reading Theodolites.</span>&mdash;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
-<span class="pagenum"><a name="Page_260" id="Page_260">[260]</a></span>
-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<span class="pagenum"><a name="Page_261" id="Page_261">[261]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe22_625" id="i261">
-  <img class="w100" src="images/i_261.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 183.&mdash;<i>Stanley's micrometer transit theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_261a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-<p>A full micrometer reading instrument is shown at Fig. 184,<span class="pagenum"><a name="Page_262" id="Page_262">[262]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe25_5625" id="i262">
-  <img class="w100" src="images/i_262.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 184.&mdash;<i>Stanley's full micrometer transit theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_262a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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 4&frac12;-inch horizontal
-circle reading by micrometers to 20 seconds of arc which may
-be approximately read by mental subdivision to 5 seconds,<span class="pagenum"><a name="Page_263" id="Page_263">[263]</a></span>
-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 &frac14;-degrees, which may easily be
-estimated to a third of this.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe30" id="i263">
-  <img class="w100" src="images/i_263.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 185.&mdash;<i>Stanley's light micrometer transit.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_263a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe21_375" id="i264">
-  <img class="w100" src="images/i_264.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 186.&mdash;<i>Dr. Deville's transit.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_264a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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
-<span class="pagenum"><a name="Page_264" id="Page_264">[264]</a></span>
-level for ordinary use. The telescope is 14 inches solar focus
-with large object glass so that observations may be taken of
-<span class="pagenum"><a name="Page_265" id="Page_265">[265]</a></span>
-stars up to the sixth magnitude; it has a revolving micrometer
-<span class="pagenum"><a name="Page_266" id="Page_266">[266]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe25_4375" id="i265">
-  <img class="w100" src="images/i_265.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 187.&mdash;<i>Stanley's patent universal transit theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_265a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>The universal transit designed by the reviser is shown at
-Fig. 187.</p>
-<p>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.</p>
-<p>A description of the larger geodetic instruments is given
-in a subsequent chapter.</p>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_267" id="Page_267">[267]</a></span></p>
-<h2>CHAPTER IX.</h2>
-</div>
-<p class="ch">PLAIN THEODOLITES IN WHICH THE TRANSIT PRINCIPLE IS
-NOT EMPLOYED&mdash;THE PLAIN THEODOLITE&mdash;IMPROVED
-CONSTRUCTION&mdash;EVEREST'S&mdash;SIMPLE&mdash;ADJUSTMENTS AND
-EXAMINATION OF THEODOLITES.</p>
-<p>437.&mdash;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.</p>
-<p>438.&mdash;<span class="large bold">The Plain Theodolite.</span>&mdash;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.</p>
-<p>The standards or A-frames in the ordinary plain theodolite
-are attached to the vernier plate, but not generally to<span class="pagenum"><a name="Page_268" id="Page_268">[268]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe25_3125" id="i268">
-  <img class="w100" src="images/i_268.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 188.&mdash;<i>5-inch plain theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_268a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>439.&mdash;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<span class="pagenum"><a name="Page_269" id="Page_269">[269]</a></span>
-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.</p>
-<p>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.</p>
-<p>440.&mdash;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.</p>
-<p>441.&mdash;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<span class="pagenum"><a name="Page_270" id="Page_270">[270]</a></span>
-weight and of greater portability. The weights of the three
-sizes in general use are as follows:&mdash;</p>
-
-<div class="m10" style="padding: 1em 0;">
-<p class="center" style="padding-bottom: .5em;"><i>Weights of Plain Theodolites.</i></p>
-<table summary="" style="border: 1px solid black; border-collapse: collapse;" width="100%" class="med90">
-  <tr>
-    <th class="tdc" style="padding: 1.5em; border: 1px solid black;"></th>
-    <th class="tdc" colspan="2" style="border: 1px solid black;">Instrument.</th>
-    <th class="tdc" colspan="2" style="border: 1px solid black;">Case.</th>
-    <th class="tdc" colspan="2" style="border: 1px solid black;">Outer Case.</th>
-    <th class="tdc" colspan="2" style="border: 1px solid black;">Tripod.</th>
-  </tr>
-  <tr>
-    <td class="tdc pt1">4-inch</td>
-    <td class="tdrbl pt1">7</td>
-    <td class="tdc pt1">lbs.</td>
-    <td class="tdrbl pt1">7&frac12;</td>
-    <td class="tdc pt1">lbs.</td>
-    <td class="tdrbl pt1">3&frac12;</td>
-    <td class="tdc pt1">lbs.</td>
-    <td class="tdrbl pt1">8</td>
-    <td class="tdc pt1">lbs.</td>
-  </tr>
-  <tr>
-    <td class="tdc">5-inch</td>
-    <td class="tdrbl">11</td>
-    <td class="tdc">"</td>
-    <td class="tdrbl">8&frac12;</td>
-    <td class="tdc">"</td>
-    <td class="tdrbl">4</td>
-    <td class="tdc">"</td>
-    <td class="tdrbl">9</td>
-    <td class="tdc">"</td>
-  </tr>
-  <tr>
-    <td class="tdc pb1">6-inch</td>
-    <td class="tdrbl pb1">17</td>
-    <td class="tdc pb1">"</td>
-    <td class="tdrbl pb1">10</td>
-    <td class="tdc pb1">"</td>
-    <td class="tdrbl pb1">5</td>
-    <td class="tdc pb1">"</td>
-    <td class="tdrbl pb1">11</td>
-    <td class="tdc pb1">"</td>
-  </tr>
-</table>
-</div>
-
-<p class="noindent">Very light 3-inch and 4-inch plain theodolites of from 5 lbs.
-to 7 lbs. complete are made occasionally for travellers.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe19_0625" id="i270">
-  <img class="w100" src="images/i_270.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 189.&mdash;<i>Stanley's new model plain theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_270a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>442.&mdash;The author has recently modified the plain theodolite,
-Fig. 189, for which there still remains a small demand<span class="pagenum"><a name="Page_271" id="Page_271">[271]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i271">
-  <img class="w100" src="images/i_271.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 190.&mdash;<i>Everest's theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_271a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>443.&mdash;<span class="large bold">Everest's Theodolite</span>, 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<span class="pagenum"><a name="Page_272" id="Page_272">[272]</a></span>
-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, <a href="#i186b">Fig. 128</a>. 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, <a href="#i186a">Fig. 127</a>, p. 186.
-The verniers trisect the circle, and are marked <i>A</i>, <i>B</i>, and <i>C</i>.
-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.</p>
-<p>444.&mdash;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.</p>
-<p>445.&mdash;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:&mdash;</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe33_875" id="i273">
-  <img class="w100" src="images/i_273.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 191.&mdash;<i>Everest's locking plate tribrach.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_273a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>446.&mdash;<i>Everest's Tribrach.</i>&mdash;The upper part of the engraving,<span class="pagenum"><a name="Page_273" id="Page_273">[273]</a></span>
-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 <i>feet</i>, 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 <i>locking plate</i>, is centred upon the hollow
-axis of the head, so that it will move laterally. The locking
-plate has a <i>hole and slot</i> 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<span class="pagenum"><a name="Page_274" id="Page_274">[274]</a></span>
-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 <i>ride</i>. 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe34_625" id="i274">
-  <img class="w100" src="images/i_274.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 192.&mdash;<i>Stanley's Everest theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_274a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p><span class="pagenum"><a name="Page_275" id="Page_275">[275]</a></span></p>
-<p>447.&mdash;<i>The Framed Tripod</i> of Sir Geo. Everest's design
-is made of straight-grained mahogany, each leg being formed
-of two <i>side-pieces</i>, 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 <i>strap plates</i>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe36_625" id="i275">
-  <img class="w100" src="images/i_275.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 193.&mdash;<i>Simple theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_275a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>448.&mdash;<span class="large bold">Simple Theodolite.</span>&mdash;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<span class="pagenum"><a name="Page_276" id="Page_276">[276]</a></span>
-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, <a href="#Art_249">art. 249</a>.</p>
-<p>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 4&frac34; lbs.</p>
-<p>449.&mdash;<span class="large bold">Examination and Adjustment of the Theodolite.</span>&mdash;The
-description given of a transit theodolite, <a href="#Art_369">arts.
-369</a> 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,
-<a href="#Art_369">arts. 369</a> to 389, noting only where variations occur from
-partial differences between this and others.</p>
-<p>450.&mdash;A theodolite as it comes from a respectable maker<span class="pagenum"><a name="Page_277" id="Page_277">[277]</a></span>
-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.</p>
-<p>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, <a href="#Art_42">art. 42</a>.</p>
-<p>451.&mdash;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<span class="pagenum"><a name="Page_278" id="Page_278">[278]</a></span>
-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.</p>
-<p>452.&mdash;<i>Examination for Coincidence of Exterior and
-Interior Vertical Axes.</i>&mdash;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, <a href="#Art_193">art. 193</a>, or
-one level parallel with one pair of foot screws if it is made on
-the tribrach system, <a href="#Art_234">art. 234</a>. 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 <i>tommy</i> 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 <i>always</i> to observe the bubbles after the hands have
-left the instrument, <i>not during the adjustment</i>, 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<span class="pagenum"><a name="Page_279" id="Page_279">[279]</a></span>
-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.</p>
-<p>453.&mdash;<i>Examination of the Azimuthal Level.</i>&mdash;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.</p>
-<p>454.&mdash;<i>Examination of the Divisions and Centring.</i>&mdash;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<span class="pagenum"><a name="Page_280" id="Page_280">[280]</a></span>
-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 <i>half points</i>, 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.</p>
-<p>Examination of the telescope has been discussed <a href="#Art_107">arts. 107</a>
-to 115.</p>
-<p>455.&mdash;<i>Testing an Instrument for its Stability.</i>&mdash;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<span class="pagenum"><a name="Page_281" id="Page_281">[281]</a></span>
-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.</p>
-<p>456.&mdash;<i>Tripod Head Examination.</i>&mdash;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.</p>
-<p>457.&mdash;<i>General Examination of Fixed Parts.</i>&mdash;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<span class="pagenum"><a name="Page_282" id="Page_282">[282]</a></span>
-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.</p>
-<p>458.&mdash;<i>Examination of the Transit Axis.</i>&mdash;The best
-means of adjusting this axis in a theodolite is by a <i>striding
-level</i>, <a href="#Art_400">art. 400</a>. 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,<span class="pagenum"><a name="Page_283" id="Page_283">[283]</a></span>
-and is not subject to change, especially if solid without an
-adjustable V.</p>
-<p>459.&mdash;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.</p>
-<p>460.&mdash;<i>Examination and Adjustment of Webs, Lines on
-Glass, or Points.</i>&mdash;The ordinary manner of webbing the
-diaphragm of a theodolite was shown <a href="#i050">Fig. 23</a>. 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<span class="pagenum"><a name="Page_284" id="Page_284">[284]</a></span>
-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.</p>
-<p>461.&mdash;<i>Adjustment of the Telescope to Vertical Collimation.</i>&mdash;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, <a href="#Art_200">art. 200</a>. The
-only difference with the transit theodolite is that instead of
-turning the instrument in its Y's, the telescope is <i>transitted</i>, 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.</p>
-<p>For the transit theodolite, adjustment by means of a
-collimator, <a href="#Art_229">art. 229</a>, 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.</p>
-<p>462.&mdash;<i>Examination for Perpendicularity of Transit Axis
-and Telescope.</i>&mdash;The whole of the lower part of the instrument
-retaining its position with all clamps firm, open the cleats<span class="pagenum"><a name="Page_285" id="Page_285">[285]</a></span>
-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.</p>
-<p>463.&mdash;<i>Examination of the Magnetic Needle.</i>&mdash;If the
-needle be placed in a circular box, as shown in the engraving,
-<a href="#i065">Fig. 30</a>, it admits of no adjustment. If it is placed in a trough,
-<a href="#i236">Fig. 161</a>, 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, <a href="#Art_132">art. 132</a>. 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<span class="pagenum"><a name="Page_286" id="Page_286">[286]</a></span>
-magnetic meridian, in order to preserve its magnetism as
-much as possible.</p>
-<p>464&mdash;<span class="large bold">Use of the Theodolite.</span>&mdash;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 <i>picket</i>, 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.</p>
-<p>465.&mdash;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.</p>
-<p>466.&mdash;It may be observed that if the tripod be set up out<span class="pagenum"><a name="Page_287" id="Page_287">[287]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe14_3125" id="i287">
-  <img class="w100" src="images/i_287.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 194.&mdash;<i>False centre for a tripod head.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_287a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>467.&mdash;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<span class="pagenum"><a name="Page_288" id="Page_288">[288]</a></span>
-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
-<i>dance</i>, 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 <i>face</i> 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&mdash;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<span class="pagenum"><a name="Page_289" id="Page_289">[289]</a></span>
-they form a check to positions if taken with pickets afterwards
-more definitely. These may be marked in the field-book
-<i>inx.</i> for <i>inexact</i>.</p>
-<p>468.&mdash;<span class="large bold">Field Book.</span>&mdash;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, &frac34; 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.</p>
-<p>469.&mdash;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.</p>
-<p><span class="pagenum"><a name="Page_290" id="Page_290">[290]</a></span></p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe25" id="i290">
-  <img class="w100" src="images/i_290.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 195.&mdash;<i>Diagram bisection of circle.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_290a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>470.&mdash;<i>Elimination of Instrumental Errors during Triangulation&mdash;Changing
-Face.</i>&mdash;It is generally advised to
-<i>change face</i> with the theodolite after angles are taken in
-the ordinary way, that is, to take first the initial angles
-reading from the <i>face</i> 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:&mdash;In Fig. 195 let a be zero (360°), the
-reading of the face vernier. Let the opposite reading (180°)
-be at <i>a′</i>. Suppose at 180° on the left-hand side of the
-instrument the 180° reads at <i>b</i>, 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 <i>c</i>, and the
-telescope must traverse <i>cb</i> to come to the first direction.
-The instrumental error is half <i>bc</i>, which bisected in <i>a′</i> 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.</p>
-<p>471.&mdash;<i>Repeating Angles.</i>&mdash;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:&mdash;Take the angular positions of two
-objects in azimuth, commencing with the zero of the horizontal<span class="pagenum"><a name="Page_291" id="Page_291">[291]</a></span>
-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.</p>
-<p>472.&mdash;It may be observed that if the horizontal circle is
-placed with its zero constantly to magnetic north&mdash;not
-necessarily for taking angles in reference to this&mdash;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&mdash;it is quite otherwise.
-It is best to have some distinct, sharply defined object to
-which all angles are referred, and therefore called a <i>referring
-object</i>, as the general index. The magnetic bearing need
-only be the initial position of the horizontal circle of the
-instrument.</p>
-<p><span class="pagenum"><a name="Page_292" id="Page_292">[292]</a></span></p>
-<p>473.&mdash;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.</p>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_293" id="Page_293">[293]</a></span></p>
-<h2>CHAPTER X.</h2>
-</div>
-<p class="ch">LARGE THEODOLITES USED ONLY FOR GEODETIC SURVEYS&mdash;STANLEY'S
-10- AND 12-INCH&mdash;14-INCH ALTAZIMUTH&mdash;COLONEL
-STRANGE'S 36-INCH THEODOLITE.</p>
-<p>474.&mdash;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.</p>
-<p>475.&mdash;The construction of large theodolites is varied very
-<span class="pagenum"><a name="Page_294" id="Page_294">[294]</a></span>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
-<span class="pagenum"><a name="Page_295" id="Page_295">[295]</a></span>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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe19_4375" id="i294">
-  <img class="w100" src="images/i_294.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 196.&mdash;<i>Stanley's 10-inch transit theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_294a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>476.&mdash;<span class="large bold">10- or 12-inch Theodolite.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe23_1875" id="i297">
-  <img class="w100" src="images/i_297.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 197.&mdash;<i>14-inch altazimuth theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_297a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>477.&mdash;<span class="large bold">14-inch Theodolite.</span>&mdash;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 <i>Encyclopædia Britannica</i>, 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<span class="pagenum"><a name="Page_296" id="Page_296">[296]</a></span>
-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<span class="pagenum"><a name="Page_297" id="Page_297">[297]</a></span>
-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&mdash;it is perhaps
-the worst feature in the instrument, some modification of<span class="pagenum"><a name="Page_298" id="Page_298">[298]</a></span>
-the plan shown, <a href="#i294">Fig. 196</a>, being much better for large
-instruments.</p>
-<p>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.</p>
-<p>478.&mdash;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&mdash;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.</p>
-<p>479.&mdash;<span class="large bold">36-inch Theodolite</span>, Fig. 198, was designed by
-the late Colonel A. Strange and constructed by Messrs.
-Troughton &amp; 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe21_75" id="i299">
-  <img class="w100" src="images/i_299.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 198.&mdash;<i>36-inch theodolite&mdash;Great Indian Survey. From a photograph.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_299a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>480.&mdash;<i>The Stand</i> has three massive mahogany legs <i>AA</i>
-braced together with horizontal and oblique wrought-iron<span class="pagenum"><a name="Page_299" id="Page_299">[299]</a></span>
-bars <i>B</i>. Each leg is divided vertically, and contains a long,
-gun-metal, square-threaded screw <i>C</i> which is made to rotate
-by means of a worm-wheel and endless screw worked by a
-winch handle <i>D</i>, and capable of being firmly clamped after<span class="pagenum"><a name="Page_300" id="Page_300">[300]</a></span>
-adjustment at points about 15 inches apart <i>E</i>. 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 <i>F</i> which
-pass through the side of this circle are intended to adjust the
-centre of the instrument over the station mark. A lever <i>G</i>
-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.</p>
-<p>481.&mdash;<i>The Foot Screws</i> 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<span class="pagenum"><a name="Page_301" id="Page_301">[301]</a></span>
-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 <i>H</i> 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.</p>
-<p>482.&mdash;<i>The Horizontal Circles.</i>&mdash;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<span class="pagenum"><a name="Page_302" id="Page_302">[302]</a></span>
-centre to the tribrach, but everywhere else is perfectly free.
-The outer or <i>guard circle</i> 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.</p>
-<p>483.&mdash;<i>The Horizontal Tangent Screws.</i>&mdash;It will be seen
-at <i>II′</i> 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 <i>divided nut</i> 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<span class="pagenum"><a name="Page_303" id="Page_303">[303]</a></span>
-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.</p>
-<p>484.&mdash;<i>The Vertical Axis</i> 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.</p>
-<p>485.&mdash;<i>The Telescope</i> is furnished with two separate eye-ends,
-carrying respectively a vertical and a horizontal parallel
-wire micrometer <i>J</i>. It is also supplied with both bright and
-dark field illumination, the latter being employed when faint
-stars are observed. The vertical circle <i>K</i> 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 <i>LL′</i> 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<span class="pagenum"><a name="Page_304" id="Page_304">[304]</a></span>
-perfect as practicable through any diametrical section of the
-vertical axis.</p>
-<p>486.&mdash;<i>The Spirit Levels</i>, both horizontal <i>M</i> and vertical
-<i>N</i>, 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.</p>
-<p>487.&mdash;<i>The Five Micrometer Microscopes O</i> 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 <i>S</i> 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<span class="pagenum"><a name="Page_305" id="Page_305">[305]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i305">
-  <img class="w100" src="images/i_305.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 199.&mdash;<i>Robinson's micrometer.</i></p>
-    <p class="caption float-right">Fig. 200.&mdash;<i>Webs of micrometer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_305a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>488.&mdash;<i>Relieving Apparatus.</i>&mdash;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<span class="pagenum"><a name="Page_306" id="Page_306">[306]</a></span>
-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.</p>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_307" id="Page_307">[307]</a></span></p>
-<h2>CHAPTER XI.</h2>
-</div>
-<p class="ch">MINING SURVEY INSTRUMENTS&mdash;CIRCUMFERENTORS&mdash;PLAIN
-MINER'S DIAL&mdash;SIGHTS&mdash;TRIPOD STAND&mdash;ADJUSTMENTS&mdash;HENDERSON'S
-DIAL&mdash;LEAN'S DIAL&mdash;ADJUSTMENTS&mdash;HEDLEY'S
-DIAL&mdash;ADDITIONAL TELESCOPE&mdash;IMPROVED HEDLEY TRIBRACH
-AND BALL ADJUSTMENT&mdash;REFLECTORS&mdash;CONTINENTAL
-FORMS&mdash;THEODOLITE SOUTERRAIN&mdash;TRIPOD TABLES&mdash;STANLEY'S
-MINING THEODOLITE&mdash;PASTORELLI'S AND HOFFMANN'S
-ADJUSTABLE TRIPOD HEADS&mdash;MINING TRANSIT
-THEODOLITES&mdash;STANLEY'S PRISMATIC MINING COMPASS&mdash;HANGING
-DIAL&mdash;HANGING CLINOMETER&mdash;SEMI-CIRCUMFERENTOR&mdash;MINING
-LAMPS.</p>
-<p>489.&mdash;<span class="large bold">Miner's Circumferentor.</span>&mdash;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 <i>circumferentor</i>;
-and subsequently, being best adapted to underground surveying,<span class="pagenum"><a name="Page_308" id="Page_308">[308]</a></span>
-it became, with some slight alterations, the <i>miner's
-dial</i>.</p>
-<p id="Art_490">490.&mdash;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:&mdash;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 <i>vice versa</i>, 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<span class="pagenum"><a name="Page_309" id="Page_309">[309]</a></span>
-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.</p>
-<p id="Art_491">491.&mdash;<span class="large bold">Plain Miner's Dial.</span>&mdash;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, <a href="#Art_130">art. 130</a>, 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe29_25" id="i310">
-  <img class="w100" src="images/i_310.png"  alt="" />
-</div>
-  <div class="caption2">
-    <p class="caption2">Fig. 201.&mdash;<i>Mining dial.</i></p>
-    <p class="caption2">Fig. 202.&mdash;<i>Cover to the same.</i></p>
-    <p class="caption2">Fig. 203.&mdash;<i>Sight.</i></p>
-    <p class="caption2">Fig. 204.&mdash;<i>Section of ball and socket joint.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_310a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>492.&mdash;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 <i>limb</i>. The limb of the instrument is mounted upon a <i>ball
-and socket joint</i> 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.</p>
-<p>493.&mdash;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<span class="pagenum"><a name="Page_310" id="Page_310">[310]</a></span>
-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,<span class="pagenum"><a name="Page_311" id="Page_311">[311]</a></span>
-and thus form a reading index to the arc, giving thereby
-approximately the vertical angle at which the sights are
-set to degrees.</p>
-<p>494.&mdash;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.</p>
-<p>495.&mdash;<i>Sights</i>, one of which is shown separately, Fig. 203,
-are common to mining instruments. They are constructed
-essentially in two parts, technically termed the <i>slit</i> and the
-<i>window</i>. The <i>slit</i> <i>A</i> 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 <i>A′</i>. 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 <i>window</i> <i>B</i> 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<span class="pagenum"><a name="Page_312" id="Page_312">[312]</a></span>
-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.</p>
-<p>496.&mdash;<i>In the use of the Sight</i> 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.</p>
-<p>497.&mdash;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.</p>
-<p>498.&mdash;<i>Universal Sight</i>, termed technically <i>hole and cross
-sight</i>, consists of a small hole <i>C′</i>, 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 <i>C</i> 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.</p>
-<p>499.&mdash;<i>Ball and Socket Joint.</i>&mdash;This is shown in elevation
-Fig. 201 at <i>F</i>, and in section Fig. 204 <i>F, D</i>. It is one of<span class="pagenum"><a name="Page_313" id="Page_313">[313]</a></span>
-the oldest forms of adjustment, and is common to many dials.
-When the clamping screw <i>G</i> is released the ball is free in its
-socket <i>F</i> to move about its centre, to the extent of the opening
-at the top of the socket, in any direction. A <i>plug</i> <i>E</i>, which
-really forms the lower half of the socket, is screwed into the
-part <i>F′</i> at the lower part of what is technically called the
-<i>socket-piece</i>. The plug is turned upwards by its screws so as to
-tighten the ball by means of a tangent screw <i>G</i> which works
-in a rack thread cut in a part of the circumference of the plug,
-thus forming a <i>screw and cross screw</i>, 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.</p>
-<p>500.&mdash;<i>The Tripod Stand of an Ordinary Miner's Dial.</i>&mdash;The
-upper part is shown in Fig. 205. This form of
-tripod is common to many dials. The legs are made about
-1&frac14; inches in diameter. The heads of the legs are fitted
-directly without brasswork between the <i>book-plates</i> <i>A</i>, 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 <i>L</i>. 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. <i>C</i> the male screw, which is fitted to the
-woodwork by a socket and cross pinned to it. This piece has a<span class="pagenum"><a name="Page_314" id="Page_314">[314]</a></span>
-point at its lower end. <i>D</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i314">
-  <img class="w100" src="images/i_314.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 205.&mdash;<i>Jointed tripod legs of a miner's dial.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_314a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>501.&mdash;<i>Examination and Adjustment of the Plain Miner's
-Dial.</i>&mdash;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<span class="pagenum"><a name="Page_315" id="Page_315">[315]</a></span>
-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&mdash;a plumb-line is best&mdash;a piece of string suspending
-a stone answers&mdash;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.</p>
-<p>502.&mdash;<span class="large bold">Henderson's Dial.</span>&mdash;This is an improvement
-upon an old form of circumferentor,<a name="FNanchor_19_19" id="FNanchor_19_19"></a><a href="#Footnote_19_19" class="fnanchor">[19]</a> 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.<a name="FNanchor_20_20" id="FNanchor_20_20"></a><a href="#Footnote_20_20" class="fnanchor">[20]</a> 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 <i>Mine Surveying</i>.</p>
-<p>503.&mdash;<span class="large bold">Lean's Dial.</span>&mdash;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, <a href="#Art_491">art. 491</a>. The legs are also</p>
-<p><span class="pagenum"><a name="Page_316" id="Page_316">[316]</a></span></p>
-<p>the same&mdash;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:&mdash;</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe21_8125" id="i316">
-  <img class="w100" src="images/i_316.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 206.&mdash;<i>Mining circumferentor or Lean's dial.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_316a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>504.&mdash;<i>The Tripod</i>&mdash;of the mining circumferentor, in common
-with many other forms of dial, has the legs fitted directly<span class="pagenum"><a name="Page_317" id="Page_317">[317]</a></span>
-between <i>book-pieces</i>, 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, <a href="#Art_193">art. 193</a>, 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, <a href="#i140">Fig. 85</a>, 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i318">
-  <img class="w100" src="images/i_318.png"  alt="" />
-</div>
-
-  <div class="caption">
-    <p class="caption">Fig. 207.&mdash;<i>Section of compass-box and axis of Lean's dial.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_318a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>505.&mdash;<i>Revolving Compass</i> 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 <i>A</i> is
-ground to fit the male axis <i>S</i>, and at the same time it is
-shouldered to fit the surface of the parallel plate <i>T</i> 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 <i>D</i> 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 <i>D</i> 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<span class="pagenum"><a name="Page_318" id="Page_318">[318]</a></span>
-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 <i>B</i>, 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 <i>R</i> is fixed in a box upon the arm plate
-that works by means of a large milled-head screw <i>P</i>. 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, <i>not shown</i>; and
-when thus fixed the needle only is used as in the plain dial.
-Between the collar-piece <i>C</i> and the socket-piece <i>A</i> a wedge-shaped<span class="pagenum"><a name="Page_319" id="Page_319">[319]</a></span>
-lift raises the needle off its centre by pressing in a
-slide shown at <i>L</i>.</p>
-<p>506.&mdash;<i>The Vertical Arc</i> 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° + <i>n</i> will
-indicate a perfect vertical to the station of the instrument
-above, the + <i>n</i> 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°.</p>
-<p><span class="pagenum"><a name="Page_320" id="Page_320">[320]</a></span></p>
-<p>507.&mdash;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.</p>
-<p>508.&mdash;Lean's dial possesses the qualities 1 and 4, pointed
-out in <a href="#Art_490">art. 490</a> 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 9&frac12; inches; to the top of the sights placed in a
-level position, 8 inches; weight of instrument only, 6&frac12; lbs.
-The 6-inch instrument is about 1 inch higher, and weighs
-1 lb. more.</p>
-<p>509.&mdash;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,<a name="FNanchor_21_21" id="FNanchor_21_21"></a><a href="#Footnote_21_21" class="fnanchor">[21]</a> 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.</p>
-<p>Messrs. Newton &amp; 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
-<span class="pagenum"><a name="Page_321" id="Page_321">[321]</a></span>
-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.</p>
-<p>510.&mdash;<i>Examination of Lean's Dial.</i>&mdash;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 <i>P</i>, <a href="#i318">Fig.
-207</a>, of the pinion wheel <i>R</i> 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.</p>
-<p>511.&mdash;<i>The Adjustment of Lean's Dial</i> 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<span class="pagenum"><a name="Page_322" id="Page_322">[322]</a></span>
-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.</p>
-<p>512.&mdash;<i>To set a line in Azimuth with one taken above
-Ground.</i>&mdash;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.</p>
-<p>513.&mdash;<span class="large bold">Hedley's Dial</span>, 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<span class="pagenum"><a name="Page_323" id="Page_323">[323]</a></span>
-take horizontal angles within a wide azimuth without obstruction
-to the sight of the compass.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe31_3125" id="i323">
-  <img class="w100" src="images/i_323.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 208.&mdash;<i>Hedley's dial.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_323a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>514.&mdash;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.</p>
-<p><span class="pagenum"><a name="Page_324" id="Page_324">[324]</a></span></p>
-<p>515.&mdash;<i>The Rocking Centre</i> 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 <i>zero</i>
-(360°). The pivots form the axes of a stout ring&mdash;<i>rocking
-ring</i>&mdash;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 &frac34; 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.</p>
-<p>516.&mdash;<i>The Vertical Arc</i>, 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.</p>
-<p>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 <i>latch-piece</i> so as to convert it into a
-plain dial.</p>
-<p>517.&mdash;The great merit of Hedley's dial is that the rocking<span class="pagenum"><a name="Page_325" id="Page_325">[325]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe27_625" id="i325">
-  <img class="w100" src="images/i_325.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 209.&mdash;<i>Hedley's dial with ball clamp.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_325a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>518.&mdash;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<span class="pagenum"><a name="Page_326" id="Page_326">[326]</a></span>
-is required. It is a very cheap form of dial, but substantially
-made. It answers for a small mine survey.</p>
-<p>519.&mdash;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.<a name="FNanchor_22_22" id="FNanchor_22_22"></a><a href="#Footnote_22_22" class="fnanchor">[22]</a> 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.</p>
-<p>520.&mdash;<i>Examination and Adjustment of Hedley's Dial.</i>&mdash;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 <i>no loss of time</i>
-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.</p>
-<p>521.&mdash;<span class="large bold">Improvement in Hedley's Dial</span>, <i>by Addition
-of Telescope</i>.&mdash;Surface work being generally performed with
-<span class="pagenum"><a name="Page_327" id="Page_327">[327]</a></span>
-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, <a href="#Art_193">art. 193</a>, p. 99, suitable for fairly level
-workings. A ball and socket joint is sometimes fitted to this
-instrument in place of these.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i327">
-  <img class="w100" src="images/i_327.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 210.&mdash;<i>Hedley's dial with telescope.</i></p>
-    <p class="caption float-right">Fig. 211.&mdash;<i>Bracket sight.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_327a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>522.&mdash;<i>The Telescope</i> is placed on Y's, and is of exactly<span class="pagenum"><a name="Page_328" id="Page_328">[328]</a></span>
-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. <i>Its examination
-and adjustment</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe28_375" id="i328">
-  <img class="w100" src="images/i_328.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 212.&mdash;<i>Improved miner's dial.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_328a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>523.&mdash;<span class="large bold">Improved Miner's Dial.</span>&mdash;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, <i>not shown</i>, 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,<span class="pagenum"><a name="Page_329" id="Page_329">[329]</a></span>
-and reads with two verniers&mdash;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.<a name="FNanchor_23_23" id="FNanchor_23_23"></a><a href="#Footnote_23_23" class="fnanchor">[23]</a>
-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.</p>
-<p>524.&mdash;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 <i>B</i>. 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 6&frac12; inches;
-weight, 11 lbs. for both parallel plate and tribrach adjustments.</p>
-<p>525.&mdash;<i>Adjustable Tripod for Dials.</i>&mdash;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
-<span class="pagenum"><a name="Page_330" id="Page_330">[330]</a></span>
-section, about 1&frac14; inches by 5/8 inch, and a third bar or leg <i>G′</i>
-of about 1&frac14; 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 <i>SS′</i>
-are fixed near the ends of the bars. One of these <i>S′</i> is
-firmly soldered to a boss-piece that takes a thumb-screw,
-which has quite sufficient power to hold the leg <i>G′</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i330">
-  <img class="w100" src="images/i_330.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 213.&mdash;<i>The author's adjustable ball joint and socket tribrach stand.</i></p>
-    <p class="caption float-right">Fig. 214.&mdash;<i>Adjustment to leg of tripod.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_330a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>526.&mdash;<span class="large bold">Hedley's Dials, with Pastorelli's and Hoffmann's
-Ball Arrangements.</span>&mdash;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<span class="pagenum"><a name="Page_331" id="Page_331">[331]</a></span>
-ball and socket is clamped by the same screws that bring the
-instrument to final position. In Pastorelli's arrangement<a name="FNanchor_24_24" id="FNanchor_24_24"></a><a href="#Footnote_24_24" class="fnanchor">[24]</a> the
-socket is drawn down upon the ball by the adjusting screws.
-In Hoffmann's<a name="FNanchor_25_25" id="FNanchor_25_25"></a><a href="#Footnote_25_25" class="fnanchor">[25]</a> 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, <i>va</i>, the axis of the instrument terminates
-in a ball <i>e</i> which works in a cup <i>f</i>. The axis has also a portion
-of a ball of greater radius <i>b</i> concentric with the lower ball <i>e</i>.
-The upper parallel plate <i>d</i> is cupped over this ball. When
-the parallel plate is moderately free on <i>b</i>, the axis <i>va</i> may be
-set to any angle within the range of the central opening of <i>d</i>;
-and as the friction upon <i>bd</i> is greater than that upon <i>fe</i>, the
-axis moves by the adjustment of the parallel plate screws <i>aa</i>.
-In Fig. 216 the action is precisely the same, except that the
-pressure is upwards instead of downwards. In Fig. 215 there
-are springs <i>s</i> under the parallel plate screw heads to keep contact
-when the screws are loosened. In Fig. 216 the spring
-<span class="pagenum"><a name="Page_332" id="Page_332">[332]</a></span>
-is a plate under the screws <i>s</i>, the action being the same in
-both cases.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i331">
-  <img class="w100" src="images/i_331.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 215.&mdash;<i>Pastorelli's ball and socket adjustment.</i></p>
-    <p class="caption float-right">Fig. 216.&mdash;<i>Hoffmann's ball and socket adjustment.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_331a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>527.&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe25_5625" id="i332">
-  <img class="w100" src="images/i_332.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 217.&mdash;<i>Improved Hedley's dial, mounted on Hoffmann's head.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_332a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>528.&mdash;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.<span class="pagenum"><a name="Page_333" id="Page_333">[333]</a></span>
-The height of this dial is 9&frac12; inches; the weight 8 lbs. for
-a 6-inch instrument, in aluminium 5 lbs.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe32_625" id="i333">
-  <img class="w100" src="images/i_333.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 218.&mdash;<i>Improved Hedley, with cradle ring.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_333a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>529.&mdash;<span class="large bold">Hedley's Dial with Cranked Rocking Centre.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe29_4375" id="i334">
-  <img class="w100" src="images/i_334.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 219.&mdash;<i>Stanley's improved dial.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_334a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>This instrument has tribrach levelling with quick-setting
-spherical lower plate, a sliding tribrach for centring over any<span class="pagenum"><a name="Page_334" id="Page_334">[334]</a></span>
-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.</p>
-<p>530.&mdash;<span class="large bold">Accessories Common to Hedley's Dials</span> are
-a vertical reflector and a diaphragm illuminator.</p>
-<p><i>Reflecting Cap.</i>&mdash;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,<span class="pagenum"><a name="Page_335" id="Page_335">[335]</a></span>
-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 <i>H</i> and <i>H′</i>. When turned up it
-leaves the tube open for direct vision. A reflector <i>R</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_1875" id="i335">
-  <img class="w100" src="images/i_335.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 220.&mdash;<i>Reflecting cap to miner's dial.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_335a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>531.&mdash;<i>Illumination of the Diaphragm</i> 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<span class="pagenum"><a name="Page_336" id="Page_336">[336]</a></span>
-reflector, Fig. 220, goes on the same fitting. The reflector
-Fig. 221 <i>R</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i336">
-  <img class="w100" src="images/i_336.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 221.&mdash;<i>Conical reflector to illuminate axis of telescope.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_336a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>532.&mdash;<span class="large bold">Continental Forms of Miner's Dials.</span>&mdash;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.</p>
-<p>533.&mdash;<span class="large bold">French Miner's Compasses.</span>&mdash;Fig. 222 shows
-the simpler form of this instrument. The needle is open and
-quite free from obstruction. The telescope is centred about<span class="pagenum"><a name="Page_337" id="Page_337">[337]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i337">
-  <img class="w100" src="images/i_337.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 222.&mdash;<i>French form of miner's dial.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_337a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>534.&mdash;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.</p>
-<p><span class="pagenum"><a name="Page_338" id="Page_338">[338]</a></span></p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i338">
-  <img class="w100" src="images/i_338.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 223.&mdash;<i>French miner's transit survey instrument.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_338a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>535.&mdash;<span class="large bold">Miner's Transit Instrument.</span>&mdash;This is the
-<i>théodolite souterrain</i> of the French, and is of a construction
-very general throughout the Continent&mdash;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 6&frac14; inches; the weight without
-the tripod table is about 14 lbs. The tripod table is constructed
-in various ways by different makers.</p>
-<p>536.&mdash;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<span class="pagenum"><a name="Page_339" id="Page_339">[339]</a></span>
-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,
-<i>right</i> or <i>left</i>. For this a column should be placed in the field-book.
-As a rule fore sights are taken with the telescope <i>left</i>;
-back sights with the telescope <i>right</i>, 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.</p>
-<p>537.&mdash;<i>The Tripod Table</i> 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<span class="pagenum"><a name="Page_340" id="Page_340">[340]</a></span>
-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, <a href="#i273">Fig. 191</a>, p. 273, on this particular
-point.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i340">
-  <img class="w100" src="images/i_340.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 224.&mdash;<i>Stanley's improved mining survey transit.</i></p>
-    <p class="caption float-right">Fig. 225.&mdash;<i>Stand for the same.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_340a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>538.&mdash;<span class="large bold">Improved Mining Survey Transit.</span>&mdash;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<span class="pagenum"><a name="Page_341" id="Page_341">[341]</a></span>
-usual, to take a wide field of view; therefore it forms a
-good level.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i341">
-  <img class="w100" src="images/i_341.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 226.&mdash;<i>Stanley's miner's dial sight.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_341a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>539.&mdash;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. <i>ab</i> represent the pair of sights,
-<i>c</i> 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, <a href="#i158b">Fig. 105</a>, 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.</p>
-<p>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<span class="pagenum"><a name="Page_342" id="Page_342">[342]</a></span>
-tripods would be 1 foot 6 inches, 3 feet 6 inches, and 5 feet
-4 inches.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i342">
-  <img class="w100" src="images/i_342.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 227.&mdash;<i>Stanley's underground theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_342a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>540.&mdash;<span class="large bold">Mining Theodolite.</span>&mdash;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 1&frac14; inches
-about the centre of the tripod and be clamped to its position.
-The horizontal axis is pierced to permit the diaphragm to be<span class="pagenum"><a name="Page_343" id="Page_343">[343]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i343">
-  <img class="w100" src="images/i_343.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 228.&mdash;<i>Stanley's prismatic mining compass.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_343a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>541&mdash;<span class="large bold">Prismatic Mining Survey Compass.</span>&mdash;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 &frac14; degree or nearer.
-The principle of the compass is described <a href="#Art_148">art. 148</a>, the prism
-<a href="#Art_55">art. 55</a>; 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<span class="pagenum"><a name="Page_344" id="Page_344">[344]</a></span>
-of a large prism, Fig. 229 <i>R</i>, placed under the compass-box in
-a square tube, and a small movable lamp to throw light into
-it, Fig. 228 <i>L</i>. The floating ring, Fig. 229 <i>C</i>, 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 <i>W</i> is jointed in two folds <i>jj</i>,
-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&mdash;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,
-4&frac14; lbs. without the tripod stand.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i344">
-  <img class="w100" src="images/i_344.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 229.&mdash;<i>Section of prismatic mining compass.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_344a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>542.&mdash;<span class="large bold">Hanging Compass.</span>&mdash;A very general method of
-underground surveying in mineral districts upon the Continent
-is by means of the <i>hanging compass</i>; this instrument is therefore
-generally found in catalogues of surveying instruments in<span class="pagenum"><a name="Page_345" id="Page_345">[345]</a></span>
-France, Germany, and Italy. The original hanging compass
-was invented by Balthasar Rössler about 1660.<a name="FNanchor_26_26" id="FNanchor_26_26"></a><a href="#Footnote_26_26" class="fnanchor">[26]</a> 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&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_1875" id="i345">
-  <img class="w100" src="images/i_345.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 230.&mdash;<i>Stanley's hanging dial.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_345a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>543.&mdash;<span class="large bold">Hanging Dial.</span>&mdash;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.</p>
-<p>544.&mdash;In the construction of the instrument a circle of
-brass about 6 inches diameter, &frac12; inch wide, and 1/8 inch thick,
-<span class="pagenum"><a name="Page_346" id="Page_346">[346]</a></span>
-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 <i>fork-piece</i>, 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i346">
-  <img class="w100" src="images/i_346.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 231.&mdash;<i>Hanging clinometer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_346a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>545.&mdash;<span class="large bold">A Light Hanging Clinometer</span>, 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 <i>Mine Surveying</i>.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i347">
-  <img class="w100" src="images/i_347.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 232.&mdash;<i>French semi-circumferentor.</i></p>
-    <p class="caption float-right">Fig. 233.&mdash;<i>Tripod head.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_347a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>546.&mdash;<span class="large bold">Semi-circumferentor.</span>&mdash;This simple instrument<span class="pagenum"><a name="Page_347" id="Page_347">[347]</a></span>
-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<span class="pagenum"><a name="Page_348" id="Page_348">[348]</a></span>
-instrument with 6-inch circle is about 2 lbs.; height above
-tripod, 7 inches.</p>
-<p>547.&mdash;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.</p>
-<p>548.&mdash;<span class="large bold">Lighting Underground.</span>&mdash;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,<a name="FNanchor_27_27" id="FNanchor_27_27"></a><a href="#Footnote_27_27" class="fnanchor">[27]</a> 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.</p>
-<p>549.&mdash;<span class="large bold">Mining Survey Lamp.</span>&mdash;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
-<span class="pagenum"><a name="Page_349" id="Page_349">[349]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe21_9375" id="i349">
-  <img class="w100" src="images/i_349.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 234.&mdash;<i>Mining survey lamp.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_349a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe34_4375" id="i350">
-  <img class="w100" src="images/i_350.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 235.&mdash;<i>Stanley's complete mining outfit.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_350a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>550.&mdash;<span class="large bold">Mining Targets.</span>&mdash;The three tripod system has
-been much improved by the introduction of accurate targets
-made specially for the instrument used, and interchangeable<span class="pagenum"><a name="Page_350" id="Page_350">[350]</a></span>
-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<span class="pagenum"><a name="Page_351" id="Page_351">[351]</a></span>
-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.</p>
-<p>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.</p>
-<p>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.</p>
-<p>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.</p>
-<p><span class="pagenum"><a name="Page_352" id="Page_352">[352]</a></span></p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe19_625" id="i352">
-  <img class="w100" src="images/i_352.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 236.&mdash;<i>Stanley's Dunbar Scott auxiliary.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_352a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-<p>For vertical sighting it is also most useful and accurate, as<span class="pagenum"><a name="Page_353" id="Page_353">[353]</a></span>
-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.</p>
-<p>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.</p>
-<p>In Fig. 235 the auxiliary telescope is shown at top; Fig.
-236 shows it attached at the side.</p>
-<p>551.&mdash;<span class="large bold">Pocket Instruments.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i353">
-  <img class="w100" src="images/i_353.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 237.&mdash;<i>Pocket mine transit.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_353a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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<span class="pagenum"><a name="Page_354" id="Page_354">[354]</a></span>
-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.</p>
-<p>552.&mdash;<span class="large bold">Dip Compass.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe36_6875" id="i354">
-  <img class="w100" src="images/i_354.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 238.&mdash;<i>Dip compass.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_354a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_355" id="Page_355">[355]</a></span></p>
-<h2>CHAPTER XII.</h2>
-</div>
-<p class="ch">INSTRUMENTS TO MEASURE SUBTENSE OR TANGENTIAL
-ANGLES TO ASCERTAIN DISTANCES&mdash;HISTORICAL NOTES OF
-THE METHOD&mdash;PRINCIPLES INVOLVED&mdash;STADIUM MEASUREMENT,
-DIRECT AND BY THE ORDINARY TELESCOPE&mdash;CORRECTIONS
-FOR REFRACTION OF THE OBJECT-GLASS&mdash;STANLEY'S
-SUBTENSE DIAPHRAGM&mdash;ANALLATIC TELESCOPE
-OF PORRO&mdash;TACHEOMETERS&mdash;STADIUM&mdash;FIELD-BOOK&mdash;OMNIMETER
-AND ITS FIELD-BOOK&mdash;BAKEWELL's SUBTENSE
-ARRANGEMENT.</p>
-<p>553.&mdash;<span class="large bold">Direct Subtense Measurement of Distances</span>,
-<i>by an Instrument</i>, 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.</p>
-<p>554.&mdash;<i>The Origin of the Invention of Subtense Surveying</i>
-was thought to be due to Wm. Green, an optician<span class="pagenum"><a name="Page_356" id="Page_356">[356]</a></span>
-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.<a name="FNanchor_28_28" id="FNanchor_28_28"></a><a href="#Footnote_28_28" class="fnanchor">[28]</a> 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&mdash;tacheometers, omnimeters, etc.&mdash;and this is worthy of
-note, as the invention, though generally attributed to him,
-was not his:&mdash;</p>
-<p>555.&mdash;"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 (<i>staff</i>) 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 (<i>passing</i>) 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 (<i>by measurement of
-the image of the micrometer</i>) and all the angles included betwixt
-them, with the theodolite, plot it out in the usual manner, <i>e.g.</i>,
-<span class="pagenum"><a name="Page_357" id="Page_357">[357]</a></span>
-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.</p>
-<p>"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."</p>
-<p>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.</p>
-<p>"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.</p>
-<p>"Thus may any surveyor in less than two hours take all<span class="pagenum"><a name="Page_358" id="Page_358">[358]</a></span>
-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."</p>
-<p>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.</p>
-<p>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 <i>Life of
-James Watt</i>, he gives a statement by Watt himself that he
-constructed his instrument in 1770 and showed it to Smeaton
-in 1772.</p>
-<p id="Art_556">556.&mdash;<span class="large bold">Subtense Instruments</span>, 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:&mdash;</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i358">
-  <img class="w100" src="images/i_358.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 239.&mdash;<i>Diagram of tangential angle measurement.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_358a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p><span class="pagenum"><a name="Page_359" id="Page_359">[359]</a></span></p>
-<p>Let <i>AC</i>, Fig. 239, be a horizontal line; <i>BC</i> a stadium
-set up vertically. Then if the angle <i>BAC</i> and the height
-<i>BC</i> are known, the distance of <i>AC</i> can be easily calculated.
-For any intermediate distance between <i>A</i> and <i>C</i> a vertical will
-be in length proportional to this distance. Let <i>de</i> be at one-third
-the distance from <i>A</i>; then the line <i>de</i> will be one-third
-the length of <i>BC</i>. If we divide <i>BC</i> into three parts and
-place the stadium at <i>fg</i> two-thirds the distance from <i>A</i>, the
-angle <i>dAe</i> 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.</p>
-<p>If the tangent be made a constant equal to the
-length of the stadium <i>BC</i>, and this stadium be placed at
-another position, say <i>de</i> or <i>fg</i>; then the angle subtended by
-its entire length will vary in a manner that can only be estimated
-by trigonometrical calculation.</p>
-<p>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:&mdash;</p>
-<p>Given the tangent <i>BC</i> and the angle <i>BAC</i>, required
-the distance <i>AC</i>. Let the angle <i>BAC</i> be represented
-by <i>D</i>; then&mdash;</p>
-<div class="m25">
-<table summary="">
-  <tr>
-    <td class="tdc" style="border-bottom: 1px solid black;"><i>CA</i></td>
-    <td class="tdc" rowspan="2" style="padding-left: .1em;">= cotan <i>D</i>, or <i>CA</i> = <i>CB</i> × cotan <i>D</i>.</td>
-  </tr>
-  <tr>
-    <td class="tdc"><i>CB</i></td>
-  </tr>
-</table>
-</div>
-<p>Reducing by logarithms, we have&mdash;</p>
-<p class="noindent center">
-log <i>CA</i> = log <i>CB</i> + <i>L</i> cotan <i>D</i> - 10.<br />
-</p>
-<p>For example, make <i>CB</i> 14 feet, and the angle <i>D</i> 2° 45′
-50″, thus:&mdash;</p>
-<div class="m15">
-<table summary="">
-  <tr>
-    <td class="tdr">log <i>CB</i></td>
-    <td>= 1·146128</td>
-    <td></td>
-  </tr>
-  <tr>
-    <td class="tdr"><i>L</i> cotan <i>D</i> - 10</td>
-    <td style="border-bottom: 1px solid black;">= 1·316265</td>
-    <td></td>
-  </tr>
-  <tr>
-    <td class="tdr">log <i>CA</i></td>
-    <td>= 2·462393,</td>
-    <td>or <i>CA</i> = 290 feet.</td>
-  </tr>
-</table>
-</div>
-<p>The above gives the principles followed with instruments of<span class="pagenum"><a name="Page_360" id="Page_360">[360]</a></span>
-the theodolite class simply; but arrangements are made in
-omnimeters and similar instruments to read the tangent
-directly and determine the height <i>CB</i> in equal parts, so that
-observation of the heights <i>BC</i> gives rectangular co-ordinates
-and thus saves reduction from degrees of arc.</p>
-<p>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.</p>
-<p>557.&mdash;<i>Measuring Distances by the Ordinary Telescope by
-Measurement of its Focal Image.</i>&mdash;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, <a href="#Art_58">art. 58</a>, 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 <i>A</i> and <i>C</i> 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.</p>
-<p id="Art_558">558.&mdash;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<span class="pagenum"><a name="Page_361" id="Page_361">[361]</a></span>
-kindness of Lord Rayleigh for the following demonstration
-of Riechenbach's formula:&mdash;</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i361">
-  <img class="w100" src="images/i_361.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 240.&mdash;<i>Subtense diagram.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_361a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>Let Fig. 240 <i>AB</i> = <i>s</i>, <i>ab</i> = <i>i</i>, <i>OA</i> = <i>d</i>, <i>Ob</i> = <i>r</i>. <i>O</i> is the
-optical centre of the object-glass; <i>ab</i> a pair of webs at variable
-distance <i>r</i> from <i>O</i> according to telescopic focus; <i>f</i> focus for
-parallel rays. Then by similar triangles <i>s</i>/<i>d</i> = <i>i</i>/<i>r</i> or <i>d</i> = <i>rs</i>/<i>i</i>, <i>r</i>
-is found by optical laws to vary in the proportion of
-1/<i>r</i> + 1/<i>d</i> = 1/<i>f</i>. We may therefore eliminate the variable <i>r</i> by
-substituting its value <i>r</i> = <i>fd</i>/(<i>d</i> - <i>f</i>), by which we find <i>d</i> = <i>sf</i>/<i>i</i> + <i>f</i>,
-which gives the true correction; and the distance from
-the axis of the instrument will be <i>d</i> = <i>sf</i>/<i>i</i> + <i>f</i> + <i>c</i> where <i>c</i> 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 <i>c</i> becomes <i>f</i>/2.</p>
-<p>It is seen that <i>sf</i>/<i>i</i> represents the direct subtense, whereas
-the refraction, which is a constant, gives f and the position
-of the object-glass <i>f</i>/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 1&frac12;<i>f</i>, which added to the apparent subtense is
-found to produce no error. Thus with a telescope of 1 foot<span class="pagenum"><a name="Page_362" id="Page_362">[362]</a></span>
-solar focus, and using the decimal system of notation, as
-before mentioned, if a stadium or distinct scale be placed at
-301&frac12; 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 + 1&frac12; 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 1&frac12; feet always.</p>
-<p>559.&mdash;When the line of sight is inclined from the horizon
-and the stadium is held erect&mdash;a convenient method commonly
-followed upon the Continent&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i362">
-  <img class="w100" src="images/i_362.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 241.&mdash;<i>Diagram of vertical stadium on an incline.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_362a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>Thus, Fig. 241, let the portion cut by the lines <i>AB</i>, <i>S′</i> be
-the reading of the stadium; then</p>
-<p class="center">
-<i>S′</i>(cos <i>a</i>) = <i>S</i>.<br />
-</p>
-<p>The inclined distance is then equal to</p>
-<p class="center">
-(<i>f</i>/<i>i</i>)<i>S′</i>(cos <i>a</i>) + <i>f</i> + <i>c</i><br />
-</p>
-<p><span class="pagenum"><a name="Page_363" id="Page_363">[363]</a></span></p>
-<p class="noindent">and the horizontal projection of that distance or</p>
-<p class="center">
-<i>a</i> = ((<i>f</i>/<i>i</i>)<i>S′</i>(cos <i>a</i>) + <i>f</i> + <i>c</i>)cos <i>a</i>;<br />
-</p>
-<p>or as <i>f</i> + <i>c</i> is small and the angle generally small also, <i>f</i> + <i>c</i>
-may be taken equal to (<i>f</i> + <i>c</i>) cos <i>a</i>. Then</p>
-<p class="center">
-<i>a</i>=(<i>f</i>/i)<i>S′</i> cos<sup>2</sup> <i>a</i> + <i>f</i> + <i>c</i>.<br />
-</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe23_875" id="i363">
-  <img class="w100" src="images/i_363.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 242.&mdash;<i>Stanley's patent subtense diaphragm.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_363a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>560.&mdash;<span class="large bold">The Subtense-diaphragm</span> 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.</p>
-<p>561.&mdash;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.<span class="pagenum"><a name="Page_364" id="Page_364">[364]</a></span>
-The means of doing this, devised by the author, is to place
-a <i>sight director</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe21_5625" id="i364">
-  <img class="w100" src="images/i_364.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 243.&mdash;<i>Sight director for stadium.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_364a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>562.&mdash;<span class="large bold">The Anallatic Telescope.</span>&mdash;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,<a name="FNanchor_29_29" id="FNanchor_29_29"></a><a href="#Footnote_29_29" class="fnanchor">[29]</a> in an instrument termed a tacheometer.
-The telescope will be best understood by the
-following details:&mdash;</p>
-<p>The object-glass <i>O</i>, Fig. 244, is made of a focus that falls
-well in front of the axis of the instrument <i>CC′</i>, so that the
-rays cross before falling upon the anallatic lens <i>A</i>, the optical
-arrangement being such that if the rays fell direct without any
-<span class="pagenum"><a name="Page_365" id="Page_365">[365]</a></span>
-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 <i>A</i> to <i>M</i>. The stop at <i>S</i> and at the axis
-<i>CC′</i> cuts off eccentric rays that would otherwise give internal
-reflections from the telescope tube. The eye-piece, represented
-by <i>MF</i>, 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i365">
-  <img class="w100" src="images/i_365.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 244.&mdash;<i>Diagram of anallatic telescope.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_365a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>563.&mdash;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<span class="pagenum"><a name="Page_366" id="Page_366">[366]</a></span>
-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&mdash;by
-rack and pinion.</p>
-<p>564.&mdash;The eye-piece of the anallatic telescope is generally
-made of much higher power than those ordinarily employed
-for levels and theodolites&mdash;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 <a href="#i335">Fig. 220</a>, 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i366">
-  <img class="w100" src="images/i_366.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Figs. 245, 246, 247.&mdash;<i>Subtense lines ruled on glass.</i></p>
-    <p class="caption float-right">Fig. 248.&mdash;<i>Adjustable point diaphragm with stadia points.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_366a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>565.&mdash;While many civil engineers are satisfied with a single
-percentage pair of subtense lines the author much prefers using
-the point system, <a href="#Art_237">arts. 237</a> 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 <i>ss</i> for subtense
-angles. These points adjust by separate screws top and bottom<span class="pagenum"><a name="Page_367" id="Page_367">[367]</a></span>
-with a milled-headed key <i>f</i>. 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.</p>
-<p>566.&mdash;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, <a href="#i163">Fig. 109</a>,
-p. 163.</p>
-<p>567.&mdash;It is well to note that with the anallatic telescope
-the stadium must not be so near that the rays from
-the object-glass <i>do not cross</i> 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<span class="pagenum"><a name="Page_368" id="Page_368">[368]</a></span>
-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>i</i>/<i>f′</i> = the ratio <i>l</i>/<i>D</i>;
-where <i>i</i> is the space between the stadia points, <i>l</i> the height on
-the staff which these points appear to intercept when viewed
-through the eye-piece accurately focussed on them, <i>D</i> the
-distance of the staff from the object-glass, and <i>f′</i> the distance
-of the diaphragm from the object-glass. Now in this equation
-<i>i</i> is a fixed space, <i>l</i> 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/<i>f′</i> + 1/<i>D</i> = 1/<i>F</i> where <i>F</i> is the principal focal length of the lens.<span class="pagenum"><a name="Page_369" id="Page_369">[369]</a></span>
-Therefore <i>f′</i> = <i>FD</i>/(<i>D</i> - <i>F</i>) for all values of <i>D</i>. Substituting this
-value of <i>f′</i> in equation (1) we get <i>i</i> × (<i>D</i> - <i>F</i>)/<i>FD</i> = l/<i>D</i>; and
-multiplying both sides by <i>D</i>, <i>i</i> × (<i>D</i> - <i>F</i>)/<i>F</i> = <i>l</i>. ∴ <i>D</i> - <i>F</i> = (<i>F</i>/<i>i</i>)<i>l</i> and
-<i>D</i> = (<i>F</i>/<i>i</i>)<i>l</i> + <i>F</i> which is true for all distances. But this
-distance is measured from the object-glass, and the distance <i>S</i>
-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 <i>d</i>. ∴ <i>S</i> = <i>D</i> + <i>d</i> = (<i>F</i>/<i>i</i>)<i>l</i> + <i>F</i> + <i>d</i>, and
-<i>F</i> + <i>d</i> is the constant of the instrument = <i>c</i>. ∴ <i>S</i> = (<i>F</i>/<i>i</i>)<i>l</i> + <i>c</i>.</p>
-<p>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,<span class="pagenum"><a name="Page_370" id="Page_370">[370]</a></span>
-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 <i>S</i> = 100,000<i>l</i>/<i>x</i> + <i>c</i> where <i>x</i> is the micrometer
-reading, and <i>l</i> 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.</p>
-<p>568.&mdash;<span class="large bold">Tacheometers</span> 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 <i>tacheos</i> (quickly),
-and <i>metreo</i> (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<span class="pagenum"><a name="Page_371" id="Page_371">[371]</a></span>
-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,<a name="FNanchor_30_30" id="FNanchor_30_30"></a><a href="#Footnote_30_30" class="fnanchor">[30]</a> 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, <a href="#i247">Fig. 169</a>, 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.</p>
-<p>569.&mdash;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 1&frac34; 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
-<span class="pagenum"><a name="Page_372" id="Page_372">[372]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe18_5" id="i372">
-  <img class="w100" src="images/i_372.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 249.&mdash;<i>Stanley's 6-inch tacheometer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_372a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>570.&mdash;Where points are not used in the diaphragm or
-where lines are preferred, these may be divided upon glass<span class="pagenum"><a name="Page_373" id="Page_373">[373]</a></span>
-in fine lines as <a href="#i366">Fig. 246</a>; or spider webs may be used, but
-these are more difficult to set exact for stadia.</p>
-<p>571.&mdash;<span class="large bold">Stadium.</span>&mdash;Any accurate levelling staff will answer
-for the stadium, but the ordinary Sopwith, <a href="#i152">Fig. 99</a>, is slightly
-confusing. A more open reading is generally recommended&mdash;that
-shown <a href="#i155">Fig. 102</a>, 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&mdash;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.</p>
-<p>572.&mdash;<i>The General System of Working the Tacheometer</i>,
-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 <i>The Tacheometer:
-Its Theory and Practice</i>, by Mr. Neil Kennedy;
-<i>Surveying</i>, by Whitelaw; <i>Aid to Survey Practice</i>, by L. D'A.
-Jackson, &amp;c. There is a small work published in New York
-giving some details.<a name="FNanchor_31_31" id="FNanchor_31_31"></a><a href="#Footnote_31_31" class="fnanchor">[31]</a> There are complete works in French,
-Italian, German, and Spanish. In French, <i>Leves de Plans
-a la Stadia</i>, 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.</p>
-<p>There are several tacheometers made upon the Continent,
-of more complicated forms than those herein described, but
-they do not produce better work.</p>
-<p><span class="pagenum"><a name="Page_374" id="Page_374">[374]</a></span></p>
-<p>573.&mdash;<span class="large bold">Field-books</span> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i374">
-  <img class="w100" src="images/i_374.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 249<i>a</i>.</p>
-    <p class="caption ebhide clear"><a href="images/i_374a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>574.&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe17_4375" id="i375">
-  <img class="w100" src="images/i_375.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 250.&mdash;<i>Perspective view of 5-inch omnimeter.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_375a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>575.&mdash;<span class="large bold">The Omnimeter</span> 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<a name="FNanchor_32_32" id="FNanchor_32_32"></a><a href="#Footnote_32_32" class="fnanchor">[32]</a>
-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
-<span class="pagenum"><a name="Page_375" id="Page_375">[375]</a></span>
-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<span class="pagenum"><a name="Page_376" id="Page_376">[376]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe31_6875" id="i376">
-  <img class="w100" src="images/i_376.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 251.&mdash;<i>Details of omnimeter, showing section of microscope and scale.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_376a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>576.&mdash;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<span class="pagenum"><a name="Page_377" id="Page_377">[377]</a></span>
-placing the tangent scale in a horizontal position, where it
-could be firmly fixed upon the vernier plate as shown Fig. 251
-<i>S</i>, and reading the scale by means of a reflecting prism <i>P</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i377">
-  <img class="w100" src="images/i_377.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 252.&mdash;<i>Details of prismatic eye-piece.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_377a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p><span class="pagenum"><a name="Page_378" id="Page_378">[378]</a></span></p>
-<p>577.&mdash;The general appearance of the instrument resembles
-the transit theodolite, already described <a href="#Art_368">art. 368</a>, 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. <i>T</i> telescope
-with sensitive level <i>B</i> mounted upon it; <i>R</i> 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 <i>P</i> 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 <i>S</i> with the micrometer
-with edge reading vernier at <i>M</i>. The compass of the
-instrument <i>C</i> 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 <i>S</i>.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i378">
-  <img class="w100" src="images/i_378.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 253.&mdash;<i>Omnimeter webs; a telescope, b microscope.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_378a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>578.&mdash;The telescope diaphragm is generally webbed with
-one horizontal and two vertical webs, Fig. 253 <i>a</i>, 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 <i>b</i>
-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.</p>
-<p><span class="pagenum"><a name="Page_379" id="Page_379">[379]</a></span></p>
-<p>579.&mdash;<i>Reading of the Tangent Scale.</i>&mdash;As the micrometer
-divides half a principal division into 500, the complete <i>figured</i>
-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 65&frac12; 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.</p>
-<p>580.&mdash;<i>Value of the Scale taken in Rectangular Coordinates.</i>&mdash;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.</p>
-<p>581.&mdash;<i>The Stadium</i> 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<span class="pagenum"><a name="Page_380" id="Page_380">[380]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i380">
-  <img class="w100" src="images/i_380.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 254.&mdash;<i>Ruling of omnimeter field-book.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_380a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>582.&mdash;<i>Field-book.</i>&mdash;The field-book as shown above, Fig.
-254, was recommended by the inventor.</p>
-<p>583.&mdash;<i>Mode of Operating with the Omnimeter.</i>&mdash;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<span class="pagenum"><a name="Page_381" id="Page_381">[381]</a></span>
-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.</p>
-<p>584.&mdash;<i>To Determine the Horizontal Distance in Feet.</i>&mdash;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:&mdash;</p>
-<div class="m10">
-<table summary="">
-  <tr>
-    <td>First reading</td>
-    <td>of scale</td>
-    <td>67,500,</td>
-    <td class="tdc">micrometer</td>
-    <td class="tdr">235 =</td>
-    <td class="tdl">67,735</td>
-  </tr>
-  <tr>
-    <td>Second</td>
-    <td>"</td>
-    <td>64,000,</td>
-    <td class="tdc">"</td>
-    <td class="tdr">450 =</td>
-    <td class="tdl" style="border-bottom: 1px solid black;">64,450</td>
-  </tr>
-  <tr>
-    <td></td>
-    <td></td>
-    <td></td>
-    <td></td>
-    <td>Difference</td>
-    <td class="tdr">3,285;</td>
-  </tr>
-</table>
-</div>
-<p class="noindent">then</p>
-
-<div class="m20">
-<p class="noindent center"  style="padding-right: 1em;">
-<span class="division" style="padding: 0 .5em;">
-  <span class="numerator">1,500,000</span>
-  <span class="denominator">3285</span>
-</span>
-= 456·6 feet distance.</p>
-</div>
-
-
-<p>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&mdash;</p>
-<div class="m20">
-<table summary="">
-  <tr>
-    <td style="padding-right: 1em;">log. 1,500,000</td>
-    <td>6·1760913</td>
-    <td></td>
-  </tr>
-  <tr>
-    <td>log. 3,285,000</td>
-    <td style="border-bottom: 1px solid black;">3·5165354</td>
-    <td></td>
-  </tr>
-  <tr>
-    <td></td>
-    <td>2·6595559</td>
-    <td>= 456·6 feet.</td>
-  </tr>
-</table>
-</div>
-<p>585.&mdash;<i>To Determine Horizontal Distance in Chains</i> 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&mdash;</p>
-<div class="m15">
-<p class="noindent center" style="padding-right: 1em;">
-<span class="division" style="padding: 0 .5em;">
-  <span class="numerator">3,000,000</span>
-  <span class="denominator">3285</span>
-</span>
-= 913·2, or 9 chains 13·2 links distance.</p>
-</div>
-
-<p><i>To Determine Horizontal Distance in Metres</i>, the stadium
-is divided to 4 metres. Then radius 150,000 × 4 = 600,000.
-Taking, for example, difference of reading as before 3285 then</p>
-<div class="m20">
-<p class="noindent center" style="padding-right: 1em;">
-<span class="division" style="padding: 0 .5em;">
-  <span class="numerator">600,000</span>
-  <span class="denominator">3285</span>
-</span>
-= 182·64 metres.</p>
-</div>
-
-<p><span class="pagenum"><a name="Page_382" id="Page_382">[382]</a></span></p>
-<p>586.&mdash;<i>Levelling&mdash;Taking Altitudes.</i>&mdash;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&mdash;</p>
-<div class="m25">
-<table summary="">
-  <tr>
-    <td style="padding-right: 1em;">Lower</td>
-    <td>reading</td>
-    <td>64,450</td>
-  </tr>
-  <tr>
-    <td>Level</td>
-    <td class="tdc">"</td>
-    <td style="border-bottom: 1px solid black;">50,010</td>
-  </tr>
-  <tr>
-    <td></td>
-    <td  style="padding-right: .5em;">Difference</td>
-    <td>14,440</td>
-  </tr>
-</table>
-</div>
-<p class="noindent">then</p>
-<div class="m20">
-<p class="noindent center"  style="padding-right: 1em;">
-<span class="division" style="padding: 0 .5em;">
-  <span class="numerator">14,440</span>
-  <span class="denominator">3285</span>
-</span>
-× 10 = 43·96 feet nearly.</p>
-</div>
-
-<p class="noindent">The heights, in relation to the position of the instrument, are
-<i>positive</i> or <i>negative</i> according as the scale readings are greater
-or less than the constant level reading or departure point.</p>
-<p>587.&mdash;<i>Work of the Omnimeter.</i>&mdash;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&mdash;"It
-has been found to give very accurate heights of buildings, etc.,
-also to be wonderfully accurate when used as a levelling
-instrument; <i>but it is not so accurate for measuring distances
-over</i> 600 <i>feet</i>, and even at this distance the error sometimes
-amounts to as much as 1 <i>foot</i>. It is recommended as admirably
-adapted for city surveys and traversing, also in hilly and
-jungly countries, and for railway and similar purposes."<a name="FNanchor_33_33" id="FNanchor_33_33"></a><a href="#Footnote_33_33" class="fnanchor">[33]</a></p>
-<p>588.&mdash;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,
-<span class="pagenum"><a name="Page_383" id="Page_383">[383]</a></span>
-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.</p>
-<p>589.&mdash;<i>Improvement in the Omnimeter.</i>&mdash;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.</p>
-<p><span class="pagenum"><a name="Page_384" id="Page_384">[384]</a></span></p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe32_0625" id="i384">
-  <img class="w100" src="images/i_384.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 255.&mdash;<i>Bakewell's tangential arrangement to a theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_384a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>590.&mdash;<span class="large bold">Bakewell's Tangential Arrangement</span> <i>to a
-Theodolite for Measuring Distances</i>.&mdash;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&mdash;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.<a name="FNanchor_34_34" id="FNanchor_34_34"></a><a href="#Footnote_34_34" class="fnanchor">[34]</a> 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.</p>
-<p>591.&mdash;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
-<span class="pagenum"><a name="Page_385" id="Page_385">[385]</a></span>
-the pivots. A collar <i>A</i>, 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 <i>B</i>. The collar is
-connected in the same gun-metal casting with the radial arm
-<i>C</i> that terminates at <i>T</i> in a plane, which is made truly radial
-with the transverse axis of the telescope. This radial arm <i>C</i>
-has a long German-silver spring <i>S</i> 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 <i>D</i>; on the spiral the scale of distances is
-engraved; and readings are taken from a line on the index <i>I</i>
-which slides on the bar <i>E</i>. 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 <i>D</i> is divided into 200, and reads by
-vernier <i>V</i> carried by the arm <i>E</i> in 5 or thousandths of a
-revolution. The micrometer screw has twenty-five threads to
-an inch, and the radius of the arm <i>C</i> 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.</p>
-<p>592.&mdash;<span class="large bold">The Gradienter Screw.</span>&mdash;This is no doubt a<span class="pagenum"><a name="Page_386" id="Page_386">[386]</a></span>
-simplified copy of Bakewell's tangential arrangement and is
-shown at Fig. 256.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe32_625" id="i386">
-  <img class="w100" src="images/i_386.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 256.&mdash;<i>Gradienter screw.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_386a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-<p>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.</p>
-<p><i>To establish any grade with this screw.</i>&mdash;Set the gradienter<span class="pagenum"><a name="Page_387" id="Page_387">[387]</a></span>
-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.</p>
-<p><i>For Measuring Distance.</i>&mdash;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.</p>
-<p><i>Second Method.</i>&mdash;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&mdash;</p>
-<div class="m20">
-<p class="noindent center"  style="padding-right: 1em;">
-<span class="division" style="padding: 0 .5em;">
-  <span class="numerator">20·00 feet</span>
-  <span class="denominator">1·45</span>
-</span>
- × 100 = 1379·3 feet.</p>
-</div>
-
-<p>Another instance.&mdash;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&mdash;</p>
-<div class="m20">
-<p class="noindent center" style="padding-right: 1em;">
-<span class="division" style="padding: 0 .5em;">
-  <span class="numerator">3·25 feet</span>
-  <span class="denominator">0·78</span>
-</span>
-× 100 = 416·6 feet.</p>
-</div>
-
-<p>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<span class="pagenum"><a name="Page_388" id="Page_388">[388]</a></span>
-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.</p>
-<p>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.</p>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_389" id="Page_389">[389]</a></span></p>
-<h2>CHAPTER XIII.</h2>
-</div>
-<p class="ch">INSTRUMENTS CONSTRUCTED ESPECIALLY FOR OFFERING FACILITY
-OF TAKING INCLINES&mdash;INCLINOMETER&mdash;THEODOLITE&mdash;GRADIOMETER&mdash;CLINOMETERS&mdash;ABNEY'S,
-TROUGHTON'S, DE
-LISLE'S, STANLEY'S, BARKER'S, BURNIER'S, WATKINS'&mdash;CLINOMETER
-SIGHTS&mdash;RULE CLINOMETERS&mdash;ROAD TRACER.</p>
-<p>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.</p>
-<p>593.&mdash;<span class="large bold">Lister's Inclinometer Theodolite.</span><a name="FNanchor_35_35" id="FNanchor_35_35"></a><a href="#Footnote_35_35" class="fnanchor">[35]</a>&mdash;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,
-<a href="#Art_370">arts. 370</a> 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
-<span class="pagenum"><a name="Page_390" id="Page_390">[390]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe24_6875" id="i390">
-  <img class="w100" src="images/i_390.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 257.&mdash;<i>Lister's inclinometer theodolite.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_390a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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."</p>
-<p>The main difference between the method of taking cross
-sections by the level and by the inclinometer theodolite is in<span class="pagenum"><a name="Page_391" id="Page_391">[391]</a></span>
-substituting inclined bases for horizontal ones, which will be
-clearly understood by reference to the following diagrams,
-which illustrate somewhat extreme surface inclination.</p>
-
-<div class="figcenter padding1">
-<div class="caption">
-  <p class="caption">Fig. 258.</p>
-</div>
-<div class="figcenter illowe37_5" id="i391">
-  <img class="w100" src="images/i_391.png"  alt="" />
-</div>
-
-  <div class="caption">
-    <p class="caption">Fig. 259.</p>
-    <p class="caption ebhide clear"><a href="images/i_391a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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<span class="pagenum"><a name="Page_392" id="Page_392">[392]</a></span>
-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.</p>
-<p>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.</p>
-<p>594.&mdash;<i>Explanation of the Method of Operating with the
-Inclinometer Theodolite.</i>&mdash;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.</p>
-<p>595.&mdash;<i>To take Cross Sections when the Line is Straight.</i>&mdash;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<span class="pagenum"><a name="Page_393" id="Page_393">[393]</a></span>
-in the direction of the section lines, the method of procedure
-is as follows:&mdash;</p>
-<p>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.</p>
-<p>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<span class="pagenum"><a name="Page_394" id="Page_394">[394]</a></span>
-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:&mdash;Fig. 260.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i394">
-  <img class="w100" src="images/i_394.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 260.</p>
-    <p class="caption ebhide clear"><a href="images/i_394a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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:&mdash;if the angle of the tilt be 10°, and the
-vertical arc angle 25°&mdash;Referring to tables, cosine 10° = ·98481,
-tangent 25° = ·46631. ·46631 × ·98481 = ·45924 = tangent
-24° 40′, the corrected angle making a variation of 20′.</p>
-<p><span class="pagenum"><a name="Page_395" id="Page_395">[395]</a></span></p>
-<p>596.&mdash;<i>To take Cross Sections when the Line is on a
-Curve.</i>&mdash;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.</p>
-<p>Diagram (Fig. 261) showing the adjustment of the instrument
-for taking sections on curves and the variation of the
-tangential angles for each section.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i396">
-  <img class="w100" src="images/i_396.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 261. If the centre pegs be taken as slope pegs, the diagram applies to illustrate
-the setting out of half widths.</p>
-    <p class="caption ebhide clear"><a href="images/i_396a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-<p>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
-<span class="pagenum"><a name="Page_396" id="Page_396">[396]</a></span>peg. Release the telescope from the arc and turn it at right
-angles thereto in the direction of the zero line AD. Now,
-<span class="pagenum"><a name="Page_397" id="Page_397">[397]</a></span>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.</p>
-<p>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.</p>
-<p>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.</p>
-<p>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.</p>
-<p>597.&mdash;<i>To set out Half Widths or Slope Pegs when the
-Line is straight.</i>&mdash;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<span class="pagenum"><a name="Page_398" id="Page_398">[398]</a></span>
-"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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i398">
-  <img class="w100" src="images/i_398.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 262.</p>
-    <p class="caption ebhide clear"><a href="images/i_398a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-<p>In speaking of half-mile distances we are assuming the<span class="pagenum"><a name="Page_399" id="Page_399">[399]</a></span>
-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.</p>
-<p>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.</p>
-<p>598.&mdash;<i>To set out Slope Pegs when the Line is on a
-Curve.</i>&mdash;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.</p>
-<p>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.</p>
-<p>To put in the first peg from the normal, make one movement
-of the angle repeater and adjust the bubble. To put in<span class="pagenum"><a name="Page_400" id="Page_400">[400]</a></span>
-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.</p>
-<p>599.&mdash;<i>Alternative method of setting out the Normal
-Pegs.</i>&mdash;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 1&frac12; to 1, or at an inclination
-of 56° 18′. The distance <i>bc</i> for a 1&frac12; to 1 slope is one-third
-the formation width, or 10 feet. The data required for the
-operation is the distance <i>ad</i> from the centre peg to the plane
-of the slope, which is found by multiplying <i>ac</i> by the natural
-sine of the slope angle 56° 18′, thus: 26 × ·831 = 21·60 feet.</p>
-<p>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, <i>viz.</i>, 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.</p>
-<p>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 <i>ag</i>
-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.</p>
-<p><span class="pagenum"><a name="Page_401" id="Page_401">[401]</a></span></p>
-<p>In this example, when the required reading is higher than
-the ordinary staff, lower the tilt and take an intermediate
-reading, as at <i>f</i> in the diagram, Fig. 263, which may read,
-say, 12·00, when the required reading on the peg will be
-reduced to 9·60.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i401">
-  <img class="w100" src="images/i_401.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 263.</p>
-    <p class="caption ebhide clear"><a href="images/i_401a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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>i.e.</i>, at double the tangential angle for the distance
-the instrument is from the peg, as before explained in detail
-for operations on curves.</p>
-<p>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<span class="pagenum"><a name="Page_402" id="Page_402">[402]</a></span>
-contingent difficulties of ground surface is an advantage of
-considerable importance.</p>
-<p>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.</p>
-<p>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 <i>a</i> on the sketch (Fig. 264), and at
-the point read, as at <i>b</i>, 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i402">
-  <img class="w100" src="images/i_402.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 264.</p>
-    <p class="caption ebhide clear"><a href="images/i_402a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-<p>600.&mdash;<i>To set out Slope Pegs on both sides of the Line
-simultaneously without moving the Instrument from the Centre<span class="pagenum"><a name="Page_403" id="Page_403">[403]</a></span>
-Line.</i>&mdash;<span class="smcap">Conditions.</span> Single Line. (<i>ab</i>) Formation 15 feet.
-(<i>cd</i>) Depth of cutting 14 feet. Slope 1 to 1.</p>
-<p>The point <i>e</i>, 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″.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i403">
-  <img class="w100" src="images/i_403.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 265.</p>
-    <p class="caption ebhide clear"><a href="images/i_403a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p><span class="smcap">Operation.</span>&mdash;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 <i>c f</i>).
-Take the section depth <i>cd</i> (14 feet), to which add <i>de</i> (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 <i>g</i> 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, <i>but</i> if the telescope be now
-changed to the angle of the slope on the other side of the line
-<i>ch</i>, the peg <i>i</i> is instantly found by the same reading (15·20).</p>
-<p>601.&mdash;<i>The Use of the Inclinometer in Mining.</i>&mdash;A lode
-having been discovered, it is required to mark out on the<span class="pagenum"><a name="Page_404" id="Page_404">[404]</a></span>
-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.</p>
-<p>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.</p>
-<p>602.&mdash;<span class="large bold">The Gradiometer.</span>&mdash;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.</p>
-<p>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<span class="pagenum"><a name="Page_405" id="Page_405">[405]</a></span>
-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.</p>
-<p>The additional parts do not increase the bulk of the case
-and add very little to the weight.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i405">
-  <img class="w100" src="images/i_405.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 266.&mdash;<i>Stanley's gradiometer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_405a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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<span class="pagenum"><a name="Page_406" id="Page_406">[406]</a></span>
-instrument, and taking the reading of the drum at the position
-of the indicator.</p>
-<p>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.</p>
-<p>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.</p>
-<p>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.</p>
-<p>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.</p>
-<p>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<span class="pagenum"><a name="Page_407" id="Page_407">[407]</a></span>
-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.</p>
-<p>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 37&frac12; | 50 and 33-1/3 | 33-1/3 and 25 | 25 and 20 | 20
-and 16-2/3 | 12&frac12; and 11-1/9 | 11-1/9 and 10.</p>
-<p>
-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 27&frac12; 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</p>
-<div class="m25">
-<table summary="">
-  <tr>
-    <td>12·75</td>
-  </tr>
-  <tr>
-    <td style="border-bottom: 1px solid black;">- 3·40</td>
-  </tr>
-  <tr>
-    <td>= 9·35</td>
-  </tr>
-</table>
-</div>
-<p>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.</p>
-<p>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.</p>
-<p>
-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.</p>
-
-<p class="noindent center">650 ÷ 10 = 65</p>
-<p class="noindent center" style="padding-left: .9em;">650 ÷ 20 = 32&frac12;</p>
-
-<p>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<span class="pagenum"><a name="Page_408" id="Page_408">[408]</a></span>
-out in the required direction with a 10-feet rod (preferably
-having <img style="height: 1em;" src="images/t1.png" alt="T symbol" /> ends,
-thus <img style="height: 1em;" src="images/t2.png" alt="T symbol" />,
-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 32&frac12;.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe36_75" id="i408">
-  <img class="w100" src="images/i_408.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 267.&mdash;<i>Stanley's gradioplane.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_408a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-<p><span class="pagenum"><a name="Page_409" id="Page_409">[409]</a></span></p>
-<p>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.</p>
-<p>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.</p>
-<p>603.&mdash;<span class="large bold">Gradioplane.</span>&mdash;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.</p>
-<p>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.</p>
-<p>In the former case it carries a floating bevelled aluminium
-ring compass divided to &frac14; degrees, reading by microscope, and
-in the latter a long trough compass.</p>
-<p>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 1&frac34; 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.</p>
-<p>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<span class="pagenum"><a name="Page_410" id="Page_410">[410]</a></span>
-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.</p>
-<p>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.</p>
-<p>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<span class="pagenum"><a name="Page_411" id="Page_411">[411]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i411">
-  <img class="w100" src="images/i_411.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 268.&mdash;<i>Stanley's gradioplane.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_411a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-<p>604.&mdash;<span class="large bold">Abney's Clinometer.</span>&mdash;This very popular little
-instrument, the invention of Captain Abney, Fig. 269, embraces
-the same form of sighted level with reflector as that<span class="pagenum"><a name="Page_412" id="Page_412">[412]</a></span>
-shown in section, <a href="#i142">Fig. 87</a>, 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 2&frac12; by 1&frac12;
-inches; weight, 8 oz.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i412">
-  <img class="w100" src="images/i_412.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 269.&mdash;<i>Abney's clinometer..</i></p>
-    <p class="caption float-right">Fig. 270.&mdash;<i>Troughton's clinometer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_412a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>605.&mdash;<span class="large bold">Troughton's Abney's Clinometer.</span>&mdash;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.</p>
-<p>606.&mdash;<span class="large bold">Telescopic Hand Clinometer.</span>&mdash;The author
-has recently added a telescope to the Abney form of clinometer,
-as shown Fig. 271. The arc is moved by rack and<span class="pagenum"><a name="Page_413" id="Page_413">[413]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i413">
-  <img class="w100" src="images/i_413.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 271.&mdash;<i>Telescopic Abney clinometer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_413a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>607.&mdash;<span class="large bold">De Lisle's Reflecting Clinometer.</span>&mdash;There
-have been several arrangements made for converting the
-Burel level, <a href="#i144">Fig. 89</a>, 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 <i>C</i> 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<span class="pagenum"><a name="Page_414" id="Page_414">[414]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe19_625" id="i414">
-  <img class="w100" src="images/i_414.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 272.&mdash;<i>De Lisle's reflecting clinometer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_414a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>608.&mdash;<span class="large bold">Prismatic Clinometer.</span>&mdash;This instrument was
-originally devised by the author about 1860. The form of the
-instrument, Fig. 273, is that of a prismatic compass, <a href="#Art_155">art. 155</a>.
-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<span class="pagenum"><a name="Page_415" id="Page_415">[415]</a></span>
-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&mdash;weight, 8 oz.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i415">
-  <img class="w100" src="images/i_415.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 273.&mdash;<i>Stanley's prismatic clinometer.</i></p>
-    <p class="caption float-right">Fig. 274.&mdash;<i>Barker's clinometer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_415a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p><i>In Using this Form of Clinometer</i> 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.</p>
-<p>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.</p>
-<p>609.&mdash;<span class="large bold">Barker's Combined Prismatic Compass and
-Clinometer</span>,<a name="FNanchor_36_36" id="FNanchor_36_36"></a><a href="#Footnote_36_36" class="fnanchor">[36]</a> Fig. 274.&mdash;The prismatic compass of this
-arrangement is that of Hutchison's form, <a href="#Art_155">art. 155</a>. The clinometer
-is of the same kind as that just described, but this,
-instead of being a separate part of the instrument capable of
-<span class="pagenum"><a name="Page_416" id="Page_416">[416]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i416">
-  <img class="w100" src="images/i_416.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 275.&mdash;<i>Continental form of clinometer (Burnier).</i></p>
-    <p class="caption float-right">Fig. 276.&mdash;<i>Section of the same.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_416a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>610.&mdash;<span class="large bold">Continental Form of Clinometer.</span>&mdash;Hand
-clinometers on the Continent are generally made on Captain
-Burnier's plan, Fig. 275, which was explained for the prismatic
-compass, <a href="#Art_156">art. 156</a>. 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<span class="pagenum"><a name="Page_417" id="Page_417">[417]</a></span>
-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, <i>B</i>, when this is brought coincident
-with the sights <i>D′W′</i> as described for Burnier's compass.
-When the clinometer and compass are combined the vertical
-rims stand opposite to each other, <i>AC</i>. A lifter, Fig. 275, <i>L</i>, is
-provided to take the working parts out of bearing, and a stop
-<i>S′</i> to prevent oscillation. The illustrations show the combined
-instrument: <i>B</i> cylindrical lens reading the drums; <i>A</i>
-clinometer; <i>C</i> compass; <i>DD′</i> fore sight; <i>WW′</i> windows,
-both of which fold down on the top of the instrument.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe32" id="i417">
-  <img class="w100" src="images/i_417.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 277.&mdash;<i>Major Watkins clinometer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_417a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>611.&mdash;<span class="large bold">Major Watkins' Clinometer.</span><a name="FNanchor_37_37" id="FNanchor_37_37"></a><a href="#Footnote_37_37" class="fnanchor">[37]</a>&mdash;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 <i>R</i>, which reads to a line on a slip of
-ivory placed just beside the eye-hole <i>E</i> 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
-<span class="pagenum"><a name="Page_418" id="Page_418">[418]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i418">
-  <img class="w100" src="images/i_418.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 278.&mdash;<i>Compass with clinometer sight.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_418a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>612.&mdash;<span class="large bold">Clinometer Sights.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i419a">
-  <img class="w100" src="images/i_419a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 279.&mdash;<i>Rule form clinometer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_419aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>613.&mdash;<span class="large bold">Rule Form Clinometer.</span>&mdash;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<span class="pagenum"><a name="Page_419" id="Page_419">[419]</a></span>
-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<span class="pagenum"><a name="Page_420" id="Page_420">[420]</a></span>
-shown at the ends of the upper part of the instrument. Its
-size is 6&frac34; by 1&frac34; by &frac12; inches; weight 9 oz. There are several
-varieties of this instrument.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i419b">
-  <img class="w100" src="images/i_419b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 280.&mdash;<i>Road tracer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_419ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>614.&mdash;<span class="large bold">The Road Tracer</span> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe18_1875" id="i420">
-  <img class="w100" src="images/i_420.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 281.&mdash;<i>Bellamy's road tracer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_420a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>This instrument has been improved by Mr. C. V. Bellamy,
-M.I.C.E., M.I.M.E., F.G.S., &amp;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.</p>
-<p>The chief feature of this pattern lies in the adoption of
-the arc of a circle instead of a straight scale, and a pendulum<span class="pagenum"><a name="Page_421" id="Page_421">[421]</a></span>
-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.</p>
-<p>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.</p>
-<p>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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe21_25" id="i421">
-  <img class="w100" src="images/i_421.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 282.&mdash;<i>Bellamy's improved road tracer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_421a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_422" id="Page_422">[422]</a></span></p>
-<h2>CHAPTER XIV.</h2>
-</div>
-<p class="ch">INSTRUMENTS OF REFLECTION&mdash;OCTANT OR QUADRANT&mdash;REFLECTING
-CIRCLE&mdash;SEXTANT&mdash;PRINCIPLE&mdash;PARALLAX&mdash;CONSTRUCTION&mdash;EXAMINATION&mdash;ADJUSTMENT&mdash;ARTIFICIAL
-HORIZON&mdash;SOUNDING SEXTANT&mdash;BOX SEXTANT&mdash;SUPPLEMENTARY
-ARC&mdash;IMPROVEMENTS UPON THIS&mdash;OPTICAL
-SQUARE&mdash;OPTICAL CROSS&mdash;APOMECOMETER.</p>
-<p>615.&mdash;<span class="large bold">The Octant or Quadrant</span> measures angles
-within 90° by an arc of 45°. This instrument is generally
-termed an <i>octant</i> 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,<a name="FNanchor_38_38" id="FNanchor_38_38"></a><a href="#Footnote_38_38" class="fnanchor">[38]</a> and also
-by Newton.<a name="FNanchor_39_39" id="FNanchor_39_39"></a><a href="#Footnote_39_39" class="fnanchor">[39]</a> 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.</p>
-<p>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
-<span class="pagenum"><a name="Page_423" id="Page_423">[423]</a></span>
-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:&mdash;</p>
-<p><i>That the angle between two reflections in the same plane is
-equal to twice the inclination of the reflecting surfaces to each
-other.</i></p>
-<p>616.&mdash;<span class="large bold">Hadley's Quadrant.</span>&mdash;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.<a name="FNanchor_40_40" id="FNanchor_40_40"></a><a href="#Footnote_40_40" class="fnanchor">[40]</a> It was tried experimentally by the Astronomer
-Royal, August, 1732, in a yacht excursion, when readings
-were taken satisfactorily within a minute of arc.<a name="FNanchor_41_41" id="FNanchor_41_41"></a><a href="#Footnote_41_41" class="fnanchor">[41]</a> It afterwards
-came into general use.</p>
-<p>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
-<span class="pagenum"><a name="Page_424" id="Page_424">[424]</a></span>
-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 <i>back sight</i> to 220°. The means he suggested, which
-were commonly carried out in instruments of the period,
-were found to be too complicated for practice.<a name="FNanchor_42_42" id="FNanchor_42_42"></a><a href="#Footnote_42_42" class="fnanchor">[42]</a> 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,<a name="FNanchor_43_43" id="FNanchor_43_43"></a><a href="#Footnote_43_43" class="fnanchor">[43]</a> became the
-modern sextant.</p>
-<p>617.&mdash;<span class="large bold">Reflecting Circle.</span>&mdash;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. <i>Reflecting circles</i>, 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.<a name="FNanchor_44_44" id="FNanchor_44_44"></a><a href="#Footnote_44_44" class="fnanchor">[44]</a> We have also
-meritorious reflecting circles by Pistor and Martins, and by
-Amici.<a name="FNanchor_45_45" id="FNanchor_45_45"></a><a href="#Footnote_45_45" class="fnanchor">[45]</a> 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
-<span class="pagenum"><a name="Page_425" id="Page_425">[425]</a></span>
-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.</p>
-<p>618.&mdash;<span class="large bold">The Sextant</span>, 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&mdash;it may be used with or without a tripod or
-stand&mdash;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 <i>sounding
-sextant</i> and the <i>box sextant</i>. 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.</p>
-<p>619.&mdash;<i>Optical Arrangements of the Sextant.</i>&mdash;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<span class="pagenum"><a name="Page_426" id="Page_426">[426]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i426">
-  <img class="w100" src="images/i_426.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 283.&mdash;<i>Reflection in direct line from two plain mirrors.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_426a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>620.&mdash;<i>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.</i></p>
-<p>Let <i>MM′</i>, Fig. 283, be two mirrors placed with their
-faces opposite and parallel to each other. Let the incident
-ray <i>IM</i> fall on the mirror <i>M</i> whose normal is <i>a</i>. 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 <i>M′</i>.
-Let the normal of <i>M′</i> be <i>a′</i>. Then again, the incident line
-<i>MM′</i> will be reflected at equal angles to the normal to <i>D′</i>,
-that is, as shown by the diagram, it will continue parallel with
-the incident ray and in such a position that an object at <i>P</i>
-would appear to the eye, placed at <i>D′</i>, as though it were at
-<i>P′</i> in the direct line of sight.</p>
-<p id="Art_621">621.&mdash;<i>Parallax.</i>&mdash;It will be seen by the figure that the
-point <i>P</i> does not appear to the eye at <i>D′</i> in its true position
-but at <i>P′</i> therefore with the mirrors <i>MM′</i> quite parallel, the
-points <i>P</i> and <i>P′</i> 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<span class="pagenum"><a name="Page_427" id="Page_427">[427]</a></span>
-the points <i>P</i> and <i>P′</i> really subtend a small angle if direct
-lines be drawn from them to <i>D′</i>. 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 <i>error
-of parallax</i>. 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.</p>
-<p>622.&mdash;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.</p>
-<p>623.&mdash;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 <i>M′</i> so that the planes <i>M</i> and
-<i>M′</i> continued to subtend an angle to each other, then the
-normal of <i>M′</i> must also be changed in direction equal to
-this; but the ray <i>MM′</i> remaining constant, as there is no
-movement of <i>M</i>, this ray will therefore be displaced in its
-reflection from <i>M′</i> an amount equal to the angle of incidence
-on <i>M′</i> from its normal, plus the angle of reflection from the<span class="pagenum"><a name="Page_428" id="Page_428">[428]</a></span>
-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.&mdash;</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe34_875" id="i428">
-  <img class="w100" src="images/i_428.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 284.&mdash;<i>Principles of reflection of the sextant.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_428a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>624.&mdash;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 <i>SR</i> directed
-to a plane mirror <i>R</i> is reflected therefrom to a plane mirror
-<i>R′</i>, following a plane of reflection perpendicular to the
-intersection of the two mirrors. The direction <i>R′T</i> of the
-ray reflected by the second mirror falls into the same plane of
-reflection, and makes with the direction <i>SA</i> of the incident
-ray an angle double that which is comprised between the
-two mirrors.</p>
-<p>The two planes of reflection <i>SAB</i> and <i>ABT</i> unite in<span class="pagenum"><a name="Page_429" id="Page_429">[429]</a></span>
-one because they both contain the line <i>AB</i> and the normal
-<i>BP</i> to the mirror <i>R′</i>.</p>
-<p>In prolonging the normals of the mirrors to their point of
-intersection <i>P</i> we find that&mdash;</p>
-<p class="center"><i>BTS</i> = <i>BAS</i> - <i>ABT</i>;</p>
-<p class="noindent left">but as <span style="margin: 0 20%;">&frac12; <i>BAS</i> - &frac12; <i>ABT</i> = <i>BPA</i> = <i>BDA</i>,</span></p>
-<p class="noindent left">therefore <span style="margin: 0 30%;"><i>BTS</i> = 2 <i>BDA</i>.</span></p>
-<p>625.&mdash;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 <i>ET</i>, with its objective to the mirror <i>R′</i>,
-we see in the centre of the field of view the image of the
-object <i>S</i> reflected consecutively by the mirrors <i>R</i> and <i>R′</i>.
-We also see in the telescope whether the mirror <i>R′</i> 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 <i>E</i> situated in the prolongation of the line <i>TB</i>, also the
-image of <i>E</i> which is necessarily coincident with that of <i>S</i>,
-because the rays by which each image is formed enter the
-telescope in the same direction <i>BT</i>. Therefore when the
-images of the two objects <i>E</i> and <i>S</i> 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 <i>T</i> from
-the same objects, and when one is known the other is
-easily deduced.</p>
-<p>626.&mdash;<span class="large bold">Nautical Sextant.</span>&mdash;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 <i>AA″</i> including within its extreme radii
-about 155°.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe33_125" id="i430">
-  <img class="w100" src="images/i_430.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 285.&mdash;<i>Nautical or astronomical sextant.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_430a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>627.&mdash;<i>The Limb G</i>, which is made only about 1/12 inch in
-thickness, has generally a face of about &frac34; inch in width, which
-is inlaid with silver or platinum, as <a href="#i186a">Fig. 127</a>, p. 186, to take
-the graduation to about 140°. The limb is stiffened by a
-deep, thin rib about &frac12; inch wide, supported by a corner<span class="pagenum"><a name="Page_430" id="Page_430">[430]</a></span>
-hollow. The exterior radial arms and interspace framing, Fig.
-285 <i>MM</i>, 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 <i>L</i>, made
-generally of ebony, is supported on two standards or <i>brace-pieces</i>
-<i>N</i>, 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 <i>Q</i>, to support it conveniently
-on a table to take the reading of an observation just
-made.</p>
-<p>628.&mdash;At the centre of the arc a female axis of about
-1&frac12; inches in depth <i>E</i> 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 <i>M</i>.<span class="pagenum"><a name="Page_431" id="Page_431">[431]</a></span>
-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 &frac34; inch in width.
-This is stiffened by a light rib on its upper side.</p>
-<p>629.&mdash;<i>The Vernier V</i> 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, <a href="#Art_318">art. 318</a>. The vernier falls upon
-the arc on the plan shown <a href="#i186a">Fig. 127</a>, p. 186. It is clamped
-near to position by the milled-headed screw <i>H</i>, and is adjusted
-by the tangent <i>I</i>. A magnifier <i>J</i> is placed on a jointed sling-piece
-<i>K</i> 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.</p>
-<p>630.&mdash;Over the axis of the vernier arm a large, oblong
-mirror, termed the <i>index glass</i>, <i>A</i>, is fixed with its face in a
-plane cutting the centre of the axis. <i>The index glass</i> 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 <i>horizon glass B</i>.</p>
-<p>631.&mdash;<i>The Horizon Glass B</i> 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.</p>
-<p>632.&mdash;<i>The Telescope</i> screws into a ring fitted at <i>R</i>, which
-stands upon a bar erect from near the edge of the frame. The<span class="pagenum"><a name="Page_432" id="Page_432">[432]</a></span>
-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.</p>
-<p>633.&mdash;<i>Four Circular Shades</i>, carried in square frames
-fitted with dark bluish-grey glasses, are jointed to the frame at
-<i>C</i>. 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 <i>D</i>, 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.</p>
-<p>634.&mdash;<i>The Telescopes</i> used as a part of the sextant are
-generally two in number. One for <i>direct vision</i> 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,
-<a href="#i040">Fig. 14</a>. 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.</p>
-<p><span class="pagenum"><a name="Page_433" id="Page_433">[433]</a></span></p>
-<p>635.&mdash;<i>The Case</i> 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.</p>
-<p>636.&mdash;<i>Manufacture and Examination of the Nautical
-Sextant.</i>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i434">
-  <img class="w100" src="images/i_434.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 286.&mdash;<i>Section of axis and index glass of sextant.</i></p>
-    <p class="caption float-right">Fig. 287.&mdash;<i>Section of limb and clamp and tangent.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_434a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>637.&mdash;<i>Axis.</i>&mdash;This is the most important part of the<span class="pagenum"><a name="Page_434" id="Page_434">[434]</a></span>
-instrument, and requires the greatest care in construction.
-Fig. 286 represents this to a scale half size. <i>a</i> 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 <i>S</i> 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 <i>B</i> attached upon an angular or tight conical
-fitting by the screw <i>D</i>, which prevents the axis rising out of
-its socket. The axis is covered by a cap <i>L</i> which protects it
-from injury, and this at the same time forms a leg to the
-instrument as before mentioned. The index glass <i>I</i> is
-mounted in a tray <i>T</i> 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
-<i>G</i> by a spring <i>C</i> in front, acting <i>contra</i> to a screw at the
-back <i>E</i>, which adjusts only a small distance to bring the index
-glass to perpendicularity. The flange-piece <i>F</i> is adjusted in<span class="pagenum"><a name="Page_435" id="Page_435">[435]</a></span>
-the manufacture so as to leave very small separate adjusting
-to the index glass necessary.</p>
-<p>638.&mdash;<i>Section of the Limb and Clamp and Tangent.</i>&mdash;The
-general arrangement is shown in Fig. 287. <i>M</i> arms of
-the frame; <i>J</i> section of the limb; <i>C</i> clamp attached to the
-tangent <i>N</i> for clamp and tangent motion, described <a href="#Art_346">art. 346</a>;
-<i>O</i> milled head to clamp; <i>N</i> milled head to tangent. The
-vernier is shown at <i>V</i>, reading through an opening on
-the face of the index arm <i>P</i>. The rib to stiffen this arm is
-shown at <i>R</i>.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i435">
-  <img class="w100" src="images/i_435.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 288.&mdash;<i>Vertical section of horizon glass.</i></p>
-    <p class="caption float-right">Fig. 289.&mdash;<i>Plan of section A to B.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_435a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>639.&mdash;<i>The Adjustment Arrangement of the Horizon
-Glass.</i>&mdash;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 <i>FF</i> is made
-in one casting, which has its base collar firmly fixed to the
-frame of the sextant. Fig. 289 is a cross section <i>A</i> to <i>B</i>.
-<i>H</i> the horizon glass is held upon its face by three points, one
-of which is shown at <i>L</i>, which is placed in the centre of the<span class="pagenum"><a name="Page_436" id="Page_436">[436]</a></span>
-top. The lower front points are the exterior corners of a
-plate which is cut away between. This plate is held by the
-screw <i>G</i>. The screw <i>G</i> 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 <i>J</i> and <i>Q</i>. The screw <i>J</i> resists this pressure lightly
-and permits adjustment of the horizon glass <i>H</i> 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 <i>J</i>.
-The perpendicular position of the horizon glass, <i>H</i>, is
-secured by slight adjustment of the capstan head <i>K</i>, which
-moves against a spring <i>L</i> in the vertical centre of the top of
-<i>H</i>. This piece, with screw and spring, is attached to the
-horizon glass frame <i>FF′</i> 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 <i>H</i> with a
-razor.</p>
-<p>640.&mdash;<i>Testing the Parallelism of the Surfaces of the
-Glasses.</i>&mdash;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.</p>
-<p><span class="pagenum"><a name="Page_437" id="Page_437">[437]</a></span></p>
-<p>641.&mdash;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.</p>
-<p>642.&mdash;<i>The Quality of the Surfaces of the Glasses</i> 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.</p>
-<p>643.&mdash;<i>To Silver the Index or Horizon Glass with
-Mercury.</i>&mdash;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&mdash;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<span class="pagenum"><a name="Page_438" id="Page_438">[438]</a></span>
-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.</p>
-<p>644.&mdash;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.</p>
-<p><span class="pagenum"><a name="Page_439" id="Page_439">[439]</a></span></p>
-<p>645.&mdash;<i>Adjustment of the Index Glass.</i>&mdash;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, <a href="#i434">Fig. 286</a> <i>E</i>, very gently.</p>
-<p>646.&mdash;<i>Adjustment of the Horizon Glass to Perpendicularity.</i>&mdash;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.</p>
-<p>647.&mdash;<i>Adjustment for Index.</i>&mdash;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, <a href="#i435">Fig.
-288</a>, at <i>G</i>.</p>
-<p><span class="pagenum"><a name="Page_440" id="Page_440">[440]</a></span></p>
-<p id="Art_648">648.&mdash;<i>Adjustment of the Horizon Glass by the Sun.</i>&mdash;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 <a href="#i435">Fig. 288</a> <i>K</i>. If notches
-appear at the sides of the limb when it is held horizontally
-there is an index error, which may be adjusted at <i>G</i> if it be
-small.</p>
-<p>649.&mdash;<i>Index Error after Adjustment Allowance.</i>&mdash;The
-limb of the sextant is graduated 5° beyond the zero position
-when the glasses are parallel to each other. This is called
-the <i>arc of excess</i>. 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<span class="pagenum"><a name="Page_441" id="Page_441">[441]</a></span>
-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.</p>
-<p>650.&mdash;<i>Adjustment of the Telescope to Set its Axis Parallel
-to the Plane of the Sextant.</i>&mdash;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,&mdash;as the sun and
-moon, or the moon and a bright star,&mdash;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<span class="pagenum"><a name="Page_442" id="Page_442">[442]</a></span>
-little to make the reflected and direct images appear equally
-clear.</p>
-<p>651.&mdash;<i>Final Examination of the Sextant.</i>&mdash;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
-<i>Nautical Almanac</i>, 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, <a href="#Art_229">art. 229</a>. 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.</p>
-<p>652.&mdash;<i>To Use the Sextant</i> 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<span class="pagenum"><a name="Page_443" id="Page_443">[443]</a></span>
-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 <i>Spherical and Practical
-Astronomy</i>.</p>
-<p>653.&mdash;<span class="large bold">Artificial Horizon.</span>&mdash;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,<a name="FNanchor_46_46" id="FNanchor_46_46"></a><a href="#Footnote_46_46" class="fnanchor">[46]</a> 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 <i>artificial horizon</i><a name="FNanchor_47_47" id="FNanchor_47_47"></a><a href="#Footnote_47_47" class="fnanchor">[47]</a> 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
-<span class="pagenum"><a name="Page_444" id="Page_444">[444]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i444">
-  <img class="w100" src="images/i_444.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 290.&mdash;<i>Diagram of artificial horizon.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_444a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>654.&mdash;<i>Theory of the Artificial Horizon.</i>&mdash;A ray <i>M′</i> Fig.
-290, from a luminous body, at infinite distance will have its
-image reflected from a level reflecting surface <i>SS′</i> at an angle
-equal and opposite to the incident ray, the angles <i>M′AS</i>
-and <i>EAS′</i> being equal. Let <i>E</i> be the place of the eye or
-the sextant: this will receive a ray from the same distant body
-in direction <i>ME</i>, which is sensibly parallel with <i>M′A</i>. The
-angle <i>MEA</i> being double the angle of incidence <i>M′AS</i>,
-the half of this angle will therefore produce the horizontal
-line <i>EH</i> at the height of the observer's eye if the plane of
-reflection <i>SS′</i> be level. Therefore if we take half this angle
-<i>MEA</i> 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
-<i>M′AS</i> be 30°, the angle <i>AEM</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i445a">
-  <img class="w100" src="images/i_445a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 291.&mdash;<i>Artificial horizon of black glass.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_445aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>655.&mdash;<span class="large bold">Artificial Horizon in Black Glass.</span>&mdash;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<span class="pagenum"><a name="Page_445" id="Page_445">[445]</a></span>
-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 <i>AA′A″</i>. It is
-adjusted to level by a loose level tube ground on its under
-face <i>P</i>. The level tube shown in detail <a href="#i094">Fig. 51</a>, p. 94, is
-placed on the surface lineally with the two screws, Fig. 291
-<i>AA′</i>, and afterwards at a right angle to its first position with one
-end of the tube towards <i>A″</i>. 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<span class="pagenum"><a name="Page_446" id="Page_446">[446]</a></span>
-presents a more perfectly level plane. The circular artificial
-horizons are commonly made 3&frac14; inches diameter; weight,
-&frac34; lb.; the oblong, Fig. 291, 4 inches by 3 inches; weight 2 lbs.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i445b">
-  <img class="w100" src="images/i_445b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 292.&mdash;<i>Artificial horizon, mercury.</i></p>
-    <p class="caption float-right">Fig. 293.&mdash;<i>Mercury bottle to the same.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_445ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>656.&mdash;<span class="large bold">Artificial Horizon of Mercury</span>, Fig. 292. This
-instrument consists of an oblong tray of about 6 inches by 3
-inches by &frac34; 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 7&frac12; inches by 6 inches by
-5 inches; weight, with 1 lb. of mercury, about 4&frac34; lbs.</p>
-<p>657.&mdash;<i>The Bottle</i>, 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i447">
-  <img class="w100" src="images/i_447.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 294.&mdash;<i>Captain George's artificial horizon.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_447a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>658.&mdash;<span class="large bold">Captain George's Artificial Horizon</span>,<a name="FNanchor_48_48" id="FNanchor_48_48"></a><a href="#Footnote_48_48" class="fnanchor">[48]</a> Fig.
-294. This is a great improvement on that last described.
-<span class="pagenum"><a name="Page_447" id="Page_447">[447]</a></span>
-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 <i>E</i> and <i>M</i> are
-connected together by a tube through a stem-piece in which
-there is a strong iron cock at <i>a</i>. 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 <i>B</i>. The chamber
-<i>M</i> 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 <i>C</i> forms an air plug. The cock moves
-very stiffly by the leverage given by a tommy-pin, shown <i>a′</i>,
-which is inserted in the hole at <i>a</i>. The chamber <i>E</i> is slightly
-elevated to cause the mercury to flow from it to <i>M</i>, the cock
-being turned on at the same time and the air screw <i>C</i> released
-a little. By the same arrangement, <i>M</i> being raised, the
-mercury flows back into the bottle for storage.</p>
-<p>659.&mdash;<i>For Using this Artificial Horizon</i>, when the mercury
-is poured out in the tray <i>M</i>, it is levelled by the three
-screws <i>AA′A″</i> 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 <i>M</i> 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<span class="pagenum"><a name="Page_448" id="Page_448">[448]</a></span>
-soft leather bag which fits in the tray <i>M</i>. This artificial
-horizon is generally carried in a solid leather case with sling
-to go over the shoulder. Its weight complete is about 4&frac12; lbs.;
-size, 9&frac12; inches by 4 inches by 1&frac12; inches. The surface of
-mercury is a circle of 3 inches diameter.</p>
-<p>660.&mdash;<span class="large bold">Improved Captain George's Artificial
-Horizon.</span>&mdash;Mr. S. A. Ionides, C.E., has devised an improved
-form of the foregoing instrument shown at Fig. 295.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i448">
-  <img class="w100" src="images/i_448.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 295.&mdash;<i>Ionides's artificial horizon.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_448a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-<p>661.&mdash;<i>In Using the Artificial Horizon with the Sextant</i>
-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<span class="pagenum"><a name="Page_449" id="Page_449">[449]</a></span>
-is used as an approximate correction. For solar and
-stellar refraction, works on astronomy should be consulted.</p>
-<p>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.</p>
-<p>662.&mdash;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.<a name="FNanchor_49_49" id="FNanchor_49_49"></a><a href="#Footnote_49_49" class="fnanchor">[49]</a> The
-matter is mentioned here as the recurrence of the idea
-appears to be frequent.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i450">
-  <img class="w100" src="images/i_450.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 296.&mdash;<i>Sounding sextant.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_450a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>663.&mdash;<span class="large bold">The Sounding Sextant.</span>&mdash;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
-<span class="pagenum"><a name="Page_450" id="Page_450">[450]</a></span>
-required as may afterwards be plotted on a chart. This
-instrument is shown in perspective, Fig. 296. The index
-glass is large&mdash;about 2&frac14; inches by 1&frac14; 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 1&frac12; inches
-in width and &frac34; 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<span class="pagenum"><a name="Page_451" id="Page_451">[451]</a></span>
-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 4&frac12; 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 2&frac34; 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.</p>
-<p id="Art_664">664.&mdash;<span class="large bold">Box Sextant.</span>&mdash;This very neat and portable
-instrument was invented by the late William Jones.<a name="FNanchor_50_50" id="FNanchor_50_50"></a><a href="#Footnote_50_50" class="fnanchor">[50]</a> 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&mdash;as a surveying
-instrument constantly in hand&mdash;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
-<span class="pagenum"><a name="Page_452" id="Page_452">[452]</a></span>
-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 <i>cross
-thread</i>. The general description of the outer parts is as
-follows:&mdash;</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i452">
-  <img class="w100" src="images/i_452.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 297.&mdash;<i>Perspective view of the box sextant ready for use.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_452a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>665.&mdash;<i>C</i> 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 1&frac12; inches. <i>B</i> box containing
-the optical and moving parts of the sextant. <i>A</i> 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<span class="pagenum"><a name="Page_453" id="Page_453">[453]</a></span>
-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. <i>O</i> 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. <i>S</i> two nibs, part of two levers for putting the
-shades in or out of action.</p>
-<p>666.&mdash;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.</p>
-<p>667.&mdash;<i>The Key K</i> 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 <i>b</i>, 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.</p>
-<p>668.&mdash;<i>The Telescope</i> is achromatic, with draw tube for
-focussing. It magnifies about 2&frac12; diameters. It has a
-concave eye-glass, and therefore gives an erect image, <a href="#i040">Fig. 14</a>.
-A sun-glass <i>E</i> 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 <i>T′</i> and two steady pins.
-The crank-piece screws in reverse position upon the telescope
-for portability before putting it by in its case.</p>
-<p><span class="pagenum"><a name="Page_454" id="Page_454">[454]</a></span></p>
-<p>669.&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i454">
-  <img class="w100" src="images/i_454.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 298.&mdash;<i>Box sextant under the face.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_454a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>670.&mdash;<i>The Interior or Optical and Mechanical part of
-the Sextant</i> is shown Fig. 298. <i>I</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 <i>O</i> of
-Fig. 297 on the face of the sextant. Fig. 298: horizon glass,
-cut by <i>ED</i>, adjusts to the vertical by screws <i>CC′</i>, 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 <i>P</i>. This adjustment acts by screwing against
-a helical spring, shown at <i>Q</i>. The reflected rays enter by a
-wide window in the side of the box, Fig. 298 <i>d</i>, the direct
-rays by a small window <i>f</i>. The path of a ray is shown by
-fine lines from <i>R</i> to <i>E</i>, for the positions in which the index and
-horizon glasses are placed. The pin-hole opposite which the
-eye is placed is shown white. <i>S</i> shades with their axis are<span class="pagenum"><a name="Page_455" id="Page_455">[455]</a></span>
-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 <i>S</i>.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i455">
-  <img class="w100" src="images/i_455.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 299.&mdash;<i>Plan of horizon glass.</i></p>
-    <p class="caption float-right">Fig. 300.&mdash;<i>Section of the same.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_455a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>671.&mdash;<i>The Construction of the Box Sextant</i> 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 <i>F</i> 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 <i>cc′</i> which protrude
-in square heads to the face of the instrument. The
-horizon glass, <i>H</i>, 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 <i>a</i>. 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<span class="pagenum"><a name="Page_456" id="Page_456">[456]</a></span>
-<a href="#i186a">Fig. 127</a>. The vernier is soldered closely on the index and
-should read down to a fine clean edge.</p>
-<p>672.&mdash;<i>Examination of the Box Sextant.</i>&mdash;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.</p>
-<p>673.&mdash;<i>Adjustment.</i>&mdash;The box sextant is best adjusted by
-the sun upon the plan described <a href="#Art_648">art. 648</a>. The adjusting
-screws, as already stated, are moved by the key, which unscrews
-from the face of the sextant, <a href="#i452">Fig. 297</a> <i>K</i>. 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 <i>b</i>; adjustment to zero of arc by the
-screw at the side <i>a</i>. 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, <a href="#Art_621">art. 621</a>.</p>
-<p>674.&mdash;<i>Use of the Box Sextant.</i>&mdash;The sextant has its<span class="pagenum"><a name="Page_457" id="Page_457">[457]</a></span>
-under shutter opened by pressing the stud attached over in its
-slot. The nibs of the shade levers, <a href="#i452">Fig. 297</a> <i>S</i>, 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.</p>
-<p>675.&mdash;It must always be remembered that the sextant
-takes angular positions <i>actually</i>, whereas plans are made in
-<i>azimuthal</i> 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<span class="pagenum"><a name="Page_458" id="Page_458">[458]</a></span>
-equal heights. For sketch plans of very hilly or mountainous
-districts the prismatic compass, <a href="#Art_148">art. 148</a>, is better, as this
-gives, although with less precision than the sextant, its angles
-in azimuth.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i458">
-  <img class="w100" src="images/i_458.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 301.&mdash;<i>Interior construction of box sextant with supplementary arc.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_458a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>676.&mdash;<span class="large bold">Box Sextant with Supplementary Arc.</span>&mdash;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°&mdash;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 <i>sole plate</i> exactly under the position
-of the index glass. This mirror is termed the <i>supplementary
-index glass</i>. 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: <i>MM′</i> 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<span class="pagenum"><a name="Page_459" id="Page_459">[459]</a></span>
-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 <i>reverse direction</i>, 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 <i>two reflections</i>, 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i459">
-  <img class="w100" src="images/i_459.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Figs. 302, 303.&mdash;<i>Diagram of supplementary arc sextant.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_459a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>677.&mdash;<i>Theory of Supplementary Angles to the Sextant.</i>&mdash;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 <i>II′</i> be the surface of a mirror (<i>index glass</i>) which is
-movable to any angle in relation to the face of the mirror <i>SS′</i>
-(<i>supplementary index</i>). 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 <i>FC</i> and <i>BC</i> form a right line (180°); <i>F</i> fore
-sight and <i>B</i> back sight. An object at <i>F</i> would be reflected
-from the mirror <i>II′</i> to the eye at <i>E</i>, the angles <i>FCI</i> and<span class="pagenum"><a name="Page_460" id="Page_460">[460]</a></span>
-<i>ECI′</i> being equal. Another object at <i>B</i> reflected from the
-face of the mirror <i>SS′</i> would also reach the eye at <i>E</i>,
-the angles <i>BCS′</i> and <i>ECS′</i> being equal. And as the
-angles <i>FCI</i> and <i>BCI′</i> are equal in crossing a right line,
-the line <i>FCB</i> must be also a right line (180°) which is
-indicated by the angle of coincidence of the two reflections to
-<i>E</i>. The positions of the reflections are shown as angular
-measurements upon the graduated arc.</p>
-<p>678.&mdash;In Fig. 303 let <i>SS′</i> remain as before, angle <i>BCE</i>
-will remain as shown in both figures. Move the index glass
-from the position <i>II′</i> of Fig. 302 to the position <i>JJ′</i> of
-Fig. 303, so that after this movement the eye at <i>E</i> would
-receive the image of an object at a new position <i>F′</i> as reflected
-from the mirror <i>JJ′</i>, <i>F′CJ</i> and <i>ECJ′</i> being equal. In
-this process, as the reflector <i>JJ′</i> in the angle <i>ICJ</i> would
-have moved half the angle <i>JCF</i>, the record of this movement
-upon the index, which moves with <i>JJ′</i>, 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 <i>pro ratâ</i>. 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 <i>EC</i>; consequently this increase is read
-backward on the sextant, that is, right to left, and is indicated
-by the outer line of numerals.</p>
-<p>679.&mdash;<i>Manufacture.</i>&mdash;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
-&frac14; 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<span class="pagenum"><a name="Page_461" id="Page_461">[461]</a></span>
-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.</p>
-<p>680.&mdash;<i>Examination and Adjustment.</i>&mdash;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.</p>
-<p>681.&mdash;<i>In using this instrument</i> 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 <i>reverse way to increase the angle</i>, 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.</p>
-<p>682.&mdash;<span class="large bold">Box Sextant, with Continuous Arc to 240°.</span>&mdash;This
-instrument is an improvement by the author upon
-one originally designed by Mr. W. Franklin. The reading<span class="pagenum"><a name="Page_462" id="Page_462">[462]</a></span>
-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°.</p>
-<p>683.&mdash;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<span class="pagenum"><a name="Page_463" id="Page_463">[463]</a></span>
-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, <i>E</i> place of the eye with direct ray through
-the horizon glass <i>H</i> to <i>O</i>. The index glass <i>I</i> is that of the
-ordinary sextant, shown by dotted lines, throwing the image of
-an object at <i>P</i> to the upper horizon glass and thence to the
-eye at <i>E</i>. <i>B</i> is the fixed supplementary glass with its surface
-at 60° to the lower horizon glass at <i>A</i>. The sight lines from
-an object at <i>Q</i> are reflected from <i>B</i> to <i>A</i> and thence to <i>E</i>.
-A spring arrangement shown <i>SS</i> with a milled head underneath
-permits the lower glass <i>A</i> to be drawn down to convert
-the instrument into a simple box sextant.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i463">
-  <img class="w100" src="images/i_463.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 304.&mdash;<i>Stanley's continuous arc box sextant.</i></p>
-    <p class="caption float-right">Fig. 305.&mdash;<i>Section of supplementary horizon arrangement.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_463a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>684.&mdash;<i>Details of Spring Arrangement</i> to the supplementary
-horizon glass are shown in Fig. 305 full size in
-section. The springs <i>SS</i> in Fig. 304 and <i>S</i> Fig. 305 form
-two points of support to the horizon glass, the silvered face
-of which is shown at <i>A</i>. A third point of contact is near <i>D</i>,
-placed in the centre of the end of the supporting plate for the
-horizon glass. When the screw <i>R</i>, which is placed in a loose
-fitting, is released, the springs bring the supporting plate tight
-up to <i>D</i> and hold the horizon glass firmly in an elevated<span class="pagenum"><a name="Page_464" id="Page_464">[464]</a></span>
-position. When the screw <i>R</i> is tightened it brings this glass
-down. The horizon glass is adjusted over a rocking centre by
-the screws <i>CC′</i>. A screw and collar b prevent the loss of the
-screw <i>R</i>. 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i464">
-  <img class="w100" src="images/i_464.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 306.&mdash;<i>Stanley's portable surveying sextant.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_464a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>685.&mdash;<span class="large bold">Open Surveying Sextants</span>, 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<span class="pagenum"><a name="Page_465" id="Page_465">[465]</a></span>
-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.</p>
-<p>A handy form of portable surveying sextant has been
-devised by the author and is shown at Fig. 306.</p>
-<p>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 × 2&frac12; inches.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i465">
-  <img class="w100" src="images/i_465.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 307.&mdash;<i>Optical square.</i></p>
-    <p class="caption float-right">Fig. 308.&mdash;<i>Double optical square.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_465a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>686.&mdash;<span class="large bold">Optical Square.</span>&mdash;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<span class="pagenum"><a name="Page_466" id="Page_466">[466]</a></span>
-manipulation to place the adjustments to the larger glass, that
-is, the index glass. The horizon glass, Fig. 307, <i>h</i> is therefore
-fixed firmly, like the index glass of the box sextant, by two screws
-to the sole plate. The index glass <i>i</i> is held and adjusted in
-exactly the same manner as the horizon glass of the box
-sextant, as shown in detail, <a href="#i455">Figs. 299, 300</a>, 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 <i>Q</i> for horizon sight, <i>o</i> for
-index sight, and <i>e</i> for pin-hole or eye sight, are cut through
-the two tubes.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe20_4375" id="i466">
-  <img class="w100" src="images/i_466.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 309.&mdash;<i>Optical square.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_466.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>687.&mdash;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 <i>k</i>. The weight of the entire instrument
-is about 4 oz. if of ordinary make; but smaller ones are made
-in German-silver or silver, 1&frac14; 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.</p>
-<p><span class="pagenum"><a name="Page_467" id="Page_467">[467]</a></span></p>
-<p>688.&mdash;<i>Examination and Adjustment of the Optical
-Square.</i>&mdash;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° <i>picket</i>, 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 <i>k</i>, Fig. 307, and this
-observation repeated until the 90° is correct.</p>
-<p>689.&mdash;<i>In Using the Optical Square</i> 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 <i>h</i> 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.</p>
-<p>690.&mdash;<span class="large bold">Double Optical Square.</span>&mdash;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 <i>optical cross</i>. 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<span class="pagenum"><a name="Page_468" id="Page_468">[468]</a></span>
-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.</p>
-<p>691.&mdash;The arrangement of the optical part of the instrument
-is shown Fig. 308. The two index glasses <i>CD</i> are fixed
-at equal angles to the direct line of sight <i>EO</i>. The two
-horizon glasses <i>AB</i> 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 2&frac14; 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.</p>
-<p>692.&mdash;<i>Examination and Adjustment of the Double Optical
-Square.</i>&mdash;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<span class="pagenum"><a name="Page_469" id="Page_469">[469]</a></span>
-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.</p>
-<p id="Art_693">693.&mdash;<span class="large bold">Apomecometer.</span>&mdash;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.</p>
-<p>694.&mdash;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, <i>A</i> is the index
-glass, <i>B</i> the horizon glass, <i>E</i> 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 <i>E</i> to <i>H</i>. 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 1&frac14; inches diameter,
-3/8 inch in thickness, weight 2 oz. in German silver.</p>
-<p>695.&mdash;<i>The Use of the Apomecometer.</i>&mdash;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<span class="pagenum"><a name="Page_470" id="Page_470">[470]</a></span>
-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 <i>OH</i>, being equal to <i>FH</i>. 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 <i>ab</i> being = <i>ed</i>, as the base <i>ab</i> can easily be
-measured. An approximate may be found by dropping a
-small pebble at <i>a</i> and at <i>b</i> and then measuring the distance
-apart of these pebbles.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i470">
-  <img class="w100" src="images/i_470.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 310.&mdash;<i>Optical details of the apomecometer.</i></p>
-    <p class="caption float-right">Fig. 311.&mdash;<i>Scheme for measuring heights.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_470a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p><span class="pagenum"><a name="Page_471" id="Page_471">[471]</a></span></p>
-<p>696.&mdash;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, <i>b</i> being a buoy at sea, Fig. 312, walk from <i>e</i>, at
-which a walking-stick may be set up, towards an object <i>o</i>.
-At <i>E</i> the buoy and object <i>o</i> will appear to be coincident.
-Then drop a stone or make a mark directly under the
-instrument. Walk on till beyond <i>E′</i> and turn to face <i>e</i>. Now
-in returning, the buoy and the object e will appear coincident
-at <i>E′</i>. The distance <i>EE′</i> is double that of the intermediate
-<i>a</i> to <i>b</i>.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i471">
-  <img class="w100" src="images/i_471.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 312.&mdash;<i>Scheme for measuring distances.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_471a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_472" id="Page_472">[472]</a></span></p>
-<h2>CHAPTER XV.</h2>
-</div>
-<p class="ch">GRAPHIC SURVEYING INSTRUMENTS AND APPLIANCES CONNECTED
-THEREWITH&mdash;PLANE TABLES&mdash;ALIDADES&mdash;TELESCOPIC
-ARRANGEMENTS&mdash;SUBTENSE MEASUREMENTS&mdash;VARIOUS
-DEVICES FOR HOLDING THE PAPER&mdash;CONTINUOUS
-PAPERS&mdash;ADJUSTMENT OF TRIPOD HEADS&mdash;METHOD
-OF USING&mdash;EDGEWORTH'S STADIOMETER&mdash;SKETCHING
-PROTRACTOR&mdash;SKETCHING CASE&mdash;CAMERA
-LUCIDA, ETC.</p>
-<p>697.&mdash;<span class="large bold">Plane Tables.</span>&mdash;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<span class="pagenum"><a name="Page_473" id="Page_473">[473]</a></span>
-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.<a name="FNanchor_51_51" id="FNanchor_51_51"></a><a href="#Footnote_51_51" class="fnanchor">[51]</a></p>
-<p>698.&mdash;<i>The Plane Table</i> in its simplest form consists of a
-small drawing-board mounted upon a firm tripod stand, and is
-shown at Fig. 313.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i473">
-  <img class="w100" src="images/i_473.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 313.&mdash;<i>Simple plane table.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_473a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>A rule termed an <i>alidade</i>, 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 <i>fiducial</i> or
-ruling edge to give a magnetic north to south line, to which
-all other lines are assumed to take angular direction. A loose
-<span class="pagenum"><a name="Page_474" id="Page_474">[474]</a></span>
-spirit level is also provided, by means of which the board may
-be set level by shifting the legs of the tripod.</p>
-<p>699.&mdash;<span class="large bold">Plane Table with Telescope.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i474">
-  <img class="w100" src="images/i_474.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 314.&mdash;<i>Plane table.</i></p>
-    <p class="caption float-right">Fig. 315.&mdash;<i>Tripod stand.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_474a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>700.&mdash;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<span class="pagenum"><a name="Page_475" id="Page_475">[475]</a></span>
-rule that the edge <i>W</i> should always take a north to south
-direction. Three screws <i>sss</i> 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, <a href="#i477">Fig. 319</a>, is a convenient
-addition.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i475">
-  <img class="w100" src="images/i_475.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 316.&mdash;<i>Panel board of plane table.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_475a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>701.&mdash;<i>The Telescopic Arrangement</i> 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<span class="pagenum"><a name="Page_476" id="Page_476">[476]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i476a">
-  <img class="w100" src="images/i_476a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 317.&mdash;<i>Stanley's plane table.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_476aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i476b">
-  <img class="w100" src="images/i_476b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 318.&mdash;<i>Alidade to plane table.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_476ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>702.&mdash;<i>Lateral Adjustment to the Alidade.</i>&mdash;The author's<span class="pagenum"><a name="Page_477" id="Page_477">[477]</a></span>
-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 <i>A′</i> 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 <i>B</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe15_8125" id="i477">
-  <img class="w100" src="images/i_477.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 319.&mdash;<i>Subtense points.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_477a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>703.&mdash;<i>The Telescope Arranged for Subtense Measurements.</i>&mdash;Where
-a stadium, <a href="#Art_556">art. 556</a>, 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<span class="pagenum"><a name="Page_478" id="Page_478">[478]</a></span>
-upon the alidade in Fig. 317. This has a degree scale
-reading by vernier to about 3 minutes.</p>
-<p>704.&mdash;<i>Various Devices for Fixing the paper on the
-Surface of the Table</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i478">
-  <img class="w100" src="images/i_478.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 320.&mdash;<i>Plane table with rollers.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_478a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p><span class="pagenum"><a name="Page_479" id="Page_479">[479]</a></span></p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i479">
-  <img class="w100" src="images/i_479.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 321.&mdash;<i>Gurley's plane table adjustment.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_479a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>705.&mdash;<i>Adjustment of the Plane Table.</i>&mdash;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, <i>D</i> the table top; <i>A</i> a ball fitting turned inside and
-out, and attached firmly to the table top; <i>C</i> a socket fixed
-firmly in the head of the tripod; <i>B</i> a bolt with globular
-head fitting the interior of <i>A</i>, 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 <i>B</i> and <i>C</i> with
-moderate firmness when the table is being set to an angle.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i480a">
-  <img class="w100" src="images/i_480a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 322.&mdash;<i>Stanley's high-class plane table.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_480aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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<span class="pagenum"><a name="Page_480" id="Page_480">[480]</a></span>
-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<span class="pagenum"><a name="Page_481" id="Page_481">[481]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i480b">
-  <img class="w100" src="images/i_480b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 323.&mdash;<i>Stanley's high-class alidade with bubble on verniers.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_480ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>706.&mdash;<i>Method of Using the Plane Table.</i>&mdash;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 <i>abcdef</i>. 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<span class="pagenum"><a name="Page_482" id="Page_482">[482]</a></span>
-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 <i>abcde</i>, cutting the former
-lines as represented by dotted lines in the figure, and the
-intersections of these lines will give the true positions of
-<i>abcde</i>, 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i481">
-  <img class="w100" src="images/i_481.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 324.&mdash;<i>Diagram of plane table work.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_481a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>707.&mdash;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,
-<a href="#i478">Fig. 320</a>, 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.</p>
-<p>708.&mdash;<span class="large bold">Edgeworth's Stadiometer.</span><a name="FNanchor_52_52" id="FNanchor_52_52"></a><a href="#Footnote_52_52" class="fnanchor">[52]</a>&mdash;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 &frac14;°. The part representing the
-limb of a theodolite is carried out from its axis by two arms
-only: upon these the standards <i>RR</i> 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
-<span class="pagenum"><a name="Page_483" id="Page_483">[483]</a></span>
-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, <a href="#Art_558">art. 558</a>. 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.<a name="FNanchor_53_53" id="FNanchor_53_53"></a><a href="#Footnote_53_53" class="fnanchor">[53]</a></p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i483">
-  <img class="w100" src="images/i_483.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 325.&mdash;<i>Edgeworth's stadiometer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_483a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>709.&mdash;<i>To Use Edgeworth's Stadiometer.</i>&mdash;After it is set up,
-a circular disc of paper of about an inch less diameter than the
-<span class="pagenum"><a name="Page_484" id="Page_484">[484]</a></span>
-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, <a href="#Art_558">art. 558</a>. 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&mdash;</p>
-<p class="center">
-<i>stadium reading</i> + <i>constant</i> - <i>altitude correction</i>.
-</p>
-<p class="noindent">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.</p>
-<p>710.&mdash;<span class="large bold">The Sandhurst Protractor</span>, 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<span class="pagenum"><a name="Page_485" id="Page_485">[485]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe28_25" id="i485a">
-  <img class="w100" src="images/i_485a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 326.&mdash;<i>Sandhurst Sketching clinometer protractor.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_485aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i485b">
-  <img class="w100" src="images/i_485b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 327.&mdash;<i>Example of scale of shades for slopes.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_485ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>711.&mdash;<span class="large bold">Military Sketching Board.</span>&mdash;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,<span class="pagenum"><a name="Page_486" id="Page_486">[486]</a></span>
-and it will also be found of great use to surveyors, explorers,
-and other travellers.</p>
-<p>It consists of a mahogany board revolving on a circular
-metal plate attached to a handle held in the operator's left
-hand.</p>
-<p>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.</p>
-<p>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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i486a">
-  <img class="w100" src="images/i_486a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Top view.</p>
-    <p class="caption ebhide clear"><a href="images/i_486aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i486b">
-  <img class="w100" src="images/i_486b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Under view.</p>
-
-    <p class="caption ebhide clear"><a href="images/i_486ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-    <p class="caption">Fig. 328.</p>
-</div>
-
-<p>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.</p>
-<p><span class="pagenum"><a name="Page_487" id="Page_487">[487]</a></span></p>
-<p>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.</p>
-<p>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.</p>
-<p>712.&mdash;The method of using is simple and ensures a great
-degree of accuracy with a minimum amount of time and
-trouble:&mdash;</p>
-<p>(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<span class="pagenum"><a name="Page_488" id="Page_488">[488]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i488">
-  <img class="w100" src="images/i_488.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 329.&mdash;<i>Cavalry sketching case.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_488a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>713.&mdash;<span class="large bold">Cavalry Sketching Case.</span>&mdash;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 9&frac14; inches by 7&frac12; 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.</p>
-<p>714.&mdash;<span class="large bold">Camera Lucida&mdash;Optical Compass.</span>&mdash;In new<span class="pagenum"><a name="Page_489" id="Page_489">[489]</a></span>
-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 <i>Treatise
-on Drawing Instruments</i>, seventh edition.</p>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_490" id="Page_490">[490]</a></span></p>
-<h2>CHAPTER XVI.</h2>
-</div>
-<p class="ch">INSTRUMENTS FOR MEASURING LAND AND CIVIL WORKS
-DIRECTLY&mdash;CHAINS&mdash;VARIOUS TELLERS&mdash;STANDARD CHAINS&mdash;ARROWS&mdash;DROP
-ARROW&mdash;VICE FOR ADJUSTING CHAIN&mdash;CAINK'S
-RULE FOR INCLINES&mdash;STEEL BANDS&mdash;WIRE LAND
-MEASURES&mdash;COMPENSATION SYSTEMS&mdash;LINEN TAPES&mdash;OFFSET
-RODS&mdash;PINE STANDARD RODS&mdash;RODS WITH IRON
-CORE&mdash;BEAM COMPASS RODS&mdash;COINCIDENT MEASUREMENTS&mdash;COMPENSATED
-RODS&mdash;BASE LINE APPARATUS&mdash;COAST SURVEY
-LINES&mdash;PERAMBULATOR&mdash;PEDOMETER&mdash;PASSOMETER&mdash;SOUNDING
-CHAINS&mdash;SOUNDING LINES&mdash;TELEMETERS&mdash;HAND
-RODS&mdash;RULES.</p>
-<p>715.&mdash;<i>The Instruments Generally Employed for Measuring
-Land</i> 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.</p>
-<p>716.&mdash;<span class="large bold">Land Chains.</span>&mdash;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<span class="pagenum"><a name="Page_491" id="Page_491">[491]</a></span>
-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 <i>light</i> and <i>strong</i>. 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i491">
-  <img class="w100" src="images/i_491.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 330.&mdash;<i>Land chain and arrows.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_491a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-<p>717.&mdash;<span class="large bold">Tellers</span> are small pieces of brass suspended to the<span class="pagenum"><a name="Page_492" id="Page_492">[492]</a></span>
-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. <i>S</i> inserted swivel. The
-50 teller shows the link attachment. <i>A</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i492a">
-  <img class="w100" src="images/i_492a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 331.&mdash;<i>Gunter's land chains.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_492aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>718.&mdash;<i>Inserted Tellers.</i>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i492b">
-  <img class="w100" src="images/i_492b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 332.&mdash;<i>Inserted tellers.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_492ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>719.&mdash;The author's design for inserted tellers is shown<span class="pagenum"><a name="Page_493" id="Page_493">[493]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i493">
-  <img class="w100" src="images/i_493.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 333.&mdash;<i>Stanley's inserted tellers.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_493a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>720.&mdash;<span class="large bold">Feet Chains</span> 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.</p>
-<p>721.&mdash;<span class="large bold">Mining Chains</span> 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&mdash;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.</p>
-<p>722.&mdash;<span class="large bold">Metre Chains</span> 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 4&frac12; lbs.; strong, in No. 8 B.W.G.,
-9 lbs. 25-metre, light, 6 lbs.; strong, 11 lbs.</p>
-<p>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.</p>
-<p><span class="pagenum"><a name="Page_494" id="Page_494">[494]</a></span></p>
-<p>723.&mdash;<span class="large bold">Standard Chains.</span>&mdash;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.</p>
-<p>724.&mdash;<span class="large bold">Arrows.</span>&mdash;These are sometimes called <i>pins</i>. Ten
-form a set. They are shown with the chain in Fig. 330,
-and are commonly made of the same wire as the chain&mdash;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.</p>
-<p>725.&mdash;<span class="large bold">Drop Arrow</span>, 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<span class="pagenum"><a name="Page_495" id="Page_495">[495]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i495">
-  <img class="w100" src="images/i_495.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 334.&mdash;<i>Quiver with arrows.</i></p>
-    <p class="caption float-right">Fig. 335.&mdash;<i>Drop arrow.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_495a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>726.&mdash;<i>Examination and Adjustment of Chains.</i>&mdash;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 2&frac12; 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.</p>
-<p>727.&mdash;<i>The Chain to be Adjusted</i> should be first examined<span class="pagenum"><a name="Page_496" id="Page_496">[496]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i496">
-  <img class="w100" src="images/i_496.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 336.&mdash;<i>Stanley's vice for adjusting and repairing land chains.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_496a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>728.&mdash;<span class="large bold">Chain Vice.</span>&mdash;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 <i>brass links</i>. 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&mdash;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 <i>B</i> is used for an anvil for straightening
-the links. The vice <i>V</i> holds the link edgewise very firmly by
-bringing up the slide <i>J</i> by means of the screw <i>S</i>. 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<span class="pagenum"><a name="Page_497" id="Page_497">[497]</a></span>
-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.</p>
-<p>729.&mdash;<i>Opening and Closing the Chain for Use.</i>&mdash;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.</p>
-<p>730.&mdash;<i>Chaining</i> is performed by two chainmen, termed the
-<i>leader and follower</i>. 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<span class="pagenum"><a name="Page_498" id="Page_498">[498]</a></span>
-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, <i>the follower having ten
-counts nine only for the first ten</i>. To prevent accident it is
-therefore safer to start from a stake or other landmark, <i>not one
-of the arrows</i>. 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i498">
-  <img class="w100" src="images/i_498.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 337.&mdash;<i>Caink's rule for correcting inclines.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_498a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>731.&mdash;<span class="large bold">Caink's Rule</span> 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.</p>
-<p>732.&mdash;<i>To Use Caink's Rule.</i>&mdash;The follower has a clinometer
-of one of the kinds shown, Figs. <a href="#i394">260</a> or <a href="#i402">264</a>. He<span class="pagenum"><a name="Page_499" id="Page_499">[499]</a></span>
-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.</p>
-<p>733.&mdash;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 <a href="#Page_355">Chapter XII</a>.; 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°.</p>
-<p>734.&mdash;<span class="large bold">Steel Bands</span> for measuring, termed <i>steel band
-chains</i>, 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<span class="pagenum"><a name="Page_500" id="Page_500">[500]</a></span>
-by many to be a compensation that they are always of true
-length.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i500a">
-  <img class="w100" src="images/i_500a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Figs. 338, 339, 340.&mdash;<i>Steel bands and tapes.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_500aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i500b">
-  <img class="w100" src="images/i_500b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 341.&mdash;<i>One link of steel band.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_500ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>735.&mdash;The bands commonly used for land measuring are
-made 3/8, &frac12;, 5/8, and &frac34; 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 <i>b</i>, or perforated
-with holes indicating the number of tens. These band
-chains are made in links, feet, metres, or to any foreign<span class="pagenum"><a name="Page_501" id="Page_501">[501]</a></span>
-measure to order, and of any length corresponding with land
-chains. Weights, approximately&mdash;100 feet: &frac34; inch, 7 lbs.;
-5/8 inch, 4&frac34; lbs.; &frac12; inch, 4 lbs. 100 links: &frac34; inch, 4&frac34; lbs.;
-5/8 inch, 2&frac34; lbs.; &frac12; inch, 2&frac14; lbs. 20 metres: &frac34; inch, 5 lbs.;
-5/8 inch, 4 lbs.</p>
-<p>736.&mdash;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.</p>
-<p>737.&mdash;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.</p>
-<p>738.&mdash;The French make the handle generally T-shaped<span class="pagenum"><a name="Page_502" id="Page_502">[502]</a></span>
-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.</p>
-<p>739.&mdash;<span class="large bold">Wire Land Measures.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i502">
-  <img class="w100" src="images/i_502.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 342.&mdash;<i>French land measure.</i></p>
-    <p class="caption float-right">Figs. 343, 344.&mdash;<i>Marchant's 500-feet band.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_502a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>740.&mdash;The author has made many chains of 500 links;
-in Fig. 344 a part of one is shown full size. This <i>band</i>,
-as we may term it, is wound upon a reel in an iron case,
-Fig. 343. A spring brake is placed at the position <i>A</i>, 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&mdash;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, 3&frac12; 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<span class="pagenum"><a name="Page_503" id="Page_503">[503]</a></span>
-stock of 2, 3, 4, or 5 chains, or 200, 300, or 400 feet wound
-upon a steel cross.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i503">
-  <img class="w100" src="images/i_503.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 345.&mdash;<i>Richmond's tension handle.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_503a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>741.&mdash;<span class="large bold">Richmond's Tension Handle.</span>&mdash;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.<a name="FNanchor_54_54" id="FNanchor_54_54"></a><a href="#Footnote_54_54" class="fnanchor">[54]</a></p>
-<p>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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i504a">
-  <img class="w100" src="images/i_504a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 346.&mdash;<i>Copper case thermometer for suspending to a band chain.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_504aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>742.&mdash;<span class="large bold">Chain and Band Thermometer.</span>&mdash;Where very
-<span class="pagenum"><a name="Page_504" id="Page_504">[504]</a></span>
-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 <i>clinical</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i504b">
-  <img class="w100" src="images/i_504b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 347.&mdash;<i>Littlejohn's temperature handle.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_504ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p><span class="pagenum"><a name="Page_505" id="Page_505">[505]</a></span></p>
-<p>743.&mdash;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.</p>
-<p>744.&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i505">
-  <img class="w100" src="images/i_505.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 348.&mdash;<i>Stanley's repairing sleeve.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_505a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>745.&mdash;<span class="large bold">Repairing Sleeve for Steel Bands.</span>&mdash;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.</p>
-<p>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.</p>
-<p>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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i506">
-  <img class="w100" src="images/i_506.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 349.&mdash;<i>Linen Tape.</i></p>
-    <p class="caption float-right">Fig. 350.&mdash;<i>Small steel pocket tape.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_506a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>746.&mdash;<span class="large bold">Linen Tapes.</span>&mdash;This most useful implement,
-Fig. 349, is one of the most unsatisfactory measures the trader<span class="pagenum"><a name="Page_506" id="Page_506">[506]</a></span>
-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&mdash;often valueless or
-worse&mdash;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&mdash;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.</p>
-<p>Tapes are divided into links, feet and inches, metres, and
-all measures as required. A decimal yard is commonly<span class="pagenum"><a name="Page_507" id="Page_507">[507]</a></span>
-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.</p>
-<p>747.&mdash;<span class="large bold">Steel Tapes.</span>&mdash;Thin steel tapes, 3/8, &frac12;, 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.</p>
-<p>748.&mdash;<span class="large bold">Pocket Steel Tapes</span> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i507">
-  <img class="w100" src="images/i_507.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 351.&mdash;<i>Jointed offset rod, top and centre.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_507a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>749.&mdash;<span class="large bold">Offset Rods</span> 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 <i>H</i>. 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.</p>
-<p><span class="pagenum"><a name="Page_508" id="Page_508">[508]</a></span></p>
-<p><i>The offset is Used</i> 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.</p>
-<p>750.&mdash;<span class="large bold">Measurement by Rods</span> 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.</p>
-<p>751.&mdash;<span class="large bold">Pine Standard Rods</span>, 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 1&frac34; 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&mdash;·0000085, average of total length per
-degree centigrade, which is about three-fourths that of iron.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i508">
-  <img class="w100" src="images/i_508.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 352.&mdash;<i>One end of a pinewood butt rod.</i></p>
-    <p class="caption float-right">Fig. 353.&mdash;<i>S&mdash;Block square.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_508a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>752.&mdash;Where butt rods are used for continuous measurement,
-it is necessary that they be brought very carefully<span class="pagenum"><a name="Page_509" id="Page_509">[509]</a></span>
-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.</p>
-<p>753.&mdash;<span class="large bold">Angle-piece.</span>&mdash;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.</p>
-<p>754.&mdash;<span class="large bold">Butt Rods with Iron Core.</span>&mdash;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 2&frac14; inches square, sawn down and turned cut
-sides outwards to prevent warping. A 10-feet length of iron
-steam tube about &frac12; 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.</p>
-<p>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.</p>
-<p>755.&mdash;<i>The 5-feet Rule</i> is of steel, &frac34; inch by &frac14; inch, inlaid<span class="pagenum"><a name="Page_510" id="Page_510">[510]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i510">
-  <img class="w100" src="images/i_510.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Figs. 354, 355, 356.&mdash;<i>Butt rods with iron core.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_510a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-<p>756.&mdash;<i>Beam Compass Measurements</i> 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<span class="pagenum"><a name="Page_511" id="Page_511">[511]</a></span>
-the punch mark. Rods of pine are commonly employed.
-Figs. 357, 358 will sufficiently illustrate the instruments.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i511a">
-  <img class="w100" src="images/i_511a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 357.&mdash;<i>Beam compasses.</i></p>
-    <p class="caption float-right">Fig. 358.&mdash;<i>Standard scale.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_511aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i511b">
-  <img class="w100" src="images/i_511b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 359.&mdash;<i>Coincidence rods.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_511ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>757.&mdash;<span class="large bold">The Method of Coincidence</span> 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 <i>B</i> has a fixed scale <i>b</i> placed on top of
-it at one end. The rod <i>A</i> has a scale protruding from it.<span class="pagenum"><a name="Page_512" id="Page_512">[512]</a></span>
-This scale may be jointed with a good ground joint at <i>J</i> 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 <i>P</i> until exact
-coincidence of the lines shown at <i>b</i> is brought about. This
-tapping operation appears a rather rough process, but
-practically it is very exact.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i512">
-  <img class="w100" src="images/i_512.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 360.&mdash;<i>Bessel compensated rod.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_512a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>758.&mdash;<span class="large bold">Compensated Rods.</span>&mdash;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&mdash;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
-<i>II′</i> are the iron bars, <i>Z</i> zinc. The length of the zinc required
-for compensation between the junctions is found in the
-equation&mdash;</p>
-<p class="center">
-(<i>S</i> + <i>Z</i>)(0000119) - <i>Z</i>(0000292) = <i>0</i>,
-</p>
-<p><i>S</i> being the total length of the standard rod in feet, and <i>Z</i> the
-length of zinc in feet required for compensation. This plan
-is that adopted for the compensation of pendulums. For the<span class="pagenum"><a name="Page_513" id="Page_513">[513]</a></span>
-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.</p>
-<p>759.&mdash;<span class="large bold">Colby Compensated Rods</span>, 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.</p>
-<p><i>The Rods</i> are each made 10 feet 1·5 inches long, 5 inches
-broad, and 1·5 inches deep. Fig. 362 <i>i</i> is a side elevation of
-one rod, Fig. 363 <i>ib</i> plan of iron and brass rods, Fig. 365 <i>ib</i>
-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 <i>F</i>. They
-are firmly fixed together at their centres by transverse steel
-cylinders, Fig. 363 <i>RR′</i> 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 <i>E</i>, Fig. 363, fixed firmly on the bottom of the box <i>bx</i>.
-At the extremity, and at right angles to each of these bars, is a
-flat steel tongue, Figs. 364, 365 <i>A</i>, 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>i</i>. The tongue <i>A</i> is jointed by double
-conical pivots at <i>f</i> and <i>f′</i>, which form axes perpendicular to<span class="pagenum"><a name="Page_514" id="Page_514">[514]</a></span>
-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
-<i>P</i>, 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i514">
-  <img class="w100" src="images/i_514.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption"><i>Colby Compensated Measuring Rods.</i></p>
-    <p class="caption">Fig. 361.&mdash;<i>End of rod mounted with microscopes, trestles and ground plate.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_514a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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 <i>F</i>, and the
-central stay <i>E</i> mentioned before prevents any displacement<span class="pagenum"><a name="Page_515" id="Page_515">[515]</a></span>
-of the bars when the rods are held by the rollers <i>RR′</i>. To
-protect the tongue <i>A</i>, 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 <i>D</i>, employed to observe
-the standard points of one pair of rods brought by adjustment
-to true position <i>MM′</i>. A pair of sight vanes which shut
-down are placed on the ends of the box for setting the rods
-approximately in line.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i515">
-  <img class="w100" src="images/i_515.png"  alt="" />
-</div>
-  <div class="caption2">
-    <p class="caption"><i>Colby Compensated Measuring Rods.</i></p>
-    <p class="caption2">Fig. 362.&mdash;<i>Side elevation of point of support of rod.</i></p>
-    <p class="caption2">Fig. 363.&mdash;<i>Side elevation of centre, with section of box bx.</i></p>
-    <p class="caption2">Fig. 364.&mdash;<i>Plan of rods and compensating arm.</i></p>
-    <p class="caption2">Fig. 365.&mdash;<i>Perspective view of the same.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_515a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p><i>Two Rigid Tripod Stands</i> Fig. 361 <i>S</i> are used to each
-of the rods placed under the rollers Fig. 362 <i>F</i> upon which
-the bars are supported in the box. The tripods carry a<span class="pagenum"><a name="Page_516" id="Page_516">[516]</a></span>
-universal slide-rest by which the rod may be adjusted to
-position both in horizontal and vertical planes Fig. 361 <i>A</i>.
-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.</p>
-<p><i>Compensated Microscopes.</i>&mdash;The compound microscopes,
-Fig. 361 <i>MM′</i>, 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 <i>T</i> is fixed on the same piece of apparatus,
-with adjustment for reading a point on the ground <i>G</i> 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."</p>
-<p>In measuring a base line a piece of nearly level land
-is selected, and the rods are supported upon the trestles or<span class="pagenum"><a name="Page_517" id="Page_517">[517]</a></span>
-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 <i>HH′</i>. The cases containing the
-rods, or the rods themselves, are made sufficiently strong to be
-supported upon two points only without serious deflection.</p>
-<p>The Colby system of measurement of base lines varied
-in detail has been employed by nearly all the nations of Europe
-and in America.</p>
-<p>760.&mdash;<span class="large bold">Modern Base-line Apparatus.</span>&mdash;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.</p>
-<p>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.</p>
-<p>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<span class="pagenum"><a name="Page_518" id="Page_518">[518]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i518">
-  <img class="w100" src="images/i_518.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 366.&mdash;<i>One of the two end supports of the band, showing tension weight,
-with cord running over the ball-bearing pulley.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_518a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>To prevent catenery light intermediate stands, as shown at
-<i>B</i> 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,
-<i>C</i> 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,
-<i>D</i> Fig. 367, which is over the plate let into the ground.</p>
-<p><span class="pagenum"><a name="Page_519" id="Page_519">[519]</a></span></p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i519">
-  <img class="w100" src="images/i_519.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 367.&mdash;<i>Two reading and plumbing instruments, C, C; transferring
-instrument, D; and one of the adjustable intermediate supports, B.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_519a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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<span class="pagenum"><a name="Page_520" id="Page_520">[520]</a></span>
-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<span class="pagenum"><a name="Page_521" id="Page_521">[521]</a></span>
-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.</p>
-<p>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.</p>
-<p>761.&mdash;<span class="large bold">Perambulator.</span>&mdash;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<span class="pagenum"><a name="Page_522" id="Page_522">[522]</a></span>
-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 &frac14; 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 1&frac12; 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i522">
-  <img class="w100" src="images/i_522.png"  alt="" />
-</div>
-  <div class="caption2">
-    <p class="caption2">Fig. 368.&mdash;<i>Perambulator.</i></p>
-    <p class="caption2">Fig. 369.&mdash;<i>Details of registering box.</i></p>
-    <p class="caption2">Fig. 370.&mdash;<i>Section.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_522a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p><i>The Registering Part of the Instrument</i>, 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 <i>S</i>, of
-about sixteen threads to the inch. The screw works in the
-edges of a pair of discs <i>R</i>, 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<span class="pagenum"><a name="Page_523" id="Page_523">[523]</a></span>
-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 <i>O</i>. 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 13&frac12; miles.</p>
-<p><i>The Measuring Box</i> 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.</p>
-<p>762.&mdash;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.<span class="pagenum"><a name="Page_524" id="Page_524">[524]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i524a">
-  <img class="w100" src="images/i_524a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 371.</p>
-    <p class="caption ebhide clear"><a href="images/i_524aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>763.&mdash;<span class="large bold">Pedometer.</span>&mdash;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<span class="pagenum"><a name="Page_525" id="Page_525">[525]</a></span>
-are four divisions only, to indicate quarter miles. The pedometer
-is slung up by a loop, Fig. 371, <i>H</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i524b">
-  <img class="w100" src="images/i_524b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 372.&mdash;<i>Construction of pedometer.</i></p>
-    <p class="caption float-right">Fig. 373.&mdash;<i>Face of passometer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_524ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>764.&mdash;<i>The Registering Apparatus</i> consists of a pendulum,
-Fig. 372, <i>P</i> placed horizontally by being supported by a
-delicate spring <i>L</i> 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 <i>S</i>, shown under it.
-The axis of the pendulum is free upon the axis of the ratchet
-wheel <i>R</i>. 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 <i>D</i>. 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, <i>not shown</i>, 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 <i>S</i> 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.</p>
-<p>765.&mdash;<span class="large bold">Passometer.</span>&mdash;This instrument was originally
-invented by the author as an improvement upon the pedometer
-(1868). The instrument, Fig. 373, is not intended to<span class="pagenum"><a name="Page_526" id="Page_526">[526]</a></span>
-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.</p>
-<p>766.&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i526">
-  <img class="w100" src="images/i_526.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 374.&mdash;<i>Sounding chain.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_526a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>767.&mdash;<span class="large bold">Sounding Chains</span> 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&mdash;of 28 lbs., for ordinary coast work, or<span class="pagenum"><a name="Page_527" id="Page_527">[527]</a></span>
-heavier if there are strong currents. The chain is contained
-in a strong wooden box.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i527">
-  <img class="w100" src="images/i_527.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 375.&mdash;<i>Sounding line and weight.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_527a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-<p>768.&mdash;<span class="large bold">Sounding Lines</span>, used for survey of shallow
-coasts and harbours, are made of water-laid line of fine green
-hemp, about &frac34; 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.</p>
-<p>769.&mdash;<span class="large bold">Coast Survey Lines.</span>&mdash;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<span class="pagenum"><a name="Page_528" id="Page_528">[528]</a></span>
-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.</p>
-<p>770.&mdash;<span class="large bold">Telemeters.</span>&mdash;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.<a name="FNanchor_55_55" id="FNanchor_55_55"></a><a href="#Footnote_55_55" class="fnanchor">[55]</a> 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.</p>
-<p>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, <a href="#Art_693">art. 693</a>, but with a tangent screw to give a
-<span class="pagenum"><a name="Page_529" id="Page_529">[529]</a></span>
-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, <a href="#Art_664">art. 664</a>, being in every
-way a superior telemeter for the purpose when a measured base
-can be fixed and well-known trigonometrical calculation used.</p>
-<p>771.&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i529">
-  <img class="w100" src="images/i_529.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 376.</p>
-    <p class="caption ebhide clear"><a href="images/i_529a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p><span class="pagenum"><a name="Page_530" id="Page_530">[530]</a></span></p>
-<p>772.&mdash;<span class="large bold">Hand Rods</span>, 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i530">
-  <img class="w100" src="images/i_530.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 377.&mdash;<i>Ordinary 5-feet jointed rods&mdash;plan and section of joint.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_530a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>773.&mdash;<span class="large bold">Ordinary 5-feet Rods</span> 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 (<i>housing</i>) 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
-&frac12; 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.</p>
-<p>774.&mdash;<span class="large bold">Fully Divided Rods.</span>&mdash;The author has made rods
-for many years divided to single inches. These measure from
-both ends&mdash;one end direct as Fig. 378 and the other end
-reversed by turning the rod over as Fig. 379. By this plan<span class="pagenum"><a name="Page_531" id="Page_531">[531]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i531a">
-  <img class="w100" src="images/i_531a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Figs. 378, 379.&mdash;<i>Stanley's surveyors' rods.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_531aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p id="Art_775">775.&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i531b">
-  <img class="w100" src="images/i_531b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 380.&mdash;<i>Connecting link for rods.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_531ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i531c">
-  <img class="w100" src="images/i_531c.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 381.&mdash;<i>Slip jointed rod.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_531ca.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>776.&mdash;<span class="large bold">Slip Jointed Rod.</span>&mdash;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<span class="pagenum"><a name="Page_532" id="Page_532">[532]</a></span>
-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:&mdash;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.</p>
-<p>777.&mdash;<span class="large bold">Brace-piece.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i532">
-  <img class="w100" src="images/i_532.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 382.&mdash;<i>Civil engineer's rule.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_532a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>778.&mdash;<span class="large bold">Civil Engineer's Rule</span> 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&mdash;&frac34; inch; and some wide for strength&mdash;1&frac14; 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, &frac14;, &frac12;, 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.</p>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_533" id="Page_533">[533]</a></span></p>
-<h2>CHAPTER XVII.</h2>
-</div>
-<p class="ch">STATIONS OF OBSERVATION&mdash;PICKETS&mdash;FALSE PICKET&mdash;PERMANENT
-STATIONS&mdash;REFERRING OBJECT&mdash;HELIOTROPE&mdash;HELIOSTAT&mdash;HELIOGRAPH&mdash;SIGNALLING&mdash;MORSE
-ALPHABET&mdash;NIGHT
-LIGHTS&mdash;OIL LANTERNS&mdash;MAGNESIUM LIGHT.</p>
-<p>779.&mdash;<span class="large bold">Stations of Observation</span> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i533">
-  <img class="w100" src="images/i_533.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 383.&mdash;<i>Ranging pole or picket.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_533a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>780.&mdash;<span class="large bold">Pickets or Ranging Poles</span>, 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.</p>
-<p>781.&mdash;The picket (Fr. <i>piquet</i>) is a straight, slightly tapering<span class="pagenum"><a name="Page_534" id="Page_534">[534]</a></span>
-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: <i>B</i> black, <i>W</i> white, <i>R</i> red. It is usual
-to have six pickets at least out in use with a theodolite in
-open country.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i534">
-  <img class="w100" src="images/i_534.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 384.&mdash;<i>False picket.</i></p>
-    <p class="caption float-right">Fig. 385.&mdash;<i>Spur-shod picket.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_534a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>782.&mdash;<span class="large bold">False Picket.</span>&mdash;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<span class="pagenum"><a name="Page_535" id="Page_535">[535]</a></span>
-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.</p>
-<p>783.&mdash;<span class="large bold">Spur-shod Picket.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe32_75" id="i535">
-  <img class="w100" src="images/i_535.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 386.&mdash;<i>Socket for station pole.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_535a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>784.&mdash;<span class="large bold">Permanent Stations</span> 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<span class="pagenum"><a name="Page_536" id="Page_536">[536]</a></span>
-way to do this is to have a slightly tapered wooden socket,
-Fig. 386 <i>S</i>, constructed of stout boards, say 1&frac12; inches
-thick, made into a hollow square with a cross of boards,
-<i>WWWW</i> 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 <i>P</i> 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.</p>
-<p>785.&mdash;<span class="large bold">Referring Object.</span>&mdash;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.</p>
-<p><i>Stations Visible at Great Distances</i> are formed by means
-of reflection of the sun's rays or by artificial light.</p>
-<p><span class="pagenum"><a name="Page_537" id="Page_537">[537]</a></span></p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i537">
-  <img class="w100" src="images/i_537.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 387.&mdash;<i>Stanley's heliotrope.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_537a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>786.&mdash;<span class="large bold">Heliotrope</span>, or <i>heliostat</i> 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 <i>M</i>
-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 <i>B</i> is attached upon
-one side that works into a tangent screw which is moved by<span class="pagenum"><a name="Page_538" id="Page_538">[538]</a></span>
-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 <i>A</i>. 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.</p>
-<p>787.&mdash;<i>The Base Board</i> is of &frac34; 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 &frac34; inch thick, is hinged, so as to
-be held erect by means of a stay bar <i>E</i>. In the centre of
-the screen an opening is turned out 3&frac12; 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 <i>abc</i> in the figure.</p>
-<p>788.&mdash;<i>The Discs abc</i>, are of thin brass and have
-openings respectively &frac14;, &frac34;, and 1&frac12; 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.</p>
-<p>789.&mdash;<i>To Pack the Instrument</i>, the screen is turned down
-the index frame, falling into the opening <i>F</i>; 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.</p>
-<p><span class="pagenum"><a name="Page_539" id="Page_539">[539]</a></span></p>
-<p>790.&mdash;<i>To Use the Heliotrope</i>, 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 <i>P</i> is cut away to admit of the suspension of a
-plummet.</p>
-<p>791.&mdash;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."<a name="FNanchor_56_56" id="FNanchor_56_56"></a><a href="#Footnote_56_56" class="fnanchor">[56]</a></p>
-<p>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.</p>
-<p><i>Signalling with the Heliotrope.</i>&mdash;A thin wooden bat <i>D</i> is
-<span class="pagenum"><a name="Page_540" id="Page_540">[540]</a></span>
-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.</p>
-<p>792.&mdash;<span class="large bold">Heliostat.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i540">
-  <img class="w100" src="images/i_540.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 388.&mdash;<i>Heliograph.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_540a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>793.&mdash;<span class="large bold">Heliograph.</span>&mdash;This instrument is the invention
-of Sir H. C. Mance,<a name="FNanchor_57_57" id="FNanchor_57_57"></a><a href="#Footnote_57_57" class="fnanchor">[57]</a> 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. <i>B</i> is the back of a plain circular
-<span class="pagenum"><a name="Page_541" id="Page_541">[541]</a></span>
-mirror of 5 inches diameter, supported upon pivots on a
-fork frame <i>J</i>, 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 <i>A</i> which
-moves the mirror and the entire apparatus above in horizontal
-revolution.</p>
-<p>794.&mdash;<i>The Sighting Arm L</i> 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
-<i>C</i>. The arm <i>L</i> has a supplementary extension by the piece
-<i>Sj</i>, 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>I</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.</p>
-<p>795.&mdash;<i>The Sighting Vane</i> is a piece of white metal
-upon which there is placed a black dot termed the <i>sighting
-spot</i>. 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 <i>shadow
-spot</i>. 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.</p>
-<p>796.&mdash;<i>The Supplementary Mirror M</i> is similar to that
-already described, centred also on pivots and placed in a forked
-frame. This is mounted on a cone <i>S′</i> which fits into a socket
-at <i>S</i>, when the extension arm <i>J</i> is removed. This mirror is
-intended to receive the image of the sun when placed towards<span class="pagenum"><a name="Page_542" id="Page_542">[542]</a></span>
-the back of the pointing of the instrument to throw the sun's
-image from the mirror <i>M</i> to <i>B</i>, 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>I</i>.</p>
-<p>797.&mdash;<i>Telegraphing Apparatus</i>, called technically <i>flashing</i>
-apparatus. This consists of a rod <i>R</i> 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
-<i>R</i>, which forms a part of the tube. The Morse key is hinged
-at <i>J</i> to the stem of the instrument, and is kept up to a fixed
-stop by means of a spring <i>P</i> extended by an arm from the
-stem of the instrument, so that pressure upon the disc <i>F</i>
-moves the key down to its stop <i>P</i>, 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 <i>D</i>, is more certain for
-signalling words.</p>
-<p>798.&mdash;<i>The Tripod of the Heliograph TT′T″</i> 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<span class="pagenum"><a name="Page_543" id="Page_543">[543]</a></span>
-sink the toes, or to have a heavy stone suspended under the
-centre of the head.</p>
-<p>799.&mdash;<i>The Case for the Heliograph</i> 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.</p>
-<p>800.&mdash;<i>To use the Heliograph with a Single Mirror.</i>&mdash;In
-this case the reflection is direct. The instrument is
-approximately directed by looking through the mirror from
-behind, moving the arm <i>L</i> and the sight <i>I</i> to cut
-the distant station, and then clamping the screw <i>C</i>. After
-this is done the exact position is found by placing the head
-nearly in <i>front</i> 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>I</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.</p>
-<p>801.&mdash;<i>To Adjust the Mirror</i>, stand behind the instrument
-and adjust the vertical screw <i>R</i> and the horizontal pinion
-A until the black spot, as it appears on the mirror from the<span class="pagenum"><a name="Page_544" id="Page_544">[544]</a></span>
-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 <i>R</i> and pinion <i>A</i>, following the apparent
-path of the sun.</p>
-<p>802.&mdash;<i>To Use the Heliograph with Two Mirrors</i>, 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 <i>S</i>.
-This has a white paper vane cemented upon it, as shown at
-<i>M</i>. The mirror <i>B</i> 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 <i>B</i>, 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 <i>M</i> until the reflection
-of the distant station appears in the centres of the mirrors.
-Now clamp the mirror <i>M</i> in this position, from which it must
-not be moved so long as it is required to keep the same
-station in communication.</p>
-<p>To keep the reflection following the sun a position is
-taken at the back of the mirror <i>B</i>, 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
-<i>M</i> takes the place of the metal vane <i>I</i>.</p>
-<p id="Art_803">803.&mdash;<i>Telegraphing by the Heliograph.</i>&mdash;The communication
-is made by the alternate pressure and release of the
-Morse key <i>F</i>, 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<span class="pagenum"><a name="Page_545" id="Page_545">[545]</a></span>
-of a touch represented by dashes. The following arrangement
-forms the alphabet:&mdash;</p>
-<div class="m25" style="padding: 2em 0;">
-
-<table summary="" style="border-collapse: collapse;">
-<tr><td style="width: 10%;">A</td><td class="tdl xxlarger br" style="width: 40%;"> · &ndash;</td>
-    <td style="width: 10%; padding-left: 3em;">N&nbsp; </td><td class="tdl xxlarger" style="width: 40%; padding-left: .25em;"> &ndash; ·</td>
-</tr>
-<tr><td>B</td><td class="tdl xxlarger br">&ndash;···</td>
-    <td class="td03">O</td><td class="tdl xxlarger pl25"> &ndash; &ndash; &ndash;</td>
-</tr>
-<tr><td>C</td><td class="tdl xxlarger br">&ndash;·&ndash;·</td>
-    <td class="td03">P</td><td class="tdl xxlarger pl25"> ·&ndash; &ndash;·</td>
-</tr>
-<tr><td>D</td><td class="tdl xxlarger br">&ndash;··</td>
-    <td class="td03">Q</td><td class="tdl xxlarger pl25"> &ndash; &ndash;·&ndash;</td>
-</tr>
-<tr><td>E</td><td class="tdl xxlarger br">·</td>
-    <td class="td03">R</td><td class="tdl xxlarger pl25"> ·&ndash;·</td>
-</tr>
-<tr><td>F</td><td class="tdl xxlarger br">··&ndash;·</td>
-    <td class="td03">S</td><td class="tdl xxlarger pl25"> ···</td>
-</tr>
-<tr><td>G</td><td class="tdl xxlarger br">&ndash; &ndash;·</td>
-    <td class="td03">T</td><td class="tdl xxlarger pl25"> &ndash;</td>
-</tr>
-<tr><td>H</td><td class="tdl xxlarger br">····</td>
-    <td class="td03">U</td><td class="tdl xxlarger pl25"> ··&ndash;</td>
-</tr>
-<tr><td>I</td><td class="tdl xxlarger br">··</td>
-    <td class="td03">V</td><td class="tdl xxlarger pl25"> ···&ndash;</td>
-</tr>
-<tr><td>J</td><td class="tdl xxlarger br">·&ndash; &ndash; &ndash;</td>
-    <td class="td03">W</td><td class="tdl xxlarger pl25"> ·&ndash; &ndash;</td>
-</tr>
-<tr><td>K</td><td class="tdl xxlarger br">&ndash;·&ndash;</td>
-    <td class="td03">X</td><td class="tdl xxlarger pl25"> &ndash;··&ndash;</td>
-</tr>
-<tr><td>L</td><td class="tdl xxlarger br">·&ndash;··</td>
-    <td class="td03">Y</td><td class="tdl xxlarger pl25"> &ndash;·&ndash; &ndash;</td>
-</tr>
-<tr><td>M</td><td class="tdl xxlarger br">&ndash; &ndash;</td>
-    <td class="td03">Z</td><td class="tdl xxlarger pl25"> &ndash; &ndash;··</td>
-</tr>
-</table>
-</div>
-<p>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 <i>The Manual of Instructions in Army
-Signalling</i>. 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.</p>
-<p>804.&mdash;<span class="large bold">Lights for Observations by Night.</span>&mdash;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.</p>
-<p>805.&mdash;<span class="large bold">Oil Lanterns.</span>&mdash;In the great trigonometrical<span class="pagenum"><a name="Page_546" id="Page_546">[546]</a></span>
-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.<a name="FNanchor_58_58" id="FNanchor_58_58"></a><a href="#Footnote_58_58" class="fnanchor">[58]</a></p>
-<p>806.&mdash;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&mdash;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 <a href="#i537">Fig. 387</a>, <i>D</i>. 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.</p>
-<p>807.&mdash;<span class="large bold">Magnesium.</span>&mdash;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
-<span class="pagenum"><a name="Page_547" id="Page_547">[547]</a></span>
-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.</p>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_548" id="Page_548">[548]</a></span></p>
-<h2>CHAPTER XVIII.</h2>
-</div>
-<p class="ch">MEASUREMENT OF ALTITUDES BY DIFFERENCES OF ATMOSPHERIC
-PRESSURE&mdash;HISTORICAL NOTE&mdash;MERCURIAL
-BAROMETER&mdash;CONSTRUCTION&mdash;OPERATION&mdash;ANEROID
-BAROMETER&mdash;CONSTRUCTION&mdash;VARIOUS IMPROVEMENTS&mdash;HYPSOMETER.</p>
-<p>808.&mdash;<i>Historical Note.</i>&mdash;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 58&frac12; 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<span class="pagenum"><a name="Page_549" id="Page_549">[549]</a></span>
-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.</p>
-<p>809.&mdash;<span class="large bold">The Mercurial Barometer.</span>&mdash;The principle of
-the barometer is generally understood. If a glass tube,
-closed at one end, 33 inches long, say of &frac14; 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&mdash;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 <i>Torricellian vacuum</i>.</p>
-<p>810.&mdash;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<span class="pagenum"><a name="Page_550" id="Page_550">[550]</a></span>
-<i>basin</i>, or what is technically termed the <i>cistern</i>. 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 <i>per
-area</i> 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.</p>
-<p>811.&mdash;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</p>
-<p class="center">
-29·95 × 0·48967 = 14·66 lbs.
-</p>
-<p class="noindent">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.</p>
-<p>812.&mdash;<span class="large bold">Mountain Barometer.</span>&mdash;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,<span class="pagenum"><a name="Page_551" id="Page_551">[551]</a></span>
-in whatever position the barometer may be placed. The
-closing is effected by means of an adjusting screw, <a href="#i553">Fig. 390</a> <i>F</i>,
-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 <i>X</i> 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.</p>
-<p>813.&mdash;<i>The Glass Tube</i> 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.</p>
-<p>814.&mdash;<i>Mercury&mdash;Filling the Barometer Tube.</i>&mdash;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,<span class="pagenum"><a name="Page_552" id="Page_552">[552]</a></span>
-in which there is left sufficient clean mercury to complete
-the barometer.</p>
-<p>815.&mdash;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, <i>D</i>. Upon the under side of
-the collar an ivory gauge peg <i>X</i> is inserted, which forms the
-index point for reading the surface of the mercury in the
-cistern upon the Fortin principle.</p>
-<p>816.&mdash;<i>The Cistern.</i>&mdash;The glass sighting tube, Fig. 390
-<i>H</i>, of the cistern, through which the mercury and gauge point
-<i>X</i> are visible, is made about 1&frac12; inches long and from 1 inch
-to 1&frac12; 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 <i>D</i>, 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>I</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 <i>E</i>
-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 <i>F</i> presses for adjustment of the
-mercury, or to close the tube.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe23_625" id="i553">
-  <img class="w100" src="images/i_553.png"  alt="" />
-</div>
-  <div class="caption2">
-    <p class="caption2">Fig. 389.&mdash;<i>Mountain barometer erected for use.</i></p>
-    <p class="caption2">Fig. 390.&mdash;<i>Section through the cistern.</i></p>
-    <p class="caption2">Fig. 391.&mdash;<i>Vernier reading, showing gauge point S.</i></p>
-    <p class="caption2">Fig. 392.&mdash;<i>Sling case for carrying.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_553a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>817.&mdash;<i>The Cistern Casing</i>, which is of brass, consists of
-upper and lower collar pieces, Fig. 390 <i>AA′</i> and <i>BB′</i>, 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 <i>D</i> and makes soft contact between these parts.
-The lower collar has been partly described with the cistern.
-This has a brass tube <i>E</i> screwed upon it, covering the
-<span class="pagenum"><a name="Page_553" id="Page_553">[553]</a><br /><a name="Page_554" id="Page_554">[554]</a></span>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 <i>F</i> placed in the axis of the tube.
-There are four bolts or screws <i>GG′</i> 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.</p>
-<p>818.&mdash;<i>The Stem, or Barometer Casing Tube</i>, is made of
-brass, about &frac34; inch diameter. This has a slot, of about &frac14; 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, <i>rr′</i>. 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 <i>S</i>. 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
-<i>cock-piece</i>, Fig. 389 <i>m</i>, on the outer tube in the same manner
-as before described for telescope racking, <a href="#Art_96">art. 96</a>. Two <i>stay-pieces</i>
-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.</p>
-<p><span class="pagenum"><a name="Page_555" id="Page_555">[555]</a></span></p>
-<p>819.&mdash;<i>Mounting of the Barometer.</i>&mdash;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.</p>
-<p>820.&mdash;<i>The Thermometer</i>, shown at Fig. 389 <i>t</i>, 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.</p>
-<p>821.&mdash;<i>The Packing Case</i>, 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.</p>
-<p>822.&mdash;<i>Reading the Barometer.</i>&mdash;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 <i>beading</i>, as it is termed, varies
-according to whether the mercury is rising or falling. It<span class="pagenum"><a name="Page_556" id="Page_556">[556]</a></span>
-is always necessary before taking an observation to raise
-the mercury, by turning the screw <i>F</i>, until its surface just
-touches the peg <i>X</i>, 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 <i>S</i>, 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&mdash;</p>
-<div class="m25">
-<table summary="">
-  <tr>
-    <td class="tdc">26·45</td>
-  </tr>
-  <tr>
-    <td class="tdc" style="padding-left: 1.8em; border-bottom: 1px solid black;">·025</td>
-  </tr>
-  <tr>
-    <td class="tdc" style="padding-left: .8em;">26·475</td>
-  </tr>
-</table>
-</div>
-<p>For altitude the upper and lower stations are taken, and the
-difference subtracted for difference of barometrical scale.</p>
-<p>823.&mdash;<i>Difference in Altitude in feet taken from Barometrical
-Inches.</i>&mdash;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 <i>Meteorological
-Magazine</i>, as follows:&mdash;</p>
-<p>"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:&mdash;</p>
-<div class="m25">
-<table summary="">
-  <tr>
-<td class="tdc">Lower</td>
-<td class="tdc">station</td>
-    <td class="tdr">29·25</td>
-<td class="tdc">inches</td>
-  </tr>
-  <tr>
-<td class="tdc">Upper</td>
-<td class="tdc">"</td>
-    <td class="tdr" style="border-bottom: 1px solid black;">28·02</td>
-<td class="tdc">"</td>
-  </tr>
-  <tr>
-<td class="tdc"></td>
-<td class="tdc"></td>
-    <td class="tdr">123</td>
-  </tr>
-  <tr>
-<td class="tdc"></td>
-<td class="tdc"></td>
-    <td class="tdr" style="border-bottom: 1px solid black;">9</td>
-  </tr>
-  <tr>
-<td class="tdc"></td>
-<td class="tdc">Elevation</td>
-    <td class="tdr">1107</td>
-<td class="tdc">feet."</td>
-  </tr>
-</table>
-</div>
-<p><span class="pagenum"><a name="Page_557" id="Page_557">[557]</a></span></p>
-<p>824.&mdash;<i>Capillarity.</i>&mdash;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:&mdash;</p>
-
-<div class="m5">
-<table summary="" style="border: 1px solid black; border-collapse: collapse;">
-<caption style="padding: 1em 0 .5em 0;"><i>Correction of Capillarity to be Added to the Reading.</i></caption>
-  <tr>
-    <td class="medium" colspan="3" style="padding: .5em .5em 0 .5em;">Diameter of Tube in Inches</td>
-    <td class="td05a">·6</td>
-    <td class="td05a">·55</td>
-    <td class="td05a">·5</td>
-    <td class="td05a">·45</td>
-    <td class="td05a">·4</td>
-    <td class="td05a">·35</td>
-    <td class="td05a">·3</td>
-    <td class="td05a">·25</td>
-    <td class="td05a">·2</td>
-  </tr>
-  <tr>
-    <td class="medium" style="padding: 0 0 0 .5em;">Unboiled</td>
-    <td class="medium">Tube,</td>
-    <td class="medium">Inches</td>
-    <td class="td05">·004</td>
-    <td class="td05">·005</td>
-    <td class="td05">·007</td>
-    <td class="td05">·01</td>
-    <td class="td05">·014</td>
-    <td class="td05">·02</td>
-    <td class="td05">·025</td>
-    <td class="td05">·04</td>
-    <td class="td05">·059</td>
-  </tr>
-  <tr>
-    <td class="td05b">Boiled</td>
-    <td class="medium">"</td>
-    <td class="medium">"</td>
-    <td class="td05b">·002</td>
-    <td class="td05b">·003</td>
-    <td class="td05b">·004</td>
-    <td class="td05b">·005</td>
-    <td class="td05b">·007</td>
-    <td class="td05b">·01</td>
-    <td class="td05b">·013</td>
-    <td class="td05b">·02</td>
-    <td class="td05b">·029</td>
-  </tr>
-</table>
-</div>
-<p style="padding-top: 1em;">825.&mdash;<i>Temperature Correction.</i>&mdash;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 <a href="#i553">Fig.
-389</a> <i>t</i>. 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&mdash;thermometer,
-52° Fahr.; barometer, 30 inches</p>
-<p class="center">
--(52 - 32) × 30 × ·00014 = ·084,<br />
-</p>
-<p class="noindent">making the true reading 30 - ·084 = 29·916 inches at 32°
-Fahr.</p>
-<p>Tables for correction without any calculation will be found
-in Molesworth's and other pocket-books.</p>
-<p>826.&mdash;<i>Gravity Correction.</i>&mdash;The force of gravity decreases
-as we ascend to a higher level in proportion to the square of<span class="pagenum"><a name="Page_558" id="Page_558">[558]</a></span>
-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&mdash;on an average it may be taken at about 0·001 inch of
-mercury per 400 feet of ascent.</p>
-<p><i>Time.</i>&mdash;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.</p>
-<p>827.&mdash;<span class="large bold">Aneroid Barometer.</span>&mdash;The first introduction of
-this instrument into England was by Pierre Armand, le Comte
-de Fontainmareau.<a name="FNanchor_59_59" id="FNanchor_59_59"></a><a href="#Footnote_59_59" class="fnanchor">[59]</a> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i559">
-  <img class="w100" src="images/i_559.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 393.&mdash;<i>Stanley's civil engineer's aneroid.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_559a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>The aneroid practically in its present form was devised
-by Lucien Vidie from 1848 to 1862.<a name="FNanchor_60_60" id="FNanchor_60_60"></a><a href="#Footnote_60_60" class="fnanchor">[60]</a> 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
-<span class="pagenum"><a name="Page_559" id="Page_559">[559]</a></span>
-exterior spring, the point of communication or tension being
-placed at the centre of its corrugated sides only.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i560">
-  <img class="w100" src="images/i_560.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 394.&mdash;<i>Perspective view of the interior of an aneroid.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_560a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>828.&mdash;The construction of this aneroid is shown in Fig.
-394, which is of a 4&frac12;-inch instrument, aneroids made for
-surveying being of two sizes, 3 inches and 4&frac12; inches. <i>A</i> is a
-solid plate of metal 1/8 inch in thickness, termed the base
-plate; <i>B</i> the vacuum chamber, circularly corrugated on both
-sides, made of thin, hard-rolled German silver containing a
-large percentage of nickel.</p>
-<p>829.&mdash;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 <i>D</i> above it, to be described. A
-bridge-piece <i>EE</i> of steel of strong section strides over the
-vacuum chamber. This piece has a stout arm-piece projecting
-from it towards <i>A</i>, which is secured to the base plate
-by a screw that is left open to a hole indicated near <i>A</i> through
-the outer case of the instrument, by means of which the
-bridge-piece can be rocked so as to produce more or less<span class="pagenum"><a name="Page_560" id="Page_560">[560]</a></span>
-tension of the spring <i>D</i> upon the vacuum chamber for final
-adjustment. The bridge-piece has two points of rigid support
-in right line, which form a primary&mdash;adjusted when the
-instrument is made&mdash;of the spring <i>contra</i> to the pull of the
-vacuum chamber. The <i>main spring D</i> 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 <i>C</i> 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 <i>EE</i>. A <i>lever arm G</i>
-is fixed to the main spring <i>D</i> 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 <i>HK</i>, which communicates through the axis to a second<span class="pagenum"><a name="Page_561" id="Page_561">[561]</a></span>
-cranked arm placed at right angles to the first <i>I</i>. This pulls a
-chain <i>Q</i> attached to the arm <i>J</i>. The chain is wound round a
-small drum fixed upon the axis which carries the hand near <i>R</i>.
-The drum keeps the hand in one direction <i>contra</i> to the pull
-of the chain by a hair spring <i>R</i> which is just sufficient to overcome
-the friction of the axis of the hand <i>F</i>. The hand and
-drum and their fixings are carried by the plate <i>M</i>, which is a
-light piece of brass projected from a stiff standard fixed from
-the base plate <i>K</i>. 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.</p>
-<p>830.&mdash;<i>Compensation for Temperature.</i>&mdash;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 <i>G</i> 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&mdash;iron and brass&mdash;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.</p>
-<p>831.&mdash;<i>Dial and Hand.</i>&mdash;From the delicacy of the structure<span class="pagenum"><a name="Page_562" id="Page_562">[562]</a></span>
-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.</p>
-<p>832.&mdash;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.</p>
-<p>Instruments made with care in the points just indicated
-must necessarily become expensive. Where the aneroid is to<span class="pagenum"><a name="Page_563" id="Page_563">[563]</a></span>
-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.</p>
-<p>833.&mdash;<i>The Altitude Scale</i> 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:&mdash;</p>
-
-<div class="m15 pb1">
-<table summary="" style="border: 1px solid black; border-collapse: collapse;" class="med90">
-<caption style="padding: 1em 0 .5em 0;"><i>Table of Altitude with Barometrical Scale.</i></caption>
-    <tr>
-      <td class="td01a">Height in Feet.</td>
-      <td class="td01a">Barometer in<br />Inches.</td>
-      <td class="td01a">Height in Feet.</td>
-      <td class="td01a">Barometer in<br />Inches.</td>
-    </tr>
-    <tr>
-      <td class="td01caa">0</td>
-      <td class="td01caa" style="padding-right: 2em;">31</td>
-      <td class="td01caa" style="padding-left: .75em;">6000</td>
-      <td class="td01caa">24&middot;875</td>
-    </tr>
-    <tr>
-      <td class="td01cb">250</td>
-      <td class="td01cb">30&middot;717</td>
-      <td class="td01cb" style="padding-left: .75em;">7000</td>
-      <td class="td01cb">23&middot;979</td>
-    </tr>
-    <tr>
-      <td class="td01cb">500</td>
-      <td class="td01cb">30&middot;436</td>
-      <td class="td01cb" style="padding-left: .75em;">8000</td>
-      <td class="td01cb">23&middot;125</td>
-    </tr>
-    <tr>
-      <td class="td01cb">750</td>
-      <td class="td01cb">30&middot;159</td>
-      <td class="td01cb" style="padding-left: .75em;">9000</td>
-      <td class="td01cb">22&middot;282</td>
-    </tr>
-    <tr>
-      <td class="td01cb">1000</td>
-      <td class="td01cb">29&middot;883</td>
-      <td class="td01cb">10,000</td>
-      <td class="td01cb">21&middot;479</td>
-    </tr>
-    <tr>
-      <td class="td01cb">1500</td>
-      <td class="td01cb">29&middot;340</td>
-      <td class="td01cb">11,000</td>
-      <td class="td01cb">20&middot;706</td>
-    </tr>
-    <tr>
-      <td class="td01cb">2000</td>
-      <td class="td01cb">28&middot;807</td>
-      <td class="td01cb">12,000</td>
-      <td class="td01cb">19&middot;959</td>
-    </tr>
-    <tr>
-      <td class="td01cb">2500</td>
-      <td class="td01cb">28&middot;283</td>
-      <td class="td01cb">13,000</td>
-      <td class="td01cb">19&middot;236</td>
-    </tr>
-    <tr>
-      <td class="td01cb">3000</td>
-      <td class="td01cb">27&middot;769</td>
-      <td class="td01cb">14,000</td>
-      <td class="td01cb">18&middot;535</td>
-    </tr>
-    <tr>
-      <td class="td01cb">4000</td>
-      <td class="td01cb">26&middot;769</td>
-      <td class="td01cb">15,000</td>
-      <td class="td01cb">17&middot;853</td>
-    </tr>
-    <tr>
-      <td class="td01c">5000</td>
-      <td class="td01c">25&middot;804</td>
-      <td class="td01c"></td>
-      <td class="td01c"></td>
-    </tr>
-  </table>
-</div>
-<p>It may be generally observed that the more open the scale
-the less altitude can be obtained by a single revolution of the<span class="pagenum"><a name="Page_564" id="Page_564">[564]</a></span>
-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.</p>
-<p>834.&mdash;<i>Movable Altitude Scale.</i>&mdash;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.</p>
-<p>835.&mdash;<i>Adjustment of the Aneroid.</i>&mdash;There is a screw at
-the back of every aneroid somewhere under the point <i>A</i>,
-<a href="#i560">Fig. 394</a>, 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.</p>
-<p>836.&mdash;<i>Directions for Measuring Altitudes.</i>&mdash;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<span class="pagenum"><a name="Page_565" id="Page_565">[565]</a></span>
-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.</p>
-<p>837.&mdash;<i>Various Improvements in the Aneroid.</i>&mdash;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<span class="pagenum"><a name="Page_566" id="Page_566">[566]</a></span>
-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<a name="FNanchor_61_61" id="FNanchor_61_61"></a><a href="#Footnote_61_61" class="fnanchor">[61]</a>
-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<a name="FNanchor_62_62" id="FNanchor_62_62"></a><a href="#Footnote_62_62" class="fnanchor">[62]</a> 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.<a name="FNanchor_63_63" id="FNanchor_63_63"></a><a href="#Footnote_63_63" class="fnanchor">[63]</a></p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i566">
-  <img class="w100" src="images/i_566.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 395.&mdash;<i>Watkin's extended scale surveying aneroid.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_566a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>838.&mdash;<span class="large bold">Watkin's Extended Scale Aneroid.</span>&mdash;This
-instrument is shown at Fig. 395, and has a very extended reading,
-consisting of <i>three complete</i> circles, in place of the usual
-single scale, with a hand or pointer sufficiently long to extend
-<span class="pagenum"><a name="Page_567" id="Page_567">[567]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i567">
-  <img class="w100" src="images/i_567.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 396.&mdash;<i>Face.</i></p>
-    <p class="caption float-right">Fig. 397.&mdash;<i>Back.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_567a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>839.&mdash;<span class="large bold">Watkin's New Patent Mountain Aneroid
-Barometer.</span>&mdash;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<span class="pagenum"><a name="Page_568" id="Page_568">[568]</a></span>
-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.</p>
-<p>It has an aluminium case for lightness, is made in two
-sizes (3 inch and 4&frac12; inch), and has a sling leather case.</p>
-<p>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.</p>
-<p>840.&mdash;An improvement was made in the aneroid in one
-direction by the late Thomas Cooke<a name="FNanchor_64_64" id="FNanchor_64_64"></a><a href="#Footnote_64_64" class="fnanchor">[64]</a> 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.</p>
-<p>841.&mdash;<span class="large bold">Bourdon's Aneroid</span>, invented by C. Bourdon in
-1849.<a name="FNanchor_65_65" id="FNanchor_65_65"></a><a href="#Footnote_65_65" class="fnanchor">[65]</a> The motor of this instrument consists of a flat,
-oval tube bent into a circular form. This tube opens to
-<span class="pagenum"><a name="Page_569" id="Page_569">[569]</a></span>
-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.</p>
-<p>842.&mdash;<span class="large bold">Hypsometer</span>, <i>or Boiling-point Thermometer</i>.&mdash;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.</p>
-
-<div class="figcenter padding1">
-
-<div class="figcenter illowe31" id="i570">
-  <img class="w100" src="images/i_570.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 398.&mdash;<i>Hypsometer, or boiling point thermometer.</i></p>
-    <p class="caption float-right">Fig. 399.&mdash;<i>Case for hypsometer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_570a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>843.&mdash;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 <i>C</i>. The covering tube has a smaller tube, about 3 inches
-long and &frac12; inch diameter leading upwards from it, through
-which the thermometer bulb is passed into the boiler. This
-tube is covered by the <i>jacket J</i>, 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<span class="pagenum"><a name="Page_570" id="Page_570">[570]</a></span>
-&frac34; 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 <i>O</i>. 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 <i>A</i> 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 <i>O</i>, 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<span class="pagenum"><a name="Page_571" id="Page_571">[571]</a></span>
-this arrangement the flame is not seriously disturbed by wind
-or rain.</p>
-<p>844.&mdash;<i>The Thermometer</i>, upon which the action of the
-instrument depends, has a stout stem about 6 inches long and
-&frac14; 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 <i>T</i> when
-in use is surrounded by a vulcanized indiarubber collar <i>I</i> which
-slips over its stem to adjust it to position in the boiler tube as
-shown.</p>
-<p>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.</p>
-<p>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.</p>
-<p>845.&mdash;<i>Use of the Hypsometer.</i>&mdash;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<span class="pagenum"><a name="Page_572" id="Page_572">[572]</a></span>
-temperature above or below 5·5° centigrade at any two stations
-of observation, of which the difference of level is required.
-Thus:&mdash;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.</p>
-<p>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&mdash;</p>
-<p class="center">
-60° Fahr. = 5/9 (60 - 32) = 15·55° centigrade.<br />
-</p>
-<p>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&mdash;</p>
-<div class="m10">
-<table summary="">
-  <tr>
-    <td>211°</td>
-    <td>boil point</td>
-    <td><i>h</i> + 511 feet.</td>
-  </tr>
-  <tr>
-    <td>210°</td>
-    <td class="tdc">"</td>
-    <td><i>h</i> + 511 + 513 = <i>h</i> + 1024 feet.</td>
-  </tr>
-  <tr>
-    <td>209°</td>
-    <td class="tdc">"</td>
-    <td><i>h</i> + 511 + 513 + 515 = <i>h</i> + 1539 feet.</td>
-  </tr>
-</table>
-</div>
-
-<div class="chapter">
-<hr class="chap" />
-<p><span class="pagenum"><a name="Page_573" id="Page_573">[573]</a></span></p>
-<h2>CHAPTER XIX.</h2>
-</div>
-<p class="ch">MISCELLANEOUS SURVEYORS' AND ENGINEERS' INSTRUMENTS,
-APPLIANCES, AND ACCESSORIES&mdash;CROSS STAFF&mdash;MECHANICS'
-LEVELS AND CLINOMETERS&mdash;BONING RODS&mdash;FOOTNER'S
-RAILWAY GAUGE&mdash;GIRTH STRAP FOR TIMBER MEASUREMENT&mdash;GIRTH
-TAPES&mdash;TIMBER MARKER&mdash;SLASHING KNIFE&mdash;BILL-HOOK&mdash;RECONNOITRING
-GLASS&mdash;TELESCOPE&mdash;SUN
-SPECTACLES&mdash;WHISTLES&mdash;PIONEER TOOLS&mdash;SKETCH BLOCK
-BOOK&mdash;CAMERA&mdash;GEOLOGICAL TOOLS&mdash;WEALEMEFNA&mdash;OPISOMETER&mdash;BOUCHER'S
-CALCULATOR&mdash;SLIDE RULES&mdash;FULLER'S
-CALCULATOR&mdash;ENGINEERS' POCKET BOOKS&mdash;CHRONOMETER&mdash;OUTFITS.</p>
-
-<p>846.&mdash;<span class="large bold">Cross Staff.</span>&mdash;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.</p>
-<p>847.&mdash;Cylindrical heads superseded the open cross-head.<span class="pagenum"><a name="Page_574" id="Page_574">[574]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i574">
-  <img class="w100" src="images/i_574.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 400.&mdash;<i>Open cross-head.</i></p>
-    <p class="caption float-right">Fig. 401.&mdash;<i>French form.</i></p>
-    <p class="caption">Fig. 402.&mdash;<i>Adjustable cross staff head.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_574a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>848.&mdash;<span class="large bold">Adjustable Cross Staff Head.</span>&mdash;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 <a href="#i347">Fig. 232</a>, p. 347,<span class="pagenum"><a name="Page_575" id="Page_575">[575]</a></span>
-and very inferior to that instrument owing to the extreme
-closeness of the sights. Its use is obvious.</p>
-<p>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.</p>
-<p>849.&mdash;<span class="large bold">Mechanics' Levels.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i575">
-  <img class="w100" src="images/i_575.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Figs. 403, 404.&mdash;<i>Mechanics' Levels.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_575a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>850.&mdash;<span class="large bold">The Author's Hand Level</span> is shown Fig. 404&mdash;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<span class="pagenum"><a name="Page_576" id="Page_576">[576]</a></span>
-at the other, which is adjustable, so that the tube may be
-easily replaced if broken.</p>
-<p>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.</p>
-<p>851.&mdash;<span class="large bold">Square Level&mdash;Circular Level.</span>&mdash;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&mdash;1&frac12; 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 <a href="#Art_187">p. 96</a>,
-which appears to answer very well.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i576">
-  <img class="w100" src="images/i_576.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 405.&mdash;<i>Square level.</i></p>
-    <p class="caption float-right">Fig. 406.&mdash;<i>Surface level and clinometer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_576a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>852.&mdash;<span class="large bold">Incline Level.</span>&mdash;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 <i>S</i> is commonly
-divided upon the adjustable end. The tube is raised or<span class="pagenum"><a name="Page_577" id="Page_577">[577]</a></span>
-lowered by the key <i>A</i>, which is removed after setting and
-cannot be tampered with.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i577a">
-  <img class="w100" src="images/i_577a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 407.&mdash;<i>Stanley's sight for mechanics' levels.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_577aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<div class="figcenter padding1">
-
-<div class="figcenter illowe33" id="i577b">
-  <img class="w100" src="images/i_577b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 408.&mdash;<i>Section.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_577ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>853.&mdash;<span class="large bold">Sighted Levels.</span>&mdash;A mechanic's level is commonly
-made with a hole longitudinally through it of about &frac12; 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,
-<i>P S</i> one of the pair of points. This, when turned up,
-shoulders on the stop-piece <i>A B</i>. The stop-piece is made of
-sufficient thickness to admit the point in the hole near <i>B</i> for
-protection when it is folded away out of use. The section of<span class="pagenum"><a name="Page_578" id="Page_578">[578]</a></span>
-the level, as shown by the end view <i>D</i>, 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i578">
-  <img class="w100" src="images/i_578.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 409.&mdash;<i>Boning-rod.</i></p>
-    <p class="caption float-right">Fig. 410.&mdash;<i>Boning-rod with standard.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_578a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>854.&mdash;<span class="large bold">Boning-Rods</span>, 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 &frac34; 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 <i>boning forward</i> 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<span class="pagenum"><a name="Page_579" id="Page_579">[579]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i579">
-  <img class="w100" src="images/i_579.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 411.&mdash;<i>Footner's railway gauge and clinometer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_579a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>855.&mdash;<span class="large bold">Railway Gauge</span>, 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 &frac12; 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.</p>
-<p>856.&mdash;<span class="large bold">Timber Girth Strap.</span>&mdash;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, <a href="#Art_775">art. 775</a>, or by the
-apomecometer, <a href="#Art_693">art. 693</a>. The girth is most conveniently taken<span class="pagenum"><a name="Page_580" id="Page_580">[580]</a></span>
-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 <i>quarter-girth</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i580a">
-  <img class="w100" src="images/i_580a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 412.&mdash;<i>Leather girth strap with throwing reel.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_580aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i580b">
-  <img class="w100" src="images/i_580b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 413.&mdash;<i>Leather girth strap with clutch hook.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_580ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>857.&mdash;<span class="large bold">Girth Tapes</span>, similar to measuring tapes, <a href="#i506">Fig. 349</a>,
-p. 506, are occasionally used, but these are more convenient
-for felled timber. Tapes for the purpose are made from
-&frac34; inch to 1 inch wide, and 6, 12, and 24 feet long. They<span class="pagenum"><a name="Page_581" id="Page_581">[581]</a></span>
-have the ordinary feet and inches on one side and quarter-girths
-on the other.</p>
-<p>It is customary to allow 1 or 1&frac12; inches, and sometimes
-more for bark, according to the species of tree and the custom
-of the country.</p>
-<p>858.&mdash;<span class="large bold">Marking off Timber.</span>&mdash;For this a special tool
-with a gouge point, Fig. 414, and strong buck-horn handle,
-termed a <i>timber-marker</i>, 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe35_75" id="i581">
-  <img class="w100" src="images/i_581.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 414.&mdash;<i>Timber marker, nearly full size.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_581a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>859.&mdash;The author makes a very small, neat surveyor's
-knife, with marker, for the waistcoat pocket, Fig. 415, which
-combines&mdash;<i>M</i> tree marker (small); <i>S</i> screw-driver for small
-screws of instruments; <i>P</i> tommy-pin for turning capstan heads;
-<i>F</i> file for sharpening lead of pencil, when this is used for the
-field-book; and <i>E</i> <i>R</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i581b">
-  <img class="w100" src="images/i_581b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 415.&mdash;<i>Surveyor's pocket knife.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_581ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p><span class="pagenum"><a name="Page_582" id="Page_582">[582]</a></span></p>
-<p>860.&mdash;<span class="large bold">Slashing Knife&mdash;Bill-Hook&mdash;Axe.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i582">
-  <img class="w100" src="images/i_582.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 416.&mdash;<i>Slashing knife.</i></p>
-    <p class="caption float-right">Fig. 417.&mdash;<i>Bill-hook.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_582a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>861.&mdash;<i>Hedging Gloves&mdash;Iron Hooks for Climbing Trees.</i>&mdash;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.</p>
-<p>862.&mdash;<span class="large bold">Rods for Measuring Standing Timber.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i583a">
-  <img class="w100" src="images/i_583a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 418.&mdash;<i>Reconnoitring glass, India pattern.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_583aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>863.&mdash;<span class="large bold">Reconnoitring Glass.</span>&mdash;At present it is customary
-to use a binocular field-glass in preference to a
-telescope. The telescope gives greater penetration from its<span class="pagenum"><a name="Page_583" id="Page_583">[583]</a></span>
-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 1&frac34; inches, not over this.
-Where a telescope is used, the 30-inch&mdash;the original, not the
-present&mdash;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<span class="pagenum"><a name="Page_584" id="Page_584">[584]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i583b">
-  <img class="w100" src="images/i_583b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 419.&mdash;<i>Army telescope.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_583ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>864.&mdash;<span class="large bold">Prism Binoculars.</span>&mdash;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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i584">
-  <img class="w100" src="images/i_584.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 420.&mdash;<i>Stanley's prism binocular.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_584a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>865.&mdash;<span class="large bold">Dome Spectacles&mdash;Bogles.</span>&mdash;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 <i>bogles</i>. 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.</p>
-<p><span class="pagenum"><a name="Page_585" id="Page_585">[585]</a></span></p>
-<p>866.&mdash;<span class="large bold">Whistles</span> made very powerful are much used in
-exploring abroad to bring the party together, and for signalling
-generally by sound, using the Morse signals, <a href="#Art_803">art. 803</a>.</p>
-<p>867.&mdash;<span class="large bold">Pioneers' Tools.</span>&mdash;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 2&frac12; inches; it weighs 1&frac34; 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.</p>
-<p>868.&mdash;<span class="large bold">Sketch Block Book&mdash;Pocket Book.</span>&mdash;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.</p>
-<p>869.&mdash;<span class="large bold">Camera.</span>&mdash;Recently the camera has been much
-used for reconnoitring. These are now made very light and
-portable to take &frac14; plate or 3 × 3 inch films, either on rollers
-or in separate films.</p>
-<p>870.&mdash;<span class="large bold">Cement Testers</span> 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&mdash;it tests the adhesion of the cement to<span class="pagenum"><a name="Page_586" id="Page_586">[586]</a></span>
-stone, which appears to the author to be its most important
-function; it is always hard enough.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe34_875" id="i586a">
-  <img class="w100" src="images/i_586a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 421.&mdash;<i>Mann's cement tester.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_586aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>871.&mdash;<span class="large bold">Watson's Improved Vicat Needle</span> 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<span class="pagenum"><a name="Page_587" id="Page_587">[587]</a></span>
-lowered into it by means of the handle at the top. The
-depth of penetration is shown in millimetres on the divided
-arc.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe30_9375" id="i586b">
-  <img class="w100" src="images/i_586b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 422.&mdash;<i>Watson's vicat needle.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_586ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>872.&mdash;<span class="large bold">Geological Tools.</span>&mdash;<i>Acid-bottle&mdash;Blow-pipe&mdash;Touch-stone.</i>&mdash;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&mdash;sulphuric
-and nitric&mdash;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.</p>
-<p>873.&mdash;<span class="large bold">Wealemefna&mdash;Opisometer.</span>&mdash;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.</p>
-<p><span class="pagenum"><a name="Page_588" id="Page_588">[588]</a></span></p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe32_625" id="i588">
-  <img class="w100" src="images/i_588.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 423.&mdash;<i>Wealemefna.</i></p>
-    <p class="caption float-right">Fig. 424.&mdash;<i>Opisometer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_588a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>874.&mdash;Boucher Calculator, the invention of M. Alex.
-E. M. Boucher, engineer, of Paris.<a name="FNanchor_66_66" id="FNanchor_66_66"></a><a href="#Footnote_66_66" class="fnanchor">[66]</a> 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,
-<span class="pagenum"><a name="Page_589" id="Page_589">[589]</a></span>
-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:&mdash;</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i589">
-  <img class="w100" src="images/i_589.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption float-left">Fig. 425.&mdash;<i>Boucher's calculator.</i></p>
-    <p class="caption float-right">Fig. 426.&mdash;<i>Stanley-Boucher calculator.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_589a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>Multiplication, using the second circle of divisions from
-the outside of the front dial:&mdash;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.</p>
-<p>Division is performed on the same scale as follows:&mdash;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.</p>
-<p>For proportion the second circle is also used:&mdash;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.</p>
-<p><span class="pagenum"><a name="Page_590" id="Page_590">[590]</a></span></p>
-<p>Square roots, using the same scale:&mdash;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.</p>
-<p>Cube root:&mdash;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.</p>
-<p>To use the trigonometrical dial:&mdash;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.</p>
-<p>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.</p>
-<p>875.&mdash;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.</p>
-<p>876.&mdash;<span class="large bold">Slide Rules</span>, 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 <i>Gunter's lines</i>, are placed upon most
-slide rules. The arithmetical lines are lettered <i>A</i>, <i>B</i>, <i>C</i>, <i>D</i>,
-and <i>E</i>. <i>A</i> and <i>B</i> are alike: these are technically termed
-<i>double radius log. lines</i>. They are used for all processes of
-multiplication and division. <i>C</i> and <i>D</i> are also alike and are
-termed <i>single radius log. lines</i>. They are used together for
-ordinary multiplication and division, and in conjunction with
-A and B scales for squares and square roots. The <i>E</i>
-line, not originally a Gunter's line, but found early in the
-century on several rules, is termed a <i>triple radius log. line</i>.<span class="pagenum"><a name="Page_591" id="Page_591">[591]</a></span>
-The numbers of the divisions on this line are the cubes of the
-numbers of the corresponding divisions of the <i>D</i> 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:&mdash;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 <i>A</i> to
-<i>C</i> 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.</p>
-<p>877.&mdash;<i>The Slide Rules</i> 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.</p>
-<p>878.&mdash;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.</p>
-<p>A great number of slide rules are made for special
-purposes only: some of these are very useful to the civil
-engineer.</p>
-<p>879.&mdash;<i>Hudson's Slide Rules</i> give strength of shafts, beams,
-and girders; pump duty; and computation of horse-power in
-engines.</p>
-<p>880.&mdash;<i>Honeysett's Hydraulic Slide Rule</i> gives discharge of<span class="pagenum"><a name="Page_592" id="Page_592">[592]</a></span>
-water from channels and pipes of different forms and
-inclinations.</p>
-<p>881.&mdash;<i>Tacheometrical Slide Rules</i> with scale of sine<sup>2</sup> 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.</p>
-<p>882.&mdash;<i>Sheppard's Slide Rule</i> has duodecimal lines, double
-reading, for squaring and cubing timber.</p>
-<p>883.&mdash;<i>Young's Slide Rule</i> is designed for squaring and
-valuing timber simultaneously, which operations it performs
-in a very expeditious manner.</p>
-<p>884.&mdash;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.</p>
-<p>885.&mdash;<span class="large bold">The Slide Rule of Prof. Geo. Fuller, C.E.</span>,
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i592">
-  <img class="w100" src="images/i_592.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 427.&mdash;<i>Professor Fuller's calculating slide scale.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_592a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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,<span class="pagenum"><a name="Page_593" id="Page_593">[593]</a></span>
-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<span class="pagenum"><a name="Page_594" id="Page_594">[594]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe22_3125" id="i593">
-  <img class="w100" src="images/i_593.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 428.&mdash;<i>Improved Fuller's slide rule.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_593a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-<p>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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i595a">
-  <img class="w100" src="images/i_595a.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 429.&mdash;<i>Barnard's co-ordinate spiral slide rule.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_595aa.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>886.&mdash;<span class="large bold">The Co-ordinate Spiral Slide Rule</span> has been
-designed to meet these requirements by Mr. H. O. Barnard,
-A.C.H., F.R.A.S., etc., Superintendent of Trigonometrical<span class="pagenum"><a name="Page_595" id="Page_595">[595]</a></span>
-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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i595b">
-  <img class="w100" src="images/i_595b.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 430.&mdash;<i>Thacher's slide rule.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_595ba.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>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.</p>
-<p>887.&mdash;<span class="large bold">Thacher's Slide Rule.</span>&mdash;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<span class="pagenum"><a name="Page_596" id="Page_596">[596]</a></span>
-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.</p>
-<p>888.&mdash;<span class="large bold">Pocket Sets of Chain Scales.</span>&mdash;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.</p>
-
-<div class="figcenter padding-top1">
-
-<div class="figcenter illowe37_5" id="i596">
-  <img class="w100" src="images/i_596.png"  alt="" />
-</div>
-
-  <div class="caption">
-    <p class="caption float-left">Fig. 431.&mdash;<i>Biram's anemometer.</i></p>
-    <p class="caption float-right">Fig. 432.&mdash;<i>Lowne's anemometer.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_596a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>889.&mdash;<span class="large bold">Anemometers</span> 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<span class="pagenum"><a name="Page_597" id="Page_597">[597]</a></span>
-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.</p>
-<p>890.&mdash;<span class="large bold">Books of Tables and Formulæ.</span>&mdash;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&mdash;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 <i>Civil Engineer's
-Pocket-book</i> (American) is the most complete, but it is of
-double the weight of the Molesworth. Spon's <i>Engineers'
-Tables for the Waistcoat Pocket</i>&mdash;weight, little over &frac12; oz.&mdash;is
-a very useful little book. Of <i>Traverse Tables</i> both
-Gurden's and Boileau's are comprehensive and reliable.
-There are several pocket-books of <i>Curve Tables</i>, those of
-Cutler &amp; Edge, Beazeley, and Kennedy &amp; Hackwood being
-perhaps in the most general use.</p>
-<p>891.&mdash;<span class="large bold">Technical Books&mdash;Ordnance Maps</span> 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.</p>
-<p>892.&mdash;<span class="large bold">Sling Case for Drawings.</span>&mdash;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.</p>
-<p><span class="pagenum"><a name="Page_598" id="Page_598">[598]</a></span></p>
-<p>893.&mdash;<span class="large bold">Chronometer.</span>&mdash;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 <i>pro ratâ</i> 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.</p>
-
-<div class="figcenter padding1">
-<div class="figcenter illowe37_5" id="i598">
-  <img class="w100" src="images/i_598.png"  alt="" />
-</div>
-  <div class="caption">
-    <p class="caption">Fig. 433.&mdash;<i>Sling case for drawings.</i></p>
-    <p class="caption ebhide clear"><a href="images/i_598a.png" rel="nofollow">Larger image</a></p>
-  </div>
-</div>
-
-<p>894.&mdash;<span class="large bold">Chronograph.</span>&mdash;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.</p>
-<p>895.&mdash;<span class="large bold">Outfit of a Surveyor for Work in a New
-Country.</span>&mdash;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&mdash;the sextant,<span class="pagenum"><a name="Page_599" id="Page_599">[599]</a></span>
-or box sextant with glass artificial horizon, good pocket
-chronometer, <i>telescope</i>, 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.</p>
-
-<hr class="chap" />
-
-<h2>INDEX</h2>
-<p><span class="pagenum"><a name="Page_601" id="Page_601">[601]</a></span></p>
-
-<div class="figcenter">
-<img src="images/i_hr.png" width="57" height="8" alt="" />
-</div>
-
-<div class="center padding-top1 padding-bottom0">
-<table style="width:75%; border-collapse: collapse;" border="1" summary="alpha jump table">
-	<tr>
-		<td class="ix"><a href="#IX_A">A</a></td>
-		<td class="ix"><a href="#IX_B">B</a></td>
-		<td class="ix"><a href="#IX_C">C</a></td>
-		<td class="ix"><a href="#IX_D">D</a></td>
-		<td class="ix"><a href="#IX_E">E</a></td>
-		<td class="ix"><a href="#IX_F">F</a></td>
-		<td class="ix"><a href="#IX_G">G</a></td>
-		<td class="ix"><a href="#IX_H">H</a></td>
-		<td class="ix"><a href="#IX_I">I</a></td>
-		<td class="ix"><a href="#IX_L">L</a></td>
-		<td class="ix"><a href="#IX_M">M</a></td>
-	</tr>
-	<tr>
-		<td class="ix"><a href="#IX_N">N</a></td>
-		<td class="ix"><a href="#IX_O">O</a></td>
-		<td class="ix"><a href="#IX_P">P</a></td>
-		<td class="ix"><a href="#IX_Q">Q</a></td>
-		<td class="ix"><a href="#IX_R">R</a></td>
-		<td class="ix"><a href="#IX_S">S</a></td>
-		<td class="ix"><a href="#IX_T">T</a></td>
-		<td class="ix"><a href="#IX_V">V</a></td>
-		<td class="ix"><a href="#IX_W">W</a></td>
-		<td class="ix"><a href="#IX_Y">Y</a></td>
-	</tr>
-</table>
-</div>
-
-
-<ul class="IX">
-<li><a id="IX_A" name="IX_A"></a>Abney's clinometer, <a href="#Page_411">411</a></li>
-<li>Achromatism explained, <a href="#Page_35">35</a></li>
-<li>Adjustable axis, of plane table, <a href="#Page_479">479</a>
-  <ul class="IXa">
-  <li>of theodolite, <a href="#Page_237">237</a></li>
-  </ul></li>
-<li>Adjustable tripod, <a href="#Page_329">329</a></li>
-<li>Alidades for plane tables, <a href="#Page_473">473</a></li>
-<li>Alloys used for surveying instruments, <a href="#Page_7">7</a></li>
-<li>Altazimuth theodolite, <a href="#Page_295">295</a></li>
-<li>Altitudes, measurements of, <a href="#Page_550">550</a></li>
-<li>Aluminium alloys, <a href="#Page_8">8</a></li>
-<li>Anallatic telescope, <a href="#Page_364">364</a></li>
-<li>Anemometers, <a href="#Page_596">596</a></li>
-<li>Aneroid barometers, Vidie's, <a href="#Page_558">558</a>
-  <ul class="IXa">
-  <li>Bourdon's, <a href="#Page_568">568</a></li>
-  </ul></li>
-<li>Apomecometer, <a href="#Page_469">469</a></li>
-<li>Arrows, for chain, <a href="#Page_494">494</a></li>
-<li>Artificial horizons, <a href="#Page_443">443</a></li>
-<li>Atmospheric pressure, measurements of, <a href="#Page_550">550</a></li>
-<li>Axes, workmanship in, <a href="#Page_11">11</a></li>
-</ul>
-
-<ul class="IX">
-<li><a id="IX_B" name="IX_B"></a>Bakewell's tangential index, <a href="#Page_384">384</a></li>
-<li>Ball and socket adjustments: Hoffmann's, Pastorelli's, <a href="#Page_330">330</a></li>
-<li>Bands, steel, for measuring land, <a href="#Page_449">449</a></li>
-<li>Barker's clinometer, <a href="#Page_415">415</a></li>
-<li>Barometer, aneroid, <a href="#Page_558">558</a>
-  <ul class="IXa">
-  <li>mountain, <a href="#Page_550">550</a></li>
-  <li>mercurial, <a href="#Page_549">549</a></li>
-  </ul></li>
-<li>Base line apparatus, <a href="#Page_517">517</a></li>
-<li>Beam compass measurements, <a href="#Page_510">510</a></li>
-<li>Bellamy's road tracer, <a href="#Page_420">420</a></li>
-<li>Bill-hook, <a href="#Page_582">582</a></li>
-<li>Binoculars, prism, <a href="#Page_584">584</a></li>
-<li>Black, optical, <a href="#Page_14">14</a></li>
-<li>Boiling-point thermometer, hypsometer, <a href="#Page_569">569</a></li>
-<li>Boning rods, <a href="#Page_578">578</a></li>
-<li>Books, levelling, <a href="#Page_173">173</a></li>
-<li>Boucher's calculator, <a href="#Page_587">587</a>
-  <ul class="IXa">
-  <li>improved, <a href="#Page_590">590</a></li>
-  </ul></li>
-<li>Box sextant, <a href="#Page_451">451</a>
-  <ul class="IXa">
-  <li>with continuous arc, <a href="#Page_461">461</a></li>
-  <li>with supplementary arc, <a href="#Page_458">458</a></li>
-  </ul></li>
-<li>Bronzing instruments, <a href="#Page_14">14</a></li>
-<li>Brunton mine transit, <a href="#Page_353">353</a></li>
-<li>Bubble trier, <a href="#Page_88">88</a></li>
-<li>Burel's reflecting level, <a href="#Page_144">144</a></li>
-<li>Burnier's clinometer, <a href="#Page_416">416</a></li>
-</ul>
-
-<ul class="IX">
-<li><a id="IX_C" name="IX_C"></a>Caink's rule for correcting inclines, <a href="#Page_498">498</a></li>
-<li>Calculators: Barnard's, <a href="#Page_594">594</a>
-  <ul class="IXa">
-  <li>Boucher's, <a href="#Page_587">587</a></li>
-  <li>Fuller's, <a href="#Page_592">592</a></li>
-  <li>Thacher's, <a href="#Page_595">595</a></li>
-  </ul></li>
-<li>Camera, <a href="#Page_243">243</a>, <a href="#Page_585">585</a></li>
-<li>Cases, for carrying maps, <a href="#Page_597">597</a>
-  <ul class="IXa">
-  <li>leather, for instruments, <a href="#Page_23">23</a></li>
-  </ul></li>
-<li>Cavalry sketching case, <a href="#Page_488">488</a></li>
-<li>Cement tester, Mann's, <a href="#Page_585">585</a></li>
-<li>Centesimal division, <a href="#Page_185">185</a></li>
-<li>Chain scales, pocket sets, <a href="#Page_596">596</a></li>
-<li>Chain vice, <a href="#Page_496">496</a></li>
-<li>Chaining, <a href="#Page_497">497</a></li>
-<li>Chains, land, various, <a href="#Page_490">490</a></li>
-<li>Chains, sounding, <a href="#Page_526">526</a></li>
-<li>Chronometer and chronograph, <a href="#Page_598">598</a></li>
-<li>Circumferentor, <a href="#Page_307">307</a></li>
-<li>Clamp and tangent motions, various, <a href="#Page_202">202</a></li>
-<li>Classification of instruments, <a href="#Page_5">5</a></li>
-<li>Clinometer compasses, <a href="#Page_418">418</a>
-  <ul class="IXa">
-  <li>hanging, <a href="#Page_344">344</a></li>
-  </ul></li>
-<li>Clinometers, various, <a href="#Page_411">411</a></li>
-<li>Coast survey lines, <a href="#Page_527">527</a></li>
-<li>Coincidence rods, <a href="#Page_511">511</a></li>
-<li>Collimation, <a href="#Page_55">55</a></li>
-<li>Collimator, <a href="#Page_121">121</a></li>
-<li>Compass, surveying with, <a href="#Page_80">80</a></li>
-<li>Compasses: magnetic, bar, <a href="#Page_59">59</a>
-  <ul class="IXa">
-  <li>Barker's, <a href="#Page_84">84</a></li>
-  <li>Burnier's, <a href="#Page_80">80</a></li>
-  <li>hanging, <a href="#Page_344">344</a></li>
-  <li>Hutchinson's, <a href="#Page_79">79</a></li>
-  <li>luminous, <a href="#Page_84">84</a></li>
-  <li>mariners', <a href="#Page_73">73</a></li>
-  <li>prismatic, <a href="#Page_75">75</a></li>
-  <li>pocket, <a href="#Page_82">82</a></li>
-  <li>ring, <a href="#Page_72">72</a></li>
-  <li>trough, <a href="#Page_74">74</a>, <a href="#Page_83">83</a></li>
-  </ul></li>
-<li>Compensated rods, <a href="#Page_512">512</a></li>
-<li>Connecting link, to extend hand rods, <a href="#Page_531">531</a></li>
-<li>Convex and concave lenses, <a href="#Page_32">32</a></li>
-<li>Cooke's level, <a href="#Page_138">138</a></li>
-<li>Co-ordinate slide rule, <a href="#Page_594">594</a></li>
-<li>Cross-staff heads, <a href="#Page_573">573</a></li>
-<li>Curvature, correction for, <a href="#Page_170">170</a></li>
-<li>Cushing's level, <a href="#Page_136">136</a></li>
-</ul>
-
-<ul class="IX">
-<li><a id="IX_D" name="IX_D"></a>De Lisle's reflecting clinometer, <a href="#Page_413">413</a></li>
-<li>Declination of needles, <a href="#Page_67">67</a></li>
-<li>Deville's theodolite, <a href="#Page_263">263</a></li>
-<li>Diagonal eye-piece, <a href="#Page_45">45</a></li>
-<li>Dials, mining, <a href="#Page_309">309</a></li>
-<li>Diaphragm of telescope, <a href="#Page_50">50</a>, <a href="#Page_114">114</a>, <a href="#Page_135">135</a></li>
-<li>Dip compass, <a href="#Page_354">354</a></li>
-<li>Dip of needles, <a href="#Page_66">66</a></li>
-<li>Dispersion of light, <a href="#Page_35">35</a></li>
-<li>Dividing engine, <a href="#Page_176">176</a></li>
-<li>Division of the circle, <a href="#Page_175">175</a></li>
-<li>Double optical square, <a href="#Page_467">467</a></li>
-<li>Drop arrow, <a href="#Page_494">494</a></li>
-<li>Dumpy level, <a href="#Page_110">110</a>
-  <ul class="IXa">
-  <li>improved, <a href="#Page_123">123</a></li>
-  </ul></li>
-<li>Dynameter, <a href="#Page_43">43</a></li>
-</ul>
-
-<ul class="IX">
-<li><a id="IX_E" name="IX_E"></a>Edgeworth's stadiometer, <a href="#Page_482">482</a></li>
-<li>Engineer's level, <a href="#Page_133">133</a></li>
-<li>Engraving, note on, <a href="#Page_16">16</a></li>
-<li>Everest's theodolite, <a href="#Page_271">271</a>
-  <ul class="IXa">
-  <li>tripod, <a href="#Page_273">273</a></li>
-  </ul></li>
-<li>Excise ink bottle, <a href="#Page_174">174</a></li>
-<li>Eye-pieces: Ramsden, <a href="#Page_41">41</a>
-  <ul class="IXa">
-  <li>erecting, <a href="#Page_44">44</a></li>
-  <li>diagonal, <a href="#Page_45">45</a></li>
-  <li>reflecting, <a href="#Page_46">46</a></li>
-  </ul></li>
-</ul>
-
-<ul class="IX">
-<li><a id="IX_F" name="IX_F"></a>Field-books, <a href="#Page_289">289</a>, <a href="#Page_374">374</a>, <a href="#Page_380">380</a></li>
-<li>Field-glasses, <a href="#Page_582">582</a></li>
-<li>Finishing of surveying instruments, <a href="#Page_14">14</a></li>
-<li>Formation of images in a telescope, <a href="#Page_33">33</a></li>
-<li>French forms of miners' dials, <a href="#Page_336">336</a></li>
-<li>Fuller's rule, <a href="#Page_592">592</a></li>
-</ul>
-
-<ul class="IX">
-<li><a id="IX_G" name="IX_G"></a>Geological tools, <a href="#Page_587">587</a></li>
-<li>George's artificial horizon, <a href="#Page_446">446</a></li>
-<li>Girth straps, tapes, etc., <a href="#Page_579">579</a></li>
-<li>Glass diaphragm, <a href="#Page_53">53</a></li>
-<li>Glass, working, 16 refraction of, <a href="#Page_25">25</a></li>
-<li>Gradient scale, <a href="#Page_213">213</a></li>
-<li>Gradienter Screw, <a href="#Page_386">386</a></li>
-<li>Gradiometer, <a href="#Page_404">404</a></li>
-<li>Gradioplane, <a href="#Page_409">409</a></li>
-<li>Graduation, <a href="#Page_179">179</a></li>
-<li>Green, William, Subtense instruments, <a href="#Page_355">355</a></li>
-</ul>
-
-<ul class="IX">
-<li><a id="IX_H" name="IX_H"></a>Hadley's quadrant, <a href="#Page_423">423</a></li>
-<li>Hanging mining compass, <a href="#Page_344">344</a></li>
-<li>Hedley's dial, <a href="#Page_322">322</a>
-  <ul class="IXa">
-  <li>improved, <a href="#Page_326">326</a>, <a href="#Page_329">329</a>, <a href="#Page_333">333</a></li>
-  </ul></li>
-<li>Heliograph, <a href="#Page_540">540</a></li>
-<li>Heliostat and heliotrope, <a href="#Page_537">537</a></li>
-<li>Henderson's miners' dial, <a href="#Page_315">315</a></li>
-<li>Hick's patent level, <a href="#Page_96">96</a></li>
-<li>Historical sketch of surveying instruments, <a href="#Page_1">1</a></li>
-<li>Hoffmann's ball and socket head, <a href="#Page_330">330</a></li>
-<li>Horizontal scale of tangents, <a href="#Page_213">213</a></li>
-<li>Hypotenuse and base, <a href="#Page_212">212</a></li>
-<li>Hypsometer, <a href="#Page_569">569</a></li>
-</ul>
-
-<ul class="IX">
-<li><a id="IX_I" name="IX_I"></a>Illumination of axis of telescope, <a href="#Page_234">234</a></li>
-<li>Inclinometer: Lister's, <a href="#Page_389">389</a></li>
-</ul>
-
-<ul class="IX">
-<li><a id="IX_L" name="IX_L"></a>Lacquering work, <a href="#Page_15">15</a></li>
-<li>Lamp, magnesium, <a href="#Page_545">545</a>
-  <ul class="IXa">
-  <li>for levelling, <a href="#Page_169">169</a></li>
-  <li>mining, <a href="#Page_348">348</a></li>
-  <li>theodolite, <a href="#Page_235">235</a></li>
-  </ul></li>
-<li>Land chains, <a href="#Page_490">490</a>
-  <ul class="IXa">
-  <li>vice for adjusting, <a href="#Page_496">496</a></li>
-  </ul></li>
-<li>Lanterns, oil, <a href="#Page_545">545</a></li>
-<li>Lean's miners' dial, <a href="#Page_315">315</a></li>
-<li>Leather cases, <a href="#Page_23">23</a></li>
-<li>Lenses, <a href="#Page_33">33</a>
-  <ul class="IXa">
-  <li>achromatic, <a href="#Page_36">36</a></li>
-  </ul></li>
-<li>Level: for levelling staff, <a href="#Page_163">163</a>
-  <ul class="IXa">
-  <li>mechanics', <a href="#Page_575">575</a></li>
-  <li>with inclines, <a href="#Page_576">576</a></li>
-  </ul></li>
-<li>Levels: surveyors', <a href="#Page_97">97</a>
-  <ul class="IXa">
-  <li>Cooke's, <a href="#Page_138">138</a></li>
-  <li>Cushing's, <a href="#Page_136">136</a></li>
-  <li>dumpy, <a href="#Page_110">110</a></li>
-  <li>same improved, <a href="#Page_123">123</a></li>
-  <li>engineers', <a href="#Page_133">133</a></li>
-  <li>reflecting, <a href="#Page_144">144</a></li>
-  <li>pocket, <a href="#Page_142">142</a></li>
-  <li>simple construction of, <a href="#Page_141">141</a></li>
-  <li>supplementary parts to, <a href="#Page_139">139</a></li>
-  <li>water, <a href="#Page_146">146</a></li>
-  <li>Y-form, <a href="#Page_98">98</a></li>
-  <li>same improved, <a href="#Page_107">107</a></li>
-  </ul></li>
-<li>Level tubes, <a href="#Page_86">86</a>
-  <ul class="IXa">
-  <li>circular, <a href="#Page_96">96</a>, <a href="#Page_576">576</a></li>
-  <li>curvature of, <a href="#Page_87">87</a></li>
-  <li>divisions upon, <a href="#Page_90">90</a></li>
-  <li>readers for, <a href="#Page_95">95</a></li>
-  <li>Scott's, <a href="#Page_93">93</a></li>
-  <li>sensitiveness of, <a href="#Page_89">89</a></li>
-  <li>Strange's, <a href="#Page_92">92</a></li>
-  <li>with air cell, <a href="#Page_93">93</a></li>
-  </ul></li>
-<li>Level tube trier, <a href="#Page_88">88</a></li>
-<li>Levelling: books, <a href="#Page_172">172</a>
-  <ul class="IXa">
-  <li>staves, telescopic, <a href="#Page_148">148</a></li>
-  <li>semicircular, <a href="#Page_150">150</a></li>
-  <li>mining, <a href="#Page_158">158</a></li>
-  <li>papering of, <a href="#Page_159">159</a></li>
-  <li>preservation of, <a href="#Page_161">161</a></li>
-  <li>various patterns of, <a href="#Page_151">151</a></li>
-  <li>holder for, <a href="#Page_163">163</a></li>
-  <li>pads for, <a href="#Page_161">161</a></li>
-  <li>pegs for, <a href="#Page_171">171</a></li>
-  <li>practice of, <a href="#Page_163">163</a></li>
-  </ul></li>
-<li>Light for night observations, <a href="#Page_169">169</a>, <a href="#Page_545">545</a></li>
-<li>Light, refraction of, <a href="#Page_27">27</a></li>
-<li>Line, sounding, <a href="#Page_527">527</a></li>
-<li>Lubrication of joints, etc., <a href="#Page_20">20</a></li>
-<li>Luminous compass, <a href="#Page_84">84</a></li>
-</ul>
-
-<ul class="IX">
-<li><a id="IX_M" name="IX_M"></a>Magnesium lamp, <a href="#Page_546">546</a></li>
-<li>Magnetic compasses, <a href="#Page_59">59</a>
-  <ul class="IXa">
-  <li>correction of, <a href="#Page_64">64</a></li>
-  <li>declination of, <a href="#Page_67">67</a></li>
-  <li>inclination of, <a href="#Page_66">66</a></li>
-  <li>trough, <a href="#Page_74">74</a></li>
-  <li>variation of, <a href="#Page_68">68</a></li>
-  <li>various forms, <a href="#Page_82">82</a></li>
-  </ul></li>
-<li>Magnetic needles, <a href="#Page_59">59</a>
-  <ul class="IXa">
-  <li>lifting, <a href="#Page_65">65</a></li>
-  <li>mounting, <a href="#Page_64">64</a></li>
-  </ul></li>
-<li>Magnetic needles, various, <a href="#Page_59">59</a></li>
-<li>Magnetism, <a href="#Page_59">59</a>
-  <ul class="IXa">
-  <li>preservation of, <a href="#Page_71">71</a></li>
-  </ul></li>
-<li>Magnifying power of telescope, <a href="#Page_43">43</a></li>
-<li>Measuring rods, <a href="#Page_530">530</a></li>
-<li>Mechanics' levels, <a href="#Page_575">575</a></li>
-<li>Mercurial barometer, <a href="#Page_549">549</a></li>
-<li>Metals employed in surveying instruments, <a href="#Page_7">7</a></li>
-<li>Micrometer microscopes: various, <a href="#Page_192">192</a>
-  <ul class="IXa">
-  <li>Stanley's, <a href="#Page_197">197</a></li>
-  </ul></li>
-<li>Micrometer theodolites, <a href="#Page_259">259</a></li>
-<li>Military sketching board, <a href="#Page_485">485</a>
-  <ul class="IXa">
-  <li>cavalry, <a href="#Page_488">488</a></li>
-  </ul></li>
-<li>Miners' circumferentor, <a href="#Page_307">307</a></li>
-<li>Miners' compasses: French, <a href="#Page_336">336</a>
-  <ul class="IXa">
-  <li>hanging, <a href="#Page_344">344</a></li>
-  <li>Stanley's prismatic, <a href="#Page_343">343</a></li>
-  </ul></li>
-<li>Miners' dials: various, <a href="#Page_309">309</a>
-  <ul class="IXa">
-  <li>hanging, <a href="#Page_344">344</a></li>
-  <li>Hedley's, <a href="#Page_322">322</a></li>
-  <li>Henderson's, <a href="#Page_315">315</a></li>
-  <li>Lean's, <a href="#Page_315">315</a></li>
-  <li>improvements in Hedley's dial, <a href="#Page_326">326</a>, <a href="#Page_329">329</a>, <a href="#Page_333">333</a></li>
-  </ul></li>
-<li>Mining, survey lamp, <a href="#Page_348">348</a>
-  <ul class="IXa">
-  <li>targets, <a href="#Page_349">349</a></li>
-  <li>theodolite, <a href="#Page_342">342</a></li>
-  </ul></li>
-<li>Morse signaling, <a href="#Page_544">544</a></li>
-<li>Mountain barometer, <a href="#Page_550">550</a>
-  <ul class="IXa">
-  <li>theodolite, <a href="#Page_258">258</a></li>
-  </ul></li>
-</ul>
-
-<ul class="IX">
-<li><a id="IX_N" name="IX_N"></a>Nautical sextant, <a href="#Page_429">429</a></li>
-<li>Needles, magnetic, <a href="#Page_59">59</a></li>
-<li>Night signalling stations, <a href="#Page_545">545</a></li>
-</ul>
-
-<ul class="IX">
-<li><a id="IX_O" name="IX_O"></a>Octant or quadrant, <a href="#Page_422">422</a></li>
-<li>Offset rods, <a href="#Page_507">507</a></li>
-<li>Omnimeter, <a href="#Page_374">374</a></li>
-<li>Opisometer, <a href="#Page_587">587</a></li>
-<li>Optical black, <a href="#Page_14">14</a></li>
-<li>Optical principles of telescope, <a href="#Page_25">25</a></li>
-<li>Optical square, <a href="#Page_465">465</a></li>
-<li>Outfits for surveyors abroad, <a href="#Page_598">598</a></li>
-</ul>
-
-<ul class="IX">
-<li><a id="IX_P" name="IX_P"></a>Packing of instruments, <a href="#Page_21">21</a></li>
-<li>Parallax, in eye-piece, <a href="#Page_55">55</a></li>
-<li>Parallel plates, to level, <a href="#Page_99">99</a>
-  <ul class="IXa">
-  <li>to theodolite, <a href="#Page_219">219</a></li>
-  </ul></li>
-<li>Passometer, <a href="#Page_525">525</a></li>
-<li>Pastorelli's ball and socket head, <a href="#Page_330">330</a></li>
-<li>Pedometer, <a href="#Page_524">524</a></li>
-<li>Perambulator, <a href="#Page_521">521</a></li>
-<li>Permanent stations, <a href="#Page_535">535</a></li>
-<li>Pickets or ranging poles, <a href="#Page_533">533</a></li>
-<li>Pine measuring rods, <a href="#Page_508">508</a></li>
-<li>Pioneer tools, <a href="#Page_585">585</a></li>
-<li>Photographic camera, <a href="#Page_243">243</a>, <a href="#Page_585">585</a></li>
-<li>Plain theodolite, <a href="#Page_215">215</a>, <a href="#Page_267">267</a></li>
-<li>Plane tables, <a href="#Page_472">472</a></li>
-<li>Platinum-iridium points, <a href="#Page_53">53</a>, <a href="#Page_129">129</a>, <a href="#Page_135">135</a></li>
-<li>Plummets, <a href="#Page_232">232</a></li>
-<li>Pocket-books, <a href="#Page_534">534</a>, <a href="#Page_596">596</a></li>
-<li>Pocket levels, <a href="#Page_96">96</a>
-  <ul class="IXa">
-  <li>sighted, <a href="#Page_142">142</a>, <a href="#Page_525">525</a></li>
-  </ul></li>
-<li>Pocket magnetic compasses, <a href="#Page_83">83</a></li>
-<li>Point diaphragm, <a href="#Page_53">53</a>, <a href="#Page_129">129</a>, <a href="#Page_135">135</a></li>
-<li>Polishing work, <a href="#Page_14">14</a></li>
-<li>Preservation of instruments, <a href="#Page_20">20</a></li>
-<li>Prismatic clinometers, <a href="#Page_414">414</a></li>
-<li>Prismatic compasses, <a href="#Page_75">75</a>
-  <ul class="IXa">
-  <li>Hutchinson's, <a href="#Page_79">79</a></li>
-  <li>stands, <a href="#Page_78">78</a></li>
-  </ul></li>
-<li>Prismatic mining survey compass, <a href="#Page_343">343</a></li>
-<li>Prisms as reflectors, <a href="#Page_29">29</a></li>
-<li>Protectors for the eyes, <a href="#Page_584">584</a></li>
-<li>Protractors, sketching, <a href="#Page_82">82</a>, <a href="#Page_374">374</a>, <a href="#Page_485">485</a></li>
-</ul>
-
-<ul class="IX">
-<li><a id="IX_Q" name="IX_Q"></a>Quadrant, <a href="#Page_422">422</a></li>
-<li>Qualities of work, <a href="#Page_7">7</a>
-  <ul class="IXa">
-  <li>of a telescope, <a href="#Page_56">56</a></li>
-  </ul></li>
-<li>Quick-setting surveyor's level, <a href="#Page_132">132</a></li>
-<li>Quick-setting theodolites, <a href="#Page_257">257</a></li>
-<li>Quiver for arrows, <a href="#Page_494">494</a></li>
-</ul>
-
-<ul class="IX">
-<li><a id="IX_R" name="IX_R"></a>Railway gauge, <a href="#Page_579">579</a>
-  <ul class="IXa">
-  <li>theodolite, <a href="#Page_258">258</a></li>
-  </ul></li>
-<li>Ramsden eye-piece, <a href="#Page_41">41</a></li>
-<li>Ranging poles, <a href="#Page_533">533</a></li>
-<li>Ray shade, <a href="#Page_129">129</a></li>
-<li>Reader for level tube, <a href="#Page_95">95</a></li>
-<li>Reading microscopes, <a href="#Page_188">188</a></li>
-<li>Reconnoitring glass and telescope, <a href="#Page_582">582</a></li>
-<li>Reflecting cap to telescope, <a href="#Page_334">334</a></li>
-<li>Reflecting circle, <a href="#Page_424">424</a></li>
-<li>Reflecting clinometers, <a href="#Page_413">413</a></li>
-<li>Reflecting levels, <a href="#Page_144">144</a></li>
-<li>Reflection of glass, <a href="#Page_25">25</a></li>
-<li>Reflector in eye-piece, <a href="#Page_46">46</a></li>
-<li>Refraction of light, <a href="#Page_25">25</a></li>
-<li>Repairing sleeves for steel bands, <a href="#Page_505">505</a></li>
-<li>Revolving compass to dial, <a href="#Page_318">318</a></li>
-<li>Richmond's tension handle, for steel band, <a href="#Page_503">503</a></li>
-<li>Road tracer, <a href="#Page_420">420</a></li>
-<li>Rods: coincidence, <a href="#Page_511">511</a>
-  <ul class="IXa">
-  <li>compensated, <a href="#Page_512">512</a></li>
-  <li>hand, <a href="#Page_530">530</a></li>
-  <li>standard, <a href="#Page_508">508</a></li>
-  </ul></li>
-<li>Rule, civil engineer's, <a href="#Page_532">532</a></li>
-<li>Rule for correcting inclined measurement, <a href="#Page_498">498</a></li>
-<li>Rule form clinometer, <a href="#Page_418">418</a></li>
-</ul>
-
-<ul class="IX">
-<li><a id="IX_S" name="IX_S"></a>Semi-circumferentor, <a href="#Page_346">346</a></li>
-<li>Sextants, <a href="#Page_425">425</a>
-  <ul class="IXa">
-  <li>box, <a href="#Page_451">451</a></li>
-  <li>with supplementary arc, <a href="#Page_461">461</a></li>
-  <li>continuous arc, <a href="#Page_458">458</a></li>
-  <li>sounding, <a href="#Page_449">449</a></li>
-  <li>surveying (open), <a href="#Page_464">464</a></li>
-  </ul></li>
-<li>Sight director to stadium, <a href="#Page_364">364</a></li>
-<li>Sighted pocket level, <a href="#Page_142">142</a></li>
-<li>Silvering sextant glasses, <a href="#Page_437">437</a></li>
-<li>Sketch books, etc., <a href="#Page_585">585</a></li>
-<li>Sketching board, military, <a href="#Page_485">485</a></li>
-<li>Slashing knife, <a href="#Page_582">582</a></li>
-<li>Slide rules, various, <a href="#Page_590">590</a></li>
-<li>Sliding stage to theodolite, <a href="#Page_249">249</a></li>
-<li>Socket for station pole, <a href="#Page_535">535</a></li>
-<li>Solar attachment to theodolite, <a href="#Page_239">239</a>, <a href="#Page_259">259</a></li>
-<li>Soldering, <a href="#Page_13">13</a></li>
-<li>Sounding chain, <a href="#Page_526">526</a>
-  <ul class="IXa">
-  <li>lines, <a href="#Page_527">527</a></li>
-  </ul></li>
-<li>Sounding sextant, <a href="#Page_449">449</a></li>
-<li>Spectacles for protecting the eyes, <a href="#Page_584">584</a></li>
-<li>Spherical aberration, <a href="#Page_33">33</a></li>
-<li>Spur shod picket, <a href="#Page_535">535</a></li>
-<li>Stadia points, <a href="#Page_131">131</a>
-  <ul class="IXa">
-  <li>webs, <a href="#Page_114">114</a></li>
-  </ul></li>
-<li>Stadium for tacheometer, <a href="#Page_155">155</a>, <a href="#Page_373">373</a></li>
-<li>Stadiometer, <a href="#Page_482">482</a></li>
-<li>Standard rods, <a href="#Page_508">508</a></li>
-<li>Stands of instruments, <a href="#Page_19">19</a></li>
-<li>Stations for observation, <a href="#Page_533">533</a></li>
-<li>Staves, levelling, <a href="#Page_149">149</a></li>
-<li>Steel bands and tapes, <a href="#Page_499">499</a>, <a href="#Page_507">507</a></li>
-<li>Striding level, <a href="#Page_237">237</a></li>
-<li>Style of work, <a href="#Page_16">16</a></li>
-<li>Subtense, instruments, <a href="#Page_355">355</a>
-  <ul class="IXa">
-  <li>diaphragm, <a href="#Page_114">114</a>, <a href="#Page_363">363</a></li>
-  </ul></li>
-<li>Supplementary arc to box sextant, <a href="#Page_461">461</a></li>
-<li>Sun glass to telescope, etc., <a href="#Page_47">47</a></li>
-</ul>
-
-<ul class="IX">
-<li><a id="IX_T" name="IX_T"></a>Tacheometers: general description, <a href="#Page_370">370</a>
-  <ul class="IXa">
-  <li>Stanley's, etc., <a href="#Page_371">371</a></li>
-  </ul></li>
-<li>Tacheometers: stadium for, <a href="#Page_155">155</a>, <a href="#Page_373">373</a>
-  <ul class="IXa">
-  <li>field book, <a href="#Page_374">374</a></li>
-  </ul></li>
-<li>Tangent motions, <a href="#Page_202">202</a></li>
-<li>Tapes, linen, etc., <a href="#Page_505">505</a></li>
-<li>Targets, mining, <a href="#Page_349">349</a></li>
-<li>Telemeters, <a href="#Page_528">528</a></li>
-<li>Telescope: general description of, <a href="#Page_24">24</a>
-  <ul class="IXa">
-  <li>Kepler's, Galileo's, <a href="#Page_40">40</a></li>
-  <li>body of, <a href="#Page_47">47</a></li>
-  </ul></li>
-<li>Telescope: optical arrangements, <a href="#Page_47">47</a>
-  <ul class="IXa">
-  <li>optical principles, <a href="#Page_25">25</a></li>
-  <li>qualities, <a href="#Page_56">56</a></li>
-  <li>reconnoitring, <a href="#Page_582">582</a></li>
-  </ul></li>
-<li>Telescopic pocket level, <a href="#Page_143">143</a></li>
-<li>Tension handles for steel bands, <a href="#Page_503">503</a></li>
-<li>Theodolites, <a href="#Page_214">214</a>
-  <ul class="IXa">
-  <li>adjustment, <a href="#Page_276">276</a></li>
-  <li>adjustable axis, <a href="#Page_237">237</a>, <a href="#Page_248">248</a></li>
-  <li>Deville's, <a href="#Page_263">263</a></li>
-  <li>Everest's, <a href="#Page_271">271</a></li>
-  <li>micrometer, <a href="#Page_259">259</a></li>
-  <li>mountain, <a href="#Page_258">258</a></li>
-  <li>plain, <a href="#Page_265">265</a>, <a href="#Page_267">267</a></li>
-  <li>railway, <a href="#Page_258">258</a></li>
-  <li>simple construction, <a href="#Page_275">275</a></li>
-  <li>solar attachment to, <a href="#Page_239">239</a></li>
-  <li>Souterrain 348</li>
-  <li>Stanley's, <a href="#Page_247">247</a></li>
-  <li>transit, <a href="#Page_215">215</a>, <a href="#Page_231">231</a>, <a href="#Page_247">247</a></li>
-  <li>14-inch, <a href="#Page_295">295</a></li>
-  <li>36-inch Colonel Strange's, <a href="#Page_298">298</a></li>
-  <li>Universal, <a href="#Page_265">265</a></li>
-  </ul></li>
-<li>Thermometer for steel band, <a href="#Page_503">503</a>
-  <ul class="IXa">
-  <li>boiling point, <a href="#Page_569">569</a></li>
-  </ul></li>
-<li>Timber girth strap, <a href="#Page_579">579</a>
-  <ul class="IXa">
-  <li>marking knife, <a href="#Page_581">581</a></li>
-  <li>rods, <a href="#Page_582">582</a></li>
-  </ul></li>
-<li>Tools used in manufacture of instruments, <a href="#Page_11">11</a></li>
-<li>Triangle for levelling staff, <a href="#Page_162">162</a></li>
-<li>Tribrach adjustments, <a href="#Page_126">126</a>
-  <ul class="IXa">
-  <li>Everest's, <a href="#Page_272">272</a></li>
-  <li>with mechanical stage, <a href="#Page_251">251</a></li>
-  </ul></li>
-<li>Tripods, <a href="#Page_114">114</a>, <a href="#Page_217">217</a>, <a href="#Page_322">322</a>
-  <ul class="IXa">
-  <li>framed, <a href="#Page_250">250</a></li>
-  <li>miners', <a href="#Page_313">313</a></li>
-  </ul></li>
-<li>Tripods, jointed, for mining instruments, <a href="#Page_313">313</a></li>
-<li>Trough compass, <a href="#Page_74">74</a>, <a href="#Page_83">83</a>, <a href="#Page_236">236</a></li>
-</ul>
-
-<ul class="IX">
-<li><a id="IX_V" name="IX_V"></a>Vernier scale readings, <a href="#Page_180">180</a></li>
-<li>Vicat needle, <a href="#Page_586">586</a></li>
-<li>Vice for adjusting land chain, <a href="#Page_496">496</a></li>
-</ul>
-
-<ul class="IX">
-<li><a id="IX_W" name="IX_W"></a>Water levels, <a href="#Page_146">146</a></li>
-<li>Waterproof covers, <a href="#Page_23">23</a></li>
-<li>Watkin's aneroid, <a href="#Page_567">567</a></li>
-<li>Watkin's clinometer, <a href="#Page_417">417</a></li>
-<li>Wealemefna, <a href="#Page_587">587</a></li>
-<li>Webs, collecting and mounting, <a href="#Page_51">51</a></li>
-<li>Whistles, <a href="#Page_585">585</a></li>
-</ul>
-
-<ul class="IX">
-<li><a id="IX_Y" name="IX_Y"></a>Y-levels, <a href="#Page_98">98</a>
-  <ul class="IXa">
-  <li>improved construction, <a href="#Page_107">107</a></li>
-  </ul></li>
-</ul>
-
-<hr class="chap" />
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-<div class="figcenter illowe37_5" id="i609">
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-<p class="noindent center large bold margin-top0 margin-bottom5">Shows you in detail how to install<br />
-electric wires. Read the contents.</p>
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-<p class="p1">Contents of chapters: 1, Introduction; 2, Planning
-the wiring; 3, Completing the installation; 4, Installing
-the lights; 5, Other methods of wiring; 6, Materials and
-notes; 7, Conduit and protected wiring, armored cables,
-pipe conduits, latest condulet fittings and concentric
-wiring; 8, Digest of 1916 edition of the National Code,
-Underwriters rules and notes. 128 pages, 45 illustrations
-and 9 plates, 12 mo, cloth.</p>
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-<li class="ad4">3. Electrical Circuits and Diagrams, Part 1.</li>
-<li class="ad2">*  4. Electric Bells, Annunciators and Alarms.</li>
-<li class="ad4">5. Modern Primary Batteries.</li>
-<li class="ad4">6. Experimenting with Induction Coils.</li>
-<li class="ad2">*  7. Electric Gas Igniting Apparatus.</li>
-<li class="ad2">*  8. Small Accumulators, How to Make and Use.</li>
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-<li class="ad1">* 10. Practical Electrics.</li>
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-<li class="ad1">* 13. The Fireman's Guide to the Care of Boilers.</li>
-<li class="ad1">* 14. The Slide Valve Simply Explained.</li>
-<li class="ad1">* 15. The Magneto Telephone.</li>
-<li class="ad1">* 16. The Corliss Engine and Its Management.</li>
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-<li class="ad1">* 31. Gas Engine Management.</li>
-<li class="ad3"><b>37. Collin's Wireless Plans, Part 1.</b></li>
-<li class="ad3"><b>38. Collin's Wireless Plans, Part 2.</b></li>
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-
-<div class="footnotes"><h3>FOOTNOTES:</h3>
-<div class="footnote">
-<p><a name="Footnote_1_1" id="Footnote_1_1"></a><a href="#FNanchor_1_1"><span class="label">[1]</span></a> <i>Proc. Royal Institution</i>, vol. xi. p. 413.</p></div>
-<div class="footnote">
-<p><a name="Footnote_2_2" id="Footnote_2_2"></a><a href="#FNanchor_2_2"><span class="label">[2]</span></a> See <i>Phil. Trans.</i> 1896, vol. 188, Map. 9.</p></div>
-<div class="footnote">
-<p><a name="Footnote_3_3" id="Footnote_3_3"></a><a href="#FNanchor_3_3"><span class="label">[3]</span></a> See Simms' <i>Mathematical Instruments</i>, p. 3.</p></div>
-<div class="footnote">
-<p><a name="Footnote_4_4" id="Footnote_4_4"></a><a href="#FNanchor_4_4"><span class="label">[4]</span></a> See pamphlet on <i>A New Form of Levelling Instrument</i>, by Thos.
-Cushing, F.R.A.S., 1879.</p></div>
-<div class="footnote">
-<p><a name="Footnote_5_5" id="Footnote_5_5"></a><a href="#FNanchor_5_5"><span class="label">[5]</span></a> Patent No. 69, Wm. Barrie, 1856.</p></div>
-<div class="footnote">
-<p><a name="Footnote_6_6" id="Footnote_6_6"></a><a href="#FNanchor_6_6"><span class="label">[6]</span></a> Patent No. 6742, John Browne, June, 1834.</p></div>
-<div class="footnote">
-<p><a name="Footnote_7_7" id="Footnote_7_7"></a><a href="#FNanchor_7_7"><span class="label">[7]</span></a> <i>Brit. Assoc. Report</i>, 1838, p. 154.</p></div>
-<div class="footnote">
-<p><a name="Footnote_8_8" id="Footnote_8_8"></a><a href="#FNanchor_8_8"><span class="label">[8]</span></a> Patent No. 12590, 1889.</p></div>
-<div class="footnote">
-<p><a name="Footnote_9_9" id="Footnote_9_9"></a><a href="#FNanchor_9_9"><span class="label">[9]</span></a> <i>Colliery Guardian</i>, vol. xxxviii. p. 576, 1879.</p></div>
-<div class="footnote">
-<p><a name="Footnote_10_10" id="Footnote_10_10"></a><a href="#FNanchor_10_10"><span class="label">[10]</span></a> <i>A Treatise of the Principles and Practice of Levelling</i>, by F. W.
-Simms, 1842; <i>A Treatise on Land Surveying</i>, by John Ainsley, revised
-by William Galbraith, 1849. Quite modern works&mdash;<i>Aid to Survey
-Practice</i>, L. D'A. Jackson, Crosby Lockwood, 1910; <i>On Levelling and
-its General Application</i>, by Thomas Holloway, Spon, 1887; revised 1914.</p></div>
-<div class="footnote">
-<p><a name="Footnote_11_11" id="Footnote_11_11"></a><a href="#FNanchor_11_11"><span class="label">[11]</span></a> <i>Levelling</i>, p. 49.</p></div>
-<div class="footnote">
-<p><a name="Footnote_12_12" id="Footnote_12_12"></a><a href="#FNanchor_12_12"><span class="label">[12]</span></a> Deschanel's Natural Philosophy, by Prof. Everett, p. 1018, 1876.</p></div>
-<div class="footnote">
-<p><a name="Footnote_13_13" id="Footnote_13_13"></a><a href="#FNanchor_13_13"><span class="label">[13]</span></a> <i>A Manual of Surveying for India</i>, by Colonel H. L. Thuillier,
-C.S.I., F.R.S., etc., and Lieutenant-Colonel R. Smith. Thacker,
-Calcutta, 1875. (Now out of print).</p></div>
-<div class="footnote">
-<p><a name="Footnote_14_14" id="Footnote_14_14"></a><a href="#FNanchor_14_14"><span class="label">[14]</span></a> The illustration is taken from <i>Die geometrischen Instrumente</i>, Dr.
-G. Chr. K. Hunäus. Hanover, 1864.</p></div>
-<div class="footnote">
-<p><a name="Footnote_15_15" id="Footnote_15_15"></a><a href="#FNanchor_15_15"><span class="label">[15]</span></a> Digges's <i>Pantometria</i>, see p. 2.</p></div>
-<div class="footnote">
-<p><a name="Footnote_16_16" id="Footnote_16_16"></a><a href="#FNanchor_16_16"><span class="label">[16]</span></a> Gardiner's <i>Practical Surveying</i>, p. 59, 1737.</p></div>
-<div class="footnote">
-<p><a name="Footnote_17_17" id="Footnote_17_17"></a><a href="#FNanchor_17_17"><span class="label">[17]</span></a> Adam's <i>Geometrical Essays</i>, pp. 217&ndash;229, 1803.</p></div>
-<div class="footnote">
-<p><a name="Footnote_18_18" id="Footnote_18_18"></a><a href="#FNanchor_18_18"><span class="label">[18]</span></a> <i>Civil Engineers' Pocket-Book</i>, by J. C. Trautwine, C.E.</p></div>
-<div class="footnote">
-<p><a name="Footnote_19_19" id="Footnote_19_19"></a><a href="#FNanchor_19_19"><span class="label">[19]</span></a> Plate xiv., fig. 5. <i>Geometrical Essays</i>, Geo. Adams, 1803.</p></div>
-<div class="footnote">
-<p><a name="Footnote_20_20" id="Footnote_20_20"></a><a href="#FNanchor_20_20"><span class="label">[20]</span></a> <i>Proc. Min. Inst.</i>, Cornwall, 1883, vol. i. p. 317.</p></div>
-<div class="footnote">
-<p><a name="Footnote_21_21" id="Footnote_21_21"></a><a href="#FNanchor_21_21"><span class="label">[21]</span></a> Patent No. 1592, April 1878.</p></div>
-<div class="footnote">
-<p><a name="Footnote_22_22" id="Footnote_22_22"></a><a href="#FNanchor_22_22"><span class="label">[22]</span></a> Patent No. 1857, J. L Casartelli, May, 1874.</p></div>
-<div class="footnote">
-<p><a name="Footnote_23_23" id="Footnote_23_23"></a><a href="#FNanchor_23_23"><span class="label">[23]</span></a> Illustrated plate xv. Fig. 1., <i>Geometrical Essays</i>, John Adams, 1803.</p></div>
-<div class="footnote">
-<p><a name="Footnote_24_24" id="Footnote_24_24"></a><a href="#FNanchor_24_24"><span class="label">[24]</span></a> Pastorelli's patent, No. 2714, 1863.</p></div>
-<div class="footnote">
-<p><a name="Footnote_25_25" id="Footnote_25_25"></a><a href="#FNanchor_25_25"><span class="label">[25]</span></a> Hoffmann's patent, No. 2084, 1878.</p></div>
-<div class="footnote">
-<p><a name="Footnote_26_26" id="Footnote_26_26"></a><a href="#FNanchor_26_26"><span class="label">[26]</span></a> <i>Geometria Subterranea</i>, Voitel, 1686.</p></div>
-<div class="footnote">
-<p><a name="Footnote_27_27" id="Footnote_27_27"></a><a href="#FNanchor_27_27"><span class="label">[27]</span></a> <i>Subterranean Surveying</i>, Thos. Fenwick, Lockwood.</p></div>
-<div class="footnote">
-<p><a name="Footnote_28_28" id="Footnote_28_28"></a><a href="#FNanchor_28_28"><span class="label">[28]</span></a> <i>Description and use of an Improved Reflecting and Refracting
-Telescope and Scales for Surveying</i>, by William Green, 1778.</p></div>
-<div class="footnote">
-<p><a name="Footnote_29_29" id="Footnote_29_29"></a><a href="#FNanchor_29_29"><span class="label">[29]</span></a> <i>La Tachéomètre, ou l'Art de Lever les Plans et de Faire les
-Nivellements</i>, Paris, 1858.</p></div>
-<div class="footnote">
-<p><a name="Footnote_30_30" id="Footnote_30_30"></a><a href="#FNanchor_30_30"><span class="label">[30]</span></a> <i>Tables Trigonométriques Centésimales</i>, by J. L. Sanguet, Paris.</p></div>
-<div class="footnote">
-<p><a name="Footnote_31_31" id="Footnote_31_31"></a><a href="#FNanchor_31_31"><span class="label">[31]</span></a> <i>Manual of the Theory and Practice of Topographical Surveying by
-Means of the Transit and Stadia</i>, by J. B. Johnson. New York.</p></div>
-<div class="footnote">
-<p><a name="Footnote_32_32" id="Footnote_32_32"></a><a href="#FNanchor_32_32"><span class="label">[32]</span></a> Patent, prov., No. 1859, June, 1868; patent No. 3759, Dec., 1868.</p></div>
-<div class="footnote">
-<p><a name="Footnote_33_33" id="Footnote_33_33"></a><a href="#FNanchor_33_33"><span class="label">[33]</span></a> <i>Report on Omnimeter</i>, by Major G. A. Laughton, Superintendent,
-Bombay Revenue Survey.</p></div>
-<div class="footnote">
-<p><a name="Footnote_34_34" id="Footnote_34_34"></a><a href="#FNanchor_34_34"><span class="label">[34]</span></a> <i>Proc. Inst. C.E.</i>, vol. xcii. part ii. p. 248, 1887&ndash;1888.</p></div>
-<div class="footnote">
-<p><a name="Footnote_35_35" id="Footnote_35_35"></a><a href="#FNanchor_35_35"><span class="label">[35]</span></a> Lister's Patent, No. 2375, 1864.</p></div>
-<div class="footnote">
-<p><a name="Footnote_36_36" id="Footnote_36_36"></a><a href="#FNanchor_36_36"><span class="label">[36]</span></a> Francis Barker's patent, No. 1926, 1881.</p></div>
-<div class="footnote">
-<p><a name="Footnote_37_37" id="Footnote_37_37"></a><a href="#FNanchor_37_37"><span class="label">[37]</span></a> British patent, No. 217, 1884.</p></div>
-<div class="footnote">
-<p><a name="Footnote_38_38" id="Footnote_38_38"></a><a href="#FNanchor_38_38"><span class="label">[38]</span></a> <i>Posthumous Works</i>, p. 502; also <i>Animadversions to the</i> Machina
-Cælestis <i>of Helvetius</i>, p. 49.</p></div>
-<div class="footnote">
-<p><a name="Footnote_39_39" id="Footnote_39_39"></a><a href="#FNanchor_39_39"><span class="label">[39]</span></a> <i>Phil. Trans.</i>, vol. xlii. p. 155.</p></div>
-<div class="footnote">
-<p><a name="Footnote_40_40" id="Footnote_40_40"></a><a href="#FNanchor_40_40"><span class="label">[40]</span></a> <i>Phil. Trans.</i>, vol. xxxvii. p. 147.</p></div>
-<div class="footnote">
-<p><a name="Footnote_41_41" id="Footnote_41_41"></a><a href="#FNanchor_41_41"><span class="label">[41]</span></a> <i>Ibid.</i> p. 340.</p></div>
-<div class="footnote">
-<p><a name="Footnote_42_42" id="Footnote_42_42"></a><a href="#FNanchor_42_42"><span class="label">[42]</span></a> See Nicholson's <i>Navigator's Assistant</i>.</p></div>
-<div class="footnote">
-<p><a name="Footnote_43_43" id="Footnote_43_43"></a><a href="#FNanchor_43_43"><span class="label">[43]</span></a> Pearson's Practical Astronomy, p. 537.</p></div>
-<div class="footnote">
-<p><a name="Footnote_44_44" id="Footnote_44_44"></a><a href="#FNanchor_44_44"><span class="label">[44]</span></a> <i>Ibid.</i> p. 577.</p></div>
-<div class="footnote">
-<p><a name="Footnote_45_45" id="Footnote_45_45"></a><a href="#FNanchor_45_45"><span class="label">[45]</span></a> <i>Gli Strumenti a Reflessione per Mesurare Angoli</i>, by G. B.
-Magnaghi, 1875.</p></div>
-<div class="footnote">
-<p><a name="Footnote_46_46" id="Footnote_46_46"></a><a href="#FNanchor_46_46"><span class="label">[46]</span></a> <i>Description of a New Quadrant</i>, by George Adams, 1748.</p></div>
-<div class="footnote">
-<p><a name="Footnote_47_47" id="Footnote_47_47"></a><a href="#FNanchor_47_47"><span class="label">[47]</span></a> Adams' <i>Geometrical Essays</i>, edited by William Jones, 1803.</p></div>
-<div class="footnote">
-<p><a name="Footnote_48_48" id="Footnote_48_48"></a><a href="#FNanchor_48_48"><span class="label">[48]</span></a> Prov. Patent No. 2624; Christopher George, 1868.</p></div>
-<div class="footnote">
-<p><a name="Footnote_49_49" id="Footnote_49_49"></a><a href="#FNanchor_49_49"><span class="label">[49]</span></a> See British patents&mdash;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.</p></div>
-<div class="footnote">
-<p><a name="Footnote_50_50" id="Footnote_50_50"></a><a href="#FNanchor_50_50"><span class="label">[50]</span></a> Adams' <i>Geometrical Essays</i>, p. 264, 1803.</p></div>
-<div class="footnote">
-<p><a name="Footnote_51_51" id="Footnote_51_51"></a><a href="#FNanchor_51_51"><span class="label">[51]</span></a> <i>Proc. Inst. Civil Engineers</i>, vol. xciii. part iii. paper No. 2308.
-See also <i>Military Surveying in the Field</i>, by Major The Hon. M. G.
-Talbot, Prof.; <i>Papers Royal Engineers</i>, vol. xiv. p. 25.</p></div>
-<div class="footnote">
-<p><a name="Footnote_52_52" id="Footnote_52_52"></a><a href="#FNanchor_52_52"><span class="label">[52]</span></a> Patent No. 1202, D. R. Edgeworth, April 1866.</p></div>
-<div class="footnote">
-<p><a name="Footnote_53_53" id="Footnote_53_53"></a><a href="#FNanchor_53_53"><span class="label">[53]</span></a> Heather's <i>Surveying Instruments</i>, 1870, p. 85.</p></div>
-<div class="footnote">
-<p><a name="Footnote_54_54" id="Footnote_54_54"></a><a href="#FNanchor_54_54"><span class="label">[54]</span></a> <i>The Surveyor</i>, vol. ii. No. 5. Sydney, Nov. 1889.</p></div>
-<div class="footnote">
-<p><a name="Footnote_55_55" id="Footnote_55_55"></a><a href="#FNanchor_55_55"><span class="label">[55]</span></a> Patent No. 2142, May, 1880.</p></div>
-<div class="footnote">
-<p><a name="Footnote_56_56" id="Footnote_56_56"></a><a href="#FNanchor_56_56"><span class="label">[56]</span></a> <i>Manual of Surveying for India</i>, p. 478, 1875.</p></div>
-<div class="footnote">
-<p><a name="Footnote_57_57" id="Footnote_57_57"></a><a href="#FNanchor_57_57"><span class="label">[57]</span></a> Patent No. 3390, October 1874.</p></div>
-<div class="footnote">
-<p><a name="Footnote_58_58" id="Footnote_58_58"></a><a href="#FNanchor_58_58"><span class="label">[58]</span></a> For full description and plate, see Everest's <i>Measurement of the
-Meridional Arc of India</i>, Introd. p. cxv.</p></div>
-<div class="footnote">
-<p><a name="Footnote_59_59" id="Footnote_59_59"></a><a href="#FNanchor_59_59"><span class="label">[59]</span></a> British patent, No. 10157, April, 1844.</p></div>
-<div class="footnote">
-<p><a name="Footnote_60_60" id="Footnote_60_60"></a><a href="#FNanchor_60_60"><span class="label">[60]</span></a> British patents&mdash;No. 13332, November, 1850; and No. 682,
-March, 1862.</p></div>
-<div class="footnote">
-<p><a name="Footnote_61_61" id="Footnote_61_61"></a><a href="#FNanchor_61_61"><span class="label">[61]</span></a> Patent, No. 13332, May, 1850.</p></div>
-<div class="footnote">
-<p><a name="Footnote_62_62" id="Footnote_62_62"></a><a href="#FNanchor_62_62"><span class="label">[62]</span></a> Patent No. 3454, December, 1862.</p></div>
-<div class="footnote">
-<p><a name="Footnote_63_63" id="Footnote_63_63"></a><a href="#FNanchor_63_63"><span class="label">[63]</span></a> Patent No. 3425, March, 1886.</p></div>
-<div class="footnote">
-<p><a name="Footnote_64_64" id="Footnote_64_64"></a><a href="#FNanchor_64_64"><span class="label">[64]</span></a> Patent No. 2714, October, 1865.</p></div>
-<div class="footnote">
-<p><a name="Footnote_65_65" id="Footnote_65_65"></a><a href="#FNanchor_65_65"><span class="label">[65]</span></a> Patent No. 12889, December, 1849.</p></div>
-<div class="footnote">
-<p><a name="Footnote_66_66" id="Footnote_66_66"></a><a href="#FNanchor_66_66"><span class="label">[66]</span></a> Patent, No. 4310, November, 1876.</p></div></div>
-
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-
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