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Transcriber's Note:

  Punctuation has been standardised, and possible typographical errors
    have been changed.
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  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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    20. Simple Experiments in Static Electricity.

    21. Small Electrical Measuring Instruments.

    22. Electrical Circuits and Diagrams, Part 2.

  * 23. Induction Coils, How to Make Them.

    24. Model Vaudeville Theatres.

  * 25. Alternating Currents, Simply Explained.

  * 26. How to Build a 20 foot Bi-plane Glider.

  * 27. A B C of the Steam Engine.

  * 28. Simple Soldering, Hard and Soft.

  * 29. Telegraphy for Beginners.

    30. Low Voltage Lighting with Storage Batteries.

    33. House Wiring for Electric Light.

  * 34. Magnets and Magnetism.

  * 36. Small Windmills and How to Make Them.

  * 31. Gas Engine Management.

    =37. Collin's Wireless Plans, Part 1.=

    =38. Collin's Wireless Plans, Part 2.=

  In paper covers Price 25c each Postpaid.

  * These books can also be had in cloth binding at 55c each postpaid

  SPON & CHAMBERLAIN

  PUBLISHERS OF TECHNICAL BOOKS

  123-5 LIBERTY ST., NEW YORK