CHAPTER XIX._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.

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°.

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. · 第 19 / 26 章