Transcriber's Note:

Punctuation has been standardised, and possible typographical errors have been changed.

Archaic, variable and inconsistent spelling and hyphenation have been preserved.

SURVEYING AND LEVELLING

INSTRUMENTS

SURVEYING AND LEVELLING
INSTRUMENTS
Theoretically and Practically Described.

FOR CONSTRUCTION, QUALITIES, SELECTION, PRESERVATION, ADJUSTMENTS, AND USES; WITH OTHER APPARATUS AND APPLIANCES USED BY CIVIL ENGINEERS AND SURVEYORS IN THE FIELD.

BY

WILLIAM FORD STANLEY

OPTICIAN, MANUFACTURER OF SURVEYING AND DRAWING INSTRUMENTS,

AUTHOR OF A TREATISE ON DRAWING INSTRUMENTS, PROPERTIES AND MOTIONS OF FLUIDS, NEBULAR THEORY, ETC.

FOURTH EDITION

Revised by H. T. TALLACK.

LONDON: E. & F. N. SPON, LTD., 57, HAYMARKET, S.W.

NEW YORK: 123, LIBERTY STREET

AND OF

W. F. STANLEY & CO., LIMITED

286, High Holborn, London, W.C.

1914

PREFACE TO FIRST EDITION.

Notes were taken for many years before the production of this work of queries that came before the author for reply relative to functional parts of surveying instruments. These bore most frequently reference to optical and magnetic subjects, and to the qualities and action of spirit level tubes, also occasionally to graduation and the qualities of clamp and tangent motions. It was therefore thought that it would be useful to give notes upon these subjects in detail as far as possible in the early chapters. As the work proceeded it was found that this plan saved much space in avoiding the necessity for separate descriptions when parts of complex instruments were afterwards described.

To show the state of the art and render the work useful, it was necessary that the structure of surveying instruments should be given with sufficient detail to be worked out by the skilful manufacturer. Beyond this it was thought to be most important that the professional man, who must have limited experience of the qualities of workmanship, should be supplied with as many simple tests as possible for assuring the qualities of the instruments he might purchase or use, with details also of their adjustments. This matter is therefore carried into detail for one instrument at least of each class, as very little general information is to be found on the subject in our literature. In fact, large groups of instruments in extensive use, such as those used for mining surveying, and subtense measuring instruments, have remained heretofore nearly undescribed in our language.

The technical principles followed in working out details in these pages are given by illustrations of such parts of important instruments as present any difficulty of observation from an exterior view of the engraving of the entire instrument. The plans of construction in general use are selected for illustration. Certain constructions that are liable to failure are pointed out. Many recent improvements in instruments are recognised and some are suggested, but no attempt has been made to record the little differences of construction, often meritorious, which give only a certain amount of style to the work of each country and of each individual. Upon this point it must occur that the work done in any workshop must vary from other work according to the skill and judgment of the master. It is intended, therefore, that distinctly typical instruments only should be described, in a manner that details may be worked out therefrom. To make this matter as clear as possible, with few exceptions these pages were written with the instruments described upon my table, and the illustrations, when not taken directly from the instruments, were taken from workshop drawings to a reduced scale.

In practice it is found that instruments performing similar functions may be very much varied in construction, bearing reference frequently to the conditions under which they are to be used. The same may be said of the functional parts of instruments. We may also observe that English instruments differ in detail from foreign ones, and upon this point there is no doubt much may be learned by comparison of some details of English with foreign work, although our own is admitted to rank high. Comparisons are therefore freely made in the following pages, and suggestions offered after study abroad of foreign work, and careful inspection of nearly the whole literature upon the subject, in which it is very observable that some modern continental books, treating upon parts of the subject, are much in advance of our own.

The surveying instruments described in these pages are nearly limited to those used in the field. Instruments for plan drawing and calculation of areas, which the surveyor uses in the office, have been described in the author's work on Drawing Instruments (now in Seventh Edition), to which this is intended to be the complement of the subject.

To render the work as complete as possible, it was thought necessary to give briefly the manner of using many instruments in practical surveying. This part of the subject, from the author's very limited experience in the field, is largely taken from inspection of the best works on surveying. The author, however, is very pleased to acknowledge the kindness of many professional friends for assistance on this and many other points, and for historical notes. For the description of the 36-inch theodolite, given in Chapter VII. (now X.), the author is indebted to the late Col. A. Strange, F.R.S., who gave every detail of his design and discussed many points. The author is also indebted to Mr. Thomas Cushing, F.R.A.S., Inspector of Scientific Instruments for India, who has given information and his opinions upon many subjects from his large practical experience. Also to Prof. George Fuller, C.E., who has kindly read proofs, examined formulæ, and made some technical points clearer. Also to Mr. W. N. Bakewell, M.Inst.C.E.; Major-General A. De Lisle, R.E.; Right Hon. Lord Rayleigh, F.R.S., for assistance on several technical points.

In this First Edition, entirely from manuscript, there will no doubt be errors and omissions; therefore the author will feel obliged by the receipt of any notes that he may make use of for future corrections, should another Edition be demanded.

W. F. S.

Great Turnstile, 1890.

PREFACE TO THIRD EDITION.

The note at the end of the First Edition of this work referred to on the preceding page has brought the author many letters from professional men, who have kindly taken interest in the work by offering suggestions which are now incorporated as far as practical in this Edition, and for which thanks are tendered.

One important improvement of late years in the construction of surveying instruments is due to the greater perfection of modern machinery, and the adoption of special machines to shape out many parts of the work from the solid which were formerly screwed together in many pieces, which made the instruments heavier and also liable to become loose in parts by jars, so as to cause the necessity of frequent readjustments.

Another important improvement in modern surveying instruments is in their lightness, due to the discovery of permanent aluminium alloys, by which many parts of instruments that are shaped out in the solid may be reduced to one-third the weight of the gun-metal castings formerly used entirely for these parts.

In the present Edition, which represents forty-seven years of experience of the author's life devoted to the details of the subject, it is hoped that some permanent improvements in surveying instruments may be shown, and that many new designs now first described, founded upon this experience, may merit trial.

The author is pleased to acknowledge the zealous aid his working manager and at present co-director, Mr. H. T. Tallack, has given in perfecting this work to bring it to its present state.

W. F. S.

Great Turnstile, 1901.

PREFACE TO FOURTH EDITION.

Since the publication of the Third Edition of this work, the author has been taken from us, and it has fallen to my lot to revise it and bring it up to the present time. This work I have approached with the greatest diffidence, having to follow one who had such profound knowledge of the subject, and I have earnestly endeavoured, as closely as possible, to act as I think he would have done had he been alive, and having enjoyed over twenty years of the happiest and closest business relations with him—actively co-operating in bringing many of the instruments to their present state, I venture to hope that I have to some extent carried out what his wishes would have been.

I have carefully read over and corrected the whole work, and the additions to it are only in the nature of bringing it up to date.

H. T. Tallack.

286, High Holborn,

June, 1914.

CONTENTS.

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:—

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.

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.

Fig. 1.—Diagram of Refraction and Reflection.

Larger image

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.

Fig. 2.—Diagram reflections from a plane.

Fig. 3.—Reflection from a prism.

Larger image

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.

Fig. 4.—Measurement of angle of reflection in optics.

Larger image

Fig. 5.—Diagram illustrating the principle of the lens.

Larger image

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.

Fig. 6.—Diagram convex lens.

Fig. 7.—Diagram concave lens.

Larger image

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.

Fig. 8.—Diagram of the convergence of rays of light.

Larger image

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:—

Fig. 9.—Diagram showing chromatism of light by the prism.

Larger image

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.

Fig. 10.—Diagram perfect achromatism.

Larger image

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.

Fig. 11.—Showing principles of achromatism.

Larger image

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.

Fig. 12.—Showing achromatic objective.

Larger image

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,

2nd.—Inside " f 3 convex,

crown.

3rd.—Outside " f 3 concave,

4th.—Inside " 4f convex,

flint.

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.

Fig. 13.—Kepler's telescope.

Fig. 14.—Galileo's telescope.

Larger image

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.

Fig. 15.—Diagram of arrangement of lenses.

Larger image

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.

Fig. 16.—Ramsden eye-piece.

Larger image

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.

Fig. 17.—Dynameter.

Larger image

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.

Fig. 18.—Optical arrangement of erecting eye-piece.

Larger image

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.

Fig. 19.—Diagonal eye-piece, full size; S G sun-glass.

Larger image

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.

Fig. 20.—Reflector in eye-piece to illuminate the front of diaphragm.

Larger image

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.

Fig. 21.—Body of surveying telescope.

Larger image

Fig. 22.—Section Fig. 21, A to B.

Larger image

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.

Fig. 23.—Elevation of diaphragm.

Fig. 24.—Section of diaphragm.

Larger image

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.

Fig. 25.—Webs wound off for use.

Larger image

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.

Fig. 26.—Broad needle.

Larger image

Fig. 27.—Edge-bar needle.

Larger image

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.

Fig. 28.—Author's plan of needle reading.

Larger image

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.