GIFT OF MICHAEL REESE A DESCRIPTIVE TREATISE ON MATHEMATICAL RAWING INSTRUMENTS, THEffi CONSTRUCTION, USES, QUALITIES, SELECTION, ESERVATION, AND SUGGESTIONS FOE IMPROVEMENTS. \VITH Joints upon JBratomg anlr Colouring, WILLIAM FORD STANLEY, M.R.L, Mathematical Instrument Maker to H.M. Government, Science and Art Department, Council of India, Admiralty, Tithe Commission Office, Royal School of Naval Architecture t Eoyal Military Academy, Royal Geological Society, etc., etc. "C'^tait la main de 1'homme qm Stait la seule machine de 1'esprit." A. DE LAMABTIITB. FIFTH EDITION. PUBLISHED BY 2. & F. N. SPON, 46, CHARING CROSS. NEW YORK: 446, BROOME STREET; AXD THE AUTHOR, AT 5, GREAT TURNSTILE HOLBORN, LONDON, W.C 1878. Price Five Shillings. BFTLEB & TANNER, THE SELWOOD FEINTING WOEKS, FEOME, AND LONDOKT. ~ PREFACE, TO THE FIRST EDITION, OUR scientific literature has become so diffuse and universal, that we expect to find an outline of all the little mysteries of any particular art, somewhere in print. If such is not to be found, the restless inquiry that demand proclaims, will generally tempt some indi- vidual to become the teacher, however far he may fall short of perfect mastery. Certainly, the author of the following pages, who could only spare desultory hours from active business, would not have attempted to write a description of the qualities and uses of Mathematical Drawing Instru- ments, being conscious that his powers were greater with the lathe and file than in the " ways of gentle rhetoric/' had he not felt that there was really a want of such a work, much of his time being constantly required to describe by letter instruments which, from their extensive use by some of the profession, ought to be known of at least by all : this particularly applies to such instruments as the Eidograph, Centrolinead, Com- puting Scale, and some others of like utility. Further, IV PREFACE. it appears so much, more English to purchase complete information on any subject if you can, than to be compelled to ask small particulars of any person in detail. It happened that a treatise upon Mathematical Instruments really must be written, to be produced at all ; scissors could do no more. The ignorance of the mere compiler, in this line, had become so striking as to be only ridiculous. Here is an instance. A very silly triangular compass, which consisted of three jointed arms, moveable upon a horizontal centre, was illus- trated in a work upon mathematical instruments published over a hundred years since. It is not very certain whether the instrument was ever made; but the next writer who wrote upon the subject extracted the description, also the engraving, except that his engraver, accidentally no doubt, made the joint very small. The next writer who recommended the instru- ment left out the joint altogether, whereby it ceased to be a triangular compass, except in the faint historical similarity to the original. Subsequent writers, finding the stereotype to hand, unfortunately followed the last description, and also the last engraving, very much to the perplexity of the more philosophical reader. It is not intended that the above should infer that we have no original works upon mathematical instru- ments. We have several but they are of the far past. PREFACE. V It will be attempted in the following pages to review the merits of a few of the possibly useful instruments to be found in them. Keally the best work we have is the " Geometrical and Graphical Essays " by George Adams, published in 1791. This was a rather complete work in its day. It embraced some description of all the instruments then in use. It was practical too, written by a workman and a shopkeeper in constant intercourse with the user. There is one deficiency which the writer appears to have felt that of his not being a draughtsman. He made, however, an excellent apology by offering very copious opinions of professional men. Of more modern works, the only one of this class with any claim to originality is a " Treatise on the Principal Mathematical Instruments," by F. W. Sims, 1844. This is practical one way ; the writer is a pro- fessional draughtsman. The work, however, is limited to instruments for the use of the land surveyor ; and of these there is the omission of some of the most important. After consideration of all that has been done, the writer of these pages determined to place before his readers only his own opinions and experiences of draw- ing instruments. The plan is egotistical, but it offers the reader all the writer really knows on the subject, with perhaps some of his fancies and ideas, described of PREFACE TO THE FIFTH EDITION, SOME few matters are added in this edition, and some further remarks on principles of construction and pro- fessional values and uses of certain instruments; also, some further hints on drawing and colouring. The conditions under which the first edition was produced, after twelve years, no longer remain. This Treatise, independent of its steady moderate sale, has also met with suck an amount of literary patronage, that its contents may now be found, in various stages of dilu- tion, widely diffused in works that touch upon its subject. The old stereotype of imaginary triangular compasses described in the first Preface, has been put by. Instruments, and ideas of them, introduced for the first time in these pages, have been very generally accepted by the profession, and the patterns and prin- ciples imitated by the trade. Therefore the first Pre- face could now very well be omitted, but it is left intact, as being quite true at the time it was written ; and it may be now used as a mark of our progress in small things. This change of circumstances calls forth these few supplementary remarks. GREAT TURNSTILE, Aug., 1878. SECTION I. Relates to Drawing Instruments used to produce Lines and Geometrical Figures, some of which are also used to set off Spaces. CHAPTER I. PAGB Introduction Arrangement of Instruments Definitions Metals Qualities and Finish 1 CHAPTER H. Instruments for producing Fine Lines Drawing Pens . . 8 CHAPTER IH. Instruments for producing Broad Lines, Double Lines, Dotted Lines, Transfer, etc. Bordering Pen Road Pen and Pencil Wheel Pen Tracer Pricker 14 CHAPTER IV. Instruments for dividing and marking off Distances Dividers Description of Joints, etc. Hair Dividers Portable Dividers Brick Gauges 21 CHAPTER V. Instruments for producing Circles Compasses and Points Tu- bular Compasses 29 CHAPTER VI. Instruments for producing Small Circles Bows Spring Bows Pump Bow 38 CHAPTER VH. Portable Compasses Napier Compasses Pillar Compasses, etc. 46 X CONTENTS. \ CHAPTEE VIII. PAGE Instruments for striking Large Circles, or setting off Distances Beam Compasses and Standards 51 CHAPTEK IX. Instruments for striking Arcs of Circles of high Radii Hooke's Instrument Centrograph, etc 59 CHAPTEE X. Instruments for striking Ellipses Elliptic Trammel Semi- elliptic Trammel Elliptograph, etc 66 CHAPTEE XI. Instruments for producing Spiral Lines Helicograph . . 76 CHAPTEE XII. Instruments for producing the Parabola and Hyperbola . . 80 CHAPTEE XIII. Instruments for producing Conchoids, Flutes of Columns, the Wave-line, etc. Conchoidograph 84 CHAPTEE XIV. Instruments for the Production of Eegular Geometrical or Ornamental Figures Geometrical Pens .... 89 CHAPTEE XV. Instruments for producing Opposite-handed Equal Forms Antigraph Other Practical Means . 97 CHAPTEE XVI. Instruments for Copying Drawings Triangular Compasses- Triangular Beam Compasses, etc 100 CHAPTEE XVII. Instruments principally used for Enlarging or Reducing Draw- ings Wholes and Halves Proportional Compasses, etc. Proportional Callipers 103 CONTENTS. CHAPTEE XVIIL Instruments f or Eeducing and Enlarging Drawings of considerable Size The Pantagraph The Eidograph The Cymograph . 110 CHAPTEE XIX. Instruments intended to facilitate the Delineation of Natural Objects, Buildings, etc. Camera Lucida Optical Compasses Perspective Director, etc. 130 SECTION II. Relates to Drawing Instruments used as Grinding Edges, Instruments for Measuring, and Drawing Materials. CHAPTEE XX. Surfaces to Draw upon Drawing Boards Tracing Frames Sketching Boards and Blocks Trestles, etc. . . .144 CHAPTEE XXI. Euling Edges for producing Straight Lines Straight-Edges Bow Line Picket Line 153 CHAPTEE XXII. Ruling Edges for producing Parallel Lines at Set Angles, guided by the Edge of the Drawing Board Tee-Square, Isogon, etc 158 CHAPTEE XXHI. Euling Edges for producing Parallel Lines Parallel Eules Eolling Parallels 164 CHAPTEE XXIV. Euling Edges for producing Eadial or Vanishing Lines The Centrolinead Eolling Centrolinead Excentrolinead . 169 CHAPTEE XXV. Euling Edges used to raise Angles from the Edge of another Instrument Set Squares Slopes and Batters Lettering Set Squares Sectioning Set Squares Isograph, etc. . 182 Xll CONTENTS. CHAPTEE XXVI. PAGE Euling Edges for producing Curved Lines Eailway or Eadii Curves Ship Curves French Curves Weights and Splines Curve Bow 190 CHAPTEE XXVII. General Description of Drawing and Mathematical Scales Material Divisions, etc 197 CHAPTEE XXVHI. Description of Scales in common use Chain Scales and Offsets Engineers' and Architects' Scales Marquois' Scales Mili- tary Scales 203 CHAPTEE XXIX. Mathematical Lines or Scales principally deduced from Geometri- cal Figures Diagonal Scale Gunter's Scale Plain Scale Sector Slide Eule, etc 215 CHAPTEE XXX. Instruments to divide the Circle General Description Vernier Eeadings Protractors of various kinds Station Pointer . 224 CHAPTEE XXXI. Instruments for computing the Area of Surfaces of Drawings Computing Scale Planimeter Opisometer . . . 242 CHAPTEE XXXH. Drawing Paper and Methods of Fixing it Tracing Paper and Cloth Carbonic and Blacklead Paper Drawing Pins Pin Lifter Stationers' Eule Cutting Gauge Lead Weights Varnishing, etc 260 CHAPTEE XXXIII. Drawing Pencils Qualities Manner of Cutting India-rubber Erasing Lines, etc . . . 271 CHAPTEE XXXIV. Indian Ink Colours Brushes Palettes Chromo-lithographs, etc. ... 275 CHAPTEE XXXV. Stencil Plates, etc. ... ... 289 MATHEMATICAL DRAWING INSTRUMENTS. SECTION I. Relates to Drawing Instruments used to produce Lines and Geometrical Figures, some of which are also used to set off Spaces. CHAPTER I. INTRODUCTION ARRANGEMENT OF INSTRUMENTS- DEFINITIONS QUALITIES AND FINISH. THIS chapter is devoted to desultory matters relating to drawing instruments generally, and is intended to introduce and unite the subject consistently. The plan of the work to be followed in all future chap- ters will be to separate each subject, by placing all the relative instruments, or those intended to produce like results or like forms, separately in consecutive chapters. As a case of drawing instruments generally embraces our first ideas of mathematical instruments, and at the present time belongs almost as much to our school re- quirements as the slate and pencil, it may be well, by way of introduction, to give a slight technical descrip- tion of these cases as they are arranged for professional purposes, particularly as the instruments contained in a case form a collection of those most useful and import- B Z MATHEMATICAL DRAWING INSTRUMENTS. ant, and therefore should not be lost sight of. The simplest cases contain the most necessary instruments, and the more expensive and complete contain what may be termed the draughtsman's luxuries. If we presume the reader to be acquainted with the names of the ordinary drawing instruments, the cases of instruments, as they are technically named, are the Half -set Case, which contains a pair of compasses with movable leg, ink point, pencil point and lengthening bar, and drawing pen ; the Set Case, which contains the same as the half-set case, and in addition, a pair of dividers, ink bow, and pencil bow ; the Full-set Case, which contains, in addition to the instruments in the set case, a set of spring bows, a pricker, and one extra drawing pen : this last case, containing all the instru- ments constantly required, is sufficiently complete for ordinary professional purposes. Cases with a greater number of instruments, containing proportional com- passes, road pen, wheel pen, tracer, beam compasses, etc., are termed Long-set Cases, which term is indefinite as to the quantity of instruments. The above cases also generally contain three rules of very little use a protractor, sector, and parallel. The above is the general arrangement of instruments in cases, which is however sometimes varied ; as, for instance, tubular compasses may be put in the place of the half-set, which will answer in practice for the same purposes ; or other changes may be made, to the taste of the draughtsman. Persons with limited means will find it better to procure good instruments separately of any respectable maker, as they may be able to afford them, than to pur- ARRANGEMENTS, QUALITIES. chase a complete set of inferior instruments in a case. With an idea of economy, some will purchase second- hand instruments, which generally leads to disappoint- ment, from the fact that inferior instruments are manufactured upon a large scale, purposely to be sold as second-hand to purchasers, principally from the country, who are frequently both unacquainted with the workmanship of the instruments and of the system practised. Inferior instruments will never wear satisfactorily, whereas those well made improve by use, and attain a peculiar working smoothness. The extra cost of pur- chasing the case and the nearly useless rules would, in many instances, be equal to the difference between a good and an inferior set of instruments without the case. Further, if the case be dispensed with for eco- nomy the instruments may be carefully preserved by merely rolling them up in a piece of wash leather, leaving space between them that they may not rub each other ; or, what is better, by having some loops sewn on the leather to slip each instrument separately under. Before leaving the subject of cases of instruments, a few words may be said upon the various kinds of cases made to contain drawing instruments, as it would be difficult to return to the subject in an advanced part of the work. The cases in most common use are made seven inches long, by from four to six inches wide, and about one inch and a half deep ; they are generally made of mahogany, frequently veneered with rosewood or wal- nut. They are much better if made of solid wood, with dovetailed corners, as the veneers, although very 4 MATHEMATICAL DRAWING INSTRUMENTS. pretty at first, through the necessity of laying them upon the plain wood, by soaking them with glue, slowly contract and very generally draw ( the tops hollow and the sides out of square. Oak is a very suitable material, looks nice, and stands well. The cases that are found practically most convenient are made thirteen inches long ; these are termed maga- zine cases, and will contain 12-inch scales, angles, curves, and other useful instruments. They are gene- rally made in an elegant and costly manner, veneered, with metal bands and capped corners; they may, how- ever, be made plainly in the solid, at a very moderate cost. They possess one advantage over the 7-inch cases, that is, they will contain nearly all the necessary drawing materials, and will be found, upon the whole, cheaper to the professional draughtsman than the cost of several separate boxes. Many draughtsmen, for the convenience of having their instruments at hand when required, prefer a pocket-case. This is a thin wood case, covered with Russia or Morocco leather, and is generally made to contain the set or full set of instruments. Pocket- cases should be made with the corners properly rounded ; the fastening should be a spring clip or a bolt, as adopted by the French : we often see them fastened by hooks, which catch in everything. The French make pocket-cases very tastily; they wear much better and are thinner than the old style of English ones, the sides and corners being entirely rounded. Lately the English case-makers have imi- tated the French, nearly equalling them in appearance, and perhaps surpassing them in the solidity of the leather work and hinging. METALS EMPLOYED, s 5 Such instruments as are generally included in the ordinary cases are made of two sizes only, which are called 6-inch sets and 4>^-inchsets; one of these terms is applied to the whole set, whichever it may be, although only the compasses and drawing pen are of the length from which the set is named. The ink and pencil bows of a 6-inch set are only three inches long, but are called 6-inch bows. The same rule is, for convenience, applied to all the instruments, the term indicating in proportion with 6-inch or 4^-inch compasses. Six-inch sets of instruments are best suited and most used by mechanical engineers. Four-and-a-half-inch sets are placed in pocket-cases exclusively, and are used almost entirely by architects, and civil engineers. The METALS generally used in making drawing instruments are brass, electrum, or silver, the points and joints being made of steel. Silver is little used of late years, being costly and possessing little merit over electrum, which is at present the most popular. Elec- trum, as it is called, should be an alloy composed of pure nickel and copper; in colour it should nearly equal the whiteness of standard silver, with the advan- tage of being stiffer and of less specific gravity. Its merit over brass is that it will not soil the fingers by forming verdigris from the action of the perspiration of the hand; neither does it emit the odour peculiar to brass, which is very disagreeable to some few sensitive persons. Electrum of inferior quality approaches the colour of pale brass. Attempts have been made to introduce aluminium and its alloy, aluminium-bronze, into the manufacture of drawing -instruments it must be admitted, with MATHEMATICAL DRAWING INSTRUMENTS. little success. Aluminium would undoubtedly in some respects be very excellent, especially for its non-cor- rosive quality and extreme lightness ; but it requires some genius to discover the method of soldering it to steel, to render it at all adapted to drawing instru- ments. With regard to aluminium-bronze, after many experiments, the writer has been unable to discover any peculiar merit that it possesses over brass. As the steel of instruments is very liable to rust, no greater part of the instrument should be made of that metal than is necessary for strength or fineness of edge. In concluding these remarks, which apply to drawing instruments generally, a few observations may be made on what is technically termed finishj as it is this which marks the taste of the workman, and is considered a test of good work ; so that many professional gentle- men select their instruments by observation of the finish only, relying upon the work being well done if pains have been taken in this particular. By finish is understood the grace and correspondence in form of each side and opposite part of the instru- ment, and of the quality of the surfaces, which should be perfectly flat, or straight, in one direction, and show equally sharp angles. The grain left from finishing the surface should be at right angles with the length of the instrument ; it should in all parts show an equal and very fine-grained surface, but not a burnished gloss. The French and Swiss instruments were very popu- lar some few years since, but seem to have gone out of favour ; they appear to have owed their popularity to their glossy, burnished surfaces, easily produced by the buff wheel. It is creditable to the English work- CHAEACTEE OF man that he never adopted this fashion, although it was making inroads upon his trade; had he done so, it would have degraded his work of " hand and eye " to the rank of ironmongery. It must, however, in justice be remarked that although the French and Swiss ordinary cheap work, such as is commonly sent to this country, is highly polished, their better class of work is hand- finished, as our own; and in such instruments as the theodolite and microscope they leave the grain more distinct than it is left by our English workmen. CHAPTER II. INSTRUMENTS FOR PRODUCING FINE LINES DRAWING PENS. THE DRAWING PEN is perhaps the most important instrument to the draughtsman, being used to render nearly all the lines of a drawing permanent with Indian ink after the first outline has been produced with the blacklead pencil. The general construction of the drawing pen is perhaps too well known to need parti- cular description. It consists of two pointed blades of metal, which are fixed or jointed over each other in such a manner as to leave a space sufficient to support the ink by capillary attraction. The distance of the points is adjusted by a milled-head screw ; the line to be produced by the pen corresponding in thickness with the adjustment. Drawing pens are differently constructed, both for economy and convenience ; each of the various kinds being frequently adapted to a special purpose. Fine Drawing Pen. 1 The FINE DRAWING PEN is cut out of a piece of steel wire, the whole working part of the pen being in one piece. It is generally preferred for fine-line drawing, from the fact that the nibs are each equally firm when DKAWING PENS. y iu contact with the drawing-paper; this is an impor- tant consideration, difficult to attain with any form of jointed pen. The fine pen is much used for plotting surveys; it is lighter than the jointed pen and less angular, thereby turning more readily in the fingers to follow irregular lines. The fault of the pen is the dif- ficulty of cleaning between the nibs, and of setting it. For these reasons one handle is frequently adapted to six pens, for the convenience of draughtsmen having them all set at one time by the maker. The setting is undoubtedly a difficulty, but pens will retaji their working condition for a considerable time if they be kept perfectly clean. The light coating of rust which occasionally accumulates between the nibs may be easily removed by folding a narrow piece of No. glass paper, and drawing it between the nibs until they ap- pear bright ; this should be done without touching the extreme points. It will also be found to keep the pen in good working order.