This is a reproduction of a library book that was digitized by Google as part of an ongoing effort to preserve the information in books and make it universally accessible. https://books.google.com of tbe inntversit^ of Wisconsin MATHEMATICAL DRAWING and MEASURING INSTRUMENTS, CONSTRUCTION, USES, QUALITIES,. SELECTION, PRESERVATION, and SUGGESTIONS for IMPROVEMENTS, WITH HINTS UPON DRAWING, COLOURING, CALCULATING SUN PRINTING, LETTERING, &c. WILLIAM FORD STANLEY. " La main de l'homme, la seule machine dp lVsprit." A. Dk Lamartine. SEVENTH EDITION. PUBLISHED BY E. & F. N. SPON, 125 STRAND. NEW YORK: SPON & CHAMBERLAIN, 12 Cohtlandt Street; AND BY THIS AUTHOR, at r, GREAT TURXSTILE, HOLBORN, LONDON", W.C. 1900 Price Five Shillings, PREFACE TO THE SEVENTH EDITION. In this edition about one hundred pages of new matter with many illustrations have been added, from the desire to embrace all recent improve ments in drawing instruments up-to-date. The whole matter has also been revised, to drop out descriptions of many instruments that have become obsolete, the defects of which were pointed out in early editions, when suggestions were made for improvements which were at the time original, but have now become general, and are adopted by the profession and the trade. W. F. S. Great Turnstile, June, 1 900. 4 4 I CONTEN T S. CHAPTER I. PAGE Introduction — Arrangement of Instruments in Cases — Defini tions — Metals Used — Qualities and Finish ... 1 CHAPTER II. Instruments for producing Fine Lines — Drawing Pens — Mapping Pens, etc. .11 CHAPTER III. Instruments for producing Broad Lines, Double Lines, Dotted Lines, Transfer, etc. — Bordering Pen — Road Pon and Pencil — Wheel Pens — Tracer — Pricker . 20 CHAPTER IV. Instruments for Dividing and Marking oil' Distances — Dividers — Description of .Joints, etc. — Hair Dividers — Portable Dividers — Brick Gauges . .28 CHAPTER V. Instruments for producing Circles — Compasses with Movable Points — Tubular Compasses ...... 37 CHAPTER YI. Instruments for producing Small Circles — Bows — Spring liows — Pump Bow, etc . .47 CHAPTER VII. Portable Compasses — Napier Compasses — Pillar Compasses, etc. 56 CHAPTER VIII. Instruments for Striking Large Circles or Setting oil' Distances — Beam Compasses — Standards ..... 61 vi CONTENTS. CHAPTER IX. paok Iustrumenta for Striking Arcs or Circles of High Radii Hooke's Instrument -Oentrograph, etc. ..... 71 CHAPTER X. Instruments for Striking Ellipses — Elliptic Trammel— Semi- elliptic Trammel — Elliptographs — Oograph, etc. 77 CHAPTER XI. Instruments for producing Spiral Lines — Ilelicograiihs . 92 CHAPTER XII. Instruments for producing the Parabola and Hyperbola . 96 CHAPTER XIII. Instruments for producing Conchoids, Flutes of Columns, the Wave-line, etc. — Conchoidograph ..... 102 CHAPTER XIV. Instruments for the production of Regular ( ieometrical or Ornamental Figures —(ieometrical Pens . , .107 CHAPTER XV. Instruments for producing Opposite-handed Equal Forms Antigraph — Other Practical Means . ll'i CHAPTER XVI. Compasses for Copying, Enlarging, or Reducing Drawings - Triangular Compasses — Triangular Beam Compasses — Wholes and Halves — Proportional Compasses —Proportional Calipers, etc lis CHAPTER XVII. Instruments for Reducing, Enlarging, and Copying Drawings of considerable size —The Pantagraph — The Eidograph — The Cymograph 128 CHAPTER XVIII. Instruments intended to facilitate the Delineation of Natural Objects, Buildings, etc. — Camera Lucida — Optical Coin- passes — Perspective Sighting Instruments, etc. 149 CONTENTS. Vll CHAPTER XIX. PAUE Surfaces to Draw upon — Drawing Boards — Tracing Frames — Plane Tables — Sketching Boards and Blocks — Engraver's Tray— Trestles, etc 164 CHAPTER XX. Ruling Edges for producing Straight Lines — Straight-edges — Bow Line — Picket Line . 1 79 CHAPTER XXI. Ruling Edges for producing Parallel Lines at Set Angles, guided by the Edge of the Drawing Board — Tee-squares — Isogon, etc 184 CHAPTER XXII. Ruling Edges for producing Parallel Lines — Parallel Rules — Rolling Parallels- Space Divider 192 CHAPTER XXIII. Killing Edges for producing Radial or Vanishing Lines — The Centrolinead — Rolling Centrolinead — Notes on Perspective — Excentrolinead ........ 200 CHAPTER XXIV. Ruling Edges used to Raise Angles from the Edge of another Instrument — Set-squares — Slopes and Batters — Sectioning Set-squares — Isograph, etc. .21:3 CHAPTER XXV. Ruling Edges for producing Curved Lines — Railway or Radii Curves — Curve Radiator — Ship Curves — French Curves — Weights and Splines — Curve Bow, etc. .... 222 CHAPTER XXVI. General Description of Drawing and Mathematical Scales — Materials — Divisions, etc. — Chain Scales and Offsets — Engineers' and Architects' Scales — Marquois' Scales — Mili tary Scales 232 viii CONTENTS. CHAPTER XXVII. ,.a,;k Mathematical Lines or Scales principally deduced from Geo metrical Figures — Diagonal Scale— Gun ter's Scale — Plain Scale — Sector — Slide Rules — Calculating Rules, etc. 252 CHAPTER XXVIII. Instruments to Divide the Circle — General Description — Ver nier Readings, etc. — Protractors of various kinds — Station Pointer, etc. ......... 264 CHAPTER XXIX. Instruments for Computing the Area of Surfaces of Drawings — Computing Scale — Planimeter — Integrator — Opisometer, etc , - - 286 CHAPTER XXX. Drawing Paper, and Methods of Fixing it — Tracing Paper and Cloth — Carbonic and Black-lead Paper — Drawing Pins — Pin Lifter — Stationer's Rule — Cutting Gauge — Lead Weights — Varnishing, etc. " . 307 CHAPTER XXXI. Drawing Pencils— Qualities — Maimer of Cutting — India-rubber — Erasing Lines — Professional Knife, etc. 319 CHAPTER XXXII. Indian Ink — Colours — Brushes — Sketching — Palettes — Chromo lithographs — Photographs, etc. ..... 325 CHAPTER XXXIII. Lettering Drawings -Lettering Set-squares — Stencil Plates — Stamps, etc. ......... 346 MATHEMATICAL DRAWING INSTRUMENTS. CHAPTER I. INTRODUCTION — ARRANGEMENT OF INSTRUMENTS IN CASES— DEFINITIONS— METALS USED — 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 chapters will be to separate each subject by plaoing 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 in some simple form belongs almost as much to our school requirements as the slate and pencil, it may be well, by way of introduction, to give a slight technical description of instrument cases as they are arranged for professional purposes, particularly as the instruments contained in a case B 2 MATHEMATICAL DRAWING INSTRUMENTS. form a collection of those most useful and important, 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-net Case, which contains a pair of compasses which has one movable leg, an ink point, a pencil point, and a lengthening bar, fitted to ic; also one drawing pen. The Set Case, which contains the same as the half-set case, and iu addition, a pair of dividers, ink Full-set Case. 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 instruments constantly required, is sufficiently complete for ordinary professional purposes. The above instrument cases often contain three rules of very little use —a protractor, a sector, and a parallel ARRANGEMENTS, QUALITIES. 3 rule. Cases with a greater number of instruments, containing proportional compasses, road pen, wheel pen, tracer, beam compasses, etc., are termed Long-set Cases, which term is indefinite as to the quantity of instruments. Some variations are occasionally made in full-set and long-set cases, 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 can 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 purchase a complete set of inferior instruments in a case, With an idea of economy, some will purchase second-hand instruments, which generally leads to disappointment, 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 purchasing the case 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 economy, 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