ji&Binnn 
 
ahr 0. R Bill Etbrarsj 
 
 iN'nrtli itarolma t*tatr llninprmlij 
 
 SMITH REYNOLDS 
 FOUNDATION 
 
Digitized by the Internet Archive 
 
 in 2010 with funding from 
 
 NCSU Libraries 
 
 http://www.archive.org/details/practicaldraughOOarme 
 
THE 
 
 PRACTICAL DRAUGHTSMAN'S 
 
 BOOK OF INDUSTRIAL DESIGN, 
 
 AND 
 
 MACHINIST'S AND ENGINEER'S DRAWING COMPANION: 
 
 FORMING A COMPLETE COURSE OF 
 
 IPttjnmital, (feghiecring, mtfr ^rtjjiicctaral gralrag. 
 
 TRANSLATED FROM THE FRENCH OF 
 
 M. ARMENGAUD, THE ELDER, 
 
 PROFESSOR OF DESIGN IN THE CONSERVATOIRE OF ARTS AND INDUSTRY, PARIS, 
 AND 
 
 MM. ARMENGAUD, THE YOUNGER, AND AMOUROUX, 
 
 CIVIL ENGINEERS. 
 
 REWRITTEN AND ARRANGED, WITH ADDITIONAL MATTER AND PLATES, SELECTIONS FROM AND EXAMPLES OF 
 THE MOST USEFUL AND GENERALLY EMPLOYED MECHANISM CF THE DAY. 
 
 BY 
 
 WILLIAM JOHNSON, Assoc. Inst., C.E , 
 
 EDITOR OF "THE PRACTICAL MECHANIC'S JOURNAL." 
 
 PRILADELPniA: 
 
 HENRY CAREY B A I R D, 
 
 INDUSTRIAL PUBLISHER, 
 
 No. 406 "WALNUT STREET. 
 
 1865. 
 
PREFACE. 
 
 Industrial Design is destined to become a universal language ; for in our material age of rapid transition 
 from abstract, to applied, Science — in the midst of our extraordinary tendency towards the perfection of the 
 means of conversion, or manufacturing production — it must soon pass current in every land. It is, indeed, 
 the medium between thought and Execution ; by it alone can the genius of Conception convey its meaning to 
 the skill which executes — or suggestive ideas become living, practical realities. It is emphatically the 
 exponent of the projected works of the Practical Engineer, the Manufacturer, and the Builder ; and by its 
 aid only, is the Inventor enabled to express his views before he attempts to realise them. 
 
 Boyle has remarked, in his early times, that the excellence of manufactures, and the facility of labour, 
 would be much promoted, if the various expedients and contrivances which lie concealed in private hands, 
 were, by reciprocal communications, made generally known ; for there are few operations that are not 
 performed by one or other with some peculiar advantages, which, though singly of little importance, would, 
 by conjunction and concurrence, open new inlets to knowledge, and give new powers to diligence ; and 
 llersehel, in our own days, has told us that, next to the establishment of scientific institutions, nothing has 
 exercised so powerful an influence on the progress of modern science, as the publication of scientific periodicals, 
 ia directing the course of general observation, and holding conspicuously forward models for emulative 
 imitation. Yet, without the aid of Drawing, how can this desired reciprocity of information be attained ; or 
 how would our scientific literature fulfil its purpose, if denied the benefit of the graphic labours of tin- 
 Draughtsman? Our verbal interchanges would, in truth, be vague and barren details, and our printed 
 knowledge, misty and unconvincing. 
 
 Independently of its utility as a precise art, Drawing really interests the student, whilst it instructs him. 
 It instils sound and accurate ideas into his mind, and develops his intellectual powers in compelling him to 
 observe — as if the objects he delineates were really before his eyes. Besides, he always does that the best, 
 which he best understands ; and in this respect, the art of Drawing operates as a powerful stimulant to 
 progress, in continually yielding new and varied results. 
 
 A chance sketch — a rude combination of carelessly considered pencillings — the jotted memoranda of a 
 contemplative brain, prying into the corners of contrivance — often form the nucleus of a splendid invention. 
 An idea thus preserved at the moment of its birth, may become of incalculable value, when rescued from the 
 desultory train of fancy, and treated as the sober offspring of reason. In nice gradations, it receives the 
 refining touches of leisure — becoming, first, a finished sketch, — then a drawing by the practised hand so that 
 many minds may find easy access to it, for their joint counsellings to improvement — until it finally emerges 
 from the workshop, as a practical triumph of mechanical invention— an illustrious example of a happy 
 

 combination opp- men arc barely able even to Mart th 
 
 r furnish that tr . 
 umortal. i 
 ,| »n iu Object ; for it will at least add I I the ladder of Intelligence, 
 
 and form a few more I '.Vction — 
 
 "Thou hut not W an hour »h*r«>f ihrr* u * Ml _ 
 
 A wniuu thought mt midnight will roJeem th« livelong d»y." 
 
 T , v necessary as the ordinary rudiment* of ]ear- 
 
 ,. in the edl :uent 
 
 iy intend I i; tor without a know 
 
 Manufactures, can be a 
 and the routines of study in all varicti 
 j the introduction of fas 
 
 The special mi--ion . .f the Practical Draughtsman's Book of Industrial Design may a: ered from 
 
 I to furnish gradually di BJOtrical I ►rawing, applied directly 
 
 of the Industrial \ Hag Linear Design pr 
 
 ■ >ns ; the Prawn E aiag and C 
 
 tod the study ..f parallel and • 
 
 f Mechanics, Architecture, Foundry-W 
 
 •ally. 11yd: I Mill-Work. In 
 
 ipilation. • ncrally ot: toy foraffc .fully 
 
 brieal problem, a practical exampl i lieation has be- 1 
 
 facili' -.due. 
 
 The work is comprised within nine divisions, appropriated to the different branches of Industrial D 
 The first, vkieb • irticularh 
 
 apple 
 
 • ident t" the proper ase of I - 
 exampl. -s of different nethoda of oonBtrnctiiig plain i 
 i n ni . the ellipse, the oral, the pai and the roluti 
 
 accura 
 
 lloetratei the geometri station of 
 
 practicallj considered. It shows thai 
 
 : initiation of all tl 
 
 for the die .;ion of internal : 
 
 D points OOl tionnl colours and tin! 
 
 ofol to their nature ; famishing, at the rimple and ca-v examples, which I 
 
 I the pupil, and hmniajt— bjffl with the u-e of the ; 
 
 In the foarth di'. 
 
 . with the ' '."pnicnt, hi 
 
 appl Cocke. 
 
 and cluai ' lus « 
 
PREFACE. 
 
 The fifth division is devoted to special classes of curves relating to the teeth of Spur Wheels, Screws 
 and Racks, and the details of the construction of their patterns. The latter branch is of peculiar importance 
 here, inasmuch as it has not been fully treated of in any existing work, whilst it is of the highest value to the 
 pattern maker, who ought to be acquainted with the most workmanlike plan of cutting his wood, and 
 effecting the necessary junctions, as well as the general course to take in executing his pattern, for facilitating 
 the moulding process. 
 
 The sixth division is, in effect, a continuation of the fifth. It comprises the theory and practice of 
 drawing Bevil. Conical, or Angular Wheels, with details of the construction of the wood patterns, and 
 notices of peculiar forms of sonic gearing, as well as the eccentrics employed in mechanical construction. 
 
 The seventh division comprises the studies of the shading and shadows of the principal solids — Prisms, 
 Pyramids, Cylinders, and Spheres, together with their applications to mechanical and architectural details, 
 as screws, spur and bevil wheels, coppers and furnaces, columns and entablatures. These studies naturally 
 lead to that of colours — single, as those of China Ink or Sepia, or varied ; also of graduated shades produced 
 by successive flat tints, according to one method, or by the softening manipulation of the brush, according 
 to another. 
 
 The pupil may now undertake designs of greater complexity, leading him in the eighth division to various 
 figures representing combined or general elevations, as well as sections and details of various complete 
 machines, to which are added some geometrical drawings, explanatory of the action of the moving parts 
 of machinery. 
 
 The ninth completes the study of Industrial Design, with oblique projections and parallels, and exact 
 perspective. In the study of exact perspective, special applications of its rules are made to architecture and 
 machinery by the aid of a perspective elevation of a corn mill supported on columns, and fitted up with all 
 the necessary gearing. A series of Plates, marked A, B, <fec, are also interspersed throughout the work, as 
 examples of finished drawings of machinery. The Letterpress relating to these Plates, together with an 
 illustrated chapter on Drawing Instruments, will form an appropriate Appendix to the Volume. The general 
 explanatory text embraces not only a description of the objects and their movements, but also tables and 
 practical rules, more particularly those relating to the dimensions of the principal details of machinery, as 
 facilitating actual construction. 
 
 Such is the scope, and such are the objects, of the Practical Draughtsman's Book of Industrial Design. 
 
 Such is the course now submitted to the consideration of all who are in the slightest degree connected 
 with the Constructive Arts. It aims at the dissemination of those fundamental teachings which are so 
 essentially necessary at every stage in the application of the forces lent to us by Nature for the conversion 
 of her materials. For ;1 man can only act upon Nature, and appropriate her forces to his use, by compreheuding 
 her laws, and knowing those forces in relative value and measure." All art is the true application of 
 knowledge to a practical end. We have outlived the times of random construction, and the mere heaping 
 together of natural substances. We must now design carefully and delineate accurately before we proceed 
 to execute — and the quick pencil of the ready draughtsman is a proud possession for our purpose. Let the 
 youthful student think on this ; and whether in the workshop of the Engineer, the studio of the Architect, 
 or the factory of the Manufacturer, let him remember that, to spare the blighting of his fondest hopes, and 
 the marring of his fairest prospects — to achieve, indeed, his higher aspirations, and verify his loftier thoughts, 
 which point to eminence — he must give his days and nights, his business and his leisure, to the study of 
 
 iJnbustrial DtBtgn. 
 
ABBREVIATIONS AND CONVENTIONAL SIGNS. 
 
 In order to simplifv the language or expression of arithmetical ami geometrical operations, the following conventional 
 •ign» are used : — 
 
 The »ign + signifies plus or more, and is pl.t « o or more terms to indicate additior. 
 
 Eia v 4 + 3, is 4 plus 3, that is, 4 added to 3, or 7. 
 
 fie* minus or Itss, and indicates su! 'traction. 
 Ex. : 4 — 3, is 4 minus 3, that is, 3 taken from 4, or 1. 
 
 The sign X signifies multiplied by, and, placed between two terms indicates mullip) 
 
 5 x 3, is 5 multiplied bj 8, or 15. 
 quantities are expressed i mippi eased Hun we writ.-, indifferently — 
 
 a x b, or ab. 
 The sign : or (as it is more commonly used i - Uwidtd by, and, placed between two qua it. -* division. 
 
 Bx 
 
 12 
 12 : 4, or 12 -J- 4, or — , I by 4. 
 
 The si-- '* or aawaJ to, and b -ions t.> indi tality. 
 
 + 2 = 8, meaning, tli.it ] i to 8. 
 
 • >n of these eigne, : :: I indicatea geometrical proportion. 
 
 : : i : ,; , nn an ng, thai 8 a to 8 .■« 4 is to 0. 
 The sign V — indicates the extraction of a root; as, 
 
 Vi)-^. meaning, thai the equate root of 9 is equal to 3. 
 The ml rpoaition of a Tin 
 
 ■J/J7 = 3, expresses that the cube root of 27 ii equal to 3. 
 The signs ^ and 7 indica'- i and pnagfcr than. 
 
 3 / 4, = 3 mii.iINt than 1 , ai y, 4 7 8, = 4 greater than 3. 
 
 Fig. signifies figure; and pL, 
 
 
 
 
 10 Millimetre* 
 
 = 
 
 
 
 = 
 
 
 10 DetJraetm 
 
 = 
 
 1 M.T, 
 
 10 Metra 
 
 = 
 
 1 I ►' ■ am»'tr« 
 
 
 = 
 
 1 !!••.• 
 
 
 = 
 
 
 lo Kumwtm 
 
 ■ 
 
 -.rnrtr* 
 
 FRENCH AND ENGLISH LINEAR MEASURES n»M!'\l:i.I>. 
 
 •0894 Inolic*. 
 •S9S7 " 
 **•»»* 1 " 
 
 rarda 
 
 ■• 
 
 -ng*. 
 : I 6J|:- ' 
 : 6213>' 
 
 
 
 
 
 m \ 
 
 •- 
 thnetm, 
 
 II In. he. 
 
 = 
 
 
 
 = 
 
 • 
 
 
 = 
 
 1 Y*rJ 
 
 
 = 
 
 '.-in 
 
 1 .rJ« 
 
 = 
 
 1 Pol* or 
 
 
 = 
 
 
 
 = 
 
 1 Furlong 
 
 
 - 
 
 • 
 
 rlong* ) 
 
 i aide i 
 
 = 
 
 
 
 = 
 
 1 ■ !" I ; 
 
CONTENTS. 
 
 Preface, - 
 
 Abbreviations and Conventional signs, 
 
 Tiar. 
 
 iii 
 
 CHAPTER I. 
 
 LINEAR DRAWING, - 
 Definitions and Problems : Plate I. 
 Lines and surfaces, - 
 
 Applications. 
 
 Designs for inlaid pavements, ceilings, and balconies 
 
 Plate II., - 
 
 Sweeps, sections, and mouldings : Plate III., 
 Elementary Gothic forms and rosettes : Plate IV, 
 Ovals, Ellipses, Parabolas, and Volutes : Plate V, 
 
 Rules and Practical Data. 
 Lines and surfaces, - 
 
 - ib. 
 
 - II 
 
 - 13 
 . 14 
 
 , 15 
 
 - 19 
 
 CHAPTER II. 
 
 THE STUDY OF PROJECTIONS, - - - 22 
 
 Elementary Principles : Plate VI. 
 
 Projections of a poiDt, - - - ib. 
 
 Projections of a straight line, - - - 23 
 
 Projections of a plane surface, - - - tb. 
 
 Op Prisms and Other Solids : Plate VII., - - 24 
 
 Projections of a cube : Fig. lh, - - - ib. 
 
 Projections of a right square-based prism, or rectan- 
 gular parallelopipcd : Fig. [§, - - 25 
 
 Projections of a quadrangular pyramid ; Fig. ©, - ib. 
 
 Projections of a right prism, partially hollowed, as 
 
 Fig.®, ib. 
 
 Projections of a right cylinder : Fig. H, - - ib. 
 
 Projections of a right cone : Fig. \f, - - ib. 
 
 Projections of a sphere : Fig. (g, - - 26 
 
 Of shadow lines, - - - - - ib. 
 
 Projections of grooved or fluted cylinders and 
 
 ratchet-wheels : Plate VIII., - - - 27 
 
 The elements of architecture : Plate IX., - - 28 
 
 Outline of the Tuscan order, - - - 29 
 Rules and Practical Data. 
 
 The measurement of solids, - - - - 30 
 
 CHAPTER HT. 
 
 ON COLORING SECTIONS, WITH APPLICA- 
 TIONS. 
 
 Conventional colors, - . - - - 
 
 Composition or mixture of colors : Plate X., 
 Continuation of the Study of Projections. 
 
 Use of sections — details of machinery : Plate XL, 
 
 Simple applications — spindles, shafts, couplings, 
 wooden patterns : Plate XII., - 
 
 Method of constructing a wooden model or pattern 
 of a coupling, - 
 
 Elementary applications — rails and chairs for rail- 
 ways : Plate XIII. , - 
 Rules and Practical Data. 
 
 Strength of materials, - 
 
 Resistance to compression or crushing force, 
 
 Tensional resistance, - 
 
 Resistance to flexure, - 
 
 Resistance to tordon, - 
 
 Friction of surfaces in contact, - 
 
 35 
 ib. 
 
 36 
 
 CHAPTER IV. 
 
 THE INTERSECTION AND DEVELOPMENT OF 
 SURFACES, WITH APPLICATIONS, - 
 The Intersections of Cylinders and Cones : Plate 
 XIV. 
 Pipes and boilers, - 
 Intersection of a cone with a sphere, 
 Developments, ------ 
 
 Development of the cylinder, - 
 
 Development of the cone, - 
 The Delineation and Development of Helices, 
 Screws" and Serpentines: Plate XV. 
 
 Helices, ------ 
 
 Development of the helix, - - - - 
 
 Screws, - - - - - 
 
 Internal screws, - 
 
 Serpentines, ------ 
 
 Application of the helix — the construction of a 
 staircase : Plate XVI., - - - - 
 
 - 49 
 
 52 
 53 
 ib. 
 
 54 
 ib. 
 
 55 
 

 The intersection of sarTacca application* to - 
 cock. - a 
 
 Be LX« AID I'» . 
 
 
 
 f heat, .... 
 
 ng swrtace, - - II 
 
 Atioa of the dxiemsioM of bodeta, - ib. 
 
 Ihsaensions of firegrate, -61 
 
 ;< • 
 Safety-valves, 
 
 CHAPTER V. 
 
 63 
 
 '.oid. an.l epicycloid: Plates XVIII. 
 and I 
 
 VIII. - - - i%. 
 
 »ti XVIII.. - - - 64 
 
 ; described by a circle rolling 
 aboc- 
 
 - ib. 
 Alien of a rack and pinion in gear : Fig. 4, 
 
 - ib. 
 Gearing of a worm with a worm-wheel : Figs. 5 and 
 
 I, Pun TOIL, 67 
 
 bbical ob Srra QsaMm : Pun 
 
 ml delineation of two (par-wheels in gear: 
 
 ib. 
 
 v.ion of a couple of wheels gearing internal! v : 
 
 68 
 
 I »1 delineation of a couple of spur-wheels : 
 
 . 69 
 T»r MB PaT- 
 
 tsess roa Toothed Wuku : Flats X\i.. 
 • .eel patterns, 
 
 rn of the pinion, - - - • ib. 
 
 • :.e wooden-toothed spur-» ! - 71 
 
 - |0. 
 ' vTA. 
 
 Toothed gearing, .... 
 
 Angalar and circumferential Telocity of wheels, - 74 
 asiuas of gear.- .- 
 ♦* of the teeth. 
 
 f the teeth, - - - - - 7« 
 
 .on* of the web, . -77 
 
 •er and dimensioos of the arms, - ib. 
 
 icn patterns, - 
 
 CHAPTER VI. 
 
 . V TOOTHXD 
 
 Pi (TI 
 
 .'. or beril gearinr. 
 Design for a pair of ben]. wheels in gear 
 
 . 
 
 Ct ; * rf>den patterns for a pair of beril- 
 
 III.. - 
 I 
 
 » beels. with involute 
 
 Helical gear; 14.. 
 
 ComiTixr- , ;.i»T] kLMoTKYtxra. 
 
 • a. 
 
 - o>. 
 
 ■ - i 
 
 The delineation of eccentrics and cams: Flati 
 
 \w 
 
 . - ... 
 
 rt-»haped cam: Fig. 1. - 
 Car rn and intermittent 
 
 morement : Fig* 2 and 3, ... 
 
 Triangular cam : Figs. 4 and 5, - 
 Inrolnte cam : Figs. 6 at i 7. - - - 
 
 Cam to produce intermittent and **i«*imil*r move- 
 ments : Figs. 6 and 9, - 
 Rcxks ASP Fsi 
 
 The simple machines, .... 
 
 Centre of gravity, ..... 
 On estimating the power of prime movers, - 
 
 .lation for tbe brak- - . - ib. 
 
 The fall of bodies, - - - - - 95 
 
 Momentum, .... . ib. 
 
 ral forces, - - - - - i 
 
 rnAiira vu. 
 KI.KMrNTAP.V PItIN< - 96 
 
 Shadows or Faisxs, Ptrakids. axd Ctuxdies : Flati 
 WVl. 
 
 . 
 .mi.l. ..... 
 
 Truncated pyramid, - - - - M 
 
 - ib. 
 w cast by one cylinder on an otb< r. - - if>. 
 m cast by a cylinder on a pr:-m, - - ib 
 
 low cast by one prism on Mot] r . 99 
 
 •v cast by a prism on a cyhn-i r. - - ib. 
 
 Pbixctplbs Pi HI \\V1I.. . . M0 
 
 rfcee*, ■*. 
 
 - i7.. 
 Ml 
 
 Shading by soft. ■:. 
 
 ■ x or THB - ' krt 
 
 XWIII. 
 
 I caM upon the interior of a cylinder, - 103 
 
 Shadow ca-- far upon another, • ib. 
 
 - lows of cone- - • ib. 
 
 - 
 
 v cast upon the interior of a hollow cone, • 106 
 
 - ib. 
 
 rus, - - • ib. 
 
 m cast by a straight line upon a tor 
 
 quarter round, ..... |n7 
 
 * s of surfaces of revolution. - - - if.. 
 
 Re: - 
 
 Pumps. . . . . . . : ' ■- 
 
 ',•■■• AV 
 
 T'«. - - - - 10. 
 
 r pump*, ... 
 Tbe hydrostatic press, - - - ib. 
 
 i! calculations and data — discharge of 
 water throi.. BcM, - - • ib. 
 
 rm section and fall. 110 
 . - - - - ib. 
 
 Calculation of the discharge of water through rect- 
 angular orifice* of narrow edge*, - - 111 
 
CONTENTS. 
 
 Calculation of the discharge of water through over- 
 shot outlets, - 
 To determiue the width of an overshot outlet, 
 To determine the depth of tho outlet, 
 Outlet with a spout or duct, - 
 
 - ib. 
 
 - 116 
 
 CHATTER VIII. 
 
 ArrUCATION OF SHADOWS TO TOOTHED 
 GEAR: Plate XXX. 
 
 Spur-wheels : Figs. 1 and 2, - - - - ib. 
 
 licvil-whccls : Figs. 3 aud 4, - - -117 
 
 Application of Shadows to Screws : Plate XXXI., 118 
 Cylindrical square-threaded screw : Figs. 1, 2, 2", 
 
 and 3, - - - - - ib. 
 
 Screw with several rectangular threads: Fig?. 4 and .">. ib. 
 
 Triangular-threaded screw : Figs. 6, 6°, 7, and 8, - ib, 
 
 Shndows upon a round-threaded screw : Figs. 9 and 10, 119 
 
 Application of Shadows to a Boiler and its Furnace : 
 
 Plate XXXII. 
 
 Shadow of the sphere : Fig. 1, ... ib. 
 
 Shadow cast upon a hollow sphere : Fig. 2, - 120 
 
 Applications, ..... ib. 
 
 Shading in Black — Shading in Colours : Plate 
 
 XXXIII., 122 
 
 CIIAMER IX. 
 
 THE CUTTING AND SHAPING OF MASONRY: 
 
 Plate XXXI V., 
 
 The Marseilles arch, or arriZre-voussxire : Figs. 1 
 and 2, 
 Br/l.ES and Practical Data. 
 Hydraulic motors, - 
 
 I udershot water-wheels, with plane floats and a 
 circular channel, - 
 
 •Width, 
 
 Diameter, ...... 
 
 Velocity, ...... 
 
 Number and capacity of the buckets, 
 
 Useful effect of the water-wheel, ... 
 
 Overshot water-wheels, - , , . 
 
 Water-wheels, with radial floats, - 
 
 Water-wheels with curved buckets, 
 
 Turbines, ...... 
 
 Remarks oh Machine Tools, - - , . 
 
 123 
 ib. 
 
 ib. 
 ib. 
 127 
 ib. 
 
 ib. 
 
 ib. 
 128 
 129 
 130 
 
 ib. 
 131 
 
 CHAPTER X. 
 
 THE STUDY OF MAOHIN KEY AND SKETCHING. 
 
 Various applications and combinations, - - 133 
 The Sketching of Machines? : Plates XXXV. and 
 
 XXXVI., ib. 
 
 Drilling Machine, - - - - - ib. 
 
 Motive Machines. 
 
 Water-wheels, ...... 135 
 
 Construction ami setting up of water-wheels, - ib. 
 Delineation of water-wheels, - - -136 
 
 Design for a water-wheel, .... 137 
 
 Sketch of a water-wheel, - - - - ib. 
 
 Overshot Water- Wheels : Fig. 12, ... ib. 
 Delineating, sketching, and designing overshot 
 
 water-wheels, ..... 138 
 
 Water-Pumps : Plate XXX VII. 
 
 Geometrical delineation, .... 138 
 Action of the pomp, - .... 139 
 
 Steam Motors. 
 
 High-pressure expansive steam-engine: Plates 
 XXXV in., XX XIX, and XL., - - - 141 
 
 Action of the engine, - - - -142 
 
 Parallel motion, - - - - - ib. 
 
 Details of Construction. 
 
 Steam cylinder, ..... 143 
 
 Piston, - - - - - - ib. 
 
 Connecting-rod and crank, - - - - ib. 
 
 Fly-wheel, - - - - - - ib. 
 
 Feed pump, ..... ib. 
 
 Ball or rotating pendulum governor, - 144 
 
 Movements of the Distribution and Expansion Valves, ib. 
 
 Lead and lap, ..... 145 
 
 Rules and Practical Data. 
 
 Strum-engines: low pressure condensing engine 
 without expansion valve, ... - 146 
 
 Diameter of piston, ----- 147 
 
 Velocities, ------ 148 
 
 Steam-pipes and passages, ... - ib. 
 
 Air-pump and condenser, .... ib. 
 
 Cold-water and feed-pumps, ... - 149 
 
 High pressure expansive engines, ... 2 "j. 
 
 Medium pressure condensing and expansive steam- 
 engine, ...... 151 
 
 Conical pendulum, or centrifugal governor, - 153 
 
 CnAFTER XI. 
 
 OBLIQUE PROJECTIONS. 
 
 Application of rules to the delineation of an oscilla. 
 ting cylinder : Plate XLI, 
 
 - 154 
 
 chapter xii. 
 PARALLEL PERSPECTIVE. 
 
 Principles aud applications : Plate XLIL, 
 
 CHArTER XIII. 
 
 TBUE PERSPECTIVE. 
 
 Elementary principles : Plate XLIII, - -158 
 
 First problem — the perspective of a hollow prism : 
 
 Pigs. 1 and 2, - - - - - ib. 
 
 Second problem — the perspective of- a cylinder: 
 
 3 and 4, - - - - 159 
 
 Third problem — the perspective of a regular solid, 
 
 when the point of sight is situated in a plane 
 
 passing through its axis, and perpendicular to the 
 
 plane of the picture : Figs. 5 and G, 
 Fourth problem — the perspective of a bearing brass, 
 
 placed with its axis vertical : Figs. 7 and 8, 
 Fifth problem — the perspective of a stopcock with 
 
 a spherical boss : Figs. 9 and 10, - 
 Sixth problem — the perspective of an object placed 
 
 in an] position with regard to the plane of the 
 
 picture: Figs. 11 and 12, - 
 Applications — Sour-mill driven bv belts: Plates 
 
 Xl.IV. and XI.V. 
 
 Description of the mill, 
 
 ICO 
 
 ib. 
 
 - ib. 
 
 161 
 
 - ib. 
 

 Representation of the Bill b 
 
 ' recent improvement* la luar-mill*, 
 
 - 
 -ullstone," • 
 
 - 
 
 i 
 
 
 Work p e l f o rme d bj ranon* machines, 
 
 - 
 
 : - - 
 : saw». 
 
 ICO 
 
 a. 
 
 171 
 
 •1. 
 
 cn.wTi R i 
 
 MA- 
 CUIJi 
 
 i!ance water- meter. . 1TJ 
 
 ng machine, • 174 
 
 i vrens locomotire engine, 17i* 
 
 aning machine. . 
 
 - i-hiiir machine lor pine* goods, 183 
 
 •m. 
 
 
 
 I .'•-. 
 
 
 Eiamj I't-actmg manac engine*. 
 
 rn.MTn xv. 
 I'RAW I 
 
 1-i 
 
 I N D KX TO T II K TA 15 1 - 
 
 - 
 . 
 
 ' .ta! m. -asur - h millime- 
 
 tres and English fcet, 
 
 and volume* of regular po! 
 
 •0*1 meaaor I 
 (m, .... 
 
 •nal ni< i-up mint- 
 Tuscn: .... 
 
 \ <-och ascoluu supports, 
 
 - 
 
 ..n when 
 
 submitted to » lcn>Uc strain. 
 
 Diameter* of the joarnali of water-wheel and other shafts 
 
 for heary work. - . - - - 
 
 r* for shaft journals calcu! rence to 
 
 . 
 
 Ratio* of irnals in !•■-.. 
 
 Pi imuu , temperatures, w> 
 
 aeas of plate* in cylindrical i 
 
 of ire »tm-.'|l,ir«, .... 
 
 IHajMtm ..l.^'j-iilin, . 
 
 - 
 I' 
 
 6- 
 
 21 
 30 
 
 33 
 
 a 
 
 u 
 4$ 
 
 I*. 
 
 MM 
 
 Dime: rms. 
 
 Average amount of mechanical i 
 
 and animal*. - • - W 
 
 • nndinc to various velocities of falling bodies, 94 
 
 measures of capacity. . 110 
 
 ' water through an orifice one mMre in width. Ill 
 
 v metre in width, 1 1 3 
 
 - 115 
 1 irinus kinds of turbine*. 131 
 
 i pressure of maehir Mr*, 
 
 :.s steam engine*, with the quantities of steam 
 
 - It" 
 I \ en out with various degrees of 
 
 expansion, by a cobic metre of steam, at rations pres- 
 sure. ..... . 150 
 
 engines, condensing and 
 the steam 
 r atmosphere* in the coo- 
 ing, and at fire atmospheres in the other engine' 
 m pressure condensing and expa- 
 
 - ib. 
 
 ..•ns of the arm*, a: f the balls of the 
 
 >l pendulum, or cen'- 
 1' I and number of pair* of 
 
 .t-alus, required in £ 
 
 ■ 16» 
 
PRACTICAL DRAUGHTSMAN'S 
 
 BOOK OF INDUSTRIAL DESIGN. 
 
 CHAPTER I. 
 LINEAR DRAWING. 
 
 In Drawing, as applied to Mechanics and Architecture, and to tho 
 Industrial Arts in general, it is necessary to consider not only the 
 mere representation of objects, but also the relative principles of 
 action of their several parts. 
 
 The principles and methods concerned in that division of tho 
 art which is termed linear drawing, and which is the foundation of 
 all drawing, whether industrial or artistic, are, for the most part, 
 derived from elementary geometry. This branch of drawing has 
 for its object the accurate delineation of surfaces and the con- 
 struction of figures, obtainable by the studied combinations of 
 lines; and, with a view to render it easier, and at tho same timo 
 more attractive and intelligible to tho student, the present work 
 'i arranged to treat successively of definitions, principles, 
 and problems, and of tho various applications of which these are 
 capable. 
 
 Many treatises on linear drawing already exist, but all these, 
 red apart from their several objects, seem to fail in the due 
 
 development of tho subject, and do not manifest that general ad- 
 vancement and increased precision in details which are called for 
 at tho present day. It has therefore been deemed necessan to 
 begin with these rudimentary exercises, and such exemplifications 
 have been selected as, with their varieties, are most frequently 
 met with in practice. 
 
 Many of the methods of construction will be necessarily such as 
 are already known; but they will be limited to those which are 
 absolutely indispensable to the development of the principles 
 and their applications. 
 
 DEFINITIONS. 
 
 OF LltlES AND SURFACES. 
 PLATE I. 
 
 In Geometry, apace is described, in the terms of its threi dimen- 
 sions — length, oreadth or thickness, and height or depth. 
 
 The combination of two of these dimensions represents surface. 
 
 and one dimension takes the form of a line. 
 
 Mats. — There are several kinds of lines used in drawing— 
 straight or right lines, curved lines, and irregular or broken lines. 
 
 Right lines are vertical, horizontal, or inclined. Curved lines are 
 circular, elliptic, parabulic, tSfC. 
 
 Surfaces. — Surfaces, which are always bounded by lines, aro 
 plane, concave, or convex. A surface is plane when a straight-edge 
 is in contact in every point, in whatever position it is applied to it. 
 If the surface is hollow so that the straiuht-edge only touches at 
 each extremity, it is called concave; and if it swells out so that 
 the straight-edge only touches in one point, it is called convex. 
 
 Vertical liars. — By a vertical line is meant one in the position 
 which is assumed by a thread freely suspended from its upper ex- 
 tremity, and having a weight attached at the other; such is the 
 line AB represented in fig. ^. This line is always straight, and 
 
 the shortest that can be drawn between its extreme points. 
 
 Plumb-line. — -The instrument indicated in tig. .A is called a 
 plumb-line. It is much employed in building and the erection 
 
 of machinery, as a guide to the construction of vertical lines and 
 surfaces. 
 
 Horizontal line. — When a liquid is at rest in an open vessel, its 
 
 upper surface forms a horizontal plane, and all lines drawn upon 
 such surface are called horizontal lines. 
 
 Levels. — It is on this principle that what arc called fluid levels 
 are constructed. One description of fluid level consists of two 
 
 upright glass tubes, connected by a pipe communicating with the 
 
 bottom of each. When the instrument is partly tilled with water, 
 the water will stand at the same height in both tubes, and thereby 
 indicate the true level. Another torn), and more generally 
 
 used, denominated a spirit level — spirit being usually employed— 
 consists of a glass tube (fig. ©) enclosed in a metal case. ,/, 
 
 d by two supports, b, to a plate, c. The tube is almost 
 filled with liquid, and the bubble of air, d, which remains, is 
 
 exact]] in the centre of the tube when any surface, c d, os 
 
 Which the instrument is placed, is perfectly level. 
 
 Masons, carpenters, joiners, and other mechanics, are in (he 
 habit of using the instrument represented in t'vj. Q. em 
 simply of a plumb line attached to the point of junction of the two 
 
 inclined side pieces, ah. Ac, of equal length, and connected near 
 their free ends by the cr.i-s-pi.ee, An, which has a mark at its 
 
Tin: ; 
 
 V. . thr jWumb lin. h Ou» mark, 0.. 
 
 lOOteL 
 
 licular 1", aud 
 
 . always 
 
 Thus 
 
 Deal. 
 
 ■ 
 ■ 
 
 i < umfcrmcr. — TIip eMiUbUOtU 
 
 • 
 
 ■ t-idently 
 
 the fixed a i/rr, o. 
 Radius. — 11, 
 ■ 
 
 all lino*, m o Imrn from tin- centra to the 
 
 il radii. 
 
 • li::r, I. II, |m.i*in£ through tl 
 
 and liii. by the circui r. The 
 
 . ■ ■( tin- radius. 
 ' thin ilir ebnamfen i" 
 
 plane ntrfact, :■■ any pari of the circui 
 
 ranti. 
 
 I - (he cirrumfor- 
 
 • 
 
 ■ at the point of contact, ti. 
 
 I 
 i the an- which count • 
 
 ■ of the 
 ■1 wiiliin an arc and the chord which 
 
 I of the 
 
 ire |» r- 
 al their inter- 
 i other withoul 
 
 otfuar I 
 
 ir when formed 
 I fortni 'I by two 
 
 pn<trai'tura, and rv pnwntvd in ti;r«. | 
 
 tin- nir . anj^c are a- 
 
 of Ilia!!. 
 
 - 
 
 ■ 
 
 When ma mcaMirv of the a: 
 
 quentl) 
 
 r when the «ir, 
 
 and taili inih . 
 
 l 
 
 ■ 
 I 
 
 • .'ii the 
 circle indicating the no It 
 
 will l«- aeen thai the 60*. 
 
 those tl 
 
 other. Tlir ri 
 
 t.> the m -rtir.-il line, ic, or the horizontal lint 
 
 /' i 
 
 other when tl 
 
 length ; the II • Del 
 
 / 
 
 i . when tlir i 1 
 
 . 
 and '. : 
 when tli<' tlir. i 
 
 it wiim an) i 
 funn n I 
 subtend Irumcnt 
 
 i 
 
 . 
 i| the other 
 
 /■ \ 
 
 I o when all the 
 
 and il>- \ 
 
 ,\ 
 \ 
 
 ■ 
 
BOOK 'IF INDUSTRIAL DESIGN. 
 
 aai da, Bg. 10. are equal and perpendicular to one another, the 
 angles consequently also being equal, and all right angles. 
 
 A rectangle is a quadrilateral, having two aides equal, as a b 
 and r n, fig. 14. and perpendicular to two other equal and parallel 
 sides, as a y ami E N. 
 
 A parallelogram is a quadrilateral, of which the opposite sides 
 and angles are equal ; and a lozenge is a quadrilateral with all the 
 sides, but only the opposite angles equal 
 
 A trapezium is a quadrilateral, of which only two sides, as a i 
 and M i.. fig. 9. are parallel. 
 
 Polygons are regular when all their sides and angles arc equal, 
 and are otherwise irregular. All regular polygons are capable 'if 
 being inscribed in a circle, hence the great facility with which they 
 may be accurately delineated, 
 
 OBSERVATIONS. 
 
 Wo have deemed it necessary to give these definitions, in order 
 to make our descriptions more readily understood, and we propose 
 DOW to proceed to the solution of those elementary problems with 
 which, from their frequent occurrence in practice, it is important 
 that the student should be Well acquainted. The first step, how- 
 ever, to be taken, is to prepare the paper to be drawn upon, so 
 that it shall be Well stretched on the board. To effect this, it 
 
 must be slightly but equally moistened on one aide with a sponge; 
 
 the moistened Side is then applied to the board, and the edges of 
 the paper glued or pasted down, commencing with the middle of 
 
 the sides, and then Becnring the corners. When the Bheel is dry, 
 it will bo uniformly stretched, and the drawing may be executed, 
 being fust made in faint pencil lines, and afterwards redelineatcd 
 pi ii. To distinguish those lines 
 which may be termed working lines, as being but guides to the 
 in o( the actual outlines of the drawing, we have in the 
 
 plates represented the former bj i itted I nea, and the latter by full 
 
 continuous lines. 
 
 PROBLEMS. 
 
 1. To erect a perpendicular on the centre of a given right I 
 c D, Jig. 1. — From the extreme points, c,' n, as centres, and with a 
 radius greater than half the line, describe the ares which cr 
 
 other in a and u, on either side of the line to be divided. A line. 
 a is, joining these points, will be a perpendicular bisecting the line, 
 
 C D, in G. Proceeding in the same manner with each half of the line, 
 I G D, we obtain the perpendiculars, I K and i. M, dividing 
 
 the line into four equal parts, and we can thus divide any given 
 right line into 2, 1,8, 16, &c., equal parts. This problem is of 
 
 ml application iii drawing. For instance, in order to obtain 
 
 the principal lines, V X and V /.. which divide tho sheet of paper 
 into four equal parts; with the points, r s I u, taken as near the 
 edge of the paper a3 possible, as centres, we describe tin arcs 
 which intersect each other in p and q: and with these last as 
 centres, describe also the arcs which cut each other in y, z. The 
 right lines, v x and Y z, drawn through tho points, P, Q, and ;/. :. 
 respectively, are perpendicular to each other, and serve as guides 
 in drawing on different parts of the paper, and are merely pencilled 
 in, to be afterwards effaced. 
 
 2. To erect a perpendicular on any given point, as H, in the line c D, 
 
 fig. 1 — Mark oil* on the line, on each side of the point, two equal 
 distances, as c h and kg, and with the centres c and g describe 
 the arcs crossing at I or ic. and the line drawn through them, and 
 lie 'in h the point it. will be the line required. 
 
 3. To let fa ular from a point, as L, apart from 
 
 (he right line, c n. — With the point l, as a centre, describe an 
 arc which cuts the line, c D, in G and d, and with these points as 
 centres, describe two other ares cutting each other in u, and the 
 right line joining L and M will be the perpendicular required. In 
 practice, such perpendiculars are generally drawn by means of an 
 an e and a square, or T-square, such as fig. (p 1 . 
 
 ■I. To <li mi- parallels to any given li7ies, as vx and r z. — For 
 regularity's sake, it is well to construct a rectangle, such as rst tj, 
 on the paper that is being drawn upon, which is thus done: — From 
 the points v and x, describe the arcs R, s, T, u, and applying tho 
 rule tangentially to the two first, draw the line r s, and then in tho 
 the line t u. The lines r t and s u are also obtained 
 in a similar manner. In general, however, such parallels are moro 
 quickly drawn by means of the T-square, which may be slid along 
 the edge of the board. Short parallel lines may be drawn with 
 the angle and rule. 
 
 5. To dh ide a given right line, as a b, Jig. 3, into several equal 
 parts. — We have already shown bow a line may be divided into 2 
 or 1 equal parts. We shall now give a simple method for dividing 
 a line into any number of equal parts. From the point a, draw 
 
 a o, making any convenient angle with a b ; mark off on A C 
 as many equal distances as it is wished to divide the line A u into; 
 in the present instance seven. Join c B, and from the several 
 points marked off on a c, draw parallels to c B, using the rule and 
 angle for this purpose. The line a b will be divided into seven 
 equal parts by the intersections of the parallel lines just dmwn. 
 Any Line making any angle with a e, as A i. may be employed in- 
 of a e. with exactly the same results. This is a very useful 
 problem, especially applicable to the formation of scales for the 
 reduction of drawings. 
 
 6. A scab is a straight line divided and subdivided into feet, 
 inches, and parte to English measures; or into 
 
 li ii.s. centimetres, and millimetres, according to 
 French :i e divisions hearing the same proportion to 
 
 each other, as in the system of measurement from which they are 
 derived. The object of the scale is to indicate the prop trtiou the 
 drawing bears to the object represented. 
 
 7. To construct a scale. — The French scale being the on* 
 adopted in this work, it will be necessary to state that the mitr» 
 (=39-371 English inches) is the unit of measurement, and is 
 
 divided into In deeiuii lies, i •, minu'-tres, and 1000 millimetre*. 
 
 If it is intended to execute the drawing to a scale of i or J; llie 
 
 metre is divided by 4 or 5, one of the divisions being the ten 
 metre on the reduced scale. A line of this length is drawn on the 
 paper, and is divided into reduced decimetres. &c. just as the. 
 in.tre is itself. Fig. 7 is part of a scale for reducing a drawing to 
 In this scale an extra divisi in is placed to the left of 
 zer... wbi.-li is subdivided, to facilitate the obtainment of any re- 
 quired measure. F..r example, if we want a length corresponding 
 to 33 centimetres, we place one point of the compasses on the 
 division marked 3 to the right of zero, and the other on the second 
 
I 
 
 Tiir. pn\<Ti«\i. DRAroirrsMAVS 
 
 drrbtoa to the left, and the length comprised between these points 
 will be 3 dVrimAtrrv 3 een ime-tre*. = S3 centimetres. 
 
 The ahiigissci ttmte :nnule im-»«un ments are n- 
 
 qiuosi greater precision is obtained with a diagonal scale, such aa 
 fig. ft. It b thu» constructed : — Having drawn a line ami i 
 it. at in fig 7, draw, parallel and equal to it, tin 
 c <£ a./, if., at c^aal distances apart, 
 dkrulan at tl I 
 
 dKWooa to tl . draw the flBMjnnal. .'■ i. and draw 
 
 pualleb to it from the mnainii 
 From the di». 
 
 to the point on the extreme parallel. ■ 4. rut by '' 
 dicular, and draw also the parallel diagonals, 1 — 2. 2 — 3. aa I 
 
 It will be evident, that aa in the space of the ten borizoata] line % 
 
 the left, it w: 
 intermediate 11: .1. 3d, die., at • 1.2.3. 
 
 h» of such di\i«i.>n. in the same direction, so that the 
 diagonal line, 3'. will cut the 5th line at a point 2,*, of ■ d 
 diatant from zero. Tl 
 on the point i, and tin- other on Iha Intersection of 111 
 
 la] line with the perpendicular of il 
 the measure compriaed between t ii - m will be 3 <1< 
 
 ■ad ,'.. .T 5 millimetre* = 325 mili.: 
 / I angle, as T c n, fig. 2, inln tw» eipiu 
 
 !ie apex, c, as a centra, deeeribe tha arc, h i. and willi Iha 
 
 - cutting 
 each other in ; ; join ; c, and the right line, j < . will bifida tha 
 
 - ii i j and i i i. Tl. 
 be sublividcd in the aame manner, aa shown in '! 
 angle may alao be divided by BMaoa of either of i: 
 
 D. *■ 
 
 9. To drate a tangent m n _ n D H, fig. X 
 
 required to draw iha in the 
 
 . radius, c D, must be drawn meeting llie point, and be pro- 
 duced beyond it, «ay to e. Then, by Iha method dread] 
 draw 2 |<vndicular to c E, cutting it in t>, anil it 
 
 will be , linst If. h •• 
 
 the ta: I given point, a* a, oataidl Iha circle, a 
 
 awn joining the point, a, an : 
 of the I ' the point, 0, with this 
 
 point »• - nl»' a circle passing through A nn-; 
 
 " in n and it : right lines joining a ii and 
 A M wi ' •, circle, and lb 
 
 • ad and a ii respectively. 
 ' -ill u-ith irhirh 
 
 • drawn. — With an;. 
 aa centres, describe arcs of equal limiaa, entdng each othi 
 throogh the ;. .. to and L0J 
 
 o, the 
 
 11/ "-It through any three points ru* in a right 
 
 irelo can |«ss through the aa:; 
 and sir. g (he centre :- 
 
 and a point in the cir 
 exactly the ami • 
 
 /'. iiucn&r a cirxle m a guen triangle, as a ■ r, fig. 6. — 
 
 srribej in a figure, when all ,; 
 
 latter an 
 
 lines, as a a B ' 
 
 fall per;- — e per- 
 
 ..il, and radii of the r. 
 
 Ii V . i jV .i :'i.j'i_->. .i< u. ' - ,ual }<arts. — If 
 
 the parts an- n le, as g t, in the 
 with which, aa 
 
 i 
 
 k, b] the perpenr hc ahg I . equal 
 
 and draw ma One, i. m. |wralM to ii i. Tha trtangli 
 ■ 
 ■ half the Mangle, g ii t. If the given triangle were cm, 
 
 it eroold alao be dhrhlad into two equal parti i m. 
 
 I I Ih ilrair a tmttn diruhle (Ac > I [uarr, A B r D, 
 
 rtrnara any two sidea 
 
 srUefa are at ri.-tit angina to each other, a" n A and D C, to n and L, 
 
 with Iha ci utre, n, and radius, i. n. .1. rjn ai laf 
 
 and through llie pot 
 -. i> a and D i.. draw parallels to d l and da reapectirejy, or 
 i g e p, will be double 
 i of Iha given square, a bc d; and in the aama manner a 
 
 ii K I. n, may be drawn double the area of On • 
 Il i* evident that the diagonal of ■ • iual to 
 
 one -i le of a square twice (hi 
 
 15. Tn ittCtibt a rirrlr half the tea) nf a giien rirrle. ihkid, 
 •Draw two diameters, a n and r t», at right ai 
 each other; join an extremit] the chord) ac 
 
 tl is chord by tin- perpendkolar, r. r. The radius of tin 
 
 '. circle will l« ■ It follow, that the annulai 
 
 rnal to Iha amaOer oirde wHUn it. 
 
 11. '/'• I',-.-!' 13, 
 
 ii — Draw any diameter, r, and with 
 g, as a centre, oV aariba Iha an-, inn. its radius being equal to thai 
 
 of the gi\m circle; join D r. I r, and I D, and D »"• T will be the 
 r.qiiinsl. The ~i.le of a M gular hi to the 
 
 r the eirenmacribing drele, and, therefore, in order to in- 
 
 sci-ilic it in a drele, all that is necessary is to mark olT 00 lln- cir- 
 cunili nncc the length of the radius, and, joining the |K.ints of in- 
 
 n, as k 1 1. ii m j, the naulaTuH, figure will Is- iha i 
 T ■ - -i' • H • ■■■ i of 19 or '2i -il. «. ii i- mi 
 to dhrlde or lubdiride the ■ 
 
 i ;is alM.ve. and to join the |>oitits of intl 
 ■ 
 mil. and bottb I 
 
 I '■<• , Hi whi.l .. or the stjuara. 
 
 in differ - bdtaatod m " 
 
 17. T ' '■ ''- 13 — 
 
 - a ii. D, perpaooaaahv to one another, aru 
 join the |>oini- • ■<■. and A i; ii i> will be 
 
 ind. 
 1» 7'. • I i.V a regular octagon abrntt a 
 
 II .nig. as in the last OBCC, ilr.iun '«•> 
 i i, ,. ii. draw other tw... i j. k : 
 ■ mud l,y the t'..niur; through the i igh! p..inls ol u.ierws;- 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 tion with the circle draw the tangents, e, k, e, j, f, i.. i — these tan- 
 gents "ill cut each other and form the regular octagon required. 
 This figure may also be drawn by means of the square, and angle 
 of 45", ©. 
 
 19. To construct a regular octagon of which one side is given, as 
 A V,fig. 14. — Draw the perpendicular, o u, bisecting a b ; draw A F 
 parallel to o d, produce a n to C, and bisect the angle, c a f, by the 
 line e a, making E a equal to a b. Draw the line og, perpendi- 
 cular to, and bisecting e a. oq will cut the vertical, o d, in o, 
 which will be the centre of the circle circumscribing the required 
 octagon. This may, therefore, at once bo drawn by simply mark- 
 ing oft' arcs, as E H, H f, &c, equal to A B, and joining the points, 
 F.. h, f, &c. Be dividing and subdividing the arcs tints obtained 
 we can draw regular figures of 16 or 32 sides. The octagon is 
 a figure of frequent application, as for drawing bosses, bearing 
 brasses, &c. 
 
 20. To construct a regular pentagon in a g inn < ircle, as A B c D F, 
 also a decagon in a gken circte, as E R to, fig. 15. — The pentagon 
 is thus obtained : draw the diameters, A t, B J. perpendicular to each 
 other; bisecting OE in K. with K as a centre, and k a as radius. 
 describe the arc, a l ; the chord, a l, will be equal to a side of the 
 pentagon, which may accordingly be drawn by making the chords 
 which form its sides, as a e, f d, d c, c b, and b a, equal to a l. 
 By bisecting these arcs, the sides of a decagon may be at once 
 obtained. A decagon may also be constructed thus : — Draw two 
 radii perpendicular to each other, as o M and o R ; next, the tan- 
 gents, N M and N R. Describe a circle having N H for its diameter ; 
 join K, and f the centre of this circle, the line, R p, cutting the 
 eircle in a ; r a is the length of a sido of the decagon, and applying 
 it to the circle, as r6, &c., the required figure will be obtained. 
 The distance, r a or rc, is a mean proportional between an entire 
 radius, as r n, and the difference, c N, between it and the radius. 
 A mean proportional between two lines is one having such relation 
 to them that the square, of which it is the one side, is equal to tire 
 rectangle, of which the Other two are the dimensions, 
 
 21. To construct a rectangle of which the sides shall be mean pro- 
 portionals between a given line, as A c, fig. 16, and oiw a third or 
 two-thirds of it. — A c, the given line, will be the diagonal of the 
 required rectangle; with it a-s a diameter describe the circle abcd. 
 Divide A c into three equal parts in the points, m, n, and from these 
 points draw the perpendiculars, m D and n B ; the lines which join 
 the points of intersection of these lines with the circle, as A B, a d, 
 c b, c d, will form the required rectangle, the side of which, c D, is 
 a mean proportional between c m and c A, or — 
 
 Cm: CD::CD:CA; 
 that is to say, the square of which C D is a side, is equal to a rec- 
 tangle of which c a is the length, and c m the height, because 
 
 CDxCD = CmxCA* 
 In like manner, a d is a mean proportional between c a and m a. 
 This problem often occurs in practice, in measuring timber. Thus 
 the rectangle inscribed in the circle, fig. 16, which may be con- 
 sidered as representing the section of a tree, is the form of the 
 beam of the greatest strength which can bo obtained from the 
 tree. 
 
 * See the notes and rules given at the end of thu chapter 
 
 APPLICATIONS. 
 
 DESIGNS FOR INLAID PAVEMENTS, CEILINGS, AND BALCONIES. 
 
 PLATE II. 
 
 The problems just considered are capable of a great variety of 
 applications, and in Plate II. will be found a collection of some of 
 those more frequently met with in mechanical and architectural 
 constructions and erections. In order, however, that the student 
 may perfectly understand the different operations, we Would 
 recommend him to draw the various designs on a much larger 
 scalo than that we have adopted, and to which we aro necessarily 
 limited by space. Tho figures distinguished by numbers, and 
 showing the method of forming the outlines, arc drawn to a larger 
 scale than the figures distinguished by letters, and representing tho 
 complete designs. 
 
 22. To draw a pavement consisting of equal squares, figs. A and 
 1. — Taking the length, a b, equal to half the diagonal of tho 
 required squares, mark it off a number of times on a horizontal 
 line, as from A to B, B to c, &e. At A erect the perpendicular 
 I h, and draw parallels to it, as D E, G f, &c, through the several 
 points of division. On the perpendicular, i H, mark off a number 
 of distances equal to A B, and draw parallels to A B, through tho 
 points of division, as h g, I f, &c. A series of small squares will 
 thus be formed, and the larger ones are obtained simply by draw- 
 ing the diagonals to these, as shown. 
 
 23. To draw a pavement composed of squares and interlaced 
 rectangles, figs. (5) and 2. — Let the side, as c d, of the square bo 
 given, and describe the circle, L M q B, the radius of which is equal 
 to half the given side. With the same centre, o, describe also 
 the larger circle, K N P i, the radius of which is equal to half the 
 side of the square, plus the breadth of the rectangle, a b. Draw 
 the diameters, a c, e d, perpendicular to each other ; draw tan- 
 gents through the points, a, d, c, e, forming the square, jhfo; 
 draw the diagonals J F, g, h, cutting the two circles 'n the points, 
 I, B, K, L, M, N, P, Q, through which draw parallels to the diagonals. 
 It will be perceived that the lines, a e, e c, c d, and D a, aro 
 exactly in the centre of the rectangles, and consequently serve to 
 verily their correctness. The operation just described is repeated, 
 as far as it is wished to extend the pattern or design, many of the 
 lines being obtained by simply prolonging those already drawn. 
 In inking this in, the student must be very careful not to cross tho 
 lines. This design, though analogous to the first, is somewhat 
 different in appearance, and is applicable to tile construction of 
 trellis-work, and other devices. 
 
 24. To draw a Grecian border or frieze, figs. © and 3. — On two 
 straight lines, as a b, ac, perpendicular to each other, mark off, 
 as often as necessary, a distance, a t, representing the width, ef, 
 of the ribbon forming the pattern. Through all the points of 
 division, draw parallels to a b, a c — thus forming a series of small 
 squares, guided by which the pattern may be at once inked in, 
 equal distances being maintained between the sets of lines, as in 
 fig. ©. This ornament is frequently met with in architecture, 
 being used for ceilings, cornices, railings, and balconies; also in 
 cabinet work and machinery for borders, and for wood and irori 
 gratings. 
 
 25. To draw a pavement composed of squares and regular octa. 
 
' 
 
 gvm.fig*. D atj i.— W 
 
 in»!e I., draw 
 i: — iuc »quare, a a c D, being timt obtained, mii-i 
 ICID, drawn 
 bring then -ir.. 
 be formed by marking off from each • 
 
 pattern u extended rimpty by 
 
 ride* of four 
 which an- inclined at an an 
 ThU pt ■ •»!'• marble, 
 
 Bl CuluUTH, «). 
 
 36. 7' icti/ composnl 
 
 and 5.- 
 
 6 
 '. 
 
 ■ 
 the hexagon* are plain and shad. : m their 
 
 arranj> :: • !"iir. 
 
 . 
 Bqvarti, 
 
 nala, A c, B d ; i 
 
 the firv. ' rial, r d, mark the equal rthrtanceo, or, if, and 
 
 through c and /draw parallel* tn tlir diagonal, a c ; join th* 
 
 ' ilea, i /. 
 m n, erl 1 to form Ihi | 
 
 requirir - 
 
 !h Formed in 
 
 I f..r furnitiu. 
 
 On a ■trai' r rht line, A B. mark off Ihi 
 
 aw Ike due 1 d, 
 
 •■ad: and draw a i 
 I r parallel to A B. C . i . cut- 
 
 i jobi a ii. In Ihii 
 
 ■ I by continuing 
 the line* and drawing parallel! n - 
 
 remain . - rn will In- r> 
 
 I 
 
 ami 12. — If in ' 
 
 diagnnv shall obtain 
 
 ■ 
 
 I be tlir 
 *]*•% of 
 
 • lint*. 
 
 vrangeinent* of >ari»u< regular pol 
 
 pattern* may be produced by combining these d 
 
 ■! many art*, particularly for 
 
 .mental 
 
 / aVair an open-work •ting of Uaenget and 
 
 'i.'». H andS- . 
 
 I 
 
 lii.li mast ihi li.'ular 
 
 ./, draw parallela to 
 ■ 
 
 • .i|ur1. The i' lie the 
 
 • r mat 
 
 ti radii. 
 
 I •.,••.... I by ad • -. and to 
 
 • a, parallel* to 
 drawn, then ■ cora- 
 
 ttern. 
 
 . composed if imall squares or 
 md 9.— 
 1 
 nt' roar of the amall loxcngea, draw tl • 
 
 Into t'"Ur equal part* 
 iil" the I ^ ii. ami join 
 
 . /«, are 
 ..ml tin- appropriate iiarallel- I 
 drawn. In extending the pattern bj repetition, Ihi 
 ponding t.> i ai 
 parallel line*, as i i and 
 
 I 
 i aeh, a Dumber of pattern* may l«- | 
 
 though formed of tie 
 
 rn, eom- 
 : rililxins intrrla 
 
 1 
 
 l«- drawn. uilh 
 
 vertical i ■ -. make i i equal t" i a. and «.■ 
 
 the circle havL 
 
 equal ■ ■!.-■ I ' 
 
 which will complete the lit 
 of tlir pattern, |, u, the left. Ti. 
 
 duplex, fig 9, may 1- "n tlio 
 
 V. - are run 
 
 int.. pal I tin-in 
 
 join «•■!!. aa the beauty of Ihe dra 
 
 mk in the • H i* practieaDy 
 
 Kan tn draw a 
 
 • line. 
 
 / mjnifrii 
 
 1 I 1 WO 
 
 i.tli aba 
 
 ■ - ..i the other, dm Brat the 
 
 • I tin' inner and coneen tri c one, *fgn. Tlio 
 
 I tin' latter being eul bj tie and ID, la the 
 
 i. ;. k. I, IhrOUgh (heme draw |>nrallcl» to the ride* of tho 
 
 aquare, abcd, and finally, with the centre, o, describe a amaV 
 
ROOK OF INDUSTRIAL DESIGN. 
 
 circle, the diameter of which is equal to the width of the ind 
 crosses, the sides of these being drawn tangent to this circle. 
 Tims are obtained all the Hues accessary to delineate this pattern : 
 the relievo aud intaglio portions are contrasted by the latter being 
 shaded. 
 
 In the foregoing problems, we have shown a few of the manj 
 varieties of patterns producible by the combination of 
 
 regular figures, lines, and circles. There is DO limit to the multi- 
 plication iif these designs; the processes of construction, however, 
 being analogous to those just treated of, the student will be able 
 to produce them with every facility. 
 
 SWEEPS, SECTIONS, AND MOULDINGS. 
 PLATE III. 
 
 34. To draw in a square a a rtss of arcs, relisted by semicircular 
 mouldings, figs. A and 1. — Let a B be a side of the square ; draw 
 the diagonals cutting each other in the point, o, through which 
 draw parallels. D E, c F, to the sides; with the corners of the 
 square as centres, and with a given radius, a <;, describe the four 
 quadrants, and with the points, D, F, B, describe the small semicircks 
 of the given radius. D <;, which must be less than the distance, D b. 
 This completes the figure, the symmetry of which may be verified 
 by drawing circles of the radii, c G, c H, which should touch, the 
 former the larger quadrants, and the latter the smaller semi- 
 circles. If. instead of the smaller semicircles, larger ones had 
 been drawn with the radius. D i, the outline would have formed a 
 perfect sweep, being free from angles. This figure is often met 
 with in machinery, for instance, as representing the section of a 
 beam, connecting-rod, or frame standard. 
 
 35. To draw an arc tangent to two straight lines. — First, lei the 
 radius, a b. fig. 3, be given; with the centre, A, being the point 
 of intersection of the two lines, A B, A c, and a radius equal 
 to a b, describe arcs cutting theso lines, and through the points of 
 intersection draw parallels to them, B o, c o, cutting each other in 
 o, which will be the centre of the required arc. Draw perpen- 
 diculars from it to the straight lines, A B, AC, meeting them in 
 D and E, which will be the points of contact of the required arc. 
 Secondly, if a point of contact be given, as B, tig. 3, tie lb* a 
 being A B, AC mating any angle with each other, bisect the 
 angle by the straight line, a d ; draw B o perpendicular to a n, from 
 
 the point, b, and the point, o, of its intersection with a d, will be 
 the centre of the required arc. If. as in figs. - and :i. we draw 
 arcs, of radii somewhat less than o B, we shall form conges, which 
 stand out from, instead of being tangents to. the ui\ >n straight 
 lines. This problem meets with an application in drawing fig. 2- 
 which represents a section of various descriptions of castings. 
 
 36. To draw a circle tangent to three given straight lines, which 
 make any angles with cocA other. Jig. 4. — Bisect the angle of the 
 lines, ab and A c, by the straight line, A E. and the angle formed 
 by c d and c a, by the line, c f. a e and c f will cut each other 
 
 in the point, o, which is at an equal distance & -a.h side, and 
 
 is consequently the centre of the required circle, which may be 
 drawn with a radius, equal to a line from the point, o, perpendi- 
 cular to any of the sides. This problem is necessary for the com- 
 pletion of n>. @. 
 
 37. To draw the section of a stair rail, Jig. ©. — This gives riso 
 to the problems considered in tigs. 5 and 6. First, let it be ro- 
 quired to draw- an arc tangent tii a given arc, as a b, and to the 
 
 given straight line, CD, tig. •> — D being the point, of contact wi h 
 the latter. Through u draw E F perpendicular to CD; make FD 
 equal to OB, the radius of the given arc, and join or, thlOUgh 
 the centre of which draw the perpendicular, G E, and the point, E, of 
 its intersection with i: r, will be the centre of the required arc, 
 aud ED the radius. Further, join o E, and the point of intersec- 
 tion, i), with the arc, A n, will be the point of junction of the two 
 arcs. Secondly, let it be required to draw an arc tangential to a 
 given arc, as All, and to two straight lines, as bc,cd, fig. 5. 
 Bisect the angle, ii c D, by the straight line, C E ; with the centre, C, 
 
 ami the radius, en. equal to that of the given arc, b a, describe 
 the an', o a ; parallel to ti <• draw t it J, cutting E c in J. Join o J, 
 the line, o j, cutting the arc, H g, in g ; join c G, and draw o K pa- 
 rallel to cg; tho point, k. of its intersection with E J, will be 
 the centre of tin' required arc, and a line. K L or K H, perpendicular 
 to c ither of the given Btraight lines, will be the radius. 
 
 38. To draw the section, (J an acorn, Jig. ©. — This figure calls 
 for the solution of the two problems considered in tigs. ;> and 10. 
 
 First, it is required to draw an arc. passing through a given point, 
 A, fig. 9, in a line, a b, in which also is to be the centre of the 
 are, this arc at the same time being a tangent to the given arc. 0, 
 .Make a I) equal to o c, the radius of the given arc ; join o D, and 
 draw the perpendicular, f b, bisecting it B, the point of inter- 
 section of the latter line, with A B, is the centre of the required ale, 
 a e c, a b being the radius. Secondly, it is required to draw an arc 
 passing through a given point, A, fig. 10, tangential to a given are, 
 bcd, and having a radius equal to a. With the centre, o, of the 
 given arc, and with a radius, o E, equal to o c, plus the given radius, 
 a. draw the arc B ; and with the given point, a. as a centre, and 
 with a radius equal to <;. describe an arc cutting the former in E 
 — E will be the centre of the required are. and its point of contact 
 with the given arc will be in c, on the line, o E. It will be seen 
 that ill fig. r £). these problems arise in drawing either side of the 
 object. The two sides are precisely the same, but reversed, and 
 the outline of each is equidistant from the centre line, which should 
 
 always be pencilled in when drawing similar figures, it being diffi- 
 cult to make them symmetrical without such a guide. This is an 
 ornament frequently met with in machinery, aud iu articles of 
 vai ious materials and uses, 
 
 39. To tlruic a wan run, .formed by arcs, equal and tangent to 
 each other, and passing n jioinls, a, b, their radius being 
 
 distance, a b. figs. 2 and 7. — Join A B, and draw 
 the perpendicular, E F, bisecting it in C. With the centres, A and 
 i'. and radius, a C, describe arcs cutting each other in Co and with 
 the centres, 11 and c, oilier two cutting each other in li ; g and H 
 will be the centres of the required arcs, forming the curve or 
 sweep, Air.. This curve is very common iu architecture, and is 
 styled the eyinu redo. 
 
 40. To draw a similar curve to the preceding, but formed by 
 tires of n gixen radius, as a t.figs. G? and 11. — Divide the straight 
 line into four equal parts by the perpendiculars, E F, Q B, and 
 c D ; then, with the centre, a, and given radius, A I, which must 
 always be greater than tho quarter of A B, describe the arv 
 

 0» ia c: alar, w-iih ate centre, a. » aa nil i r are or.mg 
 • a ia a ; c aad ■ will be lb* centre* uf ibe am forawag the re- 
 quired evil Whalrter be the given radios, protidrd it at not 
 too small, lha centres of tha arc* w ill *!»*>» be ia the fine*, c D 
 aad • a. It will be aeca that the area, c t and a i, cut the straight 
 anas, c» aad e a. io two points raa piru lafca the 
 
 aw mill poiata, uu centres. w« ahall form a ainalar cane to the 
 laat, bat with the concavity and convexity tranepused. aad called 
 tha n/ma rrwra*. The two mill be found ia fig . f, the firat at a, 
 aad the second at a. This figure represents the aertioo of a 
 door, or window bane — it is one well known to carpenter* aad 
 
 The little iaairamrot ksowa as the - Cvmameter." afford* a 
 coot cnirnt mean* of obtaining rough niraaareiDeiita of contours 
 of rariooa classes, as mouldings aad bas-refiefa. It is amply a 
 Ight adnsatsble frame, acting as a apnea of holding socket fur a 
 dim of paraDet slips of wood or metal— a handle of straight 
 , for example. Previous to applying tins for taking an ho- 
 of measurement, the whole aggregation of pieces is 
 diwsid in M • at surface, so that their eods form s 
 plane, like the cads of the bristles in a square rut brush ; and 
 these component piecea are held in close parallel contact, with just 
 anoafh of stiff friction to keep them from slipping and falling 
 a» it. The ends of the piecea are then applied well op to the 
 »«— t*»g or surface whose cavities and projections are to be mea- 
 sured, and the frame is then acrewed up to retain the slips in the 
 araetfon thus aaiian il The surface thus moulds ha sectional 
 rontour upon the needle coda, as if the surface made up of theae 
 arsis waa of a plaatie material, and a perfect impression is there- 
 for* earned a-»av on the instrument. Toe nicety of de l in e ation is 
 .■■J by the rels 
 41 TodiwbaluMtrafm&iflexamltmr,fig*.Qmti' 
 here neeeaaary to draw an -• 
 
 know* arcs, a i and c r>. and <i bori- 
 
 lootal, t i Eitend t i to B. making i B equal to c n. the radius 
 of the are. c o. Join c a. biaectin.- ■;.» ndicular; this 
 
 will cat r B in the point, e, which is tbr crntrr of the required arc — 
 « i being it* radius. A line joining e a ruts c D in c the point of 
 contact of the two area. The arc. t> r, which is required to be a 
 tangent to c n, and to pass through the point, r, is drawn with the 
 centre, o, obtained by biaecting th< era ndkabv 
 
 which cuts the radius of the - ken, in fig. Q. to 
 
 b* repeated both on each aide of the t crural line, m n. and of the 
 t. ■ aid ;.:,• ,fg. 
 
 i;, irate tar aerriow of* halajfer c/siavair owtirar, as fig. X- 
 ■ * an air passing through two points, a, a, 
 ' ' r* bring in a straight line, • c ; this are, moreover, 
 
 n^uinnjr to join at n. and form a sweep with another. :■ i. hating 
 rut centre in a line, r i >. pars.' i ■ ; « ndicu- 
 
 IV hiaertiag ■ A. will rut a c in o, which will br the centre of the 
 firat arc. and that of the second may now be obtained, aa in 
 prohlaat 37. fig. 6 
 
 .'-•* base of the baluster, fig. H. ia in the form of I 
 tanned a aces*. It may be drawn by t ai t o wa untbuda. The 
 fallowing are two of the airnptrwl areording to the firat. the 
 aajre* may be formed by area awerping into each other, and tan- 
 
 geataat a aad c U tare given aaraMs, a, a, en, fig. IX Through 
 fiaaj the prrpcadkaars, c o aad a k, aad divide the latter 
 into three equal parts. With one drriaoa, F a, aa a radian, 
 • U first arc, a c b ; totX.tr c t eqaal to r A. join l r, aad 
 bisect I r bj the n vr prad ka hu - . o x. which cuts c ia a o will 
 br the eratre of the other arc required. The Bar, o a, paeanf 
 through the centres, o and r, wil] cat the area in the point of junc- 
 tion, a. It is at this manner that the cunre ia fig. N a ibtaaii 
 The aeroad method a to form the carve by two area sweeping 
 into each other and pawning through the given poiata. a a, fig. 14, 
 their centres. b»w r » er. being in the anae b. <m ■ •atal fine, c n, 
 parallel to two ai eight lines, x r aad a c, pawning t a t o a g h tha 
 given poiata. Throagfa a, draw the pcrprocacwlnr, A L I. a* point 
 of interarcaoo with c It, ia the eratre of oar are, a t>. Ml it draw 
 the chord, a n, the perpendicular brarrting whs-h. will cut c n ia o, 
 the centre of the other arc, the rail us being o D or o a. Thia curve 
 is more particalarly met with in the conatraraoa of bases of tat 
 i riiriusn. and Cocnposite order* of arduteeture. 
 
 ••• Tcustom the stodrnt to propca-aoa hi* d e a iga a 
 to the rules adopted ia practice ia the awre u l nio a * ap priratvt na, 
 we bate indiratrd on each of the figs. A- 3- C &<-. aad oa tha 
 •ding outlines, the measurrmen t» of the varioa* pans, ia 
 aaftaaetrea. It mast, however, at the same time ha understood, 
 that the various p i o bWra are equally capable of a u laa u a with 
 other data: and. indeed, the number of appli c ations of which tha 
 : • - • -■-. ..• *--•,-• .._-■--•- - . -.. 
 ■ 
 
 : KNTARY ' R06 TK& 
 
 PLATE IV. 
 4* Having solved the foregoing pi iiblian, tha i taial may 
 
 i! : 
 
 - 
 to the accurate determination of tha p ra ain al lines, 
 which serve aa guides to the minor details of the drawing. 
 
 ■ Gothic arrhitecture that we meet with the more Burner- 
 aai a; • . ati m :' aad aaaf n •■: : . <;. - ::■ > ; .:«v! aaalai xr.J 
 inea, and we give a few trample* of this order ia Plate IT. 
 Fig. 5 repreaeau the upper portion of a window, cca np ooed of a 
 aerie* of area, combed ao aa to form what are denominated ewepaf 
 The width or apaa. A a. being git en. aad the apex, c . 
 i . draw the bisecting perpendiculars, cutting a > in 
 p and r_ Theae Utter are the centre* of the sundry concentric 
 arcs. mh..-h. Ktrrally rutting each other oa the TerticaL c r. form 
 the arch of the window. The small interior eaapi 
 in the same manner, aa indicated ia the figure ; t 
 c B. being git en. also the apaa aad apnea. Theae mterior archee 
 are manuana sumvunied by the nranarat. a, termed aa «a(-ew> 
 •as/. rniwwatiag •imply of concentrk rirrle*. 
 
 tscoU a rowrtte, f orated by cone 
 the outer intrrsta-.es containing a series of smaller circlra. fa 
 an interlaced fillet or ribbon. The radio*. A o, of the circle, coa- 
 taining the orotres of all the wnall circles, is •apposed lobe given. 
 amber of equal parta. With the poiata of 
 ditision. 1. i X Ac aa centres, deaeribe the cocbm tangeataal la 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 each other, forming the fillet, making the ra.lii of the alternate 
 ones in anv proportion to each other. Then, with the centre, 0, 
 describe concentric circles, tangential to the larger of the fillet 
 circles of the radius, A b. The central ornament is formed by 
 arcs of circles, tangential to the radii, drawn to the centres of the 
 fillet circles, their convexities being towards the centre, o: and the 
 arcs, joining the extremities of tfae radii, are drawn with the actual 
 centres of the fillet circles. 
 
 46. Fig. 6 represents a quadrant of a Gothic rosette, distin- 
 guished as radiating. It is formed by a series of cuspid arches and 
 radiating mulliuns. In the figure are indicated tie' centra lines of 
 the seven] arches and mullions. and in fig. 6', the capital, con- 
 electing the niullion to the arch, is represented drawn to dottble 
 the scale. With the given radii, a b, a r, a d, a e, describe the 
 different quadrants, and divide each into eight equal parts, thus 
 obtaining the centres for the trefoil and quadrefoii ornaments in 
 and between the different arches. We have drawn these orna- 
 ments to a larger scale, in figs. t>>, t;>', atui 6°, in which are indi- 
 cated the several operations required. 
 
 47. Fig. 4 also represents a rosette, composed of cuspid arches 
 and trefoil and quadrefoii ornaments, but disposed in a different 
 manner. The operations are so similar to those just considered, 
 
 that it is unnecessary to enter into further details. 
 
 48. Fig. 7 represents a cast-iron grating, ornamented with 
 Gothic devices. Fig. 7* is a portion of the details on a larger 
 scale, from which it will be seen that the entire pattern is made 
 up dimply of arcs, straight lines, and sweeps formed of Ihese two. 
 
 the problems arising comprehending the division of lines aid 
 
 angles, and the iibtainment of the various centres. 
 
 49. Figs. 2 and 3 are sections of tail-pieces, such as are sus- 
 pended, as it were, from the centres of Gothic vimlts. They also 
 represent sections of certain Gothic columns, met with in the 
 architecture •if the twelfth and thirteenth centuries. In order to 
 draw them, it is merely necessary to determine the radii and centres 
 of the various arcs composing them. 
 
 Several of the figures in Plate IV. are partially shaded, to 
 indicate the degree of relief of the various portion*. \\'e have in 
 
 this plate endeavoured to collect a few of the minor difficulties, 
 
 our object being to familiarize the student to the use of his instru- 
 ment*, espi eiallj the compasses. These exercises will, at the same 
 time, qualify him for the representation of a vast number of forms 
 met with in machinery and architecture. 
 
 OVALS, ELLIPSES, PARABOLAS, VOLUTES, dec 
 
 TLATE V. 
 50. The ore is an ornament of the shape "I an egg, and is 
 formed of arcs of circles. It is frequently employed in architecture, 
 and is thus drawn: — The axes, a b and c D, fig. 1, being given, 
 Perpendicular to each other; with the point of intersection, o, as a 
 centre. tirst describe the circle, cade, half of which forms the 
 upper portion of the ove. Joining no, make it equal to BE, 
 the difference between the radii, o c, o b. Bisect F B by the per- 
 pendicular. G II. cutting c D in H. rt will be the centre, and II c 
 the radius of the arc. c I ; and i, the point of intersection of HC 
 with a B, will be the centre, ant! I B the radius of the smaller arc, 
 
 I B K, which, together with the arc, II K, described with the centre. 
 I., and radius, id, equal to lie, form the lower portion of the 
 required figure ; the lines, G H, L K, which pass through the 
 respective e, litres, also cut the arcs in the points of junction. 
 
 J and K. This ove will he found in the fragment of a ei e, 
 
 fig- A- A more accurate and beautiful ove may be dm ami by 
 rf the instrument represented in elevation and plan in the 
 annexed engraving. 
 
 The pencil is at a, in an adjustable holder, capable of sliding 
 along the connecting-rod, b, one end of which is jointed at c, to a 
 slider on the horizontal bar, D, whilst the opposite end is similarly 
 joint, il to the crank arm. e. revolving on the fixed centre, F, on 
 tin 'oar. By altering the length of the crank, and the position of 
 the pencil on the connecting-rod, the shape and size of the ovn 
 may ' •< varied as required. 
 
 51. The oral differs from the ove in having the upper portion 
 symmetrical with the lower; and to draw it. it is only nec< ssarv to 
 repeal the operations gone through in obtaining the curve, l b f 
 fig. 1. 
 
 52. The ellipse is a figure which possesses the following pro- 
 perty : — The sum of the distances from any point, a, fig. 2, in the 
 circumference, to two constant points, n, c, in the longer axis, is 
 alu.-,ys equal to that axis, he, The two points, b, i - are b mied 
 foci. The curvi forming the ellipse is i ymmetrir witf referenci 
 
 botU to the horizontal line or axis. D E, and to the vertical line, F O. 
 bisecting the former in 0, the centre of the ellipse. Lines, as 
 
 B a, c a, b t, c f, &c., joining anj point in the circumference with 
 the foci, B and c, are called vectors, and any pair proceeding from 
 one point are togi ther equal to the longer axis, d e. which is called 
 the fransreri . po being the conjugate axis. There are different 
 
 methods of drawing this curve, which we will proceed to in 
 
 dicate. 
 
 53. First Method. — This is based on the definition given above, 
 
 and requires that the two axes be given, as he and F G, fig. 3. 
 
 Tie foci, b and c, are tir-t obtained by describing an arc, with the 
 
 extremity. G or F, of the conjugate axis as a centre, and with a 
 radius, fc, equal to half the transverse axis; the an will cut tho 
 latter in the points, r. and r. the foci. If now we divide D E 
 unequally iu M. and with the radii, n H, E II. and the foci as centr- -a, 
 we describe ares severally cutting each (■ther in i. j, k. a ; tin « 
 four points will lie in the circumference. If, further, wo agdB 
 unequally divide d e. say in l, we can similarly obtain four ot lei 
 
M 
 
 Tllr'. M \VS 
 
 poteta in the rinrutnfrrt oc and we ran. in Ekr manner, ..(tain any 
 number of p>4aU, when the eifipae mar 1- 
 • h% hand. Tne Ur,-> etHpara which are sometimes required in eoo- 
 atrarojooa, are generally draw a with a tmmmrl instead of com paw, 
 the trammH being ■ ■ :h adjustal... 
 
 gmlt mr 'i tUtpr: To ubtain this, place a rod in each ol 
 of the required ellipse; round theae place an endleiw cord 
 when stretched by a tracer. 
 wiD be drawn hj es 
 
 *» 4 b, and on half the 
 
 |QaJ to half ll 
 v.l Place til. - so tlial ill. 
 
 longer meaaurvm«nt. r point, 
 
 Daa transverse axis, DC I: 
 
 axes — : a point 
 
 in the circumference which may be narked »itl> a |» n.il. the 
 ellipae being alVrwanU traced throagfa the pointi tint— nbt 
 55. Third MrthitL 
 
 genHM-tr. 
 
 :i will Iw >n My lliat 
 
 the pr. 
 
 being given, as a B and c i>. lh< r in tin- . 
 
 draw ao; 
 
 11,111 dial 
 1 n. an.! ' 
 
 • • "1 
 
 '. 
 the semicircle, and. :.' 
 a a, «■•• 
 equal t. 
 ' 
 
 iili the 
 - 
 
 i. Draw radii, cut) 
 
 'V that 
 the radii ahould !»• al 
 
 the latter 
 a n. nn.l throagfa the 
 I 
 ■ 
 
 which may. . traced throogil tli. m It 
 
 ■ I a point in tl I • 
 
 mint a 
 
 A a. and 
 
 'j in j ; j.hd ; u i»: vflj rut rj in / 0/ will be 
 
 equal U 
 
 . - raar. having 
 the ami 
 
 . 
 half th. 
 
 1 with the eonv 
 
 ubtain 
 
 I lw> seen that 
 
 :.rca of circle*, 
 
 and that thoe Jarl* an - and by 
 
 - axia ia 
 drawn 
 nln, the 
 
 : 
 
 but witii onlj 
 
 'liout, but tlio 
 
 must alwaya 1« within, ami. i 
 ■ r be a ithoul 
 
 • all poa- 
 
 ii and n..t to 
 
 ■ 
 
 be tli" 
 
 I 
 
 li..n ; ami al-". that it " """l '"' l lo 
 
 another, it en 
 
 Lei i 
 both in ' »»d ■, and make a r equal 
 
 • i draw I ll parallel to C a. 
 
 1 ii I. a J. and c t\ equal to it G : J'in i x. and baaaSl it in a, 
 ami at i DxateuaW, eottBf, I Pi Of I D pTOlfonad, at at; 
 
 - of the 
 
 ! .ii M !< and I ra«iii of 
 
 tin- pointi U cntart 
 -. drawn thr- 
 ipse. 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 Several instruments have been invented "for drawing ellipses, 
 many of them very ingeniously contrived. The best known of 
 these contrivances, are those of Farey, Wilson, and I lick — tho 
 last of which we present in the annexed engraving: It is shown 
 as in working order, 
 with a pen for drawing 
 ellipses in ink. It con- 
 sists of a rectangular base 
 plate, A, having sharp 
 countersunk points on 
 its lower surface, to hold 
 the instrument steady, 
 and cut out to leave a 
 Sufficient area of tho 
 paper uncovered for the 
 traverse of the pen. 
 It is adjusted in position 
 by four index lines, 
 setting out the trans- 
 verse and conjugate 
 axes of the intended 
 ellipse — these lines 
 being cut on the inner 
 edges of the base. Near 
 »ne end of the latter, a vertical pillar, b, is screwed down, for the 
 purpose of carrying the traversing slide-arm, c, adjustable at any 
 height, by a milled head, D, the spindle of which carries a pinion 
 in gear with a rack on the outside of the pillar. The outer end 
 of the ami, c, terminates in a ring, with a universal joint, e, 
 through which the pen or pencil-holder, F, is passed. The pillar, 
 B, also carries at its upper end a fixed arm, g, formed as an ellip- 
 tical guide-frame, being accurately cut out to an elliptical figure, as 
 the nucleus* of all the varieties of ellipse to be drawn. The centre 
 of this ellipse is, of course, set directly over the centre of the 
 universal joint, E, and the pen-holder is passed through the guide 
 aud through the joint, the fiat-sided sliding-piece, h, being kept in 
 contact with the guide, in traversing the pen over the paper. Tho 
 pen thus turns upon its joint, E, as a centre, and is always held in 
 its proper line of motion by the action of the slider, h. The dis- 
 tance between the guide ellipse and the universal joint determines 
 the size of the ellipse, which, in the instrument here delineated, 
 ranges from 2J inches by 1J, to j g by \ inch. In general, how- 
 ever, these instruments do not appear to be sufficiently simple, or 
 convenient, to be used with advantage in geometrical drawing. 
 
 57. Tangents to ellipses. — It is frequently necessary to deter- 
 mine the position and inclination of a straight line which shall 
 be a tangent to an elliptic curve. Three cases of this nature 
 occur : when a point in the ellipse is given ; when some external 
 point is given apart from the ellipse ; and when a straight lino 
 is given, to which it is necessary that the tangent should bo 
 parallel. 
 
 First, then, let the point, A, in the ellipse, fig. 2, be given ; 
 draw the two vectors, c A, B A, and produce the latter to M"; bisect 
 the angle, mac, by the straight line, N p ; this line, it p, will be 
 'vie tangent required; that is, it will touch the curve in the point, 
 A, and in that point alone. 
 
 Secondly, let the point, i, be given, apart from thjs elli 
 3. Join l with i, the nearest focus to it, and with i. as ,, . 
 
 and a radius equal to i. i, describe an are, si I >'. Next, with tho 
 more distant focus, h, as a centre, and with a radius equal in the 
 transverse axis, a b, describe a second arc, cutting the first in h 
 ami n. Join m h and n ii, and the ellipse will be cul iii ill' 
 
 r and ,c; a straight line drawn through either of these points from 
 the given point, L, will be a tangent t" tli.- ellipse. 
 
 58. Thirdly, lei the straight fine, q r, fig. 2, be given, parallo 
 to which it is required to draw a tangent to the ellip.-o. From the 
 nearest focus, b, let fall on q H the perpendicular, s b; then with 
 the further focus, c, as a centre, and with a radius equal to tho 
 transverse axis, d e, describe an arc cutting b s in s : join I -. and 
 the straight line, c s, will cut the ellipse in the point, T. of contact 
 of the required tangent. All that is then necessary is, to draw 
 through that point a line parallel to the given line, ij r, tho 
 accuracy of which may be verified by observing whether ii I' 
 the line, s b, which it should. 
 
 59. — The oval of fine centres, fig. 4. — As in previous cases, the 
 transverse and conjugate axes are given, and we commence by 
 obtaining a mean proportional between their halves; for this 
 purpose, with the centre, o, and the semi-conjugate axis, o c, as 
 radius, we describe the arc, c I K, and then the semi-circle, a l k, of 
 which A K is the diameter, and further prolong o c to i., l being 
 the mean proportional required. Next construct the parallelo- 
 gram, a g c o, the semi-axes constituting its dimensions; joining 
 c A, let fall from the point, G, on the diagonal, c a, the per- 
 pendicular, g ii d — which, being prolonged, cuts the conjugate axis 
 or its continuation in D. Having made c M equal to the mean 
 proportional, o i„ with the centre, n, and radius, u M, describe 
 an arc, a U Ii ; and having also made a n equal to the mean pro- 
 portional, L, with the centre, Ii, and radius, n \. describe tie 
 arc, n a, cutting the former in a. The points, n. ti, on 01 
 and n', b, obtained in a similar manner on the other, to) i thi r 
 with the point, D, will be the five centres of the oval : and 1 
 
 lines, R H a, s h' b, and p a D, q b D, passing through the r. ; 
 centres, will meet the curve in the points of junction of the various 
 oomponent arcs, as at R, P, q, s. 
 
 This beautiful curve is adopted in the construction of many 
 kinds of arches, bridges, ami vaulls : an example of its use is _i\. n 
 in fig. ©. 
 
 60. The parabola, fig. 5, is an open curve, that is. one which 
 does not return to any assumed starting point, to how. 
 
 a length it may be extended; and which, consequently, can nevei 
 enclose a space. It is so constituted, that any point in it, d, is at 
 an equal distance from a constant point. . . termed the focus, and 
 in a perpendicular direction, from a straight line, a k. cal 
 directrix. The straight line, F G, perpendicular to the directrix, 
 A B, and passing through the focus, c, IS the axis of the curve, 
 which it divides into two symmetrical portions. The point. A, 
 midway between F and r, is the apex of the curve. Thi 
 
 several methods of drawing thi- curve. 
 
 61. First method: — This is based on the definition jusl 
 
 and requires that the focus and directrix be known, as e. and a p. 
 Take any points on thi' directrix, A B, as a. e, II. I. and thronin 
 them draw parallels to the axis, f g, as also the straight linen 
 
niii: 1 
 
 i 
 
 ■•ui.n„» para! 
 .kill be in the 
 
 nam 
 
 : drawn, cu! 
 
 ■ 
 I 
 
 ■taking h c equal to e c, ati 
 
 I 
 . 
 
 ■ 
 
 . lit Tail 
 
 puts, as 
 
 I'.irall.-N tn :' 
 • 
 
 r..m the 
 m, n, ii, 
 
 parabola, 
 
 •ad pnr D Bna, J K, we let fall a [n riiendieular, C L, 
 
 drawn parallel I cut the cam in tin- tN.in- 
 
 tact, n. 
 
 • 
 
 -■ 
 
 ' iple of 
 I /' 
 
 and ar> 
 
 - from llii- pnu 
 "f oue tnirp.r, b /, Ibj Sat 
 
 )-. a*, ..!' 
 
 ' 
 
 lane* apart; fur all t!i |„. ulnar, J/J 
 
 -. nnd arc nir-. 
 
 • / / • 
 
 rammit to ili 
 . il parte, ninl with ll,. 
 
 I- 
 1 
 
 ! nnd 4 — 2, pan 
 
 I 
 
 • t., the 
 J With ihi-. 
 
 I ■ i 
 
 i a lirw 
 drawn 
 radian, 1' a', a I 
 
 . — liiill 
 
 !' 
 
 carta. J 
 
 and/' will he uthir t. 
 
 » 
 In- mil with in 
 
 feet a c 
 
 s ,\\l) PRACTICAL DATA 
 i. i a ii 
 
 • 
 
 rut the 111 
 
 dhridod into tbi 
 
 \ ■ 
 
 ■ 
 
 m uail- 
 
 ■ 
 In the aune manner ! 
 
 ■ 
 And tli- 
 for, 
 
 ■ 
 It in in ' 
 ■ 
 
 0) i» the iiin: 
 a square raid. ; for 
 
 4 1 foot as \ yard X { yn.nl - J wjiiu 
 
 A •v|n.'«T inch i' the i nth part of ■ 
 
 . fur 
 
 I Inch x I men ,'. fool > toot, 
 
 nnd 
 
 1 men x 1 Inch — ,', \nnl > 
 Thi* Diustral ■ t lha 
 
 of other methoda, 
 
 ■ nr an a "f ■ 
 ea and | 
 ; llano ur length, and 
 
BOOK OF INDUSTRUL DES1UN. 
 
 perpendicularly from the base. Thus the area of a rectangle, the 
 base of which measures 1-25 metres, and the height -75, is equal to 
 1-25 x -75 = -9375 square metres. 
 The area of a rectangle being known, and one of its dimensions, 
 the other mav be obtained by dividing the area by the given, 
 dimension. 
 
 Example. — The area of a rectangle being -9375 sq. m., and the 
 base 125 m., the height is 
 
 =: - 7o m. 
 
 l-as 
 
 -This operation is constantly needed in actual construction ; as, for 
 instance, when it is necessary to make a rectangular aperture of a 
 certain area, one of the dimensions being predetermined. 
 
 The area of a trapezium is equal to the product of half the sum 
 of the parallel sides into the perpendicular breadth. 
 
 Example. — The parallel sides ot a trapezium being respectively 
 
 1-3 in., and 1-5 in., and the breadth -8 m., the area will be 
 
 1-3 + 15 „ 
 
 ^ x -8 = 1-12 sq. m. 
 
 The area of a triangle is obtained by multiplying the base by 
 half the perpendicular height. 
 
 Example. — -The base of a triangle being 23 in., and the perpen- 
 dicular height 1-15 m., the area will be 
 
 23 x 
 
 115 
 
 2 
 
 13225 sq. m. 
 
 The area of a triangle being known, and one of tlft dimensions 
 given — that is, the base or the perpendicular height — the other 
 dimension can be ascertained by dividing double the area by the 
 given dimension. Thus, in the above example, the division of 
 (1-3225 sq. in. x 2) by the height 1-15 m. gives for quotient the base 
 2-3 m.. and its division by the base 2-3 m. gives the height 1-15 m. 
 
 70. It is demonstrated in geometry, that the square of the 
 hypothenuse, or longest side of a right-angled triangle, is equal to 
 
 the sum of the squares of the two sides forming the right angle. 
 It follows from this property, that if any two of the sides of a 
 right-angled triangle be given, the third may be at onei ascertained. 
 
 First, If the sidos forming the right angle be given, the hypo. 
 thenuse is determined by adding together their squares, ami 
 extracting the square root. 
 
 Example.— The side, A B, of the triangle, a b C, tig. Hi, II. I., 
 being 3 in., tho side B c, 4 m., the hypothenuse, A e, will be 
 A c = l / 3 a +4- = V'y + 16 = 1 / 25 = 5 m. 
 
 Secondly, If tho hypothenuse,. as a c, be known, and one of 
 the other sides, as a b, the third side, B c, will be equal to tho 
 square root of the difference between the squares of a c and A B. 
 
 Thus assuming the above measures — 
 
 Be = V25 — 9 = Vl6 = 4 m. 
 
 The diagonal of a square is always equal to one of the sides mul 
 tiplied by y-2; therefore, as Vi = 1-414 nearly, the diagonal is 
 obtained by multiplying a side by 1-414. 
 
 Example. — The side of a square being 6 metres, its diagonal 
 = 6 X 1-414 = 8-484 m. 
 The sum of the squares of the four sides of a parallelogram is 
 equal to the sum of the squares of its diagonals. 
 
 71. Regular polygons. — The area of a regular polygon is 
 obtained by multiplying its perimeter by half the apothegm or pet 
 pendicular, let fall from the centre to one of the sides. 
 
 A regular polygon of 5 sides, one of which is 9-8 m., and the 
 perpendicular distance from the centre to one of the sides 5-t; in., 
 will have for area — 
 
 9-8 x 5 x 51= 137-2 sq. in. 
 The area of an irregular polygon will be obtained by dividing it 
 into triangles, rectangles, or trapeziums, and then adding together 
 the areas of the various component figures. 
 
 TADLE OF MULTIPLIERS FOR REGULAR POLYGONS OF FROM 3 TO 12 SIDES. 
 
 Names. 
 
 Sides. 
 
 Multipliers. 
 
 D 
 
 Area 
 
 . 1 side = 1. 
 
 E 
 
 liil< nutl Angle. 
 
 F 
 
 Apothegm 
 
 A 
 
 B 
 
 c 
 
 Pi I i ndicnlar. 
 
 
 3 
 
 4 
 5 
 6 
 7 
 8 
 9 
 10 
 11 
 12 
 
 2-000 
 1-414 
 1-238 
 1156 
 1.111 
 1-080 
 1-062 
 1-050 
 1-040 
 1-037 
 
 1-730 
 1-412 
 1-174 
 
 radius. 
 •867 
 •765 
 •681 
 •616 
 •561 
 •516 
 
 •579 
 •705 
 •852 
 side. 
 1-160 
 1-307 
 
 1-470 
 
 1-625 
 1-777 
 1-940 
 
 •433 
 1-000 
 1-720 
 2-598 
 3-634 
 4-828 
 6-182 
 7-694 
 9-365 
 11-196 
 
 60° 0' 
 
 90° 0' 
 108° 0' 
 120° 0' 
 128° 3 1' = 
 135° 0' 
 140° 0' 
 144° 0' 
 147° 16V r 
 150° 0' 
 
 •l'nnoT.'jI 
 ■5000000 
 ■6881910 
 ■8660264 
 1 '0382607 
 1-2071069 
 1-3737387 
 1-5388418 
 1-7028436 
 1-8660234 
 
 
 
 
 
 
 
 
 
 By means of this table, we can easily solve many interesting 
 problems connected with regular polygons, from the triangle up to 
 the duodecagon. Such are the following : — 
 
 First, The width of a polygon being given, to find the radius of 
 the circumscribing circle. — When the number of sides is even, the 
 width is understood as the perpendicular distance between two 
 opposite and parallel sides; when the number is uneven, it is 
 twice the perpendicular distance from the centre to one side. 
 
 Rule. — Multiply half the width of the polygon by tin factor, in 
 
 column A, corresponding to the number of sides, and the product 
 will be the required radius. * 
 
 Example. — Let 18-5 m. be the width of an octagon; then. 
 
 18^5 
 2 
 
 x 1-08 =9-99 m.; 
 or say 10 metres, the rudius of the circumscribing circle. 
 

 •. 7V rasSai «/ m circle krimg gim. to fad At Itngm tf 
 tir nsVo/ am itucrikml pttjgtm. 
 
 ply the radio* by the factor in column B, curre- 
 sr*>odmf to the number of •idea of tl>c required polygon. 
 
 TIM radius bang 10 m, the side of an inscribed 
 .. ktj -. »... U — 
 
 "65 m. 
 Third. TV naV of « pcifgtm being gitta, u> find Ike radius tf 
 V* citrvmuerikmg circle. 
 
 pij the side by thi 
 • number of aides. 
 Exat ii. be the aide of an octagon ; then 
 
 := loo, nearly. 
 TV rssV if a polugtm brtnt; giren, to find Ike area. 
 
 side by the (actor in column D, 
 e u ne a p u oding to the number of airlea. 
 
 I*. — The aide of an octagon being 7-65 m., the area win 
 
 I 828 = 36-93 >q. m. 
 
 Tlir l AtD AKEA OF A CIKCLE. 
 
 . diame- 
 I* a numU r *otio tf 
 
 tie ctmimftrcnce to Ike diameter. The ratio is found to be (ap- 
 I 
 
 3 1116. or -J.: - 
 that is, the circumference equals 31 4 16 time* the 
 raie> formula*. 
 - 
 and ili dans ula, 
 
 - 
 
 -. if the 
 D radius II = 1-35 m., 
 
 the circumference will be equal to— 
 
 ■ 
 
 cir „:..:. :. ;► ■ f » s 8 i-J ID . . 
 
 and the radius, R. is — 
 
 
 = 1 35 m. 
 
 • .- - 
 
 TV arm tf a circle iiftmmd bm multiphfing Ike circumference km 
 kalf ike radiut. — This rale i» expressed in the following formula : — 
 
 The ana of a circle = i«Rxi = , 
 
 i 
 
 ■• rtn, k R*, is merely the simpmVatioej of the formahv 
 TV number U U-in_- ■ r and divisor, may be can- 
 
 celled, and the produ .or tha. 
 
 square of the radius. It follows, then, that the area of a circle is 
 equal to the square of the radius multiplied by the cin-uiiifcrcnce, 
 
 Example. — The radius of a circle being 1-05 m.. the area win 
 be— 
 
 t-Mlfl x l -j. m. 
 
 The .-.- .the radius is determu>-d by 
 
 . :he area by 3-1416, and extracting the square ruot of tha 
 
 Example. — The area of a circle being 34635 sq. m.. the radios 
 
 V 
 
 
 The area of a circle i- . 
 
 . x I> 
 Area = , or 
 
 '. - 
 
 ;D» . 
 
 •1 ' 
 
 4 
 
 That ia 1 the square of 
 
 the diai: :«■ the area. 
 
 Example. — h mea- 
 
 m. 
 ■Iial if the ana of a Mjuare is l:..»n. that 
 of an inscribe-! I; that 
 
 ia, the ana of a sanan i . as, 
 
 4 : . 
 
 TABLE Of ArTBOXIXATE RATIOS Bt7 
 
 
 X 
 
 
 
 X 
 
 ... X 
 
 . (mQu- 
 
 Lb* side of a square of equal area is 
 
 14141 
 
 »! area. 
 = thr- - 
 
 
 Qg 860*/., the aid* of 
 
 860 > 
 TIM *'•"•'.. the diameter of 
 
 in . irBs»»assrJbta*j ,•;-> '. Ii 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 Tin' radii and diameters of circles are to each other as the cir- 
 cumferences, and vice versa. The areas, therefore, of circles are to 
 each other as the squares of their respective radii or diameters. 
 
 It follows, hence, that if the radius or diameter be doubled, the 
 circumference will only be doubled, but the area will be quadrupled ; 
 thus, a drawing reduced to one-half the length, and half the 
 breadth, only occupies a quarter of the area of that from which it 
 is reduced. 
 
 73. Sectors — Segments. — In order to obtain the area of a sector 
 or segment, it is necessary to know the length of the arc subtend- 
 ' big it. This is found by multiplying the whole circumference by 
 the number of degrees contained in the arc, and dividing by 360°. 
 
 Example. — The circumference of a circle being 3-5 in., an arc of 
 4 ' will be 
 
 3-5 x 45 
 
 360 
 
 = -4375 m. 
 
 The length of an arc may be obtained approximately when the 
 
 chord is known, and the chord of half the arc, by subtracting the 
 
 chord of the whole arc from eight times the chord of the semi-arc, 
 
 and taking a third of the remainder. 
 
 Example. — The chord of an arc being -344 m., and that of half 
 
 the arc "198, the length of the are is 
 
 •198 x 8— -344 
 
 = 4133 m. 
 
 3 
 
 The area of a sector is equal to the length of the arc multiplied 
 
 into half the radius. 
 
 Example. — The radius being -169 in., and the are -_iiii; 
 
 •266 x -169 „,,. ' 
 
 = -0225 sq. m., the area ol the sector. 
 
 The area of a segment is obtained by multiplying the width ; that 
 is, the perpendicular between the centre of the chord, and tho 
 centre of the are, by -626, then adding to the square of the pro- 
 duct the square of half the chord, and multiplying twice the 
 square root of the sum by two-thirds of the width. 
 
 Example.— let 48 in. be the length of the chord of the are, 
 and 18 in. the width of the arc, then we have 
 
 18 x -626 = 11-268, and (11-268)-' = 126-9678; whilst 
 
 2x18 
 
 : 576; therefore, 2 x V 126-9678 + 576 x —— = 630-24 
 
 sq. m., the area of the segment. 
 
 The area of a segment may also bo obtained very approximately 
 by dividing the cube of tho width by twice the length of the chord, 
 and adding to tho quotient the product of the width into two 
 tliirds of the chord. Thus, with the foregoing data, we have 
 
 (?)' 
 
 and, . 
 
 = 576-0 
 
 Total, 636-7 sq. m. 
 
 A still simpler method, is to obtain the area of the sector of 
 which the segment is a part, and then subtract the area of the 
 
 COMPARISON* OF CONTINENTAL MEASURES, WITH FRENCH MILLIMETRES AND ENGLISH FEET. 
 
 Value in 
 
 Value in 
 
 MiLhnielres. 
 
 Feet. 
 
 S16-103 
 
 1-037 
 
 296-416 
 
 ■970 
 
 435-185 
 
 1-460 
 
 ■■,;:■■■::■•■ 
 
 1-140 
 
 3 96 -500 
 
 1-301 
 
 300-000 
 
 •984 
 
 291-859 
 
 •958 
 
 296-168 
 
 •972 
 
 1,000-000 
 
 3281 
 
 285-588 
 
 •937 
 
 289-197 
 
 •949 
 
 285-362 
 
 •936 
 
 35(5-421 
 
 1-169 
 
 313-821 
 
 1-029 
 
 282-655 
 
 •927 
 
 635-906 
 
 2742 
 
 B47-965 
 
 2-782 
 
 297-896 
 
 ■977 
 
 ti-j:;-422 
 
 •733 
 
 294-246 
 
 ■968 
 
 284-610 
 
 •933 
 
 286-490 
 
 •940 
 
 291-995 
 
 •958 
 
 300-000 
 
 •984 
 
 Designation of Me 
 
 Austria 
 
 Baden, 
 
 Bavaria, .... 
 
 Belgium 
 
 Bremen, .... 
 
 Brunswick, . , 
 
 Cracovia, 
 
 Denmark, 
 
 Spain, 
 
 Papal States,, -j 
 
 Frankfort 
 
 Hamburg 
 
 Hanover, , 
 
 Hesse 
 
 (Vienna) Foot or Fuss = 1 
 
 inches = 144 lines 
 
 (Bohemia) Foot, 
 
 (Venice) Foot, 
 
 Foot (Paliuo) 
 
 " Foot (Architect's Meas.) 
 (Cai-lsruhe) Foot (new) = 10 
 
 inches = 100 lines 
 
 (Munich) Foot = 12 inches = 
 
 144 lines, 
 
 (Augsburg) F"oot 
 
 (Brussels) Ell or Aline = 1 metre, 
 
 Foot, 
 
 (Bremen) Foot = 12 inches = 
 
 144 lines, 
 
 (Brunswick) Foot = 12 inche 
 
 = 144 lines 
 
 (Cracow) Foot, 
 
 ( Copenhagen) Foot 
 
 (Mini rid) Foot (according to Loh 
 
 Castilian Vara ( " Liscar), 
 (Havana) Yara= 3 Madrid feet. 
 
 (Pome) Foot 
 
 Architect's Span = * foot, 
 
 Ancient F'oot 
 
 Pool 
 
 Foot = 3 spans = 12 inches = 
 
 96 parts 
 
 (Hanover) Foot = 12 inches = 
 
 144 lines, 
 
 (Darmstadt) Foot = lo inches 
 
 100 lines, 
 
 Lubeck, . . 
 Mecklenburg, 
 
 Modena,. 
 
 (Amsterdam) Foot 
 
 | =11 inches 
 
 (Rhine) Foot 
 
 ( Lubeck) Fout,. . . . 
 
 3 spans 
 
 I 
 
 I 
 
 Ottoman Enipin 
 Parma 
 
 Poland 
 
 Portugal, . 
 
 Prussia,. . . 
 
 Russia, . . . 
 
 Sardinia,. . 
 •Saxc 
 
 Sicilies,. . . 
 
 Switzerland, . 
 
 Tuscany, 
 
 Wui-temburg,.. 
 
 I oot, 
 
 (Modena j Foot, 
 
 
 
 I I onstantinople) Grand | u . 
 Anns-length = 12 inches = 172s 
 
 atoini 
 
 ( Varsox ie) Foot = 12 inches 
 
 144 lines 
 
 (Lisbon) Ft. (ArchitecfsMeasure) 
 
 " Vara = 40 inches 
 
 (Berlin) Foot = 12 inches 
 
 (St. Petersburg) Russian Foot; 
 
 " Archine 
 
 (Cagliari) Span, 
 
 ( Weimar) Foot 
 
 Span = 12 inches (ounces = 6o 
 
 niinuti) 
 
 (Stockholm) Foot, 
 
 i Bale and Zurich) Foot 
 
 (Berne and Neufchatel) Fool - 
 
 •i inches 
 
 (Geneva) Foot 
 
 i Lausanne) Foot = 10 inches = 
 
 100 lines 
 
 (Lucerne and other Cantons) Ft.. 
 
 Foot, 
 
 Foot = 10 inches = 100 
 
 813864 
 
 623-048 
 
 66S I , 
 
 oil 670 
 
 297-769 
 
 388-6 
 
 1,008-868 
 309-726 
 
 711-480 
 202-678 
 281-97J 
 
 268-670 
 
 1-080 
 
 i 
 1-718 
 1-742 
 2-196 
 
 1787 
 
 1-111 
 
 1-766 
 2-884 
 
 ■60 l 
 
 .-865 
 
 •97 1 
 •999 
 
 ■962 
 1-600 
 
 ■984 
 
 1-O30 
 
• 
 
 ■ 
 
 
 J the area of an annular space contain. <: 
 •MMBtrie rirvi.-*, multiply the »um of iho duu. 
 dil!«rroc< , and 
 
 100 -f 60) X (1 '"• Iho 
 
 ' tha annular (face. 
 TV» arcs ul annular apace 
 
 needy, by tin- are which is a niraii |irop.,rtiiinal to .. 
 Un AREA OF AX (LI.:. 
 
 n U equal to I 
 of wtikh the diameter ia a mean proportional between Ibe tn 
 
 ■ 
 
 Uonal by 
 
 - 
 tiff u 
 
 i 
 The arrsa of 
 
 ' : and tho 
 - area ol 
 
 / | • 
 
 truil arU, an. I |«rticiilarly i\ 
 
 Oft The ejBJ | 
 
 ^, as well ea -. 
 
 problem.-.. 
 
 CHAPTER II. 
 THE STUDY OF PROJECTIONS. 
 
 > all the dimensions of an • 
 ■ 
 
 mprehended under the 
 of P 
 and aa I lone, or 
 
 lion "!i papi r of the appear- 
 i from diflerant 
 
 ■ a body on two 
 pr in c ip al plain*, ••:.«■ of which is distinguished as Ibe horizontal 
 plant, and the I 
 
 planes are alan Thoj an' 
 
 h other, tho horizontal plan In ■in;; the lower; Ibe 
 d the Ixise li/ir, and i- 
 to one l : 
 
 .i thorough Imowli dge of tin' 
 -. . in order to In' able 
 terminate forma, the eontotui 
 1 now i nter npon tn h up 
 u axe Meeaaarj primarily with Ibe projectiona 
 
 of a potet and Of 
 
 [ENTARY PRINCIPLES 
 . tiii: rBojBOTtoaa or a poikt. 
 
 I'l.MK VI. 
 
 ■ l and f, !«• ■ horlsontaj : 
 ird on which Ui- dri 
 made, or parhaj let a n e r bo 
 
 plane. Meg at a wall at one side of tin 
 in- nt , the »trai(fht I 
 
 r ' ■ .. 
 
 of which it i- ■ 
 
 i perpendicular, o o, to !>>• Icl fail on the l- 
 plane, Dm pohrl ndicoJar, 
 
 will be what is mid. i . ..f the 
 
 given point Similarly, If from ibe point, o, we • 
 pendictil i, tho 
 
 point ol or fool of ti • ar, will be th« 
 
 vertioal projection "i the tame point TI Jim are 
 
 ■ d in the Vertical and borixo 
 
 6 n and . |uir;i]!rl and eipial I 
 
 ". Il follow! .ii-truetii in, that, when the I 
 
 of any point are given, the position in spa* I 
 
 ■ letertninalile, it being necessarily the |>"int 
 
 of narpendieul of the 
 
 point 
 
 A* in dm* 
 of paper, and ■ 
 plane, it la customary t" rapp 
 ils forming a eontinnation of the ho 
 
 turned on the baM On ith il — ■ 
 
 il.it mi a labli \\ i 
 thua obtain tie 
 
 tin- two lad b] the base line, a b, and 
 
 the poinl 
 
 of the given |K,int. 
 
 It will l»' remarked, thai these pointa 1" 
 (li.-ular lo the b ■ . in the turnine; down 
 
 Of the previously verticil plane, the | 
 t i. .ii of Ihe line, n 0. It is I!cvo>-siry to obasfTa, that tin 
 
 poinl from the horizontal plane, 
 whilst n a measures 
 
 other sjnras, if on ■ m arjaot a nsfnaadaNlai kg la* plane, and 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 measure the distance, n o', on this perpendicular, we shall obtain 
 the exact position of the point in space. It is thus obvious, that 
 the position of a point in space is fully determinable by means of 
 two projections, these being in planes at right angles to each 
 other. 
 
 THE PROJECTIONS OF A STRAIGHT LINE. 
 
 78. In general, if, from several points in the given line, perpen- 
 diculars be let fall on to each of the planes of projection, and 
 their points of contact with these planes be joined, the resulting 
 lines will be the respective projections of the given line. 
 
 . When the line is straight, it will be sufficient to find the pro- 
 jections of its extreme points, and then join these respectively by 
 straight lines. 
 
 79. Let M o, fig. 2, represent a given straight line in space, 
 which we shall suppose to be, in this instance, perpendicular to 
 the horizontal, and, consequently, parallel to the vertical plane of 
 projection. To obtain its projection on the latter, perpendiculars, 
 M m', o o', must bo let fall from its extremities, m, o ; the straight 
 line, w! o', joining the extremities of these perpendiculars, will be 
 the required projection in the vertical plane, and in the present 
 case it will be equal to the given line. 
 
 The horizontal projection of the given line, M o, is a mere 
 point, m, because the line lies wholly in a perpendicular, M m, to 
 the plane, and it is the point of contact of this line which consti- 
 tutes the projection. In drawing, when the two planes are 
 converted into one, as indicated in fig. 2°, the horizontal and ver- 
 tical projections of the given right lines, in o, are respectively the 
 point, m, and the right line, m' u'. 
 
 80. If we suppose that the given straight line, M o, is horizon- 
 tal, and at the same time perpendicular to the vertical plane, as 
 in figs. 3 and 3% the projections will be similar to the last, but 
 transposed; that is, the point, e/, will be the vertical, whilst the 
 straight line, m o, will be the horizontal projection. 
 
 In both the preceding cases, the projections lie in the same 
 perpendicular line, m m, fig. 2", and o' o. fig. 5". 
 
 81. When the given straight line, M o, is parallel to both the 
 horizontal and the vertical plane, as in figs. 4 and 4", its two pro- 
 jections, m o and ?n' o', will be parallel to the base Hue, and they 
 will each be equal to the given line. 
 
 82. When the given straight line, M o, figs. 5 and 5", is parallel 
 to the vertical plane, abef, only, the vertical projection, m o', 
 will be parallel to the given line, whilst the horizontal projection, 
 m y, will be parallel to the base line. Inversely, if the given straight 
 line be parallel to the horizontal plane, its horizontal projection will 
 be parallel to it, whilst its vertical projection will be parallel to 
 the base line. 
 
 83. Finally, if the given straight line, M o, figs.. 6 and' 6°, is 
 inclined. to both planes, the projections of it, mo, m' o', will hoth 
 be inclined to the base line, A B. These projections are in all 
 cases obtained by 'letting fall, from each extremity of the line, per- 
 pendioulars to each plane. 
 
 The projections of a straight line being given, its position in 
 space is determined by erecting perpendiculars to the horizontal 
 plane, from the extremities, m o, of the projected line, and making 
 them equal to the verticals, n m' and p u'. The same result 
 follows, if from the points, m', u', in the vertical plane, \vc erect 
 
 perpendiculars, respectively equal to the horizontal distances 
 mn and po. The free extremities of these perpendiculars meet 
 each other in the respective extremities of the line in space. 
 
 THE PROJECTIONS Of A TI.ANE SURFACE. 
 
 84. Since all plane surfaces are bounded by straight lines, as 
 
 soon as the student has learned how to obtain the projections of 
 these, he will lie able to represent any plane surface in Hie two 
 planes of projection. It is, in fact, merely necessary to let fall 
 perpendiculars to each of the planes, from the extremities of the 
 various lines bounding the surface to be represented; in other 
 words, from each of the angles or points of junction of these lines, 
 by which means the corresponding points will be obtained in the 
 planes of projection, which, being joined, will complete the repre- 
 sentations. It is by such means that are obtained the projections 
 of the square, represented in different positions in figs. 7, 7", 8, 8% 
 and 9, 9". It will be remarked, that, in the two first instances, the 
 projection is in one or other of the planes an exact counterpart of 
 the given square, becau.se it is parallel to one or other of the 
 planes. 
 
 85. Thus, in fig. 7, we have supposed the given surface to be 
 parallel to the horizontal plane; consequently, its projection in 
 that plane will be a figure, m o /' 7, equal and parallel to itself, 
 whilst the vertical projection will be a straight line, p' <>', parallel to 
 the base line, a b. 
 
 86. Similarly, in fig. 8, the object being supposed to be paralle. 
 to the vertical plane, its projection in that plane will be the equa, 
 and parallel figure, m'dp'q', whilst that in the horizontal plane 
 will be the straight line, m 0. When the two planes of pri 
 
 are converted into one. the respective projections will assume the 
 forms and positions represented in figs. 7", 8". 
 
 87. If the given surface is not parallel to either plane, but yet 
 perpendicular to one or the other, its projection in the plane to 
 which it is perpendicular will still be a straight line, as j.' ,,', figs, 
 9 and 9", whilst its projection in the other plane will assume the 
 form, mo pa, being a representation of the object somewhat forjx- 
 shortened in the direction of the inclination. 
 
 The cases just treated of have been those of rectangular Bur- 
 faces, but the same principles are equally applicable to on) poly. 
 gonal figures, as maybe seen in figs. 1- and 12*, which will b< 
 easily understood, the same letters in various charm 
 corresponding points and perpendiculars. Nor does (lie ubtain- 
 ment of the projections of surfaces hounded by curved lines, as 
 circles, require the consideration of oilier principles, as we shall 
 proceed to show, in reference to tigs. Ill and 11. 
 
 88. In the first of these, fig. 10, the circular disc, m o p <;. is siq>- 
 posed to bo parallel to the vertical plane, a b 6 1. and its projec- 
 tion on that plane will be a eircle, m 1 o' //</', equal and paralle) to 
 itself, whilst its projection on the horizontal plane. A H e i>„will he 
 
 a straight line, </ m 0, equal to its diameter. If. on the other hand, 
 
 thi' disc is parallel to the horizontal plane, as in lie. |J, its vertical 
 
 projection will be the straight lino, p'&m 1 , whilst its horizontal 
 
 projection will he the circle, op 1,1 7. 
 
 If the given circular disc he inclined to either plane, ifa 
 
 tion in that plane will be an ellipse; and if it i> inclined I h 
 
 planes, both projections will be ellipses. This will he made e'. i- 
 

 ■ • 
 
 SSL WW maati tilling Dm projections of regular figures, it 
 fariiiute* th. pr o ce— considerably if projections of the centres and 
 
 <■. -■■ .n.. - I..-.: f , ■ ■>.. i. in i'i ■-. I ■ ll.aoiM, 
 
 \; ft .. B*\ !,'..• ;<•>•.. :i -n ..!"».! pUlM SUrfacaa may bt !'• ir. i. 
 ■■ u how in obtain the ppjertions of points and line*. 
 ' objects bounded by surfaces 
 •ad lines, the f uDitn., 
 
 PRISMS \\l> OTHER BOJJ 
 
 I'LATK VII. 
 
 90. Before entering 1 in the rrpre- 
 
 — ntitino of solids, the student should make hini- 
 «:-:i -h- imcjiy ■ • ..-. . adopted in aaaam and a". 
 
 with re fe r en ce to inch objects; and we here sabjoin such as will 
 b.- n-v.-ra-y. 
 
 t having thi 
 that i«. lprucs length, iriMK and height. a - 
 
 sJbs |.^„^_, ■afnttode, rolmne, or capacity. 
 
 There are ■ i 
 
 bounded by plane anrfaeea; the earn, the cylinder, and the sphere, 
 are bounded ■ KM. Those are termed solids i/ re. 
 
 taluJun, which may be defined as generat.Hl by the f i ulilll 
 plane a- ;ued the axis. Thus, a rin^', 
 
 or annular torus, U a - a circle 
 
 angles to the plane •• \ -..n. the 
 
 lateral fa ,,al and 
 
 '■ 
 fiscea, or facets, are p- 
 when the ends are r 
 pmrmlUofiped, when the ends are r 
 and wte equal and squ. 
 
 r regular kexakedrtm. 
 
 .mlar polyhedra, be- diod by 
 
 appropriate names; an :tid the 
 
 inaaSedmn, whkh ar. 
 ■ 
 
 '. 
 m a polyhedron, of whkh all th.- 
 aniiing in one point, the o/>r.r, and having. a« bow- 
 
 I 
 and pyramid are triangular, quadrantriilar. | 
 
 rdinif aa the p!y.'..n- forming the bawi are b 
 aa .-. a, pentagons, hi cagona, he 
 
 By the htlgk 
 eular let fall ft 
 
 !•••"■•• Iwaentl ■;-->■ ilar meets the centre of the baam, 
 A tntmrmttJ pyram ti of a pyr:. 
 
 a plane para! 
 
 may be demr 
 g about, and at any . from, a 
 
 r. ■ : ik :.r ai ■ 
 
 A eon*, fig. j 
 
 termin;. ti 
 the ba>. 
 
 a |nt- 
 
 • 
 
 ti.. baaa. 
 
 A sphere is a solid gener..:- 
 sbout its dioi. £j. 
 
 A spheric u 
 
 '■ 
 
 ■ 
 obtained will be annular or 
 an-, Li.'. 
 
 ; 
 
 A spheric w- 
 
 - 
 twined .i 
 A sal • 
 
 . by tlie 
 
 ■ 
 
 •-res. 
 A segmental anmili. on of a 
 
 1 
 
 . 
 on the ai 
 
 A »rV Of pyram itlal I 
 
 THE rKOJF. .. A- 
 
 91. A Clll-e, of « ; 
 ■ 
 
 I" and I. 
 
 W 
 - parallel to th 
 
 on the 
 
 . ■ nlar to t-o'li 
 straight linos, as A D .< I. snd a' r ai. I 
 
BOOK OF INDUSTRIAL DESK IN. 
 
 85 
 
 hfing respectively in the same straight lines perpendicular to the 
 base line, l T. It will also bo perceived, that the base, f e g h, 
 fig- <A, cannot be represented in the horizontal projection, nor the 
 side, d c g H, in the vertical, sinco they are respectively immedi- 
 ately behind and hidden by the sides, a b c d and aief, repre- 
 sented in the projections by the squares, a b c d, fig. 1*, and 
 A' b' e' f', fig. 1. They are, however, indicated in the planes to 
 which they are perpendicular, by the straight lines, f' e' and D c. 
 
 92. "It will bo evident from these remarks, that in order to 
 design a cube so that a model may be constructed, it is sufficient 
 to know one of the sides, for all the sides are equal to each other. 
 
 When the plans are intended to be used in the actual construc- 
 tion of machinery or buildings, the objects should be represented 
 in the projections as having their principal sides parallel or per- 
 pendicular to the horizontal and vertical plane respectively, in 
 order to avoid the foreshortening occasioned by an oblique or in- 
 clined position of the object with reference to these planes, because 
 the actual measurements of the different parts cannot be readily 
 ascertained where there is such foreshortening. 
 
 To obtain, then, the projections of the cube, fig. ^, a square 
 must be constructed, as a b c d, fig. 1*, having its sides equal to 
 the given side or edge, the sides a b and d c being disposed parallel 
 to the base line ; next, the square must be reproduced as at a' b' e' f', 
 fig. 1, on the prolongations of the sides, A D and B c, which are 
 perpendicular to the base line. 
 
 the projections of a eight square-eased prism, or 
 rectangular paeallelopiped, fig. [b. 
 
 93. The representation of this solid is obtained in precisely the 
 same manner as that of the cube, the sides being supposed to be 
 parallel or perpendicular to tho respective planes of projection. 
 The base of tho prism being square, its horizontal projection is 
 necessarily also a square, A B c D, fig. 2"; but its vertical pro- 
 jection will be the rectangle, a' b' e' f', fig. 2, equal to one of the 
 sides of the prism. For the construction of these projections, the 
 same datum as in the preceding case is required ; namely, a side of 
 the base, and in addition, the height of the parallelopiped, or 
 prism. 
 
 THE PROJECTIONS OF A QUADRANGULAR PYRAMID, FIG. ©. 
 
 94. This pyramid is supposed to be inverted, and having its 
 base, A B c D, parallel to the horizontal plane : it follows upon this 
 assumption, that its horizontal projection is represented by the 
 square, a B c D, fig. 3°. The axis, or centre line, o s, which is 
 supposed to be vertical, and consequently passes through the centre 
 of the base, is projected on the horizontal plane as a point, o, fig. 
 "", and on the vertical plane as a line, o' s ; drawing through the 
 point, o', of this line, the horizontal line, a' b', equal to a side of 
 the ba«e, which is supposed to be parallel to tho vertical plane, we 
 shaU obtain the vertical projection of the base ; and joining a's, b's', 
 that of the whole pyramid, the points a' and b' may be found by 
 prolonging the parallels, A d, b c, fig. 3 d . This may be conveniently 
 done with the square, and tho operation is usually termed squaring 
 over a measurement — that is, from one projection to another. Tho 
 lateral facets, sic and sab, aro represented in the vertical pro- 
 jection by the straight lines, a' s, b' s, fig. 1, since they are per- 
 
 pendicular to the vertical plain'; and the projection of the facet. 
 
 d s c, is identical with a' s b', that of the front facet, a s ii, imme- 
 diately behind which it is. Since' each of the inclined con 
 
 facets is bidden by the base, they cannot he drawn in sharp lines 
 in tho horizontal projection ; wo have, however, indicated their 
 positions in faint lines, fig. 3". Were these lines full, the projec- 
 tion would be that of a pyramid with the apex uppermost, or of 
 a hollow, baseless pyramid, in the same position as fig. ©. 
 
 THE PROJECTIONS OF A RIGHT PRISM, PARTIALLY HOLLOWED, 
 AS FIG. ©. 
 
 95. The vertical and horizontal projections of the exterior ..I' 
 this solid, are precisely the same as those of fig. 13; they are re- 
 presented respectively by tho square, a b c d, fig. 4", and the rec- 
 tangle, a' b' e' f', fig. 4. It will be perceived, that the internal 
 
 surfaces of this figure are such as may be supp J 
 
 of the sides of a smaller prism ; the sides, chu and t L M It, are 
 parallel to the vertical plane, and G K N J and H I M L perpendicular 
 to it, and it follows that the projections of this lesser figure 
 will assume the forms, g' h' i' j', fig. 4, and a H L k, fig. f. 
 The lines, K g, l h, are faint dotted lines, instead of being slurp 
 and full, as being hid by the base, A B c D, of the external prism. 
 These lines will be found to be different to the projection lines, or 
 working lines. The latter are composed of irregular dots, whilst 
 those which indicate parts of the figure which actually exist, hut 
 are hidden behind more prominent portions, are composed of regu- 
 lar dots. This distinction has been adhered to throughout tho 
 entire series of Plates. 
 
 97. On examining tho examples just treated of, it will be ob- 
 served, from the horizontal projections, that the contour, or out- 
 line, is in every case square, whilst, from the vertical projections, 
 it will be seen that each object is different This demonstrates 
 that one projection is not sufficient for the determination of all the 
 dimensions of an object; and that, even in the simplest casi a, 1 o 
 different projections are absolutely necessary. It will, moreover, 
 bo seen, as we advance, that in many cases, three, and at times 
 more, projections are required, as well as sections through two or 
 more planes. 
 
 THE PROJECTIONS OF A RIGHT CYLINDER, FIG. g. 
 
 98. The axis, o m, of this cylinder is supposed to be vertical, 
 and its bases, a b, e f, will consequently be horizontal. Its pro- 
 jections in figs. 5 and o" are represented by tho rectangle, a' d' l> i ', 
 on the one hand, and the circle, A c b d, on the other. It is evi- 
 dent, that to draw these figures, it is quite sufficient to know the 
 radius, o a, of the base, and the height, o m; with I he given 
 radius, we describe the circle, a c b d, which is the horizontal pro- 
 jection of the whole cylinder; then making the vertical, of ■ 
 
 to the given height, and squaring over by means of the parallels, 
 A A', b B', the diameter of the circle, we draw, through o' and 
 m, the horizontals, a' b', e' f', completing the parallelogram, 
 a' b' e' f', which is the vertical projection of the cylinder. 
 
 THE PROJECTIONS OF A RIGHT CONE, FIG. [j?. 
 
 99. The projections of aright cone differ from those of the cyliii- 
 
 ' der solely as far as regards the vertical plane. Tims it will he get n, 
 
' 
 
 la fcja. duJC, that the horiioatal pr.;.vjon of the com, » A B, ■ 
 
 •'*- taar ••• that of a <■;, ',;n !.-r bun,- an e>jual line ; but 
 liit tcrtica. prujertioa. V *' > - mj» a nvlajr, i* an 
 
 i«ii !■■ triangle, of whirh the baa* ia equal I 
 
 isJaf the boruontal projection, whuat Ifae height ia that 
 
 . M S .1 -i 
 
 know I .ircular 
 
 Tiir. rsojccnon or a snirnr, n<;. ft. 
 
 - 
 
 ■ 
 
 radius equal to that, o I 
 
 - 
 - i- a further illustration of the in- 
 
 we approach I 
 
 »'>.-!i aaldad projection would equally represent that of a cylinder 
 
 with a h. mi -;■!;• -ii-;i! termination, 'i 
 
 •h. riantad proj etions of cylinder and >■■• :10a, mod, indeed, to a!l 
 
 aaldbodata. 
 
 • which 
 
 repreae: I 
 
 ■ 
 
 'i of lines are 
 
 • maintenane. 
 
 •it and 
 particular dire. I 
 
 tliat some par- 
 •*hil»t others ai Hitherto, a nniform 
 
 that it - il. a 0, of ill" 
 
 ■ 
 
 V. 
 ■r, and on wliat account it H 
 
 ia the r. ,.n— 
 
 i roJ, ia our drs • 
 
 . k and a', in ; aa the 
 
 and uu;> 
 
 tical or horizontal plane, the turning avii ! 
 the baae tine. Let us in the. lir.-t (dace. - 
 
 |>lanc at o, and in Ili<> vertical at a'. 
 and rail 
 
 f..ldi*l ■: 
 
 - 
 
 elination ion ihu 
 
 ■ 
 1 
 part ol 
 
 - 
 
 . 
 
 the lines, B 1 . 
 ' : .'. It moat b 
 ■ 
 projection, ia 1 
 
 _ r in a similar manner. What ha* jnat 
 - 
 
 parti which . 
 
 tit and in the ahadi 
 rhich are illuminated, from '., not. 
 
 ■ '■ 
 
 I 
 not be employed as that fori 
 minent surface. Thm " the line*, b' ' 
 
 N 
 
 those on the ilhllllillM.il ride of - 
 - 
 
 i* in the shade. In other * 
 
 fully illuminati'd outline, a t da, an. I 
 
 that portion . in the 
 
 aavily l«. full • 
 anea entirely ; 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 In the horizontal projection of the cylinder, fig. 5°, the illumi- 
 nated portion corresponds to the semi-circle, o rf 4, whilst that in 
 the shade is the other semi-circle, a c b; the points, a, b, of 
 separation of the two halves, are obtained by drawing through 
 the centre, o, a diameter, a b, perpendicular to the ray of light, 
 d o, or by drawing a couple of tangents to the circle parallel 
 to this ray. The straight line, a b, is inclined to the base line 
 at an angle of 45°. Great care is necessary in producing the 
 circular shadow-line, acb, and the nibs of the drawing-pen should 
 be gradually brought closer as the extremities, a and b, of the 
 shadow-line are approached, so that it may gradually die away 
 into the thickness of the illuminated line. By inclining the 
 drawing-pen, or by pressing it sideways against the paper, the 
 desired effect may be produced; the_ exact method, however, being 
 obtained rather by practice than by following any particular in- 
 structions. A very good effect may also, in some instances, be 
 produced, by first drawing the entire circle with the fine line, and 
 then retracing the part to be shadow-lined with a centre slightly 
 to one side of the first centre, and repeating this until the desirefl 
 strength of the shadow-line is obtained. 
 
 104. In the plan of a cone, fig. 6°, the part in the shade is always 
 less than the part illuminated ; but it requires an especial con- 
 struction, which will be found in the chapter treating of Shadows, 
 for the determination of the lines of separation, se; and it is sel- 
 dom that smh extreme nicety is observed in outline drawings, the 
 shadow-line of the plan of the cone being generally made the 
 same as that of a' cylinder, or perhaps a little less, according to 
 the judgment of the artist. Yet, if the height of the cone be 
 less than the radius of the base, the whole conical surface will be 
 Llumina:cd, and consequently its outline should have no shadow- 
 iine. 
 
 105. In explanation of the motives which have guided us in 
 the adoption of the diagonal of a cube, as projected in the lines, 
 R, r', fig. 8, as the direction of the rays of light, in preference to 
 the other systems proposed, we shall proceed to point out some 
 of the inconveniences attending the latter. 
 
 In the first place it must be observed, that if we adopt, as the 
 direction of the rays of light, the diagonals projected in a' e' and 
 D B. figs. 1 and 1", that part of the object which is represented in 
 the plan as illuminated, does not correspond with the part repre- 
 sented as illuminated in the elevation : in such case, the shadow- 
 lines would be A B and B c in the horizontal projection, and f' e', 
 d' e' in the vertical, so that ihere is no distinction made between 
 the plan and the elevation; whereas, according to the" system 
 adopted by us, it is at first sight apparent which is the plan, and 
 which the elevation, from the mere shadow-lines, which are in the 
 latter at the lower parts of the object ; whilst, in the former, they 
 are, on the contrary, at the upper parts. It is not natural, more- 
 over, to suppose, that in the representation of any object, the light 
 can be made to come as it were from behind the object, for in that 
 case the side nearest the spectator would evidently be in the 
 shade ; and yet it is only on such a supposition that the projections 
 of the ray of light can be such as D b and a' e'. Thus a double 
 inconvenience may be urged against this system. 
 
 If, on the other hand, the rays of light are supposed to be per- 
 pendicular to either plane, such confusion will result as to render 
 
 it impossible to ascertain, by any reference to 1 1 r< • shadow-linos 
 what is, or what is not, illuminated, and thus the object of employ- 
 ing shadow-lines would be lost sight of. Thus let US suppose, for 
 
 example, that the light is perpendicular to the vertical plane, 
 whence it follows that the whole of the anterior facet, tigs. 1 to 1, 
 is fully illuminated ; but, at the same time, all the facets perpen- 
 dicular to the vertical plane are equally in the shade, and it would 
 consequently bo necessary to use shadow-lines all round, or el e not 
 at all; and whichever plan was adopted, would lie quite unintelligi- 
 ble. Besides this, it is unnatural to suppose that the spectator 
 should place himself between the light and the object. Indeed, it 
 is unquestionable that the most appropriate direction to he given to 
 the ray of light, is as before stated, that of the diagonal of a cube, 
 of which the facets are respectively parallel to the two plane, of 
 projection; and tho projections of this diagonal are, consequently, 
 inclined to (he base line at an angle of 45°, hut proceeding from 
 above in the vertical projection, and from below in the horizontal 
 projection, as shown by the arrows, R and r', fig. 8. 
 
 PROJECTIONS OF GROOVED OR FLUTED CYLINDERS 
 AND RATCHET WHEELS. 
 
 PLATE YIII. 
 106. The various diagrams in this plate are designed principally 
 with the view of making the student practically conversant with 
 the construction of the projections of objects: an I. besides teach- 
 ing him how to delineate their external contours, to enable him to 
 represent them in section, that their iutei ire maj also lie 
 
 recorded on tho»drawing. 
 
 Fi |f s. 1 and 1° are, respectively, the plan and elevation of a 
 right cylinder, which is grooved on its entire external surface. The 
 grooves on one-half of the circumference are supposed to I" 
 pointed, being formed by isosceles triangles of regular dinioii 
 sions, and may represent the rollers used in Sax machinery, i:i 
 apparatus for preparing food for animals, and in inanj 
 machines. Tho other half of the circumference is ton u 
 square or rectangular grooves, the lateral faces of which are I ithi t 
 parallel to the centre lines which radiate from tin i 
 themselves radiating. 
 
 107. To construct the horizontal projection of this e; 
 that is, as seen from above, we must first ascertain bow many 
 grooves are contained in the whole circumference ; then drai 
 circle with a radius, A o, which should always be greater than that 
 of the given cylinder, divide it into twice as many equal parte as 
 there are grooves. If the student will refer back to the section 
 treating of linear drawing, illustrated in Plate I., he will find simple 
 methods of dividing circles into 2, 3, 4, 6, 8, and 12 equal ports, 
 and, further, of subdividing these. Thus, as the cylinder, fig. l, 
 contains 24 grooves, its circumference must be divided into 48 equal 
 parts. To obtain these, begin by drawing two diameters, a b, c n, 
 
 perpendicular to each other; then, from each extremity, mark oil' the 
 
 length of the radius, to, thus obtaining the four points numbered 
 
 8 on one side, and the points numbered 4 on the other — making, 
 With the points Of intersection Of the two diameters with the cir- 
 cumference, in all, 12 points. It remains simply to bisect each 
 space, as a 1, b — 4, or 4 — 8, &e., as well as the lesser spaces 
 
' 
 
 thus toand; thu will r>e the 48 divisions required. I 
 the potato of dm*..o draw li, which will ditide 
 
 the inner cirri* iWrilii il with the radiu- ■• tame 
 
 noiaUr of equal part*. The depth of the grooves is limited 
 ..-vriDHl with Uir radius, o E, whilst the outside 
 omening ridge* is defined bg 
 All the opera!. 
 
 i: Mm .- :-••!>.' :. . : ■ ■■.•'.■ ' ..-., irah4 hvlan.'ulal .t.-uv 
 Id pro ceding, we mu«t. in the former case. 
 
 ti. a. I. r. d. «lih h are in earn circumference alternately; 
 
 it have simply 
 % as well as the radial 
 
 •■••■• 
 the depth ahould be given, aay m i 
 two horizontals, M f. ■ 
 
 to • •!•. 
 
 iiid draw parallels : 
 
 rior of Out [tirt of the 
 /ontal, M r. 
 
 m not 
 ■■ 
 
 1 and P. that 
 tin- interior of the cylinder. 
 ivntral citvu!. - Dot ap- 
 
 parent 
 
 1 1'. It i-. im- 
 of the 
 
 through 
 
 to the pi 
 
 ■ 
 
 - 
 tin- in- 
 
 in an • •'■• 
 
 . t from 
 
 Th»t » hich 
 
 •n*l piano passe*, i- 
 
 ,'irtn which the plane 
 \v the 
 parts in 
 
 iron, a 
 
 • :..■»•' -t. . :• . .i~ I. W'liiUt .1 lighter "tie ilnlicati « wood or .ti.tie ; 
 
 r. indicates 
 
 the object to be made of copper, whilst tiui b fig. J* correspond* 
 to cast-iron, and in fig. 3* to wood or masonry. 
 
 that the actio* Una, of whatever 
 deacriptiiin they may be, are always inclined at an angle of 45* 
 with the baae line ; this is to distinguish the anrttonmg from fiat 
 
 - 
 less prominent than another: this latter flat-tinting it generally 
 
 ■ ;■ ndirular or horizontal lines. Tike 
 
 mdiralwa the base of the internal cylinder, cat, ahould not be 
 a shadow-tine equal in strength to tie bases of the sectional parts, 
 for the latter are more prominent. This point is seldom attended 
 to as it slum Id be; greater beanty and •' 
 
 This remark applies equally to all projertiona 
 
 •' portion is more prominent than another. 
 
 Thus, ;- .'. the vertical lines passing through r are 
 
 considerably in I than those passing through H w , 
 
 and lying in a poaawinr flan*. It is the more important to 
 
 u in rapraw • ' 
 least as much as poe>j 
 
 ■ ■.n-jderatioD • 1 and 3, 
 representing ratchet wbeab ami fl 
 
 intelligi rationa a* an- a 
 
 d quite obvious by the view! th«m~ 
 
 THE ELEMENTS OF ARCHITECTURE. 
 
 H.ATK IX. 
 111. Columns of tl 
 quently employed in buildings, and also in mcvliani. .. 
 
 i 
 I. Ti,. Taw 
 D 
 
 3. Th 
 
 4. Tie ' 
 
 5. Ti. 
 
 I 
 11.' I 
 
 ■ 
 
 ami the 
 
 - 
 
 nine time*: the Corinthian and I The 
 
 ■ 
 ent pari - 
 
 • he lower pari 
 
 ■ 
 
 ir» ».!h»r»J to is* fin. h*w i»,n f of n . 
 
 a sstWnir . bvt »• on i4 fol i s , is th • 
 i r« on.r» rru.it. a asjat is 
 
 IS* Ant . ■* j.r.. ,.g 
 r.rk, Ron.,,. uJ M •!. r» 
 loauc . sail Um laird. C-i.>il.u uut ( uaiaal*. 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 into i2 parts, in the Tuscan and Doric orders; and into 18 parts, 
 in the Ionic, Corinthian, and Composite. The whole height of 
 the Tuscan order is 22 modules 2 parts, apportioned as follows : — 
 The column is 14 modules; the pedestal, 4 modules 8 parts ; and 
 the entablature, 3 modules 6 parts. The whole height of the 
 Doric order is 25 modules 4 parts — the column being 16 modules; 
 the pedestal, 5 modules 4 parts ; and the entablature, 4 modules. 
 The whole height of the Ionic order is 28 modules 9 parts — the 
 pedestal, 6 modules; the column, 18 modules; and the entablature, 
 4 modules 9 parts. The wfiole height of the Corinthian and 
 Composite orders is 31 modules 12 parts — of which 6 modules 12 
 parts form the pedestal, 20 modules the column, and 5 modules 
 the entablature. 
 
 As we do not propose to treat especially of architecture, we 
 have not given drawings of all the various orders, but have con- 
 fined ourselves to the Tuscan, as being the simplest, as well as the 
 one more generally adopted in the construction of machinery. 
 At the end of this Chapter, will be found tables of the dimensions 
 of the various components of the Tuscan order, and we also there 
 give a similar tab:3 for the Doric order. 
 
 OUTLINE OF THE TUSCAN ORDEK. 
 
 113. The whole height being given, as M n, the proportions of 
 the different parts may always be determined. Let tins height 
 be, for example, 4 metres 272 millimetres, fig. 7. First, divide it 
 into 19 equal parts, then take 4 such parts for the height of the 
 pedestal, 12 for that of the column, and the remaining 3 for the 
 entablature. Then, according to the order which it is intended to 
 follow, the height, m n, of the column, is divided into 7, 8, 9, or 10 
 equal parts, and the diameter of the lower part of the column will 
 be equal to one of these divisions : thus, in the Tuscan order, the 
 diameter, a ft, is \ of the height, m n ; the half of this diameter, 
 or the radius of the shaft, is the unit of proportional measurement, 
 called the module, and with which all the components of the order 
 are measured : it follows then, that in the Tuscan order this mo- 
 dule is T ' T of the height of the column, in the Doric ~j, in the 
 Ionic T ' s , and —^ in the Corinthian and Composite. 
 
 114. The three members of an order are each subdivided into 
 three divisions. Thus the Pedestal is composed of the Socle, 
 or lower Plinth, a ; of the Dado, B ; and Cornice, c : the column 
 consists of the Base, or Plinth, D ; the Shaft, E ; and the Capital, f ; 
 and in the entablature are the Architrave, G ; the Frieze, H ; and 
 the Cornice, L 
 
 115. Before proceeding to delineate these different parts, and 
 the mouldings with which they are ornamented, it is expedient to 
 set off a scale of modules, determined in the manner just stated, 
 the module being, of course, subdivided into 12 equal parts. 
 
 To make the mouldings and various details more intelligible, 
 we have drawn the various portions of the order, separately, to a 
 larger scale. Thus the socle and pedestal of the column are repre-. 
 sented in elevation in fig. 2, and in plan in fig. 3, to a scale 2 \ times 
 that of the complete view, fig. 1, and the module will, of course, be 
 proportionately larger. All the numbers indicated on these figures, 
 give the exact measurements of each part and each moulding, so 
 that they may be drawn in perfect accordance with the scale given. 
 It conduces considerably to the symmetry and exactitude of the 
 
 drawing, to set off all the measurements from the axis or. Centre 
 line, c ■/. The module being but an arbitrary measurement, ii is 
 necessary, in practically carrying out any design, to ascertain the 
 
 different measures in metres and parts of metres ; and for this 
 reason we have given additional scales in metres, to correspond to 
 those in modules ; and we have also expressed in millimetres, on 
 each figure, tho measurements of the various details, placing the 
 metrical in juxtaposition with the modular ones. And, to give a 
 distinct idea as to the degrees of prominence or relief of the 
 various members, a part of tho elevation is shown as sectioned 
 by a plane passing through the axis of the shaft, this part being 
 sufficiently distinguishable from the sectional fiat-tinting. In 
 the horizontal projection, fig. 3, are also represented portions of 
 sections in two different planes, one being at tho height of I he 
 line, 5 — 6, and the other at that of 7 — 8. The first shows that the 
 shaft is round, as well as the fillet,/, and the torus, g, whilst the 
 base, h, and cornice, ij, are square: tho second section shows, 
 in a similar manner, that the dado, b, the socle, a, and its fillet, /), 
 are square. The tlat-tintings sufficiently indicate the parts in 
 section. 
 
 Fig. 4 represents the entablature and the capital of the column 
 in elevation and in section. Fig. 5 is a horizontal section of the 
 column with its capital, as it were inverted, and is supposed to be 
 half through the line, 1 — 2, and half through 3 — I. The whole 
 is what is termed a false section, the parts in section bring in 
 parallel, but not identical planes. The different measurements 
 are given in modules and metres, as in the other figures; they 
 indicate tho respective distances from the axis. <■' </'. 
 
 116. The execution of this design offers little or no difficulty] 
 but all the operations required, as well as the parts to which the 
 measurements apply, are carefully indicated. It is, therefore, 
 unnecessary to enter into further details, except as far as relates 
 to such parts as involve some peculiarity : the shaft of the column, 
 for example, and one or two of the mouldings. 
 
 Referring, in the first place, to the column, it is to be observed 
 that it is customary to make the shaft cylindrical for one third of 
 the height, that is, of equal diameter throughout that, extent : 
 above that point, however, it diminishes gradually in diameter up 
 to the capital. This taper is not regular throughout, being 
 scarcely perceptible at the lower part, and becoming more and 
 more convergent towards the top. Its contour is consequently a 
 curve, instead of a straight lino. This curvature constitutes what 
 is termed the entasis, and is employed to correct the appaient 
 narrowness of a rectilinear column at the middle. Such defective 
 appearance onl*takes place "hen the cylindrical piece, or column, 
 is between a pedestal and an entablature having plane surfaces 
 A cylinder, or sphere, always seems to occupy less space than a 
 plane surface equal to its greatest section. Thus the outline of a 
 
 cylinder or sphere, appears to grow less when it is shaded. \..\\, 
 where the column is in contact with the plane surface of the pe- 
 destal or entablature, it cannot appear less in proportion, the 
 proximity of the latter correcting such appearance, whilst tho 
 
 influence is less felt at the central part, which is farthest from the 
 pedestal and entablature. A true cylinder, therefore, in sach 
 position, appears to be thinner at the middle, and this is corrected 
 bf the entasis, or curved contour. 
 

 «nJ it 
 
 eolunuu for m. 
 
 and ihr ci.luii ■. 
 
 meduvtiad entasis, \- ■ 
 
 - 
 »nd increaiwxl width in tin- middle 
 •uch r»\ U 
 
 height 
 
 oft, int. i any SI :ti Iht 
 
 ■ 
 uucof i rir ,ual to 9} nar - - 
 
 .-. C </", tiii.n [Kindle! Kali 
 •. j- : divide t)n- are, r j, into *i\ equal porta, 
 and then th fOW g h the | 
 
 ■ tin- horicontal 
 «n throu^ li. 
 
 od through d the ra- 
 
 the ahaft Thi - 
 
 • J, will 
 shaft 
 In tfa ' will 1«. found t«" 
 
 . • . . i of the cijmn 
 
 lii peculiaritiee 
 1 Bopm the • 
 ! /- and accompanying minor mould- 
 
 ■ 
 teparately, and on a larger scale, in figs. 9 H 
 
 ftl I i:s and PRACTICAL DATA. 
 
 Tlli 
 
 117. V. that the Yolumeoreolidity of abody, 
 
 ■pace enthral —length, 
 
 width, i I .1. ptli, 
 
 of a »oud ia d 
 
 a unit ■• it u I square 
 
 timetre, and tin* eul. 
 
 ■ 
 
 \\1iil-.t i mi 
 
 I i iMla (10* x 10* x 10*-=) 100 
 
 ..■• x loir = 
 = ( Iikhj -/. x 1000 */. x 1000"/. = ) i '. euhfa 
 
 inillimr' 
 
 ■ 1 <T , , ', , 
 
 B 
 
 . 
 and in for — 
 
 1 euhk foot — 1 yard x 1 yard >. | 
 
 and an I: 
 
 119. Para >. — The volumi 
 
 • 
 : PL 7. Let A] 
 
 and K II 11 bet Than the lm.-w = 14 X 14 a 1 
 .' 
 ! 
 ■sod by the I 
 
 • which one aide UK 
 
 . - 1 I • 1 l ■; 1 1. or II': j T . 
 ■ ral, tin- \ • •! mm- of a ri^'lil prism, v. 
 
 equal t.. tin- product of tlir baae into il»' height 
 
 TABLE OF SURFACES, A5D VOLUMES OF REOl I IB ! - •: '. III.HU 4. 
 
 Ntniu or Sidi.. 
 4 . . . . 
 
 19 ... . 
 
 N»irs Svirici. Vomi 
 
 adron l-TM >oa "11 
 
 ii v dron, or Cube I 
 
 Iron B'4641016 -ft 
 
 ♦ 1 I ■ 
 
 •M . . . . I oi ' B-660U&40 - 
 
 120. Pyram jonal pyramid ■ 
 
 to it» ba». 
 
 ' I Band AD 
 
 ■f the pyramid 
 1-4x1 
 
 Ml.ll.-1. 
 
 
 Tow •■ 
 
 |iri«in. hating »• 
 
 equal t.. the product of a third of the height, int.> Iht ana 
 tw.. l.i-. ■ added to li of their product 
 
 » Time. \ onl the volume of a truneated pyramid, of 
 
 which tli. hi ■. II. 8 R • '. ill" lowi r I 
 i . we hart — 
 
 V=^ x (11+ !!'+♦ UTT') = 
 
 — x (8 a f. + 4 a. f. + 4/0 x 4) = I 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 In practice, when there is little difference between the areas of 
 the bases, a close approximation to the volume is obtained by- 
 taking the half of the sum of tho bases, multiplied into the 
 height. Thus, with the preceding data, we have 
 
 /B + B'\ 
 V = II X ^— \ — J = 15 sq. ft. 
 
 121. Cylinders. — The cubic contents of any cylinder, as fig. g, 
 is equal to the product of the base into the height. Thus, in the 
 case of a cylinder of a circular base, we have B = n R 2 (72) ;* 
 consequently, the volume, V, = jt R 2 X H. 
 
 First Example. — What is the volume of a cast-iron cylinder, 
 of which the radius, R, = 20 inches, and the length, H,- = 108 
 inches? 
 
 V— 3-1416 X 20 s X 108 = 135,717 cubic inches. 
 The volume may also be derived from the diameter of the cylin- 
 der, in which case we have — 
 
 :D a 
 
 V = 
 
 X II; or, 
 
 V = -7854 x 40- X 108 = 135,717 cubic in. 
 The convex surface of a right cylinder, when developed, is equal 
 to the area of a rectangle, having for base the rectilinear develop- 
 ment of the circumference, and for height that of the- cylinder. 
 It is therefore obtained by multiplying the circumference into 
 the height or length. With the data of the preceding case, the 
 convex surface is expressed by the formula — 
 
 S = -2n R X H, or n D X II = 31416 X 40 X 108 = 
 13,571-7 cubic inches. 
 The volume of a hollow cylinder is equal to the difference between 
 that of a solid cylinder of the same external radius, and that of 
 one whose radius is equal to the internal radius of the hollow 
 cylinder. Or, it is equal to the product of the sectional area into 
 the height, such area being equal to the difference between two 
 circles of the external and internal radius, respectively. 
 
 Example. — It is required to find the volume, V, and the internal 
 surface, S', of a steam-engine cylinder, including its top and bottom 
 flanges in the volume. Let the following be the dimensions : — 
 External diameter, D, = 56 inches ; internal diameter, D', =: 50 
 inches; length or height, H, = 120 inches; external projection 
 of the flanges, F, = 5 inches, and their thickness, E, = 4 inches. 
 Then, for the internal surface, we have — 
 
 S' = 3-1416 x 50 x 120 = 18,850 sq. in. 
 
 For the volume of the body of the cylinder, we have — ■ 
 
 «56 2 7to0- 
 V' = — t j- x 120= (-7854 x 56=)— (-7854 x 50 2 ) x 
 
 120 = 60,000 cubic inches. 
 And for the additional volume of the flanges — 
 
 y . = n (56 + 10)= _ 156 2 x 4 x 2 = (.7854 x 66=) - 
 4 4 
 
 (-7854 x 56 2 ) x 8 = 7666 cubic inches. 
 Whence the whole volume — 
 
 V + V* = 67,666 cubic inches. 
 
 • When we wish to refer the student to any role or principle already giv> 
 w# do so by means of the number of the paragraph containing such rule or priri 
 pie. In Ihr present instance, what is refeired to will be found at page 20. 
 
 122. Corns. — The cubic content of a cone is equal to the pro- 
 duct of its base into a third of its height ; or, 
 
 V = B x *L 
 3 
 
 In the right cone, fig. \?, of which the base is circular — 
 
 V^R^xH-^x^ 
 3 ~ 4 3 
 
 and as n, or 3-1416 -=- (4 x 3) = -2618, the formula resolves 
 itself into — 
 
 V = -2618 x D 2 x H. 
 
 Example. — What is the volume of a right cone, of which the 
 height, H, = 24 inches, and the diameter of the base, or D, = 
 17 inches? 
 
 We have — 
 
 V=-2618 x 17 2 x 24 = 1816 cubic inches. 
 
 As wo shall demonstrate, at a more advanced stage, the 
 
 development of the convex surface of a right cone is equal to tno 
 
 sector of a circle, of which tho radius is the generatrix, and the 
 
 arc the circumference of the base of the cone — consequently, tho 
 
 conical surface is equal to the product of the circumference of 
 
 the base into the half of tho generatrix: whence is derived the 
 
 following formula. : — 
 
 G 
 S = In R x ■7j-=x R x G. 
 
 Willi the data of the foregoing example, and allowing (ho 
 generatrix to be equal to 25| indies, we have — 
 
 S = 3-1416 x 8-5 x 25-5 = 681 cubic inches. 
 
 123. Frustum of a cone. — The volume of the frustum of a cone 
 may be obtained in the same manner a» that of the truncated 
 pyramid (120). The convex surface of a truncated cone is equal 
 to the product of half the generatrix of the frustum into the sum 
 of the circumferences of the bases, and is expressed in the follow- 
 ing formula : 
 
 S =^ x In (R + R') = L x * (R + R'). 
 
 Example. — Let the length, L, of the generatrix of the couie 
 frustum, = 14 inches; the radius, R, of the lower base, = 8-5 
 inches; the radius, R', of the upper base, = 3-8 inches; then tho 
 convex surface— 
 
 S = 14 x 3-1416, x (8-5 + 3-8) = 54 square inches. 
 
 124. Splure. — The volume of a sphere may 1 e ascertained as 
 soon as its radius is known. Its surface is equal t" foul times 
 that of a circle of equal diameter. This is expressed by the 
 formula — 
 
 S = in R 2 = n D 2 = 31416 x D-, 
 or the square of the diameter multiplied by 3-1416. 
 
 The volume is equal to the product of the surface into one-third 
 of the radius, as in the formula — 
 
 V = 1* R 2 
 
 R 
 
 = — x rt R J , or V : 
 3 3 
 
 4188 x R»: 
 
 or, if we employ the diametral ratio — 
 D 
 
 D 2 x 
 
 — — -5236 x D 3 
 6 
 
-. 
 
 TMK l'K\<TI«\I. I>K.V 
 
 VsTm;ir.—\\'e w.u!J kaow whs! i. the surface and the volume 
 V a •]**•«», of which the ifianutsr ■ ■ ■■■ll SS inches. 
 
 The mutt * 4 
 
 • 1416= 1963-5 sq. inchea 
 IWiiIibi 
 
 cubic inch**. 
 . 1 the nJitt* or diameter of a sphere, of which the volume 
 :ivert the preceding operation*, the 
 
 V V 
 
 R' = 
 
 R = 
 
 
 
 D' = 
 
 D = 
 
 which, with the preceding data, gives R = 125 inches, and D = 
 
 •_:, | :.. v 
 
 The raiios is derived Mm the surface by means of the follow. 
 ing formula : — 
 
 U«' 
 
 R' = 
 
 » ).- m. 
 
 vhr aes, 
 
 R " \ 
 
 D' = 
 
 V 31416' 
 
 N/Arric actors, ferments, and zones. — The surface of a* 
 fooe or spheric segment, is equal t - , rvurn- 
 
 fereoee the sphere, i: f the zone or 
 
 ■ 
 
 S = V B X H. 
 - 
 
 'udiu*, R, of the sjihfrc, 75 inches, the surface— 
 
 . - . 
 
 • >r is equal to the pr. duct "f 
 -ical base, into one-third the radius of the sphere 
 of which it » a [• 
 
 I re— 
 
 R 3 
 
 -«xB*B . ■; ■ IT II 
 
 ' .me of the spheric sector, whose spheric 
 
 baa* is equal to the surface considered in the previous example, is— 
 V = 3094 x 7 5' X 15 = 17668 cubic inches. 
 The volume of s sfharfa •epment is equal to the pr 
 
 :>c-aixth 
 
 ... II 
 
 Esamjir.—X. Sea, and II 15 inrhrs; the then 
 
 aBO 
 
 V = -5»96 x 6-5' x 1 5 = S3 56 cubic inches. 
 
 The volume of a spheric aagwk is equal to the orodocl of lh* 
 gore, which is Ha base, into a third of the radius. 
 The formula b — 
 
 V ■ 
 
 3 
 
 where A = the area of the get*. 
 
 The volume of a zonk segment ia equal to half the sum of 
 Ha basea* multiplied by ita height, paws the volume of a sphere 
 of which that height is the diameter ; whence the formula — 
 
 v-(-»!±*^)xi " 
 
 Ooas-vstKsss. — The volumes of spheres are pr op ortional 
 to the cubes of their radfi, or diameters. Law V s 
 culiic inches, and r = 4-188 cubic inches. It will he found 
 that the respective radn are— 
 
 r ~ v < 188 ~ V * ls8 ~ : 
 
 and, consequently. D = 3 and J — ± 
 
 The cubes of these numbers, that is, 37 and 8, have the same 
 ratio to each other as the volumes given ; that is to say — 
 
 137 : V188. 
 
 When of equ . l.-rs are to each other, as well as 
 
 as the. squares of the radii of their bases. 
 
 of equal diameter, these solids are to each other as 
 
 First, then, we ha 
 
 V = « R» x H, andr = « r» > H. 
 
 whence, 
 
 V : t :: R : : r> 
 
 And, aecon I 
 
 V = «R' x II, andr = * R> x a; 
 
 vw *»■ • . 
 
 V : i :: H : K 
 
 TV volume of a sphere is to that of the circumscribed rrSndni 
 as 3 to 3. A sphere is said to be inscribed in a cylinder, when 
 its diameter is equal to the height and diame te r of the cylinder. 
 
 The volume of an annular I is equal to the product 
 
 of its section into the mean circumference. We have 
 that an annular torus is a solid, generate-! 
 a circle about an axis, situated in the plane of the circle, 
 and at right angles U> the plane of revolution. 
 
 radius of the generating circle, and r the i 
 of its centre from the axis, we have— 
 
 \ « R' x 3« r = 19-73 R» x r. 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 PROPORTIONAL MEASUREMENTS OF THE VARIOUS PARTS OF AN ENTIRE ORDER. 
 THE (MODERN) DORIC ORDER. 
 
 .J i 
 
 Cornice, . 
 
 Frieze, 
 
 f Reglet, . . 
 Cavetto, . 
 
 Fillet, . . 
 
 Cymatium, 
 
 Corona, . 
 Fillet, . . 
 Mutules, . 
 Guttte, . . 
 Fillet, . . 
 
 Cyinatium, 
 
 Capitals of the Triglyphs, 
 
 . ( Ta?nia, 
 
 Architrave,-! p . ' 
 
 ( r acia, 
 
 Catital, 
 
 Shaft, . 
 
 Base,. . 
 
 Cornice, 
 
 Dado, 
 
 Base, . 
 
 Reglet, . . , 
 Cymatium, . 
 
 Abacus, .... 
 Echinus, .... 
 
 Three Annulets, 
 
 ^ Necking, .... 
 
 Beading or Astragal, 
 Cincture, 
 
 Shaft Proper, .... 
 
 Fillet,. . 
 Beading, 
 Torus, . 
 Plinth, . 
 
 Reglet, 
 
 Quarter-Round, 
 
 Fillet, 
 
 Corona, .... 
 
 Cymatium, . . . 
 
 Fillet, 
 
 Beading, 
 
 Cyma Reversa, . . . 
 
 Plinth, 
 
 Sub-Plinth or Socle, 
 
 2 
 
 <u 
 
 2 
 
 6 
 
 2 
 
 5 
 
 a 
 
 4A 
 
 2 
 
 2 
 
 2 
 
 l! 
 
 1 
 
 3 
 
 1 
 
 Oi 
 
 
 iU 
 
 
 n 
 
 11* 
 
 Total height of the Orde 
 
 1 31 
 
 1 3i 
 
 1 2^ 
 
 1 2 
 
 1 1| 
 
 111 
 
 10| 
 
 10" 
 
 1 
 
 m 
 
 10" 
 1 
 
 i U 
 
 1 2 
 1 5 
 1 5 
 
 1 11 
 
 1 10| 
 1 9| 
 
 1 5 
 
 2! 
 
 2 ' 1 
 
 10 $ ' 
 
 1 
 
 u 
 
 4 
 
 M6 
 
 13 10i 
 
 2-833 
 2.583 
 2-542 
 2-500 
 2-417 
 2-375 
 2-167 
 2-125 
 1-250 
 1-083 
 1-042 
 •959 
 •917 
 
 •833 
 
 •959 
 •833 
 
 > ' 6 
 
 4 4 
 
 1-292 
 1-271 
 1-188 
 1-167 
 1-146 
 •959 
 •875 
 •833 
 
 1-000 
 •959 
 •833 
 
 1-000 
 
 1-104 
 1-167 
 1-417 
 1-417 
 
 1-917 
 1-889 
 1-806 
 1-750 
 1-542 
 1-459 
 
 1-417 
 
 1-500 
 1-583 
 1-583 
 1-708 
 1-750 
 1-792 
 
 •083 
 
 
 ■250 
 
 
 •042 
 
 
 •125 
 
 
 •333 
 •042 
 
 ■ 1-500 
 
 •042 
 
 
 ■209 
 
 
 ■042 
 
 
 •16G 
 
 
 •ICG, 
 
 
 1-500 
 
 1-500 
 
 •107 
 •833 
 
 . 1-000 
 
 •042") 
 
 •083 
 
 •209 
 ■209 
 
 ■124 
 
 •333 
 
 •0S3 
 •042 
 
 •0831 
 •083 I. 
 •334 f 
 ■500 J 
 
 4-000 4-000 I 16 000 
 
 4 25 333 
 
. 
 
 '. IIUUUS PART8 OF AN ENTIRE ORDER. 
 
 THE T08C A ■ K n I it. 
 
 i J is. M..Wn ...I M<xMi>f* 
 — bag ik* IW.J. 
 
 
 
 Ttw Mud.U - I. 
 
 
 P 
 
 Qujuiit-i: 
 
 I ! 
 
 
 
 I - 
 
 Cymatium, 
 
 A«CinT«ATX, ■ 
 
 fVU, 
 
 
 
 
 
 R •iiii.1, 
 
 
 
 
 
 fAatngal, . . . 
 stmft Pi 
 
 
 I 
 
 linth. 
 
 I ' 
 
 ) Cymatium, 
 
 
 I Socle or ninth, 
 
 Total baLgH ..f d I 
 
 a 3} 
 
 1 111 
 
 10 
 
 m. r. 
 
 i 
 1 
 
 f * V 
 
 
 ■a 
 
 '21 
 
 1 
 
 1 H 
 
 II 
 
 i . B 
 
 •'.'17 
 1000 
 
 i :r.:> 
 
 i fij 
 1 8 
 
 1 <■' 
 1 - 
 
 ! '} 
 
 3 8 
 
 '. 
 
 i 881 
 
 1 117 
 
 i :. i -j 
 
 l : I 
 
 •333' 
 
 . 
 
 •333 
 
 
 
 i Iff] 
 
 
 ■181 
 
 
 3600 
 
 1-000 
 •331 J 
 
 11875 
 
 •181 1 
 
 I -333 I 
 
 117 
 
 
 
 •• Ubln we tan eaiuly H. -tcmiinr Im prOfMf 
 nMMimimt for any member <<r monldiiig, in (I 
 
 hen the height of d Pot tl,i. 
 
 U an jlw., ih. tnt . n I... u IS. q rl »r portm, IS. 
 
 hi moat t-- divided by the decimal • 
 mi'iil in tin' talili « lor tin 1 t"i I to the 
 
 i .ill of the module proportioned to audi height. Tlicn 
 that of any required i I by multiplying th - 
 
 into the decimal in tin- ' 
 
 II It ii required to know » ' 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 tin' lower part of the shaft according to the Tuscan order, tho 
 
 height of the entire order being 15 feet. 
 
 The height of the entire order being 22167 when the modulo 
 
 '22-167 
 = 1 . we have — tt~ 
 
 feet, the diameter of the lower part of the shaft. 
 
 = 1 -4778 the module, and 1 -4778 x 2 = 2-9556 
 
 Second Example. — What is the height of the socle or lowor 
 plinth according to the Tuscan order, supposing the module to be 
 1-4778 feet ? We have 1-4778 x -417 = -616. 
 
 In like manner the dimensions of all the' other details may bo 
 easily determined according to tho Tuscan or Doric order. 
 
 CHAPTER in. 
 ON COLOURING SECTIONS, WITH APPLICATIONS. 
 
 CONVENTIONAL COLOURS. 
 
 127. Hitherto we have indicated the sectional portions of 
 objects by means of linear flat-tinting. This is a very tedious 
 process, whilst it demands a large amount of artistic skill — only 
 obtainable by long practice — to enable the draughtsman to pro- 
 duce pleasing and regular effects; and although, by varying the 
 strength or closeness of the lines, as we have already pointed out, 
 it is possible to express approximately the nature of the material, 
 yet the extent of such variation is extremely limited, and the dis- 
 tinction it gives is not sufficiently intelligible for all purposes. If, 
 however, in place of-such line sectioning, we substitute colours 
 laid on with a brush, we at once obtain a means of rapidly tinting 
 the sectional parts of an object, and also of distinctly pointing 
 out the nature of the materials of which it is composed, however 
 numerous and varied such materials may be. Such colours are 
 generally adopted in geometrical drawings; they are conventional 
 — that is, certain colours are generally understood to indicate par- 
 ticular materials. 
 
 In Plate X. we give examples of the principal materials in use, 
 with their several distinctive colours; such as stone and brick, steel 
 and cast-iron, copper and brass, wood and leather. Wo propose 
 now to enter into some details of the composition of the various 
 colours given in this plate. 
 
 THE COMPOSITION OR MIXTURE OF COLOURS. 
 PLATE X. 
 
 128. Stone. — Fig. 1. This material is represented by a light dull 
 yellow, which is obtained from Roman ochre, with a trifling addi- 
 ton of China ink. 
 
 129. Brick. — Fig. 2. A light red is employed for this material, 
 and may be obtained from vermilion, which may sometimes be 
 brightened by the addition of a little carmine. A pigment found 
 in most colour-boxes, and termed Light Red, may also be used when 
 great purity and brightness of tint is not wanted. If it is desired 
 to distinguish firebrick from the ordinary kind, since the former is 
 lighter in colour and inclined to yellow, some gamboge must be 
 mixed with the vermilion, tho whole being laid on more faintly. 
 In external views it is customary to indicate the outlines of the 
 individual bricks, but in the section of a mass of brickwork this 
 "efinement may be dispensed with, except in cases where it is 
 
 intended to show the disposition or method of building up. Thus, 
 in furnaces, as also in other structures, the strength depends greatly 
 on the method of laying the bricks. When vermilion is used in 
 combination with other colours, the colour should be constantly 
 mixed up by tho brush — as, from its greater weight, the vermilion 
 has a tendency to sink and separate itself from the others; and if 
 this is overlooked, a varying tint of unpleasing effect will he 
 imparted to tho object coloured. 
 
 130. Steel or Wrought Iron. — Fig. 3. The colour by which these, 
 metals are expressed is obtained from pure Prussian blue laid on 
 light — being lighter and perhaps brighter for steel than fi >r wrought- 
 iron. The Prussian blue generally met with in cakes has a con- 
 siderable inclination to a greenish hue, arising from the gum with 
 which it is made up. This defect may be considerably amended 
 by the addition of a little carmine or crimson lake — the proper 
 proportion depending on the taste of the artist. 
 
 131. Cast-iron. — Indigo is tho colour employed for this metal ; 
 the addition of a little carmine improves it. The colours termed 
 Neutral Tint, or Payne's Gray, are frequentl] used in place of the 
 above, and need no further mixture. They are not, however, 30 
 easy to work with, and do not produce so equable a tint. 
 
 132. Lead and Tin are represented by similar means, the 
 colour being rendered more dull and gray by the addition of China 
 ink and carmine or lake. 
 
 133. Copper. — Fig. 5. Fortius metal, pure carmine or crimson 
 lake is proper. A more exact imitation of the reality may be ob- 
 tained by the mixture, with either of these colours, of a little China 
 ink or burnt sienna — the carmine or lake, of course, considerably 
 predominating. 
 
 134. Brass or Bronze. — Fig. 6. These arc expressed by an orange 
 colour, the former being the brighter of the two; burnt Roman 
 ochre is the simplest pigment for producing this colour. Where, 
 however, a very bright tint is desired, a mixture should be made 
 of gamboge with a little vermilion— care being taken to keep it 
 constantly agitated, as before recommended. Mam draughtsmen 
 use simple gamboge or other yellow. 
 
 135. — Wood. — Fig. 7. It will bo observable, from preceding 
 examples, that the tints havo been chosen with reference to the 
 actual colours of the materials which they are intended to express — 
 earning out the same principle, we should have a very wide range 
 in the case of wood. Tho colour generally used, however, is 
 

 burnt • irpth oratreogth wit' 
 
 ■at* be cofcj.i. -ual to epidy 
 
 •hade first, aubacqoently showing the graining with a 
 
 with burnt «i.-nn». Throe poinU are »u«- 
 
 it variation, and very mock mu»t be left to the 
 
 ju'l^rirtit of it- 
 
 / I Jut-Rubber, and Gutta Perrha. — 
 
 . 
 
 r.ha by dark • I india- 
 
 ■ 
 
 V. - a little 
 
 i at readineaa am! facility tlion if hi* 
 
 ' ir«. — Wo hnve aeen by what 
 
 •i. It tnay In- imagined (hat 
 .1 is ai. . — t li:it ia, limply 
 
 itjon t.. the fi 
 i lent may tl. 
 
 . id which >t i .. 
 
 ■ 
 quired quantity 
 
 dour in 
 
 ■ ■ 
 
 ■••. !i'. Ii it 
 fl i tint, it i-> will to | 
 
 • 
 
 Wly obtain tl, 
 
 applied 
 When the di 
 
 ir Will, 
 
 ■uall ', 
 
 ■ I t.i fill 
 .' in ii-: !-■ r. | ■ 
 
 It 
 
 I ' it will 
 It la a vii, .1 with 
 
 I 
 
 rath be 
 
 a fine eveo ahade, for the leaftt quantity of aaliva which may be 
 
 taki ti uj, by th«- l.r.i.h baa the i rT.v ..:id altogether 
 
 apnilne; the wmah of I 
 
 cleanly method, the artiat should have a piece of bl 
 
 Ui ride— (kt bom abaorbeal Km better. Bj paerief th, break 
 
 I . u* colour DM '' and a» line a 
 
 ua. The bru- 1 
 paaaed i -.urn- [art of Un 
 
 try; ai.d when th<- Wniiiiiati..n of a large ahade ia 
 ■ 
 , be left dark.-r at tliat \<ur- 
 idwuld In- taki-n to ki.p i \artlv t.. tl..- ..inline; and ai 
 ..-. Ji"u!.l Ih- wbollj 
 
 • mark at Ike jun.-ti..n of tin- tWO |»Tti..n«. Finally, 
 
 I ii, .1 l« 
 id the colour should li 
 for th. 
 
 tin- better r. -nil of the «..rL. undei 
 
 CONTINUATION OF THE BTJ l>\ I >!' PROJECTIONa 
 
 lin. i - 
 
 TI.MK XI. 
 
 i \'. -. ihown, whi • 
 
 \ ill., thai ' or cut 
 
 ► 
 ' \\i:b th. Plate XL, 
 
 tli.it in ; 
 
 * 
 - 
 
 be divided by ■ 
 dona] < 
 
 .1. j t)i of tl u alao th.- 
 
 r ; lhir.il . 
 
 Thai 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 centre-bit, which, of course, should not turn with the spindle-foot, 
 is prevented from doing so by means of the key, c, which fits 
 
 into a cross groove in its under side, the key itself being' held 
 firmly by the grooves, b, into which its projecting ends are made 
 to tit. Of these details, the cup-piece, A, is of east-iron, the 
 footstep, B, of gun-metal or brass, the centre-piece, c, of tempered 
 Steel, and the small key, c, of WTOUght-iron. Therefore, bearing 
 in mind what lias already been said, we may indicate these various 
 materials in the sections, either by line-shading, of different 
 strengths, as in the figure, or by means of colours, corresponding 
 to those employed in Plate X.; and we may here remark, that 
 where line-sectioning is used, brass, guh-mctal, or bronze, is 
 frequently expressed by a series of lines, which are alternately 
 full and dotted. There are, besides, many ways of varying the 
 effect produced by line-shading. For example, the spaces between 
 the lines may be alternately of different widths, or the lines may 
 be alternately of different strengths. 
 
 Strictly speaking, figs. 1 and 1* are all that are necessary for 
 the representation of the object under discussion. The cup- 
 piece, a, however, which is externally cylindrical, has, at four 
 points, diametrically opposite to each other, certain projecting 
 rectangular plane surfaces, d, which are provided to receive the 
 thrust of the screws which adjust the footstep accurately in the 
 centre. The width of these facets is shown in the plan, fig. 1 
 whilst then depth is obtainable from the elevation, fig. 1". If, 
 instead of these facets, d, being, as they are, tangential to the 
 cylinder, a, they had projected, in the least, at their centres, then 
 depth would necessarily have been given in the section, fig. I s , 
 and in such case the elevation, fig. 1", might have been altogether 
 dispensed with. Whilst referring to the representation of the 
 •projecting facets, in connection with the cylinder, a, we may 
 remark, that when a cylinder is intersected by a plane, which is 
 parallel to its axis, the fine of intersection is always a straight 
 line, as efi figs. 1 and 1". 
 
 140. Stuffing-box cover, or gland. — In pumps and steam-engine 
 cylinders, the cover is furnished, at the opening through which 
 the piston-rod passes, with a stuffing-box, to prevent leakage. 
 The hemp, or other material used as packing, is contained in an 
 enlargement of the piston-rod passage, and is tightly pressed down 
 by a species of hollow bush with flanges, as reoresented in plan 
 in fig. 2, and in elevation in fig. 2". In this instance, the neces- 
 sity of a sectional view is still more obvious than in the case of 
 the footstep already treated of. In the vertical section, fig. 2*, 
 it is shown, that the internal diameter is not uniform throughout, 
 and that there is a ring or ferule, b', let in at the lower part of 
 the interior. The cylindrical opening, a, of the gland, coincides 
 exactly with the diameter of the piston-rod : the internal diameter 
 of a portion, b, of the ring, e\ is also the same. -The part, e, 
 however, comprised between these two, is greater in diameter, so 
 as to lessen the extent of surface in frictions] contact with the 
 piston-rod, and it also serves for. the lodgment of lubricating 
 mailer. It is further discernible in the section, that the flanges 
 or lugs, <l, which project on either side of the upper portion of the 
 gland, have each a cylindrical opening, e, throughout their whole 
 depth. These are the holes fur the bolts, which force down the 
 gland, and secure it'to the corresponding flanges, or lugs, on the 
 
 Btuffing-b6x. The annular hollowing out, /, at the upper and 
 internal part, of the gland, acts as a reservoir, into which llio 
 lubricating oil is first poured, and whence it gradually oozes ItO 
 tho interior. The ring, b', is forcibly fitted into the bottom 
 the gland, and terminates below in a Wedge, in lie- same manner 
 as the gland itself, the double Wedge jamming the packing against 
 the piston-rod and the sides of the Stuffing-box, and thus forming 
 a steam-tight joint. The ring, B', is generally made of brass, 
 both with a view to lessen the friction, ami to iis being 
 with facility when worn, without the necessity of renewing the 
 whole gland. The latter is generally made of cast-iron, though 
 the whole is sometimes made of brass or jjuii-hh ital. 
 
 141. Spherical Joint. — In some cases, a locomotive receives water 
 from its tender by means of pipes which are tilted with spherical 
 joints, as a considerable play is necessary in consequence of the 
 engine and tender not being rigidly connected together, and 
 obviate any difficulty of attachment from the pipes in the locomo- 
 tive not being exactly opposite to those in the tender, 'i'lii- 
 of joint, represented in plan and elevation in tigs. 3 and 3', gives 
 a free passage to the water, in whatever position, within < I 
 limits, one part may be with respect to the other. For its con- 
 struction to be thoroughly understood, tin- vertical section fig. 3' is 
 needed. This view, indeed, at once explains the various i 
 nent parts, consisting — first, of a hollow sphere, a, of i| ; , 
 thickness as the pipe, b, of which it forms the prolongation ; ami, 
 second, of two hemispherical sockets, C, D, which embrace tho ball. 
 
 a, and which are firmly held together by bolts passing through 
 
 lugs, a, a. When this species of joint is used of a small i 
 the junction of a gas chandelier with the ceiling, the two half- 
 sockets are simply screwed together — this method, indee 
 adopted in many locomotives. It must be borne in mind, that our 
 
 object in this work is simply to instruct the student to i [irately 
 
 represent mechanical and other objects, and for this purpi 
 employ both precept and example; but such examples do not 
 necessarily comprise tho latest and most improved or efficient 
 forms. The half-socket, c, forms part of the continuation, s, of 
 the feed-pipe, whilst the half-socket, d, is a detached piece, neces- 
 sarily moveable, to allow of the introduction of the sphcri 
 A. This half-socket, D, is partially cut away at the lower part, 
 and does not fit closely to the neck of the ball. This aih.ws t lit: 
 pipe, b, to move to a slight extent from side to side in anydu 
 and flic upper end of the ball, a, is cut away to a corresponding 
 extent, to prevent any diminution of the Opening in 
 when the two portions are thus inclined to each other. The pipe, 
 e, with its half-socket, c, is an example of the combination of a 
 cylinder with a sphere, and gives us occasion thai the 
 
 intersection formed by the meeting or junction of these solids is 
 always a circle in one projection, and a straight line in the Other. 
 
 The subject of such intersections will be discussed more in detail 
 
 in reference to Plate XIV. 
 
 The sockets, r and n, are formed with four external lugs, or eye- 
 pieces. </. for connection by bolts, as before stated. The 
 outlines of these logs, which glide tangentiolly into that of the 
 
 ho.lv of the socket, give rise to the solution OI a problem which 
 
 ni.e. lie thus put : To draw with a given radius an arc tangential In 
 
 n arcs. The solution is thus obtained: with the centres 
 
Tin: i nu\i(iHT 
 
 s 
 
 i «.f the 
 
 and ti-.-iK.tjil .. 
 
 • *>ure gauge*, 
 
 ■ 
 to the Mcam aa soon a- pro ore tlian i 
 
 deUrsained oa lad for whioh the valre la loaded. I' _- I I*, and 
 
 ..Ii J \l-r- 
 
 th-al aertion of a aafi 
 
 eonaSatx a, jur- 
 
 Banantl] 
 
 ivm and 
 
 !. at ill.- 
 
 n in an 
 
 - 
 
 ■•\;lh tliat c.f ifae latt. r. Tl»- upper 
 
 ■ 
 
 •mil the 
 ■ 
 and lb 
 
 / I ■ \ 
 
 net with In Cornwall, 
 a* mar,' 
 
 1he atnun, with a \.ry lit:! 
 I 
 
 I 
 . and a loll- 
 with a r ■ 
 
 ! when it i« li!' 
 art- nimultan. 
 
 •nil |urt of l! - tpimlte 
 
 in .-tn- with i! 
 ..:.,-!..-. c. The seal U anmU 
 ihre pmeota a 
 
 : 
 
 i the curird junction ff tKr body • •/ 
 
 .1/ ;«n\ Ti 
 of in r. : - drawn 
 
 1 of tiu> branch, c with the 1 
 
 as, an.1 passing 
 -jinple: 
 
 and the 
 
 1 \\ liii-h tlv an 
 
 - 
 
 the ajv 
 
 it, a, an- drawi. 
 
 ajul act nee alw) 
 
 ti'-n will show llut t! 
 
 ■ 
 
 external outline. 
 
 nt who ha* a 
 III. 
 
 SIMPLE APPUCATfi 
 
 run: xu. 
 111. l 
 
 and wood, arc 
 Ok, and 
 
 in all m 
 
 ■ 
 \ ■ 
 
 • the main 
 . ■ u lanla^u 
 
 than cast, and of possessing g 
 
 1 ij w I V p l, 1. :>. ■ I • Bflnrcol 
 
BOOK OF INDUSTRIAL DESiGN. 
 
 projections of a wooden shaft, such as is used for a water-wheel. 
 Fig. 4 shows, on one side, a lateral elevation of the shaft, furnished 
 with its iron ferules or collars, and its spindle ; and at the same 
 time, on the other side, a vertical section, passing through the 
 centre of the shaft, giving the ferules in section, but supposing 
 the central spindle, with its feathers, to be in external elevation. 
 Generally, in longitudinal sections of objects enclosing one or more 
 pieces, the innermost or central piece should not be sectioned, 
 unless it has some internal peculiarity — the object of a section be- 
 ing to show and explain such peculiarity where it exists, and being 
 quite unnecessary where the object is simply solid. In the same 
 manner, it is not worth while sectioning the various minutiae of 
 machinery, such as bolts and nuts, simple cylindrical shafts and 
 rods and screws, unless these are constructed with some intrinsic 
 peculiarity. 
 
 Fig. 5 is a transverse section through the middle of the shaft, 
 and merely shows that it is solid, and that it lias the external con- 
 tour of a regular octagon. Fig. 6 is an end view of the same 
 shaft, showing the fitting of the spindle, with its feathers, into the 
 socket and grooves, funned in the end of the shaft to receive 
 them, and the binding of the whole together by the ferules or 
 hoops. These views are what are required to determine all the 
 various parts of the shaft. It manifestly consists, in fact, of a 
 long prismatic beam of oak, A, of an octagonal section, and of 
 which the extremities, b, are rounded, and slightly conical. The 
 spindles, B, which are let into the ends, are each cast with four 
 feathers, c, and a long tail-piece, d, uniting and strengthening 
 them. Some engineers construct the spindles without the addi- 
 tional tail-piece, d. Though this simplifies the thing considerably, 
 it is an arrangement which does not possess so much strength as 
 when the spindle is longer. The beam-ends are turned out and 
 grooved to receive these spindles, the grooves for the feathers 
 being made rather wider than the feathers themselves. When 
 the spindles are introduced into the sockets, b, thus formed for 
 them, the whole are bound together by means of the iron hoops, 
 f, which are forced on whilst hot. After this, hard wooden 
 wedges are jammed in on each side of the feathers, thus tightening 
 and solidifying the whole mass. In addition to this, iron spikes, 
 g, are sometimes hammered in, to jam up the fibres of the wood 
 still closer. Fig. 1, which is a shaded and finished elevation of 
 one end of the shaft, gives an accurate idea of its appearance when 
 complete and ready for adjustment. 
 
 146. Cast-iron Shaft. — There are several descriptions of cast- 
 iron shafts. Some are cast hollow, others quite solid, and cylin- 
 drical or prismatical in cross section. Such as are intended to 
 sustain very great strains, are generally strengthened by the addi- 
 tion of feathers, which project more towards the middle. These 
 give great rigidity to the piece. A shaft of this description is 
 represented in elevation in fig. 7, half being sectioned through the 
 irregular line, 1 — 2 — 3 — 4, and half in external elevation. Fig. 8 
 is an end-view of it ; and fig. 9 a transverse section through the 
 line, 5 — 6, in fig. 7. In practice, it is not considered absolutely 
 necessary that a section should follow a straight line. Frequently 
 a much greater amount of explanation may be given in one view, 
 by supposing the object sectioned by portions of planes at differ- 
 ent parts, and solid and, easily comprehended portions are generally 
 
 shown in elevation, as the feathers of the shaft, in the present in- 
 stance, or the spokes of a spur-wheel or pulley. The shaft under 
 consideration is SUeh a one as is employed for hydraulic motors. 
 The body, a, is cylindrical and hollow, and it is cast with four 
 feathers, b, disposed at right angles to each other, and of an ex- 
 ternal parabolic outline, so as to present an equal resistance to 
 torsion and flexure throughout. Near the extremities of these 
 feathers, four projections are cast, for the attachment of the bosses 
 of the water-wheel. These projections are formed with facets, 
 so as to form the corners of a circumscribing square, as shown in 
 fig. 8; and they are planed to receive the keys, i, by which they 
 are fixed and adjusted to the bosses or naves, which are grooved 
 at the proper places to receive them. The spindles, n, which 
 terminate the shaft at each end, are cast with it, and are afterwards 
 finished by turning. The shaft thus consists of only one piece, or 
 casting. 
 
 147. Although we have already shown tho method of drawing a 
 parabola, in Plate V., the outline of tho shaft feathers affords a 
 practical exemplification, which it will be useful to illustrate. We 
 here also give the method generally adopted — because of its sim- 
 plicity — when the curve is a very slow or obtuse one, such as is 
 given to the feathers of shafts, beams, side-levers, connecting-rods, 
 and similar pieces. It is understood, in these cases, that two points 
 in the curve are given; the one, a, fig. 7, being at the summit, 
 and at the same time in the middle of the piece, and the Other, A, 
 situated at the extremity. In the present instance, wo suppose 
 the heights, a c and b d, from the axial line, m n, of the shaft to be 
 given. This line, mn, may also be taken as the centre line of a 
 beam, or connecting-rod. After having drawn through the point, 
 b, a line, e b, parallel to the axis, divide tho perpendicular, a e, into 
 any number of equal parts, and transfer these divisions to the line, 
 hi, the prolongation of the line, db; then draw lines from the 
 points, 1, 2, 3, to the summit, a. Further, divide also the length, 
 cd, into the same number of equal parts as the perpendicular, 
 and, through the divisions, 1', 2/ 3', draw other perpendiculars, 
 the respective points,/, g, h, of intersection of these with the lines 
 already drawn, will bo points in the required curve. As the 
 lower feather is an exact counterpart of the upper one. the perpen- 
 diculars may be prolonged downwards, and corresponding di 
 
 as 1'— /', 2'— <g', 3 — h', set off on them. To draw, also, the '<■ If 
 of each feather to the left, it is merely necessary to erect perpen- 
 diculars of corresponding lengths, at corresponding points ill the 
 axis. A ditferent method of drawing this curve is sometimes 
 adopted; namely, the one which we have already given in Plate 
 IX., for the entasis of the Tuscan column. As, however, it does 
 not possess the advantages of the true parabolic form, and as tho 
 curve becomes too sudden towards the extremities, we think the 
 method given in Plate XII. is to be preferred. 
 
 Fig. 3 represents a portion of the shaft just discussed, shaded 
 and finished, the lines running in ditferent directions, the better to 
 distinguish the flat from the round surfaces. 
 
 148. Shaft Coupling. — In extensive factories, and other works, 
 where considerable lengths of shafting are necessary, thej bave 
 to be constructed in several pieces, and coupled together. These 
 couplings are generally of cast-iron, and formed of one or moro 
 pieces, according to their size. One form consists of a species or" 
 
. 
 
 c j fo dn ual »«**t, arcurstely turned bteraaDy, which receive* 
 the rod> of i!m* two shaft* to beVoutccted, these being scarfed or 
 htt* ana other, *e a* to be bound wail together, and re- 
 volve like om coatianoaa piece. According to another form, two 
 ire employed, of increased diameter at the part wV-re they 
 and at this part into quadrant-ehaped dutches, 
 -. The coupling repreaented in aid. 
 i kind ; and in front elevation, a* separated, 
 
 , ,. u pling waa designed for a shaft, of w hi.-h the diameter 
 at the collar* waa 88 centimetre*. The sock 
 is adjusted on the end of the first part of the shaft, c T 
 
 »', b similarly adjusted on the end 
 of ti..- >!iaft. The** •■ -■ -|iooea gear »i!i each otfcsr, 
 
 ■ ..-ans of the projection* or . 
 
 • and »'. c •!.- tit the 
 
 one into the I 
 
 ■ . A, shows the 
 exact ahape and dimensions of theae projecting dutches, each 
 ...' a quadrant of the circle on the face of the socket-piece. 
 Those of the second |*vce, a', are precisely the same, or. 
 "-« on a, au tliat 1 - 
 -, as shown 
 accnrati 
 
 shafting is obtained, in the first place, by means •■' 
 diamctr '. and let half into the shaft, 
 
 and hal; 
 
 .ludiual 
 j ; «ling. 
 
 nix a: vs a woode* model or rArrtta 
 
 or i 
 
 ■ nny piece of mechanism which it is 
 
 ' - 
 . ■ 
 
 - 
 •nsiderable sU rt of th» 
 
 as also a knowlisl^e of the >. 
 p i upil a t i 
 
 ■ 
 
 etjaanaaah BatNd , however, plane-tree or sreun r.- ..r i...k 
 
 b u~-J ; and fur small patterns, and - _Tvat precision, 
 
 mabog> i u*ed, it 
 
 ehouM ry, and well seasoned. The pattern ia made 
 
 ■ according to the dimensions of the 
 
 Lance, a column of any eonaiderahle 
 
 - far a coupling of large ,aUe, 
 
 aoch aa that rcpro* and 14, the pattern ia 
 
 • ing the 
 up, there ia leaa ri»k of warp- 
 
 upling-pioc* ia represented. ; 
 nal aide elevation, and partly in longitudinal section, bein | 
 
 through the axis. rV 1 J is ■ 
 elevation, ebowing the project. 
 
 ti].— • ».. a- Ihal lb* path nj a hraMal >>t ta • i--*.-<iv ■ ay, maad 
 the circumference* of which a- 
 
 aa atare* i* li 
 up into piece* of the repaired thirlmei, and the aide* an 
 
 il, to coincide with the radii, cd.cr.Uf. 
 then fitted to the board*, t> n', and at this stage present the ap- 
 pearance of the left-hand aort The drum .- 
 ward* put int.. the lithe, and the circumference ia rcdu - 
 a] surface, like the right-hand portion of the aame I 
 On one of the ends, D, of thia drum, i- jrcting 
 clutch-piece, a, whirh baa U • of a board of 
 >. mi v in present the outline of fig. li On the 
 
 .'. are turned down to a di~ ..le to 
 
 Ihhi in the coupting- 
 '. 
 
 - lirface aa amooth as p oaai b la, 
 • loam of which the mould is 
 
 -. particularly when of small size, are more- 
 ii I4ack-lcad. ■ polish 
 
 and hardness to the surface. The diameter of the con -. 
 ia leaa than thai 
 
 -'me margin in the casting for turning and grinding 
 down i iirncnaiona. The oor> 
 
 - of loam placed in the centre 
 
 structed on end, and I ■ d not require 
 
 further - or placed in a 
 
 horizontal poatfaa, it require* to be aupported at both end*, and, 
 
 •rengtheoed by wires or roda pn a kg throegfa iu 
 
 ■ .is reason, a core-piece, aa r, is only attached to 
 
 I of the drum. It will be observed that this ia slightly 
 
 ..m is so also, but to a leas extent ; the core itself, 
 
 driest. 
 
 J Shjusk, or AOmtmet f 
 traction- -fted from the mould 
 
 essary to form 
 Ha aides with a alight tap**, or dram, a* it is technical , . 
 
 -.-piece, r, aa Well a» that of 
 the drum itself, must be less at the lower extremity, or at the part 
 Lrodoced into the mould, than at the opp • 
 
 .. .Terence of diameter i* euff; |Hi*e. 
 
 -.n. as b the case with all the metal* of the engio. • 
 
 leaa bulk when culd than w hen in a atate of fusion, and, bam an) : 
 
 .Le the patterns of somewhat 
 
 i.ineniions than the resting ia to be when finished. It 
 
 •hen. tluit when the pieces to be cast bare afterward* to 
 
 be planed, tamed, ground, or grooved, it is necessary to bear in 
 
 in::..!, in Mnaatiajeling lb* wonrlw asttara, not oal] the ati. r •• - 
 
 itraction. or, as it is termed, the *k 
 the metal, but also that which is occasioned by the rednring pnv 
 eaaats umdved in finishing the article. In general, § 
 require* an allowance for ahrink of from 1 # : L.; «r*ii» 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 iron, however, requires a much larger allowance. The allowance 
 to be made for the reduction caused by tho finishing processes, 
 depends entirely on their nature. 
 
 When, with a view to avoid tho expense of constructing a 
 pattern, the mould is formed from the actual object which is to bo 
 reproduced or multiplied, the mould-makers obtain the necessary 
 margin by shifting tho model slightly during the formation of tho 
 mould. This, of course, can only be done with advantage when 
 tho piece is not of intricate shape. 
 
 ELEMENTARY APPLICATIONS 
 
 RAILS AND CHAIKS FOR RAILWAYS. 
 PLATE XIII. 
 
 151. In railways, the two iron rails on which the trains run are 
 placed at the distance apart, or gauge, of lj metres, and are 
 generally formed of lengths of 4| to 5 metres. In England, the 
 gauge is generally 4 feet 84 inches, and the rails are rolled in 
 lengths of from 12 to 15 feet. These rails are supported by 
 cast-iron chairs, placed at from 9 to 10 decimetres asunder, and 
 adjusted and bolted on oak sleepers, lying across the rails, imbed- 
 ded even with the surface. Those chairs which occur at the 
 junctions of the lengths of rails are made wider at the base, and 
 of greater length, so as to embrace the end of each length of rail, 
 and render their rectilinear adjustment and union as perfect as 
 possible. 
 
 In Plate XIII. we give details of a very common form of rail and 
 chair. There arc many different forms in use ; but the method of 
 drawing or designing each will be similar, and may be thoroughly 
 understood from the exemplification here given. Figs. 1 and 2 
 represent the elevation and plan of a chair, with a portion of 
 the rail which it supports. Fig. 3 is a vertical section through 
 the line, 1 — 2. in the plan; but supposing the chair to be turned 
 round, or to belong to the right-hand rail — showing, in connexion 
 with fig. 1, the relative positions of the two lines of rails, with 
 their respective chairs. Fig. 4 is a side view of the chair alone, and 
 fig. 5 is an end view of a length of rail. This chair, which is de- 
 signed with the view of combining solidity and strength with 
 economy of material, consists of a wide base, a, by which it is 
 seated on the sleeper, and of two lateral jaws, B, b', strengthened 
 by double feathers, c, c'. The base, B, is perforated at a — the 
 holes being cylindrical, and slightly rounded at their upper edges. 
 These holes are for the reception of the bolts which secure the 
 chair to the sleeper. The space between the jaws of the chair is 
 for the reception of the rail, D, and the wooden wedge, E, which 
 holds it in position. 
 
 In this example, the vertical section of the rail, D, presents an 
 outline which is symmetrica] with reference both to the vertical 
 centre line, be, and also to the horizontal line, de, fig. 5. This 
 permits of the rail being turned when one of the running surfaces 
 is worn. The section of the wedge, e, is also symmetrical with 
 reference to Its diagonals, so that it is immaterial which way it 
 is introduced, whilst it also fits equally well to the rail when the 
 latter is reversed. 
 
 Tho outline of tho rail is composed of Btraigb.1 lines and arcs, 
 which are geometrically and evenly joined, as shown in fig. 5. 
 The necessary operations are fully indicated on the drawing itself. 
 Theso operations are, for tho most part, but the repetition and 
 combination of the problems treated of in the first division of tho 
 subject. We have, moreover, given somo of tho problems do 
 tached, and on a larger scale, in figs. 6, 7, 8. Fig. (J recalls tho 
 problem (35), which has for its object tho drawing of an arc, ij k. 
 tangent to the straight lines,/"' and gh, the radius, ok, being 
 given, equal to 31-5"'/„. (fig. 2, Plate III.) This problem meets 
 with an application at fgh, fig. 5. In fig. 7 we have the problem 
 (37), which requires that an arc, Imn, be drawn tangent to a 
 straight line, nip, and to a given arc, q r t, the point of contact, n, 
 being known (fig. 6, Plate III.) This meets with its application at 
 I m n, fig. 5. 
 
 The problem illustrated by fig. 8 is, to draw a tangent, g'f, 
 to two given circles of radii, st and o 1 A\ respectively. In 
 this problem (9), we require to find a common point, u, on tho 
 line, os, which joins the centres of the two circles. To effect 
 tins, we draw through the centres, o and s, any two diameters, vx 
 and v' x', parallel to each other. Join two opposite extremi 
 each, as v and x', by the straight line, ii', which will cut the line, 
 d s, in the point, u. The problem then reduces itself to the draw- 
 ing of a tangent to any single circumference (fig. 1, Plate I.), from 
 a given point, u. The tangents obtained, in the present instance, 
 will lie in one straight line, and be the line required — tangent to 
 both circles. The application of this problem is at x k' I in 
 fig. 4. 
 
 On fig. 9 we have also indicated the solution of a problem (41), 
 which is — to draw an arc, y z, of a given radius, a b', tangent to 
 two other arcs, having the radii, e' d' and e'f* (fig. 8, Plate 111.) 
 This problem is called for in drawing the outliue of the jaw of the 
 chair, where it runs into the base, A, near the edge of the bolt- 
 hole, a, fig. 3. 
 
 To complete the outline of the chair, it remains for us to show 
 how to determine the lines, g' h', which represent the inter 
 of portions of cylindrical surfaces, as will be gathered from tigs. 1 
 to 4. To avoid a confusion of lines, we have reproduced this 
 portion in figs. 10, 11, and 12, which represent — the two former, 
 vertical sections of each cylindrical portion, and the latter, the line 
 of intersection in plan. 
 
 We must first determine on fig. 12, wliich corresponds to fig. 2, 
 the horizontal projection, i, of any point, as i, taken on the arc, 
 g' V, in fig. 10 ; letting fall from this point, on the base line, L T, a 
 perpendicular, i i, and also drawing from it a horizontal line, i i*. 
 Tins latter line meets the cylindrical outline, g k', fig. 11, in i'. 
 Project t 3 in i' on the baso line, transferring it to a line at right 
 angles to the base line, by means of a quadrant of a circle, and 
 draw through tho point thus obtained a line parallel to the base 
 line, and meeting the line ii in ?, which will be a point in the 
 curve required ; other points, as /', n', are found in a similar 
 manner. 
 
 It must be observed, that when the two cylindrical portions are 
 of equal diameters, their intersection with each other, g'hf, as will 
 be demonstrated hereafter, is projected horizontally :is a straight 
 line; the greater the difference between the two cylinders, the more 
 

 
 > -I the line of their intersection be, a* U apparent in fig*. 
 
 The outlines of the feathers, r and c', glide into th..' 
 base, a whirh, in the plan, i- lha are, 
 
 tlic preceding figures, 
 
 i.ere remark, r 
 
 may br ii many of the problem already discussed, 
 
 and also with ■ 
 
 the draughtsman in the 
 . actiee. In such olijecta as tl 
 
 ud the 
 ■rs with eaffip 
 
 I in their chair- irly, but 
 
 an> in.-' each other, in such a MfJ 
 
 rtical, <ri*: this. 
 .! the carriages 
 may have to run off the rails, as is the case more particularly in 
 runes, from the effort made by tin- wheel* to run in :i - 
 
 r than tho < 
 for the lik 
 
 RULES AND PRACTICAL DATA 
 
 ■ MATERIALS. 
 
 The various materials employed in mechanical m 
 
 - -tli with 
 
 injured, 
 
 tkm of force or mo to which tiny 
 
 • are termed, — ""Ung to tin- mode in which they 
 ' 
 
 I Ir.iin often rt> 
 Brj calculating 
 tensioD* of uj •■ to the 
 
 •i and degree ol 
 
 BUtSTASCE TO COJlntE*- 
 153. Compression is a for. • ,-!i. or n inl.r 
 
 Gbre* or molecule* of any suh-tam-c which is sub- 
 : ••> iu action. 
 
 ■its, a prism of oak, of such 
 dimensions thai 
 
 ' •! by a 
 -tiinclre 
 of transverse m -hi of from 5. 1 | square 
 
 f (ransveme section. 
 ■ era], with oak of cast-iron, I' 
 
 • irea, as soon as the !• 
 
 nt, the resistance to compression m 
 
 - to be eompreaeed u f 4,900 
 
 • >r of nearly "K 
 • crushing, as so.. n as the 
 of the |*. ve aneada three time* the least dimension of the traas- 
 
 W* may safely load bodies of various substance*. 
 
 Table tf the Wmgktl which Solid* — such as C.iumns, Ptiastert, 
 S -<rts — iciU sustain tcilnout bring crushed. 
 
 WOOD* AM> URALS. 
 
 Drornntios 
 
 MsMtBsL 
 
 Sound oak, . . 
 oak,. 
 
 i 
 
 PrepottMa of Uaftb to Uost Jim*u 
 
 Up to It. Abo». II Abmo 14 Ab.... *l 
 
 
 
 TM! 
 
 
 
 . 
 
 SToS'ES, BUCKS, AM> VIoETABS. 
 
 Deornptios of Ma 
 
 • M 
 
 Granite t V96 
 
 gSJ 
 
 S25 
 
 
 
 in 
 
 Marl.le, hard, .'. 
 
 whiU 
 
 Freestone, hanl, 
 
 
 
 m Chatillon, near Paris 
 
 U 1'aris, 
 
 185 
 
 S&fi 
 
 from ■ 
 
 711 
 
 * trdinar) ■ 427 
 
 ■ 
 
 171 
 
 An i 1 1 )"■ 
 
 1 1,1 
 
 or 
 
 bard and ».ll baked 
 
 1 
 
 ., . . i 
 
 • I with lime •rater 
 
 Mortar, 1 ■ Id 
 
 " " of lime and sand, . . . 
 
 ■ B 
 
 /.' —To Bad, bj means of thi- • 
 
 • may ba I 
 
 Multiply the transient sectional itrra of the pitta r>v the n< 
 
 I 
 
 i 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 the table corresponding to the material., and to the proportionate 
 lengtli of the piece. And inversely, from the weight which a piece 
 is to support, its smallest transverse section may be determined. 
 By dividing this weight, expressed in pounds, by the number in the 
 table corresponding to the material, and to the proportionate length. 
 
 First Example. — What weight can be put with safety upon a 
 pillar constructed of ordinary bricks, the pillar being of a rectan- 
 gular section, of 50 inches by 60, and the height being below 12 
 times the length of this cross section ? 
 
 We have 50 x 60 = 3000 square inches of transverse sectional 
 area. Then, according to the table, we have — ■ 
 3000 X 57 = 171,000 lbs. 
 
 Second Example. — What must be the transverse sectional area 
 of a square post of sound oak, 19 feet 8 inches in height, and 
 which will safely bear a load of 60,000 lbs. ? 
 
 According to the table, if we suppose the length to be not more 
 than 12 times the least cross section, the number or coefficient of 
 compression, in pounds per square inch, is 426'75. 
 
 Then, 
 and 
 
 60,000 . , 
 
 ;_„„. = 140 square inches; 
 42b' to 
 
 Vl40 = 11-8 inches, the length of tho supposed side. 
 Comparing tliis 11-8 inches with the given height, we find that 
 
 19 ft, 8 in. 
 11-8 in. 
 
 236 
 11-8 
 
 = 20. 
 
 This shows — and we have constructed the example with this 
 
 view — that in this instance the proportionate length has not been 
 
 correctly estimated ; and therefore, instead of taking the number 
 
 426-75, as in the first column, we must take that in the second 
 
 column, for a proportionate length of between 12 and 24 times the 
 
 cross section. The calculation will, consequently, have to be 
 
 rectified thus — 
 
 60.000 . , 
 
 = 168-7 square inches, 
 
 and VT6S-7 = 13 inches nearly, the proper dimension for the 
 cross section of the post. 
 
 Third Example. — What is the greatest load that can be borne 
 with safety by a solid cast-iron column, 3 inches in diameter, and 
 12 feet in height? 
 
 It is, in the first place, evident that the ratio of tho diameter to 
 the height is 12 feet, or 144 inches, -5- 3 inches = 48. 
 
 Consequently, 
 the section -785 x 3 2 x 4741-666 = 33,500 lbs. 
 
 In shops and warehouses, builders employ solid cast-iron 
 columns, instead of brick pillars, so as to take up less space. These 
 columns are generally calculated to support loads of above 
 33,000 lbs. each. They are usually about 3 inches in diameter, 
 and 12 feet high. In which case, supposing a cubic foot of cast- 
 iron weighs 452 lbs., they will weigh (3 inches being equal to -25 
 foot)— 
 
 •785 x -25 2 x 12 x 452 = 266 lbs. 
 
 If, instead of these columns being massive or solid, we employ, 
 m place of two of them, a hollow one, to support the proportionate 
 load of 66,000 lbs., and being 6 inches in diameter, this increase 
 
 in tho diameter makes tho ratio of the length to it 24, instead of 
 48 ; and the coefficient to be taken from tho table will conse- 
 quently be 14,225, instead of 4742. 
 
 Now, 66,000 -H 14,225 = 4-64 square inches, would be tho 
 cross section of a solid pillar, equivalent to that of which tho 
 thickness is sought. Since, however, the diameter of the tatter is 
 6 inches, its section of solidity would be — 
 
 •785 x 6 2 = 28-26 square inches. 
 Then, deducting from this area 4-64 square inches, as above 
 determined, we have 28-26 — 4-64 = 23-62, for the cross sectional 
 area of the central hollow. From tliis we deduce the internal 
 diametor, thus — 
 
 /23-62 
 
 J 
 
 7S0 
 
 = 5'485 inches. 
 
 And, finally, the thickness of the column will bo — 
 
 6 ~ 5 " 485 = -2575 inches. 
 2 
 
 The weight of such a column, if 12 feet in height, will be — 
 
 4-64 
 
 — — X 12 X 452 = 174-77 lbs. 
 144 
 
 This result shows very markedly how great an economy results 
 from the employment of hollow in place of solid cast-in. n columns. 
 The thickness, determined as above, of -2575 inch, is theoretically 
 sufficient, but in practice we seldom find such castings under half 
 an inch thick. 
 
 In the above examples, too, the mouldings usually added to the 
 columns are not taken into the account, With these, the weight 
 will bo a tenth or so more, according to the description of moulding. 
 
 TENSIONAL RESISTANCE. 
 
 155. A tensile force is one which acts on a body in the direc- 
 tion of its length, tending to increase the length, and when carried 
 to a sufficient extent, to cause rupture. 
 
 As with reference to compression, many experiments have been 
 made to determine the sectional area to be given to bodies i f 
 various materials submitted to a tensile strain, so that they may 
 safely resist a given force. 
 
 First Example. — Required the sectional area for four square 
 tension rods of wrought-iron, to connect the top and bottom of a 
 hydraulic press, in which tho force which tends to separate these 
 two ends, and consequently to rupture the rods, is equal to 500,000 
 lbs. 
 
 Each rod must be capable of resisting 
 
 500.000 , ., 
 
 = 125,000 lbs. 
 
 4 
 
 According to the table, the best wrought-iron may be safely 
 
 subjected to a strain of 14,225 lbs. per square inch of cross section. 
 
 We have, consequently, 
 
 125.000 _„ . , 
 
 = 8-79 square mches. 
 
 14,225 H 
 
 for tho area of the cross section ; and 
 
 V879 = 2-964, or nearly 3 inches, 
 
 for a side of the square rod. If the rod were round, we should have — 
 
 /8-79 
 D =V : 785 = 
 
 3-345 inches, for the diameter. 
 

 la the aamc maanar, the rfkra et cr proper for air— engine 
 pi»t • >o -r odi mar be ralmlalod, when the preaaure on the puton ia 
 known. 
 
 ' J sustain u-hrn 
 
 submitted ■ S 11/1. 
 
 DMcnpfca U V.u, ^ 
 
 • 
 
 
 
 
 
 
 ' _r»in 
 
 
 
 
 
 M 
 
 Mi- 
 
 I 
 
 . 
 oar u i 
 
 ' 
 
 j to tin-. 
 
 
 
 M3*/. 
 
 
 
 
 
 
 I to - 1S inch, 
 k or 1 !<• :. •/■ in dial 
 
 
 
 
 
 
 
 
 
 
 
 
 I 
 
 . 
 
 
 
 ... 
 
 
 
 i 
 
 
 
 
 
 
 
 
 
 11 
 
 
 
 
 
 
 
 
 
 
 1 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 7.1 IS 
 
 
 
 
 417 
 
 l.llrt 
 
 In. I 
 
 440 
 
 826 
 
 110 
 
 v / . d the amount of lenale or I 
 
 , a carriage draw-ahad, inada 
 I ruaa-aeclional area of 166 etjuara inehea. 
 
 hatt — 
 : Iba. x 15 5 = 36-400 Iba, 
 155. Pulby B ila mar gene- 
 
 rally be employed in practice, to determine the dui 
 .»: — 
 
 20_x II I' 
 • 
 in «rU h I 'i "f 8m land in boaM; 11 P, the : 
 
 «rer; and r, tl,- mute. 
 
 •ii Iba., raiiied 
 I font Ufljb in a uiinui. .uumea, 
 
 •>ame aa 
 
 inula would be — 
 
 _ 1.V' • ■ II I' 
 v 
 r, in this ntkoetrai pel - 
 
 and I, the width in itntiin.: kaaat «( the 
 
 Of 6"/.. 
 
 the htirse puirer by the constant mv. dnide the pro- 
 duct by the iclucily in fret per minute., and the (fuotienl trill be the 
 u-idih <y" tht Iximl in i 
 
 / Let II F niinute, 
 
 then, 
 
 10 
 
 - 
 j which it embrace*; tint b 
 ii ; and that ll 
 
 I !i_\ it. 
 It i- 
 of two | 
 
 KUM. 
 
 effort w I 
 
 - 
 B I 
 
 i 
 
 wliilit Ii 
 
 ! in the 
 - pported ut the centre, and h 
 applied at both 
 
 u . der the caae ■ 
 
 .i ttraln at the 
 'A Ih. iha ». i-l, t la ; 
 
 in wU Ii tin- piece und< i 
 ■ 
 diuienaion in b 
 auuilarly ezprea*ed ; — then tliv great.- 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 bear, without undergoing alteration, will be determinable by tho 
 following formula, the piece being of rectangular section, aud fixed 
 at one end, and weighted at the other. 
 
 C X ab 3 
 
 W = 
 
 6L 
 
 Now, 
 
 C == 8,535, for wrought-iron ; 
 10,668, for cast-iron ; 
 854, for oak and deal. 
 Substituting these values of C, in the preceding formula, we 
 shall have, for pieces of rectangular section, according to the 
 material — 
 
 For Wrought-iron. 
 
 TbTT 
 
 For Cast-iron. 
 
 p ^ 10,668 IX«i', or more simp]yi = 
 6 L 
 
 1778 X ab 3 
 
 P = 
 
 854 x ab- 
 6L 
 
 , or more simply, : 
 
 142 x ab 3 
 
 Tliese formulae lead us to the following rule for pieces of rect- 
 angular section : — Multiply the horizontal dimension in inches of 
 cross section, by the square of the vertical dimension in inches, and 
 by a coefficient depending on the material: then divide the product 
 by the length in inches, and the quotient will be the weight in pounds, 
 which the piece will sustain without alteration. 
 
 This rule is derived from the fact, that the transverse resistance 
 of pieces submitted to a deflective strain is inversely as their 
 length, directly as their width, and as the square of their vertical 
 thickness. 
 
 According to tliis, pieces fixed at one end, and intended to bear 
 a strain at the other, should be placed on edge ; in other worus, 
 the greatest cross section should be parallel to the direction of the 
 strain. 
 
 First Example. — What weight can be suspended, without causing 
 deflection, to the free end of a wrought-iron bar, fixed horizontally 
 into a wall at one end, and projecting 5 feet (== 60 inches) from it; 
 the bar being of a rectangular cross section, having its horizontal 
 dimension, a = 1-2 inches, and its vertical dimension, b = 1-6 
 inches ? 
 
 We have 
 
 1422-5 x 1-2 x 1-6 3 
 
 P = 
 
 72-8 lbs. 
 
 This result is obtained on the supposition that the bar is placed 
 on edge ; but what would be the weight, other things being equal, 
 supposing the bar to be placed on its side — that is, when 1-6 inches 
 is its horizontal dimension, a, and 1*2 its vertical dimension, bl 
 
 We have, in this case, 
 
 P = 
 
 14225 x 1-6 x 1-2 3 
 
 6U 
 
 = 54-6 lbs. 
 
 This inferior result shows the advantage of placing the bar on 
 edge. 
 
 When the piece under experiment is of square instead of oblong 
 section, a necessarily = b, and a b- becomes b', and tins is conse- 
 quently to be substituted in the formual for the former. 
 
 If, however, tho piece is cylindrical, the formula will be — D 
 
 representing tho diameter, 
 
 „ . . . _ 854 x D 3 
 r or wrought-iron, P = — — • 
 
 For cast-iron, 
 For wood, 
 
 P = 
 
 JL 
 
 1066 x D 3 
 
 P = 
 
 L 
 
 35 x D 3 
 T ' 
 
 In each of the cases just referred to, the transverse sectional. 
 dimensions of pieces fixed at ono end, and submitted to a strain 
 at the other, are determined by the following formula! : — 
 
 
 Form of Section. 
 
 
 
 
 
 
 
 Rectangular. 
 
 Square. 
 
 Circular. 
 
 Wrought-iron, . . 
 
 ■— 1& 
 
 6 3 
 
 PL 
 1,422-5 
 
 I) 3 = 
 
 PL 
 
 854 
 
 
 M PL 
 
 b 3 
 
 PL 
 
 1,778 
 
 D 3 = 
 
 PL 
 
 1066 
 
 Wood 
 
 ■"-£ 
 
 b 3 
 
 PL 
 
 142 
 
 D 3 = 
 
 PL 
 
 so 
 
 The rule derivable from these formula? for the determination of 
 the transverse section, whether rectangular, square, or circular, of a 
 bar or beam fixed by one end and loaded at the other is thus stated : — ■ 
 Multiply the weight in pounds by its distance in indies from the siijt- 
 port ; divide the product by a coefficient varying with the material 
 and form of section; and extract the cube root, which will give <" 
 inches the vertical dimension, the side of the square, or the diameter 
 of the circle, according as the bar or beam is rectangular, square, »r 
 circular in cross section. 
 
 First application : What should bo the transverse section of a 
 rectangular wrought-iron bar, intended to cany at its free end. and 
 at a distance of 5 feet from its support, a weight of 72'8 lbs., tno 
 bar being supposed to be placed on edge ? 
 
 We have here, 
 
 72-8 lbs. x 60 in. 
 
 ab 3 — 
 
 1,42 
 
 =3071; 
 
 then, if a be taken = 1-2 inches, 
 
 b = x I "."'* = 1-6 inches, the vertical dimension. 
 
 /3-071 
 
 V w" : 
 
 Second application : 'What should the side of the cross section 
 measure, of a square bar, under similar circumstances otherwise ? 
 
 b 3 = 
 
 = 3-071, and 
 
 11225 
 
 3 
 
 b = v 3-07-i = 1-454 in., the thickness of the bar. 
 157. Observations. — When tho bar, or beam, under erperi 
 ment possesses in itself any weight capable of influencing its 
 resistance ; or, besides the weight suspended or acting at one end, 
 has a weight equally distributed throughout its length ; the trans- 
 verse-sectional dimensions are, in the first place, determined with- 
 
4 
 
 M \\S 
 
 art taking the additional weight into consider., 
 fee*. calculated app :..iimaie!y. and the half of it added to the 
 suspended l««d, a fn«h calculation being made with this stun a* 
 a Ua.i. 
 
 A bar, or beam, fixed by one end, and loaded at the other, ha* 
 always a tendency to break off at the ahoi. 
 
 - ;.j«.rt. becatue it is on that point th .: thi 
 rfr atrain acta with the greatest leverage. V. 
 
 the piece has been determined, in a.-. 
 with the formula) gh u\ch are calculated I 
 
 dimension* of the piece at the shoulder; the section may bt 
 firiauy diminished towards the free i 
 
 ing the material, and leasenin.- I The 
 
 curve y the parabola, as described in 
 
 i and XII. It may also be obtained in the 
 following man: ticular case nnder consideration: — 
 
 Calculate the t- 
 
 piece, the other data remaining as 1- 1 curve 
 
 ■ne which pa*- i, when 
 
 they are |4accd at distano •» from the load equal t" : 
 
 'ivy are calculated. This curve is also given to bars, 
 beams, or shafts, filed at both ends and loaded in their mi 
 throughout their length. T 
 1 ' . ■ • \ 1 1 
 of thi*. S • beams and side levers are a' - 
 
 - shaDS) as it gives them a uniform r- 
 
 '. it. so that they are not liable to break or give way in 
 any on. - .'.an another. 
 
 A bar, or beam, supi~.rt.-d in the centre, and loaded at either 
 
 support double the weight ca|*ble of being carried by 
 
 -imilar dimensions, supported at one, and loaded at the 
 
 ■I; it is, ind..-d. e\ident llial each weight will only act 
 
 with half the leverage, being only half the **i*'*irr*> from the point 
 
 -•rt. 
 
 ..-ly, a bar, or beam, ' •• mitiea, 
 
 and loaded in the MB) lible that sus- 
 
 .,. amine dimensions fixed at one, and loaded 
 at tlie other end. Therefore, in calculate 
 
 theae two last-mentioned rases, it is necessary simply to dooble 
 . for the first case. 
 A bar, or beam, firmly and solidly fixed by both ends, »ill sap. 
 port a load four times as great aa one of the same <tinf t «M»i»« 
 1. and loaded at the 
 
 | ...druple the above coefficient in thia 
 MM, 
 
 iials, of 
 shafts for hydraulf 
 tain gn at weights, the following j articular formula may be 
 ■ 1: — 
 
 D= I 
 -ses the diameter in inches, and \Y 
 be sustained in pounds. 
 
 TABLE Ol 
 
 THE DIAXETERS OF 
 
 .VIM OF WATER-WHEEL AID OTHER 
 
 sHxrrs ro« heavt 
 
 WORK. 
 
 
 Diuuttl of Journal in Inch**. 
 
 
 Diaawur *f Josraal is tars— 
 
 Tout basis 
 
 
 
 vl is 
 
 
 ■ ..... 
 
 
 
 
 
 
 OaaVtan, 
 
 Wroufht-Irwa. 
 
 
 Osavbaa. 
 
 WiMfkt-Ina. . 
 
 
 ; 
 
 •4315 
 
 
 8 
 
 
 
 l 
 
 
 1 
 
 8. 
 
 
 
 i} 
 
 
 
 :< 
 
 
 1099-0 
 
 a 
 
 
 
 9» 
 
 
 
 2J 
 
 
 
 10 
 
 
 
 3 
 
 
 
 10, 
 
 
 
 3} 
 
 
 
 11 
 
 
 
 i 
 
 
 
 IM 
 
 
 
 4 
 
 
 
 19 
 
 
 mi 
 
 6 
 
 
 
 
 1 ' 
 
 
 6. 
 
 
 
 13 
 
 
 
 '. 
 
 61780 
 
 
 
 11 ' 
 
 : so-0 
 
 61 
 
 
 
 11 
 
 
 730 
 
 7 
 
 
 
 Hi 
 
 1.(5 
 
 
 - 1 
 
 
 ...35 
 
 15 
 
 
 inula, the dial] 
 or journal, i« ! 
 strain, in pounds, and multiplying it by the constant, i 
 
 : indli «, <t Joan 
 
 froa tliat for 
 
 mula. 
 
 ' Of what dial: spindle of a 
 
 Mfl l«'. the t"tal strain b> ■'.: 10 lbs,! 
 
 a ^___ 
 D= ♦'70,000 X 193* nearly. 
 
 f (7-987 X -863 =) 6 9 inches, will 
 
 j-oee. 
 
 RESISTAXiE TO TO - 
 
 tially to any solid, tending to turn iu opposite ends in different 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 47 
 
 directions, or to twist it, it is said to be subjected to torsion, and 
 offers moro or loss resistance to tins action according to its form 
 and composition. Taking, for example, the main shaft of a steam- 
 engine, at one end of which the power acts through a crank, set 
 at right angles to it, and at the other the load, by means of wheel 
 gear — the resistance which tins load presents, on the one hand, 
 and on the other, the power applied to the crank, represent two 
 forces which tend to twist the shaft, subjecting it to the action of 
 torsion. 
 
 In machinery, all shafts and spindles whieh communicate power 
 by a rotatory, or partially rotatory, movement on their axes, are 
 subject to a torsional strain. Those which sustain the greatest 
 torsional efforts are those shafts denominated first movers, the 
 first recipients of the power. Such are the fly-wheel shafts of 
 land engines, and (he paddle-shafts of marine engines. In these 
 the action is further complicated and heightened by the irregularity 
 witli which, in reciprocating engines, the power is communicated 
 to them. Such shafts as carry very heavy toothed gearing, but 
 receive and transmit the powor in an equable manner, and without 
 a fly-wheel, are termed second movers ; and finally, such as carry 
 only pulleys, or comparatively small toothed wheels, are comprised 
 in the class of third movers. Such shafts, again, as meet with an 
 intermittent resistance, as is the case with all cam movements, 
 require increased strength to meet this irregularity of action. 
 
 In constructing formulae for the determination of the diameters 
 of shafts, regard must always be had to the class to which they 
 belong, and also to the description of work they have to perform. 
 
 As the journals are the parts of a shaft on which the greatest 
 strain is concentrated, it is obviously to the determination of their 
 dimensions that our investigation should be directed. The prac- 
 tical formula, for ascertaining the diameter proper for the journal 
 of a cast-iron first-mover shaft, is — 
 
 
 x 419. 
 
 Here, d = diameter of journal in inches. 
 
 H P = the horse power transmitted by the shaft. 
 
 R = the number of revolutions of the shaft per minute. 
 
 This formula is expressed in the following rule. 
 
 159. To determine the diameter at the journals of a cast-iron 
 first-mover shaft : — Divide the horse power of the engine by the 
 number of revolutions of the shaft per minute, multiply the quotient 
 by the constant, 419, and extract (lie cubic root, which will be the 
 diameter required in inches. 
 
 For the journals of cast-iron shafts whieh are second movers, 
 the formula is — 
 
 a/HP 
 V-R- 
 
 X206; 
 
 and for third movers- 
 
 3 /iTp 
 
 106. 
 
 These are, in fact, similar to the formula given for first movers, 
 with the exception, that for these the constant multiplier is 41-9, 
 whilst, for the latter it is 206 and 106, respectively. 
 
 160. For the journals of wrought-iron shafts the same formula: 
 are employed, the multipliers only being changed; these are 249 for 
 first movers, 134 for second movers, and 676 for tlurd movers. 
 
 If, with a view of suppressing the radical sign in (lie above for- 
 mula, we raise both sides of the equation to their third or cubic 
 power, and further express the multiplier by m, we have 
 
 d 3 = — - Xm; ) 
 
 from which formula it will be seen, that the cube of the diameter 
 of the journal is proportional to the force transmitted. Similarly, 
 the resistance of a journal is proportional to tho cube of its dia-" 
 meter. In other words, one journal, of which the diameter is 
 double that of another, is capable of sustaining a strain eight times 
 greater, since the cube of 2 is 8. 
 
 161. As, in consequenco of tho necessity of extracting cubic 
 roots, the calculation, according to these formula?, becomes very 
 tedious and complex, wo have rendered it much simpler by 
 means of the table on the next page. 
 
 We may, however, first observe, that the formula, 
 
 J3 HP ^ 
 a J = -rf- X m, 
 
 may be put in the form — 
 
 (P_HP 
 m R ' 
 or again, reversing the terms, 
 
 m R 
 
 T 3 ~ HP' 
 If now we divide the coefficient, m, by the cubes of the series, 
 1, 2, 3, 4, &c., representing the diameters of the journals in inches, 
 we shall obtain a series of numbers corresponding to 
 R 
 HP' 
 Thus, if 419 be successively divided by tho cubes, 1, 8, 27, 64, 
 &c, the numbers in the second column of the tablo will bo 
 obtained; and by dealing with tho other multipliers in like manner, 
 the numbers in the 3d, 4th, 5th, 6th, and 7th columns, will be. 
 found. 
 
 Rule. — When the table is used, the rule for determining tho 
 diameter of the journal of a shaft is thus stated: — 
 
 Divide the number of revolutions per minute of the shaft by the 
 horse power, and find the number in the table which is nearest to the 
 quotient thus obtained, bearing in mind the class and man rial, and 
 the corresponding number in the first column will be thediaimUr 
 required. 
 
 First Example. — What should be the diameter at the journals 
 of a cast-iron first-motion shaft, for an engine of 20 horse power, 
 the shaft in question to make 31 revolutions per minute? 
 We have — 
 
 Jl 31 
 
 H P ~ 20 
 
 It will be observed that this quotient is the nearest to tue 
 number 1-526 in the second column of the table, nnd that 1-526 is 
 opposite to 6i ; the diameter, d, of the shaft journal should con- 
 sequently be 6i inches in diameter. 
 
 If a shaft for the same purpose as the above be made of 
 wrought-iron, we must look in the fifth column lor the number to 
 which 1-55 approaches nearest It will he observed that it lios 
 between the numbers 1-992 and 1-497, respectively opposite to 5 
 and 51 inches ; the diameter of the journal should consequently Ikj 
 between these — sny about 5J inches. 
 
 1-55. 
 
• 
 
 taile or w a* etch rot matt jocixal*, cau-clatcd with BirrtExcE to toemoxal - 
 
 : . • ••■ 
 
 falHkrfCMlM CWfM. 
 
 A»um*U u Wrasfkt-tna »L«ru. 
 
 u£» 
 
 
 
 
 
 
 
 
 
 ■ -Mm. 
 
 f— .. ' 
 
 Tk.nl M«r*t«. 
 
 FuM Vina 
 
 ?** :.. M .»-». 
 
 Tklnl 
 
 
 T 
 
 MM 000 
 
 1568-000 
 
 848-000 
 
 .'00 
 
 .000 
 
 «oo 
 
 
 I 
 
 •00 
 
 906-000 
 
 •00 
 
 •00 
 
 
 
 
 If 
 
 
 
 
 
 
 . 
 
 
 3 
 
 
 . 
 
 
 31 125 
 
 
 
 
 
 
 
 
 
 
 
 
 3 
 
 
 
 
 
 4-963 
 
 
 
 1 
 
 
 
 
 
 3 1J3 
 
 
 
 4 
 
 
 
 
 
 
 
 
 41 
 
 
 
 
 
 
 
 
 5 
 
 sua 
 
 
 ■848 
 
 
 
 
 
 II 
 
 
 
 •637 
 
 
 ■806 
 
 
 
 
 
 
 
 1153 
 
 
 •313 
 
 
 
 
 •750 
 
 
 
 
 
 
 1 
 
 
 •601 
 
 
 
 
 
 
 7j 
 
 
 
 •253 
 
 
 •325 
 
 
 
 8 
 
 ■838 
 
 
 
 
 
 
 
 
 •683 
 
 •335 
 
 173 
 
 
 
 •no 
 
 
 9 
 
 ■575 
 
 
 1 14 
 
 •Ml 
 
 1-1 
 
 
 
 
 
 
 ■121 
 
 
 156 
 
 
 
 10 
 
 
 
 
 
 
 
 
 >o, 
 
 - 
 
 •178 
 
 • 
 
 •J 15 
 
 ■110 
 
 
 
 II 
 
 ■314 
 
 155 
 
 
 
 
 
 
 II 
 
 
 135 
 
 
 
 •089 
 
 
 
 II 
 
 
 119 
 
 
 111 
 
 •078 
 
 • 
 
 
 
 
 
 
 127 
 
 •068 
 
 . 
 
 
 13 
 
 
 
 049 
 
 111 
 
 
 
 
 
 
 •084 
 
 
 
 
 
 
 II 
 
 153 
 
 
 
 
 •049 
 
 . 
 
 
 Hi 
 
 137 
 
 
 
 
 
 
 
 15 
 
 
 •061 
 
 031 
 
 
 039 
 
 
 
 1 
 
 3 
 
 3 
 
 4 
 
 6 
 
 6 
 
 - 
 
 1 Example, — We require to ascertain flu d 
 urnala of a ahaft of the second claan. Intended to trans. 
 -*-e, i~jiia1 to 15 horee power, at the rate of 40 rev 
 
 iota. 
 
 R <" ._ 
 - = 3-67. 
 
 third column, a- 
 
 than, that if the ahaft ia to b 
 
 I 
 wn-d 3j and 1 ..tiout half axi 
 
 two mali-riala in thia inittanrc. 
 I 
 tranamit a force equal to C homo power, v 
 
 Tiola in. 
 • ..-• ■ »r>. ..t.un.ri ! 
 
 B 60 
 
 nr - 
 
 
 - MS, 
 
 Dtnnbar, in tin- tliinl • 
 
 - :ind 3|, 
 
 inches,** tin- number, - 
 
 journalii and i! 
 
 ■ 
 
 '-ip>n journal, . 
 
 - 
 
 tonal and a ladral or 
 
 wiih r. ■ ' -tr-.iiii which hi the paail I 
 
 ahaft* are not of any great Itogffa — 3 to <i ' 
 
 I raaMron ahafta of a). 
 
 greater 
 than tli .' tiaJa. 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 FRICTION OF SURFACES IN CONTACT. 
 
 162. Friction is the resistance which ono surface offers to 
 another — moving or sliding on it. Friction may be distinguished 
 as sliding friction, and the friction of rotation. The former is that 
 which arises from the simple rubbing of ono surface upon another; 
 the latter, from the rotation of one surface upon another. 
 
 The friction caused by the rubbing of plane surfaces is inde- 
 pendent of the extent of surface or velocity of movement ; it 
 depends essentially on the weight of the body, or, more accurately, 
 the pressure binding the two surfaces together. It may therefore 
 be said, that the friction is in proportion to the pressure. 
 
 Similarly, the friction of a journal in its bearings is independent 
 of the length of these, but is proportional to the diameter and to 
 the pressure. 
 
 We give tables for each of these classes of friction, indicating 
 the ratio (if the friction to the pressure, and consisting of a series 
 of coefficients, whereby the pressure must be multiplied in order 
 to ascertain the amount of resistance due to friction. 
 
 Table of Ike Ratios of Friction for Plane Surfaces. 
 
 Description of Materials 
 
 of the Fibres. 
 
 Condition 
 of the Surfaces. 
 
 Ratio of Friction 
 to Pressure. 
 
 At 
 Starting. 
 
 In 
 Motion. 
 
 r 
 ! 
 
 Oak on oak J 
 
 Parallel. 
 Do. | 
 
 Across. 
 
 Do. 
 
 Endwise 
 (on one piece). 
 Parallel. 
 Do. 
 Do. 
 Do. 
 Do. 
 
 Flat or on edge, 
 j Flat. 
 
 Dry. 
 
 Lubricated with 
 
 dry soap. 
 
 Dry. 
 
 Wet with water. 
 
 { Bry. 
 
 Do. 
 
 Do. 
 
 Do. 
 
 Do. 
 
 Wet with water, 
 
 > Do. 
 
 | Oiled or greased. 
 
 Dry. 
 
 Do. 
 
 Do. 
 
 ■62 
 | -44 
 •44 
 •71 
 ■43 
 •38 
 •53 
 •80 
 ■62 
 05 
 •62 
 •12 
 < -47 
 | -28 
 •16 
 •19 
 
 •48 
 •16 
 •34 
 ■25 
 •19 
 
 Ash, beech, or deal on oak, . . 
 
 ■38 
 
 Wrought-iron on oak, 
 
 ■49 
 
 Ftimp leather on cast-iron,. . . 
 1 on cast-iron pulleys,... 
 
 •27 
 •15 
 
 
 
 
 Example. — What power is necessary to raise an oaken flood- 
 gate weighing 30 lbs., and against which a pressure is exerted 
 equal to 700 lbs. ? 
 
 We have 
 
 (•71 x 700 =) 497 + 30 = 527 lbs. at starting, 
 and (-25 x 700 =) 1 i 5 + 30 = 205 when in motion, 
 
 supposing the pressure continues the same. 
 
 Table of the Rutins if Pridian for Journals in Beari 
 
 Cast or wrought-iron journals, 
 in oast orwrought-iroii, brass, 
 or gun-metal bearings, 
 
 Cast-iron in cast-iron < 
 
 Cast-iron in brass or gun-metal, 
 
 Cast-iron in lignumvita; < 
 
 Wrought-iron in brass or gun- ' 
 metal 
 
 Wrought-iron in lignumvita:, . - 
 
 Lubricated with oil 
 or lard, 
 
 Similarly lubricated 
 and wctwitli water 
 
 Lubricated with or- 
 dinary oil, and wet 
 with water, 
 
 Greased 
 
 1 1 reased and wet, . . 
 
 (Jnlubrioated 
 
 Lubricated with oil and 
 lard 
 
 Lubricated with o pre- 
 paration of lard and 
 plumbago, 
 
 I I leased, 
 
 i ireaaed and wet, ». . . 
 
 Badly lubricated, 7. . . 
 
 Lubricated with oil and 
 
 lard 
 
 Lubricated with ordi- 
 nary oil 
 
 Rule. — To determine the frietional pressure, f, acting on the 
 bearings of a journal, always bearing in mind the weigh! of the 
 shaft and the gear carried by it, the power transmitted, as also the 
 resisting load: Multiply the product of these, p, by the coejjh 
 to obtain tlie amount of friction; next multiply this by the constant 
 •08, and by the diameter d., in inches, (or by -08 ( /..) to obtain the 
 amount per revolution ; and, final! y, multiply this by the numbi r of 
 revolutions in a minute, which will give the amount of power con- 
 sumed by friction during this unit of time. 
 
 Example. — What amount of power, A, is absorbed by the 
 friction of the journals of a east-iron shaft revolving in bearings ; 
 also, of cast-iron, under the following conditions? 
 
 The diameter at the journals = 5 inches. 
 
 The pressure of the shaft and gear = 20,000 lbs. 
 
 The velocity = 5 revolutions per minute. 
 
 According to the table, the coefficient, c, is - 075. 
 
 Here we have — ■ 
 
 F = -08 d x c x P, 
 = -08 x 5 x -075 x 20,000 = 3,000 lbs. 
 
 CHAPTER IV. 
 THE INTERSECTION AND DEVELOPMENT OF SURFACES, WITH APPLICATIONS. 
 
 163. Nowhere is descriptive geometry more useful, in its appli- 
 cation to the industrial arts, than in the determination of the lines 
 of intersection, or junction, of the various solids, whether the in- 
 tersection be that of two similar solids with each other, as a 
 cylinder with a cylinder ; or of dissimilar ones, as a cylinder with 
 
 a sphere or a cone. Willi the aid, however, of this branch ot 
 geometry, we can determine, in the most exact manner, the pro- 
 portions of all the curves — of double as of single curvature — which 
 may bo produced by the intersections of surfaces of revolution, 
 the constructive or generative data of which arc known. 
 
T1IK I 
 
 Ana b which aoch care* occur are execed- 
 •agtv n„a« r . . n» , tl, rj abuuo I 
 
 .,;„(, of the I 
 
 • ■ 
 
 ablr to 
 
 al and arvliilectural coo- 
 
 Tin: I.N ' 0N8 AND DEVELOPMENT OF 
 
 [NDERS AND CONEB, 
 
 PLATE XIV. 
 
 AMD BOILERS. 
 
 I .is said 
 
 ■ 
 
 "uitiiiti.m in tooc*— ion 
 
 •"•n. by 
 
 - 
 
 000 and 
 
 1 and 2, draw 
 
 - 
 
 1 t', and/ 1 /*. 
 
 and in r* J' in the vertical pr< 
 
 - dmWB in plan 
 -', it will 
 - ■ if the 
 throuirh 
 
 intersection of thin Una, r' ./. with t>. 
 
 r. A. 
 
 - m n, parallel 
 
 I 
 \ 
 
 in', p. when, ait in ill!- 
 •jmt, ||n 
 
 A* n 
 
 ■ 
 
 wliich an n a plane a! 
 
 other — ;- 
 
 nth. 
 
 -. and i:, 
 
 ■ 
 
 that in 
 
 - 
 
 1 5, which n 
 is a species of man ! 
 
 Tin; n 
 
 '■' 
 
 ■ 
 ntained within • 
 
 ii will l»' tin- outline of that |«irt ■•: 
 . 
 
 ■ ', by any plane wh.v. 
 itting plane, a' f, for in»!.. h 
 
 ■ 
 straight line, as in fig. 3*. and as a i 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 of projection to which it is parallel. It follows, from the existence 
 of these respective properties, that we have at hand a very simple 
 nn thod for determining the curve of intersection of a cone with a 
 sphere, whatever may be the relative position of their axes. This 
 method consists in supposing a series of parallel planes to cut 
 both the cone and the sphere, so as to produce circular sections 
 of both — the intersections of the oudines of which will conse- 
 quently be points in the curve sought, as indicated in fig. 3. 
 
 The intersection, a 1 b', is a circle, the diameter of which is limited 
 bv the extreme generatrices, s' a', s' b, of the cone, where they 
 encounter the great circle of the sphere, c. The same method 
 holds good' when the cone is cut by any plane, a! g, inclined to the 
 base, the outline of the section being in this case an ellipse, which 
 is projected in the plan, fig. 3, by the line, a i" g' n', the resultant 
 of the various intersections in the planes adopted in die construc- 
 tion and obtaiument of the curve. 
 
 The same occurs with the intersection of a cone, a' e' s', with a 
 cylinder, a'b' if; and when dicir axes lie in the same straight 
 line, the intersection, a b', is also a circle, the ditmeter of which 
 is equal to that of the cylinder. 
 
 167. If their axes are parallel, though not in the same straight 
 line, the intersection of these two surfaces becomes a carve of 
 double curvature, which may be determined either according to 
 the method adopted in reference to figs. 1 and 3, or by supposing 
 a series of plains to cut the cone parallel to it.s base, and conse- 
 quently at right angles to the generatrix lines of the cylinder; by 
 this means circular sections will be produced, those of the cylinder 
 being always tin same, but those of the cone varying according to 
 
 • if the planes from its apex. The points of intersec- 
 tion of he various circles representing, respectively, sections of 
 the cone and cylinder, will be points hi the curve of intersection 
 
 S U il< lit. 
 
 DEVELOPMENTS. 
 
 168. By this term is meant the unrolling, extending, or flatten- 
 upon a plane, of any curved surface, in order to ascertain 
 
 its exact superficial measurement. 
 
 i The more generally used surfaces or forms which are capable 
 of development in this manner, are — the cylinder, the cone, prisms, 
 pyramids, and the frus/a, or fragments of these solids. 
 
 Tin and copper-smiths and boiler-makers, who operate upon 
 metals which come into their hands in the form of thin sheets, 
 have continually to transform these sheets into objects which are 
 analogous in form to these solids. 
 
 To do their work with skill and exactitude, and not by mere 
 guess, and also to avoid the cutting of the material to waste, they 
 should make plans of the whole or part of the object as finished, 
 so that they may calculate the exact development of the surface, 
 both as to form and size, and cut it at once from the sheet of 
 metal with all possible precision. 
 
 THE DEVELOPMENT OF THE CYLINDER. 
 
 169. Here, taking fig. 2, which we have on a former < 
 considered as a couple of solid cylinders, to represent, in the 
 present case, two pipes or hollow cylinders formed of thin sheet 
 metal, let us set about ascertaining what should be the shape and 
 size of the pieces of metal as extended out flat, of which these 
 
 two cylinders are to be formed. It is to be observed, in the first 
 
 place, that the rectification or development into a straight line of 
 a circle, is equal to its diameter multiplied by 3-1416. &c; whence 
 
 tin- development of the base, r q, of the right vertical cylinder, A. 
 fig. 2} of which the diameter measures -322 metres, is obviously 
 equal to 3-22 X 31416 = 1012 m. 
 
 This length, then, 1-012 m., is set off on the fine, M M. fig. 10, 
 and the circumference having been divided into a Dumber of equal 
 part-, as was done to obtain the curve of intersection of the two 
 cylinders in fig. 1 ; the line, M M, is divided into the like number 
 of equal divisions. Through each of these points of di 
 perpendiculars are erected upon the line, m H, representing so 
 many generatrix lines corresponding to those of the cylinder, a, 
 fig. 2; and for the sake of greater intelligibility, we have marked 
 the corresponding lines bv the same letters. Next, on each of 
 these are set off distances, M 4', e' e-, I' I 2 , P a',ff 2 , u' u-, q 
 equal to the respective distances in fig. 2. By this means are 
 obtained die points, b 1 , e, X, &e., in fig. 10, through which the can e 
 passes which forms the contour of intersection correspi Hiding to that 
 portion of the senii-cylhider, V a b", fig. 1, which is intersected by 
 the horizontal cylinder, b; and as the other half of the cylinder is 
 precisely the same, the curve has simply to be repeated, as shown 
 in fig. 10. 
 
 It is unnecessary to detail the method of finding this d 
 ment of the horizontal cylinder, B, as it is identical hi principle 
 to that just discussed. 
 
 It may be gathered from the above iv: lhat the 
 
 principle generally to be followed in i 
 cylindrical surfaces, is, first, to unfold it in a di • 
 angles to one of its generatrici i.eratiix 
 
 takes in the construction of the solid, and ther to set < ff from the 
 straight line thus produced, at equal distances apart, any number 
 of distances previously obtained hum the projections of ihe out- 
 line or line of intersection when the cylinder is joined to another, 
 or of its section when cut by any plane. The curve of this out- 
 line is finallv obtained by tracing a line through the exti 
 of die generatrices, drawn perpendicular to thi 
 
 THE DEVELOPMENT OP THE 
 170. As in the case of the cylinder, so likewise, in order t" find 
 
 the development of tin- cone, do we unfold it, as it were, in the 
 
 direction of motion of its generatrix. Now, as all the generatrices 
 . of a right cone an- equal, and converge to one point, the apex, it 
 follows that, when the conical surface is developed upon a plane, 
 these ge, U form radii of a portion of ad 
 
 quently, if with one of the generatrices, as a radius, we describe 
 a circle, and cut off as much of the circumference as shall be equal 
 to that of the base of the developed cone, we shall obtain a 
 sector of a circle equal in area to the lateral surface of the cone, BS 
 developed upon a plane. 
 
 Fi". 9 represents the development of the frustum, or truncated 
 cone,° a' I", a' b', as projected in fig. 3% and of which the apex 
 would bo s', were the cone entire. The operation is as fol- 
 lows: — 
 
 We dial] suppose the cone to be developed in the direction 
 taken by the generatrix, s' a', fig. 3'; therefore, with a radius equal 
 
>M\VS 
 
 ■', describe the fragm) nl of a circle, 
 
 /' ■» A r . 
 
 ■ ireular !«•.■ I 
 •ante arbitrary number of equal part*, aay 1 1 drawn 
 
 •In- arc, 
 a ■ a 1 , fitf. 9. an equal nun. 
 
 t 
 ! lraw the radii, 
 
 ■ 
 
 .ireular 
 
 . t.. the 
 
 .ire, a' b' a'. 
 
 radius drawn with the same I with a radius equal to 
 
 away. 
 iSlc •!■ 
 
 an ani 
 
 171 I e, of which the dividing plana 
 
 - 
 Irii;d or spherical body, and 1 1 >«- Hue 
 ed in any «ny. the development of tl 
 
 take the f"nn of the are, a e 6. 
 • .tT. on 
 
 . 
 
 ■ 
 
 ■ 
 
 I 
 
 i "in«t !»• 
 
 . 
 
 Cor the 
 
 ■■ ncrally 
 
 I 
 
 the development of one of euch goree; th- : -awing 
 
 (/, an are, m n, corr> - 
 
 • • 
 
 .-. a« wo in tl i ' tin- arc, m n, 
 
 fig. 6, mark an arbitrary III la, at equal dialancea 
 
 ; 
 
 the varioua r 
 ■ kfcfc arc* are drawn a* indicated ; the ix-etifica- 
 
 I. and transferred to )> ■]« ndiculara 
 drawn th 
 
 Ihe arc, m n. wj 
 Thus, from tin- an-, ;. <j. - ' </', and 
 
 siniilarh 
 
 tin- aurl The 
 
 necessary allowance, for lap is superadded. a» shown bj 
 
 '. 
 - tin n hammered to a pr- , 
 an til, w -irface. 
 
 THE DELINEATION AND DEVELOPMENT OF ID I 
 BCREWS, AND BERPENTLNEa 
 
 P L a T 1 xv. 
 
 id i 
 n:t. That emrj is called a eylii 
 
 ■ 
 
 and in tl 
 
 ■ 
 rum it - ' 
 
 time .-< ; 
 
 int.. tl ■ 
 drawn ; 
 
 Let 
 
 point pn.jivt.il in n >l 
 
 I. a m r- 
 I I 
 
 ;. irta, ami a •' 
 drawn ■ . theea 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 S3 
 
 points are next connected by the continuous line, a', 1', 3', 6', 9', 
 a-, which forms the vertical or lateral projection of the helix. 
 
 Half of this curve is indicated by a sharp full line, as being on 
 the front surface, a, 3, 6, of the cylinder, whilst the other half is 
 in dotted lines, representing the portion of the curve which is on 
 the other side, a, 9, 6. 
 
 The number of divisions of the circumference of the cylinder 
 is a matter of indifference as regards the accurate delineation of 
 the curve, and it is therefore natural to choose a number that 
 calls for the simplest operations — an even number, for example, 
 as 6, 8, or 12; and in the present instance, wherein the starting 
 point, a, lies in the horizontal diameter, a 6, of the base, it will 
 be observed that two points occur in the same vertical line, as 
 2 — 10, which gives the points, 2', 10', in the vertical projection. 
 
 The operations will be similar, if the given starting point be 
 diametrically opposite to a, as b', the pitch, b l b 2 , being equal to 
 a 1 a 2 . 
 
 174. The conical helix is different from the cylindrical one, 
 simply in that it is described on the surface of a cone instead 
 of on that of a cylinder, and the operation consequently differs 
 very slightly from the one before described ; the horizontal and 
 vertical projections of the cone are given, and also the pitch. 
 Fig. 3 is the vertical projection of a truncated cone, c, the bases 
 of which, a' b', c' d', are represented in the plan, fig. 1, by the 
 concentric circles described, with the respective radii, a o and c o. 
 The outer circle having been divided as already shown, radii are 
 drawn to the centre, o, from all the points of division, 1, 2, 3, 
 &c., which cut the inner circle in the points, e,f,g, &c. These 
 points are then projected upon the upper base, c' d', in fig. 3, those 
 on the outer circle being similarly projected on the lower base, 
 a' b' ; the respective points in each base are next joined, thus forming 
 a series of generatrices of the cone, as l 2 — e 2 , 2 2 — /-, o 1 — o 2 , &c, 
 which would all converge in the apex, if the cone were complete. 
 These lines are cut by horizontals drawn through a corresponding 
 number of divisions in the length of the given pitch, a' c', and the 
 points of intersection thus obtained lie in the curve which it is 
 required to draw. The horizontal projection of the curve is then 
 obtained by letting fall from the points of intersection last 
 obtained, a series of verticals which cut the respective radii in the 
 plan, fig. 1. This produces a species of spiral, or volute, e 3 ,/ 3 , g 3 , 
 A 3 , 2 3 , &c. By following out the same principle's, helices may bo 
 represented as lying upon spheres, or any other surfaces of revo- 
 lution. 
 
 THE DEVELOPMENT OF THE HELIX. 
 
 175. It will be recollected that a cylinder, and also a cone, are 
 capable of being developed upon a plane surface, and that the 
 h;i-e of either, when rectified, or converted into a straight line, is 
 equal to the diameter multiplied by 3-1416. Let, then, a 6, fig. 
 4, be a portion of tho development of the base of the cylinder, 
 A, figs. 1 and 2; to obtain the development of the helix drawn 
 upon ibis cylinder, we must first divide it oft' into lengths, corre- 
 sponding and equal to the arcs obtained by the division of the 
 circle, a o. On each of the divisions thus obtained, as 1, 2, 3, 
 &... we then erect perpendiculars, making them equal respectively 
 to the distances from the starting point) (7, of the several divisions 
 
 of tho pitch. The extremities of these perpendiculars, as 1', 2', 
 3', &c, will be found to lio in the same straight line, a G', which 
 consequently represents the development of a portion of lire 
 helix. In general, the development of a helix is a straight line, 
 forming the hypolhcnuse of a right-angled triangle, the base .,1' 
 which is equal to the circumference of the cylinder, and the 
 height to the pitch of the helix. 
 
 Several helices drawn upon the same cylinder, and having tho 
 same pitch, or a helix which makes several convolutions about a 
 cylinder, is represented by a series of parallel curves, the distance 
 between which, measured on any lino parallel to the axis, is 
 always equal to the pitch. 
 
 The development of the conical helix may be obtained by means 
 of an operation analogous to that employed for the development 
 of the cone (Plate XIV.) ; and in this case the result will he a 
 curve, instead of a straight line. 
 
 We meet with numerous applications of the helical curve in the 
 arts, for all descriptions of screws; and staircases, and serpentines. 
 
 SCREWS. 
 
 176. Screws are employed in machinery, and in mechanical 
 combinations, either for seeming various pieces to each other, so 
 as to produce contact pressufe, or for communicating motion. 
 Screws are formed with triangular, square, or rounded threads or 
 fillets. 
 
 A screw is said to have a triangular thread, when it is generated 
 by a triangle, isosceles or not, the three angles of which describe 
 helices about the same given axis, situate in the same plane as I ho 
 triangle. Figs. 5 and 5" represent the projections of a triangular- 
 threaded screw, such as would be generated by the helical move- 
 ment of the triangle, a' b' c', of winch the apex, a', is situate on 
 a cylinder of a radius equal to a o, and of which the other angles, 
 b', c', are both situate on the internal cylinder, Inning the radius, 
 b o, winch is called the core of the screw, and is concentric with 
 the first. The Wfference, a b, between the radii, a o and b o, indi- 
 cates the depth of the thread. 
 
 When, as in the case taken for illustration, the screw is single- 
 threaded, the pitch is equal to the distance between the two points, 
 
 V and c'; that is, to the base of the triangle. The screw is "i f 
 
 2, 3, 4, or 5 threads, according as the pitch is equal to •!. 
 5 times the base of the generating triangle. From what has 
 already been discussed, tho method of delineating the triangular- 
 threaded screw will be easily comprehended ; for all that is neces- 
 sary is to draw the helices, generated by the three angular points, 
 in the manner shown in reference to figs. 1 and 2. We have, 
 notwithstanding, given the entire operation for one semi-convolu- 
 tion of the thread, in figs. 5 and 5*. When one of the exu 
 o' 3' 6', is obtained, it is repeated as many times as there are COS 
 volutions of the thread on the length of the screw. To do this 
 with facility, and without repeating the entire operation, it is 
 customary to cut out a pattern of the curve in hard card-board, 
 or, by preference, in veneer wood; then setting this pattern i" the 
 points of division, d' e f, previously set oil", the curves an 
 drawn parallel to one another. The same may be done with tho 
 inner helical Curves. 
 
 It nius! I» observed, that, to complete the outline of the screw, 
 

 J by :!»■ portion*, f -f. J' "'■ 
 an drWB aa Min}>!< 
 
 ■ 
 
 •kin, a' I/, */ •''-•'<•. Ill |t 
 
 ided aerew — Ih 
 
 a' d\ marks ti • 
 
 I 
 casual ' 
 
 r, in the 
 
 ■ 
 
 :. in ail nuu-s having as in.. 
 
 - 
 
 BWE 
 
 '.tl out 
 
 cut away from it — in anch a manner thai it- more i:> 
 
 t 
 
 ■ ' 
 
 9 ■ 
 Meea*-./ by a |>lane pan 
 
 6* and '•' 
 
 I into it ; 
 
 ■ 
 !■. E; and aa '■■ 
 
 \>\ Uie 
 
 ■ 
 
 Thia form 'u oftrn employ . » a, such 
 
 I 
 
 tin- ml. 
 
 I| 
 
 I 
 
 . an. I already 
 
 - 
 ■ 
 
 Of ili-tinet ; til u 
 
 in the point, J, "n lb 
 
 . OJ the 
 
 'n i • ■ i 
 
 ■ 
 r i 
 
 ■ 
 
 In tl: 
 
 lerv « •units are - 
 
 ..njjular- 
 - 
 I 
 ■ 
 ■hould • 
 
 atl I smaller, at 
 
 ' 
 
 For tl 
 
 ; 
 ■ 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 THE APPLICATION OF THE HELIX. 
 
 THE CONSTRUCTION OF A STAIRCASE. 
 
 PLATE XVI. 
 
 181. The staircases, which afford a means of communication 
 between the various floors of houses, are constructed alter various 
 systems, the greater number of which comprise exemplifications . 
 
 of the helix. The cage, or space set apart for the staircase, varies 
 in form with the locality. It may be rectangular, circular, or 
 elliptic. 
 
 Fii's. 1 and 2 represent a staircase, the cage of which is rec- 
 tangular; tills space being provided for the construction of the 
 main frame of the stair, with its steps and balustrade, and with a 
 central space left sufficient for tho admission of light from above. 
 Li the ease of a cylindrical cage, the curve with which the steps 
 rise is helical from bottom to top ; but in a staircase within a rec- 
 tangular cage, the steps rise for some distance in a straight line, 
 and only take the helical twist at the part forming the junction 
 between the rectilinear portions running up alternate sides of the 
 rectangle. Stairs are sometimes made without this curved part, 
 a simple platform, or " *estiiig-plaec," connecting the two side 
 portions. 
 
 For the division of the steps, we take the line, efg h i, passing 
 through tho centre of their width, and taking exactly the direction 
 it is intended to give the stairs. The first or lowest step, A, 
 which lies on the ground, is generally of stone, and is larger and 
 wider than the others. 
 
 For the stairs, as for the helix, the pitch or height, say 3-38 m., 
 from the basement to the floor above, is divided into as many 
 equal ['arts as it is wished to have steps. The centre line, efg h i, 
 is also divided into a like number of equal parts. In general, the 
 number of steps should be such, thai the height of each does not 
 exceed 19 or 20 centimetres. The larger the staircase is, the 
 mure may this height be reduced — say, perhaps, as low as 15 or 
 16 centimetres. The width, 1 — 2, of the step should not be under 
 18 to 20 centimetres. 
 
 If, for example, in the given height of 3'38 m., we wish to make 
 21 steps, we must divide this height into 21 equal parts, and draw 
 a series of horizontal lines through the points of division, which 
 will represent the horizontal surfaces of tho steps. 
 
 For those steps which lie parallel to each other, it is simply 
 requisite to erect verticals upon the points of division on the 
 centre line in the plan. The points of intersection of these with 
 the horizontals above, as 1, 2, 3, 4, fig. 2, indicate the edges of ihese 
 steps. For the turning steps, however, or winders, as those steps 
 are called which are not parallel to each other, a particular opera- 
 tion is necessary, termed the balancing of the steps, the object of 
 which is to make the steps as nearly equal in width as possible, 
 without, at the same time, making them very narrow on the inner 
 edges, or rendering the twist or curve too sharp or sudden. 
 Where the stairs are narrow, as in the case we have illustrated, 
 the balancing should commence a step or two before reaching the 
 curved portions. This balancing may be obtained in the follow- 
 ing manner: — A part of the rectilinear portion, p I, equal to three 
 stops, is developed, and then a part of the curved portion, I in n. 
 
 equal to three more steps. On the vertical, t q, Bg. 3, set off tho 
 heights of the first three steps; and through the point, q, draw 
 the horizontal, (/ -1, representing the development of the widths of 
 the steps in a straight line. Also, on the prolongation, / q 1 , of the 
 
 vertical, t q, set off the heights of other three steps. Through the 
 point, <;', draw a horizontal, and make </ 10 equal to the are, / in n, 
 in the plan, fig. 1, as rectified. The straight line,/ 10, will then 
 be the development corresponding to the curve of the framepiece. 
 At the latter point, ?i, erect a perpendicular on this line, and at the 
 point, 5, a perpendicular to the straight line,/ 4. The point of 
 intersection, o, of these two perpendiculars, gives the centre of 
 the arc, p h n, which is drawn tangentiaUy to these lines. Then, 
 through each point of division on the vertical, q q>, draw horizon- 
 tals, meeting this curve in the points, j, k, I, in, through which 
 draw parallels to q q'. Then transfer the respective distance,. 
 j 6, k t, I 8, m 9, comprised between the arc and the two straight 
 lines, ( 4 and / u, on the line of the framepiece, /; /.• n, in the plan, 
 fig. 1, as at_; k, k I, I m, m n. Next, draw straight lines through 
 the points,/, k, I, m, and through the respective points of division, 
 6, 7, 8, 9, on tho centre line, which will give the proper incli- 
 nation for the steps as balanced. The second half of the curvutl 
 portion is obviously precisely the same as the first in plan, and 
 may easily be copied from it. 
 
 Having thus determined the position of the steps in the hori- 
 zontal projection, they must next be projected on the vertical 
 plane, by means of a series of verticals, which cut the respective 
 horizontals drawn through the points of division, 1, 2, 3, 1. As 
 in tig. 2, the anterior wall of the cage is supposed io be CUl a« J 
 by the line, a 6' 10', in the plan, the outer edges of the steps are 
 seen and are determined by erecting verticals on the correspond 
 ing points, 6', 7', 8', 9', &c. 
 
 The perpendicular portions, v i', of the steps, which are over- 
 hung by the horizontal portions, and consequently invisible in the 
 plan, tig. 1, are, nevertheless indicated there in dotted lines, 
 parallel to the edges of the steps. To render them quite distinct, 
 however, and at the same time to show the manner in which they 
 are fitted into the framepiece, we have represented them, in ti u- I, 
 without the actual steps, supposing them to be cut in succession, 
 horizontally, through their middles. 
 
 The framepiece is the principal piece in the staircase. It is 
 situated in the centre of the cage, and sustains each step, and, 
 consequently, must he constructed \ciy accurately, lor upou it, in 
 a great measure, depends the strength and solidity of the stairca>e. 
 For a staircase of proportions, like those of the one represented in 
 the plate, the framepiece is generally made of oak, in three pieces ; 
 the middle piece, c, corresponding to the curved portion, whilst 
 the other two, B and D, joined to that one, form the rectilinear 
 portions. A special set of diagrams is necessary, to determine 
 the shape and proportions of the various parts of this framepiece. 
 The method here to be followed is in the first place, to draw the 
 joints, by Which the vertical portions of the steps are attached Io 
 the framepiece, These can easily be obtained by squaring them 
 over from fig. 4' to fig. 5, in which last are the horizontal division 
 
 lines, corresponding to fig. 2. It will I bserved, that th 
 
 referred to are beville.l oil', so as not to l«- apparent externally, 
 The faces on the framepiece are seen on tig. 5. at the parts, B, c, 
 

 and the method of obtaining them U nufT . 
 
 The i'taii.t i-i-v.- ha* a certain rrjjuUr i 
 
 ■ 
 
 - <i' It and «*/■, are naturally pa 
 
 •. d' <•', 
 
 ■l- r 3 . If, ill • 
 ■ the r 
 
 IS, ami 14, 1 
 
 ■ 
 
 rallelopipad, in which ; 
 
 a the junction of iliis 
 ; -. ■ and d, they an- connected bj ir. 
 
 or bin. I In, or by bulla pausing through, th 
 
 tnickneai of the. wood. 
 
 in plan ami elevation, the di I 
 tlio Ian . • of the 
 
 ■taire, ;. ,1 with th.- upper floor. It ba «illi thin 
 
 lI the upper portion, d, of tin 
 
 the other port 
 
 through the line, 1 — 'J, 
 
 B — <;. Tin- form, dim 
 all fully imli.-ii^l ii. 
 I 
 
 ipied by ■ balustrade, formed by ■ 
 of iron or wood, attached at their lower exti 
 
 16, an.) united abort by a Mat 
 bar of U I of poliahed fumjtnn 
 
 1 . ii;'. 0. The position of the r.«l-, 
 I 
 • 
 
 Till; INTERSECTION OF 81 ELFACER 
 
 41 I 
 
 i-i.vn: xvii. 
 
 - 
 
 m pro- 
 -.My met. with, 
 
 •i Iflnetmtkm. 
 
 of which 
 
 • BM .•..!Miiiii:ii.-:ii; .11 Hipm-fl 
 
 I A,..||- 
 
 ■ 
 ■i. Tin- 
 
 |«rt of : 
 
 - 
 
 \ 
 III tin 
 
 the key, ilu- i 
 
 . 
 handle, r,by meena of which it i» turned. 
 
 i.'i tin- r.H-k by a nut. '•. work 
 
 projecting end of thi 
 cock, end fig. 
 
 i 
 through the Bne, 1 — 3 
 ction through the llni 
 It wfll 
 • 
 
 to And, ■ ■ •.. the projeeti i of the, 
 
 elliptic shoulder, i>, with the external 
 
 ■ of tin- cylind 
 .- well when th 
 
 tlti— pfau '.'. .;,„. i|„, 
 
 i with tin- i 
 
 . 
 section oi ■ prism with ■ iph of the 
 
 ill.- koy in il 
 dona 1.' 
 
 I to explain. 
 I :t and :i' show n of Ilia Inter. 
 
 '. "f the handle, with ii 
 cal cytlnder, i.', of the key. The curri 
 according i" Il i 
 
 i \ iv. We here, how 
 ■ 
 
 . yllndor, i '. Bga. 8 1 and 8*, 1 
 Inclined I a Ith the 
 
 . . lindi r. i '. aaaumea a dlflbrenl aj 
 in ilii-. i I ■ itruction, h..»< 
 
 follows : — To obtain any |*.int iii the curve, «.■ proi 
 
 ■ ample, .In." 
 t.. the axel of tho cylinders, tlii-« puu ■ 
 tlir..iiL'h the In • 
 
 I ■ i the vertical |>r.> 
 
 • 
 on h ii, th. hi 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 line, d e. drawn through the poiut, ft', represents the intersection 
 of the plane with the horizontal cylinder, ft ft', being, of course, 
 measured from its rxis. It will be seen that the line, d e, is cut 
 by the vertical lines, a" /and e g, in the points, d, e, which lie in 
 the curve sought ; and the same construction will apply to every 
 other point in the curve, dbec. 
 
 181. Figs. 4 and 5 represent the intersection of an elliptical 
 cylinder wilh a right cone of circular base, corresponding to the 
 external conical surface, A, of the cock, at its junction with the 
 shoulders, d. Fig. 5 is a plan, looking on the cock from below, 
 and which shows the horizontal projection of the intersectioual 
 curves. 
 
 The solution of the problem requiring the determination of these 
 curves consists in applying a method already given — namely, in 
 taking any horizontal plane which cuts the cone, so as to present a 
 circular section on the one hand, and the cylinder in two straight 
 lines on the other — the points of intersection of these straight lines 
 with 'lie circle representing the section of the cone. Thus, by 
 drawing Ihe plane, c d, fig. 4, we obtain a circle of the diameter, c d, 
 which is projected horizontally, as with the centre, o, fig. 5; we 
 have also two generatrices of the cylinder, both projected in the 
 vertical plane in the line, a A, and in the horizontal plane in the lines, 
 a' ft' and a- ft 3 . Having drawn the semibase of the cylinder, d e, as 
 at d"/e', and having taken the distance,/ g, fig. 4°, and set it off, in 
 fig. 5, from the axis, as from g' to a', and to a 2 , we thereby obtain 
 the generatrices, a' b' and a ' 6 s , which cut the circle of the dia- 
 meter, c' d', in the four points, ft' i', which are squared across to, 
 and projected in, the vertical plane in the points, ft, i. In the 
 same manner we obtain any other points, as m, n; k I being the 
 plane taken for this purpose. The extreme points of the curve 
 are obtained in a very simple and obvious manner, as /, g, r, s, 
 being the points of intersection of the extreme generatrices, or 
 ■ the outlines of the two solids. With regard to the points, t, u, 
 which form the apices of the two curves, their position may be 
 obtained from the diagram, fig. 4", by drawing from the point, s, 
 which would be the apex of the entire cone, a tangent, s t, to the 
 base, d' fe', of the cylinder, and projecting the point of contact, t, 
 in the line, x y, representing a plane cutting the cone, which must 
 be projected in the horizontal plane. Then, making g' x', fig. 5, 
 equal to t r, fig. 4', and drawing horizontals through x', their 
 intersections, ( u', with the circular section of the cone, will 
 be the points sought, which are accordingly squared over to 
 fig. 4. The operations just described are analogous, it will be 
 observed, to those employed in obtaining the intersection of two 
 cylinders. 
 
 If, in the case of the cone and cylinder, the latter had been one 
 of circular instead of elliptical base, as is frequently the case, still 
 the construction, as a little consideration will show, must be pre- 
 . isoly the same, and the resulting curves would be analogous — that 
 i> when the diameter of the cylinder is less than that of the cone 
 at Jie part where it meets the low T est generatrix of the cylinder; 
 the curves, however, assume a different appearance when the dia- 
 meter of the cylinder exceeds this, as is shown in figs. 6 and 7. 
 In this case the intersections are represented by the curves, sir 
 and p u q; the method of obtaining these is fully indicated on the 
 diagrams. 
 
 185. The opening or slot, H, cut through the key of Ihe stop- 
 cock, is generally rectangular, rather than circular, or similar to 
 the tubular portions of the cock. The object of this shape is to 
 make the key as small as possible, and yet retain the required 
 extent of passage. This rectangular opening gives rise, in Bg. 2*, 
 to the intersectional curves, a b, c d, which are portions of the 
 hyperbola, resulting from the section made by a plane, cutting tin- 
 cone parallel to its axis. The operations whereby they are deter- 
 mined are indicated in figs. 10, 11, and 12. 
 
 To render the character of the curve more apparent, we have, 
 in these figures, supposed the generatrices of tho cone to make a 
 greater angle with the axis than in fig. 2'. The line, a ft, ivprc- 
 sents the vertical plane in which the curve of intersection lies. 
 It is evident that, if we delineate a series of horizontal plains, as 
 c d, ef, g ft, i k, fig. 10, we shall obtain a corresponding series of 
 circles in the horizontal projection, these circles cutting the plane, 
 a b, in the points, /', m', n', p', &c. These points are squared over- 
 to the vertical projection, fig. 10, giving the points, I, m, n, p ; and 
 the apex, o, of the curve is obtained, by drawing in the plan, 
 fig. 12, with the centre, s, a circle tangent to the plane, a b, and 
 then projecting this on the vertical plane, fig. 10, as shown. 
 From these diagrams, it is easy to see that the opening, h, will be 
 partly visible when the key is seen from below, as in fig. 2'. 
 
 186. Figs. 8 and 9 represent the vertical and horizontal pro- 
 jections of the nut, a, which secures and adjusts the key in its 
 socket. This nut is hexagonal, being terminated by a portion of 
 a sphere, the centre of which lies in the axis of the prism. Each 
 of the facets of the prism cuts the surface of the sphere, so as to 
 present at their intersection portions of equal circles, which should 
 be determined in lateral projection. The diameter of the sphere 
 is generally three or four times that of (he circle circuml 
 the nut, but, to render the curves more distinct, we have adopted 
 a smaller proportion in the case under examination. Tin- sphere, 
 y, is represented by two circles of the radius, o a; and the nut by 
 an hexagonal prism, the axis of which passes through the eentre of 
 the sphere. The anterior facet, a' b', of this nut, cuts the 
 so as to show a circle of the diameter, c' d'. This circle, projected 
 vertically on fig. 8, cuts the straight lines, a e and hi, ni the 
 prism, in the points, a and b ; and the portion of the circle com- 
 prised between these two points, consequently, represents the 
 intersection of this facet with the sphere. The other two facets, 
 a g' and b' h', which are inclined to the vertical plane, also cut 
 the sphere, so as to produce, at their intersection with the surface, 
 arcs of equal radii with that of the facet, a 4. From their incli- 
 nation, these ares become slightly elliptical, being comprised, on 
 the one hand, between the points, a and g, and ft, ft, on tb 
 The summits of these ellipses are obtained by drawing horizontal 
 lines tangential to the arc, a ft, and cutting it in the points, '.. /. 
 by perpendiculars drawn through the middle of the lateral facts. 
 In practice, it is quite sufficient to describe circular arcs. \>. ssing 
 through the points, g, k, a, and ft, I, ft. 
 
 We have already seen, in reference to Plate XIV.. that Ihe 
 intersection of a right cylinder with a sphere, through thi 
 of which its axis passes, gives a circle projected laterally as a 
 straight line. Thus, the opening o', which passes through the nut. 
 
 being cylindrical, produces, by its intersection with the sphere, a 
 
Tin: i 
 
 eirc!* of the diameter, aV W, in the j Jan. projected vertically in the 
 airtight fine, m n. 
 
 -• jmfiml— lb* ■— lognea operations required to .!- 
 the mm int«wrti«iiu when the nnt ia wn with ooe of the 
 angles fat the centre, and only two faceU visible, aa represented in 
 
 fi«c >•• 
 
 The eluptfc ranre, b' /» a', eoniwpiinitinp I . H. tim-t 
 
 obrlu— ly he eompr U - tal line* 
 
 pansinr; through theae points, and an are ia drawn thrun. 
 
 ay here observe, that the proficient draughtsman will, 
 doabtleaa, deem it unnwi— it. swept in extraordinary cases, to 
 Ut atirh minute details <.|" ! far the \ari.-u* 
 
 llllllaw I tiniial runes as turn 
 
 :. and the appesranco prescntnl by 
 different experimental All draughtsmen, ) 
 
 will find that some practice in "rtrtrilihig tl ntetfon 
 
 of the various cunes, accor 
 rolea laid down, will t- 
 them, from possessing a thorough theoretical knowledge of the n-la- 
 
 .irious forma of solids to eat 
 much ix-an r Initli, wlien, at a more advanced stage, they r< 
 the aid uf such constructive | 
 
 \\U PRACTICAL DATA 
 
 All liquids become change.) 
 I« ratlin- is sul! 
 
 - 
 
 Ttoe prasauri 
 
 in a vacuum, a i 
 
 cury 3" - iijiial to a u 
 
 IB 'I... par ■qoara mek 
 
 Thus, taking the square inch as tl rtirial measure- 
 
 ment, the pre.- , of the atvain 
 
 also equal to 15 lbs. 
 
 ntaining vessel is hermetically closed, as in a 
 
 if the t ^ 
 
 . 
 not loin;.' directly pr- : 
 The t. n-i..n or <■> 
 
 al the pressor, 
 volume of II • 
 one enj Mie quantity q) 
 
 half the sjiace at a pressure ol 
 
 TATiLE OF PRESSURES, TEMPEBATfRES, WEIGHTS, ASD VOLfMES OF STEAM. 
 
 PrMMrw is 
 
 Pi— mn is It><-he« 
 
 runs r»r So,ssr« 
 
 Tfii>i»r*lMri 
 
 Traiprretarj 
 
 ' .'.< uUr Fu* 
 
 Vuloai. •* . r...»a 
 
 *'—'•'"'"- 
 
 of Maresry. 
 
 
 Fahr*&h«tu 
 
 rata. 
 
 of 8USBU 
 
 af M..m 
 
 
 
 
 
 
 Lb. 
 
 
 100 
 
 
 
 219 
 
 
 
 
 
 375 
 
 
 
 
 
 
 160 
 
 450 
 
 
 
 119-4 
 
 
 
 175 
 
 
 
 ■Ji:t 
 
 117 1 
 
 
 1 '..'-1 
 
 
 
 
 250 
 
 
 
 
 
 
 3375 
 
 
 
 
 
 350 
 
 
 
 
 
 
 1 1777 
 
 
 
 
 870 
 
 
 
 I 9771 
 
 300 
 
 90-0 
 
 
 
 1 
 
 
 
 
 
 
 •J- i 
 
 1377 
 
 
 
 3 50 
 
 
 
 
 
 
 
 4-00 
 
 
 
 
 1 1 •. 1 
 
 
 
 4 50 
 
 135-0 
 
 
 
 1 19 l 
 
 
 
 6-00 
 
 1600 
 
 
 
 
 
 
 650 
 
 
 
 114 
 
 
 l 7494 
 
 ■«716 
 
 6-00 
 
 1800 
 
 n oo 
 
 
 
 
 
 
 
 
 
 
 
 
 
 310 
 
 
 331 
 
 
 •J 1777 
 
 
 800 
 
 B40-0 
 
 19 
 
 141 
 
 179-1 
 
 •J 1669 
 
 •4071 . 
 
 the aaak t an c e of this table, wo esj 
 
 a:— 
 
 First F.xamjit. — What is the amount of ■team pressor 
 on a piston of 10 inches diai 
 
 ■'■■■grcest It will I*. Ntn that the pressure corresponding 
 is equal to three atmospheres, or to 45 lbs. per aquaro 
 
 The area of a bJbJm "f in inches in diameter is equal to 
 10* x -7854 = 78-51 sq. b 
 
 78 54 • 18 Nt4 3 Ids. 
 
 Thn- ■ 
 
 indlng t" Km given temperature, and multiply It by the 
 Second F.ramflr.— \\ ! .luring 
 
 \\ . : • '-'.lin the volume • <|> ii'l.-l, 
 \- 
 
 x 3 — 19 635 cubic feet. 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 At a pressure of three atmospheres, a cubic foot of steam weighs 
 1-0058 lb. ; consequently, 
 
 19-635 x 1-0058 = 1975 lbs. 
 
 To solve this problem, then, we ascertain the volume expended 
 in cubic feet, and multiply it by the weight corresponding to the 
 given temperature, or pressure — the product is the weight in 
 pounds. 
 
 UNITY OF HEAT. 
 
 188. With a view to facilitate various comparisons connected 
 with the subject of steam, the French experimentalists have 
 adopted the term calorie, or unity of heat. This is defined as the 
 amount of heat necessary to raise the temperature of a kilogramme 
 (= 2-205 lbs.) of water, one degree centigrade. 
 
 Thus, a kilogramme of water at 25° contains 25 unities of heat ; 
 and, in the same manner, 60 kilog. of water at 50° contains 
 50 x 60 = 3000 unities. 
 
 The number of unities of heat is obtained by multiplying its 
 weight in kilogrammes by the temperature in degrees centigrade. 
 
 The amount of heat developed by different descriptions of fuel 
 varies according to their quality, and according to the construction 
 of the furnaces. 
 
 According to M. Pcclet, the mean quantity of heat developed 
 by a kilogramme of coal is equal to 7500 calories, or unities of 
 heat. 
 
 According to M. Berihier, that developed by a kilogramme of 
 wood charcoal varies from 5000 to 7000 unities. 
 
 In the following table will be found the results of experiments 
 with different descriptions of fuel : — 
 
 Table of the Amount of Heal developed by one Kilogramme of Fuel. 
 
 Description of Fuel. 
 
 
 
 Number of 
 unities of heat 
 developed by 
 
 Quantity of 
 
 steam practically 
 
 obtainable from 
 
 1 kdog. 
 
 
 6000 to 7000 
 6000 
 7500 
 4800 
 
 3000 
 
 1500 
 3600 
 
 2800 
 
 5800 
 
 Kilo?. 
 5-6 to 6 
 
 
 7- " 8 
 
 
 575 " 7 
 
 Drv Turf, 
 
 
 Common Turf, containing 20 per 
 
 :ent 
 
 1 
 
 1-8 " 2 
 
 
 
 
 « 
 
 Dry Wood of all 
 Common wood, 
 
 
 
 
 3-7 
 
 containing 20 
 
 per 
 
 I 
 
 27 
 
 Tint' Charcoal,. . 
 
 
 
 28 to 3 
 
 
 
 In the last column of this table, we have given the quantities 
 of steam produced by the combustion of one kilogramme of fuel, 
 being such as are practically obtainable in apparatus most com- 
 monly met with. 
 
 Example. — What is the quantity of coal necessary for the sup- 
 ply of a furnace intended to produce 250 kilog. of steam ' 
 
 The average produce of 1 kilog. of coal being 6-5 kilog., we 
 have 
 
 250 
 
 -r-r = 84 kilog. of coal. 
 
 189. The boilers in which the steam is to be produced, may be 
 
 of the shape represented in figs. 4 and 5, Plate XIV. — that is, 
 cylindrical, and terminated by hemispheres. They tire frequently 
 accompanied by two or three tubular pieces in connection with tlio 
 main portion of the boiler by pipes. Boilors answering to tliis 
 description are termed French boilers, being of French origin ; they 
 are found very effective, and are much used in the manufacturing 
 districts of England. These boilers are made of plates of wrought- 
 iron, the thickness of which varies, not only according to the sizo 
 of the boilers, but also according to the pressure at which it is 
 intended to produce steam. 
 
 The proper thickness for the plates of cylindrical boilers may 
 be determined by the following formula, which is the one adopted 
 by the French Government in their police regulations : — 
 
 _ 18 x d x p 
 
 + 3; 
 
 where 
 
 T = thickness in millimetres; 
 
 d = diameter of boiler in metres ; 
 
 p = pressure in atmospheres, less one. 
 
 The rule derivable from the formula is — . 
 
 To multiply the effective pressure of fJie steam in atmospheres 
 by the diameter of the boiler, and by the constant 18, dividing the 
 product by 10, and augmenting the quotient by 3, which will give 
 the thickness in millimetres. 
 
 To simplify these calculations, we give a table showing the 
 thickness proper for boiler plates, calculated up to a diameter 
 of 2 metres, and to a pressure of 8 atmospheres above tin- atmo- 
 sphere : — 
 
 Table of Thicknesses of Plates in Cylindrical Rollers. 
 
 Diameter 
 of Boiler. 
 
 
 Pre 
 
 ssure of Steam in Atmoaphe 
 
 
 
 2. 
 
 3. 
 
 4. 
 
 5. 
 
 6. 
 
 7. 
 
 8. 
 
 Metres. 
 
 Millim. 
 
 Millim. 
 
 Millim. 
 
 Millim. 
 
 Millim. 
 
 Millim. 
 
 Millim. 
 
 •50 
 
 3-9 
 
 4-8 
 
 5-7 
 
 6-6 
 
 7-5 
 
 8-4 
 
 9-3 
 
 •55 
 
 4-0 
 
 5-0 
 
 6-0 
 
 7-0 
 
 7-9 
 
 8-9 
 
 9-9 
 
 •60 
 
 41 
 
 5-1 
 
 6-2 
 
 7-3 
 
 8-4 
 
 9-5 
 
 10-5 
 
 ■65 
 
 4-2 
 
 5-3 
 
 6-5 
 
 7-7 
 
 8-8 
 
 lii-ii 
 
 11-2 
 
 •70 
 
 4-3 
 
 5-5 
 
 6-8 
 
 8-0 
 
 9-3 
 
 10-5 
 
 1 1-8 
 
 •75 
 
 4-3 
 
 5-7 
 
 7-0 
 
 8-4 
 
 9-7 
 
 111 
 
 12-4 
 
 ■80 
 
 4-4 
 
 5-9 
 
 7-3 
 
 8-8 
 
 10-2 
 
 11-6 
 
 131 
 
 •85 
 
 4-5 
 
 61 
 
 7-6 
 
 91 
 
 10-6 
 
 12-2 
 
 13-7 
 
 •90 
 
 4-6 
 
 6-2 
 
 7-9 
 
 9-5 
 
 111 
 
 12-7 
 
 14-3 
 
 •95 
 
 4-7 
 
 6-4 
 
 8-1 
 
 9-8 
 
 1 1-5 
 
 13-3 
 
 15-0 
 
 1 <>0 
 
 4-8 
 
 6-6 
 
 8-4 
 
 10-2 
 
 12-0 
 
 13-8 
 
 15-6 
 
 1-10 
 
 5-0 
 
 7-0 
 
 8-9 
 
 10-9 
 
 12-9 
 
 1 III 
 
 " 
 
 1-20 
 
 52 
 
 73 
 
 9-5 
 
 11-6 
 
 13-8 
 
 10-0 
 
 " 
 
 1-30 
 
 5-3 
 
 7-7 
 
 10-0 
 
 124 
 
 14-7 
 
 " 
 
 " 
 
 1-40 
 
 5-5 
 
 8-0 
 
 10-6 
 
 131 
 
 15-6 
 
 " 
 
 " 
 
 1-50 
 
 5-7 
 
 8-4 
 
 111 
 
 13-8 
 
 " 
 
 " 
 
 " 
 
 1-60 
 
 5-9 
 
 8-8 
 
 11-6 
 
 11-5 
 
 " 
 
 " 
 
 " 
 
 1-70 
 
 61 
 
 91 
 
 12-2 
 
 152 
 
 " 
 
 " 
 
 " 
 
 i-flb 
 
 6-2 
 
 9-5 
 
 12-7 
 
 160 
 
 " 
 
 " 
 
 " 
 
 1-90 
 
 6-4 
 
 9-8 
 
 13-3 
 
 " 
 
 " 
 
 " 
 
 " 
 
 2-00 
 
 6-6 
 
 10-2 
 
 138 
 
 " 
 
 " 
 
 
 11 
 
 To suit English measures, the foqjula is — 
 18 xd x p 
 
 10,000 
 
 + -1182. 
 
Tin: r i>it \ii.iii 
 
 And lure, 
 
 --in Inches; 
 J = diameter in Inches ; 
 • = prvaaure in »Unu»}4nn-», low one. 
 
 Ill: ATI** mi 
 
 d ili.il a square metro 
 
 .in per 
 
 h<>ur, » indlical, with or 
 
 . 
 
 l<i I- y in.lwl.<l tli.it whi.h is .iirft-lly 
 
 • 
 fn>m tli. 
 
 si tin- production of -' 
 
 hbalf "r a third of tbja 
 I t.i tin- direct action "f tin- tin-, which will give, 
 f..r the whole b 
 
 In tl. "■ principal dimension! 
 
 I ■■- ■ - j- a. i ol i i era ■•! the French dcecrip- 
 ti.ui — that in, cylindrical with two 
 
 dp 
 
 1 1 ■ I! I /' • fi-r a 
 
 /' I 
 
 
 
 L»iw1h nf 
 
 
 1 
 
 
 ■he Tuba. 
 
 
 • M. 
 
 II. 
 
 H. 
 
 at 
 
 - 
 
 I 
 
 4 
 
 •J in 
 
 
 
 
 
 
 A 
 
 
 
 
 
 '.' 
 
 In 
 
 
 
 
 
 
 R 
 
 10 
 
 10 
 
 
 
 
 
 10 
 
 111 
 
 li 
 
 
 
 
 
 1" 
 
 1<I 
 
 
 
 
 
 
 111 
 
 10 
 
 
 
 
 
 
 1" 
 
 111 
 
 * 
 
 
 
 
 
 10 
 
 111 
 
 
 
 
 
 
 
 111 
 
 
 
 
 
 
 11 
 
 10 
 
 
 
 1 
 
 
 
 11 
 
 111 
 
 .without additional tubes, the water ahonld 
 
 lwo4hirda of tin- whole apace, and in boilers, with the 
 
 i occupy aboul one-half the main cylindrical body 
 
 I til till' tiling. 
 
 Iii order that (he with it small 
 
 lich sction is termed "ftriminii" the Im.iI.t 
 
 i» anriB ■ dome, In which the 
 
 ;..rt of Which II 
 
 thrown op by the obullitioff 
 
 ' ' '■'■ ■ r n cylindrical 
 
 e>- 'i"i' "f 
 
 be luat- 
 in\i surface 13 sq. tn., par li 
 
 I x 6 = 7* sq. nx^total heating surface. 
 1 tliat 
 
 7-8 aq. m. = L 
 
 J , i -, K 
 ^r = L x — — , 
 
 3 3 
 
 Ji nought, nn I El the I 
 = '4 m.; so that, nulmtiluting fur K sud It : 
 
 7-8 aq. m. = L x 314 x -4 x — = L > 
 
 
 L = 
 
 
 • i ■ .". ■ 
 
 An it may In- an 11 i fin watca. 
 
 DA, this may : 
 
 I 
 Tin- boQar being terminated by bamisphari of the 
 
 cylindrical iHirtiuii will be aqua] to 
 
 — (4 x 2) = 385. 
 
 iH bare, th.n, fur the \ to iho 
 
 cylindrical portfoo — 
 
 iitnl for thai of tl .J ends — 
 
 2^ 
 
 The whole volume of •>■ |nently, 
 
 I 189 1 ihl 
 The remainder of the volume, whi 
 is obviously 
 
 2 
 
 inlill'T, 
 
 II' 
 This result might bave been obtained by the following 
 formula i — 
 
 t 
 .) 
 
 = -731 cubic ■ 
 
 v = L x i i; i 
 
 R' = 
 
 14 , 
 
 191. Wo I" r. quote the portion of the n 
 the French Governmi nt, relal 
 what condition I 
 
 of public .-.ili iv, and 
 • 
 
 ire divided Into f"iir 1 1 
 
 "Tli. the boiler, ine'ndlng thai of the tnl 
 
 mere \*- any, must b 
 
 ii i in it ati tnd tl 
 
 two quantitlea multiplied Into each other. • 
 
 •• it tin- product < n 
 
 ..II. lull 
 
 : fifteen. < »f tin- third, whan mora than tl. 
 fourth, when uol i <i 
 
 •• If two in i to work in corn 
 
 :iini.'ati..|) wr: 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 81 
 
 term taken to represent the capacity "must be tho sum of the 
 capacities of each. 
 
 " (34.) Steam-boilers of the first class must bo stationed outside 
 of idl dwelling-houses or workshops. 
 
 " (35.) Nevertheless, in order that tho heat, which would other- 
 wise be dissipated by radiation, may bo better economised, the 
 officer may allow a boiler of the first class to be stationed inside a 
 workshop, provided this does not form part of a dwelling-house. 
 
 "(36.) Whenever there is less than 10 metres in distance 
 between a boiler of the first class and a dwelling-house or public 
 road, a wall of defence must be built, in good and solid masonry, 
 and 1 mitre thick. Tho other dimensions are specified in article 
 41: This wall of defence must, in all cases, be distinct from the 
 masonry of the furnaces, and separated from it by a space of at 
 least 50 centimetres in width. It must, in a like manner, be 
 separated from the intermediate walls of the neighbouring houses. 
 
 " If the boiler be sunk into the ground,' in such a manner that 
 no part of it is less than 1 metre below the level of the ground, 
 the wall of defence shall not be required, unless the boiler is within 
 5 metres of a dwelling-house or of the public road. 
 
 " (38.) Steam-boilers of the second elass may be stationed inside 
 a workshop which does not form part of a dwelling-house, or of 
 a factory or establishment consisting of several stories. 
 
 " (39.) If a boiler of the second elass be within 5 metres from a 
 dwelling-house or the public road, an intermediate wall of defence 
 shall be erected, as prescribed in article 36. 
 
 "(41.) The authority given by the inspecting-offieer for boilers 
 of tho first and second class, shall indicate the situation of the 
 boiler, its distance from dwelling-houses and the public roads, and 
 shall determine, if there be space enough, the direction to be given 
 to the axis of the boiler. 
 
 " This authority shall also specify the situation and dimensions, 
 as to length and height, of the wall of defence, where this is 
 required, in conformity with the above regulations. 
 
 " In determining these dimensions, regard must be had to the 
 capacity of the boiler, to the pressure of the steam, as well as to 
 all circumstances tending to make the boiler more or less danger- 
 ous or inconvenient. 
 
 " (42.) Steam-boilers of the' third class may be stationed in 
 workshops which do not form parts of dwelling-houses, and it is 
 not necessary to erect a wall of defence. 
 
 " (43.) Steam-boilers of the fourth class may be stationed in 
 any workshop, even if tins forms part of a dwelling-house. 
 
 " In this caso, the boilers must be furnished with an open 
 manometer. 
 
 " (44.) Tho furnaces of steam-boilers of the third and fourth 
 class shall be entirely separated, by a space of at least 50 centi- 
 metres, from any dwelling-house." 
 
 According to these regulations, a boiler of the dimensions taken 
 fir illustration, and supposing tho maximum pressure to be 3 
 atmospheres, would be in the second class, for — 2-203 x 3 = 
 6-609, winch is below 7. 
 
 Second Example. — What should be the dimensions of a cylin- 
 drical boiler, with two additional tubes, intended to supply an 
 engine of 16 horses power, tho diameter of the main body being 
 •9 m., and that of the tubes -45 m. ? 
 
 Assuming 1-2 sq. m., per horse power, fur the heating surface, 
 wo shall havo 1-2 X 16 = 192 sq. m., for the entire heating sur- 
 face. Half of tho surface of the main cylinder of the boiler, and 
 three-fourths of that of the tubes, is the best disposition of this 
 heating surface. These data give riso to tho following formula :— 
 
 , . „ 2« R x L , 3 
 
 19:2 sq. m. = + r2*xLx2x — = 
 
 J, 4 
 
 n R L 4- 3rt r L— . 
 
 L here represents tho length of tho boiler and tubes, which is 
 
 the only unknown term. 
 
 Substituting for R and r their numerical values, -45 and -225, 
 
 we have — 
 
 19-2 sq. m. = 3'14 x -45 x L + 3 x 3-14 x -225 x L; or 
 
 19-2 sq. m. = L (3-14 x -45) 4- 3 x 3-14 x -225 = 
 
 L (1-413 + 2-12); 
 
 whence, 
 
 19-2 19-2 
 
 3-533 
 
 = 5-43 m. 
 
 1-413 + 212 
 
 Thus, the total length of the boiler is 5-43 m., but the ends 
 being hemispherical, the length of the cylindrical portion is 
 equal to — 
 
 5-43 — -9 = 4-53 m. 
 The tubes usually project in front of the main body, to a dis- 
 tance of about 50 centimetres; but, for convenience in constructing 
 the return flues, they do not extend as far back, so that they aru 
 of about the same length as the main body. 
 
 192. In distillery boilers, a horse power is understood to mean 
 the capability of evaporating 25 kilogrammes of water in an hour. 
 Thus, a boiler of 10 horses power should be capable of evaporating 
 250 kilog. of water in that time. Now, assuming l-f2 sq. m. of 
 heating surface, per horse power, for a steam-engine, we should 
 only have an evaporation of from 18 to 20 kilog. per hour, per 
 horse power, and per square metre of heating surface. 
 
 DIMENSIONS OF FIRE-GRATE. 
 
 193. In practice, 1 square metre of grate will burn from 40 to 
 45 kilog. of coal per hour. Thus, a boiler intended to produce 
 280 kilog. of steam per hour, will require, for this purpose — 
 assuming that 1 kilog. of coal produces 6-65 of steam — 
 
 280 
 
 ' . „ = 43 kilogrammes of coal ; 
 oo5 
 
 and tho furnace of tins boiler should have a grate, measuring 1 
 
 square metre. 
 
 Tho grate-bars are generally of cast-iron, of from 30 to 35 
 millimetres in width, but having between them a space of only 
 7 or 8 millimetres, so that tho intervals only occupy a fourth or 
 a fifth of the whole area. 
 
 It has been found that greater strength and durability is 
 obtained by making the bars straight above, and strengthened by 
 parabolic feathers below. 
 
 CHIMNEYS. 
 
 194. The height of chimneys is very variable, and cannot bo 
 subjected to any fixed rule. The cross section at the summit 
 depends upon the size of the grate, and is generally about a sixth of 
 
TJIK I 
 
 this. In the f.41owing application will be found calculations 
 respecting chkuncy*, and examples of the various rule* « 
 
 Ami 
 
 -opoae calrula'in.- the dimensions i.f the funu. 
 - an engine of 8 bone* poi 
 example, to be worked on the higb-preasure system, consuming, aa 
 a maiimiim, 5 kilogramme* of coal, : -. par hour, the 
 
 amount of beating aurfare being taken at 1 Ul eq. in., p 
 power. 
 
 For 8 horaea power, the boa' 
 
 . 
 Da, »e have— 
 
 : 218-88 kilog. of steam. 
 Aa 5 kilog. of steam are produced by 1 Uog. of coal, I 
 
 — s — = «-8k;: 
 
 representing the quanti:;, r hour. 
 
 TT>e grate ;.- 
 that one square decimetre L> sufficient fur 1*3 Idlog. par hour, will 
 
 l J 
 
 = 36 square dt • 
 
 rth of this area to U .-sage of air. 
 
 - to calculate the cross sectional ana of the 
 must remark, that 1 - 
 
 of coal; 
 ,'iiro 
 43 8 x 18 = "7881 . 
 
 I of its 
 >(.- acid "a* nii- 
 
 f to M. P( • *. at tlie 
 
 • hoar. If wi drrfcV - 
 
 ohlain the quantity which em-apes per second ; nan 
 1< 
 
 
 
 aaaume, aa is. ] r..|~.r- 
 
 dl of the aa* - inula:— 
 
 \ 
 In the case II = oj ,„ „ j. th. i-..n-t.int 
 
 r numerical ij 
 \ ' ■ • (300 — 15) = 91. 
 
 ■gnttM that t ,n theehfanni 
 
 actual 
 rale. I _., r , 
 
 T It 7 m. 
 •be rate .-., that time, 
 
 i 
 
 •hall obtain the croa* sectional area proper for the upper part of 
 the chimney ; as thus— 
 
 Tliu« is. supposed to be aquare, will only 
 
 internally, something leas than tw 
 metres each way at t: ■ ■ mini- 
 
 mum dimension, and il ' .Traler dimen- 
 
 square, 
 
 • 
 - in manufactories. A dnin. 
 
 should I 
 
 
 
 Table 
 
 / 1 I triers of Safety 
 
 1 
 
 
 
 EiUst »f 
 
 Fiwwi Is AiawybirM 
 
 
 
 
 
 
 
 
 
 
 
 
 
 % 
 
 ■i\ 
 
 S 
 
 »t 
 
 ! 
 
 
 
 
 
 
 *U 
 
 */ 
 
 "/. 
 
 "/ 
 
 »/ 
 
 * 1 
 
 "/ 
 
 "/.. 
 
 
 ■ / 
 
 •v *■ 
 
 
 
 
 
 
 
 1 
 
 
 it 
 
 
 
 
 
 
 11 
 
 
 9 
 
 1 
 
 
 
 
 
 
 
 
 
 
 13 
 
 
 
 
 
 
 
 
 
 
 
 
 4 
 
 
 11 
 
 
 
 
 
 
 
 
 
 3 
 
 66 
 
 
 
 36 
 
 
 
 
 
 
 
 
 
 61 
 
 
 II 
 
 
 
 
 
 
 
 
 7 
 
 66 
 
 
 
 
 39 
 
 36 
 
 
 
 
 
 8 
 
 
 
 
 
 
 39 
 
 
 
 
 
 I 
 
 
 
 64 
 
 
 II 
 
 41 
 
 36 
 
 
 
 
 10 
 
 79 
 
 66 
 
 17 
 
 
 
 43 
 
 
 
 
 
 It 
 
 83 
 
 68 
 
 60 
 
 
 
 43 
 
 
 
 33 
 
 
 11 
 
 
 
 
 66 
 
 
 
 
 
 
 
 
 
 
 63 
 
 
 
 49 
 
 
 
 
 
 It 
 
 M 
 
 
 67 
 
 
 
 61 
 
 
 41 
 
 
 33 
 
 
 96 
 
 
 
 
 
 33 
 
 
 
 
 36 
 
 ia 
 
 
 63 
 
 
 63 
 
 39 
 
 66 
 
 
 
 
 
 17 
 
 
 83 
 
 74 
 
 
 
 66 
 
 
 
 
 
 If 
 
 
 87 
 
 76 
 
 68 
 
 63 
 
 68 
 
 
 
 
 
 
 
 90 
 
 
 
 64 
 
 60 
 
 
 
 
 41 
 
 
 HI 
 
 93 
 
 
 
 66 
 
 61 
 
 
 
 
 
 •J I 
 
 111 
 
 
 
 
 68 
 
 63 
 
 
 
 
 
 
 117 
 
 97 
 
 84 
 
 76 
 
 69 
 
 64 
 
 
 
 
 II 
 
 
 
 99 
 
 86 
 
 
 
 66 
 
 38 
 
 
 
 
 
 
 
 
 
 
 67 
 
 39 
 
 
 
 
 
 
 
 90 
 
 
 
 69 
 
 60 
 
 
 
 
 
 
 
 91 
 
 
 
 
 63 
 
 
 
 
 
 
 
 
 
 
 
 63 
 
 
 
 
 
 
 
 
 
 
 73 
 
 64 
 
 
 
 
 
 
 111 
 
 97 
 
 
 
 
 
 
 
 
 
 136 
 
 
 
 
 -1 
 
 
 66 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 84 
 
 
 
 
 
 
 
 69 
 
 
 
 
 
 149 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 83 
 
 
 
 
 
 
 
 
 
 101 
 
 
 86 
 
 
 
 
 
 
 
 
 
 101 
 
 
 
 
 
 
 63 
 
 
 
 
 
 111 
 
 lo| 
 
 
 
 
 
 
 
 
 
 
 
 
 101 
 
 
 
 
 
 60 
 
 
 
 
 IS! 
 
 
 
 
 
 
 73 
 
 •ceea*. ' .;/j, alarm ir/i 
 
 .1 instrument which MTTM to indicate tho 
 the In.iler in al 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 63 
 
 The float serves to indicate the level of the water, and the 
 whistle to give the alarm when the water is much below the pro- 
 per level. 
 
 The safety valve provides fm exit for the steam when the pres- 
 sure is too high. 
 
 We have given a drawing of one at fig. 4, Plate XI. Their 
 diameters vary with the dimensions of the boilers and the pres- 
 sure of the steam. 
 
 The regulations of the French Government contain the following 
 rules and the above table for their determination. To find the proper 
 diameter for the safety valve, the heating surface of the boiler, 
 expressed in square metres, must be divided by the maximum 
 
 pressure of steam intended to be maintained, expressed in atmo- 
 spheres, previously diminished by the constant "412: the square 
 root of the quotient being extracted, is to bo multiplied by :2-(J, 
 and the product will be the diameter sought, expressed in centi- 
 metres. This rule may be put as a formula, thus: — ■ 
 
 2-6 
 
 V^T 
 
 11 2 
 
 where d is the diameter of the valve in centimetres, s the healing 
 surface of the boiler, including both tire and Hue surface, expressed 
 in square metres, and n the number expressing tho pressure iu 
 atmospheres. 
 
 CHAPTER V. 
 
 THE STUDY AND CONSTRUCTION OF TOOTHED GEAR. 
 
 196. Toothed gear is a mechanical expedient, universally 
 employed for the transmission of motion. It is met with of all 
 proportions, from the minute movements of the watch, to the 
 gigantic fittings of manufacturing workshops. Toothed gear is 
 generally constructed with a view to the following principle of 
 action — that the lateral acting-surfaces develop the same arc during 
 the same duration of contact, whilst their angular velocities 
 vary inversely as their diameters. By the angular velocity of 
 any body, turning about a centre, is meant the angle passed 
 through by tho body in a unit of time ; whilst the real or linear 
 velocity of any point is the space passed through by this point, 
 whether the direction of motion be rectilinear or circular. Thus, 
 various points on a crank, taken at different distances from the 
 centre of the shaft, have all the same angular velocity, whilst their 
 actual velocity differs considerably, because of their respective 
 distances from the centre. It is the same with a pendulum, which 
 vibrates through an angle, or has an angular motion about its 
 centre of suspension. The angular velocity of a body is greater, 
 as the angle passed through in the same time is greater. Two 
 points may have the same angular velocity, although the space 
 passed through by each may be very different. Thus, all the 
 points in the pendulum are affected with an equal angular motion, 
 whilst their actual velocities, or the course traversed by each, 
 vary as the distance from the centre of motion. 
 
 This description of gear consists of a series of projections, or 
 teeth, regularly arranged on straight, cylindrical, or conical sur- 
 faces, termed webs, and disposed so as to act on each other, during 
 a limited time. 
 
 In order, however, that the gearing action may take place in a 
 regular, even manner, it is indispensably necessary that tho sur- 
 faces of the teeth should bear upon each other tangcntially, 
 throughout the entire duration of their contact; and for this pur- 
 pose, far from being arbitrarily designed, their form should be 
 determined with the utmost geometrical exactitude, for on their 
 form entirely depends their accurate and easy working. It is, 
 
 therefore, obviously incumbent on the student to give particular 
 attention to the delineation of these teeth. 
 
 The curves generally adopted in practice for the outline of 
 teeth, are the involute, the cycloid, and the epicycloid. 
 
 It is useful to investigate the nature and construction of tneso 
 curves, both on account of then- application to the teeth of wheels, 
 and also because of their employment in several other mccnanical 
 contrivances. 
 
 INVOLUTE, CYCLOID, AND EPICYCLOID. 
 
 PLATES XVIII. AND XIX. 
 
 I>-\OLUTE. 
 
 Figure 1.— Plate XVIII. 
 
 197. When a thread is unwound from the circumference of a 
 circle, and i3 kept uniformly extended, its extremity will <! 
 the curve known as the involute. 
 
 This definition serves as a basis for obtaining the geometrical 
 delineation of the involute. Let a b c ho the given circle of 
 the radius, a o, and a the extremity of a thread wound upon it. 
 Starting from the point, a, mark off, at equal distances apart, 
 several points, as a, b, c, so near to each other, that the interven- 
 ing arcs may he taken for straight lines without sensible error. 
 Through each of these points draw tangents to the circle, or per- 
 pendiculars to the corresponding radii; and on these tangents set 
 off distances, equal to the rectifications of the respective arcs 
 A b, A c, &c. ; by which means are obtained the points. <;', />'. , ', &c, 
 and the curve passing through these points is a portion of the 
 involute. By continuing the development or unwinding of tho 
 thread, the curve may be extended to a series of convolutions, 
 increasing more and more in radius, and becoming a species of 
 spiral. After one complete evolution of the circumference, '!"■ 
 shortest distance between two consecutive convolutions is always 
 the same, and equal to the development or rectification of the 
 
THE PRACl 
 
 of -i*- faaalm afcast. wh»b h 
 
 TU puiata, a, ft, e, U-inj taken at equal 
 circomfrn n», Ik* tan.-rnt* in r c, triple, Ac, 
 
 thai of Ike first, A a : and if. a* we directed, these poiota are sufli- 
 cimtly Dear to < may Im drawn, with closely 
 
 approximate .- bribing a ■u o rt — ion of arcs, hating 
 
 these tangent* for radii. Thus, with the point, a, aa centre, and 
 radiaa, a a*, the fint arc, a a', is drawn ; a: < ntre, b, 
 
 and radius, b ft', the aectbd arc, m ft, in like manner; and similarly 
 with the real. 
 
 la Uk. Uied gear, 
 ., wi sjau fu, cams and eccentrics. 
 
 . crt XV1IL 
 
 196. 9 af due is rolled upon a plane surface in a 
 
 rectilinear direction, any point in the circumference of this dine 
 generates the nine called the cycloid. Thus, any point bd 
 the ouUide of a loco: :i motion, describes as many 
 
 r ■ ; ■ i' as the wheel make!- r 
 
 In order that 
 
 I -aary that Ike I : take place without . 
 
 . the plane; ii. 
 
 should be equal 
 
 I with, the pb 
 
 of a circle of the given radius, a o, and rolling upon a given 
 na, b c 
 There arc several metl .- this problem. 
 
 .inference, starting from the 
 
 .'lances equal to a a, ao small that the arcs 
 
 .- 1 may be taken as straight lines. Set off.the same <hV 
 
 lance a . snd at 
 
 • 
 
 r , which arc th in the 
 
 . 
 on each of which successively Mt off tl.- ma area, 
 
 - . and so 
 on tlir r o' c', paa-M' 
 
 |oirad. 
 irve may a!». ■ ' - 
 
 the original circle, and then intersecting these by the area drawn 
 
 ' 
 
 i wing area of circles « 
 centres, a» mdl .rid aide of flg 
 
 1 icaj, A o, 
 
 on the ho r ltonla U , a- ..:.<•<•» equal I 
 
 r ''r ■' '• '••' bet*" :i i!.. original circl< and lhi> f« rpentli- 
 
 culars through tin- several i 
 
 thus, the distance*, r e './/, p g>, » a , Ac. are set off from I to a' 
 
 a to i ', 3 to c 
 
 ing to .this last solution to the left-hand aids of fig. S, which akowa 
 n of a aecood cycloid similar to the first. 
 
 '.lined, aa at d', the poiat riiirr— pnajdhrg to 
 the diameter, A D. The length. A c, of the gij en a Ua igs U line, is 
 obviously equal to the rectificalioD of the atstavihiaaafiiumis of tho 
 generating circle, wboae radius ia a a 
 
 obtained, having equal and symmetrical portions oo either aid* of 
 
 .. al, c 0, and having for ita base a line* double the length 
 
 .-cquentJy equal to the rectification of the enure 
 
 The cycloid is the curve more generally given to the teeth of 
 w heel gear and endless screws. 
 
 EXTEBXAL IHCTC! 
 
 N 1.— run XIX. 
 
 dmVfs from the cycloid, in that the 
 a a straight fine, doea 
 hieh is fixed. \\ 
 
 an- in the sain- .'. taken generate-, a right or eylistJri- 
 
 - are situate in different planes, 
 but maintaining a uniform angle to each ot) 
 
 butumis a tjmrric ap ■ rating circle m 
 
 auppos. ntre, at the aame time mmng 
 
 the stationary < 
 
 ►I. the 
 •1 are analog- - 
 I o be the radius of the g» : ■ 
 circle, and a c the nu! 
 
 a number of equal pan 1 on the 
 
 H as many arcs equal to the a- r. staru 
 
 : A. as at a. ft, r. </. Ac. Thr- 
 - 
 lb* rad .- circle U ing genera!- 
 
 - n Oation about the stationary 
 . which are tl 
 
 - 
 :'. of the 
 :tli tht-w p.ints a- 
 .ircs of i-jiia! radii w ' rig circle, max 
 
 --tiding arcs, x a', x V, x c', aa from 
 •e pa*»ing tlir 
 O*, ft*. - 
 
 ! ..'ion. — Tin p ■ rmined 
 
 by >ir:. r, area paasiri. 
 
 in a', ft*, c', a", which are ao many , 
 ■ 
 
 ". ti rated by tnaaferrmg 
 
 I 
 i its original position, and the radii, c a, c i, c L, passing 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 through the different points of contact on the stationary circle, 
 measured upon the ares described with the centre, c, to the same 
 ares, but so that the extremities of the whole may lie in the pro- 
 longation of the radius, c B. •Thus the distances, ee',ff,gii' ,& c, 
 are set off, from 1 to a', 2 to b', 3 to c', &e. The diagram refec- 
 ting to this construction forms the right-hand portion of fig. 1. 
 
 When the generating circle lias made an entire revolution, the 
 euro obtained is an entire epicycloid, a d b, comprising two equal 
 ind symmetrica] portions on either side of the line, d e, which is 
 iqual to tlie diameter of the moving circle. 
 
 EXTERNAL EPICYCLOID DESCRIBED BT A CIRCLE ROLLING ABOUT 
 A FIXED CIRCLE INSIDE IT. 
 
 Figure 3. — Plate XIX. 
 
 200. For this diagram, which is analogous to the preceding one, 
 ' the radii of the circles are given, c A being that of the fixed circle, 
 
 and b a that of the moving one. Divide the first circle into any 
 number of equal parts, in the points, a, i, c, d, &c, and divide off, 
 on the larger circle of the radius, b a, a like number of arcs, equal 
 to those on the other circle, as from a to a 1 , a' to b, &c. Then 
 with the point c as centre, and with the radius b c, describe a 
 circle, cutting the radii, c A, c a, c 4, c c, in the points, b, b', b 2 , b 3 , 
 and with each of the last as centres, and with the radius, A B, 
 describe arcs, which will be tangents to the fixed circle, at the 
 different points of contact, a, b. c, in succession. Then, with the 
 centre, c, describe arcs, passing successively through the points, 
 a', J', c', d', on the moving circles, as in its first position. These 
 last will cut the arcs tangential to the given circle, in the points, 
 r 2 , b", c-, d-, and the curve passing through these points is the 
 rpicycloid sought. 
 
 The other two methods given, of drawing the common epicy- 
 cloid, are also applicable \o this last case. 
 
 INTERNAL EPICYCLOID. 
 Figure 2. — Plate XIX. 
 
 201. The epicycloid is termed internal, when the generating 
 circle rolls along the concave side of the circumference of a fixed 
 circle. 
 
 Let c A be the radius of the fixed circle, and B A that of the 
 generating circle. As in preceding cases, so also here, we 
 commence by dividing the moving circle into a certain number of 
 equal pails, and then dividing the fixed circle correspondingly, so 
 that the arcs thus obtained in each may be equal. We then pro- 
 ceed as in the ease of the external epicycloid, according to which- 
 ever of the three solutions we propose adopting, all being alike 
 applicable. The operations are fully indicated on fig. 2, and the 
 same distinguishing letters are employed as in fig. 1. 
 
 When the generating circle is equal to half of the fixed circle, 
 the epicycloid generated by a point in the circumference is a 
 straight line, equal to the diameter of the fixed circle. Thus, in 
 fig. 3, Plate XVIII., the epicycloid generated by the point, A, of 
 the moving circle of the radius, a c, after a semi-revolution, coin- 
 cides exactly with the diameter, a b. 
 
 If, with circles of the same proportions as those in fig. 3, 
 Pla,te XVIII., we take a point, D, outside the generating circle, 
 but preserving a constant distance from it, the epicycloid generated 
 
 by it will be the ellipse, D F E G, having for its transverse axis the 
 line, d e, equal to the diameter, a b, of the fixed circle, augment d 
 by twice the distance, n a, of the point, i>, from its extremity; and 
 for conjugate axis, the line, g t, equal to twice the same distance, 
 
 D A, alone. If it is wished to determine this curve ace on 
 its properties as an epicycloid, and without having recourse to the 
 methods given in reference to Plate V., and proper to the ellipse, 
 it may bo done by adding the distance, a d, to that of the radius, 
 c A, in each successive position occupied by the generating circle 
 during its rotation. If the generating point be taken inside the 
 moving circle, the curve produced will also be an ellipse. 
 
 The epicycloid is the curve most employed for the form of 
 the teeth, whether of external or internal spur or bevil wheels. 
 
 Toothed gearing may be divided generally into two categories; 
 namely, right, cylindrical, or "spur" wheels, and conical, angular, 
 or "bevil" wheels. In the first are comprehended the action of a 
 rack and pinion, that of a worm or tangent-screw with a worm- 
 wheel, and finally, that of two wheels. We may remark, that in 
 all these modes the teeth are so formed and arranged, as to act 
 equally well whichever of each couple he the driver, and in which- 
 ever direction the motion takes place. 
 
 THE DELINEATION OF A RACK AND PINION IN GEAR. 
 
 Figure 4. — Plats XVm. 
 
 202. A rack is a species of straight and rigid rod or bar, formed 
 with teeth on one side, so as to take into or gear with the teetn of 
 a right wheel, generally of small diameter, and in such case termi 1 
 a pinion. Such a rack is represented at A E in the figure. 
 
 In proceeding to construct this design, a.s well as for all kinds 
 of toothed gear, it is necessary to have determined beforehand 
 the thickness, a b, of the teeth, as this dimension varies accord- 
 ing to the power or strain to be transmitted; and rules and 
 for this purpose, will be found at the end of the chapter. 
 
 When the rack and pinion are made of the same metal, the 
 thickness of the teeth should be the same in both. The spaces or 
 intervals between the teeth ought also to be equal in such case. 
 Theoretically speaking, the intervals should he equal to the thick- 
 ness of the teeth; but in practice, they are made a little v 
 admit of freer action. 
 
 203. The pilch of the teeth comprises the width of n 
 
 and that of the interval. In a wheel this pitch is measured upon 
 a cucle of a given radius, termed the primitive or pitch circle, and 
 in the rack on a straight line tangent to the pitch circle of the 
 pinion, and also called the primilire or pitch line. 
 
 204. Let o c be the radius of the pitch circle of a pinion gear- 
 ing with a rack, of which the pitch line is a b. We propose, in 
 the first place, to determine the curve of the teeth of the pinion, 
 so as to gear with and drivo the rack, and we shall subse |uentiy 
 determine the curve of the teeth of the rack, enabling it to gear 
 with and drive the pinion. 
 
 The operations consist in rolling the straight line, a c, tangen- 
 tially to the pitch circle, O c; during this mo-vement, the point, c. 
 will generate an involute, c D, which may be drawn in the manner 
 indicated in fig. 1 — a construction Which is further repeated at 
 a' ,1'. on one of the teeth of the pinion, fig. 4. 
 
 This curve possesses this property, that if the teeth are formed 
 

 la it. and the pinion b> turn. 
 
 wiB alwayt be in the strai;rhl line. a. b, tra 
 
 (Batty the aatn. 
 
 r. ntrr, that k at th» 
 
 pilrh rin-le mi:.. s« many e<]aal part* 
 
 intma - 
 
 • 
 
 fted U ■ vh line, a b, of the rack, an many times as 
 
 trically 
 
 indicated at o if, no that the pinion may ■ 
 
 they may 
 
 ■ 
 
 ■ 
 
 - 
 
 I B. 
 
 ■ 
 
 tooth, II, <>(" the 
 rack, should continue to impel it nnl * 
 
 .... 
 
 all th. ' :re. 
 
 To a rtino of tin ' 
 
 '.its, bf, 
 ne, a n, nnil | 
 ■ 
 
 «. at the same time, f..rm tbj 
 
 .lit line, m ». I 
 
 Ih nf the 
 
 the t. ••■th with 
 iriUv, which, ai 
 
 h cima, 
 tln in to ilri\. 
 
 i k at it- pitch i 
 
 ■ • 
 
 - 
 
 Lh nf the rail. ■ and to 
 
 then !«• in th- 
 linn, if Iron th.. i>. -int. L, tl 
 
 . 
 
 tat, l. If, tl 
 
 • 
 
 ]iitch line of the rack, as was aln:i. 
 ]4niim. 
 To ffa 
 
 c '<*, ami through tl • 
 
 i line, m !c, parallel to a r.. I 
 
 ■ 
 i j. k I, &«•., which an 
 
 - 
 . 
 . nd the side* of the ' 
 joined ' 
 
 ribod with a n uu Uiat 
 
 lad drawn. 
 ■ would be a ti 
 dotatnfaimg tin- runes in lb th, it i* 
 
 .-•I ..r tliiu h o 
 n nr template, by the 
 
 . 
 - 
 • 
 
 uith, ami, in i ir arc is 
 
 i radius 
 
 With thin 
 
 view the are should b the tooth, sn.l 
 
 I 
 'i an- f.r tin- tnie . 
 
 nee this arc I 
 point, r, l iual to 
 
 I. q, ami to be a tan, 
 o r, an! 
 
 . 
 
 ij afterwards i- 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 with the same radius, care being taken to keep the centres in the 
 line, a b. 
 
 An analogous operation will give the proportions of the are, 
 substituting the curve of the pinion teeth. 
 
 THE GEARING OF A WORM WITH A WORM-WHEEL. 
 Figures 5 and 6. — Plate XVIII. 
 
 207. This system of gear is constructed on tho same principles 
 as that of a rack and pinion, which method requires that, in the 
 first place, the worm and worm-wheel be supposed to be sectioned 
 by a plane passing through tho axis of the former, and at right 
 angles to that of the latter. The representation of this section 
 becomes analogous to the diagram, tig. 4 ; that is to say, tho pitch 
 circle, g c j, of the worm-wheel being given, and also the straight 
 pitch line, A B, of the worm tangential to this circle, and parallel 
 to the axis of the worm, the involute curve, c D, is sought for the 
 teeth of the wheel, and the cycloid, c k, for those of the worm. 
 The lengths of these curves are limited, as in the preceding exam- 
 ple, and when the whole is complete, an outline will be produced 
 similar to the tinted portions of fig. 6. It is in this manner that 
 the gearing of the worm and worm-wheel is made to depend upon 
 the same principles as that of a rack and pinion, and the same 
 method may be employed in construction in determining the outline 
 of the teeth, as we have shown. 
 
 To represent the worm and worm-wheel geometrically in exter- 
 nal elevation, instead of a section of the teeth alone, it is necessary 
 to know the diameter and pitch of the worm on the one hand, and 
 the thickness of the worm-wheel, fig. 5, on the other. 
 
 Let iu' a' be the distance of the pitch line, a b, from the axis, 
 M' n, of the worm, and a b the width of the wheel. When the 
 worm is single-threaded (177), the pitch of the helix is the same 
 as that of the teeth, and, therefore, the thickness of a tooth, added 
 to the width of an interval. In this case, each revolution of the 
 worm turns the wheel to the extent of one tooth, and this is the 
 arrangement represented in the figures. If the worm, however, 
 is double or triple-threaded, its helical pitch will bo correspond- 
 ingly two or three times the pitch of the teeth; and in such case, 
 each revolution will turn the wheel to the extent of two or three 
 teeth. 
 
 The worm-wheel being of a certain thickness, and requiring to 
 gear with the convolutions of the worm, must necessarily have its 
 teeth inclined to correspond with the obliquity of the worm-thread. 
 It is _ further to be observed, that the sides of the wheel-teeth 
 being simply tangential to the worm-thread, contact cannot, 
 rigorously speaking, take place in more than one point of each 
 tooth and convolution. This point constantly changes with the 
 motion, but always lies in the plane, o' m', of the section. 
 
 In delineating the convolutions of the worm-thread, helices 
 have to be drawn passing through the external corners, d, e, and 
 internal corners, /, g. We have repeated these points to the left- 
 hand side of fig. 6, where the required operations are fully indi- 
 cated, in connection with the projection, fig. 5, and in accordance 
 with the principles already explained (173). The corresponding 
 points in the two figs. (5 and 6) are distinguished by the same 
 letters and numbers. 
 
 208. For the representation, in external elevation, of the teeth 
 of tho worm-wheel, it is required to develop a portion of the 
 cylindrical surface generated by the revolution of the pitch-line, 
 
 A B, about the axis of the worm, and containing the portion, 
 A.iklm, for example, of the helix, described by the central point 
 of contact, A. To obtain this, make the line, e' a', fig. 7, equal to 
 the semi-circumference, a' m e 2 , rectified. At the point, e', erect 
 the perpendicular, c' e', and make it equal to c e, fig. G, or half 
 tho pitch, and join e' a', whereby will be obtained the actual 
 inclination of the worm-thread. On each side of the point, m, on 
 e' a', mark distances, m a' and m b', equal to mf a and m b, tig. 5, 
 and through these points draw parallels to c' e', and tie portion, 
 p q, of the enclosed line comprised within them, will serve to deter- 
 mine the width and inclination of the teeth of the worm-wheel. 
 Through tho points, ;>, r, draw p t and r s parallel to e' a', arid 
 mark otl* the distances, I s and s q, which are equal, on the pitch 
 circle of the wheel, fig. 6, from s to t and q, after having drawn 
 through the points, s, but only in faint pencil or dotted lines, tho 
 contours of the teeth as sectioned at f and g'. It is then sufficient 
 to repeat theso outlines through the points, t and q, limiting their 
 length by the same internal and external circles. 
 
 Finally, the edge view of the worm-wheel, fig. 5,. being the 
 lateral projection of the teeth, is determined by squaring across the 
 points, u, v, x, to «', t>\ x l , which give the interiors of the teeth : 
 and the points, u-, v", x", being squared over to u 3 , v 3 , x 3 , give tin ir 
 exterior edges. 
 
 Worm-wheels are sometimes constructed with the form of the 
 teeth concave, and concentric with the axis of the worm, with the 
 view of their being in contact with the convolutions ol the worm- 
 thread throughout a certain extent, in place of onJIJ Couching at 
 single points. 
 
 This arrangement, which requires a particular operation for its 
 construction, is generally adopted when great precision is required, 
 and when it is wished to avoid, as much as possible, any play 
 betw-een the teeth and the worm-thread during the transmission "I' 
 motion. 
 
 CYLINDRICAL OR SPUR GEARING. 
 
 PLATE XIX. 
 THE EXTERNAL DELINEATION OF TWO SFUR-WHEELS IN GKak. 
 
 Figure 4. 
 209. Spur-toothed wheels are such as have their teeth parallel, 
 and lying upon a cylindrical surface or web. When a couple of 
 such wheels are of unequal size, the smaller one is generally 
 called a pinion, and the larger one a Bpur-whee). Two wheels, 
 which are intended to gear together, cannot work satisfactorily in 
 concert, unless their radii or pitch circles are exactly proportional 
 
 to the number of teeth contained by each. Consequently, in 
 order to construct designs for couples of toothed wheels, it i» 
 necessary to know — tho number of teeth of each, and the radian 
 of one or other of then ; or the radii or diameters of both, and the 
 number of teeth of one; or the distance between their centres, and 
 the radius or number of teeth of one; or finally, the number <>i 
 revolutions of each in the same time, and the distance between 
 

 tSrir eeatrea. or lb* radios and numU-r of teeth ofoMof thesn. 
 la lb* rules and data at the rod . • f t hi. chapter, will be found the 
 .1. : ii. .. >. al problems involved in tbcee various cases. 
 
 lowing data, I -= 400, 
 
 dm* bring tba isapeetive radfl " f '" 
 . the number af 
 .•Main Ibe nnmbrr of . by tbo 
 
 ag proportions! furmuU : — 
 
 '. m 40. 
 Then describe the pitch circlca of the radii, A a and * c, and 
 
 ■btaining the pitch, or the central point of each I 
 • c name on b 
 
 i e<)nal porta, i -■ and, at 
 
 the sai 
 
 l c,aa a 
 ' o, and 
 roll round t. 
 
 . in rafcranea t" li^'. 1 ; and 
 
 ■ 
 
 •lla^nun. It 
 
 mil round the 
 . 
 
 b o, as 
 ! a por- 
 
 'urniny 
 | 
 
 .il tune 
 
 I 
 
 j 
 
 r ra.lhv 
 
 ■ 
 is intended alw.. 
 
 ..c teeth of the spur-wheel would only require to be 
 
 ' J, and those of the pinion, like the portion of 
 
 • 1 for the naif ..f distinction ; but generally, 
 
 - reasons, all epur gear is ao cooatructed ■ 
 
 ally, and equally well, whichever be the driver, and we 
 
 ',h of the pinion, so tint it may, in 
 
 - rf.irm that fui 
 
 i ;« a circle with the centre, &, of the radium 
 
 a i , taken aa a diameter ; and suppose that circle to n.ll round the 
 
 i point, a, at present in cob. 
 
 tact, will generate the epicycloid, a u which is the propai curve 
 
 to be . i ■ .. con- 
 
 . 
 the name manner round (he 
 i B D, and tl> - 
 
 > in the aame 
 
 : 
 
 ..rv, b/*, equal I 
 
 scribed with tl 
 iuit >h"rt n| ' .J circle 
 
 paaaage, as air. 
 
 cat, and 
 
 similar I 
 
 In !L< 
 
 - Dcceaaary ft ;. 
 
 . 
 : 
 g. "hi. h alalia, 
 
 \*ar. 
 
 ■ 
 - 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 same operations, modified to suit the different positions of the 
 parts with respect to each other. Thus the curve, B I., of the 
 pinion tooth, is generated by the rolling round the pitch circle, 
 G b H, of the circle described with the centre, o, and radius, o B, 
 equal to the half of b c, the radius of the pitch circle, d b e, of the 
 larger wheel. Tills is an application of the operations explained 
 in reference to fig. 3. The flanks, B a, or the sides of the teeth, 
 are obtained by simply drawing radii, or lines converging in the 
 point, e. 
 
 In the same manner, the curve, b f, of the teeth of the large 
 wheel, is generated by rolling along the interior of its pitch circle, 
 b d e, a circle described from the centre, o', and radius, B o', equal 
 to half the radius, B A, of the pitch circle, G B H, of the pinion. 
 These curves being obtained, the outlines of the teeth are com- 
 pleted in the manlier explained in reference to fig. 4. It may, 
 however, be observed that, in the diagram, fig. 5, though the teeth 
 might be cut off by a circle passing through the point, / and 
 described with the centre, a, they are prolonged beyond that, so 
 that the teeth remain longer in contact, and a greater number of 
 teeth are, consequently, engaged at one time, allowing the strain 
 to be distributed over a greater number of points. It is the fact 
 of the curvatures of the two lines of. teeth being in the same direc- 
 tion, which admits of a greater number of teeth being engaged at 
 once, without that increase of friction, and other disadvantages, 
 which would result from such an arrangement with wheels like 
 fig. 4. 
 
 THE PRACTICAL DELINEATION OF A COUPLE OF SFUK-WHEELS. 
 Plate XX. 
 
 213. In the cases treated of in the preceding sections, which 
 comprehend the general principles involved in rack and wheel 
 gearing, we have assumed that the rack and pinion, or pinion and 
 spur-wheel, are constructed of the same material, and in this case 
 the thickness of the teeth is the same in any two working together. 
 It very often happens, however, in actual construction, that one 
 of the,two has wooden, and the other cast-iron teeth, or of other 
 dissimilar material. When this is the case, the thickness of the 
 one description must necessarily be greater than that of the other, 
 to compensate for the difference in, the strength of the materials. 
 The pitch, however, will still be the same for both wheels; for, 
 since the intervals on one wheel correspond to the teeth on the 
 other, a tooth and an interval on one must obviously be equal to 
 an interval and a tooth on the other. A couple of wheels of this 
 description are represented in plan and elevation, in figs. 1 and '2. 
 
 We here assume the wheels to be in the ratio to one another of 
 3:4; whence, giving the pinion 36 teeth, the spur-wheel must 
 have 48. After dividing the pitch circle of the spur-wheel, drawn 
 with the radius, c b, into 96 equal parts, the points of division 
 representing the centres of the teeth and of the intervals, and the 
 pitch circle of the pinion drawn with the radius, a b, likewise, into 
 72 equal parts — with the centres, o and o', describe the circles 
 • wii'ch generate the epicyeloidal curves, e f and B l. Take 4y of 
 the pitch, b c, for the thickness of the wooden tooth, d e, and ,' T 
 for that of the cast-iron tooth, allowing the remaining Jy for the 
 play in working. Next draw a series of radii, to indicate the 
 
 Hanks of the teeth, both of the pinion and spur-wheel, and at the 
 point of their junction with the pitch circle, draw the curved por- 
 tion of each, with the aid of a small pattern or template, cut to 
 the curves, n l and c f; and, finally, limit the lengths of the teeth 
 and the depths of the hollows in the manner already pointed out, 
 in reference to Plate XIX. 
 
 As draughtsmen are generally satisfied with representing the 
 epicyeloidal curves by area of circles which almost coincide with 
 them, and nearly fulfil the same conditions, such arcs imi-l he 
 tangential to the radial sides of the teeth at their points of inter- 
 section with the pitch circle. They are determined in the follow- 
 ing manner: — Let fig. 10 represent one of the pinion teeth, drawn 
 to a larger scale. Through the point of contact, b, draw* a tan- 
 gent, B o, to the pitch circle; then bisect the chord, !i n, which 
 passes through the extremities of the curve, by a perpendicular, 
 which will cut the tangent, B o, in the point, v. This is the centre 
 of the arc, b m n, which very nearly coincides with the epicj - 
 curve. The same arc is repeated for each side of all the teeth "f 
 the pinion, the radius, b o, being preserved throughout. An 
 analogous operation determines the radius of the arc to be suliMi- 
 tuted for the curve in the teeth of the spur-wheel. 
 
 It is generally advisable to make wooden teeth about three- 
 fourths as long as the pitch, and east-iron teeth about two-thirds 
 as long. In no case, however, should the lengths of the teeth in 
 the two wheels geared together be less than those obtained by 
 calculation, and determined by the points,/,/ 1 , situated on the 
 circles described with the centres, o, o', by which the epicycloids 
 are generated. The ratio of the curved external portion, " m, of 
 the tooth to the flank, n p, is 4:5. In other words, the whole 
 height or length of the tooth bi-in lT divided into '.' equal parts, 4 of 
 these are to be taken for the length of the curved portion, and 5 
 for the rectilinear flanks. When the teeth are of cast-iron, the 
 thickness, p q, of the web should be equal to the thickness, r s, of 
 the tooth. Sometimes it is made only ,'ths of this; but in that 
 case it is strengthened by a feather on the interior. 
 
 For wooden-toothed wheels, since it is necessary that the tenon, 
 t, of the tooth be firmly secured, the web is made of a thickness, 
 p q, often double that of the tooth. The tenons of the teeth must 
 be adjusted very carefully and accurately in the web. They are 
 made with a slight taper, and are secured on the interior of the 
 wch either by iron pegs, as at u, passing through them, or bj a 
 series of wooden keys or wedges, r, driven in between tin 
 forming strong dove-tail joints. These two methods of fixing the 
 teeth are shown at different parts on fig. 1. and more in detail in 
 fig. 7. There is a third modification, which also possesses some 
 advantages. We have represented it at T, fig. 3, whence it will 
 he seen that it consists in forming the teeth with a couple of 
 shoulders, :. which allow of the tenons. I, being made much 
 stronger, and also take away thereby some of the weight of metal, 
 two objects of great importance. 
 
 The width, x y, of the teoth is equal to two or three times their 
 pitch. In wheels entirely of cast-iron, the web is of the same 
 width as the teeth: but it is much broader when the teeth a y of 
 wood, for it requires to be mortised, to receive the tenons of the 
 teeth, and should have a width equal to that of the teeth, plus an 
 amount equal to once and a half or twice their thickness. We 
 

 • in »Wb of moderate - 
 the boat, r\ by arm*, v. The t. 
 tb**e inn vai 
 
 In the preaeot raae uV vanna; thia tp. 
 
 other uaaiina. being more particu'.. 
 number of !•« :h are d 'list the 
 
 concave quarter -round moul. 
 
 cated in fitf*. 5 and 6, which rcorc- 
 
 - are united : ■',(• inn 
 
 ! 
 
 •till, an 
 
 feathers being united, M it were, to the body uf tin- ami without 
 any additions; 
 In all caar*. 
 
 radnally 
 
 . rdly . 
 
 '.•■, 3 — 1 — .">. 00 fig. I. W 
 
 -. that at the upper part of • 
 I* parallel t«i tli«- arm, or (be ami it, 
 
 ■■r a a', 
 
 mat it may I*- pr oj ec te d in d a whh- 
 
 the am- as in the ob nted in 
 
 In ll 
 
 ■ 
 
 THE DELINEATION AND CONSTRUCTION OF WOODEN 
 PATTERNS FOB TOOTHED WHEELS 
 
 1'I.ATK XXI. 
 
 •want iai i 
 
 mon the 
 • ii pai- 
 
 •h.n .if the |. 
 
 ■ of ill.- 
 
 |*rta — an that 
 
 mat make allowance, nut only (or lb 
 
 away l.y turning and finishing afterward*. M 
 
 I Zeroed with a 
 
 I difficult — «m.. 
 
 actual luam • 
 
 mind tin ~- various c -n-M. rati on*, we may proce e d 
 
 '«. »u Ii aa are 
 \ \ 
 
 r*TTXJi« oi 
 
 cipal pii 
 
 I ;ort» in succ< -- 
 
 - 
 in thiil. 
 
 built u|i like brickwork, the 
 
 r. 
 quite dry. is put into a lathe, ami there i 
 
 | arallcl, and tie 
 detenu .mi upon a 
 
 ai-tual - a 
 
 At t!. 
 
 or naDed on. i 
 
 BOM, 
 
 Tin' l>oi« i- i , 
 
 . I when the «' 
 
 ; .irati ly to ti'. 
 
 ncaa oi '■!' the arm. 
 
 lu of a 
 
 I 
 of that part of the arm which i» afterward* the only part 
 
BOOK OP INDUSTRIAL DESIGN. 
 
 in the casting, but also comprising, above and beyond this, the 
 projections by which, in the pattern, it is attached to the boss on 
 the one hand, and to the crown on the other. The extremity, a, 
 of the boss end of the arm is in the form of a sector, correspond- 
 ing to a sixth part of the circle of the boss, the pinion having six 
 arms; the lateral facets, /), of this part are grooved out, to receive 
 small tongue-pieces, or keys, c, fig. 1, so as to form a strong joint 
 when glued together. The other extremity, d, of the arm is cut 
 circularly, to the form of the crown, or web, into which it is fitted, 
 penetrating to a slight extent, tho crown being previously formed 
 with a socket to receive it. 
 
 Next, the feathers have to be attached to the body, c, of the 
 arm. These feathers, B, are each cut out in separate pieces, to . 
 (he shape indicated in fig. 5 : they have supplementary projec- 
 tions, e and f, at their opposite extremities, whereby they are fixed 
 into the crown and boss. When all these feathers are in their 
 place, and the arms glued into the crown, the two portions, D, d, 
 of the boss are fixed to them, the grooves for the reception of the 
 ends of the feathers being glued, as well as the other parts, to 
 give greater solidity. Finally, the boss is surmounted by the 
 conical projecting pieces, f, f, which serve to produce in the mould 
 the cavities, or sockets, which retain the loam core in position, the 
 core being provided to produce the eye of the wheel, into which 
 the shaft is fitted. 
 
 To give compactness and strength to the whole, a bolt, G, is 
 passed through the centre; and this method of securing permits 
 of the core projections, f, f, being changed for larger or smaller 
 ones, if desired, without having to pull the entire wheel to pieces. 
 If, to add to the elegance of the shape of the wheel, it is wished to 
 ornament the arms with mouldings, as at i, these are applied at 
 the angles of junction of the feathers with the body of the arm. 
 These are simply glued or nailed on. The sectional view, fig. 6, 
 shows the form and position of these mouldings. 
 
 It is to be observed that, in wheels of a moderate size, when 
 oast-iron teeth are to work on casHron, they are at once cast to 
 the exact shape, and the pattern is constructed accordingly ; but 
 it is almost always indispensable, where cast-iron and wooden 
 teeth have to work together, to finish and reduce the former after 
 being cast ; and the projections, B, on the pattern answering to 
 them, must consequently be made of larger proportions every way, 
 to provide for the quantity of metal taken away in the finishing 
 process. 
 
 PATTERN OF THE WOODEN-TOOTHED STOR-WHEEL. 
 
 216. Figs. 7, 8, and 9 represent, in elevation, plan, and vertical 
 section, the wooden pattern of the spur-wheel, which gears with 
 the pinion just described. It consists, like that wheel, of the 
 crown or web, the boss, and the arms ; and these various parts, 
 which are designated by letters corresponding to those employed 
 in the preceding example, are constructed exactly in the same 
 manner. 
 
 There is, however, an essential difference in the exterior of the 
 crown : in place of this carrying the projections, B, cut to the 
 shape of the teeth, and such as will actually be produced on the 
 casting, it has other projections, b', of a simpler form, intended to 
 produce in the mould the sockets for receiving the core-pieces 
 
 which form the mortises in the casting, to receive the tenons of 
 the wooden teeth. These projections are let into the crown, or 
 simply applied thereto, and fixed by nails, as at /. or by screws, as 
 
 at m, the latter method being preferable, as it has the advantago 
 
 of permitting the number of teeth to be changed without injury to 
 themselves or to the crown. In the Wooden pattern, the length 
 of the projections, B', is carried to the edge of the face of the 
 crown, on that side which descends into the lower half of the 
 mould-frame, to allow of the more accurate adjustment of the coro- 
 pieces, and also to facilitate the recovery of the pattern from the 
 mould. These core-pieces, however, are so formed as to make the 
 mortises no wider than is necessary, and to leave a sufficient thick- 
 ness of metal for the strength of the crown, as already pointed out 
 in reference to Plato XX. 
 
 CORE-MOULDS. 
 
 217. The core-pieces for the mortises should not only he placed 
 at equal distances apart throughout the circumference of the crown, 
 but they must all also be of precisely the same form and dimen- 
 sions throughout, so that the mortises may he perfectly equal. 
 With this view, a wooden core-box or mould is made ; and there 
 are several methods of doing this. Thus, fig. 10 represents a thro 
 view, and fig. 11 a horizontal section, through the line 3 — 1 in 
 fig. 10, of one form of core-mould, consisting of a single piece. Tho 
 portion, n, of the cavity corresponds to the projecting core-piece, 
 b', outside the crown, and the portion marked n,v tho mortise, or 
 hollow socket, in the crown : this last has the same section as the 
 crown in the width of the cut-out part. The moulder fills tho 
 cavity of the core-mould with loam, previously prepared, and after 
 pressing it well in, levels it oft' with a straight-edged doctor or 
 scraper; he finally inverts the mould, thus releasing the core com- 
 plete. The operation is repeated as many times as there are teeth ; 
 and when the cores are all dry. they are placed with "Teat care in 
 the mould, their supplementary projections, b', being let into the 
 sockets formed to receive them— thereby insuring the accuracy of 
 their adjustment. 
 
 Fios. 12, 13, and 14, show another construction of wooden core- 
 mould, formed in two separate pieces, h and i. These have be- 
 tween them the cavity, n o, corresponding to that in the one just 
 described. In this last case, the surface of the core which re- 
 quires to be levelled oft" with a scraper, is only at one of the extre- 
 mities instead of on the lateral faces, as in the other, and the eon -> 
 are released by separating the two pieces, n, i. which are render! I 
 capable of accurate adjustment to each other by means of marking. 
 pins, k. 
 
 To return to the wheel itself: when it is of very large dimen- 
 sions, the blocks, P, of the boss are secured together by two or 
 more bolts, c;, in place of one. 
 
 The mould for the wheel is in two pieces, the lower frame, or 
 "drag," being let into the ground in the moulding shop; the upper 
 frame or top part, is moveable, and it will be obvious that very 
 great care is required to lift this oil' the pattern, so as not to injure 
 the regularity and sharpness of the impression; and for this pur- 
 pose, sufficient "draw" or taper must he given to the various parts, 
 as the crown, the boss, and the feathers on the arms, as already 
 pointed out. 
 
' 
 
 
 two arrvw-atii; 
 
 or bnua, «ro countersunk into 
 
 >,Tnmis and to 
 ■ 
 
 : plana, made fur ui'tual 
 
 ■ 
 
 .:> PI VCT1CAL DATA. 
 
 IHISG. 
 
 i fundamental rale, thai 
 
 r luii-t 
 
 tofl 
 
 • 
 It follows from ilii- a the radii of 
 
 tha ii iimlxr of !<i Hi of one of 
 In r, and reciprocally. 
 al tin- Dumber of teeth of a wheel of 
 U)o nuliu-s R ; and n : ■ Dumber "l ii . lli of :i wheel 
 
 of the ■ re me direct proportionals, i : n :: ■ : r; 
 
 i, alany time, ascertain anyone of the terms when 
 ■vn. . 
 / .■!«• "I" :i s|.ur- 
 
 . i the Dumber of teeth on ii 76, what should 
 ■ h "ii a pinion gearing with it, 
 
 _ 
 
 : : 19 : 9 . whence 
 
 75 x 8 
 
 ia 
 
 
 lively, be the somber 
 of the teeth • ■!" a ■par-wheel and pinion, and 19 inches th 
 «>f the pitch circle «f the Former, the mdma of the piteh • 
 •Ji« latu-r maj be found by meana of the proportion — 
 70 : SO :: i- : r; whence, 
 
 W x 12 o . , 
 r = — — — = 8 n 
 76 
 
 ii the Dnmbera of revolutions 
 
 ir-wheel and pinlbn in gear with each other, 
 
 are In U -. radii, or nnn> 
 
 I 
 
 1 . ■ ni tl»- velocity of rol 
 
 ■ which eqnala r, 
 
 and the nomber of the teeth n, and patting i the relo- 
 
 il whieh the pitch drela radk 
 
 R .11! 
 
 V : , :: r: R, 
 and 
 
 V : i : 
 
 1 ramie, as hi the format 
 
 when the tlir>-<- others are known. 
 
 I I \ | ulii.-h 
 
 - 
 a lth il, and i 
 
 D 
 
 . 
 
 
 
 
 I circle radius of the pinion. 
 
 a a pinion at the riIo 
 tinute, uliat hlinul.i he the nomber 
 of the 
 
 : n ; 
 
 ■ 
 
 78 
 
 = 20, 
 
 thr namber of teeth the pinion mast ; 
 
 ii oom- 
 mnnieation with one another by eordi 
 
 s i known 
 
 is the distance apart of their centres, the namber of teeth which 
 ry, orthe nber of their revolutions In Ii 
 
 time. In Ilii- • 
 
 ili.- .—mil of their revolutions, 
 nnd between their r< ■ and revolutions; and, on the 
 
 other hand* a direct proportion between the i 
 the — < j it i of tin- teeth on I •. . t Ii whoels, radii, oi 
 
 tin- nomber of teeth ol 
 
 ■ ■ apart u|" lli. 
 
 pinion of the respective radii, K. r, and Dumber of teeth, v 
 
 \ t the following 
 
 inverse proportion, 
 
 D: V + t::R: V; 
 
 Ii : N - - :: N : It. 
 / • / Lot 40 inches l«- tha distsne* between iii» 
 
 . »f a apur-wheel and pinion, the former of which i- t" make 
 
 ■j-2 revolutions per minute to the others t.'»J. what should be thou 
 ■ radii f 
 We Ii... i 
 
 >:: R:S9; 
 whence, 
 
 and 
 
 win I , 
 
 ,: MM often, 
 
 
 •22 + 15 5 
 
 When the pitch eirehj radios of one of tin 
 
 for the other radini bj 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 of the second proportion, for it is sufficient to subtract the one 
 found from the sum of both; thus, 
 
 45 — 26-4 =18-6; or, 
 45 — 18-6 = 264. 
 Second Example. — The distance, d, between the two centres 
 being known =45 inches, and one wheel carrying 31 teeth and 
 the other 44, what are their respective radii ? 
 We have here, in the first place, 
 
 45 : 31 + 44 :: R : 44; 
 
 whence, 
 
 and 
 
 wdience, 
 
 „ 45 x 44 
 R=— — - = 264, 
 31 + 44 ' 
 
 45 : 31 + 44 :: r : 31; 
 
 45 x 31 
 31 + 44 
 
 186, 
 
 or, more simply, 
 
 r = 45 — 26-4 = 18-6 inches. 
 
 In like manner, the respective radii of a spur-wheel and pinion, 
 to gear together, may be determined geometrically, when the dis- 
 
 tance between their centres is known, sa well as the numbers of 
 revolutions of each, by the following rule: — 
 
 Divide the distance into as many equal parts as there are of any 
 measure contained exactly in the sum of the velocities, such mea- 
 sure being also contained exactly any number of times in each of 
 the velocities alone. Then, for the pinion radius, take as many of 
 these measures as are contained in the lesser velocity, and for the 
 radius of the spur-wheel, tbje remainder of them. 
 
 Example. — Let 16 inches be the distanco between the centres 
 of a spur-wheel and pinion which make 6 and 4 revolutions re- 
 spectively, or any equi-multiples or equi-submultiples of these, as 
 12 and 8, or 3 and 2. Divide the distance into 10 equal parts, 
 and take 4 of these for the pinion radius, and 6 for the spur-wheel 
 radius. 
 
 This rule is of very simple application when the ratios of tho 
 numbers of revolutions are whole numbers, such as 1 : 4, or 2 : 5 ; 
 for all that is necessary is to add the two together, to divide the 
 distance between the centres to correspond, and to take the re- 
 spective numbers of measures for each wheel. 
 
 The following table will be of great assistance in the solution 
 of various problems connected with systems of gearing, when tho 
 number of teeth, the pitch, or the radius are known. 
 
 TABLE FOR CALCULATING THE NUMBERS OF TEETH AND DIAMETERS OF SPUR GEAR, FROM THE FITrH, OR VICE VERSA. 
 
 Namber. 
 
 Coefficient. 
 
 Number. 
 
 Coefficient. 
 
 Number. 
 
 Coefficient. ' 
 
 Nu.be, 
 
 Coefficient. 
 
 Number. 
 
 Coefficient 
 
 10 
 
 3- 183 
 
 39 
 
 12-414 
 
 68 
 
 21-644 
 
 97 
 
 30-875 
 
 126 
 
 40- 106 
 
 11 
 
 3501 
 
 40 
 
 12-732 
 
 69 
 
 21-963 
 
 98 * 
 
 31193 
 
 127 
 
 40-424 
 
 12 
 
 3-820 
 
 41 
 
 13-050 
 
 70 
 
 22-281 
 
 99 
 
 31-512 
 
 128 
 
 40-742 
 
 13 
 
 4-138 
 
 42 
 
 13-369 
 
 71 
 
 22-599 
 
 100 
 
 31-830 
 
 129 
 
 41-061 
 
 14 
 
 4-456 
 
 43 
 
 13-687 
 
 72 
 
 22-917 
 
 101 
 
 32-148 
 
 130 
 
 41-379 
 
 15 
 
 4-774 
 
 44 
 
 14-005 
 
 73 
 
 23-236 
 
 102 
 
 32-467 
 
 . 131 
 
 41-697 
 
 16 
 
 5-093 
 
 45 
 
 14-323 
 
 74 
 
 23-554 
 
 103 
 
 32-785 
 
 132 
 
 12-016 
 
 17 
 
 5-111 
 
 46 
 
 14-642 
 
 75 
 
 23-872 
 
 104 
 
 33-103 
 
 133 
 
 42-334 
 
 18 
 
 5-729 
 
 47 
 
 14-960 
 
 76 
 
 24191 
 
 105 
 
 33-421 
 
 134 
 
 42-652 
 
 19 
 
 6-048 
 
 48 
 
 15-278 
 
 77 
 
 24-509 
 
 106 
 
 33-7411 
 
 135 
 
 42-970 
 
 20 
 
 6-366 
 
 49 
 
 15-597 
 
 78 
 
 24-827 
 
 107 
 
 34058 
 
 136 
 
 43289 
 
 21 
 
 6-684 
 
 50 
 
 15-915 
 
 79 
 
 25146 
 
 108 
 
 34-376 
 
 137 
 
 43-607 
 
 22 
 
 7-002 
 
 51 
 
 16-233 
 
 80 
 
 25-464 
 
 10!' 
 
 34-695 
 
 138 
 
 43-925 
 
 23 
 
 7-321 
 
 52 
 
 16-552 
 
 81 
 
 25-782 
 
 110 
 
 35-013 
 
 139 
 
 44214 . 
 
 24 
 
 7-639 
 
 53 
 
 16-870 
 
 82 
 
 26-100 
 
 111 
 
 35331 
 
 140 
 
 44-562 
 
 25 
 
 7-957 
 
 54 
 
 17-188 
 
 83 
 
 26-419 
 
 112 
 
 35-650 
 
 141 
 
 44880 
 
 26 
 
 8-276 
 
 55 
 
 17-506 
 
 84 
 
 26-737 
 
 113 
 
 35968 
 
 142 
 
 45- 199 
 
 27 
 
 8-594 
 
 56 
 
 17-825 
 
 85 
 
 27-055 
 
 114 
 
 36-286 
 
 143 
 
 45-517 
 
 28 
 
 8-912 
 
 57 
 
 18143 
 
 86 
 
 27-374 
 
 115 
 
 36-604 
 
 1 14 
 
 45835 
 
 29 
 
 9231 
 
 58 
 
 18-461 
 
 87 
 
 27-692 
 
 116 
 
 36-923 
 
 145 
 
 46-153 
 
 30 
 
 9-549 
 
 59 
 
 18-780 
 
 88 
 
 28-010 
 
 117 
 
 37-241 
 
 146 
 
 46-472 
 
 31 
 
 9-867 
 
 60 
 
 19098 
 
 89 
 
 28-329 
 
 118 
 
 37-559 
 
 147 
 
 46-790 
 
 32 
 
 10186 
 
 61 
 
 19-416 
 
 90 
 
 28-647 
 
 119 
 
 37-878 
 
 148 
 
 47-108 
 
 33 
 
 10-504 
 
 62 
 
 19-734 
 
 91 
 
 28-965 
 
 120 
 
 38196 
 
 149 
 
 47-427 
 
 34 
 
 10-822 
 
 63 
 
 20-053 
 
 92 
 
 29-284 
 
 121 
 
 38-514 
 
 150 
 
 47-745 
 
 35 
 
 11-140 
 
 64 
 
 20-371 
 
 93 
 
 29-602 
 
 122 
 
 38-833 
 
 151 
 
 48-063 
 
 36 
 
 11-459 
 
 65 
 
 20-689 
 
 94 
 
 29-920 
 
 123 
 
 39151 
 
 152 
 
 18-382 
 
 37 
 
 11-777 
 
 66 
 
 21-008 
 
 95 
 
 30-238 
 
 124 
 
 39-469 
 
 153 
 
 48-700 
 
 38 
 
 12095 
 
 67 
 
 21-326 
 
 96 
 
 30-557 
 
 125 
 
 39788 
 
 154 
 
 49020 
 
 RULES CONNECTED WITH THE PRECEDING TABLE. 
 
 I. To find the diameter of a spur-wheel, when the number and 
 pitch of the teeth are known. 
 
 M 'fiply the coefficient in the table, corresponding to the number yf 
 teeth, by the given pitch in feet, inches, metres, or other measures, and the 
 product u-ill be the diameter in feet, inches, or metres, to correspond. 
 

 teeth, hartrtg a filch of I* inches! 
 
 Oppo.it* lb* number 60, ia lb* table, w* find the caa ffirl n't, 
 50-053. Then— 
 
 20fi53 x 1 i - 30-08 inches 
 the diameter of the spur-wheel. 
 
 What an the diameter* of two -.heels, of 41 
 :*eth respectively, their pilch (gang j iocs ! 
 On the one band, we have 
 
 -.:, = 9-7875 inch**, 
 ■ the ilaiaiilii of the pinion of 41 t« ih ; and on the other, 
 : 358 inches, 
 the diameter of the spar-wheel of 15" 
 
 II. To find ' . spur-wheel, when the diameter and 
 
 . are known. 
 Ihnde tie firm diameter ey (Jke aorju x nt in (he faaJe um — su ms ' 
 ny to tie number tf tie Met*, and tie quatitmt via be tie pitch 
 tvmgkL 
 
 I ! Wmm u the pilch of a wheel of 30-08 inrbee 
 
 diameter, and of 63 U-eth ! 
 
 30-08 : 30-053 = 15 inch, 
 the pitch n-]u:n-<l. 
 
 SeetmJ Example. — It is required to construct a »pur-w heel, of 
 136 teeth, to work with the preceding, what must be its diameter? 
 
 
 
 1-5 x 40-106 = 60-159 ir 
 :.' 
 
 I 'I. T-. Bad tin- t. hen the pitch 
 
 and diameter are known. 
 
 lie giien diameter by tie piirn juA. tie number in tie 
 
 Isj •> ogrramaeJiaj /•■ tm fmttmwt iri.. i« : : - mtmhtr e/lsjn • ._- ; .'. 
 
 If ll I in the table, take the number earreapond- 
 
 •>at nearcct V- 
 /Vsf Examjle. — "Hie di»n is, 30-08 inches, 
 
 and the pilch of the teeth u 1'5 inch, what number of teeth should 
 
 30-8 : 15= I 
 -:">nd* to 63 t. 
 Se e tm J Example. — What should be the number of teeth of a 
 pinion, the diameter of »l„. h u> 875 millimetres, and » 
 intended to gear with a rack. :»h u 35 millimetres ■ 
 
 35. 
 The number most nearly corresponding to this is 110, the 
 to the pinion. 
 
 r.LocJTT or vntLi 
 
 *■ what i« the anjrvT me abaft 
 
 of * fly-wheel •. r , iitud velocity 
 
 rule :— 
 
 m by tie number of* reredutjemt per 
 
 rnd tie prod,. - ,porr pasted through n lie 
 
 tame time ; and tiit product bring divided by 60, via gim tie tab. 
 
 - nreumferenre per tertmd. 
 
 •fiameter of a wheel be 4 feet, and the 
 
 number of its ret olutioos par minute 20, what u the v . 
 th» I M IHfl n rx*»r ! 
 
 The circumference of the wheel = 4 x 11416= 1*5664; 
 U.. I 
 
 MM x 20 = 251 328 fret, 
 the apace paaaed through per minute by any poial in the lin — 
 f ervnee ; and 
 
 60 
 
 = 4% 
 
 ■ 
 
 ..: the eirenmference ia known, the angnlai 
 or the number of turns in a given lime, may be a-ocr- 
 tamed by the following rale :— 
 
 Diride tie eire^tm/errmtial Telocity by tit eireutn/eremee, and dm 
 quotient trifl be He angular teiocity, or number rf read uIhm in lit 
 giren time. 
 
 In the preceding rase, 4-3 feet being the circumferential 
 per second, and 4 feet the diameter, we hare 
 
 — -il-=33t, 
 
 4 X 3U16 * 
 
 the angular velocity per second ; and 
 
 •334 x 60 = 90, 
 ■ linute. 
 In practice, it is easy to asce-tan. f a wheel, the 
 
 motion of which is uniform. Y - marked 
 
 with chalk on the rim of the •• w often 
 
 in a .-inn time; then 
 this nui by the eircur 
 
 described by the marked point, and the product ditided by the 
 duration of the observation expressed in seconds. The result 
 will be :' the circumference* of the wheel. 
 
 I have a AS rent ti 
 to its distance from the centre of motion. 
 Example. — A wheel, 2 feet in diameter, baring, atc o id ng to 
 obeu intion. made 75 revolutions per minute, what b its cirenm- 
 ferential velocity (per second) ! 
 
 ■ 3 11x8 
 
 \ 
 
 
 
 circumferential velocity of the wheel. 
 
 - «-ally. when the circumferential velocity (per secood) is 
 known, the ni ■ .ns per minute is found by means 
 
 ntda — 
 
 V x W 
 N ". ( :i • 1' • 
 or, w ith the data of the preceding esse, 
 
 \ itions per minute. 
 
 . several spar-wheels or pulleys are placed on the same 
 shaft, the cin- ' 
 
 in the name m. 
 the respective rircumfcreriees, and dividing lb* product* by 60. 
 
 Example. — Three wheels on on* 
 
 shaft ; the radios of the pulley, a, is equal to 1 1 feet ; that of tho 
 pulley. I that of the pulley. vod the - 
 
 shaft makes 13 turns par minute, — what is the 
 velocity of these three pulleys ! 
 
BOOK OF INDUSTRIAL DESIGN 
 
 For the pulley, a, we have — 
 
 6-28 x 11 x 12 
 
 V = 
 
 for the pulley, 
 
 60 
 
 6-28 x 1-6 x 12 
 60 
 
 1-38 feet per minute ; 
 
 = 2 feet ; 
 
 arid for the pulley, c — 
 
 628 x 215 x 12 
 
 = 2-7 feet. 
 
 DIMENSIONS OF GEARING. 
 
 220. In designing tooth-gearing of all descriptions, it is neces- 
 sary to determine — first, the strength and dimensions of the teeth ; 
 second, the dimensions of the weh which carries the teeth ; and, 
 third, the dimensions of the arms. 
 
 THICKNESS OF THE TEETH. 
 
 221. The resistance opposed to the motion of the wheel or the 
 load, may be considered as a force applied to the crown, to pre- 
 vent its turning, and the power, during its greater strain, as applied 
 to the extremities of the teeth. The teeth then should be con- 
 sidered as solids fixed at one end, and loaded at the other ; and 
 the equation of equilibrium for thenj is — 
 
 P x l = ix i 1 xjc; 
 in which formula, P signifies the pressure in kilogrammes at the 
 extremity of the tooth ; h, the amount of projection of the teeth 
 from the web in centimetres ; A', a numerical coefficient ; t, the thick- 
 ness of the teeth in centimetres ; w, their width in centimetres. 
 
 In this formula, the numerical coefficient, A", which is calculated 
 with reference to the motion of toothed gearing, varies with the 
 material of which the teeth are constructed. 
 
 From Tredgold's experiments with well-constructed cast-iron 
 wheels, this coefficient has been calculated to be 25 for that 
 metal ; and adopting it, the preceding formula will then become 
 
 P xl = 25 xl' x »; 
 whence, 
 
 _ 25 x P to 
 h ' 
 a lormula in which three dimensions are variable. 
 
 The following ratios usually exist between these quantities : — 
 
 w varies between 3 t and 8 t. 
 
 h = l-it to 15 t. 
 
 Let, then, w = bt, and k = 1'2 I, so that, substituting these values 
 
 in the equation, it becomes — 
 
 P = 
 
 25 x 5 x t x( 
 1-2 x t 
 
 = 104- x C; 
 
 whence, 
 
 lot 
 
 and I = -098 \Tp 
 
 11 tne above ratio between the thickness, I, and width, w, be 
 adopted for all proportions ; for low pressures or small loads, we 
 shall have teeth much too thin and small ; and for high pres- 
 sures, on the other hand, the defects of too great thickness and 
 
 pitch. To retain, then, the thicknesses within convenient limits, it 
 is well to vary the ratio of t to w, according to the pressures; and 
 in order that the pitch may not be too great, the width of the teeth 
 is determined at the outset, according to the pressure or load 
 which they have to sustain, in the following manner : — 
 
 I. 
 
 For 100 to 
 
 200 lb., 
 
 make w = 3 t; when 
 
 = 
 
 1361 I' 
 
 II. 
 
 " 200 
 
 300 
 
 " w = 3-5 t " 
 
 = 
 
 117 ♦'F 
 
 ni. 
 
 " 300 
 
 400 
 
 " w = 4 t " 
 
 = 
 
 no^F 
 
 IV. 
 
 400 
 
 500 
 
 " w = 45 1 " 
 
 = 
 
 104 1 P 
 
 v. 
 
 500 
 
 1,000 
 
 " w = 5 1 " 
 
 = 
 
 098 fF 
 
 VI. 
 
 " 1,000 
 
 1,500 
 
 " w = 55 t " 
 
 = 
 
 093 ^F 
 
 VII. 
 
 " 1,500 
 
 2,000 
 
 " w = 6 t " 
 
 ( = 
 
 089 VF 
 
 VIII. 
 
 " 2,000 
 
 3,000 
 
 " w = 6-5 I " 
 
 = 
 
 084 ^F 
 
 IX. 
 
 " 3,000 
 
 5,000 
 
 " w = 7 1 " 
 
 = 
 
 082 ♦'F 
 
 X. 
 
 " 5,000 and upwards 
 
 " w = 8 1 " 
 
 = 
 
 077 ♦'F 
 
 The height, or projection, h, should be comprised between 12 I 
 and 15 t, the latter applicable to low powers or loads, and the 
 former to high ones. 
 
 For teeth of wood, which are ordinarily mado of beech or elm, 
 the coefficient should be augmented by a tliird in each of the last 
 given formula, which become — 
 
 I. I = -1G8 /F making w = 3-0 I. 
 
 II. «=156VF 
 
 III. i = -147 VF" 
 
 IV. i = -139VF" 
 V. Z = -131VF 
 
 VI. t'=-124VF' 
 
 vii. t = -mVP~ 
 
 VIII. * = -112VF" 
 
 IX. t = -109 VW 
 
 X. t = -WA>/F 
 
 to = 3-5 (. 
 w = 4-0 (. 
 w = 4-5 L 
 w = 50 1. 
 w = bb t. 
 w = 6-0 t. 
 w = 6-5 I. 
 w = 7-0 I. 
 w = 80 t. 
 
 All these formulas aro constructed on the supposition that, 
 although there are generally several teeth in contact at tin- same 
 time, yet each should be capable of sustaining the whole strain as if 
 there were only one in contact, and they should be strong enough 
 to compensate for wear, and sustain shocks and irregularities in the 
 strain for a considerable length of time. 
 
 The pressure, P, on the teeth may be determined according to 
 the amount of power transmitted by the wheels per second at the 
 pitch circumference. 
 
 This pressure is obtained by di tiding (he strain to be transmitted, 
 expressed in kilogrammitre, by the velocity per second of the pitch 
 circumference. A kilogrammetre is a term corresponding to the 
 English expression, "one pound raised one foot high per minute." 
 A kilograminetro is equal to one kilogramme raised one metro 
 high per second : it is written shortly thus — k. m. 
 
 First Example. — A spur-wheel is intended to transmit a force 
 equal to a power acting at the pitch circumference of 500 kilo- 
 grammetres, at the rate of 2-09 m. per second, what pressure have 
 the teeth to sustain ! 
 

 
 BOO k ■ 
 
 
 tli» strain that each I without 
 
 risk of breakage, even after eooaiderahle use and ■ 
 
 SacattJ Example. — \ "nnamita 
 
 tea 86 n 
 
 minute, what i- 
 
 • i r. = 75 x 30 = 1500 kilugramm. I 
 and 
 
 V = 
 
 3 14 X a 
 60 
 
 . per second; 
 
 1000 
 
 = 573 kilo;-., 
 
 the preaaure on the tooth. 
 
 ri at Ite crmumferenee 
 
 * for tin- (••■•til mav !«• oalcn 
 
 rding to the material of which 
 
 hi tin- former of the last two examples, in which P = 239 
 
 iDMal of ttio tOOfh, If of Ctat-iroil, should be making 
 . .» I : 
 
 ' = •117 ♦ / 239 = 1-8 cent = 18 millitn. • 
 
 tample, when 1' = 573 kil., the t> 
 •Mil be, supposing tin- teeth t.. 1»- of l» ech, ud «• = 5/, 
 
 I = -131 » 673 = B'M c, or 32 3 millim. 
 
 w = 5 ■ 833 loi :, ml 
 
 / ■' 
 
 ■ 
 
 It of a spur-v. ,, of wlii.-li i- I 
 
 to detarmini — h of this 
 
 apOl w 
 
 In 1 
 
 7j= 1875 ki: 
 
 V 
 
 1q5 x 2. 
 
 
 
 i. ' 8 ™ 
 
 1' — = 2113 k,! 
 
 . a 6*5 1, the thickness of the tooth will be 
 
 ' = I Ml.., 
 
 and 
 
 u>- MO'SmOUm. 
 
 11 ' ' ir..n pioJon of a powerful maohhia 
 
 B. in .liamot.T, il ii li\.-.| OB I abaft Which should transmit 
 
 ■Unions 
 
 - tih nd ti.. ir .inn. 
 
 T5 = 15,000 kilogram. 
 4ii,| 
 
 . I ' 
 
 N par second. 
 
 Tbe pre*- 'h i»— 
 
 P 
 
 1 1 inking te = 6l; we bars, for the tlii. Liuu of the 
 i,n, 
 
 l = -077 4'ti333 = 613 */«. 
 and • v = B 
 
 For a pinion of tin ted, jhq 
 
 ■ was made 75 millim., and the width US nullim. 
 
 . 
 •par-wheel teeth, me asur ed on tin- pitch chvumforeoee, rompriaea 
 the tlii.-kn.— -, I, of tin- tooth, and tin- width of (ha int.nal, whi.h 
 
 i bj oin.ti -mli ; 
 -If. • 
 
 In tin- 1st, p — 31 x 18 = 378 "/. 
 
 3.1 p = 2 1 x 37 = 777 */_. 
 
 ■llli •• = 2-1 x 61-3 = 128-5 ■/«, 
 
 When tin- spur-wl* 
 
 ii, 1 of il,,- preceding examplea, it wil 
 with a pinion, bsring eesf-iron teeth, which shook) !><• of about 
 Ihree-fourtha tin- Ihlrilmnea of tin- a 
 )iit.-li will Ik- equal to • 
 
 / + -75/ + -1 i = 1 + -85 r = 1 
 ,n this example, wa thoukj hsvi 
 
 p = 323 X l-85 = 5'.»8-/_ 
 After this i- ■ I li.-ii tin- pHofa ;. wlii.li, 
 
 as has aln on the 
 
 pitch drclea of nny two wbeola woridng togatbar, the Dumber of 
 tooth of one of the wheel* ma** be obtained bj tl»- following 
 formula — 
 
 , of tin. spur. win .1 ; U. tho 
 
 i the pitch circle ; and /'. the pitch, meaaured on ii. - 
 
 / / What i» tin- nni - D .1 spiir-wlii-i-l 
 
 of two metres diameter, ami the pit.li of wh 
 
 Ili-r. — 
 
 14 X 1 
 
 N= ■.,,.,. 
 
 It will be easily undent I. thai the faction ariaing fr..m the 
 
 D DlUBl I 
 
 tooth. I fore, where I 
 
 must be slightly iocn I 
 
 deration, (he pitch becomea 
 
 P = N — «»■, 
 
 . - m. 
 
 S / ' I rat) ,'■ .1 to dl i. nninr tin- mi' 
 
 w I. ii t. .id t-. i»- BarnV .1 l.y a spnr-wheal of two mi 
 
 the pitch b 
 
 II. n, 
 
 I I ■ | 
 
 105. 
 
BOOK. OF INDUSTRIAL DESIGN. 
 
 When a spur-wheel is to have wooden teeth, it is necessary 
 tnat the nuiujjer of these be some multiple of the number of anus 
 of the wheel, in, order that they may be conveniently attached to 
 the web ; thus, in the present example, if the wheel is to have 
 6 arms, the number of teeth must be 102 or 108, to be divisible 
 bv that number; and if the former be adopted instead of _105, the 
 pitch will be slightly augmented in consequence. 
 
 To obviate the necessity of making long and tedious calcula- 
 tions, .a table is subjoined, showing the thickness and pitch of 
 teeth of spur-wheels, in which is adopted the coefficient "105 of 
 M. Morin, which makes the formula, 
 
 for cast-iron teeth, and 
 
 t — -145 VT 
 for wooden teeth : the width being constantly equal to nearly 4'5 
 the thickness. 
 
 Table of the Pitch and Thickness of Spur Teeth for different 
 Pressures. 
 
 
 Of Cast-iron. 
 
 Of Wood. 
 
 Kilogrammes. 
 
 Thickness of 
 
 Teelh 111 
 Millimetres. 
 
 Pitch in 
 Millimetres. 
 
 Thickness of 
 
 Teeth in 
 Millimetres. 
 
 Pitch in 
 Millimetres. 
 
 * 
 
 
 
 
 
 5 
 
 23 
 
 4-9 
 
 32 
 
 5-9 
 
 10 
 
 3 3 
 
 6-9 
 
 4-7 
 
 8-7 
 
 15 
 
 4-0 
 
 8-5 
 
 5-6 
 
 KV4 
 
 20 
 
 4-6 
 
 97 
 
 6-4 
 
 11-8 
 
 30 
 
 5-7 
 
 12-0 
 
 7-9 
 
 144 
 
 40 
 
 6-6 
 
 13-9 
 
 9-1 
 
 16-9 
 
 50 
 
 7-4 
 
 15-6 
 
 10-2 
 
 18-9 
 
 60 
 
 8-1 
 
 17-u 
 
 11-2 
 
 20-8 
 
 70 
 
 8-7 
 
 18-4 
 
 12-1 
 
 22-4 
 
 80 
 
 9-4 
 
 19-7 
 
 12-9 
 
 23-9 m 
 
 90 
 
 9-9 
 
 20-8 
 
 137 
 
 253 
 
 100 
 
 10'5 
 
 22 
 
 14'5 
 
 26-8 
 
 125 
 
 11-6 
 
 24-4 
 
 16-1 
 
 29-8 
 
 150 
 
 12-8 
 
 269 
 
 17-7 
 
 32-7 
 
 175 
 
 13-8 < 
 
 29-1 
 
 191 
 
 34-8 
 
 •Joo 
 
 14-8 
 
 31-1 
 
 . 20-2 . 
 
 37-4 
 
 225 
 
 15-7 
 
 330 
 
 21-7 
 
 40-1 
 
 'J .'in 
 
 166 
 
 348 
 
 22-9 
 
 42-4 
 
 27 5 
 
 173. 
 
 36-3 
 
 23-9 
 
 412 
 
 300 
 
 18-2 
 
 381 
 
 25-1 
 
 46-4 
 
 S50 
 
 19-6 
 
 41'2 
 
 27-1 
 
 5(rl 
 
 •4no 
 
 21-0 
 
 43-2 
 
 29-0 . 
 
 53-6 
 
 : 
 
 23-4 
 
 49-1 
 
 32-4 
 
 59-9 
 
 600 
 
 25-7 
 
 640 
 
 355 
 
 65-7 
 
 700 
 
 27 '7 
 
 582 
 
 37-2 
 
 69-1 
 
 soo 
 
 29-7 
 
 G2-4 
 
 41-0. 
 
 75-8 
 
 900 
 
 315 
 
 66-1 
 
 43-8 
 
 83-0 
 
 1000 
 
 332 
 
 69-6 
 
 45-8 
 
 84-7 
 
 • With the assistance of this table, and the preceding rules, we 
 can always determine, not only the thickness and pitch of the teeth, 
 but also their height and width, since these are in proportion to 
 their thickness. 
 
 DIMENSIONS OF THE WEB. 
 
 223. The width of the web is ordinarily equal to that of the teeth 
 when the whole is of cast-iron. Nevertheless, in some cases — such 
 as. for example, where very great irregularities in the pressure and 
 speed, and reiterated shocks have to be borne in the heavy ma- 
 jhinerv in engine shops — the web is made wider than the teeth, 
 
 projecting also on either side of the teeth, so that these are wholly 
 or partially imbedded, which increases their power of red 
 very considerably. These lateral webs are generally each made 
 oT about half the thickness of the tooth. 
 
 The thickness of the web, or crown, is never made less thai! 
 three-fourths that of the tooth, and very frequently it is further 
 strengthened by an internal feather, as already mentioned 
 
 213. When the teeth are of wood, the web is much thicker, to 
 give sufficient hold to the tenons of the teeth; it is generally 
 made about l - 5 to 2' times the thickness of the tooth. 
 
 NUMBER AND DIMENSIONS OF THE Aims. 
 
 224. The number of arms, or spokes, which a Bpur-wheel 
 to have, has not, up to the present time, been precisely aid 
 scientifically determined. According to general experience, up in 
 a diameter of 1 me:tre, or about 3. feet, four arms are sufficient; 
 from 1 metre to 2 metres, or 3 feet to 6 or 7 feet, aix are 
 necessary and sufficient ; beyond 2'5 m., or 8 feet, eight arms ai e 
 used: and for 5 m., or 16 feet, ten are given; it is seM 
 last number is exceeded, except for wheels of extraordinary di- 
 mensions. 
 
 The section of the arms of the wheel is always in the form of 
 a cross, the stronger portion of which lies in the plane of the cir- 
 cumferential strain, whether these aims are cast in one piece with 
 the boss and the crown, as is the case with wheels oi small 
 diameter — that is, of such as have not a greater radius than 2 m. or 
 6i feet; or whether they are cast in separate pieces, and after- 
 wards fitted together. The thicker part, then, of the arm must he 
 strong enough to bear the circumferential strain. Experience 
 has shown, that when a spur-wheel is in motion, and acted upon 
 by a considerable force, this strain has a tendency to make the 
 arms assume a twisted shape, and produce on them a lateral 
 inflexion. It is to obviate and prevent this, that the arms aro 
 strengthened by feathers. 
 
 The power acts with greatest effect near the boss of the wheel, 
 so that it is necessary to make them wider at this part than near 
 the crown, so as to approximate to the form which presents an 
 equal resistance throughout This will be observed in the 
 figures in Plate XX. The boss must have such a thickness as 
 will allow of the wheels being solidly fixed on the shall. A 
 thickness of 5 inches maybe considered a maximum for the bossi s 
 of moderately-sized wheels. The dimensions of the arm- 
 be in proportion to the width of the web or crown, their thickness 
 being ordinarily about J that of the crown. This proportion i^ a 
 good one for wheels under 6* feet in diameter. For larger sizes, 
 i the width of the web is considered sufficient 
 
 The lateral feathers should have, at the very most, only the 
 thickness of the arm. Generally, the width of the arm near the 
 web is made about § of its width near the boss. The following 
 table, calculated from Tredgold's experiments, shows the propor- 
 tions to be given to the arms or spokes of spur-wheels, ace 
 to the strain acting at their circumferences; supposing the dia- 
 meter of the wheels to be 1 m., and the number of arms 
 thickness being taken equal to J the width of the crown. The 
 dimensions given are the averages, or those to be applied to tlio 
 arm, half-way between the boss and the crown. 
 
Tin: I'iimth'ai. imu ciirsMws 
 
 Tabk e/fJkt Dimauiau </ Spur.r\nl Arms. 
 
 • a.i-t 
 
 IV -Iik »f lk* Arm u 
 fMUawm 
 
 W«hk om aft, of lk. 
 
 I'..'.h»r« la fatiaWllaa. 
 
 
 4 "DO 
 
 1 .'1 
 
 
 6-00 
 
 
 SO 
 
 
 
 
 8-50 
 
 
 144 
 
 1 
 
 
 
 
 
 ■ 
 
 1! • I 
 
 
 
 is ia 
 
 
 
 1310 
 
 1 
 
 
 
 
 • 
 
 
 
 1310 
 
 
 II M 
 
 
 
 
 
 
 
 
 ■ 
 
 
 
 i: I ' 
 
 
 
 
 11 ■ 
 
 
 
 
 
 l • 
 
 
 
 
 
 To »p[>!v the numbers in t ; 
 
 I » It, R In iiii.' tho ra.lius of (lie whc.-l 
 fur which ill- dimensions arc to bo calculated. 
 
 W0ODCI riTTEBX*. 
 
 I canting has 
 doced, :. 
 
 be turtn-d, I 
 
 this laal MM, an lli« 
 allownm 
 
 uld Iw 
 given. 
 
 j mathematical precision — w 
 i«, that, 
 
 :. that, in liH. 
 loam, tin- moo 
 
 y at all 
 part*. Willi regard !•> (In- la 
 
 1 1 n foaiid thai tho diameter of a win 
 tin- line of the amis, i« noaibly less tluin M 
 
 • 
 - . that in ttle I 
 - a M\t!i of an ineli. 
 
 nanifeat, that all il> ma moat be bona in 
 
 mind whan constructing wooi y 
 
 errors at magnitada will arise. 
 
 CHAPTER VI. 
 
 ITINUATION OF THE STUDY OF TOOTHED GEAR, 
 
 
 • only capable of tnmamitting 
 
 which are |ianillil to each other; and when 
 
 1. ..r form any angle with each other, tin- 
 
 to be made conical, ami are than caBad l«-vil- 
 
 ■ of gear may In- capable of working 
 ■!v. ami of ti riderable power whan 
 
 • ar, it i* eaaontial iliat the ahafta or as ■ of 
 
 any pair work! ■ in tins 
 
 v.il mi«t in a point which i< tl»- apei common to 
 
 n throogh 
 
 khaTU i: • . other at right 
 
 ■ couple 
 barn for teeth, paaaing from one to tie- other 
 
 parallel to the axis ; and the wheal to guar with thi- • 
 10 parnllil with the n\i-, 1"'' 
 from a - 
 
 it when 
 
 at for aome d- - .ning machinery — the 
 
 ■ frame, for example — bvvil-wheele are 
 
 i ahnata in the eame plane ; th< 
 termed "-ki « bevila," from the teeth having a hyporboloida) twist 
 in order that they may net pr I kind of 
 
 wheel doM not work well, and la asldom employed, except 
 
 ■ 
 mlttod : the pwliT fonn rd (hi b I 
 difficult to eonatrnet Their dm it so limited, that ftvtai i 
 
 for. Indeed, they ought rather to lw 
 avoidi 'i m Im\ il- 
 
 wli. ela cannot I for them with adranl 
 
 teeth of bovB ie of wood or meUl, abnOarly 
 
 to epur-wbeel teeth, and thou rma are detera 
 
 axa i* unit. 
 I'i.in: xmi. 
 
 • 
 
 «Ih al a Ian t. eth, and thi 
 
 I ii the pair of •pur-wl 
 Let I the two wheala 
 
 aaaumed here to be at right anglca to aaah "tier . though we 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 71 
 
 must observe, that what follows will apply equally well to the 
 construction of a couple of wheels, the axes of which make any 
 angle with each other, acute or obtuse. 
 
 Let B D = '220 m., and ef = -440 m., the radii of the pitch 
 circles of the two wheels. It is, in the first place, necessary to 
 determine the position these circles should occupy on their respec- 
 tive axes. With this view, on any point, B, taken on the axis, A B, 
 erect a perpendicular, B D, and make' it equal to the radius of the 
 smailer wheel, and through the extremity, D, draw a line, D L, 
 parallel to this axis ; in the same way, at any point, e, taken on 
 the axis, A c, erect the perpendicular, E F, equal to the radius of 
 the larger wheel, and through the extremity, r, draw F n parallel 
 to A o. The point of intersection, G, of these two lines, F H and 
 n l, is the point of contact of the two pitch circles, the radii of 
 which are g i and g k. Blake i h and k l, respectively, equal to 
 the radii, and join the points, H G L, to the common apex, A, thereby 
 determining what are termed the " pitch " cones, A H G and A G L, 
 of the two wheels, the straight line or generatrix, A G, being the 
 line of contact of the two cones. These pitch cones possess the 
 same properties as the pitch circles, or, more correctly, pitch 
 cylinders, of spur-wheels ; that is to say, their rotative velocity is 
 in the inverse ratio of their diameters, and their diameters are pro- 
 portional to the respective numbers of their teeth. 
 
 The proportions of the pitch cones being thus obtained, with the 
 centres, o and o', figs. 2 and 3, taken on the prolongation of the 
 given axes, describe the pitch circles, A h' i' and g' k' l'. Divide 
 these circles into as many equal parts as there should be teeth ; 
 that is to say, in the present case, 24 and 48, respectively, which 
 operation will give the pitch; each part is then bisected to obtain 
 the centres of the teeth and of the intervals, and on each side of 
 the centre lines are set off the demi-widths of the teeth, regard 
 being had to the difference to be made between the wooden and 
 cast-iron teeth, as already explained (213). 
 
 The external contours of the teeth will be situated in cones, the 
 generatrices of which are perpendicular to those of the pitch cones ; 
 they are obtained by drawing through the point of contact, G, on 
 the line, a g, a perpendicular, b c, meeting the axis of the smaller 
 wheel in B, and that of the larger one in c ; the points, B and c, are 
 the apices of the two cones, B H G and c G L. 
 
 If these last-mentioned cones be developed upon a plane, it will 
 be easy to draw upon it the exact forms of the teeth. Now, we 
 have seen (170) that the development of a cone on a plane surface 
 takes the form of a sector of a circle, which has for radius the 
 generatrix of the cone, and for arc the development of the base of 
 the cone. As it is unnecessary to develop the entire cone in the 
 present case, it is sufficient to describe with any point, b', fig. 4, 
 with a radius equal to b g, an arc, a e b, on which, starting from 
 the point, c, are divided off distances — one, c d, equal to the thick- 
 ness of the tooth of the smaller wheel, fig. 3, and the other, c e, to 
 that of the tooth of the larger wheel, fig. 2. The same operation 
 is performed for the larger wheel ; that is, with the point, c', 
 situated on the prolongation of b' c, and with a radius equal to c g, 
 describe the arc, / eg, on which are measured the distances, 
 respectively, equal to the" former ones, e d and c e. 
 
 This dune, the outlines of the teeth are obtained by means of 
 precisely the same operations as those explained in reference to 
 
 tho spur-wheels. Thus, on the radius, e' <-, considered as a 
 diameter, describe a circle, i cj, which, in rolling round the circle, 
 f e g, considered as the pitch circle of the larger wheel, determines 
 the epicycloid, e h, which gives the curvature of the teeth of the 
 larger wheel ; in (he same manner, the circle, k e I, described on" 
 the radius, e c', as a diameter, and rolling round the circle, a c b, 
 gives the epicycloid, c m, which is taken for the curve of the teeth 
 of tho smaller wheel. After having repeated these curves 
 metrically on each side of the teeth, these are limited by drawing 
 chords in tho generating circles from the point, e, each equal to 
 the pitch of tho teeth, as c n, c k, and then with c' and i,' as centi i - 
 describe circles passing, one just outside the point, n, and tho othvr 
 just i«itside tho point, k ; and to indicate tho line of the web, describe 
 a second couple of circles, nearly tangents to the preceding. Then 
 project the points, o and p, which indicate the depth and extre- 
 mities of the teeth, over to the line, B c, in o and p ; through theso 
 last draw straight lines to the apex, a, which will represent the 
 extreme generatrices of the teeth, as in vertical section. 
 
 As all the teeth converge in one point, it is obvii us that tho 
 contour of the inner ends of the teeth cannot be the same as that 
 of the outer ends ; the difference is the greater, according as the 
 width, g r, on the generatrix line of contact is itself greater, in 
 proportion to the entire cone, and to the greater or less angle 
 formed by the extreme generatrices. 
 
 In other respects, this contour is determined in the same manner 
 as the first, Thus, through tho point, r, is drawn the straight 
 line, s t, perpendicular to a g, which cuts the two axes, and givi 9 
 the proportions of the two cones, on the surface of which lie the 
 contours of tho inner ends of the teeth. Continuing the opera- 
 tion as above, portions of the cones are developed, arcs being 
 described with the points, s' and (', as centres, and radii equal to 
 r s and r I. The diagram, fig. 5, which is analogous to fig. 4, fully 
 explains what further is to be done. 
 
 What has been said so far, has referred only to one tooth of 
 each wheel. In proceeding with the execution of the design, after 
 cutting out templates to tho form of the teeth as obtained by 
 means of them, the outline is repeated, as often as is necessary, on 
 the external cones, the generatrices of which are B G and G c, for 
 the outer ends of the teeth, and on the internal cones, the genera- 
 trices of which are r s and r t, for the outlines of the inner 
 the teeth. At tho same time, and in order that the operation 
 may be performed with regularity, a series of lines should be 
 drawn through the points, o, p, of the two wheels, lying on the 
 surface of the external cones, a h g, a g l, and uniting at tho 
 apex, A, by means of a "false square." of a form analogous to that 
 represented at x, in fig. 3, Plate XXIII., for the smaller wheel, 
 and like that represented at T, fig. 4, of the same Plate, for the 
 larger wheel. 
 
 The forms of the teeth being thus obtained, the partial section, 
 fig. 1, of fhe two wheels is drawn, the radii of the shafts being 
 given, as well as the thickness of the bosses and Webs, the propOf 
 tions employed in the present example being indicated on tho 
 
 drawings. It will be observed that those teeth which are of« 1 
 
 are adjusted in the web of the larger wheel, in the same luaniiet 
 as in the spur or cylindrical wheels, the forms of the tenons being 
 modified, so that their sides all incline to the common apex, a 
 
TIIK I 
 
 TV erctioasv together wtth the developnienta, fig*. 4 and S. are 
 •urfirirol for the parpeeea of construction, a* all the required mea. 
 earesaeata en be obtained from them ; but when it b desired to 
 
 will be 
 ■ns of the teeth and other parta. ' 
 
 • tally drawn D| 
 -• - of tin- whc. K M 
 
 Ij bean 
 
 - . als, and mart 
 
 i and I • ' ' 
 
 , limit* the lower ntel oul 
 
 ■ • 
 
 t I which the p In thi* 
 
 circle, a - 
 
 ■ 
 ■ 
 
 • to the centre, 
 . found in a similar HaW, draw similarly 
 ■ 
 
 ir an- to represent tin- epicycloids! curve, 
 une time 
 
 TV ' in fio-. 3 : It OOMbta in dmw- 
 
 or. and rd, r i/, by a pcr|>eiiiiicular i 
 
 • 
 
 'i on the 
 mpleted by d 
 area for the corresponding i 
 
 drawn i ling to r anil | ' 
 
 tweea lha teeth — thai 
 drawn, 1 1 1 • » proj< ctiu/ia of the 
 • ■ 
 ii. It will V obaarred that, on i 
 I a view of n quarter "f the lower and inner 
 portion of thl 
 :li a* in plan ; in the former • 
 ■ 
 I web on which wt are look rat ud 
 
 ■ ■I the teeth of the mall 
 
 ling or squaring orer, from 
 
 to tli- pit. h line, ■• n ; nn.l 
 over thi to the 
 
 I 
 • 
 
 flank* at 
 
 . ami it 
 
 termediate brtwprn u, p, and e, e, may be obt.. 
 
 Ii are 
 ■ 
 in fie;. 3. Tin. 
 
 in^' In the apex. A, and find the latere 
 of the • 
 and jf . 
 
 I the teeth m 
 
 I 
 
 ■|>er left -haii d 
 
 whole 
 
 r. of the arc, whi. !. 
 portion of each tooth, is shown in fig. H". Kr..iu th • 
 are obti lir.-d to produce ti- 
 
 i in fig. I. TV operation* an 
 
 wheel; -ire also used to | 
 
 ■irity. 
 
 ■ nds at K a second quadrant 
 of tin- win-el. drawn as seen from U 
 
 - Mrh all 
 \ third quadrant, r. 
 
 :. so that the mordant art - :ant, r, 
 
 ■ 
 I i th" amis ot - 
 
 rough the li- i of the 
 
 web made through Dm Baa, :t — i. igh the 
 
 centre r.f the mortise ; and fig. 8 comprehends a lateral i 
 and !'• 
 
 r-wheela, an- t I 
 
 Tin- n . -ill enable tin 
 
 to fom an accurate id. a ot the actual proportiona of 1 1 . . 
 
 mi. . oatrat • ma n an* < i-air 
 
 OF III 
 
 Will. 
 
 • 
 
 -till, at lha ... 
 
 the difference in the form of the l. 
 
 y.. in. 
 
 I -i 2 repn - nl ;>,. • iwttern 
 
 of the two wheels in the p 1 
 
 is a \ i : ' 
 
 , nt roughly log*. Ihar, ud tnu 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 form the crown ; and on the other, a view of the same as finished, 
 with the arm and its feathers. 
 
 It will bo seen from these figures that the crown is built up in 
 the same manner as that of the pinion in Plate NXI. ; the layers 
 of wood are, however, in steps, increasing iu diameter downwards, 
 so as to give the required conical form when turned. When these 
 pieces are glued together, the whole is turned externally and 
 internally in such a manner as to conform exactly to the full-sized 
 drawing, previously made on a board planed smooth for the pur- 
 pose. " Squares," also, should be made from the drawings, to 
 serve as guides in producing the correct conical inclination. 
 
 After turning the top face, b> b', perpendicular to the axis of the 
 cone, the pattern-maker proceeds to turn the external conical 
 surface, a' b', of the web or crown. As a guide in doing this, he 
 takes a " false square," T, fig. 4, of which one side, b b, corresponds 
 to the plane face, 4' b', and the other, a b, to the inclination 
 of the conical generatrix, a' b' : it is very easy with this to take 
 off just as much of the wood as is necessary, without the liability 
 of going too far. It is also necessary to determine the inclination 
 of the generatrix, b a', of the outer cone, perpendicular, it will be 
 recollected, to the contact generatrix, G r, by means of the square, 
 x, fig. 3, the side, a b, of which is applied exactly to the conical 
 surface, a' b', and the side, a c, then gives the inclination of the 
 conical surface, a' c' ; and the same square being turned round will 
 give the inclination of the internal conical surface, b' d', the gene- 
 ratrix of this, the smaller cone, being s r, parallel to B G, that of 
 the larger one. " 
 
 Finally, the thickness at a' c' and V d', is measured on the 
 wooden web, so as to obtain the proportions of the internal conical 
 surface, c d', to be turned out in a similar manner. 
 
 Mortises have now to be cut in the crown to receive the ends of 
 the arms, c, and their feathers, E. As the wheel under considera- 
 tion is of very small diameter, the number of arms is limited to 
 four; these arms are so placed inside the crown that the feathers 
 are all on one side, and towards the wider end of the cone. Their 
 attachment to the web is by means of a circular groove or mortise, 
 seen at e'f, fig. 2, and at g' d', fig. 3, and they are united at the 
 centre to each other and to the boss, in the same manner as the 
 arms of the pinion, described in reference to Plate XXI. The 
 arms are not placed in the middle of the boss, as in the spur-wheel 
 and pinion, but are simply applied to the base of the boss, which 
 may, consequently, be of a single piece ; and the feathers are let 
 into a groove extending their whole length, and are fixed into the 
 boss and crown at either extremity. The boss is slightly coned, 
 so as to give the "draw" necessary in the construction of the 
 mould. Its outer edges are indicated by the lines, m n, m n, whilst 
 the other lines, o p, which are, on the contrary, parallel to the axis, 
 show the depth of the grooves cut to receive the feathers of the 
 arm. These last, as shown in the section, fig. 10, are thicker near 
 the arms. 
 
 The core pieces, E, are added on either end of the boss, and the 
 whole is held firmly together by means of a central bolt. 
 
 The pattern being so far advanced, the external conical surface 
 is divided into as many equal parts as there are to be teeth and 
 intervals, and, with the assistance of the "false square," t, lines 
 which represent generatrices of the cone, are drawn through the 
 
 points of division, to indicate the positions of the teeth or of the 
 grooves to receive them. 
 
 Each tooth is cut out separately according to the fall-size draw- 
 ing made, as already mentioned, which, besides containing the ver- 
 tical section, fig. 3, should also show the exact form of each end of 
 the tooth, e', and of the dovetail joint attaching them to the web. 
 Fig. 5 shows a portion of this drawing for the larger ends of tho 
 teeth. 
 
 PATTERN OF THE LARGER BEVIL WHEEL. 
 
 230. Figs. 6 and 7 represent the elevation and plan of tho 
 pattern of the larger bevil wheel, with wooden teeth, represented 
 in Plate XXII. Fig. 8 is a vertical section through the axis of the 
 wheel, showing on one side the arrangement of the pines of wood 
 built up upon one another, and forming the crown, a, and on tho 
 other side, the same piece, turned and finished, attached by tho 
 arm, c, to the boss, D. 
 
 Fig. 9 represents the false square, T, employed as a guide for 
 giving the proper inclination to the external conical surface, <i //, 
 of the crown. 
 
 Fig. 1 1 is a transverse seetion of one of the arms, or spokes, 
 taken through the line 7 — 8 in fig. 7. 
 
 Whatever explanations are called for regarding the construction 
 of the crown, a, the arms, c, and the boss, D, as well as the uniting 
 of these parts with each other, have already been given in reference 
 to preceding examples. We have distinguished all corresponding 
 parts and working lines by the same letters. 
 
 The only difference between this last and the preceding example 
 consists in the disposition of the tooth pieces, b', placed on the out- 
 side of the crown, to form the sockets in the mould for i. 
 the core pieces for the mortises, into which the wooden teeth are 
 to be fixed after the piece is cast. 
 
 It must be observed, in the first place, that these projections 
 must be shaped so that the end, k I, is inclined to the surface, b' a, 
 instead of being perpendicular to it. This inclination must be 
 sufficient to allow of the easy disengagement of the piec 
 the mould. This disposition is necessary, because th 
 half of the mould takes the impression of the outside of the crown, 
 with the tooth pieces and the upper portions of the arms, whilst 
 the top part of the mould takes the inside of the crown, the 
 feathers of the anus, and the boss, the position of the who 
 the reverse of that in which they are represented in the drawing. 
 
 The core pieces for the teeth are formed by the moulder in core 
 boxes, similar to those described in reference to figs. 10 and 11, 
 Plate XXI., which we have reproduced in Plate XAjLLL, figs. 12, 
 13, and 14, as modified to suit the different form of tooth. Fig. 
 12 is a face view, and figs. 13 and 14 are sections made through 
 the lines 9—10 and 11—12 of fig. 12. It will be observed that, 
 at the larger end of the tooth, the part to project is formed with 
 an inclination corresponding to k I, in fig. 7, already referred to as 
 required in this case. 
 
 The operations called for in delineating these patterns are all 
 fully indicated, and are analogous to those in the preceding 
 The observations, also (149 and 214), already made, with reference 
 to calculating tin- allowance to be made for shrinking, and for tho 
 turning and finishing processes, are equally applicable to the case 
 before us. 
 
N 
 
 T1IK PRACTICAL 
 
 I\\ > HELICAL TEETH 
 
 SSBXJ with 
 
 i— «■»!. win-rein 
 rved — 
 
 •ii- without dc-tcriunit- 
 
 3ti. ■; 
 
 it varies throughout the duration I : from 
 
 which i' egubrity in the action and inequality 
 
 .mount of friction. 
 
 1USM have induced a 
 
 ■ of the 
 m tried. Tin- ban in question possesses the fol- 
 lowing : 
 
 1 bo ban of thi ' i wheel hi quite Independent 
 
 o ■ • 
 
 . Uiu centres of the wheels, may be 
 I 
 
 author* also attribute to this form the property <>f trans- 
 mitting ' . boot the duration of I 
 
 tact. 'I' 
 
 of tin- ; ■ wheeb is constantly 
 
 ariation not being accurately proportions] in the two 
 1 
 
 -••so and o', fig. 1, uf tlie two wheeb be given, 
 raiiii, o a and a of, ol cb circles; also, 
 
 •. a n, passing througb 
 
 -, a. and prolong it indefinitely b \ Prom 
 
 - line a perpeodbubr, o* <•, ><n which 
 
 will accordingly !»• tin- radius of u SOOOnd circle tangent tO Uiu 
 
 same line. These cir. 
 
 . re d< ris.-.i the bvol i and c </. forming the 
 
 outline I the wheeb nro drawn just as 
 
 KVHL ('197.) 
 It nwst be obeerred tbat the eurve, a 6, which i* th>- bvolata 
 ■ a, i- thai for tl»- both of the apur- 
 h i' the MnMi and the radius, o a ; and, in 
 
 i eurve, r (I, tin- inviiliit.- nf tin- amaller • 
 
 D of the radius, n' a. It tliu- | 
 
 that the f..nn ; the apm>whee) ■ qnJb bdependi nt 
 
 of the dbmeter of the pinion, whflat that of ma |>iiii..n both is 
 
 ; of the tpmvwbeeL from whbh b 
 
 notrnctod in this manner nan, 
 
 witii at • ', an formed on the name prindpbi 
 
 and wfaOH pibfa is tlie sainc, w|i: :■■ 
 
 - n..t nilrnit 
 
 I .-obi are large, and t - 
 
 ■ -, a b and e J. 
 
 I 
 ' ■ 
 
 the common tangent, a b, a < 
 
 ./.li the 
 
 will 1«- tin- externa] limit uf the pinion 
 
 In like ruann on, a - . of |] 
 
 • a distance, A c', also eqneJ b the pitch, /g, and with tlu< 
 ■ 
 
 th. It is I'urtl,- • 
 paeilim a little within 
 on tin- other, «iil determine the depth of t) the lino 
 
 b nf the pinion and spur-wheel respectively. 
 
 I is a diagram to show — first, how thai tin 
 
 I omtnofl 
 
 . ii i-. Thus, n 
 pbion tn turn in the ilir.s-li.in of the 
 as A of the involute! a h, ia m the 
 
 . of the pinion, whilst it ui : 
 
 the centre, o, of the spar-wheoL Returning to Bg. 3. it is ahowBi 
 in the eeeond place, that the distal 
 
 , Is- v.-iri.-.l without it- 
 but, in in h case, the inclination of the t..-, 
 
 xs u i , when Uie two centres are : 
 nearer to 
 
 In practise, I rmining the radius, o B, arbitrarily, 
 
 and then deriving tlu- other radius, n o, from it, or mm tma, th» 
 efaebe which am for generating the bvotutee may !»• found, an 
 well as the inclination of the tangent, by the following method i — 
 On one of the pitch circles, thai of the pinion, for example, take 
 an are, a i, anajaj to the pitch of the teeth; draw the r.i 
 and on it let fall a perpendicular, a m. from the point, a : o m will 
 then Ih- tin- radius of the g eneratin g circle for the mvolota sum 
 
 Of the teeth of the pinion, and by prolonging m A to n, which is in 
 
 common tangent, and drawing the radhm, o a, porpon dl - 
 
 cular to it, or. what is the same thing, parallel to o' m, <i n will Ixj 
 
 the radius of tin ■ the involute of the teeth of 
 
 the spiir-wlli-el. 
 
 If this rale i- applied b t ill give 
 
 curies diffeti- .Is. 
 
 Ilv taking for the generating curbs, n- in the Q 
 o B and o' c, sensibly less than the radii of the pitch eb 
 inclination of the common tangent to the Unejobb 
 
 . and the n -nltin_' form of tooth possesses greater propot* 
 width and strength at na roots, whbh i- ibelialile for 
 gearin transmit great or irregular st. 
 
 It will Ih- observed further, that, — "f^g b this lystem, tlm 
 
 on of the tlank of the both 
 
 indeed the curve may be continued down b th.- line ..f the 
 weh with a.|\ tooth will, in I ' • much 
 
 near the web, whbh is n..t the nam 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 teeth, for in these the flanks all convergo towards the centre of the 
 wlurl, and the tooth is, in consequence, narrower at the neck, close 
 to the web, than at tho pitch circle. 
 
 Fig. 2 is a fully shaded elevation, or vertical projection of the 
 spur-wheel separated from the pinion. The portions of these 
 wheels not particularly referred to, are constructed on tho same 
 general principles as those previously discussed. 
 
 helical gearing. 
 
 Figures 4 and 6. 
 
 232. If to a worm-wheel we apply, instead of a worm, a pinion 
 with teeth helically inclined to correspond to the similarly inclined 
 teeth of the worm-wheel, we shall have a spur-wheel and pinion 
 constructed on the helical principle. 
 
 This svstem, invented in the seventeenth century by Hooke, 
 but reprodifced since by White and others, claims to possess two 
 properties which have been often thought to be incompatible with 
 each other — namely, uniformity of angular velocity, and freedom 
 from other than rolling friction between the teeth. In other words, 
 the arcs described by driver and follower will be equal in equal 
 times, and the contact between the teeth will resemble that of 
 circles rolling on planes. 
 
 Added to these properties, and consequent to them, are the 
 advantages of a constant contact, and of an insusceptibility to the 
 play between the teeth, which invariably exists more or less 
 palpably in gearing constructed according to the systems before 
 described. 
 
 The form of the helical teeth, as taken in a sectional plane at 
 right angles to the axis of the wheel, may be derived either from a 
 couple of epicycloids, or a couple of involutes ; it is only the sides 
 which, in common spur-gearing, are parallel to the axis that here 
 follow the inclination of a succession of helices coming in contact 
 one after the other. The arrangement is such that the contact of 
 each tooth commences at one side of the wheel and crosses over 
 to the other, and does not cease until the following tooth shall 
 have commenced a fresh contact. 
 
 The helicoidal system may be applied either to wheels having 
 their axes parallel, as spur-wheels, or intersecting, as bevil-wheels, 
 or again inclined, but not intersecting, as skew bevils. 
 
 In figs. 4 and 5 are represented, in face and edge viow, a spur- 
 wheel and pinion, constructed according to this system of Hooke's, 
 this being its simplest and most common application : — Let A o and 
 a' o be the radii of the respective pitch circles of the two wheels, 
 these radii being, of course, in the same ratio as the numbers of 
 the teeth, as in common gearing. The radii are supposed to lie 
 in a vertical plane, b' c', and it is on this plane, as turned at right 
 angles, that the operations represented in fig. 4 are supposed to be 
 performed. 
 
 These operations have for then- object the obtainment of the 
 outline of the teeth, and are precisely the same as for any other 
 epieycloidal system of gearing. Thus, the curves, A b and A c, 
 are derive'd from the generating circles, o d a and A d' o 7 , as also 
 the flanks, A d and a e ; but it is unnecessary to repeat a detailed 
 explanation of the proceeding. 
 
 Supposing, then, the outline of the teeth to be drawn as on the 
 
 plane, b' c', representing say the anterior face or base of the wheels, 
 next draw the line, E f, (fig. 5,) representing the opposite face, and 
 parallel to the first, limiting also the breadth of the wheels. 
 
 To proceed methodically, the teeth should also be drawn as seen 
 on this plane, E F being behind the outlines of the anterior ends of 
 the teeth, a distance equal to a a', or rather more than the pitch. 
 These last outlines need only be represented in faint dotted or 
 pencil lines in fig. 4, as the parts they represent are not actually 
 seen in that view when complete. Thus, starting from the point, 
 a', on the pitch circle of the spur-wheel, and from the point, g', 
 on the pitch circle of the pinion, wo repeat the contours of tho 
 teeth, as obtained at e A i and d A n, respectively. 
 
 As the result of this disposition, it will be observed, that if tho 
 curve, A i, of the tooth, A, of the spur-wheel is in contact, at the 
 pitch circle, with the flank, g d, of the tooth, g, of the pinion at 
 the anterior face, b' c', and if the wheels be made to turn to a cer- 
 tain extent in the direction of the arrows, the curve, a' i', on the 
 opposite face, E F, will in time be found to be in contact with tho 
 corresponding flank, g' d', of the pinion. In other words, if tho 
 space between the curves, A i and a' i', be filled up by a helicoidal 
 surface, as also the space between the flanks, g d and ef d', all the 
 points of one'such surface will be in contact successively with the 
 corresponding points on the other ; so that when, for example, the 
 curve a V, shall have reached the position, A 2 i 3 ; that is, when it 
 shall have passed through a distance equal to a a', the posterior 
 curve, a' i, will have assumed the position held originally by a i; 
 or rather, a position directly behind this in the plane passing 
 through the axis, and the point of contact between a' i' and a' d' 
 will then obviously be in the line of centres, o o'. It thus follows, 
 that any two teeth which act on each other will be constantly in 
 contact on the line of centres throughout a space equal to a a'. 
 This space, A a', is, as before stated, somewhat greater than the 
 pitch of the teeth, so as to allow a following couple of teeth to act 
 on each other, and be in contact on the line of centres before the 
 eouple in advance shall bo quite free, and thus a constant contact 
 on the line of centres is preserved throughout the entire revolu- 
 tion. 
 
 In order to delineate the lateral projection, fig. 5, it will bo 
 necessary to find the curves which form the outline of the helicoidal 
 surfaces of the teeth. The principle, according to which this" is 
 to be done, is precisely what has already been explained (208). In 
 the present case, however, as we have but fragments of helices to 
 draw, in place of finding the pitch of the helix, and then dividing 
 it and the circumference proportionately, it will be sufficient to 
 divide the width, b' e, of the wheels, into a certain number of 
 equal parts ; and through the points of division, to draw lines 
 parallel to b' c'. Further, the arcs, a a', e e', i i', must be divided 
 into a like number of equal parts. 
 
 To render the diagram clearer, these divisions are transferred 
 to 1,2, 3, 4, &c, andl', 2', 3',4',&c. (fig. 4.) Each point, 1,2,3,4, 
 being squared over, in succession, to the corresponding lines in 
 fig. 5 — namely, the lines of division first obtained, and lying 
 parallel to the faces of the wheels, the operation will give the 
 curve, 1, 3, 5, 6, (fig. 5,) corresponding to the outline of the exter- 
 nal edge, extending from i to i'. The curve, I', 3', 5', C, similarly 
 gives the other edge. It is also obvious that the line of junction 
 

 af the tooth »ith tla* web "ill be represented by the babY.- 
 
 - lb* laet, bat lying on 
 liar of • aoatewbat afaallar diameter. 
 
 iteral |-r. ;.«■!: n. of all the teeth are determined in the 
 mow manner, but tat ana, aarame various aspect*, 
 
 fr.<n the djfT.r. ct positions in which they lie with reapect to the 
 iir'ki) Bana* 
 
 - ruction, in order to determine the exact inclination 
 
 The 
 ■ 
 
 ■ nd the 
 i' : A o : : ■' I 
 
 may be 
 oV...:,..l _■■ ^n. •-..:•. . .imply thu. : — Maki lln straight ;i;i, , m >i. 
 • 'jual to the arc, a a'. 
 
 lar, I L, equal : ■' E, of 
 
 the wheel. : join i M. * iiulioD of the 
 
 • 
 
 • , ial to the ar. 
 nationi, L I au<J I. l. (SUning 
 
 Lh, and tin- line, c, of junction 
 ■ ■ 
 
 ■ 
 
 lh, with 
 ■ -. difler- 
 . iiua ia amaller, and tbi . >rtional 
 
 ': A o* ::■'■: x. 
 
 ■ 
 
 action, 
 
 ■.ill pressure n| 
 
 . of the nurl':. 
 
 tudinal 
 
 • r iho 
 
 ■ • 
 ■ 
 
 of a m 
 
 ■ 
 
 . in the 
 ■ 
 
 * of tlio 
 ■ 
 
 involute and 
 
 rtfaw of 
 
 i 
 
 If a • 
 
 i* tra»i lllng along a curve, 
 
 forma of the respective teeth on each ah 
 I made to ti. 
 glass " • <:milar to lh..- the piston-rod 
 
 attachm parallel motion, and also exhibits! 
 
 vibration of a atrai^ht wire, a how breadth i 
 •.lined in this manner 
 
 • that whilst according to Ihi 
 rloidal an.l im li made 
 
 up of 1 • natures, whoa .not, in 
 
 or passage trot 
 
 preeiai-K ■- h-.ur- 
 
 gtaaa " e I ntinuou* ana' . I 
 
 any way, 
 
 - of the same | 
 
 - and nicety obtainal. 
 • 
 
 ..rdinary mail 
 - and machinist will Dot !«• at the I 
 • 
 
 in. tii- .• i 
 
 or thin board* are cut to ha 
 
 llkh U 
 
 trial with a |»air of com]«Kst-s, a centre and radii. - 
 ■ 
 
 - 
 trie with the | 
 
 ■ 
 
 ' ,-ira ago 
 
 iniinary 
 
 ■ 
 another, of the 
 
 I in the 
 
 | i 
 
 calculati 
 
 the graduated arale. . | Ick and 
 
 ■ 
 
 ■ 
 
 ■ 
 • ahould be ■, 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 to design practical arrangements and combinations of toothed gear 
 according to whichever of the systems may be preferred. 
 
 CONTRIVANCES FOR OBTAINING DIFFERENTIAL 
 MOVEMENTS. 
 
 THE DELINEATION OF ECCENTRICS AND CAMS. 
 PLATE XXV. 
 
 234. Eccentrics and cams are employed to convert motion, 
 whilst toothed-wheel work is for the simple transmission of it. 
 
 Endued themselves with a continuous circular movement, they 
 are so constructed as to give to what they act upon, an alternate 
 rectilinear movement, or an alternate circular movement, as the 
 case may be, the motion so produced being obtainable in any 
 desired direction. 
 
 CIRCULAR ECCENTRIC. 
 
 235. There are several descriptions of eccentrics. The simplest 
 and most generally employed, consists of a circular disc, completely 
 filled up, or open and with arms, according to its size, and made to 
 turn in a uniform manner, being fixed on a shaft which does not 
 pass through its centre. Such eccentrics are represented in 
 Plate XXXIX. 
 
 The stroke of such a piece of mechanism is always equal to 
 twice the distance of its centre from that of the shaft on which it 
 turns ; that is to say, to the diameter of the circle described by its 
 centre during a revolution of the shaft. The motion of the piece 
 acted upon is uninterrupted during either back or forward stroke, 
 but it is not uniform throughout the stroke, although that of the 
 actuating shaft is so ; the velocity, in fact, increasing during the 
 first half of the stroke, and decreasing during the second half. 
 
 heart-shaped cam. 
 Figure 1. 
 
 236. When it is required to produce an alternate rectilinear 
 motion which shall bo uniform throughout the stroke, the shape of 
 the eccentric or cam is no longer circular; it is differentially 
 curved, and its outline may always be determined geometrically 
 when the length of the stroke is known, together with the radius 
 of the cam, or the distance of its centre from the nearest point of 
 contact. 
 
 An example of this form of cam is represented in the figure. 
 
 Let a a' be the rectilinear distance to be traversed, and o, the 
 centre of the shaft on which the cam is fixed, it is required to 
 make the point, a, advance to the point, a', in a uniform manner 
 during a semi-revolution of the shaft, and to return it to its original 
 position in the same manner during a second semi-revolution. 
 
 With the centre, o, and radii, o a, and o a', describe a couple of 
 circles, and divide them into a certain number of equal parts by 
 radii passing through the points, 1, 2, 3, 4, &c. ' Also divide the 
 length, a a', into half as many equal parts as the circles, as in the 
 points, 1', 2', '3', &c. Describe circles passing through these 
 points, and concentric with the first. These circles will succes- 
 sively intersect the radii, o 1, o 2, o 3, &£., in the points, h, c, d, r, 
 &c, and the continuous curve passing through these points will 
 
 he the theoretical outlino of the cam, which will cause the point, 
 a, to traverse to a', in a uniform manner, for the equal distances, 
 a' 1', 1' 2', 2' 3', &c, passed through by the point, a, correspond 
 in succession to tho equal angular spaces, a' 1, 1 — 2, 2 — 3, &c, 
 passed through by the cam during its rotation. 
 
 As it is not possible to employ a mathematical point in prac- 
 tice, it is usually replaced by a friction roller of the radius, o i, 
 which has its centre constantly where the point should he ; and it 
 will be seen, that in order that this centre may be made to travel 
 along the path already determined, it will be necessary to modify 
 the cam, and this is done in tho following manner : — With each of 
 the points, b, c, d, &c., on the primitive curve as a centre, describe 
 a series of arcs of the radius, a i, of the roller, anil draw a curve 
 tangent to these, and such curve will bo the actual outline to be 
 given to tho cam, B. 
 
 It will be seen from the drawing, that tho curve is symmetrical, 
 with reference to the line, a e, which passes through its centre; 
 in other words, the first half which pushes (he roller, and conse- 
 quently tho rod, a, to the end of which the roller is lilted, from 
 a to a', is precisely the same as tho second half, with which the 
 roller keeps in contact during the descent of the rod from a' to a. 
 Thus the regular and continuous rotation of the cam, b, produces 
 a uniform alternate movement of the roller, and its rod, a, which 
 is maintained in a vertical position by suitable guides. 
 
 In actual construction, such a cam is made open, and with ono 
 or more arms, like a common wheel, or filled up, and consisting of 
 a simple disc, according to its dimensions ; and it has a boss, by 
 means of which it is fixed on the shaft. When it. is made open, 
 it is cast with a crown, of equal thickness all round, and strength- 
 ened by an internal feather, curved into the boss at one side, and 
 into the arm or arms at the other. 
 
 Examples of the heart-shaped cam are ,found in an endless 
 variety of machines, and particularly in spinning machinery. 
 
 cam for producing a tjniform and intermittent movement. 
 Figures 2 and 3. 
 
 In certain machines, as, for example, in looms for the " picking 
 motion," cases occur where it is necessary to produce a uniform 
 rectilinear and alternate motion, but with a pause at each extremity 
 of the stroke. The duration of the pause maj he equal to, oi 
 greater, or less, than that of the action. Fig. 2 represents tho 
 plan of a cam designed to produce a movement of this description; 
 and in this case the angular space passed through by the cam, in 
 making the point, o, traverse to the position, «', is supposed to bo 
 equal to half the angular space described by it, whilst the point. ,;, 
 is stationary, whether in its position nearest to the centre, or 
 its furthest, a', from it. For this reason, the circles of tho 
 radii, n a, and o a' are each divided into six equal pints in tho 
 points, a', 1, /, g, ft, and j. Of these portions, the two opposite, 
 1 /'and j ft, correspond to the eccentric curves, h j and I It, which 
 produce the movement, whilst the other portions correspond to tho 
 pauses. 
 
 After having drawn the diameters, 1 ft, and f j, the eccentric 
 curves, ft /', anil / It, are determined in precise!) the same manner 
 as tho continuous curve already discussed, and represented in fig. 
 1. That is to say, the arcs 1 /, and j ft, are to be divided into a 
 
M 
 
 
 certain Damber of f-qual parts by radial line.; and tho 1. 
 -.- onmbar of aqoal parU in 
 ■clee are to be drawn through the*, 
 which will be iatarneeted in the point*, c, <L r, bt the radial 
 liaea. Lines paeaiaa; through theee point* of intersection a 
 • sought, »/. and I a. 
 The in, eat and f g a, which unite tl 
 
 era concentric with the abaft, and conaeque 
 the point remain* to contact with these an- I with- 
 
 out motion, aJ 
 
 of a ca-v the one, c, ui>!> r I — that 
 
 derived 
 
 from tli' 
 
 mathematical p >n is fully indicated - 
 
 a !»•«• , i» made \ • 
 
 cut awav, and 
 
 crown, anna, and a gnat part of the boat ill of a 
 
 tK»fc»».» l aa will be more plainly aMB iti i 
 
 I 
 ■iodic. 
 
 - • 
 
 ns In which they are ctetennmad an 
 
 - lis of the an 1 , 
 which takes the place of the straight lino, a <r\ 
 
 TIUISVUI CAM. 
 I-* \ AXD 5. 
 
 ■ of a curvilinear equilateral 
 
 • 
 
 rrcumgular form, a* at T, fig*. A and IS- It ii hollowed out in 
 
 planed edges, to a surface, a b, on tin' cylinder, i>. also 
 true, n'i ; Ita I m.te.n is I" allow ii .. 
 
 to pass alternate.) to ih.- nffjar pari of the cylinder, by the |»>rt, 
 
 ■ 
 the ts. 
 
 i.tuaN-d wllli nn alter- 
 
 . attached to a vertical rod, I 
 
 the Tall 1 in ti";. 
 
 ©. and ■ 
 which • am, o. 
 
 of tlie valve a certain distance and intomiitti ntly, in sm-h a man- 
 ner that the | 
 •team for a certain til 
 
 ■ which it traverses; with . and with this 
 
 ii! *lTrr». o a, for a radius, describe a i into six 
 
 equal pacta, in ll 
 
 ita, aa I and '2, and with Die same ra 
 area, o 'J, and ■ l I unilinear Irian;;!.', ..— 1 — 2, 
 
 ■ 
 
 the parallels, i — I and 4 — A, tangential to the two sides 
 
 of the !r..i:-._!. . o, and we -Kail thus obtain the uj.|« r and 
 
 M th* two aides of the frame, 
 I' 
 
 abaft, J, as shown in I 
 
 ■hat if I lie shaft lur:. 
 ■ 
 the upj- will cause i: I 
 
 ■ 
 
 l 
 lion, m n. then hv tod 
 
 ance equal to i. 
 d. ii umo.ered. so as to allow 
 of tlie oyundc* (fig. B); whiUt. on the oil,. . :mnica- 
 
 .ind the aaampi 
 
 E, so th . D |iai.s out from the upper end of th 
 
 dor. Li the moTomenl of tbi ■ 
 ■tab. of a revolution, I 
 
 Me with tlie avis, dooa 
 not chat frame, as lot 
 
 with it- ■ al MOB, bowOTOr, M t 
 
 1, will ba in i: 
 and it will, in ■ ■ tact with the lower 
 
 h i- in tin- position of the horizontal cent 
 3 — i. Tin- further revolution of t 
 
 from ita pressure on the lower side, until tl 
 I, "I I 
 
 the tana will occupy the position, m' «'. i to lha 
 
 tad in tig. 3. 
 It follow-, from toil arra- remain 
 
 \ when it arr and the 
 
 pause each time will 
 
 rotation of the i-atii abaft 'Hie n| Miwanl 
 
 . tring a third •■: and tho 
 
 . ,11 not !»• unifonn. although the r..: 
 
 In actual construction, the angles of tin' 
 
 I to avoid a too -ud.lin change of 
 
 • • frame. 
 
 C A M. 
 
 i- | AM. 7. 
 
 In certain industrial arts, an instrument b 
 poundin 
 tnnl.ark. for evani|.le. in which the • : 
 
 ■ through 
 . a well 
 known working application of this ei: 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 la these cases, the stamp, or hammer, lias to be raised or tilted 
 up preparatory to each succeeding stroke, and it is obvious that 
 this may be most economically done in a gradual manner. It is 
 generally effected by a cam, the outline of which is the involute 
 curve already described ; this form being preferable on account of 
 tne uniformity of its action. 
 
 The office, then, which the cam under consideration has to 
 fultil, is the raising of the stamp, or load, to a certain height, and 
 then the letting it fall, without impediment, upon the object sub- 
 mitted to its action. 
 
 The diameter of the cam-shaft being predetermined, as well as 
 that of the generating circle, which last is usually the same as that 
 of the boss of the cam, the design is proceeded with as follows : — 
 Letting A be the cam-shaft, and taking A o as the radius of the 
 generating circle, whilst a a! is the height to which the projection, 
 B, fig. 03, formed on the stamp, c, is to be raised, develop the 
 circumference (197) of the circle of the radius, A o, by means 
 of a series of tangents which give the points, c, d, e, &c, the curve 
 passing through which forms the involute, bfi. The inner por- 
 tion, b o, is not a continuation of the involute, but simply joins the 
 boss with a circular turn, because the stamp projection, B, does 
 not approach the cam-shaft, a, nearer than the point, a, to which 
 b corresponds. Through the point, a, draw the vertical, a a', and 
 make it equal to the height to which the stamp has to be raised ; 
 then with the centre, A, and a radius equal to a a', describe the 
 arc, a' m i, which will cut the involute in the point, i, and this 
 point is consequently the outer limit of the cam. A little con- 
 sideration will show that if the cam-shaft, a, be turned in the 
 direction of the arrow, supposing that it is originally placed, so 
 that the point b, coincides with a, it must necessarily raise the 
 lifting-piece, b, the lower side of which is indicated by the line, 
 m ft, and wall carry it by equal increments up to the position, m' a'. 
 The point, i', will then have attained the position, a 1 , and the rota- 
 tion continuing, the next moment it will pass it, when the cam will 
 be entirely clear of the lifting-piece, B, and this last being unsup- 
 ported, must fall by its own weight. 
 
 The involute might have been derived from a generating circle 
 of the radius, a a, and had this radius been adopted, the resulting 
 curve would have been shorter, notwithstanding that it would give 
 the same extent of lift. The angular space passed over would 
 also be less, and this would admit of a higher velocity of the cam- 
 shaft, and the strokes might be given in more rapid succession, 
 whilst on the other hand, a greater power would be required to 
 raise the same weight. 
 
 The cam we have represented in fig. |B), is such as is employed 
 to actuate the chopping stamp of mills for reducing oak, or other 
 bark, for the preparation of tan. The bark is placed in a land of 
 wooden trough, e, solidly fixed into the floor. The stamps are 
 armed with a series of cutters, n, in the form of crosses. The side 
 of the trough next to the stamp is vertical, whilst the opposite side 
 is elliptical in shape, and the matter under operation has, con- 
 sequently, always a tendency to fall under the stamp. The stamps 
 are kept vertical bv slides in which they work. They are generally 
 from 450 to 700 pounds weight, and fall through a height of from 
 16 to 20 inches. 
 
 Fig 7 is a plan of the cam as seen from below, and fully 
 
 indicates the width of the rim, and of the boss, and the thickness 
 of the feather or disc uniting the two. 
 
 A series of such cams are frequently employed in different 
 planes on the same shall, actuating a corresponding scries ..(' 
 stamps, and in such ease they are arranged in steps so as to come 
 into action one after the other. Two or more are also sometimes 
 employed in the same plane, and working a single stamp. In this 
 latter case, the generating circle requires to bo of much larger 
 diameter in proportion, but the principle of construction is how- 
 ever the same. 
 
 CAM TO PRODUCE INTERMITTENT AND DISSIMILAR MOVEMENTS. 
 FlUUKES 8 AND 9. 
 
 240. In certain 'examples of steam engines, the valve movement 
 is obtained from a species of duplex cam, which being formed of 
 two distinct thicknesses, affords a means of adjustment whereby 
 the valve may be made to move intermittently and at different 
 rates, the proportions of which are variable at pleasure. Tho 
 object of this is to form and shut oft' tho communication between 
 the cylinder with the steam-pipe, at any required point of tho 
 stroke. In other words, the arrangement permits of the winking 
 of the machine on the expansive principle, and of varying the 
 "cut-oft'" point at pleasure within certain limits. We shall see, 
 at a more advanced period, what is to be understood by the fore- 
 going expressions. In designing cams of this class, we primarily 
 determine the radius o a, of the cam boss, and the entire length] 
 b c, of the stroke to be given to the valve-rod. This distance, 
 which in the present instance we shall take as equal to three limes 
 the height of the port, must not be traversed at one movement 
 On tho contrary, a third only of this is at first passed 111 
 with some rapidity, and the remaining two-thirds are traversed at 
 a later period, in a continuous manner: in other words, after a 
 third of the stroke lias been traversed, a slight pause takes place 
 before the remainder is traversed, and a second pause also occurs 
 before the commencement of the return stroke. 
 
 After describing a couple of concentric circles with the respec- 
 tive radii, o a, and o c, and having determined the angular spaces, 
 a d, and f g, corresponding to the times during which the valve is 
 to remain stationary, and the spaces, o- h, and c/, corresponding to 
 the duration of the movements; divide the whole Stroke, ' 
 three equal parts in the points, i,j, through which descril e 
 concentric with tho preceding. Through the points,/, »-, h, draw- 
 radii, and produce them to/", g', and /;'. 
 
 As the cam will act on two friction rollers, g, diametrically 
 opposite to each other, their radius is determined, as a e ; one is 
 drawn with its centre, e, on the radius, o a produced, and tangen- 
 tial to the circle described with that radius: the other, with its 
 centre, e , on the radius, o c produced, is, in like manner, tangential 
 to the circle described with this radius. 
 
 Between the two points, d and k, and comprised within tho 
 given angle, g o h, a curve. /. / </. is drawn and united by tangential 
 arcs at either extremity with the circles of the radii, a <i and o i, 
 respectively, in such a manner as to avoid any sudden change of 
 direction. Next divide the arc, g h, into a certain number of equal 
 parts in the points, 1, 2, &c., and carry the radii across to 1', 3, 
 &c. ; then, on each of these radii, as a centre line, describe an arc 
 
T1IK I 
 
 ' to the radio* of the roller, o, and tangential to the 
 
 bl obtained the pointa. r t t, 
 
 indicating the MKceeaive poaitiaaa of the centre of the roller on 
 
 the foe, e r*. when impelled I -tailing 
 
 from these aeveral pointa, we meaaure on the corresponding croea 
 
 . frifiy equal to I - 
 
 - .« .- ahaD obtaia the poaitiona, r, r*. I , of l) - 
 
 • • -. '-.■•■■ 'I 
 time poiata, r, a, I. m 
 
 .J to them, and unite 
 the radii, c o uxij a, in a aunilar DM 
 ■ 
 
 -t, i I It, 
 
 In w may maintain 
 
 the M 
 
 - 
 lira.!-. the ram and an ' planed 
 
 !' the frame is bolted the cast-iron • 
 I 
 on the centre u. and 
 
 . ••■ T. fig. B. above. In th. : 
 • the ram and r.>!l.-r frame, in fig. S, the fltfi 
 
 • |«rt, <r\ and this remains ojx-n whilst I 
 arc, a A, and Etl 
 mi shaft, o. 
 /. shall have arrival at the | 
 
 ■ ■ 
 v pass thmu^h th<- anLnV. J o g, and 
 
 r 
 
 • 
 
 • will, in 
 fact, be 
 
 V 
 
 - 1 1 • .rt time, during which 1 1 , - 
 
 in, hew. 
 
 actuating gear, will :i. intil the 
 
 open. 'lliis mov< men! will tal 
 
 i >>y the 
 -. ■;. and th'- frame >tiil farther 
 n to the 
 ■ and o r, in the Mime manner at t!i 
 
 . a in n, 
 i* ubla 
 
 • ire fully 
 
 in, and it baa in mind 
 
 that th< -.ict with 
 
 hi haa paw. 
 
 iry during an 
 Umawaad, and then If* 
 nwnre to art iij«.d the roller, o\ and cause it, with the frame, to 
 
 return from right to left, and the movemente and inter \a)s will take 
 
 iii) it ree/hta 
 
 rt-aperta, and laid u|- 
 
 aa m attd 
 
 ■ 
 
 that half of the cam » 
 
 a., that. 
 
 • 
 
 manner ia obtained a i rate of expat 
 
 which ll 
 
 t m'. of 
 ■ 
 
 . it i. 
 
 An innumi r: I by the 
 
 RULES AND PRACTICAL DATA 
 
 •j ll T • . during 
 
 •■! draw 
 
 a force 
 upon n ■ 1 t.i it. and 
 
 continui 
 
 It followa from 
 tlint the 
 two in-! 
 
 passed through in a given time, or the 
 
 Tin- amount of mechanical work increase* directly as the increase 
 
 i ..f the 
 ■ 
 
 ■ 
 »..rk m 1x1=4. II 
 
 dan; and if, with the 
 
 - 
 
 well—- 16, or 
 
 il amount. 
 
 In th. f "8 that. ! n fact 
 
 just a- - 
 
LOOK OF INDUSTRIAL DESIGN. 
 
 length, breadth, and depth, so also is mechanical effect defined by 
 the three terms representing pressure, distance, and time. This 
 analogy gives rise to the possibility of treating many questions 
 and problems, relating to mechanical effects, by means of geometri- 
 iul diagrams and theorems. 
 
 The unit of mechanical effect (corresponding to the geometrical 
 cubical unit) adopted in England, is the horse power, winch is 
 equal to 33,000 lbs. weight, or pressure, raised or moved through 
 a space of 1 foot in a minute of time. The corresponding unit 
 employed in France is the kilograuimetre, which is equal to a 
 kilogramme, raised one metre high In a second. Thus, supposing 
 the pressure exerted be 20 kilog., and the distanco traversed by 
 the point of application be 2 metres in a second, the mechanical 
 effect is represented by 40 k. m. ; that is, 40 kilog., raised 1 metro 
 high. This unit is much more convenient than the English one, 
 from its lesser magnitude. Indeed, when small amounts of me- 
 chanical effect are spoken of in English terms, it is generally said 
 that they are equal to so many pounds raised so many feet high. 
 That is to say, this takes place in some given time, as a minute, 
 for example. The time must always be expressed or understood. 
 It is impossible to express or state intelligibly an amount of 
 mechanical effect, without indicating all the three terms — pressure, 
 distance, and time. It is to the losing sight of this indispensable 
 defiuition, that we may attribute the vagueness and unintelligibility 
 
 of many treatises on this subject Tlio French engineers make 
 
 the horse power equal to 75 kilogramme ties ; thai is, to 7.0 kilog., 
 raised one metre high per second. 
 
 The motors generally employed in manufactures and industrial 
 arts are of two kinds — living, as men and animals ; and inanimate, 
 as air, water, gas, and steam. 
 
 The latter class, being subject only to mechanical laws, can 
 continue their action without limit. This is not the case with 
 the first, which are susceptible of fatigue, after acting for a certain 
 length of time, or duration of exertion, and require refreshment 
 and repose. 
 
 Wliat may be termed the amount of a day's work, producible 
 by men and animals, is the product of the force exerted, multiplied 
 into the distance or space passed over, and the time during which 
 the action is sustained. There will, however, in all cases, be a 
 certain proportion of effort, in relation to the velocity and duration 
 which will yield tho largest possible product, or day's work, for 
 any one individual, and this product may be termed the maximum 
 effect. In other words, a man will produce a greater mechanical 
 effect by exerting a certain effort, at a certain velocity, than he 
 will by exerting a greater effort at a less velocity, or a less effort 
 at a greater velocity, and the proportion of effort and velocity 
 which will yield the maximum effect is different in different 
 individuals. 
 
 TABLE OF THE AVERAGE AMOUNT OF MECHANICAL EFFECT PF.ODUCIELE BY MEN AND ANIMALS. 
 
 A man ascending a slight incline, or a stair, without a burden, his work 
 
 consisting simply in the elevation of his own weight, 
 
 A labourer elevating a weight by means of a cord and pulley, tho cord 
 
 being pulled downwards, 
 
 A labourer elevating a weight directly, with a cord, or by the hand,. 
 A labourer lifting or carrying a weight on his back, up a slight incline, or 
 
 stair, and returning unladen, 
 
 A labourer carrying materials in a wheel-barrow, up an incline of 1 in 1: 
 
 and returning unladen, 
 
 A labourer raising earth with a spade to a mean height of five feet,. . . 
 
 ACTION ON MACHINES. 
 
 A labourer acting on a spoke-wheel, or inside a large drum. 
 
 At the level of the axis, 
 
 Near the bottom of the wheel, 
 
 A labourer pushing or pulling horizontally, 
 
 A labourer working at a winch handle, 
 
 A labourer pushing and pulling alternately in a vertical direction,. . . . 
 
 A horse drawing a carriage at an ordinary pace, 
 
 A horse turning a mill at an ordinary pace, 
 
 A horse turning a mill at a trot 
 
 An ox doing the same at an ordinary pace, 
 
 A mule do. do. 
 
 ^n ass do. do. 
 
 143 
 
 40 
 44 
 
 143 
 
 132 
 
 132 
 
 •50 
 
 26 
 
 2-30 
 
 26 
 
 1-97 
 
 Hi 
 
 3-46 
 
 11 
 
 361 
 
 154 
 
 2-95 
 
 90 
 
 3-96 
 
 66 
 
 6-56 
 
 1 13 
 
 197 
 
 66 
 
 2-95 
 
 31 
 
 262 
 
 1 tout hi-h. 
 
 715 
 
 26-0 
 246 
 
 8-5 
 
 7-8 
 
 660 
 59-8 
 512 
 430 
 39-7 
 454-3 
 
 •JIlL'-O 
 
 4330 
 281-7 
 194-7 
 81-2 
 
 8 
 10 
 8 
 4i 
 
 I 
 
 561,600 
 531,360 
 
 401,760 
 
 306,000 
 
 2S0.00O 
 
 1,900,800 
 
 I.T-Jl'.-JIO 
 1,474,560 
 1,238,400 
 I.I I.: 360 
 16,354,800 
 
 7,01 1,600 
 S.I 12,960 
 
 2,338,560 
 
 It may be gathered from this table that a labourer turning a 
 winch handle can make its extremity pass through a distance of 
 2 - 46 feet per second, or 60 x 2-46 = 147-6 feet per minute. 
 Then, supposing the handle has 133 inches, = 1-147 feet radius, 
 which corresponds to a enrnnjference of 6-28 x 1-147 = 72 feet 
 
 at the point of application, the labourer is capable of an average 
 velocity of 
 
 ■ = 20 turns (nearly) per minute. 
 
 Also, the same labourer exerting a force equal to 17J lbs. with 
 
■I 
 
 TIIK 1 
 
 ftaft par second, will produce a mechanical 
 •fleet equal to 
 
 ha raiM>d I foot high per second, or of 
 43 x 60 = 2580 |- 
 
 858" hour. 
 
 And a* he cm work at this b I \nnical 
 
 be, as' indicated in Uie table, equal 
 - tOO Iba. raised 1 foot 
 W. may then calculate Out, aa a day's work, a I 
 
 a » inch-hand ■ ..inner 17J \\n. 
 
 par aooond; wbj Iba labonraf lias only 
 
 to api to a crane, a windlass, or a 
 
 capstan, he can develop a m 
 
 . 
 crane, a man can in 90' raise a load of 10480 lbs. to ■ !, 
 npan this with die tabuL 
 
 pounds raised 
 1 foot high in a ageood, to which tl,. | jnal. 
 
 It bai i by experiments, that mdar the moat 
 
 favourable cm - ..- 
 
 • exertion, raise to the same height, 1CJ : 
 
 h is equal to a mechanical • :' 
 
 1474 x 1W „ . , . 
 
 J.'j lbs. raised 1 tool Ugh \*-r - 
 
 A man can evidently only axerl itwfa a force daring 
 lin.it. -1 | kind of labour 
 
 with tliat which eoBl hours. 
 
 ■ the l..ail in.. I velocity as given in the table are those 
 h oil., r. still, when U 
 requires it, they might l>o altered I ' . thus, if it is 
 
 neccsaary to apply I In ■u.iiy of the 
 
 winch-handle i it] w..uM be i 
 
 and would become 
 43 
 
 : 3 16. 
 
 35 
 
 It ha- 1 from actual obeervationa, thai a horse, 
 
 going at the n • r hour, 
 
 cannot exert a greater UetlUft forea than the O Or ro apun dlng 
 
 draw anything 
 
 appreciable when going at the rate of 16 miles |*r hour. 
 
 Thus, when it ■ warned to ineraua the i 
 takes place in the veloertj ; an. I reciprocally, when it i- 
 to gain time ami apeed, it ran only ba done at the expense of the 
 load. 'Pin-, in the eaae of the winch-handle, the two tnetore 
 must ahrayi prod u ea 
 
 'her. 
 In al! 
 impressed, for without mumnnit there con!. I DO) I- 
 I '.. r . • 
 
 - ..f motion — uniform. I on, 
 
 I ■ niiifonii 
 
 ii equal times. 
 TVon, f.>r example, if a body b 
 
 (' " n is iiml'oriii. | 
 
 i T the 
 .mee is 
 equal to I 
 
 Firit Example. — T 
 
 h what distance will it liavo 
 
 D = 3 x 15 = 4S 
 
 I) 
 
 From the preceding formula, D = V x T, is obi. 
 
 that is ' : .1 is equal to the distance 
 
 ■ 
 / -fir. — Tin' distance passed through in 13 
 
 45 
 V =,6= ; ' 
 
 machinery, as well as mar 
 .-, for the most | M rt, actuated in a uiiilorm 
 
 •J II. Vakiip IfoTKML — Wh.n a body pass,.* in equal timi-s 
 
 through ii augment or deereaae by equal qui 
 
 Uie motion is called uniform!* 
 
 The distance in motion uniform' . ..d to half the 
 
 .sum of the extreme v< locitiea multiplied b] the time in »• 
 
 First I What is the d I through in 4 
 
 by a body in motion, the velocity of whiel 
 
 second at starting, and '. 
 
 3 + 6 
 D = -^ x 4= l 
 
 / V. |«ss4sl thr.o 
 
 by a body in motion, which 
 
 I. ft . t per sjeond, hut which is gradually red i. 
 
 D = 
 
 x 4 = 1 
 
 It will 1m> seen from thee* two axamplea, that, with like i di 
 
 tions, th,. total ilisiance la the s;iiiie for notiona onifohx 
 - !■ i. 
 The velootty at the tod of a given time, in uniform)} 
 
 DOB, is equal to the Velocity at starting, plus tin- prodooj 
 of the ii. 'id into the time in s,c..n.ls. 
 
 / / ...— \\ hat reloelty will a body have at th. 
 
 the initial Velocity — I, and that it il 
 at the rate ot lid ? 
 
 V = 1 + (8 x 3) = . 
 
 The Velocity which, at the . 'iiiica body uniformly 
 
 : should ban Ity minus the 
 
 produol of the dimiiiu 1*0 the tune in 
 
 / .jir — \ bod] in noi 
 
 m.i, and ii- reloeHj docreenea at tit 
 • nil, what will !-■ the velocity at the end oi I 
 V = 23 — (3 x 10) = a i 
 r which the varloni | 
 two prtneipal kinds — oontinuoua, mid alt. 
 ad forward mot 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 These two kinds of motion may take place either in straight or 
 curved lines, the latter generally being circular. 
 
 In the actual construction of machinery, wo find that, from 
 these principal descriptions of motions, the following combinations 
 are derived : — 
 
 t Continuous rectilinear. 
 Continuous rectilinear motion is converted into } Continuous circular. 
 
 t Alternate circular. 
 
 r Continuous rectilinear. 
 Alternate rectilinear motion is converted into \ Continuous circular. 
 
 < Alternate circular. 
 
 r Continuous rectilinear. 
 « .. , . , ■ . I Alternate rectilinear. 
 
 Continuous circular motion is converted into 4 Continuous circular 
 
 I Alternate circular. 
 
 Alternate circular motion is converted i 
 
 ' Alternate rectilinea 
 . Alternate circular. 
 
 THE SIMPLE MACHINES. 
 
 246. This term is applied to those mechanical agents which 
 enter as elements into the composition of all machinery, whether 
 their function be to elevate loads, or to overcome resistances. 
 
 The simple machines are generally considered to be six — the 
 lever, the wheel and axle, the pulley, the inclined plane, the 
 screw, and the wedge. 
 
 A much more scientific and comprehensive arrangement of the 
 elementary machines is (hat lately suggested by Mr. G. P. Ren-, 
 shaw, C.E., of Nottingham. According to his system, the elemen- 
 tary machines, or mechanical powers, are five — namely, the lever, 
 the incline, the toggle or knee-joint, the pulley, and the ram. 
 
 The wheel and axle, of the first system, is evidently but a 
 modification of the lever, and the screw and wedge are modifi- 
 cations of the inclined plane ; whilst no mention is made of the 
 toggle-joint and ram — the last so well represented by the hydro- 
 static press. 
 
 All these machines act on the fundamental principle, known as 
 that of virtual velocities. According to this principle, the pressure 
 or resistance is inversely as the velocity or space passed through, 
 or that would be passed through, if the piece were put in motion. 
 The momentum of the power and resistance is equal when the 
 machine is in equililtrio. By momentum Is understood the pro- 
 duct of the power by the space passed through by the point of 
 application. 
 
 Time is occupied in the transmission of all mechanical force. 
 In any mechanical action we do not see the effect and the cause 
 at the same instant. Thus, in continuous motion, in which the 
 time expended is not apparent at first sight, each succeeding por- 
 tion of the motion is due to a portion of tho impelling action 
 exerted a certain time previously. This will bo moro obvious on 
 observing the commencement and termination of any motion. 
 The motion does not commence at the instant that the power is 
 applied, nor does it cease at the exact moment of the power's 
 cessation. The fiction of the vis inertia; has been invented to 
 account for these latter observed facts, but it explains them very 
 awkwardly. Thus, bodies are said to possess a certain force 
 ■ which is opposed to a change of state, whether from rest to motion 
 or motion to rest. If such a resistive force existed, it would 
 require an effort to overcome it, in addition to what is actually 
 
 accounted for by the motion. If it is said that this is again given 
 back at the termination of tlio motion, another fiction is required 
 to account for it in tho meantime, that is, during tho continuation 
 of the motion. Moreover, there is nothing analogous to it 
 throughout tho ontiro range of physical science. 
 
 The facts are described in a much more simplo and philosophi- 
 cal manner, when they are said to arise from tho lime taken in the 
 transmission of motive force. Why thero should bo this expen- 
 diture of time is a more abstruse question. It probably arises 
 from tho elasticity of the component particles of bodies and 
 resisting media, and is regulated by the laws which govern the 
 relation to time of the vibrations of tho pendulum. 
 
 In all machines, a portion of tho actuating power is lost or 
 misapplied in overcoming the friction of the parts. . 
 
 247. The Lever. — Tho lever, in its simplest form, is an 
 inflexible bar, capable of oscillation about a fixed centre, termed 
 the fulcrum. A lever transmits the action of a power and a 
 resistance, or load; the distance of the power, or load, from tho 
 centre of oscillation, is called an arm of the lever. 
 
 There are two kinds of power lovers, distinguished by tho posi- 
 tion of the fulcrum as regards the power and the resistance. 
 These become speed levers, by transposing the power and resist- 
 ance. By a potter machine, is meant one which gives an increase 
 of power at the expense of speed, and by a speed machine, ono 
 that gives an increase of speed at the expense of power, and .ill 
 tho simple machines are one or the other, according to the relative 
 position of the power and resistance. 
 
 In all cases of the lever, the ■power und lie resistance are in the 
 inverse ratio to each other of their distances from the em/re qfoseil- 
 lation. That is to say, that when, in equilibria, the momentum 
 of tho power, P X A, or the product of this power into the space 
 described by the lever ami, A, is equal to the product, R x B, of 
 the resistance, into the space described by the lever arm, B : whence 
 the following inverse propoi tioii : — 
 
 P : R :: B : A; 
 
 Any three of which terms being known, the fourth can he found 
 at once. 
 
 248. The wheel and axle is a perpetual lever. As a power, the 
 advantage gained is in the proportion of tho radius of the circum- 
 ference of the wheel to that of the axle. That is to say. the power, 
 p, is to the resistance, R, as the radius, b, of the axle, is to the 
 radius, a, of the wheel, or the length of the winch handh — in the 
 simpler form of this machine, consisting of an axle and a winch 
 handle. The same rules and formulae obviously apply to this, as 
 to the first described form of lever. 
 
 Thus, multiply the resistance by the radius of the axle, and 
 divide by that of lie- handle, and die quotient will be the power. 
 
 In windlasses and cranes, consisting of a system of wheel-work, 
 the power is applied to a handle fixed on the spindle of a pinion, 
 which transmits the power to a spur-wheel, fixed in the spindle ot 
 the barrel, about which the cord, or rope, carrying the load to bo 
 raised, is wound. 
 
 Where there are several pairs of such wheels, it is necessary to 
 include in the calculations the ratios of the pinions to the spur- 
 
 wheela 
 
TilK VU\< 
 
 •porlioeal formula will, iu thin caae, be the «ain. 
 
 P:l::tx V < y ■. a * • 
 
 ■ 
 
 i 1/ 
 
 .mrf i/fruir M- 
 />y .'■"■ prrduct of Ote radius <f the handle into the ru./ 
 
 i ' paoriatf rill oe /Ac potter, ttkick, rken applied to rte 
 
 li W ' - ;■ 
 
 trrd, and by f ■ . and the quotient will 
 
 III. 1/ i I barrel, and Jiiulr the 
 
 . :nd the quutirnl 
 
 —When ■ b 
 
 plane, i - - . r, and 
 
 .- none of the weight of t!" ..», but manly 
 
 ■ 
 
 mi up im inettned plane, Ihi 
 hi proportionate to the Inclination of ma 
 
 '. that 
 
 f ihr flam trill 
 
 - 
 — 
 
 / ON the 
 II 7 
 III. 7 
 
 i of the 
 
 ombinod wttfa a 
 
 ■• nda upon tlm 
 
 Unll ply the 
 
 the i nd of the 
 
 arm <r 
 
 1 by the 
 nda <>f 
 
 - 
 
 .' »|a. <■ [ rl 
 
 ■ 
 
 — Tln-rv art- two kim tlie one 
 
 trawnjnj; cclitrra. 
 
 ng ilio 
 
 A mii. I at the 
 
 eord, ii will be the axis 
 
 i tlir arrange- 
 
 paaaod through l>y I the latter joae 
 
 . illey will onlj 
 iror, in x ti. will be eqnal to thai of the 
 in eqafltbriam. 
 Though tip i u i 
 
 tnechan 
 it affordi 
 
 ■ pa.! downward! than npwai 
 ■ In the formal • 
 Whan several pulleys or viiitja 
 
 ndtahje frame, it la oallod ■ blodt Where two • •r mon 
 ■re empJoyi d, it i^ onlj lb 
 power, and thht 
 or pill!' 
 
 Tin' iin.liaiiiial advantage of the b i 
 
 ■ 
 tin- ~un. . round the pul 
 
 pi txOng t" ii 
 divided bj the Dombi i 
 
 which the Hni ■ pulley 
 
 li\. .1 in the w 
 
 h the power, i 
 or tnoti 
 
 I I 
 
 I 
 from tin' division nt • 
 
 I 
 over which tin | 
 
 understand, that when, i ; 
 
 "t the pow< i 
 ■ 
 
 tahed, v 
 rxtirlhj I 
 
 What? 
 
 Iml to 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 circumstances in which the power is to be used. Thus we can 
 make a very small force, as that of a man, elevate an enormous 
 weight, but with a speed proportionately slow. 
 
 Finally, The mechanical effect developed in a given time by a given 
 force, through the instrumentality of machinery, must always equal the 
 useful effect obtained, plus the amount lost in overcoming frictional 
 and other resistances ; and the. useful effect of machinery icill he the 
 greater, according as the causes of these resistances are diminished-. 
 
 CENTRE OF GRAVITY. 
 
 254. All bodies are equally subjected to the action of weight. 
 Gravity, or weight, is the action of that universal attraction which 
 draws all bodies towards each other, and by which, in the case of 
 bodies on the surface of the earth, these are drawn towards its 
 centre. The power, of whatever nature it may be, which balances 
 this action, is equal to the weight of the body. 
 
 The curvature of the surface of the earth being quite inap- 
 preciable for small distances, gravity is considered as acting in 
 parallel lines, and its direction is given by the plumbline. 
 
 The centre of gravity is that point in any body in which the 
 action of its entire weight may be said to be concentrated. If 
 the body be suspended by this point it will be in equilibria, in 
 whatever position it is put. 
 
 The position of the centre of gravity depends upon the nature 
 and form of any body ; it may generally be found in the follow- 
 ing manner : — 
 
 Suspend the body by a thread attached to any point whatever 
 in it ; when tho body is motionless, the line of the suspension 
 thread will pass directly through the centre of gravity. Suspend 
 the body by any other point, and the centre of gravity will also 
 be in the continuation of the line of the thread, so that the actual 
 centre must be at the point of intersection of the two lines thus 
 obtained. This simple expedient reminds us of the application of 
 the square to the finding of the centres of circles — the unknown 
 centre on the endface of a shaft, for example — where the inter- 
 section of any two lines, drawn along the blade of the square, 
 when the head is laid against the periphery of the shaft iu two 
 different positions, gives the required point of centre. 
 
 The centre of gravity of regular bodies, as spheres, cylinders, 
 prisms, is in the centre of their configuration. 
 
 The centre of gravity of an isosceles triangle is one third up 
 the centre line which bisects the base. 
 
 The centre of gravity of a pyramid, with a triangular or poly- 
 gonal base, is one fourth up the line which joins the summit with 
 the centre of gravity of the base. It is the same with a cone. 
 
 The centre of gravity of a hemisphere is situated three-eighths 
 up the radius at right angles to the base. 
 
 The centre of gravity of an ellipse is in the point of intersection 
 of the axes. 
 
 When a body is placed in a vertical or inclined position on a 
 plane, it is necessary, in order that it may rest upon it in that po- 
 sition without falling, that the vertical line passing through tho 
 centre of gravity shall fall within the external outline of the side 
 in contact with the plane. This limit, however, allows of consi- 
 derable deviation from the. vertical in the general contour of bodies, 
 as is instanced in the case of [canine or inclined edifices. The 
 
 stability of bodies increases as the extent of their bases is greater 
 
 in comparison with their height, and also, as the vertical line, 
 passing through the centre of gravity, meets the plane on which 
 the body rests nearer to the centre of the base. A body is said 
 to be more stable when it requires a greater force to overturn it. 
 A cone is more stable than a cylinder of tho same height and base. 
 The stability of walls depends greatly on the kind of foundations 
 given to them, and on the proportionate extension of their bases. 
 
 ON ESTIMATING THE POWER OF PRIME MOVERS. 
 
 255. As we shall see further on, the power of prime movers 
 may be calculated from the dimensions of the various parts of tho 
 engine. Still, the many different modes of construction tend to 
 modify considerably the actual useful effect, and engineers have 
 endeavoured to construct an apparatus, by means of which the 
 actual power, or useful effect of engines, may be measured with 
 exactitude. 
 
 Prony's brake, which is the instrument most generally used for 
 this purpose, acts on the principle of the lever, and consists of a 
 cast-iron pulley in two halves, united by screws. This is fixed on 
 the main shaft of the prime mover, the force of which it is wished 
 to measure. It is embraced by two jaws, which may be tightened 
 down upon the pulley by screws. To the lower jaw is attached 
 a long lever, from the end of which is suspended a scale fi.r 
 weights. If it is known what power the engine was designed to 
 possess, it is simply necessary to put into tho scale the weight 
 corresponding to this power, that is, the weight which, by tho 
 action of the lever, will give a pressure equal to the supposed 
 power of the machine. 
 
 Having fixed the apparatus on the engine, and provided means 
 of efficiently lubricating the frictional surface of the pulley with 
 soap and water, and having balanced the apparatus in such a 
 manner that it will not be necessary to take into tho calci 
 anything but. the weight placed in the scale, the steam may be 
 gradually let on.- Tho engine will perhaps shortly acquire a 
 greater velocity than that for which it was designed : it' tlii- is the 
 case, the jaws are gradually screwed closer and closer upon the 
 pulley. As the friction thereby increases, the velocity will dimi- 
 nish, and full steam may be let on. After a short time, and when 
 the friction is so great that the lever is raised slight]] 
 the horizontal line, and the engine is going at its proper velocity, 
 and the pressure of tho steam at its correct point, so that tho 
 power of the engine balances the load on the lever, it may fie con- 
 cluded that the engine develops the power for which it was in- 
 tended. If the lever rises considerably, it will !«• necessary to 
 increase the weight in the scale, so as to obtain the actual maxi- 
 mum power of the engine ; and, on the contrary, if the engh 
 not appear to have the desired power, the weight must be reduced, 
 by which means its actual p.>wcr will be ascertainable. 
 
 CALCULATION FOR THE BRAKE. 
 
 256. The weight which will balance the force of a machine may 
 1„- calculated when the length of the lever arm is known, or, m..ro 
 correctly, the radius from the centre of the shaft to tin- point of 
 suspension of the weight, and the nominal horse-power, by the 
 following rule : — 
 
TIIK 1 
 
 . > At nominal lonr-pomr by 33.000, «nJ Win* the pro. 
 duel ty At cimmfrrmet drteribtd by Ae end of At brer, and by 
 At number <i reiviutwni per ana**, <m<i Ike fuofvaf riU bt At 
 
 for . -uun|i!v, the main ahaft of a atom-engine of 
 r, which run* it the rate of 30 revolution*, per 
 minute, tho miiiu of the brake U-it 
 
 ! ! 'iave w = 
 
 ■ = 311 
 
 the bra- lUaotd by being au-j-rmh-d ..n il» 
 
 centre of gravity. 
 
 The actual | I an engine, n-. 
 
 r.ile : — 
 !y Ac cireum/rrrnct described by At lexer, by At number 
 • / mvlutiuni <f At tkafi per minute aiJ by At weight ta At 
 teak, and dindt At prudmct by 3X000 and At amUuml trill to 
 At actual /uret <f At engine in bona potter. 
 
 ■ tho main ahaft of a atram- 
 ' tat the ratiiua of the 
 I 4 lba>, 
 « kit i» tin maximum : 
 
 114 
 
 F = 
 
 
 I'll P. 
 
 TABLE OF I'" 
 
 
 
 V.lunly. 
 
 l|r,.ht 
 
 1 
 
 
 
 
 1 
 
 ii. atl 
 
 Urkw. 
 
 
 IwfcM. 
 
 lack**. 
 
 l-.s.. 
 
 l.rW 
 
 lack**. 
 
 ■artm. 
 
 lartiM. 
 
 Ik>.« 
 
 
 
 
 
 
 
 
 
 
 
 
 
 6-8 
 
 171 
 
 
 1-473 
 
 
 
 
 
 •8 
 
 
 5-9 
 
 177 
 
 
 
 
 
 
 
 •4 
 
 
 0-0 
 
 1-4 
 
 
 
 
 
 
 
 •J 
 
 
 61 
 
 
 
 
 
 
 
 
 •-. 
 
 
 6 2 
 
 
 19-0 
 
 
 
 
 
 
 
 
 6-S 
 
 
 19-5 
 
 1-938 
 
 
 
 
 
 •8 
 
 
 64 
 
 
 
 
 
 
 
 
 t 
 
 
 85 
 
 -215 
 
 
 
 
 
 
 
 
 
 66 
 
 
 
 
 
 
 
 
 11 
 
 
 8-7 
 
 
 
 
 
 
 
 
 
 
 6-8 
 
 
 
 
 
 
 
 
 18 
 
 
 6-9 
 
 
 
 
 
 
 
 
 1 I 
 
 
 
 
 
 
 
 
 
 
 15 
 
 ■oll5 
 
 7 1 
 
 
 18-5 
 
 . 
 
 61 5 
 
 
 
 
 iTt 
 
 
 
 
 
 21*86 
 
 
 
 
 
 17 
 
 
 7-8 
 
 
 
 
 
 
 
 
 
 
 7 1 
 
 
 
 
 63-0 
 
 
 
 
 1-9 
 
 
 
 
 
 8-316 
 
 63'5 
 
 
 
 
 s-o 
 
 
 
 
 
 
 
 
 
 
 Jl 
 
 
 
 
 
 
 
 i:. in 
 
 
 34-6V5 
 
 
 
 
 
 
 
 
 
 
 86116 
 
 S-8 * 
 
 
 7-9 
 
 - 
 
 
 
 
 
 
 
 
 
 
 •328 . 
 
 
 3-V96 
 
 
 
 
 16 ■.■•■« 
 
 
 -0319 
 
 
 
 
 
 
 
 
 
 86 
 
 
 8-3 
 
 
 
 
 
 
 
 
 
 
 88 
 
 
 
 
 
 
 
 
 • 
 
 
 
 
 
 
 
 
 
 
 2-9 
 
 
 
 
 
 
 
 
 
 
 8-0 
 
 
 8« 
 
 
 
 
 
 
 
 
 81 
 
 
 
 •886 
 
 81 5 
 
 
 
 
 
 
 8-3 
 
 
 
 ■896 
 
 
 
 
 
 
 
 8'8- 
 
 
 89 
 
 
 
 
 
 
 
 
 81 
 
 
 
 
 88 -0 
 
 
 
 
 
 
 85 
 
 
 1 1 
 
 
 885 
 
 
 
 
 
 
 8< 
 
 
 9-3 
 
 
 
 
 
 
 
 
 8-7 
 
 ■0697 
 
 9-8 
 
 111 
 
 84-5 
 
 
 
 
 
 
 8-8 
 
 
 
 
 
 
 
 
 
 
 8-9 
 
 
 96 
 
 
 86-6 
 
 
 
 
 VI S 
 
 
 
 
 9< 
 
 
 86-0 
 
 
 
 
 
 
 41 
 
 
 
 
 
 
 
 
 
 
 
 
 9'8 
 
 
 
 
 
 
 
 
 4 8 
 
 
 9-9 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 6«-6 
 
 
 
 
 
 
 11" 
 
 
 
 
 
 
 
 
 4 7 
 
 
 
 
 
 
 
 
 
 
 
 1174 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4Hi 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 •999 
 
 
 
 
 
 
 
 58 
 
 
 
 
 
 
 
 -:. :.:..-. 
 
 
 
 
 
 
 
 
 
 7H> 
 
 S5-6V6 
 
 
 
 55 
 
 
 
 
 
 9C46 
 
 
 
 99-6 
 
 6" 466 
 
 M 
 
 1598 
 
 16D 
 
 
 
 
 
 
 
 *60?75 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 THE FALL OF BODIES. 
 
 258. Whon bodies fall freely of their own weight, the velocities 
 which they acquire are proportionate to the time during which 
 they have fallen, whilst the spaces passed through are as the 
 squares of the times. 
 
 It has been ascertained by experiment that a body falling- freely 
 from a state of rest, passes through a distance of 16 feet and a 
 small fraction, in the first second of time. At the end of this 
 tune it has a velocity equal to twice this distance per second. 
 
 From this it follows that if the tunes of observation are — 
 
 3" 
 
 4" 
 28 ft. 
 
 "... 256" 
 
 "... 112" 
 
 2, 3, 4 
 
 2, 3, 4 
 4, 9, 16 
 
 3, 5, 7 
 
 The corresponding velocities will be 32 ft.... 64 ft.... 96 ft.. 
 The spaces passed through from the ) . „ „ fi . ,, . ,, 
 
 commencement, ( 
 
 The spaces passed through during each f , fi « 48 » on « 
 second, j 
 
 That, is to say, that the times are as the numbers, 1, 5 
 *The velocities also as, 1, S 
 
 The spaces passed through as the squares, 1, 
 
 Aud the space for each interval as the odd numbers, 1, 
 
 These principles apply equally to all bodies, whatever may be 
 their specific gravity, for gravity acts equally on all bodies ; the 
 effect, however, being modified by the resistance of the media 
 through which the bodies pass, which is greater in proportion, as 
 the specific gravity is less. 
 
 259. The velocity which a body will acquire in a given time 
 when falling freely, will be found by multiplying the time ex- 
 piessed in seconds by 32 feet. 
 
 Example. — Let it be required to ascertain the velocity acquired 
 by a body falling during 12 seconds. 
 
 V = 12 x 32 = 384 feet per second. 
 
 When a body falls from a given height, H, the ultimate velo- 
 city, or that acquired by the time the base is reached, will be given 
 by the formula (g being the velocity gravity causes a body to 
 acquire in the first second) 
 
 V = Vigil, or V = V64x H, 
 which leads to the following rule : — Multiply the given height in 
 feet by 64, and extract the square root, which will be the velocity 
 in feet per second by the time the body shall have fallen through 
 the height, H, not taking resistance into consideration. * 
 
 Example. — What will be the ultimate velocity of a body falling 
 a distance of 215 feet t 
 
 H = — = 
 
 V = V64 x 215 = 117-3 feet per second. 
 From the above formula, 
 
 \ = V2g-R, 
 we obtain V J = 2 g H, then 
 
 64' 
 
 whence we have this rule : — Divide the square of the velocity in 
 feet per second by 64, and the quotient will express the height 
 through which a body must fall unimpeded, from a state of rest, in 
 order to obtain that velocity. 
 
 Example. — A body has acquired a velocity of 1173 feet per 
 second, through what height must it have fallen ? 
 
 H= =^- = 215 feet, the height of the fall. 
 64 
 
 To obviate the necessity of calculating the corresponding heights 
 
 and velocities, we give a very extensive table, calculated for 
 
 tenths of inches The numbers, however, being equally correct 
 
 as representing feet or yards, thoso of both columns being of tlio 
 siune denomination. 
 
 MOMENTUM. 
 
 260. Tho force with which a body in motion strikes upon 
 one in a state of rest, is equal to tho product of tho mass of 
 the moving body multiplied into the velocity; this product is 
 termed its momentum. If a body with a mass, m, is animated 
 with a velocity, v, its momentum is equal to m v. The term, m, 
 however, may be taken as signifying the mechanical effect of a 
 weight falling during a second of time, or through 32 feet, there- 
 
 20 
 
 fore, m = — , that is, tho weight in pounds divided by 32 feet, 
 
 w x v 
 
 whence, m v = • 
 
 What distinguishes the simple momentum or force of impact of 
 a body from the mechanical effect of a prime mover is, that 
 whilst the former is due to a single impulse, we have in the latter 
 to consider the continuous action of the impelling force. 
 
 261. When a motive force imparts continuously a certain velo- 
 city to a body, the result of its action is what may be termed I is 
 viva, or continuous momentum; it is numerically the product of 
 the (moving) mass multiplied into the square of the velocity im- 
 parted to it. 
 
 Putting M to represent the mass of a body, and V the velocity 
 impressed upon it, 
 
 M V J or 
 
 WV 
 g 
 
 is the expression of the ozs viva of the body. This force is doublo 
 that developed by gravity. For, in fact, when a body of the 
 weight, W, falls from a height, II, it acquires from its fall an 
 ultimate velocity, V, which we have already shown to be equal to 
 
 and the mechanical effect, W H, is consequently expressed by 
 
 WV 
 
 *g ' 
 
 U v 
 now, putting for P, its value, Mir, the formula becomes — g— • 
 
 Thus, the mechanical effect developed by gravit] is equal to 
 
 half the vis viva imparted to a body. 
 
 CENTRAL FORCES. 
 
 262. When a body revolves freely about an axis, it is said to 
 be subjected to two central forces; tin * one, termed "centripetal," 
 tends to draw the body to the axis; the other, termed " centri- 
 fugal," or tangential, and due to the tendency of bodies in motion 
 to proceed in straight lines, strives to carry the body away from 
 the centre. These forces aro equal, and act transversely to each 
 other. 
 
 The centrifugal effort exerted by a body in rotative motion, and 
 
 which tends to separate the component particles, is e\pn - 
 
 the following formula : — 
 
 W V 
 
 F . 
 
 i'xR' 
 
 in which W represent.- the weigh! of the body; V, the velocity in 
 
Tin: i 
 
 - orcuad ; and U, the radius, or distanc* at the centre of 
 
 : 
 
 I of the Wei r 
 radius, It, Hi. .. rotate with a velocity, V = . 
 
 ball oa 
 Uk r» . 
 
 F = 
 
 •J3 X 40 X 40 
 Si x a 
 
 = 230 lbs. raise! 
 
 rilUTF.K VII. 
 
 ELEMENTARY PEINCIPLES OF SHADOWS. 
 
 trical drawing, that Uu 
 ■ 
 
 from tin- upper left hand ooi 
 
 :!iai tli«- horizontal at 
 cubic diagonal make angles of 45' with tin 
 I 
 The . this assumption of the <iir. eiion of the my* 
 
 it has the merit of n' 
 
 is parts of an object, even with 
 or view. 
 
 rtnined, on considering an ob- 
 
 ■"■ tiii ■ cyiindri- 
 of which will In' tin' Ulaminod 
 The part ni.-t by the** rmyi of 
 Iflumined, whOal the )>orti..: 
 entire!) (hi* latter |iart 
 
 I roptr «f the object — I 
 
 • ray* surrounding the 
 ted by I 
 
 will hi' unillu- 
 
 ■ "f the interception of -•< f the r.;\- by the 
 
 Hon will be limited by, 
 
 ned tlie 
 
 ■ i any virfai-e. 
 ■ 'In- illumine.) from the litiilliimiued 
 | . or (lie 
 
 ihadow. Tlii" ii modified by the form of the red. 
 •rail aa by thai of the object which 
 l 'a Usee when • 
 
 are plain.; and by rum - wh.n either or b"lh tire cylindrical, 
 
 • 
 
 ■ ■• rniitiati.in of tli Uloi •. ,,f 
 
 • proper, and i ■ Boding 
 
 tlii- |H.n ' • a straight lite 
 
 with a ; I 
 
 ■ by tli" 
 '-, and it i. neeoaaarj 
 
 • \ plain the aunt 
 which n a due regard 
 
 ■ 
 
 i, ainl bounded 
 
 ally cylindrical ; ainl we shall proa 
 
 complex form*. The objecta which 
 
 '.lv met 
 with in machinery and architecture; they will, n 
 afford quite sufficient illustration in i 
 
 XXVI. 
 
 the horizontal and ra> 
 tieal projection* of a cube,!! b required to determine the fonn 
 
 In th' 
 
 wliieli are in tin light are tie by a D ainl A C, in the 
 
 horizontal projection, anJ p ly in a' t' u 
 
 The op; 1 o, are 
 
 in the n pri -i ntations, the - 
 can only l»- ahown l>y a thick shadow line, produced by China ink 
 
 in line d/nwii • -r..k, of the l.ru-li in w.iler- 
 
 Coliiiir ilr- 
 
 i • lines, which distinguish the illumii 
 from tie 
 
 ation of Ugbl and shade. It now • find Um 
 
 shallow cast by the cube on the plane, i. t. 
 When the obji cl r. ita on thi 
 
 • from the rerl 
 |i equal ' by it will !»■ in the 
 
 ■ I plane; and to '!• tenuine it- outline bi 
 
 . u K in/, parallel to i 
 
 liliil the l-'int.", c h, ,1, in which tie *•• line BMaj tie 
 
 To •fled thla, through the points, o*, and a', flg, i <;. the pro. 
 
 .1 the tWO lir-t. H D, 'haw t 1 n.l a' b', |*rsl- 
 
 lel to it', ami meeting the baa* line, i. T, in e* and ■'. I 
 
 through th*** points, w* 'haw p. rpeadfcnlar* to the l 
 
 ... «in ,-nt thi i lour "f 
 
 . liinite.l by tl" 
 /• ./, ami i/ o. 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 The faro, e' e', being that on which the cube rests, has no pro- 
 minence, and caunot therefore cast any shadow. It follows, then, 
 that the shadow, as above determined, is all that is apparent. It 
 is generally represented by a flat, uniform shade, laid on with the 
 brush, and produced by a greyish wash of China ink. 
 
 269. It will be observed that the lines, d b and b c, are parallel 
 to the straight lines, D B and B c. This is because these are 
 themselves parallel to the horizontal plane ; for when a line is 
 parallel to a plane (82), its projection on this plane is a line paral- 
 lel to itself; and hence we have this first consequence, that — 
 
 ]\~hen a straight tine is parallel to the plane of projection, it casts 
 a shadow on llie plane, in the form of an equal and parallel straight 
 line. 
 
 270. It will also be observed, that the straight lines, d d, b b, c c, 
 which are the shadows east by the verticals, projected in D, B, and 
 c, are inclined at an angle of 45° to the base lino ; whence we 
 derive the second consequence, that — 
 
 When a straight line is perpendicular to the plane of projection, 
 it casts a shadow on the plane in the form of a straight line, parallel 
 to the raijs of light, and consequently inclined at an angle of 45" to 
 the base line. 
 
 271. These observations suggest a means of considerably simpli- 
 fying the operations. Thus, in place of searching separately for 
 each of the points, e, b, d, where the rays of light pierce the hori- 
 zontal plane, it is sufficient to determine one of these points, such 
 as 6, for example, and through it to draw the straight lines, b d, b c, 
 parallel and equal to the sides, D B and B c, of the cube and 
 intersecting lines, inclined at an angle of 45° drawn from the 
 points, D c. 
 
 In the actual case before us, we may even entirely dispense with 
 the vertical projection, fig. 1", since it would have been sufficient 
 to prolong the diagonal, a b, to b, making b B equal to n a. or to 
 make the inclined lines, d d, or b b, equal to the diagonal, A B ; 
 because the vertical projection, c' c', and horizontal projection, c c, 
 of the same ray of light, are always of the same length, which fol- 
 lows from our having taken the diagonal of the cube for the direc- 
 tion of this ray, the two projections, a b and a' b', of this diagonal 
 being obviously equal. Whence follows the third consequence, 
 that — 
 
 //', through any point of which the two projections are given, we 
 draw a straight line, representing the ray of light, and if we ascer- 
 tain the point in which this ray meets either plane, the length <f the 
 ray in the other plane of projection will be the same. 
 
 2T2. Finally, it is to be observed that the distance, b d, taken 
 on the prolongation of the vertical line, c b, is equal to the entire 
 height, c' b', namely, that of the cube ; and consequently, in place 
 of employing the diagonal to obtain the various points, d, b, c, we 
 may make the distance, B d, equal to the height of the cube, and 
 draw, through d, a straight line, d b, parallel and equal to db, 
 and through b a second, b c, parallel and equal to b c, and then 
 join d D, c c. 
 
 Thus the shadow cast on a plane by a' point, is at a distance 
 from the projection of the point, equal to the distance of the point 
 itself from the plane. 
 
 273. Figs. 2 and 2" represent a prism of hexagonal base, sup- 
 posed to be elevated above the base line, but at the same time at 
 
 such a distance from the \crtical plane, that all tin- shadow i;tst 
 will be in the horizontal plane. 
 
 It will be seen that the vertical faces, a b, b C, and A F, aro 
 
 illumined, whilst the opposite ones, e d, d c, and Br, are in the 
 shade. 
 
 Of these latter faces, c D is the only one visiblo in the vertical 
 projection, fig. 2*, and represented by the rectangles c' d' H g, 
 which should be shaded to a deeper tint than the CflBl shadows, 
 to distinguish it. 
 
 274. The operation by which we determine the shadow cast 
 upon the horizontal plane, is evidently the same as in the preced- 
 ing case; still, since the lower base, j h, does not rest upon the 
 horizontal plane, it will not be sufficient merely to draw the rays 
 of light through the points, c, d, E, f, of the upper side ; it is, in 
 addition, necessary to draw corresponding rays through the points, 
 J, I, G, H, of the base. 
 
 It is to be observed, as in the preceding case, that as these two 
 faces are parallel to the horizontal plane, the Bhadow cast by each 
 upon this plane will be a figure equal and parallel to itself; so that, 
 in place of seeking all the points of the shadow, it would ha\e 
 been quite sufficient to obtain one of these points, as d. for 
 example, of the upper side, and k, of the lower side, and then, 
 starting from them, to draw a couple of hexagons, parallel and 
 equal to a n c D E F. 
 
 It will also be understood, that as it is only the outside lines, 
 those of the separation of the light and shade, which make up the 
 contour of the shadow, it is not necessary to determine the points 
 which fall within this contour, and correspond to those points 
 in the object itself which do not lie in the lines of separation of 
 the illuminated and shaded parts. 
 
 275. Thus it is unnecessary to find the points, a, b. e, h ; and 
 generally, in making drawings, we do not seek tin- shadows cast 
 by points fully illuminated, or within the borders of the shaded 
 portion; and the contour of the shadow is derived simply from 
 points lying in the line of separation of the light and shade on the 
 object. 
 
 276. From what we have already explained, it will In- gi 
 
 that the projection in one plane of the Bhadow, cast by a point, •■■■■ i 
 be obtained by drawing the diagonal of the Bquare, a Bide of which 
 is equal to the distance of the point from the plane, as shown in 
 the other projection. 
 
 For example, the shadow, k, on the horizontal plane of the 
 print the two pi-j.-_i! ms ot win- h air i and I. li. >. .. an! .: in:' 
 
 be got by forming the Bquare, i Ik, a side of which, r /. i 
 to the distance, i /', of the point from tie- horizontal plane. 
 
 In the same way, we have the points, g, i,f, corresponding to 
 g. t, r. whi.h are the same height as the first above the plane. 
 
 For the points, c,d, e,f, which correspond to the upp 
 a'd', of the prism, we draw the diagonal, 1/ </', of l!,. 
 
 having for a side the height, o'tn, of the poist, d', above the 
 
 horizontal plane, and set out this diagonal from C to c, D to a, 
 E to e, &c 
 
 277. When several straight lines converge to a point, the 
 shadows they cast on either plane of projection must necessarily 
 
TIIK. PRACTICAL I»It M'lillT- 
 
 ■bo, cu nio tga to • p"ir.t. Thus, in the p> raroid, figa. 3 and 3*. 
 Ib» aprx of whirs U projected in the pointa, « and »'. Ihc edgea of 
 all the aide* brine directed to thia point, caat shadow, on tho 
 horizontal plane, bounded by line* corner. '. a, the 
 
 ahadow caat by the »|»v on the name plane. In OfdaT, then, to 
 find the ahadow east by a \-\ n 
 
 • . draw the ray of li^'ht through the apex, 
 
 ■ ' 
 draw linea to thin point fr- tn all 1 1 • la- of the 
 
 pyramid, if thia mil U|>on the plat;. I 
 
 b raiaed above the plane, it will !-■ neceHw. ladowa 
 
 caat by the various angles of tin- base, and thin draw straight 
 linea from tbeae to the ahadow of tin- apex. 
 
 • rVKAMID. 
 
 of a pyramid I 
 with, and the ■) i. it is neeeaaary lo Bod tin - 
 
 ban, ami by t 
 truncation. Tims tli. 
 
 - on the borizotttal plana, in the \- 
 whteh are obtained by drawing nroogh each point, in tin- 
 I 
 
 - './..IT. •*, which are wjna: 
 
 In Ibc borizonb - aa t<> meet the com 
 
 drawn through tin- pointa, r., f, q, ii. Then, it' «r dm lines 
 from t! I in tho 
 
 la] plan.-, wc hhall ohtain tl.- • by null of the 
 
 lateral edges of the pyramid. 
 
 W aamc reason that these edj.'es are diver* ly inclined to 
 
 -t by tin-in on tins plane have 
 
 r. nt inclinations to the base lino; but the adgoa of the 
 
 paraDal to tl. - 
 : parallel to tl - 
 been the rase bail i' i to the 
 
 l • rident that, in tbe position in which the pyramid in 
 
 - A E H D 
 
 and a r. r n, an- in the li^'lit, whilst tin -ir oppoaites, D 11 
 c o r b, are in the abode. This bat, wbJafa ia tlie only oni 
 in fig. 3*, ia there dbtinguished by a nodi rate abada of colour. 
 
 ■her. 
 !i n circular bna being a regular solid, all 
 that is I ■ running tbe Bam of separation of lieffit and 
 
 shade, in, nli.-n tin- cylinder is \ertical, to draw a couple • ■' 
 tangential to it, ami |mrallel to tin- a, 4 and 
 
 4*. n a the borlsontal plane, 
 
 in the linen, ao, it, tangent* to tbe cfaele, and inclined at the 
 
 By with tbe i-in 
 
 iration of lighl and shade, which are 
 
 ally in a' c and a* D i b appa- 
 
 V. • hajaa tlmi thl . 
 
 a r. a, o in the light, at . a r n, in tbe 
 
 aluule. A very small portion of tbii lout r. anil is 
 
 • 
 
 hailo«, it i« t,, l„. remarked, 
 that for the very reason Oiat Be line* of separation of light and 
 
 aluule are vertical, the ahad- 
 
 plane w I Baa, e a and J b, with an in. 
 
 . 
 l-arallel to the horizontal pla: 
 - Ives ; and all that ii 
 caat b\ ' —, x and &, and w ith tbe pointa, a, a, 
 
 - with a radii;- L The 
 
 ■iln, c a, J b. 
 
 . Villi AloTHIft. 
 
 ML Hitherto we I. . -i by an 
 
 I 
 r, that one bod) 
 
 a of the 1h«1i at one part of it caata 
 
 ■ iln-r. 
 
 •: of a short ,- 
 
 '•'■ 
 
 linil the line of eeparation i abada npoo tb 
 
 cylinder* ; and lor tl. • 
 tbe] projeedon, 
 
 ofitanx ' Jit also 
 
 I 
 ilniw tb 
 
 a' and B , anil i '. r* and 
 
 (/', to Bg. I and D tl. which separate tho 
 
 tight iVom tie - I drawing 
 
 draws 
 
 I. n, upon tlio 
 cylinder, a, is limited to that due to the |>ortion. <f r' ir\ of tbe 
 cin-uiui. I nt poiaia in the on: low are 
 
 determined, by first taking any pot . upon the arc, 
 
 i/' • li', and drawing throogh each of them 
 parallel rays of light, and lie 
 der, a', in tbe point-, c\ r\ /", a*. Ha\i 
 mention. si |„,inis on ti 
 
 • parallel to the first, and 
 - of light, and square on r lb 
 wbi.-h will | 
 
 - the onijiii- of the abadow*apoo tb 
 
 Aa jieen in a fonm r exainple, bjataad nrot tbe 
 
 | . »e can obtain bV log the 
 
 ■lidino rays I 
 
 MIAMiW I *ST BY A CVLI5nr.K fro* a ruts*. 
 383. Figa. 7 1 anaofa prism, 
 
 a, of an nulagnn a l ban '. »• 
 
 \ draw tbe ra.i 
 
 a of liirii'.. tiienby obtaining tbe point of contact, if, and, 
 tlio line of «e|»aratioii. n J,,,f hght and - 
 
 tbe oyhndrical 1 1 
 
 • the prisra. being in tbe dir. ■ 
 the ray of light, ami, consequently, bclined at an angle of I 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 the vertical plane, is considered to be completely in tho shade. 
 The edge line, a b, fig. 7, is therefore the lino of separation of 
 light and shade on the prism-shaped portion of the object, and 
 the surface, a bid, is consequently tinted. The shadow cast upon 
 the prism by the overhanging head, e, reduces itself to that due to 
 the portion, c' f' h', merely, of the circumference of the latter, and 
 it falls upon the two faces, c' f and/" ft', of the latter. 
 
 The lines indicated on the diagram, with their corresponding 
 letters, when compared with those of the preceding example, will 
 show that the operations are precisely the same in both cases, and, 
 in the latter, the curves, c ef and fg h, are the resulting outlines 
 of the shadow. In general, it is unnecessary to obtain more than 
 the extreme points of the curve, and another near the middle. 
 • Through the three points thus obtained, ares of circles can then be 
 drawn. The curves are, however, in reality elliptical. 
 
 SHADOW CAST BY ONE PRISM UPON ANOTHER. 
 
 284. Figs. 8 and 8" represent a couple of vertical projections, at 
 right angles to each other, of a prism of an octagonal base, sur- 
 mounted by a similar and concentric, but larger prism. Although 
 the operations called for in this case are precisely the same as in the 
 two preceding, still it is an exemplification which cannot be omitted; 
 and its chief use is to show, that 
 
 The shadow cast by a straight line upon a plane surface is inva- 
 riably a straight line ; and, consequently, it is sufficient to determine 
 its extreme points, in order to obtain tlie entire shadow in any one 
 plane. 
 
 Thus, the straight line, e' c', easts a shadow upon the plane 
 facet, fc, which is represented by the straight line, ec. 
 
 It is further obvious, that 
 
 The shadow cast upoti a plane surface, by any line parallel to it, 
 must be parallel to that line. 
 
 Thus, the straight line, e' g', of the larger prism, B, being paral- 
 lel to the plane facet, f g', of the prism, a, casts a shadow upon 
 the hitter, which is represented by the straight linc,/g-, parallel to 
 the line, F G, the vertical projection of the edge, f' g'. It is not, 
 however, the same with the portion, ef, because the coiTesponding 
 portion, e' f', of the edge of the larger prism, is not parallel to the 
 facet,/ e 1 . 
 
 SHADOW CAST BY A PRISM UPON A CYLINDER. 
 
 285. Figs. 9 and 9" represent vertical projections, at right angles 
 to each other, of a portion of an iron rod, a, surmounted by a con- 
 centric head, B, of a hexagonal base. The main object of tliis 
 diagram is to show, that 
 
 When a right cylinder is parallel, or perpendicular, to a plane of 
 projection, any straight line, which is perpendicular to the axis of the 
 cylinder, and parallel to the plane of projection-, casts a shadow upon 
 the cylindrical surface, which is represented by a curve, similar to 
 the cross section of such surface. 
 
 If, therefore, the cylinder is of circular base or cross section, as 
 we have supposed in the present case, the shadow cast upon it 
 will be a portion of a circle, of the same radius as the cylinder. 
 Thus, the straight line, d' f', situated in a plane, at right angles to 
 tho axis of the cylinder, a, and being, at the same time, parallel to 
 the vertical plane, casts a shadow upon the cylinder, which is re- 
 
 presented by the portion, c c/, of a circle, the centre, «', of which is 
 obtained by drawing through the point, o, a line, o i, representing 
 tho ray of light, and extending to the prolongation of the edge, d' 
 f'. Tho line, o I, cuts the circumference of tho cylinder in the 
 point, i', which is squared over to i, upon tho other projection, h i, 
 fig. 9, of the ray, o I. The lower point, c, is obtained from tin- 
 upper one, t', being symmetrical with reference to the axis of the 
 cylinder. Tho ray, H t, being continued to the axis, cuts it in the 
 point, o', which is, consequently, the centre of tho arc, c i ■ i, the 
 radius, io'or co', of which is equal to that, o i', of the cylinder. 
 
 286. The edge, f' h', although situated in a plane perpendicular 
 to the axis of the cylinder, is not parallel to the vertical plane, and 
 does not, therefore, cast a shadow of a circular outline upon tho 
 cylinder, but one of an elliptical outline, as fg h, which is obtain- 
 ed by means of points, tho operations being fully indicated on tho 
 diagrams. If the head, b, which casts a shadow upon the cylin- 
 der, were square, instead of hexagonal, as is often the case, one 
 of tho sides of the square, as I n', fig. 9*, being perpendicular to 
 the vertical plane, would cast a shadow on the cylinder, having 
 for outline the straight line, H i, making the angle of 45° u ith the 
 axis. 
 
 Thus, wlienever a straight line is perpendicular to the plane if 
 projection, not only is Us shadow, as cast upon this plane, a straight 
 line, inclined at the angle of 45°, but it is also the same on an object 
 projected in this plane, no matter of whafform. 
 
 Observation. — In the four examples last discussed, we have only 
 represented half views of the objects in the auxiliary vertical pro- 
 jections, figs. 6", 7," 8", and 9*, this being quite sullicienl for deter- 
 mining the shadow, as it is only that produced bj this half which is 
 seen. It is obvious, that the same operations will answer the pur- 
 pose, whether the axis of the object be horizontal or vertical. 
 
 SHADOW CAST BY A CYLINDER IN AN OBLIQUE POSITION. 
 
 287. In figs. 5 and 5', we have given the horizontal and vertical 
 projections of a right cylinder, having its axis horizontal, but 
 inclined to the vertical plane. As in this oblique projection we 
 cannot obtain the points of contact of the luminous rays with tho 
 base in a direct manner, it becomes necessary to make an especia. 
 diagram, in order to determine the lines of separation of light and 
 shade, which are always straight lines, parallel to the axis of the 
 cylinder. 
 
 To this effect, we shall make use of a general construction, sus- 
 ceptible of application to a variety of such cases. This construction 
 consists in determining the projection of the luminous ray, in any 
 
 given plane, perpendicular to either of the geometrical planes, w hence 
 
 may be derived its form and aspect in either of the latter planes. 
 It follows, that if we have any curve in the given plane, we can 
 easily find the point of separation of the light and shade situated 
 upon this curve, by drawing a couple of tangents to it, parallel to 
 the ray of light projected in this plane, and transferred to the otlier 
 plane of projection. 
 
 Thus, let r o and r' o' be the projections of the luminous ray . 
 it is proposed to find the projection of this ray upon the plane, a b, 
 of the base of the cylinder. To obtain this, project the point, R 
 to r, by means of a perpendicular to a b, and r o represents tho 
 horizontal projection of the ray of light upon the plane, a b; and 
 
' 
 
 .-.Iby •qu«riri. 
 *-.- lrn<\ tmi /■•utal. 
 
 • Ittpeea, 
 
 »', .-'. :. ■ -. .. nl '' • *• r- ..-.i! |« .yvtii.ru (.f the .I'd' .-I ill.- . Win. I. r. 
 taking three Uageota far:. 
 
 - 
 
 I and/e, 
 
 ; independently 
 5", in the Colli 
 i- at a" b\ haril 
 • 
 the raj 
 
 • 
 
 > of the 
 
 <i' m //*, 
 
 paraJli-l t.> •> r\ ami tl • - nt the 
 
 .nl.-. ulii.h are 
 the horizontal | ..iiculara 
 
 drawn from tl 
 
 en thus 
 be difficult t<> find tin 
 i 
 ■ 
 
 .. those 
 
 - 
 
 -• parallel to the line, r* o. 
 
 I, in the ho riAnnt.il pro- 
 1 with the extn 
 
 I 
 ■ 
 and « paria. 
 
 PRINCIPLES OP SHADING. 
 
 Purr XXVII. 
 
 -should 
 
 difficult • .wily Miniii.tn ■ 
 
 light and iJia.1- 
 
 - 
 II an illumined surface has all its points at an equal 
 
 from the eye, it must rceru* a clear shade of uniform inten- 
 sity Aroughnut. 
 
 - ippoaed 
 to be parallel nii.l perpendicular to tl all »ur- 
 
 • 
 
 ■ 
 
 ' I - illel to tarn ether, and 
 
 illumin manner, that which is nearer to the eye should 
 
 ■nsity. 
 \ '. inclined to the plane of tfte picture, 
 
 .•lances from the ry. 
 
 ■ ■ : 
 
 portion of an ob ur; thi* 
 
 ■ 
 i at which is mitrr directly pre- 
 
 - 
 - 
 still, at i 
 
 - 
 
 H 
 
 m inten- 
 sity throm 
 
 • \ VIII., whi h 
 
 pon i ho 
 
 more pi 
 
 i. in- in ; tj with the tw 
 
 I 
 
 • - tint. 
 .-! upon the t x Will . 
 
 M 
 
 \ 
 
 li-rably 
 • ■ £*• 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 297. IV7ien two surfaces in the shade are unequally inclined, 
 u-ith reference to the direction of the rays of light, the shadow cast 
 tnj any object should be deeper upon that which receives it more 
 a i recti y. 
 
 Thus, the shadow, a dfe, east upon the faee, f, of the prism, 
 fig. 1, Plate XXVI., should be slightly stronger than that cast 
 upon the face, g, because the first is more directly presented to 
 the light than the second, as shown by the lines, /' h' and /' c', 
 fig. 7". 
 
 These first principles are exemplified in the finished figures on 
 Plate XXVI., XXVII., and subsequent ones. 
 
 As, in order to produce the gradations of shades, it is important 
 to have some knowledge of actual colouring or shading by means 
 of the brush, we shall proceed to give a few short explanations of 
 this matter. 
 
 Two methods of producing the graduated shades are in use — 
 one consisting in laying on a succession of flat tints ; the other, in 
 softening oft* the shade by the manipulation of the brush. 
 
 We have already said two or three words about the laying on of 
 flat tints, when treating of representing sections by distinguishing 
 colours. (137.) These first precepts may serve as a basis for the 
 first method of shading, which is the less difficult of the two for 
 beginners. In fact, according to it, the graduated shade is produced 
 by the simple superposition of a number of flat tints. 
 
 FLAT-TINTED SHADING, 
 
 298. Let it be required to shade a prism, A, Plate XVIL, with 
 flat tints : — 
 
 According to the position of this prism, with reference to the 
 plane of projection, as seen in fig. 1, it appears that the face, a' b'i 
 is parallel to the vertical plane, and is fully illumined ; it should, 
 consequently, receive a clear uniform tint, spread over it by the 
 brush, and made either from China ink or sepia, as has been done 
 upon the rectangle, a, b, c, d, fig. A. When the surface to be 
 washed is of considerable extent, the paper should first be prepared 
 by a very light wash, the full intensity required being arrived at by 
 a second or third. (137.) 
 
 The face, V g', being inclined to the vertical plane, and com- 
 pletely in the shade, should receive a tint (294) deepest at the 
 edge, b c, and gradually less intense towards g h ; this is obtained 
 by laying on several flat shades, each of different extent. For this 
 purpose, and to proceed in a regular manner, we recommend the 
 student to divide the face, V g', fig. 1, into several equal parts, as 
 in the points, 1', 2', and through these points to draw lines parallel 
 to the sides, b c, g h, fig. A. These lines should bo drawn very 
 lightly indeed, in pencil, as they are merely for guides. A first 
 greyish tint is then spread over the surface comprised between the 
 first line, 1 — -1, and tho side, b c, as in fig. 2; when this is quite 
 dry, a second like it is laid on, covering the first, and extending 
 from the side, b c, to the line, 2 — 2. as in fig. 3. Finally, these 
 are covered with a third wash, as in liir. A, extending to the outer 
 edge, g h, and completing the graduated shade of the rectangle, 
 b r g h. 
 
 The number of washes by which tin' gradation is expressed, 
 evidently depends upon the width of the surface to be shaded ; 
 and it will be seen that the greater the number of washes used, 
 
 tho lighter they should be, and the lines produced by the ed •, - of 
 
 each will he less hard, and a more beautiful effect will result 
 
 The student must remember to efface the pencilled guide-lines, 
 as soon as the washes are sufficiently dry. 
 
 299. This method of overlaying the washes, and covering a 
 greater extent of surface at each succeeding time, is preferable to 
 the one sometimes adopted, according to which the whole surfaee, 
 bg h c, is first covered by a uniform wash; a second h, in 
 
 laid over b 2—2 c; and finally, a third over the narrow strip, 
 b 1 — 1 c. When the shade is produced in this manner, theei 
 the washes are always harder than when the washes are laid on as 
 we recommend — tho narrowest first — for the subsequent washes, 
 coming over the edge of each preceding one, soften it to a consi- 
 derable extent. 
 
 The face, e° a 1 , fig. 1, being likewise inclined to the vertical plane, 
 but being wholly illumined, should receive a very lighi shade I 392 ), 
 being, however, a little holder towards the outer edge, e /', fig, A. 
 The shade is produced in the same way as that of the face, I g , 
 but with much fainter washes. 
 
 300. Let it be proposed to shade a cylinder, fig. [3, with a 
 of flat tints :— 
 
 In a cylinder, it is necessary to give the gradations of shade, both 
 of the illumined and of the non-illumined portion. In reference to 
 this, it will be recollected that the line of separation, a A, of fight 
 and shade, is determined by the radius inclined at an angle of 45°, 
 as o a, fig. 4, perpendicular to the ray of light; consequently, all 
 the shadow proper, which is apparent in the vertical projection, fig, 
 [§, is comprised between the line, a b, and the extreme gen 
 c d. Consequently, according to the principle already laid down 
 (296), the shade of this portion of the surface should he graduated 
 from a b to c d, as was the case with the inclined plane surface. // e '. 
 fig. 1, the greater intensity being towards ah. 
 
 On the other hand, all that part of the cylinder comprise 1 1„. 
 tween the line, a b, and the extreme generatrix, fg, is in the liglit : 
 at the same time, from its rounded form, each generatrix is at a 
 different distance from the vertical plane of projection, and makes 
 different angles with the ray of light. Consequently, this portion 
 of the surface should receive graduated shades. (292.) To i 
 the effect in a proper manner, it is necessary to know what pari of 
 the surface is the clearest and most brilliant ; and this is evidently 
 the part about the generatrix, e i, fig. [IB, situated in the vertical 
 plane of the ray of light, k o, fig. 4. In consequence, In 
 of the visual rays being perpendicular to the vertical plane and 
 parallel to the line, v o, the portion which appears to the eye to 
 be the clearest will be nearer to this line, v o, and may be limited, 
 on the one hand, by the line, T o, bisecting the angle made by the 
 lines, B and v o, and on the other, by tin- line, K o: squaring 
 over, then, the points, e 1 and m', fig. 4. and drawing the lines, t i 
 ami hi n, fig. 3, we obtain the surface, e i m n, which is the most 
 illumined. 
 
 301. This surface is bright, and remains white, when the cylinder 
 is polished, as a turned iron shaft, for example, or a marble column ; 
 it is covered with a light shade, being always clearer, however, than 
 tin' rest of the surface, when the cylinder is unpoltt 
 
 302. Alter these preliminary observations, we may proceed to 
 

 the i 
 
 sttadr the ry«nu>r, f m' «" e*. fig . 4, dSridtng il int.. a c-rUin nun*- 
 bar of eqaal parts, the not numerous Meaning m the cylinder u 
 |TMlif. Tk.»din*.»iff squared over to the vertical projection, 
 ■ad .traijfct tnr. drawn H.+tly witfc the pencil, aa limiting guides 
 fur the eoloor. We thro lay ■ fight gray ahade on the surface, 
 m c i b, fig. 5. to laiiiph* at once the put in tar ahade ; whea 
 this b dry, we lay oa a eeeood covering, the fine, a k, of arparatinn 
 of light and ahade, aad extending over a dhriaioa oa either aide of 
 it, aa abown in fi,'. 6 . we afterward* lay oo a third ahade, covering 
 two divisions to the right aad to the left, aa in fig. 7 ; and proeeed 
 at the seme manner, eorering more aad more each time, always 
 keeping to Ate pencil lines. IV d fl ere n t stages are u pi ea t u ted 
 in fig*. 8, 9, and 10. 
 
 ,t .hade the part,/? i g, laying on an tc aaaire ahadea, 
 bat fighter than the preceding, as indicated in figs. S. 9, and 10. 
 
 Trio operation is finally terminated by laying a light « 
 the whole, leaving untouched only a very small portion of th< 
 earftm, e at a i, fig. B- This last wash has a beautiful and i 
 
 MIAMI.; BT SOfTEXED U 
 
 -torn of shading differs from tho former in pt 
 
 .ht and >h:ui. I 
 by manipulation with th<- brush in U. .r: this 
 
 system possesses the adrantage over the first, of not leaving any 
 !.'■•«. bMbbs* :!.'■ bsssbTsbJ aaasaaa of sssvJa, wkkh aonaetasss*. ■•;•- 
 pear ban . and seem to represent facets or (lutings, 
 
 - 
 jchimry, however, the former «;.-' 
 bringing out the oljects so shaded in a remarkable manr 
 
 .ail machinery to be sluuled in thai manner, 
 whilst architectural subjects will lo> .1 according to 
 
 •bade L« miii b more diffiou'v 
 ing considers!. _• in the 
 
 .' systematic course. 
 
 -< d to shade a truncated hexagonal pyramid, 
 . WII 
 
 - solid, with r ■ • vertical plane 
 
 of projection, i» the aame aa that of the prism, fig. A- Thus the 
 face, abed,*!. uniform flat a! 
 
 rigorously kee; 
 
 ■•■ttom, aa the lace is not quite parallel ' 
 |>l.in«\ 
 The ' 
 
 ply a first 
 
 I — 1. as a limi 
 this »..ft. run _- i. prod ..-. -i '■■. . l.-arin^ the braeh, ■ • thai the colour 
 
 toe aha.: .) be taken up in the brush 
 
 once or • 
 
 being t. ,j ^ ou t|j r ,, 
 
 abject, 
 
 Wkn this first wash ia w«D dry. a second is laid over it. produc- 
 . m tin- same manner, and extending further to the right, 
 covering the apace, b e 8 — A aa shown ia fig. 16. Pi mailing 
 in the same manner, 1-PfTnaig to the Bomber of divisions of the 
 fa a, asj aj '.. i _-.:. aaai r m* ••>!. • ■:.-, BfoaVjata| aa mmimtm aaaaa, 
 »g»cfig. O. 
 
 The oprralions are the same for the tore, « a a/, which b nearly 
 parpendicular to the rays of fight, bat b considerably inclined to the 
 a|aaj ..t" probtssom. 
 
 on this face should be gradua' m ef to a J, but also 
 
 (rum r a to/ A Abo, on the face, b g h c, in the shade, the tint 
 should be a trine darker at the base, c a. being graduated off 
 tow arda b g. 1 -so simple in form as the one under 
 
 considi I :y may be neglected— at any rata, by the 
 
 beginner— a- only increasing hi* difficulties ; the proficiec'. 
 other It. • ,eee refinement* assists 
 
 and truthful representations. 
 
 .- with softened waahea, 
 \\VI1. 
 
 ■ the indications gi\. • ilar im- 
 
 -:. jl.-s. as explained with reference to the hat- wash 
 sliading, the desired effect may lie similarly pt 
 
 - irvcly necos.tr i irrutn- 
 
 many ports aa I I ; a first shade 
 
 Baa, a A, of separati d shade, 
 
 and th;- ff in both directions, as in fig. 1 1 . a 
 
 . 
 off, and in this manner we attain th. 
 13, and O. 
 Wa I .1 it nn i near) -..ms of all the 
 
 preceding cxai ;racti*e these n 
 
 . rajsviiiy 
 
 ..! can-. If they i-rr on the dark aid 
 
 • 
 
 dry, and then slightly moarton 
 
 i a clean rag. lighta 
 
 taken out in ' > their minuteness or 
 
 a flat ah 
 
 "ff tlie 
 s-aah. 
 
 - 
 bave already been discussed, as in-ti- 
 cated in _ uidea, also, in sharBno; 
 
 with w.i' shades in that pbte are pro- 
 
 \ \\ II. represent the 
 actual appear . -.i -shading mei! 
 
 Fina: f a much Urger 
 
 ..Me to produie largo 
 waahea with similarity and smoothness of I 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 CONTINUATION OF THE STUDY OF SHADOWS. 
 
 Plate XXVHL 
 
 SHADOW CAST UPON THE INTERIOR OF A CYLINDER. 
 
 308. When a hollow cylinder, as a steam-engine cylinder, a cast- 
 iron column, or a pipe, is cut by a plane passing through its axis, 
 we have, on the one hand, a straight projecting edge, and, On the 
 other, a portion of one of the ends, which cast shadows upon the 
 internal surface of the cylinder. 
 
 We propose, then, to determine the form, as projected, of the 
 shadow cast upon its interior by a steam-engine cylinder, a, sec- 
 tioned by a plane passing through its axis, figs. 1 and 1". In the 
 first place, we seek the position of the shadow cast by the rectilinear 
 projecting edge, B c, which is, in fact, produced by the intersecting 
 plane, b' a'. This straight line, B c, being vertical, is projected 
 horizontally in the point, b', and casts a shadow upon the cylinder, 
 as represented by the straight line, bf, which is also vertical, and 
 is determined by the point, b , of intersection of the ray of light, 
 b' 4', with the surface of the cylinder, b' b' o'. Thus, when a 
 straight line is parallel to a generatrix of the cylinder, the shadow 
 cast by it will be a straight line parallel to the axis. It is, therefore, 
 evidently quite sufficient to find a single point, whence the entire 
 shadow may be derived. 
 
 309. We next proceed to determine the shadow cast upon the 
 interior of the cylinder by the circular portion, b' e' f', of the upper 
 end. If we take any point, e', on this circle, and square it over to 
 E in the vertical projection, and draw through this point a ray of 
 light, e' e', e e, it will be found to meet the cylindrical surface in 
 the point, e', which is squared over to e, the length of the ray being 
 equal in both projections, according to the well known rule. This 
 applies to any point in the arc, e' f'. The extreme point on one 
 side is obtained by a tangent to the circle in the point, f', giving 
 the point, f, in the vertical projection ; the opposite extreme point, 
 b, being already given as the top point of the straight edge, B c ; we 
 have, therefore, the curve, Feb, for the upper outline of the shadow 
 due to the circular portion, b' e' f'. 
 
 310. If, as in figs. 1 and I", we suppose the piston, p, with its 
 rod, T, to be retained unsectioned in the cylinder, we shall have to 
 determine the form of the shadow cast by the projecting part of 
 the piston upon the interior of the cylinder, and represented by the 
 curve, d ho. For this purpose we take any points, b', h', o', on the 
 circumference of the piston, and draw through them, in both pro- 
 jections, the rays of light which meet the surface of the cylinder, 
 b' b' o, in the points, V h! o', which are projected vertically in dho: 
 the curve passing through these points is the outline of the shadow 
 sought. The curved portions of these shadows are elliptical. 
 
 The piston-rod, T, being cylindrical and vertical, casts a shadow, 
 of a rectangular form, upon the interior of the cylinder, the vertical 
 sides, if, k I, being determined by the luminar tangents, i' t', k' K, 
 parallel to the axis. 
 
 SHADOW CAST BY ONE CYLINDER UPON ANOTHER. 
 
 311. Let figs. 2 and 2* be the projections of a convex semi- 
 
 cylinder, A, tangential to a concave semicylinder, B, forming a pat- 
 tern often met with in mouldings. 
 
 This problem, which consists in determining the shadow proper 
 of a convex cylinder, together with that cast by it upon the surface 
 of a concave cylinder, in addition to that cast by the latter upon 
 itself, is a combination of the cases discussed in reference to figs. 4 
 and 4*, Plate XXVI., and to figs. 1 and 1' in the presenl plate. The 
 operations called for here are fulrj indicated nn the diagram; and 
 we have merely to remark, that it is always well to start by deter- 
 mining the extreme points, as c', D,' which limit the shadow propel 
 c g, and cast shadow, v> c g: these points may be obtained more 
 exactly, as already pointed out, by drawing the radii, o c' and W a, 
 perpendicular to the luminous rays. 
 
 shadows of cones. 
 
 312. In this branch of the study, we propose to determine, first, 
 the shadow proper, or the line of separation of light and shade upon 
 the surface of the cone ; second, the shadow cast by the cone upon 
 the vertical plane of projection; and, third, the shadow cast upon 
 the cone, and upon the vertical plane of projection, by a prism of a 
 square base, placed horizontally over the cone. 
 
 313. First: We have laid it down as a general principle, that, in 
 order to determine the shadow proper of any surface, it is necessary 
 to draw a series of parallel luminous rays tangential to this surface. 
 When, however, the body is a solid of revolution generated by a 
 straight line, as a cylinder or a cone, it is sufficient to draw tangen- 
 tial planes parallel to the luminous rays, to obtain the lines of sepa- 
 ration of light and shade. 
 
 In the case of the cone represented in figs. 3 and 3% and of which 
 the axis, s T, is vertical, the operation consists in drawing from the, 
 apex, s and s', two lines, making angles of 45", as s s and s' s\ 
 giving, in the point, s', the shadow cast by this apex upon the hori- 
 zontal plane. From this point we draw a straight line, a' s', tan- 
 gential to the base, a' c' b', r.f the cone. This straight line repre- 
 sents the plane, tangential to the cone, as intersecting the horizontal 
 plane of the base; and the contact generatrix is then obtained by 
 letting fall from the centre, s', a radius, s' a', perpendicular to the 
 line, a' s' ; and this line, s' a', is the horizontal projection of 
 the lines of separation of light and shade. The vertical pr- 
 of this straight line is obtained by squaring over the point of con- 
 tact, a', to a, and then drawing the straight line, s a. The othei 
 line, s b, of the separation of light and shade, is similarly obtained 
 by means of the tangent, s' b'. Its vertical projection is, however, 
 not apparent in fig. 3°. 
 
 314. Second: The shadow cast by the cone upon the vertical 
 plane is limited, on the one hand, by the line of separation of light 
 and shade, and, on the other, by the portion of the illumined base 
 comprised between the two separation lines. Now. the straight 
 line, s a, casts a shadow, represented by the straight line, ** a', as 
 indicated in the diagram ; and the base, a' e' c' b', casts a shadow, 
 represented by the elliptic curve, fe d a', which is determined by 
 points, as in the case considered in reference to fig. 5, Plate XXVI. 
 
 315. Third: The shadow cast by the lower side, <; it, of the 
 rectangular prism, p, upon the convex surface of the cone, is found 
 in accordance with the principle already enunciated — that when a 
 straight line is parallel to a plane of projection, it casts a shadow 
 
TIIK I <MAV8 
 
 u;> ■-,•'..» |'.v •.•■>■ \ • n SjajHBti I . ^ -■-.. .' IhM, i-jua! lad 
 paralli | a plan.-, 
 
 M V parallel to iU baar, the shadow 
 upon ti..« pta: 1 by drawing from t). 
 
 ban, itn tad ■;• ■•-. the a\i- ■ •!' V.i- rone, sin! projected borizonUlly 
 iaooi ray. which nm ti this pUm 
 at, t", upon Um 
 
 ' draw the sir. In- tlu< 
 
 sliadow cut I' 
 
 rizontally in M 
 
 ! ' 
 
 _'tlt lilH-, 
 
 its in tlu- outline of the aha 
 ■ 
 
 manner, and taking »• 
 • m r>, any number of point! may be 
 obtaini-d. It ken at a 
 
 ..i^'lit line, i. ii, 
 this, much use- 
 - letermining the limiting 
 • before us, v. 
 
 n draw a luminous ray. and ll 
 
 of the eons, it 
 ■quart- i 
 
 W 
 V, of the same shadow, by i |nal to 
 
 I 
 iminoui ray, a.s situate, in a 
 
 ■ 
 ■ 
 
 by tlif Imiiiii 
 i ind drawn through the points, i and u, in the 
 
 . V, tiii- limit* of the ennro sought, 
 
 -m. r. upon tin- virti.-.-i! plai 
 rity apart from the principles alroad) : 
 
 SHADOW or ATI IMVEBTED COKE. 
 
 31" V. 
 
 : 
 
 ami 4*. ' 
 
 lined by draw. 
 - linen at an ni. 
 
 • 
 
 I be observe- i 
 
 I 
 - 
 
 The ra-. 
 
 rid shnw that U rti.m of tin . 
 
 the sha 
 
 less than that ii • , running 
 
 - 
 -ininates 
 at tin- i 
 
 . 
 square plinth, I 
 
 - 
 •I". i~ perpendicular t-. 
 - 
 
 ■ 
 
 •1, ami than drawing through the |>oiiit, o*, the straight Ik 
 paralU-l to the ray of light, as in Ihi ' is, at sn 
 
 boriaon; nasi draw the horisooUJ D 
 and it will Im- interaecti >l by I 
 which is consequent!) 
 
 ■ 
 of tin- body «'. 
 
 cal plain . in which tin- ray of light Ik tgn the 
 
 point whose - -lit as 
 
 • 
 drill U- the pi 
 
 of tin- |>oillt. 
 
 • a Irian- 
 
 I J 
 then, If a straight lino 
 
 ; by tin- luminous ray, 
 ■ 
 
 [f ti,. • likewise pass 
 
 through the ufa 
 
 wbothi r I s or not, an-l th 
 
 ral projection will, in I 
 
 tin- whl 
 
 and one or twi 
 in tin- . 
 oienl let 
 the laminous ray. a- 
 
 Aj U mil) g, of the ■ 
 
 f of the fruit 
 
 ■ 
 
 at iii tin- euro, x* f, i< a!V 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 105 
 
 by means of (he sectional plane, M N ; G 8 H, fig. 4, is the shadow of 
 the edge, g h, in that plane, and it cuts the circle representing the 
 section of the cone in the same plane in the point, i", which is ob- 
 viously a point in the outline of the shadow. 
 
 SHADOW CAST UPON THE INTERIOR OF A HOLLOW CONE. 
 
 318. Fig. 5 represents a plan of a hollow truncated cone, and 
 hi/. 5" is a vertical section through the axis of the object. It is 
 required to determine the horizontal projection of the shadow cast 
 upon the internal surface of the cone hy the portion of the edge, 
 a' b c, and the vertical projection of the shadow cast by the sec- 
 tional edge, D s, and by the small circular portion, a' d', projected 
 vertically in A D. 
 
 It is to be observed, in the first place, that the straight line, D s, 
 which is a generatrix of the cone, casts a shadow upon the latter, 
 in the form of a straight line, for the plane parallel to the ray of 
 light, and passing through this line, D s, must cut the cone in a 
 generatrix ; we therefore draw through the point, d', the ray of 
 light, d' d', making an angle of 45° with the base line, and from 
 the centre, s', let fall the perpendicular, s' e', this straight line 
 representing the horizontal projection of the intersection of the cone 
 by the plane passing through the line, d' s', and at the same time 
 parallel to the ray of light. By squaring over the point, e', to e, 
 fig. 5°, and joining e s, we have the vertical projection of this line 
 of intersection, and consequently the shadow cast by the line, D s. 
 The diagonal ray of light, d d, drawn through the point, D, deter- 
 mines the limit, d, of the shadow. The horizontal projection of the 
 extreme points, a' and c, of the curved outline of the shadow, is 
 also obtained by means of the tangents, s' a' and s' c, drawn from 
 the point, s, in which the ray of light passing through the apex 
 intersects the plane of the base of the cone. The determination 
 of the central or symmetrical point, b', of the same curve, is derived 
 from the straight line, D b, drawn from the point, D, parallel to the 
 ray of light, s R", as in the diagonal plane, that is, as at s R 1 ; the 
 point, b, in which this straight line meets the generatrix directly 
 opposite to that passing through the point, D, is projected horizon- 
 tally in the point, b', upon the prolongation of the diagonal ray of 
 light, s' s'. 
 
 319. The operation for finding any intermediate point in the 
 curve, is based on principles already explained ; namely, that when 
 
 a line or a surface is parallel to a plane, the shadow cast is also " 
 a line or a surface equal and parallel to the first. If, then, we 
 draw a plane, M n, parallel to the base, D F, of the cone, the 
 shadow cast by this base upon the plane, m N, will be a circle ; it 
 will consequently be sufficient to draw through the centre, o, fig. 
 5°, a ray, o a, which will meet the plane, M n, in a, which must 
 be squared over to a', on the horizontal projection of the same 
 ray. Next, with the point, a', for a centre, and with a radius 
 equal to D o, describe a circle, h'ii; this will represent the entire 
 shadow that would be cast by the base, D F, of the cone upon the 
 plane, M N ; this plane, however, cuts the cone in the circle, of 
 which M N is the diameter and vertical projection, whilst h' m' j n' 
 is the horizontal projection : this circle is cut by the former in the 
 points, h' and j, which are consequently two points in the outline 
 of the shadow in fig. 5, and the one of these which is seen in the 
 vertical projection is squared over to ft, upon the line, H N. 
 
 AITLICATIONS. 
 
 320. In this plate, as well as in Plate XXVI., we have given 
 shaded and finished representations of several objects, which servo 
 as applications of the several principles we have just pointed Out, 
 whether referring to shadows proper, or east, or to graduated shad- 
 ing. Thus, fig. /& represents flu- interior of a steam-engine cylinder 
 with piston and rod. In this example, regard has been had to the 
 general principle, that shadows are the stronger the brighter the 
 surfaces on which they fall would be, if illumined — that is, when 
 such surfaces are perpendicular to the rays of light, any shadow 
 cast upon them will be most intense ; the shade is consequently 
 made deepest about the generatrix, corresponding to g ft, in lig. 1 ', 
 and situate in the vertical plane of the rays of light passing through 
 the axis of the cylinder : to the right and left of this line, the shado 
 is softened oft*. 
 
 321. In the graduation of the shade, regard has also been had 
 to the effects of the reflected light, which prevents a surface in the 
 shade from being quite black. In a hollow cylinder, for the por- 
 tion in the shade, it is the generatrix, F f", fig. 1", which should 
 receive the shade of least intensity, as it receives the reflected 
 rays of light more directly. It will he recollected that the point, 
 f', is obtained by means of the radius, T F', perpendicular to the 
 ray of light. 
 
 Fi'T. [g represents a portion of a common moulding, and shows 
 how the distinction made between the shadow proper, and the east, 
 shadow, tends to bring out and show the form of the object. 
 
 Fig. © is an architectural fragment from the Doric order, given 
 as an application of shadows cast upon cones, as well as those cast 
 by cones upon a vertical plane. 
 
 This example also shows how necessary it is, in producing an 
 effectivs representation to make a iiSirenc* in tin intenai; f 
 shadows cast upon planes parallel to the plane of projection, and at 
 different distances from the eye; and also to give gradations to 
 such shadows when cast upon rounded Burfaces. 
 
 Fig. © is a combination of a cylinder with a couple of cones, 
 with their apices in opposite directions, showing how differently the 
 effects of light and shade have to be rendered upon each. 
 
 There is less shadow upon the upper cone than upon the cylin- 
 der, whilst there is more upon the lower cone ; the reasons of those 
 differences have already been explained in reference to tigs. 3" 
 and 4". 
 
 Fig. g represents an inverted and truncated cone, showing the 
 manner of shading the same, and the form of the shadow cast by 
 me square tablet above ; and fig. [Fis % aview of a hollow cone, sec- 
 tioned across the axis, presenting a further variety of combinations. 
 
 TUSCAN ORDER. 
 Plate XXIX. 
 SHADOW OF THE TORUS. 
 322. In geometry, the torus is a solid, generated by a circle, re- 
 viving about an axis, continuing constantly in the plane of tins 
 axis, in BUeh a manner, that all sections made hy planes passing 
 through the axis are equal circles, anil all sections by planes perpen- 
 dicular to the axis will also be circles, but of variable diameters. 
 
I 
 
 Tim rRuTH'M. i 
 
 .• « . n. that in architecture, the torus U on. 
 I/ p»ru of the ba~ . and <•!" the racial • 
 
 ■U „• das -^-1 »■• ^i- ■ •!■ or onnl l>3 ■■■ > r > "■'• V* ' K,-,t : ' : - ! ,: ' "'• 
 
 . in;,' about the 
 t.al sur- 
 
 k till' |.rilH-i|«l 
 
 Thus, by 
 
 . 
 
 the st-mkin 1. «, afc, which limit the contour <.f the loroa In tho 
 
 I 
 
 Km of st-pora- 
 
 . 
 
 ■ 
 •!.•.. ntal, b f. I': ■•■ cune will be 
 
 tdefa will lie in . 
 
 :.. the ray, I 
 ■ the torns, in the point, 
 
 I \. rti.-.illy in tli.- hori- 
 zon Ul li 
 Ulil tli I" 
 
 ■ 
 «nJ wfa in the rertieal plane pairing tbroogh the 
 
 l — J, we pro- 
 toned 
 
 ■ 
 ■ 
 
 parallel t" tfai i ..l piano, 
 
 .1 is, at an m 
 
 ht Hut it I. . 
 tnuinf. " 
 
 .. r t.. i*. in tl I 
 
 ,- i. drawn throngfa i" 1 . 
 I 
 an.l d, in the eurred I • but H 
 
 because of the large leala of tin- drawing, it k ■•■ 
 be done bj ■ 
 
 aa »' a', which 
 in a da 
 
 t,, the i Plato XXVI. ; that is 
 
 to say, »c seek tli" projection "t tli.- Ituninoui ray npon tl 
 
 o' a'. I lot fall u|xin ,: |.iiji.n. 
 
 Inr. «' i t taken upon tin- hnrinooa ray, • 
 
 U I npon the pi 
 
 '. until it 
 idblg with r'. Tln-n, aa tho 
 
 !<•, i- i-,ua! In 
 that of the point, a, tl I ..-#* uf 
 
 .lid tlie 
 | 
 
 ration. If. tin 
 
 light ainl shade, at in I I 
 
 . in n*. 
 Lai, n n*, 
 iwn the 
 ■ 
 
 which v 
 \ \\ I . ; and ■ 
 
 in l»>lh cases. 
 If tin- drenlar an- 1m- proton 
 npon it . 
 
 which iaal 
 
 the luminous ray. '1. . in tho 
 
 .'. drawn at a • 
 op, above tin- centre line, //, equal t-> t - . uf tho 
 
 horizontal paaalim Ihrongh the point, a*, below it. 
 
 When tin- shadow | la (a known", tl 
 
 plane — the plinth or | 
 
 number of linea parallel to tin- luminous ray. an.l then fii 
 
 i|-.>n the 
 I which la a cum- ; boil 
 Hon, 
 
 . /■', in tlii-> curvi 
 
 mi from the- point, / /', with the | 
 *I"li.- half of the line "f separation ■ ipon tho 
 
 il portion uft! 
 
 n, Is similar to the ai 
 
 :i..n.f J, whDat 
 ■ 
 
 rumounted by a eyflndrieal lilh-t, tlm 
 
 U f separation of de npon the latter « 
 
 the t..ruv Ti I -". Una 
 
 «i!l be the case with the Diet, i>. the Due ofaeparal 
 
 Tl.ii One, I 
 which it n »tr:. luminous rs\ 
 
 ,t./. a luminous ray. I 
 bortzontal plane, <i ./. in i, which |>-- otoj t<« 
 
 "the horizontal projection. Il 
 by tin- circular portion./'^', wkleh i* in lb 
 ■ 
 
 \ \ \ 1 . ■ 
 i v of the ] 
 
 iloation ..f tl..- shadow, nj, ■ ' 
 by (he cyllndl npon the annular got 
 
 li the fillet, l>. 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 SHADOW CAST BY A. STRAIGHT LINE UPON A TORUS OR 
 ,.,_ QUARTER-ROUND. 
 
 ■ 326. Fig. 3 represents the horizontal projection, as seen from 
 below, of a fragment of a Tuscan capital, of winch fig. 3" is the 
 vertical projection, the object of these figures being to show the 
 form of the shadow cast by the larmier, F, which is a square prism, 
 upon the quarter-round, A, which is annular. 
 
 We yet again recall the general principle, that when a straight 
 line is parallel to a plane, its shadow upon this plane is a straight 
 line parallel to itself. For the rest, it will be sufficient to compare 
 the operations indicated with those of figs. 3 and 3", Plate XXVIII., 
 to see that they are precisely the same : thus, on the onejiand, we 
 have the diagonal, g/, for the shadow east upon the quarter-round, 
 where it is limited by the curve, b el, the line of separation of light 
 and shade upon this ; and, on the other hand, we have the curve, 
 i" g V, likewise limited by the same curve, for the shadow cast by 
 the edge, g h, of the larmier upon the quarter-round. 
 
 Figs. 3 and 3" complete what refers to the shadow of the capital 
 of a column ; they show the operations necessary to determine the' 
 shadow cast by the line of separation of light and shade of the 
 quarter-round upon a cylinder, as well as that cast on the same 
 jylindef by a portion of the larmier. The operation, in fact, simply 
 consists in drawing the luminous rays through various points, i" e, 
 in a portion of the line of separation of light and shade upon the 
 quarter-round, finding their intersection with the cylindrical surface 
 of the shaft, e, bymeans of the horizontal projection. There is 
 no peculiarity or difficulty in this procedure, and the whole being 
 fully indicated upon the diagrams, we need not pause to detail it 
 further. 
 
 To render the diagrams just discussed more generally applicable 
 tnd intelligible, we have not given to the different parts the precise 
 proportions prescribed by this or that architectural order ; such pro- 
 portions, however, will be found in fig. &,, which represents the 
 model fully shaded and finished, being the entablature and column 
 vf the Tuscan order. A double object is intended to be gained by 
 this beautiful example of drawing ; namely, to show the application 
 of the principles laid down regarding shadows, and the distinctness 
 and niceties to be observed in the various intensities of the washes, 
 and in the general shading. 
 
 SHADOWS OF SURFACES OF REVOLUTION. 
 
 327. It will be recollected, that a solid or surface of revolution 
 is that which may be said to be generated by a straight or curved 
 line, caused to turn about a given fixed axis, and maintaining a uni- 
 form distance therefrom ; thus, the cylinder, the cone, the sphere, 
 the torus, are all surfaces of revolution ; so, also, is the surface 
 generated by the curve, a b c, revolving about the axis, a b, figs. 4 
 and 4*. It follows, from the above definition, that every section 
 made perpendicularly to the axis will be a circle, and all such sec- 
 tions w r ill be parallel. Every section made by a plane passing 
 through the axis will give an outline equal to the generating curve, 
 and which may be termed a ?neridian. 
 
 328. The shadow of a surface of revolution may be determined 
 in two different ways : by drawing sectional planes perpendicular 
 to the axis, and then considering the sections made by these 
 plunes as bases of so many right cones ; or by imagining a series 
 
 of planes passing through the axis, and then projecting the ray of 
 Ughl Upon these planes, so as to draw lines tangential to (he dif- 
 ferent parts of the outline, and parallel to the projections 
 ray of light, the points of contact of which will be points in the 
 line of separation of light and shade sought. This latter method 
 having been applied in the preceding figs. 1 and 1", Plate XXIX., 
 and figs. 3 and 4, Plate XXVIII., we deem it more useful, in the 
 present instance, to explain the operations called fur in the first 
 method. * 
 
 Take, then, any horizontal plane, b d, figs. 4 and 4', cutting the 
 surface of revolution in a circle, the radius of which is b e, and tho 
 horizontal projection, V e! d', through the points, b and d, draw a 
 couplo of tangents to the generating curve which forms tho outline 
 of the surface of revolution. These tangents will cut each other 
 in the point, s, upon tho axis, this point being the apex of an im- 
 aginary cone, s b d; through this apex draw a luminous ray, s / 
 and a' b', meeting the horizontal plane of the section, b df,\af,f; 
 from this latter point, the horizontal projection, draw two straight 
 lines,/' g 1 and/' i', tangents to the circle, V c d' ; then the points 
 of contact, g' and i', will be the two points of the line of separa- 
 tion of light and shade intersected by the plane, b d, and they are 
 therefore squared over to the vertical projection, fig. 4°, i, only 
 being there visible. 
 
 It is in a similar manner that the points, h and j', are deter- 
 mined, these points being situated in planes, c d and E F. parallel 
 to the first. R is to be observed, however, that, in these two last 
 cases, the imaginary cones will be inverted, and the lumino 
 must consequently be drawn to the left instead of l" the right, aa 
 has already been explained in reference to figs. 3* and 4", Plato 
 XXVIII. 
 
 329. When the tangents to the generating curve are v< il 
 is the ease with the sectional planes, M n and a I. the points, m and 
 n, o& the line of separation of light and shade, are determined by 
 lines, inclined at an angle of 45°, and tangential to the circular sec- 
 tions in the horizontal projection, because these circular sections are 
 the bases of imaginary cylinders and not cones. 
 
 When a sufficient number of points have been obtained in this 
 manner, as in fig. 4", a curved line is drawn through them all, which 
 will 'give the visible portion, m i n hj E, of the line of separation 
 of light and shade upon the surface of revolution. This method is 
 general, and may be applied to surfaces of revolution of any outline 
 whatever. 
 
 As it is w ell to determine directly the lowest point, /.. of this and 
 similar curves, it may be done in the same manner as for the torus' 
 figs. 1 and 1", namely, by drawing the ray of light, r b, at the same 
 inclination to tho base line, as it is in the diagonal and vertical 
 plane, and then drawing parallel to it a tangent to the outline of 
 the surface of revolution, the projection for the moment 
 supposed to be in a plane parallel to the ray of light, r.' a' ; th • 
 distance of the point of contact, A', from the axis, being then mea- 
 sured upon the horizontal projection, r' a', of the luminous ray 
 oives the point, k', which is finally squared over to /.. in the hori- 
 zontal line in the vertical projection passing through the same point 
 of contact. 
 
 A portion of this curve, namely, the lower part, t. k j, casts a 
 shadow upon the cylindrical fillet, co; to determine this shadow 
 
1 1 
 
 
 it wffl. u» U* fin4 |iar*. be ■ in — i y to d e laea t i the boruoatal 
 a of the run r. il;.u>j thro to draw lumir 
 
 t!ir- a.* • *«• or two p- »nU la the 
 
 thr borUoetal pr-^c. txm of the filifl. The p.. lD u ia ■ 
 
 I— it ami rare interwrt lb* rirrlr. an- thrr 
 
 thr vertical pro)-rtioa of 0» ow rare, wheaee i» drrived the 
 
 : f. The varioue operation Hue* art not indicated no the 
 
 1 coafaaioa, bat the pmwxding will be tmmij eon. 
 
 UO, Pig. 4* repreeenta the vertical projection of a bam*-. 
 m b often aeeo in balroniea of atone or marble, and eometimea 
 ng a* an avolated standard, or a* a j 
 ! ..an annular | 
 
 aortace of aliirh the baae of the fillrt raaU a aha-: 
 to •»■<■ that thai ahado* 
 a* thow occurring la fig*. 3 and 3*, Plata X\\ III . M well aa in 
 
 •■■.•' • • 
 
 ■ 
 r.f loiu.tir, eoaaWag of aartaeea of revo iti W< m amend 
 
 the etodrnt to draw them upon a large scale, and to determine the 
 imtflne of the ahadou - 
 
 which we have laid down. Such ba -vie of 
 
 W 
 - .uppoeed them to be drawn to a ».. 
 ml aiie. 
 
 ■ad combinati 
 wU br • tuil practice; but our labour-, would ba 
 
 ir.'.< naiaable wcrr »c to give them all. Our exemplification* involve 
 aD the | 
 
 \M> PRACTICAL DATA. 
 
 fin* dr-i 
 
 : ump*, in »li 
 . 
 
 . \ I \ 
 III l.il't if and /urn'itg pvmpu, in which l*.;!i the al«.%e actiuna 
 are combined. 
 
 :rt.ta. 
 
 '■' 
 - 
 
 ■ 
 
 I 
 
 -•■preeont the 
 
 .--■.■ 
 
 the diameter of the piatoa, and P for the weight or p raa m » oa tat 
 paaoa — -* 
 
 ipreaa tbia p i i aa an ia powada, it most ba 
 
 .at bring the weight ia pound, of a cubic foot of 
 
 formula then becomee— 
 
 ., D» II 
 P ba* 
 
 Bal n,. bbbuj n,. :.t I. .r _• . \|*. «-U ■ f.-.t. 
 
 333. Independently of thia load, which eorreapoada to the ueeful 
 •fleet of -the machine, the power an '.ng the piatoa 
 
 - paaaire reaiatancea to overcome, n.. 
 
 :1k- pUtoo against the aidea of the pump. 
 ' in the pipe*. 
 3d. The n-lanlation uf the water in its peaaage to the pump by 
 
 ■ 
 4th . live. 
 
 Theae reaiatancea can onh 
 
 ■I d'AubUson, that the load to 
 laJ to 
 
 II • 1-08; 
 
 ■ 
 
 l>- II 
 I • - - ' •! aud r.-d. 
 
 ■ 
 
 • rmula, 
 
 : t /. 
 
 icnuinrd by an expression 
 
 - 
 
 i of thai 
 .up. 
 
 . i Iba. to 
 the equ 
 
 I 
 
 •iiu. 
 
 Mr*. 
 335 W 
 
 m with 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 ail valves having a great body of water above them, and with their 
 uppeRsurfacc greater than the area of the orifice above. 
 
 LIFTING AND FORCING PUMPS. 
 
 336. A pump of this description ordinarily consists of a cylinder 
 with a short suction pipe, a discharge pipe, a solid piston, termed a 
 plunger, and suction and discharge valves. 
 
 Two such pumps are frequently coupled together, in which ease 
 a single suction and discharge pipe serves for both. 
 
 337. The power necessary to work one or more pumps is ex- 
 pressed by 52-5 D 2 II v, or, taking into account the force necessary 
 to work the piston by itself, 557 D'Hi; v signifying the velocity 
 in fret per minute. 
 
 This velocity is obviously obtained by multiplying the number 
 of strokes per minute by the length of stroke ; thus — 
 
 v = 2n I, 
 n being the number of baek-and-fonvard movements per minute ; 
 consequently, the power required is equal to 
 
 55-7 D 1 H x 2nl = 1114 D J H n I; 
 this product representing pounds raised one foot high per minute, 
 the measurements being in feet. 
 
 With these premises, w 7 e can solve such problems as the fol- 
 lowing : — 
 
 First : What force, F, is required to work a pump, having a 
 piston 6 inches in diameter, a stroke of 18 inches, and a velocity of 
 15 double-strokes per minute; the whole height between the well 
 • and the point of delivery being 70 feet ? 
 
 The velocity v = 2n I = 30 x U = 45 feet. Then F = 557 
 D a x H x v = 55-7 X -25 x 74 x 45 = 46,997 lbs. raised one 
 foot high per minute. 
 
 To express this in horses power, we must simply divide it by 
 33,000 ; therefore, 
 
 _ 46,997 
 
 33 000 = ' = horses power, nearly. 
 
 Second : What quantity will the same pump raise in ten hours ] 
 Assuming, according to the formula (333), the effective volume, 
 V = -6 D 2 I, or V='«x -25 x 15 = -225 cubic feet per 
 stroke ; 
 and the volume per minute, 
 
 •225 x 15 = 3-375 cubic feet ; 
 and per hour, 
 
 . 3-375 x 60 = 202-5 cubic feet. 
 The quantity of water raised in ten hours will consequently be 
 202-5 X 10 = 2,025 cubic feet. 
 Third: What diameter should be given to the piston of a pump 
 which raises 202-5 cubic feet of water per hour, the velocity being 
 45 feet per minute, the length of stroke 18 inches, and the height 
 to which the water is raised 75 feet? 
 
 The formula above, relative to the effective discharge per stroke, 
 V=-6D' x /, 
 by transposition, becomes 
 
 D ^nrx-r 
 
 Now, the volume, 202-5 cubic feet, discharged per hour, is, per 
 
 minute, 20-2-5 
 
 - 60 = 3375 cubic feet. 
 
 This hist again reduces itself to 
 2 x 1-5 x 3-375 
 
 225 cubic feet per stroke; 
 
 consequently, 
 
 D' = 
 
 Whence, 
 
 D =V / -JxV5 = 
 
 6 inches. 
 
 THE HYDF.OSTATIC PRESS. 
 
 338. This powerful machine is an application of the lifting and 
 forcing pump. It consists of a bulky piston, or plunger, termed a 
 ram, working in a cylinder to correspond, and communicating, by a 
 pipe of small bore, with a small but very strong forcing pump. 
 To the top of the large piston is fixed a table or platform, which 
 compresses or crushes what is submitted to the action of the 
 machine. 
 
 The pressure exerted upon the water by the smaller piston, is, 
 by means of the fluid contained in the pipe, transmitted to the base 
 of the ram; and as, according to the well-known hydrostatic law, 
 the pressure is equal on all points, the total force acting on each 
 piston will be in proportion to their area ; so that if, for example, 
 the diameters of the pistons are to each other as 1 to 5, the pres- 
 sure on the larger one, the ram, will be 25 times as great as that 
 exerted by the pump-piston. Suppose a man can apply a force 
 equal to 60 lbs. to the end of a lever 3 feet long, and that the point 
 of connection with the piston-rod is only'li inch from the fulcrum, 
 the leverage of the power will be 24 times as great as that of the 
 resistance, and the pressure upon the ram will consequently be 
 24 x 25 x 60 = 36,000 lbs., an effort equal to that of 600 men 
 acting at once. 
 
 In the hydrostatic press, we have, consequently, to consider two 
 mechanical advantages — that of the simple machine, the lever, and 
 that of the ram : these advantages are, however, necessarily com- 
 pensated for by the diminution in the velocity of the ram. 
 
 On these principles, enormously powerful presses and lifting- 
 machines have been constructed. The one capable of lilting 18,000 
 tons, at the Menai Tubular Bridge, is an unparalleled example. 
 
 HYDROSTATICAL CALCULATIONS AND DATA — DISCHARGE OF 
 WATER THROUGH DIFFERENT ORD7ICES. 
 
 339. The discharge of a volume of water, in a given time, varies 
 according to the velocity of the water, and depends upon the area 
 and form of the discharge orifice. 
 
 Surface Velocity. — The velocity of water at the surface of a water- 
 course or river, of which it is wished to ascertain the discharge, is 
 obtained by means of a float, which is thrown into the part where 
 the current is strongest. As the wind, if there is any, affects the 
 result very considerably, the float must project above the surface as 
 little as possible. A distance of as great a length as convenient is 
 measured on the part of the stream where the current is most regu- 
 lar, and the time occupied by the float in passing that distance is 
 noted by a seconds watch. The space passed through is then divided 
 by the time expressed in seconds, and the quotient will be the sur. 
 face velocity per second. 
 
Tin: i 
 
 •aaJ U> try aeveral fl *U in diftntl perta of the runroL 
 / -ore pwacd through by each float is 
 
 .3 ij «v «oJ> 
 
 \ 
 
 If the velority i< not uniform throw fth of the canal, 
 
 mr point du ■ * nul " 
 
 padJl^wnwI. the IwU uf which ju«t <ii|> into the water. The 
 
 • thin iiintnirncnt tK-ii 
 plani by it» moan rircumfiTei 
 
 [»■«**»«; |o the centra of the unmerf*ed part of the tl ..it — 1 1 1 ■ - pro* 
 dart npn — - 
 • 
 / 
 
 jihI tliat tin- i ll to IJfoOt, wh.it 
 
 i« the aur' UTOOt! 
 
 VI. •;!>• tliat 
 
 irhola body of 
 
 • I w for Iha ganging .if lha 
 
 dplying it by n 
 coefficient, wl 
 
 Tm m • ■■ 
 
 • ( iftj !• 
 of V U. 
 
 / ity of a current of which the 
 
 I- . , . • 88 x S 1*10 mat 
 
 Tlir i 'i» »" Op«l mtatvoOtUM or river of 
 
 ■;. tin- following formula: — 
 
 /A II 
 V* = 66 86 x \/ 
 
 V V I. 
 
 ■ hudnmtnt of lha exact level of tha 
 
 aurfare I iter lha 
 
 ■ 
 
 lit of lha GUI, II dot- 
 •li, L 
 / • tha irate in ■ wate- 
 
 .i width of •(■'> 
 
 ■ 
 
 •^MHvtioruil area. A, 
 
 = 35 X li = 43ii 
 
 r. 
 
 ■ 
 
 -oTft -8 
 
 V = 56B6> \ , ,_ , - -30 = 339 
 
 i una formula, it n neoeaaary ao aartnol lha 
 
 I under lha rmli- 
 . ■ multiply thia root by th« co-efficient 58 88 ; 
 
 and. finally, to auolmct from the p* 
 
 i are iii > 
 
 kiaoa or rur.v ii av 
 
 • ■•jii.nl to a cubic Dl 
 
 1 1 ' -99-29 litre- or cubic 
 Tin aw aECTtOH 
 
 AMi ! 
 
 :ui. w 
 
 inlform fall, tli. 
 
 ruiiiln : — D = A X V , in v. h 
 
 \ 1 area 
 
 < ity. 
 / V* 
 
 ■ . and the mean 
 D u ■ 1*065 s- 4*478 eabie in.ir.-, or 4-478 litre- par aacond 
 
 IV AT THE BOTTOM ' 
 
 849. Tin- velocity ■•(' irate at the bottom of water-couraea b> 
 
 ■ t > i -• 1 1 the mean *i loclty. 
 Pntfit \ .ist the -uri'aee velocity, \ me moai 
 
 eity, ati.l \" the ground velocity, (he relation of the three will !•« 
 erraoaaod by V" 8 V — V. Hud i- to -ay. tha vebcil 
 bottom • , i.il t" twice lha moan velocity minna tho 
 
 aarfaoa velocity. 
 
 / 1 rdodty of a wate-way at found to be 
 
 ■ . ami the mean relodty calculated t 
 la the ground velocity I 
 
 V* = a x 1-55 — 2= 110 i 
 l ■ velocity at the bottom of a water-eouraa leoda bo 
 
 nd carry' aw ay the bed, millennium:.' Ihe -i'b- ami OBaabjg 
 
 deal of damage; too -mall a velocity, on the other hand, by 
 allowing the matter raapandad in the water to aettli 
 
 1 
 
 The following (able ahowa the limit of velocity aooorani • 
 al the bed, which eannot be exoeeded without danger: — 
 
 N.lurr 
 
 Limit of tllP Vrlerit jf per tocond. 
 
 Ih 
 
 
 
 
 
 
 
 
 
 
 
 Rock friiL'm. nt« 
 
 N.h.l ro.k 
 
 313. /' T'.e prodooa "I" any -niree may alao 
 
 Bred by ilaiiiiiiim..' up the entire width of the -Iream with 
 thin pi.. 
 
 no, Tboaa ' 
 
 •ii. until the level of the water within them 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 is maintained above their centres ; so that when this is affected, 
 the discharge is calculated from the number of orifices which 
 require to be open. 
 
 The quantity of water discharged by each orifice of '02 m. in 
 diameter, in a board -017 m. thick, and under a column - 03 m. 
 e the centre, is 20 cubic metres in 24 hours. 
 
 Another method of gauging a stream of water, consists in setting 
 up an under or overshot sluice-gate at a similar dam, the discharge 
 being calculated according to the following rules in refereneo to 
 this subject : — 
 
 CALCULATION OF THE DISCHARGE OF WATER THROUGH 
 RECTANGULAR ORIFICES OF NARROW EDGES. 
 
 344. As it is of importance, in a majority of circumstances, to bo 
 able to calculate the discharge of water by sluice-gates, or by tlio 
 vertical discharge-gates of hydraulic motors, so as to know the 
 volume, and, consequently, the value of a stream of Water, We shall 
 commence by giving a table, which enables us to determine this 
 discharge in a very simple manner, and places these operations 
 within the capacity even of labourers and working mechanics. 
 
 TABLE OF THE DISCHARGES OF WATER THROUGH AN ORIFICE ONE METRE IN WIDTH. 
 
 Height 
 
 of the 
 
 
 
 
 
 
 Volume discharged in 
 
 itres per 
 
 second, co 
 
 responding to the b 
 
 eights:— 
 
 
 
 
 
 metres. 
 
 •2 m. 
 
 ■3 m. 
 
 •4 m. 
 
 ■5 m. 
 
 '6 m 
 
 •7 m. 
 
 •8 m. 
 
 10 m. 
 
 1-2 m. 
 
 |l,m. 
 
 1'fn. 
 
 1-8 m. 
 
 2 m. 
 
 2 5 m. 
 
 3'0 m. 
 
 3-5 m. 
 
 40 m. 
 
 4 
 
 50 
 
 61 
 
 71 
 
 79 
 
 86 
 
 93 
 
 99 
 
 110 
 
 121 
 
 130 
 
 138 
 
 146 
 
 154 
 
 172 
 
 188 
 
 201 
 
 215 
 
 5 
 
 62 
 
 76 
 
 88 
 
 98 
 
 107 
 
 116 
 
 124 
 
 138 
 
 151 
 
 162 
 
 173 
 
 182 
 
 191 
 
 214 
 
 255 
 
 251 
 
 268 
 
 6 
 
 75 
 
 91 
 
 107 
 
 117 
 
 128 
 
 139 
 
 148 
 
 165 
 
 181 
 
 194 
 
 207 
 
 218 
 
 229 
 
 257 
 
 281 
 
 301 
 
 321 
 
 7 
 
 86 
 
 106 
 
 122 
 
 136 
 
 148 
 
 161 
 
 172 
 
 192 
 
 210 
 
 226 
 
 241 
 
 255 
 
 267 
 
 299 
 
 327 
 
 350 
 
 374 
 
 8 
 
 98 
 
 120 
 
 139 
 
 155 
 
 170 
 
 184 
 
 196 
 
 219 
 
 240 
 
 258 
 
 275 
 
 290 
 
 305 
 
 341 
 
 374 
 
 400 
 
 427 
 
 9 
 
 109 
 
 135 
 
 156 
 
 174 
 
 191 
 
 208 
 
 220 
 
 246 
 
 267 
 
 289 
 
 309 
 
 326 
 
 343 
 
 382 
 
 420 
 
 450 
 
 481 
 
 10 
 
 122 
 
 149 
 
 173 
 
 193 
 
 212 
 
 228 
 
 246 
 
 272 
 
 298 
 
 321 
 
 342 
 
 362 
 
 380 
 
 424 
 
 466 
 
 500 
 
 533 
 
 11 
 
 133 
 
 161 
 
 189 
 
 212 
 
 230 
 
 249 
 
 267 
 
 299 
 
 327 
 
 353 
 
 376 
 
 398 
 
 418 
 
 466 
 
 511 
 
 550 
 
 587 
 
 12 
 
 145 
 
 178 
 
 206 
 
 230 
 
 251 
 
 272 
 
 291 
 
 321) 
 
 356 
 
 384 
 
 409 
 
 434 
 
 455 
 
 507 
 
 557 
 
 599 
 
 640 
 
 13 
 
 157 
 
 192 
 
 222 
 
 249 
 
 272 
 
 294 
 
 314 
 
 352 
 
 385 
 
 416 
 
 443 
 
 469 
 
 492 
 
 549 
 
 602 
 
 647 
 
 693 
 
 14 
 
 168 
 
 206 
 
 238 
 
 267 
 
 292 
 
 316 
 
 338 
 
 379 
 
 414 
 
 446 
 
 476 
 
 504 
 
 530 
 
 590 
 
 648 
 
 697 
 
 715 
 
 15 
 
 179 
 
 220 
 
 255 
 
 285 
 
 312 
 
 338 
 
 361 
 
 405 
 
 443 
 
 477 
 
 509 
 
 539 
 
 566 
 
 631 
 
 693 
 
 747 
 
 7 '.Hi 
 
 16 
 
 190 
 
 ,234 
 
 271 
 
 304 
 
 330 
 
 360 
 
 385 
 
 432 
 
 472 
 
 509 
 
 542 
 
 574 
 
 603 
 
 673 
 
 739 
 
 797 
 
 852 
 
 17 
 
 201 
 
 248 
 
 2S7 
 
 322 
 
 350 
 
 382 
 
 414 
 
 456 
 
 501 
 
 540 
 
 575 
 
 610 
 
 638 
 
 715 
 
 784 
 
 847 
 
 905 
 
 18 
 
 213 
 
 262 
 
 304 
 
 340 
 
 370 
 
 403 
 
 432 
 
 484 
 
 529 
 
 571 
 
 608 
 
 644 
 
 677 
 
 757 
 
 830 
 
 896 
 
 958 
 
 19 
 
 223 
 
 276 
 
 324 
 
 358 
 
 392 
 
 425 
 
 454 
 
 510 
 
 558 
 
 601 
 
 641 
 
 680 
 
 715 
 
 799 
 
 876 
 
 946 
 
 1011 
 
 20 
 
 235 
 
 29] 
 
 3£7 
 
 377 
 
 414 
 
 447 
 
 485 
 
 536 
 
 586 
 
 627 
 
 675 
 
 715 
 
 753 
 
 841 
 
 922 
 
 996 
 
 1Q66 
 
 21 
 
 247 
 
 305 
 
 354 
 
 396 
 
 431 
 
 470 
 
 512 
 
 563 
 
 615 
 
 664 
 
 708 
 
 751 
 
 790 
 
 884 
 
 96 ! 
 
 1046 
 
 1118 
 
 22 
 
 259 
 
 320 
 
 370 
 
 417 
 
 451 
 
 492 
 
 538 
 
 590 
 
 645 
 
 695 
 
 742 
 
 787 
 
 828 
 
 926 
 
 1014 
 
 1096 
 
 U71 
 
 23 
 
 271 
 
 334 
 
 388 
 
 434 
 
 472 
 
 515 
 
 550 
 
 616 
 
 674 
 
 726 
 
 776 
 
 823 
 
 865 
 
 968 
 
 1060 
 
 1146 
 
 1 22 1 
 
 24 
 
 282 
 
 348 
 
 404 
 
 452 
 
 492 
 
 537 
 
 574 
 
 643 
 
 703 
 
 758 
 
 809 
 
 859 
 
 903 
 
 1010 
 
 1 106 
 
 1 195 
 
 1278 
 
 25 
 
 294 
 
 363 
 
 420 
 
 471 
 
 516 
 
 559 
 
 598 
 
 670 
 
 733 
 
 790 
 
 843 
 
 895 
 
 911 
 
 1052 
 
 1 152 
 
 1215 
 
 1331 
 
 26 
 
 306 
 
 377 
 
 437 
 
 490 
 
 538 
 
 581 
 
 626 
 
 697 
 
 762 
 
 822 
 
 877 
 
 930 
 
 978 
 
 1094 
 
 1 198 
 
 1295 
 
 1 38 1 
 
 27 
 
 318 
 
 392 
 
 454 
 
 509 
 
 559 
 
 604 
 
 645 
 
 724 
 
 791 
 
 853 
 
 911 
 
 966 
 
 1016 
 
 1136 
 
 12 15 
 
 1345 
 
 1437 
 
 28 
 
 329 
 
 406 
 
 471 
 
 527 
 
 573 
 
 626 
 
 679 
 
 740 
 
 820 
 
 885 
 
 914 
 
 1001 
 
 1 05 1 
 
 1172 
 
 1291 
 
 1395 
 
 1 191 
 
 29 
 
 340 
 
 421 
 
 487 
 
 546 
 
 602 
 
 649 
 
 693 
 
 777 
 
 850 
 
 916 
 
 978 
 
 1037 
 
 1092 
 
 1220 
 
 1337 
 
 14 14 
 
 15 14 
 
 30 
 
 353 
 
 434 
 
 504 
 
 564 
 
 624 
 
 670 
 
 718 
 
 804 
 
 880 
 
 948 
 
 1010 
 
 1073 
 
 1129 
 
 1262 
 
 1385 
 
 1 194 
 
 15: 17 
 
 31 
 
 364 
 
 449 
 
 521 
 
 583 
 
 635- 
 
 694 
 
 741 
 
 831 
 
 909 
 
 980 
 
 1046 
 
 1109 
 
 1167 
 
 1305 
 
 1 129 
 
 1544 
 
 1650 
 
 32 
 
 376 
 
 463 
 
 538 
 
 602 
 
 655 
 
 715 
 
 765 
 
 857 
 
 939 
 
 1011 
 
 1079 
 
 1144 
 
 1205 
 
 1366 
 
 1 175 
 
 1594 
 
 17113 
 
 33 
 
 388 
 
 477 
 
 555 
 
 622 
 
 676 
 
 737 
 
 789 
 
 884 
 
 969 
 
 1043 
 
 1113 
 
 1180 
 
 12 12 
 
 1389 
 
 1521 
 
 164 l 
 
 1756 
 
 34 
 
 400 
 
 491 
 
 572 
 
 640 
 
 696 
 
 759 
 
 813 
 
 911 
 
 998 
 
 1074 
 
 1147 
 
 1216 
 
 1279 
 
 1431 
 
 1568 
 
 1693 
 
 1810 
 
 35 
 
 415 
 
 507 
 
 588 
 
 659 
 
 717 
 
 782 
 
 837 
 
 938 
 
 1027 
 
 1103 
 
 1180 
 
 1252 
 
 1317 
 
 1473 
 
 1614 
 
 1743 
 
 1863 
 
 36 
 
 424 
 
 520 
 
 605 
 
 677 
 
 737 
 
 804 
 
 861 
 
 965 
 
 1057 
 
 1138 
 
 1214 
 
 1288 
 
 1355 
 
 1515 
 
 1660 
 
 17: i:; 
 
 1916 
 
 37 
 
 436 
 
 534 
 
 622 
 
 696 
 
 758 
 
 826 
 
 885 
 
 981 
 
 1086 
 
 1169 
 
 1248 
 
 1324 
 
 1392 
 
 1557 
 
 1706 
 
 1843 
 
 I96g 
 
 38 
 
 450 
 
 549 
 
 638 
 
 715 
 
 778 
 
 849 
 
 909 
 
 1018 
 
 1115 
 
 1201 
 
 1283 
 
 1359 
 
 1430 
 
 1599 
 
 1 752 
 
 1893 
 
 2023 
 
 39 
 
 462' 
 
 564 
 
 653 
 
 734 
 
 798 
 
 872 
 
 933 
 
 1045 
 
 1145 
 
 1232 
 
 1315 
 
 1395 
 
 1 168 
 
 16U. 
 
 1798 
 
 1943 
 
 2U76 
 
 40 
 
 484 
 
 577 
 
 671 
 
 753 
 
 819 
 
 894 
 
 957 
 
 1070 
 
 1174 
 
 1266 
 
 1351 
 
 1431 
 
 1506 
 
 1683 
 
 1844 
 
 1992 
 
 2129 
 
 41 
 
 .. 
 
 591 
 
 688 
 
 772 
 
 840 
 
 915 
 
 981 
 
 1097 
 
 1203 
 
 1298 
 
 1384 
 
 1467 
 
 1543 
 
 1725 
 
 1890 
 
 2012 
 
 2182 
 
 42 
 
 
 . 
 
 606 
 
 705 
 
 790 
 
 860 
 
 936 
 
 1005 
 
 1124 
 
 1233 
 
 1329 
 
 1419 
 
 1503 
 
 1581 
 
 1768 
 
 1936 
 
 2092 
 
 2236 
 
 43 
 
 
 , 
 
 620 
 
 722 
 
 809 
 
 881 
 
 961 
 
 1028 
 
 1151 
 
 1262 
 
 1361 
 
 1453 
 
 1538 
 
 1618 
 
 1809 
 
 1982 
 
 2142 
 
 2289 
 
 44 
 
 
 , 
 
 635 
 
 737 
 
 828 
 
 901 
 
 983 
 
 1053 
 
 1171 
 
 1291 
 
 1393 
 
 1486 
 
 1574 
 
 1656 
 
 1851 
 
 2029 
 
 2192 
 
 2343 
 
 45 
 
 
 , 
 
 649 
 
 754 
 
 847 
 
 920 
 
 1005 
 
 1076 
 
 1204 
 
 1321 
 
 1424 
 
 1520 
 
 1609' 
 
 1694 
 
 1894 
 
 2075 
 
 2241 
 
 2394 
 
 46 
 
 
 , 
 
 663 
 
 771 
 
 866 
 
 941 
 
 1028 
 
 1100 
 
 1231 
 
 1350 
 
 1456 
 
 1554 
 
 1636 
 
 1731 
 
 1936 
 
 2121 
 
 2291 
 
 2 1 19 
 
 47 
 
 
 . 
 
 677 
 
 787 
 
 885 
 
 961 
 
 1050 
 
 1124 
 
 1257 
 
 1380 
 
 1488 
 
 1588 
 
 1681 
 
 1769 
 
 1978 
 
 2167 
 
 2341 
 
 2504 
 
 48 
 
 
 . 
 
 691 
 
 801 
 
 903 
 
 982 
 
 1072 
 
 1148 
 
 1284 
 
 1409 
 
 1519 
 
 1622 
 
 1716 
 
 1807 
 
 2020 
 
 2213 
 
 2391 
 
 3659 
 
 49 
 
 
 , 
 
 706 
 
 820 
 
 922 
 
 1002 
 
 1095 
 
 1172 
 
 1311 
 
 1438 
 
 1551 
 
 1656 
 
 1753 
 
 1845 
 
 2062 
 
 23.-S!! 
 
 2440 
 
 261 1 
 
 50 
 
 
 ' 
 
 719 
 
 B36 
 
 940 
 
 1023 
 
 1115 
 
 1194 
 
 1337 
 
 1468 
 
 1583 
 
 16! HI 
 
 1789 
 
 1882 
 
 2104 
 
 2395 
 
 2490 
 
 2669 
 
Tin: i'K\< : 
 
 TNa Ubic hm bran calculated by m«n» of tli< 
 
 I» - rk x ♦'StfH x 1000; 
 n which 
 
 • volume of wat.-r divlurptl in litres per ■ 
 toatreo; 
 
 ;.rcwitiro, in mrtre«, measured 
 • ■ f lln- rv- 
 
 > 1 1 US) ; sn-l, 
 
 m ii a i 
 
 * ai 
 
 ..11 four 
 nJc- 
 
 ' imn of tin* table wo pive tin 
 and in the following columns: the n raid of 8m >li~ 
 chsrge effected, in III - of the 
 
 I 
 
 • in now ilit<rtnim\ by I W r . 
 
 : through a vortical Bood- 
 
 • orifice, of which thi 
 
 ■ the top of the orifice, 
 \V. bare, in I'.i. t. aimply \» find the 
 
 and to the cnlumn ••/ ir- El centre, and lluii mullijily this 
 
 I ■ .1 by the orifice 
 
 .: of the orifice 
 
 • i ihc column, from t li •- centre of the 
 
 rvoir, 8*6 m., and the oontrso- 
 ■ 
 In tin Una with (he I nitres, and la 
 
 . will be found the number 
 
 • r the actual d GOod, 
 
 It will !«• equally i 
 
 h ii" not happen i" !»• 
 
 II ed by :i 
 - m. In width, the height "f Ll 
 
 H tnn ii |~ -ii the centre i ' 
 
 not in the table, bul 
 
 itiy, the 
 for I ■ ' 
 
 ! ii will be about 706; therefore the 
 
 I 
 
 \- 
 ■ In- dia- 
 the numbers ' : 
 
 M Ilillll- 
 
 ■ 
 ■ 
 
 •i of the aidea of the reservoir 
 
 - 
 In tlii* ease, in order t" cslculati 
 moat In- multiplied by 
 1*126, If the contraction la 
 
 " 
 
 / I the volume "f water diacharged I . 
 
 height, 1*1 in. in width, and «iih a eolnma 
 • I fri'in the centre of the orifice, the bottom 
 . ■ line with the bottom of the reservoir; i! 
 ■ on taking place only <>n the I 
 It will !»■ found, according t" the table, thai 
 
 Ires for a width of one metre, and consequently 098 • I i 
 = 777 litres, is the dit I .in., when the contraction is 
 
 i iplete. We have, then R 7TJ I 
 
 actual discharge sought. 
 
 — Ii mtv often bappaaa that tlio 
 sluicegate i* Inclined. In thii case, If there i- no contraction <>n tlio 
 
 to !»• oonaklera. 
 1.1 v augmented. 'Ilui". to calculate the effective diachai 
 
 \ to multiply tin- numbera in the pri 
 If the sluice ia inclined i «itli l main 
 
 u< l in hi ight and bj 1*23, it the inclination ia 60 , <t l n i 
 3 in lii ight 
 / | know the vblui 
 
 through an orifice inelinod at an angle of 41 . having 1" m. in 
 liii^-lii vi rtically, 1*21 m. in width, and at ■ d a below 
 
 voir; the !«•• 
 being in :i line «iili the »idi - of the n - 
 
 Fn.in the tabl 
 dischsrge %<> i 1 1 ■ a vertical ortfiee ;uul eompli 
 quently, I "ill 1"' il»' effective di 
 
 sought, 
 
 :i n. When vertical il I rati - have tlnir lower • I 
 
 the bottom of the reservoir, at hi general!) the oa* . t" di termlne 
 the dim i 
 
 M ,lii the number* xiirn in tht tmble by 1*04. 
 / 
 
 orifice of which is opened to ■ hi 
 8 in. in width, and - •'< n. 1* lag the distance from thi 
 I., the upper Ii 
 
 10 litrsa for tin 
 ■■.in width. Whence 1,698 x *8 x 1*04 
 ought 
 
 not mora titan three n 
 h other, and i ifja ■■'" 
 
 Ik- nlilaiiH •! 1 ■>' 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 Multiplying the numbers given in (he table by '915. 
 Example. — If the orifices of two sluices, situated at a couple of 
 metres distance from each other, have together a width equal to 
 1-5 m., and are both opened to a height of -45 m., the column of 
 
 water upon their centres being 1-8 m., what will be the effective' 
 discharge of the two together per second? 
 
 In the table, we find that 1609 litres corresponds to a column 
 of 1-8 m., and a width of 1 m. Therefore, 1609 x 15 x 915 
 = 2208-35 litres is the required discharge. 
 
 TABLE OF THE DISCHARGE OF WATER BY OVERSHOT OUTLETS OF ONE METRE IN WIDTH. 
 
 Heishts 
 of the 
 
 Discharge 
 
 Heights 
 of the 
 
 Disc 
 
 n"' 6 
 
 Heights 
 
 of the 
 
 Discharge 
 
 the bottom 
 of the outlet. 
 
 litres per second. 
 
 level above 
 
 litres pe 
 
 r second. 
 
 level above 
 
 litres per second. 
 
 1st Case. 
 
 2d Case. 
 
 the bottom 
 of the outlet. 
 
 1st Case. 
 
 2d Case. 
 
 the bottom 
 of the outlet. 
 
 1st Case, 
 
 2d Case. 
 
 5-0 
 
 20 
 
 21 
 
 28-5 
 
 259 
 
 283 
 
 52-0 
 
 639 
 
 698 
 
 5-5 
 
 23 
 
 24 
 
 29-0 
 
 266 
 
 290 
 
 52-5 
 
 648 
 
 708 
 
 60 
 
 26 
 
 27 
 
 295 
 
 273 
 
 298 
 
 530 
 
 658 
 
 718 
 
 6-5 
 
 29 
 
 31 
 
 30-0 
 
 280 
 
 306 
 
 53-5 
 
 667 
 
 728 
 
 7-0 
 
 32 
 
 34 
 
 30-5 
 
 287 
 
 313 
 
 54-0 
 
 676 
 
 738 
 
 7-5 
 
 36 
 
 38 
 
 31-0 
 
 293 
 
 321 
 
 54-5 
 
 685 
 
 748 
 
 8-0 
 
 40 
 
 42 
 
 31-5 
 
 301 
 
 329 
 
 55-0 
 
 694 
 
 758 
 
 8-5 
 
 43 
 
 46 
 
 32-0 
 
 309 
 
 337 
 
 555 
 
 704 
 
 769 
 
 90 
 
 47 
 
 50 
 
 32-5 
 
 315 
 
 344 
 
 560 
 
 713 
 
 779 
 
 95 
 
 51 
 
 54 
 
 330 
 
 323 
 
 353 
 
 56-5 
 
 72 1 
 
 790 
 
 " 10-0 
 
 56 
 
 59 
 
 33-5 
 
 330 
 
 361 
 
 57-0 
 
 733 
 
 800 
 
 105 
 
 60 
 
 63 
 
 34-0 
 
 338 
 
 369 
 
 57-5 
 
 743 
 
 811 
 
 11-0 
 
 64 
 
 68 
 
 34-5 
 
 345 
 
 377 
 
 580 
 
 753 
 
 822 
 
 11-5 
 
 68 
 
 73 
 
 350 
 
 353 
 
 385 
 
 58-5 
 
 762 
 
 832 
 
 12-0 
 
 72 
 
 77 
 
 35'5 
 
 360 
 
 393 
 
 59-0 
 
 771 
 
 842 
 
 12-5 
 
 .77 
 
 82 
 
 36-0 
 
 368 
 
 402 
 
 59-5 
 
 781 
 
 853 
 
 130 
 
 82 
 
 87 
 
 36-5 
 
 375 
 
 410 
 
 600 
 
 791 
 
 864 
 
 135 
 
 86 
 
 92 
 
 37-0 
 
 382 
 
 419 
 
 60-5 
 
 801 
 
 875 
 
 14-0 
 
 92 
 
 98 
 
 37-5 
 
 392 
 
 428 
 
 61-0 
 
 811 
 
 886 
 
 14-5 
 
 97 
 
 103 
 
 38-0 
 
 399 
 
 436 
 
 61-5 
 
 821 
 
 896 
 
 150 
 
 101 
 
 108 
 
 38-5 
 
 408 
 
 445 
 
 62-0 
 
 831 
 
 907 
 
 15-5 
 
 107 
 
 114 
 
 390 
 
 415 
 
 453 
 
 62-5 
 
 811 
 
 918 
 
 160 
 
 111 
 
 119 
 
 39-5 
 
 423 
 
 462 
 
 630 
 
 851 
 
 929 
 
 16-5 
 
 117 
 
 125 
 
 40-0 
 
 431 
 
 471 
 
 635 
 
 861 
 
 940 
 
 17-0 
 
 121 
 
 130 
 
 40-5 
 
 439 
 
 479 
 
 64-0 
 
 871 
 
 951 
 
 17-5 
 
 127 
 
 136 
 
 41-0 
 
 447 
 
 488 
 
 645 
 
 882 
 
 963 
 
 180 
 
 132 
 
 142 
 
 415 
 
 455 
 
 497 
 
 650 
 
 892 
 
 974 
 
 18-5 
 
 138 
 
 148 
 
 42-0 
 
 463 
 
 506 
 
 65-5 
 
 902 
 
 985 
 
 190 
 
 143 
 
 154 
 
 42-5 
 
 472 
 
 515 
 
 66-0 
 
 912 
 
 996 
 
 195 
 
 149 
 
 160 
 
 43-0 
 
 481 
 
 525 
 
 66-5 
 
 922 
 
 1007 
 
 20-0 
 
 154 
 
 166 
 
 43-5 
 
 488 
 
 533 
 
 67-0 
 
 932 
 
 1018 
 
 20-5 
 
 160 
 
 173 
 
 44-0 
 
 497 
 
 543 
 
 67-5 
 
 943 
 
 1030 
 
 21-0 
 
 166 
 
 179 
 
 44-5 
 
 506 
 
 552 
 
 68-0 
 
 954 
 
 1042 
 
 21-5 
 
 171 
 
 185 
 
 45-0 
 
 514 
 
 561 
 
 68-5 
 
 965 
 
 1054 
 
 22-0 
 
 176 
 
 192 
 
 45-5 
 
 523 
 
 571 
 
 69-0 
 
 976 
 
 1066 
 
 22-5 
 
 182 
 
 199 
 
 46-0 
 
 531 
 
 581 
 
 695 
 
 * 987 
 
 1078 
 
 23-0 
 
 188 
 
 205 
 
 465 
 
 540 
 
 590 
 
 70-0 
 
 998 
 
 1090 
 
 23-5 
 
 194 
 
 212 
 
 47-0 
 
 549 
 
 599 
 
 70-5 
 
 1008 
 
 1101 
 
 240 
 
 202 
 
 219 
 
 47-5 
 
 • 558 
 
 609 
 
 71-0 
 
 1019 
 
 1113 
 
 24-5 
 
 207 
 
 226 
 
 48-0 
 
 567 
 
 619 
 
 715 
 
 1030 
 
 1125 
 
 25-0 
 
 212 
 
 233 
 
 48-5 
 
 576 
 
 629 
 
 72-0 
 
 1041 
 
 1137 
 
 25-5 
 
 220 
 
 240 
 
 490 
 
 584 
 
 638 
 
 73-5 
 
 1052 
 
 1149 
 
 260 
 
 226 
 
 247 
 
 495 
 
 593 
 
 648 
 
 730 
 
 1063 
 
 1161 
 
 26-5 
 
 233 
 
 254 
 
 50-0 
 
 603 
 
 658 
 
 735 
 
 1073 
 
 1172 
 
 270 
 
 239 
 
 261 
 
 50-5 
 
 612 
 
 668 
 
 74-0 
 
 1084 
 
 1184 
 
 27-5 
 
 245 
 
 268 
 
 51-0 
 
 621 
 
 678 
 
 74-5 
 
 1095 
 
 1196 
 
 28-0 
 
 253 
 
 276 
 
 515 
 
 630 
 
 688 
 
 750 
 
 1106 
 
 1208 
 
THE I 
 
 LATUM Or TW DMCftAKGt Of WITH TWBOCGB 0T««- 
 
 The practical formula 
 
 Uw qua- mm/m in a* 
 
 ■ 
 
 1) w II ■ < ..II • m x 1000; 
 Id which formula, 
 
 \V, tiic width of 
 II. Uie drpth • ■ 
 
 edge to the level of (he water in the IN 
 The Mlu»ing table ia calculated by weans of tills formula, it 
 being supposed, 
 
 :. Tliat the I Rata "•' 
 
 •005 m M front ■■ 
 
 • column of thi 
 
 Third, That ' 
 
 M \L P • t and Leabroe 
 
 I the term m. : — 
 
 TW l»n». I 
 
 jn, , iliis case nro given in the 
 
 i tan "f tin- labia. Tie j 
 
 • 
 
 - virtually of the MOM wi.llh as tlie 
 
 only a little, if 
 
 M d'An- 
 
 ■ Bt, in. is equal to -43 
 
 on the n iwUlbe found in die 
 
 loan of the fa 
 
 the afcl of ti ikolatloii for determin- 
 
 ing the • I ' "■*•» by u overshot outlet, reduoM 
 
 I — 
 
 V ■ If the tritlth "f the m. mitrer, hy the mtmhrr 
 
 mn, awl oom I '/ 'A' 
 
 ou/Zrt in lAc fral nJumn, when the outlet i- narrower than tlie water- 
 . and wlen foe Vital - HM A* •''""• 
 
 And by DM mimVr in the ihirj column OOfTI tptmduig to ffce Mm* 
 
 is of the Mine width as toe outlet, 
 • than thai of flu lower 
 
 ■ 
 
 • -mine the vol 
 
 : hy an overshot outlet, the width of 
 
 jhj of the overflow '99 m.. • 
 ription. 
 It will bi mm fr I mm of the table, thai 
 
 h nn outlet of n metre in width, and of -"- 
 
 - 
 
 a ith tlie 
 
 Remark. — I: 
 
 a mean 
 
 / the qnantit] 
 
 ■ In width, and of a depth ■ 
 
 In th. lad, for 1 metre in width, will 
 
 U- beta 
 
 136. 
 
 | 
 
 And in the ■ 
 width, b 1 143 and I 18, will l>o 
 
 about I 
 
 Win rue. 1 |ii K 3 — 438 lit) 
 
 TO DETERMINE THE WTOTB 1HOT IUTI.ET. 
 
 349. When the role ed per leeond is 
 
 known, and it ia wiahed to calculate Ihe width to be given to an 
 oTorahol outlet, t the deeired discharge 
 
 \\i:h a given height "t water, this may !*• done in the following 
 
 - : — 
 
 ■i height 
 (this nn: • • for a wi.llh of I metre), sad 
 
 litres, it trill gi\e lh< 
 icitlth in i 
 
 I I What width must be given to nn 
 
 quired to discharge BOO litree per eeoond, with a depth al 
 ■ ! ■:•■ of '13m. .' 
 
 In the s ii.l column of the table, and o] wDI l>o 
 
 found the nun. 
 W. have, then — 
 
 : T2 = 8-33 m.. the width - 
 S / What width must be given to an open stains, 
 
 required wd, with ■ depth 
 
 . m. .' 
 
 find that 180 litres is the e ffe ctual d 
 ■ ■ a wi.lih of i metre. 
 Whence — 
 
 . th.- width sought 
 
 to Dl iii HOT in! i ! i i ii "i rffl "1 ti.et. 
 ' i iv < K-.nr where we are limited as to width. It is 
 
 then in vi s..irv to ascertain the least depth necessary to effect tlm 
 required discharge, which maj 1~- done by means of the following 
 
 rule : — 
 
 /),,„;. / in hir> < ]tt anond, If th' wUfk m 
 
 mi Com the mmtbtr in the meani omowi wMol it w 
 
 the MOM ii' iJitmnnl, (he number in the firtl column UN IMUUwJuU/ 
 '.', or very nearly to. 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 115 
 
 Example. — With what depth of outlet will a discharge of 350 
 litres per second be effected, the width being limited to 2 metres 1 
 
 We have 
 
 350 -=- 2 = 175 litres. 
 
 In the second column of the table will be found the number 176, 
 corresponding to a height of '22 m. in the first column, which will 
 therefore be the required height, witliin a millimetre. 
 
 351. Observation. — When it is not possible to measure the 
 depth, H, with exactness, the lesser depth, h, must be taken im- 
 mediately over the lower edge of the outlet, and multiplied by 1-178, 
 so as to obtain the actual value of H, corresponding to the num- 
 
 bers given in-the table, according as the outlet is narrower than the 
 reservoir, or water-course, or equal to it in width. 
 
 First Example. — Determino the discharge effected through an 
 outlet, 4 metres wide, the depth, k, immediately above the lower 
 edge being equal to '11 in., the width being about four-fifths of 
 that of the reservoir. 
 
 We have '11 m. x 1-178 = -13 m., for the assumed height, H, 
 of the reservoir level. 
 
 Corresponding to this height, we have, in the second column, the 
 quantity, 82 litres. 
 
 Then 82 x 4 = 328 litres, the effective discbarge sought. 
 
 TABLE OF THE DISCHARGE OF WATER THROUGH PIPES. 
 
 
 Diameters of the Pipes. 
 
 Mean 
 
 
 
 
 
 
 
 
 
 
 
 velocity 
 
 '10 
 
 
 ■15 
 
 
 •20 
 
 m. 
 
 ■25 
 
 m. 
 
 •30 
 
 m. 
 
 metres 
 
 
 
 
 
 
 
 
 
 
 
 per 
 
 Discharge 
 
 Fall 
 
 Discharge 
 
 Fall 
 
 Discharge 
 
 Fall 
 
 Discharge 
 
 Fall 
 
 Discharge 
 
 Fall 
 
 second. 
 
 
 
 
 per metre 
 
 
 per metre 
 
 
 per metre 
 
 
 per metre 
 
 
 litres 
 
 in length 
 
 litres 
 
 in length 
 
 litres 
 
 in length 
 
 litres 
 
 in length 
 
 litres 
 
 in length 
 
 
 per 
 
 
 
 
 
 
 per 
 
 
 per 
 
 
 
 second. 
 
 centimetres. 
 
 second. 
 
 centimetres. 
 
 second. 
 
 centimetres. 
 
 second. 
 
 centimetres. 
 
 second. 
 
 centimetres. 
 
 o-io 
 
 0-8 
 
 0-02 
 
 1-8 
 
 001 
 
 31 
 
 o-oi 
 
 4-9 
 
 o-oi 
 
 7-07 
 
 o-oi 
 
 0-15 
 
 1-2 
 
 0-04 
 
 2-6 
 
 0-03 
 
 4-7 
 
 0-02 
 
 7-4 
 
 0-02 
 
 10-60 
 
 o-o 1 
 
 0-20 
 
 1-6 
 
 0-07 
 
 3-5 
 
 0-05 
 
 6-3 
 
 0-03 
 
 9-8 
 
 0-03 
 
 1414 
 
 0-02 
 
 0-25 
 
 2-0 
 
 0-10 
 
 4-4 
 
 0-07 
 
 7-8 
 
 0-05 
 
 12-3 
 
 0-04 
 
 17-67 
 
 0.03 
 
 0-30 
 
 2-3 
 
 0-15 
 
 5-3 
 
 o-io 
 
 9-4 
 
 0-07 
 
 14-7 
 
 0-06 
 
 21-20 
 
 0-05 
 
 0-35 
 
 2-7 
 
 0-19 
 
 61 
 
 0-13 
 
 110 
 
 o-io 
 
 17-2 
 
 0-08 
 
 21-74 
 
 0-07 
 
 0-40 
 
 31 
 
 0-25 
 
 7-1 
 
 0-17 
 
 12-6 
 
 0-12 
 
 19-6 
 
 o-io 
 
 28-27 
 
 0-08 
 
 045 
 
 3-5 
 
 0-31 
 
 8-0 
 
 0-21 
 
 141 
 
 016 
 
 22-0 
 
 0-12 
 
 31-81 
 
 o-io 
 
 0-50 
 
 3-9 
 
 0-38 
 
 8-8 
 
 0-25 
 
 157 
 
 0-19 
 
 24-5 
 
 015 
 
 35-34 
 
 0-13 
 
 055 
 
 4-3 
 
 0-46 
 
 9-7 
 
 0-30 
 
 17-3 
 
 0-23 
 
 27-0 
 
 018 
 
 38-88 
 
 0-15 
 
 0-60 
 
 4-7 
 
 0-54 
 
 10-6 
 
 0-36 
 
 18-8 
 
 0-27 
 
 29-4 
 
 0-22 
 
 42-41 
 
 0-18 
 
 0-65 
 
 51 
 
 0-63 
 
 1 1-5 
 
 0-42 
 
 20-4 
 
 032 
 
 31-9 
 
 0-25 
 
 45-95 
 
 0-21 
 
 0'70 
 
 5-5 
 
 0-73 
 
 12-4 
 
 0-49 
 
 L'l'll 
 
 036 
 
 34-4 
 
 0-29 
 
 49-48 
 
 0-24 
 
 0-75 
 
 5-9 
 
 0-83 
 
 13-2 
 
 0-56 
 
 23-6 
 
 0-42 
 
 36-8 
 
 0-33 
 
 53-01 
 
 0-28 
 
 0-80 
 
 63 
 
 0-95 
 
 141 
 
 0-63 
 
 25-1 
 
 0-47 
 
 39-3 
 
 0-38 
 
 56-55 
 
 0-31 
 
 0-85 
 
 6-7 
 
 1-06 
 
 15-0 
 
 0-71 
 
 26-7 
 
 053 
 
 41-7 
 
 0-43 
 
 60-08 
 
 0-35 
 
 0-90 
 
 7-0 
 
 119 
 
 15-9 
 
 0-79 
 
 28-3 
 
 0-59 
 
 44-2 
 
 0-48 
 
 63-62 
 
 0-40 
 
 0-95 
 
 75 
 
 1-32 
 
 16-8 
 
 0-88 
 
 29-8 
 
 0-66 
 
 46-6 
 
 0-53 
 
 67-15 
 
 0-44 
 
 1-00 
 
 7-8 
 
 1-46 
 
 17-7 
 
 0-97 
 
 31*4 • 
 
 0-73 
 
 49-1 
 
 0-58 
 
 70-7 
 
 0-49 
 
 1-10 
 
 8-6 
 
 1-76 
 
 19-4 
 
 117 
 
 345 
 
 0-88 
 
 54-0 
 
 0-70 
 
 77-7 
 
 0-59 
 
 1-20 
 
 94 
 
 2-09 
 
 21-2 
 
 1-39 
 
 37-7 
 
 1-04 
 
 58-9 
 
 0-83 
 
 84-8 
 
 0-69 
 
 1-30 
 
 10-2 
 
 2-44 
 
 23-0 
 
 1-63 
 
 40-8 
 
 1-22 
 
 63-8 
 
 0-98 
 
 91-9 
 
 0-81 
 
 1-40 
 
 110 
 
 2-82 
 
 247 
 
 1-88 
 
 44-0 
 
 1-41 
 
 68-7 
 
 1-13 
 
 98-9 
 
 0-94 
 
 1-50 
 
 118 
 
 3-24 
 
 26-5 
 
 2-16 
 
 47-1 
 
 1-62 
 
 73-6 
 
 1-29 
 
 1060 
 
 108 
 
 1-60 
 
 12-6 
 
 3-68 
 
 28-3 
 
 2-45 
 
 50-3 
 
 1-84 
 
 78-5 
 
 1-47 
 
 1131 
 
 1-22 
 
 1-70 
 
 133 
 
 4-14 
 
 306 
 
 2-76 
 
 53-4 
 
 2-07 
 
 83-4 
 
 1-66 
 
 120-2 
 
 1-38 
 
 1-80 
 
 141 
 
 4-64 
 
 318 
 
 309 
 
 56-5 
 
 2-32 
 
 88-3 
 
 1-85 
 
 127-2 
 
 1-55 
 
 1-90 
 
 149 
 
 5-16 
 
 33-6 
 
 3-44 
 
 59-7 
 
 2-58 
 
 93-3 
 
 2-06 
 
 134-3 
 
 1-72 
 
 2 00 
 
 157 
 
 5-71 
 
 353 
 
 3-80 
 
 628 
 
 2-85 
 
 98-2 
 
 2-28 
 
 141-4 
 
 1-90 
 
 2-10 
 
 164 
 
 6-29 
 
 37-1 
 
 4-19 
 
 660 
 
 314 
 
 1031 
 
 2-51 
 
 148-4 
 
 2-10 
 
 2-20 
 
 17-2 
 
 6-89 
 
 389 
 
 4-60 
 
 691 
 
 3-45 
 
 108-0 
 
 2-76 
 
 155-5 
 
 2-30 
 
 2-30 
 
 18-0 
 
 7-53 
 
 40-6 
 
 5-02 
 
 72-2 
 
 3-76 
 
 112-9 
 
 301 
 
 162-6 ' 
 
 2-50 
 
 2-40 
 
 18-8 
 
 819 
 
 42-4 
 
 5-46 
 
 754 
 
 4-09 
 
 117-8 
 
 3-28 
 
 169-6 
 
 2-73 
 
 2-50 
 
 196 
 
 8-88 
 
 44-2 
 
 5-91 
 
 78-5 
 
 4-44 
 
 122-7 
 
 3-55 
 
 176-7 
 
 2-96 
 
 260 
 
 20-4 
 
 9-60 
 
 45-9 
 
 6-40 
 
 81-7 
 
 480 
 
 127-6 
 
 3-83 
 
 183-8 
 
 3-20 
 
 2-70 
 
 212 
 
 10-34 
 
 47-7 
 
 6-89 
 
 84-8 
 
 517 
 
 132-5 
 
 414 
 
 190-8 
 
 344 
 
 280 
 
 22-0 
 
 1111 
 
 494 
 
 7-41 
 
 88-0 
 
 556 
 
 1374 
 
 4-45 
 
 197-9 
 
 3-70 
 
 290 
 
 22-8 
 
 11-92 
 
 si -a 
 
 7-94 
 
 911 
 
 595 
 
 142-3 
 
 " 4-77 
 
 205-0 
 
 3-97 
 
 300 
 
 236 
 
 12-74 
 
 530 
 
 8-50 
 
 942 
 
 637 
 
 1473 
 
 510 
 
 212-1 
 
 4-25 
 
. ICAL DRAUGHTS 
 
 I ExoavatV.— \\~ Hi tli. like data, « I 
 U»r diM-har.t-, supposing lb. ilh and 
 
 d. pa »» UM reservoir ' 
 
 H = 13 m. f..r 
 
 M ill tile liiird 
 column. 
 
 ..■*— 
 
 67 x 4 = 348 litre*, (he actual discharge. 
 
 OCTLET WITH A STOUT, Or: 
 
 I: may happen that a iipiiut or duct, slightly ioi 
 
 ■ ■ - more oontraet- 
 rd, both at the bottom and at ' - v. ■ .ir. Ineuch, 
 
 eaae, the discharge Li aenaibly dim-rent; ami to determine it, it it 
 neeesasry to multiply tin- nun nd column of tin- table 
 
 when the hi ■- upwards; by -8, when the 
 
 blight is -15 m.; and by "ti, when the height is only -1 m. 
 
 TOES FOR 71 v OF WATER. 
 
 353. The formula* employed in calculating the proportion* of a 
 conduit I . indrieel tubes, 
 
 V = 53 58 
 
 / dY 
 \ i -»■ 
 
 
 ..:..! 
 
 D = S V " 
 
 4 
 
 In wUohi 
 
 ■ lodty ; 
 D, the rolnme is 
 
 d, th>- internal diune I luit; 
 
 i ■ ■ ■ • i nit, Abided by 
 
 the lcw-ls at either extremity ; and 
 I the conduit 
 In ordiT to abri.l_'.- the calculations, we five a table, with the 
 aid of which, stive to the laying down of 
 
 water-ducta, formed by cylindrical tubes, may be solved very 
 speedily. 
 
 / Example, — What fall must Is- given to a conduit, 1 in. in 
 
 diameter! in ur.lcr that it may diacharge n litre.-, of water pet 
 nmond ? 
 
 From tin- table it will Ik> Been, that the fall, in this case, should 
 l»- 1 i-., or 1 millimetre. |mt i 
 
 Second Example. — What diameter must be Lri \ • ■ 1 1 to a conduit, 
 600 metres in length, in order thai it may discharge 168 cobi 
 of water i*-r hour, the whole Ball being 460 m.1 
 
 We hare 168 onbic metres. ,, r 168,000 litres, -=- (60 x 60) = 
 46-65 litres, discharged per leoond; 
 and : '63c, the mil per o 
 
 It will be seen from the table, thai the dia ter 
 
 this discharge, and with this (all, [a ■•_'.') in., or SS eentimi I 
 
 CHAPTER Vin. 
 AMPLICATION OF SHADOWS TO TOOTHED GEAR. 
 
 I'l.ATK XXX. 
 
 
 I - I \ v I. J . 
 
 ... . 
 
 in a fin to lav down tl at. 
 
 ;. happen to be 
 
 pply the finishing ihadea to the tpnr- 
 
 ■■ lv, on 
 
 each wheel, both the shadow proper of tin- external rarmoe of tin- 
 
 "f the tilth apon it, end als., upon them- 
 
 I fat with one of the wbeela are in.li- 
 
 • wheal, 
 
 ■01 In. 
 
 to lie- luminous pay, 
 
 -. by the radl | . maring 
 
 I projection, wi 
 
 Hon. Similarly, by tqnarlng 
 bl line, i ... for th< 
 
 separation of light and atuule on tin- outer end. of tl 
 
 Which are likewise cylindrical. A portion of the lateral m. 
 
 the tec tb is also in the shade, aa will easily Ih- determined, by draw* 
 - through the extreme . parallel to the 
 
 luminous rays. Thus the surfac. ■>. n </, /' *, and r I. do Ml 
 
 any light, and are. therefore, shaded in the elevation, as within the 
 
 outlines, a' if g ft, b' e ij, and <■'/' k I. 
 
 shadow ii|Kin the cylindrical 
 ' . »'/, r' I. an 
 
 their shadows on the web are also vertical, These last an 
 mined bj drawing the laminar lines through I '. .-. and 
 
 «', />', i-', and thi - of contact, at, n, ... t.. 
 
 ru', ;i', '/. 
 
 To complete the thadovi i of the t- eth upon the web, it is farther 
 
 ) t.i obtain the outline correeponding to the edges, a d, l< a, 
 
 extreme points, ./,»'./. and »»'. n, <>'. 
 
 and in n Where, however, greater 
 
 • quired, it i« well to find ■ few intermedial. 
 The lower edge of the tooth, shadow upon the web, 
 
 which is obtained in U er, by drawing laminar Bnea 
 
 throuoh tin- points. ;.../. r. tn. • . . ofthoweb 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 Some of the teeth, also, cast shadows upon each other ; but as 
 their surfaces are vertical, these shadows are simply determined by 
 the contact of the luminal lines with them. Thus, the edges pro- 
 jected in s, I, y, &c, have for shadows the straight lines projected 
 vertically in u' u', x' x', z' z 3 . 
 
 Finally, when we have drawn the horizontal projection of the 
 wheel, as in the present example, we have to determine the shadow 
 east by the web upon the tenons of the teeth, and upon the arms, 
 or spokes. All these surfaces being horizontal and parallel, the 
 shadow cast upon each will be a circle equal to the one, hil, 
 which is the projection of the inner edge of the web. All that is 
 necessary, then, is to draw through the centre, o, o', a line parallel 
 to the luminous ray; and to find the points of intersection, o 3 and 
 o 3 , with the planes, iw o" and N o"', in which lie the upper surfaces 
 of the tenons and of the arms, and to describe arcs with the points, 
 o 3 and o s , as centres, and with the common radius, o h (280). In 
 the same manner we obtain the shadows cast by the boss of the 
 wh.el, and by the feathers upon the arms. 
 
 When we have thus gone through the requisite operations for 
 eaeh wheel, we proceed with the shading, according to the prin- 
 ciples laid down (289, et seq.), covering first the portions which 
 require a more pronounced shade, and leaving the lighter parts to 
 the last. 
 
 The specimen, fig. A, which we recommend to be copied on a 
 arger scale, indicates the various gradations of shade required to 
 produce the proper effect, according to the different positions of the 
 planes, and to the contour of the surfaces. These wheels are also 
 supposed to be mounted upon their shafts, which are shaded as 
 polished cylinders. 
 
 bevil wheels. 
 Figures 3 axd 4. 
 
 355. The procedure here called for will be the same as in the 
 preceding case— that is to say, we must first draw the outlines of 
 the shadows, proper and cast, for each wheel. The figures repre- 
 sent a horizontal and vertical projection of a bevil wheel with east- 
 iron teeth, the shadows being indicated on the different surfaces. 
 
 The external surfaces of the teeth and of the web being conical, 
 the shadows proper are determined in the same manner as for the 
 cone, by drawing through the apex a plane parallel to the luminous 
 ray, and finding the generatrix at which this plane touches the 
 conical surface (313). 
 
 It is in this manner that, for the outer ends of the teeth, we ob- 
 tain the generatrix projected in o a, fig. 3, and for the outer surface 
 of the web. that projected in o B. These generatrices, which are the 
 lines of separation of light and shade, are projected vertically in tho 
 straight lines, o' a' and d' b', converging to the apex of the cone; 
 since, however, these lines occur between two teeth in the present 
 example, they are not apparent in fig. 4. 
 
 Some of the teeth have their lateral faces in the shade, whilst all 
 the lower conical surface corresponding to the wider ends of the 
 teeth is in deep shade, as indicated in fig. 4 by a darker tint. 
 
 We have, besides, merely to determine the shadows cast by 
 the outer edges, a d, b e, cf, and by the curved portions, d g, e h, 
 and f i. Now, the outer edges, a d, b e, cf, cast shadows upon 
 the conical surface of the web, which are represented by straight 
 
 lines coinciding with generatrices on this surface ; and therefore, 
 to determine them, we must draw through the corresponding edges 
 a series of planes parallel to the luminous ray ; the whole of these 
 necessarily passing through the common apex, o, it is simply re- 
 quisite, therefore, to find the shadow east by any ono point in 
 these edges. Let us take, for example, the points, d, e, /. all 
 situate in the same circle, E d F ; the operation, then, is to find 
 the shadow of this circle upon the conical surface, and is the same 
 as that which we have already indicated and explained several 
 times ; it consists, in fact, in drawing any planes, G h and I J, per- 
 pendicular to the cone's axis, and, consequently, parallel to the plane 
 of the circle, e d f. 
 
 356. We have seen that the shadow cast by the circle, e d f, 
 upon each of the planes, will be a circle equal to itself; and it is, 
 therefore, simply necessary to find the shadow cast by the centre, 
 o, o'. This shadow falls in o, o', on the plane, G H, and in o 3 , o 3 , on 
 the plane, I I ; if, then, with the points, o and & 3 , as centres, and 
 with the radii, o k' and o* ]', equal to the radius, o E, we draw a 
 couple of arcs, these arcs will cut the circles, g' k' h' and I' l' j', <h ) 
 projections of the sectional planes, in the points, k' and j', wlrvl ., 
 being squared over to the vertical projection in the points, K and <, 
 will give two points in the curve, J K M N, representing the shado v 
 cast by the circle, E d f, upon the conical surface of tho wej. 
 Consequently, if we draw the luminar lines through the points, 
 d\ e',f, &c, the respective points of their intersection with the 
 curve, as M, p, Q, will represent their shadows cast upon the web 
 surface.. These points are squared over to m', p', q', in the h >ri- 
 zontal projection. 
 
 The points, g, h, i, situated upon the upper base of the cone, 
 obviously cast no shadows, the shadows of the teeth, however, 
 springing from them ; if it is wished to determine any points be- 
 tween these and those already found, it will be necessary to de- 
 scribe an imaginary circle, such as g', k', h', passing between the 
 points, d and g, the cuter and inner angles of the teeth. Tho 
 curve, r s T, as projected in the elevation, will be found to repre- 
 sent the shadow cast by this circle upon the conical surface of tho 
 web. 
 
 As the edges, ad,be,cf, cast shadows which coincide with 
 generatrices of the cone, they may be obtained simply by drawing 
 straight lines through the several points, m\ q', and p', converging 
 in the apex of the cone in both planes of projection. 
 
 Finally, the shadows cast by some of the outer edges of the 
 teeth, such as/c, upon the teeth immediately behind, are defined 
 by drawing the luminar line,//, through the point,/, meeting the 
 flank, / m, of the other tooth, which lies in a vertical plane. This 
 point of contact is projected vertically in V, on the vertical projec- 
 tion,/ f, of the luminar line. It now remains to draw a line, I' n, 
 through this point, V, and through the apex of the cone, and this 
 line will represent the shadow cast by the edge,/c. 
 
 357. In the case where the luminar line passing through the 
 extremity of the tooth— as that, for example, drawn through the 
 point, p — falls upon a curved portion of the tooth behind, it is 
 necessary, if great accuracy is required, to imagine a vertical 
 plane passing through this point and through the luminar line, 
 and then to find the intersection of this plane with the curved sur- 
 face of the tooth. This would require a separate diagram; but 
 

 THE I «IAVH 
 
 -unpfe, 0£. B ' 
 
 It ■•'. ili»t 
 
 ■ 
 
 Id sb 
 
 ■ :. that, from I 
 
 - 
 in uV »luul.-, ■ I end of the other i» illumi- 
 
 nalt-d. 
 
 APPUCATiON OF SHADOWS TO SCREWS 
 PLAT! XXXI. 
 
 by at' 
 
 ■ 
 .1 i«th. TK- ntly, called bri 
 
 1 
 cast »h*J'>»« u|hiii tin- .-..rv ■•! tbe KNW, nr opon the twisti 
 
 I Itself. If the 
 anew in surmounted by n head, there will !»•, in addition, the 
 ►ha.1.. • • of the thread 
 
 "a, U |« v. i to explain the methodi 
 
 esrewe. 
 
 Tim limit of the ehadow proper np in tbe screw, i- 
 
 - tlmt iijH.n a right cylinder, by drawing the 
 
 nuliui, o a, »t right engtea t" the ray "f light, r ". and then squar- 
 
 : lint, a, to a' and a*, and drawing aline through theae 
 
 1 1 1 1 •• - mum manner we obtain, 
 
 the i-'int, n, tbi light and shade, 
 
 1' B*. u|»in tl 
 
 'n„. the Ibreadi ir[...n the 
 
 :i|i!v determined l.y n 
 D i/, drawn parallel t" tbe Ini 
 i ./ n. the projection of (be core, in t and •/: 
 
 ti,r- I.-,". /', paralli I t" I 
 
 ■ • 
 
 ■ r\. i| outline of the -■ 
 
 i to the left, :i 
 8* en<l I and 'J, 
 
 ihadowa 
 
 ■ 
 
 1 1.. be tbe tun 
 
 ■ ' 
 
 ■ ■f tlir I 
 
 in both • ' 
 
 which \* borixi 
 
 I . I. i a ii i. whicl 
 
 from the left-banded portioa i upon a 
 
 which will lx- i 
 termined, in aecordanci' \\th j 
 tbe principal polnta in which 13. 
 
 
 J AM' 5. 
 
 861. Tin' construction of the shadows of a roctangular-l 
 • the same, win ther it bo in a horizontal i>r \. 
 or whether it Ii' right-handed nr left-handed. Tim-, tl.. 
 with eevi I and A, has 
 
 in tin- Brat puce a shadow proper, limited by tbe vertical line, a' a', 
 
 i r from tbe point, a, and next, the shadow, 
 cast upon the core bj lb< out* i i dge of tbe dm ad, i ' d* i.' ; tl» re 
 over, :i |N.rti.m of tin' shadow cast by the circular shoulder, 
 i. ii i, upon the Ihreada, inn! also upon the core. Tin- onl 
 . idowa are fonnd in | 
 . and 3 (361). 
 
 1i:i urot LAI • uw. 
 
 Fun sal t, i'.', 7, am. s. 
 
 \: 
 
 ■ of which the height, a A, ia greater than tbi 
 the base, e </. there "ill be a shadow cast by the outer edgi 
 thread upon tbe twisted surface oft] involution. In 
 
 proceeding to determine tl ntline of t } i i -. shadow, 
 
 with the genera] method, which eonaiata in finding die i 
 eontael of the luminous rays with tbe surface, we are I"! 
 in the lir-t place, the curre of intersection ol a, with n 
 
 plain- passing through tin' luminous ray, and parallel t" tl" 
 
 tip- screw. 
 
 i purpose, lot ■ o,ftg. 1 ; Ma lo- 
 in with tli I Mhti ad will I*. 
 
 in the i 8 and 7. and similarly it> intersection with 
 
 tlir inside, n 1 g, will lx' in tbe point, r,r. To obtain mtertne- 
 ■ onal curve, we i 
 
 with tl" I r.-lilii. o m, o 
 
 . indora, on which UetheheUi between 
 
 the inner one, « / g, nm' outermost, •/ 1 ' ■>. I 
 
 • !. r \\ . tin reb] obtain lion, A. i, 
 
 i ..\. r to h . r. in fig. ii. and men, by 
 
 of Inter- 
 
 ■ 
 
 i aw » luminal Una, ».' • '. through tin- point, i '. in the mum 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 plane, its intersection with the curve, e" h' i' r, will give a point, e', 
 in the outline of the shadow sought. 
 
 In like manner, by drawing other planes, as f h and g r, parallel 
 to the Hist, e o, wo shall obtain (he intersection*! curves, f 2 /' h' 
 and o 2 / g I, and further upon these the points,/' and g', of the 
 outline of the shadow. By proceeding thus, we can obtain as many 
 points as may be deemed necessary for the construction of the 
 shadow cast by the outer edge, c g' p, of the thread, and the curve 
 obtained is, of course, repeated on the several convolutions of the 
 thread. We would remark, that there is no shadow cast when the 
 depth of the thread is such, only that a b, fig. 6, is less than the half 
 of the base, c d, of the generating triangle. 
 
 The diagrams, figs. 6" and 8, which represent a portion of a left- 
 handed screw, will show that the operations required in this modi- 
 fication, to determine the outlines of the shadows, are precisely the 
 same as those last explained. 
 
 The core, N, which separates the two portions of the double 
 screw, as well as the end, n', receives a shadow cast by the outer 
 edge of the adjacent convolution of the thread. 
 
 shadows upon a round-threaded screw. 
 Figures 9 and 10. 
 
 363. These figures represent a species of screw generated by a 
 circle, abed, the plane of which passes through the screw's axis, 
 and of which each point describes a helix about the same axis. 
 The intervals or hollows between the convolutions of the thread 
 are also formed with a helical surface generated by a semicircle, 
 d e f, tangential to the first. We have, then, to determine the 
 limiting line of the shadow proper upon the screw, and the shadow 
 cast by this line upon the hollows. 
 
 The projecting thread being a species of spiral torus or serpen- 
 tine, the determination of its shadow will be similar to that of the 
 shadow of the ring (323). 
 
 Thus, if the screw be sectioned by a vertical plane, G o, passing 
 through its axis, iU intersection with the thread will evidently be a 
 circle, as projected in/ I', fig. 9. This circle, being inclined to the 
 vertical plane of projection, fig. 10, is projected therein in the form 
 of an ellipse, the principal points,/ k, I, of which are obtained by 
 squaring over the points,/, k\ V, respectively, upon the helices cor- 
 responding to the points, a, b, c. If, then, upon the plane, G o, 
 which we suppose to be reproduced at o g, fig. 10*, we project the 
 luminous ray, R o, it will be sufficient to determine the point of 
 contact of this ray with the curve,,;' A: I; for this purpose, find tho 
 projection of the ray upon the vertical plane in g' o', fig. 10"; then 
 draw a line, g 3 <?, tangential to the ellipse, j k I, and parallel to the 
 straight line, g 1 o, its point of contact, m, with the ellipse will be a 
 point in the line of separation of light and shade upon the outer 
 surface of the screw-thread. By proceeding in this manner, any 
 number of points in this line may be obtained. 
 
 By continuing the sectional plane, G o, across the hollow of the 
 screw, we shall likewise obtain the elliptic curve, n o", the principal 
 points in which are. equally situated upon the helices which pass 
 through the points, d, e,/; it is sufficient to prolong the luminar 
 line, g 1 o 3 , until it cuts the ellipse, n o' p, so as to obtain the point, 
 <A which is the shallow cast by the corresponding point, m, of the 
 
 line of separation of light and shade upon the hollows or intervals 
 between the convolutions of the thread. 
 
 It is to he remarked, that the prolongation of the line of separa- 
 tion of light and shade, s I, casts a shadow upon the outer surface 
 of the convolution immediately below; and, in the same manner, 
 the shoulder above casts a shadow over the projection and hollow 
 of thr adjacent thread. 
 
 APPLICATION OF SHADOWS TO A BOILER AND ITS 
 FURNACE. 
 
 PLATE XXXII. 
 
 shadow of the sphere. 
 
 Figure 1. 
 
 364. It will be recollected, that a sphere is a regular solid, gene- 
 rated by the revolution of a semicircle about its diameter. From 
 this definition it follows, that its convex or concave surface, ac- 
 cording as it is considered solid or hollow, is a surface of revolution, 
 of which every point is equally distant from the centre of the gene- 
 rating circle. To determine, then, the shadow proper, upon the 
 surface of a sphere, we can proceed according to the general prin- 
 ciple (328) ; but, in this particular case, the following will be the 
 simpler method. 
 
 Let us suppose the sphere to be enveloped in a right cylinder, 
 having its axis parallel to the luminous ray ; this cylinder will touch 
 the sphere at a great circle, which is, in fact, the line of separation 
 of light and shade, and the plane of which is perpendicular to tho 
 luminous ray, and, consequently, inclined to the planes of projec- 
 tion ; it follows, therefore, that the projection of this line upon those 
 planes will be an ellipse. 
 
 Thus, let fig. 1 represent the horizontal projection of a sphere, 
 whose radius is o a, the projections of the extreme generatrices, B c 
 and D E, of the cylinder, parallel to the luminous ray, touch the 
 external contour of the sphere in the points, c, E, which are dia- 
 metrically opposite to each other, and are the extremities of the 
 transverse axis of the ellipse. 
 
 As, in general, this curve can be drawn when its two axes are 
 determined, it merely remains to find the length of its conjugate 
 axis. To this effect let us imagine a vertical plane to pass through 
 the luminous ray, R 0, and let us take two lines tangent to the 
 section of the sphere in this plane, and parallel to the luminous 
 ray ; if now we turn this plane about the line, R o, considered as 
 an axis, so as to fold it over upon, and make it coincide with, the 
 horizontal plane, the great circle, which is its section with tho 
 sphere, wall obviously coincide with the circle drawn with the 
 radius, a o. The luminous ray will, as already seen (287), be 
 turned over to r' o, making an angle of 35° 16' with the line, R o. 
 It may also be obtained by making the line, r' r, perpendicular to 
 r o, and equal to a side of the square, as G K, and then joining 
 r' o. The two luminous rays tangential to the sphere will then 
 coincide with the straight lines, H L and M N, parallel to r' o, 
 their points of contact with the great circle will be the extremities 
 of the diameter, L N, perpendicular to r' o. If now we imagine 
 the plane to be returned to its original position, the points, l and 
 

 TIIK I 
 
 *.»;:: br pr..j,<-i«-d in l' at-: ng the length 
 
 tin- conjugal* utt of the elbpae aought. 
 
 364. If, in place ••: ■ rdinary 
 
 ■ 
 a arrira of an- 
 
 ' ■ 
 
 B Ot end 
 luriursl In :..-• plane, so that it shall coincide uilli tin- I. 
 
 with the 
 ". of the »)•: 
 
 the radius, e o, equal to a c. Next draw the tan- 
 »' u, and then project the point, i, on tlie 
 thamcU-r, I. a, ' original line of section, ami 
 
 - manner, as many points ma;. 
 lained .1- lO cef,<f 
 
 . now apparent 
 part of the ellipse. 
 
 If tl:. poaed l" 1"- upon the 
 
 r.. would, on 
 
 arr, be in the direction, a t, jieriK'nilicular ; 
 fig. 3, representing the Itenilenhwrical end of a boiler, shaded and 
 
 siui" L BOIXOW n HERB. 
 
 - 
 
 866. When i by* plane passing through ita 
 
 centre, and parallel to the plane of projection, the inner edge of the 
 aviD east a shadow u|H,n tin- concave «*", the outline 
 ■ will U- an elliptic curve, which may be determini 
 
 :• ral principle of pa already 
 
 ■ of the simpler I 'lis and 
 
 auiiliar;. nple, md of which wu 
 
 ahall pi another inatai , in li::. 2. 
 
 re np.n 
 
 ■ - • -«■ ti» • ri throogfa the line. 1 — 3, 
 
 of the boiler, i '. and 6. It' this bemisphera be 
 
 ••, a b, parallel to the lominoni r«y, 
 
 ■ ; in the auxiliary view, fig. 3, will b< 
 
 - ray, lying in this plane, and passing 
 ; >int, a, a', will, in fig. 8, Is- repn seated by tin- line, 
 
 - indicated in | 
 I ill line, a' i ', • 
 
 ■ ', Which muit l>e - 
 
 d o will !»• tic • by tlio 
 
 point, A. 
 
 In the earne > tela the pointa, >'. ,/, bj m ua of the 
 
 a n, and catting the sphere in 
 
 I 
 
 ■i' li', parallel I 
 
 ■ 
 
 0M tra: 
 
 ml aii,| mechanical subject* ; as, for i 
 n niches, domes, and boilers. 
 
 arrucATioss. 
 
 sal section, at the line, 3 — I, 
 
 ends, ai I f cylindrical ch 
 
 - .. . 
 
 ii ii)«.ii it, ami 
 
 .•■n, made at the line, 5 — 6, in fig*. 4 
 and 5. 
 Fur thin boUer, we have to deteramu — 
 
 I |"'n the 
 
 andj k A upon the cyliodrical surface, together with tlie ■ 
 cast on the i' • ndrieal chan. 
 
 • rnal cylindrical 
 
 and spherical porb'ona of the boOer, and Ih -; uj».n 
 
 . the cylindrical chambara, 
 
 1 letter* as to the analogous diagram, 
 
 fig, 3, this view being drawn for the pn >ing the elliptic 
 
 carve, n J c, of the shadow east by the ciivular portion, a c d, up»n 
 
 the internal spherical surface <>f tlie end of the boiler. 
 
 In the same manner ia obtained the portion, e h c 1, by means of 
 
 the diagram, fig. 8, observing that the sections made parallel to (lis 
 
 rav of light! above the line, " 
 
 below, Mieli aa y c, give the circular portion to the righl of the 
 . but an elliptical portion to the left of t!, - 
 
 the cylindrical port of 
 the boiler obliquely. It must U- remarked, that the ejrlindrieal 
 chambera, sttnatea on tne top of the boiler, give rise to the nit er. 
 
 i, i j E r, which i i upon the interior of tin 
 
 instead of the rectilinear portion, i r, of the i -atrix . >f 
 
 the cylinder, which would have cast a shadow, bad the cj 
 
 chambers not been ' 
 
 -i ladoVI east bj 
 
 limited to the curves, jki, which may be • 
 the aid i ■ by squaring over 0m i 
 
 to the are. j' k' l' I ', and then drawing a aerial of lamia 
 through that i«, lines parallel to tin 
 
 These will meet the internal surface of the cylinder in lb 
 j', A', /', which an- squared over again t" the longitudinal - 
 fig. I, b\ nu ans i.t horizontals 
 
 through the com ■ponding points in I " ■■ h chamb e r , in 
 
 tin- points, j, /.. I. The rectilinear portion, t i, of tin- nppermosl 
 \ of the cylinder, lias for Its shadow, on the internal sur- 
 [Ual straiglit line. / i. which e> 
 in the projection, with the axis, o 
 
 neratrix, I *, of each cylindri- 
 cal chamber, li! -h.ul.iw upon tlie internal Burl 
 
 tin- boUer, tl atlin* of which h ■ ourve, i mj t wb 
 
 • !re, ii. and Wtthj 
 
 equal to that, c <>, ••( the boQer. 11 
 
 lit line i n. which i - i.dieulnr to ti- 
 
 the cylinder; whilst : ; 
 ■'.mi. 
 \\ . . : . . ■:.. points, i, m,j, of tlie enrxe, 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 independently, with the assistance of the auxiliary projection, fig. 6, 
 at right angles to fig. 4. 
 
 It is the same with the curve, n p q, which is likewise an arc. of 
 a circle, because the straight line, n p, the edge of the cover which 
 closes the top of the chamber, is at right angles to the axis of the 
 latter, and at the same time parallel to the vertical plane of projec- 
 tion. The edges, n r and r m, being vertical, have for shadows 
 upon the internal surface of the chamber, a couple of vertical 
 straight lines, parallel to themselves (309). The chamber to the 
 right having a circular opening in the cover, has a shadow upon its 
 internal surface, necessarily different from that in the other cham- 
 ber. It is, however, easily obtained, and in the same manner as in 
 figs. 1 and 1°, Plate XXVIII. It must be observed, however, that 
 a portion, s ( u, of this shadow is due to the under edge, s T u, of 
 the cover-piece : whilst the other part, s v, takes its contour from 
 the upper edge, v x, of the same piece. A comparison of figs. 4 
 and 5 will render these points ea§y of comprehension. 
 
 There remains, finally, the curve, c e g h, and the rectilinear por- 
 tion, h i, together extending from the first, d d c, to the straight 
 line, i i, and which represents the shadow cast by the arc, A F, g h, 
 of the hemispherical end of the boiler, and the straight part, H I, of 
 the upper edge of the cylindrical portion. 
 
 The whole curve, D d, c g i, representing the shadow cast by 
 the edge of the section of the boiler upon the internal surface of 
 the latter, is precisely the same as that distinguished in architecture 
 by the name of the niche shadow. It is to be observed, however, 
 that the position in this case is different, as the axis of the niche is 
 vertical. 
 
 We have now to draw the shadows, proper and cast, upon the 
 outer surface of the boiler, as seen in horizontal projection, fig. 5. 
 As for the shadow proper, it consists partly in that limited by the 
 line of separation of light and shade, d d, obtained by the tangential 
 line, making an angle of 45° with the horizon, and touching the 
 circle in the point, c, and partly in that bounded by the elliptic 
 curves, c d and d c' E, upon the spherical ends of the boiler, the' 
 manner of determining which has already been thoroughly discussed 
 in reference to fig. 1. 
 
 . 368. As to the shadows cast by the cylindrical chambers, either 
 oil their neck pieces, or upon the outside of the boiler itself, they 
 are simply represented by lines inclined at an angle of 45°, as a' d', 
 B' g E', drawn tangential to the outsides of the cylinders, and which 
 are prolonged in straight lines, as far as the line of separation of 
 light and shade, upon the cylindrical portion of the boiler; that is, 
 in case they stand out far enough from the boiler surface. If, on 
 the contrary, they do not rise very high, as exemplified in the 
 end view, fig. 9, it will be necessary to determine the outline of 
 the shadow cast by a portion of the upper edge, b' c', as lyino- 
 either upon the cylindrical part of the boiler, or upon one of the 
 spherical ends. To find the shadow in this last case, we have 
 supposed an imaginary vertical plane to pass through the luminous 
 ray, r' o',^fig. 5, producing an elliptical section of the cylinder, 
 and a circular one of the spherical part. This plan being repro- 
 duced at r 3 o", fig. 9, and turned about, to coincide with the hori- 
 zontal plane, we have the curve, F 3 G a h 2 , representing the section 
 in question. The point of contact, b', being transferred to b 2 , is 
 also turned down, as it were, upon the horizontal plane, to the 
 
 point, B 3 ; so that if we draw a line, E s I*, through this point, B* 
 parallel to the luminous ray, r 3 o 3 , similarly brought into the hori- 
 zontal plane, this line, b 3 i 2 , will cut the intersectional curve in the 
 point, I s ; the horizontal projection, I 3 , of this point, upon the line, 
 R 3 h 2 , being obtained by letting fall the perpendicular, I 3 i 3 , upon 
 the latter. The corresponding point, i', in fig. 5, is taken at a dis- 
 tance from b', equal to b 2 i 3 , in fig. 9. Proceed in the same manner 
 with another sectional plane, parallel to the first, and passing 
 through the point, o', in order to obtain" a second point, c', of the 
 shadow. The operations necessary for determining the intersec- 
 tional curves are sufficiently indicated in figs. 5 and 9. 
 
 369. The cylindrical steam-boiler, represented in longitudinal 
 section in fig. A, in end elevation in fig. g}, and in transverse 
 section in fig. ©, conjoins the various applications of shadows, of 
 which we have been treating, in reference to spheres and cylin- 
 ders ; whilst, at the same time, they serve as examples of shading, 
 by lines or by washes, indicating the effects to be aimed at, and to 
 be attained by the following out of the various principles already 
 laid down. 
 
 370. We must remind the student, that, in order to produce tnese 
 effects, he 'must not always confine himself to the representation 
 of the shadows proper and cast merely. lie must, further, show 
 the gradations of the light or shadow upon each part, as has already 
 been explained with reference to solid and hollow cylinders. As 
 upon a cylinder or a cone, there is always a line of pre-eminent 
 brilliancy, so likewise, upon the surface of a sphere, will there be a 
 point of greater brilliancy than the rest. 
 
 This point is actually situated upon the luminous ray, passing 
 through the centre of the sphere, fig. 1. Since, however, the visual 
 rays are cot coincident with the luminous rays, the apparent posi- 
 tion of this point is somewhat changed. Thus, if we bring the 
 vertical plane, R o, fig. 1, into the horizontal plane, the luminous 
 ray will coincide, as has been seen, with the line, r' o', ami, conse- 
 quently, its point of intersection with the sphere will coincide with 
 the point, i. On the other hand, the visual rays which are perpen- 
 dicular to the horizontal plane will coincide with parallels to c o, 
 when brought into the horizontal plane. This latter line intersects 
 the sphere in the point, c ; and as the light is reflected from any 
 surface in the direction of the visual rays, so as to make the angle 
 of incidence equal to the angle of reflection, if we divide the angle, 
 toe, into two equal angles, by the line, n o, the point, n, will bo 
 that which will appear to the eye most brilliantly illuminated. The 
 positions, n' and i', in the vertical plane of the points, n and i, are 
 obtained by letting fall perpendiculars upon the line, o A, repre- 
 senting this plane. 
 
 In shading up a drawing it is preferable to place the bright or 
 lightest part between the two points, n' and i', a more pleasing effect 
 being obtained thereby. When the sphere is polished, as a steel, 
 brass, or ivory ball, a circular spot, of pure white, must be left about 
 the point in question. When, however, the body is rough, as is 
 supposed in fig. (g, this part is always lighter than the rest ; but, at 
 the same time, it is covered by a faint wash. 
 
 In the case of a hollow sphere, figs. 2 and 3, we have to bear in 
 mind, not only to indicate the position of the bright spot, which 
 is projected, in the same maimer, upon the luminous ray, a b, and 
 lies between the points, n\ I', but also the point in the cast shadow, 
 
m 
 
 THE I'll \( 1 
 
 whk-h .hookl be the least prominent. Ti. •■ found 
 
 U> be at '"• n S- 3 - drawn 
 
 ..-. into the same 
 j.'jmr H |g 3 
 
 Tbe boQer i» rrpre*- I ta Hi furnace, which 
 
 i, baiJt • rilh s diaphragm pawing down tho 
 
 middle "•"< and gs- 
 
 the grata to pass slot .. than '" return by that 
 
 U> Um right, and pa— 
 
 ■ . ... r, full 
 
 . a pipe 
 pawn,- ' teach. In ' 
 
 water Itroro. - • as not 
 
 to reduce the tempera- : . u I ,on 
 
 ita introduction intu it. 
 
 ted as half full of w.itor. It should 
 geotnl . ' ; >ia] f lu " ! so 
 
 that a greater p ntarior may !>>• 
 
 Tin- remain 
 chambers, is suppose i I '"• The base of the 
 
 is of brick. Tne foundations 
 of the furnace :. 
 
 ... tain which 
 
 as large, ao as to sequin the proper skill an J facility of treatment. 
 
 SHADING IN I'.I.VX.- SHADING IN COLOURS 
 
 PLATE XXXIII. 
 
 la* great numl*r of drawir ilariy in those 
 
 I drawing*, and intended for us,- in tetoal eonstrao- 
 shading thi 
 na ink — son, ring 1 1 » i -* with a faint 
 
 : the material. The 
 t the parts in relief, and ren- 
 ■ the eye ; a 
 tiie other han . indicate ..i" what material they are 
 
 made. This duplex arii-ti. - tin- drawing 
 
 much ti. bended, A drawing 
 
 may be . ' phut il first to 
 
 ■hade op tho various surfaces with China ink, hat b 
 
 ■ ording t.. the 
 
 lights and shades, as has been done in the preceding plate*, The 
 
 entire surface • red with an ■ 
 
 wash of clour, the line of which b onal 11 must 
 
 ■n in flat W*l | to Hi" Inatmctiona given in 
 
 i 
 
 ease*, but it leaves out mod In the effective 
 
 without 
 
 old and monotonous. A better reeull i- obtainable by 
 
 • China ink ■ depth, and by 
 
 '■■iir. laid on in 
 
 . with the Ch produce 
 
 put*, whil-t I 1 
 
 parts ar, l,» pure 
 
 the bril- 
 V softer and I .an bo 
 
 il n.utra! tint, instead of tl 
 ink, for the pr 
 difficult to mix, ami to ke, p uniform. 
 
 -kill and facility in the 
 .in may 
 in a more direct and vigorous n 
 out altogether the preliminary shading with China ink, and laying 
 
 time, tl. 
 
 material. This last method he* the merit I 
 
 of the drawing a richer transiuoence, more warmth, and i 
 tory fulfilment of all deeirabh 
 
 I ;;, ra!. all drawings intended t.. be shaded should \»- d.!i- 
 with faint graj instead of ' 
 outline drawing; the faintnees of such line* avoids the ui 
 of making them very fin.-, and their greater breadth affords a much 
 tide to the shading-brush. A black outline, however tine 
 it may be, always produce* a too sharp and I 
 then la much greater ri-k of overstepping it in laying on the 
 ■ 
 373. In Plat.- XXXIII. we 
 shaded i prising the m ri In ma in con- 
 
 struction. 
 
 though tin- wo... Is are naturally verj different in clour, still, in 
 mechanical lira' indiscriminately : it i-, 
 
 have said, entirely conventional. 
 
 In fixing upon these colours, the obj< ct in view has bean to avoid 
 on, and to employ a distinct and intelligible colour for 
 the representation of i oopy the 
 
 natural colour in all It 
 
 In colouring this wooden capital, after the preliminary 
 th.ns which we have mentioned, for determining the out 
 
 the shadow*, | '. it is first sha.l.sl throughout with 
 
 China ink. and when this shading has reach, d a coincident depth, 
 and is thoroughly dry, the whole surface is to be covered with a 
 light wash, which may he a mixture of gamboge, lake, and China 
 
 ink. or burnt nmbi r alone. The colour, in fact, should be analo- 
 
 I. Plate X. ; it should, however, ah 
 fainter than In that example, which represents the mater,.. 
 ti..n. and is, therefor 
 
 This proceeding may be easily modified, and mi 
 the effect of the second method, by leaving certain parts of the 
 
 incolound, and by softening off the -hade in th-- 
 wh.re the light i tli a marly dry brush. If, however, 
 
 the draught-man has become soinew hat familiarized with the ttSS 
 Of the hrii-h and the mixture of the colour-, he may. Si WS have 
 said, omit the preliminary shading in black, by modify : 
 ■hade as laid on, mixing the China ink directly with the 
 nlid th.n gradually bringing npthe shades, cither accor.li: 
 
 »\ -t. in of Bat washes, ..r the more difficult o f - 
 
 . • ikl n in lav ing on tie -■ shades tO commence at the 
 
 part*, and then to c\er ti. 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 123 
 
 quent washes, which gradually approach the bright part of the 
 object ; for in this way a more brilliant and translucent effect will 
 bo obtained. 
 
 When the objects are of wood, it is customary to represent the 
 graining in faint irregular streaks, care being taken to make these 
 as varied as possible. A general idea of the effect to be produced 
 will be obtained from fig. 1. 
 
 Following out these principles, the draughtsman may proceed to 
 colour various other objects composed of different materials, merely 
 varying the mixtures of colour according to the instructions given 
 in reference to Plate X. 
 
 Fig. 2 represents the top of a chimney of brickwork, the form 
 being circular. In this external view, the outline of each brick is 
 indicated ; and to render them more distinct from each other, a 
 line of reflected light has been shown on the edges towards the 
 light, near the brighter part of the chimney. Indeed, it is generally 
 advisable to leave a narrow, pure white light at the edges of an 
 object which are fully illuminated, as it gives an effective sharp 
 appearance. 
 
 Fig. 3 represents the base of a Doric column in stone, showing 
 the flutings. This being an external view, the tint to represent the 
 stone is not made nearly so strong as for the sectional stone-work, 
 represented in Plate X. A yellowish grey may be used for it, made 
 by mixing gamboge, the predominant colour, with a little China ink, 
 adding a little lake to give warmth. 
 
 These three examples of wood, brick, and stone, represent bodies 
 
 with rough surfaces, and which, therefore, can never receive such 
 brilliant lights as objects in polished metal ; no part, indeed, should 
 be entirely free from some faint colour. 
 
 Fig. 4 represents a nut or bolt-head of wrought-iron ; and, as 
 we have supposed it to be turned and planed, and polished upon 
 its entire surface, it has been necessary to leave pure white lights 
 at the brighter parts, to distinguish the surfaces from those which 
 are rough and dull. It is the same in the example, fig. 5, repre- 
 senting the base of a polished cast-iron column, and in the lateral 
 projection, fig. 6, of polished brass upper and lower shafUbearings 
 or brasses. 
 
 We would hope that the principles of shadows and shading, ex- 
 plained and exemplified in the last two chapters, may serve as 
 sufficient guides for the various applications which may present 
 themselves to the draughtsman — whether his skill be called forth 
 to render the simple effects of light and shadow, or to produce the 
 gradations of shade and colour due to roundness or obliquity of 
 surface — to the various positions of the objects in their polished or 
 unpolished state, and to the various materials of which they may 
 
 Thus, it will be understood, that although two objects are pre- 
 cisely alike in material and form, if they are situated at unequal 
 distances from the spectator, the nearer one of the two must be 
 coloured more strongly and brilliantly than the more distant, more 
 force and depth being given to the darker shades. 
 
 CHAPTER IX. 
 THE CUTTING AND SHAPING OF MASONRY. 
 
 PLATE XXXIV. 
 
 374. The operation of stone-cutting has for its object, the pre- 
 paring and shaping stones in such manner that they may be built 
 up into any desired form in a compact and solid manner ; great 
 care and skill, as well as mathematical knowledge, is more parti- 
 cularly required in the preparation of stones for arches, vaults, 
 arcades, and such like structures. 
 
 The study of the shaping of stones is based entirely upon descrip- 
 tive geometry, being indeed but a particular application or branch 
 of it, and in it have to be considered the generation of surfaces, as 
 well as their intersections and developments. 
 
 In proceeding to adapt the stones to the position they are to 
 occupy, the mason should prepare a preliminary drawing of the 
 actual size of each stone, as well as a general view of the entire 
 erection, indicating the joints of each stone ; these, according to 
 the various positions to be occupied by them, are called key stones, 
 arch stones, &c. 
 
 It is not our intention to give a complete treatise on the shaping 
 of masonry ; but, as this study seems to belong, in part, to geome- 
 trical drawing, we have thought it quite within the design of the 
 present work to give a few applications, sufficient to show the line 
 of procedure to be followed out in operations of this nature. 
 
 the marseilles arch, or arriere-vu„.ssure. 
 Figures 1 and 2. 
 
 375. Wo propose to prepare the designs for the bay and arch 
 of a door or window, to be built of stonework, the upper part 
 being cut away, so as to present a twisted surface, analogous to 
 that known as the arriere-voussiire of Marseilles. 
 
 This surface is such as would be generated by a straight lino, 
 c a, kept constantly upon the horizontal, c' k', projected vertically 
 in the point, c, and moved, on the one hand, upon the semi-base, 
 B E D, of a right cylinder, having c' k' for its axis ; and, on the 
 other, upon the circular arc, F e a, situated in a plane parallel to 
 that of the base, bed. 
 
 The lateral faces, f b l n and A R Q D, of the bay, are vertical, 
 and are projected horizontally in f' b' and a' d', fig. 2. These 
 faces intersect the twisted surface at the curves, F B and A D, which 
 we shall proceed to determine. 
 
 For this purpose, the first thing to be done is to seek the pro- 
 jections of the straight generator line, c a, as occupying different 
 positions, so as to obtain their points of intersection with one of 
 the oblique planes. 
 

 ay rrmark, thai if Up 
 
 for I ioj. J' • . of !:.• I. and • 
 
 liraJ p.— j««ti.-n» of Um> g*t. 
 
 . 
 
 aaJM liaea abo rui the cirvular are. I 
 
 ••!' thb 
 
 tbaae bat. an.: 
 
 •ac generatrix, c a. and eon 
 
 I 
 
 ! M lines, 
 
 . A M / I D, p 
 
 I, sou U> avoid :l. 
 
 full size, it a 
 
 ■ 
 
 an are of a . 
 
 ■ 
 
 over the 
 ■mi the 
 
 iodivi- 
 
 : up. 
 
 - 
 
 the key- 
 
 i with the tw 
 
 th i-. the 
 
 I 
 
 \i. n /i andoi, • - 
 
 "BED ami r • 
 
 ■ 
 
 It i* the eta i e and J C, in which lie the 
 
 :i«, k g and I » of the 
 led hori- 
 : a' t. 
 - 
 nhoiiUl ■: hashed from r 
 
 • joint), ami be 
 tin ii taki 
 from an 
 roughly in thi 
 
 lane the 
 
 Tim-. 
 
 : in front view ami 
 
 :.ikes a paralleloniped, of wlm-h the 
 i ..f firvimwnliitiL' the two parallel I 
 tin- upper part of the key-stone, and of « hieh th.- 1. 
 equal to tin- length, i it. After having eat ami finished the two 
 .. and u' r. of the prism, as well as tin- li ■ • 
 at off upon tin- anterior face, fig. 8, the 
 and vertical sidis. ( o and a r. ami then the obfiqtM lims o f> and 
 p {, which, it wHl be nuu-inl- 
 
 ire. Mr ni-xt seta off np.ui a tamp 
 - them thence opon th 
 
 :. ti.'. 3. at ;i and h I. After this preliminary marking 
 
 out, tin- itoneentter reduces ami takes away all tin- mati rial opon 
 
 parallelopiped which lies ootaide tin- tines, i 1 
 
 r l ; tl.. - • finished, the shape-d it upon 
 
 them id i at n h ami o /. In order that thi I 
 
 • inav Ih- more easily comprehended, we have brought the 
 . 
 if projection, 
 new, H will ' ined; for, on tin- one 
 
 hand, we h.i\.- tin- line, t J y. equal to k k\ i Ihe thick. 
 
 ■ tin- arch; and. on tin- other hand, nil the 
 other dii ' !,lt ,l "' 
 
 >n of ;lu- line, d I , can be determined with tin- mi 
 
 - 
 
 tide to tin- st i-utter in reducing 
 
 ■ 
 
 affording a ti- 'on. it may 1h> 
 
 ihould In- cut in tuch a manner, thai a 
 
 l, v t |„. . r of which splits from the 
 
 •:,.• latter from tin- | 
 
 ither of tin- tw 
 
 ted in their full dimei 
 
 . 
 
 trail l to thi- 1 
 Thus, to obtain tin- actual dhneni •..•joint 
 
 1 at h, with tin- poll 
 
 .. u; u i/-, h w. *« a» to reproduce tlio 
 ... u, h, at u\ h', V, upon tin- vertical, o" ir ; then, bj 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 off, ft" K', equal to n' h', fig. 2, and joining the points, h' n", fig. 7, 
 we get the inclination of the generatrix line, if h', which is project- 
 ed vertically at n h, fig. 1. The form of the joint face is completed 
 by drawing the horizontal lines, o 1 w , h' z', y' i', and the verticals, 
 ■u v' and z' y', which last are already given full size in fig. 6. It 
 will be observed that fig. 7 is on the plate removed a little to the 
 right of the vertical, o a w ; but this is a matter of no importance, and 
 is merely done for convenience sake. 
 
 The same system of auxiliary projections is applicable to the 
 determination of the dimensions of the other face of this piece — 
 namely, that projected at m g, which is brought round to the hori- 
 zontal, m' g 2 , and drawn with full dimensions in fig. 8 ; only, for 
 this last face, it is necessary to bear in mind the portion of the line 
 of intersection of the sides with the arched part which it contains, 
 and which is obtained in its actual proportions, as at c? m 3 , by 
 means of a template formed to the curve, a" m", in fig. 1. The 
 stone, T, beneath, of course, contains the remainder of the inter- 
 sectional curve. 
 
 The methods just explained, in regard to the shaping of the key- 
 stone and one of the corner-stones, may be extended, without diffi- 
 culty, to the remaining portions of this Marseilles arch. 
 
 In this application it has been necessary to determine the propor- 
 tions of the twisted bay of the arch, as well as the faces of the 
 joints ; but in the more general case of straight, bays, such as that 
 represented in fig. I 1 ", the operations are considerably simplified, 
 and the designer has merely to attend to the form of the joint faces, 
 making use, for this purpose, of the auxiliary projections, as above 
 described. The delineation of the various parts of this figure pre- 
 senting no new peculiarity, it need not further detain us. 
 
 378. Let it be proposed to delineate a circular vault with a full 
 centering, bounded by two plane surfaces oblique to its axis, figs. 
 9 and 10. This example is taken from the entrance to the tunnel 
 on the Strasbourg Railway, near the Paris terminus, and it is a form 
 frequently met with in the construction of railways. 
 
 In the representation of this vault, we have supposed one of the 
 oblique planes to be parallel to the vertical plane of projection! and 
 it consequently follows that the axis of the arch is inclined to this 
 plane. 
 
 Let a B he this axis, and c D the horizontal projection of a 
 plane at right angles to it ; with the point, e, as a centre, describe 
 the semicircle, cad, representing the arch in its true proportions, 
 as brought into the plane of the picture. Let us suppose this 
 semicircle to be divided into some uneven number of equal parts, 
 as in the points, a, b, c, d, e,f ; through each of these points draw 
 straight lines, passing also through the centre, E, and representing 
 the joints, a g,b h, c i, of the arch stones, being, of course, normal 
 to the circular curvature of the arch, and being limited in depth, as 
 we shall suppose, by the second outer semicircle, g i I, concentric 
 with the first. Each of these joint faces intersects the centering 
 of the arch in a straight line parallel with its axis, and the horizon- 
 tal projections of these intersections, as seen from below, are ob- 
 tained simply by drawing through the points, a, b, c, d, lines parallel 
 to the axis, B a; these last extend as far as the vertical plane, a e, 
 which bounds a portion of the vault. The external faces of the 
 key and arch stones are limited by straight vertical lines, such as 
 m h, i n, oj, and horizontals, as m i and n o. 
 
 We have now to obtain the projections on the vertical plane, 
 fig. 10, of the intersection of each of the arch stones by the plane, 
 a e. 
 
 We may remark, in the first place, that since this plane is 
 oblique tp the axis of the cylindrical arch, it produces an elliptical 
 section, having for its semi-transverse axis the length, c' a, and for 
 its semi-conjngate axis, the length, a b , equal to the radius, a' e. 
 As much of this ellipse as is required is drawn according to one 
 or other of the many methods given (53, et seq.) — say as at c' i s b' 
 fig. 9, which curve is reproduced at c" o" a", in the elevation, 
 fig. 10. 
 
 If we, in like manner, obtain the projection of the semicircle, F i I, 
 which limits the radial joints, we shall also obtain the portion of an 
 ellipse, f" g" i\ and we have further merely to project the points, 
 a', b', c', upon the first ellipse, in a" b" c" ; as also on the second 
 one, the points, g", h", i", corresponding to g ft and i. The straight 
 lines, f" c", g" a", h" b", i" c", represent the intersections of the 
 faces of the arch stone joints, with the plane, a e. 
 
 The vault being supposed to extend no further back than the 
 plane, c D, it will be necessary to represent the intersection of this 
 last with the arch stones which extend thus far upon this plane, 
 c D. We have, therefore, to project the elliptic curves, c'" b'" c" 
 and f"' g'" i", corresponding to the quarter circles of the radii, 
 F B and c b. As the arch stones cannot extend the entire length 
 of the vault, they are limited by planes, M N, perpendicular to the 
 axis, and, consequently, parallel to c D. so that the projections of 
 these joints will be but repetitions of portions of the same elliptic 
 curve ; care is taken so to dispose the blocks of stone, that no two 
 joints form a continuous line, the joints in one course being brought 
 between those in the adjacent ones, as is customary in all brick and 
 stone work. 
 
 379. We have now to determine the intersection of the oblique 
 plane, a g, with the remaining half of the same circular vault, and 
 then to obtain the projection of this intersection upon the vertical 
 plane. 
 
 The plane, A G, also produces an elliptical section of the van't ; 
 this is represented at g' gt, as brought into the picture in the auxiliary 
 diagram, fig. 11, which gives its actual proportions ; the semi-trans- 
 verse axis, g' o, of this ellipse is equal to G A, and its semi-conjugate 
 axis is equal to the radius, a' b, of the vault. 
 
 After having divided this curve into a certain uneven number of 
 equal parts, draw normals* p u, q v, r x, s y, and I z, through I ho 
 points of division representing the joints of .the arch stones, the 
 remaining sides of the external faces of which are limited b) hori- 
 zontals and verticals, as before. 
 
 If the vault is supposed not to extend beyond the plane, a g, 
 the arch stones will have to be shaped as facing stones, and their 
 joints will require to be set off upon the first ellipse, g' q l, and to 
 be limited by the second, h' q* C, obtained from the intersectional 
 plane, H i, drawn parallel to A G ; by drawing straight lines from 
 the points of division obtained upon the ellipse, g' q I, to the centre, 
 o, we obtain the points, p', q*, r\ s', of intersection of these line? 
 upon the second -ellipse, and the straight lines, p p\ q q', r r 3 , s s a , fe- 
 presenting the intersections of the arch stones with the inside of the 
 
 • A line is said to be normal to a curve, when it is perpendicular to a t intent t« 
 the curve passing through its point of intersection with the curve (73). 
 
m 
 
 
 iaaa sre projected horizontally in f /, cr* o*. 
 . fig. 9, si,. -.!•»«■. bxua toe diagram is 
 
 Mp|>arU to U f the vault, aa seen from below ; the 
 
 two dasgram*, figs. 9 and It. wiU reader the determination of the 
 vortical projection, fie;. 10. very easy, the asm* lines there being 
 d— igsslrd by the — e letters. 
 
 To limit the arch lacing atones, and unite them coavenW r 
 the regular unit— of tin- vault, th« y must be cut by planes, aneh 
 aa J I and L r, fig. 9, psrpendirolar to the aii.% A a. TV 
 tioaa of thee* planea with the vault produce |-.rti,.n- 
 are projected aa ellipses in fig. 1 1, such as l' if v and v' r* x'. for 
 the inside of the vault, and >' q «' and l' s' i j . fbf 
 trccnitics, them various ellipses corresponding to the radii, c ■ and 
 r a. The joints of tbeae stones are finally completed by planes, 
 each aa t r* a Q, fig. II. passing through the axi-. a b, and through 
 horizontal lines. T z' and o a, in the vault, the latter and i. 
 of which only ia risible in tii- : 10. 
 
 380. In constructing this vault, it is necessary to make detailed 
 drawing* of each part: •» ing the dimensions of all the 
 
 foes*, In las, IS :■ 16, va !.^-.,- rapreaaxted oaa ••; m -<• a.-.-h 
 at now, O. in pun and elevation, aa detached from I 
 10, and showing more particularly such lines as are not apparent in 
 Thus, in these views may be distinguished: — 
 
 bee, ■ q r x, which i« : .ontally 
 
 upon the line of the plane, a g ; mil inhered, 
 
 intersect* the vault at the elliptic cur - q r. 
 
 3d. The fao M edge, x r. is 
 
 : upon the same plane, c A, at x - 
 
 : upon the line, r' r', parallel lor, i; and 
 
 • r edge, r r*, the line of int» n I th the 
 
 Hat, finally, the 
 upper and fourth edge, x w, is projected at . 
 
 3d. Tiit second joint face, r q / w, U opposite to the first, and 
 
 4th. Toe face, n « z t, lhi> horizontal ; 
 
 . ; this face is situated in a plane pas the axis 
 
 of the vault, and is additions.' :i the diagnu. 
 
 on the radius, r q*. 
 
 6th. The species of dovetail joint, q <f t z r* r, of «. 
 edge*, o o* and r r*. are projected, as has been Men, at q q* and 
 .ilst the sides, q r and z r\ are similarly projected at q" r 
 and z r', and : 
 
 6th. I. 
 render an account by mean- eh are 
 
 invariably the same for the same points, altii 
 mark* are snperadded to obviate eoi various 
 
 nave added the subsid. 
 of the block in the plane, ir.u I • 
 picture ; we have thus the actual pr ; 
 in the p l anea , a* r* sn 1 
 
 ■> , it is sufficient to * I -a] distances I 
 
 line, o o, of the elevation, figs. II and 13, obtaining in this man- 
 
 • instance, the points r*, 7'. 
 ■ '. ' and x. 
 
 "Ni example* chosen for this plat. \ \ \ I V . .rnoine the more 
 
 difficult problems and applications met with in the shaping aad 
 arrangement of stonework, and will make the student aoqn 
 with the operations upon which design* for these purpose* are 
 based, aa wed aa with the general method* to be adopted in obtain, 
 ing oblique projections by the employment of auxiliary projections, 
 taken, a* it were, in planes parallel to the different surfaces, and 
 then brought into the plane of the picture ; this system, at the same 
 time, being of much use in ascertaining the exact proportions of 
 various surfaces, such as the joints of masonry. 
 
 RUI . MTHAL DATA. 
 
 BYDBACUC MOTORS. 
 
 3S1. Tin- fall of a stream of water varies with the locality, and 
 rent kinds of hydraulic motors, 
 which are denominated as follows, according to their several pe- 
 culiarities. 
 
 Undershot water-wheels, which receive the water below 
 .-.res, and the buckets or floats of which pass through an 
 enclosed circular channel, at the part where the water acta upon 
 them. 
 
 i. Overshot 1 iuch receive the water from 
 
 above. 
 
 Thirl vertical axes, known as turbines, and which 
 
 are capable of working at various depths. 
 
 Fourth. Wial h plane floats or buckets, receivTig 
 
 the wat> - and working in enclosed channels, 
 
 through a portion of their circumference. 
 
 irved buckets. 
 anted on barges, and suspended in 
 the currenL 
 
 U5DERSH0T WATER-WHEELS, WITH PLANE FLOATS A5D A 
 CIRCULAR CHA55EL. 
 
 mtageous arrangemeot that can be adopted 
 
 in the construction of an and htfa plane floats, 
 
 riving in an enclosed circular channel, is that in which the 
 
 - formed by an 'nd when the bottom 
 
 of this - J tu., or about 8 inches, below the general 
 
 Lei it bv re-juirvd to determine the width of an undershot water- 
 ing data: — 
 
 : 1<H) litre* per second. 
 l.Jl is 2 475 mi 
 Thini. ' the water at the sluice-gate is to 1- 
 
 WIDTH OF THE WHEEL. 
 
 ':«■ seen, in the table at page 113, that, with an outlet of 
 
 •23 in depth, a discharge can - of water per 
 
 for a width of 1 metre; consequently, the width to be 
 
 1 the sluice, to enable it to discharge 1,200 litres per second, 
 
 should be— 
 
 1200 ■+- 188 = fi 39 metres. 
 
BOOK OP INDUSTRIAL DESIGN. 
 
 DIAMETER OF THE WHEEL. 
 
 383. The diameter to be given to a wheel of this description has 
 not been accurately determined, because it has not a direct influence 
 upon the useful effect that may be obtained from it. Nevertheless, 
 it is manifest that it should not be too small ; for in that case the 
 water would be admitted too nearly in the horizontal line passing 
 through the centre, or even above it, which would cause great loss 
 of power. Neither should it be too great, for in that case the ex- 
 aggerated dimensions would but involve an increased bulk and 
 weight, and, consequently, a greafer load and more friction, without 
 any compensating advantage. 
 
 In general, for a fall of from 2 to 3 metres, it is advisable to make 
 the extreme radius of the wheel at least equal to the mean height 
 of the fall, augmented by twiee the depth of the water upon the 
 edge of the outlet. 
 
 Thus, in the case before us, the height of the fall being limited 
 to 2-475 m., the outer radius of the wheel should Tiot be less than 
 2-475 m. plus twice the depth of the overflowing body of water 
 when at its fullest — say '6 m. ; that is to say, in all, 3075 m., which 
 corresponds to a diameter of 6-15 metres. 
 
 Water-wheels, on the same system, with a fall of water of from 
 2-6 to 2-7 metres, have often an extreme diameter no greater than 
 this. 
 
 VELOCITY OF THE WHEEL. 
 
 384. Theoretically speaking, the velocity which it is convenient 
 to give to an undershot water-wheel should be equal to half that 
 due to the height of the overflow of the water ; that is to say, equal 
 to from 1- to 1-1 in. in the present case. Nevertheless, practice 
 shows that this rule may be departed from without inconvenience, 
 and the wheel may be made to attain a velocity of from 1*5 to l"6m. 
 per second at pleasure, which is a very great advantage in many 
 circumstances. 
 
 If the wheel makes three turns per minute, the mean velocity at 
 
 the outer circumference, and at the edges of the floats, will be — 
 
 615 x 31416 x 3 
 . s; = 1-021 m. per second. 
 
 Thus, when the height of the overflow is -24 in., the correspond- 
 ing velocity of the water being 2-17 m. nearly, as shown in the 
 table at page 94, which gives the heights, 2356 and 24-67 cent., 
 therefore, the ratio of the velocity of the wheel to that of the water 
 is -47 : 1. 
 
 If the height of the overflow were reduced to - 15 m., which sup- 
 poses that the discharge would only be 
 
 101 litres x 6-32 m. = 638 litres per second, 
 the corresponding velocity of the water would not be more than 
 1-72 ; and in this case, the ratio of the velocity of the wheel, sup- 
 posing it to be still the same, to that of the water, would be — 
 •595 : 1. 
 
 NUMBER AND CAPACITY OF THE BUCKETS. 
 
 385. Although the number of buckets cannot be determined in 
 accordance with any exact rule, it is, nevertheless, of importance 
 that their pitch should not be much greater than the depth, or 
 thickness, of the overflowing body of water acting upon them. It 
 
 is also necessary that the number of the buckets should be divisible 
 by that of the arms of the wheel, so that the whole may be put 
 together conveniently. 
 
 Now, since the outer circumference of the wheel is 
 G15 x 31416= 19-32 metres, 
 we can very conveniently give it 8 arms and 64 buckets ; and the 
 pitch of these last will be -32 m. With this distance between the 
 buckets, there should not generally be a greater depth of overflow 
 than -25 or -26 m. ; because, at -27 m. the water will begin to choke, 
 as it will not be admitted easily into the buckets, and will rebound 
 against the interior of the channel, giving rise to a continual shak- 
 ing action. 
 
 Thus, then, in determining the number of buckets for an under- 
 shot water-wheel, receiving the water from an overshot outlet, it is 
 necessary to calculate the spaces between them, so as to be about 
 a third, or at least a fourth, greater than the depth of the water at 
 the outlet, whilst their number must be divisible by the number of 
 arms of the wheel. 
 
 For water-wheels of from 3-5 to 4-75 metres in diameter, six 
 arms for each rim or shrouding ; for wheels of 5 to 7 metres in 
 diameter, there should always be eight arms for each shrouding; 
 and the number of arms should obviously increase for wheels of 
 greater diameters than 7 metres, of which, however, there are but 
 few examples. 
 
 With regard to the capacity of the buckets, and the channel, 
 taken together, it should be equal to at least double the volume of 
 water discharged. Therefore, on this basis, we can always easily 
 determine the depth to be given to the buckets, when the maximum ' 
 discharge is known. 
 
 Thus allowing, in the present instance, the maximum discharge 
 to be 1,340 litres per second, instead of 1,200, since the velocity at 
 the outer circumference is 1-021 m. per second, the number of 
 buckets contained in this space is equal to 
 1-021 -=--32 = 3-19. 
 Then— 
 
 T340 -i- 3-19 = -43 cubic metres nearly, 
 the quantity which should be in each bucket during thi> revolution 
 of tin- wheel. If, then, the capacity is to be double this, it will bo 
 equal to -86 cubic metres. The product, however, of the width, 
 6-38 m., of the wheel, multiplied by the space between two consecu- 
 tive buckets, -32 m., is equal to 2-022 m. 
 
 We have, then, -86 -=- 2-022 = -42 m., for the depth of the 
 buckets. The distance between the buckets, however, is not the 
 same at the inside as at the extremities, and the capacity is also 
 further diminished by the thickness of the sides of the buckets, and 
 by the inner portions, which make an angle of 45° with the outer 
 portions. For these reasons, the depth should be somewhat 
 increased. When the discharge of water is considerable, and we 
 are limited as to the width of the wheel, it is preferable to do awai 
 with the inner inclined portion of the buckets, as indicated in the ■ 
 drawing, Plate XXXVI., prolonging them considerably towards 
 the centre of the wheel. 
 
 USEFUL EFFECT OF THE WATER-WHEEL. 
 
 386. The absolute force of a stream of water is the product 
 of the water discharged per second, expressed in kilogrammes, bv 
 

 THE I 
 
 la» >...».! •..'!»«• U/1 erpieeai I ia aita, or tit* wri^l In p., nod* 
 lafcet. 
 T!.c«. >l«i the diarharg* h> UOOUlraaor kBoff- pec eeoood, and 
 •I I- i.+l of It. 
 
 .imrir. • llic . V.l.nuiy 
 
 .md 3217 -I- 75 = 43 I 
 
 U' .t.jr...i Whl ii v«. . . I .Iru.lc-l. arr r.i|. . ! .■ .- lr in 
 
 ovi«» 
 
 fail, nr the 
 
 ■ 
 
 : by a vertical sluice-gate, with 
 
 • i ■.;. . i. aaatro. ■■■■■■< a: tl.. hui • t. 
 
 : v ; alM.\« 
 
 nt | .._••• 1 1 1. of tin- diachi 
 
 b tba quantity which 
 ■ ■ a pe a at an orifice 1 1 tn. in hi i^ni. by 1 I A with 
 
 880 x -5 
 
 • v partt. 
 
 ** If" ■' .'in-utii- 
 
 I 
 
 ■ 
 
 ild In- counterbalanced by the 
 ■ 
 
 1 of the 
 
 Don ii will be 
 
 ■ 
 
 ' ll fall. 
 
 • * ti.»t the depth of tl 
 •""T '" ' - much 
 
 ! I 
 
 mutt be add 
 ' the wale* in 1 1 ■.- dm t i- bh>d 
 
 ' 
 
 Ing all tli< x- quanti:. 
 
 ■• +- 03 + -01 + -01) = 4305 m. 
 
 IV ■ and lli.' 
 
 width ■ ' 
 
 • • with contraction from the tali 
 ■ again to bV 
 
 II I, tip 
 
 * 
 
 : 1 ISO I 
 
 l M in. for tin' width 
 what I. 
 Tba .1. ptfa of Um be lined thu» i — 
 
 8 x -I M in. 
 
 .f the 
 
 = Jl I in.; 
 
 1 
 
 lently, the internal diameter, il, of th< i..a— 
 
 d' :: m. 
 
 Py ii' depth ali. hi n fifth, which will maka it 
 
 to Ih- allowed berwi > n tin- 
 interna] i-i rx-«i 1 1 1 " J to — 
 
 19*174 nx, 
 (livi.li: 
 
 18-174 , , 
 
 rater-wheel, howovi ■ 
 
 and If ii i-« inU ndod to maka lha 
 ■hroudin thai lha 
 
 ihiiiiIk r "I buck) la bo divisible by S; it will, th< 
 
 to havi I 17. an. I in llii- 
 
 t«> . n each will Ih- reduced to — 
 
 l _: i . i in. 
 
 Ii iniw merely nana wheel; for tlii» porpi 
 
 thd lie. 
 
 il ii ill. n to Ih. divided into I 
 and ra.lii are drawn ii nl af diviaion, 
 
 \ \ \\ I . on ■ . outward from the 
 
 I equal l<. a lit 1 1 « - DOM llinn Imlf Ui<> 
 
 depth of the b to indicau the bottoma of il». 
 
 Tl aairuuta d in llii» iii.iiiiht, may give 
 
 ,,iV7'i ..r mi par .-''lit. ..i tl.. wain r. 
 
 N..w il. I.. — 
 
 v .il li..r». H-|H.wrr. 
 
 1 1 in of wafer. 
 
 wilh .•■•rtainly. 
 tl.ai the |h.». r inarntttad by tlii-. wheal wU I 
 
 tO ~ I ..r '. 
 
 ■ 
 wbiofa tliin « .nike per 
 
 niinuic ia — 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 129 
 
 GO -~ 4-305 x 314 = 4-44, 
 since its velocity, r, is 1 metre per seeond, or 60 metres per 
 minute. 
 
 In tracing out the preceding solution, it will have been seen that 
 the width to be given to the wheel is 1-76 m. ; a much less width 
 might have been obtained, by making the wheel revolve faster, and 
 by augmenting the velocity of the water also. Let us suppose, for 
 example, that the question has to be solved on the hypothesis, that 
 the velocity of the water-wheel is to be 1-5, instead of 1 metre, per 
 second; it will then be necessary, in order that the water may 
 escape from the orifice at double this velocity, that it be equal to 3 
 metres per second. 
 
 For this velocity, the height of the upper level, above the centre 
 of the orifice, should be -46 in. 
 
 Allowing -06 m. for the height of the open part of the sluice-gate, 
 
 the whole height above the wheel will be 
 
 •46 + -03 + -02 = -51 metres; 
 
 consequently, the outer diameter of the latter should bo 
 
 d = 4-56 — -51 = 4-05 metres, 
 
 the width of the sluice-gate, or 
 
 •140 
 
 w = -^ ^ = I'll metres, 
 
 ■06 x 3 x -7 
 
 and consequently the width of the wheel 
 
 = 1-11 + -10 = 1-21 metres. 
 
 This width, it will be seen, is considerably less than that first 
 calculated. This wheel, however, which is narrower, and revolves 
 at the rate of 1-5 metres per second, will not be capable of trans- 
 mitting so great a useful effect, by four or five per cent. Never- 
 theless, it may be preferable in many circumstances to adopt this 
 lesser width, either to render the wheel lighter and less costly in 
 construction, or to avoid the necessity of much intermediate gear 
 between the wheel and the machinery to be actuated. Thus, it is 
 evident that tins wheel should make 
 
 (60 x 1-5) -=- (4-305 x 314) = 666 revolutions per minute, 
 whilst the first wheel only made 4-44.., 
 
 The other parts of the wheel are proportioned according to the 
 above rules ; they will, however, differ but slightly from those of 
 the first wheel. 
 
 The proportions of the water-wheel might still be otherwise 
 modified; thus, the depth of water at the outlet might'be allowed 
 to be greater than that taken for a basis in the preceding cal- 
 culations. Thus, the outlet might be opened to the height of 
 •1 m. instead of only -06 m. : in this case, the width of the outlet 
 and of the wheel would be much less. But this arrangement 
 would have many disadvantages, for it would be necessary to make 
 the buckets more open ; that is to say, the angle made by the 
 outer portion of the bottom of the bucket with the tangent to the 
 circumference passing through its extremity, instead of being 15° 
 or 16°, as is usual, would have to be 30° or 32°; the buckets 
 would have to be deeper and more capacious ; they would empty 
 themselves sooner : from all which causes would follow a decrease 
 in the useful effect given out, which might reach even to 15 per 
 cent 
 
 It is true, on the other hand, that the width of the outlet would 
 be reduced to 1 metre, supposing the wheel to revolve at the | 
 
 rate of 1 metre per second, and that it would not he more than 
 ■67 m. when the wheel revolves at the rate of 1-5 m. per second ; 
 in which case, the depth of the buckets would be about -34, and 
 the spaces between them -4 m. each. 
 
 It will be easily conceived that such an arrangement cannot be 
 advantageously adopted, except where there is plenty of water to 
 spare, and when the constructor is limited as to the width of the 
 wheel. 
 
 WATER-WHEELS WITH RADIAL FLOATS. 
 
 388. In old mills we sometimes meet with water-wheels which 
 have plane floats placed radially, working in straight inclined chan- 
 nels, with a vertical outlet more or less distant from the centre of 
 the wheel. 
 
 These wheels generally give out 25 to 35 per cent, of useful 
 effect of the absolute force of the stream. In them the floats are 
 three or four centimetres clear of the sides of the channel ; when 
 a greater space than this is allowed, the useful effect is sensibly 
 diminished. Generally, the width of such wheels is equal to that 
 of the outlet. 
 
 At the present day, water-wheels are never constructed with 
 plane floats arranged in this way. When a wheel is required to 
 have a great velocity, it is preferable to construct it to work in an 
 enclosed circular channel, and to receive the water from above, or 
 from an orifice with a sufficient column above it, to give the propor- 
 tionate velocity to the water. 
 
 Such wheels are constructed in the same manner and with the 
 same care as undershot water-wheels ; in fact, they do not differ 
 from the latter, except in that these receive the water from an open- 
 topped or overshot duct. The useful effect given out by them 
 varies from 40 to 50 per cent., according as the sluice-sate is more 
 or less near to the upper level of the water. Thus, the nearer the 
 channel approaches to the upper level, the more Iiko the wncel 
 becomes to a commoi, undershot one, and, in consequence, the use- 
 ful effect is greater. 
 
 In the construction of a water-wheel of this kind, the same rules 
 are followed as are already laid down for common undershot wheels 
 with open outlets. 
 
 Thus, let it be proposed to construct a wheel for a fall of 1-75 
 metres, and with a discharge of 440 litres of water per second ; let 
 the centre of the outlet orifice be at -4 m. below the upper level, 
 and the height of the orifice itself, -15 m. 
 
 By referring to the table on page 111, it will be seen that the 
 discharge of water through an orifice, under these circumstances, is 
 255 litres per second for a width of one metre, and it will therefore 
 be evident that the wheel should have 
 
 440 
 
 ijgg = 1-72 metres in width. 
 
 The velocity of the water at the sluice-gate, corresponding t.. 
 the column of -4 m.. is 2 -81 12 per seeond ; consequently, if we make 
 the velocity of the wheel equal to -55 times that of the water, it 
 will be 
 
 2-802 x -55 = 1-54 metres per second. 
 
 The diameter of the wheel is of itself a matter of indifference ; 
 it should be reduced as much as possible, so as to lessen the cost 
 of construction; notwithstanding, it should never be less than twieo 
 
Ill 
 
 TI1K l'tt\< : 
 
 Um «*><•:. bright of the fit" ; tbua. in Uie prr- 
 
 •hoold Boll* Iras than 4 D 
 
 II ha. cftrn been asserted that the power b Increase 
 
 ; the rsamrlnr; it •.« iii» inr ' that the 
 
 ' trarsunitti*! mint be b lb) fall, 
 
 jl:.1 !•■ 8m ,aa •.:. ■ I ataa r .!.-. .'..-ir.-. •!. Il the diameter of the 
 m Wl k increased, the angular or I 
 
 sad, roasequeolly, the momentum and actual force communicated 
 nwh the same. 
 
 Taking the diameter at 4 m< 
 • 60 
 
 If a wheel uf this dinm. t. - 
 overshot duct, with a 
 
 - 
 1 would not be moro 
 than 
 
 1-981 x S5 = l-Ofl 
 and, consequently, the num'. r of bun 
 ' 60 
 
 par Bbnta. 
 
 But then, as the diach I ntlet of 
 
 -J m. in depth and 1 mi In- in width, 
 
 table, page 111 | .al to 
 
 = 2-7 i ■ 
 
 Thue, it will be seen that 11 M more 
 
 rapidly ia nan-, arga of wufc r 
 
 by an open outlet, and ntly, leal costly in n 
 
 t only gives out, at 
 
 • •ut by 
 may reach, a* ■ :ls much as 70 
 
 : the wheel, « 
 
 . ::li n: the common under- 
 
 WATtE-WIII.I.Ls »l: 
 
 389. Tbcac wheels are fated wttb 
 the inclination being equal to a bane of 1 Batn (or every 1 or 2 
 metre* b height — daw 
 fur a short distance in a circular channel, . 
 walla. 
 
 ! f..r low IUb of from -5 to 
 
 . . • 
 
 ppaaJbbi an^l tli.it, nt r 
 part, it should havo al or 15 centimi 
 
 fsrilitate the dbenga. action 
 
 is enlarge tn. ■-.,„, | n „ 
 
 line passing tl ■ ,; n { \„. 
 
 apace I- 
 
 • UM waler at 
 from tl • 
 
 Mo be calculated in the aarae manner 
 
 as that : ■ » ; as to the diameter, it ma 
 
 •In -. - 1 ■• r be leas than 
 
 : ptli of lb) il -.Hiding 
 
 - oald be i.jnal to one- 
 fourth •rnled by the fa 
 
 i.l be fr..m -2 to -J2 m. : it may bo 
 or ■!'. in. for bib of from 1-- to 1-5 m. 
 
 or float! are in the f..rm of n cylindrical curve, 
 ■ ircular arr, tai . !iu» al the it, 
 
 and making an angb ofabool h the stream ■ 
 
 wn of the wb 
 
 - i-ireum- 
 by an angle of 25", and their thl 
 
 vhen made of WTOUght-irOn plates, and 32 to 35 when of 
 
 wood The bottom of Ibl channel ihoald have a fall or in.-liua- 
 
 abont /.th ..r , * - 111 — thai i- I to that of the 
 
 f a triangle, the base of which il 12 or l.'i. and tlio 
 
 height 1 mcire. 
 
 RW 
 
 390. Among the varieties' of turbines widen receive the action 
 
 of the water throughout their whole circmiitcr. DBS, may be distin- 
 guished those which discharge the water al their outer cii 
 
 .1 those which allow il to escape behind. The nsefnleflbet 
 given out by these wh pot cent, of tlie 
 
 •• am of water. 
 i'..r these riont liptionn ..t' wheel, I 
 eniated in accordance with tin 
 the tir^t kind, termed centrifugal t ur i ma] dbmetet i» 
 
 ...1 by multiplying the fourth or fifth of the velocity doe to 
 the t..t:il fall by 7 s ji ; then dividing the quantity of water t.. bt 
 
 discharged by Ihe reenlt obtained, and finally extracting the square 
 rool Of the quotient. 
 
 / nppoas that the mil b 8*8 m.. and the db- 
 
 id. It will l>e gathered From 
 the table on page 1 11, that the velocity due to the height, 
 
 , as o 57 ill. 
 then, 
 
 ■ n 
 
 =1642, and-. =1314; 
 
 and further, 
 
 / 80t > 
 
 D ^V 7854X1G42 = - 787 ' 
 
 / 800 
 D =V785Tx-i 
 
 
 = -874 . 
 
 t".r the internal diameter of (he cylindrical tank above the turbine. 
 
 A.l.l I or So Ihe internal dbmetet >•( t! 
 
 which _■ 
 
 •83 to !'l m. 
 
 I be equal to the internal ■ ; 
 multiplied b] f*S8 "r I l.'i. and is. tie • 
 
 to 1189 m.; 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 1-137 to 1-319 m. 
 
 When the height of the fall and the discharge of water are 
 variable, the diameters should be calculated for the extreme cases, 
 so that the most advantageous proportion may be adopted — that is, 
 the one which will give the best result throughout the greater part 
 of the year. 
 
 If the variation is very considerable, there should be two or more 
 turbines employed, some calculated for the lowest discharges, others 
 for the mean, and others again for the maximum discharges. 
 
 The height of the buckets — that is to say, the vertical distance 
 between the two discs which form their top and bottom — is gene- 
 rally about a fifth, or a fourth at most, of the radius of the interior 
 of the wheel. 
 
 Tims, in the case before us, the diameter being -787 or -874, the 
 radius is -3985 or -437, and, consequently, the height of the buckets 
 should be -1 to - 11 m. 
 
 The buckets being cylindrical in form, their entrance is normal 
 to the conducting channels which direct the water against tliem, 
 and for these low discharges of water should make angles of 68° to 
 70° with the internal circumference of the wheel — that is to say, 
 the conducting channels should make angles of 20° to 22" with the 
 circumference. When the discharges are large, this angle may bo 
 increased to 30° or 45° ; thus, for a discharge of 600 to 700 litres 
 per second, it is considered that the angle should be about 30°. 
 
 In order to obtain the maximum useful effect, the velocity of the 
 wheel should be equal to about -7 times that of the water; in prac- 
 tice, one-tenth may be added to this ratio, or one-fifth to one-sixth, 
 without materially diminishing the useful effect. 
 
 The space between each bucket, taken at the internal circum- 
 ference, should be nearly equal to the distance between the top and 
 bottom discs of the turbine; it should, however, never exceed 18 
 to 20 centimetres. The internal and external distances between 
 the buckets are necessarily in the ratio of the internal and external 
 diameters of the wheel. 
 
 In the following table we give the principal dimensions, data, and 
 results of several descriptions of turbines, constructed, within the 
 last few years, by MM. Fourneyron, Fontaine, and Andre Koechlin. 
 
 These results have been selected under circumstances where the 
 best useful effects were given out : — 
 
 FABLE OF DIMENSIONS AND PRACTICAL RESULTS OF VARIOUS 
 KINDS OF TURBINES. 
 
 Total fall, 
 
 Discharge per second, 
 
 External diameter, 
 
 Depth of shrouding, 
 
 Height of outlet. 
 
 Number of liuckets, 
 
 Numher of director curves 
 
 Number of revolutions per minute, 
 
 Useful effect 
 
 Ratio of useful effect to absolute 
 
 35 H. P. 
 70°f„ 
 
 100 m 
 218 111 
 133 m 
 
 2h. P. 
 
 71°/ 
 
 1-40 
 
 111 10 1 
 
 I 'l in , 
 
 Data and Results. 
 
 Jonval Turbines, constructed by M 
 Andre KoBChlin, Mulhouse 
 
 
 2-720 m. 
 684 lit. 
 ■800 ra. 
 •410 m. 
 
 16 
 •290 sq. m. 
 •450 sq. m. 
 90 to 158 
 
 13 H. P. 
 
 2-77 m. 
 470 lit. 
 ■800 m. 
 .100 m. 
 
 18 
 •220 sq. III. 
 
 90 to 108 
 15 H. p. 
 72°/ 
 
 1-70 m 
 
 
 
 
 
 
 •120 m. 
 
 
 
 
 ■0706 sq. in 
 2977 sq. in 
 90 
 6 H. p. 
 
 Area of escape outlet helow the wheel, . . . 
 
 Ratio of useful effect to absolute force, . . . 
 
 72°/„ 
 
 REMARKS ON MACHINE TOOLS. 
 
 VELOCITY OF THE TOOL, OR OPERATING PIECE, IN MACHINES 
 INTENDED TO WORK IN WOOD AND METAL. 
 
 391. The principal machine tools, employed in machine shops, 
 are — 
 
 1. The simple lathe, the self-acting lathe, and the wheel-cutting 
 lathe, with adjustable table. 
 
 2. Boring machines of various dimensions, and radial drilling 
 machines. 
 
 3. Horizontal and vertical shaping machines. 
 
 4. Planing machines with a fixed tool, or with a moveable one, 
 so as to work both ways. 
 
 5. Mortising or slotting machines, having a vertical tool with a 
 revolving table below. 
 
 6. Machines for finishing nuts and screws. 
 
 7. Machines for cutting screws and bolts. 
 
 8. Dividing engines, for dividing and cutting toothed-wheels 
 of all dimensions. 
 
 9. Straight and curved shears, for shearing plates. 
 
 10. Punching and riveting machines. 
 
 11. Steam and other hammers. 
 
 12. Straight and circular saws.* 
 
 The velocity of the cutting tools, in -these machines, varies 
 according to the nature of the material, arid the quality of work 
 desired. 
 
 In general, for soft cast-iron, it is convenient to give a velocity 
 of seven to eight centimetres per second to the tool, in sucli ma- 
 chines as lathes, and planing and slotting machines. This velocity 
 should be reduced, at least, to four or five centimetres in shaping, 
 drilling, and screwing machines. When the cast-iron is hard, the 
 velocity is considerably diminished. 
 
 For wrought-iron, the velocity may be advantageously increased 
 one half, because the tool is kept well lubricated with oil, or with 
 soap and water ; thus, in turning or planing, the velocity may be 
 raised to eleven or twelve centimetres ; and in shaping and screw- 
 ing, to about six centimetres per second. 
 
 For copper, brass, and other analogous metals, with which the 
 tool does not become heated whilst working, the velocity may be 
 very much greater ; and for wood, its only limits are those deter- 
 mined by the size of the tool, and by the powers of the machine. 
 
 With regard to the pressure and rate of advance of the tool per 
 revolution, or per stroke, it necessarily varies according to the 
 dimensions of the machine itself, and also according to the degree 
 
nj 
 
 THE l DRAUGin 
 
 of tauh »*•* U to be gtreo to the mirfsr. 
 
 &\r u murh nrt»»*o,r> -snail lalhr an to that 
 
 apoa a krf» one — to a amatl drill, aa t 
 
 marhioe. Tbi» tariai. fmm a 
 
 iMth o/a BkQlinieUv, in aorne caam, to aa much aa i 
 
 \ 
 
 ■! — wl» ii ii nvohi-s and the 
 ttar wlitn it rtv..|\ts. an J thr cutting 
 1 shaping and drilling machines. 
 
 TAR! TV AND PR M MTllM) TOOLS OR CI i 
 
 
 Tarmibf. 
 
 Drilling ud Shapiiuj. 
 
 D «rr.-,t 
 
 ... 
 
 •'■■mied per hour 
 
 Numlter 
 
 Wurl performed per hoar 
 
 
 of re» 
 
 
 
 luii'ini 
 
 wilh 
 
 111111 " ' 
 
 per BJlOtll*. 
 
 } m lmo{ prcMara. 
 
 per Ullnillr. 
 
 f */■ of pretsura. 
 
 
 CM 
 
 
 
 
 
 Wrought 
 
 Cut 
 
 Wrought 
 
 
 
 
 
 
 Iron. 
 
 
 
 Iron. 
 
 
 
 
 
 rent. 
 
 
 
 cent. 
 
 
 1 
 
 
 
 
 
 71 i 
 
 ii i ■<; 
 
 
 
 
 
 ii i •; 
 
 
 
 
 573 
 
 ii P6 
 
 171 ■;• 
 
 3 
 
 
 78 i 
 
 
 
 
 
 7i. 1 
 
 li 1-6 
 
 
 
 
 ii i ■■; 
 
 171 B 
 
 19-1 
 
 98 7 
 
 
 
 .'. 
 
 
 45-8 
 
 !U-7 
 
 i .■-:, 
 
 15-3 
 
 99-9 
 
 
 
 6 
 
 
 
 78 i 
 
 ii i ■•; 
 
 19-7 
 
 19-1 
 
 
 673 
 
 8 
 
 1 • 1 
 
 
 673 
 
 
 9-S 
 
 113 
 
 
 49-9 
 
 10 
 
 15-3 
 
 
 45 8 
 
 
 7-8 
 
 ii :. 
 
 99-9 
 
 B4-8 
 
 11 
 
 IS 7 
 
 IS 1 
 
 
 
 6-4 
 
 
 I'M 
 
 38-6 
 
 10 
 
 
 15 3 
 
 
 
 51 
 
 7 
 
 lfr9 
 
 39 B 
 
 
 
 
 Willi 1 »;„ „f pmuura. 
 
 
 
 With 1 "i* '■( i -■ 
 
 
 " 
 
 1 1 r, 
 
 - 
 
 
 8-8 
 
 B 7 
 
 33-9 
 
 
 
 6 1 
 
 
 
 
 
 46 
 
 
 97-4 
 
 
 .VI 
 
 
 
 
 2-fl 
 
 38 
 
 I.VJ 
 
 
 
 i l 
 
 
 Sfl 1 
 
 
 9-9 
 
 33 • 
 
 
 19 8 
 
 
 
 
 
 313 
 
 1-9 
 
 
 iiv 
 
 17 1 
 
 
 
 :, i 
 
 
 
 ] 7 
 
 .'.'. 
 
 10-1 
 
 15-9 
 
 
 31 
 
 
 183 
 
 •J7 1 
 
 1-5 
 
 
 9-1 
 
 
 
 
 i B 
 
 
 .94 9 
 
 II 
 
 21 
 
 B B 
 
 [9-8 
 
 
 
 
 16-9 
 
 
 13 
 
 i B 
 
 7-6 
 
 Hi 
 
 
 
 
 1 IT 
 
 -J 11 
 
 11 
 
 l - 
 
 7-0 
 
 
 
 
 
 
 19-6 
 
 11 
 
 n; 
 
 
 
 
 
 
 1J1 
 
 18 -3 
 
 I'O 
 
 i .. 
 
 
 90 
 
 
 1 1 
 
 
 hi 
 
 17 1 
 
 B 
 
 ii 
 
 
 8-5 
 
 90 
 
 1-7 
 
 
 I- i 
 
 lfi-9 
 
 •8 
 
 1 8 
 
 50 
 
 7-6 
 
 
 Ifi 
 
 
 9 i 
 
 
 •8 
 
 11 
 
 
 
 
 1 1 
 
 •j l 
 
 
 13-6 
 
 ■7 
 
 1-0 
 
 11 
 
 8-9 
 
 
 
 i I 
 
 
 111 
 
 'ii 
 
 
 37 
 
 7 
 
 
 1 1 
 
 1 B 
 
 
 
 ■8 
 
 >9 
 
 
 
 i i 1 
 
 II 
 
 1 8 
 
 ■ ■ 
 
 
 
 •8 
 
 B-9 
 
 i 9 
 
 
 l-,i 
 
 i :, 
 
 
 90 
 
 '8 
 
 •8 
 
 
 
 
 
 i i 
 
 B i 
 
 ;> 
 
 i 
 
 
 
 
 
 
 i l 
 
 
 
 •i 
 
 
 
 
 
 •7 
 
 I <> 
 
 
 
 •3 
 
 B 
 
 i B 
 
 
 
 
 ■ 
 
 
 6-4 
 
 •8 
 
 v 1 
 
 
 
 
 
 •8 
 
 8 .t 
 
 i B 
 
 •8 
 
 •1 
 
 1 ii 
 
 9-4 
 
 
 
 ■7 
 
 
 
 -1 
 
 •1 
 
 i • 
 
 
 
 1 
 
 
 
 
 ■1 
 
 ■:i 
 
 I 8 
 
 i B 
 
 400 
 
 •3 
 
 •5 
 
 
 
 -2 
 
 •3 
 
 11 
 
 in 
 
 • 
 
 ■ ing machine tools for 
 w» tar. i which 
 
 may be railed fur according I ..f the 
 
 - .-uti..n. Thuit, a latin- v/hl h 
 ! 10 turn ar' 
 
 a diameter, should have a considerable rol 
 ana thai it t^ ba chiefly applied to turning and 
 bulky pieces, or snch as neasnra from ono to two matron In dia- 
 meter, ahould, on ma contrary, be aotnated by n combii 
 low, bat, at ii,. 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 CHAPTER X. 
 THE STUDY OF MACHINERY AND SKETCHING. 
 
 VARIOUS APPLICATIONS AND COMBINATIONS. 
 
 392. Hitherto we have had to occupy ourselves with industrial 
 drawing, as regards only the geometrical delineation of the princi- 
 pal elements of machinery and architecture. This preliminary study 
 being of great importance, we have thought it well to dwell more 
 particularly upon it, since also it is the very basis of all designing, 
 with a view to actual construction, comprehending not only the 
 mere outline of objects, but also the proportions between the vari- 
 ous parts, as dependent upon the functions which each is required 
 to perform. 
 
 Machines are, indeed, but well calculated and thoughtfully ar- 
 ranged combinations of these elements, and afford innumerable 
 applications of the rules and instructions laid down in reference to 
 them. The study, therefore, of machines in their complete state, 
 naturally suggests itself as the next step to be taken. 
 
 393. Machines may, in general, be classified under three catego- 
 ries — machine tools, productive or manufacturing machinery, and 
 prime movers. 
 
 By machine tools are meant those by the instrumentality of 
 which we work upon raw materials, as wood, metal, stone ; lathes, 
 wheel-cutting machines ; drilling, boring, and shaping machines ; 
 mortising, slotting, planing, and grooving machines ; riveting ma- 
 chines ; shears, saws, hammers — are of this class. The movements 
 jf these machines should be so combined, that the tool or cutting 
 instrument — that is, that part which attacks the material — should 
 move with a velocity properly proportioned to the nature of the 
 work. 
 
 In the few notes accompanying our text will be found some 
 experimental deductions, which may serve as guides for adjusting 
 the movements in designing and constructing machinery of this 
 description. 
 
 Amongst productive or manufacturing machinery, are comprised 
 spinning, weaving, and printing machines; pumps, presses, com, 
 and oil mills ; and, finally, prime movers consist of those worked by 
 animals ; windmills, water-wheels, turbines, and steam-engines. 
 * For the study of complete machines, we have selected from each 
 of these categories those possessing most interest and generality — 
 as a drilling machine, an instrument so very useful and so much 
 employed in machine-shops and railway works; a pump for raisino- 
 water, serving for domestic purposes as well as for important manu- 
 facturing establishments; two examples of water-wheels, showing 
 various arrangements and forms of floats or buckets ; a high pres- 
 sure expansive steajn-engine, with geometrical diagrams, determin- 
 ing the relative positions of the principal pieces in various circum- 
 stances ; and, finally, a set of belt-driven flour mills, constructed on 
 a system recently adopted. 
 
 Before proceeding to the description of these machines, it will 
 be necessary to habituate the student to draw from the reality, 
 for up to the present time he will have done nothing but copy 
 the various graphic examples to this or that scale. The operation 
 iu question consists .in drawing with the hand, the elevation, plan, 
 
 sections, and details of a machine, preserving, as much as possible, 
 the forms and proportions of each part ; and then taking the actual 
 measurement of each part, and laying it down in figures in its par- 
 ticular position upon the drawing : this duplex operation of sketch- 
 ing and measuring constitutes the study of the rough draughting 
 of machinery. 
 
 THE SKETCHING OF MACHINERY. 
 
 PLATES XXXV. AND XXXVI. 
 
 394. Before commencing the sketch or rough draught of a 
 machine, it is absolutely necessary to look carefully into its organi- 
 zation, the action of the various working parts, the motion of the 
 intermediate mechanical connections, and finally, its object and 
 results. The object of this preliminary examination is to give the 
 draughtsman a good general idea of the more important parts — 
 those which he will have to render most prominent and detailed 
 when he comes to make a complete. drawing of the whole; such 
 drawing comprising a series of combined views, together with sepa- 
 rate diagrams of such details as may not be apparent in the former, 
 or require to be drawn to a different scale to render them intelligi- 
 ble. In fact, this must be done in such a manner, that, with tho 
 aid of the sketch, a perfect representation of the machine may be 
 got up, which, if necessary, may serve in the construction of other 
 similar machines. 
 
 DRILLING MACHINE. 
 PLATE XXXV. 
 
 395. In order to give an exact idea of tho manner of sketching 
 machinery, we take a simple machine as an example ; this we sup- 
 pose to be represented in perspective* in fig. ^\, this view being 
 instead of the machine itself. 
 
 This machine is for chilling metals : it consists of a vertical cast- 
 iron column, A, which forms part of the building or workshop. 
 This column is hollow, and rests by an enlarged base upon a stono 
 plinth, e, imbedded in the ground, and at its upper end it supports 
 the beam, c. 
 
 Upon one side of this column is cast the vertical face, D, which 
 is planed to receive three cast-iron brackets, e, f, g, attached to 
 it by bolt9. To the opposite side, d', of the same column, is in 
 like manner attached the bracket, H, which, witli the middle one, 
 F, on the other side, serves to carry the horizontal spindle, r. 
 This spindle carries on one side the cone-pulley, J, over which 
 passes the driving-belt, K, and on the other extremity it has 
 keyed upon it the bevil-pinion, l, which gears with a larger 
 bevil-wheel, M. This last is attached to the vertical shaft, N, 
 
 * In a subsequent chapter, we shall explain the general principles of par&lleJ %al 
 exact perspective. 
 
I.lt\l ..III 
 
 '•JU,.4.i.f. and i. BMrreahle in the brark-l- 
 keaifcyi r aad o. TV. •haft rmimi duple* moirrrwii' 
 <• -.:.:. u ... r •_ . ■> ■ • i . -re ..r !.■« rapid, »••■■ ■r.l.r,.- ». if- 
 Wl, K, i. .* IS* U-a» or greater dkueotor of lb* cone-pulley ; and 
 Um other mtirai and rectilinear, due to lh« acUon pi 
 whira Work* la aa interna] arrew In the cod of the In 
 That arrrw earrie* at iu upper rod a 
 
 ■mail pWoa, o> the abaft, «, of »h.h i. prolonged downwarda, and 
 terminate* in a amall hand-wheel, a. 
 
 To* object to be drill. ,1 U I pair of jaWB, 
 
 '•a groove* upon the table, T, and capable of adjustment bock and 
 !bnrard by meana of the arrew, A, t 
 
 aaodJ*. The table, T, i« made in two piece*, »o aa to f-nii a collar 
 a>- ut the rolumn, A, and il ia bad at any I hi upon 
 
 thk colanin by aeana of the praaauro nh \\, r, i i ■■ i 
 of the table from the drill, J. ■ 
 
 pinioo on the abaft, a, ■ 
 
 •station of thia handle and Um pinion neceiwarily et 
 
 or drarenl of ibe tafah. 
 
 TV drilling machine, then, fulfil- the folk na : on 
 
 ibe one hand, the drill, J, ia worked at a gn 
 ■ 
 
 with tin 1 nature of tho maleri 
 upon; .i • r luuul, the lalile Which BUTi 
 
 I ia .a|al.!e oi 
 nwlpg to the foraw and din - whilst it may 
 
 alao be net eccentrically, when ncccaaary, by turning it lo the le- 
 imn. 
 
 anatraction and action 
 dI tin- machine, tho .1; 
 man rur. H 
 
 ■ 
 I'ifoaa. 
 
 Irical elevation 
 
 iimn, a, with ■ and the lablo, 
 
 I 
 
 iiraii_-ht.au well aa in I with it without the 
 
 aaaiatatx a of a rata, I . thus, 
 
 • Um ooJnmn, a, draw 
 nr ; then draw 
 parallel I ..f lha drill-etock, > ; than the hori- 
 
 zontal, '. -I tin' bartt-wbeel, i.. 
 
 and tb< 
 • p, o » 
 
 o; Anally, dr.. i I / nu<l I i, 
 
 of Uw bracket, it ; an 
 
 the bnttum am) top of tin- BohUDB. At thin atagt 
 aary ktl lay down tlie meaeuretnent* opon the 
 column principal |«rt» of thi 
 
 .ml upon it for the 
 
 height to be meaaur. 
 
 ' 
 
 :• nt at the baaa 
 and aui 
 
 • it tliat they • 
 
 . the aini.uiit ..f i'|« ning U in;; t!.. 
 rule, and w ritti n down upon I 
 ra may l«- oh 
 rule, to the eb - alwaya 
 
 ter, when it ii 
 obtain thi r baaa. In thk 
 
 ii nccesaary, aa haa I- 
 i. bj I [416. 
 To obtain Ua utra lluo 
 
 ■iliimn, place toe extremity of Um rule at ?, agalnat tlio 
 oolnmn, and lit it Bi i, of 1 1 1«* 
 
 «|nir.«' '1 tin riilr will 
 
 b« that nf t' i, tn which moat lie addi-d Uu' radium i i" 1 , uf the 
 column. 
 If the centre, i, wara not approachabla with Um i 
 
 Um Interna] dietanea between. Hw nrfiei 
 column nnd that of tin- acrow, and (hen add the 
 of tin' BCrOW and column. Whan tin H 
 
 than the length of the meaarxring-nile, a rod or tape moat I«j 
 I. When, Indeed, the ■: 
 
 • iint of skill, h" may take t ant, i i*, 
 
 directly, by applying the rule opon lha - column 
 
 Um avis of Uu 
 in aneh I manner that the rule ihall to the column, 
 
 «li. ii tl. en Um two pointa wU bo Um meaanroment 
 
 ■ 
 ■ m horizontal linea, at n, o ;■. o f, » L 
 The moaaaramenti indlcatod opon I •• bow all thaai 
 
 are obtained. 
 'I'll. |.i. ■ • ding operationj will allow 
 
 laying off the relaUn Um main |«rt« 
 
 which go t tnpoat Um machine to be akotrhed. We have nest 
 
 • ll! the iniii'.r 
 
 of the machine. To t li i~, effect, and t.i avoid eonfoston, it >- 
 
 diffbront 
 f ili. in, opon «liiili Um dim. n 
 properly bjdk 
 
 I • nt, in eleradon and plan, the detail of tlia 
 
 1'i.uki i, i, which npporta Um >liati-. i and >, with Um 
 
 beril-wbi > Umm rlowi are not lurBcienl t" 
 
 ..I the dlmenaloni of tlii- braefcel ; thm it 
 
 * 
 
 I — \i, nnd projl ' l.'nn ..I the 
 
 • r . ii !■• Ilka* 
 
 I Um t r**fng 1 '-', which Inil'l- up the abaft, ••, t" Um 
 
 Il at the line, 
 
 ■how the braaas* which ■ >amal of tho 
 
 ■ 
 a larger ecolc. ao aa to indk and to 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 give room for the measurements ; and it may be observed, that, for 
 a draughtsman who has not much practical knowledge of machine- 
 ry details, it will be necessary to take down or separate various 
 parts, such as the cap and the upper brass. With regard to wheel- 
 work, it will be sufficient to give the section of the web and boss, 
 as indicated in figs. 2 and 7, and a section, as tig. S, of one of the 
 arms when the wheel has any, and then the numbers of teeth and 
 arms must be counted and set down. 
 
 When all the parts of any detail are thus sketched out in 
 elevation, plan, or section, the draughtsman must take the 
 measurements of each, and set them down in their appropriate 
 positions upon the sketches, as indicated in the figures ; being 
 mindful to see that the principal measurements coincide with those 
 laid oft' in the complete general view already commenced. The 
 measurements of the diameter of the pitch-circle, and of the width 
 of the teeth, will be sufficient, in addition to what has already 
 been directed to be done in reference to wheel-work, the proper 
 ratios being maintained between those in gear with each other. 
 As many parts of machinery require to be in proportion to 
 each other, a knowledge of such relations will enable the 
 draughtsman to dispense with a great deal of tedious measuring 
 and sketching, as in the case just alluded to, of wheels working 
 together. 
 
 The remaining parts of the machine are to be detailed in the 
 same manner. Thus, figs. 9, 10, and 11, represent a vertical sec- 
 tion, a plan, and a side view of a portion of the table, T, with its 
 holding-jaws, and its elevating pinion and shaft. Fig. 1:2 is a ver- 
 tical section of the lower extremity of the drill-stock, or spindle, n, 
 with the drill, d, in elevation. Fig. 13 is *a section of the cone- 
 pulley, J. Figs. 14 and 15 show, in vertical and horizontal section, 
 the mauner of jointing the screw, o, into the upper end of the 
 spindle, n. Finally, figs. 16 and 17 give* complete detail of the 
 mechanism for elevating the table, T, as well as that for fixing or 
 adjusting it at any required height. 
 
 397. On all the preceding details, we have quoted the measure- 
 ments of the different parts exactly as they should be upon an 
 actual machine. These measurements are expressed in millimetres, 
 as in former examples, this measuring unit being adopted because 
 its minute scale renders fractions unnecessary. We have also 
 slightly shaded various parts, as is generally done where the com- 
 plication and variety of forms would otherwise lead to confusion 
 and error. Besides, in this manner, a few touches of the pencil 
 show at once whether this or that portion is round or square, and, 
 in many instances, the labour of drawing additional views will 
 thereby be dispensed with. 
 
 In order to facilitate the proceedings of beginners in sketching, 
 we would recommend them to delineate the main centre lines with 
 the aid of a rule, and the circles with compasses, though the dimen- 
 sions of the latter need not be exact. This will give the sketch a 
 much neater appearance, and render the various objects or details 
 more regular. It is with this view that sketchers frequently employ 
 cross-ruled paper, with horizontal and vertical lines equally spaced. 
 That portion of Plate XXXV., upon which are sketched figs. 9, 10, 
 and 11, is of this description. 
 
 It will be understood, that, if the lines ruled upon the paper are 
 at equal distances apart, corresponding to one or more units of the 
 
 scale to which the sketches are being nride, these may be drawn in 
 correct proportions at once, in which case it will be unnecessary to 
 write on the various measurements. 
 
 The example which we have given as an introduction to the 
 study of sketching machines, will have somewhat familiarized the 
 stu lent with his operations even now. The applications contained 
 in the subsequent examples will suffice to complete this study, 
 which is one of great importance to the draughtsman and construct- 
 ive engineer. 
 
 MOTIVE MACHINES. 
 
 WATER-WHEELS. 
 
 PLATE XXXVI. 
 
 398. The water-wheel, represented in fig. 1, has plane floats, and 
 works, through a portion of its circumference, in a concentric cir- 
 cular channel. It receives the water from over a sluice-gate, a 
 little below its centre, and is of the undershot description. 
 
 The wheel is composed of several parallel shroudings, A, in 
 which are fitted the radial wooden bearers, B, carrying the floats, c. 
 When the shroudings are of east-iron, as is supposed in the present 
 example, they are cast in one piece with the arms, D, and central 
 boss, E, and are firmly secured by keys, a, upon the shaft, F, also 
 of cast-iron. 
 
 The head of the channel, G, which embraces the lower part of 
 the wheel, is constructed with a piece, h, in cast-iron, called tin? 
 neck-piece, which is fitted upon the cross timber, i, and let into the 
 two lateral walls. Against this neck-piece works the wooden 
 sluice, J, above which overflows a certain depth of water, falling, 
 in succession, upon each float of the wheel as it comes round, 
 causing it to turn in the direction of the arrow. The rotatory 
 movement of this water-wheel is taken off by the cast-iron spur- 
 wheel, K, mounted upon the end of the shaft, F, and gearing with 
 the east-iron pinion, L, the shaft of which communicates with the 
 machinery to be set in motion. 
 
 In giving this example, our object has been to examine this motor, 
 not only with reference to its accurate delineation, but also with a 
 view to sketching similar wheels, as well as to constructing and 
 setting them up, with their channel and sluice gear. 
 
 THE CONSTRUCTION AND SETTING UP* OF THE WATER-WHEEL. 
 
 399. The channel, G,is built up of hewn stones, the lateral joints 
 of which converge towards the centre, o, of the wheel, and they are 
 imbedded upon a foundation of ordinary stone-work. All thu 
 masonry is put together with mortar, made with hydraulic lime, 
 the joints being finished with Roman cement. In some localities 
 the channel is of bricks or freestone, and sometimes even of 'wood. 
 The apparent concave surface of the channel should be perfectly 
 cylindrical, and concentric with the external circumference of the 
 wheel. Also, before placing the latter in its proper position, this 
 surface should be finished, and rendered quite smooth and true, 
 which may be done with the assistance of a temporary shaft, o. 
 with the actual shaft of the wheel, in the following manner: — 
 
 The shaft, F (146), is adjusted to the exaet height at which it is 
 to be afterwards, and it is made capable of rotation in appro 
 

 Till: 1 
 
 .■ ■ : ■ .. 
 
 ::... shaft are fitted tbe sh rn M in gi, A. each connected to 
 i . tbe outside of Um anna are then 
 tsaapsraray attached two ladaal pieces of wood, baring a cross piece 
 : to Ihs^ the c*ler edge rfw1sk*Ue*ade true aiid parallel 
 ,'jft. sad rotarsirot with tbe external edges of the c 
 at that, if the abaft i» now made to I 
 v 1 describe a cylindrical surface, ■ 
 precisely that which the ehaaoel should posse*. 
 theref o re, as so accurate guide in giving the channel its appropriate 
 . • h .r 
 
 Tbe lower part of the channel U continued on in a straight line, 
 i waliiaii ilSJ at the vertical, o 4, and in a din%-li<>n. b r. - 
 iodiaed to a short distance away from the ■ tato the 
 
 escape of the water. 
 
 The cross timber, t, which surmounts tbe masonry of the ch.in- 
 d< I. and which recedes the ae 
 
 he channel, so as to allow the sluice-gate to be 
 broaght closer up to tbe wheel. The neck-piece, a, which forma 
 the crest of the channeljis more frequently constru.: 
 than of either wood or atone, as that material does not require to 
 be so thick, for resisting the pitas un of tbe - 
 neck-piece is at a distance below the Bpp 
 • 
 
 I 
 i imsiifa rilily. according to the quantity 
 and the width I 
 
 neck-piece, a ea Bed in the ma- 
 
 ■ 
 
 IS . ... so that it may n.-l ':- 
 ii.i- smalt raw . 
 this, again, ser- iting bodies, as tree*. •'■ 
 
 ently of a grating placed further behind, and prat 
 1 injuring the wheel. 
 Tbe sluice eonsista of two strong oaken planks, haring 
 and toagaed jointa, and being made thicker at the middle than at 
 tbe extremities, where the wheel is of a greater width than 1 , 
 metre. The amount of inclt: 
 by drawing a perpendicular to tlw- • 
 
 drawn near the middle, or, perhaps, I i of the 
 
 'Hie sluice i« I 
 
 rml wall*. 
 At the upper parta of these an 
 
 • cast-iron re- 
 attached to tbe two side-posta, a. These racks r> - 
 
 . which also guide them, and, on the 
 - 
 tal axi- 
 
 wheel, q, actuated b] a, which ma;, 
 
 p lan—re from ah, it e— a winrh-handle, or hand-mi 
 uf»-n aba appar • rtmnity of its wrlir.il spindle f^r thin purpose. 
 
 •luire, and. eonaeqoi I 
 
 with the greatest nicety, as well aa of the total shutting ofT of the 
 
 »»•• r (r m th<- wheel. 
 
 The shroudi: j 
 
 panes! in it, as at s, i. shown in the 
 
 r ends, of the 
 ... to which the tl at* are boll 
 
 ' • - ■ 
 
 « only the case when the di s c har ge, and 
 rj small, 
 the can 
 
 - 
 C and i.'. 
 
 in the U| 1 In both 
 
 thecarri- - 
 
 rder to facilitate the adjust- 
 
 them in: 
 
 retains: N 
 
 . 
 
 .-•> are of wo.- necessarily be 
 
 -. as shown in figs. 5 and ti ; 
 
 . 
 
 - can at all timi - 
 should they begin I 
 
 are adjust 
 
 I 
 shroudi: . iron straps, as 
 
 - and are 
 ■ nans of last b 
 1 fn>m the h 
 
 I are nailed down upon : 
 bastsgal 
 
 n of the 
 rataav II 
 
 ■ ' 
 
 h ■ .- 
 arfgh „ and channel 
 
 • - - ' - ' : ' *■*■ Tbe 
 
 I 
 
 •pace in 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 lines passing through the centre, and representing the sides of the 
 carrier-pieces upon which each float is placed. Two circles must 
 next be described, expressing the depth of the shrouding. Then 
 the complete outline of one of tho carrier-pieces must be drawn, 
 with the dimensions quoted on the figure ; and the key and bolts 
 may also be indicated upon it. Afterwards, to complete the 
 drawing, it will be sufficient to describe a series of circles, passing 
 through the bolts, the ends of the floats and carrier-pieces of the 
 key. and of the counter-float. With regard to the floats, and to 
 the arms of the shrouding, as well as to the spur-gear for trans- 
 mitting the motion, the student may refer back to the diagrams 
 and explanations already given concerning similar objects. The 
 same remark applies to the lifting apparatus of the sluice-gate, 
 which is also composed of gearing already treated of in the course 
 of the studies. 
 
 DESIGN FOR A WATER-WHEEL. 
 
 401. If it is in contemplation to make a design for the con- 
 struction of a water-wheel, analogous, we shall suppose, to the one 
 above described, it is simply necessary to ascertain the height of 
 fall, and the amount of discharge per second, of the water at our 
 disposal, and to refer to the calculations and practical rules which 
 accompany our text, to be able to determine, on the one hand, the 
 diameter and width of the wheel, and, on the other, the depth and 
 interstices of the floats, and their number. By referring back, also, 
 to the tables and notes relating to the resistance of materials 
 (Chapter III.), we shall be able to complete the remaining dimen- 
 sions for the shaft and its journals, the shrouding and its arms. 
 
 The study of water-wheels of this description will be much sim- 
 plified, if we consider that certain dimensions, such as the thickness 
 of the floats, the section of the carrier-pieces and shrouding, and 
 the diameter of the bolts, as well as the details of the sluice appa- 
 ratus, do not sensibly vary; and for them the draughtsman may 
 refer entirely to those indicated upon the drawing, which are 
 themselves examples of actual construction. 
 
 SKETCH OF A WATER-WHEEL. 
 
 402. The sketch of a water-wheel, already constructed and set 
 up, is a very simple matter; for the apparatus consists of a repeti- 
 tion of various pieces, and it is sufficient to obtain the measure- 
 ments of one only of each kind. Thus, after having measured the 
 diameter and extreme width of the wheel wilh the aid of a long 
 rule or tape, and counted the number of buckets or floats, of the 
 shroudings, and of the arms, we have merely to take the sketch of 
 a single float, with its carrier-piece and accompaniments, then to 
 make a section of one of the shroudings, another of one of the 
 arms, and, finally, a third of the boss and shaft. 
 
 The details given in figs. 2 to 10 show the various parts of 
 which the sketches have to be made, as detached, together with. the 
 corresponding measurements. Fig. 20 is a transverse section of 
 one of the arms, d, of cast-iron, taken near the boss. 
 
 The sketching of the sluice apparatus consists in making a 
 section of the side-posts, with their cap-piece, and of the sluice 
 itself; then a detailed view of one of the racks, with its pinion 
 and friction-pulley, and of the worm-wheel and worm. As to the 
 amount of inclbation of the sluice and side-posts, it has already 
 
 been seen that it is determined by a perpendicular to the radius, 
 entering near the middle of the depth of water at the outlet, at 
 the circumference of the wheel. It may, however, be found by 
 means of a plumb-line, let fall from one of the edges of the cap- 
 piece down to the level of the water, by measuring the horizontal 
 distance, r s, of the plumb-line, from one of the sides of the side- 
 post, and then the vertical height, r I. By applying a rule against 
 the side-post, and down to the neck-piece. H, we can always obtain 
 the actual distance of the top of the latter, either from the pro- 
 longation of the horizontal, r s, «r from the cap-piece, P. of the 
 sluice. To obtain the horizontal distance, r s, with exactitude, it 
 should generally be taken at a given distance above the level of 
 the water, and chalked upon one of the side-walls of the channel ; 
 it is also advisable to make use of a spirit-level. (Plate I.) 
 
 In order to take an accurate sketch of the neck-piece and the 
 channel, it is almost always necessary to stop the water behind 
 by means of a dam, so that the parts requiring to be examined 
 may be dry and open. The sluice must also be taken away, as 
 well as a few of the floats of the wiieel. We may remark, that 
 this labour may be avoided, when it is known that the' height and 
 thickness of the neck-piece are nearly always equal to those indi- 
 cated in fig. 11; and as to the arrangement of the masonry or 
 brickwork, of which the channel may be constructed, it will be 
 recollected that all the lateral joints are pointed towards the centra 
 of the wheel. 
 
 OVERSHOT WATER-WHEEL. 
 
 Figure 12. 
 
 construction of the wheel, and its sluice apparatus. 
 
 403. Overshot water-wheels, with buckets, receive the water 
 from a duct placed immediately above them, and allow it to escape 
 from as low a part only as possible. They are constructed of 
 wood, or of cast-iron. In the first ease, which is the simpler and 
 more economical, the shaft, the arms, and the shroudings are of 
 oak. The lower part of the wheel, represented in the drawing, 
 fig. 12, is of this description. The buckets and the inner-rim are 
 likewise of oak, or of iron plates. As this wheel is of small dia- 
 meter, its shaft, f, has only six sides ; and consequently, each 
 shrouding, A, of the wheel has only six aims, d, which are recessed 
 into, and bolted upon, a central cast-iron frame, e, which is itself 
 keyed upon the shaft. The transverse section, fig. 13, shows the 
 manner in which the arms are attached to this frame. The wooden 
 shroudings, A, are generally composed of two rings, placed one on 
 the other in such a manner that the joints of each are opposite to 
 solid portions of the other, to "break bond," and obviate tie ten- 
 dency to warp. A portion of the shrouding is represented as de- 
 tached in figs. 14 and 15. These rings are held together by screw s, 
 v, or by nails or pegs ; and at their junction with the arms, a couple 
 of bolts are passed through all, as indicated in the transverse sec- 
 tion, fig. 16. The buckets, c, are either let into grooves of smai. 
 depth, upon the inner face of the shrouding, as seen at c', in figs. 14 
 and 15, or they are retained by bracket-pieces, c: and. added to ties, 
 strong tension-rods, b, hold the whole together, being secured to 
 

 
 Ot» *ft>«tta~«, A. as cither side of the borkeU. These tco.ion- 
 
 rods Sfs ftlrd, ■ hcB the inner nui. «. . .r I- • ! t-tu of the bu. 
 
 btaa Mil. J or •rresrrd to tbo inn. r edges of Ute »hr..udi n g«. The 
 
 ■tan pilot! are further •treogthrned externally by a n: 
 
 trap. n. klfir V the f. ll.-e ..fan ordinary wheel, and c- 
 
 tbo c«ou of the .lu; J.» «hr..oding. 
 
 Bonntim— the backets ar. partly, of wood, and parti) 
 p'atr. to giro th. m greater «!r. ngth. 11m- edfi - 
 • bo defended with metal, aa they an 
 
 the wheel i» of cast- r. at dia- 
 
 meter, bat of the size represented in tin- u] l_'. I lie 
 
 anna and the boa*, f, may !■■ 
 
 . 
 »', ai.-i ilxjut Jth inch in thick- 
 
 ness. To arrorc th' 
 
 -. tn which Ihey 
 the wheel, the buckets 
 
 it i, or arc ti\< : 
 by amall acrew-bulta, i', figs. 17 a! 
 Tbo advantage of 1n.1l.l11/ 
 
 rm, which enlai 
 capacity, and . 
 
 whilst the ww »ni i—i lily eooaial of two rectilinear 
 
 re of tlir wheal, 
 
 Tne a -1. n channel, m, to the top of 
 
 -. moving in aide 
 
 if virtual racks, o, and 
 
 nies the winch-handle. Q. The 
 
 fond the 
 
 actual .urunii: oold lie a 
 
 ■ ■I the wheel, with the 
 r into tin' I'n 
 splashing and loM "f water by allowing the air to 
 escape bit, rally. The depth of the outflow of water •!• ; 
 the distance ot ttom of 
 
 the channel, and should alw . 
 
 existing betwi ■ la. The | ,.| ii„. 
 
 Ihe wheel in the 
 ■i .if the arrow, and II by an intcrn.'ill v- 
 
 I'-UllillgK. 
 
 Thi» • the drawing ii simply tndioated by its pitch 
 
 • i'.ar» »iili ill. pinion, i., mounted on th.- ■ 
 
 with the machinery in the i. 
 
 H'T WATER- 
 
 rincipal parts of an ■ ■ 
 
 way aa thai nf tin. 
 
 tl al when (In at 
 
 - 
 
 an angle 
 
 mity, aa 
 
 • 
 
 ntiMir ia a ciiiilinui'ii- may be 
 
 ■ IS, 17, 
 and 18. 
 
 - tching this wl i n in tin- pn 
 
 case may be lik 
 
 - and taking an accurate sketch of one of them, l< 
 with tin- accompanying mcasurcim ■ • - 
 
 mal and external diameters of the shroudings; tlun the 
 
 depth from t tn ■/, Bg. 17. Finally, if it ia itain iho 
 
 'in or curvature of the bucket, it will In. iieoeaaarj 
 one down, and I pattern of it, by app 
 
 ■ 
 t'.ir the forma of a beaJ-b eta, . a bJefa are difficult to 
 
 Aa i" the sketch of the oi 
 
 as the boas, the arm*, and also the sluice a| i uliarity 
 
 ordiflionlty can present itaelf which need detain aa lure. Tim 
 drawing, moreover, indicates all It trementa 
 
 which are nocoaoiry. 
 In designing an overshot water-wheel il to know 
 
 hi of fall, and the daily discbarge of the water. With 
 ■ these partienlara, we must sm.j Ij refer to irfh- . 
 ..id Practical I 1 
 
 W ,\T E R-PUM PS. 
 PLATH XXXVII. 
 
 GEOMETRICAL StllHlTlnX. 
 
 405. We have already indicated, i; 
 tin ii-, the \ari" M ' mips, with their proper dimi 
 
 in proportion t.. the quantitioa of water to be Furnished by them. 
 We new pro p one t" enter npon mori 
 
 ;lnir eonstroction, actton, and performance, 
 I'ur this purpi.se we mbined 
 
 lifting and forcing pump, the discbarge of wl 1 1 ■ •utiriu- 
 
 i.ns, although it- Bonatruction 
 
 I imp. 
 
 I, on Plata \ XX VII., repreaenta a n 
 
 taken throngfa the axia'of this pump. I; 
 
 cylinder, a, tamed out fur the greater |»>rti..n ••! • 
 
 • 
 or lift-pipe, c, below. Thin lwise is bolted down either i 
 
 liml.. r-. 0, ..r to I stonework 
 
 r frame, dividi 
 partition, at, and having the aidaa formed • Iwoia- 
 
 npOO which the hra-s . D shut. 
 
 The pip below in a i! - of which the 
 
 iuction-fj ed, extending down to the water to 
 
 Towarda the nppat sujnp eyhndar, i 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 a curved outlet, g, likewise terminating in flanges, to which the 
 discharge-pipe is secured. The piston, or bucket, of this pump is 
 composed of a brass ring, or short cylinder, H, upon the outer cir- 
 cumference of which is formed a groove, b, (fig. 2,) to receive a 
 packing-ring, c, which fits, air-tight, to the inside of the pump 
 cylinder. The bucket, H, has also a central partition, d, to the top 
 of which arc jointed the two clacks, I, which rest upon inclined seats, 
 formed by the elevated sides, e, of the bucket. This is further cast 
 with a bridle,/, perforated in the middle, to receive the screw-bolt, 
 g, which secures it to' the stout hollow piston-rod, j. This rod, 
 which, in the generality of pumps, is made of but small diameter, 
 like the upper part, K, of the one represented in the plate, is, in the 
 present instance, of a sectional area, equal to half that of the pump 
 cylinder. It follows from this, as will be more particularly ex- 
 plained further on, that the water is discharged during both the up 
 and down stroke of the piston. 
 
 The clacks, F, have projections, h, cast upon them, which pre- 
 vent their opening too far, and falling over against the sides of 
 the casing, B, so as not to shut again when required to do so. 
 The clacks, I, in the bucket, have similar projections, i, for a like 
 purpose, these projections striking against the top of the bridle,/, 
 when the clacks open. It will have been observed, that the seats 
 of these valves are inclined at an angle of 45°, with the view of 
 facilitating their opening movement, and diminishing the concus- 
 sive action of their own weight. The edges of the valve-seats are 
 generally defended with a strip of leather, to facilitate their tight 
 closing. 
 
 Figure 2 represents, detached and in elevation, the bucket, H, 
 with it? chicks, i. Fig. 3 is a horizontal section of the bucket, taken 
 at the line, 1 — 2. Figs. 4 and 5 give the details of the valve-scat, 
 E, in elevation and plan, the clacks being removed. 
 
 To prevent the entrance of air to the pump cylinder, it is closed 
 at the top by a cast-iron cover, L, which is fitted with a stuffing- 
 box for the passage of the piston-rod ; the packing is compressed 
 by the gland, M, similar in general form to that represented in 
 .Plate XI. (81.) 
 
 ACTION OF THE PUMP. 
 
 406. The upper extremity of the piston-rod, K, carries a cross- 
 head, 1, (fig. 6,) and is there jointed to the lower extremity of a 
 connecting-rod, N, which is itself jointed to the pin of a crank, o ; 
 this latter is mounted on the end of a horizontal shaft, p, actuated 
 by a continuous rotatory movement. This movement is trans- 
 formed by means of the crank and connecting-rod into an alternate 
 rectilinear motion — that is, into the up-and-down strokes of the 
 pump bucket — this last being forced to move in a straight line, the 
 cross-head, I, sliding in vertical guide-grooves, to maintain the 
 piston-rod, K, in the same line with it. 
 
 It follows, from this disposition of parts, that when- the crank, 
 o, is in the position, p — o, fig. 6, the piston will be at the bottom 
 of its stroke, that is, at h' ; consequently, during the time the 
 crank turns, the piston must rise, tending to leave a vacuum below 
 it, because the space between the clacks, f, and its under side 
 increases, as well as the volume of air that may be therein en- 
 closed. Consequently, the pressure of. this air upon the clacks 
 k diminished, whilst that upon the surface of the water remains 
 
 the same, and causes the water to rise up the suction-pipe, and, 
 raising the clacks, F, to enter the pump cylinder, filling it up nearly 
 to the under side of the piston ; or if the apparatus is in a perfectly 
 air-tight condition, it will rise quite up to the piston. 
 
 When the crank has reached the position, p — 12, — that is, 
 when it shall have described a semi-revolution, — the piston itself 
 will likewise be at the highest point of its stroke, and, in this 
 position, all the space left behind it in the body of the pump will 
 be filled with water; if now the crank, continuing its rotation, 
 makes a second semi-revolution, the piston will descend, and, 
 pressing upon the water below it, will cause the clacks, f, to 
 shut. Now, as the water is incompressible, it must find an exit, 
 or else prevent the descent of the piston ; and it therefore raises 
 the bucket-clacks, i, thus opening up for itself a passage through 
 the piston, h, above which it then lodges. But as the piston-rod, 
 J, is of a large diameter, and therefore occupies a considerable 
 space in the pump cylinder, a part of the water must necessarily 
 escape through the outlet, g, in such a. manner that, when the 
 piston shall have reached the bottom of its stroke, there will not 
 remain in the pump cylinder more than half the quantity of water 
 which was contained in it when the piston was at the top of its 
 stroke. 
 
 Such is the effect produced by the first turn of the crank, which 
 corresponds to a double stroke of the piston — that is, an ascent and 
 a descent. 
 
 At the second turn, when the piston again rises, it sucks up, as 
 it were, anew, a volume of water about equal to the length of 
 cylinder through which it passes, because the suction-clacks, f, 
 u hich were shut, now open again, and the bucket-clacks, i, w hicli 
 were open during the descent, are now shut by the upward move- 
 ment of the piston. 
 
 During this stroke, all the water which previously remained above 
 the piston, finds itself forced to pass off through the pipe, G, so 
 that, with this arrangement of piston and rod, or plunger, of large 
 dimeter, it follows that, at each up-stroke of the piston, the quan- 
 tity of water which rises into the pump is equal to the length of 
 cylinder through which the piston passes, the half of which quantity 
 rises in the discharge-pipe during the descent, and the other half 
 during the subsequent ascent of the piston, and the jet is conse- 
 quently rendered almost continuous and uniform. 
 
 When, on the contrary, the piston-rod is made very small in 
 diameter, as in ordinary pumps (fig. 6), the discharge of the water 
 only takes place during the ascent of the piston, and it is conse- 
 quently intermittent. 
 
 In a pump, as in all other machines in which an alternate rec- 
 tilinear is derived from a continuous rotatory motion, by means 
 of a crank and connecting-rod, the spaces passed through in a 
 straight line by the piston do not correspond to the angular 
 spaces described by the crank-pin ; in fact, it will be seen 'from 
 the diagram, fig. 6, that if the crank-pin is supposed to describe 
 a series of equal arcs, beginning from the point, 0, the correspond- 
 ing distances, 0' 1', 1' 2', 2' 3', passed through by the piston will 
 not be uniform ; very small at the commencement of the stroke, 
 they will gradually increase towards the middle, after passing 
 winch they will simUarly decrease whilst the piston approaches 
 the other end of its stroke. The successive positions of the 
 
140 
 
 
 pUtno may be obtained by desrriblne; villi rarli 
 
 lr.-«, u» i » ilh a rm.hu. equal ' 
 •rn. . of arc. 
 
 - i -iU-'l" of u. 
 
 oa the same brie, at diioano • 
 
 the length of the piaton-rod, measured from tin- j-.int. . 
 
 bottom of the pi%ton. 
 
 -1, that, in Co: 
 
 of the 
 
 endtarouml to abow the Ml 
 
 ■paratrra *olu : watar 
 
 at »oec. Je-aclino pump, such as lb' 
 
 upon any lino, x y, as 
 many equal parts as we have taken in diriaions on tin- circle <lc- 
 - 
 3, 4, dr.. ll of the 
 
 the pi-' -. tin-re i- nothing to indicate 
 
 - 
 
 ..■ i :.. | -• :. b I. i'. «ill pro- 
 
 ■ ■:• r. d tli' n, that when it Ins 
 
 i .' to 1 1 , tin' ijimutity 
 
 t may l«- represented by it- : 
 
 1 1 — I j'. It i- off from 
 
 >r drawn through the point, 13; in 
 
 di Kcnda from 11' to In', it is 
 
 iltiplied by the height, 
 
 11' — l" - iff from the point, 14 to b. It 
 
 i proceed _•■■•. hi the dia {ram, it is 
 
 *imply ■ i of the perpeudiculara drawn 
 
 15, 16, 17, 1 
 
 I for each portion 
 e prop irtional to the d 
 
 the cylinder remaining 
 wmrtint 
 if. through the vnr 7, obtained in this 
 
 i surface 
 
 ide, and which will give 
 
 , orrt ipondcDce 
 
 with at I I (be rotation of 
 
 this up- 
 « tin- down-at 
 
 tar then 
 : i curve equal I 
 
 ■ 
 
 ■ . pumping ap 
 ■I ini ia tooh/thal the , 
 
 ibcd by 
 
 - i rideat that the product ol i 
 
 that "He at the pistons, hat 
 . brj . the eurve, a 
 
 niie linn.' 
 
 abed; so that tin* diagram only d 7, ill that the 
 
 i and lit to 1-. ill the latter, are 
 
 In the formor filled up by an equal h. ■■• an equal llal 
 
 diagram of the perfutniaaM of a two<yiinder pomp may 
 
 ting that of the |'Uiup. fig. I. whieh, 
 of it-s trunk piston-rod, acta as a duubloacling pump, as 
 already explained, 
 
 • nis the diagram of the perfbrmai 
 cylinder pomp, of whieh the pistons, n. a', n', represented, tor 
 eonvenii i in the same cylinder, occupy the i 
 
 eorr. jponding I three crank-pins, u. 0*, 0', at 
 
 at the angles of an equilateral triangle, inscribed in i 
 described by them with the centre, p. In of Una 
 
 disposition, there are at one time two and one 
 
 . and at another time, on the contrary, only one 
 ascending ami two deaoendi to represent the com- 
 
 him .1 performanoe of these pumps in a diagram, by tising different 
 ei. h.urs, or different di ptha of dude, for tin !■< n. in 
 
 dent upon tie • liTaken up by 
 
 . crank-pins, l nfuaion will be 
 
 . and it will be necessary to timl the positions, a, ■ 
 the attachment of tin- connecting-rod to the piston-rod upon the 
 
 Vertical line penning through the centre, i, 01 
 
 a* the distances will he the same for all, being mi 
 
 different parts of the diagram. 
 
 In the diagram, t i ^ . l". we haw laid down the performance of 
 each of tin- three pumps, supposing them all to he of the asms 
 diameter, and taking care, when two pumps aredischai 
 gether, to add together their performanoe ; thus, for example, w Inn 
 on,- of tin- pis ruantitj of wati r, ■ • , 
 
 the perpendicular, 13a, that which . 
 time furnishes a qnantil] expressed bj the diatani 
 
 quently, the total rolun f tl 
 
 aented In the total height, 18a : when, on the other hand, 
 
 of the three pumps d 
 
 byaaingli length of perpendicular, such ai It will be 
 
 I, thai il is precisel] at the moment when onlj 
 
 out its maximum performani 
 
 which it follows, that the jet of water is continuous, an. I almost 
 
 uniform throughout its duration, as will he \rr\ evident ir'.m a 
 consideration of the >■■. i I, tin- outline <.t which ii 
 
 mined by pcrpendioulara, or ordinab -. n to the 
 
 str.ii-ht line, m ii, thro 
 
 mpars the oombinod ofleel of a three-cylinder pump with 
 pumps, we have, in i 
 
 . 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 141 
 
 merits; and it will be remarked, that although, with cylinders of 
 an equal sectional area, we necessarily obtain a much larger dis- 
 charge, yet the regularity of volume is not so great as in the 
 previous example. 
 
 STEAM MOTORS. 
 
 HIGH-FF.ESSURE EXPANSIVE STEAM-ENGINE. 
 
 Plates XXXVIII, XXXIX., and XL. 
 
 407. When the steam generated in a boiler is led into a vase or 
 cylinder which is hermetically closed, it acts with its entire expansive 
 force upon the sides and ends of the cylinder, so that, if this en- 
 closes a diaphragm, or piston, capable of moving through the cylin- 
 der in an air-tight manner, the force of the steam, in seeking to 
 enlarge its volume, will make the piston move. It is in this way 
 that a mechanical effect is derived from the expansive action of the 
 steam, and it is on the same principle that the generality of steam- 
 engines are constructed. 
 
 Thus, in most apparatus to which this name is given, the action 
 of the steam is caused to exert itself alternately on the upper and 
 under surface of the piston, enclosed in the cylinder, thereby caus- 
 ing it to make a rectilinear back and forward movement or stroke. 
 (187.) 
 
 Steam-engines are said to be low or high pressure engines, 
 according as the tension of the steam is only of about 1 atmosphere 
 on the one hand, or of 2, 3, and upwards, on the other. Low- 
 pressure engines are generally condensing engines, and high-pres- 
 sure ones non-condensing ; so that the terms, low pressure or con- 
 densing, high pressure or non-condensing, are used indiscriminately, 
 although, in modern engineering practice, what are called high- 
 pressure condensing engines are extensively employed. 
 
 When the steam is made to act alternately above and below the 
 piston, the engine is said to be double-acting ; and of this description 
 are most of those employed at the present day ; but if the steam 
 acts only on one side of the piston, as is the case in many mine- 
 pumping engines, the engine is called a single-acting one. 
 
 Low-pressure engines are generally also condensing engines; 
 that is to say, that after the steam has exerted its expansive action 
 upon the piston, and is on its way out of the cylinder, it passes into 
 a chamber immersed in cold water, and termed a condenser, where 
 it is condensed or reduced to the state of water. This condensa- 
 tion produces a partial vacuum in the cylinder, and consequently 
 considerably diminishes the resistance to the movement of the 
 piston. 
 
 In high-pressure engines, the steam which has produced its effect 
 upon the piston escapes directly to the atmosphere, so that the pis- 
 ton has always to overcome a resistance equal to one atmosphere, 
 or about 15 lbs. per square inch, acting in a direction opposite to 
 its motion. 
 
 Steam-engines are further distinguished as expansive and non- 
 expansive ; of the latter description are those wherein the steam 
 enters the cylinder throughout the entire stroke of the piston ; so 
 that the pressure is uniform, since the volume of steam of a given 
 pressure which enters is always equal to the space passed through 
 by the piston. 
 
 In expansive engines, on the contraiy, the steam is only allowed 
 to enter the cylinder during a portion of the stroke ; so that the 
 expansive power of the steam is called into action during the 
 remainder of the movement. 
 
 The machine detailed in Plates XXXVIII., XXXIX., and XL., 
 is a high-pressure engine, with a variable expansion valve. 
 
 Fig. 1, Plate XXXVIII., represents an external elevation or front 
 view of the machine, the frame of which consists of a hollow column, 
 with lateral openings. 
 
 Fig. 2 is a horizontal section, taken at the height of the line, 
 1—2. 
 
 Fig. 3 is an elevation of a fragment of the lower part of the 
 column. 
 
 Fig. 4 is another horizontal section, taken at the line, 3 — 4; and 
 fig. 5 is an elevation of the capital of the column. 
 
 Figs. 6 and 7 are diagrams, relating to the movement of the 
 governor, with its balls. 
 
 Fig. 8, Plate XXXIX., represents a vertical section, taken 
 through the axes of the column and the steam cylinder, at the plane, 
 5 — 6, parallel to that of the fly-wheel. 
 
 Fig. 9 is another vertical section, at right angles to the preceding 
 figure. 
 
 And, finally, fig. 10 is a horizontal section, taken at the broken 
 line, 7 — 8—9—10. 
 
 This machine consists of a cast-iron cylinder, a, truly boied out, 
 and enclosing the piston, B. On one side of the cylinder are tast 
 the passages, a, A, by which the steam enters alternately above :.nd 
 below the piston. These passages are successively covered over 
 by a cup or valve, d, the details of which are given in figs. 28 to 
 31, Plate XL.; and the valve is itself contained in the cast-iron 
 chamber, E, called the valve casing, and communicating with a 
 second chamber, F, called the expansion-valce casing ; it is inio 
 this latter chamber that the steam is first conducted by the pipe, 
 G, from the boiler. The communication between the two vah o 
 casings is intercepted for short periods during the action of the 
 machine, by the expansion valve, h, detailed in figs. 38 to 4 1 > 
 Plate XL. 
 
 The vertical rod, i, of the piston, b, is attached at its upper ex- 
 tremity to a short cross pin, e% which connects it to the wrought- 
 iron connecting-rod, j, hung on the pin, /, of the crank, k ; this is 
 adjusted and keyed upon the extremity of the horizontal shaft, t, 
 which carries on one side the fly-wheel, in, and on the other the 
 eccentrics, n, o, p. The first of these eccentrics is intended to ac- 
 tuate the distributing valve, D, the rod, g, of which is connected to 
 it by the intermediate adjustable rod, n'. The second works the 
 expansion valve, H, by means of the rods, o' and h ; and, finally, the 
 third eccentric, p, gives an alternate movement to the piston or 
 plunger, Q, of the feed-pump, r. 
 
 The steam cylinder is bolted in a firm and solid manner, by 
 its upper flanges, to the top of the hollow, cast-iron plinth or pe- 
 destal, s, on which also rests, and is bolted, the column, t. The 
 pedestal is square ; and, at the corners of its base, lugs are east, 
 by means of which it is firmly bolted down to a solid stone 
 foundation. • 
 
 The column, T, is cast hollow, and with four large lateral open- 
 ings diametrically opposite to each other, their object J»einc t« 
 

 THE 1 
 
 the m r.-^.i of the column, and to afford the a«reaaary 
 > for the mtr.-lu U a ..f th. various piece* when b. h 
 
 arfcaa uJu-d down. This coluraa aiao serves aa a 
 frame for la* aotira machine, and abovs the capital in placed a east- 
 anas piDow-hlcMk, i\ furoi»h.d with bearing braaat - 
 
 . jownal of the first motion shaft, aa well aa the supporting 
 bracks**, a, f, of the spindle, /, of the bail f 
 
 ■ida are alao boiled the two supports, i, of the parallel inolion, and 
 ■dig- 
 
 I or THE MX 
 
 408. Before proeee i I shall give some idea of tho 
 
 fee era! action of the machine. Aa already mentioned, the steam 
 ia generated in a bod-" uiije, as that represented in 
 
 QT, 189 . i'-l - ■ tondneted by t: <;, into 
 
 tne first chamber, r ; « 
 toe orifice, or port, ,1. the steam finds its way into 1 
 
 .•it passes either to the nj bwat and ..I" 
 
 •r other 
 of the : ~ loaaagea, a, b. Now, whe n the | , 
 
 is almost fully 
 nel, b, U in communication with 
 
 ■•■.lli.h the tWl ' tdocl it tO thl 
 
 I • it i to the cylinder, it has 
 
 a pressure of, nay four ' will set upon 
 
 - • ■ oe, bow- 
 
 in commtuiea- 
 ■ , • ■ | iial to 
 
 M>e atmosphere oppo- ire the actual 
 
 l>ressur» acting on tlie lop ..f the piston will ba I 
 
 • rs the 
 Km psasage, 6, te , allow the - 
 of the ej ■■ .it. is |nit in communication with the 
 
 . the rup of • Bar the 
 
 steam which has just acted on the upper tide of Liu- pist.jn during 
 
 ■ be remarked, that if the intr.xlurti.>n of the steam takes 
 
 place do up-and-down stroke of the piston, which 
 
 . communicated directly with 
 
 !'. k. pi one of the porta oneo- 
 
 i would 
 
 i arid that the machine 
 
 waa a hi —'.hat is to say, tli.it it 
 
 I with a full ■ ■ .un. 
 
 In the mnli 
 
 ■ 
 
 with lie 
 
 • 
 at the | the passage, d, mu-t ngOMBl in ^ 
 
 expand |ng the 
 
 I to be 
 
 in this rn.se a 
 
 a (bird, half. 
 
 thirds of the capacity of the cylinder, aeeordiug as the intro- . 
 
 iiird, ouc-haJl 
 il is the ratio between tin- qnantitj 
 re ssun- Ultluduued, and lie ■ 
 der, which expresses the degree of expansion at which the 
 
 works. 
 
 rARALLEL MOT10*. 
 
 409. Tlie rectilinear altsmal ■ trans- 
 
 Ibnned into a eontinuoui circular motion on the Beat motion abaft, 
 I. ley the interv, utii.n of tie- nnnnffflrtlia; rnd, J, and crank, i; hut 
 with this arrni is naturally a lateral strain u|sen the 
 
 top of the pisteo-rodt I, ami in onlrr tliat its movement may be 
 . rcctiliuear and vertical, it la jointed : articu- 
 
 lated levers, fanning what i- termed a parallel motion. 
 
 • I of two wrought mm rod- 
 
 i, and are articu- 
 lated at tin ir opposite BXtreflaif -. x. mar their middle, 
 
 nnd are jointed at one end to the I ross pin, e", fig. 9, of Um 
 
 rod end ; and at tl tin r to the rod, v, attached to a cross. 
 
 o a, and oscillating in 1« snogs, in ■ * 
 bolted to the lower part of th* 
 Xlii- heed of this laet-mentioned — Hiatt»g rod is ,i. ..died sepa- 
 
 ratelj, hi XL 1 1 has brasses, to < 
 
 the journal of i : ' by which U ia eonneoted to the ends 
 
 Of tlie II ■ 
 
 •mbination of this n inch, that the point of 
 
 attachment, r, constantly mo?i ' line throughout the 
 
 entire stroke. It ma;, metrical prim 
 
 : in the diagrams, li^'s. 8 and 11. T 
 •opposed, that alter baring drawn the horizontal line, t 1 /\ and tho 
 vortical, t >', distances, e t? and t c', are set off 00 the ktttl 
 to the half stroke ..I the piston, or to the radius of the crank ; then, 
 with the points, r r\ describe Bfl are. with a radius, e /-equal to the 
 
 length of the lever, x. which is taken at pleasure, but should never 
 man the stroke of the piston. If we nasi lay off this 
 
 from e" to /»', the space. ;/ ;.', will express the amount of 
 oscillation of the rod, Y, the centre I Inch wo 
 
 place below, on the vertical line, drawn at an equal disl.-ua N (rom 
 
 and between tin- two points, a, p*. We next As the point, n, of 
 
 attachment of the rccU, \. ]., the h\c r, x. This point, n, during 
 ■ inc tit of the parallel motion, nisessarily decicribes a circu- 
 lar arc, of which it is requisite tec find the centre. In invi - 
 ibis problem, it ia tec !*• observed that, whatever may l><- • 
 tic.n cci the- Icier, the point, " ■■ from 
 
 the eatreml t y , ;■. or tl th.-r one,* If, then, we in in 
 
 draw ti.- ';'''• indkwHng the difierei 
 
 : the lc \er, c-.crr ■ '. ■*. «*, of tie- 
 
 r's! cii'l. we shall, on each "t tie SS lines, obtain the- s. \cral posi- 
 
 m', a*, ii', by laying off oa fliem dhoai ««f tin- d 
 
 ;> n or r n. We can then M ry easily linel the centre of tho sro 
 
 passing through tin M points. (10.) 
 
 cm of an snalogOUl parallel motion, 
 :n which the riMls, V, art so eli-pose.l. that their point of 
 :it is exactly iii the D x; aid in this 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 case, their axis of oscillation lies in a plane passing through the 
 vertical axis, e e 3 . 
 
 DETAILS OF CONSTRUCTION. 
 
 STEAM CYLINDER. 
 
 410. The cylinder is cast in one piece with its bottom cover and 
 lateral steam passages. As it should be bored with great care, so 
 as to be perfectly cylindrical in the interior, a central opening is 
 made in the bottom for the passage of the spindle of the boring 
 tool ; this opening, however, is afterwards closed by the small 
 cover, a 3 , cemented at its junction surfaces, and bolted down to the 
 bottom of the cylinder. The upper end of the cylinder is closed 
 by a cast-iron cover, a', which is formed into a stuffing-box in the 
 centre, to embrace the piston-rod, which works steam-tight through 
 it. The packing is compressed or forced down for this purpose 
 by a gland (140), bolted to the stuffing-box, and hollowed out at 
 the top to receive the lubricating oil. The valve-face, on the out- 
 side of the cylinder, and on which the valve works, is planed very 
 carefully, so as to be a true plane throughout. The same is done 
 with the valve-casing at the flanges, where it is fitted to the valve- 
 face. 
 
 The piston (figs. 8, 9,-19, and 20) is composed of two cast-iron 
 plates, which have an annular space between them for the recep- 
 tion of two concentric cast or wrought-iron or brass packing-rings, 
 c'. These rings are cut through at one side, and are placed one 
 within the other in such a manner, that the breaks in each are 
 diametrically opposite to each other; their thickness gradually 
 diminishes on each side towards the break, and they are hammered 
 on the inside in a cold state, which renders them elastic, giving 
 them a constant tendency to open. Since the diameter of the 
 outer ring is equal toihat of the cylinder when the two edges are 
 brought together, the elasticity of the inner ring, combining with 
 that of the outer one, tending constantly to enlarge them, it 
 follows that there must be a perfect coincidence between the 
 outside of the ring and the inside of the cylinder throughout the 
 whole extent of the latter. Thus the contact of the piston with 
 the sides of the cylinder only takes place through the packing- 
 ring, and not by the plates, which are of a slightly less diameter. 
 To prevent the passage of the steam through the break in the 
 outer packing-ring, a rectangular opening is made in the two edges 
 of the ring, and in this is placed a small tongue-piece, a', screwed 
 to the inner ring, this piece serving to close or break the joint 
 without preventing the play of the rings. The principal plate of 
 the piston is fixed to the piston-rod by means of a key (fig. 9)- 
 The piston-rod is consequently of increased diameter at its lower 
 end. The upper end of the piston-rod is likewise fixed in a socket, 
 l', (figs. 9 and 13,) which terminates in two vertical branches to 
 receive the middle of the spindle, e 1 , which is held down by 
 means of a key. 
 
 CONNECTING-ROD AND CRANE. 
 
 411. Tne connecting-rod, J, (figs. 8, 9, 14, and 15,) terminates 
 at its lower end in a fork, by means of which it is jointed to the 
 
 spindle, e 3 , brasses being fitted in either side, and secured by bridle- 
 pieces passing under them and keyed above. The fork is jointed 
 to the spindle, e a , on each side of the piston-rod head, sufficient 
 space, however, being left between them for the levers, x. The 
 head of the connecting-rod (figs. 15 and 16) is likewise fitted with 
 brasses to embrace the pin, /, of the crank ; these brasses are ' 
 tightened up by means of the pressure screw,/'. 
 
 The crank, K, like the connecting-rod, J, is of wrought-iron, 
 being adjusted on the end of the first motion shaft, and secured to 
 it by a key. This crank is very often made of casHron in sta- 
 tionary engines, but in marine and locomotive engines it is gene- 
 rally forged, so as to be better suited for resisting severe strains 
 and shocks. 
 
 The first motion shaft, l, is likewise either of cast or wrought- 
 iron. In the notes, we have already given u.bles and rules for 
 determining the respective dimensions of this detail. It is not 
 only supported by the brasses of the pillow-block, v, but also by 
 those of a similar one v fixed, we shall suppose, upon the wall 
 which divides the engine-house from the workshop or factory. It 
 should always be larger in diameter where it receives the fly- 
 wheel, M. 
 
 FLY-WHEEL. 
 
 412. The fly-wheel is of cast-iron — of a single piece in the pre- 
 sent example, because its diameter is only 3-5 metres. When of 
 larger dimensions, the rim and the arms are cast in separate pieces, 
 and then bolted together. For wheels of from 5 to 8 metres in 
 diameter, the rim is made in several pieces, and the arms are also 
 cast separate from the boss, and all the parts are then bolted 
 together. The arms are sometimes made of wrought-iron of small 
 dimensions, with the view of reducing the weight near the centre, 
 without reducing the effect of the wheel. 
 
 FEED-PUMP. 
 
 413. This pump serves to force into the boiler a certain quantity 
 of water, to replace that which is converted into steam and expend- 
 ed in actuating the engine. It is a simple force-pump, consisting 
 of a cylinder, R, in which works the solid piston or plungci, q. 
 The piston is not in contact with the sides of the pump cylinder, 
 and the latter consequently only requires to be turned out at its 
 upper part, where it is formed into a stuffing-box aud guide for 
 the plunger, being necessarily air-tight. 
 
 On one side of the pump is cast a short pipe, to which is atl..Ji- 
 ed the valve-box, R, generally made of brass. To the lower part 
 of this is secured the suction-pipe, t', communicating with a cistern 
 of water, and having a stopcock, s', upon it, like the one repre- 
 sented in detail in Plate XVII. To one side of. the valve-box is 
 likewise fitted the discharge-pipe, carrying a similar stopcock, s 3 ; 
 this last pipe is generally passed through the pipe which carries 
 off the waste steam, so that the water may take up some of the 
 heat of this steam before entering the boiler. 
 
 It will be seen, from figs. 9 and 23, that this valve-box contains 
 two valves, s', s 2 ; the lower one of which, s', is the suction valve, 
 and the upper one, s', is the discharge-valve. The latter is much 
 larger in diameter than the former, so that its seat may be wide 
 enough for the lower valve to be passed through it. The upper 
 
Tin. ! nit.\i cut: 
 
 ecsJ of thr tilii -■<>! U tlowd b> I 
 dowa I . sod ir..n bndlr, o*. 
 
 .1 MM to 
 6l ■<*• ravly. Th* nodrr part ol il,MM 
 
 jiaasage 
 
 tal, nml 
 ujx>n the li 
 
 Th* ■ 1 null rod, t, adjust- 
 
 !.! i r< >n rod, 1', 
 :i cullnr, 
 ■ 
 
 thai ><( the pumps of 
 
 ■ >ii. Tim*, wb< n tha 
 
 and 1", are open, the 
 
 pipe, k', the valve, a*, opening, 
 
 lj "i" the pump, into which ii H 
 
 v. 
 
 ■ 
 
 - along the discharge-pipe to 
 i 
 
 entirely shot off by closing them ; but 
 die, p, with it.-, rod, 1 •', will continue 
 
 ■ bicb is 
 - \. 1, by which the piston-rod 
 
 Uittatl. d, in such a manner thai the socket, 
 
 ■■ rod, r', will simply slide iij> 
 
 BALL nil lOTATDra I 
 
 41 1. '.' tton "f 
 
 • proportion t" tin- n 
 
 1 valve, 
 throttle-valve. Just 
 for I 
 
 ■ •in. hi. and i- actuated by ■ r. .'1. passing 
 
 ■ steam 
 der mors or 1. r.- ; sod, similarly, thu 
 
 ■ ■I the piston, 
 
 li"ll Willi it 
 1 as - .-ii in li:.' 1, of n nil 
 
 lupport, /.'. mid 
 
 1 ■ . j .( .. r 1 11.1 are 
 
 In cast- 
 
 1 
 
 1 ■-./.!.. tli.' wroogbtiroo "r e ipper 
 
 iDudle: 
 
 ind tli" 
 balls l» .nil with it, will bavi 
 
 •ril f,.rce 
 - 
 • 
 
 up»n tl 
 is to SSJ 
 ■ 
 
 the bolls will fly bai. 
 
 I 
 will lx circular 
 
 tod bell- 
 s 1I1 the throtl 
 
 <■'. drawn with it-, bos, a', in I 
 
 ralre will be slmt. I 
 
 d below tin- |ir.i|N r point, owing t.j an iin-r. ..- 
 the balls will approach 1 ad assume Ihi 1 • 
 
 nend, and, consequently, the 
 throttle-valre will become 1. 1- to allow ■ 
 
 quantity of ah am t" enb r the vain 
 Uir c) Under. 'I 
 which they cann 
 the spindle, /. 
 
 The motion of tliis spindle is derived from the lirst motion slmft, 
 i„ by in' '. fixed upon the inti n 
 
 spindle, r*, pUo capital of the column, t. and by the 
 
 bevil-whi ng their motion from the pulley, r 4 , • 
 
 t rati" is maintained between the r.itr of the mai 
 that of the governor. 
 
 and ". will sufficiently explain 
 tin- respective ] 10I tl" i" ndulum, and 
 
 will show how tin- ri- el upon the spindle li 
 
 li_v. and is in proportion t". tli" flying asundor of t 
 im; to 'lie number of n 
 
 tin- BUS] ■ 
 
 MOVEMENTS OF THE DISTRIBUTION AND EXPAN- 
 SION \ M.\ is 
 
 11;, \'. tli.it tli.- valve, D, represented in different 
 
 and "i. and i» l«- ■ r i 
 is attached, by Its rod, g, !•> tli" vertical rod, nf, which is joined t.. 
 
 the rod, a*, of tli" circular "< Dtrie,n, figs. Bo^and 84. Winn, 
 
 sn was customary until lately, tha «-«-ntr«. «»t* Iheecc 
 
 riuliiis perpendicular t.' the direction nf tli" crank, the movements 
 
 "i tli" st. inn piston and reive ar" different t" < ach oaher — that is 
 
 when tha crank passes from the lefl boriaontal t" tk 
 ■ 
 
 I 
 of tli" vertical line, drawn ilir..u„'li the centre of tl>" firsl 
 
 ,:.l eonsequenl 
 tl" rslvi 11 'it quite differonl (■. thai ol 
 
 too, in - " that, when il" 
 
 »tr..k", tli. valve, "" tli" otfai r band, 
 
BOOK OF INDUSTRIAL DESIGN.- 
 
 porta are consequently fully open, to give the steam the freest 
 passage into the cylinder. 
 
 Whilst the piston is accomplishing its stroke in one direction, 
 the valve moves up or down, and returns again to its central po- 
 sition, the part which it covered being opened and again shut; 
 when, however, the crank makes two fourths of a revolution in 
 different directions, the piston rises and falls half a stroke each 
 way, whilst the valve makes a single rectilinear movement in one 
 direction. * 
 
 Finally, for each of these movements, whilst the velocities of the 
 piston are increasing from the commencement towards 4he middle 
 of its stroke, those of the valve are decreasing, and reciprocally. It 
 therefore follows, that the maximum space passed through by the 
 piston, for a given portion of a revolution of the crank, corresponds 
 to the minimum passed through by the valve. 
 
 LEAD AND LAP OF THE VALVE. 
 
 416. Of late years, engineers ha re- recognised the advantage of 
 inclining the radius of the eccentric, with regard to the radius of the 
 crank, instead of placing them perpendicular to one another, in such 
 a manner that, at the dead points — that is, the extreme high and 
 low positions of the piston — the valve shall already have passed 
 the middle of its stroke to a slight extent; it is this advance of the 
 valve which is termed the lead. 
 
 The effect of giving this lead to the valve, is to facilitate the 
 introduction of the steam into the cylinder at the commencement 
 of the piston's stroke, and at the same time to allow a freer exit 
 to the waste steam on the other side of the piston ; a greater uni- 
 formity of motion is in consequence obtained, whilst less force is 
 lost. 
 
 In order to avoid as much as possible the back pressure due to 
 the slow exit of the waste steam, it is likewise customary, in addi- 
 tion to the lead, to give the valve more or less lap ; that is to say, 
 to make the width of that part of the valve which covers the ports, 
 a, i, fig. 28, sensibly greater than that of the ports themselves. 
 
 In explanation of the effects due to the lead and lap of the valve, 
 we have, in fig. 35, given a geometrical diagram, indicating the 
 relative positions of the crank, the piston, the eccentric, and of the 
 valve. 
 
 Let o o represent the radius of the crank ; with this distance as 
 a radius, and with the centre, o, describe a semicircle, which divide 
 into a certain number of equal parts. From each of the points of 
 division, let fall perpendiculars upon the diameter, o c. The points 
 of contact, 1, 2, 3, 4, &c, represent upon this diameter, considered 
 ss the stroke of the piston, the respective positions of the piston, 
 corresponding to those, 2 2 , 3", 4 a , &c, of the crank pin. It is un- 
 necessary to take into account the length of the connecting-rod, 
 which connects the latter to the piston, because, in the present case, 
 the connecting-rod is supposed to be of an indefinite length, and 
 to remain constantly parallel to itself, so that it cannot modify the 
 results. 
 
 With the centre, o, likewise describe a circle with a radius, 
 o a', equal to that of the eccentric, N. We have assumed the 
 point, a', to be the position the centre of the eccentric should 
 have at the moment when the piston v at the end of its stroke — 
 
 that is to say, at o; the distance of this point, a', from Hi" vertical 
 m n, oxpresses the lead of the valve, and consequently the angle 
 m o a', is called the angle of lead. The position of the point, a' 
 may likewise be obtained, after .the following data arc decided on— 
 namely, the height of the ports, a, b, fig. 28, the width, r s, of the 
 flange of the valve, which is equal to the height of opening, I r 
 which properly expresses the amount of lead given to the port 
 augmented by twice the lap, together with the amount of the intro- 
 duction of the steam to the cylinder, and the amount of opening, 
 s' l', expressing the lead given to the escaping steam, and which is 
 always greater than the former, so that the exit passages may he in 
 communication as long as possible. 
 
 The diameter of the eccentric, N, is equal to the height of the 
 port, augmented by the width, r s, of the flange of the valve, and 
 the difference which exists between the two amounts of lead, .s' l' 
 and r t; it is, then, with the half of this as radius that the circle, 
 a' b' c d', must be described ; and we then obtain the point, «', by 
 setting off from the centre, o, to the right of the vertical, m n, a 
 distance equal to the lead of introduction, r I, augmented by the lap. 
 Starting from this point, a', we then divide this circle into as many 
 equal parts as we previously divided the one into, described by the 
 crank pin, and then through each of the points of division we draw 
 perpendiculars to the vertical, m n. 
 
 We further draw the straight line, a' g', parallel to m n, when 
 the distance of the several points of division from this line «iil 
 indicate the successive positions of the valve in relation to those 
 of the piston. Thus, after having drawn the horizontals, r u, 
 through the extreme point, r, of the valve, at the moment when 
 the piston is at the extremity of its stroke, make 1'— 1' equal to 
 b' J 2 , and the point, 1', indicates how far the valve has descended 
 during the time the piston has traversed the space, 1, whilst the 
 crank has described the first arc, o 1'. In like manner, set off 
 the distances, c 1 c 3 , d l d 2 , &c, which correspond to the third and 
 fifth divisions, reckoning from the horizontal line, r n, from j 2 to 3', 
 and from h* to 5', on the verticals corresponding to the third and 
 fifth positions of the piston, and consequently the positions, 3* 
 and 5", of the crank. It will then be seen that the valve con- 
 tinues to descend until the moment the centre of the eccentric, 
 reaches the point,/', upon the horizontal line, of, corresponding 
 to the sixth position, and the valve then wholly uncovers the 
 port, a, as shown in fig. 29. During the continued revolution of 
 the eccentric, on passing this point the distances of the points of 
 division from the line, a' g', diminish, and the valve reascends, in 
 such a manner as that, w : hen the centre attains the point, p — that 
 is to say, when the crank shall have performed a semi-revolution, 
 and the piston have arrived at 18, at the other end of its stroke — 
 the valvo will occupy the position indicated in fig. 30. This 
 figure shows that it uncovers the lower port, b, for the introduc- 
 tion of the fresh steam, and the upper one, a, for the escape of 
 the used steam. If the respective positions, 6', 7', 8', 9', ecc, of 
 the valve, be determined throughout the entire stroke, by setting 
 off upon the verticals, 6, 7, 8, 9, &c, the distances of the points 
 of division of the eccentric from the straight line, a' g', as already 
 explained, a curve will be formed, as at u 3' 6' 9' 18', which is a 
 species of ellipse. This diagram has the advantage of bringing 
 into a single view the relative positions of the crank, piston, eccen- 
 

 ■ 
 
 tnr. ia.1 valre, » n J brtHulca th* determination of tf.* pad 
 lite vslte, <wm»puadin£ to any r» - 
 
 p. of the -*— ■t-f 8 -'— . U U aofficirnt to dnw the vertical, y x\ 
 
 »h^h will enl the Ml 
 
 Dais point, (ram the horizontal, I ■*, 
 
 • 
 by the boruooUl, f u. 
 
 •, wiih a valve 
 is lead and lap, dvely to 
 
 it off at four- 
 
 -1 that, if the machine contio 
 
 c which 
 ■ 
 attain tl I soon as 
 
 ■ :. In llii- | 
 
 open — tho fir^t to the exit aperture, 
 
 . whilst the valve ta at 
 
 found by continuing 
 
 ,18 - l BtV, is exactly 
 
 u 16". On iho same 
 
 diagram '9' 18', 
 
 • •juil an 1 par.. 
 
 : the v;iH«-. in : 
 
 poaitioni 
 
 upon the verti- 
 
 <..!-, drawn till 
 It m. . 
 
 iran'. It i». I reduce it x- g 
 
 . miuish the surface of the valve, and 
 
 ii the hack of it- In 
 the axil port, e, 
 •• r Uuui tliat nf the introduction ; mtity at 
 
 be lap an. I the 
 lead, ( i and I r. 
 
 ■ 
 417 The actios of - 
 that of • n of iU 
 
 • ilated in the - 
 
 ■ 
 1 u|N, n tha main shaft, u n- ■ .th the 
 
 to the adjuatab 
 u*. Thia arrangement allowi 
 ihn.w being increased or din 
 
 . . 
 
 • It To thi- 
 central 
 
 If •*• • !«• in the MOM 
 
 tioo aa the cm: 
 drawn i 
 35, that 
 
 tlian would oil 
 
 .1 partis 
 starting from i • through the point, v 1 , draw a i 
 
 lino, ami then eel off OH the varietal 
 
 from tl.. Urolith the D . of the 
 
 ii m' ■' ;.', the 
 : which i« Sal — tinted with . 
 
 - 
 
 ■ i ill Una 
 drawn throngh the npj port,d, in the point, n, whi Ii 
 
 - at what time the va entrance port 
 
 It will be Been tliat thu the poaitian, <V, of the 
 
 ■team-piston, tl ; that tho cu 
 
 a has performed no more than a fourth of lot I 
 
 tinning the movement) it will be observed that the valve, ■, b)bm 
 bigber and higher, so that it b rer the entranei 
 
 little before tin - the sad of Ha stroke; but it i* evi- 
 
 dent thai ilie steam cannot find ita wsj into the eyiindar at this 
 point, for the distribution vajve is in its turn dosed, as s... i 
 
 bv the I ■ and of 
 
 88 and 40, and h shown also in iho 
 i 
 
 n of it* 
 ■• lativaly with the rsdiui of the orank, it wQI In- easily nn- 
 
 !. that within certain i lltoT the time when the 
 
 ■ ■ port, and an 
 in vary the d 
 I traa 41 and 19 sho* that the rod of the valve ii attached to 
 
 it by a T joint, which leaves the valve sufficiently free for \> 
 
 it constant]] i hoe; and a similar 
 
 adjustment is adopted with the distribution valve. 
 
 :ii..ns w lii. !i we have given in tho pn 
 to the construction and notion of thisi 
 evidently appl] to other s yst e ms, which merely differ in some of 
 the srrangementa and forma of the compom at pk •■• a Iforeow r, 
 
 in <>iir n Hi vvill find the rules and tables coin-erne.! 
 
 in Ihe eslenlationa and designs of these engin es, 
 
 aUl BS \M» PRACTICAL DATA 
 BTJ 
 
 l.ovv-.ri. -v u vi . 
 
 118. In 'li- 
 ra i- pro d noad at n tamparatore very lillle over that of 
 
 boding wat.r. or 100 i I iisuheit) M la, m fast, 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 generally 105° cent.— in which case the tension of the steam will 
 sustain a column of mercury of 90 centimetres in height ; that is to 
 say, 14 centimetres above that due to atmospheric pressure. It is, 
 consequently, equal to a pressure of 117 atmospheres, or 1-2 kilog. 
 per square centimetre. It is for this pressure that what are gene- 
 rally known as Watt's engines, without cut-off valves, are calculated; 
 and the one we have been examining is regulated upon this datum. 
 
 There is, however, a great difference between the pressure of 
 the steam in the boiler, and that to which the effective power of the 
 machine is due. It is evident that a part of the pressure will be 
 absorbed by the back pressure due to an imperfect vacuum, as well 
 as by the friction of the piston, and other moving parts, aud the 
 leakage and condensation in the steam passages. So that, taking 
 into consideration these various causes of loss, the effective force 
 may be estimated at -5 kilog. only, per square centimetre, in the 
 majority of engines, whilst it may reach, perhaps, -65 kilog. in the 
 most efficient. 
 
 The rule for calculating the power of low-pressure steam-engines 
 consists in — - 
 
 Multiplying the mean effective -pressure of the steam upon the piston 
 by the area of the latter, expressed in square centimetres, and the pro- 
 duct by the velocity in metres per second. 
 
 The result of this calculation will be the useful effect of the 
 eno-ine in kilogrammetres. 
 
 To obtain the horses power, this result must be divided by 75. 
 
 Thus, the diameter of the cylinder of a low-pressure non-expan- 
 sive steam-engine being -856, and its section 5755 square centi- 
 metres, if the effective pressure upon the piston is -63 kilog. per 
 square centimetre, and the velocity 1-1076 — 
 
 We have 
 
 •63 x 5755 x 11076 = 401567 k. m. 
 ^Whence— 
 
 4015-67 -=- 75 = 53-54 II. P. 
 
 But the effective pressure upon the piston is not always -63 
 kilog. per square centimetre ; it is more frequently below than above 
 this amount. It varies not only according to the power of the 
 machine, but also according to the state of repair. Thus, some- 
 times the effective pressure will not be more than -45 kilog. in 
 small engines, whilst in large, powerful ones, it may at times reach 
 •65 kilog. 
 
 Single-acting engines, such as are employed in mines, are of the 
 same dimensions as double-acting ones, but of only half the power. 
 Thus, the cylinder of a low-pressure steam-engine, of 50 horses 
 power, and only single-acting— that is to say, receiving the action 
 of the steam during the descent only of the piston — is exactly the 
 same as in a machine of 100 horses power, in which the steam acts 
 alternately on both sides of the piston. 
 
 In the following table, which applies to this kind of steam-engine, 
 we have given the diameters and velocities of the steam-piston 
 from 1 to 200 horses power. 
 
 TABLE OF DIAMETERS, AREAS, AND VELOCITIES OF PISTONS, IN LOW-PRESSURE DOUBLE-ACTING STEAM-ENGINES, WITH 
 THE QUANTITIES OF STEAM EXPENDED PER HORSE POWER. 
 
 
 Diameter 
 
 of 
 
 piston. 
 
 Area of Piston. 
 
 Length of 
 
 Number 
 vf 
 
 revolutions. 
 
 Velocity of 
 piston 
 
 Velocity of 
 
 piston 
 per minute. 
 
 Effective 
 I lie piston 
 
 per square 
 
 Weigh! .if 
 
 power. 
 
 Total. 
 
 Per 
 horse power. 
 
 lower per lioui 
 
 1 
 
 2 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 16 
 
 20 
 
 24 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 120 
 
 160 
 
 200 
 
 15 
 •21 
 ■30 
 •35 
 ■40 
 ■45 
 •49 
 •55 
 •61 
 •66 
 •73 
 •83 
 ■91 
 1-00 
 1-07 
 114 
 1-21 
 1-27 
 1-39 
 1-60 
 1-78 
 
 sq. m. 
 ■018 
 ■036 
 ■068 
 ■098 
 ■128 
 •159 
 •189 
 •240 
 •292 
 •346 
 •414 
 ■535 
 ■658 
 ■779 
 •903 
 1032 
 T138 
 1-264 
 1512 
 2-005 
 2-480 
 
 sq. cent. 
 •181 
 ■178 
 •171 
 •163 
 •160 
 •159 
 •157 
 •150 
 •146 
 •144 
 •137 
 •134 
 •132 
 •130 
 •129 
 •W'i 
 •126 
 •126 
 •126 
 •125 
 •124 
 
 •52 
 ■61 
 •76 
 •91 
 1-07 
 1-22 
 1-22 
 1-37 
 1-52 
 1-69 
 1-83 
 1-99 
 213 
 2-28 
 2-44 
 2-44 
 2-59 
 2-59 
 2-74 
 3-00 
 3-00 
 
 50 
 42 
 34 
 31 
 
 27 
 24 
 24 
 
 20 
 18 
 17 
 16 
 15 
 14 
 13 
 13 
 12 
 12 
 11 
 10 
 10 
 
 •85 
 •86 
 •90 
 •94 
 •96 
 •98 
 •98 
 1-01 
 1-02 
 1-02 
 1-04 
 1-06 
 1-07 
 1-07 
 1-06 
 1-06 
 1-04 
 1-04 
 1-00 
 1-00 
 1-00 
 
 51 
 52 
 54 
 57 
 58 
 59 
 59 
 60 
 61 
 61 
 62 
 64 
 64 
 64 
 63 
 63 
 62 
 62 
 60 
 60 
 60 
 
 kilog. 
 •49 
 •49 
 ■49 
 •49 
 •49 
 •49 
 •49 
 •50 
 •51 
 •52 
 ■53 
 •53 
 •54 
 54 
 •55 
 •56 
 •57 
 ■58 
 •59 
 ■60 
 •61 
 
 kilog. 
 
 38-81 
 38-77 
 38-77 
 38-72 
 38-72 
 38-64 
 3864 
 37-80 
 37-38 
 36-88 
 36-04 
 35-70 
 35-32 
 34-94 
 34-30 
 3431 
 3301 
 32-97 
 31-92 
 31-67 
 31-47 
 
 . 
 
 
 
 
 
 
 
 
 
 
 DIAMETER OF THE PISTON. 
 
 By means of the above table, we can, in a very simple manner, 
 determine the diameter and velocity of the piston of a low-pressure 
 
 double-acting steam-engine, supposing the steam to be of the 
 pressure of 1-17 atmospheres in the boiler, corresponding to a 
 column of mercury of 90 eentimAtws in height. 
 

 
 -Up lhc att« • 
 
 of th«- c.-iw l«> be <■• n«lru. '■ 
 * ..f |...l«.o. 
 
 f a low. 
 pnwor> .1 ubl* -arux.g aUam-eogio* of 25 horses p 
 
 In i(,. IheJ the ana 
 
 ■ 
 bona | - '"• 1" r 
 
 • for tho total 
 
 \ ' ■ ; GT 
 
 Thus, tii-- dun 
 
 ;riE». 
 and per minute, given in the 
 andu, 1 erally adopted ae 
 
 Um rr_- la and Inanu;. 
 
 number 
 
 piston, p«i minute, for 
 
 tli.- number va ■ '■ ll > H 
 
 . 
 ■ 
 : .. itter (he 
 
 oca the height of the 
 [uently, mu.b ihorter for the 
 - 
 
 rare by 
 ■ 
 
 make a few .- mioate 
 
 iti« i lui.i Bowd 
 
 I . work 
 
 i of (be 
 
 i tin' ri-'jiiiri-.l power. 
 
 mil by « very 
 
 ■ 
 
 proper- 
 
 1 : I'M 111-, 
 
 uiil 
 
 t phi 
 
 - uditure |nr : r hour. 
 
 i • - the expeajas- 
 
 i araall 
 a. rt'ul 0O«a — tbf reason of « 
 
 I I J boraea power, th,e ezpenditore of* 
 ■ r per h'-ur : wtulat for an 
 the expenditure on!;. 
 for a like power in tl.- 
 
 bta of the steam have been ea 
 from tli. | uila: — 
 
 W A x S x to x 3 N x 60. 
 •rw power j 
 
 u>, the weight of a cubic metre of steam at the pressure en.; 
 N, the Dumber ol 
 
 ■ .1 not ban I leiatkm the una of -• 
 
 from leakage and onnrtonaatlon in the steam ] 
 
 passages, w hi. h i- generally estimated at one tenth of Um 
 expenditure, aa thia Item should evidently enter into the caleula- 
 ipecting the boiler. 
 
 BTxaavnna ami ta- 
 Tho section of the pipe which conveys the steam to the i 
 
 as w. II aa that of the iniro.i.- 
 
 ■ the piston. 
 Wh. ■ ii.it the diameter of the steam-pip- 
 
 Bfth of that of the ej 
 Wo i remark, that tl • of the 
 
 ■ 
 of thia that, in locomotive ■ 
 :i i- somatii nth or a ninth of th.it of the 
 
 cylinder, ma time (be preaaure of thi 
 
 more, in 
 
 AIK-I'I'MP AM 
 
 The stroke of the air-pun I of the 
 
 be saine number of strokes. 
 • a quantity ol 
 ■ 
 
 l> in. ; and the 
 
 - 
 ibic in., it followa that the pump ■ J a littlo 
 
 more ;!. I the volume ••« ut oul bj tin 
 
 of lie- 
 angina. 
 
 1 ar.a of tie ! of the 
 
 pump, and in length ia abonl :yis,at 
 
 • r \ ari. * 
 . vv.it. r. it will be Well 
 to know bow I 
 
 To i;. I uswaf : — 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 Rule. — Take the excess of the temperature of the steam over that 
 of the injected water, and, after adding 550 to it, multiply it by the 
 weight of sltam to be condensed, and divide the product by the differ- 
 ence of temperature between (lie discharged and the injected water. 
 The quotient will be the weight of cold water to be injected. 
 
 Thus, let w represent the weight of the steam to be condensed; 
 /, its temperature ; W, the weight of the cold water to be injected 
 into the condenser ; t', its temperature ; and T, that of the water 
 discharged : — 
 
 We have 
 
 w (550 + * — T) 
 
 W 
 
 If we make w 
 we shall have 
 
 W = 
 
 T — t' 
 16, V — 12° cent., T = 38°, and t — 105°, 
 
 26-16(550 + 105" — 38°) 
 
 38° — 12° 
 
 Whence, W =; 621 kilog. or litres, for the expenditure per 
 minute of cold water in the condenser. 
 
 That is to say, the quantity of water to be injected into the con- 
 denser should, in this case, be about 24 times the weight of the 
 steam expended. 
 
 If the discharged water were of the temperature of 55°, the cold 
 water remaining at 12° — 
 
 We should then have 
 
 26-16(550+ 105° — 55°) 
 55° — 12° 
 Whence — 
 
 W = 365 kilog. or litres. 
 
 That is to say, that in the last case the water injected would not 
 be more than 14 times the steam expended. 
 
 But it is to be remarked, that in this case the force of the steam 
 in the condenser, at a temperature of 55°, is equal to a column of 
 mercury of 12-75 centimetres in height; whilst, in the first case, it 
 would only be equal to a column of 5-5 cent. There is, therefore, 
 an advantage in employing sufficient injection-water to produce the 
 lower of the two temperatures. 
 
 From the preceding results, we may deduce what follows : — 
 
 First, That the stroke of the air-pump piston, in low-pressure 
 double-acting steam-engines, is ordinarily equal to half the stroke 
 of the steam-piston. ^ 
 
 Second, That the diameter-of the air-pump piston is equal to 
 about two thirds of the diameter of the steam piston ; and, conse- 
 quently, its area is about half that of the latter. 
 
 Third, That the effective displacement of the air-pump piston — 
 that is, the cubic contents of the cylinder generated by the disc of 
 the piston — is equal to an eighth, or at least a ninth, of the contents 
 of the cylinder generated by a double stroke of the steam-piston. 
 
 Fourth^ That the capacity of the condenser is at least equal to 
 that of the air-pump. 
 
 Fifth, That the sectional area of the passage communicating 
 between the condenser and air-pump is equal to one-fourtli the area 
 of its piston. 
 
 Sixth, That the quantity of cold water to be injected into the 
 condenser varies according to its temperature, and to the tempera- 
 ture of the water discharged. 
 
 Seventh, That this quantity is equal to 24 times tht weight of 
 
 steam expended by the cylinder, where the mean temperature of 
 the cold water is 12°, and that of the water of condensation 38°, 
 which are generally what exist in low-pressure double-acting 
 engines. 
 
 COLD-WATER AND FEED PUMPa. 
 
 The capacity of the cold-water pump should be the 24th or 18th 
 of that of the steam cylinder. The capacity of the feed or hot- 
 water pump should be the 230th or 240th, at least, of that of the 
 steam cylinder. 
 
 HIGH-PRESSURE EXPANSIVE ENGINES. 
 
 Let the following dimensions be given for an engine analogous 
 to that which we have just described : — 
 
 Diameter of the cylinder, = -275 m. 
 
 Stroke of the piston, = - 680 m. 
 
 Area of the piston, = -0594 square m. 
 
 Number of double strokes per minute, = -40 . 
 
 Let us suppose, in the first place, that when the steam reaches 
 the cylinder, its pressure is equal to 5 atmospheres, and that it is 
 cut off during three-fourths of the stroke ; that is to say, that tho 
 cylinder only receives the steam during the first quarter of the 
 stroke. 
 
 This pressure of 5 atmospheres is equal to 5 x 1-033 = 5-165 
 kilog. per square centimetre. Consequently, the total pressure 
 exerted upon the surface of the piston is — 
 
 5-165 x 594 sq. cent. = 3068 kilog. 
 
 And as with this pressure the piston passes through a space 
 equal to one-fourth of its stroke, or 
 
 ■680 -7- 4 = -170 m., 
 it is capable, theoretically speaking, of transmitting an amount of 
 force expressed by 
 
 3068 x -17 = 521-56 kilogiammetres. 
 
 Next, dividing the length, -51 m., or the remaining three-fourths 
 of the stroke, into an even number of equal parts — as four, for 
 example — each of these parts will be equal to 
 
 — = -1275 m. 
 
 4 
 
 Now we know that, according to Mariotte'a law, the successive 
 volumes of a given quantity of any gas are in the inverse ratio of 
 their tension or pressure, provided the gas is in the samo condition 
 throughout. This principle may be regarded as quite true in steam- 
 engines, because the expansion is never carried very far, and as tho 
 strain passes through the cylinder with great rapidity, and is con- 
 tinually being renewed, after a certain time and when the cylinder 
 has become warm, its temperature is very little below that of the 
 steam itself, and the latter suffers no appreciable change in passing 
 through it. Putting P for the pressure, 3068 kilog., as found for 
 the first quarter of the stroke, we may state the relations of the 
 volumes and pressures in the following manner; that is, at the 
 points, 1, 2, 3, 4, 5, of the stroke, or for the successive spaces, 
 •170 hi., -295 m., -425 m., -5525 m., -680 m. 
 
IM 
 
 
 TV» rurreapuadaaf pwwii will be— 
 
 - 
 of leaa*-, 
 
 3068 a, 1761 k, 
 
 ■«««*t to Simpson'* method, wt hare 
 
 TV. ... WUW iii imi i i h ii i i, • - »"»+ W7 » *«» 
 
 T-t~ U» HMIIHIlUl^ i»uim .' tXl»= MM 
 
 r«f iim ta» f ■■-■~ «f tW «■»■ 1(1*14+ M 
 
 T«tal, ITIil 
 
 Taking the third of this quantity, and multipl; 
 re ahall have the work pun out during the cut-otT. Thus — 
 
 = 727-64 k. m. 
 
 Adding to thi-i 621 56 k. m., the work given out before tin- cut- 
 
 off, we •hall have ll ■ i by the ateam 
 
 during ' '»■ piaton — 
 
 = 1241*2 k. m. 
 . thia the effect of the atmospheric pressure, 
 • :i throughout the stroke, and 
 . il equal to 
 
 Ik. x 594 sq. c x -68 m. = 417 25 k. m., 
 
 ; ]),•• |,'|. t. ill 
 
 m., 
 nearly, ; - ; and as th> | 
 
 per minute, th<- effective force per minute becomes 
 in. ; tiiat b, 56660 kili-grainiues, raised one 
 
 -. as well as of most other expansive 
 ■tsssavengines, will b* obtaiaed in a much more siru|>lc and leas 
 -. bj taking advantage of the following tab 
 
 TABI.F. OF Tli: Kll.'H;i:\MMiTi:i>. GIVES OUT WITH VARIOUS 1'D.l.: a il BIO 
 
 I . Al:l"l - 1 .. 
 
 
 
 
 Fore* pTro oat, eurrcipaadiQf with thr prewar* of 
 
 
 
 V4«a» 
 
 
 
 
 
 
 
 
 
 
 l 
 
 11 
 
 1 
 
 t| 
 
 l 
 
 4 
 
 i 
 
 6 
 
 
 • :i sat), 
 
 •• . , -i 
 
 ■1 
 
 f ■ q i.. 
 
 ■H BJ '.. 
 
 ■tSMS] Bi 
 
 »!n. •; h. 
 
 >■■ . • 
 
 •»t»c M*lnm 
 
 k. si. 
 
 k. m. 
 
 km. 
 
 k. m. 
 
 k. DJ. 
 
 turn. 
 
 turn. 
 
 k. m. 
 
 
 
 
 
 
 
 41333 
 
 
 
 
 
 
 
 
 • 
 
 
 ■ 
 
 
 
 
 
 
 " 
 
 
 
 
 
 
 
 84174 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1-71 t 
 
 
 
 
 
 
 
 119978 
 
 
 
 
 
 
 
 
 
 116819 
 
 
 
 
 4 1 57 i 
 
 
 
 
 
 194799 
 
 
 
 
 
 54918 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 
 
 
 
 
 71976 
 
 
 
 . 
 
 
 
 
 
 
 
 
 
 1 17946 
 
 
 
 
 
 6S9I9 
 
 " 
 
 1011 I" 
 
 
 161710 
 
 450 
 
 
 - 
 
 617 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 
 
 
 
 67410 
 
 
 
 
 161784 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ' 
 
 111796 
 
 
 167694 
 
 
 
 43619 
 
 
 
 
 
 
 1704 18 
 
 
 
 
 
 79190 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 7 11-7 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 121764 
 
 
 189646 
 
 
 
 
 
 77010 
 
 99 1 1 2 
 
 193916 
 
 
 • 
 
 
 
 
 
 
 
 194616 
 
 
 • 
 
 
 
 
 
 
 94479 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 96417 
 
 
 
 ■ 
 
 
 
 
 
 81117 
 
 97341 
 
 
 
 1 ,|, -j 
 
 
 
 
 
 
 98941 
 
 
 
 
 
 
 
 
 
 •"ill 
 
 
 
 198338 
 
 9-25 
 
 
 
 
 
 
 
 
 
 9-50 
 
 
 
 
 
 
 
 
 - 
 
 
 
 
 
 
 
 
 
 
 l 
 
 
 
 68254 
 
 
 
 
 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 According to this table, if we have, to calculate the force acting 
 upon the piston in this engine, in the same circumstances, we must, 
 in the first place, ascertain the original volume of the steam intro- 
 duced into the cylinder during the first quarter of the stroke of the 
 piston. This volume is equal to 
 
 •0594 x -17 = -010098eubie metres. 
 
 Now it will be seen from the table, that the force given out when 
 a cubic metre of steam, of a pressure of 5 atmospheres, expands to 
 four times its original volume, is equal to 
 123290 k. m. 
 
 Consequently, that corresponding to a volume of -010098 cubic 
 metres will be — ■ 
 
 123290 x -010098 = 1245 k. m., 
 
 And deducting from this the atmospheric pressure, which resists 
 the motion of the piston, wo have 
 
 1245 — 417 = 828 k. m., 
 a quantity which differs very little from that obtained by the more 
 tedious calculation. Thus, the calculation for determining the 
 effective power of a steam-engine, of which we know the diameter 
 and stroke of the piston, the pressure of the steam, and the amount 
 of cut-off, reduces itself to the following rule : — 
 
 Rule. — Multiply the area of the piston by the portion of the length 
 of the stroke, during which the steam acts with full pressure, and you 
 will determine the volume of steam expended. Multiply this volume 
 by the amount of kilogrammetres in the table, corresponding to the 
 pressure of the steam and to the final volume, and then deduct from 
 the product the amount, in kilogrammetres, of the atmospheric pressure 
 opposed to the piston during the entire stroke, and the result will be 
 the theoretic amount of force, in kilogrammetres, given out by the 
 steam during a single stroke of the piston. 
 
 A MEDIUM-PRESSUKE CONDENSING AND EXPANSIVE STEAM- 
 ENGINE. 
 
 Let the- following data be assumed : — 
 
 The diameter of the steam-cylinder = -330 m. 
 
 The stroke of the piston = -650 m. 
 
 The diameter of the air-pump = -180 m. 
 
 The stroke of its piston = -325 m. 
 
 The diameter of the feed-pump . . . . = -035 m. 
 The stroke of its plunger = -235 m. 
 
 It follows, from these dimensions, that we shall have — 
 
 The area of the steam-piston = 855-30 sq. cent. 
 
 The area of the air-pump piston . . . = 254-47 " 
 The area of the feed-pump = 9.62 " 
 
 And for the displacement, or volumes of the cylinders generated 
 by the pistons — 
 
 That of the steam cylinder . . . . = 55-594 cubic decim. 
 
 That of the air-pump = 8-270 " 
 
 That of the feed-pump = -226 " 
 
 We shall suppose that, when the engine is in regular working 
 condition, the pressure of tho steam is 31 atmospheres; and we 
 must ascertain what is the actual force given out, supposing the 
 steam to be cut off during three-fourths of the stroke of the piston. 
 
 That is to say, that the steam is admitted into the cylinder only 
 during a quarter of the stroke, which corresponds to -1G25 m. 
 
 Since the sectional area of the cylinder is -0885 m., the volnmo 
 of steam expended during a fourth of the stroke will be equal to 
 •0885 x -1G25 = -0139 cubic metres; or, 
 13-9 cubic decimetres. 
 
 Now, according to the table of the amounts of force given out by 
 the steam at various pressures, it will be found that the force due 
 to a cubic metre of steam, of an initial pressure of 3j atmospheres, 
 when allowed to expand to four times its volume, is equal to 8G303 
 kilogrammetres. As the table does not give the actual amount foi 
 3| atmospheres, it may be taken by adding together that for 2' 2 
 and 1 atmospheres. Thus — 
 
 61645 + 24658 = 86303 k. m. 
 
 We have, therefore, in the present case — • 
 
 ■0139 x 86303 = 11996 k. m., 
 as tho force due to a single stroke of the piston. 
 
 From this quantity, however, .we must deduct the back pressure 
 due to the imperfect vacuum in the condenser. This back pressure 
 is, in the generality of cases, equal to about -27 kilog. per square 
 centimetre, when the temperature of the water of condensation is 
 about 65° cent. 
 
 Allowing this to be the case in the present example, we shall 
 have to deduct from the preceding result the action of this back 
 pressure upon tho whole surface of the piston, and during the entire 
 stroke. This is 
 
 ■27 x -0885 x -65 x 150-1 k. m., 
 
 We have, consequently, 
 
 ,1199-6 — 150-1 = 1049-5 k. m., 
 for the actual force given out by the piston during a single stroke ; 
 and if this engine works at the rate of 42 revolutions per minute, 
 which supposes the velocity of the piston to be -9 m. per second, 
 wo shall find that the mechanical effect per minute will be equal to 
 1049-5 x 84 = 981588 k. in ; or, 
 881598 -f- 4500 = 1959 horses power. 
 
 It is well known, however, that this amount is far from being all 
 transmitted by the first-motion shaft, for a portion is absorbed in 
 overcoming the friction of the various moving parts of the engine, 
 and there are also other causes of loss. 
 
 If we reckon that the force which is really utilised is not more 
 than four-tenths of that theoretically due to the steam, in which 
 case we must suppose that six-tenths are completely lost, we shall 
 have for the effective force transmitted to the first-motion shaft— 
 
 19-59 x -4 = 7-84 horses power; 
 or almost 8 horses power, of 75 kilogrammetres each. 
 
 If it is desired to know the quantity of fuel consumed per hour 
 in producing this mechanical effect, we may remark, that a cubic 
 metre of steam, at a pressure equal to 3 J atmospheres, weighs 1 -85 1 8 
 kilog. ; and at a pressure of 4 atmospheres, it weighs 2-0291 kilog. 
 
 Now, although we have supposed the pressure in the cylinder to 
 be 3| atmospheres, we, nevertheless, allow that it will be conside- 
 rably more in the boiler, to cdrnpensate for the leakage in the valve- 
 easing, passages, and valves. 
 
 Taking 4 atmospheres as the pressure in the boiler, it will be 
 found that the weight of steam expended for each single stroke of 
 the piston is — 
 

 hit: rn.v : 
 
 •oi» x 9<*i = -©»i i 
 
 •Atl prr • 
 
 I kflofl. 
 
 Frwn 
 
 .... that Uio quantity I 
 
 I ;• . < 1 . <; ■ h"ur. 
 
 Ad<1 • 
 \\ 
 
 Jill -4- 7-84 = 3 1 
 
 -. pa? li.nir. 
 npleto the r en, we add u. 
 
 - 
 of dilVcrriit kinds: — 
 
 . \\l I M.IN M> WITH oil 
 
 i ATMOSPHERES I.N TUJ >D Al' 
 
 
 
 
 
 
 '■ 
 
 
 
 Su..k. 
 
 »i i-.'.^. 
 
 • 
 
 rotlmj off 
 
 •Irak*. 
 
 nj ulT ti uatvfuunh. 
 
 
 
 
 
 
 
 
 
 
 
 p.l^O. 
 
 I-T K« H.J. 
 
 •■*' ■■"""•• 
 
 _. 
 
 1 
 
 
 
 
 
 
 
 
 
 
 ■ 
 
 
 i-' 
 
 
 ■ 
 
 
 
 
 
 
 ,.i.:..u. 
 
 hiTW uiiwcr. 
 
 
 ■ 
 
 
 Ml 
 
 
 
 ML 
 
 ■q. mil. 
 
 kii «. 
 
 
 -\ rrnU 
 
 cent. 
 
 Ular. 
 
 1 
 
 
 
 
 10 
 
 
 94-90 
 
 1 1 
 
 1 18 
 
 10 
 
 
 
 
 
 
 so 
 
 too 
 
 
 19 
 
 i 6 
 
 l 1 
 
 
 I 
 
 
 
 
 
 1 IS 
 
 
 
 194 
 
 18 
 
 
 
 
 
 
 
 
 
 SI 
 
 198 
 
 •ji 
 
 
 8 
 
 
 
 337 
 
 
 1J7 
 
 
 38 
 
 11 '. 
 
 - 
 
 
 
 
 
 31-7 
 
 ' 
 
 119 
 
 91-36 
 
 
 
 
 
 IJ 
 
 
 
 BO-0 
 
 41 
 
 li j 
 
 91-18 
 
 38 
 
 
 SO 
 
 
 
 110 
 
 
 28-6 
 
 ■I.. 
 
 mi 
 
 
 19 
 
 *7 
 
 
 
 
 190 
 
 no 
 
 
 
 hi 
 
 
 10 
 
 81 
 
 81 
 
 
 
 
 
 
 64 
 
 99 
 
 
 49 
 
 78 
 
 84 
 
 
 
 
 ISO 
 
 
 rn 
 
 
 
 69 
 
 79 
 
 
 
 
 
 
 
 69 
 
 71 
 
 18-64 
 
 
 68 
 
 38 
 
 
 
 
 
 
 
 - ■ 
 
 
 67 
 
 • i 
 
 
 
 
 170 
 
 
 
 
 70 
 
 17-98 
 
 69 
 
 
 43 
 
 
 
 
 1 10 
 
 
 7J 
 
 68 
 
 17-99 
 
 66 
 
 58 
 
 
 
 
 
 
 sa g 
 
 
 87 
 
 17-10 
 
 7J 
 
 .,i 
 
 60 
 
 
 
 
 16 ■ 
 
 
 85 
 
 67 
 
 16-69 
 
 84 
 
 66 
 
 66 
 
 
 rABLK OF PROPORTIONS OP MEDIUM l ^ IT 11 TWO 
 
 CYLINDERS OH WOO} '■ - BYSTJ M; PBJ 
 
 
 >r* in 
 
 Arei of jnitoni id square centimctroi. 
 
 Stroke of puloni in n>. 1 
 
 
 
 
 
 
 
 
 
 
 
 
 4. 
 
 D 
 
 
 IVr ltor»- j*i*rr. 
 
 t. 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 a. 
 
 A. 
 
 " 
 
 A. 
 
 
 
 
 4 
 
 I«, 
 
 
 
 
 60 
 
 l i : 
 
 
 ■90 
 
 
 
 |i 
 
 ■ 
 
 
 
 17 
 
 160 
 
 ■67 
 
 •:mi 
 
 
 
 91 
 
 
 
 1 184 
 
 
 1 II 
 
 - 1 
 
 i i i 
 
 300 
 
 
 
 
 416 
 
 
 II 
 
 188 
 
 
 
 
 IJ 
 
 
 46 
 
 491 
 
 
 40 
 
 
 ■89 
 
 1-10 
 
 97-a 
 
 16 
 
 
 
 816 
 
 •J 1 .' 1 
 
 88 
 
 i . 
 
 
 1-90 
 
 
 
 
 
 
 9990 
 
 
 n i 
 
 ■''7 
 
 1-80 
 
 
 
 
 • 
 
 
 
 33 
 
 118 
 
 
 1-30 
 
 
 
 
 
 
 8117 
 
 80 
 
 108 
 
 
 
 91-6 
 
 
 
 
 1076 
 
 
 
 98 
 
 1-Jil 
 
 1-80 
 
 •Jl <i 
 
 
 
 '- 
 
 
 
 96 
 
 88 
 
 1-97 
 
 i 70 
 
 89-1 
 
 
 
 71 
 
 1 194 
 
 
 
 >7 
 
 1-97 
 
 1 7(1 
 
 L'J 1 
 
 
 41 
 
 
 
 ins 
 
 
 
 
 I B0 
 
 
 
 
 
 
 
 l£«i 
 
 
 i ■ 
 
 
 
 
 
 
 
 ■ 
 
 26 
 
 34 
 
 i ' 
 
 
 
 
 51 
 
 
 3048 
 
 
 
 -i 
 
 i 60 
 
 
 
 
 
 
 
 
 
 
 i VI 
 
 •j in 
 
 18*0 
 
 
 
 104 
 
 
 
 
 
 1 .7 
 
 9-10 
 
 1- 8 
 
 110 
 
 
 
 
 
 
 84 
 
 i 67 
 
 I i" 
 
 i- B 
 
 
 
 II 1 
 
 B019 
 
 
 
 
 1-67 
 
 9-10 
 
 
 
 05 
 
 118 
 
 
 
 
 84 
 
 i .: 
 
 •J in 
 
 18-6 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 CONICAL PENDULUM, OR CENTRIFUGAL GOVERNOR. 
 
 The centrifugal ball-governor is compared, in physics, to a 
 simple pendulum, the length of which is equal to the distance of 
 the point of suspension from the horizontal plane passing through 
 the centres of the balls ; and the duration of an entire revolution of 
 the ball-governor is equal to that of a completo oscillation of the 
 pendulum. 
 
 The formula for determining the vertical height or the distance 
 of the point of suspension above the plane of the balls is, conse- 
 quently, the same as that employed to find the width of a pendu- 
 lum, of which we know the number of oscillations. It may be 
 reduced to the following rule: — 
 
 Rule. — Divide the constant number, 89,478, by the square of the 
 number of revolutions per minute. The quotient will give the height 
 in centimetres. 
 
 Example. — What is the vertical height or distance of the point 
 of attachment, from the horizontal plane passing through the 
 centres of the balls of a governor, revolving at the rate of 40 turns 
 per minute? 
 
 We have 40 s = 1600, 
 
 and 89478 -4- 1600 = 56 centimetres, 
 
 for the height sought. 
 
 With this rule, it will be easy for us to calculate the heights of 
 conical pendulums, from the velocity of 25 revolutions per minute, 
 to that of 67 ; and within these will be found the rates of combi- 
 nations more generally met with iu practice. We have given 
 them in the following table, adding a column, which gives the 
 difference iu height for each revolution. And as the angle which 
 the arms of the governor make with the spindle is generally one 
 of 30°, when the balls are in a state of repose, or are going at 
 their minimum velocity, we have given, iu the fifth column of the 
 table, the lengths of these arms, from their point of suspension to 
 the centres of the balls, assuming the angle of 30°, and making 
 them to correspond with the number of revolutions given in the 
 first column. 
 
 In calculating the lengths of the arms, we have employed the 
 following practical rule : — 
 
 Rule. — Divide the cdnstant number, 103,320, by the square of the 
 number of revolutions per minute, and the quotient will be the length 
 in centimetres. 
 
 Example. — Assuming the angle to be 30°, what should be the 
 length of the arms of a conical pendulum, making 37 revolutions 
 per minute? 
 
 We have 3V = 1369. 
 
 mi. 10-3320 
 
 Then — ■ ,^» = 75 ' 46 centimetres, 
 
 13o9 
 
 for the length of the arms of the pendulum, or the diameter of the 
 
 circle described by the balls. 
 
 It is evident, that if, on the other hand, the length of the arms, 
 with this angle of 30°, is known, the number of revolutions which 
 the balls make in a minute, will be found by dividing the number, 
 103,320, by the length of the arms expressed in centimetres, and then 
 extracting the square root of the quotient. 
 
 The weight of the balls, according to the resistance they have 
 to encounter, is as important to determine as the length of the 
 
 suspending-arms, in order that the governing action of the pendu- 
 lum may be sufficiently powerful and quick. It often happens, in 
 badly designed engines, that the governor produces no effect, be- 
 cause, the length of the suspending-arms is not proportionate to 
 the velocity, or because the weight of the balls is not proportionate 
 to the resistance to.be overcome. 
 
 We have considered that it would be a great convenience to 
 engineers and artisans to possess a table, showing at sight the ve- 
 locities and corresponding lengths, for the conical pendulums, or 
 ball-governors, generally employed in steam-engines, so as to 
 enable them to determine with certainty the exact proportions to 
 be given thotn, in relation to their spindles and driving-gear. 
 When these points are determined, the weights of the balls may be 
 easily adjusted. 
 
 TABLE RELATIVE TO THE DIMENSIONS OF THE ARMS AND TO THE 
 VELOCITIES OF THE BALLS OF THE CONICAL PENDULUM OR 
 CENTRIFUGAL GOVERNOR. 
 
 Number of 
 Revolutions 
 per Minute. 
 
 Square of the 
 Velocities. 
 
 Length of 
 Pendulum in 
 CentimetreR. 
 
 Difference of 
 
 Length for one 
 
 Revolution. 
 
 Length of Amu 
 
 with an Angle 
 
 of 3u°. 
 
 
 
 Cent. 
 
 Milt. 
 
 Cent. 
 
 25 
 
 625 
 
 143-1 
 
 108 
 
 16 
 
 26 
 
 676 
 
 132-4 
 
 96 
 
 153 
 
 27 
 
 729 
 
 122-7 
 
 86 
 
 142 
 
 28 
 
 784 
 
 114-1 
 
 77 
 
 132 
 
 29 
 
 841 
 
 106-4 
 
 70 
 
 123 
 
 SO 
 
 900 
 
 99-4 
 
 63 
 
 116 
 
 31 
 
 961 
 
 93-1 
 
 57 
 
 107 
 
 32 
 
 1024 
 
 87-3 
 
 52 
 
 101 
 
 33 
 
 1089 
 
 82-1 
 
 48 
 
 95 
 
 34 
 
 1156 
 
 77-4 
 
 44 
 
 89 
 
 35 
 
 1225 
 
 73-0 
 
 40 
 
 84 
 
 36 
 
 1296 
 
 69-0 
 
 37 
 
 80 
 
 37 
 
 1 369 
 
 65-3 
 
 34 
 
 75 
 
 38 
 
 1414 
 
 61-9 
 
 31 
 
 71 
 
 39 
 
 1521 
 
 58-8 
 
 29 
 
 68 
 
 40 
 
 1600 
 
 55-9 
 
 27 
 
 64 
 
 41 
 
 1681 
 
 53-2 
 
 25 
 
 61 
 
 42 
 
 17 64 
 
 50-7 
 
 23 
 
 68 
 
 43 
 
 1849 
 
 48'4 
 
 22 ■ 
 
 56 
 
 44 
 
 1936 
 
 46-2 
 
 20 
 
 63 
 
 45 
 
 2025 
 
 44-2 
 
 19 
 
 51 
 
 46 
 
 2116 
 
 42-3 
 
 18 
 
 4 'J 
 
 47 
 
 2209 
 
 40-5 
 
 17 
 
 47 
 
 48 
 
 2304 
 
 38-8 
 
 16 
 
 45 
 
 49 
 
 2401 
 
 37-3 
 
 15 
 
 43 
 
 50 
 
 2500 
 
 35-8 
 
 14 
 
 41 
 
 51 
 
 2601 
 
 34-4 
 
 13 
 
 40 
 
 52 
 
 27n4 
 
 33-1 
 
 12 
 
 38 
 
 53 
 
 2809 
 
 31-8 
 
 12 
 
 37 
 
 54 
 
 2916 
 
 30-7 
 
 11 
 
 33 
 
 55 
 
 3025 
 
 29-6 
 
 10 
 
 34 
 
 56 
 
 813B 
 
 28-5 
 
 10 
 
 35 
 
 57 
 
 3249 
 
 27-5 
 
 9 
 
 32 
 
 58 
 
 3364 
 
 26-6 
 
 9 
 
 3) 
 
 59 
 
 3481 
 
 25-7 
 
 8 
 
 30 
 
 60 
 
 3600 
 
 24-8 
 
 8 
 
 29 
 
 61 
 
 3721 
 
 24-8 
 
 8 
 
 28 
 
 62 
 
 :;s44 
 
 23-3 
 
 7 
 
 27 
 
 63 
 
 3969 
 
 22-5 
 
 7- 
 
 26 
 
 64 
 
 4096 
 
 21-9 
 
 7 
 
 25 
 
 65 
 
 4225 
 
 21-2 
 
 6 
 
 24 
 
 66 
 
 4356 
 
 20-5 
 
 6 
 
 24 
 
 67 
 
 4489 
 
 19-9 
 
 6 
 
 ' 23 
 
 68 
 
 4624 
 
 19-3 
 
 
 23. 
 
 Note. — With an angle of 30°, the centrifugal force is the same for 
 all lengths of pendulum. 
 
 This table may also be consulted in the case of single-armed pendu- 
 lums, which are occasionally employed, instead of centrifugal gover- 
 
the rn actical it. \> <:iir 
 
 CHAPTER XI. 
 
 OBLIQD i: PROJ EJ3TI0 
 
 AmxATta* or iruf 10 thi deliseatios or ah oscillatisi; stiam < vi-isdes. 
 II \TK M.I. 
 
 tr>-»i drawing, (he plane* .. o which 
 
 the ob. ' M to be 
 
 |nr»:'. ' which it folio 
 
 : the machine it 
 
 »;■!«.•»• 
 
 thai til cannot Ik- |«imllrl to II planes. 
 
 ju.ntly, 
 
 ■ vidently appli- 
 li i-., however, 
 
 l parallel tn t 1 - 
 portions and ilinif n- 
 
 • the production of tlm oblique 
 
 - 
 
 ■ both the liori- 
 
 nt this nut. in Bg. i. as placed with ita base 
 parallel to an auxiliary horizontal pit I .1 bj the due, 
 
 .; /. C </ t f. 
 
 ■ make the vertical projection of this j>ri- • ; 
 I'lano, parallel to one of the fact i. nr t.i a <l. we should, in 
 bare the projection of the edgi a, 
 
 he lii f inb : 
 
 In iii.ii aotaal position 
 
 the nut ; and it is, therefore, tin- base Une of the two 
 
 I is, we shall suppose, the angle, i. <> i.', 
 
 *itii tin. base line nf tin- actual drawing in hand, which angle, 
 
 amount of inclination of the top ami bottom 
 
 prism, with the actual horizontal plane; whilet the angle, 
 
 ■ mod by the perpendiculars, drawn tn each of the lines 
 
 amount nf inclination of tin' 
 
 of tin- prism with regard to the vertical plane. After 
 
 nr.liT In nb'ain III.' [mints, ,l',h\r\it, 
 
 nd Lit of tin- point, -., on the line, t.' t', the 
 i ./...mi. I b g or eg, derived Iron li^'. I. D 
 nlara tn tin. Una, l't", through each of the points, .i'.V,. ■'../', 
 »n«l limiting them by tin- In. -, ,1' ,ft an. I a* ./\ Bg, •_'. parallel tn Ihe 
 
 upon the ainiiinry ptane, parallel to one of tin Winn 
 
 - ■■! ii..- urn brouided, or terminated by s - 
 
 .- already seen (186), Ita eqn- 
 
 tmir Is 
 
 if tin. two projeotioni 
 
 * : ... I. 1 ; 
 
 fig. 1 giving the widths, tin- distances of each of the poinl 
 
 1 lino, a ,/, whk Dgfa tin. centre, o, :. 
 defining tin- *• - ■ ■( tin- varl 
 
 the horizontal plane, 
 'I'.. this in. I, through snj 
 
 ; tin- horizontal |ir..j. 1 1 
 line, and througb tin- correapondin( ' Bg. :!. draw a 
 
 conple nf horizontal linos, cutting ii The 
 
 Deration is performed with regard to ,l,\r, 
 
 which an- projected in /- , • i. Tne wholi 
 
 consists, therefore, in drawing vertical linos through each of tlm 
 
 i'i ii;;. 1, ami horizontal lines through Ihe corresponding 
 points in Bg. -. Tin intersections of tin 
 tions of tin- extremities of each ..t tin- • Igea in tin- oblique view, 
 
 If it is wished tn obtain t! ■ if tin- eirculai 
 
 with minute exactness, it will : to determine, s 
 
 three points in each an-: and as we have the extremities already, 
 we ..ill) require now to find tin- middle of each. It i» tin 
 tin- circle representing tin- central opening nf tin- nut. It*, oblique 
 projection Men are 
 
 obtained by tin' projection nf the two diameters perpendiculsr to 
 inn- another, one of which, m n, is parallel to the vertical pis 
 
 lalter In magni uently, giving tin- tranavemo 
 
 axis of the ellipse, while) Ihe other is inclined ami foreshortened, 
 
 ■ :i\is. 
 
 431. In general, tin- oblique projection of any circle is always an 
 ellipse, tin' transverse axis nf which is equal tn tin' actual diameter 
 of tin- I'iivli'. whilst tin- conjugate .i\is is variable, according tn the 
 Inclination or angle which the plane nf tin' circle makes with one 
 of the pi '"ii. The application of this principle will 
 
 b The two fust nf tins,- figures ropro- 
 
 s. iii ii..- horizontal ami vertical projections made upon the auxiliary 
 plains i. fa portion of the cylindrical rod, a, nf tin- piston, n. w..rk- 
 ing in tin- oscillating steam-cylinder, c; ami the last. fig. ". is tlm 
 oblique projection nf this part nf tin- piston-rod npon lbs vertical 
 Tin:.' tn that <i( tlm drawing. 
 
 It will In- remarked, that tin- upper part nf the fragment nf the 
 r- ■■ 1 being limited by a plan.-. /. /, perpendicular tn its axis, 
 i 'lips.., tin- transversa axis,/. ./. nf which is ■ 
 A /, whll axis. /'/,', is equal tn tlm projection •■! this 
 
 line, A /. i.n liu r . ". Tlm cylindrical fillets, r .«, i u, dtc, nf (his rod, 
 an- projected obliquely, as similar ellipses, of whi I 
 ere apparent For tlm tome, or ring, which is comprised i 
 
 the*) two fillets, tl blique projection is a curve, which results 
 
 from tlm Int er se c tion nf an elliptical cylindi i 
 
 which are horizontal, ami tangent tn tin- external surf; f tlm 
 
 turns. If, ih. i. ].. determine this eurve witti 
 
 n, we must use the verj same method adopted in determining 
 the shadow propel of tlm external surface nf the ■■ i 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 155 
 
 practice, however, when the drawing is on but a small scale, we 
 may content ourselves with determining the principal points in the 
 curve, by projecting first the point, v, situated upon the middle of 
 tne diameter, y y, of the torus, and drawing through it the line, 
 v 1 v\ equal to the diameter ; and, secondly, drawing the horizontal 
 lines touching the external contour of the torus in the points, z, z', 
 fig. 6, over to z a , z 3 , upon the axial line, I' o', fig. 7 ; then draw an 
 ellipse with these two lines, v 1 v* and z J z a , for the transverse and 
 conjugate axes respectively. The key, D, which passes through 
 the rod, a, being rectangular in section, is projected in fig. 7, by 
 a couple of rectangles, as indicated by the dotted projection lines. 
 
 422. Proceeding upon these principles, we can make obliquo 
 projections, in a very simple manner, of various objects, more or 
 less complicated in form, when we have already the projections of 
 these objects upon auxiliary planes, making any known angle with 
 the actual plane of the drawing. Thus, figs. 10 and 13 are the 
 oblique projections of an oscillating steam-cylinder, the first repre- 
 senting the cylinder in external elevation, whilst the second is a 
 section made through the axis of the cylinder. 
 
 It is easy to see that these projections have been obtained in the 
 same manner as those already given in figs. 4 and 7 ; that is to say, 
 the external projection, fig. 10, is derived from the two right pro- 
 jections, figs. 8 and 9 — one made upon an auxiliary vertical plane, 
 parallel to the axis of the piston-rod, and perpendicular to the axial 
 lines of the trunnions, and the other upon a horizontal plane, 
 parallel to the cylinder ends, and, consequently, perpendicular to its 
 axis. All the different parts of this cylinder are, in fig. 10, project- 
 ed by straight lines and ellipses, accordingly as they are rectilinear 
 r. r circular in contour. It is the same with the section, fig. 13, 
 ind tin- horizontal projection, fig. 14, which are derived from the 
 two right projections, figs. 11 and 12, made upon auxiliary planes; 
 one vertical, and passing through the axis of the cylinder, and 
 through the valve-casing, whilst the other is perpendicular to this 
 axis, and passes through the line, 1 — 2, fig. 11. The dotted work- 
 ing lines, indicated upon tire various figures, show sufficiently 
 clearly the various constructions necessary to obtain these oblique 
 projections. We have, moreover, applied numbers to the different 
 parts projected, and more particularly to the axes or centre lines, 
 which show at sight what parts correspond with each other upon 
 the different projections. 
 
 423. These drawings represent the cylinder of a steam-engine, 
 
 different from that which we have already described. The pre- 
 sent one is called an oscillating steam-engine, because, instead of 
 the cylinder being vertical and immovable, it oscillates during the 
 motion of its piston, b, upon the two trunnions, E, carried in suita- 
 ble bearings in the engine-framing. This arrangement of oscillat- 
 ing cylinder has the advantage of dispensing with the parallel 
 motion, and of attaching the rod, A, of the piston, directly to 
 the crank-pin, to which its motion is transmitted, without the 
 intervention of any connecting-rod. In the head, H, of the rod, 
 there is, consequently, formed a bearing, which embraces the 
 crank-pin. 
 
 The bottom of the cylinder is east in the same piece with it, but 
 it has a small central opening, for the passage of the spindle of the 
 boring tool, by means of which the interior of the cylinder is turned 
 smooth and true. This opening is closed by a cast-iron cap, f, 
 bolted to the bottom of the cylinder. Against a planed face, upon 
 one side of the cylinder, is fitted the valve-casing, G, which receives 
 the steam direct from the boiler, and has within it the valve, H, 
 which has an alternate rectilinear movement, at the" same time 
 oscillating along with the cylinder. During this movement, the 
 valve alternately uncovers the ports, a, b, fig. 11, which conduct 
 the steam to the top and bottom of the cylinder. A blade 
 spring, l, attached to the inside of the valve-casing, at the back of 
 the valve, constantly keeps the latter well up against the planed 
 valve face. 
 
 The steam coming from the boiler introduces itself into the cas- 
 ing through the passage, c, fig. 12, which communicates with one 
 of the trunnions, E, and the escape of the steam, when it has acted 
 upon the piston, is effected through the exit channel, d, which com- 
 municates with the other trunnion. 
 
 The piston, B, is composed of a cast-iron body, on the outer sur- 
 face of which is cut out a groove, to receive the hempen packing, 
 i, partly covered by an elastic metal ring, h, coinciding exactly with 
 the inside of the cylinder. 
 
 Oscillating cylinder-engines have always been admired for their 
 simplicity and beautiful action ; but it is only of late years, and 
 now that such superior workmanship is attainable, that siu-h en- 
 gines have been constructed of considerable size. The aptness of 
 this arrangement for engines of the largest size has lately been 
 demonstrated by Penn, in the case of the Great Britain, and other 
 large vessels. 
 
 CHAPTER XII. 
 PARALLEL PERSPECTIVE 
 
 PRINCIPLES AND APPLICATIONS. 
 
 PLATE XLIL 
 
 424. We give the name of parallel perspective to the represen- 
 tation of objects by oblique projections, which differ from the 
 preceding, in so far that the visual rays, which we have hitherto 
 •supposed to be always perpendicular to the geometrical planes, 
 form, on the contrary, a certain angle with these planes, remain- 
 
 ing, however, constantly parallel to each other ; from which it . 
 follows, that all the straight lines, which are parallel in the object, 
 maintain their parallelism in the picture, according to this system 
 of perspective. Although, in general, it is immaterial what the 
 angle of inclination is, it is nevertheless preferable, in regular 
 
\i>; 
 
 
 stowaaf. to adopt aoase particular angle aa • nutter of o. 
 which will U<r Ik* advantage of kiun; Iha mure dui*i - 
 i «iaglr projection ur I 
 i ■ and a' ■', figi 1 and J, be the two projections of a 
 we wish to m... myn all parallel ; 
 
 rma an angle, 
 cat. with the ground line. : 
 
 that the 
 instance of U ■ 
 horuontal plane, is equal to ' 
 
 .. the point, a, being that at which it Ion fa 
 
 .ins of the various figures in 
 it, in taking the above straight lii.< - 
 
 - Bcient to 
 h.sUjad of making the 
 
 b the actual pr which we bare 
 
 these aame lines round at an an^'le of 80 ; . Than, I 
 i a", k' 1', fig. 3, are the strai. 
 
 1 lo the angle in question; whilst, on the 
 
 linea properly parallel I .tinn, a' b , in 
 
 on in parallel, 
 or, as, .• \\\ed, false p. prism,' B, with a 
 
 ■ 
 
 I I in the 
 
 a be stand g h ij. T 
 
 cular to 
 
 ■ qua! to 
 
 I 
 
 ealty projected, to a b, fig. I. Consequently, if thr... 
 
 linea, parallel Ion, the; ■• | ;l |[ the 
 
 . :ls we 
 
 have a! 
 equal lo 
 
 '. h a* and h f, 
 » *"• »"'• 10 hall' lli.- lengths, u' m and 
 
 aa all tbl 
 
 hilst all linea 
 parallel to the base lir . 
 
 edges, «./.'■• 
 
 -. a' </*, 4" t*, V 
 para. :ie. 
 
 It will be eaiily seen, tliat bj adapting the anj.'lc He have indi- 
 ■ ■ ■ • 
 
 ray, thai the in parallel |* n 
 
 sown all the dimensions of ' 
 ■..• hand, we I widths and 1 
 
 ieh are para, 
 
 ■ r from an on: 
 in which the n be |» r- 
 
 pandirnlar to tl other hud, the oblique linsa 
 
 ■ually pi r|« ndicular to ih. 
 plane, and which are exactly equal to lialf the actual lengths of 
 the latter. 
 
 I square, 
 -. M I and 9 '.. -, h> f or I k. < 
 
 quentlr, in order to construct the perspective or oblique pr 
 fig. 1. the pfan 
 
 the purpose equally well to have made tile '.. 
 
 to the half of a J or h i. 
 
 The shaded view, fig. j3. r. ; 
 
 pyramid, a, the horixontal pro- 
 
 of Which is indicated ill full, sharp linea, in fig. 5, and the 
 
 vertical projection in dotted linea, in 
 
 ling to the principle thus hud down, the pi 
 
 ad, in the tir>t place, by drawing all the linea which are 
 
 perpendicular and parallel lo the bai 
 
 through the oj | 
 
 the upper and lower bases of the pyramidal frustum, and 
 
 plinth. I 
 
 to the I bdeh are 
 
 likewise paralli 1 to the former, remain horuontal in tin- \« ■ 
 1 the other hand, all the straight lines, f 
 
 1/ r', (' 
 
 pendicular to thi 
 
 or, in other v. 
 
 I 
 of the two bases of the pyramidal frustum, a 
 straight line in I then mark off Iron. 
 
 . ..I on each side of them, the 1 p*, ***, 
 
 i 
 straight 
 
 joining the extreme p 
 
 the linea repreeenting the contours of the tw further, 
 
 by joiuix 
 
 ami eompli te the w> iw, 
 
 i.'T. i ition of a •', 
 
 ular to the ^' 
 in the finished 1 tamp "it the 
 
 f the borixontal projection ; thai is, when the fa 
 
 1. r is known, a» w. II other prt whkh may 
 
 Licular to the 
 Ixi ti l> c d| leal projection of thl 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 the perspective of its base, abed, will bo parallel to a b. Tbo 
 circles which have their centres at o, being parallel to the vertical 
 plane, are represented in perspective by two circles equal to them- 
 selves ; and their position is obtained by drawing through the 
 point, o, the straight line, o' o\ parallel to A b, fig. 1, and marking 
 off a distance, lying equally on both sides of the point, o, equal to 
 half the length of the cylinder, measured in the direction of the 
 axis, perpendicular to the vertical plane. Then with the points, 
 o', </\ as centres, describe the circles with the equal radii, o' f and 
 u /', straight lines,/ 1 / 5 and i 1 p, drawn tangential to the circles, 
 and parallel to the axis, o 1 o J , express in perspective the genera- 
 trices of the two cylinders forming the contour of the object. 
 The cylindrical pieces which join the cylinder to the base are 
 determined in the same manner by means of the line, n n a , drawn 
 through the centre, n, of the circle, d g, parallel to o l o\ and by 
 the distances, n n\ n n', together equal to half the actual length of 
 these cylindrical surfaces. The base is drawn as in the preceding 
 example. 
 
 428. The example, fig. ®, represents a cone resting upon a 
 cylindrical base, both cone and base having the same axis perpen- 
 dicular to the horizontal plane. This cone and cylinder are pro- 
 jected on the plan, fig. 8, in sharp lines, and in the elevation, fig. 9, 
 in dotted lines. 
 
 The circles, fig. 8, representing the bases of the cone and cylin- 
 der, are to be divided into a certain number of equal parts ; and 
 through the points of division, 1, 2, 3, &c, perpendiculars are drawn 
 to the ground line, and are prolonged as far as the horizontal line, 
 a' o', which is the vertical projection of the two bases. Through 
 the points, a', b', c', o', are drawn straight lines parallel to A B, fig. 
 1 ; and on each of these are set off the distances, d 2', b' 3', c' 4', 
 o' 5', &c, respectively equal to half the lengths of the perpendicu- 
 lars, 2 a, 3 6, 4 c, 5 o. &c, which operation gives the points, 2', 3', 
 4', 5', &c, through which an ellipse must be traced, to represent 
 the perspective of the base of the cylinder. In the same manner 
 we obtain the points through which passes the ellipse, representing 
 the perspective of the base of the cone. 
 
 The heights of the cone and its base remain precisely what they 
 really are, in consequence of their common axis being parallel to 
 the vertical piano.; but this is not the case with their bases, which, 
 being horizontal, are projected obliquely, in the form of the ellipses 
 we have just drawn. The apex of the cone, at the upper extre- 
 mity of the vertical axis, does not change, and for the generatrices, 
 or sides of the cone, it is simply necessary to draw through the 
 apex the straight lines, o" m and (? n, tangents to the ellipse repre- 
 senting the base of the cone, whilst the generatrices of the cylinder 
 are tangents to the two ellipses representing its upper and lower 
 bases. 
 
 429. The example, fig. H, is the parallel-perspective representa- 
 tion of a metal sphere or knob, attached to a polygonal base by n 
 circular gorge, forming altogether an ornamental head for a screw. 
 Figs. 10 and 11 are the horizontal and vertical projections of this 
 piece. 
 
 We must, in the first place, remark that the sphere, the radius 
 of which is o a, may be determined in its perspective representa- 
 tion in several ways. First, by imagining the horizontal sections, 
 « b,c d, ef, which give in plan the circles, with the radii, a' o, 
 
 c' o\ and e' o', and the perspectives of each of these circles may 
 be obtained by operations similar to the preceding, which will give 
 a series of ellipses, to be circumscribed by another ellipse, tangen- 
 tial to them all. Second, by drawing the planes, g h, ij, parallel 
 to the vertical plane, and which are projected in perspective as 
 circles, with the radii, I" g, i m, the centres being upon the oblique 
 line, n n', parallel to the line, A B, fig. 1, and passing through the 
 centre, o, of the sphere. The external curve, drawn tangential to 
 all these circles, will be elliptical, as in the preceding method, and 
 represent the perspective of the sphere. Thirdly, by at first 
 drawing through the centre, o, an oblique line, n ri ; then a per- 
 pendicular, e e", passing through the same point. Then set out 
 from the centre, o, and on each side, the distances, o e, o e", equal 
 to the radius, o a, of the sphere, which gives the conjugate axis of 
 the ellipse. To obtain the transverse axis, it will be necessary to 
 draw tangents t» the great circle of the sphere, parallel to the 
 oblique ray of projection, A e, fig. 1, as brought into the vertical 
 plane. This line is brought into the vertical plane, as at a" b. in 
 the following manner : — At the, point, a, a perpendicular to A B is 
 erected, and the distance, a* a, is made equal to a a', when a" b is 
 joined. 
 
 These tangents touch the sphere in the points,/ /', which may 
 be obtained directly by drawing through tho centre, o, the line,//, 
 perpendicular to a" b. These tangents, further, meet the line, n n', 
 in the points, n, n' ; and the distance between these points is, con- 
 sequently, the transverse axis of the ellipse, which represents tho 
 perspective of the sphere, and which may be drawn according to 
 any of the known methods. 
 
 This last method is evidently the shortest and simplest of the 
 three for obtaining the perspective of the sphere, but it is confined 
 in its application ; for any other surface of revolution, as, for exam- 
 ple, the gorge, which unites the sphere to the hexagonal base, 
 cannot be defined in this way. In cases where the axis of the 
 surface of revolution is vertical, as in this example, it will be neces- 
 sary to adopt the first general method, which consists in taking 
 horizontal sections.. When, on the other hand, the axis of the 
 surface of revolution is horizontal, we must employ the second 
 process, which consists in taking sections parallel to the vertical 
 plane, or perpendicular to the axis. Tho perspective of the thread 
 of the screw, of which the sphere is the ornamental head, is de- 
 terminable in a manner analogous to that of a circle. It is suffi- 
 cient, in fact, first to draw the two geometrical projections, figs. 8 
 and 12, of one or two convolutions of the thread, and to find the 
 perspectives of the very points which have served for the construc- 
 tion of the helices. Thus, for example, we put the circle, I p q, 
 fig. 8, into perspective, as at P p' q', fig. 13, retaining for this pur- 
 pose the same points, I, p, q, &c, which were employed in deline- 
 ating the screw, fig. 12. Through these points, P,p*, q 1 , &c, draw 
 vertical lines ; and upon them set off' the distances, V P, P P, p l p', 
 &c. Then through the points, P, P, &c, draw the curve, which 
 will be the perspective of the outer helix of the screw-thread. 
 By going through the same operation for the inner circle, r s t, ficr. 
 10, we shall obtain the similarly perspective outline of tho inner 
 helix. 
 
 An examination of fig. 13 will further show that the heights on 
 the vertical lines are precisely the same for both helices, for they 
 

 ■'I \\s 
 
 an uln upoa raJB tommcm to the two circlea, /*»* and M 
 • 
 
 ,»• J.- med it nimrrrwrr to •titer further into the devc- 
 I711I of this apscwa of perspective, of which we hare already 
 p.ra a erorrml appfieatiun in the boring-machinc, n-pn- 
 
 .1 rxatuple in which are collected almost all 
 • 
 Mechanical elements and MMI 
 
 In that example, a> figBXM in Plate \1.II , which 
 
 or lisual rara to be in all cases para. XT, uu>l to be 
 
 inclined at an ai al pro- 
 
 .reee all 
 that tw 11 do, allowing 
 
 : 
 may !*• ujs.n 1. 
 
 nd the utility 
 ing, at a 
 
 • 
 metrical ID greatly simplify the 
 
 proeeaa of sketching l.i. uncry. 
 
 CHAPTEB XIII. 
 
 T 1: r 1: p 1; i:.-1'i:cti v E. 
 
 ■■:■ APTLICATIOXS. — ELEMEXTAKY RDORla 
 
 l'l.ATE XLI1L 
 
 430. Perspe. -.ralhsl — bat here defined M 1 
 
 a (undid nr [alee perspective, in its 
 upon the actual manner in which v i-i^n tak. - 
 that is, tliat instead of being parallel to Men other, tin- visual rays 
 jcet is said to bo drawn in pen 
 tng tlie drawing fron a |urticul.ir point, it | 
 the aame appearance t.. the organ* of »i=ion as the object refjro- 
 ; we when aimila 
 
 travel from the object in 
 tig to a point at the eye, and forming a cone 
 of ray* to be intercepted bj a tnms- 
 
 parent plane, or diaphragm, of any form — tin 11. Di 
 
 « from the rations |urt- of the object pierce this 
 
 diaphragm, let us paint up-.n it t! I te me 
 
 -hull have the ev;u-t appear- 
 
 taelf, modified, as they may l»-, by 
 . ami by their U iiig in the light 
 
 in n|"'ii 
 
 the diaphragm will 11 I 00 upon lie 
 
 I 
 >l and natural manner, that the art of draw 
 • 
 
 TTie fixed point, to which the ray- lOed the point 
 
 . and in diagrams explanatory of j 
 together with • 
 
 the picture. I n of an 
 
 lathematically, we must have given us the horizontal and 
 
 and the position of the plat 
 
 ■ 
 rays as paaaing from the »arious jw.ints of 
 
 . of those rays with I 
 of the picture. 
 
 FIRST PROBLEM. 
 
 THE rEBsrECTIVE OF A HOLLOW miSM. 
 
 431. I>et A and a', figs. 1 and 2, bo the horizontal an i 
 DS of the prism which we wish to il, line ale in p- r- 
 
 the point of sight being projeeled in v and v', and the pla: 
 picture, in T and t\ p I to Ik- |wpfiidicul.ir to tlio 
 
 planes of projection, snd \ert: ally the case. 
 
 Through the point, t, in the borl 
 rays from each of the | 
 
 contour of the prfaau. The In tersecti on oi sriththe 
 
 plane of the picture determines the points, I*, a 1 , e", a", srhi 
 
 upon the hori 11, T 0, of the latter, the pi I 
 
 of the point*, ". 
 
 In like manner, through the point, v'. in the vertical projection, 
 draw the vianj 
 
 the picture in the points, «*,»',/*, and **; : 
 
 qoently, the vertical projections of I 
 
 to the plane of the picture, 
 the perspective of the object is do! \ i-il.l.-. sines all the points are 
 1 in the vertical line, T T , tie 
 
 ■ plane as turned over upon tie 
 
 .- ; whilst we mnat mppoM the line, t 0, the 
 
 horizontal projection of the picture-plane, as turned about the 
 ..- a e.ntrc, through a right angle, bringing it to coincide 
 with the ground line, L BL Winn this is done, the potntl 
 r', aP, will ill— libit ar - -.1. finally, coincide with the 
 
 1 B the ground line. Next, upon ti • 
 
 the horizontals, drawn through the 
 
 • 
 
 will be the parspectjvsa, a', b', c', d\ of the comers, o, 6, c, d, ot 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 the top of the prism. We have, likewise, the points, e'',f',g, h, for 
 the perspectives of the corners of the bottom of the prism, which 
 is parallel to the top; consequently, by joining all these points 
 together in couples, as indicated in fig. A, we obtain the entire 
 perspective of the externa! outline of the prism. As the prism is 
 hollow, we shall see in the perspective view the outline, i' m! n' o', 
 corresponding to the edges of the part hollowed out. 
 
 The point of sight, of which v and v' are the geometrical projec- 
 tions, is projected upon the picture-plane in the points, v, v"; and 
 when the picture-plane is turned over, the point will be found at i>", 
 which is the position of the point of sight upon the perspective 
 drawing. 
 
 It must be observed, that in this example the lines, a* b', a' d*, 
 and i* c', which express the perspective of the corresponding lines, 
 a b,a d, and b c, are the intersections with the plane of the picture, 
 of planes passing through these lines, and through the point of sight. 
 Now, since the intersection of two planes is always a straight line, 
 the following conclusions may be drawn ; that, 
 
 432. First, The perspective of a straight line upon a plane is a 
 straight line. 
 
 It may also be remarked, that the verticals, such as i* e',c t h,d t g, 
 are the perspectives of the vertical edges, projected in the points, 
 b, c,d; whence we deduce that, 
 
 433. Secondly, The perspectives of vertical lines are verticals, 
 when the plane of the picture is itself vertical. 
 
 It will further be seen, that the horizontals, I* c*, d* a', e' h,f g, 
 of the perspective view, correspond to the straight lines projected 
 horizontally in b c and d c, which are parallel to the picture; 
 whence it may be gathered, that, 
 
 434. Thirdly, The perspective of any straight horizontal line, 
 parallel to the picture, is itself horizontal. 
 
 Further, it follows from the two preceding principles, that all 
 lines parallel to the plane of the picture are represented, in per- 
 spective, by lines parallel to themselves. 
 
 Finally, the straight lines, a' b', d* c', e* f, and h g, which all 
 converge to the same point, v", the projection of the point of sight 
 upon the plane of the picture, correspond to the edges, ab, dc,ef 
 v. hich are horizontal, but perpendicular to the plane of the picture ; 
 whence it follows, that, 
 
 435. Fourthly, Tlie perspectives of lines which are horizontal, but 
 perpendicular to the plane of the picture, are straight lines, which 
 converge to the point of sight, and are consequently foreshortened. 
 
 It will be seen, from figs. 1 and 2, that the whole width of the 
 perspective representation, fig. A, is comprised between the points, 
 i" and <f a , which He on the outermost visual rays, drawn in the 
 horizontal projection ; and that its height is limited by the two 
 points, a" and e", which correspond to the extreme visual rays in 
 the vertical projection. The angle formed by the extreme visual 
 rays is termed the optical angle. In the present example, this angle, 
 V v d', in the horizontal projection, differs from the angle, a" v' e", 
 in the vertical projection. 
 
 The positions of the object and point of sight being given, the 
 dimensions of the perspective representation vary according to 
 the position of the plane of the picture. It will thus be seen, on 
 referring to fig. I, that if this plane be removed from if to/ t', 
 nearer to tlie object, the limits to the perspective representation 
 
 by the extreme visual rays will be enlarged ; whilst, on the con- 
 traiy, if we remove the plane of the picture to the position, /" C, 
 nearer to the point of sight, the limits will be sensibly narrowed. 
 
 Again, if, in place of moving the plane of the picture, the point 
 of sight is removed further off, or brought nearer to, the size of the 
 perspective outline will thereby be augmented or diminished. It 
 may therefore be concluded, that, 
 
 430. Fifthly, The dimensions in the perspective representation do 
 not wholly depend, cither on the actual size of the object, or on the 
 distance from which it is observed, but also on the relative distances 
 of the point of sight and of the object from the plane of the picture. 
 
 Thus the sides, d a and c b, fig. 1, are actually equal, but the 
 former is further from the plane of the picture than the latter; so 
 that whilst this is represented by the space, c' b', fig. A, that is 
 limited to the much smaller space, d* a', in the perspective view. 
 
 SECOND PROBLEM. 
 
 THE PERSPECTIVE OF A CYLINDER. 
 FlGDRES 3 AND 4. 
 
 437. To obtain the perspective outline of a vertical cylinder, such 
 as the one projected horizontally in B, fig. 4, and vertically in b', 
 fig. 3, we proceed, as in the preceding example, to draw through 
 the point of sight, v' v, a series of visual rays, extending to the 
 various points, a, b, c, d, e, taken on the upper end of the cylinder, 
 by preference at equal distances apart. These lines intersect the 
 plane, T t', of the picture, in the points, d\ c', a', g*, &c., in the 
 horizontal projection, and in the points, a", c", d", Sua., in the verti- 
 cal projection. 
 
 By bringing the plane, T t', of the picture, into that of the 
 diagram before us, or what is equivalent to it, by finding the points, 
 g', a 3 , Sic, by means of arcs, drawn with the centre, o, on which 
 the plane is supposed to turn, and drawing the horizontal lines 
 through the corresponding points in the vertical projection of the 
 picture-plane, we obtain the points, c 4 , d*, a', g*, &c, which are 
 points in an elliptic curve representing the top of the cylinder in 
 perspective, which is visible, in consequence of the point of si^ht 
 being above it. 
 
 The same points, a, b, c, d, of the horizontal projection, give, in 
 combination with their vertical projections, g 1 , f", c", &c, the per- 
 spectives, d B , e b ,f b , g b , of the bottom of the cylinder, of which, 
 obviously, only a part is visible. 
 
 The two vertical generatrices, d* d 6 ,g-'g 5 , being drawn tangential 
 to the upper and lower ellipses, complete the perspective outline 
 of the cylinder, fig. 13. 
 
 As this cylinder is hollow, an operation similar to the preceding 
 will be called for in delineating the upper visible edge of the hoi- 
 Ipwed-out portion. 
 
 It must be observed that, in taking an even number of divisions, 
 at equal distances apart, upon the horizontal projection of the 
 cylinder, and setting them off from tlie diameter, c g, parallel to 
 the plane of the picture, we have always a couple of points situated 
 upon the same perpendicular to the plane, and of which the per- 
 spectives are, consequently, situated on the same straight line, 
 drawn through the projection, v", of the point of sight. This 
 
160 
 
 TIIK PRACTICAL DRAUGI11 
 
 upoa the liar, i' J". »•• that 
 
 I... j :.. ■!.:.„• MMini tioO- 
 
 Ti: M. 
 
 THE rr 
 
 asv Rinn 
 
 BBS i A.1D A. 
 
 bt, ritu- 
 2 through thi 
 the nolid, r c', srnl j- - • picture. 
 
 J line, i ' i", repreaenting the 
 which all Uic I 
 
 and c </, which 
 of tin- picture, and which an 
 
 i' b* ami if e*i laith directed to 
 ma with the tdgm,fg, h i, of 
 • v V i', likewise oonvei 
 
 they retain their rertical position in 
 
 . ami the horizontal lines, a il. I rn. n k. e 0, parallel 
 
 ire, are rendered in the perspective view by 
 
 parallels, such as a* if, f at*, n' K', r' i'. 
 
 It nat] on of this problem, that when- 
 
 ■ through the aids of ■ 
 
 :i 1 perpendicular to the plat ore, the 
 
 imetrical with n 
 
 that it is, th< rt fore, qnita sufficient to go throngb 
 
 , ■ only of tin I 
 
 POl RTH PROBLEM. 
 
 E OF A HEARING-BRASS, PLAi r.H WITH ITS AXIS 
 . II A I.. 
 
 I1..1 m 7 1 
 
 situated, as in the pn 
 
 h the a\i- of tl bjoct, 
 
 the picture-plane, the perspective will like- 
 
 trical in reference to the centre line, i' r*j and it is 
 
 ■ uliaritv further. The Inside of Ihe 
 
 •• rmlnated by horizontal semi- 
 
 I will !"• r. nd 
 I which it will Ik> sufficient to 
 
 ' ' to tli" 
 
 ghl line, a e, which is horizontal an. I parallel 
 
 •• avis, /,* ,/•, is eqaa] to 
 i .. r /.' </', which is alsn horizontal, 
 
 .'. It will !«• remarked, that the 
 
 H the jxiint of 
 
 III II I PROB1 
 
 Till: I A SFH1EICAL BOSS. 
 
 - '.I AM' HX 
 
 tin. in carrying oat the general principle, it will be coi 
 that, in 1 
 should draw tin 
 
 1 ut in order to ascertain the i 
 tact of tl 
 
 ■ g through the sphere, producing circular - 
 ami then to find the perspective of each of these circles, 
 being found, ■ curve, drawn to oircomscribe them, will be the 
 
 the sphere. 
 
 In the example, lii--. 9 and 10, the pofa 
 chosen aa befon — that is. as situated in .. | 
 the centra of the Bphere, add perpendicular to the picture-] 
 the perspective of the sphere will, on this account, simply be an 
 ellipse, having for conjugate axis the base, o* /•', of the 
 • v A. in the horizontal projection ; and tor transvi ■ 
 the base, r' if, of the angle, e* V <P, in the vertical projection; 
 because the right cone, formed by the series of visual i 
 gential to, and enveloping the sphere, ia obliquely inter-. 
 
 the plane of the picture. If. however, the point of sight Were 
 
 situated upon a horizontal line, passing thr . . o, of 
 
 the sphere, |h of the latter Would I 
 
 The spherical pari of the 
 
 • ption of the key, an. I the edge,* /,of this 
 
 . being situated in a plane parallel to Ihe pictui 
 will, in i 1 . Bg, B, be rendered by a circle, of which the 
 
 i the cylindrical Iher side of the stopcock, for 
 
 iu junction with a lii alclrcle, ag h. is 
 
 ted by a portion of an ellipse, having the horizontal line, 
 a' h'. corresponding to .< /<: and the vertical, g*c*, being the per- 
 spective at g* '•'■ The circle, << h bg, the horizontal projection of 
 tin. surfa. I" (In- npp i- n presented in ihe perspec- 
 
 tive view by I | S« is also the upper visible ■ 
 
 the inner tubular p irtion. Bui this is the same as tin- eaai 
 the ellipses may be formed in a similar manner. 
 The perspective representation of a circle, however situated, 
 
 otherwise than parallel with regard to the plane of the picture, i- 
 
 alwaya a perfect ellipse ; but the transverse avis ol I 
 
 th, or is not the representation of, any dial 
 
 the circle ; for it is evident, that the more distant half of the circle 
 must be d must occupy 
 
 pace than the anterior half, whilst the ellipse is 
 
 iliviilnl b 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 V\ hen the point of sight is in a line perpendicular to the circle, 
 the rays from the latter will form a right cone ; and if the plane of 
 the picture is not parallel to the circle, the section determined by 
 it will be an ellipse, as is well known. Again, if the circle is not 
 perpendicular to the central visual ray, the cone of rays will be 
 elliptical, and the sections of such cone will be ellipses, of various 
 proportions, that parallel to the circle, however, being a circle. 
 
 The transverse axis of the perspective ellipse is the perspective 
 of that chord in the original circle, which is subtended by the arc, 
 between the points of contact of the extreme visual rays, as pro- 
 jected ill the plane of the circle. 
 
 SIXTH PROBLEM. 
 
 t\ie perspective of an object placed in ant position with 
 
 regard to the plane of the picture. 
 
 Figures 11 and 12. 
 
 441. In each of the preceding problems, we have supposed one 
 
 or other of the surfaces of the objects to be parallel or perpendicular 
 
 to the plane of the picture ; but it may happen that all the sides of 
 
 the object may form some angle with this plane. It is this case 
 
 which we propose examining in figs. 11 and 12. 
 
 Let a be d be the horizontal projection of a square, of which 
 the sides are inclined to the plane, t t', of the picture, and of 
 which it is proposed to determine the perspective. The point of 
 sight being projected in v and v', if we employ the method 
 adopted in figs. 1 and 2, we shall find the points, a', b 2 , c 1 , d\ 
 to be the horizontal projections, and a", b', c", d", the vertical 
 projections of the corners of the square; and when we have 
 brought the plane of the picture, T t', into the plane of the 
 present diagram, as before, we shall find the actual positions of 
 these points to be at a', ft\ c', d*. If we join these points, we 
 shall have a quadrilateral figure, of which the two opposite sides, 
 a* J 4 , c' d l , converge to the same point, /, whilst the other two 
 sides converge to the point, /'. These two points are termed 
 vanishing points. They are determined geometrically, by drawing 
 through v, the horizontal projection of the point of sicrht, the 
 itraight lines, v t and v t', parallel to the sides, a b and b c, of the 
 given square, and prolonging these lines until they cut the line, 
 T T', representing the plane of the picture. Having drawn through 
 v' the horizontal, v' v', termed the horizontal line or vanishing 
 plane, set off the distance, v t, from v" to / and the distance, 
 v T', from v" to f, and / and /' will be the required vanishing 
 points. 
 
 It follows from the preceding, that 
 
 When the straight lines which are inclined to the plane of the 
 picture are parallel to each other, their perspectives icill converge in 
 one point, situated on the horizontal line, and termed the vanishing 
 point. 
 
 When several faces or sides, situated in different planes, are 
 parallel to each other, their perspectives all converge to the same 
 vanishing point, which allows of a great simplification of the 
 operations. 
 
 Thus, the edges of the horizontal faces, h! i' and h" i', of the 
 quadrangular prism, being respectively parallel to the sides of the 
 
 square, a bed, are represented in perspective by the straight lines, 
 tV, i* e', converging to the first vanishing point,/, and the straight 
 lines, i 3 g', i* g', converging to the second point, f. 
 
 The cone, f f', which is traversed laterally by the prism, has its 
 apex projected horizontally in the point, s, fig. 12, and vertically in 
 the point, s', which, with its axis, appertains to fig. 11. The per- 
 spective of the point, s s', on the plane of the picture, is found, in 
 the usual way, to be at s in the horizontal projection, and at s' in 
 the vertical projection ; and when the plane of the picture is brought 
 into the plane of the diagram, these points are represented by the 
 points, s 2 and s", upon the same vertical, s 3 o', which is, consequently, 
 the perspective of the axis, o s', of the cone, and the point, s 2 , is 
 the perspective of the apex of the cone. 
 
 If we draw the perspectives of the two bases, k I and m n, of the 
 frustum of a cone, according to the methods already given, it will 
 only remain to draw through the point, s 3 , the two lines, s" m! and 
 s 2 n, tangential to the ellipses, representing the bases, which will 
 complete the perspective of the entire object, as in fig. [p\ 
 
 APPLICATIONS. 
 FLOUR- MILL DRIVEN BY BELTS. 
 
 PLATES XLIV AND XLV. 
 
 442. The elementary principles of perspective which we have 
 laid down, will admit of application to the most complicated sub- 
 jects, and, among other things, to complete views of mechanical 
 and architectural constructions. In Plate XLV. we have given 
 an example, which will enable the student to form a general idea 
 of this branch of drawing. This Plate is the perspective repre- 
 sentation of the machinery of a flour-mill driven by belts, and Ha 
 fitted up by M. Darblay, at Corbeil. Before proceeding, however, 
 to discuss this as a study of perspective, we propose to describe 
 the various details of the mechanism composing the mill, and 
 which we have represented, in geometrical projection, in Plato 
 
 xliv. 
 
 The construction of flour-mills has latterly undergone very in. 
 portant improvements, as well in reference to the principal driving 
 machinery, as to the minor movements, and the cleaning and 
 dressing apparatus. As such machinery belongs to a most impor- 
 tant class, we have selected a mill, as an illustrative example of the 
 subject before us, giving all the recently improved modifications 
 now at work, both in this country and on the Continent. 
 
 443. Before the introduction of what is known as the American 
 system, very large uncovered millstones, of upwards of six t'eet, or 
 two metres, in diameter, were employed ; and these gave what were 
 then considered very good and economical results. These mills 
 
 .were worked by water-wheels or wind-wheels; but as improve- 
 ments gradually crept in, not only was the entire internal mechanism 
 changed, but also the motor, and the description of stones. The 
 American flour-mills, commonly known on the Continent as 
 English mills, differed from the older mills in the employment of 
 smaller stones, with furrowed surfaces, and in their being driven 
 at a much greater speed, requiring, in consequence, more wheel- 
 gear to bring up the speed. A mill on the old system, with large 
 
I«J 
 
 
 t 'in (batter, ordlnari ly goes at the rate 
 60 rvTolutioat per nvnute, t* in* Bored, we dull .up;- 
 
 ■ V«(, caLr.; 10 ur IS turne in the «an>. 
 ■m!l »ul I'C'i ■ I and » lanterr. 
 
 or better, a av. 
 • 
 Bat a modem mil: 
 
 ' nt be imp> ' 
 
 ■aJflft/talf gear! ^t»:»i.nth' p.wcr and the w .irk. When this 
 mu'tl;-'-. .iti n is obtai: 
 
 eataaatiaf «f a ana horizontal ajmr-wh.-, ■!. drhin;; a spur-pinion 
 
 c- • •; .•->••'_» l->:i sup r~ h-i. in many 
 
 • has the 
 » ! ■ - ■ 
 the at ppafc "f » • r.J- [^ :• ■•:' -: on, w ithout ^ t ■ *i -(*"*> _r the ;■ ■-.■ n» 
 
 ■ asaj ■ i :'•..■ w 1 lie !:. . ' ! i i- J !■•; >•« nti.il point, more 
 i large and importa; I t.iany pairs of 
 
 atones an- at •• 
 
 The drawing. Plata XI.1V . mil! of thi* 
 
 1 tarblay, at Cor 
 c<npri- ■ The 
 
 ■ 
 I 
 
 - 
 
 aa Car aa the vertical al 
 
 vertical section, taken at rijjht anj. • 
 
 ■■ft. 
 
 r end of th« 
 
 - down. 
 
 ty. and 
 
 in a lira-- "ing in 
 
 - 
 ;rnal, 6, 
 of the main driving-ahaft, r. 
 
 '.oft, t, lia» fixed upon it. in U -jHnion, 
 
 • heel, c, fitted with m 
 • 
 
 wrooght-iron shaft, a', which paaaca up to U 
 
 buildin. rariooa accessory apparatus 
 
 • •f the mill, auch a* the aack-hoieta, preanit . 
 
 ■ 
 •hat shown in section at d, in 
 
 - aa at e, 
 
 - 
 aeerrer at the top, at, 
 
 -'.-lndards 
 :>ii brass 
 
 -■••■_- 
 
 necessary; aii ; the in. 
 
 »iiirh ia bolted to the croaa beams of tha 
 
 ■ 
 
 .! shafts, i. ha- 
 
 Tlie piniona gear « 
 
 - 
 shaft, E ; and tl it in commu- 
 
 These but are each keyed upon tt 
 atones, ■. A tension ; 
 
 y the two arms of a aecor 
 
 • 
 
 a eoople of guide-pulleys. /, and ai 
 
 • 
 
 communicated to the pulleys, l'. 1'. ted up, 
 
 tension 
 
 I ; and the !•• . will no 
 
 - communion- . and consequ. ; 
 
 pairs of stones, will 1- ilea o, are sup- 
 
 • bearing*, carrii-d by cast- i to the 
 
 ■a beams. T an thus 
 
 ball when 
 
 -lack, iron f .. ed at intervals, attached to 
 
 ■ 
 millstone shaft is generally made of cast-iron, its lower 
 end is fitted w ith a caj 
 
 i of a brass f. 
 
 cup, r, 
 formed in uV rfaian surmounts 
 
 ;»'n which the entire framr .■ 
 • 
 
 tbe shaft 
 • liaft is adjusted vertically, ai: 
 ■ 
 
 . has a small - a Inch a 
 
 small pa ..ndle. r, 
 
 upon its vertical spindle. By turning this handle I 
 . the small wheels are set in motion ; and a- 
 cannot otherwise turn, it i« (breed to rise or fall, and with it the 
 
 • manner 
 • 
 
 . iccording to t 
 
 .ft is also case-hardened, and 
 -ain distance into the boss • 
 - fi-ed acmes the eye of the - runner, 
 
 • -mly imbedded into the stone at either aide. On the 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 top of the boss of the centre-piece, u>, is a species of metal saucer, 
 Jito which dips the lower end of the pipe which conducts the grain 
 iown from the funnels, R, generally made of copper. These fun- 
 nels, which receive the grain, communicate by the pipes, y, with a 
 single hopper above, and rest upon the wooden cross-pieces, s, fig. 
 2, held down on one side by a hinge, z, and on the other by a 
 vertical iron rod, z', by means of winch they are raised or lowered 
 at pleasure, so as to set the bottom of their pipes at a greater or 
 less distance above the bottom of the saucer below. The object 
 of this arrangement is to allow nioro or less grain to enter between 
 the stones. The supports of the cross-pieces, s, are fixed upon a 
 wooden casing, T, which covers each pair of stones, a space being 
 left inside all round the stones, into which the produce of the 
 grinding falls, as it issues from between the stones. It is thence 
 conducted, by suitable channels, either to receiving-chests, or to the 
 elevators, by which it is carried to the upper part of the building, 
 to undergo the subsequent processes. 
 
 The lower immoveable stones, q', of the same diameter as the 
 runners above, are fitted with metal eyes, b', furnished with 
 brasses, which embrace the shafts of the runners, and assist in pre- 
 serving their perfectly vertical position. These stones are grooved, 
 as indicated in the plan of one of them, fig. 1 ; thai is to Bay, shal- 
 low channels are cut out of their working surfaces, so as to present 
 on one side a sharp edge, and act with the runner like scissors, 
 cutting each grain as it comes upon them. The fine close-lined 
 dressing, which is given to the surface between these channels, 
 completes the fracture and crashing of the grain. These lower 
 stones rest upon the cast-iron plates, u, but with the intervention 
 of the three adjusting screws, a', which allow of the obtainment 
 cf an exact level; whilst four lateral screws, a ! , fig. 1, entered 
 through the lateral cast-iron frame, serve to adjust wilh accuracy 
 the centre of the stone. 
 
 The base plate and side frames are not only bolted to the cross 
 beams of the building, but they are also supported at intervals by 
 cast-iron columns, v, placed between each pah of stones, and 
 resting upon the plates, o', and the solid masonry below them. 
 The ceiling is additionally supported by the solid wooden columns, 
 x, placed at the ends and between the two rows of stones. An 
 iron railing, v, is placed on each side of the driving-gear, to prevent 
 accidents which might arise from persons passing too near the 
 heavy wheels. Cavities are constructed in the masonry, for the 
 reception of the mechanism for adjusting the footstep-bearings of 
 the runner-shafts, already described. These openings are usually 
 covered by suitable doors. 
 
 THE REPRESENTATION OF THE MILL IN PER- 
 SPECTIVE. 
 
 PLATE XLV. 
 
 445. It was stated, in the preliminary instructions relating to 
 perspective drawing, that the perspective dimensions depend on the 
 position, both of the point of sight and of the object, from the plane 
 of the picture, which is necessarily limited in size. 
 
 In the perspective delineation of one or more objects, we should 
 r insider, not only from what distance the object should be viewed, 
 
 but also at what height the eye, or (he horizontal line, should bo 
 placed. In the example selected, we have supposed tin- point of 
 sight to be placed at the height of a man's eye ; but it is evident 
 that this height of horizon is not invariable. It depends, more or 
 less, on what part of the object we wish to develop more particu- 
 larly in the perspective representation. Thus, for a machine of but 
 little height, the point of sight should be lower; whilst it should, 
 in all cases, be at a sufficient height to enable the spectator to take 
 in the entire object, without changing his position. 
 
 In architectural subjects, the horizontal line should never be 
 taken at a less height than that of a man's eye; whilst, in general, 
 a good effect may be anticipated, when the distance of the spectator 
 from the picture is equal to about one and a half times, or twice 
 the width of the paper, provided there is, at least, as great a distance 
 between the plane of the picture, and those parts of the object 
 which are nearest to it.* Taste and practice in drawing in perspec- 
 tive will be the best guides in the choice of the dispositions leading 
 to the happiest effects. 
 
 We have at t I', figs. 1 and 2, Plate XLIV., indicated the position 
 assumed for the plane of the picture, which is supposed to be brought 
 into the plane of the diagram in fig. 5, Plato XLV. 
 
 The point of sight, agreeably to the recommendation we have 
 given, is supposed to be placed, with reference to the picture, at a 
 distance equal to about twice the width occupied by the machinery 
 of the mill in the vertical projection. It does not lie within the 
 limits of the paper in the geometrical projections, Plate XLIV.; 
 but it is projected into the plane of the perspective picture in the 
 point, r', tig. 5. 
 
 In laying out the main design of this perspective picture, we 
 must commence by finding the positions of the axial lines ot all 
 the columns, iron shafts, horizontal and vertical, and, in general, 
 of all symmetrical objects. Thus, through the points, ], 2, 3. 4, 
 &c, fig. 1, we must draw a series of visual rays, converging to the 
 point of sight, and cutting (he projection, I l 1 . of the plane of the 
 picture, in the points, 1", 2", 3", 4". &c., which, in the picture 
 itself, fig. 5, Plate XLV.. are represented by the points, 1', 2', 3', 4', 
 &c. 
 
 The vertical lines, drawn through each of these points, will be 
 the axial lines sought. We next obtain the perspective of the 
 objects situated nearest to the picture plane, as the column, .x. for 
 example. This column being very near the plane of the picture, 
 and the visual rays tangential to each side of the cylindrical sul- 
 face, being both very much inclined to Iho same side, its diameter 
 in its perspective plane seems proportionately greater than it is 
 in reality ; but this is corrected by the obliquity wilh which this 
 part of the perspective picture should be viewed. For it must he 
 borne in" mind, that all perspective pictures must be viewed from 
 the single and precise point of sight in relation to which they are 
 drawn ; otherwise, the pictures will have an untrue and distorted 
 appearance. 
 
 We next determine the perspective of the columns, v, the axes 
 of all which are situated in a plane perpendicular to the plane of 
 
 • We do not see the force of this remark, for why should not a perspective repre- 
 sentation be lirawn full size, or even to a larger scale? In one case, the object roust 
 be supposed as close to the plane of the picture, and, in the other, as between it ALd 
 the point of sight.— Translator ask Editor. 
 

 THE I 
 
 uW sirtar. ► itat they «iU dhatafa* gradual!* ill bright, being 
 iaah*<t byaroa^of faeAeonTwgiogto I 
 
 • IMM, that when the perspective of the first column baa 
 heea -*J^— <. it w>ll be aafict. nt tu draw through the principal 
 
 ■ the nv uljm.-v and other parte, a - 
 mgia the nasal >>birh will give the ptrspert: 
 
 !!■«.. of the corresponding points on the other columns, together 
 
 N.ir heights. 
 
 ■f each of the runner shafts, 
 the poller*, and other detaii- in the 
 
 vertical plane, p— ing t 
 
 X 1.1 V.. 
 
 mi eoBaaa^BBtJ] NfjresMted in r« r»i»vt.ie bj the vertical inea, 
 
 .1 t<i find thi ; 
 
 - 
 
 ■ 
 
 or Hani. - 
 
 which, however, are p 
 
 apez of 
 
 - 
 
 by lines 
 .f that 
 
 ■ 
 
 them ha« 
 
 - 
 
 h Mipfxirt the 
 
 ■ 
 
 - 
 
 ■ ion in 
 
 ■ 
 
 strict accordat , |^y ( ],,wn il 
 
 treating of aha i-ing. 
 
 NOT1 • r IMl'l!o\ i: M KN I 
 
 PLOUB.MILl 
 
 By far the I- -t millstones used, in this or any 
 an- tiLv.- -tones from t' 
 
 ■ark. and taming out 
 -. than any oil. 
 in composition, and a) 
 
 are now • ry part of tl> :;sh sys- 
 
 takerj to 
 extract • 
 
 i faces being - ! u[»>n» instead 
 
 irtificial furrows. The pm. 
 
 n such way a- 
 grinding action without interfering with th< ,-t, is an 
 
 invention, introdao I in :,_•■ II 
 
 uncertainty at;- 
 
 poo the 
 Imilding up together small fragments of - 
 i rdi ■ --. so as :•■ inson a good grinding -ml"... .- throughout — thia 
 
 l attainable in larpe masses, a 
 parts fr- makers 
 
 - 
 
 and as the manufacti.r 
 
 . n to bo 
 .<!1 carefully at 
 
 ; and 
 
 round " 
 
 i, thai 
 
 Uiron, put on hot, so as !•• 
 Tin- J •• 
 the fur: 
 
 ■ 
 
 ■ 
 ! luces annus' 
 
 and an i I 
 ■ 
 
 - 
 
 ind an important application in the 
 grindin. 
 departure 
 
 1 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 into a series of infinitely short lengths, he proposed to take a more 
 
 obtuse ic Cor carh larger portion, and in such progression, that 
 
 it would require equal pressure for every portion of the surface to 
 cause a uniform sinking of the plus '" the course of wear. The 
 contour thus obtained is of a peculiar curve, as shown in fig. 1. 
 The main feature of the generating curve for such a surface, is the 
 equality of all tangents drawn from the curve surface to the axis; 
 
 hence the use of the simple instrument illustrated by fig. 2. This 
 contrivance consists merely of a straight brass wire, A, jointed at 
 one end by a pin to the upper surface of a small wooden slider, b, 
 which is hollowed in the centre to receive the tip of the finger in 
 drawing a curve. A small drawing-pen, c, ingeniously formed 
 out of a slip of steel bent over the wire, a, and screwed to a brass 
 bush, so as to form two broad nibs, is arranged to slide from end 
 to end of the wire, being adjustable at any point by stiff friction, 
 caused by a spring, which, fitting a groove in the wire, retains the 
 vertical position of the pen. In drawing a curve, the rod or wire 
 carrying the pen is set at right angles with the slider, b, which is 
 drawn in a right line along the edge of a ruler, whilst the wire 
 carrying the pen is left to 
 find its way from its initial 
 angular position, to that of 
 a line in the same plane as 
 the slider ; and, in doing 
 this, the pen describes the 
 curve we have represented. 
 Fig. 3 is a vertical section 
 of a millstone arrangement 
 on this system, showing 
 how the gradual variation 
 of the curvature, in rela- 
 tion to the increasing dis- 
 tance of the parts from the 
 centre of motion, equalizes 
 the rubbing pressure iu the most perfect manner. The same s"ketch 
 
 also shows the adaptation of the principle to footsteps, together 
 with a new system of lubrication of these surfaces so liable to 
 extreme abrasion. The oil supply is kept in an elevated vessel, A 
 whence a pipe, B, proceeds downwards to the footsteps, upon 
 which a pressure is thus constantly kept by the oil column, a stop- 
 cock being introduced to regulate the supply. 
 
 Mr. Schiele now makes independent or self-contained flour-mills 
 of this kind, of such simplicity and compactnoss, that four com- 
 plete mills, or sets of stones, placed together, may be worked in a 
 room 10 feet square; a single shaft driving the set, from the cen- 
 tre, by means of a horizontal band-pulley, from which endless 
 bands pass to corresponding pulleys on the spindle above the 
 upper stone. In mills of this kind, when by wear the runner has 
 sunk three inches, the adjusting screws of the steps arrive at the 
 end of the 3-inch traverse allotted to them. The runner is then 
 lifted from its seat, and the thin end is shortened to this amount. 
 This plan of renovation may be repeated twice, thus allowing for 
 12 inches wear in a 2G-inch runner; and the stones, so reduced, 
 are still valuable for smaller mills. 
 
 The peculiar portability of these mills is a valuable feature of 
 improvement. No fixtures are required, as the weight of the parts 
 insures steadiness in working. Perfect uniformity of wear in the 
 grinding surfaces is attained by the use of the curved face ; and 
 the expensive dressing necessary in flat stones is here entirely ob- 
 viated, as the occasional grinding of hard substances roughens the 
 faces to an extent sufficient for grinding all the softer materials, 
 which gradually smooth down the faces. 
 
 Any of the materials ground in common mills, and u any which 
 the latter cannot properly act upon, are capable of .eduction in 
 these mills. For flour and other finely-ground substances, a few 
 air-channels are formed down the face of the runner. Their best 
 speed is only half that of common stones; and the inventor states 
 that his experimental results go to show that a two-feet runner 
 produces as much flour as a four-feet tlat millstone, the power 
 required being a minimum. If the stones run empty, no contact 
 can take place, therefore there is no firing, nor does a variation in 
 the feed or speed cause any difference in the relative position of 
 the stones, on account.of the firm and steady revolution on the 
 curved pivots. The antifrictional qualities of these pivots are 
 pretty well elucidated by the fact of the very minute consumption 
 of oil upon them. 
 
 The " Ring Millstone," invented by 
 Mr. Mullin of Gilford, Ireland, is pro- Fi »- 4 - 
 
 posed as the means of securing four 
 special advantages — economy in ma- 
 nufacture, simplicity and effective ven- 
 tilation, increased production of meal, 
 and a saving of labour in repairs. Fig. 
 4 is a vertical section of the stone, and 
 fig. 5 is a corresponding plan. The 
 " eye," a, is made excessively large in 
 proportion to the stone's diameter, ex- 
 ceeding, indeed, half the latter dimen- 
 sion. This increased area admits a 
 
 greater volume of air than is usual, and this air, coming in contact 
 with the more rapidly revolving portion of the stone, is passed 
 

 admits of thr foraasliua of thr •> the ordinary I 
 
 of 1«.Iii.,' f,ir-..»« for the il.K'.nhuli n of tin air o\. r the grin.lirig 
 anrbm. aod thu» ro^rr grain 
 
 ..rea of 
 «. . •. . .• -: -.. at •.:,.■ r.n!.T, ili. operation of (Ironing i- ob- 
 i 
 
 . a pcr- 
 nx-a'-le anafaMMO, r.-ij^.'. ■ •! Jn-vun;'»i;rial portion uf the flour 
 during lh.- actual grit 
 ■ 
 
 which i» liU-raU-d jo- 
 in tlie lower si.. in-, aii.l tin. 
 coarser pa." 
 
 1 from tin- final on. • 
 
 tin. npper atone, n - 
 
 - 
 
 thf direction of tli. 
 
 down upon thu 
 
 1 the 
 
 me. 
 
 of ■ Bopr throngfa 
 
 I that lie can 
 
 - from ordinary wheat, from one to 
 • 
 I 
 
 U 
 
 • • each pair of 
 ico-printing m i 
 Gridusl small el II 
 
 F.». 7. 
 
 
 _ 
 
 
 
 e 1 
 
 
 
 
 
 
 1 
 
 
 ,_ 
 
 
 n 
 
 ;. which form* the a\i* of the npper 
 I f the rode, c, with 
 
 ■| 
 i with a fly-wheel,/, whirl, 
 o»'t for driving floui ere ia alio an 
 
 . 
 
 i ; and 
 from tl>. 
 
 for the lower and of U arnica 
 
 i 
 longitudinally by the bearing in the 
 I, /. hut only laterally : ami there in a hard, 
 in that lower and, whi I I at tho 
 
 I 
 ■ 
 ■nd ill. 
 
 • ilt, which, I- ■ nut fitted opon the 
 
 ■crew tl 
 
 end of the lever, and thus the upper milli 
 to the inl from the lowi It fa 
 
 th«> vertical movement which is occasionally required t" I* 
 
 -. ./.that tin' ronnectii \ I 
 
 to the piston-rod by nonrenal joints. 
 
 ! by tho 
 
 both i nda of the cylinder, «. and connecting it at • . 
 with the abaft, <.'. of the upper mill-: \ to tin- pah; of 
 
 mill-ton • n that side of the stasm-engi 
 
 it should be di lime to work only one of the upper 
 
 the other maj ' 
 ereto. 
 
 ild nir with tho grain 
 tween ll of the moot im- 
 
 portant of the modern improvementa in grin 1 
 
 anrfacea are Ihm increas- 
 
 ed, whilst the quality of Boor ia very superior to that produced in 
 fiie old way. It ia thin feature which bolda a prominent place in a 
 invention by Mr. J. C < . • .w. 
 
 - of our angravin •- ia a w rtscal - 
 millstone arrangemi nta, 
 with the Foi 
 
 this par] he asea two grain feed-pipes, 
 
 wards, like a forked i m the narrow fa 
 
 the hopper, n, the n ■ pindle, c, 
 
 .;. from the main spindle, Di through a joint-hole 
 in thf fork, int.. the main un from 
 
 the hopper. After diverging downwards, until tiny reach tho 
 npper surface of the fixed atone, a, lha two I 
 vertically thron dlreotly through lha 
 
 upper - 
 tho stone. An annular portion of tho under surtsoe of tl 
 
 through 
 ■ from tin' outer aide of tin a 
 
 twei n the two 
 
 • thfa part, For the I I M grain ami air, ami 
 
 precluding Un oham f the i imencemenl of the grinding 
 
 nation, before the air has full] 
 
 lha npper fixed atone, be t ween the two 
 . over »iili :i • paaaed over the feed-spindle, 
 
 adjustment at the aye 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 as a valve. The grinding surface of the lower running stone, H, 
 is perfectly Sat throughout, and its eye at the grinding level is 
 covered over hy a metal plate, f, with a ventral aperture round 
 
 the feed-spindle, G, for the passage through of a portion of the 
 air. In this way, part of the air may be discharged at the eye of 
 the upper stone, and part down through the eye of the runner 
 beneath, whilst the main body of the air goes along with the 
 grain, and is discharged with the grained material at the periphery 
 of the stones. By this contrivance, the entire surface of both 
 stones is kept encircled by a constantly changing air-bath or 
 current, for the air, escaping at the eye of the upper stone, is 
 directed by the valve disc over its entire surface, whilst that from 
 the bottom of the lower eye passes over the whole bottom surface 
 of the runner, between it and the bottom base plate, i. This has 
 a ventilating effect ; for on the upper edge of the iron casing, j, 
 which surrounds the lower running stone, and supports the upper 
 fixed stone, is placed an annular disc of wire-cloth, K, covering 
 over the annular space left between the periphery of the stones 
 and the interior of the casing. This wire-cloth stands a short 
 distance above the level of the grinding surfaces, and from its 
 periphery a light wooden casing, l, springs upwards, surrounding 
 the upper stone, and bevilled inwards at some distance above the 
 stone's surface. Thus there is a current of cold air passing from 
 the running eye up outside the stone and inside the casing. 
 There it meets the heated current from the grinding surfaces at 
 right angles ; and breaking this heated current, whatever grained 
 material is held in suspension, falls back within the bottom casing, 
 whilst the heated air passes off through the wire-cloth, again 
 meeting at right angles with a cool current from the upper side of 
 the top stone, which, in conjunction with the bevilled top of the 
 upper case, still further separates the suspended flour, and aids 
 the ventilation. Another modification of stones relates to the 
 combination of three or more separate stones, instead of two. as 
 hitherto used. In this plan, which is represented in fig. 9, the 
 central stone, a, is the runner, the upper and lower ones, n, c, 
 being fixed, so that the grinding is performed both between the 
 under surfaeo of the upper stone at D, and the upper surface of 
 
 the central runner, and between the under surface of the latter 
 and the upper surface of the bottom fixed stone at E. The grain 
 is fed through the 
 pipe, F, into the 
 hopper, G, through 
 the adjustable feed- 
 passage into the pipe, 
 H. Hence the supply 
 for the upper grind- 
 ing surfaces passes 
 out by the inclined 
 lateral ; opcning, i.into 
 the hollow space, J, 
 in the upper stone, 
 forming the lower 
 part of the eye there- 
 of. Here it falls on 
 to the disc, K, and is 
 directed to the grind- 
 ing surfaces. The 
 
 supply of grain for the lower or secondary grinding action passes 
 out at the bottom of the pipe, H, into the eye of the runner, A, 
 and thence proceeds to the grinding surface. The upper stone is 
 supported by side brackets, these brackets being carried on the 
 lower annular casing, l, bolted down to the floor. The bottom 
 stone is sunk in a casing, m, recessed into the floor or platform, 
 being steadied late- 
 rally by an annular 
 piece of metal level 
 with the floor, whilst 
 it rests on adjusting 
 bolts, N, beneath. 
 The spindle, driven 
 by gearing from be- 
 low, rests in an ad- 
 justable balanced 
 footstep. It is fitted 
 to the runner by a 
 Ryne, made on the 
 " balance " principle. 
 The top of the spin- 
 dle is spherically 
 shaped, as at o, be- 
 ing passed through 
 the collar disc, p, 
 and fitted into a 
 spherical recess in 
 the under side of the 
 Ryne, Q, connected 
 to the stone, a. In 
 this way, as the con- 
 nection between the 
 spindle and the stone 
 is entirely formed by this ball and socket, no derangement can ansi 
 from the spindle and runner getting out of truth. 
 
 Fig. 10 is a vertical section of the "balance Ryne," on a large* 
 

 araie. a m lb* ban*- [Jav. and • lb* loner running «!•■:.• 
 fro-n »l..«r by Ibe maia aeaadle, I, which paaaga down t!. 
 cawtr* of Iba k!,u.'»kr tube* of tba d-cd-bopper, and trrnunatra 
 la a o 
 
 lb* diae pier*, D, wbirb baa famed upon Ibe epn" 
 ► ••* . » . i . r »• |. piec*. readag in a bfaai ..-r . I 
 
 I . 
 
 :nd arranged I 
 ■ 
 
 of Iba H 
 
 ruinate in an annular 
 
 .: 
 •< an u|'|it C"l!ar \>\»<h it. I 
 T - pass at 
 
 . and finally I which 
 
 . 
 
 teral adjustment, and 
 
 truth with the 
 
 - 
 ■ 
 
 I 
 
 - when 
 » [idle, ami thus 
 
 .. o, as may b. 
 
 I and a 
 
 ■ 
 
 1 
 
 of ill..- 
 
 • •t* the 
 I -rk of 
 
 Iheae maker*. 
 
 Ki l.r.s AND PRACTICAL DATA 
 W01 
 
 .r nulla, the .i 
 
 on V ■ 
 is aoax- inaged eatabhahnienU in and around Pari*, 
 
 ■ 
 
 ! in this ma- I al it rr. 
 
 quirea ai -.ilagrain- 
 
 I- r hour. Of ■ 
 gntuifm •». )u 
 
 work, n -, but also all i pparataa 
 
 mill. 
 
 from 15 ' 
 
 or 51 kDogrami 
 
 : .u, 1 bulling 
 - • 
 
 ■ 
 of 15 horsea power, w< -.nix pairs ol 
 
 ring apparatus and c W 
 
 r, that iu this i 
 - 
 is mail. 
 
 -' 
 
 an actii< 
 
 . . . ii- 1 as mucl. 
 
 In ni 
 
 - 
 of Bur^unilv al ills are 
 
 ■ 
 
 - 
 -i-cunds 
 M mills. 
 The p 
 ■lihoogl 
 
 ni. that 
 uniler thi 
 
 of 75 
 
 i actual gain, as far as 
 it ; nnd it may be said, indeed, that with a powar 
 of four boraaa, from 100 to lot kilo^r. 
 
 - 
 - :i and around I'ari.t, the san.- 
 ■ 
 
 n which, as we have 
 said, a it, 
 
 ■ 
 
 apparatii- 
 
 I of wheal 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 169 
 
 ground per horse power per hour. In fact, experimental investi- 
 gations have shown, that, with a steam-engine of from 24 to 25 
 horses power, working seven pairs of stones of 13 m. in diameter, 
 17,374 kilog. of wheat could he ground in the 24 hours. This 
 corresponds to a power of 3| horses, and 103-4 kilog. of wheat 
 ground per pair of stones, or to 29-5 kilog. per horse power per 
 hour. 
 
 We may, therefore, deduce from the preceding results : 
 
 First — That with an effective power of one horse (or 75 kilo- 
 grammes raised one metre high per second), a mill should grind a 
 minimum of 20 kilog. of wheat, and a maximum of 30 kilog. per 
 hour. 
 
 Second— That the minimum quantity applies to mills wbieh are 
 worked for commercial purposes, and particularly for the Parisian 
 consumption, producing the greatest possible quantities of the 
 higher qualities of flour. 
 
 Third— That the medium quantity (of from 25 to 26 kilog. per 
 hour) is that produced by mills likewise worked for commercial 
 purposes, but making a greater quantity of second quality flour, 
 such as those at Lyons and other places. 
 
 Fourth — Finally, that the maximum quantity corresponds to the 
 produce of those mills which only grind the coarser qualities, and 
 in which the cleansing and dressing mediums are very simple. 
 
 TABLE OF THE POWER REQUIRED, THE QUANTITY OF WHEAT GROUND, AND THE NUMBER OF PAIRS OF STONES, 
 
 WITH THEIR ACCESSORY APPARATUS. 
 
 Effect 
 
 ve Force in 
 
 Quantity of Wheat ground in kilogrammes per hour. 
 
 Nu 
 
 nber of Pairs of Stones. 
 
 Horses 
 
 
 
 
 
 
 
 
 power. 
 
 k. m. 
 
 Minimum. 
 
 Medium. 
 
 Maximum. 
 
 Minimum. 
 
 Medium. 
 
 Maximum. 
 
 1 
 
 75 
 
 20 
 
 25 
 
 30 
 
 1 
 
 1 
 
 J 
 
 2 
 
 150 
 
 40 
 
 50 
 
 60 
 
 1 
 
 1 
 
 J 
 
 3 
 
 225 
 
 60 
 
 75 
 
 90 
 
 1 
 
 1 
 
 ] 
 
 4 
 
 300 
 
 80 
 
 100 
 
 120 
 
 1 to 2 
 
 1 
 
 1 
 
 5 
 
 375 
 
 100 
 
 125 
 
 150 
 
 2 
 
 1 to 2 
 
 1 to 2 
 
 6 
 
 450 
 
 120 
 
 150 
 
 180 
 
 2 to 3 
 
 2 
 
 1 to 2 
 
 7 
 
 525 
 
 140 
 
 175 
 
 210 
 
 2 to 3 
 
 2 
 
 2 
 
 8 
 
 600 
 
 160 
 
 200 
 
 240 
 
 3 
 
 2 to 3 
 
 2 
 
 9 
 
 675 
 
 180 
 
 225 
 
 270 
 
 3 to 4 
 
 3 
 
 2 to 3 
 
 10 
 
 750 
 
 200 
 
 250 
 
 300 
 
 4 
 
 3 
 
 2 to 3 
 
 12 
 
 900 
 
 240 
 
 300 
 
 360 
 
 4 to 5 
 
 4 
 
 3 
 
 14 
 
 1050 
 
 280 
 
 350 
 
 420 
 
 5 
 
 4 to 5 
 
 4 
 
 16 
 
 1200 
 
 320 
 
 400 
 
 480 
 
 6 
 
 5 
 
 4 to 5 
 
 18 
 
 1350 
 
 360 
 
 450 
 
 540 
 
 6 to 7 
 
 6 
 
 5 
 
 20 
 
 1500 
 
 400 
 
 500 
 
 600 
 
 7 
 
 6 to 7 
 
 5 to 6 
 
 22 
 
 1650 
 
 440 
 
 550 
 
 660 
 
 8 
 
 7 
 
 6 
 
 24 
 
 1800 
 
 480 
 
 600 
 
 720 
 
 9 
 
 8 
 
 6 to 7 
 
 26 
 
 1950 
 
 520 
 
 650 
 
 780 
 
 10 
 
 8 to 9 
 
 7 
 
 28 
 
 2100 
 
 560 
 
 700 
 
 840 
 
 11 
 
 9 
 
 8 
 
 30 
 
 2250 
 
 600 
 
 750 
 
 900 
 
 12 
 
 10 
 
 8 to 9 
 
 32 
 
 2400 
 
 640 
 
 800 
 
 960 
 
 12 to 13 
 
 10 to 11 
 
 9 
 
 34 
 
 2550 
 
 680 
 
 850 
 
 1020 
 
 13 
 
 11 
 
 9 to 10 
 
 36 
 
 2700 
 
 720 
 
 900 
 
 1080 
 
 14 
 
 12 
 
 10 
 
 38 
 
 2850 
 
 760 
 
 950 
 
 1140 
 
 15 
 
 12 to 13 
 
 10 to 11 
 
 40 
 
 3000 
 
 800 
 
 1000 
 
 1200 
 
 16 
 
 13 
 
 1 1 
 
 45 
 
 3375 
 
 900 
 
 1125 
 
 1350 
 
 18 
 
 15 
 
 12 to 13 
 
 50 
 
 3750 
 
 1000 
 
 1250 
 
 1500 
 
 20 
 
 16 to 17 
 
 14 
 
 55 
 
 4125 
 
 1100 
 
 1375 
 
 1650 
 
 22 
 
 18 
 
 15 to 16 
 
 60 
 
 4500 
 
 1200 
 
 1500 
 
 1800 
 
 24 
 
 20 
 
 17 
 
 65 
 
 4875 
 
 1300 
 
 1625 
 
 1950 
 
 26 
 
 21 to 22 
 
 18 to 19 
 
 70 
 
 5250 
 
 1400 
 
 1750 
 
 2100 
 
 28 
 
 23 
 
 20 
 
 75 
 
 5625 
 
 1500 
 
 1875 
 
 2250 
 
 30 
 
 25 
 
 21 to 22 
 
 80 
 
 6000 
 
 1600 
 
 2000 
 
 2400 
 
 32 
 
 26 to 27 
 
 
 85 
 
 6375 
 
 1700 
 
 2125 
 
 2550 
 
 34 
 
 28 
 
 24 
 
 90 
 
 6750 
 
 1800 
 
 2250 
 
 2600 
 
 36 
 
 30 
 
 25 to 26 
 
 95 
 
 7125 
 
 1900 
 
 2375 
 
 2850 
 
 38 
 
 31 to 32 
 
 27 
 
 100 
 
 7500 
 
 2000 
 
 2500 
 
 3000 
 
 40 
 
 33 
 
 28 to 29 
 
 This table is calculated upon the conclusions preceding it, and 
 gives at sight, on the one hand, the quantity of wheat which can 
 be ground by a given effective power, and, on the other, the ap- 
 
 proximate number of pairs of stones which may be erected when it 
 is desired to fit up a mill with a determined power. 
 
 It is easy to see, from this table, that the number of pans ot 
 

 rfnom rnriee in arvordaoea » i:h th* three Systran ad •[»!• 
 h Hi i th. table «.::!<» somrirnt guide for tb* constru. 
 low mffl*, whatn.-r amy be the description of prim* mow . 
 ed. It BMt be remarked, thai iti» moat fre<ioeotly upon »uch data 
 that the number of stoors ought U) be determined, when an oU 
 rather than upon tli. 
 
 of the mill which pre* 
 
 H by a niill or. 
 
 known ■ 
 
 gr four pt^rs • 
 atnoea of 1-3 m. in diameter » thcr mills, six, 
 
 •••in various causes. Thus it 
 will be understood, th •' ■ '" an old mill, 
 
 t* badh ind badly arranged, it will utilize very little 
 
 of the deposable force, and re, only give out an 
 
 amount of work uju 
 
 large Preach stones, with large eyes but ungrooved, can be made 
 I little or much at ; 
 
 in fact, 
 that the quantity of wheat ground by a pair of Urge stones, in a 
 Ml ground by a pair of small 
 ataaaa, 
 
 • rence to thi- .-i-.thtr remark to Ik- 
 
 i p~t« ) which will not be without importance. In many '■■ 
 without adopting the ! 
 mills established on a ■ 
 
 the ma lb* bydrnalie prime morer, 
 
 hare been im; • B '- sufficiently advanta- 
 
 and, in fact, i: • more with a 
 
 , than they ban I producing at a later 
 
 ■ ■i l.y appanttna entirely on 
 
 the constructor 
 
 staining worse results after than before the 
 
 It niu»t be recollected, that when i French mill are 
 
 improTed — that fa) to m 
 it, and a good - 
 
 and not rncum th much aiv. -- 
 
 kv after all, when taken as a 
 
 than the English mill which is substituted for it — whoa 
 with the same amoun! 'lian the 
 
 latter, although this latter !. became the 
 
 machinery is ■ and better adapted for working in a 
 
 regular and continuous man 
 
 i»t also remark, that there are mi - stones 
 
 • f from 14 to 15 m. in diameter, at 
 
 adopting the i ral details — that 
 
 w to nay, the atones are grooved and dressed in exactly the same 
 manner as those of 1*3 m. in dian 
 
 due* n> •• Ibjaj the Utter, although they are not 
 
 ,t so rapid a rati', th.- 
 
 1'iieee larger dimensions may have the advan- 
 tage of simplifying the machinery, and diminishing the number of 
 
 . m the one hand, and perhaps, on 
 
 ■ - It 
 
 • a mill, 
 
 - .ral pairs of stones of 13 m. in diameter, may at 
 
 utilized with - 
 Again, it I 
 
 drive two pairs of small ttoi 
 one pair ; or that it is i go to the cx|- 
 
 witfa a single pair i 
 profitably employed, and ti 
 
 repairs, and keeping iti 
 
 V, remarks by a statement of l 
 
 . mills, of different epochs : — 
 
 1 1 rtt Statement of Produce, obtained from an 
 belo-.ioing to Jf. Bn< •. «o«r no longer in mU 
 
 . 
 
 Wheat flour .6*1 
 
 Flour separated from the oatmeal, .let " .. ll A " 
 
 • .. I i" = »« pel '"■' 
 
 " 3rd and 4th. " .. «J 
 
 Coarse bran SO fail 
 
 •• 
 
 Coarse meal, " 8 | — 
 
 •■• 50 " ... 4 J 
 I loss = 2 
 
 General total, 
 
 - rend Statrmmt <f Produce , 
 
 It) of \VI„at, i U liilog., obtained from a Mill, 
 
 on the Ennlith eyitem, near Paris. 
 
 Flour, 1st and 2nd quality,. . 
 
 Srdqualiti l,MO l=t-| 
 
 " 4th •• ' :.•''*•■• 1 
 
 sifiiuLT- «,8oo = •: 
 
 • 5 " 
 
 Pfaeta and loat 16,070 =»•« " 
 
 al total, fclf,in kilog. 
 
 Butheh) of Wheat, W tifki» $ 11,8 
 
 :-! quality B,«60 = "" ! ■ 
 
 tta ns % ■ 
 
 •• Irdend Ufa 411 = 4 " 
 
 Various products, MM es M 
 
 S 1 W.MILLS. 
 
 iiT Bkrw-mflk may be dhinad into Iwo dk« 
 
 Dam.lv. those in which the saws have a eontfainoai mot 
 mom in which the motion ■ rocippicatory. 
 
 The first class comprises not only circular saws, but BH 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 which consist of a thin flexible steel-plate, passed round two drums 
 or pulleys, like an ordinary pulley-belt. 
 
 The second class comprises straight saws, acting vertically or 
 horizontally, or sometimes slightly inclined. 
 
 We shall here give the notes of some experiments upon asawing- 
 machine, having several saw-plates arranged side by side in a frame, 
 weighing altogether nearly 400 kilog. 
 
 The power expended by the prime mover was, for -161 sq. m. in 
 area, sawn through per minute, in dry oak, 3-7 horses power ; and 
 4-5 horses power for an area of '131 sq. m. sawn through per 
 minute, in oak that had been cut four years. In these instances, 
 four saw-plates were worked at once, which gives for each saw- 
 plate, in the first instance, -925 horses power per plate ; and, in the 
 second, 1-125 horses power. 
 
 The width of the set of the saw is ordinarily 3 to 4 millimetres 
 at the outside. 
 
 A reciprocating saw, making, on an average, 120 strokes per 
 minute, with a length of stroke equal to -6 m., the cranks being 
 •3 m. iu radios, passes in a minute through a space equal to 
 
 120 x 2 x 6 — 144 metres ; 
 or, 
 
 2-4 m. per second. 
 
 Now, with such a stroke, we can saw through a thickness of 
 from 50 to 60 centimetres, and even more. In taking the lower 
 of these two dimensions, the work obtained per minute, with an 
 advance of 2 millimetres, is 
 
 120 x -002 x -5 = -12 sq. m., 
 for the area sawn through, measured upon one side only. 
 
 This, per hour, is 
 
 •12 x 60 = 7-8 sq. m. 
 
 WORK GOT THROUGH, WITH A LONG SAW, BY TWO MEN. 
 
 448. Two men, giving on an average 50 strokes per minute, can 
 go on, without stopping, for 3 or 4 minutes. Allowing that they 
 stop every 30 seconds, or half minute, the stroke of their saw being 
 •975 m., the entire length of the plate, 13 m., they will saw through 
 a length of '92 m. in 7 minutes. This gives for the area sawn 
 through— 
 
 •92 x -315= -2898 sq. m. ; 
 or, per minute, 
 
 •2898 -4- 7 = -0414 sq. m. 
 
 Thus, the work of these two men is very nearly equal to that 
 of one of the saw-plates in the sawing-machine first described, which 
 requires a force equal to one horse power. This difference may 
 easily be accounted for, when it is recollected that, in the sawing- 
 machine, a considerable part of the motive power is expended in 
 overcoming the friction of the various moveable parts, through 
 which the motion is communicated to the saw-frame ; whilst, in 
 manual sawing, the power is applied directly to the saw, and the 
 frame is always a very light affair, especially as compared with that 
 in the machine. 
 
 In a manually-worked saw, such as we have alluded to, the 
 teeth are '013 m. apart, so that 75 teeth come into action during 
 the stroke of -975 m. The depth of these teeth is -0065 m. ; that 
 is to say. half their pitch. They are very slightly bent to each 
 
 side, and the workmen chamfer off their inner edges, alternately on 
 one side and on the other. 
 
 As the saw only acts during its descent, it may be deduced, from 
 the preceding statements, that its mean advance is 
 ■92 m. -r-7 = -1314 m. per l'j 
 and per stroke of the saw, 
 
 •1314 -4- 50 = -00263 m.; 
 that is to say, a little above 2.' millimetres. This advance is very 
 nearly the same as that ordinarily given to a machine-saw, when 
 sawing oak. 
 
 VENEER-SAWING MACHINES. 
 
 For veneer saws, which generally work upon hard wood, and 
 which, moreover, produce sheets of peculiar thinness, and perfectly 
 equal and regular throughout, it is obviously impossible to advance 
 through the wood at such a rate as is customary in cutting deal 
 bulks into boards. 
 
 The velocity of these saws is, perhaps, greater than for any other 
 purpose. It is not less, in fact, than 280 strokes per minute, and 
 often reaches even 300 strokes, which is more than double the 
 ordinary velocity formerly adopted. 
 
 If the saw only advances through mahogany at the rate of \ 
 millimetre for each revolution, the length sawn through per minute 
 will be 
 
 300 x -0605 = -15 m.; 
 and per hour, 
 
 •15 X 60 = 9 metres. 
 
 If the width of the wood be 40 centimetres, the area sawn 
 through per hour will be 
 
 9 x -4 = 3-6 square metres; 
 and per day's work, of 12 hours, allowing 2 hours for grinding the 
 tools, fixing the wood, arranging the saw, lubricating, vie., the total 
 work done will be 
 
 3-6 x 10 — 36 sq. m., sawn through. 
 
 We may remark, that the actual juice paid to saw-mill owners 
 for sawing mahogany is, at Paris, generally 28 fr. per 100 kilog., 
 20 sheets of veneer to the inch, or 27 millimetres, of width being 
 given. 
 
 It is scarcely twenty years since the time that 10 francs per kilog., 
 or 1,000 francs per 100 kilog., was paid for this description of saw- 
 ing; and it was very rarely that so many sheets of veneer were got 
 out of the same thickness of wood. This immense difference will 
 give some idea of the effects of competition, and the improvements 
 continually made in the construction of machinery. 
 
 CIRCULAR SAWS. 
 
 450. Circular saws are, without question, the simplest, and 
 capable of the greatest number of applications in the industrial 
 arts. They are employed of all dimensions, from those of 2 or 3 
 centimetres in diameter, to those of 1 metre, and even more. The 
 smallest and weakest are generally used for cutting very minute 
 articles, in bone, horn, or ivory. In the machines tor cutting the 
 flat sides of wheel-teeth, we find circular saws employed, of from 
 6 or 8 centimetres, up to 14 or 16 centimetres in diameter, accord- 
 incr to the power of the machine, and the strength of the teeth to 
 

 DRAUGHTSMAN'S 
 
 V* cat la earpaotry. cataoeUnakinf, and coarh-makirv i 
 Stars arc . ii. ; "> diameter. ! 
 
 rralar sew. may be r..i»«i.l.r.-.l indispensable, 
 dan, and alio on account of 
 the prrfeclioo of their wort The atwt turd in theae »•• 
 
 aha at a 
 rate not leaa than 400 pat minute, and in some cases 
 
 xxrcsmtm with a cisci-lar saw, -7 m. is diameter. 
 
 J sawn: oak, one year rift. I 
 
 — 
 
 KmWi of ratolaoou of Ike mm par *M 
 
 Aim m«i ptr eiitU 1* «j m 
 
 i . — Kind of win J sawn : dry deal, in pkufa 
 
 ■ — 
 
 NumWi of nvolnuoM of th« nw ear I' t44 
 
 Araaaawu in 1' -71«q. «. 
 
 These Ibat, for ml circular 
 
 - M iiiiuli work a-- four vertical roctilinoar aw» in tliu 
 same time, and with tin- vim.' motive power. 
 
 It must b». romariud, thai I 
 
 product of the depth of the pi. cc b» the length, sawn, and not the 
 
 Mim of the two boas separated bj nsry in 
 
 calculating WOOd. 
 
 CHAPTEB \iv. 
 EXAMPLES OF FINISHED DRAWINGS OF MACHINERY. 
 
 BALAXCE WATER METER. 
 
 EXAMPLE PLATE A- 
 
 In ap| boon for the in-truc- 
 
 P I 1 . ■ :-inari in Industrial Design, We now 
 
 • :■ tails of the finished 
 
 I foi - .'lidance. 
 
 ■ clmi a ol can 
 ■n the part of the draughtsman who oom- 
 
 •- and fidelity OD the part of the 
 
 the dvlineati i 
 
 .il lights 
 
 reying 
 ■ the full aixe of a fluid mi 
 
 water, or as moeh 
 
 . -vary lor thl 
 
 It. I 
 
 ..in, » brother of Mr. E. w > ■ ft lin, the 
 
 ." both uf which gen- 
 well known to the reader! of theae pages, from 
 Ui. ir in us to physical science and the oonatractive 
 
 art-. 
 
 r" is of the rotatory kind, and I 
 i with the v Ing, within the compass of 
 
 the quantity of 
 aster flowing through n pipe, with equal accuracy at all p 
 »nd whbool ttnaons flow from the 
 
 i la a longilu i of the mater, 
 
 •hOW the 
 
 I ling longitudinal 
 
 ratun, end I ■ whole of tbi 
 
 aontaiiu I leal eaat-iron shall, a. having pluin 
 
 end nangaa, b, for bolting it in the line of the water supply-pips, 
 
 and a short cylindrical box, ' . screwed on the Up| 
 
 the Index geai -t hollow and open through- 
 
 out, l.ut with three projecting annular ribe for bori 
 for a drawn braaa lining tube, D, inaerted for the purp 
 securing a perfectly uniform area throughout the waterway; and 
 within this waterway are planed two hollow metal drum-. 
 ported on longitudinal eel in the axial lii 
 
 shell. 'I tried at their ontor ends in lx 
 
 g, in the centres of the fixed b, one of which is In 
 
 Motion, and tl ppoaite or inner spindle bearings are in i 
 
 central bracket opposite the rib, i. of tie 
 
 dinal half, from the centre line, is precisely the same in i 
 
 tion. The coins. 11. have ca.li projecting spindle 
 
 , I of tile shell, where IheV .. 
 
 cally with the shell'e uia, bj cross Lars. ;, in -hallow rii 
 
 1 into each end of the shell; whilst the c< 
 . four thin radial I 
 
 lining. The inner surfaces of theae con. nd Lha 
 
 slightly convex races of the drums, s, project s little way Into 
 
 1 iwn on the ri The 
 
 drums, K. are the prime motive dotaj - 
 
 blades, or twisted van. s, i„ sal in r. i 
 
 left-handed Motion i the drum BpL 
 
 pinions, », one on the inner end of each -pin. He. Bach pinion 
 te .ToWII Wheels. >, so that the two 
 
 are oompelled to revolve at the same rate In opposite directions. 
 
 The h.w.r crown wheel is simply . ihorl stul-shaft, 
 
 running in bearings in the centre I. racket, I.. Ing dm rely used to 
 coiin.et the t»o pinions on the lower side; whilst tb< 
 
 last on the lower end OJ ,'1' Wted 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 in the same bracket, and passed through a hole in the side of the 
 shall, to give motion to the counter above. The special object of 
 tills application of the second crown wheel, is the neutralizing the 
 lateral pressure upon the drum bearings, in the transmission of 
 motion from one drum to the other; aud to reduce the working 
 friction to the highest degree of refinement, the total weight of 
 each drum is calculated to be just equal to that of its bulk of tho 
 fluid surrounding it. The water enters the meter, as indicated by 
 the duplex spreading arrow, passing through a coarse grating, P, 
 intended to retain pieces of wood and bulky matters, but permitting 
 the water, with its ordinary impurities, to pass through. After 
 passing this grating, the fluid is collected towards the axis of the 
 shell, by the first internal conical incline, Q, of a duplex cone piece 
 inserted within the shell, aud the flow is then directed outwards 
 by the second reverse cone, R, and spread uniformly over the 
 quick external cone of the pieces, H. The object of this direction 
 of the fluid is to prevent partial currents, which would otherwise 
 disturb the motion of the working drum ; and as water, in passing 
 through pipes, sometimes acquires a rotatory motion, the conical 
 block, H, is armed with the radiating blades, K, to direct the fluid 
 in a line parallel with the axis, prior to its reaching the drums 
 beyond. 
 
 The current, thus uniformly spread and directed, now meets the 
 right-handed screw blades of the first drum, e, which is thus caused 
 to revolve, the water at the same time acquiring a certain deflection, 
 in eonsequenee partially from the resistance of the drum to rota- 
 tion, and partially from the friction of the fluid against the surface 
 of the revolving drum. 
 
 The amount of this deflection or "slip" of the water, varies 
 with the velocity of the current, and would, of course, affect the 
 accuracy of the measurement, were it not for the correcting influ- 
 ence of the second or left serew-bladed drum. The blades on this 
 drum are of precisely the same pitch as those on the first ; and as 
 they revolve, they meet the water at an angle so much greater than 
 occurs at the first drum, as is due to this angular deflection. 
 Hence the water tends to drive the second drum faster than the 
 first, and the fluid Buffers twice that amount of deflection in the 
 reverse direction. Hence the combination of the two drums pro- 
 duces a powerful water-pressure engine, upon which the slight fric- 
 tion of the apparatus exercises no appreciable retarding effect. 
 Moreover, the friction of the water on the drum surface increases 
 in the ratio of its velocity, and the result is, that the combined 
 drums move, under all circumstances, in the exact ratio of the cur- 
 rent. The outer edges of tho screw blades do not work in absolute 
 contact with the internal surface of the fixed shell, A, but no water 
 can slip through this way without impinging on the vanes, in con- 
 sequence of a slight contraction of the shell between the two drums. 
 After passing both drums, the water is again directed as in the first 
 instance, and passes off to the service-pipe at the opposite end of 
 the shell. 
 
 The counter or indicating apparatus possesses some peculiar 
 features, as regards simplicity of details, and the dispensing with 
 a stuffing-box for the commuLisating shaft, o, of the drums. It 
 is entirely contained in the cylindrical brass case, r. in the top of 
 which a strong plate-glass cover, s, is screwed in from the under 
 side. A strong brass plate, T, divides the case from the meter, 
 
 and has a central hole for the passage through of the vertical spin- 
 dle, o. A worm, or endless screw, u, upon this spindle, gives 
 motion to the wheel, v, the horizontal spindle of which has a worm, 
 w, cut upon it, and gearing with a horizontal wheel, x. Tho 
 spindle of this latter wheel carries a broad pinion, Y, which drives 
 both the horizontal spur-wheels, z, the fust of which has 101, and 
 the second 100 teeth. 
 
 The wheel with 101 teeth works loose upon its spindle, but 
 carries round with it a dial-plate, a, graduated on its circumference 
 to 100 parts. The lower wheel of 100 teeth is fixed upon tho 
 same spindle as the first, and carries an index hand, which works 
 round above the dial, and points to the divisions thereon ; and a 
 fixed hand, J, points as well to the same graduations. The train 
 of worm-wheels is so proportioned, that exactly 10 gallons of water 
 must pass through the meter, in order to move the dial-plate under 
 the fixed hand through one division. One entire revolution of the 
 dial, consequently, indicates the passage of 1,000 gallons of water, 
 for which tho moving differential hand passes through only a 
 single division on its dial. An entire revolution of the latter, 
 therefore, signifies the passage of 100,000 gallons. The reading 
 of such a dial is extremely simple. If we suppose the fixed hand 
 to point to 47, and the hand on the dial to 89, this will show that 
 89,470 gallons have passed. 
 
 The whole chamber of the counter is filled with purified mineral 
 naphtha, or other non-corrosive liquid, which communicates with 
 the impure liquid passing through the meter, only through the 
 medium of the capillary space round the upright spindle, o, and 
 does not intermingle with ^although both liquids are under the 
 same pressure. 
 
 The actual measurements by this meter have been found to* 
 agree so perfectly with the calculations, in which the frictional 
 surfaces against the water are taken into account, that llr. Siemens 
 considers any means of adjustment to be unnecessary. Much, 
 however, depends upon the formation of -perfect screw vanes upon 
 the drum, to insure uniform results : but all difficulty on this head 
 has been very successfully removed, by casting the drums in metal 
 moulds, using a peculiar composition, which does not shrink in 
 cooling, and runs very fine. 
 
 The only parts of this meter where wear and tear is to be ex- 
 pected, are the pivots of the rotatory drums, and these are made 
 of hard steel, and abut against agate plates ; 'but considering that 
 all weight is taken off the bearings, and that the water simply elides 
 over the drum surfaces, these pivots may reasonably be expected 
 to run for years without requiring attention. 
 
 An important practical advantage of this form of meter, is its 
 compact form, and the facility which it offers for adjustment in a 
 line of pipes below street pavement, or at any required elevation 
 or direction. The internal working parts are qujte self-containi d, 
 and inaccessible widiout unsoldering the ends, so that they may be 
 intrusted to the care of ordinary workmen. 
 
 In addition to the employment of the meter for water-works 
 purposes, it may be usefully applied for registering the water sup- 
 plied to steam-boilers, in order to ascertain the actual evaporation 
 going on, so as to afford a correct estimate of the value of the fuel 
 on the one hand, and the engine and boiler on the other. 
 

 Til.: 1 
 
 BB \!'IN<; M \> Hi 
 
 PLATE 3. 
 
 Oar aeeoad t ' T ** plal* is in a marc ai. 
 
 .'.usst, and, s» a work of high< r . a moat 
 
 ■J|«u|»mtl subj.-ct for the a 
 
 It goes further than Plat* A. in as lar as, in addition to it-, value 
 t , a fc^ ■ nta aome mml important 
 
 features of symmetry in ita abstract design, and • 
 
 ■mlainii al di» 
 
 trirance, and l! -° details. T>. 
 
 of to good a design U 
 
 When WaU was laying the foundation of our present magniii- 
 \. ■ I •:.. . haai a .. '-. :.• '-....- I:.- : a: ■ W -ry tuni bj | - . ■■- 
 
 lieal dimraltirs, in tin- want ■■: 
 hit ideas; and many 1 
 
 to remain mere suggestive designs. For the same 
 numberless works, which the growth of mechanical con- 
 trivances has turned into even-day opera!] ited and 
 
 > B aa simple impossibilities, in the 'i 
 were made by the crude process of wrapping a wire round a man- 
 drel, and compressing it between elastic dies. But I 
 
 • •ur farm operations have begun to 
 feel the benefit* of machinery; and, as a 1 
 we now find establishment/, for making and repairing stean. 
 and other intricate mechanistn This 
 
 substitution of machine tools for hand labour, whilst it has intro- 
 duced great accuracy of workmanship 
 that cheapoess of 1 with the ap| 
 
 of new 1 1 i materials, has made us the eminent manu- 
 
 ic are. 
 
 I is also latterly met with increased 
 - 
 tails, sjm) '.'. ; for the at 
 
 naturally cares more for an elegant macliiu- ne than 
 
 for one : ride far 
 
 - • wees. 
 
 :ithc is 
 1 most ancient, and it 
 
 applica- 
 I its action. 1 
 
 Anally accumulated st-parat- 
 planing. - 
 
 - .ially adapted tools. Each 
 1 r. and ia reatricted to a particular • 
 
 many separate I 
 
 • i mechanism. :ve of 
 
 •■ in transferrin;: and 
 .... chances of 
 readjustment. And in many branches of manufacture 
 
 . advan- 
 aae of the several kinds dis- 
 
 courages their adoption. We are, therefore, drive: 
 
 w-hich ahall 
 v. sting detached tools. 
 
 Arts, ha? 'ally alluded to this, in speaV 
 
 of " machine* much more comprtl.- -;mple in form, 
 
 by mea - in general will 
 
 :.truduced into 
 ;• of a smaller character than at present, in the same man- 
 ner as t - -aw haa e adca 
 
 - 
 upon, the common lathe a- 
 
 : -ns, arranged by Mr. 
 "«■ combination of the ordinary cirrular-cut- 
 ..:.d arrangements of the lathe, wit!, 
 1'ing machine, or f 
 I e may be applied to most of the «"*-*""« 
 ' useful and ornamental manu- 
 al in the arrangement of coo- 
 Thus, in the case of the lathe, for example, 
 1 kinds of plain 
 work, but -ranch of coro- 
 
 trical turning. For instance, if the sliding bar carry- 
 rkod by an adjustable crank-pin, u 
 a slot in the end of thi 
 
 ;he lathe nv. 
 the interposition of the ordinary chi :)ie lathe, most 
 
 . 
 kinds of lathes may bo executed — as eccentric, • 
 ■ 'idal, and 01! 
 
 - angularly, by the adjustment 
 ply ne- 
 cessary t" al'< r tin : 
 
 s a prominent feature in I 
 :\idual parts, like the machi: 
 
 - • that a lathe, 
 enitirai-i: —ess the 
 
 the ordinary plain work 
 of the amateur The engineer ami niechai: - re these 
 
 . hange- 
 
 - 
 , ams, snails, spirals, and \ 1 
 
 circular 
 or rectilinear, and for pUnir . I angular 
 
 gearing of a 
 
 . lathe, in which a • maiu sirii . 
 
 actuating the mandrel, B, of the lathe by means of a pinion, c, 
 
 ..r by a clutch: d, back gearing for 
 
 slow speed, as usuai screw, with 
 
 . guidc- 
 
 - -aft for actuating t! -ltd* of 
 
 the sli-: :ig; L, the same for moving 
 
 of the guide- v red shaft, in connection with the dif 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 ferential or barrelling motion, wjiich is attached to the vertical 
 slide, and consists of a segmental screw-wheel, embracing a mo- 
 tion of about G0°, gearing with a tangent-serow on the shaft, L. The 
 
 segment has a radial slot, in which an adjustable crank-pin is fixed, 
 the crank-pin being attached to the bearings of the screw for 
 moviug the vertical slide, by means of a connecting-rod — thn 
 
 Fig. 2. 
 
 bearings of the screw, which, slide in dovetails, and consequently 
 the vertical slide, being thus affected by the eccentricity of the 
 crank-pin. The shafts, A, H, and I, and screws, g and K, are con- 
 nected by a system of wheels, the arrangement of which is clearly 
 shown in the end view, fig. 2 ; but G, H, I, and K, may be discon- 
 nected from their respective wheels at pleasure by clutches or 
 frictions] nuts, a, g, h, i, and l, also project at the end to the 
 right hand of fig. 1, so as to carry 
 change-wheels when necessary, 
 and H and I have intermittent 
 ratchet-feeding movements at the 
 opposite end, similar to that at E, 
 for working the tangent-screw. 
 All these are worked by the re- 
 versing bar in connection with 
 the screw, K. An ordinary re- 
 versing movement, M, is interposed 
 between the guide screw, e, and 
 its driving-wheel, for reversing 
 the motion in sliding and screw- 
 cutting. When the lathe is used 
 for surfacing, this reversing motion 
 is better applied on the driving-shaft, A. Hand adjustments, not 
 shown in the figure, are applied to the boxes of the guide-screw, g, 
 and of the screws of the vertical and transverse slides of the slide- 
 rest. A composite lathe, thus geared, may be applied to all the 
 ordinary descriptions of work. For sliding, boring, and screw- 
 cutting, the mandrel is worked by the pinion, c, whilst change- 
 wheels connect a with a. The height of the tool for turning is 
 conveniently adjusted by the vertical slide of the slide-rest. Sup- 
 
 pose it is desired to stop the lathe at any particular point when 
 the attendant is absent, the screw, K, is put in gear by its clutch, 
 and by means of a detent stop-movement, it stops the lathe at 
 the precise point, by throwing the belt off the fast pulley on the 
 end of A, which travels with considerable rapidity. If it be 
 required to turn a long cone of greater taper than can conve- 
 niently be done by traversing the following head-stock, the cut- 
 ting-tool is set over the work by raising the vertical slide by its 
 hand adjustment, whilst G and i are also connected by change- 
 wheels, so that the slide rises or falls with the cut. If a con- 
 necting-rod is to be barrelled, the crank-pin of the differential 
 apparatus is adjusted for eccentricity to suit the rise of the sweep, 
 and l is connected with G by the change-wheels, to spread the are 
 over the required length. The barrelling may be used in conjunc- 
 tion with the taper adjustments, as will be evident to the practical 
 mechanic. The same parts apply equally to rectilinear cutting, 
 whether parallel or taper, in all directions of the cube, and for 
 barrelling in a vertical plane, the pinion, c, being disconnected 
 with the mandrel, and the feed being applied by the intermittent 
 ratchet motions. For cutting the hollows of connecting-rods, 
 &c, an intermittent revolving motion is given to the tool by a 
 tangent-screw movement as usual, but, in addition, applying to 
 cranks and levers held on the face-chuck ; or, instead of the latter 
 movement, the work may be set eccentrically, the hollows being 
 then worked by the tangenkserew movement in connection with 
 the mandrel. 
 
 Edge-cams, snails, volutes, of spiral curvature, with any num- 
 ber of rises, or compounds of circular and spiral arcs, of which 
 fig. 3 gives examples, may be accurately shaped or planed on the 
 edges, by connecting the tangent-screw with the transverse slide 
 

 I 
 
 L'.. ntrdcC-frxl moirmenU of r. sod I sre put in p-ar, i being 
 
 
 ninn, *, 
 . whilst I an.l ! 
 
 . una and othi i 
 may be shaped l.y va- 
 
 . it aifl diagonal work in any position mny also br I 
 
 - the satue set of 
 
 such as B a c. • 
 
 n c, or sine of the angle, whilst the 
 
 other ande traverses • r.pj.lv Ada practically, 
 
 tii»n in the rvmainin;; direeaoa >•( tlie cube. I 
 
 - introduced into tlic pair of change- 
 In many ca.v>« a crank Fit «. 
 
 in addition to I 
 
 • 
 nunt, t 
 
 whOe d 
 
 ■ i to ailju-t tlie 
 
 I 
 « 1 i — . - i< than ilriwn by a 
 bc\il pinion on I 
 A, the 
 
 ttaehed to ona 
 
 of tli<' bearingi of the 
 
 raw, which U 
 
 -imilarly 
 to tlie barrelling 
 tin nt. 
 
 •':•■ lathe, or shaping machine, con- 
 
 atmctad on the model of tha ordinary planing maebJi 
 
 irately linisliin^' tlic 
 ing tha framingi of marina 
 hi,.! other • I 
 
 appUaahla to n rariety of other wi 
 it eon tha lathe whh 
 
 i rdinary <lrii: 
 
 : 
 
 ^•■rk i^ plaa 
 
 upright itawdaHt i a a, a* in tha ordinary 
 planing machim . whflal ■ verticaJ i 
 may be given to tin 
 • ■.■k, earrying lha lathe mandrel, 
 bj two eonnecting i ■■• 'I by 
 
 crank ■ the bad, and ba 
 
 If m . i .Is are 
 
 adjustable for length by moana ofacrose 
 ■haft, • w-wheel and 
 
 1, ; D i" the ' 
 
 motion, as ii- 
 
 gulate tha eccentricity of the tool daring 
 
 turiiii h mny 
 
 be automatically fed, when requisite, by 
 
 an eooi otrio, do) shown in the I \ 
 
 - Hon, and 
 
 another ai lha baeh of the ande, s, wUofa 
 it aetnataa, adjnata lha mandrel hi a »ar« 
 Heal plane. By Um dhnjtmal p 
 wa deasribed, the ootagonaJ 
 
 for plmmniT-l.liH'k bnuwes, and 
 ilar work, may be aSeOUted with ptl 
 
 no ..t In .1. Tha baoVchnek 
 
 BO tli" side, as used for holding p!uiiiiiirr-lilo.-k- 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 their soles are pla led. A second chuck (dotted) maybe super- 
 posed for fixing work vertically; and a slide may be added to draw 
 up the work, which may then project between the bearers of the 
 
 l>ed. For long works, a bed-chuck is used at each end Levers, 
 also, may bo passed between the bed, by means of a diametric slide 
 on the face-chuck, when requisite. 
 
 We now eome to Plate 3 itself in detail. That plate repre- 
 sents a side elevation of a composite slotting and shaping ma- 
 chine, with self-acting gearing 1 , as adapted for the entire finishing 
 of large cranks, levers, wheels, and other work, ordinarily depend- 
 ent upon the efforts of several tools. The main frame consists 
 of a lasge and elegant column, with an open rectangular base, and 
 bottom flange for bolting down to the masonry. The upper por- 
 tion has east upon it, on one side, a pilaster bracket piece, with 
 two horizontal projecting arms, to carry the vertical cutting slide, 
 a ; and on the other, a pillar bracket to support one end of the 
 main crank disc shaft; on the front side of the rectangular base 
 i- I'. Ited a double-armed bracket, to carry the vertical spindle of 
 the cutting face-chuck, like the mandril and face-plate of a large 
 lathe, as set on end. The cutting slide, A, like that of a common 
 slotting machine, is fitted to traverse in dovetail faces on the 
 overhead bracket arms, being actuated by the revolution of the 
 pin iu the disc, b. At c are two pairs of bevil pinions, connected 
 to work simultaneously by an intermediate vertical shaft, D, the 
 two vertical pinions being each on the projecting end of a hori- 
 zontal screw spindle, governing the traverse motions of a pair of 
 Horizontal dovetailed slides, on which the vertical slide faces of 
 the slotting bar, a, are carried. This is for adjusting the eccen- 
 tricity of the tool in turning. Viewed from the front, the fram- 
 ing of these slides has the form, I, of which the vertical portion 
 and the two arms to the left are covered by the moving details, 
 the latter being completely thrust in when the cutting tool of the 
 slide, A, exactly coincides with the centre of the revoking work 
 en the face-chuck, as also with the crank disc, b. At E is an- 
 other shaft for giving a continuous feeding motion to the trans- 
 verse slides, by the intervention of a worm and tangent-screw, or 
 worm-wheel. This corresponds to the traverse or surfacing 
 movement in the lathe. A hand-wheel, F, is fitted on the pro- 
 longed end of the shaft, D, for manual adjustment when the worm- 
 wheel gear is disconnected by slackening the screw, g, the bear- 
 ing, H, at the other end of the spindle being constructed with a 
 joint to allow of this disengagement. Another shaft, i, carries a 
 spur pinion to actuate the rack, j, on the cutting slide, this 
 pinion being capable of traversing on the shaft by means of a 
 groove and feather, along with the slides of the cutting bar. In 
 this way a continuous vertical feed motion, for turning or boring, 
 is secured, the shaft, I, being connected with the shaft, k, by a 
 worm and wheel ; the hand-wheel, l, on the bottom end of a ver- 
 tical shaft, connected at its upper end to the shaft, K, by a pair of 
 bevil pinions, is the hand adjustment. This motion serves also 
 to adjust the cutting bar, previous to tightening the nut on tho 
 stud bolt in front, for the reciprocating action. During the 
 working of the reciprocating cutter slide, however, this adjusting 
 gear is disengaged, and is kept disengaged by an eccentric and 
 slide actuated by the hand-wheel, n, which moves the entire 
 adjustment in one mass. At the back of the cutter slide, near 
 
 the upper end, is a nut, o, whereby the crank disc connecting-rod 
 may In- detached when wide lateral ranges of the slide are wanted 
 in turning. The general details of the driving gear for the turn- 
 ing and planing actions, are fully delineated in the plate : but it 
 may be explained, that at V is a hand-lever, working over a semi- 
 circular arc, suitably notched and contrived to snift the bearing, 
 Q, of the horizontal shaft, B, by an eccentric, so as to throw 
 either of the opposed or antagonistic bevil wheels on this shaft into 
 gear with its corresponding bevil wheel. This movement enables 
 the workman to connect either the circular action of tin- face- 
 chuck, through the large bevil wheel beneath it, or the rectilinear 
 action of the cutting slide, by means of the vertical shaft passing 
 up the centre of the maiu column, and geared to the horizontal 
 crank disc shaft above, by a bevil wheel and pinion, or, by selling 
 this adjustment at an intermediate position, both may be disen- 
 gaged. At s is a foot-break lever to stop the revolution of the 
 work when heavy masses are under operation, a friction strap 
 from this lever being passed over a pulley on the shaft, R, for ibis 
 purpose. 
 
 At T is a cone pulley, working in connection with the cone pul- 
 leys on the two upper or continuous feeding shafts, for the circular 
 cutting action, the respective pulleys being set to coincide verti- 
 cally when connected. The face-chuck can be fixed during the 
 reciprocating action of the cutting slide, by the clamp, u. This 
 clamping movement consists of a worm, with a square spindle for 
 shipping on a handle, driving a worm-wheel on the end of a spin- 
 dle, connected interiorly with a segmental wedge, the sides of 
 which are portions id' a right and left screw-thread respectively. 
 The upper part of this segmental piece is flattened, to permit the 
 free revolution of the face-chuck when driven by th 
 ing, as indicated by the large worm-wheel, in gear with 
 fast on the spindle of the main front hand-wheel. Near it 
 of the tool is a hand-wheel, v, for the angular adjustment 
 mandril frame or headstock for taper work. For ibis purpose the 
 headstock is attached to the main frame by a central tenon and 
 circular dovetails, which afford a support during the slackening of 
 the holding bolts. 
 
 An eccentric chuck, having two slides at right angles to each 
 other, ami an upper worm-wheel adjustment, is titled on the facc- 
 chuek mandril. The lower slide, for giving the intermittent feed 
 in shaping the rectilinear sides, w, of a crank, has a double-acting 
 ratchet-wheel, temporarily connected by a rod with the correspond- 
 ing feeding disc of the large worm-wheel on the face chuck, when 
 the latter is fixed at u. The intermittent feed is primarily derived 
 from the edge-groove cam on the crank disc, B. This groove works 
 the upper stud-pin of a bell-crank lever, set on a stud centre in tiie 
 side <d' the main frame, and from the lower horizontal arm of this 
 lever a rod descends to the worm-wheel mechanism of tie i. > - 
 chuck. 
 
 The upper side of the eccentric chuck is limited to the ac- 
 tual adjustment of the work, and, by means of the two slides 
 conjointly, adjustments may be made for shaping the bosses of 
 the cranks, as well as the hollows at x. The obliquity of 
 the straight sides, w, of the crank is adjusted by the upper 
 screw-wheel, which need only bo of a diameter equal to tho 
 length of the crank ; or, instead of this plan, the sides, w, may 
 

 U worked .-at ilnVrrolialli by <k' 
 
 la ralti n .• . .«! a crank on : I 
 fared. TV buam an 
 
 bat fitted .- :■ v ■ leal of bj moani of i!.- : in ; '•■■ I A/li r 
 rk ha* U«-a a»Iju*tt-«! . 
 ii ilaiii|iiil ilnaii mil ■ In '" 
 I-./ x ,t..,., c b the i-lim k, >• lli- n )ci-~^l :!,r.ujli the boro ■•f each 
 bow, and thr external etamr~ I taming 
 
 »r»l .lii|»n„' protussss an- gone through. The »Tk requires no 
 further 
 
 b-»\» work tli_m ibr lal 
 
 ' 
 
 ■ •:i in a 
 plait*, a» oa a latin-, entail* w ; liability 
 
 able by 
 ■ 
 
 nee, but 
 
 i 
 
 a In. I, cannot be »<j turned in 
 
 il column, with 
 
 it. Tin- crank 
 - ' 
 -. n-turn ; ami I In (rant of thfl 
 
 mi nt to 
 I 01 
 
 r when 
 
 daaeenda into a pit, so as to bring the d derably 
 
 . in-ular 
 I 1- 1*1 down solid i*.r 
 
 .' worm "r t:in- 
 
 • with n 
 
 mail behind, an<l Iht required an- is 
 
 nk |'iti rnrlin- I 
 ■ 
 
 nil. 
 
 but the 
 
 • at right an r - 
 t" a[.p'. and tuning, 
 
 I 
 
 ■ hack, ud ■ ■ 
 
 !•. th* fa.-. • 
 either a worm at tin- fr.mt tn.l ma. turn the 
 
 : 
 
 ed, as i. 
 
 ■ 
 Ii ft thread may lw pul 
 
 for tin. 
 
 with tli- 
 
 v. 
 
 plank, 
 
 EXPRESS LOCOMOTIVE ENGINE 
 
 The three pUl . far tlio 
 
 kiml in r • \ 
 
 di pth of lining, 
 where every Individaal 
 
 f the i i 
 
 ■ 
 
 of the boiler at the steam dome, aho ■ • •! Iha 
 
 Innermost expanded p 
 section is taken at a point al 
 neck ••! I i 
 
 dbtthxl half section*, one through the mo 
 
 • r llir..il_'!i l 1 .. 
 
 ide with iosidi 
 ' tnd *i\ wheel*; the driving-wheel 
 
 diameter, and arranged In the mannoi 
 Tin- < 
 
 n|i with pistons mado of w 
 be made by lir. GoodfeUou • •! Manchester. The eylu> 
 ,1, r- 1-> be of the hardeal an 
 
 an. I Inn- when fitted The 
 
 cylinder 
 
 p.irH a- 
 
 Ibr the i 
 
 The B n ''"■ eyllnder, 
 
 and four fcet three and ■ quarter Inches i sternal d 
 
 llv i-ir.-nlar .-. I 
 
 la, '.. I.-- of the beat Lowmoi 
 qoality, with the nal 
 
 ] . rU. 1- !■■ I- 
 
 sn.l to be one and three quarter Inehi - apart from i 
 of rivet. The plat** for the cyllndi 
 
 f an inch in tlii.ktn ■■■r tl titer — 1 1« - 1 1 of 
 
 la I f Lowmooror Bowing Iron, or ol equal 
 
 • f an Inch in i' as of lh« 
 
 ! B 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 £..,11:11 quality; to be three-fourths of an inch thick. The plates 
 of tho smoke-boxes and smoke-box door to be of the best Staf- 
 fordshire iron, live-sixteenths of an inch in thickness. The chim- 
 neys tu be made also of Staffordshire iron, one quarter of an inch 
 in thickness ; and the whole of the parts of the boilers and smoke- 
 boxes to be made and fitted up in the manner shown in the draw- 
 ings, which will be supplied. 
 
 The Fire-boxes to be mado as shown in drawing, and introduced 
 as shown in tho cylinder part of tho boiler, four feet nine inches; 
 to be made of the best copper plate, free from all delects when 
 worked. The tube-plate to be three-fourths of an inch in thickness 
 where the tubes are fixed. The sides and end plates to be three- 
 eighths of an inch thick, and the roof-plates to be seven-sixteenths 
 of an inch thick. The bottom plates to be one-half inch thick. Tho 
 boxes to be made with a middle partition in them ; the plates of 
 these partitions to be of copper, made three-eighths of an inch in 
 thickness, and formed as shown in drawing. 
 
 The following are the leading inside dimensions of tho fire-box : 
 — Length on Sre-bar to be five feet ten inches and one quarter. 
 The length at roof to be ten feet six inches. Depth above fire- 
 bars at front plate, six feet fivo inches. Depth at door-plate, six 
 feet ten inches. Width on fire-bar, four feet. Length in cylinder 
 of boiler, four feet nine inches. Height at narrowest part, two feet 
 three inches. Height at tube-plate, three feet. Width at tube- 
 plate, three feet nine inches. 
 
 The top of tho box to be supported by twenty-five wrought- 
 iron bearers, twenty of which to be five inches deep by one inch 
 thick, and the five nearest tube-plate five inches deep by one and 
 a half inches thick. These bearers to res! at their ends on the 
 side plates of the fire-box ; and to be screwed to the top plate by 
 bolts one inch diameter, placed four and a half inches from centre 
 to centre, screwed into the top plate. The screw to be of fine 
 thread, next head of bolt, to be one inch and an eighth dia- 
 meter ; the head of tho bolt to be inside tho fire-box, and a nut 
 on the end of the bolts on the top of the bearers, with one inch 
 screw. 
 
 The Fire-box to be stayed to the boiler by copper bolts, seven- 
 eighths of an inch diameter, screwed into the plates with a fine- 
 threaded screw, having both ends riveted carefully, and placed four 
 inches apart from centre to centre. This also applies to the mid 
 partition. 
 
 The end plates above the fire-box to be stayed to the smoke-box 
 tube-plate, by connecting them together by two stay bolts, each one 
 inch and a quarter diameter. 
 
 The Tubes to be of brass, and made the very best quality, by 
 the manufacturer who supplies the company at present ; or of 
 other equal quality, and to the approval of the company's en- 
 gineer. There will be three hundred and three tubes in each 
 engine ; the size, one and three quarter inches outside diameter, 
 to section furnished; and the thickness of metal to be No. 12 
 wire-gauge at tire-box end, and No. 14 wire gauge at smoke-box 
 end. 
 
 The Wheels are to bo mado entirely of the best scrap wrought- 
 iron, and of tho very best workmanship. The driving-wheel, 
 without the tyre, to bo seven feet one and a half inches diameter. 
 The tyres to be of the best Lowmoor, Bowling, or of equal 
 
 quality ; to be finished five and a quarter inches wide, and two and 
 a quarter inches thick on the tread. The sizes of the wheel in all 
 its parts will be furnished by tho company's locomotive engineer at 
 Wolverton. 
 
 Tho Crank Axles to be mado of the very best iron from the Low- 
 moor, Bowling, or the Haigh foundry forges, or of other equal 
 quality, complete and perfect to the sizes given when finished. A 
 full-size drawing of the crank-axlo in its parts will be snpplied. 
 The outside bearings to bo seven inches diameter, and ten inches 
 in length. The inside bearings seven inches diameter, and four and 
 a quarter inches in length. The crank boarings to be seven inches 
 diameter, and four inches in length. 
 
 The Straight Axles to be tubular, as shown in the drawing, of 
 best quality of iron, seven and a quarter inches external diameter, 
 and one and a half inch thick of metal. Tho bearings of the lead- 
 ing and trailing axles to be the same size as the crank ; viz., seven 
 inches diameter by ten indies long. 
 
 Tho Axle Boxes and brass bearings to be mado according to the 
 drawing which will be supplied. 
 
 The Springs, links, and attachments to the axle-boxes, to be 
 supplied by the company, and applied according to the instructions 
 of their engineer at Wolverton. 
 
 The Pumps to be made of tough brass to the drawing furnished. 
 The clacks and boxes to be accurately finished and fitted. The 
 pump-rams to be made of strong tough brass, with wrought-iron 
 cross-heads, as per drawing. 
 
 The Steam Pipes, blast and feed pipes, to be made of the best, 
 copper, three-sixteenths of an inch thick, with copper flanges, as per 
 drawings to be supplied. 
 
 Regulator to be made of brass, on the equilibrium principle, ad 
 per drawing. 
 
 The Eccentric Straps to be made of the best wrought-iron, lined 
 with gun metal of die best quality, according to drawing, accurately 
 fitted, and to have all the oil siphons forged on. 
 
 The Slide Valves to be made of gun metal, and to have an out- 
 side lap of one and a quarter inch. They are to have an oil 
 or grease cup attached on each side of the smoke-box. to lubricate 
 them. 
 
 The Connecting-rods to be made of the very best quality of 
 wrought-iron, fitted accurately. The straps to be made as per 
 drawing, and the oil siphons to be forged on them. 
 
 The Expansion Gear to bo made as per drawing, all the work- 
 ing and Wearing joints and surfaces to be steeled and hardened, or 
 case-hardened. The distance from the centres of the leading wheel 
 axle to the centres of the middle axle, to be exactly eight feet four 
 inches, and from the centre of the middle to the centre of the trail- 
 ing axle, eight feet six inches. 
 
 These Engines are to be manufactured of the very best mate 
 rials and workmanship throughout, and supplied in every respect 
 with water-gauges, steam-taps for heating water in tender, whistle 
 blow-off cocks, cylinder-cocks, pet-cocks, reversing and expansion 
 gear worked from tho foot-plate ; screw draw-bars (proper and 
 in duplicate), ash-pan, damper, sand-boxes, a full set of tools, lamp- 
 in ms, &c 
 
 Detail drawings of all the parts will be supplied by the company's 
 engineer at Wolverton, previous to manufacture. 
 

 
 TV Svn s I imber, and to ban- 
 
 i - a:.. I ■ half inrhea diauivlrr, 
 
 ;lic end 
 
 oft!.. . Ii aquare inch 
 
 of I].. I 
 
 • aj» of the apring balance to bo gm . ■ hun- 
 
 dred ar. : 
 
 .', ao aa 
 to be iron tu iruo »1« :i the joint U iili.Ii- ; and tin- 
 be pbmd not mora loan three incboe apar. I 
 
 I 
 
 vtut* made in two parta, with a drop apparatus, 
 
 ■ 
 
 robbed down 
 
 . 1 itll|HT- 
 
 ! to re- 
 
 I i 'oDDcll, 
 
 r throughout; 
 t, ahaJl at 
 
 ■ 
 
 b) .Mr. 
 
 !• in (he boat 
 
 •liii-k. 
 
 of the 
 quality, 
 
 • 
 and .1 
 
 '.'iil, will 
 
 nr, aa por drawing, ofqoallt] 
 
 by the 
 
 <• irlng, and 
 
 Tbe TrrUc- 
 •ech end; In i- 
 
 : 
 
 • joint •' 
 
 \v<M>.i'i..\\i\<; m miiim:. 
 
 
 (he itadnl tn 
 - : and wbilal il 
 
 ■ 
 
 i.uliim- is il,,- prodoetion rail At 
 
 W Foundry, Jol 
 
 i iplete longitudinal elevation of tin- im| 
 
 machine, aa iii working order, with a board in the 
 through it to I- of the 
 
 machine. Tin- i-nlir. ; ii|«.n tin- lot 
 
 vertical ride ttmHiH*i a, i-.-i»t in 
 down to 
 
 . 
 
 Brat motion d 
 
 on to tin- whole of thi I 
 
 . ning in bearii 
 
 ; alley, i, from which ■ 
 dl pulley, k, on 
 . planing euttor, i.. i 
 
 liii- apindle ol 
 uatahle end-bi 
 of ili. i- ■• boltod il-i" n 
 
 i 
 
 which i-ni tin 
 
 ■ 
 tudinal centre of the machine, by tin 
 
 ■ I.- bud-wheel, v, « b 
 other ipindle, which it only tc 
 
 ,1. «, on tin - 
 
 : 
 
 Mil tl|l« 
 
BOOK OF INDUSTRIAL D] 
 
 anil thna indicates the exact "set" of the cutters for the particular 
 breadth of timber under treatment 
 
 As the dual is passed into the machine to be plane. 1, it is first 
 of all entered beneath the nipping feed cams, a, which carry it con- 
 tinuously forward to the out. Each nipping arrangement consists 
 of a horizontal traversing plate of metal, b, tongued at its opposite 
 ends, tu slide freely, but accurately, in corresponding grooves in 
 the top plates, c, of the standards; and upon these plates, c, are 
 attached a pair of vertical parallel standards, J. connected at 
 their upper ends by a light cross bar, e, which answers as well for 
 the bearings of the overhead cross-adjusting spindle, /, for the 
 '•set" of the nippers. Each standard, d, is slotted down its 
 centre, to receive and guide the traversing nut-bearings, g, of the 
 cross cam-spindle, h, a screw-spindle, i, being passed down from 
 above, and through the nuts, g, so as to enable the cam-spindles, 
 h, to be set up or down by the screw action. This screw action 
 is worked, when necessary, by handles shipped on to the end of 
 the cross-spindle,/, by the workman, who thus works the screws 
 simultaneously through the two pairs of small bevil-wheels, /. 
 Each cam-spindle, h, has an eccentric cam, a, loosely hung upon 
 it by an eye, the cam-eye being entered upon the spindle up 
 against an adjustable collar, A', on the latter; and the cam-spindle, 
 h, is set fast in the standard slots by the outside adjusting nut, I. 
 Tims arranged, the nipper forms a complete traversing frame, 
 capable of free horizontal movement along its guide grooves. 
 Beneath the level of its traverse support, two projecting eye- 
 pieces, m, are cast on the plate, b, each eye carrying a joint-stud, 
 n, whence short links, o, pass to corresponding eyes, p, on the 
 upper ends of the two sides of the vibrating lever frame-piece, q. 
 Each frame is carried on a stud centro, r, in the framing, and each 
 has a bottom joint-eye, s, for connection by a link-rod, t, to the 
 actuating cam-feed mechanism at the front or entering end of the 
 machine. Each frame has also a heavily-weighted bent lever, «, 
 attached to its bottom cross bar, and contrived so as to tend to draw 
 the tiame continually backward in the opposite direction to the 
 traverse of the wood. 
 
 The primary movement is given to the entire series of these 
 nipping feeders — of which there are six altogether, three being at 
 each end of the machine — by a toothed pinion, r, on the first 
 motion shaft. This pinion gears with a large toothed wheel, w, 
 set on a cross shaft, a\ and carrying a second pinion, y, in gear 
 with a second spur-wheel, z, fast on the actuating cam-shaft, 4. 
 On this shaft are keyed the three separate cams, or differential 
 eccentric pieces, 1, 2, 3. Opposite to, and over the periphery of 
 each cam, is set an antifriction pulley, 5, carried on the horizon- 
 tal arm of a bell-crank lever, 6, the three bell-cranks being carried 
 loosely on a stud shaft, 7. The longer vertical arms of these 
 bell-cranks are connected by eyes, 8, at their lower ends to the 
 respective rods, t, which are severally linked, as already de- 
 scribed, by end and intermediate eyes, to the bottom of each of 
 the nipping frames. The three cams are so set at starting, that 
 they aha]] each act at different periods of the revolution of their 
 carrying shaft, in such manner that a uniform feed action may bo 
 given to the board passing through the machine. In other terms, 
 they are set at equal distances asunder in the direction of revolu- 
 tion of their shaft, each cam being linked to and made to actuate 
 
 two nippers. Thus, the corresponding nippers of each pair nave 
 always the same relative position, as marked 1. 2, and 3. Then, 
 as the planing goes on, and the cams revolve, each pair of nippers 
 is made to traverse forward — -say in the direction of the arrows at 
 1 — by the upward revolving action of the corresponding cam. This 
 forward traverse is the positive feed action ; for the moment the 
 nipping frame moves in this direction, the prominent eccentric 
 portions of the cams, a 1, are thereby carried down, or jammed 
 hard upon the upper surface of the timber, squeezing it firm down 
 upon the bottom plates, h, so that the timber is carried forward to 
 the cut, as if it were permanently attached to the nipping I', ed- 
 framo. Whilst this positive feed is being given to the wood, the 
 two pairs, 2, of the nippers are being brought bach by the action 
 of their weighted levers, as their corresponding cam is descending 
 in its revolution ; these two nippers are consequently slipping over 
 the wood, for, on the instant of the return movement towards t In- 
 entering end of the machine, the prominences of the nipping cams 
 are drawn out of nipping contact, and the frames go back without 
 interfering with the feed traverse of the wood in the forward direc- 
 tion. As delineated in the plate, the third pair of Dippers are -.till 
 in forward gear, and acting, by reason of the position of their actu- 
 ating cams, to carry forward the wood in concert with the nippers, 
 1. By this means, as each cam comes round, it gives its forward 
 feed and back traverse in regular uniform succession, each succeed- 
 ing nipper gradually relieving the last in feeding action. And 
 although two nippers always thus tend to come into action at the 
 same time, derangement cannot ensue from this cause, inasmuch 
 as the quickest forward feeding nippers at any given moment carry 
 forward the wood free of the other nippers, which give way in 
 their nipping action to the higher rate of motion, by reason of the 
 consequent slip or disengagement of the nipping cam. In this 
 way the feed is constantly uniform, as although it is furnished by 
 three separate actions, yet each only comes into actual feeding play 
 at the moment that it is required to keep up the regularity of 
 movement. 
 
 As the board is thus carried forward, it comes first above uio 
 three finishing planes in the frame, 9, over which it is held down 
 by the three rollers, 10, which run in adjustable bearings held 
 down by the helical springs, 11, adjustable to any desired tcn- 
 sional pressure by the nuts, 12, on their screwed spindles, 13. 
 carried in the stationary frames, 14. After passing these press- 
 ors, the emerging end of the wood, as planed and finished on its 
 under surface, proceeds beneath the duplex pressing pulleys, 15. 
 set on a stud centre on theyfree end of a lever arm, Hi, fast to the 
 horizontal shaft, 17, carried in end bearings, 18, in the end frame, 
 and held down by the lever and weight, 19. Thence it enters 
 beneath the pair of horizontal pressing rollers, 20, similarly held 
 down by adjustable helices, 21 ; and it is between these two rollers 
 that the planing of the upper surface takes place. At the 
 moment, however, of its passage beneath the duplex pulley. 15, it 
 is first acted upon by the two cutting heads, s. Jn the present 
 example, these cutters are arranged for tongueing and grooving 
 the opposite edges of the flooring deal, as is Usual in laving floor- 
 ing. Thus, in the elevation, fig. 1, the two square cutters, 22, 
 take oft' the two angles of one edge of the deal, having the central 
 feather or tongue standing up, whilst the other double anguuir 
 
TIIK 1 
 
 ,ia«W r . off th. *liarp anglea from i!.< 
 
 A.'- ••• .iv-i!-- • -iv.r baai, f.T DM OBMf ■VJe.eanMi !!,•..• 
 
 (4ai« r»n:r»I -r—.m- < ,-l.r. .1 !•: pf-U; „• lh< plain groove, 
 
 angu- 
 
 20. ■• aabaaktcd to Um artiua of the roU 
 aaaaav," L, for bringing lit* upper net 
 
 aod npaaluiag the thirkoaaa of the deal, wax - Jn*n 
 
 sogh Um mprM't in • finished state. 
 
 nan :..- . 
 
 SE FOR PI 
 
 LMPLB PLATE Q. 
 
 TV ■ ' In P"* 1 
 
 epessim nil iilinn, mil then in 
 log good atikl 
 
 : 
 
 - .n longitudinal section on a 
 Largvr • rtion — 
 
 . body of the machine 
 eonaiata of an l-iron, which is 
 
 h irizon- 
 
 tal trail ' . c, arc pawl thro I 
 
 ■ 
 
 a by the revol 
 l third ipor-v 
 
 \ ild the diametrically 
 : parall.-l rail ban, l, which form the Hit a. 
 tag fran 
 
 whole nf the action, 
 ■-■une central wheel, c, alio drivel al 
 of aimi 
 
 har <>n I lard, *, 
 
 i roller 
 I : bat 
 
 washing movement a- plane, and Um 
 
 adjusted to fl lo be 
 
 rltau" ■ 
 
 1 1 
 
 a. an ! 
 
 i is again downward*. 
 
 a, and theno- 
 
 • 
 ■ .r.. j. It tlun rate 
 
 paaaad round Mm be 
 l, from the n; 
 
 finally n 
 
 • and is then | 
 . 
 paaaea ever Um ■. and is finally 
 
 \- 
 bowi nader treatment, U 
 
 follow lie 
 
 POWER-LOOM. 
 
 i: Z a M P I. B P I. A T B H- 
 We ! 
 
 ■ 
 
 tinting iip^n tlie main framing. The loon ■ tl 
 Mr. William Millignn, of Bradford, who baa acoornpUaned in it 
 the dot : putting any nombet 
 
 • whilal the namber ol 
 
 tion with. oil thi n of the 
 
 -T. ill Ixar. without involving any anevenneaa in the 
 ill friction o 
 that it will neither -!i|i nor (ray the cloth, at 
 - dry. 
 
 n of the 
 
 1 n in working order, looking on tl laking-up 
 
 idinal or front 
 : 
 carried on a spindle rappoited in a alol i'. I 
 
 ■ -pur-win il. n. outaide the fi 
 • i the pinion, c Tli - 
 
 I Um wheel, n, nn.l tnorea along with this wh< 
 - in gear with a pinion, a, carried ronnd along with the 
 On el, r. Inn 
 upon the fabric in 1 1 . n, and with its 
 
 upportod in v. : 
 tal rod, it. Thia r.O. a* it I 
 cloth on the I- 
 additional fold I - tin- bl am t 
 
 I -pin He of the I'loth-lx inn has 
 
 . 
 
 Inclination with the n d behind the rod, 11. This 
 
 it, to which pin i* Job ■ 
 
 I p am, with tl" 
 
 one end of the tappet-shaft, M. 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 When the loom is in action, as the horizontal rod, h, of the 
 cloth-beam gradually rises from the accumulated folds of the 
 
 cloth beneath it, it presses against the inclined side of the lever, I, 
 
 raising it by degrees to ■ vertical position. By this action, with 
 
 every slight advance of the lever, I, towards the vertical line, it 
 thus pushes back the lever, K, by the intervention of the connect- 
 ing-rod, j, so as to shorten the extent of the traverse of the lever, 
 K. The latter lever works loose in a fixed stud ventre, n, in the 
 side-frame, and, thus suspended, it is connected by its straight 
 pendant end, or lower arm, with the wheel-work which we have 
 
 just described, and by its back angular arm, with the eccentric 
 
 tappet, L, on the same shaft as the ratchet-wheel, r; and outside 
 this wheel is set the regulator, o, the lower eye of which turns 
 loosely on the ratchet. shaft as a centre. This regulator is simply 
 a slotted lever, having a sliding-pieee, F, set to move up and down 
 in the slot : and at its upper end is a short collar, acting as a bear- 
 ing for the upper end of a screwed spindle, q, the lower opposite 
 end of which is passed through a screwed hole in the sliding- 
 pieee, P. In this way the sliding-pieee, p, answers as a nut for 
 the screw, q, and the turning of the screw consequently allows of 
 the raising or lowering of the nut or slide-piece at pleasure. To 
 the top of the regulator are hinged three detents, s, each of which 
 takes into the teeth of the ratchet-wheel, f. On first setting the 
 loom to work, the height of the slide-nut, P, of the regulator, is 
 first adjusted to suit the required number of picks to be laid into 
 tho fabric per inch, and the regulator and lever, I, are pushed 
 forward by means of the lever, K, as far as the rod, H, will permit. 
 When the loom is put in motion, the eccentric. L, during one-half 
 of its first revolution, presses against the projecting angular end 
 of the lever, k, and pushes it out to an extent equal to its eccen- 
 tricity, whereby the regulator is drawn hack, to a corresponding 
 extent, by the connecting-rod, s, whilst the detents, R, bring 
 round the ratchet-wheel, F. During the remaining half of the 
 revolution of the eccentric, the angular tail of tho lever, k, de- 
 scends as far as the then degree of elevation of the cloth-beam 
 rod, H, will permit, and the detents, R, are raised out of their 
 position, and lifted as many teeth back as is equal to the distance 
 retraversed, the three detents, T, suspended from the centre of 
 the wheel, B, serving to hold the ratchet-wheel fast whilst this 
 change occurs. It will thus be seen, that whilst the detents, R, 
 are always drawn the same distance during one-half revolution of 
 the eccentric, tho distance to which they are returned in the other 
 half revolution must be less, as the cloth-beam rod, H, is raised 
 higher by the winding on of the cloth. The lever, I, should be 
 parallel with the slots in which the rod, H, works, when the 
 projecting end of the lever, k, is elevated to the top by the 
 eccentric, L, and it should rest on the rod, n, when the eccentric 
 is down. 
 
 At o is a short lever connected with the weft-motion of the 
 loom, which lever raises tho detents, T, by means of a chain, off 
 tin' ratchet-wheel, to stop the movement when the weft breaks. 
 The lever, r, is fast on one end of the horizontal rod, v, on the 
 other end of which is a balanced lever, worked by the weft thread, 
 on the principle of the ordinary well-known weft-stopping ap- 
 paratus. 
 
 DUPLEX STEAM BOILER. 
 
 EXAMrLE TLATE 0- 
 
 This, our ninth example plate, illustrates a most effective style 
 Of treatment of S stationary steam boiler, its seating and mountings. 
 In these views tiie convex and concave rounds are well brought 
 out, and considerable relief is given to the furnace doors and boiler 
 
 ends by the judicious employment of Bhadows. The water in the 
 sectional view, and more especially the 
 brickwork in the elevation, supply 
 materials for the development of the 
 
 picturesque; and the plate, upon tho 
 whole, is a fair type of a class of work 
 
 h 
 
 in which a good display is made without much elaboration. Tho 
 boiler, which is the production of Messrs. Bellhouse & Co., of 
 the Eagle Foundry. Manchester, is of the duplex or " twin" kind ; 
 that is, two distinct steam generators are combined together, to 
 work as one boiler, the two being placed side by side, with a 
 central tubular chamber between them. It is this intermediate 
 flue which forms the distinguishing feature of the contrivance, the 
 smoke and heated air from the two generators being passed 
 through this chamber, on 4>cir way from their respective furnaces, 
 to the chimney. 
 Fig. 1, on the plate, is a front end elevation of the duplex 
 
 boiler, as erected in brickwork; fig. 2 i- a transverse vertical 
 section corresponding, the section being taken through the two 
 furnaces, the brickwork and Hues, and the overhead steam-chest; 
 tig. 3, the wood engraving in the body of the description, is a lon- 
 gitudinal section ,,f the arrangement, taken through Ihe inter- 
 mediate chamber, the external flues, waterways, and the stCI in- 
 chest : and fig. 4 is a sectional plan to correspond. Both these 
 latter views are drawn to a scale of one-half the corresponding 
 views in the plate. 
 
 The two boilers or generators, a, are of the common cylindri- 
 cal, tubular class, with internal furnaces and flues. B, running ri [hi 
 through them from end to end. Tiny are set in a brick founda- 
 tion, c, suitable flues being formed in the walls id' brickwork, to 
 answer for the special arrangements of the combination. Each 
 boiler is fired separately, through the usual end furnace doors, D, 
 and the gaseous products pass off from each set of furnace bars in 
 the direction of the arrows, the two currents meeting .and forming 
 into one, in the main end transverse flue, E, in the brickwork. 
 This combined current then turns again towards the front of the 
 boiler, passing directly through the intermediate chamber oi tubes, 
 

 TilK I 
 
 rfc baae. 
 .<!i:-h eroae lh<- anj. 
 '. r-afara, Uing open »i earh mJ into the reeperU 
 
 I 
 ■ 
 ■ rmediale chamber, impart* 
 ■ 
 
 |u»«iii^ away <>f the »l«-am. 
 Boo, i, passing 
 
 til 
 
 ■ 
 
 part, tli- 
 
 I, r, and 
 
 ■ 
 I 
 
 ' le run* 
 
 '■'■ 
 
 of the 
 
 ■ 
 
 0in central . ' 
 
 i 
 
 • generator*. I 
 
 • ■ jnuj» ail Uio 
 advantage* uf an inti ... <n each. 
 
 WRECT-ACTING M \U!\i: ENGINEa 
 
 *nii-» -liading. The 
 
 imp and 
 
 NlUlll tx 
 
 in t lii-i 
 
 The /' // ■ 'lich thoae engine* arc 
 
 I 
 
 finu a-i 
 
 • !. ngth U I i 
 
 ■ 
 
 - 
 re ud iii'i tbi 
 other — ' 
 
 (KTllpV ■ 
 
 We hi 
 
 • and rivet ; .mil the 
 
 Mi «. v. 
 
 — of III. /» lulialf of lli 
 
 lie i 
 
 '.i ; whiUt nil U 
 thai tin one i 
 tber. For ii - 
 ■ action, not uncommon in old oadllatore, i 
 
 ■ 
 
 I 
 lli-r owner, Captain K 
 
 C uiilrv ; nn.l | 
 
 I 
 
 ■ 
 
 ■ C I 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 CHAPTER XV. 
 
 DRAWING INSTRUMENTS 
 
 "A good workman never complains of his tools," — although 
 a very ancient proverb, and having a poet for its advocate, is, 
 nevertheless, one which is very commonly used in an incorrect 
 sense, if it is not indeed untrue in all its applications. It is 
 certainly a very usual thing for a bad workman to throw the 
 blame of his inefficiency on his tools; but it is quite as certain 
 that a good workman will not work with any but the very best 
 tools. The draughtsman, then, who aims at excellence and accu- 
 racy in his mechanical delineations, must not only possess himself 
 of first-rate mathematical instruments, but he must preserve them 
 in perfect order. 
 
 The varieties of drawing instruments are extremely numerous. 
 We shall, however, confine our illustrations to such as are of more 
 recent invention, or more improved construction. 
 
 A Kad pencil needs no description. But the form to be given 
 to its working-point is a very important subject of consideration. 
 For drawing straight lines wit'i the assistance of a straight edge, 
 thi- point should be flat, and slightly rounded. Such a point pro- 
 duces as fine a line as a conic-al point, whilst it is much stronger, 
 and preserves its integrity for a longer time. This point may also 
 be used in describing circles of large diameter, but small circles 
 require a conical point. 
 
 Messrs'. Marion, of Regent street. London, have registered a very 
 ingenious little instrument for sharpening lead pencils and crayons. 
 Our engraving, fig. 1, represents a side elevation of the tool in the 
 act of sharpening a pencil. A projection, a, is formed on the 
 
 side of a piece of 
 Fi s- '• metal, sufficiently 
 
 large to allow of 
 a conical aper- 
 ture, b, corre- 
 sponding with the 
 required cone of 
 a pointed lead 
 pencil. One side 
 of this projection 
 is slotted to re- 
 ceive the cutting edge of the small knife, c, which is attached to 
 the inclined portion, d, of the metal block by the screw, E, passing 
 through a slot in the knife. A short projection, F, is formed upon 
 the knife for the convenience of adjustment, and when sit. it is 
 held in position by the two set-screws, g. A small handle is 
 screwed into the block at H, from behind, for the convenience of 
 holding the instrument when in use, and the end of this handle is 
 hollowed to receive the small projection, f, on the knife, c, for the 
 facility of holding it when detached for the purpose of sharpening 
 the edge. An adjustable guide, I, is secured by the pinching- 
 screw, j, by one end, beneath the block, and is furnished with two 
 arms, k. jointed on to the end of the rod of the guide, for em- 
 bracing the pencil, l, during the cutting operation. 
 
 In using this instrument, the pencil is simply passed In [ween 
 the two guide-arms, K, and its end is inserted in the conical hole, n. 
 It is then turned round between the finger and thumb, and the 
 knife-edge coming into contact with the end to be sharpened, 
 quickly pares off the material. By this simple apparatus an ex- 
 cellent poiut is given to the 'pencil in a very short time, saving 
 the draughtsman from all the troubles and inconveniences of 
 blunt penknives and fractured lead. 
 
 A mathematical drawing-pen consists of a pair of 
 flat, tapered steel-blades, fixed to a handle of ivory ''•5, 2 - 
 
 or ebony. The ink is contained between the blades, 
 and flows out from between the points, the thickness 
 of line produced being dependent on the distance 
 asunder of the points, which distance is regulated by 
 a pinching-screw. In order to maintain a uniform 
 thickness of line, care must be taken to clean the 
 outsides of the points after each fresh supply of ink. 
 It is often necessary to draw a number of lines, of 
 different thicknesses, immediately succeeding each 
 other. In this case, the inconvenience of repeatedly 
 turning the adjusting-screw of the pen may be 
 avoided by using a pen of the construction repre- 
 sented in figs. 2 and 3. This pen is the invention of 
 M. Maubert, a French engineer, and differs from the 
 ordinary drawing-pen in the shape of the points, g, A, 
 of which fig. 3 is an end view. These points are 
 made broad and rounded, and are bent at the sides, 
 so as to present convex surfaces towards each other ; 
 in other words, they touch each other at their 
 centres, but aie gradually more separate towauls 
 each side ; and in using the pen, if a fine line is 
 wanted, it is held vertically ; if a thick line is needed, 
 it is inclined moro or less to either side, so as to 
 bring the more separated portions of the acting edges 
 in contact with the paper. With the exception of 
 the shape of the points, the pen represented in fig. 2 
 may be taken as an example of the best construction 
 of a mathematical drawing-pen. The blades are 
 formed of a single piece of well-tempered steel, and 
 are lived upon an ivory handle, by means of a brass 
 socket. In si. me pens, the tips only of the blades 
 are of steel, tho remainder being of German silver, or 
 of brass, ; and one blade is jointed at its root, so as 
 to be capable of being opened out ami cleaned, when 
 necessary. A spring is fixed between the blades, 
 so as to keep them open as far as the regulating screw 
 will admit. Whilst, on the one hand, this facility in cleaning is 
 an advantage ; on the other, there is an accompanying lial 
 the joint getting loose, in which case the points can never be kept 
 
 opposite to each other, and it is quite impossible to preserve uni 
 
 2 a 
 
 
 Fig. 3. 
 
. 
 
 f r- 
 
 
 and rlranaaa of !u . 
 
 utfn*. and 
 
 T>. . t:i..i.!jr»'...n ■•( !..•■ Mmm :i ilraain^pra la II.' hwrtili n r.f 
 
 - 
 
 tin* !;»•• :• arai 
 graap of tbe f. ■ 
 
 ■part ■ 
 
 ■ 
 
 ! . • . ■■ 
 
 ■a the 
 
 ■ 
 
 ■ 
 
 i 
 ■ 
 
 - 
 
 drawiiv 
 
 ; -dace a lir • 
 
 rdinary 
 
 ■ 
 
 I variation, iw 
 • «raall acalc ; I 
 
 n.vi-««arj- rhangra, « 
 
 b 
 
 r a Ua:.«\. r- 
 
 I »t«-t-l atud, rm-lcd U> thi | lat.-. e. and of 
 conajderaUc diameter, fur Un ■>..;.. • •: ale idinaaa 
 
 ■ 
 
 down i 
 
 and fall. T: ■ 
 
 that an; 
 
 ■ 
 
 -1 aa 
 fp>m a K-ali- ; aril a 
 
 ■ ■fa |>air of I I, and 
 
 .nd a 
 
 ■ 
 
 l 
 
 . an nnplcaau I 
 
 tr.'m all cn>a» ; 
 lateral looat-ncaa. The moat ordinary kit 
 
 ■ 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 181 
 
 »nea riveted together. The better kind have a steel pin passed 
 through the leaves of the joint, upon which a flat brass or other 
 
 metal nut is passed, at the further side. This nut has two small 
 holes upon its face, for the introduction of the points of a turn- 
 screw, to be met with in most sets of instruments. The joint- 
 leaf of one leg of a pair of compasses is usually of steel, as this 
 arrangement gives a smoother action than when both sides of the 
 joint are of the same metal. The better kind are also made with 
 two steel leaves on one side, which are introduced between three 
 brass ones on the other ; but some have only one leaf on one side, 
 and two on the other. A perfect compass-joint is a thing seldom 
 met with, and draughtsmen are continually subject to annoyance, 
 arising from the inequality of action of the joints of their com- 
 passes. After some 
 Fi b- 8 - little usage, these 
 
 parts invariably im- 
 bibe the bad habit of 
 an alternate tightness 
 and looseness, so that 
 w\icn the screw is adjusted to tighten the joint for one part of 
 its movement, the objectionable slackness is only removed at the 
 expense of an equally provoking stiffness in another part. Messrs. 
 Bentley's "spiral spring compasses" aim at remedying this evil, 
 by the adaptation of a small coiled spring to the joint, in such a 
 manner as to equalize the pressure of the frictional surfaces 
 throughout the entire movement. Our sketch, fig. 8, which re- 
 presents a side view of the end of the centre joint of the compasses, 
 explains the mode of application of the spring. The centre joint, 
 A, which is sectioned to show the spring, has a recess bored out of 
 one side of it, just large enough to receive the short coiled spring, 
 
 Fig. 9. 
 
 b. When this centre joint is inserted between the two eyes 
 forming the outer joints, the spring reacts from the bottom of its 
 box against one of the eyes or cheeks of the outside joint, thus 
 keeping up a regular smooth working pressure on tho joint surface- 
 Externally, this little modification in no way affects the appear- 
 ance of the instrument, as the spring, being entirely embedded in 
 its recess, is not seen. At a mere tritle in the increase of the 
 cost, an important objection is hero remedied by very simple 
 means. 
 
 Some dividers are made with one of the legs so fitted as to be 
 capable of a slight adjustment independently 
 of the main joint. These are called "hair 
 dividers," and are represented in fig. 9. The 
 leg, A, is not, like tho other, soldered to the 
 shank, but is formed with a long thin strip of 
 metal, which lies in a groove on the inside of 
 the shank, and is fixed to the latter by a screw, 
 at its upper end, near the compasses joint. 
 This thin strip acts as a spring to bring the 
 point, a, nearer to the point of the other leg. 
 A screw, b, passed through the shank, adjusts 
 the point, A, a slight distance in or outwards, 
 thus affording a means of taking measurements 
 more minutely accurate than with the mere 
 direct action of the hand upon the main joint. 
 Our fig. 9 may be taken as the representation 
 of a very excellent style of dividers. The 
 point should be strong, and not too finely 
 tapered, and they should meet when the in- 
 strument is closed. 
 
 All sets of instruments contain a large pair 
 of compasses, in addition to the dividers, which 
 is usually of similar construction, except that 
 one of the legs is made to fit into a socket in 
 the shank, and a pencil or pen may be substi- 
 tuted, as required. The pencil-holder and pen 
 are both jointed, so that, in every case, they 
 may be put in the best position for action. In 
 the better kind, the fixed leg is also jointed; so 
 that in describing circles of large diameter, the 
 centre point may still be entered vertically into 
 the paper. A lengthening bar is also provided, which can be fitted 
 into the shank-socket, whilst the pen or pencil can be placed at 
 the end of the bar, thus giving the compasses a greater range. 
 
 In fi"s. 10 and 11, we have represented a modification of this 
 instrument, of German invention. This tool has no separate 
 pieces, but is so arranged, that a pen, pencil, or point, may be 
 brought into action as desired. The shanks are forked, and the 
 leg pieces are jointed to their extremities. One of the leg pieces 
 is formed with a steel point at one end, and a pen at the other ; 
 whilst tho other leg has a steel point at one end, and a lead pencil 
 at the other. The legs are jointed to the shanks by their longi- 
 tudinal centres, and can be turned between the fosksj so as to 
 bring into action whichever end of the leg is required. A small 
 pinching-screw is passed through one side of the shank, near its 
 extremity, to fix the leg in position. 
 
I" 
 
 
 
 
 what muller : 
 
 ■ 
 
 .1 in- 
 
 AnntliiT form of 
 
 • 
 
 - U a tpock- 
 
 . t." or " turn in " BOm- 
 
 ■ - up a 
 
 II s| :u-f when 
 
 - n iTOM uec- 
 n at the lino 
 
 1— -2. ill ' 
 
 ••nl mid 
 
 n - of the in- 
 ■tnunent when fully 
 
 oonatrooilon, ami in 
 
 il unliko 
 rmu pair ju»t 
 '. 
 I :li.ir lower i 
 
 points, 
 tl .in at th.ir extremi- 
 
 .t their 
 
 : round into « 
 
 \ r fixing 
 
 In tin' German Instniment, 
 I 
 i tin- upper ondi ol 
 ■hown in the • I i. iiinl in Umm 
 
 . 
 a» in fig. it. When in th - 
 
 ami |- !. . i'liin tlir fori 
 
 • 
 
 'v draw- 
 
 , tli. in from i 
 
 \\ •■ variuu* 
 
 peeeee of a n 
 N 
 
 . t ■ -r the 
 • umbroua 
 
 ■uuallrr and ■ 
 
 - a fruiit. aii.l fig. 18 a ado 
 ■ ' ' 
 ] IBM, to 
 
 which a unall han.l I. 
 
 it It « 
 
 bold l'T a Mnall enjww, in a Mekal formed in the tag of Ihe 
 
 • nt 'llii* ar. ids a m. aim of adj 
 
 as to length, whilat I 
 dentalrj I opnaaei of the lar.-- i 
 
 ■ 
 Imnghtamen m in tin m, if the u 
 
 not im'.. point) which, from its greater 
 
 
 Fif. IS. 
 
 F.,-. 14. 
 
 ■ injury. 
 
 I 
 
 of nn 
 
 instrument | 
 himil.ir to tin- 
 
 <vpt thai it haaa pen- 
 ril in-' 
 I 
 
 qulra to In. adjoated t.. any desired ra.iiu«. by uV 
 the ham I. In «.rk whi re gfl 
 for, it will often !*• foiin.l I i a linn 
 
 ndjnatmenl In thii manner, particular!; if the Jolnhi of tbi 
 
 mint i. ■ ["hla difficulty la go! 
 
 over In 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 Fig. 20 is a side, and fig. 21 a front view of a pair of pen com- 
 passes of this class. The use of such instruments is confined to 
 
 Fig. IT. Fig. 18. 
 
 Fig. 20. 
 
 very small circles, of half or three quarters of an inch in radius at 
 the most. In the example we have selected for illustration, the 
 emtio leg is of brass, or German silver, and is in one piece with 
 the milled handle. It is also provided 
 
 with a needle point. The pen is made 
 
 with a spring-tempered steel shank, K, 
 which lies in a groove cut in the centre 
 leg, or body, and which is fixed to the 
 latter, at its top, by a screw. A small 
 screw spindle, L, is passed through an 
 opening in the pen shank, and is jointed 
 to the centre leg, and a button, or nut, 
 is passed on to the screw spindle outside 
 the shank. This pen shank is so fixed 
 as to have a tendency to stand out from 
 the centre leg to the full extent of the 
 instrument's range, and by turning the 
 button of the screw, L, it may be forced 
 in or allowed to open, so as to give the 
 necessary adjustment. Fig. 22 is a side 
 elevation of a pair of slightly modified 
 spring-and-screw compasses ; it is shown 
 with a Socket, carrying an engraver's 
 burin. An i/ory handle is fixed to the 
 centre leg, or body of the instrument ; and 
 
 this arrangement is considered by some artists to give greater 
 control over its action. The commoner kind of spring bow com- 
 passes consists of a single piece of steel forming the two legs, and 
 
 Fig. 22. 
 
 having a small brass handle attached. The steel 
 of the legs is so tempered as to give them a ten- 
 dency to stand apart, and the radius distance is 
 regulated by a screw in the same manner as in the 
 instruments represented in figs. 20, 21, and 22. 
 
 The draughtsman lias frequently to delineate 
 circles of a radius far exceeding the range of ordi- 
 nary compasses, and for this purpose he must pro- 
 vide himself with "beam" compasses. A good 
 form of this instrument is represented in side eleva- 
 tion, in fig. 23, and in transverse vertical section, 
 in fig. 24. It consists of a wooden bar, or ruler, 
 T, of considerable length, and of a X section, being 
 formed of two strips united by a dovetail joint. 
 This construction prevents warping or bending, 
 and is necessary where a scale is cut on the bar, as 
 any deviation from a straight line would render the 
 measurement inaccurate. The compasses are pro- 
 vided with a pen, or pencil leg, and a centre leg, 
 these being fitted upon the bar with socket pieces, 
 M, m'. These socket pieces are fixed at any point 
 along the bar, by pinching screws at the side. ; but 
 to prevent the point of the screw from injuring the 
 bar, a loose plate of metal is interposed next to the 
 bar, as shown in the section, fig. 24. The socket, 
 M, is in a solid piece with its pen, or pencil- 
 holder ; but the centre leg, N, is in a separate 
 piece from its socket, m', and is capable of minute 
 adjustment back or forward in the latter. The 
 socket, m, has a cylindrical groove along its under side, in which 
 slides the head of the leg, n. This head is formed with a 
 
 Fig. 23. Fig. 24. 
 
 horizontal serew passage, or nut, to receive the screw spindle, 
 I, which is held by an eye at the end of the socket groove, 
 and is actuated by means of a bultou on the outside. By 
 
1 • 
 
 
 it at vr ary at any part of the an 
 
 a. i. Ui—owl »aJ ~i pretty near the mark, ami fi\ 
 .th of raJiu* b thea obtained by adjusting the c* 
 lij aiiiai iff am eoapaaar*. 
 
 ai—i what <ifl.-r.-nt d Vexr iption, are represented in aide alev»: 
 
 t..- M. 1:. Uui u.<tnu.i< :.'.. ■Mat b amlir >■ ..f r.« ul, Uk- onaln 
 
 - 
 ■ 
 
 ng strew underneath 
 ■ 
 which a vernier scale it rut, so thai 
 may lie taken. 
 
 filed at a convenient | or a-, i tin n tin 
 
 which carriea the moveable ; lock or 
 
 forward, a* ni it— nr, by thi 
 LS. aaaj . r « - «• l 
 
 Of the compasses cjaaa of drawing-instruments, there now re- 
 main to be •! 
 
 meat b represented, in front and aide elevation, in I 
 Ita nae b to inrreaae or reduce measurements to a 
 to that of the original drawing, of whk-fa a copy is being made ; 
 and a great deal of time may be aaved 1 
 there U much Ices risk of making mistakes with it, than « ' 
 draughtsman, in rodncing a measurement, has first to take the 
 oVtaaea, ni bV original drawing, in bb eommon diridera, and, l>y 
 applying it to the aeale of that drawing, ascertain 
 arithmetically ; and ti, »rreapooding 
 
 r., )•.*-.,! swab, mti h Im baj «.-.:•. to talu in i. : - divide ra, -• aa t.. 
 
 >'• 
 the other hand, the action of taking the measurement on the 
 original drawing, at one end of the instrument, :. 
 end to the measiiruntnt, aa increaaed or reduce.' I 
 theoopy. The instrument consists of a eou; 
 brass plates, connected by an ad 
 
 Tmitiea of each pari 
 lut, if th*. joint. : 
 
 ■ 
 between the points, at carh end. will he equal ; bag 
 ■ adjusted, aa in the | 
 ride U only half that • 
 poinu at one • 
 
 -ace will be measured 
 
 jt tha 
 ■ - a/ the same proper- 
 
 :!uU which is ■**•■*• 
 
 time being, between the 
 
 f the joint, J. To enable 
 ..ughtanun to art the inatra- 
 ment I 
 
 t has 
 
 an iii : 
 
 -responding to the desired 
 
 uaaal 
 
 - 
 
 it. Tlie instrument is n. 
 
 a purpose*, in aJ.;i- 
 
 >ine end is .*.. 
 radius of a rii 
 
 side of an in~ 
 ii 
 inatnmtent b usually grad 
 - purpose, an«i 
 
 tinding the ; 
 
 The 
 
 made, and 
 :.'>em ; 
 
 DasaV -v 
 
 ation than the prearrratinn of the 
 time is freqn- 
 
 ripal ' 
 
 ;<irtial 
 
 a no<« 
 
 in a brass socket, with an 
 
 handV h made to 
 
 • and uncovers a anaU ecrew-drivcr, which 
 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 Fi ? . 28 
 
 
 will serve to (urn the screw, e, or any of the smaller screws in the 
 other instruments. 
 
 In treating of drawing ellipses,* we have already described one 
 of the many instruments constructed for that purpose. 
 The well-known " trammel " is one of the simplest in 
 construction, but it is very defective in practice. In 
 figs. 29 and 30 we give an elevation and plan of a 
 trammel of the newest and most improved form, in which 
 tho practical defects aro very much lessened, but the 
 contrivances by which this approximate perfection is 
 attained are of such a nature as to require a more than 
 ordinary excellence and accuracy of workmanship in the 
 construction. The trammel consists of a metal bar, r, 
 on which are fitted three sliding sockets, which can be 
 adjusted at any points on the bar. Two of these sockets 
 cany centre legs, p, o, and the third carries a pen, or 
 pencil, s. In addition to these details, a guide-plate, 
 q, is required, having a couple of grooves cut in its 
 upper face, at right angles to each other. This guide- 
 plate has two short pin points, on the under side, to 
 prevent it from slipping on the paper upon which it is 
 placed. In ordinary instruments the legs, o and p, ter- 
 minate in simple points, which are respectively caused 
 to traverse the grooves in the guide-plate, Q, in describ- 
 ing the ellipse. It is, however, found to be almost 
 impossible to obtain a smooth action with this arrangement, as 
 the pressure on the points, being oblique to their line of move- 
 ment along the guide-grooves, the friction is apt to be irregular 
 and so cause a varying motion of the pen or pencil point, and produce 
 
 an uneven outline. In (lie instrument represented in fi.'s. -29 and 
 211. the parts which trav.. rso the guide-grooves in the plate, q, COD- 
 siM of small steel wheels, o,p, carried in the forked ends of the 
 
 1 See page 17. 
 
 steel spindles, o', p', which are entered loose into the socket legs, 
 o, P. Thus, whilst the wheels considerably alleviate the friction 
 arising in traversing the grooves, they always maintain their posi- 
 
 . 31. 
 
 Fig. 32. 
 
 tion with regard to the grooves, whatever he the position of the bar, 
 it, and pen, s. In adjusting the instrument, it is simply necessary 
 to set tho pen and centre legs, so that the distance of the two 
 latter from the former shall correspond respectively with the 
 semi-transverse and semi-conjugate axes of the ellipse to be 
 described. With the instrument represented in the engravings 
 it will not be possible io describe any ellipse which does not lie 
 wholly outside the guide-plate, q; and where smaller ellipses aro 
 required, a smaller guide-plate must be used. 
 
 Beyond comparison, the best instrument we have seen for 
 drawing ellipses is that invented by Mr. Webb, and represented in 
 e'cvation in fig. 31, and in plan in fig. 32. It consists of a 
 lozenge-shaped table, a, of thin metal, supported upon four 
 pointed legs. a'. Two parallel guides, b, are fixed across the top 
 of the table, a, and a disc, c, is fitted between them, in such a 
 manner as to be just capable of turning and sliding between tho 
 guides, b. The disc has a slot at one side, extending from tho 
 centre to the circumference, and in this is fixed, a( any point, by a 
 screw, d, a spindle, E, passing down through the table, a, below 
 which it has fixed to it a slight frame, F, carrying a screw spindle 
 c. This screw serves to adjust the pen, or pencil, it, back or for- 
 ward, on the frame, F. The spindle, E, works in a slot, i, in the 
 table, a, which slot is at right angles to the disc guides, b. The 
 instrument is caused to operate by turning the spindle, e, by 
 means of the button, D, which action turns the carrier frame, f 
 and also the disc. b. It then follows, that if the spindle, e, were 
 five 1 in the centre of the disc, B, the point of the pen would 
 describe a circle. If, however, the spindle, e, is fixed eccentri- 
 cally in the disc, the rotation of the latter, between its guides, r, 
 will cause the spindle to traverse the slot, 1, in the table, a. in 
 such a manner that tho point of the pen will describe a perfect 
 

 Tin: i mans 
 
 «U*jmp. la f|~ < "'3 the Instrument, two !.:>•-• are draw a 
 
 are placed upon theee Uu«-% 
 
 aiia of 
 
 •v ■ lino 
 
 l 
 
 ■ ■ 
 
 . II. is 
 
 aith the 
 
 pen, ii, 
 . 
 
 \ apindlo, 
 
 v (hi :i bo described. Tho 
 
 ■ L with < »l j"ints 
 
 ju-t eufficil »t 
 
 the act 
 
 ■ . 
 
 I overcome tli<> 
 
 : ■ . ■ : " il, to touch the 
 
 ' J"int ill 
 ngth, in 
 perfectly leveL 
 
 i rircli -, i-> the ellipti- 
 . 
 
 ■■ of which a pencil-holder . 
 wild a tulmlar locket, »■> as •■ i Ircubuiy 
 
 pencil-holder 'n jointed, m that thi 
 
 In nalng 
 older U 
 pUccd in the centra of the ellipse, and the leg ia in 
 ■ 
 
 are held 
 nix I round with the 
 
 iii,.n, it 
 U necessary ii irrying tho pencil-holder ihould be 
 
 thia, om 
 nching out "ii on . or on both 
 
 . ami til,' 
 
 aa, when 
 tba per- 
 
 ir position al I thia important 
 
 ind t'i be 
 
 make .-. 
 
 i. »r the 
 
 ■M-pante elevation*, tak, n at right angteo to 
 
 i ■:., i'l ■ all," I 
 
 in a Lnuk.-t 
 
 r , a. 
 
 r«.M 
 
 
 to an 
 
 V. 
 
 die, Hke a nut, 
 
 Tliia 
 
 and, in 
 v tra- 
 
 ■ '..I. \\ 'Ii, ii ■ 
 
 of the tho in- 
 
 atnmv nl ia ti. 
 
 the n i to that 
 
 in which it waa |wi- • 
 
 i. Thia 
 
 * k tin« 
 
 from whioh it alerted ; and 
 when tiii - point hi reachi d, the 
 
 to the 
 
 ' mil. lit 
 
 I with a 
 pin,pro|i c ting down almost to 
 the level of the bottom of the 
 dlac It !■- all ■ ■ nhonld roll arid 
 
 form pi I • instrument may be used I i 
 
 . 
 
 i a pur- 
 ■ ulii.li Ihoopiai 
 lucuilii s. Tho usual method 
 
 de it into a inn • 
 or brapexiuma — to meaanre Ifti 
 
 of lh< ir prod ! 
 
 ■ 
 tho ealculati 
 obviating fanlta in tho arithmetical pari "i Ihe worl 
 by takl 
 
 ■, this method 
 
 amount of labour of an Irkaome kind, Attempta ! 
 ! thia by entti 
 
 ' 
 r, of determinal hod — nt 
 
 ' 
 ■ 
 
 v mm 
 
BOOK OP INDUSTRIAL DESIGN. 
 
 Several " planimeters," or instruments for mechanically mea- 
 snring the area of plain surfaces, -were exhibited in the Great 
 Exhibition of 1851, and are noticed in Mr. Glaisher's admirable 
 report on Class X., " Philosophical Instruments, and pro- 
 cesses depending upon their use." All, or nearly all of these, 
 aimed at the solution of the problem by integrating the dif- 
 ferential expression of a curve, tra'ced on a plane 
 surface, being conceived on the old, and now almost 
 forgotten, view of the differential calculus, which 
 regarded the differential of a magnitude as a measure 
 of the velocity of its increase at any instant. Sup- 
 pose a straight line to be carried, with a uniform 
 motion, along the base line, or abscissa, of any curvi- 
 linear area, remaining always parallel to itself, and 
 perpendicular to the base line, and that, during this motion a 
 moveable point in the line, so carried, is always kept on the cir- 
 cumference, or boundary line, of the area. Then it is clear, that 
 the velocity of increase of the area will be proportional to, and 
 therefore measured by, the length of the ordinate, or portion of the 
 moveable line included between the base line and the describing 
 point. Again, a disc, or wheel, can be supposed to revolve with 
 an angular velocity always proportionate to the same ordinate ; 
 in which case the total angle of revolution described by it will 
 increase by similar increments with the curvilinear area, and will, 
 consequently, always be proportionate to, aud a measure of, that 
 area. The area may therefore be read off, upon its circumference, 
 by any method which keeps account of the number of revolutions 
 made by this wheel, which may be called the integrating wheel, 
 disc, or roller. If the circumferences of two circles be connected 
 by teeth, or by simple contact, so as to work together, their 
 angular velocities will be inversely as their radii ; so that, if the 
 radius of one of them be constant, the angular velocity of that 
 one will be directly as the radius of the other. Thus, any mecha- 
 nical arrangement securing the condition that a roller, or disc, 
 shall be carried round on its centre, by contact with a uniformly 
 revolving circle of a radius always equal to the length of the 
 variable ordinate, will at once be a solution of the problem. The 
 condition alluded to may be obtained by employing a couple of 
 discs at right angles to each other, or by using a cone and a disc, 
 with their axes parallel to each other. The former construction 
 is adopted in one or two instruments, invented by continental 
 mathematicians, the latter by Mr. Sang of Kirkaldy. 
 
 Mr. Sang's instrument, which is represented in perspective 
 in fig. 35, indicates the area of any figure, however irregular, 
 on merely carrying the point" of a tracer round its boundary ; 
 and. besides the advantage of not injuring the drawing, it pos- 
 sesses that of speed aud accuracy. A frame, a, carries an axle, 
 which has on it two rollers, b, of equal size, and a cone, c. It 
 is heavy, so that it maintains its parallelism on being pushed 
 along the paper. The sides of the frame are parallel to the edge 
 of the cone, and are fitted to receive the circumference of four 
 friction rollers, R, which move along a, and carry a light frame, f, 
 terminating on the tracing-point, p, to which the handle, H, is 
 attached by a universal joint. The frame, f, also carries a wheel, I, 
 which, by means of a weight, is pressed on the surface of the 
 cone, and receives motion from it as the tracer is carried along the 
 
 paper. The index-wheel, I, only touches the cone by a narrow 
 edge, the rest of its circumference being of smaller diameter, and 
 containing a silver ring divided into 200 parts, which are again 
 subdivided by a vernier into 2,000 parts. The value of each of 
 
 Fig. 36. 
 
 these divisions is the T J 3 tk part of a square inch; so that one turn 
 of the wheel represents 20 inches. Another index wheel, t, 
 moved by i, is divided into five parts, each of which represents 
 20 inches, so that a complete revolution of T values 100 inches. 
 The eye-glass, e, assists in reading the divisions aud vernier. 
 
 It is apparent, from the construction of this instrument, that if 
 the tracer be moved forward, it will cause the index to revolve, 
 not simply in proportion to that motion, but in proportion to the 
 motion of the tracer, multiplied by the distance of the edge of the 
 index-wheel, from the apex of the cone; and that the revolving 
 motion of the index will be positive or negative, according as the 
 tracer is carried backwards or forwards. Hence, if the tracer 
 be carried completely round the outline of any figure — on arriv- 
 ing at the end of its journey, the index-wheel will show the 
 algebraic sum of the breadth of the figure at every point, multi- 
 plied by the increment of the distance of the points from the 
 apex of the cone ; that is to say, the area of the figure. 
 
 This instrument possesses great simplicity of construction. 
 Both factors of the continuous multiplication are directly trans- 
 mitted from the motion of the tracing point in the simplest 
 manner. The influence of the elasticity of the parts of the 
 machine ou the accuracy of its indications, may lie discovered 
 by moving the tracer a second time over the boundary of the 
 figure, after having turned the whole instrument round 180°. 
 The effects of the imperfections in the mechanism will now have 
 changed signs, and one of the results will probably be found to 
 be a little too large, and the other a little too small. The average 
 between the two is the exact area of the figure, and is more to 
 be depended on than the results of measurements made by scale 
 and calculation in the usual way. A careful operator, in using 
 the planimeter, will always take the average of two tracings in 
 this manner; but when he experiences the rapidity with which 
 this may be done, he will find the trouble as nothing in com- 
 parison with the harassing labour of calculating by scale and 
 multiplication. 
 
 Mr. Miller, of Woolwich, has devised a very useful modifica- 
 tion of the common jointed rule. This instrument is termed a 
 "radiator," and our engraving, fig. 36, represents a portion of 
 it in plan, whilst fig. 37 is an end elevation. The inner edges of 
 the legs are used as rulers, and the joint has a transparent 
 
 2b 
 

 
 eeatre. a. which is placed direct); orer the pout to be drawn to. 
 A graJaatr J «.*.» supplied, at. J the brmM Irgs are furtu>hed 
 
 r« m 
 
 
 with m .imit of an; length of ruler being used. 
 
 1 L- r»:.j: r .« a] : ' al It to the f :. wing j arm -• - :— 
 
 For drawing lines in perspective, or geometrical drawing, to a 
 pomt or cent: off angles as a protract)-: 
 
 right-angled triangle, or an; other angles ; and for setting oat 
 yol ygu aw of different numbers of sides. In using it. the centre 
 of the giaa is placed over the centre to be drawn to. and a line 
 is drawn along the inner edge of the ruler from the point re- 
 quired. When man; lines are to be drawn to one centre, the 
 hand must be placed upon one leg, to allow the other to be 
 moved to the several ; 
 
 I -mi of protractors, or instruments for setting off or 
 r ■ . " • .• .' • . -.'_.■ • • : * 1 third, !&•! 
 
 •inch approved form, coosi- lo 360 s , 
 
 ■ 
 - in the 
 
 kearhtgi mast Irst be marl 
 
 tran-frmJ to the re 
 saamai i.!-;- t. '!:-:•• 
 aad the ac 
 
 i thence 
 trumeuts are necessary. 
 
 These bteonveaieacr- 
 
 i tig an 
 
 ' t angles, is made in one iralM bar. a, 
 
 ans of traverse bars, 
 
 • f *och 
 
 .Imit the str 
 
 -■ 6xed by th- ral transverse 
 
 piece, ». which is screwed to the t' 
 
 ■ad, for the ere of a radial straigbt-edge, r. 1. 
 
 aad clampiag plate are pn.i id- .1 to fix the radial straight bar, 
 
 r. at an; angle. Immediately, abw 
 
 r, aad I i iif<.th rod 
 
 at ltae. aad aaited togeth- i 
 p.eve embracing the socket, l. aad adjasted uw 
 
 > ». so as to be capable of being kept at all times accu- 
 
 ..rjples with the radiat bar. r. At a short distaaca 
 
 Croat the ceatre of saotioa of the radias bar, r, is a s e g mental 
 
 opening. gra«l . . an each side of the i 
 
 aad for the minute subdiviaion of the graduations of the quad- 
 rant oa the piece, x. Br this apparatus an; angles ma; be 
 measured and laid off b; the quadrant, and transferred to an; 
 point oa the paper without the aid of an; additional instrument, 
 as the whole instrument ma; be moved to an; desired point on 
 the straight-edge, r, without an; shift of position with reference 
 to the meridian line or starting point With additioaal scales 
 on the right ancle straight-edges, j. the instrument ma; be em- 
 ployed, as aa offset scale, for plotting surer;* aad laving down 
 
 Oae of the moat economical!; useful instruments of the 
 draughtsman is the Pentagraph ; but it is one which requires 
 such extreme accuracy and truthfulness in its construction, that 
 its consequent cost puts it out of the reach of the ma 
 those who need it. B; means of it, drawings may be copied oa 
 aa enlarged or reduced scale, by the mere action of carrying 
 a tracing point over the lines of the original drawing. The 
 motion of the tracing point is communicated to the delineating 
 
 pencil b; the angular movements of a series of levers o s ciPatia sT 
 upon a I -as the 
 
 ,. great. 
 
BOOK OF INDUSTRIAL DESIGN. 
 
 195 
 
 required, providing for the increase or decrease in length of the 
 
 two radii, but in such a manner that they shall continually 
 
 be in the same proportion 
 
 to each other. This is 
 
 effected by making the 
 
 main lever with joints 
 
 midway between the ex- 
 
 Fig. 40. 
 
 tremities and the 
 centre of motion. 
 It is necessary, 
 however, that the outer joints of "---. r-^^L 
 
 the lever should be maintained v ^ - 
 
 constantly parallel to each other, 
 
 and it is likewise desirable that the instrument should be capa- 
 ble of adjustment for different proportions, otherwise its scope 
 of usefulness would be sadly narrowed. These several condi- 
 tions are fulfilled in the instrument represented in our engraving, 
 fig. 40, which is a pentagraph of the most modern and approved 
 design and construction. The main lever, a, turns upon a centre 
 carried by the weight, b, which has fine points upon its under 
 side to prevent its slipping upon the paper. The lever, a, 
 passes through a socket at the centre, and may be fixed by a 
 pinching screw at any point of its length ; it is graduated at the 
 side, and the socket is formed with a vernier index for the esti- 
 mation of minute measurements. To the extremities of the 
 lever, a, are jointed the discs, c, which are formed with sockets 
 on their under sides to receive the bars, d, e. These bars are 
 graduated in a similar manner to the main lever, and vernier 
 indices are formed in the plates, c, to correspond. The paral- 
 lelism of these bars is maintained by the rods, f ; the tracing 
 point is at g, and the delineating pencil at h, or vice versa, as 
 the case may be. A string, i, is passed from the tracing point 
 through guide eyes at the joints, c, c, to a small bell-crank lever, 
 at n, by means of which the pencil is raised when it is not wished 
 to mark ; this being effected by drawing the string, i, at the 
 tracing point. As represented in the engraving, the instrument 
 is adjusted to copy a drawing upon an enlarged scale. To 
 obtain the correct action of the instrument it is necessary that 
 the tracer, g, pencil, h, and centre of motion, b, be in a straight 
 line. The proportion of reduction or enlargement being deter- 
 mined on, the main lever, a, is so adjusted in its socket, b, that 
 the portions of the lever on each side of the centre may have 
 this proportion to each other; this being indicated by the 
 graduated scale on the side of the lever. The bars, d, e, must 
 then be correspondingly adjusted in their carrying sockets, the 
 
 distance between the tracer, or pencil, and joint being always 
 ecmal to the distance between the joint and turning centre on 
 the respective side of the main lever, a. The instru- 
 ment, when adjusted, is balanced on its centre by 
 means of the sliding weight, j, upon the lever, a. 
 In some pentagraphs the rods, p, are dispensed 
 with, and the parallelism of the bars, d, e, main- 
 tained by a belt, k, indicated in 
 dotted lines, passed round the 
 peripheries of the discs, c, grooved 
 for the purpose. 
 This belt is usu- 
 ally of thin flat 
 steel wire, similar 
 to that used for 
 watch springe — a 
 belt of ordinary 
 ;<>-" ' material causing 
 
 =■*' " "■ — inaccuracies owing to its elasticity. The arrange- 
 
 ment in which the rods are used is, however, 
 superior, as the belt is apt to slip, or, if it is too tight, it occa- 
 sions an injurious strain on the joints. 
 
 Another form of pentagraph has been suggested by Mr. R. 
 Foster, jun., of Dublin, which seems susceptible of being rendered 
 a very efficient instrument. It is delineated in fig. 41. The 
 small and shallow circular box, a, contains the actuating mecha 
 nism, and is arranged to turn at pleasure upon the fixed centre 
 stud, b ; and from each side of the box, a rod, t:, d. projects, the 
 points of the rods being brought into a horizontal line with the 
 Btud centre, b. The box is in horizontal section, to exhibit the 
 
 Fig. «. 
 
 internal gearing. The end of each rod has rack-teeth upon it, 
 the teeth on the rod, o, gearing with a spur-wheel, e, fas! oil a 
 stud in the centre of the box ; whilst the other rod. d, similarly 
 gears, with a pinion, F;on the same centre. These two wheels 
 are, of course, changeable, their relative radii being always 
 determinable by the proportion to be observed between the 
 original and the copy, of any drawing to be reduced or enlarged 
 by the instrument. The same relation is also to be kept up 
 between the lengths of the two rods, in order that hoth the 
 angular and longitudinal traverse actions may coincide. It is 
 then obvious that whatever figure is traced out by the point 
 on one rod, will be delineated by the pencil on the other, in 
 the proportion determined by the wheels and the leverage of 
 tie rods. The rods may be either worked on opposite sides, 
 or both on the same side. 
 
Itt Tlli 
 
 In • put the :• nt in 
 
 ! 
 
 :i ill the « 
 
 itniiiit Bin. 
 
 • trustworthy aids in the prosecution of his ttudiet 
 
 D t" liifn in I 
 Hi ay I- nil — 
 
 where all is orderly let down." 
 
 •nd thai itory reroarl 
 
 industrial p - of the 
 
 i • u Bmall portion of the which wc I I 
 
 presd of tliat pari ition in which 
 
 • far behind. 
 •■ M tical qualifii • nt author of " M 
 
 entro. On the right side an the men <>f fact--, on t ho 
 - t In- men "f both." Let it tx i to weaken this disunion of : 
 
 or uposite class. The ri^lit and the lift may each hold to, 
 
 -, but nothing really g I can arise fr"in all ihi>, until the pra< I 
 
 upon the theoretical desi| n< r, which the hni«-r will niruiii return, in op 
 tpprehended fact* he well, " is the parent, not the proj 
 
 - in practice forma jmrt of 1 1 1 # - prelude, as well as I 
 
 by judicious theoretical comp < I 
 
 much apart " The dexterous band and the thoughtful mind," the 
 and be ■ h< oath e brain. Qnd iln-ir st 
 
 foundry it may l"- designed, or however clearly it may l"- w ritten, ran make n draughtsman. 
 
 i ns, the ambitious student must add attentive assiduity and patient toil. The first 
 
 ■ih1 are absolutely essential. Let each i the admirable words of 
 
 '• re the com n level has received two education — tb< 
 
 i and important, from himself." Thi Bacon would have 
 
 In In- "Advice on the Study nnd Practice of tl Wright lias, most happily and 
 
 ilur t'ipir. II< ■•lent may rest assured that, without industry, and u 
 
 ■ fame, and an enthusiastic desire f"r imp ail t" inspire, be will not 
 
 cut; and bo '■•it thai society form- a very different opinion of the man of sound jui 
 
 attempts, anl the fanciful and vain, who, whilst they imagine thi i 
 ii than othi r lives in indolent or trifling pursuits, without acquiring that knowledge 
 
 iracy and Buccess in practice." These are the wrll-considcrcd ideas of men who 
 hi and action. Their pithy eloquence embodies \\ hole chapters of matter \\ orthy of 
 ry, where thej must arouse him from anj dreamy and deceptive contemplal 
 
 rficial thinker is bul too apl t" !"• thus led awaj j that such compari- 
 
 litions which h<- perhaps Bopercilioui 
 i 
 
 and to further such ei written tliis book; and with such i nowcommH 
 

 
 
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