712 FURNITURE. SHERATON (T.j. The Cabinet-Maker and Upholsterer's Drawing-Book. With frontispiece and over 100 folding and other copper -engraved plates of furniture, etc. ' With Appendix. Thick 4to, new half blue calf, gilt back, gilt top, by Bayntun. London, 1793 f*?^^) * Original edition. Rare. Complete with the Appendix aud Accompanime I Digitized by the Internet Archive in 2014 https://archive.org/details/cabinetmakeruphoOOsher_0 Art<£n'cu.-Vev. r w $ 79 m . by T.S/ieraren . THE CABINET-MAKER AND UPHOLSTERER'S DRAWING-BOOK. IN THREE PARTS. b y THOMAS SHE RA TO N, CABINET-MAKER. L- O N D O N: PRINTED FOR THE AUTHOR, BY T. BENSLEY; AND SOLD BY J. MATHEWS, N° l8, STRAND; G. TERRY, N° 54, PATERNOSTER-ROW J J. S. JORDAN, N° l66, FLEET-STREET , L. WAYLAND, MIDDLE-ROW, HOLBORN ; AND BY THE AUTHOR, N^I, DAVIES- STREET, GROSVENOR- SQUARE. J 793- [ twmtts at &tatiQ\m$ ^$a\U 3 FRONTISPIECE EXPLAINED. To ftiew ::i pleafing a way as I could the liability of this Performance, and the fubje&of the book in general, I have, by the Figure on the right hand, re- prefented Geometry ftanding on a rock, with a fcroll of Diagrams in his hand, converfing with Perfpe6tive, the next figure to him, who is attentive to the prin- ciples of Geometry as the ground of his art ; which art is reprefented by the frame on which he refts his hand. On the left, feated near the window, is an Artift bufy in defigning; at v/hofe right hand is the Genius of Drawing prefenting the Artift with various patterns. The back Figure is Architecture, meafuring the fhaft of a Tuican column, and on the hack ground is the Temple of Fame, to which a knowledge of thefe Arts diredlly leads. CONTENTS OF THE THREE PARTS PART L Containing fuch Geometrical Lines and Inftrudtions as are highly ufeful to Perfons of botk Branches, illuflrated in Seven Copper-plates. To which are added the Five Orders, ex- hibited in five different Plates, proportioned by Modules, Minutes, and Aliquot Parts, according to the moft approved Authority ; together with fome Account of their Anti- quity and Origin. PART II. On Practical Perfpective, applied to the Art of reprefenting all Kinds of Furniture in dif- ferent Situations ; interfperfed with fomething of the Theory, for fuch as would know the Principles on which this ufeful Art is founded. The Whole illuflrated in Thirteen Copper-plates. PART III. A Difplay of the prefent Tafle of Houfehold Furniture ; containing alfo ufeful Remarks on the manufacturing Part of difficult Pieces. To which are added, fome Cornices drawn at large ; the Method fhewn of Gaging, Working, Contracting, and Enlarging of any Kind ; together with two Methods of reprefenting a Drawing-Room. a 2 Directions Directions for finding and binding in the Plates, with an Account of their Contents. The Frontifpicce faces its Explanation before the Title Page. PARTI. Of Geometrical Lines. PLATES. PAGES, r. To divide a Line into equal Parts, to divide a Freeze, to raife Perpendiculars, and to illuftrate the Ufe of the Sector - - Faces Page 26 2. Of Scale of Tenths, Chords, Sines on the Sector; to draw an Oval by the Sector ; and of various geometrical Figures - - 54 3. To draw Polygons, Ovals; and to find the Center of Ovals - - 78 4. To take the Plan of a Room for a Carpet - - - 80 5. Of mitcring a Comb-Tray, and Mouldings of different Projections ; of Raking Mouldings, and the Tufcan Pediment - 90 6. Various Geometrical Solids, and of finding Curve Lines to anfwer the Sec- tions of irregular figures - - - - -108 7. To find Lines for Hip and Eliptic Domes - - - - 118 8. The Tufcan Order . - - - 348 9. The Doric Order - - - - - 132 10. The Ionic Order - - - - - 154 11. The Compofite Order - - - - 160 12. The Corinthian Order - - - - - 164 13. Of. diminishing the Shaft of a Column, and of the Ionic Volute - ibid. PART vi DIRECTIONS FOR PART II. Of Perfpe&ive. PLATES. PAGES. 14. The Elementary Planes, and Nature of the Eye - - Faces Page 220 15. The Reprefentation of Squares in different Pofitions - - - 234 16. Squares in Inclined Planes . . 240 17. Ditto Ditto. - _ 24.4. 18. The Reprefentation of Cubes and Prifms - — - 256 1 9. The Reprefentation of Polygonal Figures - 264 o. The Reprefentation of a Row of Equidiftant Columns, and of Long and Short Diftances - - - - - 282 21. Curvilinear Figures - - - « - 296 22. The Reprefentation of Steps, and the Tufcan Pedeftai and Bafe - - 302 23. The Reprefentation of the Tufcan Entablature, and of Arches - - 308 24. The Reprefentation of Houfes and Chairs - - - 314 25. The Reprefentation of Tables and a Commode - - - 318 . The Reprefentation of a Cylinder Defk and Book-cafe, of a Chair oblique, and Shadows in general ; bound in by a Guard - 35G PART III. Of Pieces of Furniture. 25. The Univerfal Table. - 362 26. Sideboard Table ; marked on the Plate 54 by miftake. N. B. The Brafs Rods are made by Mr. Penton and Co. New-ftreet Square, near St. Andrew's, Holborn. - - - - - 366 27. Book-cafe Doors - - - - 370 28. A Secretary and Book-cafe - - ibid. 29. Book-cafe Doors. - - - - - ibid. 29. A Sideboard Table. - - - ibid. 30. A Library Table, binds in without a Guard. - 37.6 7 P>. A FINDING THE PLATES. vii PLATES. PAGES. A Sofa, and the Perfpe&ive Lines of it ; binds in without a Guard Faces Page 380 3*- Drawing-Room Chairs - - - - 388 33- Parlour Ditto - ibid. 34- Drawing and Parlour Ditto - ibid. 35- A Sofa - - ibid. 36. Chair Backs - ibid. 37- A Lady's Writing Table - 39° 38. Tripod Fire- Screens - - ibid. 39- Knite-Caies, and Lady s Travelling-Box 392 40. Alcove Bed - 382 4i. ii ouiimici JDcu — - *- — 3°4 42. l^r\rr\(*r T?'ji<~kr»_Nf"'nn/ic — _ _ V_/Ulllcr J_>alUil O Ltllltlo — on A 43- Wafhhand Stand Pot Cuoboard. Secretarv and Screen Table qq6 44. A Reading and Writing Table - ibid. 45- A French State-Bed - - 386 40. A Lady's Drefling-Table - - - 39 8 47- A Cylinder Defk and Book-cafe - 402 48. A Cabinet - 406 A Cabinet and Drefling-Table - ibid. to. •J A Lady's Cabinet and Writing-Table - - 408 5 1 - Window Curtains and Drapery - ibid 52. A Gentleman's Secretary - 410 53- A Cylinder Wafhhand Stand - 412 54. Pembroke Table and French Work-Table 414 55- Tripod Candle-Stands •- 416 56. A Harlequin Pembroke Table * 430 56. Ornament Ui DIRECTIONS, &c. PLATES. PAGES. 56. Ornament for a Freeze or Tablet - - Faces Page 430 57. Pediments for Book-cafes ~ - - 432 58. A Kidney Table - ibid. 59. Cornices at large - 436 60. The Lady's Drawing Table, and the Dining-Parlour - ~ 440 61. The Drawing Room * : • 444 CONTENTS, CONTENTS. Address - - - Page 5 A Book publifhed before Chippendale's - « 7 Chippendale's next in order of Time - - - ibid. Chippendale's Remark on the Ufefulnefs of Perfpective - 8 After his there appeared another Book of Defigns in Chairs only - - ibid. An Apology for a Remark made on Chippendale's Third Edition - - ibid. Ince's and Mayhew's Book of Defigns fucceeds that one of Chairs only g Hepplewhite's Upholfterer's Guide, publifhed in 1788 — Remarks on it - - io The Cabinet-maker's Book of Prices, publifhed in the fame Year — Remarks on it 1 1 The Stability of the Plan on which the Cabinet Drawing-Book is publifhed - it Miftakes to be avoided when the CompafTes are applied to the receding Parts of Furniture - - - - - - 13 PART I. Of Geometrical Lines. Introduction - - - - - The term Geometry defined - - - ' - - ibid. Regular .Geometry not necefTary to Workmen in attaining a competent Knowledge of Lines - - - - _ 16 b Geometry x CONTENTS. Geometry founded upon a few Principles of common Senfe Technical Terms propofed to be explained S E C T. I. On Geometrical Lines. Problem i. To divide a Right Line into any Number of equal Parts by the firft. Opening of the Compaffes - - -19 ■ ■ 2. To divide a Freeze - - - - -21 ■ 3. To raife a Perpendicular by different Methods - - - 22 4. Ditto - - - - - 22 Page 17 ibid. SECT. II. Of the Ufe of the common Cafe of Inftruments - - - - - 25 The ConfrTuction and Ufe of a Scale of Feet and Inches — its Derivation - - 26 ■ of a Scale of Tenths - - - 27 1 of a Scale of Chords - - ~ - 29 On the Protractor — its Derivation - - - 30 Of the Sector — its Derivation - - - - 32 Of the Line of Polygons on the Sector — its Derivation - 34 - of Chords on Ditto - - - 37 ■ of Sines on Ditto - - - 38 Of the Tangent Line on Ditto — its Derivation - - 41 SECT. III. The Names of Geometrical Figures ought to be known - - 43 Of Superficies — its Derivation - - - 44 Of various Triangles - - - - -45 Of Mixtilineal Figures - - - 48 Of Polygonal Figures — the Derivation of the Term Pentagon - 49 The CONTENTS. xi The Names of the various Sorts of Polygons page 50 What the Sections of a Cone produces - - - 5 1 A Circle and an Oval the only regular Surfaces bounded by one Line — the Deriva- tion of the Term Ellipfis - - ibid. SECT. IV. Of drawing various ufeful Geometrical Figures - - -52 Problem 5. To draw a Geometrical Square - - ~ m 53 6. To draw a Rhomb - - - - - ibid. — — 7. To draw Polygons - - - ~ S$ 8. To defcribe a Hexagon - - - -56 — — 9. To defcribe a Heptagon - ibid. ■ 10. A Circle given to find the Sides of a Pentagon - - * 57 < 1 1 . The Infcription of a Hexagon - - • > "5$ 1 12. Different Methods of drawing Ovals - - ~ 59 ■ 13. Ditto - - - - 60 14. Ditto - - - - - 61 15. Ditto - - - - 62 16. Ditto - 63 17. Ditto - - - - 65 18. To find the Center and Diameter of an Oval - 66 19. To find the Center of any Segment - - 67 — 20. To find the Diameter of a Cylinder without meafuring its End - 69 SECT. V. Problems pertaining to the Working Part. _ 2 1 . The extreme Lines are given to find any Number of mean Proportionals 7 1 Illuftration of this - - - 72 How to cut all the Steps of a Ladder to their proper Length before any Part of it is put together - - - - 73 b 2 Problem xii CONTENTS. Problem 22. How to draw an Elliptic Cornice, and to fit a Valance to it - Page 74 23. To defcribe a Segment of a large Circle without a Center - - 77 24- To take the Plan of a Room - - - 78 25. To miter any Thing of the Nature of a Comb-Tray - - 80 26. Of mitering Mouldings of different Projections - 83 27. Of mitering Raking Mouldings - - 85 28. Of the Tufcan Pediment - - 87, SECT. VI. Of the Names and Properties of various Geometrical Solids * - -91 Derivation of Hexaedron and Prifm - - 93 De rivation of Tetrahedron - - - 95 The Learned differ about the Derivation of the Term Pyramid - -97 Derivation of the Terms Hemifphere and Section - - - 99 Of the Sections and Coverings of regular and irregular Figures - - ibid. . Problem 29. Of the Covering for a Vafe - - - - IOO 30. Of the Covering of an irregular Vafe - - - 103 Of the Covering of a Sphere - - - - 105 1 31. The Section and Covering of a Knife-cafe - - -106 32. Of the Conftruction of Hip Domes - 109 General Obfervations on the Management of Domes - - 1 1 g 33. To conftruct an Elliptic Dome - - - - 116 Of the Management of Elliptic Domes - - - 118 SECT. VII. Of the Proportion of the Five Orders. Introduction - _ J2Q Of the Origin and Antiquity of the Orders - - - - 123 The Derivation of the Term Architecture - » . _ ibid. What I CONTENTS. xiii What gave rife to the Term Architecture - Page 123 Its Progrefs in building a City arid Tower to reach the Heavens - - 124 No regular Proportions afligned to any Pillars before thofe of Jachin and Boaz in Solomon's Temple - ibid. Pillars were in ufe long before Solomon's Time ; but no mention is made of their Proportion, except what Jofephus fays of their Height - - 125 The Proportions of Jachin and Boaz anfvver to the moft Ancient Doric Order - ibid. Some Particulars wherein they refemble each other - - - 126 What Vitruvius fays of the Antiquity of the Doric Order does not conuft with other Facts - - - - --128 The Tonic next in order — a Temple built of it at Ephefus - - - 130 The- Corinthian fucceeds — Vitruvius's Account of Its Origin - - 131 Who Vitruvius was - - - - - ibid. The Tufcan Order the Fourth in point of Antiquity - - - 132 The Compofite the Laft - ibid. The Compofite Capital derived from the Corinthian, and not limited to one Kind 133 The Character and Proportions of the Tufcan Order - - - 134 The Diminution of a Column - - • j^j Sir William Chambers's Remarks on Diminution - . " 13B The common Method of Diminution - * - - 139 The bell: Standard for the Quantity of Diminution - - - 140 Vignola's Method of Diminution - - - - = 141 Nicomedes's Inftrument for diminifhing Columns - - - 142 Of the principal Parts of a Column, and the Names of each Member - * 143 Of the Character and Proportions of the Doric Order - - - 150 Of the Character and Proportions of the Ionic Order - - r *53 How to defcribe the Ionic Volute «- - - - - 154 To graduate the Fillet of the Volute - - » l ^ Of the Character and Proportions of the Compofite Order - - 158 The Compofite Order fhould be placed before the Corinthian — Reafons why, fhewn rcg General X iv CONTENTS. General Proportions of the Compofite Order - Page 1 60 Of the Character and Proportions of the Corinthian Order * - 161 How to draw the Scatia, Cymarecta, and Cymainverfa - - 164 Obfervations on the Agreement of the Five Orders - - 165 Of the Proportions of Frontifpieces - ~ - - 167 General Directions for drawing the Five Orders — Indian Ink - 17Q PART II. Of VerfpeHive. Introduction - - *• - - - ~ *77 SECT. I. Of the Principles on which Perfpe&ive is founded Of die Elementary Planes - The Ground Plane - The Perfpeaive Plane - How the Appearance of Objects may be determined on Glafs The Horizontal Plane - The Directing Plane • The Vertical Plane - ■ The Vifual Plane - Ot Lines produced by the InterfecTions of the foregoing Planes Of Points produced by the InterfecTions of thefe Lines SECT. II. Of the Affinity of Optical Laws with the Principles of Perfpedtive - - 205 The Ufe of the three principal Elementary Planes in the Practice of Drawing - 21 1 ( )f various Pofitions of Lines to the Picture - - - 215 1 1 >\v a Geometrical Square appears on the Plane of the Picture in various cafes 217 SECT. 182 188 189 ibid. 190 191 196 ibid. 198 200 202 CONTENTS. XV SECT. III. Problems folved according to the preceding Principles - - Page 225 The uuial Method of teaching Perfpective is to begin with Points and Lines - ibid. Thefe unnecefTary, becaufe included in finding the Reprefentations of Superficies 226 Problem 1. To reprefent a Square lying on the Ground - - - 227 2. perpendicular to the Ground and to the Picture 228 ' 3. perpendicular to the Ground and parallel to the Picture - 230 ■ 4. inclined to the Ground, and perpendicular to the Picture - - - - - 231 5. — i inclined to the Ground and to the Picture 234 6. To find the Reprefentation of a Square lying on the Ground, having its Sides oblique to the Picture - 236 7. To find the Reprefentation of a Square perpendicular to the Ground and oblique to the Picture - - - - 238 ■ 1 8. To find the Reprefentation of a Square, having its Sides oblique to the Picture, and fituated in a Plane inclined to the Ground - 239 . 9. To find the Reprefentation of a Square fituated in a Plane oblique both to the Ground and to the Picture - - - 241 . 10. To reprefent a Floor of Squares - - 244 • 11. To reprefenc a Row of Cubes parallel to the Picture - - 246 -12. To reprefent Cub :s oblique to the Picture - - 248 ■ 13. To reprefc ">t Ejects when the Diftance and Vaniming Points exceed the Bounds of the Picture - - - - 250 ■ 14. To reduce the Point of Difiance to the Limits of the Picture - 254 SECT. IV. Of the Reprefentation of Polygonal and Curvilinear Figures - - 257 Remarks on Polygons - - - - - ibid. Problem 15. To reprefent a Hexagon having two of its Sides parallel to the Picture 259 7 Problem K*j CONTENTS. Problem 1 6. To find the Reprefcntation of an Hexangular Prifm - Page 260 17. To find the Reprefcntation of an Octagon, having two Sides parallel to the Picture - 262 18. To find the Reprefentation of an Octangular Prifm, having its fides oblique to the Picture - - 263 Remarks on the Difference between the Reprefentation of Objects on a Plane, and their Appearance to the Eye - - - 265 Of the Reprefentation of a Range of Equidiftant Columns - - 269 Of the proper Choice of the diftance of the Picture, proportioned to the Height of the Horizon - - - - - 275 How to choofe a Diftance when the whole Length of the Picture is filled with Objects on the Front - - - - - 280 How to choofe a Diftance when the Objects are drawn by a large Scale, fituated not far from the Center of the Picture - - - - 281 How to choofe a Diftance when a Piece of Furniture, not very long, is reprefented near the Middle of the Front of the Picture - - - 282 Of the Reprefentation of Curvilinear Figures - - - 283 Problem 19. To reprefent a Circle lying on the Ground Plane - - 289 20. To reprefent a Circle perpendicular to the Ground and to the Picture 291 21. To reprefent a Cylinder erect on the Ground - - 292 22. To reprefent a Cylinder lying on the Ground and oblique to the Picture 293 23. To find the Reprefentation of a Semi-ellipfis whofe tranfverfe Diameter is parallel to the Picture - 294 24. To find the Reprefentation of an Elliptic Segment inverfely . - 295 SECT. V. The Application of the preceding Problems to the Practice of drawing Pieces of Ar- chitecture and Furniture - - - „ 296 Example 1. How to reprefent a receding and returning Flight of Steps - - 297 2. How to reprefent a Tufcan Bafe and Pedeftal - 299 Example CONTENTS. xvii Example 3. How to reprefent a Tufcan Entablature and Bafe » Page 302 > 4. How to reprefent Arches - - 307 5. Ditto - 308 6. How to reprefent a Houfe having its Front parallel to the Picture - 309 7. To find the Reprefentation of a Houfe when the Gable-end is parallel to the Picture - - - - - - 311 8. How to reprefent a Chair when its Front is parallel to the Picture - 312 — 9. How to reprefent a Chair when its Front is perpendicular to the Picture - - - - -314 — 10. How to reprefent a round Pillar and Claw Table - - - 315 1 1 . How to reprefent an octagon Ditto - - 3 1 6 ' 12. To put a Commode in Perfpective when its Front is parallel to the Picture - - - - - 317 13. To reprefent a Chair when its Front is oblique to the Picture - 319 14. To puf a Cylinder Defk and Book-cafe in Perfpective when its Front is oblique to the Picture - - - 321 SECT. VI. A fhort View of the Nature and Principles of Shadows - • Preparatory Obfervations - - - - Cafe 1. To project the Shadows of Objects in various Pofitions when the Sun's Rays are parallel to the Picture - - Example 1. Ditto - 2. Ditto - 3. Ditto - - - — 4. Ditto Example 1. When one Object {lands in the Wav of the Shadow of an- other - 2. Ditto - - 326 ibid. 328 329 33° ibid. 331 33^ ibid. Cafe xviii CONTENTS. Cafe 2. To project the Shadows of Objects when the Rays come in a Direction from behind the Picture - Page 334 Obfervations on the Theory of Cafe 2. - - "335 3. To find the Projection of Shadows when the Sun's Rays come on the Front of the Picture - - 340 Example 1. When the Shadow falls on the Ground - ibid. 2. When the Shadow falls on upright, oblique, and horizontal Planes 341 Of Shadows when the Sun does not fhine - - -« 343 Of the Proportion of Tints in a Picture - 345 Of reflected Images on Water - - - - "347 PART III. Furniture in general Introduction - - - - - ~ 35 1 Of the Univerfal Table - - - - "35^ Of the Sideboard Tables - - - - - 363 Of the Book-cafe Doors ~ - - - - 368 Of the Secretary and Book-cafe - - - - 371 Of the Library Table - - ~ - - "372 Of the Kidney Table - - » - 37 8 Of the Sofa Bed ----- - 379 Of the Alcove Bed - - - - - 381 Of the Summer Bed in two Compartments - - - -382 Of the French State-Bed - - 384 Of the Drawing-Room Chairs - - - - 387 Of the Sofa - 388 Of the Lady's Writing Table - - - - ibid. Of the Tripod Fire- Screens » 390 5 Of J CONTENTS. xlx Of the Knife-Cafes and Lady's Travelling-Box - - Page 391 Of the Corner Bafon- Stands - - m « "393 A Wafhhand Stand and Pot Cupboard * " - 394 Of the Lady's Secretary and Screen Table - - « 3^ Of a Reading and Writing Table - « w - 396 Of a Lady's Drefling-Table •» « ^ ^97 Of a Cylinder Delk and Book-cafe - 399 Of a Cabinet . Of a Lady's Cabinet and Drefling-Table * - * - 405 Of a Lady's Cabinet and Writing-Table - 407 Of the Window Drapery - 408 Of the Gentleman's Secretary » * , • ■ « « Of the Cylinder Wafhhand Stand - - » - 412 Of the Pembroke Table - * » - * 413 Of the French Work-Table - = - * - 414 Remarks on Shadowing the Pembroke and French Work-Table « - Of the Tripod Candle- Stands * » '5 - 416 Of the Harlequin Pembroke Table * m « - 417 Of Pediments - - - » - -431 Of Cornices — the Method of working, contracting, and enlarging them - 432 Of the Lady's Drawing and Writing Table - - - - 437 Of the Dining-Parlour and Drawing Room * c 2 LIST LIST OF SUBSCRIBERS, Si the following Lift it is to be obferved, that the- Mailers in London are diftinguiihed by k having the Names of the Streets, and fometimes the Number of the Houfe, affixed ; but with refpeft to Mailers out of London and its vicinity we could not make this difcrimination, and therefore we hope, on this account, to be excufed by thofe who refide in t»he country. A; Allday John, Mahogany-merchant, Car- lifle-ftreet, Soho, London, 10 copies Angus, Cabinet-maker, Shug-lane, London Anderfon Henry, Cabinet-maker, ditto Anderfon Alexander, Cabinet-maker, ditto Archer William, Upholfterer, ditto Allan John, Cabinet-maker, ditto Atkinfon -Thomas, Cabinet-maker, ditto Arquart James, Profile-painter, ditto Allifon Robert, Cabinet-maker, ditto Allen i Brewer, Burr-flreet, ditto Appleby, Cabinet-maker, Stockton Aftle Thomas, Chefter Alderton, Cabinet-maker, Brighton - Angel Edward, Cabinet-maker Andrews, Cabinet-maker, Ipfwich Adams, Cabinet-maker, Strand, London 3 AppIetOn C. Cabinet-maker, Hallifax Adams Atkinfon William, Cabinet-maker, Rippon" Ambler, Bookfeller, Hallifax Alderfon, Cabinet-majcer, Newcaltle Adams, Plafterer, Briftoi Allen, Cabinet-maker, London Ackermann, Painter, Ruffel-ftreet, London B. Bentham, Colonel Barclay, Efq. Edinburgh Bouch William, Cabinet-maker, Well's- ftreet, London Beckwith, Cabinet-maker, Stockton Bream Samuel, Cabinet-maker, Yarmouth Burbury, Cabinet-maker, London ixii LIST OF SU Blackftock P. Cabinet-maker, Caftle-ftreet, Long- A ere, London Ecnfley Thomas, Printer, Bolt-court, Fleet- ftreet, ditto Bngfter J. Cabinet-maker, Piccadilly, ditto Bradley S. Cabinet-maker, ditto Bails J. Bedftead-maker, No. 434, Oxford- ftreet, ditto Brown Michael, Cabinet-maker, London Bullock William, Cabinet-maker, ditto Brnnton James, Cabinet-maker, ditto Brytam S. Cabinet-maker, ditto Balls Thomas, Cabinet-maker, ditto Binns Edward, Cabinet-maker, No. 1, Burden-ftreet, Berkley-fquare, ditto Black John, Cabinet-maker, ditto Bowman William, Cabinet-maker, ditto Bales Simon, Cabinet-maker, Norwich Blades Thomas, Upholfterer, No. 114, Jermyn-ftreet, London Bullock Richard, Cabinet-maker, ditto Bowman John, Cabinet-maker, ditto Beale John, Cabinet-maker, No. 7, Rofe- ftreet, Soho Beaumont Thomas, Carver, ditto Black Algernon, Cabinet-maker, ditto Batter, Upholfterer, Rochefter Bonington and Thorpe, Clock-cafe makers, „ No. 22, Red Lion-ftreet, Clerkenwell, London Black R. Cabinet-maker, ditto Bigger William, Upholfterer, ditto Bromridge, 'Cabinet-maker, George -yard, Hatton-garden, ditto Borthwick, Briftol Borough, Cabinet-maker, London Bifhop, Cabinet-maker, Houndfditch, do. BSCRIBERS. Baker, Cabinet-maker, Iflington Barlow, Engraver, No. 5, George- ftreet, London Blackland, Old Broad-ftreet, ditto Burnie Charles, Cabinet-maker, ditto Bower, Cabinet-maker, No. 12, Round- court, Strand, ditto Blacklock, Cabinet-maker and Undertaker, No. 79, Park-ftreet, ditto Brown James, Cabinet-maker, ditto Belfour Alexander, Cabinet-maker, ditto Browning John, Mahogany - merchant, No. 21, Southampton-ftreet, Bloomfbury, London Banks Thomas, Cabinet-maker, ditto Bennet Ebenezer, Edinburgh Blackburn William, Upholfterer, London Bunnell, Upholfterer, Colchefter Bore, Cabinet-maker, Norwich Barkworth John, Barton Bryant T. Sheffield Botcherby R. Cabinet-maker, Darlington Bings John, Cabinet-maker, Sheffield Beale Thomas, Cabinet-maker, York Braid wood and Bruce, Edinburgh Burnet and Painter, Cabinet-makers, Briftol Brailsford W. Cabinet-maker, Sheffield Brailsford T. Cabinet-maker, ditto Brafh John, Cabinet-maker, Leeds Burn James, Cabinet-maker, Hadington Baffick A. Cabinet-maker, Scarborough Benwell C. Cabinet-maker, Reading Bam and Reid, Bookfellers, Glafgow Burns, Cabinet-maker, ditto Binns, Chair-maker, New Compton-ftreet, London Barclay, at the George, Monmouth-court Benfon, Cabinet-maker, London LIST OF SUBSCRIBERS. Barton, Lincolnshire Brown, Upholfterer, Newcaftle Bell, Painter, ditto Bulmer, Cabinet-maker, ditto Brummell, Cabinet-maker, ditto Bally, Cabinet-maker and Upholfterer, No. 10, Milfom-ftreet, Bath Bland, Cabinet-maker, Halifax Baifton and Hargill, Cabinet-makers, Leeds Beal, Cabinet-maker, London Badger, Cabinet-maker, Batterly- moor, Lan- cashire Bofmand Brown, Cabinet-maker, London Binns, Shell-maker, Smithfield, London Brown, Lelburnel, and Co. Glafgow Bruce, Upholfterer, No. 307, Holborn Bland, Gowthrop, Edmond C. Campbell and Son, Cabinet-makers to the Prince of Wales, Mary-le-bone-ftreet, London Cromer James, Upholfterer, Edinburgh Chriftie R. Chair-maker, No. 2, Newman- ftreet, London Cliff, Upholfterer, London Cook William, Cabinet-maker, ditto Cryftall William, Cabinet-maker, ditto Challis John, Upholfterer, ditto Coats J. Cabinet-maker, ditto Campbell A. Cabinet-maker, ditto Chimolme T. Cabinet-maker, No. 7, Great Pultney-ftreet, ditto Cafement W. Cabinet-maker, ditto Hudfon and Corney, Cabinet-makers, No. 1 , Broad-ftreet, Soho, ditto Cragg Leonard, Cabinet-maker, London xx'.ii Cragg James, Cabinet-maker, ditto Calvert Matthew, Upholfterer, ditto Cleland Alex. Cabinet-maker, St. Ann's - court, Peter-ftree Child, Upholfterer, ditto Crockett Charles, Cabinet-maker, ditto Conyer George, Cabinet-maker, ditto Cheatham J. Cabinet-maker, Eagle-court, Clerkenwell, London Cook J. Engraver, Mill-hill, Middlefex Cerr J. Upholfterer, Glafgow Clark J. Upholfterer, London Cowin J. Cabinet-maker, ditto Cooper, Cabinet-maker, ditto Cartwright, Carver, ditto Chowles, Cabinet-maker, No. 21, North Audley-ftreet, ditto Crow Charles, Cabinet-maker, ditto Cook Edward, Cabinet-maker, Cow-crofs, near Smithfield, ditto Colborn W. Cabinet-maker, ditto Counfel, Upholfterer, ditto Corlett Edward, Cabinet-maker, ditto Cook Jofeph, Cabinet-maker, ditto Cotter W. Cabinet-maker, No. 24, Burr- ftreet, ditto Clark W. Cabinet-maker, Stockton Cubitt, Cabinet-maker, London Cooper, Cabinet-maker, Bifhopfgate-ftreet, ditto Crofs, Cabinet - maker, Blackfriars - road, ditto Chriftian Thomas, Upholfterer, ditto Cooper Jofeph, Cabinet-maker, Derby Cramp and Tollput, London Carr Richard, Sheffield Cook, Upholfterer Colchefter LIST OF SUBSCRIBERS. XXIV • Chapman, Upholftcrer, Ipfwich ■ Cartwright, Cabinet-maker, ditto .Chamberlain, Cabinet-maker, ditto Caldwell, Sheffield Cudbert John, Cabinet-maker, Whitby- Campbell John, Cabinet-maker, London -Cox Edward, Cabinet-maker, Northampton Court, Cabinet-maker, Briftol Conftantine Richard, Leeds Cravne Thomas, Derby Croft, Cabinet-maker, Leeds Crailey, Workington Craftay, Cabinet-maker, London Crowther, Cabinet-maker, Hallifax Cowley, Cabinet-maker, Liverpool Carry Chriftie, Cabinet-maker, London Crois Jofcph, Cabinet-maker, ditto Crois Aubery, Cabinet-maker, ditto D. Donald Robert, Cabinet-maker, Grofvenor- ftreet, London Daws Thomas, Upholfterer and Cabinet- maker, No. 27, Dean-ftreet, Soho, ditto Downer H. Ironmonger, Fleet-ftreet, ditto Dixon George, Cabinet-maker, ditto Dales J. Ncw-ftreet, ditto Dodrhan V/. Cabinet-maker, ditto Duncomb M. Cabinet-maker, ditto Dent Henry, Cabinet-maker, No. 27, Little Caftle-ftreet, ditto Dutton Thomas, Cabinet-maker, London Dobfon Chriflopher, Cabinet- maker, ditto Digby James, Cabinet-maker, York Davifon W. Cabinet-maker, London >)urward, ditto Dods James, Cabinet-maker, No. 34, Broa w L 1ST OF SUBSC R 1 B E R £ Rawlins, Bedftead-manufachircr, Theobald's road, London Rutherford, Cabinet-maker, Hull Rifhforth, Mufical -inftrument maker, Lon. RandeU [. Tottenham-court -road, ditto Richards, Copperplate-printer, No. 98, Long- acre, ditto Red ford, Cabinet-maker, ditto Robinfon George, Upholfterer, ditto Kols John, Cabinet-maker, ditto Robinfon Thomas, Cabinet-maker, ditto Robertfon Joliah, Cabinet-maker, ditto Robinfon Ifaac, Cabinet-maker, ditto Robfon Hiomas, Cabinet-maker, ditto Rofs R. ditto Raw, Great Marlborough -ftreet, ditto Richerley T. Cabinet-maker, Durham Reid Peter, Grocer and T ea-dealer, White- haven Rothery, Cabinet-maker, London Rowatt, Hamilton Riland, Cabinet-maker, Oxford-ftreet, Lon. Richardfon, Cabinet-maker, ditto S. Smirke, Painter, Charlotte-ftreet, London Seddons Tho. Upholfterer, Dover ftreet, ditto Stone, Cabinet-maker, Houndfditch, ditto Small, Cabinet-maker, Piccadilly, ditto Smart, Drawing - m after, W eftmoreland- buildings, ditto Small wood , Bi rm i n o ham Stiles, Cabinet-maker, Cambridge Southwell J. London Smith William, Cabinet-maker, No. 10, Beak-ftreet, London Stewart, Cabinet-maker, Bengal Sopwith, Cabinet-maker, Newcaftle Sheerwood, Cabinet-maker, ditto Semple, Cabinet-maker, Margaret-ftreet, ditto Salmon, Cabinet-maker, Chapel-ftreet, Lon. Scott Robert, Edinburgh Stovell George, Upholfterer, Grofvenor- ftreet, London Sheraton N. Cabinet-maker, ditto Scholefield Richard, Cabinet-maker, ditto Sherren Robert, Cabinet-maker, ditto Shaw William, Cabinet-maker, No. 11, George's-court, Clerkenwell, ditto Scott John, Cabinet-maker, ditto Smith T. Upholfterer, ditto Stevenfon Richard, Joiner, ditto Shepley George, Plane - maker, No. 40, Greek-ftreet, Soho, ditto Stark Wm. Cabinet-maker, ditto Smiles John, Cabinet-maker, ditto Strangeways Chriftopher, Cabinet-maker, do. Scott Robert, Edinburgh Stevens John, London Smith James, Cabinet-maker, ditto Shepherd Thomas, Cabinet-maker, ditto Shaw James, Cabinet-maker, ditto Simpfon Wm. Cabinet-maker, ditto Shepherd Beachnoft, Cabinet-maker, ditto Smith James, Upholfterer, ditto Smith Thomas, Cabinet-maker, ditto Stewart Charles, Cabinet-maker, ditto Smith, -Upholfterer, ditto Stevenfon, Printer and Bookfeller, Norwich, 6 copies Steel J. Upholfterer, London Smith John, Sheffield Scott James, Cabinet-maker, London Smith, jun. Cabinet-maker, Norwich Standage Thomas, Clerk, London Scott John, Cabinet-maker, ditto Stevens H. ditto Stenfon Matthew, Cabinet-maker, ditto Stevens, Upholfterer, ditto Shararth Lawrence, Cabinet-maker, ditto Shepherd George, Cabinet-maker, ditto L 1ST OF SUBSCRIBERS. xxxt Storcr John, Loudon Shlefcha Paul, Cabinet-maker, ditto Smith Thomas, ditto Shallis John, Cabinet-maker, ditto Standage John, Cabinet-maker, ditto Stephen ton E. Plumber, Briilol Sheriff and Oates, Cabinet-makers, Edinburgh Scott Alex. Cabinet-maker, Aberdeen Stoney Benjamin, Cabinet-maker, Notting- ham Smith John, Berwick Scott Wm. Cabinet-maker, W akeneld Stooks T. Cabinet-maker, Leeds Stevenfon David, Architect, Newcastle Screens Wortly, Cabinet-maker, Stamford Schurrey Wm. Cabinet-maker, Wakefield Smith Dan. Cabinet-maker, Windfor Spence William, Leeds Shakells and Son, Hull Scot Geo. Coach-maker, Glafgow Scott, Cabinet-maker, ditto Sandiman George, Wright, Pearth Smith, Cabinet-maker, Newcaftle Simpfon Richard, Cabinet-maker, Briftol . Standing, Cabinet-maker, London Simpfon, Cabinet-maker and Upholflerer, St. Paul's Church-yard, ditto Sanders, Cabinet-maker, ditto Shade George, Drawing- matter, Kemp's- court, Broad-ftreet, ditto Shelton and Eley, Cabinet-makers, Notting- ham Sharp, Cabinet-maker, London Summers, Cabinet-maker, ditto Summers J. ditto Stuart Alexander, ditto T. Turner, New Bond-flreet, Cabinet-maker to the Duke of Clarence 3 Taylor, Gent. Cleveland-row, London Tarn William and Son, Cabinet-makers, No. 28, London-wall, London Teede G. Bookfeller, Brook-ftreet, ditto Tatam H. Cabinet-maker, Stamford Talbot R. Upholflerer, Edinburgh ThomW, Cabinet-maker, Carpenter-flreet, near Berkley-fquare, London Taylor John, Cabinet-maker, London Tubby, Cabinet-maker, Norwich Thomfon James, York-houfe, London Tate, Cabinet-maker, ditto Thomfon James, Cabinet-maker, ditto Terry Garnet, Bookfeller, No. 54, Pater- nofler-row, ditto Tate J. ditto Thompfon William, Upholflerer, Saville- row, ditto Taylor George, Cabinet-maker, ditto Townley, Cabinet-maker, ditto Trilford Thomas-, ditto Todd James, W r right, Edinburgh Todd Henry, Upholflerer, Edinburgh Turton Richard, Sheffield Tontime G. London Thompfon John, Ewell in Surry Thompfon John, Cabinet-maker, Durham Taylor Robert, Cabinet-maker, Exeter Tate John, Cabinet-maker, Newcaftle Thompfon Wm. Cabinet-maker, Beverly Thoaker Jofeph, Leeds Torbat, Celleret-maker, No. 36, Red Lion- flreet, London Taylor, Cabinet-maker, Eafl Smithneld, ditto Turner, Workington Thompfon, Cabinet-maker, Whitehaven Trip, Barton in Lincolnfhire Tharrat Thomas, Cabinet-maker, London Thorne William, Joiner atxatn VIST OF SUBSCRIBERS. U. :V4^1 Jacobj Derby V. Verrier, Bookseller, 12 copies W. Waldron Thomaa, Upholflerer, Catharine- flrcct, London Wentworth D. Cabinet-maker, Cambridge Wright William, Cabinet-maker, No. 410, Oxford-flreet, London "Wright Francis, Cabinet-maker, No. 410, Oxford-flreet, ditto W r arrock, Joiner and Cabinet-maker, No. 5, Jermyn-flreet, ditto Way land L. Bookfeller, Middle-row, Hol- born, ditto Walker Wm. Carver and Gilder, No. 48, Albemarle-ftreet, ditto Wrightjofeph, Cabinet-maker, ditto Wilfon Wm. Cabinet-maker, ditto Whitaker Jofeph, Cabinet-maker, ditto Walker J. Carver and Gilder, Warwick- court, ditto Woolley, Architect, ditto Wyatt G. Cabinet-maker, ditto Wilkie Wm. Cabinet-maker, ditto Wright, Upholflerer, Walker David, Cabinet-maker, ditto Whitehoufe John, Cabinet-maker^ ditto Wilks W. Cabinet-maker, ditto Wilfon John, Cabinet-maker, ditto Winter, Cabinet-maker, ditto Wootton Edward, ditto White, Cabinet-maker, ditto Wright, Cabinet-maker, ditto Webb, Cabinet-maker, ditto Wetdrill Thomas, Cabinet-maker, London W ay John Wilkie James, Cabinet-maker, Hamilton, Scotland Woolley George, London Weflwood Marmaduke, Cabinet-maker, do Wilfon Robert, Gkbinet-maker, Edinburgh Webfter and Wittey, Hull Ware Robert, Cabinet-maker, Leeds Watfon J. Cabinet-maker, Newcaflle Walker T. Cabinet-maker, Hull W aflon Charles, Cabinet-maker, Edinburgh Waddell, Cabinet-maker, Glafgow Wright, Cabinet-maker, Clerkenwell, Lon. Wareham Thomas, Leeds, 4 copies Wareham John, Birmingham Wills, Cabinet maker, Montrofe Williams, Chair-maker, Ipfwich Whitelock, Hallifax Walling, Cabinet-maker, London Wright James, Teacher of Mathematics Williamfon, Cabinet-maker and Upholflerer, Bedford-court, London Wallace, Cabinet-maker, ditto Weight, Cabinet-maker, Savoy-flairs, ditto Watts, Cabinet-maker, ditto *White, Upholflerer, ditto Williams John, Frodfham Y. Young, Trotter, and Hamilton, Cabinet- makers, Edinburgh Yates John, Sheffield Yates, ditto Zeitler J. London THE CABINET-MAKER AND UPHOLSTERER'S DRAWING-BOOK, IN THREE PARTS. PART I. Containing fuch Geometrical Lines and Instructions as are highly ufeful to perfons of both branches ; including the methods of finding Lines for Hip and Elliptic Domes for State Beds, of mitring Mouldings of different Projections together, and of finding curved Lines to an- fwer the various Sections of irregular Figures. — To which are added, the Five Orders, pro- portioned by aliquot parts, and exhibited in one large Plate. PART II. On Practical Perspective, applied to the Art of reprefenting all kinds of Furniture in different lituations ; together with a little of the theory for fuch as would know feme of the reafons on which this ufeful Art is founded. N. B. The Examples in Perfpeelive are intended to exhibit the neweft Tafte of various Pieces of Furniture, and likewife to mew the necefTary Lines for defigning them. PART III. Is a Repofitory of various Ornaments, confifling of Defigns for Pediments, with Cornices* &c. drawn at large, their Springs Ihevvn, and the proper gaging marked off to work the feveral Mouldings by. — To which are added, two methods of .reprefenting a Drawing-Room, with the proper Diftribution of the Furniture. By T. S H E R A T D N, Cabinet-Maker. LONDON: printed for the author, by t. bbnsley; And fold by J. Mathews, No. i3, Strand; G. Terry, No. 54, Paternofter-Row ; J. S. Jordan, No. 166, Fleet-ftreet ; L. Wayland, Middle-Row, Holborn ; and by the Author, No. 4, Hart-ftreet, Grofvenor-fquare. *79 r - CABINET-MAKERS AND UPHOLSTERERS IN GENERAL. GENTLEMEN, I presume, that to publifh a Drawing-book anfwerable to the preceding title page will not require many words to convince you either of the neceflity or propriety of the attempt* Nor will it be requifite to ufe an oftentatious preface to recommend it to your notice, or to perfuade you of the utility of fuch an undertaking. Therefore, what I have further to fay in this Addrefs lhall be to give fome account of my plan, and point out to you the difference between this and other books which have been publiftied for the afliftance and ufe of Cabinet-makers and Upholfterers. Books ( 6 ) Books of various defigns in cabinet work, ornamented ac- cording to the tafte of the times in which they were publifhed, have already appeared. But none of thefe, as far as I know, profefs to give any inftrudtions relative to the art of making perfpedtive drawings, or to treat of fuch geometrical lines as ought to be known by perfons of both profeffions, efpecially fuch of them as have a number of men under their directions. Nor have thefe books given accurate patterns at large for orna- ments to enrich and embeliifh the various pieces of work which frequently occur in the cabinet branch. Such patterns are alfo highly neceffary to copy from by thofe who would fufficiently qualify themfelves for giving a good fketch, or regular draw- ing, of any thing they meet with, or are required to draw for others. It is granted that there are books of ornaments already publifhed fufficient for the above ends ; but it may alfo be ob- ferved, that thofe ornamental books which are good, are very extenfive, and of courfe very expenfive: on the other hand, thofe that are cheap are either fo fmall and ill drawn, or fo de- ficient through brevity, or want of examples, as to render them of little ufe to the learner. Befides, were there no other reafon for introducing ornaments into the following work, but the convenience of having a few good examples of this kind always at hand and ready to copy from, it would be fufficient to juftify the attempt. Nor indeed would this performance anfwer fo well to the title of a Drawing-book without them. I hope, therefore, C 7 } therefore, that it will be confidered as an enhancement to the real value and ufefulnefs of the Cabinet-maker and Upholfterer's Drawing-Book to compofe and fele£l fome examples of fuch ornaments as fhall ferve, both for the purpofe of the learner, and alfo to aflift the ideas of thofe who have occafion to adorn their work in this way* As I have alluded to fome books of defigns, it may be proper here juft to fay fomething of them. I have feen one which feems to have been publiflied before Chippendale's. I infer this from the antique appearance of the furniture, for there is no date to it ; but the title informs us that it was com- pofed by a fociety of Cabinet-makers in London. It gives no inftrudtions for drawing in any form, but we may venture to fay, that thofe who drew the defigns wanted a good lhare of teaching themfelves. Chippendale's book feems to be next in order to this, but the former is without comparifon to it, either as to fize or real merit. Chippendale's book has, it is true, given us the pro- portions of the Five Orders, and lines for two or three cafes, which is all it pretends to relative to rules for drawing : and, as for the defigns themfelves, they are now wholly antiquated and laid afide, though pofleffed of great merit, according to the times in which they were executed. But it may here be re- marked ( 8 ) marked to his credit, that although he has not given rules for drawing in * perfpe&ive himfelf, yet he was fenfible of their im- portance and ufe in defigning, and therefore he fays in his pre- face: " Without fome knowledge of the rules of perfpedtive, the cabinet-maker cannot make the defigns of his work intelli- gible, nor fhew, in a little compafs, the whole condu6l and effect of the piece. Thefe therefore, referring to architecture alfo, ought to be carefully ftudied by every one who would ex- cel in this branch, lince they are the very foul and bafis of his art." After Chippendale's work there appeared, in the year fixty-five, a book of defigns for chairs only, though it is called " The Cabinet-maker's real Friend and Companion," as well as the Chair-maker's. This publication profeffes to fhew the me- thod of ftriking out all kinds of bevel work, by which, as the author fays, the moil ignorant perfon will be immediately ac- quainted with what many artifts have ferved feven years to * This is ftrictly true of the third edition of Chippendale's book ; but the firft edition of it, printed in 1754, has given two chairs, a drafting table, and a book-cafe in perfpedtive, {hewing the lines for drawing them. But why thefe examples were not continued in the fucceeding editions I know not. In the laft edition of any work, we naturally expect to fee it in its be ft ftate, having received its laft revifal from the author, or fome other hand equal to the talk; and therefore it can never be thought unfair for a reader to form his judgment of a book from the Taft impreiTion. I hope, therefore, this will fufiiciently apologize foe the above obfervation. know. ( 9 ) know* But this affertion both exceeds the bounds of modefty and truth, fmce there is nothing in his directions for bevel- work, which he parades fo much about, but what an appren- tice boy may be taught by feven hours proper inftrudtions. With refpe£t to the geometrical view of the Five Orders which he has given, thefe are ufeful, and the only thing in his book which at this day is worth notice, as all his chairs are nearly as old as Chippendale's, and feem to be copied from them. The fucceeding publication to this feems to be Ince's and Mayhew's Book of Defigns in Cabinet and Chair Work, with three plates, containing fome examples of foliage ornaments, intended for the young defigner to copy from, but which can be of no fervice to any learner now, as they are fuch kind of ornaments as are wholly laid afide in the cabinet branch, accord- ing to the prefent tafle. The defigns in cabinets and chairs are, of courfe, of the fame caft, and therefore have fuffered the fame fate : yet, in juftice to the work, it may be faid to have been a book of merit in its day, though inferior to Chippendale's, which was a real original, as well as more extenfive and mafterly in its defigns. In looking over Ince's book I obferved two card-tables with fome perfpe£live lines, fhewing the manner of defigning them. Thefe, fo far as they go, are a ufeful attempt ; but .cer- b tain ( io ) tain it is to me, from fome experience in teaching, that no per- ion can have the fmalleit acquaintance with the principles of perfpe6tive, merely from feeing two or three lines joined to a plate, without proper initrudtions by letter-prefs. It is true, a defcription is given of thefe lines in the 7th page of his book, but not equal to what is abfolutely requifite to fuch as have no previous acquaintance with the art; and thofe that have, will not require that which can give them no affiftance. Properly fpeaking then, what is done in this book, relative to per- fpedtive lines, can only ferve as a hint to the workman, that this art is effential in defigning. In the year 1788 w 7 as publifhed, " The Cabinet-maker's and Upholfterer's Guide." In which are found no diredtions for drawing in any form, nor any pretenfions to it. The whole merit of the performance refls on the defigns, with a fhort de- fcription to each plate prefixed. Some of thefe defigns are not without merit, though it is evident that the perfpedtive is, in fome inftances, erroneous. But, notwithftanding the late date of I leppel white's book, if we compare fome of the defigns, particularly the chairs, with the neweft tafte, we fhall find that this work has already caught the decline, and perhaps, in a little time, will fuddenly die in the diforder. This inftance may ferve to convince us of that fate which all books of the fame kind will ever be fubjedt to. Yet it muft be owned, that books of ( II ) of this fort have their ufefulnefs for a time ; and, when through change of fafliions they are become obfolete, they ferve to {hew the tafte of former times. I fhall now conclude this account of books of defigns with obferving, that in the fame year w r as given a quarto book of different pieces of furniture, with the Cabinet-maker's London Book of Prices ; and, confidering that it did not make its appear- ance under the title of a Book of Defigns, but only to illuftrate the prices, it certainly lays claim to merit, and does honour to the publifhers. Whether they had the advantage * of feeing Heppelwhite's book before theirs was publifhed I know not ; but it may be obferved, with juftice, that their defigns are more fafhionable and ufeful than his, in proportion to their number. Upon the whole then, if the intended publication, which now petitions your patronage and fupport, be fo compiled and compofed as fully to anfwer, and alfo to merit, the title which has been given to it, I think it will be found greatly to fupply the defeats of thofe books now mentioned, and will appear to * This is not meant to infinuate any difrefpeclful idea of the abilities of thofe who drew the defigns in the Cabinet-maker's Book of Prices. I doubt not but they were capable of doing more than Heppelwhite has done, without the advantage of feeing his book ; and it may be, for any thing I know, that the advantage was given on their fide. B 2 ( 12 ) be on as lafting a foundation as can well be expedted in a work of this kind. For inftance, the firft part, which provides the workman with geometrical lines, applied to various purpofes in the cabinet branch, cannot be altered any more than reafon itfclf. The fame may be faid of Perfpedtive ; the fubjedt of the fecond part. This art, being founded on Geometry and Optics, may be improved in its practice, but its fundamental principles can never be altered, any more than the nature of vifion and thofe immutable principles upon which good fenfe is founded. With refpedt to mouldings and various ornaments, the fub- je£t of the third part, it is granted that thefe are of a changeable kind. Yet it is pretty evident that materials for proper orna- ments are now brought to fuch perfection as will not, in future, admit of much, if any, degree of improvement, though they may, by the ikill and touch of the ingenious hand, be varied, ad infinitum, to fuit any tafte at any time. It may be neceffary to obferve alfo, that this book will have the advantage of exhi- biting the prefent and neweft tafte of work ; for, whilft we are teaching the practice of Perfpedlive, the examples given fhall both fhew the neceffary lines for defigning, and likewife repre- fent, in different fituations, fome ufeful or fafhionable piece of furniture. To this advantage we jfhall alfo add another, name- ly, that every example in pieces of furniture will have the geo- metrical C *3 ) metrical dimenfions laid down on the ground, or other fcale lines adapted for that purpofe. So that no perfon, however ig- norant of Perfpe£live, fhall be liable to miftake the Perfpedtive for the geometrical meafurements, or be at any lofs to know the general fizes of fuch pieces as fhall be introduced * . And we may fay, with refpe£t to changes of fafhions, that he who is properly acquainted with lines, verfed in Perfpe£tive, and fufficiently pra6tifed in ornamental drawing, will, from a few hints, be able, at any time, to turn his hand to any fafhiom Laftly, I would entreat leave to remark, that, as the public cation of this work will be attended with very great expence, the accomplifhment of my defign will principally depend upon * The Cabinet-maker's Book of Prices advertifes thofe who are ignorant of Perfpective to take care how they apply their compafTes to the defigns, left they mould make any miftake about the fizes • But I do not fee how this can be avoided by fuch as are ignorant of the art, fince there are no directions given how to apply them, nor neceffary fcales for the purpofe of obtaining the true meafurements. They have given a fcale for the front of their defigns, which ferves to give the height and length of fuch of them as are drawn geometrically in front, but can be of no fervice in finding the width of a piece of work drawn in per- fpecTive ; becaufe its apparent breadth is much narrower than the real or geometrical one. And it may be further obferved, that we cannot determine the height of a book-cafe merely by a ground fcale, when the book-cafe is drawn in perfpective, becaufe then the top part recedes or falls back from the front, it is therefore in appearance lower than the real height. For which caufe, if any perfon was to apply the compafTes for the height of a piece of work of the above kind, they muft be totally deceived reflecting its height. Therefore, in the fol- lowing work, every difficulty of this kind mall be obviated, and proper directions given how to avoid thefe errors, and to apply the compafTes, fo as to obtain every neceffary dimenfion. the ( H ) the encouragement I meet with from you as fubferibers; and I hope, on my part, that neither care nor affiduity will be want- ing to give you all poffible fatisfadtion, and to render the book as complete as is in the power of, '.GENTLEMEN, Your humble Servant, THOMAS SHERATON. INTRO- INTRODUCTION TO PART THE FIRST: CONTAINING SOME PRELIMINARY OBSERVATIONS; G E ometry literally means, to meafure the earth-, but in practice is applied to many arts and trades, as well as fcience in general. With refpe£t to that part of it which becomes ufeful to us, it is pleafant and eafy, readily underftood, and of a me- chanical nature; fo that no workman need to be fhocked or frightened at the idea of learning fuch geometrical lines and figures as fhall be coniidered in the fubfequent pages. Nor is it requifite to the workman to begin with the ufual definitions in geometry, as thefe would be foreign to my plan, and unneceffary * Geometry ; from yn g) } the earth, and metron, to meafure, for ( i6 ) for him to know. For inftance, he needs not be told that a point is without parts or magnitude, that a line is length without breadth, or that the terms of a line are points, &cc. &c. Thefe, and a number of others of this kind, are known by the common underftanding of every one. I fliall therefore confine myfelf to fuch particulars as every candid workman will at once pronounce ufeful, and which may be applied to the pra£lice of fome parts of the ingenious art of Cabinet-making. Yet, from what I have here advanced with refpedt to geometrical defini- tions, I would not be underftood as fpeaking difrefpedl'fuily of them, much lefs to deny their ufefulnefs to fuch as learn geo- metry regularly. It is impoffible to proceed without thefe, when this ancient and divine fcience is taught as the ground- work of mathematical learning. We might as well attempt to teach logic without a method of arranging or diftinguiflxing ideas, or arithmetic without the powers and properties of num- bers, as geometry diverted of its chain of definitions and axioms, &x. by which at length we arrive to the certain knowledge of truth, and are able to demonftrate it to others. But, on the other hand, as it is poffible for a man of found fenfe to reafon well without knowing the rules of logic as they are taught in fine and regular fyftems, fo, I apprehend, it is alfo pofiible for a workman of no learning, but what is common, to attain to a ufeful knowledge of geometrical lines, without the trouble of going through a regular courfe of Euclid's definitions and de- monftrations, C 17 ) monftrations, Sec. And we may juftly fay of his definitions and demonftrations, the found of which fo often alarming the ears of the ignorant, that they are, as a certain writer obferves, " Built upon a few principles of common fenfe, without which the moft domeftic and fimple negotiations of life cannot be tranfaded, and that, what they fliun as fubjedts too fublime and intricate for their comprehenfion, are only the moft fami- liar truths made artificial by regularity and difguifed by a tech- nical language." Upon this view of Geometry, I flrall now proceed to the confideration of fuch Problems as every workman of tolerable capacity will eafily underftand, and find advantageous to him* And, for the fake of making every part of this book as in- telligible and ufeful as I am able, I fhall, in the courfe of pro- ceeding, explain fuch * technical terms as may be neceffarily ufed in the fubfequent pages, and which, for propriety's and brevity's fake, cannot well be avoided on fubje£ls of this nature. And, in attempting this, I hope not to incur the difagreeable title of a pedant ; as I pretend not to give thefe explanations as the produce of my own fkill in Etymology, but fhall recom- mend them to the reader as they are found in the writings of From. rtw>*> ttcbne, arty which belong to the terms and rules of arts and fciences.. C mem ( is ) men of unqueftionable abilities in this way *. Befides, when it is conlidered that the following work is not written for the learned, but fuch as may want feme affiftance in the derivation of particular w r ords ufed in Geometry, Architecture, and Per- fpe6tive, in order to fix their real meaning more laftingly on their memory, it is prefumed that this confideration alone will, in the view of the candid, fufficiently apologize for me. As for thofe of an oppofite caft of mind, it is not eafy to fay what would pleafe, or what difpleafe, them, * As Chambers, Johnfon, Bailey, Parkhurft, Lemon, &c. THE THE CABINET-MAKER AND UPHOLSTERER'S D R A W I N G-B O O K. PART t CONTAINING NECESSARY INSTRUCTIONS FOR OBTAINING THE KNOWLEDGE OF SUCH LINES AS ARE USED IN BOTH BRANCHES, SECT. L On dividing a Line into any Number of equal Parts — raifing a Perpendicular on a given Point — and the Method of dividing a Frieze or Pilafler into Flutes and Fillets* * Problem I. Plate I. Fig. i* A right line being given, to divide it into any number of equal parts. The line to be divided is 7.1, which is to be divided into 7 parts. Operation. — Firft,From 7, on the given line, draw a right line at pleafure, making any angle with the line to be divided. * Problem, wpofo^a, problema, " from PuX^u, hallo, to throw, and^f°> he fore, i. e. to pro-* pofe, or fet before : a proportion relating to practice, or which propofes fomething to be done; as to bifecl: a line given, to draw a circle through any three points;" or, as in the prefent cafe, to divide a line into any number of equal parts, C % Thea ( so ) Then with the foot of your compafles, fixed on 7, turn the arch * 1.8, and, without any alteration of the inftrument, place its foot in i, and turn the arch 7. 9 at pleafure. Second, Take the fpace 1.8, and place it on the arch 7.9 drawn indefinitely t. Then from 1 to 9, draw a right line, which will be parallel, to the line 7. 8. Thus far it fhould be obferved, that the problem teaches to draw two lines parallel, both with difpatch and accuracy, Laftly, with your compaffes, opened at random,, lay on the divifions 1, 2, 3, 4, 5, 6, on both lines, firft from 1 to 9, then from 7 to 8, and by drawing lines from each correfpondent point, the given line 1.7 will then be divided as required. A little reflexion will point out the reafon of this, if we confider that the lines 7.8, 1.9, are perfectly parallel to each other. For if the divifions laid on each line be greater or lefs than thofe fought for, yet lines drawn acrofs to each refpeitive divi- fion will cut the line to be divided in the fame points ; becaufe * Arch, from arcus, a bow, Lat. and, when ufed in Geometry, implies " any part of a circumference of a circle." f That is, without bounds or limits. what ( 21 ) what is loft or gained on one line, by thefe uncertain divifions, will be regained or loft, when the fame uncertain divifions are placed the contrary way on the other parallel line. This is clearly exemplified in the figure by the fmall dotted divifions on each line, which are fhorter than the proper ones on the given line. Yet, if right lines be drawn through each correfponding dot, they will cut the given line as before. The fmall dotted line drawn acrofs, from the correfpondent points near to 1.5, demonftrates this, and therefore it is unne- cefiary to fay more. Problem II. Fig. 2. To divide a frieze or pilafter, &c. 8cc. into any given num- ber of flutes and fillets: the following method is a moft certain and quick one. 1. Let A B be the fuppofed width of the pilafter required to be fluted. Operation. — Draw the right line CD indefinitely. Take then two pair of compafles, one for the flutes, and the other for the fillets ; and with the firft opening of your compafles for the flutes, lay it on C D, and divide this uncertain opening a b into three. Again, take one of thefe three parts for each fillet, as c a, and repeat ( 22 ) repeat it on the line C D, firft a fillet, then a flute, till you have the propofed number, which in this cafe is 5, (and always in pilafters fhould be an odd number*.) Second, Extend your compaffes from c to d, the whole fpace which the uncertain divifions include; and with one foot on cor d, turn the arches Ec and Ed, and from the point, where thefe two arches interfeft as at E, draw right lines to c and d, which will then form an equilateral triangle. Laftly, Draw lines from all the divifions on C D to E the angular point. After which, take A B in the compaffes and turn the arch e d> and through the two fedlions e d draw a right line, then will e d be equal A B, and the pilafter or frieze will be divided in the moft accurate manner as required. Problem III. Fig. 3. To raife a perpendicular from any given point on a line as its bafe. * Obfcrvc, any opening of one pair of compaffes will do the whole bufmefs, if a pre- vious calculation be made of the equal parts contained in all the flutes and- fillets. Thus, in the prefect cafe, we fay there are five flutes, allowing the fpace of three fillets to a flute, which make together fifteen ; and the addition of fix, the number of fillets in the pillafter, make twenty-one. Therefore lay on the compaffes at random twenty-one times, and pro- ceed as above* Operation* ( *3 5 Operation. — Let G be the given point on the bafe line G V. Take then the * radius G O, or any other at pleafure, and turn the arch O S. Fix again your compafs foot in O, and, without any alteration, interfedt the arch at P. On P, with the fame open- ing of the compafles, make another fe£tiou at S, and from thofe points S P turn an arch each way, and their interferon will form a point perpendicular with the given point G, as required. This may alfo be effected another way with more difpatch, but perhaps not always with equal accuracy. Operation.— Let ME, Fig. 14, Plate 2, be the bafe, and E the point whence you would ere6l a perpendicular. With any open- ing of the compafles, and with one of its legs fixed any where out of the line, as at S, fweep the arch £, d till it cut the bafe line, as at b. Then from b draw b s through the center S, cutting the arch at d, and their fection will form a point perpendicular to E, as required. ^ Thefe problems may be very ufeful to an Upholfterer when he is laying down the plan of a room for a carpet, as it is not convenient always to take a fquare with him. Befides, by a good line, bradaul, and chalk, a perpendicular may be raifed * Radius, a right line -drawn from the center of a circle to its circumference. This right line, I conceive, anfwers to the rays of light (in an optical fenfe), which, falling upon the eye every where in right-lined directions, form a horizon to our fight. 3 with ( 24 ) with more exa&nefs than can be drawn on a floor by a fquare. But, as I intend giving fome directions to the Upholfterer how to lay down a room in an accurate manner, fo that a carpet may be properly cut by his plan, I lhall at prefent fay nothing more on this fubjedt. Problem IV. Fig. 4. To draw a perpendicular line by a fcale of equal parts, as by a common rule, or by a rod divided. Operation. — Let the line G V be the line required to raife a perpendicular from. Let V be the propofed point, and from any fcale of equal parts lay down ten of thofe parts from the point V towards G. Take then fix of thofe parts (or fix inches of the common rule) and turn the arch 1.2 at pleafure. Again, take ten parts, or ten inches of your rule, and place the end of the rule or rod on the eighth of thofe ten parts or inches, and with the other hand, by a pencil, interfedt the arch 1.2, by which a point will be gained exactly perpendicular to V, as required. This problem will be of ufe to the Cabinet-maker and Upholfterer when neither fquare or compaffes are at hand. For inftance, if a Cabinet-maker would cut a board acrofs perfectly fquare, without compaffes, chalk line, or fquare, if he have but a rod, let him proceed thus ; 8 Divide ( *5 ) Divide the rod into ten equal parts, and by this ftraight rod ftrike a line on the fide of the board ; then lay down ten parts on this line, and proceed as above. SECTION II. On the Ufe of a common Cafe of Inftruments, together with fome Geometrical Problems conjidered. As the various inftruments found in common cafes are not commonly underftood by Cabinet-makers and Upholfterers, and as the principles by which they are devifed and conftru6led are purely geometrical, I think it neceffary and ufeful to give an explanation of them, fo far as they can any way affift the above perfons, or others, in the pradlice of drawing. The firft thing that needs be noticed is a fcale of feet and inches. The intention and ufe of a fcale is to reduce the real mea- furements of any objedt to a convenient proportion, fo that it D may ( *6 ) may be reprefented on a fheet of paper, Sec. with as much exadtnefs as if it were drawn at full fize*. A fcale of feet and inches fhould be ufed when we repre- sent any piece of furniture either geometrically or perfpeitively, becanfe fuch a fcale anfwers to our common rules ; but when we lay down any figure by the help of mathematical inftru- ments, then a fcale of tenths muft be ufed. On the Conjlru&ion and Ufe of a Scale of Feet and Inches. To underftand a fcale of feet and inches, draw feven lines - parallel to each other, and at equal diftances, as in Plate I. Fig. 9. Then, as on the line 1, 2, 3, lay down as many divifions for feet as will comprehend the largefl dimenfion of the piece you would draw. Secondly, divide one of thefe parts, which you fuppofe to be a foot, into twelve equal parts, the number of inches in a foot; to effed: which, divide that part or foot into two equal parts, as at 6: draw then the two lines 6.1, 6.12,. and the foot will be divided as required, and in the moft ac- * The term Scale feems to have been derived from the fleel-yard, and its notches or ( T '.vijions marked on. the beam, to acijuft the different degrees of weight by. 8 eurate FuMfeg as* &eA<£ afovateAugt 27. /7£/. ( *7 ) curate manner, as is clearly demonftrated by the fmall divifions on the line 12. To ufe the Scale. If you want one foot one inch, place your compafs foot 011 the fecond line from the bottom, over 1, and extend the other foot to No. 1 on the fame line. Again ; if you want one foot two inches, then place the foot of your compares on the third line from the bottom, over 1, and extend the other foot to No. 2 on this line. Laftly ; if you want three feet feven inches, place one foot of your compafles on the fixth line, over 3, and ex- tend the other foot to No. 7, and fo on for any other number of feet and inches that may be required, r On the ConJlruBion and Ufe of a Scale of Tenths. Draw eleven lines parallel to each other, and at equal dis- tances, as in Fig. 10, Plate II. Afterwards lay down eleven divifions, as you fee on the fcales found in cafes of inftruments (I have divided mine only into fix, for want of room). Take one of thofe divifions or parts, and by Prob. I. Fig. 1, divide it again into ten equal parts, placing the divifions on the bottom and top line. Then from the point 0 draw a line to the point before 2 on the top line, and fo on, as the Figure fhews. When all thefe lines are drawn, there will then be precifely one hundred equal D 2 parts. ( 23 ) parts, diftinguifliable by the dots on the feveral angles of the rhombs, becaufe, being divided into ten each way, they multiply into one hundred, by which we lhall be able to take any tenth or any hundredth part of the large divifions i, 2, 3, 4, &x. To ufe this Scale. If you want one of the large divifions and one 10th, this is afcertained by placing one foot of your compaffes on No. 1, and extending the other to the firft divifion beyond 0, and fo on, as may be required. Again, if you want one large divifion (which may be called a foot) and nine hundredth parts of a foot, place one foot of your compaffes on the line 9, and extend the other to the firft tenth on that line, and you will then have one foot and nine hundredth parts as required. Laftly, if you want five feet five tenths of a foot and five tenths of an inch, place your compafs foot on No. 6, on the right hand end of the fcale, which is the fixth line from the bottom, and extend the other foot to the fixth dot on the fame line, and the required di- menfion will be obtained. It will be evident therefore, by a little refle&ion on the nature of this fcale, that any tenth part of a foot, and any tenth part of an inch, may be accurately taken,. The fcale of chords comes next under confideration. This fcale is commonly found on the contrary fide to that whereon ( *9 > whereon the fcale of tenths is marked, which we have now de~ fcribed. The ufe of it is to lay down angles of different degrees, and to divide a circle into various proportions and parts. The Conjlru&ion and Ufe of a Scale of Chords* i. Open the compafles to fixty degrees on the fcale marked: CHO, Fig. ii, Plate II. and by this opening defcribe a femicircle, as BDA, Fig. 12. Then if the arch BD be divided into ten equal parts, thofe parts 10, 20, 30, &x. will anfwer to 10, 20, 30, &c. on the fcale of chords, Fig. 11. Hence, if you want to divide a circle into twelve parts, take thirty from the fcale of chords, and apply the compafles to the arch B D at 30, then B D will contain it three times, and confequently the whole circle will contain it twelve times. If again you want this circle di- vided into eight equal parts, then from the fcaLe take the chord of 45, and apply it to the arch B D at 45, and this will divide the quadrant into two equal parts, and therefore the whole circum- ference may, by the fame opening, be divided into eighths. In this manner any other divifion of a circle maybe certainly known at once, which a little thought will eafily make clear, and there- fore it is unneceflary to give any other example on dividing a circle into equal parts*. This ( 30 ) This icale may likewife be ufed in laying down any angle* not more than ninety degrees. Draw the line G o, Fig. 16, at pleafure ; then take the chord 6o° and fweep the arch o o at plea- fure. With your compaffes take the chord 37°! and place it on the arch 0 0 ; draw the right line G 0, and you have an angle of thirty-feven degrees and an half, and fo of any other, to ninety degrees. On the Protractor f. The Protra&or is a femicircle of brafs, divided into one hundred and eighty degrees, by the help of which we may de- fcribe an angle of any affigned quantity whatever, and likewife meafure any angle already laid down. Let the arch, divided into one hundred and eighty equal parts, on the line A B, Fig. 6, Plate I. be confidered as the brafs protra£tor, which is found in common cafes of inftru- ments. * Angle. " This feems to be from AwuAo?, ankulos, the bending of the elbow and in Geometry, implies the point in which two lines meet : but the quantity of an angle is the fpace comprehended between the two lines meeting in a point, as o c, Plate II. Fig. 1 6, and its proportion is exprefled by degrees ; which term, Degree, means fimply the three hundred and fixtieth part of a circle, whether great or fmall. f Protractor, from protraflum, " to draw out in length accordingly, by the help of this inftrument wc may draw out the legs of a triangle to any length we pleafe, Firft, ( 3i ) Firft, obferve the center of the protra&or, diftinguiftied by a fmall notch on the diameter, anfwerable to 6, on AB, Fig. 6. 2d, Let it be required to lay down an angle of ninety de- grees, and let A B be confidered as the bafe. Then place the fmall notch on the diameter of the brafs protradtor, upon 6, on the line A B, and make a mark exa£tly over 90 ; confequently a line from 6, the center, to 90, the vertical* point, will form an angle of ninety degrees, or what we commonly call a fquare. ■ Again, if an angle of forty-five be wanted, proceed as be- fore, and make a dot over 45 ; to which draw a line from the center, and it will be an angle as required ; and fo of any other to any quantity* This is fo plain, that to fay more would be needlefs. It may however be proper to obferve, that the quan- tity of any angle already laid down may alfo be found by the protractor as follows. Let Geo, Fig. 16, Plate II. be the angle to be meafured. Take the Radius, or half diameter of the protractor, and fweep the arch 0 0 ; then open the compaffes to 0 0, and apply them to the degrees marked on the inftrument, and it will im- mediately be feen how many of thofe divifions are contained in the angle, which number of divifions are called the quantity of the angle. * Vertical) " placed in a direction perpendicular to the horizon." i a? ) ■On the Sector*. The Sedfcor is a molt univerfal inftrument, and ufed for various purpofes in the different branches of mathematical learning. Nor is it without its ufefulnefs in the art of drawing, and therefore thofe who are concerned with defigning ought, in fome meafure, to be acquainted with it. To this end let us firft confider the moft fimple part of it, which is, to divide any given right line into any number of equal parts. The line to be divided by the fe<5tor is 7.7, Plate t Fig. 5, which is to be divided into feven. Firft, Look for the line of lines on the fe6tor, which may- be found by obferving two brafs centers marked with l on each limb of the inftrument. Second, Take the length of the line 7.7 in your compafles, and place one foot on the point 7 on the line of lines, and open- ing the fedtor, extend it till the other leg of the compafles co- * Sector ; it is fo called becaufe, when it is opened, it comprehends a portion of a circle between two femidiameters, making an angle at the center, as O A 4, Plate I. Fig. 6. incides ( 33 ) incides with the point 7 on the other limb of the inftrument, as Fig. 5 clearly expreffes. In this pofition keep the fe£tor, and moving the compaffes to 1.1, which is the neareft figvire to the center of the inftrument, contract their legs till you take the opening 1.1, which, if corre6lly done, will be one-feventh part of the line 7.7, as propofed. Perhaps it may be required to divide a line into fourteen ; if fo, then as there are only ten on the line of lines, you take half the length of the given line in your compaffes, and place their legs on the points 7.7 as be- fore ; and, as this opening is but half the length of the line to be divided, the compaffes muft be contracted to 1.1 as before, and then the line will be divided into fourteen, becaufe twice feven is fourteen. In this way any right line, to be divided into any number of parts, may be brought upon the feclor. To make this ftill more plain, let it be propofed that a line twice the length of the line 7.7 is to be divided into twenty-eight equal parts. Take the line 7.7 in your compaffes, and proceed in all refpedts as before, except one thing, i. e. in place of contracting the legs of the compaffes till they touch the points 1.1, you muft draw them in till they touch the lines at half the diftance of 1.1 from the center, as the dark line next the center of Fig. 5 fhews. This opening of the compaffes will turn fourteen times on the E line ( 34 ) line 7.7, confequently it will turn twenty-eight times on a line twice its length. Of the Line of Polygons * on the Se&or. This line is intended to divide a circle into equal parts, by which any kind of Polygons, from a pentagon to a duodecagon, may be formed. Hence it is diftinguilhed by the letters POL on this inftrument. Let it be required to divide the circle, Fig. 8, into five, which forms a Pentagon. Take the radius or half diameter of Fig. 8, and opening the fedtor, as defcribed by Fig. 7, place the compafs on the point 6.6, marked radius. In this pofition keep the fe6tor, and, without any variation of the inftrument, you may divide the circle 8 from 4 to 12. In the cafe before us it is into five ; therefore take the compaffes from the points 6, and extend them till they touch 5.5, and this opening will go five times on the circle 8, as will be evident if you take 5.5 in your compaffes from Fig. 7, and apply it to Fig. 8. Laftly, if you want the circle 8 divided into twelve, by which to form a Duodecagon (fee Plate II. Fig. 26), the fe£tor ftill remaining unaltered, place your compafs legs on the points * " Polygon, from aro*v$, polus, many, and gonia, a corner, having many corners or angles.'' 12.12, ( 35 ) 12.12, and apply them to the circle 8, and it will be divided as required. Obferve alfo, that a geometrical fquare may, by the fame means, be infcribed in any circle; for by keeping the fedtor extended as before, and opening the compaffes till their legs touch on 4.4, this opening will turn four times on the circle 8, and therefore will form a fquare. How this line of Polygons is divided fo as to proportion any circle in this manner, will eafily be underftood by confider- ing Fig. 6. Defcribe a circle of any radius, and draw the diameter A, B. Divide one-half of the circumference into one hundred and eighty equal parts, called degrees, and from 90 0 draw the arch 4 from the center A, then will the lines A O and A 4 reprefeat the limbs of the fedtor, Fig. 7, and 4 on Fig. 6 will anfwer to 4 on Fig. 7. Next draw the arch 5 from 72 0 , and from the center to 5 will be the chord of 72 0 , the degrees contained in the fide of a Pentagon, anfwerable to 5.5 on Fig. 7. Proceed to the arch 6, and obferve, that this is the radius E 2 of ( 36 ) of the circle, and is always equal to the chord line 6o°, and therefore contains a length equivalent to the lide of a Hexagon, or a fix-fided figure, and agrees with 6.6 on Fig. 7. After thefe remarks, I think it unneceflary to go through each chord line ; only the reader fhould obferve, that I have marked fuch chords as have fractional parts on the fine lines, or thofe drawn perpendicularly from A, B. For inftance, the chord for a Heptagon is fifty-one degrees and three-feventh parts of a degree ; and the meaning of three-feventh parts is nothing more than to divide a degree into feven, and to take three of thofe parts and add to fifty-one, which is exadtly the fide of a circle divided into feven, called a Heptagon. Thefe parts are eafily found and proved by dividing three hundred and fixty, the number of degrees contained in a whole circle, by the quantity of fides contained in any Polygon, for then the quotient will be the number of degrees which are in the arch of every fuch chord line. Thus for a Heptagon ; divide three hundred and fixty by feven, then will the quotient be fifty-one degrees and three- fevenths, equal to the fide of a heptagon. Of ( 37 J Of the Line of Chords on the Se&or* The Chords on the fixed fcale have already been con- lidered (fee page 29). Thefe chords are limited to one circle, which, to fait that fcale, muft always be drawn by the compaffes extended to fixty degrees : but the fcale of chords on the fe£lor is unlimited, becaufe the chords of circles of various radiufes may be found according as the limbs of the inftrument are more or lefs extended.. The line of Chords is on the fame fide of the fe&or with the Polygons, marked with c nigh to a brafs center on each limb : and if it be required to find the chord of thirty of any circle, take the radius of the given circle, and open the fe£lor till the compafs legs coincide with thofe brafs centers at 60.60, then contra£ling the compaffes till their legs touch 30.30, the required chord line will be found. In this manner proceed in any other cafe; always obferving that the femi-diameter of the circle muft limit the opening of the feftor at the brafs centers. By this line of Chords on the Se6lor it is evident that a* circle may be divided into feven hundred and twenty equal parts with confiderable difpatch and great accuracy. or C 3S ) Of the Line of Sines on the Secior. A Sine is a right line drawn from one end of an arch perpendicularly upon the diameter drawn from the other end of that arch, as the perpendicular line 90, drawn from the diameter B A, Fig. 1 2, Plate II. is the fine of the arch B D ; and fo likewife all the other perpendicular lines, as 1,2, 3, 4, 5, &x. on the line B A, are fines of fo many different portions of the arch BDA. The line of Sines on the fe£tor, which Fig. 13 is intended to reprefent, is marked s s nigh 90.90, with two brafs centers, one on each limb of the inftrument. The feveral divifions on this line, marked 10, 20, 30, &c. anfwer to thefe perpendicular lines 1, 2, 3, 4, 5, &x. on the line B A, Fig. 12, and the different fituations of thofe perpendicular lines are found by dividing the arch D A into nine equal divifions. Perpendiculars being then drawn from each refpeilive divifion on the circumference of the circle to the diameter A B, they are of courfe denomi- nated fines of 10, 20, 30 degrees, and fo on. To draw an Oval by the SeHor. Firft, Draw a circle that will comprehend the Iongeft dia- meter of the oval you wifh to defcribe, as the circle BDA, Fig. 12. Divide the quadrant DA into nine equal parts. Second, I 39 ) Second, Take then the fhorteft diameter in the compafles, and place one foot on the fine 90% and open the fector till the other coincides or touches 90 0 on the other limb of the inftru- ment. In this pofition keep the inftrument fixed, and contrail the compafles till their feet touch the fine 8o°.8o° ; transfer this opening of the compafles to the perpendicular line 8 at 80, which mark with the point of a pencil. Proceed to the fine 70, keeping the fedtor ftill in the fame pofition, and, after contracting the compafles till their legs touch 70.70 on the fector, transfer this opening to the perpendicular line 7 at 70 0 , and fo on of all the reft to the fine 10, by which will be obtained nine points, contracted in due proportion* from the arch D, A ; and a line, pafling through each of thefe points, and drawn by a fteady hand, will form an ellipfis perfectly true and agreeable, as is evident by the figure. From what has been faid, I prefume it will eafily be under- flood by every one how to proceed with the other quarters to complete the whole ellipfis. * This is evident by obferving, that as a right line drawn from 45 on the tangent line to the center 9, cuts the arch D A in the degree 45 ; fo likewife will a right line drawn from 10 on the tangent line to the center, cut the elliptic arch 90 A in the fame degree. A circle <( 40 ) A circle mayalfo be defcribed by the fe£tor upon the fame principle that an ellipfis is drawn by it. This, in itfelf, is not very neceffary to be known, becaufe when we have no compaffes, no ufe can be made of the fedtor, and when we have them by us, they are the beft inftrument for drawing a circle. How- ever, fince what belongs to the drawing of a circle by the fee- tor, partly belongs to the defcribing of an ellipfis by this inftru- ment, I fliall venture upon this Problem. Operation. — Draw a right line at pleafure, of length enough to contain the diameter of the circle to be drawn. Bife£t * this line, and draw a line at right angles with it of the fame length. Take then the femi-diameter of the circle, and place it on the lines each way. Open the fedtor, and on the line of fines proceed as before to take the fine 80. Transfer this to any femi-diameter, as 9 A, Fig. 12, which will extend to 1 on that line. Then proceed to take the line 70, and transfer this alfo, which will extend to 2 on that line. Proceed to the fine 60, and this opening will ex- * A line is faid to be bifected when it is divided into two equal parts, from " bis and Jeftum, to cut in two \ y an operation which is eafily performed by fweeping two arches from the extremities of the line to be thus divided ; as from b and d, in Fig, 14, where two arches interfect., which if a line be -drawn from thefe interfe&ioris, it will both bifect the given line, and will at the fame time be drawing one at right angles to it. 8 tend ( 41 ) tend to 3 on the fame line, and fo on, till you take the fine 10, which will extend from 9 to 8. The fame rauft be done on the other radius, as you take the fines from the fedtor. Having thus divided one diameter, draw perpendicular lines from each divifion each way at random. Laftly, take the fame lines again from the line 9 A, and place them upon their refpedlive fines ; that is, take from 9 to 1, which is the fine 80, and place this upoli the perpendicular line 8 at 80, and fo of all the reft, and they will form thirty-fix points for the whole circle ; through which points, if a line be corre£tly drawn, the circumference of a complete circle will be produced with as much accuracy as when we draw the circumference of an oval in the fame manner. Of the Tangent * Line on the Seffor. A tangent is a right line drawn perpendicular on the ex- tremity of fome radius, touching the circumference of the circle, but not cutting it, as A 45, Fig. 12. This line is of ufe to divide the circumference of a circle into any number of equal parts, and may be found on the fee- tor by a brafs center on each line, marked T. To this line there * Tangent, from tangens, Latin, touching. F is ( 4* ) is added another of the fame kind, marked T on each limb, but without a brafs center to it. To divide a circle by this line, proceed thus : Take the radius of the circle to be divided, and with this opening, place the compafs legs on each line T, marked 45.45, then will the fedtor be prepared for finding every degree of a circle up to 45. This, is clear ; for if the radius be laid down on the tangent line, Fig. 12, as at 45, a line drawn from 45 to 9, the center, will cut the arch D A at 45 degrees, as is obvious by infpeftion. Thus the circle may be divided into eight, fince forty-five is the half of ninety, confequently the eighth of three hundred and fixty. The fe£lor being ftill in the fame pofition, if you want to cut the arch D A at 10 degrees, contradl the legs of the compaffes till they coincide with 10.10 on the tangent line, and transfer this on the tangent line A 45, and a right line being drawn to the center as before, it will cut the arch DA at 10. Hence if the arch DA is required to be divided into nine, the extent of the compaffes at thofe ten degrees will turn nine times on the arch DA, *V^V ^irfi *nr\ l\nrn'\ <~\r\ -rcrrt t r <■ 4- f ^ r ♦ It has already been obferved, that there are two tangent • >jjTQ YTj "107 lines on the fedor. The tangent line which has not the brafs center, is to increafe that which has one np to 75, as it is marked on ( 43 ) on that line. When therefore any degree above forty-five is wanted,' take the radius of the circle to be divided, and open the feftor till the compafs legs touch 45 on the fecond tangent line on each limb ; then will the inftrument be prepared for taking the tangent of any degree up to feventy-five, by pro- ceeding in the fame manner as on the firft tangent line. SECTION HE On the Names and Properties of various ufeful Geometrical Figures of the Superficies* To have fome knowledge of the names of ufeful geome- trical figures is certainly of advantage to every one, and efpe- cially to fuch perfons as are concerned with drawing or making pieces of work of the like forms. It is certain from experience and matter of fa£fc, that many, not acquainted with names of this kind, are obliged to ufe 3 dozen words and iigns when one would be fufficient. F % Befides, ( 44 ) Befkles, a knowledge of thefe names, together with an ac- quaintance with the general properties and manner of drawing fuch figures, muft certainly be confidered as an introductory ftep to a more advanced knowledge of Geometry, by thofe young men who intend to rife higher in this fublime fcience, than can be expected to be taught in a drawing-book. I fhall therefore begin with the names and properties, and afterwards defcribe the conftrudtion, or manner of drawing, the moft generally ufeful figures. Of the Superficies *. (See Plate II.) No. i, is a Geometrical Square, fo called becaufe it has four fides of equal length, and four right angles. No. 2, is a Parallelogram. This figure receives its name from its oppofite fides and ends being all parallel to each other.. No. 3, a Rhomb, which is properly a geometrical fquare moved out of its pofition, fince all its fides are equal, but not its angles, two of them being acute, and the other obtufe. * Superficies, fuperficies, Lat. the furface or on term oft part of any thing, and in Geo- metry are fuch figures as are bounded by one or more lines, or an extenfion which has length and breadth, but no thicknefs. No, ( 45 ) No. 4, is a Rhomboides, a figure which bears the fame affi- nity to a parallelogram that a rhomb does to a geometrical fquare. A rhomboides has its fides and ends parallel to each other, but its angles differ the fame as thofe of the rhomb,; and therefore a rhomboides is a parallelogram moved out of its proper form- No. 5, is a Trapezoid, which has four fides, two of which are parallel, and two not, the fame as the feats of fome chairs. No. 6, a Trapezium, containing four fides, which are all unequal, and none of them parallel. Thefe fix figures, being all of them bounded by four right lines, are, by geometricians, called quadrangular or quadrilateral plain figures. Of various Triangles*. No. 7, is an Equilateral Triangle, fo called becaufe all its fides are equal to one another ; and, as every triangle contained under three equal fides, whether circular or mixed, are called equilateral, fo the figures u, 12, 15, are alfo of that denomi^ nation* No* ( 46 ) No. 8, is a Right-angled Triangle, becaufe two of its fides are perpendicular to each other, and confequently make an angle of ninety degrees, as the line 9.90 0 , Fig. 12, is perpendicular to B A, therefore A 9.90 0 forms a right-angled triangle, compre- hending a part of a circle equal to ninety degrees. In all right-angled triangles, the fides containing the right angle are called the Legs, as the fides 9 A, A 45 are the legs of the triangle 9 A, 45, in Fig. 12 ; and the oppofite fide to the right angle is called the Hypothenufe, as the line 9.45, in the triangle 9 A, 45, is the hypothenufe fide of that triangle. " The perpendicular height of any triangle is a line drawn from the vertex to the bafe perpendicularly :" thus if the tri- angle PEO, Fig. 15, be propofed, PO muft be confidered as its bafe, and confequently E its vertex ; and if from E you draw the line EP perpendicularly to PO, then the line EP is the height of the triangle EPO, ftanding on P O, its bafe. No. 9, is a triangle called Scalenous, becaufe none of its fides are equal, nor its angles alike in quantity. A Scalene Tri- angle is compofed of two kinds of angles, one obtufe, and the -other acute; fo alfo a right-angled triangle is compofed of two, a right one, and an acute. 8 All C 47 > All other triangles are of the acute kindl An obtufe * angle is one that is greater than ninety de- grees, or more than what we call a fquare, as a line from 9 to the point D, Fig. 12* An acute angle is lefs than ninety degrees, as a line fromi 9 to 10, confidering the lide 9 A as their bafe. No. 10. This triangle is called Ifofceles, becaufe two of its fides are equal in length, as G 0, G 0, Fig. 16 ; or if the fedtor be opened, a triangle of this kind is fitly reprefented by it* Thefe four triangles, being bounded by three right lines, are called redtilineal plain triangles ; and in general, thefe are placed before the quadrilateral, or four-fided figures, becaufe by geometricians they are confidered as more fimple, having only three fides : but as triangles generally appear more out of the way to workmen, I have affumed this liberty to place them after four-fided figures. Of mixed Triangles^ Of this kind are numbers 11,12,13,14, and they are called mixed triangles, becaufe fome of their fides are right lines, and * Obtufe fignifies flat or blunt, and acute iliarp or cutting. fome ( 48 ) fome curved ones. Three of thefe are equilateral, or equal- fided, if meafured by a right line ; and No. 14 is a fcalene tri- angle by the fame rule, as none of its fides are equal. The fides of thefe mixed triangles that are round, are called convex % but thofe that are hollow, as No. 13, 14, are called concave. Of Spherical t Triangles. A fpherical triangle is one that is curved on every fide, as No. 15 and 16. Thefe are both of the equilateral kind, becaufe their fides may be bounded by right lines of equal length. Of Mixtilineal Figures. No. 17, is of this kind; and every other figure that is bounded both by right and curved lines is called mixtilineal. Of thefe figures fome are regular, and fome irregular. When a figure of this kind is compofed of equal curved and equal right lines, then it is called a regular compound mix- * Convex is properly applicable only to any folid that has a curved or fwelled furface, and concave is the contrary. f Spherical, fomething like a fphere or globe, tilineal ( 49 ) lineal figure ; but when its fides and ends are formed of unequal curved and unequal right lines, then they are called irregular compound mixtilineal figures. Of this fort is No. 18. Of Polygonal Figures. All Figures bounded by more than four right lines are termed Polygons. The figures included between No. 19 and 26 are all of this denomination. But each of thefe figures has its parti- cular name from the number of the fides of which it is com- pofed. No. 19, is therefore called a regular Pentagon % becaufe it is bound by five right lines of equal length; but if any of thofe lines were unequal in length, then it would be termed an irre- gular Pentagon. The fame diftinftion is applicable to any other of thefe figures in fuch cafes. 1 * Pentagon, from itevfe, pente, five, and yovix, goma, a five-cornered figure. The other Polygons have all their particular names formed in the fame way, from the Greek numeral adjectives. G No. ( 50 ) No. 20 is termed a Hexagon,^ f 6 fides or angles. 21 a Heptagon, 22 an Odtagon, 23 a Nonagon, 24 a Decagon, >becaufe it has< 10 9 7 8 25 an Undecagon, 26 a Duodecagon, L12 11 No. 27, is a figure fo well known that it is unneceflary to fay any thing about it. The fame may be faid of the Semi and Quadrant, Nos. 28 and 29, the one being an half, and the other one-fourth of a complete circle. No. 30, is called the Greater Segment * of a circle, becaufe it is the greateft part of a circle cut in two by a right line ; and of courfe No. 31 is the LelTer t Segment, becaufe it is not equal to a femi. But if we fpeak of a fegment without regard to comparifon, it is a figure contained between a chord and an arch of a circle. * Segment, from fcgmentum, a piece cut off. t Letter. This way of forming the comparative adjective is by Dr. Johnfon and Lowth confidered as barbarous ; but as cuftom has fo long prevailed in the ufe of it, and as the ear feems to prefer leflcr rather than lefs, I thought it would fuit the readers bell to retain it. No. ( 5i ) No. 32, is an Ellipfis *, commonly called an oval. This figure may be confidercd, in one view, as produced by the fee- tion of a cone, by a plane cutting both fides of the cone ob- liquely to its bafe. In this cafe the ellipfis produced muft be irregular, fmce a cone is a folid which terminates to a point at the top ; and therefore any fedtion oblique to its bafe muft pro- duce an oval broader at one end than the other. To demon- ftrate this, nothing more is requifite than to get a piece of wood turned in the fliape of a fugar-loaf, and let it be fawn acrofs in a Hoping direition from the bottom of it, and the furface of the cut will be an irregular oval. But if a cylinder be cut ob- lique to its bafe, there will then be produced an Ellipfis perfectly regular, and alike at each end. It may alfo be obferved both of a circle and an oval, that they are the only regular fuperficies that are bounded by one line ; and thofe which are bounded by two, are their refpedtive fegments : as Figures 28, 30, 31, 33, 34. No. 33, is the Semi-ellipfis, or Half-oval ; and it is faid to be on the tranfverfe diameter, when the right fide is equal to the * Ellipfis, from f> Ae^K> ellipjis, a defect or omiflion. If a fuperfice be apparently round, but, on ineafuring it, if one of its diameters be found fhorter than the other, there is then a defect, and we fay that the figure is elliptic. G 2 longeft ( 5* ) longeft diameter ; but when it is only equal to the fhorteft dia- meter, then it is faid to be on the conjugate, as No. 34. No. 35, is termed an Hyperbolic Figure. When a cone, Fig. 12, Plate IV. has a fedtion parallel to its axis, the curved boundary produced by the fedtion is an Hyperbolic Figure ; and when its fedlion is parallel to the fides of the cone, then the curved boundary produced is called a Parabolic Figure. SECT. IV. Of the Manner of drawing various ufeful Geometrical Problems. In the preceding feilion, the names and fome of the pro- perties of the moft generally ufeful fuperficies have been con- fidered ; and I fliall now defcribe the method of drawing them. However, in doing this it will not be neceffary to defcribe every particular figure, fince the fame operation for one will fome- times apply to various others, Pro B o. ( 53 ) Prob. V. Fig. 14. 7b draw a Geometrical Square. By the fecond method of Prob. III. raife a perpendicular, as E d, Fig. 14, Plate II. then extend the compaffes equal to the fide of the propofed fquare. Fix one foot in E, and fweep the arch b d y which will cut the line Eb,Ed, equal to the fides of its fquare. Laftly, from d and with the fame opening of the compaffes, fweep the other arches, and their fe6tion will form a perpendicular to the points b and d, by which the fquare is completed. From what has been faid, it will eafily be underftood how to draw a Parallelogram* Prob. VI. Fig. 2 and i6> Tb draw a Rhomb. If the fides of this figure be intended to incline at an angle of fixty degrees, all that is necefTary is to draw two equilateral triangles from their oppofite bafes : and to draw an equilateral triangle is nothing more than to take in the compaffes the given fide ( 54 ) fide of the triangle, and from a right line turn an arch each way, as Fig. 2, Plate I. and their fection, as at E, by lines drawn to it, completes the figure. Then if a right line be drawn parallel to C D at E, and c d be laid on this line, fuppofed to be drawn, it will complete the Rhomb. But if a Rhomb be required to be drawn, whofe oblique fides are wanted to be inclined thirty-feven degrees and a half, take the radius of the protractor and from the center G fweep an arch, as 0 0, Fig. 16. Draw G 0, and take from the protractor thirty-feven degrees and a half, and lay it from 0 to 0. Let the right line G 0 be the given fide of the Rhomb ; and how the other fides are to be drawn, reafon itfelf will dictate. The Rhomboides, being of the fame fpecies of figure, is eafily drawn by the fame rule. Nor is it requifite to defcribe the method of drawing any other of the figures till we come to the Pentagon, becaufe fome of them are variable, and thofe that are not fo, are drawn by the fame rules that are applicable to the Square, Rhomb, and Equilateral Triangle. Prob, ( 55 ) Prob. VII. Fig. 19. How to draw the Polygons. To draw a Pentagon whofe fides fhall be equal to a given length, as the line 12.1, Fig. 19, Plate III. Operation. — Draw a right line 12.1, and take the fide 12.1 of the propofed Pentagon. Place one foot of the compaffes on 12, and with the other fweep the arch 1.1. Again, place the com- pafs foot on 1, and fweep the arch 12.1, and through the point where thefe arches meet raife a perpendicular line, and con- tinue it at pleafure. Divide the arch 12.1 into fix equal parts. Take then the firft of thefe parts, and fweep it to the perpen- dicular line downwards, as the figure clearly fhews ; and from this point on the perpendicular line extend the compaffes to 12, which will be the radius of a circle that will contain 12.1 five times: therefore, with the compaffes thus fixed, defcribe the circle, Fig. 20, and it will admit of 12.1 five times, forming a regular Pentagon. And here it fliould be obferved, that what has been done in this Problem for drawing a Pentagon, prepares the way for drawing any Polygon up to 12, whofe fides are equal to 12.1 : therefore, in defcribing the other Polygons, I fhall proceed as being thus far advanced. Pros. ( 56 ) Prob. VIII. Fig. 19. To defcribe a Hexagon, whofe fides ftiall be equal to any given length. Operation. — Take 12.1, the fuppofed dimenfion of the fide of the Hexagon, and with this radius draw a circle, whofe center is at the interfedtion of the two arches 12.1, 1.1, then will the radius turn fix times on the circumference of that circle, as the fmall daflies which are on it fpecify. It may be made a general rule without exception, that whatever the diameter of a circle be, its radius will always divide the circumference into fix. Prob. IX. Fig. 19. To defcribe a Heptagon, whofe fides fhall be equal to any given length. Operation.— Take one of the parts on the arch 12.1, and fweep it to 7 on the perpendicular line. Extend the compafles from this point 7 to 12, which will be the radius of a circle that will contain the given fide 12.1 feven times, which forms a Heptagon. If an O&agoirbe wanted whofe fides are equal to 1 2.1, take from ( 57 ) from the center two parts, and fweep the arch 2.8. Laftly, ex- tend the compaffes from 8 to 12, which, as before, will be the femi-diameter of a circle that will contain the given fide 12. 1 eight times, by which an Octagon may be formed. In the fame manner proceed with the other to a circle that will contain the given fide twelve times, as the largeft circle in the figure evidently does, as marked by the figures 1, 2, 3, &x. In the preceding diredtions for drawing the Polygons, their fides are previoully determined as to their length, but the circle that will contain the fides fo many times, is required to be found* We fhall now change the order, and propofe a given circle, in which fliall be infcribed any Polygon of the above kinds, Prob. X. Fig. 21. Therefore a circle being given, let it be required to find the fide of a Pentagon that may be infcribed within the given circle. Operation. — Let the line 9.5 be the diameter of the given circle. Bifedt the diameter, and draw a line at right angles with it ; then with the radius s 9 defcribe the circle. H Second, ( 58 ) Second, Divide any of the quadrants of this circle into five equal parts, and a chord line extended to four of thefe parts will be the fide of a Pentagon that may be infcribed in the given circle, as the figure plainly fhews. Prob. XL Fig. 21. To find the fide of a Heptagon that will infcribe within a given circle. Operation. — Let Fig. 21 be the given circle as before. Di- vide any of the quadrants into feven, as the under right hand one in the figure. Take then four of thefe divifions in your compafles, and the whole circle 21 will contain it feven times, which forms a Heptagon. In this way proceed with the other Polygons, always ob~ ferving, that whatever number of fides the Polygon is required to have, the quadrant of the given circle muft be divided into the fame number of equal parts, and four of thefe equal parts muft always be taken for the fide of the Polygon without ex- ception. This is exemplified on each quadrant of the circle, which has already been referred to, and, by a little infpe£tion and reflection, cannot fail to be underftood. The ( 59 ) The fimplicity of this method of infcribing Polygons in any circle, makes it highly ufeful to all who are any way con- cerned with defcribing fuch figures on an extenfive fcale. For inftance, how eafy is it to lay down the plan of any room, or mark out the foundation wall for any building of thefe figures, by firft drawing a circle equal to their refpe£tive areas, and dividing the quadrant of that circle into the fame number of equal parts as the room or building has fides ; and then taking four of thofe parts for each fide of the building or room. From thefe hints the Cabinet-maker alfo will eafily apply this method to any table-top, or other piece of work that is re- quired to be made of thefe figures. Of the various Methods of defcribing Ovals* Prob. XII. Fig. 22. To draw an Eliipfis by the interfedtion of two circles. Operation. — Let the line B A be the tranfverfe, or long dia- meter, which divide into three equal parts. Take one of thefe parts for the radii of the two circles, and on the centers d and s defcribe the circles interfering each other at n n. Draw from H 2 n a ( 6o ) n a right line through d to b. From n dfftw # j* to and fo of the other fide. Place the compafs foot on n, and extending the other to b, fweep the arch b e. Laftly, fix the foot of the com- pares on the other and fweeping the oppofite arch, the oval will be completed. Prob. XIII. Fig. 23. To draw an Oval whofe tranfverfe diameter fhail be equal to the diameters of two given circles. Operation.— Draw C D equal to two diameters of a given circle. Sweep the circumferences of the two circles. Then from the center of each circle, with the compaffes in the fame pofition as when the circles were drawn, fweep two arches, s dp and p 0 s y interfering in the points s and p *. To complete the Ellipfis, fix your compafs foot on s, and extend the other to n ; fweep the arch n r. Laftly, fix the compafs foot on /), and fweep the oppofite arch, and the work is done. * It is evident that the angles s d p o form a rhomb compofed of two equilateral trir angles d s o, p d o, which method of drawing a rhomb of that degree of inclination is moll quick and certain. The fame obfervation might have been made on the firffc oval, but; this being more diftindt, I chofe to mention it here. The ( 6i ) The method of drawing thefe two kinds of Ovals fuppofes that we are only confined to the length of the long diameters, without regard to the fliort one ; but the following Problem is to draw an Oval of any length and breadth as may be required. Prob. XIV. Fig. 24. To defcribe an Ellipfis whofe tranfverfe and conjugate dia- meters are pre-determined. Operation. — Let E F be the tranfverfe, and a 0 half the con- jugate. Take a 0 half of the fliort diameter, and place it on E d\ Divide then the remaining part of half the long diameter into three equal parts, as the figure fhews, and take one of thefe three parts and lay it on the other way, as from a to n. Take the diftance from n to 0, and lay it from 0 to g. Extend then the foot of the compafles from g to by which fweep two arches each way, interfering each other at p 0. From 0 to n draw a right line out at pleafure. Do the fame from 0 to g, and alfo from p to n and g on the oppofite fide ; then will every center be found for each refpedlive arch. From the center n extend the compafs foot to E, and fweep the arch E b. Do the fame from g, and fweep the arch m F. Laftly, from 0 extend the compafles to and fweep the arch b m ; and fo of the other fide, which will complete the Ellipfis as required.. Prob,. { 6a ) Prob. XV. Fig- 26. To draw an Oval of any length and breadth by means of two bradauls and a chalk line. The above methods for drawing ovals fuit well for fmall ovals defcribed on paper, or any kind of metallic furface, when very fmall ovals are wanted to be drawn on wood. But when ovals of a large fize are wanted, they become inconvenient on account of their centers. Therefore Cabinet-makers gene- rally make ufe of a tramel, by which any oval from two to about four feet may be drawn, both with more difpatch and accuracy than can be done by any other method. The method, however, which is here propofed, is not without its advantages, fince by it an oval may be drawn as large as we pleafe, both with little trouble and confiderable exadtnefs, provided that materials fufficiently ftrong and large enough were fubftituted in place of the bradauls and chalk line. Operation.— Let B D be the length of the oval, and As half the fliort diameter. Take then half of the longefl dia- meter, and place it from A to a till it touch the line a s exactly at a. Again, take the length a s and place it on the right hand at the bradaul ; then will the two centers be found in which the bradauls are to be fixed. Laftly, take a line and put it about the C 63 ) the two bradauls, and bring the ends of the line exa&ly to A, at which point fix your pencil or piece of thin chalk, and begin to defcribe in the manner that the hand exhibits, and the pen- cil, &x. will pafs through the points DBA as required., I have found the preceding method vaftly convenient in marking out the circular ends of a fet of dining-tables ; in which cafe there is always an opportunity of flicking in the bradauls at one fide of the board, after a line^ has been ftruck to make the edge of the board ftraight. Then, after drawing a perpendicular line by a fquare and pencil from half the length of your dining-table top, proceed as above, and you may draw the femi-ellipfis juft to fait the breadth of the board, if it is fo required. Prob. XVI. Fig. 27. 7b defcribe an Oval by Ordinate Lines, Where an Oval is wanted to be defcribed on a fmooth fur- fece that will not admit of any incifion or rough mark, the fol- lowing method may be recommended. Operation. — Draw the infcribed circle in Fig. 27 on a fepa- rate board or paper, that the compafs foot may not mark the fmooth furface. Divide one femi-diameter of this circle into 8 any ( 64 ) any convenient number of equal parts. From thefe divifions (fuppofe four) raife perpendicular lines to the Periphery * or circumference, which are called the Ordinates of that circle. Obferve, the diameter of this circle is always equal to the con- jugate diameter of the oval.— Proceed now to draw a line on the fuppofed fmooth furface, on which to determine the length of the long diameter ; which divide into the fame number of equal parts from the center each way as the femi-diameter of the circle is divided into. From thefe divifions draw lines acrofs, as the figure fhews. Number the ordinates of the circle, as i, 2, 3, 4, and do the fame to thofe of the intended oval. Take then the compaffes, and fixing one foot in i on the circle, ex- tend the other to the point where that line touches the circum- ference. Transfer this opening of the compaffes to the lines i.i for the oval, and make a pencil mark at the point each way from the diameter. Take the ordinate 2 from the circle, and place it each way from the diameter on the ordinates 2.2 for the oval, and mark the points with a pencil as before. In this way proceed till all the ordinate lines are taken from the circle and transferred to their correfponding ordinates for the oval ; after which nothing will remain but to draw a fmooth curved line through each point, and the oval will be complete. * Periphery, from wef», peri, about, and p^o, pbcro, I bear or carry ; which derivation, if I am not milraken, alludes to the hand bearing the radius about its center, in order to (Licribe the circumference of the circle. Prob. ( 65 ) Prob. XVII. Fig. 28. To draw an Oval by means of a notched piece of wood and a fquare. I propofe this method as a good make-fhift, where a proper tramel is not to be had, and when, perhaps, the method of drawing ovals by the foregoing rules may have efcaped the memory, and no book near at hand to affift it. Operation. — Let / i be the long diameter, and take any fquare, by means of which draw the line e t at right angles, or fquare with it. Then notch out a piece of thin deal, as a g, to fuit the thicknefs of the fquare, fo that the bottom of g may reft on the furface of the oval, and not prevent a from paffing in the circumference/ e. From the pencil point near a to the end near g muft be equal to half the long diameter gf 9 and from the notched part a to the pencil point a muft be equal to half the fhort diameter e g. Laftly, place your fquare, and with one hand keeping it unmoved on the two diameters, by the other fweep the elliptic arch e f for one quarter. How to proceed to the other qviarters muft be evident to every one, and therefore it is unneceffary to fay more. The truth of this method will appear to every one by I obferving, ( 66 ) obferving, that if b, which is the end of the notched wood or tramel flick, is moved gradually to g> the internal angle of the fquare, then will the pencil point be at /, becaufe from b to the pencil point is equal to / ' g\ half the long diameter: and again, if at the notch, be gradually turned to g\ the inner angle of the fquare, then will the pencil point be at e, becaufe from a to a is equal g e y half the fhort diameter. I have already Ihewn the method of drawing an oval by the fe£tor in Section II. page 38, and therefore I need not fay any thing on it here. Prob. XVIII. Fig. 30. To find the center and two diameters of any Oval whole circumference is already given, and whofe center and diameters are erafed or rubbed out. Operation. — Let m i q g be the circumference of the oval. Draw the right line 0 q at random, and draw m n any where parallel to 0 q, by means of two arches, as the figure fhews. Second, Bifeft the line m n from its interferon with the circumference of the oval, as at s, Alfo bife6l 0 q in the fame manner 1 ( 67 ) manner as at s. Draw the line kg through s y, and from where i g cuts the oval, bife£t i g, as at the center s. Third, On th& center s defcribe any circle large enough to interfedt the circumference of the oval, as at the points c b. Draw the line c b, and hifedt it, as at u ; then draw the long dia- meter a b through u j*, the center ; and, laftly, draw e d parallel X.o c b \ then will e d be the fliort diameter, a b the long one, and s the center, as required. This Problem will be found ufeful in many cafes. For inflance, when the face of a fire fcreen is a true oval, and it is required to put the brafs fprings on it after being covered with paper or filk, &c. in this cafe it will be very uncertain whether the oval will hang true, if the fprings are only put on by guefs. To avoid uncertainty, take a flieet of paper and lay on the face of the fcreen, drawing a pencil round its circumference, from which proceed to find the diameter as above. Prob. XIX. Fig. 17. To find the Center of any fegment or complete circle whofe circumference is already given. Operation. — Let B D A be the fegment whofe center is re- I 2 quired. ( 68 ) quired. Draw the chord lines AD. DB, any how at random. Bife£t the chord A D by fweeping two arches from the points A and D, as the figure fhews. Do the fame to D B. Laftly, draw the right lines e d and a b through the interferons of thofe arches, and where thefe two lines meet in a point, as at c r will be the center as required. It is evident, if c be the true center of the fegment B D A, that it will alfo be the true center of any complete circle of the fame radius. It is likewife farther evident, that if the chord lines AD and D B were confidered as two fides of any regular polygon* the fame method would have the fame effe£t in finding its center. The above Problem will be of ufe to the workman, when it is required of him to fit up a board into the infide of an arch> in order to afcertain its true fweep. To this end, let the line B A reprefent a lath laid acrofs the foot of the arch A D B, to find the length of its opening. Then find the middle of this lath, and from the middle of it put up another perpendicular to it, as D, to find the depth of the arch. After having proceeded thus far, take the board to be fitted up, and make one edge of it ftraight, and draw a 8 fquare ( 69 ) fquare line acrofs it, on which lay on the depth of the arch, as at the point D. From D draw the chord lines DA and DB, bife£ling them as has already been taught, and the true center will be found for the fweep of the arch ; which fweep, if it be exa&ly fawn, will fit the arch ADB, as required. Prob. XX. Fig. 18. To find the Diameter of a Cylinder, when its ends cannot be meafured, or of a circular building, when no dimenfions can be obtained from its infide. Operation. — Let the circle, Fig. 18, be confidered as the cir- cumference of the cylinder, and let h k reprefent a ftraight rod, touching the outfide of the cylinder. From any of the divi- fions on the rod h k put another rod acrofs, till it touch the outfide of the cylinder in a fquare direction from the rod h k ; which is eafily done, by keeping the crofs rod exaitly by the fide of the fquare lines which mark out the divifions. So the lines g h and / reprefenting the crofs rod, are in a fquare di- rection from the long rod, and are produced till they touch the cylinder. After proceeding thus far, take paper, or a drawing-board, as may be required, and draw a right line equal in length to h k y as ( 70 ) as h m k p No. 2. From h m k draw g h and i& 9 of the fame length and direction, as g h and i k in Fig. 18. Draw then the chord line g m at random, and from the point m draw m % the other chord. Bifedt thofe chords, as the figure fliews, and where the right lines meet in a point will be the center of the cylinder ; and any right line being drawn through the center s will deter- mine the length of the diameter as required. Thus it is evident that the diameter, and confequently the circumference of any round building, may be afcertained by this method. The lath h k, in fuch a cafe, may be confidered ten feet long, and five inches broad, and each of the divifions on it one foot: and proceeding in the manner taught above, the moft accurate dimenlions of the diameter of any fuch building will be found. SECTION ( 7i > SECTION V.. On various ufeful Problems pertaining to the working Part of both the Cabinet-making and Upholflery Branches : as the Me- thods of mitring Mouldings of different Proje&ions — of drawing large Circles, without the Trouble of extending a Lath to their Centers, to fweep their Circumferences by— of drawing fweep Cornices, and fitting up their Valances to the Cornices—of mitring the raking Mouldings of Pediments— and of the Manner of plan- ing a Room to cut a Carpet by.. Prob. XXL Fig. 15. Plate It The extreme lines P E and P 1 being given, let it be re- quired to find any number of mean proportional lines at equal, diftances from each other. Operation. — From the points of the extreme line E P to the points 1.1 of the other extreme draw right lines which will meet in O. Then let it be required to find eight mean pro- portionals, placed at equal diftances from each. other. Divide the extreme line P E into ten equal parts, which is allowing one part ( 7* ) part for each extreme. Draw the line / 9 parallel to the line P O, cutting E O in 9. Again, draw h 8 in the fame manner, cutting E O in 8 ; and fo of all the reft, as 7, 6, 5, 4, 3, 2, I. Through each of thefe points 9, 8, 7, 6, &c. draw lines parallel to PE, as the figure fhews ; then will the lines 9.9, 8.8, and fo on, be the mean proportionals as required. Obferve, in whatever proportion the extreme line EP is divided, into the fame proportion will the hypothenufe line E O be divided when lines are drawn parallel to the bafe line P O from the refpe&ive divifions on E P. Therefore if E h be one- fifth part of the line E P, then is h 8 one-fifth of the bafe line PO, and E 8 one-fifth of the hypothenufe EO. Alfo if E c be nine-tenths of the line E P, fo will a line from 1 to E be nine- tenths of the line E O, and the perpendicular line 1.1 will be one- tenth of the line E P ; fo the line 2.2 will be two-tenths of it ; and fo on proportionally of all the reft. From this little theory, the following practice may be deduced. If it be required to make a ftep-ladder of inclined fides, as they generally arc, or any thing of the fame nature, it is evi- dent, from what has been faid, and from what may be feen in the figure, that the fteps may all be cut to their proper lengths, before ( 73 ) before the ladder be put together in any part of it, which of eourfe faves both wood and time. To cut the fteps to their proper length, proceed as follows. Take a piece of deal, tw r o or three feet long, and plane it over, making at the fame time one of its edges ftraight. Then deter- mine how much the ladder is to bevel off from bottom to top. Take the difference, and having drawn a fquare line from the ftraight edge of the board, place the beveling difference, fuppofe fix inches, upon this line, which, in the figure, is reprefented by the line E P. Draw a line, as from E to O, fuppofe fix inches in length. Draw then the center line of each ftep from the edge of the board, at equal diftances, as the line 9.9, 8.8, &:c. then will the difference of the lengths of thefe perpendicular lines be equal to the difference of the length of each ftep ; that is, the ftep 8 will be the fpace between / and h fhorter than the ftep 9, and fo on to the laft ftep 1.1, which will be all the fpace between / and c fhorter than 9, as is evident from infpe£t- ing the figure. To find the bevel of the ftep-ends, divide E P, fuppofe fix inches, in the fame ratio or proportion as the fide of the ladder is divided into. If the fide pieces of the ladder be ten feet long, take one foot and place it by the edge of the before-men- tioned board. Then divide the bevel of both fides of the ftep- K ladder, ( 74 ) ladder, fuppofed to be fix inches, into ten, and take one-half of the tenth of the fix inches, and a line to a full foot in length will give the true bevel for all the fteps. Laftly, when the fteps are all plained, run a gage on the middle of their edges : upon this gage ftroke muft be placed the different lengths of the fteps, and the bevel for their ends muft be ftruck acrofs from their refpe£tive extremities. Thus it will be evident to any thinking workman, that all the fteps may be finifhed for putting together before the fides of the ladder are begun ; and how to proceed with thefe need not be mentioned. From the above little theory may alfo be deduced a ufeful practice in perfpeitive, when vanifhing lines exceed the pic- ture ; but this muft be referved for the fecond part of this work, in which I fhall treat of that art. Prob. XXII. Fig. 29. Plate III. To draw an Elliptic Cornice of any given length or depth, and to fit the valance to it. Operation. — Let 0 p be the depth of the cornice with its facia, and make 0 10 half the length of the cornice ; draw the quadrant ( 75 ) quadrant p 2, and divide its chord into nine equal parts, from whence draw lines perpendicular from the bafe of the quadrant till they cut the circumference. Divide then the half length of the cornice into ten, and draw perpendiculars from each refpedtive divifion, -marked 1, 2, 3, 4, &c. From the divifions or points on the circumference of the quadrant draw lines pa- rallel with the bafe line 10 0, till they cut the perpendicular line to which they belong ; that is, from 8 on the circle draw a pa- rallel line till it touch the perpendicular 8, and from the reft do the fame, which will form fo many points on the refpedtive perpendiculars as will be a fufficient guide for an elliptic arch to pafs through. Obferve, the ninth divifion is fubdivided, by which another point is gained in the quick part of the ellipfis, for the convenience of drawing the fweep more perfectly. The proportion of the hances may be eafily afcertained, as the figure fliews ; but in this particular fancy will generally be the rule. Method Second. It has already been obferved, that the chord line of the arch 2 p is divided into nine equal parts, from which lines are drawn till they touch the circumference ; after which draw the line p 9, as a correfpondent chord for the elliptic curve, and di- vide it into the fame number of equal parts as the chord of the circle, is divided into. Then take, for inftance, the length of K 2 the ( 76 ) the perpendicular line 8.8 in the circle, and transfer this to the perpendicular line 8 on the other chord, and mark it with a pencil. Again take 7.7 from the chord of the circle, and transfer it to 7 on the other chord, and mark it as before. In this way pioceed till all the perpendicular lines on the chord of the circle are placed on the correfpondent perpendiculars on the elliptic chord, and nine points will be obtained through which the curve is to pafs as before. Ta Jit up a Valance to a Cornice of the above Kind. The fluff for the valance fhould be tacked flraight on a board, and with a piece of foft chalk draw a line anfwerable to the line 10 0, or bottom of the facia. Divide the facia of the cornice in the manner fhewn in the figure^ and draw fquare lines up to the cornice : do the fame on the fluff for the valance, and take from the cornice the length of each perpendicular line o y 1, 2, 3, &x. &c. and transfer thofe different lengths to their re- fpeclive perpendiculars on the fluff, and mark them with chalk. JLaflly, by a fleady hand draw, with foft chalk, a curve to pafs through thefe points, which, if accurately done, and cut by the line, mufl evidently fit at the firft trial. PROR. ( 77 ) Prob. XXIIL Fig. 31. Plate III. To defcribe the Arch of a Segment of a large Circle, with- out the affiftance of a lath from its center. Operation. — Let Fig. 31 be conlldered a fegment, whofe chord is twenty feet long, and its fwell two feet, as the perpen- dicular C 10. Draw then a femi-circle, whofe radius ftiall be equal to C 10. Divide one quadrant into ten equal parts, and into the fame number divide half the chord AC. From each divifion on A C raife perpendiculars, as 1, 2, 3, and fo on. From 9 on the quadrant draw a line parallel to AC, till it touch the perpendicular 9, and mark it with a point. Again, from 8 on the quadrant draw a parallel till it touch, the perpendicular 8, and mark it as before ; and fo on, from 7 to 7, 6 to 6, till the whole are done. Through the points on the feveral perpendi- culars draw, with a fteady hand, a curve line pafling through thefe points, and it will form a regular arch. Method Second. (On the right hand of Fig. 31.) Operation. — Draw the chord of the quadrant, and divide the fame chord into ten equal parts, and raife from thefe equal divifions lines perpendicular to the chord, till they touch the. quadrant ( 78 ) quadrant arch. Divide the line C B into ten equal parts alfo, and from 10 perpendicular to C, draw the line ro B. On the chord of the quadrant take your compafies, and fixing one foot on the perpendicular 9, extend the other foot to the point where the fame perpendicular touches the arch. Transfer this to the other 9, and make a pencil mark. Again, place one foot of the compaffes on 8 of the chord of the quadrant, and ex- tend the other foot to the point where the perpendicular cuts the arch. Transfer this alfo to the other 8, on the line 10 B ; and in this way proceed for all the reft, drawing a curve line through the refpe&ive points thus found, which will form a re- gular arch as before. Prob. XXIV. Plate IV. To take the Plan of a Room in an accurate manner, fo that a Carpet may be properly cut by it. Operation.— The room being cleared of every obftrudtion, and the floor fwept clean, proceed as follows : Fir ft, Take a chalk line, and by it ftrike a line parallel to that fide of the room which feems freeft from irregularities, as d c y in Plate IV. Then by Problem III. page 23, raife a per- pendicular from c continued to b. Proceed next to the other end of the room, as at d, and by the fecond method of Pro- 8 blem ( 79 ) blem III. if moft convenient, raife another perpendicular con- tinued to a. Draw then a line from a to b, exactly parallel to d c, the oppofite fide of the room. Then will the angles abed form a true Paralelogram, proportioned to the fize of the room, by which the principal diftortions or irregularities of any of the fides of the room will at once appear. For inftance, the angle v is fomewhat out, as the line parallel to a d plainly fhews: and in this manner any other angle of the room, whe- ther obtufe or acute, may be afcertained. Second, Let the hexagon end of the room be next con- fidered ; and let it be obferved, that the plan-taker is fuppofed to have no fquare, or ftraight rule, but only a cafe of inftru- ments and line. Therefore, in order to know how much the fide i I bevels off from a fquare, take the line and ftrike it by the fide / / of the hexagon, and continue the line at pleafure beyond b. Take then the brafs protradtor, and place the center of its bafe to /, as the figure fhews. Make a pencil mark over 90, on the arch of the inftrument, and from / draw a ftraight line acrofs the pencil mark tog at pleafure. Take the fide i I of the hexagon, and place it from / to b. Draw g b parallel to the bafe of the protradtor, or to b c ; then will g b fhew how much i I is out of fquare, as required. Examine then the other fide of the hexagon by the fame rule, and if there be any variation from the oppofite fide, it will eafily be difcovered by the fame rule. Proceed ( So ) Proceed to the windows, and find the rake of the jambs in the fame manner as before, which needs not be repeated : only obferve, that the protractor cannot be placed to the architraves becaufe of their irregularity ; and therefore it muft be placed on the line ab, as the figure itfelf exprefles. Laftly, Proceed to the circular end of the room, with its windows ; and in order to find the center of the arch rop, draw p v at its foot, and parallel with a d. On the middle of pv raife a perpendicular, and continue it to t at pleafure. Draw then the chord o p, and bife£t it, whence raife a perpendicular, cut- ing o t in /, which will be the center* From the opening of each window draw the feveral radii, as fhewn in the figure, by which it will be eafily feen how much the jambs vary from thefe central lines. The room being thus lined out, take a fheet of paper, and lay down a fcale of feet and inches that will comprehend the longeft part of the room. Meafure then with your common rule the fides and ends of the Parallelogram which was chalked out on the floor, and whatever thefe meafure by the 'rule, take the fame number of feet, inches, and parts from the fcale, and draw the Parallelogram on the paper in the fame manner as was done on the floor : and in this way go on, taking off every dimenfion from the floor by the rule, and transferring them to ( 8i ) to the paper by the fcale; fo that at length the paper will have all the lines and fhapes which the room has, by which means it is evident that the moft exa£t meafurement will be obtained. The next thing to be done is to provide a place large enough to lay down the full fize of the room again. The order will now be reverfed at home; for thofe meafurements which were before taken from the room by a rule, and tranf- ferred by the fcale on the paper, muft again be taken from the paper by the fame fcale, and replaced on fome convenient place, by the fame rule that was ufed in taking the plan. If this method be purfued with accuracy, I am certain it cannot fail to anfwer the purpofe, if a proper allowance be made for ftraining the carpet. Prob. XXV. Fig. 32. Plate V. To mitre any thing of the nature of a Comb Tray, the breadth of whofe fides fhall be given, and their inclination from a perpendicular predetermined. Let b a be confidered equal to the given projection of the fide of the tray, and let the perpendicular e a be the height of the fpring of its fides. Draw the bevel line e b, and fixing one foot L of ( 82 ) of the compafles at b, fwe'ep the arch e d\ then will d on the bafe line be the mitre point of the fide of the tray g I, and db will be the required breadth of its fides, neceflary to raife it to e, perpendicular over a, the point of projection. Again, if the tray fide fhould be required to be raifed from its bafe up to m, then draw m b, which will be the breadth of the fide, and with b m in your compaffes; fweep the arch m n ; then will n be the mitre point of the fide of the tray, as required. How much fhorter the point n is than a full mitre, is feen from n to o, of the dotted lines meeting together. Whence it is evident, that as the tray fides are raifed higher and ftiil higher from their bafe, the mitres will become pro- portionably fhorter, till at length the fides will be in an upright pofition, and consequently muft iland in a perpendicular direc- tion from their bafe or bottom. On the other hand, if the fides of the tray be depreffed nearer to their bafe, and ftill nearer, their mitres will proportionably increafe, until they arrive at full length, and confequently they will be in a perfect horizontal pofition, or parallel to their bafe. A little reflection will ealily convince the reader, efpecially the Cabinet-maker, of the propriety and ufefulnefs of thefe remarks. How the edges of the fides of the tray are to be bevelled to fuit their rake, muft; be evident by infpe&ing the figure, ( 83 ) figure, and is generally known by all workmen, and therefore it is unneceffary to dwell further upon it. Prob. XXVI. Fig. 33. Plate V. To find the Lines for working the Mouldings of a Clock Bracket, &x. when the front moulding projects more than the ends. Operation. — Let a 0 b d be the plan of the clock bracket. From the center of a 0 draw the mitre lines to b and d, and from the center let fall a . perpendicular, as at f. From this perpendicular draw a profile of the cavetto and aftragal, accord- ing to the projection intended for the ends of the bracket. From the fpring of the cavetto on the top of the necking raife a perpendicular up to the line a 0 ; then from the upper part of the cavetto, as from 1, raife another perpendicular up to 1 on a 0. From where thefe perpendiculars interfedt with the mitre line, divide the intermediate fpace into any number of equal parts, as at 1, 2, 3, 4. From thefe numbers on the mitre line draw perpendiculars up to the correfpondent figures on a 0, and continue them downwards till they touch the ca- vetto at 2, 3, 4. Laftly, draw from the utmoft projection of the aftragal or necking, a perpendicular, cutting the mitre line at 5 ; then from 5, 4, 3, 2, 1 on the cavetto draw parallels out at L 2 pleafure. ( 8 4 ) pleafure. Take in your compafies d o from the plan of the bracket, and place it from d to/>, No. i. From/) let fall a per- pendicular; then from the plan, as before, take i.i and place it from i on the perpendicular line p to i on the parallel line. Again, take the line 2.2 from the plan, and place it on the pa- rallel line 2 to 2, and fo of all the reft, forming fo many points, by which a profile of the front cavetto may be formed, and which will mitre in with the end cavetto, if the mouldings are exaCtly worked to thefe profiles, and the mitres be accurately £iit. How the mitres are to be cut is eafily feen by the mitre lines on the plan. In Plate II. Fig. 12, an example of the fame kind is fhewn, as it may be performed by the SeCtor. Let the quadrant A D be confidered as one of the cavettoes to be mitred together. Then let it be propofed that another cavetto is to mitre to the former, whofe projection fhall be equal to 1.10. Proceed then to draw this cavetto by the fame directions as are given in page 39 for drawing an Oval ; after which the cavettoes are to be worked according to thefe curves. The length of the mitre for the leaft projecting cavetto is from 90 to 10, and that of the largeft projecting cavetto is from 10 to \, and the mitre line is 9.10. By ( 8 5 ) By thefe methods it is evident, that any moulding of diffe- rent projections, and conlifting of various members, may he worked, and cut fo as to mitre exactly together. Prob. XXVII. Fig. 34. Plate V. Of working and mitring raking Mouldings, Let No. 1, Fig. 34, be a level ovolo in a broken pediment. Make its projection equal to its height. Divide the height of the ovolo into any number of equal parts, and from thefe di- vifions draw parallel lines, as is fhewn in the figure. Next, from the extreme points of the ovolo draw two parallel lines, according to the rake of the pediment defcribed below, which will of courfe increafe the height of the ovolo. Draw then a perpendicular or fquare line from either of the raking lines, as at No. 2. Divide this fquare line into the fame number of equal parts, and from thefe clivifions draw lines parallel to the raking part. Take then 5.5 from No. 1, and transfer this opening of the compaffes to 5.5 on No. 2, and make a pencil mark where it extends to. Again, take in your compaffes 4.4, from No. 1, and transfer this alfo to 4.4 on No. 2, and mark it as before ; proceeding in the fame manner with the reft ; by which points will be found to enable us to draw the raking ovolo fo that it will mitre with the level one at No. 1. Laftly, if a pediment be ( 86 ) be open, then it will require returning mouldings to mitre in with the raking mouldings in front ; for which returning mem- bers there muft be another drawing made, as No. 3. The fillets, 8cc. of thefe returning mouldings ought to hang per- pendicular with the level cornice ; therefore draw, at No. 3, a line perpendicular with the level cornice. Raife then another perpendicular at a diftance from that which was firft drawn, equal to the projection of the level ovolo, as is fliewn by the dotted line in No. 3 of Fig. 35 ; and from the point where this perpendicular cuts the raking line, draw a line parallel with the level cornice, which gives the whole breadth of the returning moulding, as is apparent by infpedtion. Divide the whole breadth of the returning ovolo into the fame number of equal parts as before, and proceed exactly in the fame manner to find the curvature of the returning ovolo as was done to find that of the raking one, and the whole by thefe methods may be completed. In the fame manner may be found the raking and return- ing cyma-re£ta mouldings, defcribed in Fig. 35, which it is un- neceffary to fay any thing about, after what has been faid on the ovolo. Pros. ( 8 7 ) Prob. XXVIII. Fig. 36. Plate V. As I have in this Section defcribed the methods of drawing and mitring mouldings of different projections, and alfo of drawing and mitring raking with level mouldings, it may be proper here to defcribe the proportion of the Tufcan raking Pediment, and the manner of drawing it. It is true, according to an orderly arrangement, the Pedi- ment fhould come after the column; but this is of fmall con- fequence, if it can as well be underftood in this place. The intention of a clofe pediment, whether raking or cir- cular, is not only to ornament the front door or entrance of any building, but likewife to fhelter fuch as feek admittance from inclement weather. For this purpofe the raking clofe pediment of any order is beft calculated; for whilft we are flieltered from rain or fnow by the bold projections of the fe- veral members of each order, efpecially the Doric, the defend- ing Ihowers eafily and quickly glide off on each fide, on account of the rake of fuch pediments. It is therefore improper to have open pediments of any order at the exterior entrances of buildings : and it is con- 8 fidered ( 38 ) fidered by architects as improper to have clofe ones over interior entrances or door ways, where they are only employed as ornamental The pitch of the Tufcan pediment is the fame with the other orders, for in this refpedl they are all uniformly the fame ; but their intercolumniations, or fpaces between the pillars or pilafters, together with other particulars, vary according to the refpeclive order to which they belong ; which 1 fliall mention afterwards, in treating on the Orders. To proportion and draw the Tufcan order, proceed thus : Obferve, that Fig. 36 is exadtly half the pediment only ; and therefore, in drawing a whole pediment, the divifions fpe- cified in the figure muft be laid on each way from the central line. And obferve likewife, that the frieze and architrave are not drawn to the cornice, becaufe they are not wanted in de- fcribing the pediment. Operation. — Lay down three diameters from the center of the pediment to the center of the Ihaft, as at 1, 2, 3, in the figure. Divide a diameter into eight equal parts, and take three of thefe and place them each way from the center line of the fhaft, which gives the upper diameter of the column, as the ( 8 9 ) the figure fhews. Again, divide a diameter into four, as that diftinguifhed by the writing in the figure, and take three of thofe parts for the perpendicular height of the cornice : at this height draw a parallel line at pleafure fufficient for the whole length of the pediment, as the upper line with the numbers. Then take the perpendicular height of the cornice, and place it from the outfide line of the fhaft on the line continued out from the under edge of the cornice, which will determine its projection, as is eafily feen by the level fcale line h. Raife a perpendicular line from the whole projection, as g 9 till it cut the upper parallel line ; then will this line ferve as a fcale for the heights of each member in the cornice, the proportions of which are eafily feen by the aliquot parts on the fcales ; but if not rightly underftood, the reader may fufpend his judgment till the Tufcan order is defcribed. Divide the upper parallel line, which is equal to one-halt of the whole length, into nine equal parts, and give four of thefe for the pitch of the pediment, as the figures i, 2, 3, 4, lhew. Draw then a right line from 4 to the utmoft projection of the level cornice, and proceed to draw each member of the level cornice, as the fcale lines diredt. Note, The two upper lines, containing the nine di villous, reprefent the upper fillet of the level cyma-refta. M The ( 90 ) The next thing to be done, is to proportion the members of the raking cornice by thole of the level one. To do this, draw a fquare line from the pitch of the pediment* and con- tinue it till it pafs through the level cornice. Take then, the Ikew meafurement of the lower fillet of the level c^n± a .»rt*5ta, as a b, and transfer this to the raking cyma-re£ta downwards, from a to b. Again, take b c from the level corona, and trans- fer it from b to c for the raking corona. Laitiy, take c d,ef in the fame manner, and transfer them one after another for the raking mouldings, as before; after which, draw lines through the feveral points parallel to the pitch or raking line, and the pediment will be completed for fhading if re- quired. SECTION ( Qi ) SECTION VI Of the Names and Properties of various Geometrical Solids — Of finding curved Lines to anfwer the Sections of various irregular Figures— and of the Nature and Conflru&ion of Hip and Elliptic Domes. \ In Section iff. page 43, I have there obferved on ufeful geometrical fuperficies, that to have fome knowledge of their names and properties is certainly of advantage to every one,, efpecially to thofe who are concerned with drawing or making pieces of work of the like figures. With equal propriety the fame may be affirmed of the ufeful geometrical folids, the knowledge of whofe names and properties frequently enable us to communicate our ideas of the figures of various obje&s that occur to us, with greater pre- cifion and freedom than we otherwife Ihould be able to do, were we, for want of this knowledge, obliged to ufe a num- ber of explanatory words and figns before we could be under- flood. M 2 However, ( 92 ) However, I have not introduced more of thefe than what I think quite neceflary to be known, and which I fliall now endeavour to explain in as fliort and clear a manner as I am able. Of the Names and Properties of the General Solids. In Plate VI. No. i is termed a Cube, which is a regular folid, bounded by fix equal geometrical fquares or furfaces, from KujSof, kubos, a dye. It is alfo called by fome a Hexaedron*, becaufe it has fix feats or bafes on which it is capable of being relied. No. 2, is a Parallelopipedon, or Parallelopiped, a regular folid, contained under fix parallelograms, whofe oppofite fides are parallel and equal ; or it is by fome called a Prifm, whofe bafe is a parallelogram. If a piece of wood be feven or eight inches long, three broad, and two and a half in thicknefs, fo planed that its fides are all parallel, and cut fo that its ends are fquare to its fides, then will the piece of wood be of the figure of a Parallelo- piped. * Hcxaedron, from «|> bex 9 fix, and «fy*> hedra, a feat. No. ( 93 ) No. 3, is a Pentangular Prifm *, fo called becaufe its ends are bounded by pentagons, or five-fided furfaces, and its fides by five parallelograms. There are various kinds of Prifms ; as No. 4, is an Hexan- gular ; No. 5, a Trapezoidical ; and No. 6, a Triangular Prifm. An Hexangular Prifm is terminated at its ends by two fix- fided furfaces, and its fides by fix parallelograms. If a piece of wood, feven or eight inches long, be rounded to two or three inches diameter, and if this of round wood be planed To as to have fix fides parallel to each other, then it will be of the figure of an Hexangular Prifm. Again, a Trapezoidical Prifm is one which is bounded at its ends by two Trapezoids, (fee No. 5, Plate II.) and whofe fides are four parallelograms, two of which are equal to each other, but not parallel, and two unequal in width, yet parallel. If a piece of wood be feven or eight inches long, as before, and if one of its fides be about three inches broad, and two of them two inches and a half, inclining or beveling off alike * Prifm, from w^a, *f fomething fawn or cut off." from ( 94 ) from the fide which is. three inches, reducing the fourth fide to two inches broad, then will the piece of wood be of the figure of a Trapezoidical Prifm. Laftly, the Triangular Prifm is fo called, becaufe its ends are bounded by triangles, or three-fided fuperficies, and its fides by three parallelograms. If, as before, a piece of wood be planed fo as to have three fides, fuppofe each two inches broad, and their angles parallel, it will then be of the figure of a Triangular Prifm. No. 8, is a Tetrahedron -, called fo becaufe it compre- hends, and is bounded by four equilateral t triangles. It may alfo be conceived as a triangular pyramid of four equal faces. Hence, if a piece of wood be firft cut into the form of an equilateral triangular prifm, and then be terminated from its bafe till the three fides meet in a point perpendicular to the center of the bafe, and if the terminated or inclined fides be equal in length to their bafe, then will the wood exhibit the figure of the geometrical folid, termed a Tetrahedron. * Tetrahedron, from rty*, tetra, four, and tytc> as before, t See Plate II. No. ( 95 ) No. 7, is an 06tahedron. It receives its name from the eight equal and equilateral triangles by which it is bounded. It may alfo be conceived as two quadrangular pyramids, joined together at their bafes. If, therefore, a piece of wood be formed into an equal qua- drangular prifm, and if this prifm be terminated from its center each way, till all the fides come to a point perpendicular to the centers of the refpedtive bafes of the pyramids fuppofed to be joined together, then will the piece of wood, thus cut, give the true figure of an O&ahedron. No. 15, is a Dodecahedron, a regular folid, bounded by twelve pentagons* To form or conftru6l this regular folid, a piece of wood may firffc be turned round, and then planed into ten equal fides. Draw then a regular pentagon (Plate II. Fig. 19) on each end of the piece of wood, one of whofe fides fhall be equal to one of the fides which the wood was firii planed to. Laftly, make five faces on each end of the wood, which fh all compre- hend two of the firft-mentioned ten fides, and one of the fides of the regular pentagon drawn on each end ; then will the piece of wood form the figure of a Dodecahedron, as required. S No, ( 96 ) No. 16, is an Icofahedron, which is a regular folid, com- pofed of twenty equilateral triangles. See Plate 1L Fig. 7. This figure may be confidered as confifting of twenty tri- angular pyramids, as No. 8, whofe vertexes meet in the center of a fphere, imagined to circumfcribe it, and therefore mult all have their heights and bafes equal. To conftrudt this folid, a piece of wood fliould firft be made round, and then planed into fix equal fides. Upon each fide draw an equilateral triangle, and the fpaces between each triangle rauft be cut away to the fide of the triangle thus drawn, and when this is done, there will then be four more planes or faces for four more equilateral triangles, which will make ten. Find the center of one end of the piece of wood, and terminate each fide of the hexagon to this center, and there will be produced fix more equilateral triangles, which added to the other, make fixteen. Find the center of the other end, and terminate the before-mentioned four fides to this center, and other four equilateral triangles will be produced, which will complete the twenty as required. From what has been faid, it is evident that five of thefe folids are regular, fince they may each of them be infcribed within a fphere, fo that each angle Ihall touch the circum- fcribing ( 97 ) fcribing fphere in fome point. Hence, to form thefe regular folids, namely, the Cube, Oitahedron, Tetrahedron, Dodecahe- dron, and the Icofahedron, it is prefuppofed in the above con- ftru&ions, that the pieces of wood mentioned are all cubes, whofe fides are equal to the dimenlion of each figure. No. 13, is a Pyramid, a folid, whofe fides rife from a geo- metrical fquare as its bafe, and terminate in a vertical point. As the height of this folid is at pleafure, its fides are fome- times bounded by equilateral triangles, and fometimes by ifo- fceles, as the figure referred to. Nor are we to confine our ideas of Pyramids to fuch only as have fquare bafes, for thefe may be either triangular or poly- gonal, while yet their refpe£tive fides fliall terminate in a point perpendicular to the center of their bafes. The learned are divided in their opinions about the deri- vation of the term Pyramid : fome think the name is from mif; pur , fire, becaufe Pyramids afcend to a point like fire ; but others more confidently affirm, that it is from wygo?, wheat, or corn. " Not," fays the author of this laft opinion, " that we are to fuppofe that the Pyramids were ever intended for gra- naries; but that the Greeks, when, after many generations, N they ( 98 ) they vifited Egypt, and faw thofe amazing ftru&ures, looked on them as ftore-houfes for grain ; and knowing Egypt to be a country fruitful in corn, they called them Pyramids — corn itore buildings ; being, as they thought, the repofitories for all the produce of Egypt." No. 9, is a Cylinder. This is a folid, bounded by two equal circles at its ends, and a parallelogram revolving round their circumference. This figure is fitly reprefented by a gar- den roller, whence its name xuAsvJpo*, kulendros, a roller ; and as for its conftruition, it is fo fimple that it is unneceffary to fay any thing about it. No. 12, is a Cone ; a folid, bounded by two fuperficies, one of which is convex, and the other ftraight. The bafe of a Cone is fometimes an ellipfis, and fometimes a circle terminating to a point perpendicular to its center. From this center to its vertical point, a lirpLe is fuppofed to pafs, called its axis, on which this body might be made to revolve. And the fame may be obferved of the Cylinder, Conoid, and Sphere, each of which has its imaginary axis, or right line, palling through its center, about which they may be made to turn. No, ( 99 ) No. 14, is a Conoid ; a folid, which terminates from its bale to its vertical point in a curved or elliptic diredtion. Some- times the curve of its fide is hyperbolic, and fometimes para- bolic. See Plate II. Fig. 35, 36. Its bafe, like the Cone, is either an ellipfis or circle. No. ro, is a Hemifphere *, which is one-half of a globe cut by a plane palling through its center, and therefore is contained under two fuperficies. No. 11, is a Sphere, or whole globe, which is a body or folid, bounded by one convex furface, whofe parts are all at the fame diftance from the central point, as the perifery of a circle is to its center. Of the Se&ions and Coverings of regular and irregular Figures ; and how to find curved Lines to anfwer their various Se&ions. The Sedtion t of any folid is, when it is fuppofed to be cut by any plane paffing in fome diredtion through it, which, * Hemifphere, from fphah% a globe or fphere, and njuev£ bemtfus, half, i. e> half a globe. f Section, a cutting or dividing ; " from fcco, to cut," N 2 of ( 100 ) of covirfe produces a furface or fuperficies confonant to the nature of the fe£tion, and agreeable to the fhape of the folid hich is cut* Hence, if a cylinder be cut oblique to its bafe, this feclion will produce a furface perfectly elliptic ; and if a cone, Fig. 12, Plate VI. have a fe&ion parallel to its axis, the curved boun- daries of the fuperficies will be hyperbolic. See page 52. " If a fphere be cut in any manner, the plane of the fec- tion will be a circle, w r hofe center is in the diameter of the fphere." , But if two plains, or ftraight furfaces, cut each other, their common fedtion is a right line. I mention thefe particulars, that the reader may more readily and clearly underftand the following Problems. Prob. XXIX. Fig. 32. Plate VI. Let Fig. 32, Plate VI. be confidered a folid, of the fhape of a vafe, whofe covering and fedtion are to be found ; or, in other words, if a vafe is required to be veneered, how to cut the veneer fo as each joint fliall appear ftraight when the veneer is laid. Operation. ( ioi ) Operation. — Draw the lhape of the vafe, which, in this cafe, is a femi-elliplis on the conjugate diameter. Draw a per- pendicular line through the center of the vafe, which will be the long diameter. Divide this diameter into a number of equal parts, and on thefe divifions draw lines parallel to the conjugate diameter, as the figure fhews at i, 2, 3, 4, &c. Draw then on each of thefe right lines a femicircle, and, for the fake of greater accuracy, let the eighth fpace be fubdivided, by which another circle will be obtained near the center, as at 9. Draw next a perpendicular line at pleafure, as at No. 1. Proceed then to take the dimenfions of the curvature of the vafe thus : Place one foot of the compafles on 10, and extend the other to 9, and with the fame opening of the compafs fix one foot on 10, in No. 1, and fweep the arch 9 at pleafure. Again, fix the compafs foot on 9, and extend the other to 8 on the vafe, which transfer from 9 to 8 at No. 1, and opening the com- pafles, fix one foot on 10, and with the other fweep the arch 8 at pleafure. In this manner proceed with all the other divi- fions on the vafe, \mtil its whole curvature is laid down on the perpendicular line at No. 1. After proceeding thus far, it muft then be confidered how many pieces of veneer will cover the circumference of the vafe, and how broad the veneers may be laid ; which in this example I have fuppofed to be fourteen. Divide therefore each femicircle into ( 102 ) into feven, as fpecified by the {mail dots on each arch. Upon the femicircle 9 of the vafe, place one foot of the compafles on 9, and extend the other to the perpendicular line, which will be half the breadth of the veneer, according to the num- ber of pieces propofed. Take this opening of the compafles and place it each way from the perpendicular line at No. 1 on the arch 9. Again, on the femicircle 8, take the fpace from the perpendicular line to 8, and transfer this to the arch 8 at No. 1, placing it each way from the perpendicular as before. In this manner proceed with the reft, by which the proper breadth of the veneer on each femicircle will be determined ; and if a regular curve line be drawn through each point on the feveral arches at No. 1, the curved boundaries of thefe arches will be the exa£t fhape of the veneers, which, when properly laid down, will then have the appearance of fo many ftraight joints. And hence, by whatever rule or method we find the coverings of folids, regular or irregular, by the fame rule we alfo find curved lines to anfwer their perpendicular fec- tions ; for it is evident, if the vafe, after being veneered, was cut through its center perpendicularly, and the veneer raifed up again, that its edge would be a faint curve, like that at No. 1. Prob. / ( ) Prob. XXX. Fig. 33. Plate VI. To find the covering and perpendicular Section of a Solid partly convex and partly concave. Operation. — Draw the profile of the folid propofed, as Fig. 33. Let fall a perpendicular from the center of the top. Draw a line from 11 on the profile parallel with the top, and divide the aforefaid perpendicular line into any number of equal parts, which in this example is ten. Draw parallel lines through each of thofe divifions, and on thefe lines draw fo many femir- circles, whofe diameters lhall be equal to the length of each line. Draw a perpendicular at pleafure, as at No. 1. Fix one foot of the compafles at 1 on the profile, and extend the other to 2. With this opening fix one foot at 1, No. i, and fweep the arch 2. From 2 on the profile, extend the compafles to 3, and transfer this from 2 to 3 at No. 1. Then opening the com- pafles, fix one foot at 1, and fweep the arch 3 at No. 1, and fo on of all the other ; by which the dimenfions of the curvature of the profile will be obtained.. Laftly, take half the whole fpace from 11 on the femicircle to the perpendicular line fpecified by the dot, and place this opening of the compafles each way from the perpendicular line on the arch 11 at No. 1, and mark the phces with a pencil. Proceed ( ) Proceed to 10 on the femicircle 10, and take half of its whole fpace, and place it each way from the perpendicular on the arch 10 at No. i, as was done on the arch n before; and in this manner go through the whole, and a fufficient number of points will be found in order to draw an irregular curve an- fwerable to a perpendicular fedtion of the propofed folid, and which will alfo anfwer for its covering or veneering. But here I muft obferve to the workman, that in cafe it fhould be propofed to him to veneer any thing of the like forms of Fig. 32 and 33, it would not do to cut out the veneers fo broad that fourteen pieces would be equal to the circum- ference. It would require twenty-eight pieces at leaft, before they could be laid down with fafety and eafe, efpecially if it were required that the joints of the veneers fhould be fo clofe as to preclude the neceffity of putting in ftringing to hide them. I fpeak this not merely from theory, but praftice, hav- ing myfelf veneered knife-cafes of the fame fhape with the figures in the Plate, and where no ftringing was admiffible to hide the joints. But every thinking workman will eafily per- ceive that it makes no difference in the methods of finding the curve lines for the covering, whether the number of pieces be fourteen or twenty-eight. By thefe methods a fphere or globe may be covered, anil a curve, i ( io 5 ) curve, anfwerable to any feftion, through its center may be found. I have not given any example of this on the Plate, as it is prefumed that a few hints will ferve, after what has already been faid on the fubjeft. Operation. — Draw a circle whofe diameter fhall be equal to the axis of the fphere to be covered. Divide the femi- diameter into nine equal parts, and on thefe parts draw lines acrofs at right angles with the diameter, till they touch the circumference of the circle on each fide. From thefe feveral lines draw femicircles, as was done before in Fig. 32 and 33. Divide the feveral femicircles into eighteen degrees each, and take one degree from the largeft femicircle, and place this opening of the compa{fes on a right line eighteen times. Then from the extreme points on this line draw arches each way, till they meet in the center of the line. Laftly, transfer half a degree from each femicircle to their correfpondent arch, laid on each way from the right line, as was done on No. 1, Fig. 32 ; and the whole thus transferred, a curve line palling through each half degree laid on the feveral arches both right and left from the center line, will form the proper covering for the fphere or globe as required. Obferve, the covering will be of the figure of two feg- ments of a circle joined together, and the length of the cover- O ing ( io6 ) ing will be equal to half the circumference of the propofed fphere. I muft here entreat leave to remark, that notwithflanding the above directions are addreffed to men in the wooden way, yet it is certain that the Upholflerer may avail himfelf from what has been faid on the fubjedt: for the coverings of the like folids made of any kind of fluff, ought to be cut by the fame methods, and fewed together in feams anfwerable to the joints in wood: but the elafticity or pliablenefs of fluffs, &cc. makes it unneceffary to cut them into fuch fmall pieces as is abfo- lutely required in wood. Prob. XXXI. Fig. 34. Plate VI. To find the Se&ion and Covering of a Knife-cafe whofe front is a double oge. Draw half the plan of the front, as Fig. 34, and divide the fweep of the front into ten equal parts, as the figure ihews. Next determine how much rake the knife-cafe is to have from back to front, by which it will be eafily feen how much the fwell of the front falls at that rate, as the diago- nal line ro.i fhews in the cafe before us. Draw from 10 of the diagonal line a perpendicular at pleafure. From the feveral divifions ( 107 ) divifions on the curve of the front draw parallel lines, till they cut at the numbers on the aforefaid perpendicular. Obferve, that the numbers on the perpendicular line are placed to an- fwer the parallel lines as they proceed from each number marked on the curve of the front. Every thing being now prepared for finding the covering and fedtion of the knife- cafe, proceed to No. i, and draw a right line at pleafure, as l.i i. Take from n to 10, or any other of the divifions, on the front of the knife-cafe, and with the compafles repeat it nine times on the right line i.n at No. i. Then obferve, that from 2 to i on the front of the knife-cafe is rather a wider fpace than the other divifions, which are all equal. The intention of this is, to bring the parallel line, which proceeds from 2 on the front, a little farther on from the front line 1.1 ; therefore take from 2 to 1 on the front, and place it from 2 to 1 on the right line at No. 1, then will the whole length from 1 to n at No. 1 be equal to the whole curvature of the front of the knife-cafe, fuppofed to be ftretched out in a right fine. On the feveral divifions on the right line 1.11, at No. 1, draw perpendicular lines at pleafure. Take in the compafs the fpace 1.1 from Fig. 34, and transfer this opening to the perpendicular line 1 c at No. 1, marking it with a pencil. Then again take the fpace from 2 to the diagonal line at Fig. 34, and transfer this to the perpendicular line 2 at No. 1, and mark it with a pencil as be- fore. Do the fame from the lines 3, 4, 5, 6, 7, at Fig. 34, and O 2 obferve ( io8 ) obferve that n follows 7, becaufe it proceeds from the point 11 on the front of the cafe; therefore take the fpace from n on the perpendicular line to where the parallel cuts the diagonal, and place it on the perpendicular at No. 1. Like wife take 8 and 10 in the fame manner. As for 9, it is loft, becaufe that divifion on the front of the knife-cafe falls on the right line, and, of courfe, has no projection. Laftly, through all the points on each perpendicular at No. 1, draw a curve line, which will anfwer to the fedtion of the knife-cafe, if it be cut anfwerable to the bevel line 10. 1 on the plan of the cafe. The dark fliade e a b, at No. 1, Ihews half the veneer or covering of the knife-cafe ; and if a piece of ftrong paper be cut double, according to the boundaries of the dark fliade, it will ferve as a pattern to cut the knife-cafe open by, and likewife to cut the veneer by, before it is glued down. The infide veneer for the front of the top may alfo be cut near enough by it, though it will vary a little ; but this defe£t is not equal to the advantage of having the infide veneer pretty nearly cut to the fweep, becaufe it will then glue down much eafier, and be lefs liable to fplit. From what has been faid on this Problem, the ingenious workman may apply the rules and obfervations to other pur- pofes that may be of more importance than the cutting and veneering ( io 9 ) veneering of a knife-cafe, which I muft leave him to do as neceffity may require. Of the Nature and ConJlruBion of Hip and Elliptic Domes for Beds. Domes of various kinds have, for many ages paft, been introduced into elegant and magnificent buildings, on account of their graceful effedt and majeftic appearance. I am of opinion that the notion of employing domes for the roofs of grand buildings, was firft fuggefted by the appear- ance of the hemifphere furrounding our earth or horizon, forming a canopy or roof to the globe ; which if it were fo, domes had their origin from a truly fublime and magnificent idea. The ufe of domes for the tops of beds is of much later date than for buildings ; but it is certain, whoever he was that firft employed domes for the tops of beds, he muft be confidered as a perfon of enlarged ideas, as no other top or roof for a genteel bed can equal them : therefore we fee them generally ufed for ftate beds, where, it is certain, both grandeur and bold effe£t are effentially requifite. The < no ) The term Dome generally implies a yanked, arched, or fpherical roof. Some derive it from domus, a houfe, and others from the barbarous Latin doma, a roof or open porch. When an arched roof is raifed from a fquare or oblong plan, it is called an Hip Dome, hecaufe they require mitre ribs at each angle, uniting in a center at top. But thofe domes which take their rife from an oval plan are called Elliptic ; and, laftly, thofe which have an o£tagon or hexagon for their plan may be ftyled Polygonal Domes. Prob. XXXII. Fig. 35. Plate VII. To conftruct an Hip Dome. Operation. — Let ABCD be the under teller, upon which another tefter is to be fixed to receive the ribs of the dome. Draw the diagonals D B and A C, and their interferon will be the center for the dome. Draw a right line through the cen- ter parallel to A B ; draw another line through the center at right angles with it, then will the diagonal lines be the plans of the hip ribs, and thofe at right angles to each other will be the plans for the center ribs. Draw a circle from the center of the dome of about eight inches radius, as the figure fhews, which is intended as a ground for ornament in the center of the ( III ) the dome at the infide, and alfo to combine together the hip and center ribs. Proceed next to confider the height of the dome as may be required. Let 7.6 at No. 1 be the perpendicular height of it, and let m n be the width of the dome. Then draw a femi- ellipfis to pafs through the points m 6 n. Divide half of this femi-ellipfis into as many equ&l parts as it may be thought neceffary to have ribs in that fpace, which < * s his example is fix. Draw on thefe divifions perpendicular lines, asr the figure fhews, and fubdivide the laft fpace, from which raife a perpen- dicular as before. Proceed to No. 2, and divide half the length of the dome, as / 0, into the fame number of equal parts as half the width was divided into. From the divifions raife perpendiculars at pleafure. Take the length of the feveral perpendiculars from No. i, and place them on the correfponding perpendiculars at No. 2, and draw a curve line through each point ; then will the ellipfis thus produced be the outfide fliape of all the long ribs, the fame as No. 1 is of the fhort ribs. Laftly, proceed to No. 3, which is for the four hip ribs. Draw the dotted lines from 8, 9, 10, 11, 12 at No. 1 till they cut the diagonal line^' h at the correfponding numbers. From thefe interferons raife perpen- diculars at pleafure, as before. Transfer the length of each 8 perpen- ( II* ) perpendicular line from either No, i or 2 to No. 3 on each per- pendicular as numbered, and drawing a curve line through each point as before, it will produce an ellipfis for the outfide lhape of each hip rib. The next thing to be confidered, is the length required for each rib, according to their diftance from each angle of the dome. A little thought will make this eafily underftood ; for if No. 3 was placed in an upright pofition, being conlidered as a frame, and if the portion of the curve from n to 1 at No. 1 was placed upright to it, the two points 1 in No. 1, and 1 in No. 3, would coincide, and the point 2 of No. 1 would coincide with 2 at No. 3, and fo of all the reft. Hence, from n to 1 of No. 1 is the length of the firft fhort rib, whofe plan is at a ; from n to 2 is the fecond fhort rib, whofe plan is at b ; from n to 3 is the third fhort rib ; its plan at c : from n to 4 is the fourth fhort rib ; its plan at d : and from n to 5 is the fifth fhort rib ; its plan at e. The long ribs are taken from No. 2 in the fame manner ; each of which has its plan laid down at No. 3, as a b c d e f, fo that I need not fay any thing more on this part of the fubjecSt. For the length of the hip ribs, take from p to 5 at No. 3, and allow three-quarters of an inch for dovetailing into the center block. Genera! c m ) General Observations on the Management of Hip Domes for State Beds. Thefe kinds of domes fhould be made in four parts, for the fake of convenience in fixing up, or for more eafy convey- ance into the country. The center block fhould therefore be made in four quarter parts, on account of the hip and center ribs which are fixed into it, that the four quarters of the dome may eafily be feparated and put together again without injury; Domes in four parts mull therefore have eight hip ribs, or two at each angle, mitring together, to which the ribs of each feparate quarter are fixed. For the footing of thefe ribs a fliam or upper teller fhould be formed, about three inches in breadth, which will give room beyond the ribs to fcrew it to the under teller. When the four quarters of the dome are thus formed by ribs, a covering of thin deal, like Venetian fhade Huff, ihould be provided, and after covering both infide and outfide' of the dome, the deal may be fized over with thin glue, to ftrengthen. it. After the fize is dried, then good canvas may be glued or palled on, both infide and outfide of the dome, which will add to its ftrength, and give fmoothnefs to its furface. The outfide of the dome may then be painted, to match the furniture of the P bed < ) bed, and the infide is always lined with whatever kind of ftuff the hangings are made of. The infide of the dome fhould have neat gilt mouldings up the hips, both for ornament, and to hide the joint which is occaiion- ed by the mitring of the quarters together. And from the fpring of the dome, or round the under teller, fhould be an ornamented architrave, which w ill receive and hide the lower end of the hip- mouldings, and will alfo cover the tacking of the inner valence, as well as contribute to the grandeur of the effect of the whole. To thefe ornaments fhould be added a richly carved patera, fixed to the center block of the infide of the dome, which will alfo receive and hide the tipper ends of the hip-mouldings before mentioned. Laftly, a fluffed head-board, in a gold frame, with foliage ornaments on the top of it, in imitation of a pediment, will add greatly to the effect of the whole, and harmonize with the other enrichments abfolutely neceflary for a ftate bed. For the outfide ornaments of a bed of this kind, great care fhould be taken to avoid every thing that would appear trifling. The pillars fhould be maffy as well as tall, fuited to fupport the dome, whilft height gives room and effect to fine drapery. Sometimes the pillars are white and gold, and fometimes all gold ; or the ground of the ornaments may be of the colour of the filk, 8cc. of which the hangings are made. If enable- 7 matical / ( "5 ) matical ornaments are Introduced in the cornice, or on the top of the dome, thofe defcriptive of unity, love, and innocency, fhould be ftudied; and thofe of war, ftrife, or other irregu- larities of the human paffions, fhotikl be avoided. bos &*bft orl* 'io ogbo tulhan orft o* bov/orii t oi£lq noii gnoift Noblemen's crefts may be introduced, as ferving to diftin- gvufli the different branches of families ; but, in my opinion, not as they relate to armory. *yj*f4 rit oop^i^^gxo nwo vrn mcri^ obf*f/i zj^TArrTO't ^ii* oi3i{T The height of a ftate bed may be varied according to the different heights of rooms they are to ftand in. However, they never fhould be lefs than twelve feet to the top of the dome, including a vafe. Nor fhould they, in my opinion, exceed fifteen feet, not even where a room would admit, of it. For then the ornaments of the cornice and dome would lofe their effeft through diftance, and the whole compofition would ap- pear as if loftinefs were the greateft beauty. The length of a ftate bed may be feven, but fometimes- eight feet, when the area of a room is extenlive. The width of thefe beds is in general about one foot fliort of their length, but fometimes they are made nearly fquare. P z The < 116 ) The height of the frame, including the caftors, is fourteen inches. French caftors are the beft for the purpofe, fixed upon a ftrong iron plate, fcrewed to the under edge of the fides and ends, fo that the caftors may run clear of the pillars, and be detached from them, by which their rife is hid from the eye. Thefe are remarks made from my own experience in the bufinefs, which I offer for the affiftance of the candid workmen of both branches; but the fnarling critic may rejedt them if he pleafe. Prob. XXXIII. Fig. 36. Plate VII. 7b con/lru& an Elliptical Dome. Operation. — Let AB, DE be the plan of the tefter, whofe infide forms a true ellipfis by the help of angle pieces framed in, which mult be evident to every workman. The oval being thus formed according to the infide length and breadth of the tefter, and the two diameters being already drawn, proceed with one quarter of the dome thus : draw the plan of the upper tefter, into which the ribs are to be fixed, as the fecond elliptic line fhows. Divide then the portion of the 5 ellipfis ( "7 ) ellipfis between o and / into as many equal parts as it is required to have ribs in one quarter of the dome, as at o a h ij k £ tending to the center b. From thefe center lines draw parallel lines on each fide, which fhall determine the thicknefs of the ribs, and at the fame time fhow how broad each rib will be required, in order to give it its proper twifl fo as to fuit the ellipfis ; for here it muft be obferved, that every rib, excepting the one that is upon each femidiameter, muft have a winding form, both inlide and outfide, in proportion to the length of the oval with its breadth. Determine, next, how much the dome is to rife from the tefter, which, in this example, I confider to be equal to half the fhort diameter ; and therefore the arch of the rib B is a quadrant of a circle, drawn from the center b. This arch will ferve for two ribs, that is, B and its oppofite. Likewife, from the arch B, we determine the outline of every other rib thus : divide the femidiameter a b into five and an half equal parts, and raife perpendiculars till they touch the arch B. Divide the plan of the rib a b at No. 2 into the fame number of equal parts, and raife perpendiculars at pleafure ; to which perpendi- culars transfer the feveral lengths of thofe at No. 1 to the cor- refponding ones at No. 2, as acdefg; by which the rib A will be formed. The ribs for h ij and k are formed in the fame ( Ii8 ) fame manner, and therefore it is unuecefiary to defcribc thefe. Gbferve; C, on the plan of the elliptic tefler, is for the Jong center rib and its oppofite, as will eafily be underftood by nfpe&ing the figures, and a little reflection on the fubjedt. wJ Hum 1i oiod iol ; ^fiqiIfo odl 1'uSl o) z& 61 fflwi i-xjoiq eli li Of the Management of Elliptical Domes. Thefe domes may be made in four parts, the fame as hip domes, if required. The ribs of thefe domes are all dovetailed into a center block, which may be circular or elliptical to fuit the dome, and which ferves for the ground of a carved and gilt patera foi; the infide of the dome, as has already been mentioned on hip domes. When the ribs are all completely fixed, the fpaces between them may be filled up by glewing white deal in ; and when the pieces of deal are worked down to the ribs, the whole will form an agreeable dome, which fhould be covered with canvafs, and painted to fuit the furniture, or otherwife covered with the fame kind of fluff. And if fo, it will be unnecelTary to cover it with canvafs; but as the fluff mult be put on the dome in fo many ( "9 ) many breadths, cut fo as to anfwer its ftrape, a gimp may be ftitched on to hide the tacks and give the dome a more rich ap- pearance. But if the dome be large, it may have fmall gilt moulding in place of the gimp, which are fixed to the dome by gilt-headed fere ws. For the infide of the dome, it will be requifite to have a' gilt moulding, to hide the joining of the under and upper tefter^ and to ferve as an architrave to the dome. The. triangular compartments at each corner of the tefter, occafioned by the manner of framing it to fuit the dome, fliould have fmall mouldings put on to fuit that fhape, which will take off the flat and heavy appearance it would other wife have, and add to the efFe£t of the whole. As for any other particular with refpe£l to ornaments, what has already been obferved on hip-domes may alfo be applied here. With refpe£l to the dome defcribed by Fig. 37, I do not think it neceffary to go through an explanation of it after what has been faid on Fig. 35, which, if the reader has fully under- flood, he cannot fail to be acquainted with the lines laid down: hi Fig. 37, merely from infpe£tion, efpecially as I have marked each correfponding line with fimilar letters and numbers. SECTION ( 120 ) SECTION VII. Gf the Proportion of the five Orders, adjujied by Modules, Minutes, and aliquot Parts ; together with fome Account of their Anti-* quity and Origin. Alfo t of the general Proportions of Frontif- pieces adapted to each Order. INTRODUCTION. ' I have no doubt but it maybe thought unneceffary by fome to introduce the orders of architecture into this work, after fo many publications of this fort by men of the firft clafs in the profeffion of this art To remove this objection and unfavourable impreflion from the mind, I iliall juit mention two or three particulars which induced me to make the five orders a part of this Draw- ing-Book. Firit. — In my opinion, and it is prefumed that I am not lingular in this, nothing can appear more worthy of a place in a complete drawing-book than the five orders accu- rately laid down and neatly engraved ; by which we fee the proportions and effect of each 5 moulding arranged and con- nected ( 121 ) nedted together, according to the compofitions of thofe ancient architects of Greece and Rome, who are fo juftly famous in the world. Befides ; from a Plate of the above kind, we are not only made acquainted with the proportions and fhape of each mould- ing, but have likewife the advantage of feeing the effect of light and fliadow produced by the fun's rays falling in a certain direction on the feveral parts of a column. The knowledge of thefe particulars muft ever be confidered as effential parts of good drawing, in which architecture is often introduced, and fometimes makes the principal figure. Second, — As many cabinet-makers, and even fome ingeni- ous upholfterers, are found defirous of having a knowledge of the five orders, and the proportions of the feveral frontifpieces, I thought an attempt of this fort would be favourably received, as it undoubtedly tends to make the work more generally ufe- ful, and will prevent the trouble and expence of having recourfe to other books on the fubjeft. And this has not been merely my own opinion, but the fentiment of fome well-wifhers, who ilefired me to let the orders have a place in my book. Q Laftly. ( 122 ) Laftly. — Befides the reafons juft mentioned for publilhing the five orders, I mult frankly own myfelf a lover and admirer of thofe ancient productions of ingenuity and art, which, in my opinion, cannot be much, if in the leaft, improved by the force of modern genius. If, therefore, the author confiders himfelf as a kind of de- votee or bigot to thefe remaining monuments of ancient inge- nuity, furely he may be granted the liberty of paying the fol- lowing fmall tribute to the memory of thofe great architects who had the honour of bringing the five orders to that per- fection which we now fee them in at this day. And further, as I believe that the orders are now brought to fuch perfection in their proportions, as will bear the ftriCteft mathematical examination, I confider them as incapable of im- provement, except perhaps in fome part of their ornament, and therefore they are clafled with thofe things in this book that will remain unalterable. Of ( m ) Of the Origin and Antiquity of the Order of Architecture. Some diftin&ion is to be regarded between the origin and antiquity of the orders, and that of architecture * in general. The firft ideas of architecture in general, may perhaps be traced from thofe rude and irregular methods of building tents and huts which were the firft habitations of man. But in thefe ftruCtures, nature and neceffity were their only guides, unlefs they obtained fome inftruCtions or hints from the manner in which birds build their nefts, as Vitruvius conjectures. We are informed by Mofes, that Jabal was the father of fuch as dwelt in tents : and I fuppofe it is meant, that he was the firft maker of them likewife. And I further imagine, that the city which Enoch built about that time was an affemblage of thofe tents, perhaps furrounded by a mud wall, and fo ob- * Architecture implies the fcience of building in general, which gives rules for defign- ing and raifing all kinds of ftructures or edifices. It is from the word architect, com- pounded of archos, the principle, and te*1«v, teflon^ the chief artificer, or one who gives rules for, and directs the management of, buildings. Q 2 tained ( r&4 ) tained the name of a city in thofe days; for it can fcarcely be thought that they had at that time either difcovered ltone, or knew how to make brick, and much lefs how to put them to- gether in houfes, fo as to form a city according to thofe men- tioned in after times. But, however, very early after the flood of Noah, we read of an attempt made to build a city and tower whofe top was to reach the heavens. Their materials were then brick, and ilime for mortar. And when we confider how great their de- fign was, and how fuccefsfully they proceeded until the Divine Hand ftopt them, we mult neceffarily infer, that men in thefe days began to know the rules of building, and of courfe this may be confidered the origin of regular architecture. But the origin of that part of architecture called the five Orders^ is of much later date than this. They appear to me, and it has been the opinion of fome great architects, that they owe their beginning to Solomon's Temple. 1 do not mean that pillars or columns were never in ufe before this famous building was ereCted, but only that we do not read of certain proportions affigned to their height and diameter till thofe given to Jachin and Boaz, the names of two pillars fet up at the entrance of the porch of this building. We ( **5 ) We read of pillars above four hundred years before the days of Solomon : and we read alfo, that theft pillars had cha- piters and fillets of gold and filver ; but no mention is made of their height* or diameter; yet fomething may be known as to the intercolumniation of thefe pillars, for there were twenty pillars {landing in an hundred cubits, the length of each fide of the tabernacle. See Exod. xxxvi. 38. and xxxviii. n. flow- ever, as there are no proportions afligned to thefe pillars, I pre- fume we cannot date the origin of the orders here; yet I think there would be more plaufibility in it than what fome have ad- vanced on this fubjeit. The pillars which Solomon ere£ted at the entrance of the temple w r ere of the following proportion, according to the language of the fcriptures : — Their height was eighteen cubits, or twenty-feven feet without their chapiters or capitals; and their chapiters were five cubits ; which in all makes thirty-four and an half feet in height. A line of twelve cubits did compafs either of them about, confequently their diameter was fix feet ; and had thefe pillars been one cubit higher, their proportion would have anfwered exa&ly to the original Doric + Order, whofe height was equal to fix of its diameters. Befides * Jofephus indeed fays, " Every pillar was five cubits in height ;" and he {peaks alfo «f five pillars at the entrance of the tabernacle, that were gilded, and ftood on bafes of brafs. f For fome time after the firft invention of this order, the proportion of its diameter to the ( 126 ) Befides the llkeneft or affinity between the Doric column and thofe fet up by Solomon, will ftill appear more finking, if -we confider that the ancient Doric had no plinth or bafe ; for does not appear to have been any at the foot of Jachin and Boaz, otherwife I think they would have been mentioned as well as the chapiters. But thefe columns are faid to have fillets, whofe thicknefs was four lingers, and they were made hollow. See Jer. lii. 21. Thefe fillets feem to anfwer well enough to the Doric neck- ing at the top of the fhaft. They were hollow, and of four fingers thicknefs or projection, which is nearly the fame pro- jection as would be required in the necking of a Doric co- lumn of the dimenfion of Jachin and Boaz. There is another particular which may be mentioned which alfo bears fome likenefs to the Doric, and that is the fize of the porch or entrance, on each fide of which thefe mafly pillars were placed. This opening was twenty cubits in width, and forty in height, anfwering to the proportion of the Doric frontifpiece or door. the height was as the length of a man's foot is to the height of his whole body, which at that time was reckoned to be one fixth part \ but afterwards they added another diameter, and at length brought it to eight. 4 And ( ) And laftly.— The lily-work on the chapiters, and the ro\Vs of pomegranates round about the chapiters, were, in my opi- nion, as likely to have given rife to the ancient Doric order, and more fo than the manner of building ancient huts, by placing trunks of trees on each fide, by which the roof was fupported. Yet I will not fay but trunks of trees thus employed, might firft give exiftence to the notion of fome kind of a pillar to be ufed in the firft buildings of brick or ftone, while, at the fame time, I am inclined to think that columns were never reduced to any order till the building of Solomon's temple by God's ap- pointment. However, it is not to be underftood as if the regular Doric order could be copied from Solomon's pillars, but only fuch hints and proportions taken from them as ferved in after times to compofe the firft order of architecture* Nor can it be thought that the firft compofition of the Doric column had thefe triglyphs and mutules wdiich we now fee it has, till after it was reduced to its proper form and charac- ter. It is therefore thought to have been more fimple and mafTy in its primitive ftate ; fomething like the Tufcan order. Some imagine, ( 128 ) imagine, and not without ground, that the Tufcan, nearly as we have it now, was the firft ftate of the Doric, Vitruvius fpeaks of a ftate in which the Doric column was in hefore it was reduced to order ; for, treating of the antiquity of the Doric, that it was ufed in the temple of Juno, at Argos, he fays, that " the fame order was alfo ufed in the other cities of Achaia, before the laws of its fymmetry were eftabliftied." This indicates that it was in a more rude ftate before it was employed in that famous temple. But if that temple, dedicated to Juno, was eredted in the days of Dorus, the king of Argos, as Vitruvius intimates, it would be rather incredible to think that the Doric order fliould be in exiftence in times fo long before Solomon * : and, upon fuch a iuppofition, thofe who maintain that the firft idea of the orders was derived from Solomon's temple, would be grofsly mis- taken. A certain author, after quoting Vitruvius on the fuhjedt, fays, " Such is the account given by Vitruvius of the origin of * Dorus muft have been, at lead, four hundred years before Solomon, if he reigned at Argos before the expedition of the Argonauts* 3 improvements ( ^9 ) improvements in the proportion of columns. Had im- provements, however, exifted in fuch early times, Homer *, who was greatly pofterior to them, would certainly have made mention of fomething of the kind ; but in all his writings he gives us no account of any thing like columns of ftone, but ufes a word which would rather incline us to think that his columns were nothing more than bare ports." This account looks as if there had been neither ftone co- lumns nor temples till after Homer's days. For if the architec- ture among the Greeks in thofe days confifted of bare pofts, we cannot fuppofe that thofe magnificent temples which they dedi- cated to their gods w r ere fo poor and plain; neither can we ima- gine that if there had been fuch fine temples in his time, that he would have left them unnoticed. It would feem as if the Greeks had borrowed their firft notions of temples to worfhip their gods in, and alfo their architecture to adorn them with, from that at Jerufalem. Agreeable to this view", the above quoted author fays : " It is remarkable that improvements in architecture did not take place in any nation till after, or about, the time that Jerufalem was taken by Nebuchadnezzar. The grandeft buildings amongft the Afiyrians feem to have owed their exiftence to this mo- * Homer was born above nine hundred years before the Chrifliian aera. R narch ; ( ) narch ; and it can fcarcely be imagined that he would not en- deavour to imitate the architecture of Solomon's temple, to which, by his conqueft of Jerufalem, he had full accefs*." Upon the whole then, I think it will agree better to the above fails, if we affirm that the Doric order had its name and improvements from the Dorians, who occupied the country of Doris, a Grecian diftridt, of which Dorus had formerly been king. The Ionic order fucceeded the Doric, according to antiquity, and was an improvement from it. It had its name from Ion, the Grecian country or diftrift where it was invented, and firft employed in the temple of Diana at Ephefus. By the accounts we have of this temple, architecture muft have arrived to a con- liderable degree of perfection in thefe times. This temple at Ephefus, the metropolis of Ion, was about four hundred and forty feet long, and two hundred and thirty feet wide ; was fup- ported by one hundred and twenty-feven pillars of the above order, and about fixty-two feet high. It was built in marble, and decorated with the fineft ornaments ; and, as the hiftory fays, exhibited the moft perfect model of this order. * According to Prideaux, Nebuchadnezzar took Jerufalem fix hundred and five years before Chrift. The ( I3i ) The Corinthian comes next in order, which has its name from Corinth, a city or chief town in Achaia, a Grecian diftridt or territory. In this city the Corinthian order had its origin. The account which Vitruvius* gives of it is fomewhat curious and entertaining ; I fhall therefore tranferibe it. " The third," fays he, " which is called Corinthian, is in imi- tation of the delicacy of virgins ; for the limbs are formed more flender, and are more graceful in attire. The capital is reported to have been thus invented : — a Corinthian maid, being feized with a diforder, died ; after her interment, her nurfe collected, and difpofed in a balket, the toys which pleafed her when alive, carried it to the tomb, placed it on the top, and, that it might endure the longer in the open air, covered it with a tile. The balket chanced to be placed over the root of an acanthus, which being thus deprefled in the middle, the leaves and ftalks in the fpring feafon iflued outward, and grew round the fides of the balket ; and being preffed by the weight at the angles of the tile, were made to convolve at the extremities, like volutes. At that time Callimachus, who, for his ingenuity and excellence in the arts, was by the Athenians named Catatechnos +, happening to pafs by this tomb, took notice of the bafket, and being pleafed * Vitruvlus was an ancient Roman architect, who wrote a fyftem of architecture, it is thought, in die time of Titus, the eleventh Roman emperor, who reigned in the year 79, to whom he dedicates the work. f The firfl of artifts. R 2 with ( 132 ) with the delicacy of the foliage growing around it, as well as the novelty of the form, made fome columns near Corinth ac- cording to this model, and from thence eftablifhed the fym- metry, and determined the proportions, of the Corinthian order." The Tufcan order is the fourth in point of antiquity, but in the arrangement of the five orders it is put firft, on account of its fimplicity and plainnefs. It had its origin in Tufcany, a place remarkable in Italy, which was firft inhabited by the an- cient Lydians out of Alia. Thefe people firft built temples of this order, and dedicated them to their gods in their new plan- tations. Vitruvius calls it the ruftic order, which is confiftent enough with what I formerly conjedlured, namely, that this order was the firft ftate of the Doric column in its moft antique form. And the circumftance of its being brought from Afia by the ancient Lydians, helps to confirm it. The Compofite is the laft. Its name denotes that it was compofed from the other regular orders. It is alfo called the Roman order, becaufe it was reduced to its proportional ftandard in that country. It ( 133 ) It docs not appear to be fo ancient as the days of Vitruvius, as he makes no mention of it. He fpeaks of various capitals that might be introduced on the Corinthian column, but does not name them. " There are," fays he, " alfo other kinds of ca- pitals, called by various names, which are difpofed on the fame columns, and which have no proper fymmetry or relation to any order of columns that can be named differently ; but they are all derived and transferred from the Corinthian*." Thefe words, and the liberty they convey in favour of the compofition of varieties of capitals to the Corinthian column, it may be prefumed, gave rife to the compofition of this order, which, in any other refpeCt but the capital, is nearly the fame with the Corinthian. Some architects, however, do not incline to fpeak well of it, becaufe it appears to have been picked and culled from all the other orders, and is fometimes badly ar- ranged, on account of the liberty both taken and granted in this fpecies of architecture. However, in my opinion, it forms a very beautiful appearance when rightly managed. The original inventor of the compofite order is thought to have been one Serlio. Having now faid as much on the antiquity and origin of the five orders, as is neceffary to give a workman a proper view * See Newton's Tranflation of Vitruvms. of ( 134 ) of the fubje£t, I fhall now proceed to defcribe the proportions and chara&er of each diftinft order, and likewife explain the names of each moulding. Of the Tufcan Order. See Plate VIII. The Tufcan order is the moll limple of any of the orders. It is alfo diftinguifhable from the other, on account of its ftrong and maflive appearance. On which account, in the figurative ftyle, it has obtained the name of the ruftic order ; and in con- formity to this character it is generally employed in farm- houfes, ftables, and other buildings in the like fituations. It is, however, fometimes ufed in grander buildings, where orna- ments are not required, but where ftrength is the principal objedt. The proportion of the Tufcan column, with its pedeftal and entablature, is as follows : Divide the whole height, for the complete column, into five, as the figure fhows. Take one of thefe parts for the pe- deftal as at i, whence the line is directed that determines the height of the pedeftal. From this line divide the whole height again into five equal parts, as the fecond upright fcale fhows. 8 Take N 1 ( 135 ) Take one of thefe parts for the whole entablature, and the re- maining four is the height of the column, including its bafe and capital. Divide the height affigned for the column into feven equal parts, as is fliown on the third upright fcale. Take one of thofe feven parts for the inferior or lower diameter of the column, not including the projections of the bafe, but limply confined to what is commonly called the lhaft, or cylin- drical part of the column. Take half of the inferior diameter, and give it for the height of the bafe, and alfo for the height of the capital, not including the aftragal at the neck. Proceed next to draw a module, by which to determine the fmaller parts of the column with the heights and projections of its members, as fpecified by the upright and horizontal numbers oppofite to each member on the large fcale. Draw a right line at pleafure. Lay, on this line, a fpace equal to one diameter. Divide it into fix equal parts, and draw perpendiculars from each divifion indefinitely. Lay on five equal divifions on any of the perpendicular lines, and draw parallels through each. Draw then two oblique lines, meeting in a point at half of the firft divifion 10, which fpace will then be divided into ten, at the numbers i, 2, 3, 4, 5, 8cc. fo that any number of minutes up to fixty may be accurately taken from this fcale. I have ( 136 ) I have alfo fliown a module at the bottom of the larger pe- deftal, which is equal to two of the fmall modules, from which all the minutes are taken and placed as beforementioned, as the Plate of itfelf will make fufficiently clear by infpection. A module is confidered by fome as only half a diameter, but others extend it to a whole diameter ; which laft I have adopted, as being the moft fimple and entire, and therefore more eafily remembered by workmen. Vitruvius ufes the large module, reckoning the propor- tions of the column by the thicknefs of the lower diameter of its fliaft. And I do not fee but it anfwers as nearly to the different parts of a column as the femidiameter does, or as that of twenty minutes, which has been contrived by fome. The projection of each member is alfo denoted by aliquot, or equal parts ; and each part is equal to a minute taken from the fcale ; fo that if the reader fhould find any little inaccuracies in the aliquot parts, which it is almofl impoffible to avoid in fuch fmall fcales, he may correal thefe by the numbers. And obferve, that the cornice of the pedeftal projects Hi minutes, which is the whole fum of the projection of each member, de- noted by 2, 4, 3, 2|, and which amount to nl. The bafe of the pedeftal projects the fame. Its fillet is two parts; the ogee, or cyma-recta, feven and an half; and the fquare tw r o ; which is in all eleven and an half. The bafe of the column projects ten ; the ( 137 ) The conge, or apophyge, four ; and the torus fix. The upper conge of the neck of the capital three, and its aftragal one and an half. The capital, in all, projects twelve minutes; the firft fillet two, the ovalo feven, the abacuo one before it, and the upper fillet two. The whole projection of the architrave is five, the upper facia one and an half, and its fillet projects three and an half. The whole cornice projects forty-five minutes, and its height is equal to its projection. Of the Diminution of Columns. Some diminifli columns by a right line drawn from the inferior to the fuperior diameter ; but this is very jejune and infipid, becaufe when columns are finifhed ftridtly in this mode, they appear too flender in the middle, and lofe that graceful effect which an eafy curve line produces. It appears that fome of the ancients diminiflied the fhafts of their columns by a curve line one third from the bafe, as in Plate VIII. whilft others of them carried this point to an ex- treme, by drawing a regular curve line from the inferior to the fuperior diameter, producing a diameter in the middle of the fhaft larger than that at the bottom. This notion has been S charged ( 138 ) charged upon Vitruvius, becaufe he fpeaks of " an augmenta- tion that fliould be made in the middle of columns ;" but Mr, Newton, in a note in his book of Vitruvius, has cleared him of this charge. See page 53. And Sir William Chambers takes notice of an author who fuppofes the " addition mentioned by Vitruvius to fignify nothing but the increafe towards the middle of the column, occafioned by changing the ftraight line which at firft * was in ufe, for a curve." " This fuppofition," fays Sir William, " is extremely juft, and founded on what is obferved in the works of antiquity; where there is no inftance of columns thicker in the middle than at the bottom, though all have the fwelling hinted at by Vitruvius, all of them being terminated by curves." The method that this gentleman recommends as moft pro- per for diminifhing columns, is by an inftrument which Nico- medes invented to defcribe the firft conchoid ; for this, being applied at the bottom of the fhaft, performs at one fweep both the fwelling and the diminution ; giving fuch a graceful form to the column, that it is univerfally allowed to be the moft per- fect practice hitherto difcovered. -•■ This means, before the orders of architecture had received much improvement. This ( 139 ) This , method has been adopted in the diminution of the Ionic, Compofite, and Corinthian columns in Plate X, XI, and XII ; becaufe thefe are the moft delicate orders. But, in the Tufcan and Doric fhafts, I have followed the common method ; becaufe thefe robuft columns will admit of more apparent, or more fudden diminution than the other three. The moft common method is as follows. See Plate VIII. r\rrf\ Jk\C\ fit / { I f fYf f ' } ^Ifl f r f"}ffr I* c * e 2 * iT "TOl ■* 't frQ T r P 'i ">» "fP Divide the fliaft into three equal parts, and draw a diameter at the firft part. On this diameter defcribe a femicircle, and di- vide the femidiameter into five equal parts. From the fourth divifion raife a perpendicular line which determines the upper diameter and cuts off a portion of the femicircle, which is to be divided into four on the curve. Laftly, divide the upper two thirds of the lhaft into four equal parts, anfwerable to the four equal parts on the curve ; and from each of thefe divifions, or parts, on the curve, draw right lines to the correfponding divi- fions on the fhaft, by which, four points will be found through which the diminifhing curve line is to pafs, and, if accurately drawn, will appear fmooth. Obferve, this diminution brings the column, at its fuperior diameter, to forty-eight minutes; S 2 but ( 140 ) but in all the other orders there are uniformly fifty minutes allowed. Some architects, however, contend for various degrees of diminution, according to the chara&er of each column. They aflign to the Tufcan one fourth, to the Doric one fifth, to the Ionic one fixth, to the Compofite and Corinthian one feventh, of the inferior or largeft diameter. This makes no difference, however, in the method of di- minution above taught ; for if the Tufcan be diminifhed one fourth, then divide a fernidiameter into four parts, and take one of thofe for the diminution on each fide, and proceed as before; fo alfo of the other. I fliall now quote a few words from Sir William Chambers on this fubjeft, by which the reader, if he pleafe, may form his judgment. He fays, " In the remains of antiquity, the quantity of diminution is various; but feldom lefs than one eighth of the inferior diameter of the column, nor more than one fixth of it. The laft of thefe is by Vitruvius efteemed the moft perfect. Vignoia has employed it in four of his orders, as I have done in all of them, there being no reafon for dimi- nishing the Tufcan column more in proportion to its diameter than any of the reft." How ( i4i ) How to diminijh any Column, from the inferior to the fuperior Di- ameter, by means of an Elliptic Curve not exceeding in its Swell the inferior Diameter. Fig. i; Plate XIIL is Vignola's method of diminilhing a co- lumn, the principles of which I have taken from Sir William Chambers' Treatife on Architecture, but have here defcribed it in my own way, as follows. Determine the height of the fliaft as at c d, and draw a line for its axis. Next, draw b a at pleafure, and at right angles with the axis. Let b c be half the inferior, and nd half the fuperior diameter. Take be half the under diameter, and with the compaffes place it from n, the extreme point of the upper diameter, to any point where it falls on the axis of the column, as at o. From n draw a line through o, and proceed till it cut the bafe line b a at a. Draw a line at pleafure from b, the extreme point of the inferior diameter, parallel with c d ; and divide this line into a number of equal parts, as 2, 4, 6, 8, &c. From a, the center, draw a ray or right line to each of thefe divifions, which will pafs ob- liquely through the axis, in proportion to their diftance from the inferior diameter be. Take then be, half the diameter, and place it from 1 to 2, from 3 to 4, and fo on of all the reft. Laftly, through each of thefe points draw a curve line, and the diminution ( i#* ) diminution of one fide of the column will be thus completed, as is fhewn by the dotted line on the right hand. To determine the other fide of the fhaft, nothing is wanted but to draw a fquare line acrofs the fhaft from each point, and place the dis- tance 2 .v to x y y and / 4 to 1 9, and fo on of the reft. Fig. 2. is Nicomedes' inftrument, which, as it is here de- fcribed, is intended to perform the fame diminution as has been above explained by lines. This inftrument is made in the manner of a fquare, with a ftay to keep it firm, as at R; bp is a dovetail groove cut in the center of the upright piece, as T ; b a is its bafe, in which alfo there is a dovetail groove as at u ; iw is a ruler, or trammel, which moves by the dovetail-piece y in the groove b p, by which the diminution is performed ; gb is a plain groove cut through the trammel, and g is a center pin which guides the trammel as i pafles from p to b ; when t is at it is evident that h will be at g the center pin, becaufe hi is equal g b ; alfo g i is equal oa in Fig. 1. and found in the fame manner. The interval, or fpace, between the center / and k at the end of the trammel, is equal to the inferior diameter bm, or be, Fig. 1. As, therefore, the center i palfes to b, the center % in which a pencil is fixed, cuts all the oblique lines jj tending to 35 in the fame points as at 8 ( 143 ) at 2, 4, 6, 8, &c. of Fig. i. and at the fame time draws a perfect curve, which I take to be of the elliptic kind. Laftly, in order to make this inftrument anfwer for fliafts of various fizes, the plain groove g h muft be lengthened each way to v and w at pleafure. The upright p b, and the bafe piece N a, muft alfo be proportionably lengthened ; and if the center pin g be fixed in a moveable piece to Aide each way in the groove and fixed at any certain place by a fcrew, as may be required, then it is evident that the inftrument may be fo .conftrudted as to anfwer columns of any dimenfion* Of the principal Parts of a Column, and the Names of each Member. The principal parts of an entire order are three; the pe- deftal, fliaft, and entablature. The pedeftal is the lowermoft part of an order, compre- hended between y and F, fee Plate VIII. The column is the middle part of it, including the whole fpace between the pe- deftal and top of the capital. The entablature is the uppermoft part ( 144 ) part of the whole, and contains every member between the top of the capital, and a. Thefe principal parts are again fubdivided as follows. The pedeftal contains the plinth F, dado B, and cornice A, z,y. The column includes a bafe, fhaft, and capital ; and the entablature, an architrave, freeze, and cornice. Thus, in every entire order there arethree principal parts, and each of thefe parts are again fubdivided into three fmaller parts, which in all make nine; the origin of whofe names i$ as follows : F, the plinth, is from vxivio^ plinthos, a brick, or flat fquare ftone, on which columns, in their moft antique ftate, are fup- pofed to have flood. B, the dado or dye, fo called becaufe it is of a cubic form. A, z, 7, the cornice, from the Latin coronh, a crowning ; becaufe the cornice is the finilhing, or crowning, of the pedeftal. Xy Wy Vy 2, ( 145 ) .v, w, Vj the bafe of the column, from #*er/r, bqfis^ a founda- tion or footing for the column. The fliaft is that long and ftraight part of a column com- prehended between the bafe and capital. Some derive it from nettr]^ jkapto, to dig, in the manner of a well, round and deep, whofe infide refembles the fhape of a pillar ; and fome from the long part of an arrow or fliaft *% q, />, o, n, nt, the capital, from >ts(poi\% kephale ; or caputs the head, which the capital is to the column. /, k, /, the architrave, fo called becaufe it is the chief fup- port to the whole entablature, from arcbos, chief or prin- cipal ; and the Latin trabs, a beam. the freeze, " from pfyov^ phibron, a border or fringe ; or which the ancients ufed to call ^, the lower fillet of the capital; and q> the freeze of ditto. r, the C 148 > r, the aftragal, from a^aya\o^ qftragalos, a bone of the heel; or the curvature of the heel, which this member refembles. s- y the upper fin&ure, which it is thought was anciently an- iron hoop, or ferule, to fecure the ends of the columns, when they were ufed without capitals or bafes.^ the upper conge or apophyge, front* otTroQvyvj, apopbuge r efcape; becaufe that part of the column appears to fly off. the lower ditto ; and v, the lower findlure. w, the torus, from T^r, toros y a cable, which this member refembles. x, the plinth of the bafer jy, the fillet ; and ^ the corona, as before. A, the cyma-reverfa, or the cymatium inverted. D E, the bafe of the plinth, whofe members are named the fame as thofe of the like fliape already defcribed. In I'ully/itd a j die Act directs, T Jhemlcn. Z>ec, 6. ( T 49 ) In every other column fimilar members have the fame name, and therefore I fliall not repeat them over under the other columns. But as there are fome members in the fucceed- ing orders which differ in charadter and fliape from thofe that have been mentioned already, I fhall here point them out, to prevent future trouble, and to keep this part of the fubjedt of architecture together. The Doric, Plate IX. for inffance, has a fcotia marked A, from with the compafs foot at N, fweep NO. And laftly, on the center 12, with the compafs foot at O, fweep OP, which will; complete the volute three times round. Obferve, that the whole volute is compofed of twelve qua- drants of a circle, drawn from twelve centers, and gradually contracted in by means of the diagonal lines in the eye, fee Fig. 3. Therefore, as there are three complete turnings in the whole convolution, each of thefe turnings - is made, up of four qua- drants. 4 How ( 157 ) How to graduate the Lift or Fillet of the Volute. Make the breadth of the fillet at A equal to two minutes; or, according to fome, one and feven eighths, or one and two thirds. Conftrudt a triangle, as at Fig. 5, whofe fides AP, VP, fhall be equal to the length of the cathetus, or upright line AP, Fig. 4. Make A V, Fig. 5, equal to half the fide of the fquare in the eye of the volute, Fig. 4. Draw then the line L S, Fig. 5, at a diftanee from AV, equal to the breadth of the fillet at A, Fig. 4. Take the length L S from Fig. 5, and place it each way from S in the eye of the volute, or as from V to S in the large eye, Fig. 3. V S is divided into three equal parts, which are Ihewn by the dotted lines ; and where thefe dotted lines interfe£t with the diagonal lines in the fquare, they will find twelve new cen- ters, which will defcribe the diminution of the lift or fillet bv the fame procefs that was ufed in drawing the exterior contour or outline of the volute above explained. ')vij2 q1 lull •no/titocTf/io'j . shtfixfoi? bn£ ilputjiU t / t ? » For the other enrichments of the Ionic capital, fee the plan in Plate XII. and obferve, that over every flute in the fhaft is placed an ove, or egg, in the ovolo. of ( 158 ) Of the Character and general Proportions of the Compoflte Order. See Plate XII. This order is generally placed laft of the five, becaufe it was a compofition from them, and of the lateft invention. But, according to this reafoning, the Doric ihould be firft in order, becaufe it was the moft ancient ; however there are two rea- fons which have induced me to place the Compolite as the fourth. Firft, becaufe it is the fourth when orders are placed upon orders in large and magnificent buildings, where it is ob- fervable that the more maffive and plain columns are neareft the foundation, as firft the Tufcan, fecond the Doric, third the Ionic, fourth the Compolite, and laft the Corinthian. Second, becaufe it is the fourth in point of richnefs and delicacy, for as they decreafe in ftrength they increafe in richnefs of ornaments ; their elevation above the ground is therefore regulated both by degrees of ftrength and richnefs of compofition. But to give a proper fan&ion to this little novelty in the arrangement of the orders, it may be proper to quote fome great man of this opinion. Sir William Chambers* fays, " Moft authors give the * From whofe excellent Treatife on Architecture I have borrowed fome of the pro- portions which are found in my orders, as alfo from Mr. Richardfon's. laft ( m ) laft place to the Compofite order, as being the laft invented, and a compound, which of courfe ought to be preceded by all the fimples. I have followed Scamozzi's method ; his arrange- ment appearing to me the moft natural ; for his orders fucceed each other according to their degrees of ftrength, and in the progreflion that muft abfolutely be obferved whenever they are employed together." The proportions of the Compofite, and its enrichments and delicacy, being nearly the fame with that of the Corinthian order,, in the figurative ftyle it may be properly enough termed one of the virginal orders, and was therefore ufed in fome tem- ples of the female deities. It is, however, generally employed m triumphal arches^ for as the Romans compofed this from the Gnecian orders, fo they made ufe of it in thofe fituations to>exprefs fymbolically their conquefts over thofe nations. I have therefore, in con- formity to this, reprefented a trophy of war in the freeze, which I think would have a good effe£t placed over the center of each column, with other ornaments between them fuited to the cha- racter of this order. The Compofite may alfo be employed in monuments of fignal events, and in fuch buildings as are intended to per- 8 petuate ( ifo ) petuate the memory of the great anions of particular per- fons. The general proportions of this order are as follows ; The height of the entire order is divided into five, as ufual; one of which is appropriated for the height of the pedeftaL The remaining four is for the height of the column and en- tablature. Thefe four parts being again divided into fix, the upper one is afiigned for the height of the whole entablature, and the remaining five of thefe parts are for the height of the column, including the bafe and capital. The height of the column is divided into ten equal parts, one of which is for the inferior diameter. The bafe is thirty minutes, without the upper aftragal ; and the capital is feventy minutes high, adorned with the acanthus leaves, and volutes drawn by the fame me- thod as that of the Ionia The plan of the capital being drawn in the fame manner as that of the Corinthian, I fhall explain the particulars of it under that order. i . jL ) io io£no:j Jin tj /o bo )FAt[ ihsns boo$ £ ovnd bluo'H Miitd) I The foffit of the corona is divided into fquare compart- ments, cut out of the folid, decorated with rofes, &c. whofe re- lief rauft not projeil more than the borders which inclofe them. In rich compofitions the foffits of the modillions are alfo orna- mented, but their relief is not to exceed the horizontal furface, otherwife ( »fa ) otherwife it would greatly injure the effe£t of the modillion, and render the appearance of the profile of the entablature lefs pleafing. Of the CbaracJer and general Proportions of the Corinthian Order. See Plate XIL The Corinthian, or laft order, is certainly the moft rich and graceful in its appearance of any other. To fpeak in the figurative ftyle, it has all the delicacy of a female youth, and has therefore been termed the verginal column or order ; on which account it is employed in the apartments of young la- dies : but, for its richnefs and grandeur, it obtains a place in the palaces of kings, and the moft fuperb buildings. It is alfo ufed in public fquares, and all places of gaiety. The general proportions of this order are as follows : The whole height of the entire order is, as in all the others, divided into five, and one is given for the pedeftal. The re- maining four are then divided into fix, and one part is affigned X , to ( *8b 7 to the whole height of the entablature* The four parts which are left include the height of the column, with its bafe and ca- pital, and are divided into ten equal parts, one of which is given for the inferior diameter of the fhaft. The bafe is thirty mi- nutes high without the upper aftragal, and the capital is feventy minutes clear of the necking. The cornice is forty-eight mi- nutes in height, and its projection the fame. The foffit of the corona is worked in fquare compartments, as in the Compofite ; but the under fides of the modillions are ornamented with an olive leaf, the fame as in the capital. The abacus of the capital is fometimes fluted, and fometimes plain. The volutes fometimes rife higher than the under fide of the abacus, but the capital looks bell when thy are bounded by the: under furface of the abacus. The plan of the capital, and the pofition of the leaves as they appear on the round furface of the capital, are thus deter- mined. — Let de, in Fig. E, be equal to the inferior diameter of the column: fweep the arch eg at pleafure; then bifedt the arch by turning the fweeps do on the centers eg ■; draw do, the angular line of the capital. From the angular line place five minutes each way, as at m and n. Take m o, and place it from a too; then take the 4 whole { *6 3 ) xftiole fpace m o in the compafTes, and fweep an arch each way interfering at p. From the center />, fweep the front of the abacus mt 7 and fo of all the other fides of the capital. Take half the fuperior diameter of the fhaft, and with it fweep the arch ere; then extend the compaffes feven minutes further, and fweep the arch 7, which determines the projection of the firft row of leaves. Laftly, extend the compafTcs 10 fix minutes further, and fweep the arch 6, which will determine the fecond row of leaves. Divide the quadrant c r e into four equal parts, and draw the radii de, dr 9 de, which lines will de- termine the ftem of each leaf. From the centers e e 9 draw femi- circles, as they appear in the plan. From ere let fall perpendiculars, and the points 1,2,3,4, will determine the fituation of the leaves in the capital. There- fore take the diftances 1, 2, 3, 4, from the plan E, and place them on the capital, as 1, 2, 3, 4, each way from the center; and from thefe raife perpendiculars, which will be the apparent place of the ftem of each leaf. How the leaves are formed muft be evident by infpedlion, and therefore I fhall not enlarge far- ther on the fubjedl. How ( x*4 ) How to draw the Scotia Moulding. Fig. c is the fcotia, whofe height, without its fillets, mnft be divided into feven. On the fourth divifion draw a line r d parallel with the fillets. Take the upper three parts in the compafles and draw a circle. Make da equal dm, or four parts* From a, draw a rp indefinitely, cutting the aforefaid circle at p. Laftly, fix the compafs foot at a, and extending the other to />, fweep the arch pn y and the fcotia will be completed. The cyma-re£ta A is drawn from the fummits of equila- teral triangles thus : draw v w, and bife6t it at x. Extend the compafles x to and turn two arches at 3,, and their interfeo tion is the center for the convex part. In the fame manner y is the center for the concave part, which completes the moulding. How the cyma-inverfa B is drawn, muft be evident by in- ipedtion ; and with refpeil to any other kind of moulding, they are either confidered as quadrants, or as femicircles, or nearly fo : as the aftragals, torus, ovolo, conge, and cavetto. Obfervations ( 16s ) Obfervations on the Agreement of the Five Orders to each other. The height of every entire order is divided into five equal parts ; of which one is given for the height of the pedeftal, and the remaining four are for the column and entablature. In the Tufcan and Doric orders thefe four parts are divided into five, the uppermoft part of which is for the height of the entablature ; and the remaining four in the Tufcan, are divided into feven, and one is given for the diameter ; and in the Doric into eight, and one is afligned for the inferior diameter. In the Ionic, Compofite, and the Corinthian orders, the four remaining parts from the height of the pedeftal are divided into fix, the uppermoft of which is for the height of the en- tablature of each order ; and the remaining five, in the Ionic, are divided into nine, and one is for the inferior diameter ; but in the Compofite and Corinthian thefe five parts are divided into ten, and one is affigned for the lower diameter of each columns. fa ( 1 66 ) In every order the plinth of the pedeftal and its cornice arc equal in projection; that is, one perpendicular line ferves to determine the projection of both. In every order, without exception, the bafe of each co- lumn is thirty minutes, or half a diameter, high ; and, in the Tufcan, Doric, and Ionic, the height of the capitals is the fame; but in the Compofite and Corinthian their capitals are each of them feventy minutes. In every order the projection of the bafe at the bottom of the lhaft is ten minutes ; or, which is the fame thing, the di- ameter of each fhaft being divided into fix, one of them is fet forward for the proje&ion of the bafe* In every order its quantity of diminution may be the fame, which is ten minutes; but in my examples the Tufcan and Doric are rather more. Laftly, all the orders, except the Doric, have their cornices to project as much as they rife; but in the Doric the cornice projects one quarter part more than it rifes. Thefe ( i6y ) Thefe remarks, if retained in tfie memory, may help to facilitate the trouble which neceffarily attends in drawing the five orders. Befides, it is fometimes required of a workman to give fome anfwer to his employer refpeiting the general proportions of the orders; and, if he is not acquainted with as much of them as I have briefly laid down in the above ob- fervations, he muft of courfe look very foolifh in the eye of his querift, for he cannot then have recourfe to his book. But fur- ther, a workman who has profefledly gone through the five orders, by drawing them under the direction of fome matter, cuts but a poor figure in a converfation on the fubje£t of archi- tecture and proportion, when perhaps, after all, he is unable to recoiled: one fingle particular refpeiting them. Of the general Proportions of Frontifpieces adapted to the Five Orders. The Tufcan frontifpiece allows fix diameters from center to center of each column or pilafter, as defcribed in Plate V. and page 88. The ( i68 ) The 'Doric allows fix and a quarter, or one third. The Ionic fix and a half ; fome make it feven and a quarter. The Compofite feven; fome allow feven and a quarter. And the Corinthian feven diameters and thirty-five minutes ; or, as fome have it, eight diameters. Thefe different intercolumniations are nearly proportioned to the ftrength or delicacy of each order, fo that the aperture, or opening for the door of each frontifpiece, is much the fame in all the orders. For though the Tufcan order only allows fix diameters, yet fix of thefe are equal to fix and an half di- ameters of the Doric column. And the Corinthian, though it allows at leaft feven diameters for its intercolumniation, the opening for the door-way will not, at that rate, be quite equal to fix diameters of the Tufcan column. This fufficiently accounts for the different number of di- ameters affigned by architects for the door-ways or intercolumns of the frontifpieces adapted to each order. The proportion of doors is generally in height twice their breadth; but, in fome cafes, a little more height is re- ^uifite. The ( i«9 ) The width of the door is divided into four equal parts; one of which is for the diameter of the column, or breadth of the pilafter. Half a diameter is added to each fide of the column, for the import: or ground which receives the projections of the plinth and capitaL Half a diameter is alfo allowed above the door to the under- iide of the architrave, and one for the fub-plinth, or the fquare part on which the bafe refts. According to this proportion, from the top of the fub-plinth to the top of the column there will be feven diameters and an half; which will be within half a diameter of the full fize of the Doric column, according to the order ; but if there be a ftep up to the entrance of the door, this will increafe the column to its full height, which is eight diameters*. To the height of the column muft be added two diameters for the whole entablature above the capital : and for every other particular refpeCling the mouldings, the reader muft have re- courfe to the orders themfelves. General ( 170 ) General Dire&ions for drawing the Five Orders in Indian InL It is befl to procure wove paper, becaufe its fubftance will bear a better fliade, and its quality gives a more handfome ap- pearance to a drawing, than the more common fort. The paper fliould be regularly damped, and pafted round the edges, fo that when it dries it will become tight and even in its furface. Proceed then to draw a perpendicular line for the axis of the column, and on this line place the feveral heights required. Through each of thefe heights draw, by the pencil, lines at pleafure parallel to the bafe,. Next find the inferior diameter of the column, and after- wards the fuperior one. From the extremities of the fuperior diameter draw perpendicular lines upwards, and from the ex- treme points of the inferior diameter draw perpendicular lines downwards to the top of the pedeftal. From thefe lines place the projedtion of the bafe, and from the projedtion of the bafe each way, draw two other perpendicular lines down to the bafe of the plinth. Thus ( I7i ) Thus far the drawing is prepared for laying on the pro- jections of the feveral members which take their fpring from the above perpendicular lines, and when the mouldings are all drawn by the pencil, the ftrokes of the pencil fhould be ten- dered or made fainter by the Indian rubber, fo that the ftrokes of ink may be more clearly feen as they are drawn, and fo pre- vented from being too ftrong, which if they are, the drawing is totally fpoiled. If the drawing be on a large fcale, as thofe detached in the plates, the compafles may be fuccefsfully applied in drawing the curved members ; but if they are fmall, like the finifhed and entire orders in thofe plates, they muft be drawn by a fine pointed camel's hair pencil, guided by a fteady hand. The application of any kind of writing ink to the outlines of the drawing muft always be avoided, becaufe it neither agrees with the nature or colour of Indian ink. The writing ink not only makes an outline too harfh in appearance, but likewife deftroys the effedt of the Indian ink ; becaufe the water that is mixed with the Indian extradts the quality of the writing ink y and of courfe they blend together in one mafs, and the fhadow becomes partly blue and partly black, which deftroys the har- mony of the whole. Therefore mix good Indian ink by rub- bing it on a marble ftone, and let the ink ftand a few hours, Y-a till ( XT* ) till the grofler particles fettle to the bottom. Add a little water to a part of it, to make a light fhade with ; and with this light kind mark the outlines of the column, applying the hair pen- cil to the curved parts, and the brafs pen to thofe which are ftraight. After this procefs rub the drawing quite clean ; and ob- ferve this as a general maxim, that the fainter the outline the better, provided it can juft be difcerned. The next things to be confidered are light and fhadow, which are oppofite in themfelves ; but if difconne£led, no good effect can be produced in a drawing. Wherefore, where a ftrong light is fuppofed, there muft alfo be a ftrong fhadow agreeing with it ; and where the light is weak, the lhadow is lefs dark in proportion to it. Rays of light do not project fliadows contrary ways at the fame time. Therefore the point of light muft be fixed in the mind at leaft, if not on the paper, from whence the rays are directed in parallel lines to the object, which produce a fhadow on the contrary fide to that which the light comes from. Pro- ceed then to lay on a weak tint on that fide of the lhaft which is oppofite the light ; and the breadth of this tint muft be pro- portioned according as the light is fuppofed to come, either di- redtty ( 173 ) redtly on the front of the picture, or obliquely to it. If the light comes on the front, the tint is narrow ; but if obliquely on the pidture, the tint is broader, or comes farther on to the center of the fliaft in proportion to the degree of obliquity. After having* laid on the firft tint according to thefe principles, a fecond tint muft be applied in darker Indian ink ; but the dark tint muft not be carried plump to the outline of the dark fide, becaufe that would deftroy roundnefs ; for, in nature, all round or cylin- drical bodies have a reflected light ; but this reflected light is not equal in ftrength to the direct light, wherefore the firft or weak tint of Indian ink is fuppofed to be equal in degree to the refledted light, confequently a fmall portion of the firft tint is left on the edge of the fliaft, which is graduated or foftened into the fecond tint, which is ftrong, producing a mafs of fliade, blending itfelf in regular gradation with the firft tint towards the center of the fliaft. After the fecond tint is perfedtly dry, a third ftill ftronger lhould be applied, in order to complete a high-finifhed drawing; but care muft be taken to lay it on about the center of the fecond tint, and not broad, but plump, foftened a little off at the edges, which will produce a fufficient roundnefs, if rightly managed. If the fliaft is reprefented as fluted, its lhading will yet re- quire more management ; but the fame principles muft be ob- ferved. In managing the flutes, it will be proper to mark their boundaries, ( 174 ) boundaries firft with a nice brafs drawing-pen, filled with thin Indian ink, that it may diftribute and pafs eafily through the pen, leaving a very faint line on the light fide, fcarcely to be teen; but in ruling the dark fide the ink muft be laid on itronger, that the outhne of the flutes may not be totally loft when the fhade is laid on. After the firft tint of fhade is ap- plied, it will be requifite then to touch in the dark fides of the flutes. Thofe on the dark fide of the fhaft may be done by the hair pencil ; but if the drawing is on a fmall fcale, the brafs pen will do much better on the light fide ; becaufe, by drawing pa- rallel lines with that inftrument in imitation of graving ftrokes, it will produce a fhade in the flute more confonant, and in bet- ter tone with the light fide of the fhaft, than can be performed by the hair pencil. The flutes on the dark fide of the fhaft muft not be all black, for their concavity will reflect a dim light oppofite to their dark fide, upon the fame principles by which light is re- flected on convex furfaces. Laftly, when the flutings are thus handled, a fecond tint of Indian ink muft be laid on at the dark fide, by which the flutes and fillets muft be made to harmonize, and appear in one mafs of fhade, without deftroying their dif- tincflion. In general, the fecond tint is ftrong enough for fluted fliafts, becaufe the outlines for the flutes contribute towards a fhade themfelves. The ( m ) The mouldings muft next be confldered : and as thefe are in a different pofition from the ftiaft, confequently the light muft ftrike them differently. In the examples given, I have fuppofed the aperture, or point of light, above the top of the column ; which is a iitua- tion highly advantageous to the drawing, becaufe, upon this principle, there will be a regular ftrong fliadow under each co- vering member produdtive of a good effedt. Hence, in the Ionic, for inftance, the hollow, or upper part of the cyma-redta, has a ftrong fliade ; and the fwelling part is light in the center, bearing a fhade downwards as it recedes back* The corona is alfo light, becaufe the rays come full upon it ; but the cyma-reverfa, dentils, and ovolo, are all in fliadow, on account of the large projection of the corona, which fcreens them from the light. The left hand volute projedts a fliadow on the fliaft, and the curved top of each flute does the fame. The lower ends of the flutes are light, for the rays come full upon them ; but the upper part of the fcotia in the bafe bears a ftrong fliade, becaufe it is totally covered by the projedtion of the upper aftragal. The cornice of the pedeftal is nearly all in fliadow ; but the 4 bafe ( »76 ) bafe is nearly all light, for there is nothing to prevent the rays falling upon almoft every part of it. Thefe obfervations, with the exercife of a little tafte and; good fenfe, will, I prefume, enable the learner to accompliflx his attempt to fhade the five orders in fuch a manner as will do him credit. END OF THE FIRST PART*. PART THE CABINET-MAKER AND UPHOLSTERER'S D R A W I N G - B O O K. PART II. ON PRACTICAL PERSPECTIVE APPLIED TO THE ART OF REPRE- SENTING ALL KINDS OF FURNITURE IN DIFFERENT SITU- ATIONS : COMPREHENDING A REGULAR AND FAMILIAR TREATISE ON THIS USEFUL SCIENCE, DIGESTED AGREEABLY TO THE AUTHOR'S OWN EXPERIENCE IN THE ART FROM SOME YEARS PRACTICE, AND FROM OBSERVATIONS ON THE PRINCIPAL WRITERS ON THE SUBJECT; VIZ. DR. BROOK TAYLOR, DR. PRIESTLEY, MALTON, KIRBY, NOBLE, AND SOME OTHERS. INTRODUCTION. That the knowledge of perfpe&ive is highly ufeful to Cabinet- makers, Upholfterers, Chair-makers, Joiners, and other per- forms concerned with defigning, cannot be difputed on good grounds. And, though this is an indubitable pofition, yet many in the above profeffions are not fufficiently, if at all, ac- quainted with it. This defedt in their education, or negledt in their own application, neceffarily fubjedts fuch to confiderable Z difadvantages, ( i?8 ) difadvantages, both with refpedt to giving and receiving orders. A mafter cannot poffibly convey to the workmen fo juft an idea of a piece of furniture by a verbal defcription, as may be done by a good fketch, proportioned according to the laws of per- fpe£tive, and fituated fo as to give the moft general and clear view of the whole piece. Nor, on the other hand, can a work- man fo well underftand the meaning of a drawing, and what it is intended to reprefent, without fome knowledge of the art I am pleading for ; and confequently his progrefs in executing the work will be proportionably retarded, and, perhaps, not fo exa£lly finifhed at laft. On thefe accounts it is a matter's in- tereft to know perfpeilive himfelf, and to have men about him that underftand it. When this is the cafe, time is often gained, fluff fpared, and difgrace avoided ; fince it is matter of fail, that many alterations in pieces of work of every kind take place ; fometimes owing to bad fketches or drawings, and fometimes from want of underftanding a good delign when it is given to work by. There are fome mafters, indeed, who will fcarcely allow their foremen time to make any kind of fketch ; but, if I may offer my opinion on this head, I muft fay that fuch a me- thod of carrying on bulinefs neither reflects honour on the foreman, nor in the end turns out to any advantage to the mafter; but, on the other hand, frequently a confiderable lofs. Befides, ( 179 ) Befides, as it is the prefent mode to introduce much paint- ing in furniture, it is of great ufe to know perfpe&ive, in order to underftand when fuch painting has its proper effect, and to enable the director of work, whether mafter or foreman, to point out fuch improprieties as may efcape the notice of the painter: and which, if entirely overlooked, might prove injurious to the work, and offenfive to a cuftomer of tafte. To thefe we may mention another advantage that often arifes to a mafter from knowing this art ; fmce, by it, he may often fix the judgment and mind of a gentleman or ladyre- fpecling the piece of furniture they wifli for, by producing either a drawing that has been previouily made, or by being able, offhand, to furnifh their ideas with a good pencil fketch. In fhort, a good perfpedtive drawing may be fent to a gentle- man or lady in the country, with almoft as much confidence of fuccefs as if a model of the piece of work were fent. Laftly, if the reader confider himfelf a "gentleman, or as poffeffed of a liberal education, and at the fame time entirely unacquainted with this fine art, it will carry in it an air of con- tradiction ; becaufe perfpedtive is founded on geometrical and optical reafoning, and has therefore always been confidered as a branch of the mathematics and of a liberal education. Yet it is my intention not to treat the fubjedt mathematically, Z 2 becaufe ( i8o ) becaufe many have done it already in fuch a manner as far ex- ceeds any thing I can pretend to ; and becaufe it would not fuit workmen, for whom the following treatife is intended. If. however, any other above this fphere can reap any information . from it on account of its fimplicity, I fhall be happy to have ferved them ; but if he be above receiving inftrudtion through that channel or medium which is only intended to convey the knowledge of this art to workmen, the reader may confult fome of thofe authors referred to in the title, where he will fee problems, theorems, demonftrations, and corollaries enough to fill his leifure hours with, and to carry the fcience to any length he pleafes. However, to look into fome of thefe books would greatly difcourage many workmen, and even fome others of a higher clafs, who diflike the drudgery of perilling and com- paring an infinite number of references to a variety of fchemes, which are rather more calculated to fhew how far the fubjedt may be carried by mathematical Ikill, than to inform the reader of fuch principles as may be wanted in the practice of the art, or to give him a tolerable view of the theory on which the fcience is founded. And it may be affigned as one reafon why the fttbjedl of perfpeilive is fo little known amongft workmen, that it has been treated too mathematically. For, though geometry muft affift in ftating theories, and in making new and additional dis- coveries ( i8i ) coveries of the principles of the art, yet we muft not infer from hence that a workman cannot learn the practice of the art with- out being acquainted with that fcience. Malton fays the fame thing in the preface to his Treatife on Perfpettive. " Perhaps," he obferves, " the demonftrations of the laft (meaning the laft theorem of his fourth fedtion) may deter thofe who are not geometricians from examining it with that attention it requires ; let fuch remember, that, in order to pradtife perfpedtive, it is not abfolutely neceffary to be a geo- metrician, becaufe I pradtifed it long before I underftood geo- metry." In fine, I fliall only fay, that it has been my aim to put into the hand of the ingenious workman fuch a view of the fubjedt of perfpedtive, applied to as general a variety of cafes, as may enable him to get through with defigning any thing he meets with in the courfe of his bufinefs : and if any thing more than this be found in this treatife, the reader will fee more than what is promifed ; which may probably incline him to ac- quiefce with the author's fentiment, that it is better to do more than we fay, than fall fhort of what we have promifed. SECTION ( i8a ) SECTION L Of the Principles on which Perfpe&ive is founded^ and the Defini- tions of thofe forms neceffarily ufed on the Subje&. The principles on which the art is built are founded on the nature of our light, which invariably comprehends all obje6ls under fome angle of a lefs or greater degree, in proportion as the obje6l is at a greater or lefs diftance from the eye of the fpe&ator. Hence let A, Fig. i. Plate XIV. be confidered the human eye, which is nearly globular ; and P the pupil *, or that ex- tremely fmall point of the eye into which the rays of light if- fuing from every part of illumined objedts in right-lined direc- tions all converge. * The term pupil, in general, means a youth or minor under the tuition and manage- ment of a mafter or guardian ; but why it has been introduced into optics, and applied to the aperture or fmall opening of the eye which receives the light, is owing to the little image — or pupilla, a puppet — which is reflected in the eye, and feen by every one who looks fleadily on it, which is no other than the fpe&ator himfelf, whofe image in miniature is reflected on the cryftalline humour. Thus ( i83 ) Thus the rays BP and DP, iffuing from the Terpentine figure B D, are faid to converge, becaufe they unite in a point at P, the pupil ; and, after paffing through the pupil and con- tinuing in their diredl courfe, they diverge or fpread open as at nmr qv t, on that part of the eye called the retina *, by which an objedt is formed fimilar to the originals BD, EC, FG, and in magnitude according to their different diftances from the eye t . Therefore, as the firft obje£l BD is near eft to the pupil P, the points n t on the retina are moft extended, becaufe the angle DPB, under which the objedt BD is feen, is confiderably larger than thofe under which the objeils E C and FG are feen. And again, as the fame obje£t is removed back to EC, the rays are lefs extended on the retina as at m v ; but if the objedt be removed ftill further from the light P to F G, the rays will ftill diverge lefs, and confequently the obje£l painted on the re- tina will be proportionably fmaller as at r q. And thus, by re- moving the obje£t FC ftill further and further from the fight, it would be feen under a proportionably fmaller angle, until * Retina, from retc, a net; becaufe this part of the eye is a fine expanded membrane, fomewhat open like a net, and fpread over the bottom of the eye, on which are painted the pictures of all the objects we perceive. f The refraction of the rays of light occafioned by their paffing through the different mediums or humours of the eye, has nothing to do with perfpective ; it belongs to optics only, on which Fergufon's Lectures may be confulted, and others on the fubject. rmirf it ( i84 ) it would at length vanifh into a point, and lofe its appear- ance. That the rays of light, by which we are made fenfible of objects, make their way to the organs of fight in right-lined di- rections, is evident from a moft limple experiment ; for, if the bore of a tube or pipe be as much curved as is equal to the di- ameter of the bore, nothing can be feen through it; or if one obje£t Handing before another of equal magnitude on the fame line, be viewed by a perfon Handing on that line, the laft will be hid, provided they both Hand upright. I limply mean, if the fhafts of two columns of equal diameters were placed up- right, and a fpe£tator were Handing upright on a line paffing through the centers of each fliaft, the lafl one could not be feen; but if vifion, or the faculty of feeing, were performed by rays of light in curved directions, perhaps this would alter the cafe, but not for the better, as I am certain that the conHru£tion of our eye, and the way in which we, at prefent, difcover objects, are the perfect productions of Infinite Wifdom. From what has been faid and referred to in the figure, I prefume that the reader is not altogether ignorant of thefe two things : firfl, that all objects appear to the fpe£tator proportion- ably lefs the further they are removed from the eye; and, fecond, that the rays of light coming from every part of il- 8 lumined ( m ) himined objeCts operate on the eye in right-lined directions. Thefe two propofitions being admitted as certain truths, two very considerable points in perfpeCtive will hereby be gained. Firft, that in the reprefentations of objeCts originally of the fame dimenfions, thofe which are furtheft from the front of the piClure muft be leaft, in proportion to the fuppofed or real dif- tance of the Spectator's eye from the objeCt : and fecond, that a right line from the top and bottom of the front objeCts, ter- minating in a point on the horizon, will determine the heights of all thofe back objeCts which are originally of an equal height with thofe on the front. Hence, if a range of columns be reprefented on a picture, a right-line from the top and bottom of the firft column to fome point in the picture, will determine the heights of all thofe be- hind. Experience will convince us of the truth of this : for if we place ourfelves at a diftance from a ftraight row of columns, ftanding a little to one fide, and looking attentively from the firft to the laft column, we ftiall then fee that the pillars will appear to diminifh backward in the form of a triangle ; or, in other words, the tops and bottoms of each column will feem to tend to one point. The feme may be obferved by Handing clofe to a long brick wall, and ranging the eye along the joints of the bricks; we A a fhall ( i86 ) fliall fee each joint feemingly terminating into one point. Thofe joints below the eye will appear to rife up, and thofe above it will feem to lower ; and if the length of the wall were continued as far as we could fee, the joints would apparently unite in one point. Thefe limple experiments cannot be accounted for upon any other principle than that which 1 have already advanced on the nature of viiion; namely, that all objects, as they recede from the eye, are feen under a fmaller angle in proportion to the diftance of the obje£l from the eye. This proportion holds good, not only as it relates to the heights of objects, but alfo to their breadth and thicknefs, for thefe are diminifhed or con- tracted by the fame rules, founded on the nature of our light. Nor are thefe remarks to be reftri&ed to fuch objects as ftand upright on the ground, for thofe which are horizontal in their pofition, or which are lying in various lituations on the ground, are all fubjeil to the fame laws of diminution. But it muft here be obferved, that the various pofitions of objects give birth to moft of thofe imaginary planes which are introduced into, the fubjeil of perfpeftive ; for in thefe planes all the variety of objeils that we can conceive of, are fuppofed to be fituated, fome in the ground-plane, and others parallel to it, both above and below the horizon ; fome in upright, and fome in oblique or inclining planes. And this variety of planes fiiould be under- ftood ( 187 ) flood and carefully diftinguifhed by the learner, before he can make any good progrefs in the art, or know what he is about, when he begins to reprefent. Thefe planes are again bounded by fo many right lines, of which they are compofed ; and thefe lines have their names, anfwering to their intended ufe in the practice of perfpec- tive. Since, therefore, planes, lines, and points, comprehend the whole art of perfpeitive, it will be requifite to define- thefe in as clear a manner as poffible. The reader will, perhaps, ima- gine here, that I am drawing him into the ftudy of geometry, as an effential requifite to the practice of perfpective, and there- by contradicting what I have already advanced in the preface. If, indeed, to exercife our reafoning faculties, and to make ufe of a little common fenfe, be termed the ftudy or knowledge of geometry, I will aver that no man will ever learn perfpecftive without thefe. But, this every one knows ; that many can ex- ercife both good fenfe and reafon who never faw nor heard of Euclid. Befides, if the reader has attended to the firft part of this work, in which lines, fuperficies, and folids, have been touched on in a general way, he cannot be confidered as totally ignorant A a 2 of ( 188 ) of fome part of geometry which is ufeful to the knowledge of perfpedtive; however, as I have faid nothing of planes and their interferons, I fhall here explain them, fo far as they relate to the fubjedt of perfpe&ive. Of the Nature of Planes relative to the Subjedl of Perfpe&ive* A plane, ftri6tly fpeaking, is an even furface, neither con- cave nor convex, but which will agree with a ftraight ruler or line every where. A plane, in theory, may be confidered indefinitely, or de- finitely. When it is fuppofed to be indefinite, it admits of no bounding lines, but is imagined to be continued without limits. When it is defined, its boundaries are limited by lines, as A B, B O, O D, and D A. Fig. 2. In perfpeilive there are five planes principally in ufe, ac- cording to Dr. Brook Taylor's fyftem ; but the various circum- ftances of obje<5ts in the pidture frequently produce a variety of others, which, however, are not termed the elementary planes, as the above five may, but only accidental, depending on the circumftances of objects. Of ( &9 ) Of the Ground Plane. In the order of thefe planes I fhall confider the ground plane firft, being commonly a horizontal furface on which ori- ginal objects have, in general, their feats or foundations ; as i, 2, 3, 8, is the feat of the cafe of drawers on the ground plane AB,DO, Fig. 2. The Doctor terms the ground plane the original plane, " By which," he fays, " we mean the plane wherein is fituated any original point, line, or plain figure." I ihall, in general, however, ufe the term ground plane, as being more limple, ex- cept in cafes where no regard is paid to its being horizontal ; then, indeed, the term original plane muft be ufed, being more com- prehenfive, as it includes any pofition. Of the Perfpe&ive Plane* Second, the perfpe&ive plane, otherwife called the plane of the picture ; which, in general, is a plane perpendicular to that of the ground, as GR, HL, This plane is to perfpedlive what the retina is to optics; for the images of all original objedts are delineated on both* The ( 190 ) The perfpe&ive plane may be conlidered as fome tranfparent medium placed upright between the obje6t we view and our eye ; and as the rays of light coming from every point of il- lumined obje£ts converge, in right-lined directions, to a point on the pupil P, Fig. 2, a fe6tion of thofe rays, produced by this tranfparent medium or perfpedtive plane, is the perfpedtive reprefentation of the original objedt, be it what it may. Hence, let the learner place himfelf before a glafs window, which is, properly fpeaking, the perfpedtive plane to every ob- ject he looks at through it ; and as thofe objedts appear to him on the window, fuch is their perfpedtive reprefentations on the paper, board, or canvafs, we draw on. The appearance of ob- jects on a window may be found by gumming the glafs, which does not deftroy its tranfparency, but makes it capable of re- ceiving a mark ; and if the eye be kept perfectly fteady to one point in the window, and, with a pencil, the points or angles of a houfe, for inftance, be marked as they appear on the glafs ; and when this is done, if right lines be drawn to each point, thefe lines will form the perfpedtive of the houfe. Thus the plane GR, HL, may be confidered a piece of gummed glafs fixed upright on a table or ground A B, DO; and at P is the fpedtator's eye, viewing through the glafs the original object 1, 3, 5, 7. The right lines .iffiiing from every part of the objedt and converging at P, reprefent the rays of 8 light ( I9i ) light paffing through the tranfparent medium to the eye P. Now, as the original objedt is defcribed on the glafs by the di- rection of thefe rays, if the fpecftator, with his hand, mark the points 1,3 — 5,7,4—6, and afterwards join the points by right lines, this will be the exa£l perfpe£tive reprefentation of the original objecft. Simple experiments of this fort fliould be pra£Ufed, as I am perfuaded they are more calculated to teach the principles of the art than long and tedious theories *. Of the Horizontal Plane*. The horizontal plane, or plane of the horizon, is, in per- fpedtive, an imaginary plane paffing through the eye of the * An artift lately informed me, that a piece of ground glafs, unpolifhed, and oiled over with fweet oil, is the beft for this purpofe ; for the oil gives a degree of tranfparency to the glafs that admits of objects being feen through it, and its artificial roughnefs makes iteafyto draw on. If a fquare of glafs of this fort be put in a flight frame of wood, fixed upright on a plain board, and there be a fight-hole made in a piece of wood fixed perpendicular to the fquare of glafs ; and if the fight-hole be fixed from the glafs equal to the diftance P s, and to the height of the eye P N, then every thing which relates to Fig. 2, may be proved by ocular demonftration, provided the learner ufe this little inftrument according to the references made to this figure in the different heads of this fe&ion. fpedtator. ( i9 2 ) fpedlator, and being perfectly parallel with the ground plane, it cuts the upright pi6ture or perfpe&ive plane at right angles. Thus, in Fig. 2, Plate XIV. FH,LM, is the horizontal plane, whofe perpendicular height from the ground plane A B O D is the height of the eye at P ; hence P N is the perpen- dicular height of the eye, becaufe the line P N is perpendicular to both thefe planes. The horizontal plane FH, LM, being produced, it necef- farily cuts the perfpe6tive plane G H, L R, at right angles, and the interferon of thefe two even furfaces or planes with each other being a right line as HL; hence we have what is com- monly called the horizontal line H L ; or, more properly, the vanifhing line of a plane parallel with its original. And as the interferon of the horizontal with the perfpeitive plane pro- duces the vanifhing line H L, fo the interferon of the picture with the ground plane produces the bafe or ground line G R, All original objects, as they appear to come into the plane of the horizon, gradually vanifh into a point, and difappear. Hence the application and ufe of the term horizon in perspec- tive, which literally means the limits or boundaries of our fight, from " opfa borizo, I limit or bound." The further ob- jects are reprefented from the front of the picture, or from the ground ( 193 ) ground line GR, the nearer is their approach to this plane, and confequently their apparent magnitude will be proportionally lefs, as has been already demonftrated in page 183. For if the cafe of drawers, in Fig. 2. were removed confiderably further from the perfpedtive plane GRHL, it is evident that the rays 1 P, 3 P, 5 P, 7 P, &c. would not fubtend * fo large an angle on the plane of the pidture as they do at prefent : it is alfo manifeft that thefe rays will alfo rife higher on the pidture in proportion as the cafe of drawers or original objedt is removed back, confe- quently the image 1, 3, 5,7, of the drawers on the picture would approach nearer to the horizontal plane, until at length the image on the pidture would totally vanifh at s, the center of the pidture and height of the eye. To underftand this yet more clearly ; fuppofe the drawers to be brought forward clofe to the pidture, then the foot 1 would be at 10, and the foot 3 at 12, on the interfedtion or ground line GR, and the image of the original objedt would then appear as large on the pidture as the original itfelf ; for then the point 5 on the drawers would be at a on the pidture, and the point 7 at b ; but the whole image of the original, in this cafe, is lower on the pidture than before, and confequently farther from the horizontal plane, which was to be fhewn. * From fab and tendo, I ftrctch. The fubtenfe of an angle coincides with the chord of the arch. Thus the obje6t B D, Fig. i, fubtends an angle of 6o°, for the rays B P D P cut the arch in that proportion ; and therefore the object B D is faid to be feen under an angle of 6c°. B b From ( i94 ; From what has been faid, it is obvious that the whole fpace on the plane of the picture for delineating objects, is compre- hended between the ground line G R and the horizontal or va- nifhing line H L. No obje£t can with propriety have its feat on the picture below the line G R, for this line is the interferon of the ground plane with the plane of the pi6ture ; and there- fore, to reprefent the cafe of drawers lower than at 10 and 12 on the ground line G R, would lead us to fuppofe a new ground plane below the firft, and a new horizon to fuit it, otherwife the drawing would be unnatural and diftorted. On the other hand, no original obje<5t can have its feat in the perfpeftive plane higher than H L, for the line H L marks out the interferon of the horizontal with the perfpedtive plane; and as the plane of the horizon is generally the vanifhing plane of all original obje6ls fituated on the ground, their feats in the picture cannot be above the vanifhing line H L, without pro- ducing worfe effedts than in the other cafe juft mentioned. For if the images of all original objects, however large, vanifh into a point s in the vanifhing line H L, it would be prepofterous to fee a tall objedl feated on this line, or above it. Before I quit this head, it will be proper to obferve, that the horizontal plane, on which I have feemingly laid fo much ftrefs, does not poffefs any thing peculiar to itfelf, owing 8 to ( 195 ) to its being confidered a plane, perfectly level ; for all the vari- ous pofitions of vanifhing planes make no difference in theory, provided they are confidered as parallels to original planes. It is the pofition that thefe planes have to each other that is to be regarded. This was one principal difcovery which Dr. Brook Taylor made in his new fyftem of perfpedlive, and which has rendered his principles fo univerfal. In his book he fays, " He makes no difference between the plane of the horizon and any other plane whatfoever ; for fince planes, as planes, are alike in geometry, it is moft proper to confider them as fo, and to ex- plain their properties in general, leaving the artift himfelf to apply them." Yet it may be obferved, that we have a natural prejudice in favour of fomething peculiar to the horizontal va- nifhing plane ; becaufe, in nature, the laws of gravity fettle all folid bodies in a horizontal pofition : this being the cafe, we are accuftomed to view obje£ls in this form, and of courfe are re- quired to draw them fo ; therefore, in the pra&ice of perfpec- tive, the horizontal vanifhing plane is generally wanted ; but in principle and theory, the relation that one plane has to another is only to be regarded. Bb 2 Of ( ) Of the Directing Plane. The directing plane is imagined to be parallel with the pi£hire, whatever petition it is fuppofed to be in; and its diftance from the plane of the pi&ure is equal to the diftance of the eye of the fpe£tator ; therefore it is conlidered as a plane paffing through the eye, as the plane MFVU, Fig. 2. Hence, if any original line Z X be produced till it cut the directing plane M F V U, a line drawn from Y, where it interfe&s, to P, the place of the eye is termed the directing line of that original line ZX. And the reprefentation of any original line in the plane of the pidture is always parallel with its diredting line in the di- recting plane. Of the Vertical Plane. In perfpe&ive, the vertical plane is confidered as perpendi- cular both to the ground plane and the plane of the picSture ; confequently it cuts the other four at right angles. The plane PjQN, ( 197 ) PjQN, Fig, 2, is thus termed geometrically, becaufe it is in a diredion perpendicular to the horizon; but in perfpedtive it may be in any pofition, provided it be perpendicular to the original and perfpedtive planes, and at right angles with the other. The interfedtion of this plane with the pidture H L G R pro- duces the perpendicular line s Q, termed the vertical line of the pidture ; and the vertical plane being continued till it cut the diredting plane in the line P N, that line P N is the interfedtion of the vertical with the diredting plane ; and as s Q, the vertical line of the pidture, is parallel with P N the interfedtion of the vertical with the diredting plane : P N is therefore the diredting line of jQ, the vertical line of the pidture. Vertical planes have vertical vanifhing lines when the pic- ture is perpendicular to the ground, plane; in which cafe the vertical line sQ is continued to a length above and below the horizon H L, that will admit the neceffary vanifhing points. Of ( 198 ) Of the Vifual Plane. To thefe planes already defcribed may be added the radial or vifual planes. A vifual or radial plane, is fuch as paffes through the eye, and any original line whatever. A plane may be continued by any three points. The three points P X Y are the interferons of three right lines ; and, ac- cording to geometrical reafoning, when three fuch lines meet each other, as the lines P X, X Y, and Y P, they are all in the fame plane. This, among geometricians, is an axiom or felf- evident truth, and therefore needs no demonftration. The continuation of the plane P C Y X, which the triangle YPX is in, till it interfe£ls with the plane of the pi£ture, is therefore the vifual or radial plane of the original line Z X ; and the line i?i6, produced by the interferon of the vifual plane with the plane of the pi&ure, is termed the vifual line of the original Z X. As I have already obferved and proved that the appear- ance of objects on the retina is conveyed by rays of light flow- ( 199 ) ing from every point of any object to the eye in right-lined di- rections, fee page 184 ; let the right lines X P, Z P, be confidered as the rays of light coming from the original object Z X, and con- verging at P ; but thefe rays are cut or interfered by the plane of the picture GRHL at x z, therefore the line x z is the pro- jection of the original objedt ZX on the plane of the picture; or, in other words, it is the perfpedtive reprefentation of the original objedt ZX: for the reprefentation xz of the original line Z X is in the line v 16, which is the interferon of the vifual plane P C Y X with the plane of the pidture : and fince the line P C is the parallel of the original line Y X, where P C cuts the plane of the pidture at v 9 proves that the line v 16 is the true line of interferon produced by the vifual plane cutting the plane of the pidture. Hence the line v 16 is, in perfpedtive, termed the vifual line, from vifio^ I fee ; for the lines P Z, P X, are the rays of light by which vifion is performed, or by which we perceive objects, and as the interfedtion of thofe rays is in the line 1; 16, fo this line ^16, drawn on the pidture, is properly termed the vifual line of its origi- nal Z X, Of ( 20O ) Of the Lines in Perfpe&ive generated or produced by the fore- going Planes. I have already fpoken of thefe lines in the explanation of the feveral planes to which they are related ; but it will alfo be requilite to fum them up here, that the learner may have a more clear view of them from what has been faid. Firft. — The ground line GR, is a line produced by the in- terferon of the pi6ture or perfpe&i ve plane HLGR with the original plane ABDO. It may alfo be fimply termed the in- terferon of the pi£ture ; but fome choofe to call it the entering line. Second. — The vanilhing line HL, commonly called the horizontal line, is produced by the interferon of the vanilhing plane F H M L with the plane of the pi6lure HLGR. Third. — The parallel of the eye F M, is a line produced by the interferon of the vanifliing plane with the diredting plane UVFM ; and as this line is the interferon of a plane paffing through the eye always parallel to the pidlure, confequently FM ( 201 ) FM is always parallel to the vanifhing line HL, aud of equal height to it. Fourth.— The directing line U V is the interfe&ion of any original plane ABDO with the directing plane UVFM. Fifth. — The vertical line Qs palling through the center of "he picture s, is the interferon of the verticle or upright plane sf s Q with the plane of the picture ; and P N, the perpendi- height of the eye, is the interferon of the vertical with - diredting plane. Sixth.— The vifual line v 16, is produced by the interferon of the vifual plane P YC X with the plane of the pi&ure, and is therefore the indefinite reprefentation of the original Z X. Seventh.— The dire6tor of an original line. If any original ZX be produced till it cut the directing plane UVFM, a line P Y is termed the director of that original line ZX. Eighth.— The radial line % or parallel of any original line Z X. In whatever degree of obliquity the original line Z X in- terfedts the ground line GR, in the fame degree of inclination * Radial, from f rnbdos, or radius, a ray of light. c c will ( 202 ) will the radial P v cut the vaniftiing line H L \ for P v is parallel to the original line Z X, Of Points, in Perfpeflive, produced by the InterfeBions of the preceding Lines. As the interferons of planes with each other generate or produce lines, fo alfo lines meeting or cutting each other pro- duce points. Hence the following points in perfpedtive are produced by the interferons of the lines which we have now defined. Firft, the point of fight, or the place of the eye ; P is that point where the fpec/tator's eye ought to be placed in viewing the picture. Hence, if through the eye P a line perpendicular to the original plane be produced till it cut the parallel of the eye F M, their point of interferon is the point of light P. Second^ the center of the pi£lure. If from the point of jight P a line be drawn perpendicular to the picture, and be produced till it cut the vanifhing line HJL, their interferon will be the point s, or that point termed the center of the pic- ture ; ( 203 ) ture ; and the diftance between the point of fight P, and *} the center of the pidture, is called the diftance of the pidture ; and the line itfelf which meafures this diftance, may be termed the diredt radial. Third, the vanifhing point. If, from the point of fight P, a line be drawn parallel to any original Z X, and is produced till it cut the vanifhing line H L, their point of interferon v is the vanifhing point of the original line Z X ; becaufe, if the original line Z X were infinitely produced on the ground plane ABDO, its image ZX on the pidture would at length vanifli or difappear to the eye P in the point v. The line which mea- fures the diftance between v and P, is the diftance of that vanifh- ing points; and the line itfelf may be termed the oblique radial, becaufe its original Z X is oblique to the pidture. Fourth, the point of interferon. If the original line Z X be produced till it cut the ground line GR, that point 16 where the line G R is cut, is called the point of interferon : and if the original line Z X be ftill continued till it cut the diredling line U V, the point Y, where they interfedt, is termed the diredt- point of that original Z X. Laftly, The point of ftation. If from the place of the eye P, a line be drawn perpendicular to the ground plane C c 2 at ( 204 ) # at N, that point N is the point of ftation, or foot of the fpeo tator. I fhall conclude this fe£lion with advifing the reader to make himfelf well acquainted with the preceding planes, lines, and points, before he proceed further : which, if he do, it will enable him to read the fubfequent pages more eafily, and often prevent the trouble of referring to the plates. Add to this, it will make him underftand more readily the problems and ope- rations of both this and other publications on the fubjeih SECTION ( 20 5 ) SECTION IL 'The Affinity and Agreement between Optical Laws and the Prin- ciples of Perfpe&ive demonjlrated — And alfo of the Ufe of the three principal Elementary Planes in the Pra&ice of Draw- ing— fhowing, that all that is exhibited by the natural Pojitions of thefe Planes in Fig. 2, may be correfitly drawti on any even Surface without their Aid. — Of the various Pojitions of Lines and Planes to the Piflure, and of the Principles of Vanijhing Points agreeing therewith*. Of the Affinity of Optical Laws with the Principles of Perfpe&ive. In Sedtion I. page 183, it has been fhown that all obje£ls appear proportionably lefs as they are farther removed from the eye; and as the reader is now fuppofed to be acquainted with the planes, lines, points, and terms, which have been ex- plained in the preceding fedtion, I fhall proceed to fhow that the rules of perfpedtive agree with optical laws. Thus: \ ( 206 ) Thus : let G R, Fig. 4, be the ground line, and H L the ho- rizontal or vanifliing line, whofe height above the ground line is equal to that of the eye of the fpeftator ; s is the center of the picture, and s D the diftance of the fpedtator's eye from the ob- je£l b d. Draw db perpendicular and equal to BD, Fig. 1, and as much to the right hand of ; as D, in Fig. i 5 is to e. Then, in Fig. 4, draw the vifual lines d s and b s ; which lines are to deter- mine the heights of the two original objects, EC, FG, in Fig. 1. Then take the fpaces DC, CG 7 from Fig. 1, and transfer them to Fig. 4, from a to a, and from a to on the ground line G R. Draw the lines a 9 D, n D, cutting the vifual line d s in gc\ and laftly, from g and e on the vifual s d 9 raife perpendiculars to s b ; then will g 9 /, c, e be the perfpe£live reprefentations of G F and C B in Fig. 1. The analogy between the two figures will appear as fol- lows.— In optics, P, in Fig. 1, is the pupil, and Ve the diredt ra- dial or axis of the eye, and equal to the diftance of the firft obje£l D B from the eye. In perfpe£live, D, in Fig. 4, is the fame as P in optics, Fig. 1 ; and, in Fig. 4, i, the center of the picture in perfpe£tive, is the fame as e in Fig. 1. Therefore as P e in optics is the dire£t ray, and the diftance of the firft obje£l DB from the pupil P, fo s D, Fig. 4, in perfpe£tive, is the diftance of the fpeftator's eye from the picture. In optics, if the fecond objedl CE is removed twice as far from the eye P as the firft 8 objea ( 207 ) obje£t DB is, its image m v, on the retina, will be little more than half the length of the image / n of the firft obje£t DB on the retina; and, in perfpedtive, Fig. 4, the reprefentation c e of the fecond object C E, is exadtly half the length of the fir 11 objeft D B, as Fig. 4demonftrates, and which coincides with Fig. 1 ; for obferve, the rays of light PE, PC, coming from the fecond object to the pupil P, cut D B, their feftion, in the fame proportion as the vifual lines s d, s b 9 of Fig. 4, cut the perpendicular c e. Hence the fpace 2, 7, on D B, is equal to the reprefentation c e 9 Fig. 4 ; and in the fame manner the fpace 1, 8, where the rays of light from F G cut the picture D B, is equal to g,f, Fig. 4, the repre- fentation of G F, Fig. 1. Laftly, the reprefentations g f 9 ce, in Fig. 4, approach to the center s' 9 in the fame proportion as their originals GF, CE, in Fig. 1, approach to e, the center of the imaginary plane B D, which is fuppofed to cut the rays of light P C, P G, at 2, 1 ; for the fpace D 2 and 1 on Fig. 1, is the fame and equal to d, 2, 1, on Fig. 4; fo alfo is d, e, Fig. 4, to D Fig. 1. And hence it may be concluded, that the rays P C, P G, are to their fecftion D e 9 Fig. 1, as the vifual line d s is to its dividers or meafur- ing-lines D D n 9 Fig. 4. Before I conclude this head, it will be proper to obferve, that notwithftanding the general agreement bet een opt laws ( 208 ) laws and the rules of perfpe&ive, yet in one refpe£t there is a difference, for the perfpe&ive reprefentation of any object on a plane, is not the fame exadtly with the appearance of that object to the eye ; and therefore, in allufion to this differ- ence, I have, in the preceding page, already faid, " In optics, if the fecond object C E is removed twice as far from the eye P, Fig. i, as the firft objedt D B is, its image mv on the retina will be little more than half the length of the image t n of the firft obje£l DB; but the reprefentation 2,7, of CE on a plane D B, which is the fedtion of the rays P C, P E, is only half the length of the firft objedt DB, as the figure itfelf demon- ftrates." The reafon of this difference is owing to the eye being a fphere, but a pidture a level furface or plane ; for the rays P C, P D, cut the arch or fphere K L at 6, 5, in a different pro- portion to what they do on the plane B D, as is plain ; becaufe the fpace D 2, which is the reprefentatior^of the fpace D C on the plane B D, is greater than the fpace 6, 5, on the fphere K L ; which fpace 6, 5, is the appearance of the fpace D C to the eye ; but the fpace D 2 is its reprefentation on the pi<5hire. This difference, however, decreafes the further the objeft is removed from the eye, for then the rays do not cut the picture fo ob- liquely ; confequently the reprefentation of the original object on the plane of the picture is more natural, becaufe it has more of the appearance of that real objecSt to the eye. Thus : if the objedt EC be removed back to F G, the rays P G 5 PF, are lefs oblique ( 209 ) oblique to the picture B D ; and therefore the reprefentation i, 8, on the picture B D, is nearer to its true appearance o b on the arch K L, than the reprefentation 2, 7, is to its true appear- ance 5, 11, on that arch; but much more does this difference appear between the firft obje£l B D and its real appearance jy,6o, on the arch KL, which yet would be confideralply 1 . e if P were removed to Z. Hence the neceffity of choofing a proper diftance for the reprefentation s of objeits on a picture, that their appearance on the picture may be nearly the fame as the real obje£ts have to the eye. This will be touched on in its proper place. The difference then between the reprefentation of objects on a plane and their appearance to the eye, which is a circle, is as the difference of the tangent of the arch, which compre- hends the angle under which the obje£l is feen, is to the fub- tenfe of that angle. Thus: let DC be the object viewed at P, then will 6, 5, on the arch KL, be the opening or fubtenfe of the angle under which the obje£l D C is feen, which meafures four- teen degrees ; and D 2, the reprefentation of DC on the plane BD, is the tangent of that arch 6, 5, which comprehends the angle under which D C, the objedl, is feen. From ( aio ) From what has been faid on this fubjedt, it is evident that a perfect pidture of objects, as they appear to the human eye, cannot be delineated on a plane. It may be done on the furface of a fphere, when the eye of the fpe&ator is fup- pofed to be in its center ; for then every part of the pic- ture would be equidiftant from the eye, and every ray of light perpendicular to its own furface, as are the rays y P, ii, P, See. of the fphere KL. None of the rays, in this cafe, could cut the piiture obliquely, and confequently no diftor- tion would appear. But though this be the cafe, yet it will not afford any folid objection to the certainty of perfpe£tive rules adjufted to a plane ; for, by the help of light and fha- dow applied in different degrees of ftrength to objects' as they are more. or lefs remote from the eye, and by a judi- cious choice of the diflance, a picture may be drawn on an even furface, fo as to deceive the eye, and produce in the mind fimilar effe&s with the original or real objects. Of ( 211 ) Of the Ufe of the three principal * Elementary Planes in the Prac- tice of Drawing — alfo /hewing that every thing exhibited by the natural Pofitions of thefe Planes in Fig, 2, may be drawn on an even Surface without their Aid. It is not always underftood, even by thofe who have fome general notions of perfpe£tive, how it is that thefe planes anfwer to a level furface, fuch as the paper we draw on ; but, until there be fotoie conception of this, I will venture to fay that per- fpeftive can never be clearly comprehended. Therefore, that the reader may have a clear view of this matter, I fhall refer him to Fig. 5, Plate XV. in which are ftiewn limilar letters and nume- rals, correfponding with the fimilar planes, lines, and points of Fig. 2, as follows : The plane G O B R, Fig. 5, is the original or ground plane G O BR, Fig. 2; alfo the plane GHLR, Fig. 5, is the perfpec- * Elementary, " from the Latin elementum" the firft rudiments or principles of any fcience. Hence, in perfpe£tive, the ground plane, the plane of the picture, and the vanifliing plane, are confidered as the three chief elementary planes ; becaufe the firft principles of the art inuft be derived from them. The vertical, directing, and vifual planes, are alfo termed elementary, as has been fhewn in the firft fecYion, but not fo efTential in practice. D d 2 tive ( 212 ) tive plane denoted by the limilar letters in Fig. 2; and the plane FHLM, Fig. 5, is the vanifliing plane FHLM, Fig. 2. If, in Fig. 2, a line be extended from P to s, from s to Q, and from Q to U, that line will meafure the length of all the three planes in Fig. 5, as from P to U. Thus the ground plane, the perfpeftive plane, and vanifliing plane of Fig. 2, are fuppofed to be ftretched out of their natural pofition till they become an even furface, as in Fig. 5. The line G R, in Fig. 5, is therefore the interferon of the pi&ure with its original plane, as in Fig. 2; and the line H L, Fig. 5, is the vanifliing line, produced by the interferon of the vanifliing plane with the plane of the pic- ture, Fig. 2. The line F M, Fig. 5, is the parallel of the eye, denoted by thefe letters in Fig. 2. And laftly, Qs, Fig. 5, is the vertical line Q , the point where the line 8, P, cuts the vifual 10, j*, and the point 6 will determine the apparent breadth of the drawers ; in the feme manner as the rays P,4, P,6, cutting the vifuals a^s,b,s^ at ( 2i4 ) at the points 6, 4, determine the reprefentation of the top of the drawers 5, 7, 6, 4, at the correfponding points on the plane of the pidture, Fig. 2. By thefe operations it is manifeft that the reprefenta- tion of the drawers in Fig. 5, where the planes are ftretched out till they become an even furface, is the fame in all its parts as the image or reprefentation of the cafe of drawers on the plane of the pi£ture Fig. 2, where all the planes are in their natural pofitions. This would follow from a procefs of geometrical reafoning ; but, perhaps, it would be too tedious to the reader, and a deviation from the profeffed plan of this treatife; and, therefore, I fhall only recommend to him, to apply the com- pares to each reprefentation in the different figures, by which he will perceive the equality of parts in both ; and, if to this be added a little reflection on the preceding operations, I have not the leaft doubt of its being underftood. Of ( 2IS ) Of the various Po/itions of Lines and Planes to the Picture, and to the Ground Plane — alfo of their Reprefentation on the Pic- ture agreeing therewith, and of their various Modes of Va- nifhing. The original line ZX, in Fig. 2, is oblique to the pidture, and is therefore treated in a diverfe manner from the lines in the cheft of drawers, which are all either parallel and perpen- dicular to the pidture, or parallel to the ground plane and per- pendicular to it. Cafe 1. — When any line r, 3, Fig. 2, is parallel to the pic- ture and to the ground line G R, its reprefentation is parallel alfo. This is felf-evident by infpedting the figure. Cafe 2. — Lines in the aforefaid pofitions can have no va- nifhing line or point in the pidture, becaufe if infinitely pro- duced would never cut it ; that is, the lines 1, 3, and GR, Fig. 2, would never meet in a point, however far produced, for lines truly parallel can never cut each other. Cafe 3. — The reprefentations of lines originally parallel to each other and to the pidture, are parallel to one another. C 216 ) on the pidlure. Thus: the lines 1,3,5,7,4,6, Fig. 2, are all pa- rallel to each other and to the picture ; therefore their repre- fentations 1,3,5,7,4,6, on the pi£ture, are all parallel to one another, as is felf-evident by comparing thefe with their cor- refponding lines in Fig. 5. Cafe 4. — If any original line 1, 5, Fig. 2, be perpendicular to the ground plane, its reprefentation will be perpendicular to the ground line G R ; wherefore the reprefentation of the ori- ginal 3, 7, or any other in the like pofition, fituated any where on the ground plane, is perpendicular to the ground line GR. Hence the correfpondent lines 3, 7, 1, 5, Fig. 5, are drawn per- pendicular to G R, the ground line. From the above theory it may be concluded, that the re- prefentation of a geometrical fquare or parallelogram % is a ge- ometrical fquare or parallelogram, if it be fituated in a plane parallel to the piilure. Hence IK,LM, Fig. 6, is the true re- prefentation of the original fquare AD,BC, which is in this pofition. Cafe 5. — All lines perpendicular to the pi6lure, have their vanifhing points in the center of the pi£ture. * See its definition in page 44, and its figure Plate II. The ( 217 ) The lines 5, 4, 7, 6, of the ends of the drawers, are perpen- dicular to the picture HLGR ; confequently their reprefenta- tions 5, 4, 7, 6, on the pi£ture, appear to terminate to a point at jt, the center of the pifture. Wherefore, in reprefenting the top of the chefl of drawers at Fig. 5, b a is made equal to the length 5, 7, Fig. 2; and from ba, Fig. 5, lines are drawn to the center s. Hence the reprefentation of a geometrical fquare, fituated in any plane perpendicular to the picture, is a trapezoid, as I K, L M, Fig. 6 ; that is, two of its fides, I K, M L, are parallel, and the other two, K L, I M, not fo *. In whatever pofition an original plane may be in with re- fpeil to the ground plane, if it be but perpendicular to the picture, the reprefentation of a geometrical fquare in that plane will ftill be a trapezoid. If the planes be above or below the horizon, its appearance will be of that figure. Thus, in Fig. 3, <2, o,/>, is the reprefentation of a fquare fituated in the ground plane, which is certainly perpendicular to the picture, if the pi£lure be perpendicular to the ground ; t as N a fe£tion of the pidture, is upright to qb, one of the fides of the fquare : c i is alfo the reprefentation of a fquare, fituate in a plane raifed above the * See its definition page 44, and its figure Plate \\, E e grouiv ( 2i3 ) ground plane, but parallel with it, and therefore perpendicular to the picture in this cafe ; alfo ef is the reprefentation of the fame fquare, lituate in the plane of the horizon, which is a plane equal to the height of the eye, as the plane FMHL, Fig. 2. Wherefore in this plane the fquare does not appear, for it van ifhes into one right line, as e 2.- But if thicknefs be attri- buted to the fquare, as denoted by the double line, then, by the help of fhadow, two of its fides may be feen, as e% 1,2; but obferve, both the fides are in one right line. The fquares gh, Ik, are in planes above the horizon, ele- vated nearly as much as the other two ab, ci, are below it; their appearances are therefore trapezoids of nearly the fame dimenfions. And it is alfo evident, fince all thefe fquares are fituate in planes perpendicular to the pidture whether above or below the horizon, they muft have their vanifhing point in the center of the picture s\ and, as they are all parallel to the ground plane, their common vanifhing line will be H L. Cafe 6. — If a geometrical fquare be fituated in a plane in- clined in any angle to the ground plane, whether it be above or belo w the horizon, provided the plane be confidered perpendicular to the picture, its reprefentation will be, as before, a trapezoid ; and likewife its vanifhing point will be in the center of the pic- ture. Thus, in Fig. 8, No. 1, ADBC is the reprefentation of a geometrical fquare in a plane A E P O, inclined to the ground plane / ( 2I 9 ) plane equal to the angle n AT). Now it is evident, that the fquare will incline to any angle, by fuppofing it to revolve on its center A C in the arch u n k 5 for the fide D B of the fquare may be preffed to t k or 0 u, or to any point in thefe arches, without altering its pofition to G R, the ground line or fecSiion of the picture ; therefore, wherever the fide of the fquare D B is in thefe arches, it will ftill vanifli to x, the center of the pic- ture; and its appearance will be a trapezoid: for uo, DB, kt^ are all parallel among themfelves, and to rs> which is perpen- dicular to the picture. For the fame reafons the other fquares above the horizon, though inclined to the ground in different de- grees, and in different directions, have the fame vanifhing point. Cafe 7. — All lines oblique to the picture, but parallel to the ground plane, have their vanifhing points fomewhere in the horizontal line H L, Fig. 2 ; but not in the center of the picture, as in Cafe 6, when the line is perpendicular to the picture. Alfo if oblique lines are parallel to each other, they all have the fame vanifhing point. The original line 2 X, in Fig. 2, is ob- lique to the picture, and its vanifhing point is at v in the va- nifhing line H L, not at si the center of the picture ; for a line drawn from the eye P, and produced till it cut the picture at v 9 in a parallel direction to Z X, is the vanifhing point of that ori- ginal line Z X. Wherefore, in Fig. 5, where the elementary planes are ftretched out to an even furface, draw the original E e 2 ZX ( 220 ) ZX inclined to GR, in the angle which it is fuppofedto be in to the picture in Fig. 2. Produce X Z till it cut G R at 14 in Fig. 5 ; then lay the diftance of the eye from the picture on the vertical line at P, and from P draw Pv parallel to ZX; then will v be the true vanifhing point to the line ZX, upon the fame prin- ciples that in Fig. 2, is the vanifhing point to ZX in that figure. If a number of lines oblique to the pidture be parallel to each other, they will all have the fame vanifhing point ; for the fame reafon as a number of lines perpendicular to the picSture have but one vanifhing point in the center. Therefore, in Fig. 9, Plate XVI. the geometrical fqiaare 1, 2, 3, 4, having its fides ob- lique to the pidture, the fides which are parallel to each other are drawn to one vanifhing point. The fides db, ca y are originally parallel to each other, for they are the reprefentations of 2, 3, 1, 4, of the original fquare, wherefore they vanifh into one point at v. In like manner, and for the fame reafon, the fides b a, dc, vanifh at V. It is evident then, that the reprefentation of a fquare, having its fides oblique to the pidlure, is a tra- pezium * ; that is, none of the fides are parallel to each other. * See its figure Plate II. and its definition page 45. Cafe r^P— — = xii V C 221 ) Cafe 8, — When a fquare is fituated in a plane perpendicular to the ground, hut oblique to the pidture, only two of its fides will vanifh to a point, as BC, AD, No. 2. The other fides, AB, D C, can have no vanilhing point ; becaufe they are perpendi- cular to the ground, and parallel to the pidture. See Cafe 2, page 215. Its reprefentation is therefore a trapezoid. And becaufe the fquare is not perpendicular to the pidture, its vanifhing point is not in the center but in fome other point v in the horizon, according to the angle which the original fquare makes with the pidture, or with its interferon. Thus M A i is the angle which the fquare AB, DC, makes with the interferon, or ground line G R ; or, in other words, it is the original pofition which the fquare ftands in to the picture. Hence vd being parallel to M A, it forms the fame angle to the vanifhing line H L ; and being drawn in this direction from the place of the eye d, and produced till it cut H L at v, confequently v is its vanifhing point. Cafe 9.— If a fquare be fituated in a plane inclined to the ground plane, and its interferon with the pidture be parallel to the inter fedtion of the ground plane with the pidture, as AF, No. 3, then the vanifhing line of that plane will be parallel to the ground line G R ; and two of its fides, A N, F O, may be confidered as perpendicvilar to the pidture ; but the other two fides, ( 222 ) fides, A F, N O, are really parallel, and therefore have no vanifli- ing point in the vanifliing line HL See Cafe 2, in page 215. The fides A N, F O, are confidered perpendicular to the pi£hire ; becaufe, it is evident, that the fquare may be fuppofed to revolve on the fide AF, and be preffed or moved to 8, 10; which fhow the angles of the fame fquare in a plane ftridtly perpendicular to the picture, and therefore its fides 11, 8, 12, io, have their vanifliing point in the center s. See Cafe 4, in page 216. Wherefore, as the fquare may revolve on A F, as a table top hinged at the front, and rifing to any angle from its frame, its vanifliing point will rife on the vertical line j* d, in proportion to that angle. Hence S is the true vanifliing point of the fquare A F, N O, making the angle F A 6 with the ground plane. Cafe 10. — If a fquare be fituated in a plane of the above kind, having its fides oblique to the picture, every thing will be confidered the fame as in the foregoing cafe, only the fides will vanifli to two points in the horizon ; neither of which can be in the center j, nor in any part of the vertical line s d; be- caufe the fide A B, Fig. 10, of the original fquare, is not per- pendicular to G R. But, as the interfe&ion of this inclined plane with the picture is parallel with the ground plane, as in 8 Cafe ( 22 3 ) Cafe 9, the vanifhing points will rife in a perpendicular direc- tion above the common vanifhing line H L, in proportion to the angle which the inclined plane makes with the ground plane. Hence v v on the new horizontal line h /, are placed per- pendicular to V V in the common horizon H L ; which points V V would be the true vanifhing points of the original fquare A B, B C, were it reprefented upon the ordinary ground plane ; or, in other words, if it w r ere reprefented in a plane perpendi- cular to the picture, and parallel to the ground plane* Cafe n. — If a fquare A DBG, Fig. n, be lituated in a plane oblique both to the ground plane and to the pi£hire, its vanifhing line will be in an angle to the common horizon H L, in proportion to the angle which the inclined plane makes with the ground. For, as the original plane in this cafe is inclined both to the ground and to the picture, confequently its inter- feron with the picture will be oblique to the interferon of the ground plane with the picture. Cafe 9 has a horizontal vanifhing line, though it fuppofes the original plane to be in- clined to the ground ; but as its interferon is parallel to the ground line, fo its vanifhing line is parallel alfo. In the cafe before us, the original plane has an oblique interferon with the ( 224 ) the pidture, and t 1 -refore its vanifhing line is oblique to the horizon alfo; whia , perhaps, may be better underftood by No. i, fhowing the fame fquare in the fame pofition, confidered as the top of a table viewed angle-ways, whofe top is fuppofed to be rifing on its hinges at A C in the angle u A K. Its vanifh- ing line is therefore v V, found by drawing M V, making an angle with the horizontal line HL, equal u AK, the angle which the inclined plane makes with the ground. Or the va- nifhing line may be found as in Fig. n ; by drawing v M, cut- ting O m, which is a line perpendicular to the horizon. From the meafuring point m, draw M V parallel to the horizon, cut- ting VP at V; then will the line vV be the true vaniihing line as before. The line A X is confidered as the interferon of the inclined plane, and is therefore drawn parallel to vV, the vanifhing line ; for, in perfpe£fcive, it is a univerfal theorem, according to Dr. Brook Taylor's fyflem, that the vanifhing line, interferon, and directing line of any original plane, are pa- rallel to each other ; alfo, " the vanifhing points of all lines in any original plane, are in the vanifhing line of that plane." See his Sixth and Seventh Theorems. Wherefore the line A X is to v V the vanifhing line, the fame as the ground line G R is to the horizontal line H L. Thefe, and the other lines which I have hitherto paffed over ( "5 ) over unnoticed in the various cafes, will be explained in the different problems belonging to each particular cafe, and there- fore 1 deem it unneceffary to fay more on them at prefent. SECTION III. Containing Problems in PerfpeCtive, folved according to the pre- ceding Principles and Cafes — applied to the Methods of drawing rectangular Superficies and Solids in different Pofitions to the Picture. — Alfo, how to draw Vifual Lines, tending to vanifhing Points, out of the Picture ; and how to reduce the Point of Dif- tance to any Proportion, fo as to bring it within the Limits of the Picture* In the methods of inftru&ion generally made ufe of by moft of thofe who have written on this fubje£t, it is common for them to begin with finding the reprefentations of points and lines, proceeding afterwards to fuperficies and folids. To me, however, it appears an unneceffary prolixity, ef- pecially it would be fo to the perfons for whom this treatife is chiefly intended. For to go through all the problems neceffary for points and lines as they may be differently fituated to the ground plane and picture, and alfo to fliow how thefe lines are to be meafured off according to any given length, would take F f up ( 226 ) up as many plates and pages of letter-prefs as would be diffi- dent to explain the fuperficies of figures of which thefe lines are the boundaries. Befides, it is prefurned that the general readers of this work will underftand the various pofitions of lines, and how to meafure them off, according to their given lengths, better when they are connedled with fome figure, than when thefe fame lines are confidered abftra£tedly. And, in general, it may be faid, that when perfons fet about drawing, it is not to reprefent a line or a point nakedly, but to draw the perfpe£tive appearance of fome figure bounded by lines and points; which, when performed, muft of courfe include every thing requifite to the reprefenting or meafuring of a bare line. Therefore, in finding the reprefentation of a geometrical fquare, for inftance, the problem for this will teach us both how to find the points of its angles, and at the fame time how to reprefent and meafure a line equal to the fides of the given fquare, or any other figure of that nature. For thefe reafons I omit points and lines, and proceed to the firft problem, which is Prob, ( 227 ) Prob. I. Fig. 7. Plate XV. To reprefent a Geometrical Square lying on the Ground, havir^ two of its Sides parallel to the Pi&ure, and the other two per- pendicular to it. Operation. — Draw the ground line GE> and draw H L for the vaniftiing line, whofe height from the ground line is fuppofed to be equal to the height of the fpedtator's eye. Make s the center, or that point in the picture which is directly op- pofite to the eye when the picture is viewed. Make d the dis- tance of the eye from the picture, anfwering to Ps, in Fig. 2, Plate XIV. In this manner the paper or canvafs we draw on is prepared for delineating objects in the above fituation. The next thing to be conlidered, is the feat of the objeit in the picSture ; that is, how far the fquare, for inftance, is to be placed to the right or left of the center J, or whether it is to be diredtly under the center, and how far removed back from the pi£ture. Thefe being fixed on, lay down C A equal to the fide of the fquare to be reprefented, and draw the lines Cs, As, termed vifual lines. Determine then how far the fquare is to be removed from the picture, which in this example is equal 1 2. F f 2 Draw ( 228 ) Draw from 2 a line to the point of diftance d, cutting the vifu- als C A J, at B and A. Laftly, from thefe points of interfeo tion at B and A, draw the lines A C, B I, parallel to G R, the ground line, and the reprefentation will be completed as re- quired. Obfervations. — The fides C B, A I, of the fquare, are per- pendicular to the picture, and therefore, by Cafe 5, page 216, they muft vanifh in x i the center of the picture. The fides C A, B I, are confequently parallel to G R, the interferon of the pic- ture or ground line; wherefore, by C ( ft3* ) Prob. III. Fig. 6. Plate XV. lb reprefent a Square Jlanding upright on the Ground^ but parallel to the Pt&kre. The ground line and horizontal line, 8tc. remaining as in the preceding problem, proceed to the operation. Draw ADBC a geometrical fquare on the ground line. Draw the vifuals A j*, D s, B j", C s ; then lay on a fpace A N on the ground line equal to the diftance which the fquare is fuppofed to be from the pidture. Draw N d cutting the vifual A s in I. From I draw I M parallel to A C. Draw I K, L M, perpendicular to A D, C B. And, laffiy, draw KL parallel to DB; then will the fquare IK, L M, be the reprefentation of the original fquare ADBC, as propofed. Obfervations. — The vifual rays Aj, D j, B jr, C s 9 form a pyramid*, whofe bafe is a geometrical fquare ADBC, and whofe vertex is s, the center of the pi£lure. If this pyramid have a fe£tion parallel to its bafe, it muft be evident to every one, that the fe£lion will produce a geometrical fquare. The * See its definition page 97, and its figure Plate VI. reprefentation ( ^31 ) reprefentation 1KLM is a parallel fedtion of the pyramid of rays iffuing from each angle of the original fquare ADBC, and therefore IKLM, the fe&ion, is a geometrical fquare. See the conclufion drawn from Cafe 4, page 216, in which we fay,— " That the reprefentation of a geometrical fquare or parallelo- gram is a geometrical fquare or parallelogram, if it be fituated in a plane parallel to the picture." Prob. IV. Fig. 8. Plate XV. To reprefent a Square fituated in a Plane inclined to the Ground, and perpendicular to the Pi&ure., A OPE may reprefent the inclined plane, which is merely to aflift the imagination, or to convey what is to be underftood by the fquare ADBC, No. 1. being in a plane inclined to the ground. Operation. — OnGR, the ground line, draw the femicircle unk, whofe radius muft be equal to the lide of the original fquare. Draw n A perpendicular to the ground line ; then make n A D equal to the angle of inclination which the original fquare has to the ground. Draw then, as before, the vifuals A D j, to the center s. Let d, near L, on. the common horizontal line 8 . HL,. ( ) H L, be the diftance as in common ; draw the line u d cutting the vifual line A s in C. From C draw C B parallel to A D, then will A D C B be the reprefentation of a geometrical fquare, fitu- ated in a plane inclined to the ground, in an angle of twenty- three degrees. Method fecond.— Let Gi,Ri, be the interferon of the in- clined plane with the picture ; or, in other words, let it be con- fidered as a new ground line, and turn the plate till this line come into the fame fituation with the eye as the old ground line G R appeared to be in when the plate was upright. This will make every thing in this fecond method appear quite plain, I prefume, and will fhow that it is as eafy to reprefent a fquare in a plane inclined in any degree to the ground, if it be per- pendicular to the picture, as it is to reprefent one lying on the ground, having two of its lides perpendicular to the picture. The plate being placed to the eye as above mentioned, draw a new horizontal line h /, / /, parallel with G I, R i, palling through the center s. Make s d on this new horizontal line equal s d on the old one H L. From D lay down the fide of the fquare DA, and draw the vifuals As and Ds. From A draw A d 9 cutting the vifual D s in B. Make B C parallel to A D, and the reprefentation will be as before. In No. 2 the fame fquare is inclined to the other hand ; but the operation is ftill the fame, when the new ground line G 2, R 2, is drawn, and when a new ^ horizon ( 233 ) horizon, £2, / 2, is drawn parallel to it, palling through the center s, d near h 2 will then be its diftance, or d near / 2 will do, for they are both the fame to the fquare No. 2 ; fince both the diagonals of the fquare, if produced, will tend to each point of diftance, as is evident from infpedtion. The fquares No. 3 and No. 4 are reprefented above the horizon ; but as they are con- fidered in planes perpendicular to the picture, this makes no difference in their reprefentations, for their perpendicular fides vanifli in j", the center, and the operation is the fame above as below the horizon in all refpe6ts. As I have marked the ground lines and vanilhing lines to each fquare, diftinguifliing them by the fame numeral that the fquares are marked with, I think it unneceffary to go through the operations, as it would only be repeating what has been faid on thofe below the horizon. See Cafe 6, on Fig. 8, No. 1, in page 219. Obfervations. — From what has been faid on Fig. 8, it is evi- dent that the foregoing problem may be applied to ufeful pur- pofes in reprefenting different pieces of furniture; and that which has been frequently done at random, for want of know- ing better, may be done with great eafe and accuracy. For inftance, the riling defks of the library table, Plate XXX, are reprefented by this problem. The two femicircles fhew that the defk, raifed to any pitch, will ftill be within thefe arches, G g which ( *34 ) which are the boundaries of the defk, as it paffes round on its hinges. Prob. V. Fig. 9. Plate XVI. To reprefent a Square Jituated in a Plane inclined to the Ground and to the Pi&ure, when the Interfe&ion of the inclining Plane is parallel to the Ground Line, or when its Interfeclion is in the InterfeHion of the Ground Plane with the Piffure*. In this cafe the common ground line G R is the interfec- tion of the inclined plane with the picture ; and a line, S P 9 produced parallel to GR will be the vanifiiing line of this plane. Operation.— Let H L, the common horizon, be drawn as ufual ; and let s be the center of the picture. From s to p is the diftance of the eye from the pi6lure. Take in the com- paffes, AF, equal to the fide of the fquare, and with it fweep the arch q r from p ; then from r to q, on the arch q r, lay on the degree of inclination which the original plane has to the ground ; and draw p q produced till it cut the vertical line s d in S ; then will S be the vanilhing point of the fquare in the in- 8 dining ( *35 ) dining plane, for the fame reafon as j* is of the fquare n, 12, 10, 8, on the level ground. Make S P equal to sp> and P will be the point of diftance to the inclined plane. Draw the vifuals AS, FS, and from A draw A P, cutting the viiiial FS in O. Laftly, draw O N parallel to A F, and the reprefentation of the fquare will be found as propofed. See Cafe 9, page 221. Obfervations. — The vifuals A S, F S, may be cut by another method to the fame effedt. Thus : draw the line 5 6 parallel to S p, and take the lide of the original fquare and place it from A to 5. Draw from 5 a line to p 9 the diftance on H L, and it will cut at N, as before. The truth of this will appear by com- paring No. 1 with No. 3. At No. 1 draw GR for a ground line, and perpendicular to it draw Aj, a fe£tion of the pidhire. Lay on, from A to s 9 No. 1, the height of the common horizon ; that is, from A to J on the perpendicular line AB;, Fig. 9. From j, the center of the pidlure at No. i, draw s p equal s p the diftance at Fig. 9. Make AN, the inclined plane, of equal angle to qpr 9 the angle which the original plane makes with the ground. From A to N, No. 1, lay on A F equal to fide of the fquare No. 3. Lay the fame from A to G, No. 1. Laftly, draw Gp, N p, cutting the pidture at n and 8. Take, in the com- paffes, the fpace from A to n at No. 1, and lay it from 9 to N at No. 3, and it will be feen that they are equal. In the fame manner take A 8 at No. 1, and lay it from 9 to 8 at No. 3, and Gg 2 it ( * 3 6 ) it will be found that they are equal. This fully demonftrates the truth of the reprefeatation of the fquare AF, NO; for, be- yond all difpute, at No. i, Ihows how much the fquare on the inclined plane rifes on the picture; and 8, at No. i, as cer- tainly Ihows how much the fame fquare lying on the level ground rifes ; and Unce they both coincide with their repre- fentations at No. 3, there can remain no doubt but S is the true vanifhing point, and P the true point of diftance. N. B. This problem is of ufe to reprefent any table top hinged at the front, and riling by a horfe behind to arty pitch. Prob. VI. Fig. 9. Plate XVL To find the Reprefentation of a Square lying on the ' Ground, having its Sides, oblique to the PiSlure. Operation. — Draw the plan of the fquare propofed, as 1, 2, 3, 4, in any angle to the ground line G R, as may be required: Produce the iide 1 4 till it cut the ground line at h Alfo pro- duce the lide 1, 2 till it cut at x 4. Let s be the center of the picture as ufual, and draw s d perpendicular to H L. Let d be the diftance of the eye from the picture. From d, draw d V pa- rallel ( 237 ) rallel to 1,2, one of the fides of the fquare. From d, draw dv at right angles to dV 9 then will V v be the true vanifliing points of the fides of the fquare; for the line d V is parallel to the fide 1 2, and d v is parallel to 1, 4 ; wherefore v V are the true va- nifhing points. Hence, from 1 4, and from 3, draw right lines to V, and from k and 3 draw lines to ^; and where thefe lines' cut each other at d, b, r, will be the reprefentation of the ori- ginal fquare 1, 2, 3, 4, as- required. Method fecond. — To draw the fame fquare without the trouble of a ground plane* Operation.— Every thing remaining as before, extend the eompaffes from v to d 9 and lay v d to m on the horizon; then will m be the meafuring point to the vifuals 3, v, k, Make d 13 on the ground line equal to the fide of the fquare. From 13 draw a line to m, cutting the vifual $v at b. From b draw b V, cutting at as by the firft method. The angle of the original fquare being brought into the pidture at 3, a line from 3 to V finds the other fide dc y without any further trouble. Obfervations. — The truth of this problem will appear from what has been faid in Cafe 7, p. 219, which I would advife the reader ( 23» ) reader to examine. And I would further remark, that if vifual rays be drawn from each angle of the original fquare i, 2 5 3, 4, to the vertical line s d 9 they will cut at b 9 a 9 c 9 as in the preced- ing methods. The rays from Z X to P, in Plate XIV. Fig. 2, are the fame to the original Z X, as the rays x d $ 4 d 9 are to the fide of the fquare 1,4, in the figure before us. For c a, in this figure, is the reprefentation of t, 4 — and z 9 x 9 on the picture in Fig 2, Plate XIV. is the reprefentation of Z X. Prob. VII. Fig. 9. Plate XVI. Yb find the Reprefentation of a Square fuppofed to be fituated in a a Plane perpendicular to the Ground 9 but oblique to the Pidlure. For this problem, the pidture being completely prepared as for the preceding one, the operation will be extremely con- cife, as follows : Operation. — Raife a perpendicular line A B, No. 2. On the perpendicular A B lay the fide of the fquare from A to B. From B and A draw vifual lines to v, the vanifhing point ; found as before. From A, lay down the fide of the fquare to /; and from t draw irn, cutting the vifual line A v in D. Laftly, draw D C parallel C 239 ) parallel to A B, and the reprefentation will be found as required. See remarks in Cafe 8, page 221. Prob. VIIL Fig- 10. Plate XVI. To find the Reprefentation of a Square having its Sides oblique to the PiHure, fuppofed to be in a Plane inclined to the Ground, as in Problem V. Observations. — This problem differs in no refpedl from the fifth, except what relates to the fquares reprefented in thefe inclined planes. In the fifth problem, the fquare in that in- clihed plane, having two of its fides parallel to the pi6ture, the others of courfe vanifh in S, perpendicular to s, the center of the pi£hire. In this problem the fquare reprefented in the in- clined plane has its fides oblique to the pi6lure, and therefore they vanifh to two points in fome new vanifhing line, h /, pa- rallel to the common one H L ; becaufe the interferon of the inclined plane is parallel to the ground line. Operation. — Draw, as ufual, GR the ground line, and H L the horizon. Let s be the center, and d the diftance ©f the piilure. Draw AB, one fide of the original fquare; make. ( 240 ) .make d V parallel to A B, the fide of the fquare ; and draw rf,VL, at right angles with dV, then will V,VL, be the vanifhing points of the fquare 4,/), 5, 6, 011 the level ground. Make VM equal V d, and LV;^ equal LVrf; then will m and M be the meafuring points of the vifuals tending to V,VL, Thus far the picture is prepared only to reprefent the fquare on the level ground ; therefore we muft proceed to find the vanifhing line, points, and meafuring points, of the inclined plane, thus : — Draw perpendiculars at pleafure from V, and V L. From M draw M v, in an angle to V M equal to the angle which the inclined plane makes with the ground. Through v draw hi parallel to HL, cutting the perpendiculars at v; then will v v be the vanifhing points fought. Make v n equal v M, and n will be the meafuring point fought. Draw then the. vi- fuals 4 v and 4 vL Make 4, 0, 4, r, equal to the fides of the ori- ginal fquare B A. Ffom 0 draw 0 n, cutting at 1; and from r draw r p, cutting at 3. From 3 draw 3 v 9 and from 1 draw iv /, interfering at 2 ; then will 1, 2, 3, 4, be the reprefentation of the fquare propofed. Obfervations.— The line /B paffes through the diagonal of the original fquare, whofe fide is A B. Draw from d, the diftance, aline parallel to B /, cutting at g on the common horizon. From 4 draw a line to g 9 and it will pafs through the diagonal of the fquare T/ats. J A. f ( 241 ) fquare 4 p> 5, 6, lying on the level ground. Draw from g\ a per- pendicular to g on the new horizon h /. From 4 draw a line to the uppermoft g, and the line will pafs through the diagonal of the fquare reprefented on the inclined plane ; which is a clear demonflration of the truth of the whole. The truth of the method may be proved, alfo, by drawing a line from A to D, the diftance laid on from the new hori- zon hi; for the line cuts the vifual at 1, as in the other method. Prob. IX. Fig. 11. Plate XVII. To find the Reprefentation of a Square, fituated in a Plane oblique both to the Ground and to the Pi&ure. This figure may, to the workman, appear intricate and perplexed; but he ought not to be difcouraged at the light of an affemblage of lines, till, after having made a reafon- able attempt to underftand them, he finds it not eafily at- tained. But it is to be noticed, that there are feveral more lines than what are abfolutely neceflary for reprefenting the fquare fimply confidered ; becaufe I have fhown different me- thods to effe£t the fame thing ; and becaufe the whole procefs is fhown from firfl: to laft, that the reader might have a clear H h understanding ( 242 ) underftanding of a problem really ufeful, but rarely known amongft workmen, and even not amongft painters. Operation.— Draw G R, the ground line, and H L, the ho- rizon, as ufual ; and make s the center of the picture. Draw s d perpendicular toHL; and let d be the diftance of the pic- ture. Make the angle dvs equal to the angle which the fquare in the inclined plane makes with the picture; and draw dP at right angles to d v ; and make v m on H L equal v d. Draw at pleafure m M o perpendicular to the horizon. Make v M to in- cline in an angle equal to that which the original plane makes with the ground. Draw M, V x parallel to the horizon ; and from V X) draw V x, v, which will be the vanifhing line of the inclined plane. From the center J*, draw sS,dx perpendicular to the va- nifhing line v$ V x. From jv draw a line to d i, parallel to v S V x. Extend the compaffes from S to d i, and make S, d x, equal to S 9 di; then will S, dx be the diftance of the picture for the inclined plane. Make V x y m 2, equal V x, d x, and m % will be the measuring point. The pi£ture being thus prepared for delineating the fquare, draw from A, the vifual Av; and from A, the vifual A, V Draw A X parallel to the vanifhing line S V,x. Lay on, from A to Wj a fpace equal to the fide of the fquare ; and from w, draw iv ^ m 2, cutting at D, From D ? draw a line to % for the fide 8 of ( *43 ) of the fquare D B. Make alfo A N equal to the fide of the fquare ; and draw N m 9 cutting at G ; andlaftly, draw G V x 9 cut- ting at B ; and the fquare will be completed as required. Method fecond. — From A, fweep the arch k K, whofe radius is equal to the fide of the fquare to be reprefented. Draw A U equal to the angle of the inclined plane with the ground ; and from u, draw u t parallel to the ground line ; from t draw a vi- fual to P ; and from u, draw u M, cutting at D ; from A draw a line through the interferon of u M with / P, and produce this line till it find the vanifhing point V a; in the perpendicular P V. From D draw a line to v 9 as before; and laftly, from G, found as before, draw G V x 9 cutting at B, and the fquare will be completed, as in the other method. Obfervations. — If the original plane inclined to the ground in an angle of forty-five degrees, the vifual line of the fide of the fquare A D would pafs through the diagonal of the fquare A, k 9 n 9 8, and tend to the upper V, the vanifliing point in that cafe ; and V v would then be the vanifliing line, S would be the center of the pi£ture, m the meafuring point, and d 3 its diftance, and v 9 d 3, Q would be the angle of the inclined plane, which is the diagonal of a fquare v 9 d 3, Q, m. It is evident then, that tlie true representation of a fquare in any inclination, would H h 2 defcribe ( *44 ) defcribe a quadrant of a circle, whofe radius would be the fide of the fquare reprefented, as the figure fhows. N. B. No. i is the fame problem, diverted of all lines but fuch as are abfolutely necefTary to its reprefentation ; which, it is prefumed, will be readily underftood by infpedtion, after what has been faid on Fig. n. See page 224. Prob. X. Fig. 12. Plate XVIII. cutting at 1. Draw 1, 2, parallel to the ground line, cutting Dj at 2. From 2 raife a perpendicular, cutting C s in 5 ; from 1 raife a perpendicular to 4, cutting B s in 4. Laftly, from 4 draw a line to 5, parallel to the ground line, or to B C ; and the reprefentation of the firft cube will be completed. Next, from 2 draw 2 d> cutting at 3 ; draw 3, 8, cutting D s in 8 ; from 8 draw 8 d, and it will find the bafe of the fecond cube ; and repeating every thing as in the firft cube, any number of them may be drawn till they vanifti in the point s. Obfervations. — If a number of cubes, or prifms, are to be reprefented in various places on the pi&ure, it will be done with ( 247 ) with the moft eafe, firft, to reprefent a floor of fquares equal to the fide of the cubes, or bafe of the prifms. Thus, for in- fiance, the prifm r is eafily delineated on the back part of the pi£ture, by raifing a perpendicular M N equal to the original height of the prifm. Draw Nj, and from any fquare where it is to Hand, raife perpendiculars cutting Nj at r. From r draw a line parallel to the ground line, which will complete the prifm. In like manner the cube k i may be reprefented any where. Laflly, we may fee, in the reprefentation of a cube, that it confifts of three different cafes of geometrical fquares ; that is, A,D, i, 2, is the reprefentation of a fquare lying on the ground ; and i, 4, 5, 2, is the reprefentation of a fquare perpendicular to the ground, and parallel to the picture : and D,C, 5,2, is a fquare reprefented both perpendicular to the ground and to the pic- ture. The other three fides of the cube are refpeftively parallel to thofe we have mentioned, and therefore are the fame in all refpe£ts. Prob*. ( 348 ) Prob. XII. Fig. 13. Plate XVIII. To reprefent two Rows of Cubes oblique to the Piffure. Operation.— G R is the ground line, and H L the hori- zon. Let s be the center of the picSture, and s d the diftance. From d 9 draw dV, cutting H L in V, and parallel to that fide of the original cube; whofe reprefentation is A B C g. Draw dv at right angles with dV 9 cutting at v; then will v be the vanilhing point of the right hand fide of the fquare. Make V M equal V d y and v m equal v d ; then will M tn be the mea- furing points. From A, the angle of the firft cube, draw the vifual A v. Draw alfo A V. Make A B equal to the fide of the cube, and from B draw BV,Bu Next, lay A B to 7, and from 7 draw a line to the meafuring point m, cutting at a. Lay A B to c ; and from c draw c M, cutting at g ; from g and a raife perpendiculars to C and D ; from D draw a line to V, and from C to v 9 which will complete the reprefentation of the firft cube. The fpace between the cubes being confidered equal to the fide of the fquare, repeat A 7 each way on the ground line, as often as there is room, as at 8, 9— From each of thefe divifions ( 249 ) divifions draw lines to their refpedtive meafuring points m M, cutting A v in b and in 2, and AV in h i k. Raife perpendiculars from b and 2, cutting the upper vifuals. Do the fame from the other points h ik, and proceed in all refpe£ls as with the firft cube, and there will be two more produced. Obfervations. — If it were required to reprefent two additi- onal cubes to each row, it is evident that we muft have recourfe to fome expedient for this purpofe ; becaufe there is not room beyond 9 and / to lay on any more divifions. Therefore from 2 produce a line parallel to the ground line, and from k do the fame. And obferve, that a line from 8 to tn y and from e to M, cut thefe parallel lines at n and 1. Extend the compafles from r to 2, and repeat this at 3,4, 5, 6, and from thefe divifions draw lines to m, and they will cut the vifual A v in the fame points in which it would have been cut if thefe lines had been drawn from the original divifions on the ground line. Laftiy, a line from e to M will cut the left hand parallel at n ; repeat n k at p q r, and proceed as before. By this method, which is quite fimple, it is evident we may draw as many cubes as we pleafe, by adding parallel lines to the ground line. I i Of ( ) Of drawing Vifual Lines tending to Vanijhing Points out of the Pi&ure. In the practice of drawing it is frequently found, by expe- rience, that if we make ufe of a fhort diftance, the figure we reprefent will appear diftorted and unnatural ; and when we, to avoid this, make ufe of a long diftance, it will perhaps ex- ceed the paper or picture we draw on : alfo, in the reprefenta- tion of objedts obliquely fituated to the pidhire, their vanifliing points not being in the center, it often follows, as the confe- quence of chooling a long diftance, that the vanifhing points far exceed the limits of the pidture. To alleviate thefe dif- ficulties, we propofe the following problem* Prob. XIII. Fig. 14. Plate XVIII. To reprefent two upright Prifms obliquely fituated, whofe Biflance and Vanifhing Points exceed the Limits of the Pi&ure. Let the double line on each fide of Fig. 14 be confidered as the boundaries of the pi6hire. Draw, as ufual, the ground line G R, and the vanifhing line H L, and make s the center of 8 the ( *5* ) the picture. Let .r d be considered as only half the diftance, he- caufe there is no more fpace on the pi£ture above d. From the point d, draw a right line each way, at a diftance from s, equal s d, forming a right angle ; becaufe the fides of the prifms are originally perpendicular to each other. Make v m equal v d\ then would m be the true meafuring point, provided s d were the whole diftance of the picture ; and in this cafe v v would be the vanifliing points of the fides of the prifms ; but fince s d is only half the real diftance, take in the compaffes s and repeat that fpace to M, and make s M, s M, equal, then will M M be the true meafuring points to the whole diftance. Pro- duce the vertical line ^ to A, cutting the ground line at A. Divide s d into any number of equal parts, as x, 2, 3, 4, and, for the fake of accuracy, fubdivide thefe as in the figure. Lay on the fame divifions downwards from s to A. The next thing to be confidered, is to draw a line perpen- dicular to the horizon, of fuch a proportion to s d, at any given diftance from the center, according to the boundaries of the piihire, that when a line is drawn from d, touching the top of the faid perpendicular, it would exactly tend to the true vanifhing point, were it produced to the horizontal line. We fhall fuppofe then, that a perpendicular line is drawn from the point % which is exactly half the diftance from s the center, to V the vanifhing | I i 2 point ( ) point out of the pidlure. Make then the faid perpendicular line V4, half the length of s d; then a line palling from*/ to 4 would, if produced, terminate at V, the true vanifhing point. Divide ^,4 in the fame manner as s d, and downwards from v to 3 lay- on the fame diviiions ; for v 3 is half the length of s A. Laftly, make the other fcale on the left in the fame proportion, then will the pidture be properly prepared for delineating the pro- pofed prifms. Operation.— From A draw a line to 3, which will be the vifual for the bottoms of the prifms, for A 3 produced would tend to V. Make A c equal to the diftance which the prifm is fuppofed to be from the pi£ture ; then, from c, draw a line to M, cutting at p ; from p lay a ruler acrofs the two fcale lines, and move the ruler backward and forward till its edge coincide with/), and any correfpondent divifion on each fcale. The ruler being thus fixed, draw a line p b, cutting the fcale line s A in the fecond divifion, and the fcale line ^3 to the left in the fame divifion ; then would p b produced terminate in a point on the horizon equally diftant from s as V is. Make A a equal to the left fide of the prifm, and draw a M, cutting at b. Make c e equal A a ; and from c draw a line to M, cutting at b. From the points p, b, h, raife perpendiculars at pleafure. Confidlr ( ) Confider now the height of the prifm, which we fuppofo to be A B ; from B place the edge of the ruler, and move it till it be at fimilar divilions on each fcale line, as before. The ruler being in this polition, draw a line cutting the perpendicular p D at D; and from D; place the ruler till it coincide with fimilar diviltons on each fcale line on the left, which will complete the reprefentation of the firft prifm ; and for the fecond, proceed in the fame way, obferving that, as there is not room on the ground line GR for repeating the fide of the prifm c the fcale line, or new ground line b i muft be found, as in the preceding problem, by drawing through h a line parallel to the old ground line, cutting at ^*, then muft the fpace bg be laid to / and from which, lines being directed to M> they will cut Obfervations.— In Problem XXI. page 71, Plate II. Fig. 15^ the geometrical principle is explained, upon which this method of drawing vifuals to points out of the pidure is founded.. We there fay, in page 72, u In whatever proportion the extreme line E P is divided, into the fame proportion will the hypothenufe line EO be divided." Agreeably to which, we may obferve in the perfpeilive problem before us, that, in whatever proportion the diftance s d is divided, a line being drawn from the faid divifion parallel to the horizon, will cut the ( »54 ) the vifual d V in that fame proportion. The line s d being di- vided into two equal parts, a line from 2, parallel to the hori- zon, will cut at 4, which divides the vifual d V into two equal parts ; and a line from the point 4, perpendicular to the hori- zon, will divide s V in the fame manner. Hence it is evident, that if s d, v 4, be divided into the fame number of equal parts, a line drawn through any two correfpondent diviftons, will tend to V, the vanifhing point. It is alfo evident, by the fame mode of reafoning, that if the half diftance s d were produced to twice its prefent length, which would then be the whole diftance, a line from d to V would be equal to the fpace from Y to M, on the left the true meafuring point, in the fame manner as dv- mea- fures> v f&i which is only half that fpace. Of reducing the Point of Diftance, fo as to bring it within the Limits of the Picture* In making defigns on a large fcale, it is very common for the point of diftance to exceed the bounds of the paper or board w r e draw on : to avoid the inconvenieuee of which, let the fol- lowing problem be attended to. Prob ( ) Prob. XIV. Fig. 15- Plate XVIII. To find the Reprefentation of a Number of Squares when the Dif- tance is out of the Limits of the PidJure. The double lines which include the fquares, are the boun- daries of the paper, board, or pidture we draw on. Operation. — Let s be the center, and let sdbe fuppofed half the length of the point of diftance. Make then a fcale on the ground line, whofe equal parts fhall be equal to half the lide of the fquares to be reprefented, as 3, 4, 5. Lay on from 3 to 4 half the lide of the fquare A, and from 4 draw a line to d, half the diftance, which will cut the vifual 3 J in the fame point as it would have been cut if d had been twice its prefent diftance from /, and the whole fide of the fquare had been laid on the ground line, as at 5 ; for it is evident, that a line from 5 through t would terminate in a point on the horizon twice the diftance of s d. From 4 lay on 5, 6, equal 3, 4, and drawing lines to d, we fhall have the fquares B C. Here the learner muft obferve another difficulty arifing ; for the ground line of the picture is filled up at 6, and we are fuppofed to want the reprefentation of three more fquares ; and as the point 6 is near the extremities of ( * 5 6 > of the pi£lure or board we draw on, there can be no opportunity to lay on the fides of the fquare any further ; we mufl again there- fore reduce the -length of the* point of diftance to b, which is only one fourth of the whole diftance ; in proportion to which we muft alio reduce the fcale on the ground line to one fourth of the fide of the fquare, as I, a; or, which is the fame thing, divide the fpace 5, 6, into two equal parts, and from 6, 0, 5 draw lines to b y and three more fquares will be cut off on the vifual line 3, s } as is evident from the figure. Obfervations— The truth of the reprefentation of the three laft fquares will appear, if the whole fpace between 3 and 6 be placed from 6 to 9. Draw then from 9 a line to d, which will cut the vifual in the fame points as before, when a line was drawn from 6 to b. The advantage of this problem is very much experienced in the reprefentation of long ranges of buildings, fuch as the in- ternal views of ftreets ; in which cafe it is impoffible to find room on the ground line for the full meafurement of each front, not even when we have a very large board to draw on. I remember to have been very much embarrafled myfelf in drawing the view of a long ftreet, till I was informed of the above methods. SECTION ( *S7 ) SECTION IV. Of the reprefentations of Polygonal and Curvilinear Figures— con- taining forne further Remarks on the Difference between the Re- prefentalion of Obje&s on a Plane y and their real Appearance to the Eye— Of long and Jhort Dijlances, and the Reprefentation of a Row of Columns and Pilafters, parallel to the Pi£iure\ to- gether with fome Obfervations on the ^theory of Circular Obje&s, Of Polygonal Figures. Lines in three different pofitions to the picture, will re- prefent any polygon in any fituation whatever *. A pentagon may have one fide parallel to the piihire ; and if fo, the other four will be oblique to it ; or it may be placed fo as to have all its fides oblique. * See the definition in page 49, and the various kinds of polygons in Plate II. K k A hexagon ( *S* ) A hexagon may be fo placed as to have two fides parallel, and the other four oblique, as Fig. 16, Plate XIX. or it may have all its fides oblique. An oilagon may have two fides parallel to the picture, confequently there will alfo be two perpendicular to it, and the remaining four will be each of them oblique, as Fig. 18, Plate XIX. The oftagon in this fituation, therefore, introduces all the variety of pofitions of lines that can exift in a picture, when the figure is fuppofed to be on the ground plane, or per- pendicular to the picture ; and fince the theory of lines parallel, perpendicular, and oblique to the ground line, &c. has already been confidered and applied to pra6lice in the preceding fedtion, in the reprefentation of geometrical fquares and of cubes, no- thing is requifite here, but to apply the fame principles to the reprefentation of polygonal figures. The moft ufeful of thefe are the hexagon and o£tagon; which, for brevity's fake, I fhall confine myfelf to, taking it for granted that, after the learner is acquainted with thefe, he will be able to delineate any other, from a pentagon to a duo- decagon, as it may be found requifite. Prob. ( *59 ) Prob. XV. Fig. 16. Plate XIX. To reprefent a Hexagon having Two of its Sides parallel to the Piflure. Operation. — Draw the ground line and horizon, and make s the center of the picfture, and d the diftance. Through d 9 draw a line at pleafure parallel to the horizon. From d defcribe a fe- micircle, in which may be infcribed half a hexagon, as i, 2, 3. From d> through each angle of the hexagon, produce a line till it cut the horizontal line in V v ; then will V v be the vanifhing points of the four fides of the hexagon, which are oblique to the pidture. Draw the vifuals Fv 9 B^, and B V, F V, and make B D and FA each equal F B, the fide of the given hexagon. Draw A V, cutting the vifuals at iK; and draw D v, cutting at O N. Laftly, draw K N parallel to F B, and the reprefentation will be completed as required. Obfervations. — It is evident that a hexagon is compofed of fix equilateral triangles. The reprefentation contains fix tri- angles alfo ; and if a right line be drawn through each oppofite angle, as from FN, &c. they will all interfedt in the center e, in the fame manner as the lines from each oppofite angle on the K k 2 plan ( 260 ) plan of the hexagon Y interfedt each other in the true center, from which a circle may be defcribed that will touch each angle. - Prob. XVI. Fig. 17. Plate XIX. 7b find the Reprefentation of a hex angular Prifm, or Box, having two Sides parallel to the Pi&ure, as before. This problem may be folved by another method, which will help to confirm the truth of the laft method. Operation. — Draw the plan Y, and produce its fides up to the ground line at g,f b r c. Find the vanifhing points v V as in the preceding problem. Draw the vifuals g V,/ V, and b %\ c v v which will interfe6t each other at a, e, t. Through e the cen- ter, correfponding with e on the plan, draw h u parallel to r, on the plan. From % draw vh, produced to 0; and from V, draw V u, produced to n* Laftly, from n draw n 0, which will complete the bottom of the box. Or it may be done by drawing the vifuals 8 V, 7 V, when the other vifuals are drawn, as the figure itfelf fufficiently indicates. From each angle of the bottom perpendiculars muft be raifed, and produced at pleafure. Next, draw g p perpendicular to the ground line, and make ( 26i ) make g p equal to the height of the box ; and draw p V, and produce o to /; and from i draw i k> and from k draw a line parallel to the ground line, which will cut the aforefaid per- pendiculars drawn from 0, n, at 1, 6. The perpendiculars from h, a, were cut by p V at 2, 3. Draw 6 V, and i V, cutting the perpendiculars from u and / at 5, 4; from 5 draw 5 v 9 and from 4 draw 4, 3, and the outlines of the box will then be com- pleted^ To fhew the infide, and the thicknefs of the edges of the box, proceed thus : — produce from the plan, x w, and from zv draw a line to V, cutting t' a; from its interferon in t o, raife a perpendicular to k 1 ; and from its fe&ion on k 1, draw a line to V; and where this line cuts the diagonal 2,5, a line muft be drawn from v, the vanifhing point, to 9, the point of inter- feron, and produced till it cut the diagonal 1, 4, at 1 ; and from where it cuts this diagonal, draw a parallel to 1,6 ; and from where it cuts at 6, draw a line to V ; and from where this line cuts at 5, draw a line to -v y cutting 4; and from where it cuts, at 4, draw a line to the other interferon at 3, and the edges of each angle will be finilhed. Obfervations.— The hexagon in this figure is nearly the fame in its plan as the other in Fig. 16; but as it is removed back from the picture, its appearance is more eafy and natural 8 than. ( 262 ) than that. The hexagon in Fig. 16 has one fide, FB, in the picture, therefore F B is the full length of the fide of the ori- ginal hexagon, and the contractions of the other fides appear more fudden, and therefore more unnatural;, but its repre- fentation is equally true. The hexagon may, however, be re- prefented by this method as far back as we pleafe, by repeated- ly laying F B, the fide of the hexagon, on the ground line, as from D to E, and drawing E v, by which means we have another hexagon i, 2, 3, 4, K, Z, whofe appearance is perfectly natural. Prob. XVII. Fig. 18. Plate XIX. To find the Reprefentation of an Qciagon, having two Sides parallel to the Picture. Operation.— Draw G R, the ground line, and H L as in common ; and make s d the diftance of the pi6lure, and s the center. Draw half the plan of the octagon at A, as follows. — Make b g equal to half the breadth of the plan ; and from c fweep the arch b % /, e. Bifeft the arch in t From i draw / r, cutting at />, and p g will be half the fide of the odtagon. Lay on b p to & 1, and a line from p to 1 is one fide of the oftagon. Produce ( 263 ) Produce each fide of the o6tagon up to the ground line ; and from the points /, 8, I, 6 9 draw vifuals to s. From 8 draw a line to d, cutting at 7; from 1 draw a line to d alfo, cutting at 6. From 7 and 6 draw lines parallel to the ground line, cutting at 2, 3. Draw / d, palling through the diagonal of the fquare in which the odtagon is infcribed. Draw 4, 5, parallel to the ground tine. Laftly, draw the fides 1, 2, — 3, 4—4, 5 — 5, 6, and 7, 8 ; which completes the reprefentation., Prob. XVIII. Fig. 19. Plate XIX. $0 find the Reprefentation of an o& angular Prifm, or Box, having all its Sides oblique to the Piflure.. Operation.— Draw the ground line and horizon, and let figure A be half the plan of the odtagon. Let s be the center, and d the diftance of the picture.. Produce ne, np, to the ground line ; and draw g perpendicular to e. From b 9 g 9 1, R, draw vifuals to s: and from R draw Rd; by which a fquare will be reprefented in which the odtagon may be infcribed. Draw the other diagonal of the fquare, which will cut the vifual^ s in 8; the other diagonal R d, cuts the vifual g s in 6. From ( *6 4 ) From 6 draw a parallel to 4, cutting the diagonal at 4 ; and from 8 draw a parallel to 2, cutting the diagonal at 2; through the center of the fquare draw a parallel, cutting at 7 and 3. Laitly, draw right lines to each point, and the bottom of the box will be completed. Draw AF parallel to GR, and at a diftance from GR equal to the hefght of the box. Then -reprefent another fquare A, F, G, D, and draw the diagonal each way. Then from 8 raife a perpendicular to 10, cutting the diagonal A D at 10. In the fame manner, and to the fame efFe£l, raife a perpendicular from 6 to 11, from 5 to 13, from 4 to 14, from 3 to 15, from 2 to 16, from 1 to 0, and laftly, from 7 to 12. Draw then, as before, right lines to each point, and the whole reprefentation of the box will be finifhed, except fhewing the infide and the edges of the box : having defcribed how this is to be done in Problem XVI, I need not here repeat it ; only it will be necefiary to obferve, that as the fides of the o£tagon are drawn by this method without vanifhing points, thefe points muft be found by producing the fides of the odtagon till they cut the horizontal line HL, in the fame way as the fide 15, 14, is produced to v, which will be the vanifliing point required for drawing the infide line to, as the figure fliews. Some FuMtshcl or tk Act directs ly T.Sfieralcn , Iune. 4 • • ( s6 5 ) Some further Remarks on the Difference between the Reprefenta- tion of Objecls on a Plane, and their Appearance to the Eye. We have already, in page 210, obferved, that a perfect picture of objedts, as they appear to the eye, cannot be deline- ated on a plane ; we may conceive it to be done on the furface of a fphere, if the fpedtator's eye be in its center. But this is only a fuppolition ; for, in reality, there can be no ftridt rules given for drawing perfpedtive lines on a fpherical furface. A painter, in delineating objedts on the infide of a large dome, may make ufe of ftraight lines, and the rules of perfpedtive, as applied to a plane ; but he does this, becaufe he perceives that the dome being exceedingly large, and the objedt but fmall, the fpace which the faid objedt occupies on the dome is nearly a level furface ; and therefore common perfpedtive comes near enough to the truth for drawing that fingle objedt. But if the objedt be large, and the dome fmall, nothing of this fort can be applied. Mr. Kirby has, indeed, propofed a method to draw per- fpedtive reprefentations upon vaulted roofs and domes ; and, for L 1 any ( 266 ) any thing I know, it is as good a method as can be adopted ; yet it cannot be called perfect, much lefs a fyftem of linear per- fpedtive applicable to fpherical furfaces But the ordinary rules of perfpedtive applied to a plane is a perfect fyftem, as it relates to the reprefentation of objects ac- cording to their real appearance on a tranfparent plane inter- pofed between the eye and the original figure of any thing: for the tranfparent plane, in this cafe, is a fedtion of the rays of light coming from the objedt to the eye ; which fedtion is there- fore an infallible and moft perfedt perfpedtive reprefentation of the original figure on a plane ; but it is not fo perfedt to the eye, becaufe the eye is globular. Perfpedtive then, as it refpedts the appearance of objedt s on a plane, is perfect, and its rules are ftridtly mathematical ; but as it refpedts the appearance of thofe objects to the eye, it is a deception, and is therefore liable to defedts and imperfections, as every other deceptive art is, owing to various circumftances de- pending on the management of the artift. Thefe diftindtions have not been fufficiently attended to by fome, which has therefore been the occalion of fome difputes on this fubjedt not well founded. * As this fubjc6fc is foreign to my purpofe, and not likely to be of ufe to thofe perfons I wifh to ferve in this work, I mall not enter upon it; hut if the reader chufes, he may confult the third fe&ion, page 74, of the above gentleman's book. Hence ( ^7 ) Hence it has been faid, by a certain writer, that a row of columns, or cylinders, cannot be reprefented parallel to the picture, without producing a clumfy and bad effect, if they be drawn according to the ftri£t rules of perfpedtive ; for then thofe columns which are furtheft from the center will be the largeft, which ought rather to be the fmalleft, according to their appearance to the eye. But this depends on circumftances, and is not a fufficient reafon for charging the rules of perfpedtive with falfity, or even a defect, unlefs the laws of this art ob- liged us always to choofe a very fhort diftance ; and that, when we view r a picture, w r e muft neceflarily hold our nofe clofe to it, before we can be a judge of the merit of perfpedtive. From pretty much the fame principles another gentleman, who writes on this fubjedt, gives us an inftance of the imper- fections of perfpedtive, by reprefenting a geometrical fquare, with a very fhort diftance, which occafions the fquare to look too long one way, which he therefore terms a falfe reprefenta- tion, though he has obferved the ftridt rules of perlpedtive. Yet I will venture to fay, having made the experiment, that if this gentleman had placed his eye perpendicular to the center of the picture, and at a diftance from it equal to that by which he drew the fquare, he would not have difcerned any bad effect even in that which he calls a falfe reprefentation. But that the learner may have a proper view of this fubjedt, I fhall firft re- L 1 2 prefent ( 268 ) prefent a row of columns as they appear to the eye ; and, fecond- ly, reprefent the fame row as they appear on a plane, by which the learner will fee the difference between Mr. Kirby and Mr. Mal- ton's opinions on the fubjedt. And, thirdly, we fhall fhow the aforefaid row of columns on a plane, having the advantage of a long diftance, which, in this cafe, is recommended both by Malton and Noble ; the effedt of which being a proof that we may abide by the ftridt rules of perfpedtive in delineating a row of columns, or any other cylindrical object, and that more pleafant to the eye than when they are reprefented according to Mr. Kirby's opinion and definition of perfpedtive, which is, " to draw the reprefentations of objedts as they appear to the eye." See page 94 of his Treatife on Perfpedtive. Firft, to delineate a row of columns according to Mr. Kirby^ definition. Of the Reprefent at ion of a Range of equidijlant Columns parallel to the Pi&ure. First, Let I,K,L,M, Plate XX. Fig. 20, be confidered as a j horizontal fedtion of the four columns A, B, C, D ; and let the arch 1,2,3,4, &c. be the fedtion of a fpherical pidlure, and d the diftance of the eye from the pidlure, then will s be its cen- ter. ( *6 9 ) ter. Draw from the apparent diameters of each column vifual lines tor/; and where thefe rays cut the arch at 1,2, 3, 4, &c will be the reprefentation of the diameters of the four columns as they appear to the eye. Thefe diameters and their inter- columns, or fpaces between, rauft now be transferred to a level plane or picture, as in No. 1. Draw a line AB, and take 1, 2, from Fig. 20, and place it at 1,2, No. 1. ; then take 2, 3 from Fig. 20, and place it to 2, 3, No. 1. and fo of all the others. Draw perpendiculars from each number, and finifh them, as exhibited in the figure, and they will be the reprefentations. of the four columns A, B, C, D, as they appear to the eye. Secondly, We fhall now reprefent the fame columns as they appear on a plane, having the fame center and diftance as before. Draw the line PP, Fig. 20, parallel to the four columns, which will be the feilion of the pi6lure ; and fince the vifual rays from each column were drawn before, the reprefentations of the apparent diameters of the faid columns on a plane will be at a b, c e,fg,h L Transfer thefe diameters and their inter- columns to No, 2, as the figure ftiews ; then will A, B, C, D, be the appearance of the four original columns at Fig. 20, on the plane of the picture, according to the ftri£t rules, of per- spective, Nov/ ( 2"70 ) Now the queftion is, Which of thefe reprefentations are mod alike to the originals in Fig 20 ? If the reader will place his eye perpendicular over A, the center column in each repre- fentation, and look through his hand at a diftance equal ds, Fig. 20, 1 believe he will be able to determine for himfelf ; never- thelefs it may be proper to offer fome remarks by way of affift- iRg his enquiries. And, firft, We may obferve that the whole fpace which includes the columns at No. 2, is confiderably nearer the length of the ori- ginals at Fig. 20. than the fpace which No. t. includes. The intercolumns are nearer alike at No. 2 than they are at No. 1. And, laftly, if we look fteadily through our hand as above di- rected, we Hi all find that, at No. 2, the apparent thicknefs of the column D will be greatly reduced, and that of C will be alfo reduced, and both in proportion to their diftance from the center, fo that there will not be much difference in the thicknefs of each. But if we look in the fame manner at No. 1, we fhall find the reprefentation appear worfe, for D C will appear fmaller than they are reprefented. The reafon is obvious, for the rays of light by which vifion is performed, being confiderably ob- lique at the column D and C, the optic angles which they fub- tend are much lefs than thofe fubtended by A and B, as Fig. 20 clearly demonftrates ; for the rays G d, H d, are more oblique to 8 the ( 271 ) the pidture P P than the rays N d 9 O d\ therefore we fee that the arch 7, 8 is lefs than the arch 5, 6, and fo of the reft in pro- portion. The figure alfo demonftrates, that when thefe vifual rays are cut by a plane P P, parallel to the original columns, the ef- fect is reverfed ; for then the reprefentative diameters will in- creafe as they decline from the center /, yet the optic angles under which they are feen remain the fame as before, when the vifual rays were cut by a fpherical picture at 1, 2 — 3,4, &c. Hence it is evident, that the diameter h /, viewed by an eye at d 9 would not appear larger than the diameter 7, 8 on the arch. Wherefore the true reprefentations of the original range of co- lumns as they would appear on a tranfparent plane, interpofed between the fpe£lator's eye and the faid original columns, are at No. 2, not at No. 1, for that is their reprefentation on a fphere, as they appear to the eye, anfwering to Mr. Kirby's definition of perfpe&ive, though this is not what he means to recommend in pradlice ; for he fays, page 97, " that they" (meaning a range of equidiftant columns) " fhould be fo reprefented as not to offend " the eye of a common obferver ;" by which he means they fhould be drawn of one thicknefs, and at equal diftances. How far the reprefentation at No. 1, which is according to his defini- tion, ( 272 ) tion, will agree to this, I will leave to the judgment of the reader, and fhall proceed to fliew how thefe columns may be reprefented, according to the ftri£t rules of perfpedtive, fo as to appear of one thicknefs, and at equal diftances. We have hitherto fuppofed the eye of the fpe£lator at d> viewing the original columns A, B, C, D, Fig. 20, in which fitu- ation the vifual ray Hd, from the fartheft column D, and the eye's axis d s, form an angle of fifty-four degrees ; and fince s i is but half the piiture, the whole would be feen under an angle of one hundred and eight degrees, which is far too great for viewing any picture ; for the eye at d cannot take in a fpace twice the length of s /, without being ftrained and twifted. To convince the learner of the truth of this, let him take a pair of compaffes and extend them from d to j 1 , and placing one foot on the column A, at No. 2, let the other foot keep his right eye from A, exactly at the diftance of their opening, equal d s. Obferve, the compafs foot muft nearly touch the right eye, or the experiment will not be fo ftriking. The eye being thus placed, experience will teach him that he cannot fee the column D at No. 2 without twifting his eye ; and at the fame time he will fee, as we faid before, that the columns will be nearly equal in thicknefs. But if the eye d, at Fig. 22, be removed back to E, the ( *73 ) the whole pidture will be feen with eafe, for it will only fub- tend an angle of forty-eight degrees ; and at this diftance, the vifual rays being not fo oblique to the picture as before, they will cut it nearly at equal diftances from each other, as is de- noted by the afterifms * *, where the dotted rays cut PP. The good eftedt produced on the picture P P, by choofing E for the diftance, is clearly demonftrated by Fig. 21, which exhibits the fame row of columns drawn by the diftance £• Thus: — make s d, Fig. 21. half the fpace of Es 9 Fig. 20; becaufe there is not room for the whole diftance on the plate. From j* draw sA perpendicular to HL. Draw GR as a ground line, and proceed as before to lay on the fpaces marked by the afterifms * Fig. 20, on the line P P. Draw then the vifuals from A, B, D, C, as the figure fliews. From 1, Fig. 23, draw a line to d, cutting A s in 2. Through 2 draw a line parallel to G R, cutting the vifuals ; by which will be reprefented four geometrical fquares, in which the bafes of each column will be infcribed. Laftly, from the circles contained in each fquare, draw the fliafts, and finifh them as in the figure. Now let the reader place his eye per- pendicular over j*, and at a diftance from s equal twice sd; then I am perfuaded he will fay, that a common obferver would pronounce the columns of equal thicknefs, and their inter- columns equidiftant, although they are reprefented according M m to 4 ( 274 ) to the ftri6teft rules of perfpeCtive ; which Mr. Kirby thinks we mult not abide by in this cafe* Before I conclude this head, it may be proper to take ibme notice of the reprefentation of a row of equidiftant pi- lafters. A little reflection will make it evident, that the reprefenta- tion of a row of pilafter s parallel to the picture, are not fubjeCl to thofe awkward appearances which columns are, owing to a Ihort diftance. For, Let the dark line 9, 10, on the column D, Fig. 20, be a pi- lafter, equal in width to 13, 14, on the column A. Draw the vifuals 9, 10, to*/, cutting the picture PP at 11, 12; then will the fpace 11, 12 be equal a b, cut by the rays from the pilafter 13, 14; for as the pilafter 9, 10 is to 13, 14, fo will 11, 12, a b, their reprefentations, be to each other. The fame reafoning fhows us why columns increafe in thicknefs as they decline from the center of the picture, if we obferve where the vifual rays, drawn from their apparent diameters, cut the line pafling through their centers, as tv^kl\ wherefore, as kl is to 13, 14^ fo is h /, the reprefentation of the column D> to a b, the repre- fentation of A. kvi& hence it is evident, that in the reprefenta- tions of buildings whofe fronts are parallel to the pidture, their doors ( *75 ) doors and windows will be to each other as their originals are; that is, if the windows and fpaces between them be equal in width, their reprefentations will fee equal alfo; and, as Mr. Martin obferves, " all plane furfaces whatever, placed in a front wall or plane, will have in their perfpeitives no change of figure at all; a fquare, a parallelogram, a triangle, a pentagon, a circle, an ellipfis, Sec, will be all the fame figures on the per- fpe£live plane, and perfectly fimilar to the originals ; and this will hold good in every part of fuch a plane in front, as well above and below the horizon, as on each fide the eye -V Of the proper Choice of the Dijlance of the PiSture, proportioned to the Height of the Horizon^ and the Nature of the ObjeB to be reprefented. From what has now been hinted refpedting long and ftiort diftances, the learner will naturally wifh to know fome fixed principle about it, and what is the general rule for choofing a diftance. To give him all the fatisfadtion I can on this fubjedt, I ftiall propofe the following remarks. * See his Principles of the Genuine Theory of Perfpec"live, page 51. M m 2 There ( 2 7 6 ) There is a certain diftance fhorter than which the eye can- not eafily fee a picture ; and therefore if an object be delineated by fuch a diftance, it will appear unnatural. In Plate XIV. Fig. I, let BD be the length of the pi£ture f and Z the place of the fpe&ator's eye, and e the center of the picture, then will Z e be the diftance of the piiture ; but as Z e is very little more than half the length of the pidhire BD, therefore the angle under which the whole pi&ure would be feen at Z, is almoft ninety degrees. This is an angle which the eye cannot eafily take in, be- caufe the ray Z B is in a ftate too diverging to the pupil of the eye, and therefore the fpe£tator muft twill and ftrain his eye, before he could fee the whole extent B D. The optical reafon of this is as follows : Produce the vifual rays L P, K P. Now, it is evident, from the fcale on the arch, that thefe rays fubtend an angle of more than ninety degrees. Therefore fince v according to optical laws, rays will not unite in a point on the retina at a greater obliquity than an angle of forty-five degrees, confequently the points K L will not appear to the eye. This is probable enough from the figure ( 277 ) figure of the eye, for the image s of K, and o of L, are too far for- ward in the eye to be feen ; but by turning the eyes a little to- wards K or L, it is evident they will become vifible ; for then P e, the axis of the eye, will perhaps be turned to 20 ; or, on the other hand, at 40 ; confequently the angle of obliquity 20, P K, being confiderably lefs than forty-five degrees, the pencil of rays from the point K will unite in a point on the retina, and fo become vifible.. A fimple experiment will "convince the reader of the truth of this. Take a lath two feet long, and at the center fix a wire in a perpendicular direction, about thirteen inches long, or we fhall fay twelve inches, for then a thread ftretched from the wire to each end of the lath would form an angle of 90 ; that is, the threads will be perpendicular to each other. The end of the wire being held clofe to the eye, the experimenter muft look along each thread at once, and try if he can fee them diftin£tly at each end of the lath at the fame glance, without ftraining his eyes. If he continue to do fo a few minutes, the pain which this gives will be a fufficient proof that the eye cannot eafily take in an angle of 90 ; and that therefore twelve or thirteen inches is far too fhort a diftance for a pi£ture two feet long. Therefore, ( 2 7 8 ) Therefore, in Fig, i, if the eye be removed to P, the angle which the rays DP, BP make with the pidhire BD is coniiderably lefs, and hence the eye at P will more eaiily take in D B, the whole extent of the pidture ; becaufe the rays D P, B P do not diverge fo much at the pupil as before. If, therefore, the aforefaid wire be lengthened in the proportion of P e to B D, which will be as twenty-one inches are to twenty- four, the whole length of the lath ; and if threads be fixed as before, reprefenting the vifual rays DP, BP, the eye P, placed at the end of the wire, will eafily fee at one glance both the threads B D. This experiment, therefore, induces me to conclude that a pidture which is filled the whole length with objects on the front, fhould never be drawn by a diftance fhorter than the perpendicular of an equilateral triangle, whofe lides are equal to the whole length of the pidture. The angle B, P, D, is equi- lateral, and P e is its perpendicular ; and that I take to be the fhorteft diftance that fhould be ufed in this cafe. And I will venture to affirm, from experience, that any perfon who has never once thought on this fubjedt, when viewing a picture two feet long, will not ftand lefs than twenty-one inches from it when he wants to fee the effedt of the whole ; but if he would examine minutely fome particular part feparately, he will na- turally ( 279 ) turally approach nearer to the pidture, in proportion to the fize of the part thus examined. Whence, I alfo conclude, if nature is to be a guide in matters of delineation and painting, that the diftance of the pidlure ftiould be as 21 is to 24, fo is the proper diftance to the fpace which the front obje£ts occupy on the pi where they appear too narrow from front to back ; for the dif- tance at z forms, with the whole length of the picture, an angle only of 48 degrees ; which fliould not be admitted, except in particular cafes, as in the reprefentation of a row of columns parallel to the piiture in Fig. 20, where the eye at E is in the fame angle with the pidlure twice PP, as at Fig. 22. How to choofe a Di/lance, when the Objeffs are drawn by a large Scale, fituated not far from the Ceitter of the FiBure. Let pt, Fig. 22, ftill be confidered the whole length of th6 pidlure ; and let M be the reprefentation of a fquare, on a much larger fcale than that at C ; and let its fituation at M be much nearer to F, the center fquare. From J-, the center, extend the compafles to the extreme point of the pidlure, and fweep the arch c, then will c or b be a proper diftance in a cafe of this kind ; for the fquare M, drawn by the diftance appears perfectly natural, which would be too long were it drawn by V, the former diftance, as appears by the diagonal drawn from 10 to V, cut- ting the vifual 9, s at a. This by no means contradicts what has been advanced in page 178 ; where we fay, that " a picture filled with objects on the front, fliould never be drawn by a N n diftance ( 282 ) diftance fhorter than the perpendicular of an equilateral tri- angle, whofe fides are equal to the whole length of the pidture." For, let the line 9 be now confidered the bounds of the pidture, and it will be evident, by drawing a line from b to g, that the diftance s b is greater to the pidture at 9, than s D is to the pic- ure at /, otherwife b g would be parallel to D v. Another advantage may be obferved in this method, if we confider that a very high horizon will produce as much dif- tortion in a pidture as too fhort a diftance. Therefore if we fuppofe the horizon to be made higher by the fpace / /, the dif- tance will then be &i % in the fame proportion to it as s c is to s t. How to choofe a Diftance, when a Piece of Furniture, not very long, is reprefented by itfelf on the Center of the Front of the PiSiure* If a fingle objedl, or piece of furniture, be reprefented by itfelf on the center of the ground line, an equilateral triangle being drawn, whofe fides are equal to the length of the piece of furniture, the perpendicular of this triangle added to the height of the horizon, will be a very agreeable diftance in fuch a cafe. Thus, at the fquare F, fuppofed to be the plan of a piece of furniture reprefented on the center of the ground line, extend the compaffes from 10 to x, and fweep the arches, to form an equilateral ( 283 ) equilateral triangle, wliofe perpendicular will be at w; then will s zv be the diftance propofed in this cafe. But if the piece of furniture be of an extraordinary length in front, in propor- tion to its breadth from back to front, then it will be beft to adopt the preceding method; for if we fuppofe the piece of furniture to extend from 7 to 9, then a perpendicular of an equilateral triangle of that dimenlion added to the whole height of the horizon, would forefhorten too much. Of thefe things I am perfuaded the reader will be convinced, if he make the ex- periment as the cafes are here ftated. Of the Reprefentations of circular and curvilinear Figures^ both plain and fo/id; together with fome Remarks on their theory. The manner in which fome painters and defigners treat circular objects, would lead one to fuppofe that there is no cer- tain theory on which to build the practice of drawing objects of that kind. Sometimes we may fee a cafk, if not fliewing both ends, yet the end on which it ftands is reprefented by a curve consider- ably more flat than that by which its top is fhewn ; than which nothing can be more abfurd, for the very reverfe is the truth. Nn 2 We C 284 ) We may alfo fee, in fome cabinet defigns, the bottom of a round fronted cheft of drawers, or commode, reprefented by the fame curve as that which reprefents the top part ; which, though not fo ridiculous as the above, is far from being fcientific, or according to the rules of perfpeitive. That the learner may- avoid thefe miftakes, and have a proper conception of this mat- ter, we lhall propofe the following fliort theory. Cafe 1. — If an original circle be fituated in a plane parallel to the picture, its reprefentation will be a circle. Thus :— Let A, B, O, D, Plate XIX. Fig. 20, be an original plane parallel to the pi6ture H, I, K, in which is fituated a circle a, It, d, e, whofe reprefentation on that pi£ture is required. The vifual rays from each diameter of the original circle tending to the eye E, are cut by the picture or plane of projec- tion H, I, K, in a parallel diredtion to the original plane A,B, O, D. Wherefore we have the diameter 4, 2 drawn perpendi- cular to a d, its original. Alfo we have the diameter 1, 3 parallel to its original b e\ confequently the diameters 1,3 — 4,2, are the reprefentations of their originals ad,b e. C is the center of the original circle, and a line from C to E bifedls the triangle E, e\ confequently c is the reprefentation of the center C. Laftly, the radii or femidiameters c 1, c 2, c 3, c 4, are equal and fimilar to their originals, ( s8 5 ) originals, and therefore any one of them, as c i, will defcribe the circle i, 2, 3, 4, which will be the true reprefentation required. The truth of this may alfo be proved, by conlidering the vi- fual rays £E, dE, &cc. as the fides of a cone whofe vertex is at the eye E, and whofe bafe is the original circle a, b, d y e, and its axis C c. Now it is evident, that if a cone have a fedtion parallel to its bafe, the curved boundary of that fedtion is a circle, in like manner as a pyramid, whofe bafe is a geometrical fquare, produces a geometrical fquare, if its fedtion be parallel to its bafe. See page 230. Plate XV. Fig. 6. . By the above theory we fliall ealily judge how to proceed in the reprefentation of arches, when they reft on pillars or piers parallel to the picture. And it fliould be obferved, that in whatever lituation the original arch or circle may be in with refpedt to the center of the pidture, if they be parallel to the pidture, their reprefentations will be limilar to their ori- ginals Cafe 2.— If an original circle be fituated in a plane not pa- rallel to the pidture ; that is, if it be the reprefentation of a cir- cular objedt lying on the ground, or in any plane parallel * The reader may, if he pleafe, confult Dr. Brook Taylor's fecond corollary of theorem fourth, p. 16. 8 with. ( 286 ) with it, its reprefentation on the pidture will he an ellipfis. The reader who has previoully made this fubjedt his ftudy, may afk what I mean by the term ellipfis in this place ? fince fome have difputed whether the reprefentation of a circle in the above cafe be a regular ellipfis, or a curve of fome other fpecies of the conic fedtions. Mr. Noble has difcufled this point in oppofition to the critical reviewers, who had cenfured Mr. Ware in his tranflation of Sirigatti's perfpedtive, becaufe the tranflator had defined the reprefentation of an original circle fituated in a plane not pa- rallel to the pidture, to be a regular ellipfis. In oppofition to which definition of Mr. Ware's, the Critical Reviewers for July 1756, page 509, make the following obfervations. " In regard to his regular ellipfis for the reprefentation of a circle, it appears, from the very nature of perfpedtive, that the fore part of a circle will appear more round than the back part, w r hich being further removed from the eye, cannot appear to have the fame degree of curvature ; and confequently the whole figure, if drawn, muft be very far from having the form of fuch an ellipfis as is to be made by a tranfverfe and conjugate diameter." Mr. Noble, in oppofition to the above remarks, attempts to prove that the reprefentation in queftion muft be a regular el- lipfis; but his arguments are fo abftrufe, that if they were founded ( 287 ) founded in truth they would not be convincing to the ordinary- reader, and therefore I fhall not trouble him with them, but proceed to offer a remark or two in confirmation of thofe made by the Reviewers, which I think eafily underftood. Let A, B, C, D, Plate XXL Fig. 23, be the reprefentation of a geometrical fquare in which an odlagon and circle may be infcribed. The circle, truly reprefented, will touch every fide of both the fquare and odtagon, as fliewn by the figure. Now, I cannot fee by what mode of reafoning we can prove that the ellipfis is regular any more than we can prove that the odtagon is re- gular, becaufe it is the reprefentation of one that is fo ; but, perhaps, to ufe Mr. Noble's words, " we are ignorant of thofe few geometrical pnecognitae which alone can render vis ca- pable of conviction on this point :" and this may be the rea- fon why I have confidered Mr. Noble's arguments fo ab- ftrufe At the fame time 1 do not think the Reviewers were ignorant of thofe few firft principles of geometry, nor even wanted their recollection, when they animadverted on Mr. Ware. They juftly fay, " that the fore part of a circle will appear more round than the back part," which muft be evident to every one, by obferving that the whole curve on this fide of the diameter g is what they mean by the fore part of the circle, * The reader, if he choofe, may fee the arguments in Noble's Linear Perfpeclive, page 142. and ( 288 ) and all beyond *g c is confidered the back part of it. We may alfo obferve, that the curves contained in the quarter parts of the ellipfis are not one of them fimilar to another. How then can we pronounce it a regular ellipfis ? When we fpeak of the per- fpedtive appearance of any original objedt, do we not denomi- nate it by the figure which it aflumes upon a plane, and not as it appears to the eye ? where then is the good fenfe or propriety of calling that a regular ellipfis which, is\no way regular ? One would think Mr. Noble had forgotten the dis- tinction which he fo properly maintains in other parts of his book, namely, between the appearance of objedts to the eye, and their reprefentation on a plane ; for if we Hand at a diftance from the top of a round table, it will appear to the eye a re- gular ellipfis ; but if the top be reprefented on a picture accord- ing to that diftance, it will be an irregular ellipfis, and its irre- gularity will be in proportion to the ftiortnefs of the diftance of the pidture. But fuppofe we were to confider h d the tranfverfe diameter, and confequently bf the conjugate, yet there is a manifeft difference between the two femi-ellipfes. Nor is ,it poflible to draw a tranfverfe diameter in fuch a direction, as when the two femi-ellipfes are turned down on each other that they would coincide. Yet it muft be obferved, that if the re- prefentation were drawn in the center, and by a long diftance, it would, in this cafe, approach fo near a regular ellipfis as the difference could not be eafily difcerned. From ( *8 9 ) From what has been faid, the learner muft obferve then, that when he proceeds to draw the reprefentation of an original circle, he muft not think of applying the compaffes or trammel to draw it by ; but a number of points muft be found, through which the path of the ellipfis muft be directed by a hand fupe- rior to his who only can draw an ellipfis by a trammel or com- paffes. Of the Reprefentations of circular and curvilinear Figures, both plain and folid* Prob. XIX. Fig. 23. Plate XXI. To reprefent a Circle lying on the Ground Plane, or when it is fituated in any Plane parallel to the Horizon. Operation.— Let HL be the horizon, and GR the ground line, s is the center of the picture, and d its diftance. Make j* v equal s d, and draw d V at right angles to dv, then will v V be the vanifhing points to four fides of the o£tagon. Make V M equal Yd. Likewife make vm equal vd> and Mm will be the true meafuring points. Draw a half plan of an o£lagon, as was fhewn in Problem XVII. and Fig. 18, Make AD equal to the diameter of the given circle. Draw the vifuals 2 V, 1 inde- O o finitely. ( ) finitely. Make 2 P, 1 / equal 2 the fide of the o&agon ; and draw from / and p meafuring lines to their refpe£tive points M cutting at 3 and 8. From 3 and 8 draw 3 s, 8 s. Take the fpace 1 D, and lay it from D to 10, and from A to 12. From 12 draw a line to V, cutting at 7, 6. From 10 to v do the fame, cutting at 4, 5. Laftly, draw 5, 6 parallel to 1, 2, and the odtagon in which the given circle is to be infcribed is com- pleted. Method fecond. — In this method, which is very fimple, we proceed without regard to any of thofe lines ufed in the firft method, which was more fcientific, and according to Dr. Brook Taylor's fyftem. The ground plane F is fuppofed to remain as before. Let A, B, C, D, be the reprefentation of a geometrical fquare, found by the diagonals paffing to each vaniftiing point, confequently S will be the center. Through S draw g c, and draw as, from which we have four points, a, g, c, of the in- tended circle. Draw a line from 2 to V, and from 10 to v 9 cut- ting the diagonals at b, d, whence we have two more points. From the points b and d draw parallel lines, cutting the dia- gonals in the points h f r adding other two; which in all make eight points, fufficient for the reprefentation of the given circle. N. B. A quarter plan F is fufficient far this- method. 8 Method ( m ) Method third.— Draw the quarter plane of the circle to be reprefented, contained in the fqnare A, E, a, O. Draw the dia- gonal O A ; and from the point n, where the diagonal cuts the arch E a, raife a perpendicular to t. Reprefent a fquare as before, drawing its diagonals each way. From / draw a vifual to jj cut- ting the diagonals in the points b f. Laftly, from the points h and / draw parallels to the other diagonals, cutting at £ and d 9 by which method there will be eight points gained as before. This laft method being fo fimple, and totally divefted of every thing that can any way perplex the learner, it has been adopted in the following problems, and in moft of the repre- sentations in this book. There are, however, various other methods of effecting the fame thing, which might prove more pleafing to men of fcience, but which would not be fo advan- tageous to the workman, nor even to the artift, with whom fa- cility and difpatch are principal objedts. Prob. XX. Fig. 24. Plate XXI. 7b reprefent a Circle fituated in a Plane perpendicular to the Ground Plane. Operation.— Let the line R be the ground line, and L the horizon, s is the center of the pidlure, and s d, on the vertical line, the diftance. Draw half the original circle B, n, C Draw O o 2 the ( ; the diagonals 0 D, 0 A ; from A and D reprefent a geometrical fquare, by drawing a line from A to d, cutting at F. From i, 2, draw parallels to 3, 9; and from 3, 9, dire£t vifuals to the center and the diagonals of the fquare will be cut at 8, 5, 6, 7, forming four points, by which the reprefentation of the circle may be corre&ly drawn. Prob. XXL Fig. 25. Plate XXI. To reprefent a Cylinder ere& on the Ground Plane. After what has been faid on the preceding problem, it is fcarcely neceffary to fay any thing on this ; and therefore I fliall only obferve, that having drawn the bafe of the cylinder by the fame method as in the laft, proceed to raife perpendiculars from A, B, D, C ; and from a draw ab parallel to A B, at a dif- tance from AB equal to the original length of the cylinder. From a b reprefent another fquare, 3s b, c y q. Draw its dia- gonals and diameters. From the point 4 raife a perpendicular till it cut the diagonal b c. From the point 7 raife one till it cut the diagonal a q. Do the fame at the points 6 and 5, and eight points will be found at the top correfponding with thofe on the bafe, by which the cylinder may be completed. Prob. ( 293 ) Prob. XXII. Fig. 26. Plate XXI. 7b find the Reprefentation of a Cylinder lying on the Ground, whofe Sides are oblique to the Piffure. Operation. — Draw the ground line and horizon as ufual; and let s be the center, and d the diftance of the pidture. Make s v equal s d 9 and from d draw dV at right angles to v d 9 then will v V be the vanifhing points of the ends and fides of the cylinder. Make a half plan of the bafe of the cylinder at a 9 b 9 c 9 d 9 as in the preceding cafes. Draw C A perpendicular to the ground line, and equal to the diameter of the cylinder. Draw the vifuals C v 9 A v> and C V, A V. Make C F equal C A, and C S equal to the given length of the cylinder. Draw F m 9 S M, cutting at D and 3. Draw DB perpendicular to the ground line, and we have a fquare in which the end of the cylinder is to be infcribed. In like manner reprefent a fquare at the other end, as 1, 2, 3, 4; and having drawn the diagonals and diameters, of both fquares, draw parallel lines from 5, 6 to e f. From e and / direil vifuals to V, cutting g and h; from e 9 f, g, h, draw vifuals to v 9 which will cut the diagonals of each fquare in four points, by which each end of the cylinder may be com- pleted. N. B ( *94 ) N. B. A circle or cylinder may be reprefented without drawing a plan, by dividing the given diameter c a into feven equal parts, one of which will cut the diagonals as before, at leaft near enough for practice. Prob. XXIII. Fig. 27. Plate XXL To find the Reprefentation of a fetni-ellipfts, whofe tranfverfe Dia- meter is parallel to the Pi&ure* Operation. — Draw the ground line and horizon as in common, and let s be the center, and d the diftance of the pic- ture. Make then a plan of the femi-ellipfis, whofe tranfverfe diameter is DG, parallel to R, the ground line. Draw A B, in- cluding half the conjugate diameter. Draw the diagonals O B, OA, cutting the ellipfis at P and N. Divide AD at K, and draw E F. From E, P, N, F, O, raife perpendiculars to the ground line at 4, 5, 6, 7, 8, 9, 10, and from each of thefe draw vifuals to s. Make 3, 2, 1, each refpe£lively equal A, K, D ; and from 1, 2, 3, draw lines to d, the diftance, cutting at &. From a, >£, b, draw parallel lines to g^c\ and laftly, draw 0 a, og, then will the feveral vifvals be cut at the points requifite for defcribing the elliptic curve, "es the dotted points in the figure ihow. Prob. ; V f ^95 ) Prob. XXIV. Fig. 28. Plate XXL , 7b find the Reprefentation of an elliptic Segment inverfely. Suppose A,B, C, D, to be the fhelf of any table, &c. hol- lowed in front in the figure of an elliptic fegment, A, 1, 2, 3, 4, D. Having drawn one fide A, 1, 2, 3, 4, of the given: fegment at plea- fure, divide the curve into four equal parts, and from 1, 2, 3, 4, raife perpendiculars to c y f; then, to make the other fide of the curve fimilar to that already drawn, lay on the feveral divi- fions /, by a, to the right hand, and from thefe let fall perpen- diculars at pleafure ; then, from. % 2, 3, draw parallel lines, cut- ting the correfponding perpendiculars on the right hand, by which the other half of the fegment may be accurately drawn. The plan being thus prepared, draw vifual lines to j*, the cen- ter, and make 7/ the diftance. At a fix one foot of the com- pafles, and extend the other to 1, and with it fweep the firft arch; and in like manner ftveep the arches 2, 3^ 4. From the feveral points where thofe arches cut the line AD, direct lines to the diftance, cutting the feveral vifuals at the points 1, 2, 3, 4. Laftly, from 1 draw a parallel to 7, from 2 draw one to 6, and from 3 draw one to 5 ; thus will feven points be found through which the path of the reprefented curve muft pafs. SECTION ( age ) SECTION V. The application of the preceding Problems to thePratfice of Draw- ing the Reprefentation of Pieces of ArchiteSlure, and particu- larly various Pieces of Furniture in different Pojitions to the Pi&ure. The preceding problems, and the various figures referred to, muft be confidered as only laying the foundation for the re- prefentation of more compound objedts, confifting both of right and curvilinear parts. It becomes neceflary, therefore, to fhew the moft eafy application of thefe problems in a variety of examples, that the whole may appear practical and ufeful, and that we may alfo fee the real effect of that art which we have hitherto laboured to under ft and. Nor do I think that perfpec- tive could well be applied in many cafes without fuch ex- amples. Befides, the ufefulnefs of having a few proper ex- amples always ready to turn to, muft be of confequence to thofe who but feldom reprefent things in perfpeftive; in which cafe the rules and methods will frequently efcape the memory, and make it neceflary to have recourfe to the book ; and for the fake of more readily finding the explanation of each example, the page of letter-prefs where the explanation begins, is en- graved on the copper-plate, it being a practice fometimes to BJllAd. as the Jet directs, fy, TSkerafonAuy 4tf92. ( *97 ) to look at the plates firft for an example of what we intend drawing. Example L Fig. 29. Plate XXII. How to reprefent a receding and returning Flight of £teps whofe Rifers are parallel to the Pi&ure. Let HL be the horizontal line, s the center, and d the dis- tance of the pidture; G R is the ground line. Make A B on the ground line equal to the original length of the fteps, and draw A E perpendicular to the ground, and make the fpaces A F, F N, NO, andOE, equal the original height of the rifers. Draw vifuals from each of thefe divifions tending to s. Draw F T parallel to A B, and from B and T draw lines to s. Next, lay on the ground line the breadth of the ftep, from B to a ; and from a draw a line to d the diftance, cutting at k ; raife a perpendicu- lar from k 9 cutting at n ; and from n draw a parallel to p. Then from p raife a perpendicular to q, cutting the vifual N J* at q ; draw a parallel to r, and from r a vifual to s. Then from a to b lay the breadth of the fecond ftep, and draw a line to d 9 cut- ting at m ; raife a perpendicular from m to u, and draw a line from u to s, and a parallel from u to w 9 cutting the vifual C s at w. Laftly, lay on from b to e the breadth of the half fpace, and from e draw a line to d 9 cutting at 5, and raife a perpendi- P p cular ( ) cular to x> and from x a parallel ; which will complete the firft flight. The returning ftep leading to the fecond flight is next to be confideredc For this, draw the perpendicular y, 7, 8, 9, 10, at a diftance from A equal to the width of the returning fteps ; draw the line 6, 7, parallel to Y A, and at 6 there is an allowance made for the bearing of the ftep ; alfo at Z there is an allowance for the other half fpace to reft on. Draw the vifuals R s and E s ; and how to complete the reft of the fteps muft be evident from the figure. The returning flight comes forward until it is in the fame plane with AB, the firft rifer; therefore, after having placed the original height of the rifers at 8, 9, 10, and drawn from thefe divifions vifuals to s, it remains only to lay on the bearing of the fteps at 1,2, tending to the diftance, and cutting at 3, 4. Thefe being traced along the fteps, as fhewn by the dotted lines, till they cut the vifuals 7^, R;; how to perform the other part will appear obvious. N. B. The laft ftep of the returning flight 10, 12, does not all come into the plate, other- wife its length would be equal A B, the original length of the ftep. Thefe fteps might have alfo been reprefented oblique to the pidhire ; but as I have not plate-room for fo many examples^ the learner muft try if he can do it himfelf, by reflecting on what ( 299 ) what has already been faid and done on objefcs in oblique fili- ations ; but if he fail in his attempt, he may confult Mr. Mal- ton's complete treatife, in its pra&ical part. Example II. Fig. 30. Plate XXII. How to reprefent a Fufcan Pedejlal and Bafe parallel to the Pi&ure. Draw A firft, the profile of the pedeftal and bafe, which is taken from the large module of the Tufcan order in Plate VIII. Let H L be the horizon, and make 5 the center, and s d only half the diftance of the pidture, for want of room on the plate. Make G R the ground line, and on it, from B to C, lay a fpace equal to the length of the original plinth. Draw from thefe, lines to s. Next, confider how far the pedeftal is to be repre- fented from the pidture, w r hich in this example is equal twice C D ; becaufe the whole diftance is equal twice s d> Therefore, from D draw a line to d 9 cutting at F. Make D E equal half IB C, cutting at I. Draw F K and I O parallel to B C, by which a fquare will be reprefented equal to the plinth. Proceed now to reprefent the projection of the ogee or bafe of the plinth. For this, take 0, 1, half the original proje&ion of the plinth, and place it from B to 2. From 2 draw a line to S, cutting at 3; and from 3 draw one to d, the diftance, cutting 4. Draw next P p 2 the ( 3oo ) the diagonals K % F O. From 4 draw a parallel line, cutting the diagonals at 8, 5, and from 5 draw a line to s] cutting at 6 ; then will be projected each miter of the plinth, and alfo the lize of the dado will be determined at the fame time. Therefore from 8, 5, and 6, raife perpendiculars at pleafure, which will ferve both for the angles of the dado and the plinth of the bafe. From 0 draw a line to j-, which will cut the parallel produced from 8 at 5, and will give an internal miter at 5, K ; raife per- pendiculars from 5, K at pleafure. From c and 12 on the pro- file, draw lines to s 9 cutting the perpendiculars raifed from 5, K at /, m 9 which will give the correfpondent miter to 5, K. Draw the projecting diagonals of each moulding on the profile, as 9, 10, 11, 12, and draw ab\ from all which points in the mould- ings draw vifuals to j*, which will feverally cut the aforefaid perpendiculars at m, r. Draw then the line mn,pq, which will be the diagonal lines of the internal miters. Now draw parallels from p . . 23. ( 309 ) Example VI. Fig. 33. Plate XXIV. How to reprefent a Houfe in Perfpe&ive, having its Front parallel to the Picture. . Let H L be the horizon, and G R the ground line, s is the center, and s d the diftance of the pidture. Make A C the ori- ginal length of the front, from which draw vifuals to s. Con- fider next how far the houfe is removed back, which is here equal C 1. From 1 draw a line to d, cutting at 7; and from 7 draw a parallel to 8. Draw a plan of the roof 1,2,3,4. And from d the diftance, draw d v parallel to the lide of the roof 1,2; then will v be the vanifhing point for that fide of the roof. Take s v and place it below the horizon at V, perpendicular to s; then will V be the vanifhing point of the other fide of the roof 2, 3. From 8 and 7 raife perpendiculars at pleafure, and make A F the original height of the front. From F draw a line to j*, cutting at 9 ; draw a parallel from 9 to 10. For the windows and door, lay their original meafurements on A F and A C, drawing vifuals to s 9 as the figure Ihews; and as the front is parallel to the pidture, confequently each object on it is fimilar to their originals and therefore lines perpendicular to 8, 7, * See pages 274 and 275. and ( 3io ) and 9, 8, will form the fides, tops, and bottoms of each window and door- way. From 9, 10 draw lines to v 9 the vanifhing point of the roof; from 10 draw a line to s 9 the center. Take then 1, 3, the fpan of the roof, and place it from F to B; and from B draw a line to s, cutting at n ; from n draw a line to V, be- low the horizon, cutting at 14; from 14 draw a parallel to 13, for the top of the roof; and from 13 draw a line to V, cutting the line 10 s at 15, forming the fartheft fide of the roof; draw a perpendicular from 15 to 6, which will complete the end of the houfe. Laftly, to find the height of the chimney, draw a line from s through 14, cutting at E ; and from E lay on the original height of the chimney to D ; and from D draw a line to Sj cutting a perpendicular from 14, which will give the height required. Method fecond. — The front of the houfe being drawn as has been defcribed, to find the appearance of the roof and gable- end, draw the roof 1,2, 3, as before; and from 4 and 3 draw lines to d, cutting at 5, 6 ; from 5, 6 raife perpendiculars at plea- fure ; from 5 draw a parallel to O, cutting the vifual A j- at O, for the center of the left gable-end ; from O raife a perpendicular at pleafure. Take then the perpendicular height of the roof, from 4 to 2, and place it from F to E ; and from E draw a line to j, cutting the aforefaid perpendicular at 14, which will give both the ( 3ii ) the pitch and height of the roof. From 14 draw a parallel to 13, cutting the other perpendicular correfpondent with 14. Laftly, from 9 draw a line to 14, and from 10 draw a line to 13, and from 13 to 15, which will determine the appearance of the roof, as before. Example VII. Fig. 34. Plate XXIV. To find the Reprefentation of a Houfe whofe Gable-end is parallel to the Pi&ure. In this cafe the front that was before parallel to the pi&ure is now turned perpendicular to it. The gable is therefore pa- rallel to the picture, and is nothing more than a geometrical elevation, found by laying on the heights on a b, and the widths on a f and drawing lines from thefe to j*, the center; tnf is the diftance of the houfe from the pi£lure ; and a line from m to d, cutting at n, finds the reprefentation of that dif- tance. The other lines to the left of m 9 all tend to d alfo, by which the windows and doors, &c. are found; mq is equal to the original length of the front, a line therefore from q to d de- termines its apparent length on the piiture. For the pitch of the roof, draw e j*, cutting at p ; from which raife a perpendi- cular ; draw another perpendicular from w, the center of the other ( 3™ ) other gable-end; alfo draw the vifuals ks.ls, for the roof; which vifuals will cut perpendiculars at h and /, anfwering to the points Ik, by which the roof is formed. For the reft, the figure itfelf is fufficient, by obferving that u t is the perpendi- cular height of the roof, and / b of the chimney. Example VIII. Fig. 35. Plate XXIV. How to reprefent a Chair, having its Front parallel to the Figure. After having made afcale of feet and inches to propor- ' tion each part of the chair by, draw A, the profile of the back and fide rail ; and draw B on the right, according to the bevel of the feat ; and obferve, to diftinguifh the lines of each chair, one is marked with fmall letters, and the other with numerals. Let H L be the horizon proportioned by the fcale, about five feet high from G R the ground line. Make a b equal to the length of the front ; from which draw lines to s, the center, which, in general, ought to be perpendicular over the middle of the chair, becaufe it affords the moft eafy and natural view of its back. Next, from q, the width of the feat, draw a line to the diftance, here out of the plate, cutting the vifual a s at c ; 8 from ( 3*3 ) from c draw a parallel to e at pleafure. Take C D, the bevel of the feat, and place it from a to d; and from d draw a line to s 9 cutting c e at y 9 which gives the bevel of the feat. From a draw a line through jy, cutting the horizon at V, which will be the vanilhing point to every line originally parallel to ay 9 the fide rail ; take s V and place the fame fpace to v 9 which will be the vanifhing point to the other fide of the chair ; therefore from b draw a line to v 9 cutting at e 9 which forms the feat. For the thicknefs of the back rail, draw a line from p to the diftance, as the figure ftiews. For the height of the back, raife a perpen- dicular a g 9 and draw a parallel from r to g ; draw alfo a per- pendicular from j>, and a line from g to V will cut it at f 9 de- termining the height of the back. For the bottom of the back foot, draw a line from u to the diftance, cutting a per- pendicular from c at w. From w draw a parallel, and from z draw a line to the vanifhing point V, cutting at x 9 which will determine the place of the back foot *. How every other part is done, muft be evident from infpe<5ling the figure. * The reader will perceive that the line from z to x is not accurately drawn, for the engraver did not follow his copy, otherwife the line would have ^touched the bottom of the back foot tending to V, which the learner may prove, by drawing a line from z to V. This inftance may ferve to Jfhew the trouble there is with engravers, who in general are totally ignorant of perspective. Example ( 314 ) Example IX. Fig. 36. Plate XXIV. How to reprefent a Chair having its Front perpendicular to the Pi&ure. In this example the fame ground line, horizon, center, and diftance, is ufed as in the preceding ; therefore let the fpace 7, 1, be equal to the length of the chair front. From 7 draw a line to j, and from 1 draw a line to the diftance, cutting at 16. Make 7, 9 equal to the length of the fide rail, and from 9 draw a line to s ; make 9, 10 the thicknefs of the back foot, and from 10 draw a line to j*, as before. Draw a parallel line for the depth of the fide rail, and from 8 draw a line to j*. Next con- fider how much the back foot fweeps off from the perpendicu- lar, which is equal to the fpace 12, 13, or 2, 22 ; draw vifuals from each of thefe points, as the example directs. To find the bevel of the fides, take C D and place it from 7 to 5, and from 1 to 3 ; from which draw lines to the diftance, cutting at 1 1 and 17; from 11 and 17 draw parallels cutting the vifual 9^ at 20 and 18 ; from 7 draw a line to 20, and from 16 draw one to 18, which will finifti the outline of the feat. Laftly, from 18 and 20 let fall perpendiculars, cutting at 24, 25 ; from which draw parallels to the vifual 13 which gives the bottom of 8 each Pt.24 4 ( 3i5 ) each back foot ; and for every other particular, a little reflec- tion and obfervation will be fufficient. Example X. Fig. 37. Plate XXV. How to reprefent a round Table in Perfpe&ive^ having two of its Claws in front parallel to the Pi&ure. Draw a profile of the pillar and claw, as at A. Take a the fpring of the claw, from the center of the pillar, and with it defcribe a circle 1, 2, 3 ; divide the circle into three equal parts, fo as to fuit the intended polition of the claws, as 1, 2, 3 ; draw from thefe perpendicular lines to /, / Reprefent a fquare 4, 5, 6, 7, equal to the diameter of the top ; draw the dia- gonals and diameters of the fquare, and from // draw vifuals to s ; from C, the center, draw a perpendicular for the pillar ; and having determined the height of the table at B D, from BD reprefent a circle for the top, as has been taught in page 289, fee Fig. 23. Next find the place of the claws ; for which make f e equal / 2, and from e draw a line to the diftance cutting at g ; from g draw a parallel to h, for the other claw. To find the pflace of the back claw ; extend the compaffes from e to 3, and make 4 c equal to it ; from c draw a line to the diftance, cutting at m ; and from m draw a parallel to /, which will be the place R r 2 of C 3*6 ) of the claw. For the different parts of the pillar, draw from the profile lines to the diftance, cutting the perpendicular C F, as the figure fhews. It now remains for every part to be finifhed by a good hand and eye accompanied with judgment, as no other rules can be of any fervice in cafes of this fort. Example XL Fig. 38. Plate XXV.. How to reprefent an offagon Table having one of its Claws m Front perpendicular to the Piflure* Draw the profile of the pillar and claw, as at B ; and, as in the other example, take the fpring of the foot or claw from the center of the pillar, and with it defcribe a circle, and mark out the place of the claws at 1,2,3. Draw 1,2,3 U P to the ground line, and produce 1 up to u r for the height of the table. Reprefent a fquare both at top and bottom, and draw the dia- gonals, finding the center for the pillar. Draw now the dotted lines from the profile to k u the perpendicular, and where they cut draw lines to s, the center of the pi£lure, cutting the center of the pillar for each refpe£tive moulding. Next find the fitu- ation of the claws ; having drawn lines from k, h, a, to j-, make h b equal h i ; and from b draw a line to the diftance, cutting at which will be the place for the firft claw. Make a c equal a 3, and from c draw a line to d, as before, cutting at b ; from b draw I ( 317 ) draw a parallel to e 9 then will b e be the place of the two other claws. From 5 and 4, produced from 7, the height of the toe, draw lines to s ; and from e and b raife perpendiculars cutting thefe, which will be the height of the toes of the back claws. Laftly, we here fuppofe the top to be an irregular odtagon, wherefore let m n be equal to four of its fides ; draw from n m lines to j, from n draw a line to d y cutting at 0 ; from 0 draw a parallel to / ; finding the oppofite angle, draw m t ; and from the diftance draw a line through w 9 cutting at r ; from r draw a parallel to p ; and draw p q r which will finifh the octagon for the top. Example XII. Fig. 39. Plate XXV. 7b put a Commode Table in Perfpe£iive 9 having its Front pa- rallel to the Pi&ure. Observe, the ground line for the tables is here ufed as the horizon for the commode. Make s d half the diftance, for want of room on the plate, and make GR the ground line. Draw then the plan P of the front, according to the intended fcale. And, in cutting of each vifual line, ufe one half of a foot inftead of a whole one ; be- caufe only half the whole diftance is ufed. Therefore, having drawn ( 3*8 ) drawn the vifuals 3 s, B s 9 draw a line from 1 foot on the fcale line to d the diftance, cutting at g; then will ^g reprefent a line two feet long, equal to the breadth of the commode. From g raife a perpendicular, cutting at m, finding the apparent width of the top ; draw 5, 10 parallel and equal to the height of the foot and bottom of the commode ; draw parallel lines, alfo, for the partition below and above the drawer, and for the top, as fliewn by the figure. Proceed now to find the place of the feet and the fweep of the front : for the feet take half 3, 4, and from 3 place it to 6 ; from which draw a line to d, cutting at 2 ; from 2 draw a parallel cutting B s 9 for the other foot. Find now two points by which to dire£l the fweep of the front thus : draw perpendicular lines from the plan at 9, 12, and from 13, /, k 9 where they cut, draw lines to s ; then take half 8, 9 and place it from k to /; and from i draw a line to d 9 cutting at p, finding a point for the curve ; from p draw a parallel to t 9 finding the oppofite point, which will be fufficient for the whole. Laftly, for the recefs draw vifuals from r f 9 and, fuppofing the recefs to be a foot deep from front, make e f equal half a foot on the fcale ; draw from e a line to d 9 cutting at 0 ; and from 0 draw a parallel to the oppofite vifual. Every other thing maybe learned by obfervation, without going through a minute detail of every particular, which would become an exceeding dry tafk indeed. Example ( 319 ) Example XIIL Fig. 40. Plate XXVI. How to reprefent a Chair obliquely fituated to the Pifiure. In the two former examples of chairs in perfpedtive, the firft of thefe had its front parallel to the pidture, which is the moft ufual way of reprefenting a chair when it is wanted to be viewed as a pattern ; for the back being parallel alfo, it gives the moft natural and diftindt view of the banifter and all its parts. The fecond is put with its front perpendicular to the pidture, which is a pofition wanted in the reprefentation of in- ternal views of rooms or paffages : and this third example being put oblique, is confidered by painters moft pidturefque or fuit- able for a pidture, in which cafe the pattern of the chair is not much regarded, only its unformal fituation fuiting to the fub- jedt and circumftances of the defign. In this example I fliall therefore confider myfelf as offering fome affiftance to the painter, as well as in a few other inftances in this book. Obferve, that the vanifhing points vV 9 and meafuring points m M, of this example, are all found by laying the dis- tance downwards to D, for want of room on the plate, and which needs not here be explained, after what has been done in ( 32° ) in problem VI. page 236, as it makes no difference whether the diftance be above or below the horizon. Therefore proceed in confidering G R the ground line, drawn parallel to the horizon II L; on GR make a fcale of inches to proportion every part by. Make a f equal to the original length of the front, which ; in parlour chairs is generally 21 or 22 inches; and let a g be equafl to the width of the feat from the infide of the back to the front, commonly 16 inches. As a is confidered the neareft angle to the pi£ture, from a raife a perpendicular at pleafure, on which the original heights of each part muft be laid, as from a to nt, for the height of the feat rail, about 16 inches without the fluffing. From a and w draw vifuals tend- ing to V and v. From fc draw lines to m 9 cutting at xy; from b do the fame, cutting at 3 ; from which points raife perpendi- culars for each foot. Next, from g draw a line to M, cutting at k ; from which raife a perpendicular to 0 ; from 0 draw a line to V ; and from 4, the infide of the front foot, whofe thicknefs is fuppofed equal to the bevel of the fide rail, draw a line to v 9 cutting at p ; then from w, the outfide of the foot, draw a line to p, produced till it cut the horizon at a, which will be the va- nifhing point to every line originally parallel to the fide w p. From v extend the compaffes to 0, which lay on to O, and O will be the vanifhing point to all lines parallel to the other fide / 5. Therefore, from t draw a line to O, which will cut at 5, com- pleting the form of the feat. On the perpendicular line from w, lay ( ) lay on 21 inches for the height of the back, and diredt a line to 0, and through p draw a perpendicular at pleafure for the joint of the fide rail. Next confider how much the back foot pitches, which in this example is equal b g 9 and h i is for the thicknefs of the toe. From thefe draw lines to M, cutting at & 9 /,n; and from kj /, n 9 draw lines to V, which will cut the vifual b v in the place for the toe at 8, 6 ; from 6 raife a perpendicular cut- ting at 7, and from 7 dire£l a line to V, for the top rail; and how the reft is performed muft be obvious from what has al- ready been faid and done. Example XIV. Fig. 41. Plate XXVI. To put a Cylinder Dejk and Book-cafe in PerJpe£Hve> having its Front oblique to the Piflure. Draw firft an elevation of the cornice and pediment, and proportion the pediment according to Fig. 36, Plate V. by di- viding half the length of the cornice into nine equal parts, of which take four for the pitch. Take one of thefe parts for the height of the pedeftal, and the remaining three for the vafe. Draw lines up to the ground line at r, F,/>,/, and the vanifh- ing points having been already found, draw from r lines tend- ing to each ; from r, the neareft angle of the book-cafe, raife a S f perpendicular / C 322 ) perpendicular at pleafure, on which the feveral heights muft be laid. From r to A lay on the depth of the lower part, and direil a line to M, cutting at U, and make AB the depth of the book-cafe, and draw a line as before, cutting at X, from which raife a perpendicular. In the fame manner draw lines from F p y tending to ?n, and cutting at 3, 12, for the length and center of the book-cafe. The feveral original heights for the defk part, doors, and cornice, muft now be placed on the perpendicular, from which lines muft be drawn to each vanifliing point. And here we muft obferve, that as the neareft angle of the book-cafe comes forward to the picture *, confequently the Aider is on this lide of it. To proje£l the Aider in this cafe, a vanifliing point muft he found, from which, if a line be directed it will pafs through the diagonal of any fquare. Thus : on D, the dif- tance, fweep the arch S, and bife£t it at S, and through S dire£t a line to the horizon, cutting at d on the fmall drawers ; lay from r to g a fpace equal to the projection of the Aider; and from g dire£t a line to m % cutting at /; from / raife a perpendi- cular to y ; and from d, the aforefaid vanifliing point, draw a line through y at pleafure j and from v draw a vifual for the end of the Aider, cutting at n ; from n draw a line to V r and from v draw one through 10, for the other end of the -Aider. The opening of the door is next to be confidered. It is evident * When any object is reprefented to touch the ground-line, that part which touches it is faid to be in the picture. that ( 3*3 ) that a door turning on its hinges muft defcribe'a femicircle, and therefore if a femi is reprefented, whofe radius is equal to the breadth of the door, its circumference will determine any open- ing that can be propofed. To defcribe the femicircle proceed thus. — From the vanifli- point v draw a line through #, the center of the book-cafe, and produce it at pleafure ; then from d, the vanifliing point of any diagonal, draw a line through 12, cutting at C; from C draw a line to V; and from v draw a line through 12, cutting at K; and from K draw another diagonal to cutting at w ; from v draw a line through w, cutting at E, and produced to Q, cutting a parallel from C ; from 12 to E draw a diagonal, and if the door is intended to be opened 45 degrees more than fquare, pro- duce this diagonal, as fhewn by the dotted line, till it cut the horizon, and its interferon with it will be the vanifhing point for the top and bottom of the door. Divide CQ into feven equal parts, and from one of which at 7 dire<5t a line to m, cut- ting at 13; and from 13 draw a vifual to $, cutting at 1 ; from 1 draw a vifual to V, cutting the other diagonal at 2 ; from 2 raife a perpendicular for the apparent breadth of the door in this poiition ; and from the laft mentioned vanifhing point found by the dotted line, draw lines for the top and bottom of the door, hy which it may be completed. For the ends of the cy- linder we need not fay any thing, as this is the fame as in pro- S f 2 blem ( 3M ) blem XXII. therefore we fliall proceed with the cornice and pe- diment. Set off the projection q r of the cornice at 6, 5, on a parallel line drawn at the full height of the book-cafe, and draw lines to v y and the line 5 will cut the perpendicular raifed from X, and the line 6 will cut a perpendicular at 8, fuppofed to be raifed from the miter point of the cornice, which is found by drawing a line from d> the vanhhing point of the diagonal to X, cutting at t\ from t dire6t a line to V, cutting at a\ and from a raife a perpendicular, which will cut a line drawn from 8 to V, at the other miter point; every other part of the cornice muft be finifhed by the reader's judgment, governed by thefe prin- ciples, as it would be impoffible to apply every rule in fuch fmall examples. Laftly, for the pitch of the pediment, a vanifliing point muft be found, according to the principles in Problem IX. Plate • XVI. by drawing a line from m parallel to the pitch line at the elevation P, produced to V P, cutting a perpendicular from V ; from 8 draw a line to V P, cutting a perpendicular in the center of the front edge of its cornice ; from which draw the other fide of the pediment, which, if produced, would cut a point as much below the horizon as V P is above it. Thefe pitch lines being found, the fcroll pediment may be drawn by hand with 8 fufficient ( m ) fufficient accuracy ; but if the pediment be a ftraight pitch, then the lines for each moulding muft tend to V P, and to a point as much below the horizon. And I would here obferve, that in drawing after theic examples, it is not intended that the dif- tances made ufe of in them fliould be a precedent to the learner. Thefe are chofen to fuit the plate ; but the learner having fuf- ficient room on his drawing-board, muft choofe his diftance to give the moft natural and pleafing effe£t to his drawing, by the rules already laid down. See page 275. In thefe examples almoft every difficult part of perfpedlive is introduced, and it is prefumed that, after the learner has made himfelf fully mafter of them, nothing will occur in prac- tice that can give him much trouble, efpecially if he be pro- perly acquainted with the fhort theory that has been given. However I am fully perfuaded, that no cabinet-maker or up- holfterer will ever want to pradtife more ; and, if I am not mif- taken, there are but very few painters who are at the trouble of praitifing fo much. But if the reader's profeffion or neceffities Ihould require him to extend his fkill in this art further than what has been advanced in this treatife, I will freely refer him to Mr. Malton's complete Treatife, from which, it is here gratefully acknowledged, I have received confiderable affiftance. SECTION < 3*6 ) SECTION VI. Containing a Jhort View of the Nature and Principles of Shadows, caufed by the Sun coming in different Directions to the Pic- ture ; together with fome Remarks on the Effect of Light and Shade in general What has hitherto been done in the foregoing fe£tions is termed by artifts linear perfpedtive, which propofes rules for drawing the outlines of objects in every fituation, proportioned one to another according to their magnitude and diftance from the picture ; but the fubje£l of the prefent fe6tion is to propofe rules for giving effe6t to thefe outlines, by the different cir- cumftances of light and lhade. The mere outlines of a draw- ing is but as a fkeleton without flefh or life, but by the addi- tion of proper light and lhadow, we may almoft behold nature in a pi£ture : and that which before appeared flat and infipid, now obtains the force and effedl of the obje£ls themfelves. The do£lrine of light and fhadow may be confidered under three heads. As, Firft, when the force of the fun's rays fall on objects, and thereby produce a ftiadow ftrongly defined. Secondly, ( 3 2 7 ) Secondly, When the fun is not fuppofed to fhine, and the fhadow is only produced by light limply confidered, or by reflection. Thirdly, When the light or ftiade of one object is propor- tioned with that of another at a greater diftance in the fame pi£ture. This is termed the aerial part of perfpeCtive, or the diminution of tints according to the diftance of objeCts. The firft of thefe heads is, however, that which principally concerns us, it being reducible to ftriCt rules ; the fecond fol- lows of courfe ; and the Iaft can only be learned by obfervation and practice. In confldering the fhadows caufed by the fun's rays we may obferve the following diftinCtions. Firft, When the fun's rays are in the plane of the picture, or, which is the fame thing, when they are confidered parallel to it. Secondly, When the rays come from behind the picture. And, Thirdly, When they have their direction from the front of the picture. Case ( 3*8 > Case I. Fig. 42. Plate XXVI. 7b projeff the Shadows of ObjeBs in various Pojitions when the Surfs Rays are parallel to the PiElure. The fun, which is the great fource of light, being at an immenfe diftance from the earth, the rays of light iffuing from it in right-lined directions, are confidered as parallel to each other. The truth of this is proved by the parallel fliadows %rhich it always produces on a plane from objects which are parallel to each other and of equal thicknefs. When, therefore, the rays are confidered as parallel to the picture, the fhadows of all objects are found by parallel lines palling by the angles of each object, and in fuch a degree of inclination as the fun is fuppofed to be in, either to the right or left of the center of the picture. Thefe lines, reprefenting the fun's rays, being cut by lines from the bafes of each object drawn parallel to the ground-line, find every fliadow in this cafe. The learner will recolle£l, that in ftating the theory of lines parallel to the piiture in page 215, it is there faid, " Lines u which are parallel to the pidture can have no vaniihing line or ( 3*9 ) or point in it, becaufe if infinitely produced would never " cut it." The fame holds good in the theory of fliadows when the fun's rays are parallel to the pidlure ; for then they cannot cut it, and confequently a vanifhing point is not wanted in this cafe. Hence the fliadows of all lines perpendicular to the ground are drawn parallel to the ground line ; and as, in perfpedtive, all lines perpendicular to the pidlure vanifli into its center, fo likewife the fliadows of every fuch line will tend to it. There- fore, Example I. Fig. 42, Suppose A to be the reprefentation of a wall perpendicular to the ground and to the picture, R R is a ray from the fun in- clining to the left in an angle of forty-five degrees, therefore the fliadow 2, 3 of the perpendicular line 1, 2 is equal in length to the line itfelf. Draw the other ray rr parallel to RR, and the fliadow r 0 will be equal to the height of the wall 0 r. The line 1 r is originally perpendicular to the pi&ure, and vaniflies in jr, the center ; fo is its fliadow 3 r, which likewdfe tends to it. EXAMTLK ( 33° ) Example II. Fig. 42. Suppose EB an obje6t any where on the ground, whofe fides EB are oblique to the pidture. Draw through each angle a ray rr parallel with RR the given one, and draw lines from the foot of each perpendicular, as 4, 6, parallel to the ground line, and their fedlions with each other will form points for the outline of the fhadow. Laftly, from the point 5 draw a line to 7, and from 7 draw one to 8, and filling it up, the fhadow will be completed. Obferve, the line 4, 9, and its parallels, are not perpendicular to the piiture ; therefore its fhadow line 5 7 does not tend to $ the center, but to the fame vanifhing point neceffary for draw- ing the fide B. In the fame manner the fhadow line 7 8 vanifhes to the point requifite for drawing the fide E. Example III. Fig. 42. Let D be an objedl having the fide D inclined to the hori- zon, and the other fides oblique to the pi&ure. Draw a ray through b, and through / parallel to the given ray R R ; from g . the foot of b, and from d the foot of f 9 draw lines parallel to the ground ( 331 ) ground line, which will interfe£t the rays at a and c. To com- plete the fhadow, draw a line from the extremity of the inclined plane to a, and from a to e. Example IV. Fig. 42. Let F be the ftump of a column refting on one end, whofe fhadow is required. Find the diameter of the column each way, both at top and bottom, as the figure fhews ; and through the extremities of thefe diameters draw parallel rays as before. Laftly, from the foot of each perpendicular falling from the center and diameter, draw lines parallel to the ground line, cut- ting the rays at v, x ; draw a curve to pafs through thefe three points, and the fhadow will be projeited. Thus it is evident how eafy a matter it is to project the fliadow of any kind of object when the rays are parallel to the picture, and when the fliadow is to fall on the ground plane, as in the foregoing examples. It is, however, fometimes neceffary to proje£t fhadows fall- ing on other objects contiguous to thofe whofe fhadows are re- quired. Therefore, Tt 2 Example ( 332 ) Example L Fig. 42. Suppose the object D {landing in the way of the fliadow of A, a plane of rays parting by the end 1, 2 of the wall, will make a fe£tion of D at /, /, 3 ; which is found by drawing the line from 2 through to 3, and from 3, where it cuts the ray R R, raife a perpendicular to /, and from I draw a line to /, which will determine how far the fliadow comes in front. Laftly, the bafe line / d, of the obje£l D, cuts a line from 3 at e ; therefore, from e raife a perpendicular correfponding with 3 /, and from t draw a line to the aforefaid perpendicular, and the fliadow, fo far as it afFefts the inclined plane D, will be found. Example II. Fig. 42. Suppose the objedt C near fome inclined plane G, whofe fliadow falls upon it. To find the fliadow, draw a line h to G, parallel to the ground line, at pleafure ; draw then a ray, as before, cutting at G, where the fliadow would have terminated if the inclined plane had not been there ; draw m I parallel to n 0, cutting the ray at p ; do the fame at the other end, and the fliadow will be completed. Before ( 333 ) Before I enter upon the other cafes of fhadows, I would here remark, that this which has now been exemplified is, in my opinion, the moft ufeful, as well as moil eafily pradtifed. Particularly it is the moft ufeful to the cabinet-maker and up- holfterer, who only want it for fhading different pieces of fur- niture; becaufe the ihadows thus projected will be to the right or left of the piece, according as the light is fuppofed to come- in; but in the two following cafes of the fun's rays, the fhadows will be projected either behind, or on the front of the piece of furniture, which lituations of fliadow are liable to the folio wing objections. Firft, if the rays come from behind the picture, the front of the piece will be all in fliadow, and confequently the effeil of diftinihiefs of parts, which is always expected in furniture, will be deftroyed. Secondly, if the rays come on the front, then the fliadow will be behind the piece, and therefore little or none of it will be feen, unlefs the point of light be taken very low, which is not very agreeable. Befides, the light coming thus ftrong on the piece, leaves a glare on the front that does not produce a plealing effeft in furniture, nor fufflciently diftinguilhes the front from the white ground of paper on which it is generally drawn. Painters, ( 334 ) Painters, indeed, are faid to make this laft-mentioned poli- tical of light to the pi£ture their choice, becaufe, I fuppofe, if clears their piilure from the appearance of long black fhadows, which would frequently look too harfh, and introduce confix- fion, as is the cafe when the light comes in from behind. Yet as every cafe of lhadowing may be neceffary at times, though not out of choice, I fliall therefore proceed to the fecond cafe propofed. Case II. Fig. 43. Plate XXVI. To project the Shadows of Obje&s when the Rays come in a Direc- tion from behind the PiFture. When a ray of light comes in a direction not parallel to the pidture, it will neceffarily cut it in fome point in the hori- zontal line, or vanifhing line of the ground plane ; for the fun being at an irnmenfe diftance, and the plane of vhe horizon being confklered as infinitely extended, we may fuppofe a per- pendicular let fall from the place of the fun will touch fome- where on the horizon. And hence, the point where it touches the horizon is the vanifhing point of the fhadows, and confe- quently a line drawn through the faid point perpendicular to the horizon will be the vanifhing line of the fun's rays ; and any where on this line, if a point be fixed according to the fuppofed g altitude ( 335 ) altitude of the fun, it will be the vanifhing point of thofe rays.. Thus:— in Fig. 43, the center and diftance of the picture remaining the fame as when ufed for drawing the cube, let it be required to find its fhadow when the fun's inclination to the left is thirty-two degrees, and when its altitude is forty-five.. From d, the diftance, draw the line d h, inclining from the per- pendicular s d in an angle of thirty-two degrees ; and through h draw S S perpendicular to the horizon; then will SS be the va- nifhing line for the fun's rays. Make h M equal b d y and from M draw M S, making an angle with the horizon equal to forty- five degrees; then will S above the horizon be the vanilhing point of the rays when the fun comes from behind the pjfhire, and S below r it will fupply its place when the rays come on the front. From the vanifhing point h of the fhadow draw lines through the angles i, 3, 8, of the cube ; and from S draw lines through its upper angles 2,4,9, interfering the lines drawn, from b in the points 5, 6, 10 ; from the point 5 draw a line to 6, and from 6 a line to 10, which completes the fhadow. Obfervations on the 'Theory of the above Figure. The rays S6 and S 10, forming a triangle, may be confi- dered as a plane of rays paffing by the angle 4, 9 of the cube, and ( 33* ) and being flopped on the ground plane at 6, 10, occafions a fliadow up to the cube, which fliadow will vanifli in the line 6, 10, to V; becaufe the angle or line 4, 9, ; which projected it, was drawn to, and vanifhes in V ; confequently a line from V to S, the fuppofed place of the fun, will be the vanifliing line of the faid plane of rays. The fliadow on the other fide Is com- pofed of two lines, becaufe it is projected by two lines in dif- ferent pofitions to each other. Thus the line 2,4, originally parallel to the horizon and to the ground, projects the fliadow* line 5, 6 by the plane of rays 5, S, 6 ; which fliadow line 5, 6 will vanifli in V, becaufe the angle or line 2, 4 vanifhes there. The fliadow line 5, 1 is projected from the perpendicular line 1, 2 by the plane of rays 5, b, S, paffing by the angle or perpendicular line 1, 2, and therefore the fliadow line 5, 1 will vanifli in the feat of the luminary on the pidture; through which a line SS paffing in a perpendicular direction to the horizon, anfwerable to the perpendicular fides of the cube, is the vanifliing line of the plane of rays 5, S, b, in the fame manner, and for the fame reafon, as the horizontal v V is the vanifliing line of the flia- dows of lines originally parallel to it. The vanifliing line S S of the fun's rays may be fuppofed to move along the horizon anfwerable to the fun's inclination to the right or left of the center of the picture s, whether the fun be fuppofed on this or that fide of the picture, or, as we conceive of it by the figure, whether it be above or below the horizon. Hence, if a plane of ( 337 ) of rays be fuppofed to come from behind the picture, in a di- rection perpendicular to it, the place of the fun will be fome- *where % on a perpendicular line drawn through the center of the picture, as S d. And this place of the fun, or, which is the fame thing, the vanifhing point S, of its rays, will be above or below the horizon, according to the fuppofed altitude of the fun. If, therefore, we imagine the fun's altitude to be as before, its place will be at d when the fun is behind the picture, and at S when it is before it ; and the vanifliing point of the fhadow will be at s, the center of the pidture. This is evident, for the angle V, d, s, is the fame and equal to M, S, b. In both cafes the fines bS, od, of the angles of the fun's altitude are the fame, being equal to the diftance j* V of the pidture : for, in the fhadow of the cube, when the plane of rays from behind the piiture cut it in the oblique direction of the line d h, the line db is then confidered as the diftance of the pi6ture, ar\d being turned up to S, is equal to the diftance of the place of the fun above the horizon. And fuppofe the rays to come to the picture in the direction of d v 9 then b would be moved to v, and v d would be equal to the diftance of the picture ; and being turned up to v S, S would then be the place of the fun, or the vanifliing point of its rays, and v the vanifliing point both of the fhadow and fide of the cube 2, 4. In which cafe we fhould only have the fhadow of the fide 4, 9, 3, 8. Ii ( 338 ) It is further obfervable, that as the fun may be fuppofed to move in a circle, and if that circle be defcribed by a radius equal to the diftance of the pidhire, we may Ihow the dffFerent fhadows of the fun upon obje&s at the various times of the day. Thus:— in Fig. 44, fuppofe a line drawn from E W forming the horizon ; from the center s defcribe a circle with the dif- tance of the picture, and through s draw a line perpendicular to the horizon, and M will be the place of the fun at noon. Now let it be required to find the morning fhadow of the rod a when the fun has rifen 40 degrees above the horizon, as at 40 0 Sw From 40 0 S let fall a perpendicular to the horizon at h, and draw it through to the other femicircle ; from h, the vanifhing point of the lhadow, draw lines paffing by the bottom of the rod at pleafure; and from 40 0 S, the place of the fun, draw a ray through a, the top of the rod, cutting at 1 ; which fhews the length of the lhadow required. Suppofe the fiiadow of the fame rod be wanted at noon, s will then be the vanifhing point of the fhadow, and M the vanifhing point of the fun's rays, and the length of the fhadow will be at 5. Again, if it be required to find the fhadow of the fame rod after the fun has pafled the meridian 50 degrees, this will bring the fun to the fame degree in the afternoon as it was in the morning ; and by drawing lines in ( 339 ) in the fame manner as in the morning, the fhadow in the after- noon will be at 2. Now, if the fun be confidered on this fide the picture, the fiiadows of the fame rod at thefe different periods of the day, will be refpeilively beyond the rod at 3, 4, 6, towards the hori- zon ; which is done by tranfprojedting the place of the fun to S M S, and drawing rays from the top of the rod to each place of the fun. Thus: from a draw the dotted line to S on the left, cutting at 3, and 3 will be the length of the morning fhadow ; and from a draw the dotted line to S on the right, cutting at 4, which will be the evening lhadow. Laftly, a dotted line from a to M, cutting at 6, will be the fhadow at noon, which is hardly feen on the pidture. Thus we fee that the fhadow s of a morning or evening view are long, tending oppoflte ways ; and thofe of a view reprefenting noon-day are fhort, tending from fouth to north, nearly fo. But if we lived in a meridian on the line, then it is evident that at noon there would not be the leaft fhadow of objects of equal thicknefs ftanding perpendicular on the ground : for, fuppofe the rod a moved into the line M M, then the object would be in the fame plane with the rays of the fun; and being direftly under it, of cGurfe all fhadow would be excluded excepting fufpending objects, as No. 2, and thofe fupported like tables ; in which cafe the rays r r falling perpendicular to the V u 2 ground ( 34° ) ground, and parallel to each other, on account of the fun v s great diftance, they would form a cylinder, of which the fha~ dow would be a parallel fedtion, and therefore muft be perfe&ly fimilar to the object itfelf, both in magnitude and form, as muft be evident from the figure, and a little reflection on the fore- going principles* Case III. To find the proje&ions of Shadows when the Surfs Rays come on: the Front of the Picture. Having already explained the theory of this in what has now been advanced, it remains only to give an example or two to illuftrate it. Example £ Fig. 45. Plate XXVI. When the Shadozv falls on the Ground. In Fig. 45, A is a prifm whofe fhadow is proje£ted by the fun as above propofed, h is the vanifhing point of the fhadow, v of the fide of the cube, and S of the rays. Therefore from the angles 1, 2, 3, draw lines to h; and from 4, 5, 6, at the top, correfponding with thefe, draw lines to S, cutting at 9, c 9 b ; 8 from ( 341 ) from b draw a line to c, and from c to 9, which, when filled up, will complete the fhadow. Example II. Fig. 46. Plate XXVI. When the Shadow falls at the fame Time on upright, oblique, and horizontal Planes** This figure having the moft necefTary lines for reprefent- ing the two houfes, as well as for finding the fhadow of one houfe falling upon the other, may be confidered as an example both of perfpedtive and of fhadow.. And as the lines for both are here joined together in one view, it will fhew their relation, and the necefTary dependence they have on each other ; which, it is prefumed, will contribute more to the learner's advantage, than if many examples of fhadowing had been added without regard to the perfpedtive lines. The horizon and ground line being drawn, fix the center of the pidture as ufual; from wjhich raife a perpendicular as to d. Make d the diftance of the pidture, and, according to the obliquity fuitable for the front of the houfe, draw a line to V, for one vanifhing point ; next draw V d 9 and from d draw a line to v 9 at right angles with V d; becaufe the end and front of the houfe are originally at right angles to each other. Make v M equal to r c a\ and whatever angle the pitch of the roof makes, produce t 342 D produce a line from M equal to that angle, continued till it cut a line perpendicular to v, as at V ; then is V the vanifhing point for the fide of the roof of both houfes, and a line from V to V will be the vanifhing line of the plane which the roof is in, and H will be the vanifhing point of fhadows lying in the faid plane ; and producing V V at pleafure, and meeting it in 0 at Fig. 44, by a parallel from S, 0 will be the vanifhing point of the fun's rays on that plane. Extend the compaffes from V to v 9 and place it below the horizon, and that point will ferve for the other fide of both roofs. The houfes being completed in their outlines, according to thefe vanifhing points, proceed to fhade them upon a fuppofition that the light comes on in the front of the picture, and in a direction from the left hand pa- rallel to the dotted line d b. Therefore the point h will be the vanifhing point of the fhadows falling upon the ground plane, and producing b perpendicular to the vanifhing line V V, H will be the vanifhing point as aforefaid. The place of the fun S is fixed very low, not as a precedent, but that it might throw the fhadow of the firft houfe on the fecond, affording an occa- fion of fhewing the nature of fuch fhadows. From g the pitch of the roof on the gable-end, draw a line to S ; and from a draw a line to h, which will cut the front of the other houfe at 0 ; from 0 raife a perpendicular, cutting the line drawn from g to b in e ; from e direft a line to V, the va- nifhing ( 343 ) nifhing point for the fronts of each houfe, which gives the fhadow for the roof. From the tops of each chimney draw lines to S, and obferve that the fliadow of the firft chimney falls partly on the roof, becaufe the ray drawn to S cuts the roof, and that ray muft be cut again, by drawing a line from the top of the perpendicular fhadow o e to H, the vanifhing point of fuch fhadows as fall on the roof, and from the top of the fha- dow on the roof diredt a line to 0, in Fig. 44, which gives the complete fliadow of the chimney. Laftly, from £, at the bottom of the fecond houfe, draw a line to h ; and cut that line by twa others, one from the top of the chimney, and another from the pitch of the roof, as before ; from thefe interferons draw lines to V, the vanifhing point of the houfe, and the fhadows will he. finifhed* Of Shadows when the Sun is not fuppofed to Jhine, or thofe pro- duced by common Light. After what has been faid on fhadows produced by the fun, it will not be requifite to fay much on this head. It will, however, admit of a few remarks. . And firft, fuppofe an object a, b, c, Fig. 47, placed to the light, and confider the parallel lines as rays of common light falling on it^ for common light directs its courfe to ob- jects . ( 344 ) je&s in this manner. Now it is evident, therefore, that the fide or plane a will have moft of the light, hecaufe the rays fall nearly perpendicular on it, which confequently excludes all fhadow ; but the plane or fide b receives the faid rays obliquely, and in proportion thereto occafions a fhadow, becaufe the light partly mifles the furface. The plane e is totally in fliadow, be- caufe the ray r cannot touch that furface. Secondly, in fliadows of this kind the contrail: of light and fhade is not fo ftrong as when the fan's rays fall on objedls ; the light is not fo glaring, nor the iliadows fo black. The out- lines of fuch fhadows ought not to be ftrongly defined, but faint, and fometimes indiftindt, efpecially when the light is fup- pofed to come from different apertures, Laftly, fuch objects as are fuppofed to be viewed in a room have their upper parts lighteft ; but the lighteft parts will bear a tint, and fometimes confiderable, fo that there will not be much oppofition of light and fhade in their different furfaces. It is requifite to confider the natural colours of objects, in ©rder to fix the tone and true fcale of light fui table to them *. The lighteft part of an object that is of itfelf black, would be * This is alio necefTary when the fun is fuppofed to jfhine. a fhade ( 345 ) a {hade to one that is white, and therefore, in producing a flia- dow to any thing black or blue, it will require all the force and ftrength of the Indian ink. The other colours, as green and yellow, Sec* will alfo require a due degree of light and ihade to diftinguifh them by. Mr. Kirby confiders the colours receding from white to black in the following order i u e. yellow after white, then green, red, blue, and black, fucceffively. It is difficult, how- ever, to diftinguifli fome of thefe by the effect of Indian ink, yet it is evident fomething may be done towards it. Thus : the cube W is fuppofed to be white, Y yellow, G green, R red, B blue, and BL black Of the Proportion of Tints fuited to Obje&s at different Dijlances in the fame Pi&ure. See a View, Plate XXVI. It is evident, from the nature of perfpe£tive in general, that not only the proper dimenlions of obje£ts, but alfo the de- gree of tint, is eflential in making them appear at different dif- * This is not the order of the fimple colours, according to Sir Ifaac Newton's theory of their origin. His theory informs us, that when the rays of light are feparated by the re- fraction of a prifm, the nrlt. will be red, then orange, yellow, green, blue, indico, and violet, fucceffively. See his Optics, Book L Prop. 6. According to this, white is not a fimple colour, but a compound or mixture of all that arc ample, and black a total privation of every colour. X x tances. ( 346 ) tances. For, as in linear perfpecStive, objedts are viewed under a fmaller angle in proportion as they are at a diftance, fo in the aerial part every tint and fliadow gradually weakens as the objedt is fituated at a diftance from the front of the pidture. The reafon of this is obvious, when it is admitted that we are made to fee objects by innumerable beams of light iffuing from them to the eye. It is eafy then to conceive, that when thefe beams or rays of light have to make their way through the air from diftant parts of the horizon to the eye, they muft greatly weaken before their arrival to it, and therefore fuch diftant objects muft appear lefs diftindt and more dim in proportion to that diftance. Hence, in a pidture, as in the view given in Plate XXVI. objects on the fore ground are not only larger, but they are more made out, more diftindt, and ftrongly marked. Their lights are brighter, and their fliades are darker,, than thofe on the back ground. This will, perhaps, be more eafily underftood by the following obfervations on the view. The tree on the left is neareft to the eye of the fpectator. and is therefore moft made out ; its leaves are feen in clufters, and its fhade is ftrong. The firft tree on the right, being further back, is lefs dif- tindt in its parts, and rather fainter in its fliadow s ; and fo of the teft in proportion to their diftance. With / { 347 ) With refpedt to the houfes, we fee the fecond weaker in its parts, and its fliadow, partly on the water and on the ground, fainter than that of the firft. The laft houfe being at a vaft diftance, appears as one mafs without diftindtion of parts ; and thus objects diminifli off till they and the horizon on which they ftand mix with the fky. Of the reflected Images of ObjeSIs on Water. To afcertain the reflected images of objects on w r ater is ex- ceeding eafy, and very eflential to fome pictures. It is a law in catoptrics *, that the angle of reflection is always equal to the angle of incidence t. The angle of incidence and reflexion may be thus under- ftood and diftinguiflied. The inclined poll, and its fliadow on the water, form an angle with each other ; and at the bottom of the poft, where the line of reflection on the water and the line * Catoptrics, from xa-roTrlpot-, katoptron, a mirror or looking-glafs. Catoptrics teach the fcience of reflex vifion, and optics that of direcl vifion, though in the general and ex- tenfive meaning of the term optics, " from ottW*i, cptomai, I fee," it includes in it *' whatever relates to fight, or the doctrine of vifion;'* and therefore mull imply dioptrics alfo, which teaches the properties of refracted vifion ; that is, when rays of light pafs through ©ne medium into another, as air and water. f See fecond axiom of Sir Ifaac Newton's Optics. X x a of ( 348 ) of incident rays from the poft meet, that point is termed the poi:;t of incidence; and if from the top of the poft a perpendic- ular be let fall, it will form a triangle; and if that triangle be bife6ted; that is, by drawing a parallel line from the point of incidence b> cutting the perpendicular at then the angle c, a, b\ is the angle of incidence, and d 9 b, the angle of reflection, which are equal. Therefore if an object be perpendicular to the horizon, its reflected image on water will alfo be perpendi- cular, but in an inverted pofition to the objedt which reflects the image. And whatever angle of obliquity any obje£t makes with the ground, the fame will be its reflection to the furface of the water.. The reflections of images on water are the fame as thofe in a plain mirror. The furface of the mirror or looking-glafs is the plane of reflection; and it is evident, that in. whatever pofir tion any objeCt is prefented to it, the fame will be that of its re- flexion on the faid plane. If a rod, &c. be placed perpendicular to the mirror, its reflected image will be perpendicular to it alfo. And if one end of it touch the glafs, its image w ill alfo appear to touch the furface of it; or if it is withdrawn, its image will, appear equally removed from the reflecting plane. This expe-- riment is w r ithin the reach of every one, and will be fufficient. to convince any of the truth of the above propofition. Example 1 C 349 ) Example I. See the View, Plate XXVI. If, therefore, the reflection of the inclined poft be wanted, let fall a perpendicular at pleafure, and cut that per- pendicular by a line drawn from the bottom of the poft in- clining to the faid perpendicular in an angle equal to the ob- ject, and it will give the length and inclination of the reflected image. And obferve, that the length of the reflection on the water will be in proportion to the. diftance of the objeCt from it ; confequently if the poft were removed a little fur- ther from the edge of the water, we fhould lofe its reflection entirely. Example II. If it be required to find the reflection of any of the trees iuppofed to ftand nearly perperdicular, let fall a perpendicular from the bottom of it, and take the whole height of the tree and place it downwards from the bottom of it, then take the length of the trunk and do likewife, which will give the reflec- tion as required* . Laftly, ( 350 ) ~Laftly, it is manifeft from thefe principles, that if any obje£t be floating in the water, fuch as a piece of timber or a fliip, that its reflected image will be equal in length to the objecft itfelf, and the depth of the reflection below the fur- face of the water will be equal to the height of the objecSt above it. END OF THE SECOND PART. THE 4 i CABINET -MAKER THE AND UPHOLSTERER'S DRAWING-BOOK. PART III. CONTAINING A DESCRIPTION OF THE SEVERAL PIECES OF FURNITURE. t. OF THE USE AND STYLE OF FINISHING EACH PIECE. 2. GENERAL REMARKS ON THE MANUFAC- TURING PART OF SUCH PIECES AS MAY REQUIRE IT. 3. AN EXPLANATION OF THE PERSPECTIVE LINES WHERE THEY ARE INTRODUCED. TO WHICH IS ADDED, A CORRECT AND QUICK METHOD OF CONTRACTING AND ENLARGING COR- NICES OR OTHER MOULDINGS OF ANY GIVEN PATTERN. INTRODUCTION. Th e defign of this Part of the Book is intended to exhibit the prefent tafte of furniture, and at the fame time to give the workman fome afliftance in the manufacturing part of it. I am fenfible, however, that feveral perfons who have al- ready encouraged the work, will not want any help of this 8 • nature; ( 35* ) nature; but it is prefumed many will who are not much con- veifant in the bufinefs, and who have had no opportunity of feeing good pieces of furniture executed. For the advantage of fuch, it is hoped that the experienced workman will exercife candour and patience in reading the in- ftru6tions intended, not for himfelf, but for thofe now men- tioned. There are few but what may, with propriety, reflect on their own paft ignorance, even in things which afterwards be- come exceeding fimple and eafy by a little practice and experi- ence. Such a reflexion ought, therefore, to promote both candour and good nature in the minds of proficients, when they read the documents neceflary to young beginners. And yet, I hope, it may be faid, without arrogance, that it is probable the experienced workman may derive fome information from the fubfequent remarks, when it is confidered that they are made not merely from the knowledge and experience I have myfelf of the bufinefs, but from that of other good workmen. In converfing with cabinet-makers, I find no one individual equally experienced in every job of work. There are certain pieces made in one fhop which are not manufactured in an- other, on which account the belt of workmen are fometimes ftrangers I ( 353 ) ftrangers to particular pieces of furniture. For this reafon I have made it my bufinefs to apply to the beft workmen in dif- ferent fhops, to obtain their affiftance in the explanation of fuch pieces as they have been moft acquainted with. And, in gene- ral, my requeft has been complied with, from the generous motive of making the book as generally ufeful as poflible. The methods therefore propofed, and the remarks made, may be depended on by thofe who have not yet had an oppor- tunity of feeing the different pieces executed. This is an attempt which has not yet been made in any book of cabinet defigns, except a very few flight hints ; and, though it muft be acknowledged by every impartial mind as highly ufeful, and even in fome cafes abfolutely neceflary, yet I am apprehenfive it will not meet with the approbation of thofe who wifh to hoard up their own knowledge to them- felves, left any fliould lhare in the advantage arifing from it. In fome inftances it may be neceflary for a man to keep know- ledge to himfelf, as his own property, and upon which his bread may depend ; but I do not fee any impropriety in perfons of the fame branch informing each other. In trades where their arts depend on fecrets, it is right for men to keep them from ftrangers ; but the art of cabinet-making depends fo much on pra&ice, and requires fo many tools, that a ftraftger cannot Y y fteal ( 354 ) fleal it. But in every branch there are found men who love to keep their inferiors of the fame profeffion in ignorance, that themfelves may have an opportunity of triumphing over them. From fuch I expert no praife, but the reverfe. Their pride will not fufFer them to encourage any work which tends to make others as wife as themfelves ; and therefore it is their fixed refolution to defpife and pour contempt upon every at- tempt of this kind, in proportion as it is likely to fucceed. But thofe I will leave to themfelves as unworthy of notice, who only live to love themfelves, but not to affift others. Here I would beg leave to obferve, that it is natural for every man under a heavy burden to pour out his complaint to the firft fympathizing friend he meets with. If the reader be one of thefe, I will pour out mine, by informing him of the difficult tafk I have had to pleafe all, and to fuit the various motives which different perfons have f6r encouraging a publi- cation like this. I find fome have expected fuch defigns as never w r ere feen, heard of, nor conceived in the imagination of man; whilft others have wanted them to fuit a broker's fliop, to fave them the trouble of borrowing a bafon-ftand to fhew to a cuftomer. Some have expedted it to furnifh a country wareroom, to avoid the expence of making up a good bureau, and double cheft of drawers, ( 355 ) drawers, with canted corners, 8c c. and though it is difficult to conceive how thefe different qualities could be united in a book of fo fmall a compafs, yet, according to fome reports, the broker himfelf may find his account in it, and the country mafler will not be altogether difappointed ; , whilft others fay many of the defigns are rather calculated to fhew what may be done, than to exhibit what is or has been done in the trade* According to this, the defigns turn out to be on a more general plan than what I intended them, and anfwer, beyond my expectation, the above various defcriptions of fubfcribers. However, to be ferious, it was my firft plan, and has been my aim through the whole, to make the book in general as per- manently ufeful as I could, and to tuiite with ufefulnefs the tafte of the times ; but I could never expect to pleafe all in fo narrow a compafs : for to do this, it would be neceffary to com- pofe an entire book for each clafs of fubfcribers, and after all there would be fomething wanting ftill. Y y a A DE- ( 356 ) A DESCRIPTION OF THE SEVERAL PIECES OF FURNITURE. Of the Univerfal Table. Plate XXV. of the Cabinet Dejigns.. The life of this piece is both to anfwer the purpofe of a breakfaft and a dining-table. When both the leaves are flipped under the bed, it will then ferve as a breakfaft-table ; when one leaf is out, as in this view, it will accommodate five perfons as a dining-table ; and if both are out, it will admit of eight, being near feven feet long, and three feet fix inches in width. The drawer is divided into fix boxes at each fide, as in the plan, and are found ufeful for different forts of tea and fugar, and fometimes for notes, or the like. In this drawer is a Aider lined with green cloth to write on. The ftyle of finifhing them is plain and fimple, with ftraight tapered legs, focket caftors> and an aftrugal round the frame. Of the manufacturing Part. This table fhould be made of particularly good and well- feafoned mahogany, as a great deal depends upon its not being 8 liable X ( 357 ) liable to caft. In the befl kind of thefe tables the tops are framed and pannelled ; the bed into two pannels, and the flaps each into one, with a white firing round each pannel to hide the joint. The framing is three inches broad, and mitered at the corners ; and the pannels are fometimes glued up in three thicknefles, the middle piece being laid with the grain acrofs, and the other twx> lengthways of the pannel, to prevent its warping. The pannels are, however, often put in of folid Huff, without this kind of gluing. When the pannels are tongued into the framing, and the miters are fitted to, the tops fhould ftand to ftirink as much as poffible before they are glued for good. There are different methods of fecuring the miters of the framing. Some make fimpiy a ftraight miter, which they can fhoot with a plane ; after which they put a couple of wooden pins in. Others, again, having fitted the miters to by a plane, they flip in a tenon. But the ftrongeft method is to mortice and tenon the miters to- gether, having a fquare joint at the under, and a miter joint at the upper fide. This method, however, is the mofl tedious of the three, and where the price will not allow of much time, the above methods are more ready, and, if managed with care, are fufficiently ftrong. In gluing the miters, it will be proper, firft, to glue on the outfide of each miter a piece of deal in the fhape of a wedge, w T hich will take a hand-fcrew, fo that when they ( 3S3 ) they are putting together, the glue may be brought out, and the miters made clofe. The frame, as fhewn in the plan, is made exa6lly fquare, either of faulty mahogany, or of wainfcot veneered. In making this frame a box is formed at each end, about three inches in width, containing two Aiders apiece, which run paft each other in the faid box, as fhewn in the plan. In the bottom of each box are put two pieces, with plough grooves in them, and raking contrary to each other. In the line N O, on thofe raking pieces the Aiders run, and are flopped from coming too far out by a pin fixed in the under edge of the Aider; which pin runs in the plough grooves already mentioned, denoted in the plan by a dark line. The raking line of the Aiders is found by taking the width of the Aap, as from S to M, and making the line in- cline in that width equal to the thicknefs of the flap. This may be eafily underftood, by placing a rule from the outer point M of the flap, to S the inner point, which then will be parallel to the raking line. The Aiding pieces being in a right line their whole length at the under edge, of courfe their upper edge mvift be bevelled off, fo that when they are drawn fully out, they may be even, and in an exaft line with the top of the frame. The frame and tops being thus prepared, they are con- nected together by an iron fcrew and nut, as at A, which is about ( 359 ) about the fubftance of a bed-fcrew. This fcrew is jointed into a plate, which plate is let into the under lide of the bed, level with it ; though I have defcribed it at A with its thicknefs out, merely that the plate might be fhewn. At B the bed A is repre- fented on the frame, and the iron fcrew paffing through the rail of the table, is confined to its place by the nut, which is let into the under edge of the rail by a center-bit. And obferve, in making this center-bit hole for the nut, it rauft be iunk deeper than its thicknefs, that the bed may have liberty to rife a little, and fo give place to the flaps when they are wanted to be pufhed in. It muft be noticed alfo, from the plan of the frame, that there is a middle piece, about five inches broad, and of equal thicknefs with the flaps, fcrewed down to the frame with four fcrews at each end. This middle piece an- fwers three purpofes ; it fecures the frame, flops the flaps when they are pufhed in, and prevents the Aiding pieces from tilting. Before the bed is finally fixed to its place 5 there muft be four pieces of green cloth let into the under fide of it, to pre- vent the flaps from rubbing as they Aide under. Upon the edges of the flaps a hollow is worked all round, leaving a quarter of an inch fquare, for no other purpofe than to take off the clumfy appearance of the two thicknefles when the flaps are under ( 360 ) under the bed. At the under fide of the flaps muft be goged out finger-holes, to draw them out by. The drawer is next to be coiifi lered, which is fometimes made with two fronts, and to draw out both ways, as in the plan. On each front of the drawer is a lock, for the conveni- ence of fecuring it at either end ; for in cafe one flap be drawn out, then the drawer can be locked or pulled out at the contrary front, without the trouble of pufhing the flap in to come at the drawer. The covers of each box before mentioned, may have an oval of dark wood, and the alphabet cut out of ivory or white wood let into them, as in the plan ; or they may be white ovals and black letters ; the ufe of which is to diftinguifh the contents of each box. Laftly, the Aider to write on is made exa£lly half the inlide length of the drawer ; fo that when it is pulhed home to either front, there is immediate accefs to fix of the boxes. And here I would obferve, that fometimes the flaps of thefe tables have round corners, but they do not anfwer the bed fo well when they are in. And, to fave expence, the tops have been found to anfwer the purpofe in folid wood, without being framed* ( 36i ) framed. When they are made in this manner, particular regard fhould be had to placing the heart lide of the wood outward, which naturally draws round of itfelf, and may therefore be expedted to keep true, notwithftanding its unfavourable fitu- ation. N. B. The heart fide of a board is eafily known by plan- ing the end, and obferving the circular traces of the grain, which always tend outwards. "fbe Perfpe&ive Lines explained. In making defigns in perfpedtive, the firft thing to be at- tended to is the fcale of feet and inches, by which to proportion the different parts to each other, to determine the height of the horizon, and the diftance of the pidture. Having made the fcale, take from it about five feet fix for the height of the horizon at H L. On this line place the point of fight, fo as to give the mod favourable view of the defign, as at s. Next lay on the diftance, which is here out of the plate, and being equal to the fpace s a, agrees to the rule for choofing a diftance contained in page 281. Draw ab perpendicular to the ground line, and from a draw a line to the point of fight /, Z z Next ( 3&> ) Next confider how much the top projedls over the frame, and as much as this is, lay it from a towards e, as the firft line fhews, which is directed to the point of diftance. Where this cuts the aforefaid line drawn to i, raife a perpendicular anfwer- ing to a b. From b lay on the fpace b d, for the depth of the framing ; and from d draw a line as before to s ; and from where the line cuts the fecond perpendicular, draw a parallel for the under edge of the framing. On a parallel line from b, lay on the dimenfions of the bed and flap ; and from thefe draw lines to x, as the defign fliews. Now, as the bed of the table is fquare, nothing more is wanted to find its apparent width than to draw a line from o to the diftance which cuts at the oppofite angle ; and through this angle draw r t parallel, which com- pletes the out-line of the top. To find the place of the drawer and the boxes in it, pro- ceed thus. — On the ground line make a e equal to the whole fpace, from the drawer in the plan to the projection of the middle piece acrofs the frame. Alfo make e h the whole length of the drawer, and gf the di villous for the boxes. From each of which draw lines to the diftance, cutting at 1,2,3,4; from which draw parallels to 7, 6, 5, 8. Again, from 7 raife a per- pendicular, and make k on k equal to the height of the drawer ; from b draw a line to s ; and from m, the height of the covers of each box, do the fame. Laftly, from 6, 5, &x. 8 raife ( 3^3 ) raife perpendiculars, which will cut bs in the place for the boxes, and at n for the height of the covers. How every other thing is done, muft be obvious from infpediion. Of the Sideboard fables, Plate XXVI. and XXIX. and of Tables of tins Kind in general The fideboard in Plate XXVI. has a brafs rod to it, which is ufed to fet large dilhes againft, and to fupport a couple of candle or lamp branches in the middle, which, when lighted, give a very brillant effe£t to the filver ware. The branches are each of them fixed in one focket, w r hich Hides up and down on the fame rod to any height, and fixed any where by turning a fcrew. Thefe rods have fometimes returns at each end of the fideboard ; and fometimes they are made ftraight, the whole length of the fideboard, and have a narrow fhelf in the middle, made of full half-inch mahogany, for the purpofe of fetting fmaller difhes on, and fometimes fmall filver ware. The right-hand drawer, as in common, contains the cel- leret, which is often made to draw out feparate from the reft. It is partitioned and lined with lead, to hold nine or ten wine bottles, as in Plate XXIX. Z Z 2 The ( 3^4 ) The drawer on the left is generally plain, but fometimes divided into two ; the back divifion being lined with baize to hold plates, having a cover hinged to enclofe the whole. The front divifion is lined with lead, fo that it may hold w r ater to wafh glafles ; which may be made to take out, or have a plug- hole to let off the dirty water. This left-hand drawer is, how- ever, fometimes made very fhort, to give place to a pot-cup- board behind, which opens by a door at the end of the fide- board. This door is made to hide itfelf in the end rail as much , as poffible, both for look and fecrecy. For which reafon a turn- buckle is not ufed, but a thumb-fpring, which catches at the bottom of the door, and has a communication through the rail, fo that by a touch of the finger the door flies open, owing to the refinance of a common fpring fixed to the rabbet which the door falls againft, as is denoted by the figure A. F is for the finger, B is the brafs plate let into the rail, L is the lever, p is the fpring that prefles the lever upwards, and c is the end of it which catches the under edge of the door as it pafTes over it and ftrikes into a plate with a hole in it, and s is the fpring fcrewed to the rabbet which throws the door out when F is pufhed upwards. But the reader muft here obferve, that the fhape of this fideboard will not admit of a cupboard of this fort in the end rail* ( 3*5 ) rail. Thofe which are fquare at the ends, and only a little ihaped in front, are fitteft for this purpofe. In large circular fideboards, the left-hand drawer has fome- times been fitted up as a plate-warmer, having a rack in the middle to ftick the plates in, and lined with ftrong tin all round, and on the underfide. of the fideboard top, to prevent the heat from injuring it. In this cafe the bottom of the drawer is made partly open, under which is fixed a fmall narrow drawer, to contain a heater, which gives warmth to the plates the fame as in a pedeftah In fpacious dining-rooms the fideboards are often made without drawers of any fort, having fimply a rail a little orna- mented, and pedeftals with vafes at each end, which produce a grand effedt. One pedeftal is ufed as a plate-warmer^ and is lined with tin ; the other as a pot-cupboard, and fometimes it contains a celleret for wine. The vafes are ufed for water for the ufe of the butler, and fometimes as knife-cafes. They are fome- times made of copper japanned, but generally of mahogany. There are other fideboards for fmall dining-rooms, made without either drawers or pedeftals ; but have generally a wine- cooper to ftand under them, hooped with brafs, partitioned and lined with lead, for wine bottles, the fame as the above-men- tioned celleret drawers* The ( 366 ) The fideboard in Plate XXIX. fhews two patterns, one at each end. That on the left is intended to have four marble fhelves at each end, inclofed by two backs, and open in front. Thefe fhelves are ufed in grand fideboards to place the fmall iilver ware on. The pattern on the right is intended to have legs turned the whole length, or rounded as far as the framing and turned below it, with carved leaves and flutes. The divifion beyond the celleret-drawer is meant for a pot-cupboard. It is not ufual to make lideboards hollow in front, but in fome circumftances it is evident that advantages will arife from it. If a fideboard be required nine or ten feet long, as in fome noblemen's houfes, and if the breadth of it be in proportion to the length, it will not be eafy for a butler to reach acrofs it. I therefore think, in this cafe, a hollow front would obviate the difficulty, and at the fame time have a very good effe£t, by taking off part of the appearance of the great length of fuch a fideboard. Befides, if the fideboard be near the entering door of the dining-room, the hollow front will fometimes fecure the butler from the joflles of the other fervants. Of r ( 367 ) Of the PerfpeSlive Lines. Having drawn the plan and adjufted the height of the ho- rizon by the fcale, as was mentioned in the univerfal table re- prefent a parallelogram a, b, c, equal to the length and breadth of the table; and from every part of the plan draw lines up to the ground line, and from the ground line dire£l thefe to the point of fight. Take from the plan the fpace M N, and place it from i to 2 ; and from 2 direft a line to the point of diftance, cut- ting a point next toy; from which point draw a parallel for the place of the front legs. In like manner take the other dirnen- fions from the plan to find every other correfpondent point in the reprefentation. To find the reprefentation of the hollow and round fronts, confult the treatife on perfpedtive in pages 294 and 295, together with the lines here fliewn as hints, and it is pre fum- ed that the learner will not be at any lofs in drawing fuch a table. Of the Book-cafe Doors. Plate XXVII. and XXIX. In the execution of thefe doors, the candid and ingenious workman may exercife his judgment, both by varying fome parts of the figures, and taking other parts entirely away, when the door is thought to have too much work. No. r, K 368 ) No. 1, in Plate XXVII. might do for a plain door, if tlie ornament and fquare part in the middle were taken away. No. 2 might alfo have the fquare in the middle taken away, and look very well. No. 4 may have the upright and horizontal bars away, and No. 5 the fmall fquares ; and at each angle of the hexagon the ftraight bar might be carried through to the frame. With refpe<5t to No. 6, it may be ufeful to fay fomething of the method of making it, as well as of fome of thofe in Plate XXIX. The firft thing to be done, is to draw, on a board, an oval of the full length and breadth of the door. Then take half the oval on the fhort diameter and glue on blocks of deal at a little diftance from each other, to form a caul ; then, on the fhort diameter, glue on a couple of blocks, one to flop the ends of the veneer with at the time of gluing, and the other, being bevelled off, ferves to force the joints of the veneer clofe, and to keep all faft till fufficiently dry. Obferve, the half oval is formed by the blocks of the fize of the aftragal, and not the rabbet; there- fore confider how broad a piece of veneer will make the aftra- gals for one door, or for half a door. For a whole door, which takes ( m ) takes eight quarter ovals, it will require the veneer to be inch and quarter broad, allowing for the thicknefs of a falh faw to cut them off with. Veneers of this breadth may, by proper management, be glued quite clofe ; and if the veneer be ftraight baited, and all of one kind, no joint w 7 ill appear in the aftragal. Two half ovals thus glued up, will make aftragals for a pair of doors, which, after they are taken out of the cauls and cleaned off a little, may be glued one upon the other, and then glued on a board, to hold them faft for working the aftragals on the edge ; which may eafily be done, by forming a neat aftragal in a piece of foft ft eel, and fixing it in a notched piece of w r ood, and then work it as a gage ; but before you work it, run on a gage for the thicknefs of the aftragal ; and after you have worked the aftragal, cut it off with a fafli faw, by turning the board on which the fweep-pieces are glued on an edge ; then having fawn one aftragal off, plane the edge of your ftuff again, and proceed as before. For gluing up the rabbet part, it muft be obferved, that a piece of dry veneer, equal to the thicknefs of the rabbet, muft be force i tight into the caul ; and then proceed as before in gluing two thickneffes of veneer for the rabbet part, which will leave fufficient hiding for the glafs, on fuppofition that the aftragal was glued in five. rn r 3 A The ( 370 ) The door being framed quite fquare, without any mould- ing at the inner edge, proceed to put in the rabbet pieces* Put, firft, an entire half oval, and fcrew this to the inner edge of the door, and level with it ; then jump up the other half oval to it, and fcrew it as before ; which completes the center oval. Next, fix the Square P art ? having been before mitered round a block, and keyed together ; after which, half-lap the other quarter ovals into the entire oval where they crofs each other, and into the fquare part, liping it into the angle of the door; put in the horizontal bars for the leaves to reft on ; glue on the aftragals, firft on the entire oval, tying it with pack- thread, to keep it on; then the ftraight one on the edge of the framing, fitting it to the oval ; laftly, miter the aftragal on the fquare part, and every other particular will follow of courfe. With refpe£t to the doors in Plate XXIX. all of them may be made nearly on the fame principles, at leaft the rabbet parts muft; but the aftragals in No. i, being all of them portions of circles, lhould be cut out of folid wood, and glued on a deal board and fent to the turner's. The fame may be faid of No. 5, which, in the vafe part, may have a piece of filvered glafs. The center in No. 2, is intended to have a print or painting in it. The fweeps, in No. 6, lhould be cut out of the folid, and worked by a tool. As to fixing any part of the ornaments in- troduced in thefe doors; this is eafily done, by preparing a very Flat*. 2<9. Booms for Bookcases TShtrabn M Pi/HrjhiJ as ^Act directs- . by TSheratort TerrrSc ( m ) very ftrong gum, which will hold on glafs almoft as ftroug as glue on wood. Of the Secretary and Book-cafe, Plate XXVIII. The ufe of this piece is to hold books in the upper part, and in the lower it contains a writing-drawer and clothes-prefs fhelves. The defign is intended to be executed in fatin-wood, and the ornaments japanned. It may, however, be done in mahogany ; and in place of the ornaments in the friezes, flutes may be fubftituted. The pediment is limply a fegment of a circle, and it may be cut in the form of a fan, with leaves in the center. The vafes may be omitted to reduce the work ; but if they are introduced, the pedeftal on which the center vafe refts is merely a piece of thin wood, with a necking and bafe moulding mitered round, and planted on the pediment. The pilafters on the book-cafe doors are planted on the frame, and the door hinged as ufual. The top of the pilafters are made to imitate the Ionic capital. Of the PerfpeSiive Lines'. GR is the ground line, and HL the horizontal line, or height of the eye. Lay on the original heights of the book- 3 A 2 cafe, ( 372 ) cafe, as at &c. and draw a perpendicular line at the angle of the piece, as at A ; to which direct parallel lines as fhewn. On the ground line lay a, or two feet, for the breadth of the end; and from ba dire£l lines to the diftance, which is here out of the plate, cutting the vifuals at d e ; from e raife a perpendicular, which will determine the front of the hook-cafe,, provided it be only a foot deep. The perpendicular B is necef- fary, in order to find the perfpe£tive heights of the book-cafe ? as fhewn in the figure. Of the Library "fable. Plate XXX. This piece is intended for a gentleman to write on, or to ftand or fit to read at, having defk-drawers at each end, and Is generally employed in ftudies or library-rooms. It has already been executed for the Duke of York, excepting the deik-draw- ers, which are here added as an improvement. The ityle of finifliing it ought to be in the medium of that which may be termed plain or grand, as neither fuits their fit nation. Mahogany is the moft fuitable wood, and the orna- ments fhould be carved or inlaid, what little there is ; japanned ornaments are not fuitable, as thefe tables frequently meet with a little harfli ufage. The ( 373 ) The ftrength, folidity, and effedt of brafs mouldings are very fuitable to fuch a defign, when expence is no obje£t. For inftance, the pilafters might be a little funk, or pannelled out, and brafs beads mitered round in a margin, and folid flutes of the fame metal let in. The aftragal which feparates the upper and lower parts might be of brafs ; and likewife the edge of the top, together with the patera in the upper pannel, as fhewn on the left hand. The top is lined with leather or green cloth, and the whole refts and is moved on caftors hid by the plinth. Of the mamifaffuring Part. The top fhould be framed in inch and quarter wainfcot, in the figure of a long hexagon, which beft fuits the fhape of the oval. The pannels, which are tongued in, fhould be of at leaft three quarters hard mahogany, about nine inches fquare, and the ftiles three and an half broad. The top being thus framed of very dry wood, it iliould be planed over, and ftand for fome time at a moderate diftance from a fire, after which it may be glued together, and when hardened it ought to be planed over again, and remain in that ftate till the lower part is finifhed. If thefe methods are not purfued, the pannels will flirink, and their joints will draw down the leather or cloth, fo that the figure ( 374 ) figure of the framed top will appear, efpecially when it is lined with leather. Next, it mult be confidered how to glue on the mahogany on the framing, fo as to make the furbafe moulding appear of folid wood. Firft, plough the four ihort fides of the hexagon, and then tongue in fuitable mahogany lengthways, meeting in a ftraight joint in the center of the top ; and, laftly, after the tonguing is dry, glue in ftraight joints pieces on the two long fides of the hexagon, and when dry, the top will be prepared for cutting to its elliptic fhape. The manner of framing the upper and lower parts of the carcafe muft be learned from the plan. The upper part, framed in an entire oval, contains the defk-drawers ; and, if thought neceflary, two ftiort ones may be obtained over the fide niches. The cupboard part is framed in two, each of which has a niche at the end, and one-third of the fide niches; for the niches are all of them divided into three pannels, and the middle pannels of the fide ones ferve as doors, by which an open paf- fage is gained through the table. There are four cupboards in the whole, divided in the manner fpecified by the dotted lines in the ( 375 ) the plan, one or two of which may be fitted up in a neft of fmall drawers and letter-holes. The plinth is framed entire of itfelf, and the bafe-moulding ftands up a little to receive the whole and hide the joint. Jn putting on the bafe-moulding there are two or three methods which I would offer as the heft I know of. The frame being made fo thick as to take the projection of the bafe, it muft then be rabbeted out of the folid to receive it. This being done, proceed to glue the bafe in three or four thicknefles, con- fining them to their place by hand-fcrews, or other devices of that nature ; but obferve to let the bafe project further out than the deal plinth, that it may receive the mahogany veneer which is to be glued on lengthways to hide the deal. After the whole is glued faft to its place, the veneer on the plinth and the bafe muft be cleaned off level with each other. The convex parts of the bafe-moulding may be worked with hollows and rounds; and after thefe are finifhed, the niches fhould be worked down to them, by a tool made on purpofe. . Another method of gluing the bafe-moulding is as follows : — Prepare the inch deal, and make cauls to fit the end and fide niches of the plinth ; after which take ftraight baited three- eighths ( 376 ) eights Spanifli wood, and work the hollow part of the bafe fe- parate from the torus; then, from quarter Huff of the fame kind, cut off flips for the torus ; heat the caul well, and both wet and heat the flips, which will then eafily bend. When the hollow part is well tempered, and alfo the torus, begin at one end, and by a thin chip run glue in between them ; and as you go on drive in nails about every inch, having between the liails and the moulding a thin flip of wainfcot well heated. Obferve to let the moulding pafs beyond the caul at each end, that a pack-firing may be tied to keep it to its place when it is taken out. The torus may then be worked before it is glued on the plinth. A third method is, to make the plinth itfelf the caul, and firft work the hollows, and foak them in water a whole night. Next morning take a hand-iron and heat it well, and over the curved fide of which bend the hollow as near as may be to the fweep. Having already a flop fere wed on the plinth, jump one end of the moulding to it, and glue as you go on; at the fame time fixing fmall hand-fcrews to draw it to, or brads may be put through the fquare part to aflift: in this bufinefs, if necef- fary, for thefe will be covered by the torus. After the hollow is fufFiciently dry, the torus being worked off and well foaked, and bent round the iron as above, it will glue to the hollow without the fmalleft difficulty, by fir ft jumping it againft the flop Plate 31. . 0nf third of the real Scale of Feet and Inches -muii l u-i I I I f 1 1 .T.^lieraton del 1 (j Teny- Sculp. Fubfas tfieAct directs . Sep T 30. ijgi ~by. TSheraioTV J ( 377 ) flop before mentioned ; and after it is brought pretty near, take another flop and fcrew it againft the end of the torus, which will draw it down without further trouble. Thefe two methods are founded on experiment ; for, at my requeft, it was per- formed by fome cabinet-makers to my full fatisfadtion ; there- fore, fhould either of thefe methods fail in the hands of any, it muft be owing to fome defe6l in the management. Of the Perfpe&ive Lines. Draw firft a plan of the whole, and make GR the ground line, and H L the horizon. From the plan draw perpendicular lines from every part to G R, as ftiewn in the Plate ; make s the center, and lay on the diftance, which is here out of the plate. From each perpendicular line drawn to G R draw lines to j* ; then reprefent a parallelogram both at top and bottom, in which the ellipfis may be infcribed; and draw the diagonal correfpond- ing with that fliewn in the plan, which will cut the vifual drawn from the faid diagonal in the plan, finding a point to guide the ellipfis. For other particulars relative to the repre- fentation of an ellipfis, fee page 294, and Plate XXI ; for the re- prefentation of the niche, fee page 295 ; and for the defk-drawer, fee page 231, Prob. 4. Of ( 378 ) Of the Kidney Library fable. Plate LVIII. This piece is termed a kidney-table, on account of its re- femblance to that inteftine part of animals fo called. Its ufe* however, is the fame as that already defcribed. The drawers which appear in the defign are all real, and are ftrung and crofs-banded, with the grain of the mahogany- laid up and down. The pilafters are pannelled or crofs-banded, and the feet below turned. The view of it below Ihews the ends pannelled, and the back may be fo too, or it may be plain. With refpeit to the manufacturing part, I need not fay any thing after what has been faid on the other, except to explain the reading delk which Aides out, as fliewn below. Obferve, B is the profile of the frame which Hides out, in the edge of which there is a groove fliewn by the black ftroke, and a tongue is put into the edge of the well part to fuit it. F is the defk part which rifes by a horfe ; and A is a part of that, which rifes at the fame time to flop the book ; b is a tumbler-hinge let in flufli with the top, and hid by the cloth or leather ; c is a com- mon but-hinge let in the edge of F, and upon the frame B ; fo that when F falls to B, A does alfo. The length of the table is four feet, its width two, and its height thirty-two inches. Of ( 379 ) Of the Sofa Bed. Plate XXXI. The frames of thefe beds are fometimes painted in orna- ments to fuit the furniture. But when the furniture is of rich filk, they are done in white and gold, and the ornaments carved. The tablets may have each a feftoon of flowers or foliage, and the cornice cut out in leaves and gilt has a good effeft. The drapery under the cornice is of the French kind ; it is fringed all round, and laps on to each other like unto waves. The va- lance ferves as a ground, and is alfo fringed. The rofes which tuck up the curtains are formed by filk cord, 8cc. on the wall, to fuit the hangings ; and obferve, that the center rofe contains a brafs hook and focket, which will unhook, fo that the cur- tains will come forward and entirely enclofe the whole bed. The fofa part is fometimes made without any back, in the manner of a couch. It muft alfo be obferved, that the beft kinds of thefe beds have behind what the upholfterers call a fluting, which is done by a flight frame of wood fattened to the wall, on which is {trained, in ftraight puckers, fome of the fame fluff of which the curtains are made. The left plate fliews the plan of the tefter, and the manner of fixing the rods, which are made in two parts to pafs each 3 B 2 other, ( 38o ) other, fo that the curtains may come clofe to each other in the center. The teller rods {crew fail in front, and hook paft each other behind. The manner of fixing the tefter up is by an iron bracket at each end ; one arm of the bracket fcrews to the under- fide of the tefter, and the other againft the wall, by driving iu plugs for that purpofe. Of the Perfpe Stive Liner. The left plate fhews thefe lines, and the right fhews the fcales of proportion. Thefe beds feldom exceed twelve feet in height, including the feather at top. Their length is feven feet, and width about five. The perfpe£live lines are drawn by a contracted diftance, being only one third of the whole. The front of the fofa is merely a geometrical elevation. For the apparent width of it take five feet from the fmall fcale, which is termed one third of the real fcale of feet and inches; place this meafurement from 14 to e, and draw a line to d, cutting at 15 ; a 9 b, d, are for the tablets at each end ; and at / is laid on the full meafurement of the back tablet, from which lines are drawn to s the center, which I ( 381 ) which cuts the back of the fofa at the line 15, 16, and deter- mines its length. The back tablet being the higheft, lay on the additional height from 10, and draw a line to s, cutting a per- pendicular at n ; from which draw a parallel as fhewn. The line drawn through h is to find the front of the dome, which comes forward rather fhort of half of the breadth of the fofa. The line 4 is the back of the dome, 5 is the center line, and 3 is its front; 7 fliews the height of the under fide of it, 8 of the top of the cornice, and 9 the top of the dome ; the reft muft be un- derftood by obfervation. Of the Alcove Bed. Plate XL. The term alcove, in buildings, means a part of a room fe- parated off from the reft by columns and arches correfponding, in which is placed a bed : fo that it is not the particular form of the bed which gives rife to this name, but the place in which it ftands. The learned inform us, that the word alcove is from the Arabic eJcauf, which means a cabinet or fleeping-place. This defign is reprefented ftanding on a plinth, covered with carpet, and having a border round it fuppofed to be on the floor of the room. The fteps are introduced to fhew that beds of this fort are raifed high, and require fomething to ftep on before they can be got into. The fteps are generally covered with ( 38a ) with carpet, and framed in mahogany. Both this, the fofa, and French ftate bed, require fteps. The dome of this bed is fixed in the fame manner as the other ; but the rofes to which the curtains are tucked up are different* This is made of tin, and covered with the fluff of the bed, and unbuckles to take in the curtains behind the rofe. Upon the fluting, as before men- tioned, is fixed a drapery in this, as fhewn in the defign ; and fometimes in the arch of the alcove a drapery is introduced. Of the Summer-Bed in two Compartments. Plate XLI. These beds are intended for a nobleman or gentleman and his lady to fleep in feparately in hot weather. Some beds for this purpofe have been made entirely in one, except the bed- clothing being confined in two drawers, running on rollers, .capable of being drawn out on each fide by fervants, in order to make them. But the preference of this defign for the purpofe, mull be obvious to every one in two or three particulars. Firft, the paffage up the middle, which is about twenty- two inches in width, gives room for the circulation of air, and likewife affords an eafy accefs to the fervants when they make the beds. 8 Secondly, A 1,11© VKi (IhV 11 , JU&7i/?ied as the Art directs, by T.Shera^7iTeb.,^Jy^% ( 383 ) Secondly, the paffage gives opportunity for curtains to en- clofe each compartment, if neceflary, on account of any fudden change of weather. Thirdly, it makes the whole confiderably more ornamental, uniform, and light. The firft idea of this bed was communicated to me by Mr. Thompfon, groom of the houfliold furniture to the Duke of York, which, I prefume, is now improved, as it appears in this defign. The manufacturing part may eafily be underftood from the defign by any workman; I ftiall, however, point out a few par- ticulars. The arch which fprings from the Ionic columns fhould be glued up in thicknefs round a caul, and an architrave put on each fide afterwards. The arch fhould be tenoned into the co- lumns, with iron plates fcrewed on, fo that it may be taken off when the bed is required to come down. In this arch a drapery is fixed, with a tafTel in the center, and a vafe above. The head-board is framed all in one length, and the two inner fides of the bed tenoned into the head-rail, and fcrewed. The teller is made in one, in which there are two domes, one over each compartment. It may, however, be made without domes, but not with fo good effect. In the middle of the tefter, perpendi- cular ( 3§4 ) eular to the fides of the paffage, are fixed two rods, for the cur- tains above mentioned. Thefe rods are hid by valances, and between the valances is formed a pannel, by fewing on va- riegated margins to fuit the reft of the upholftery work. The ornamented margins, and the oval with crefts in the center of the counterpanes, may all be printed to any pattern, at a manu- factory which has been lately eftablilhed for fuch purpofes. The fcale fhews the fizes which applies to every part of the end of the bed, it being merely a geometrical elevation. Of the French State-Bed. Plate XLV. Beds of this kind have been introduced of late with great fuccefs in England. The ftyle of finifliing them, with the management of the domes, is already defcribed in general terms, in page 113, &c. I fhall, therefore, omit it here, and proceed to give fome hints relative to the manufacturing part. The dome is fupported with iron rods of about an inch diameter, curved regularly down to each pillar, where they are fixed with a ftrong fcrew and nut. Thefe iron rods are covered and entirely hid by a valance, which comes in a regular fweep, and meets in a point at I ( 385 ) at the vafes on the pillars, as the defign fkew s. Behind this va- lance, which continues all round, the drapery is drawjj up by pulleys, and tied up by a filken cord and tafifels at the head of the pillars. The head-boards of thefe beds are framed and fluffed, and covered to fuit the hangings, and the frame is white and gold, if the pillars and cornice are. The bed-frame is fome- times ornamented, and has drapery valances below. Obferve, that grooves are made in the pillars to receive the head -boards, and fcrewed at the top, by which means the whole is kept firm, and is eafily taken to pieces. Square bolfters are now often introduced, with margins of various colours ftitched all round. The counterpane has alfo thefe margins ; they are alfo fringed at bottom, and have fometimes a drapery tied up in cords and taffels on the lide. Of the Perfpedlive Lines. This defign is in an oblique lituation, fo termed becaufe none of its ends or fides are paralled to the picture. I have here taken the neareft angle of the bed for the center of the pic- ture, from which raife a perpendicular as from feven on the fcale line. Confider next the height of the horizon, which fhould be about five feet fix, taken from the fcale you draw the 3 C bed ( 3*6 ) bed by. On the perpendicular line now mentioned lay on the diftance of the picture from the horizontal line. Then deter- mine the pofition of one fide of the bed, by drawing a line from the angle E to V ; from V draw a line to the diftance here out of the plate, on the aforefaid perpendicular ; from the diftance draw a line T U at right angles with this, which produced cuts the horizon, and finds the vanifhing point for the ends of the bed ; confequently V is the vanifhing point for the fides of the bed. From 7 to A is feven feet, the length of the fide ; and from 7 to N is the width of the bed. From N A draw lines to DD, the dividing centers, or meafuring points, found as in Problem VI. Method 2. page 237, which will cut the vifuals for the apparent length and width of the bed. A perpendicular from 5 is the center of the end of the bed ; S is the original height of the dome, from which a line is directed to the right hand vanifhing point, cutting at d; a line from d finds the cen- ter of the dome, and V the top of the pine-apple ; c a give the height of the cornice; the diagonals 1, 3, 2, 4, find the center of the dome, by railing a perpendicular from their interfe£lion a Every other thing will follow of courfe to him who has previ- ouily ftudied the rules given ; without which, it would be im~ poffible to make every particular underftood here* Of 1 ] 1 1 ] 1 ] < ] ( 3«7 ) Of the Drawing-Room Chairs. Plates XXXII, XXXIV. These chairs are finifhed in white and gold, or the orna- ments may be japanned; but the French finilh them in maho- gany, with gilt mouldings. The figures in the tablets above the front rails are on French printed lilk or fatin, fewed on to the fluffing, with borders round them. The feat and back are of the fame kind, as is the ornamented tablet at the top of the left-hand chair. The top rail is pannelled out, and a fmall gold bead mitered round, and the printed filk is pafted on. Chairs of this kind have an effect which far exceeds any conception we can have of them from an uncoloured engraving, or even of a coloured one. The perfpedtive lines in the left chair may ferve as hints ; but I need not explain them, fince I have fully done this in Plate XXIV. and XXVI. The parlour chairs in Plate XXXIII. and XXXVI. need no explanation, as every one muft eafily fee how they are to be finifhed. 3 C 2 Of ( 388 ) Of the Sofa. Plate XXXV, These are done in white and gold, or japanned. Theloofe ctifliicns at the back are generally made to fill the whole lengthy which would have taken four ; but I could not make the defign fo ftriking with four, becaufe they would not have been dif- tinguifhed from the back of the fofa by a common obferver. Thefe culhions ferve at times for bolfters, being placed againft the arms to Icli againft. The feat is fluffed up in front about three inches high above the rail, denoted by the figure of the fprig running longways ; all above that is a fquab, which may be taken off occafionally. If the top rail be thought to have too much work, it can be finifhed in a ftraight tail, as the defign fhews. Of the Ladfs Writing Table. Plate XXXVII. The convenience of this table is, that a lady, when writing at it, may both receive the benefit of the fire, and have her face fcreened from its fcorching heat. The ftyle of finifhing them is neat, and rather elegant. They are frequently made of fatin-wood, crofs-banded, japan- ned, and the top lined with green leather. 8 The \ > ( 389 ) The manufacturing part is a little perplexing to a ftranger, and therefore I have been particular in fhewing as much as I well could on the plate. Obferve, that in the fide-boxes the ink-drawer is on the right, and the pen-drawer on the left. Thefe both fly out of themfelves, by the force of a common fpring, when the knob on which the candle-branch is fixed is prefled. Figure A is the fpring which is let in under the candle-branch ; C is a lever which is prefled to B, the end of the drawers, by a fpring rifing from D ; N is a part of the candle-branch, and e is the knob juft mentioned, which is capable of being prefled down ; there- fore, if P be fcrewed into E by prefling e, C rifes and relieves B, which immediately ftarts out, by a common fpring fixed on the infide of the boxes. Obferve a patera in the center of the back amidft the orna- ment. This patera communicates to a fpring of precifely the fame kind as A ; which fpring keeps down the fcreen when the weights are up : and by touching the faid patera, which has a knob in its center like the fpring is relieved, and the weights of courfe fend up the fcreen, being fomewhat aflifted by a fpring at the bottom, which may be feen in the defign. Figure T fhews the lead weight, how the pulleys are fixed, and the manner of framing the fcreen before it is covered with fluff*. The ( 390 ) The workman will obferve, that a thin piece of mahogany flides out in a groove, to afford accefs to the weights, and afterwards enclofe them. There is a drawer under the top, which extends the whole of the fpace between the legs. The fcale fhews the length of the table, b its height, a the depth of the drawer, b c the depth of the fide-boxes, and ed the height of the fwell of the fcreen part ; the width of the table is twenty inches. Of the Tripod Fire-Screens. Plate XXXVIII. Screens of this kind are termed tripod -, becaufe they have three feet or legs. The middle fcreen may be finifhed in white and gold, or japanned; and the other two of mahogany, or japanned. The rods of thefe fcreens are all fuppofed to have a hole through them, and a pulley let in near the top on which the line pafles, * Tripod, ofTff"fe treis, three; and iroho», podion, afoot. Anciently the word tripod iifed to be applied to a kind of facred three-footed ftool, on which the heathen priefts were feated to receive and deliver their oracles: from which we may learn how time alters words. and / ( 39i ) and a weight being enclofed in the taflel, the fcreen is balanced to any height. The rods are often made fquare, which indeed beft fuits thofe which have pulleys, while thofe that are made round have only rings and fprings. Such fcreens as have very fine prints, or worked fatin commonly have a glafs before them. In which cafe a frame is made, with a rabbet to receive the glafs, and another to receive the {training frame, to prevent it from breaking the glafs; and to enclofe the {training frame a bead is mitered round. Of the Knife-Cafes and Ladfs Travelling-Box. Plate XXXIX. Little need be faid refpe£ting thefe. It is only wanted to be obferved, that the corner pilafters of the left-hand cafe has fmall flutes of white holly or other coloured wood let in, and the middle pilafters have very narrow crofs-bands all round, with the pannels japanned in fmall flowers. The top is fome- times japanned, and fometimes has only an inlaid patera. The half columns of the right-hand cafe are fometimes fluted out, and fometimes the flutes are let in. The feet may be turned and twifted, which will have a good effedt. As ( 39* ) As thefe cafes are not made in regular cabinet fhops, it may be of fervice to mention where they are executed in the belt tafte, by one who makes it his main bufinefs ; u e. John Lane, No. 44, St. MartinVle-grand, London. The Lady's travelling-box in the fame plate, is intended to accommodate her in her travels with conveniences for writing, dreffing, and working. The front is divided into the appear- ance of fix fmall drawers ; the upper three fhain, and the under real. The writing-drawer takes up two of thefe fronts in length, and contains an ink-drawer, and a top hinged to the front, lined with green cloth. The top being hinged at front, by pufhing in the drawer, it will rife to any pitch. The other drawer on the left, which only takes up one front, holds a kind of windlafs or roller, for the purpofe of fixing and winding up lace as it is worked. The middle vacuity, which holds the fcilfors and other articles of that nature, takes out, which gives accefs to a convenience below it for holding fmall things. The boxes on each fide hold powder, pomatum, fcent-bottles, rings, &c. The dreiling-glafs, which is here reprefented out of the box, fits into the vacuity above the fciffor-cafe. Of ( 593 > Of the Corner Bafon-Stands. Plate XLII. The right-hand bafon-ftand contains a cupboard and a real drawer below it ; by the top folding down the bafon is inclofed and hid when it is not in ufe. The left-hand top is fixed to the fide of the bafon-ftand by a rule-joint, the fame as the flap of a Pembroke table ; but inftead of iron the hinges are made of brafs. The right-hand top is hinged to the other by common butt-hinges, by which means it will fold againft the other, and both may be turned down together. When the tops are in their place, there then appears a rule-joint on both fides. The front edges of the tops are hollowed and beaded, which hang a little over, fo that the fingers may get hold to raife them up. Short tenons are put to the under edge of the right-hand top, to keep it in its place on the end of the lower part. The bafon-ftand on the left has a rim round the top, and a" tambour door to inclofe the whole of the upper part, in which is a fmall ciftern. The lower part has a fhelf in the middle, on which ftands a veflel to receive the dirty water conveyed by a pipe from the bafon. Thefe fort are made large, and the bafon being brought clofe to the front, gives plenty of room. The advantage of yaiskia**f bafon-ftand is, that they may ftand in a 3 D genteel ( 394 ) genteel room without giving offence to the eye, their appearance being fomewhat like a cabinet. Of the Dejtgns in Plate XLIII. The drawer in the wafli-hand ftand is lined with lead, into which the bafon is emptied. The tipper part, which contains the ciftern, takes off occafionally. Below the drawer is a cup- board. Obferve, that in the delign the drawer back is fuppofed to be behind the bafon ; but before the drawer is wholly taken away, the bafon muft be taken out* Of the Pot-Cupboard. These are ufed in genteel bed-rooms, and are fometimes finifhed in fatin-wood, and in a ftyle a little elevated above their ufe. The two drawers below the cupboard are real. The par- titions may be crofs-banded, and a fixing round the corners of the drawer. Thefe feet are turned, but fometimes they are made fquare. Sometimes there are folding doors to the cup- board part, and fometimes a curtain of green filk, fixed on a brafs wire at top and bottom ; but in this defign a tambour door is ufed, as preferable. The upper cupboard contains ihelves, and is intended to keep medicines to be taken in the night, or to hold other little articles whk;h fervants are not permitted to overlook. 8 Of } ( 395 ) Of the Ladfs Secretary. These are fomctimes finiflied in black rofe-wood and tulip crofs-banding, together with brafs mouldings, which produce a fine effect. The upper fhelf is intended to be marble, fup- ported with brafs pillars, and a brafs ornamented rim round the top. The lower part may be fitted up in drawers on one fidey and the other with a fhelf to hold a lady's hat, or the like. Of the Screen-Table. This table is intended for a lady to write or work at near the fire ; the fcreen part behind fecuring her face from its in- juries. There is a drawer below the Aider, and the Aider is lined with green cloth. The back feet are grooved out for the fcreen to Aide in; in each of which grooves is fixed a fpring to balance the fcreen by. The top is firft crofs-banded all round ; then a border is put on, fo broad as to fall exadtly where the joint of the fcreen will be in the top. Beyond that again is put a narrower crofs-banding. When the fcreen is down the top appears uniform, without any joim, at leaft not fo as to be offenfive to the eye. The ftraining 3 D 2 frame ( 39 s ) frame of the fcreen is made of thin wainfcot, and framed in four pannels. When the faid frame is covered in the manner of any other fcreen, flips are got out and grooved and mitered round, and a part of the top which rifes up with the fcreen is glued on to the flip, and as of courfe the top will project over behind, fo it affords hold for the hand to raife the fcreen by. Of the two Tables, Plate XLIW The left-hand table is to write and read at. The top is lined with leather or green cloth, and crofs-banded. To flop the book there are two brafs plates let in, with key holes ; and in the moulding, which is to flop the book, are two pins, with heads and fhouiders, by which the moulding is efFe&ually fecured. The right-hand tablS is meant to write at only. The top part takes off from the under part, w hich, having a bead let in at the back and ends of the top, prevents the top part from moving out of its place. This table being made for the conve- nience of moving from one room to another, there is a handle fixed on to the upper flielf, as the drawing fliews. In the drawer is a Aider to write on, and on the right-hand of it ink, fand, and pens. The fizes are fhewn by the fcales* Of ( 397 ) Of the Lady's Dreffiing "fable. Plate XLVI. The ftyle of finifhing thefe tables is neat. They are often made of fatin-wood, and banded ; but fometimes they are made of mahogany. The fize of this table, which is here three feet, fhould be increafed in its length near fix inches when thefe folding fide-glaffes are introduced. The reafon of this is, that a lady may have more room to fit between them to drefs. It fhould, in this cafe, be made about two inches wider. But, ob- ferve, the fize here given is that which is ufed when only the rifing back-glafs is introduced ; and this has been the common way of finifhing them. Thefe fide-glafies are an addition of my "own, which I take to be an improvement; judging that, when they are finifhed in this manner, they will aniwer the end of a Rudd's table, at a lefs expence. The glafs behind rifes up like that of a fhaving-ftand. Thofe on the fide, fold down pnft each other, being hinged to a Aiding ftretcher, which is cap able of being puftied backv ^d or forward. If the right-hand glals be pufhcd to the back it will then fold down, and the other keeping its place will do the fame. A and B, in the plan, fliew thefe glafFes in their pl^ce; e is the back-glafs, and / is the top, which is hinged to a piece . of ( 398 ) of wood, which runs in a groove at each end, fo that when the top is drawn fully up, it will fall down on the frame. The other folding top on each fide have each of them a fmall tenon near the front, as may be feen at the edge of the left- hand one. Thefe tenons being let into the middle part, are the means of fecuring each fide-top, when they are folded d^w^, and the middle part is put down upon them, fo that the lock in the middle fecures the three tops. The drawer on the right is the depth of two fronts, as is eafily feen ; the ufe of which is to put caps in. The left-hand fronts are in two real drawers, for the purpofe of laying fmall things in. The cupboard in the knee- hole has its front reeded in the hollow part to imitate tambour, and the circular door in the center is veneered and quartered. This cupboard will take a lady's hat as they wear them now. The other dreffing conveniences are obvious in the plan. Of the Perfpe&ive Lines. These I only confider as hints or memorandums to fuch as have already gone through the regular treatife on the fubje£t a n is the width of the table ; and a line from a to d, the diftance, cuts the vifual n s in which gives the apparent width at that diftance. The front of the table is fuppofed to be in the pic- ture, and therefore every meafurement is purely geometrical ; that is, they are taken from the fcale. From r to c is the width of ( 399 ) of the top, except the flip behind. Therefore by drawing a perpendicular at />, and directing a line from o to s, the center, it will cut at />, and give the height of the top, fuppofing it to be raifed quite up, ready for turning down. Of the Cylinder Defk and Book-cafe. Plate XL VII. The life of this piece is plain, both from the title and de- fign. The ftyle of finifhing them is fomewhat elegant, being made of fatin-wood, crofs-banded, and varniflied. This defign fliews green filk fluting behind the glafs, and drapery put on at top before the fluting is tacked to, w hich has a good look when properly managed. The fquare figure of the door is much in fafliion now. The ornament in the diamond part is meant to be carved and gilt, laid on to fome fort of filk ground. The rim round the top is intended to be brafs ; it may, however, be done in wood. Of the manufacturing Part. The manufacturing part of this piece is a little intricate to a ftranger, for which reafoii it will require as particular a defcription as I can give to make it tolerably well under- ftood. Firft, ( 400 ) Firft, obferve the Aider is communicated with the cylinder by .an iron trammel, as I, fo that when the former comes forward, the latter rifes up and fliews the neil of the fmall drawers and letter holes, as appears in the clefign. When, therefore, the Aider is pufiied home even with the front, the cylinder is brought clofe to it at the fame time. In this ftate the lock of the long drawer under the Aider iecures both the drawer itfelf and alfo the Aider at the fame time, in the following manner :— D is the long drawer under the Aider, P the partition above it, and S is the Aider ; C is a fpring-bolt let into the partition. When, therefore, the drawer lock-bolt is out, as it rifes it drives C, the fpring-bolt, into the Aider ; and when the drawer is unlocked, then C falls down to its place in the partition, and the Aider can be pulled out. The trammel I, is a piece of iron near a quarter thick, and inch and quarter broad, with grooves cut through, as lhewn at L S, in the profile, is the Aider; and g\ 12, Z>, the cy- linder. The trammel T is fixed to the cylinder at h by a fcrew, not drove tight up, but fo as the trammel will pafs round eafy. Again, at the Aider S a fcrew is put through the groove in the trammel, which works on the neck of the fcrew, and its head keeps the trammel in its place ; fo that it muft be obferved, that the grooves or Aits in the iron trammel are not much above a quarter of an inch in width. When the Aider is pufhed in -about half way, the trammel will be at u, and its end will be below the Aider, as the plate Aiews ; but when the Aider is home ( 4°t ) home to its place, the trammel Will be at T and g. The center piece with four holes is a fquare plate of iron, having a center- pin which works in the upper flit of the trammel. It is let into the end of the cylinder, and fixed with four fcrews. To find the place of this center, lay the trammel upon the end, as T in the pofition that it will be in when the Aider is out, and, with a pencil, mark the iniide of the flits in the trammel. Again, place the trammel on the end as it will be when the Aider is in, as at T g, and do as before ; and where thefe pencil marks interfedt each other will be the place of the center-plate. The figures i, 2,3,4, fhew the place of the fmall drawers. The triangular dotted lines with three holes, is a piece of thin wood fcrewed on to the end, to which is fixed the neft of fmall drawers, forming a vacuity for the trammel to work in. F is a three-eighth piece veneered and crofs-banded, and cut behind to give room for the trammel, This piece both keeps the Aider to its place, and hides the tram- mel. The next thing to be obferved is, that the lower frame, containing two heights of drawers, is put together feparate from the upper part, which takes the cylinder. The ends of the cylinder part are tenoned with the Aip tenons into the lower frame and glued. The Aiaded part at A fliews the rail cut out to let the trammel work. The back is framed in two pannels, and the back legs are rabbetted out to let the back framing- come down to the lower drawer. The Aider is framed of ma- hogany, with a broad rail at each end about nine inches, and 3 E one ( 4°2 ) one at the front about three and an half. In the infide of the framing a rabbet is cut to receive a thin bottom. The bottom being fixed in, a flip is put at each end to receive the horfe which lupports the defk part. The ink and pen drawers at each end of the Aider have a fmall moulding mitered round them to keep them faft, without their being glued on. Gbferve, there is a fliam drawer-front fattened on to the Aider, which of courfegoes in with it, and which contains the depth of thefe ink and pen drawers, fo that they are not required to be taken out when the Aider goes in. The cylinder is jointed to its fweep in narrow Aips of ftraight-baited hard mahogany, and afterwards veneered. If the veneer be of a pliable kind it may be laid with a hammer, by firft flirinking and tempering the veneer well, which mutt not be by water, but thin glue. If the veneer be very crofs and unpliable, as many curls of mahogany are, it is in vain to at- tempt the hammer. A caul in this cafe is the fureft and beft method^ though it be attended with confiderable more trouble than the hammer. To prepare for laying it with a caul, pror ceed as follows. — Take five or fix pieces of three-inch deal, and fweep them to fit the infide of the cylinder. Fix thefe upon a board anfwerable to the length of the cylinder. Then have as many cauls for the outfide of the- cylinder, which may be made out of the fame pieces as thofe for the infide. Take then quarter mahogany for a caul to cover the whole veneer, and heat it well. Put the caul fcrews acrofs the bench, aud fiip in the board ( 4°3 ) board with the round cauls fcrewed to it ; and proceed, in every other particular, as the nature of the thing will neceffarily dictate. Of the Perfpeclive Lines. GR is the ground line, and HL the horizon; s the center, and d the diftance of the pidture. A B, on the ground line, is the breadth of the ends ; from which a line is drawn to d 9 cut- ting the vifual B j*, for the perfpedtive breadth of the end. O is the height of the lower part, and the upper part being level with the horizon, appears in one line, and therefore fhews no breadth at the top. Of the Cabinet. Plate XL VIII. The ufe of this piece is to accommodate a lady with con- veniences for writing, reading, and holding her trinkets, and other articles of that kind. The ftyle of finifhing them is elegant, being often richly japanned, and veneered with the fineft fatin-wood. The manufacturing part is not very difficult, but will ad- mit of the following remarks. — The middle drawer over the 3 E 2 knee- ( 4 flops it from com- ing entirely cut. The other figure lhews the front when it is let down, which cannot fail of making it underftood. The dotced carve line o P fhews that the under fide of the top muft be hollowed out fo that the angle of the falling front may clear itfelf as it turns.. Obferve, ( 408 ) Obferve, the writing part folds over like a card-table, and when it is open, is fupported by the drawer in the frame, Every other part muft be plain to the workman. pjj! \ N. B. Upon the fame principles the top of the drefiing- table, Plate XL VI. is managed. Of the Drapery. Plate LI. Little can be faid of this, as every part explains itfelf, as reprefented in the drawing. It is, however, neceffary to ob- ferve, that the French ftrapping and taffels in the right-hand defign is no part of the cornice, as fome cabinet-makers have already miftaken it to be. It is the upholfterer's work, and is fewed on within the valance or ground of the drapery. Thefe curtains are drawn on French rods. When the cords are drawn the curtains meet in the center at the fame time, but are no way raifed from the floor. When the fame cord is drawn the reverfe way, each curtain flies open, and comes to their place on each fide, as they are now reprefented. The cord paffes on a fide pulley fixed on the right-hand. To ( 4°9 ) To effe£t this, the rod is made in a particular manner, having two pulleys at one end, and a fmgle one at the other, which cannot well be defcribed in words without a drawing of it Of the Gentleman 9 s Secretary. Plate LIL This piece is intended for a gentleman to write at, to keep his own accounts, and ferve as a library. The ftyle of finifh- ing it is neat, and fometimes approaching to elegance, being at times made of fatin-wood, with japanned ornaments. Of the manufacturing Part. The great thing to be obferved in this, is the management of the fall A, or writing part, which is lined with green cloth. This fall is hung by an iron balance-hing^B, fo that when the fall is raifed vip by the hand a little above an angle of forty-five degrees, or in the polition it is (hewn at A, it falls to of itfelf by the balancing power of B. When A is in a horizontal pofition, B is at F, the infide of the pilafter, on which is glued a piece of cloth to prevent the 3 F iron ( 4i° ) iron from rattling. B flopping at F it is evident how firmly the fall is fupported by that means ; for the hinge is made very ftrong, about three quarters thick at the dove-tail end, and ta- pered off to about a quarter thick at the joint, and where it i& fcrewed to the fall. The hinge is made in two parts, as D and b. D has a center pin, and is fcrewed on to the infide of the pilafter, as at d; b is all in one piece, and is fcrewed on to the fall, having a center hole to receive the abovementioned pin m the other part of the hinge. It is neceflary to obferve, that there is a vacuity behind both the upper and lower pilafters in which the iron ba- lance operates, fo that nothing is feen bvit the mere joint of the hinge. Again, it is requifite to obferve, that a hollow muft be worked on the upper fide of the under carcafs, to give place to the circular motion of the under angle of the fall, as it turns upon its hinge from a perpendicular to a horizontal form. This hollow may be obferved in the plate. The fpace x contains the fall when it is up ; 2 is an open fpace, which affords room for the rings on the fmall drawers ; and 3 is the pilafter. The or- namented freeze under the cornice is, in reality, a drawer, which fprings out when the bolt of the fall-lock is relieved. This is done by a fpring-bolt let into the partition under the drawer, ( 4" ) drawer, which is forced up by the bolt of the fall-lock into the under edge of the drawer ; and when the fall is unlocked this fpring-bolt returns to its place in the partition, and a common fpring fcrewed on to the drawer-back fends it forward, fo that it may be drawn out independent of a ring or handle. When the fall is up, there appear two pannels in the form of thofe below. As for any other particular, it muft be under- ftood by a workman. Obferve, the dimenfions of every part may be accurately taken from the profile by the fcale. Of the Cylinder Wqfli-hand table. Plate LIII. These are always made of mahogany, and having a cy- linder to rife up to hide the wafhing apparatus, they look neat in any genteel dreffing-roorcu They alfo contain a bidet on the right near the front, and D, a water-drawer on the left near the back, fo that when the two are pufhed home they pafs by each other. The drawer on the front, which appears partly out, runs above the bidet and the water-drawer. The two heights of fham drawers above contain the cylinder, and the two heights of fham drawers be- 3 F 2 low ( 4 12 ) low contain the bidet and water-drawer. The bafon has a plug- hole at the bottom, by which the water is conveyed off into the drawer D, which is lined with lead. The top of the ciftern is hinged, and can be turned up at any time to fill it with frefli water. The glafs rifes up behind, in the fame manner as that of a lhaving-ftand. And when the glafs is down, the top can be turned down alfo ; and the cylinder being raifed to meet it, the whole is enclofed. The motion of the cylinder is guided by two quadrant pieces, one at each end of it, which are hinged to the top in which the bafon hangs. This is Ihewn by A in the profile ; which, when the cylinder is let fall to its place, will be at B. When the cylinder is raifed up to A, it catches at C, which is a fpring of the fame kind as thofe put on to fecretary drawers. The bidet-drawer is fometimes made to take quite out, having four legs to reft on. The end of the piece of work is cut out fo as the feet can go in without being folded up. This, in the defign, is Hopped from coming quite out, and the framed legs, which appear, fold under the drawer and flip in along with it. Of the Pembroke fable and French Work 'fable. Plate LIV. The ufe of this piece is for a gentleman or lady to break- fad on* The ( 4i3 ) The ftyle of finifhing thefe tables is very neat, fometimes bordering upon elegance, being at times made of fatin-wood, and having richly japanned borders round their tops, with or- namented drawer-fronts. The manufacturing part of this table differs but very little from thofe in common ufe. The fly brackets which fupport the flaps are made and fixed in the fame manner as any other, only I appreh nd it beft to make a dove-tail groove in the front for the drawer fides, at a diftance from each end of the drawer-front equal to the thick- nefs of the bracket and the inner lining ; fo that the front laps over and covers the whole, as appears in the defign. In this cafe the lock-bolt fhoots up into the top of the table. The top and frame may be connected to the pillar and claws, either by a fquare block glued up, or by a couple of pieces, about four inches broad, half-lapped into each other at right-angles, and double tenoned into the pillar, and fcrewed to the bottom of the frame, as the profile of the pillar and claw is intended to fuggeft. The workman is defired to obferve, that the top of the table, as fhewn in the defign, is not meant to reprefent a regu- lar ellipfis, as they are generally made a little fuller out at each corner ( 414 ) corner of the bed. The reafon of this is, that the flaps, when turned down, may better hide the joint rail. Of the French Work Table, Plate LIV. The title of this table fufficiently indicates its life. The ftyle of finifhing them is neat, being commonly made of fatin- wood, with a brafs moulding round the edge of the rim. The front part of the rim is hinged to the top, in the fame way as the front of a fecretary or defk-drawer ; fo that when it is turned up, it fallens by two thumb-fprings as they do. The brafs moulding is mitered upon the edge of the rim when the front is up, and after it is hinged ; which being cut through with a thin faw, the moulding, on the return of the front, will be fair with that on the end. The fhelf below is fhaped fomething like a boat. The bottom of it is made of inch fluff, and double tenon ned into the ftandards, as the profile plainly fhews. The top of each ftand- ard has alfo double tenons, to which crofs-bars are morticed and fcrewed to the under-fide of the top. The fcale fhews the proportions of the flandard, and the height of the table ; its breadth is fourteen or fifteen inches. 7 The ( 4*5 ) The boat part, which ferves as a convenience for fewing imple- ments, is fix inches over the middle, and three at each end. I. have, in thefe two defigns, introduced ftridt fliadowing, that the learner may better judge of its effects in fncli cafes. — But I muft obferve the fhadows here are rather too faint, be- caufe I was afraid to make the plate look heavy. The fan's rays are here confidered parallel to the picture, which is fully illu fixated, by different cafes, in the Treat ife on Shadowing, fee page 328. And, therefore, I fliall only obferve here to the learner, that, in making out the fhadows of objedts, a harfli out- line ought carefully to be avoided. In fadt, there ought to be no outline at all, except thofe firfl: drawn by a pencil to deter- mine the boundaries of the fliadow ; after which a large hair pencil fhould be ufed to fill up the fliadow. We may likewifq remark, that if Nature be obferved duly, fhe teaches us that the fhadows of objefts are ftronger neareft the foot or place where they reft, and grow fainter the further they recede from the foot of the obje£t. The reafon of this is : becaufe if fhadows are very long, as from a houfe, there is a ftrong reflection of light towards the boundaries, which mixes with the fliadow, and confequently weakens it. It is fomewhat fimilar to what aftro- nomers term a penumbra, or imperfect fliadow accompanying a total one. Laftly, ( 4i6 ) Laftly, it may alfo be obferved, that when an objedt is to- tally immerfed in the fliadow of another, as the table claws are in the fliadow of the top, there is a fort of additional fliadow, occafioned partly by reflection, and partly by the contaCt of the two furfaces, but thefe are fhort and imperfedt in their boun- daries. Of the Tripod Candle-Stand. Plate LV. These are ufed in drawing-rooms, for the convenience of affording additional light to fuch parts of the room where it w T ould neither be ornamental nor eafy to introduce any other kind. The ftyle of finifhing thefe for noblemen's drawing-rooms is exceeding rich. Sometimes they are finifhed in white and gold, and fometimes all gold, to fuit the other furniture. In inferior drawing-rooms they are japanned anfwerable to the furniture. Perfons unacquainted with the manufacturing part of thefe Hands may apprehend them to be flight and eafily broken; but this objection vaniflies, when it is confidered that the fcrolls are made of ftrong wire, and the ornaments cemented to them. I could ( 417 ) I could not fliew to advantage more than three lights, but, in reality, there are four ; one at the center, and one at each angle. The top of the left ftand is a round vafe, which can be turned and have the fquare handles put on afterwards. The handles fhould be placed parallel to two of the feet. The top of the right one is a concave fpherical triangle, having all its fides equal. As to any other part, the workman's own notions will fug- geft every thing neceffary in their manufacture. Of the Harlequin Pembroke Table. Plate LVL This piece ferves not only as a breakfaft, but alfo as a waiting table, very fuitable for a lady. It is termed a Harlequin Table, for no other reafombut becaufe, in exhibitions of that fort, there is generally a great deal of machinery introduced in the fcenery. Tables like this have already been made, but not according to the improved plan of the machinery here propofed. In this, however, I affiime very little originality or merit to myfelf, except what is due to the manner of fhewing and 3 G defcribing ( 4i8 ) defcribing the mechanifm of it : the reft is due to a friend, from whom I received my firft ideas of it. The particular advantages arifing from the machinery are as follows : Firft, the neft of drawers, or till, fhewn in the defign, can be raifed to any height, gradually, until at length the whole is out. Second, when the whole is out, as reprefented in the defign, it cannot be taken away, becaufe of three flops which keep it in ; two at one end, and one at the other, according to the grooves in No. i. Thirdly, but if neceility require that the till fhould be taken quite, away from the reft of the table, in order to come at the machinery, then one of thefe ftops at one end is fo conftru£led that it can be flipped back, and, the till being raifed up at the fame end where the flop is flipped back, the two at the other end of courfe will relieve themfelves, fo that the till can be taken quite aw r ay. Fourthly, when the till is replaced, the ftop can be pufhed into the groove again by the finger, which returns again into the groove by the force of a fmall fpring. Fifthly, ( 4*9 ) Fifthly, The till being let down again until it is perfedtly even with the reft of the table-top, it can then be fecured in its place by means of another ftop at the bottom, fo that if the whole table were turned upfide down the till would ftill keep its place. Sixthly, although the till be raifed and lowered by turning the fly-bracket which fupports the flap, yet the bracket is made to lofe this effe£t or pow r er by the turn of a key, and the bracket may then lie drawn out to fupport the flap without railing the till, and the table can then be ufed, as in common, to breakfaft upon. Thefe are all the advantages that are neceffary, or that can be looked for, in tables of this fort, to render them complete, and to obtain the approbation of the ingenious. But it will now be requifite to fhew in what manner the machinery operates fo as to effedt thefe ; and, likewife, to give fome defcription of its parts, that the workman may be able to form a proper idea of the whole* The firft and great thing to be attended to is, to fhew the manner of railing the till by turning the fly-bracket. To ac- 3 G 2 complifli ( 4 2 ° ) complifh this, I have given a perfpedtive view of the whole machinery at No. I. Suppofing the till to be taken out, and the fly-brackets and inner lining away from the framing ; a b is an upright iron axis, made in two parts, and connected together by a round pin at the joint b; of courfe, if the winch c be turned round, the axis a will turn round with it by the above pin, without moving the lower part of the axis b. Whence it is evident, that if the winch c be fere wed to the under edge of the fly-bracket, which bracket is fhewn in the defign, it will turn round without affedting any part of the machinery. This is the caufe why the flap of the top can be up whilft the till is down. But if the fquare focket a be preffed down paft the joint the two parts of the axis will then be confined together, and therefore if the winch c be moved this way, it is evident that the machinery will inftantly be put in motion in the following manner : The winch c being fere wed to the fly-bracket, and turned fquare out, it defcribes by its paffage a quadrant of a circle ; and the arm s of the crank-rod being fixed faft into the fame axis a confequently it will defcribe the fame curve as the bracket : and as the crank-rod R is jointed into its arm at and at /, in moving the arm the rod R is pufiied forward to j 9 and the hori- zontal cog-wheel H of courfe turns to the left-hand on the cen- rer C. It being then turned to the left, as exprefied by the dotted ( m ) clotted line at q, it follows that the upright cog wheel N mufl: be turned to the right-hand ; and if this be turned to the right-hand, then muft alfo the quadrant cog-wheel Q on the left turn to the right w r ith it : and, becaufe the axis A is fixed faft in the wheel Q, and the crooked levers e e into A, confequently the rollers L L, fixed by the rod o to thefe levers, will defcribe a quadrant of a circle, as denoted by the dotted line and the roller 9 ; becaufe the connecting cog-rod 5 makes Q move in the fame curve as N does. Again, if N, the upper part of the upright cog-wheel, move to the right, then muft M, the lower part of it, move to the left ; and, being con- nected with the cog-rod 6, and it again to the right-hand qua- drant cog-wheel Q, it follows, as before, that the levers//, and the roller L, will defcribe a quadrant of a circle to the left-hand, as at 8. The reader muft eafily fee now, that when the winch c is turned by the fly-bracket, that every part of the machinery will be put in motion, and that the levers and rollers, in ap- proaching gradually to 8 and 9, muft neceflauly raife up the till. But it muft alfo be obferved, that ttt6 motion of the levers f f and e e is greatly promoted by the power of the common fteel-fprings S S ; for, when the till is down, thefe are always charged ; that is, the fides of the fprings are nearly clofe to eacll other, and thefe being connedted with what may be termed the auxiliary, or affiftant cog-rods, 4 and 7, and toiifequehtly prefl ing againft their ends, the quadrant cog-wheels QQ ar~ there- by made to revolve, and the levers and rollers are raifed almoft ( 422 ) as much by this means as by the other machinery. It muft alfo be noticed, that as thefe fprings and auxiliary rods greatly affifl the other power in railing the till, fo do they alfo check the fudden fall of it, by a conftant refiftance againft the prefTure of it, fo that the paffage of the till downwards is made by this mean fmooth and eafy. Obferve, p<>p,p<>p<> are brafs pulleys fixed to keep the cog- rods hi their place, and w w are pieces of wood to keep the fprings firm to their center. The reafon why there are but three rollers, and two of them at one end, is obvious ; becaufe the till muft reft truer on three points than on four. It cannot totter on this account when it is fully raifed, becaufe there are two flops at that end where there is only one roller, which run in the grooves G G ; and if the flops chuck up to the end of the grooves when the till is up, it is impoffible that it can totter, confidering that the other end is upon two rollers. And here let it be noted, that if the work- man find any inconvenience owing to the double roller o being at the fame end with the axis b b y it can be removed by putting the double roller where the fingle one is, wiiich makes no dif- ference w r ith any other part of the machinery. And obferve, that when the rollers are nearly perpendicular to their axis A A, they enter upon an inclined plane, or on thin pieces of wood planed 1 ( 4*3 ) planed off like a wedge, of the width of the rollers, and whofe thin end is glued to meet the rollers as they rife, fo that the till can thereby be raifed as high as we pleafe. Thefe wedges being glued on the under fide of the till to fuit exadtly the place of the rollers, the projection of the wedges below the till makes it neceflary that there Ihould be a vacuity in the axis A A, for them to fall into when the till is down ; becaufe, in this filia- tion, the till refts on the three rollers, which are nearly on a level with the axis A A. And as the wedges above mentioned muft lie acrofs the axis A A when the till is down, every work- man muft fee the neceffity of a vacuity, or otherwife the till would not fettle to its place. The next thing in order is to fhew how one of the flops can be relieved, or flipped back, fo that the till maybe taken quite away. The conftru£lion of this flop is fliewn by No. 4, which fuppofes that we fee the under-flde of the till. A is a hole cut through the till, which hole is drawn by a compafs, having one foot at C the center. P is a round pin, which comes through to the infide of the bottom of the till. K is a tin key which hooks this pin. In applying this key to the pin, the writing Aider, fliewn in the defign, muft be puflied in, and the front- part which covers the letter holes turned up to its place ; and there being a groove acrofs the under fide of the Aider, exaftly 8 where ( 4H ) where the pin comes, and the Aider giving a little way for the thicknefs of the aforefaid key, the groove juft mentioned admits the key over the head of the pin P; then, when the key is drawn back again, P moves toward A by the center C ; and S, the flop ■which projects beyond the till, is by this mean drawn within. B is a plate fcrewed on to the till to keep the flop firm. Again, when the till isxlown to its place, it is neceflary that it fhould be flopped there alio, as has been already faid. The apparatus for this is fhewn at No. 3, which is a different view of the fame lock as at No. 2. 1,2, 3, 4, is fuppofed to be a part of the bottom, not of the till, but that whereon the machinery is placed at No. 1. t s is a kind of trammel with flits in it, moving on a center at s. A pin is fixed to the bolt of the lock, and there being a paffage for the pin cut out of the lock -plate, as fhewn in the defign, this pin moves up and down, according as the key is turned, a is a kind of lever, with two arms, moving at the center a. c c are ftaples which are faftened to the under- fide of the till, and as the bolt of the lock fhoots downwards, the trammel t s throws the arms of the lever out of the ftaples which are fixed to the underfide of the till ; by which means the till is relieved, and can then be raifed by drawing out the fly-bracket. And here the workman muft be careful to ob~ ferve, that when the bolt No. 1, is fhot, as it now appears, .the till is always relieved, and the bracket at the fame time has power ( 4*5 ) power to raife the till ; becaufe the fork D works in the groove d of the axis ab at No. I, and thereby prefles the focket a to b y and gives the winch c power over the machinery. And obferve further, that when the bolt b at No. 2 is up, as it is fliewn at No. 3, then it is evident that the arms of the flop-lever will pafs through the beforementioned ftaples at the underfide of the till and fecure it, while, at the fame time, the bracket will lofe its power over the machinery ; becaufe the focket a, at No. I, is thereby raifed above and of courfe as b turns on a pin, the winch c cannot affect the crank-rod s R, and therefore no part of the machinery is moved. Thus it is, I think, fufficiently clear that the till can be flopped and relieved when it is either lip or down, and alfo that the bracket can be drawn out to fup- port the flap, while, at the fame time, the till is both down and flopped, fo that the whole may be ufed as a common breakfaft table. It remains now to give fome hints refpedting the manufac- turing part. Of the Table Top. The fize of the table when opened is four feet, and two feet feven inches long ; and the rails eight and a quarter deep. 3 H The ( 426 ) The whole top is divided into four compartments, to anfwer the opening for the till. Round thefe compartments is a japan- ned border, to fill up the fpace which lies between the end of the table and the end of the till. This border muft be continued all round alike, to make the pannels appear uniform and of equal fize. The bed of the top fhould be framed in two pannels of three-quarters mahogany well feafoned, and the breadth of the ftiles to fuit the opening of the till. A pannel of half-inch fluff fhould be tongued into the other part of the bed where the till does not rife. Then, for the fake of the aftragal which is to be worked on the edge of the top all round, a piece fhould be tongued in, the long way of the grain, into each end of the bed. And obferve, that as the bed of the table will frequently have to be taken off in the courfe of the work, it is beft to put fmall tenons into the under fide of it, and mortices into the rails all round ; by which means the bed will be kept to a certain place r and taken eafy off at any time. A black fixing is put next the till, all round the infide of the border, to hide the joint. In put- ting this black firing on at the opening of the till, the infide of the mahogany frame fhould be rabbetted out to take a Hip of black veneer about three-eighths wide ; and it being left to ftand above the framing the thicknefs of the veneer, this black flip can be fliot by a rabbet-plain to the thicknefs of a neat firing, and the veneer muft be jumped to it. The ufe of this is, that when the till rifes it may not take any part of the firing away 7 with ( 4*7 ) with it, which it certainly would do if it were put on merely as a corner ftring. Of the Till. The carcafs of the till is made of half-inch mahogany; the partitions and letter-holes of thin quarter fluff, and black beads put on their edges, all of which muft be kept back about half an inch from the edge of the carcafs, to give place to the writ- ing-flider ; part of which turns up as a front to the infide of the till, and part of it remains in it : and, as a part of the writing- Aider remains in the bottom of the till below the drawers, con- fequently there muft be a joint in the Aider to anfwer it; which joint is hinged at each end, before the crofs-band is put on for the green cloth. The workman may make the hinges himfelf to fuit that purpofe. They may be made as common delk-fall hinges, only the knuckles of the hinge are made a little higher than common to receive a thin veneer ; which, when fcrewed on, the veneer for the band of the cloth lies upon and covers the ftraps, fo that a part of the knuckle is only feen : but ob- ferve, that the ends of the veneer, each meeting at the knuckle, muft be cut in a floping diredtion, fo that they and the brafs knuckle between them will be exa6lly in the form, and of the fame nature, as the rule-joint of a fly-bracket for a Pembroke 3 H 2 table ; ( 4^8 ) table ; and therefore it muft be evident to every workman that the front will turn up fquare. The Aider is fcopped into the till by a couple of pins which run in grooves ; and when it is pufhed home, before it can turn up, a hollow muft be worked in the bottom of the till, to give room for the angle of the rifing part of the Aider to turn in. When the Aider is turned up, it is kept in its place by a fpring-catch, which ftrikes into a plate put on at the under fide of the top of the till. And obferve, that when the front is up, it fiiould be rather within the carcafs of the till, both for the purpofe of letting the till go eafy dow r n, and to admit of a Aip of thin green cloth at each end, fo that when the front is turned upon the top of the Pembroke table it may not fcratch it. Another method may, however, be propofed, and which will be attended with lefs trouble ; only with this difadvantage, that it takes off a little of the height of the drawers. The Aider, being made in two parts, may be hinged in the manner of a card-table top, which, when it is folded over, can be pufhed to its place. But obferve, that the under top muft be made fo much broader than the upper one, as will admit of its being flopped in after the manner of the other ; fo that when it is drawn out, the upper top will rife and clear the drawer fronts. If the Aider be made in this manner, the draw r ers can then ( 4 2 9 ) then be brought within a little of the front edge, and what re- mains ferves to give place to a couple of thumb-nail holes to draw out the Aider by. N. B. The profpedt door is made to run in at the top like a drawer, upon the fame principles as the front of the cabinet in Plate L. Of the Frame of the 'Table. The legs are made a little ftronger than ufual, becaufe the table is pretty heavy altogether. Both the end rails are divided into four drawers each, in appearance; but, in reality, there are but two in the whole: for obferve, that, for the fake of ftrength in the frame, the lower drawer of the left hand is made real, and that above it is a fliam ; but at the other end, which is not feen in the defign, the upper drawer is real, and the under one a fham. A middle rail is tenonned, of inch fluff, into each end rail. Againft this rail the upright part of the machinery is fixed, as fliewn at No. i ; and as this rail Hands within the edge of the top-framing about an inch, it contains the whole projedtion of every part of the machinery, fo that the till pafles without obftru£tion. The ( 430 ) The inner lining for the fly-brackets to fall againft, is not lefs than three quarters thick when planed ; and it muft be the whole breadth of the end rails, i. e. eight and a quarter. The fly-bracket makes up the remaining thicknefs of the foot, and comes down low enough to anfwer the height of the upper crofs-band of the lower drawer. The part remaining below the bracket is veneered the whole length with fatin-wood, and crofs-banded, to match the drawer fronts. The workman, in making the fly-bracket to which the winch c is fcrewed, muft oDlerve to make a fhoulder pin on the turning part of it at the under edge : and this fhoulder will require to be double the ufual thicknefs, that the iron winch c may be let into the bracket without injuring the rule-joint, or interfering with the wire of its center. The lock, at No. 2 or 3, is put on at the infide of the inner lining, fo near to the axis a b, at No. 1, as that the fork D of the lock lhall extend to the groove d in the focket of the axis a b> which then will determine the place of the key-hole, as fliewn in the defign. Of I ( 43i ) Of the Pediments. Plate LVII. With refpeft to thefe pediments little can be faid, as the defigns themfelves fhew in what manner they fhould be exe- cuted. No. i. Should have the facia, or ground board, glued up in three thicknefles, having the middle piece with the grain right up and down. The foliage ornaments are cut out along with the aftragal, and planted on ; and the whole may eafily be made to take off from the cornice, by having a tenon at each end and one in the center. No. 2. The tablet part is intended to have a crofs-band round it, and the drapery may be japanned. The aftragal on the top of it is meant to return over the ogee. The fquare of the ogee may come forward, level with the tablet, to prevent too great a projection. No. 3. In the center there are two pilafters to projeil a little from the ground, which are fluted. The pannels at each end are intended to be fanned the reverfe way, or with the rounds out. No. 4. ( 43* ) No. 4. The fcrolls are continued in one piece from the foli- age, ahd planted on* No. 5. The center is intended to be veneered and crofs- banded, with an oval let in, and japanned. The pedeftal above is intended to be thrown back in a hollow carved in leaves. The foliage on the fcrolls is meant to lap on the aftragal, and to finifh off at the patera. The ground of the facia is fanned out. Of the Cornices. Plate LIX. In thefe cornices the fpring is fhewn, and the proper gaging is pointed out. The width and thicknefs alfo of the mahogany is fliewn. The aftragal, in No. 3 and 5, can be worked feparate, and glued on afterwards. The pateras, in No. 6, are turned and planted on. Of the Method of gaging and working Cornices. The explanation of this may be thought, by fome, an un- neceffary bufinefs ; but from the bungling manner in which I have feen many workmen proceed to Hick cornices, I am cer- tain ( 433 ) tain that a few hints will be of fervice, efpecially to the inex- perienced. For this purpofe I have, in No. i, lettered each gage-point, and I fliall proceed as fuppofing that it is neceffary that the whole ftiould be taught. When the pattern of any cornice is given to be worked, take the drawing and ftrike a line a n to touch as near as may be each member. From this front line ftrike one at each end fquare from it, fo as to take in the whole extent of the cornice. Then draw another line parallel to that on the front, to fhew the neceffary thicknefs of the mahogany, and proceed as fol- lows : Let the ftufF be fawn out broad enough to plane to b o ; after which, plane it true on both fides, and glue on deal of the breadth of e p, and thick enough to make out the whole fpring of the cornice. After the glue is dry, plane the mahogany to the exa6l breadth of b o. After ftriking a fquare line acrofs the mahogany, extend the compaffes from a to and to c,f, g, &c. and lay all thefe points on the fquare line, and run a gage thro* each of them. Run then a gage from a to b, and from n to o ; and taking a bevel, fix the handle of it exactly by the front line, and let the infide of the blade of it correfpond with o p. With the bevel thus fixed, plane down the wood behind till it fit the bevel in every place, and be brought down to o. Take 3 1 then ( 434 ) then a fquare, and plane down the wood at b and e till the fquare fit in every place, and the wood is brought down to b. After this lay the cornice on the fide o and fhoot off the wood a,a,b\ then lay it on the fide b e, and ftioot off the wood at n o to nu The cornice being thus properly fprung, faften it down on the fide ap, and proceed to rabbet out the feveral fquares. Begin at c and rabbet down to /; at h run on a fide gage, and, enter- ing in by a fnipe's-bill, work down to /, the fluting being laid on afterwards ; at q run on a fide gage each way for the fquare of the ovalo. From / rabbet down to and at / down to m ; and thus it is evident that the whole cornice, of whatever kind, cannot fail of being corre6lly worked.. Of the Method of contracting and enlarging Cornkef. Suppose A to be a cornice already drawn or worked, and it be required to draw and work one a third, fourth, or any other proportion narrower than A, and, at the fame time, to contract its projection in proportion to its height : Take the compaffes and extend them to a o, the whole height of the cornice A, and with this opening fweep an arch each w r ay, and where they interfedt, to that point draw right- lines from o and a, forming an equilateral triangle. In the fame manner ( 435 ) manner proceed with the projection of A, as fliewn in the figure. To the fummits of thofe triangles draw lines from the feveral heights and projections of each member. If the cornice to he drawn is to be one third lefs, then divide any one fide of the triangles into three equal parts, and take one part from o to />, and let fall a perpendicular from p ; and from where this per- pendicular cuts each line draw parallels, which will give the height of each member in exaCt proportion. For the projec- tions : o q is one third of the fide of the triangle, as before ; draw a parallel line at q, which will give the feveral projections fought. Take q /, and transfer this to p r, and fo of the reft, till you have laid on each projection ; after which let fall per- pendiculars, as fliewn at No. 7, and proceed to draw the out- lines of each member within their proper fquares, and the cor- nice wall be contracted in the moft accurate manner. Of enlarging Cornices. Suppose now the cornice A is required to be higher than what it is at prefent. Draw parallel lines from each member, and having fixed the compaffes to the height propofed, fix one foot at 0, and move the other till it touch any where on the line a /v, as at k ; draw a line from c to k, and where this line inter-* feCts with each parallel before drawn, will be the feveral heights 3 I 2 of ( 436 ) of the mouldings as required. To find the projection, proceed thus : — fweep the arch a c, cutting ok at b; take a b and place it from c to d, and from d draw a line to o, and o m will then be the whole projection of the cornice proportionable to the height o k ; confequently where the line o m interfeCts, each perpendi- cular raifed from the feveral projections of A, will be the fever al projections fought, o m is then a fcale line for the projections* and o k for the heights of each member ; and having thefe, the cornice can then be drawn on a feparate paper, in the fame man- ner as A was drawn at firfL By continuing the parallel lines of A to the right, as fliewm in the plate, and by letting fall its perpendiculars to any length* it is evident that A may be enlarged as much as we pleafe, by drawing the line o k more oblique, as at e, which then makes it rather more than one third higher. Then, by extending the compaffes from a to where o e cuts the arch, and by replacing this opening from c to g, and ftriking a line from o to g through to/, o f will be its projection as before ; on which principles of will be in a ratio with o e. This the workman can prove, for by comparing o f with the length of the projection of A, he will find it rather more than one third longer ; and by corn- pairing o e with o a, he will find it rather more than one third longer alfo. 8 Thus ( 437 ) Thus it is evident that any cornice or moulding whatever, and however complex, may be contracted and enlarged as we. pleafe, and that with the greateft mathematical nicety. Of the Lady's Drawing and Writing 'Table. Plate LX. These tables are finifhed neat, either in mahogany or fatin- wood, with a brafs rim round the top part. The upper part is made feparate from the under part, and fixes on to it by pins. The rifing defk in the middle may be made to Hide for- ward- 1 ', which will then ferve to draw upon; and the fmall drawers below the coves at each end, will be found convenient for colours. The drawer in the middle of the front ferves to put the drawings in.. The top is lined With green leather or cloth. The fcale fliews the fize of every part in the front, and the breadth is two feet three inches. The height of the upper part is eight inches. * See the directions given for the Kidney Table. of ( 433 ) Of the Dining Parlour. Plate LX. This method of reprefenting a dining or drawing-room has its advantages ; though the moll general method is by a plan and feition, as the drawing-room in Plate LXI. In this method the end wall neareft the eye is fuppofed to be laid level with the floor, without which the infide of the room could not be feen. The advantage of this is, that the walls, furniture, and every particular, are fhewn in their natural pofition, except the firft end, fo that the effeit of the whole may be better judged of than in the other method. The advantage of the method in Plate LXI. is, that the fides and ends of the room being turned down, from a geometrical plan, every thing on the walls is fhewn geometrically, and therefore the parts are more diftin£t ; but with this difadvan- tage, that it mull be viewed at four different times, by turning- each end and fide to the eye ; whereas, in the other way, the whole is feen at one view. In proceeding to draw after the method of Plate LX, make a fcale of feet as there fhewn, and draw G R for a ground line, and H L for the horizon. Let the center of the pidture be in the ( 439 ) the middle of the end ; and, as thefe are views of a fhort dis- tance, extend the compaffes from the center to 0, and turn it up to d, which will be the fhorteft diftance that can be applied. Draw vifuals from o 9 c, b, a, to the center. From 0 to 1 lay on the fize of the firft pier, and draw a line to- d 9 which, cutting the vifual drawn from 0 to the center, gives the perfpedtive of it. Then lay from 1 to 2, the breadth of the. window, and draw a line to d; and in like manner find the appearance of all the piers and windows. Obferve, that a line from R to d finds the whole length of the room. How every other part muft be drawn will be obvious to every one who underftands perfpec- tive, and no other with any propriety can attempt it.. This dining-parlour gives a general idea of the Prince of Wales's in Carlton Houfe; but in fome particulars it will be a little varied, as I had but a very tranfient view of it.. The Prince's has five windows facing St. James's Park. This alfo has five, one of which is hid by the left column. His win- dows are made to come down to the floor, which open in tw r o parts as a double door, leading to a large grafs plat to walk in; If I remember right, there are pilafters between each window. ; but this is intended to have glafs. In his is a large glafs over the chimney-piece, as this has. To thefe glafs frames are fixed candle-branches. At each end of his is a large fideboard, nearly twelve ( 44° ) twelve feet in length, Handing between a couple of Ionic co- lumns, worked in compofition to imitate fine variegated marble, which have a moft beautiful and magnificent effed:. In the middle are placed a large range of dining-tables, ftanding on pillars with four claws each, which is now the fafhionable way of making thefe tables. The chairs are of mahogany, made in the ftyle of the French, with broad top-rails hanging over each back foot ; the legs are turned, and the feats covered with red leather. I could not fhew the curtains of each window without con- fufion, but they are of the French kind. Many dining-rooms of the firft nobility have, however, only two columns and one fideboard ; and thofe of lefs note have no columns. The general ftyle of furnifhing a dining-paiiour fliould be in fubftantial and ufeful things, avoiding trifling ornaments and unneceflary decorations. The pillars are emblematic of the ufe we make of thefe rooms, in which we eat the principal meal for nature's fupport. The furniture, without exception, is of mahogany, as being the moft: fuitable for fuch apart- ments. Of (44i ) Of the Drawing Room. Plate LXI. In drawing a room of this kind very little perfpedtive is wanted. All that is required is a horizontal line on each wall. And I would not advife drawing every objedt on each wall to one point of fight, as thofe at the extremities will thereby be- come exceedingly diftorted and unnatural. For, upon fuppo- fition that the fpedtator moves along to different ftations as he views any one fide of the room, perfpedtive will admit that the defigner have as many points to draw to as the fpedtator had ftations to view from. If a room of this fort be narrow, fewer points may do for the furniture at each end, with a little ma- nagement ; but the furniture on the fide walls fhould have al- moft as many points as pieces of furniture. The line that marks out the boundaries of the floor, ferves as the proper ground line to each horizon, and the geometrical meafurement of each piece being taken from the fcale and laid down on the wall, the per- fpedtive is drawn from each point backwards, or into the room. A drawing-room is of that fort which admits of the higheft tafte and elegance ; in furnifhing of which, workmen in every nation exert the utmoft efforts of their genius. To ( 44^ ) To affift me in what I have here fhewn, I had the oppor- tunity of feeing the Prince of Wales's, the Duke of York's, and other noblemen's drawing-rooms. I have not, however, fol- lowed any one in particular, but have furnifhed my ideas from the whole, with fuch particulars as I thought beft fuited to give a difplay of the prefent tafte in fitting up fuch rooms* It may not be amifs to mention fome particulars refpefting the Prince's room, that the reader may form fome idea of its tafte and magnificence. Its proportions are as follows : — forty-eight feet fix inches long, thirty- four broad, and between eighteen and nineteen feet high, including the cove of the ceiling.. It has five windows in length, a fire-place at each end, and; five doors. Two doors are at each end, one of which is fham ; and a large arched double door nearly in the center oppofite the windows. Oppofite each window is a large glafs, with a circular top, to fuit the arches above the windows ; and over each fire-place there is alfo a glafs. In the piers between each window there are no glaffes, but a couple of richly finiflied Corinthian pilaf- ters, with their architrave and imports to fuit the tops of each 3 window. ( 443 ) window. On the fide oppofite to the windows the fame pilas- ters are employed ; for, as the before-mentioned glafles each oc- cupy a fpace equal to the width of a window, and are directly oppofite to them, this preferves a regularity in the pilafters on both fides. In like manner each end of the room has its pilaf- ters of the fame order, one on each fide of the fire-place, and of the doors. The cove and ceiling are richly ornamented in paint- ings and gold. A room of this defcription is not, however, a proper pre- cedent for drawing-rooms in general, as it partakes principally of the character and ordinance of a ftate faloon-room, in which, are entertained ambafladors, courtiers, and other perfonages of the higheft ftations. In the drawing-room which is here fhewn, every thing will appear eafily underftood to a workman in town, who is accuftomed to fee fuch apartments ; but for a ftranger, and thofe workmen who refide in the country, it will be proper to point out a few particulars. The pier tables have marble tops and gold frames, or white and gold. The glafles are often made to appear to come down to the fa:etcher of the table ; that is, a piece of glafs is fixed in behind the pier table, feparate from the upper glafs, which 3 K 2 then ( 444 ) then appears to be the continuation of the fame gla r " rr \ by reflection, makes the table to appear double. This fmall piece of glafs may be fixed either in the dado of the room, or in the frame of the table. The arches above the windows are merely artificial, being only wooden frames put up, {trained with canvas ; after which the fame kind of fluff which the curtains are made of is formed to appear like a fan, and drapery tacked on to it. The pannelling on the walls are done in paper, with orna- mented borders of various colours. The figures above the glafTes are paintings, in clare-obfcure. The fofas are bordered off in three compartments, and covered with figured filk or fatin. The ovals may be printed feparately, and fewed on. Thefe fofas may have cufliions to fill their backs, together with bolfters at each end. In France, where their draw- ing-rooms are fitted up in the moft fplendid manner, they ufe a fett of fmall and plainer chairs, referving the others merely for ornament. The commode oppofite the fire-place has four doors; its legs are intended to ftand a little clear of the wings ; and the top is marble, to match the pier tables. In the freeze part of the commode is a tablet in the center ; made of an exquifite com- pofitioa then reflet of glc fram< only the fz to ap ment< The f with i and fe togett ing-rc fett of ornarr T legs aj top is : the coi ( 445 ) pofition in imitation of ftatuary marble. Thefe are to be had, of any figure, or on any fubjedt, at Mr. Wedge wood's, near Soho- fquare. They are let into the wood, and proje£t a little forward. The commode fhould be painted to fuit the furniture, and the legs and other parts in gold to harmonize with the fofas, tables, and chairs. To fupply the Defeff of Figure 32, Plate V. It is there fliewn how to find the miter of the fides of a comb-tray at any pitch, and of any given projection ; but it was omitted to fliew how the miter is obtained in the thicknefs of the fluff, as it rifes to any pitch. Having found the breadth of the fides b c, Fig. 32, Plate V, with this opening of the compafTes defcribe a femicircle, fee Plate XXII, and make a e equal to the perpendicular height of the fide of the tray. Draw a line from e to the center ; and parallel to this, fet off a line for the thicknefs of the tray fides, and the bevel of the under edge will be at 4. Draw a fquare at the center, the length of whofe fides fliall be equal to the thick- nefs of the tray fides, as 3, 1, 2. Next draw the line B, A, E, pa- rallel to the diameter; and take a e, the fine of the angle of the tray fides, and transfer it to E A. From A draw a line to the center, cutting the fmali fquare at 1, and the fpace 1—2 will be the miter fought for; that is, when the fides are mitered in their ( 446 ) their breadth, according to Fig. 32, Plate V, fet a gage to 1—2, and run the gage along the miter, and plane it off to the gage from the outfide, and the miters will all come exactly together. If the tray fides were raifed to b, b i would then be the line of their angle ; and which being transferred to B, a line from B to the center cuts the fquare at 3 ; then is the fpace 3—2 the length of the miter fought. And thus it is evident, that as b advances to E the perpendicular, fo will the miter point B approach to D, the full miter. It is alfo evident, that by this figure the miter of any thing not exceeding the diameter E of the femicircle may be found. For inftance, if the fides of any tray be half an inch thick, and it is required to be mitered and keyed together, draw a fquare of that dimenfion, as the fecond fhewn in the fi- gure ; and if the fides bevel in an angle equal to the line e, then 1 — 2 of the fecond fquare will be the length of the miter. I proved the truth of this theory by pradice, and therefore the workman may depend on its infallibility ; but he may eafily make the fame experiment himfelf. THE END. ERRATA. Page 23, line 14, for bs, read b S. 1 i 28, 13, read it thus: — if you want five tenths of a foot, and five of the hundredth parts of a foot, place your compafs foot — >• ib. 19, for any tenth part of an inch, read any one hundredth part of a foot. S7» l6 ' fi r 9> 5* rcad IS- ib. 18, for 9, 5, rcad q — 5.. — 6 1 , 1 1 , for a to «, read d to 77. > 70, 9, for the extreme line P E and P 1, read P E and 1 1. 137, 4, for abacuo, read abacus. 152, Plate VIII, for 7 diameters, read 8 diameters. 162, line 22, Plate XII, for take m 0, read take twice m a in the companies, and with this opening find the center of the curve for the abacus as at p on Fig. B. 206, 10, for from a to read from d to a.. ■ 211, 11, for Plate XV. read Plate XIV. '273, ■ 15, for Fig. 23, rcad Fig. 21. APPENDIX TO THE CABINET-MAKER AND UPHOLSTERER'S DRAWING-BOOK. CON T A I N I NG A VARIETY OF ORIGINAL DESIGNS FOR HOUSEHOLD FURNI- TURE, IN THE NEWEST AND MOST ELEGANT STYLE; ALSO, A NUMBER OF PLAIN AND USEFUL PIECES, SUITABLE EITHER FOR TOWN OR COUNTRY ; TOGETHER WITH A DESCRIPTION AND EXPLANATION TO EACH PIECEo B Y THOMAS SHE RA TO N, CABINET-MAKER. LONDON: PRINTED FOR THE AUTHOR, BY T. BENStEY; AND SOLD BY J. MATHEWS, N° l8, STRAND; G. TERRY, N° 54, PATERNOSTER-ROW f J, S. JORDAN, N° l66, FLEET-STREET ; L. WAYLAND, MIDDLE-ROW, HOLBORN; AND BY THE AUTHOR, N° 106, WARDOUR-STREET, SOHO. *793- [ dfcntereti at ^utiwm f OIU ] T APPENDIX. Of the Elliptic Bed. Plate I. of the Appendix. As fancifulnefs feems moft peculiar to the tafte of females, I have therefore affigned the ufe of this bed for a fingle lady, though it will equally accommodate a fingle gentleman. The elliptic fhape of the frame of this bed contracts its width at each end confiderably, on which account it will not admit of more than one perfon. On the manuf alluring part of it I would offer a few hints to affift the workman. — The frame of the bedftead lhould be glued up in wainfcot three or four thickneffes, with the jump- joints croffing each other, as in the method of gluing the frames of circular card-tables, which fome ufe. For which purpofe, draw the full lize of the ellipfis upon a board, and make the diameters each way, by which one quarter will be found. ( 4 ) found. A thin mould muft then be made to agree with the quarter of the ellipfis, which will ferve for cutting out the whole by, when different portions of it is fo taken as to form croffing-joints. The frame "being thus made an entire ellipfis, as Fig. A, in Plate XXX. it is propofed to half-lap the pillars into the frame, and to have a ftretching rail at each end to tenon in oppofite to each pillar ; into which ftretcher the fcrews are to work which fix the pillars to the frame, as fliewn at a, c 9 d, in Fig. A. The workman will eafily fee that the frame made in this manner will not be defe£tive in ftrength, nor in- convenient to move from one room to another. The fluffed head-boards at each end are framed feparate, and grooved into the pillars, with a tenon in their center to flip into the bed- frame, which can be eafily done when the pillars are fere wing to. The firft tefter which fixes on the pillars, fhould form an entire ellipfis to fuit the frame, and muft be glued up in two thickneffes of good deal or wainfcot; to the edge of which fhould be glued two thickneffes of clean foft mahogany, of which to work the cornice, as expreffed by Figure B, in Plate XXX. 1 The ( 5 ) The fecond, or falfe tefter, is that to which the ribs of the dome part are fixed, as e in Fig. B ; and / is an architrave which is bent round the infide of the firft tefter, and rifes fo high above it as to receive nearly the thicknefs of the falfe tefter ; fo that the architrave is a guide to the whole dome, and is fuffici- ent of itfelf to keep it firm in its place. With refpe£t to the dome, it will be beft to make it in two parts. The cove part feparate, and the round or fpherical part feparate. This can eafily be done, by repeating the fame ope- rations as were neceflary for fixing and managing the cove part ; for it muft be obferved, that there is a light cornice or moulding where the circular part of the top begins, and which fixes on a tefter in the fame manner as the other. To the under fide of this cornice is the drapery, which hangs in the cove, tacked all round, as is the valence to the under cornice. The curtains are drawn up by pulleys fixed in the under tefter, and thus forms a drapery, by being tied to the pillars with cords. The circular part of the top is intended to be pannelled out in gilt mouldings, which cannot fail of producing a fine effecft, particularly fo if the furniture and covering of the dome be light blue. The foliage ornament that runs round the under cornice may be made either of compofition metal, or it may be cut in B wood ( 6 ) wood and fixed on wire, in the fame manner as the tops of ornamented glaffes are managed. Of the Ducheffe. The French have what they term ducheffe beds, whence I 1 iippofe we have derived our ideas of a ducheffe. What is fome- times named a ducheffe amongft us, is merely two barjier chairs fattened to a ftool in the middle ; fometimes, indeed, we add a ilight tefter and covering, but even this is very different from theirs. The French ducheffe beds are more ftately. The tefter is full and fixed to the wall, with drapery hanging clown to the bedding and floor. The head part is formed fomething like the back of a chair; at the foot there are fhort ftump pillars; and the whole frame of the bed being detached from the tefter, may be moved to any part to loll upon. The ducheffe which is here given, is intended to anfwer three different purpofes. The ends, when detached from the middle ftool, may ferve as fmall fofas. When they are connected together without the tefter, and a fquab or cufhion made to fit over the whole, it will then ferve to reft or loll upon. When it is ufed as a bed, four fhort pillars are fcrewed to each back foot, and a ftraight lath extends acrofs from pillar to pillar at each end. From thefe pillars are fixed the fweep iron rods which form the tefter, and which fupport the / ( 7 ) the drapery and covering which is thrown over the whole. The little dome or top is made feparate and entire of itfelf, with the cornice mitered round, and the taffels fixed to it as fhewn in the defign, and the whole is placed loofe on without any faften- ings. They are made narrow, between two and three feet wide, and feldom above it. Every thing is made exceeding light about the teller. The ftool is fixed to each chair with ftraps and but- tons, and the whole thus finifhed makes a pleafing appear- ance. Of the Library Cafe. Plate III. of the Appendix. The elliptic breaks of this bookcafe will produce a good effedt in the whole. The doors in the upper part are intended to have fluted green filk behind, and a drapery at top^ The pilafters are fuppofed to be glued to the ftile of the door, and are hinged as in common. n The lower middle part contains clothes-prefs flielves, and every other part may be fitted up for books ; or the lower ellip- tic ( 8 ) tic breaks may be formed into a neft of drawers, as there & depth enough. The half columns on the lower doors are glued to the ftile,, and the doors hinged as in common ; but for the fake of Ihew- ing the defign to advantage, the open door is drawn as if the columns w r ere feparate. The young workman fhould obferve, that the whole is to be made in fix carcafes, and fcrewed together, and then the plinth Ihould be made to fit it, of one entire frame; alfo the furbafe and its freeze are made all in one frame, and fcrewed down on to the carcafes ; as alfo is the cornice and its freeze* Of the Pier Tables. Plate IV. As pier tables are merely for ornament under a glafs, they are generally made very light, and the ftyle of finifhing them is rich and elegant. Sometimes the tops are folid marble, but molt commonly veneered in rich fatin, or other valuable wood, with a crofs-band oh the outfide, a border about two inches richly japanned, and a narrow crofs-band beyond it, to go all round. The frames are commonly gold, or white and burnifh- ed gold. Stretching-rails have of late been introduced to thefe 3 tables, ¥iem Tables ~I ' Sfu rafrn.de/. GTt> rry St 1 1 / / jftM/M ' ty.TSAtrufy'n.Mirck.'lJ. J/p3. ( 9 ) tables, and it muft be owned that it is with good effect, as they take off the long appearance of the legs, and make the under part appear more furniflied; befides they afford an opportunity of fixing a vafe or bafket of flowers, which, with their re- flexion when there is a glafs behind, produce a brilliant ap- pearance. Some, in place of a ftretcher, have a thin marble fhelf, with a brafs rim round it, fupported by a light frame ; in which cafe the top ought to be of marble alfo. Of the Library Steps and Table. Plate V. This defign was taken from fteps that have been made by Mr. Campbell, Upholfterer to the Prince of Wales. They were nrft made for the King, and highly approved of by him, as €very way anfwering the intended purpofe. There are other kinds of library fteps which I have feen, made by other perfons, but, in my opinion, thefe muft have the decided preference, both as to fimplicity and firmnefs when they are fet up. The fteps may be put up in half a minute, and the whole may be taken down and enclofed within the table frame in about the fame time. The table, when enclofed, ferves as a library table, and has a rifmg flap, fupported by a horfe, to write on. The C fize ( io ) lize of the table is three feet ten inches long, thirty-three inches high, and two feet one inch in width. When the fteps are out they rife thirty-three inches perpendicular from the top of the table frame, and the whole height of the laft ftep is five feet five perpendicular from the ground. The perpendicular height of the hand-rail is three feet one inch above the laft ftep ; and obferve, that on g 9 which is iron, is fixed a fmall flap on which a book may reft, fo that a gentleman, when he is looking at any book in his library, may note down a paffage from it with- out the trouble of going down again. The method of folding the whole up is as follows : The triangular iron bracket g is unlocked by a catch which keeps it firm to the hand-rail, and the defk-flap fixed to it being turned over to the infide, the whole comes for- ward, and lies level upon the upper fteps. The ftandard b may then be raifed out of its focket, and, having a joint at the top, it turns up to d 9 as fhewn by the dotted curve line. The fliort ftandard de is then, by relieving a fpring, preffed down below the edge of the table-top ; and the hand- rail and ftandard b having been folded together, as mentioned before, they both reft on the iron focket faftened to the front edge of the upper fteps. Next, the horfe o is folded by the fide of the upper fteps, and then both they and the horfe fall down within the table frame ; and it muft be obferved, that in fold- ing ( II ) ing down the fteps, the hand-rail and ftandard, which refted for a while on the focket faftened to the front of the fteps, fall into another focket of the fame kind faftened to the under lide of the table top, where they remain, and fall within the table frame when the top is folded down. Laftly, the lower fteps a are turned up to a horizontal pofition, and being hinged to a Aider which runs in a groove, the whole flips in as a drawer, and is enclofed by the flap which turns up and appears as the front of a drawer. Of the Drawing-room Chairs. Plate VI. The frame of the right-hand chair is intended to be finifhed in burnilhed gold, and the feat and back covered with printed filk. In the front rail is a tablet, with a little carving in its pan- nel. The legs and flumps have twilled flutes and fillets, done in the turning, which produce a good effedl in the gold. The chair on the left may be finifhed in japan painting, in- terfperfed with a little gilding in different parts of the banifter, which has a lively effect. The covering of the feat is of printed 5 chintz, ( 12 ) chintz, which may now be had of various patterns on purpofe for chair-feats, together with borders to fuit them. * ' * Of the Bidet Dr effing-Table, and Night-Table Bafon-Stand. Plate VII. The dreffing-table has a real drawer under the cupboard part, and the reft are fham. The right-hand cupboard door opens by a fpring-catch communicated to the patera handle in the center. The water- bottle is fupported by a round box, made of very thin wood, glued and canvaffed over to ftrengthen it, and fixed to the top. The bidet legs turn up with a joint. The deftgn fhews only legs at one end, but the other legs are fuppofed to be fold- ed up till the whole is taken out ; and when ufed, the legs are kept to their place by iron hooks and eyes. The fcale fhews the fize of the front, and its depth from front to back is fixteen inches and a half. The frame, to which the glafs is hinged, is fourteen inches in width. The night-table requires no explanation, and I fhall only obferve, that the covers with rings on them are meant for a tooth- ( 13 ) a tooth-brufh, and the ivory boxes on the right for tooth- powder. The fcale for the dreffing-table fhews the fize of the night- table, applied to the front, and its depth from front to back is eighteen inches. Of the Wardrobe. Plate VIII. The upper middle-part contains fix or feven cloth es-prefs fhelves, generally made about fix, or fix inches and an half deep, with green baize tacked to the infide of the front to cover the clothes with. The lower part confifts of real drawers. The wings have each of them arms, to hang clothes on, made of beech, with a fwivel in their center, which flips on to an iron rod fixed by plates fcrewed on to each fide of the wings, as ex- preffed in the defign. The whole is made in four feparate carcafes. The wings by themfelves, and the upper and lower middle parts feparate. The plinth is made all in one frame, and likewife the cor- nice with its freeze, and being fcrewed to each carcafs, the whole .is kept firm. D Obferve, ( 14 ) Obferve, that in the wings a bead is put up for the doors to fall againft when they are fhut to ; by which means are cleared the knuckles of the hinges on the doors of the middle part- It fhould alfo be obferved, that as the furbafe cannot go round the out ends of each wing on account of opening the doors, the moulding is returned againft the front of each door. The furbafe on the middle part returns, and flops againft the inner end of the wing ; and the edge of the door of each wing, with the furbafe which is on them, are fcribed on to the aforefaid return, which then appears as an internal miter, and gives place to the opening of the door. The fcale, applied to the middle part, gives its height and length. The wings are two feet, and fixteen or feventeen inches deep; and the depth of the middle part about twenty-three inches. Of tbe Bed. Plate IX. This defign requires no explanation, except that which re- lates to the teller. The cove of the tefter is to be formed by 8 ribs; ( 15 ) ribs; one at each miter, and other fhort ones joined to them, with the reft about five inches apart from each other. At the upper part of the cove is a fquare tefter into which the ribs are fixed. On the edge of this tefter, which is made very light, is fixed a fmall moulding mitered all round. The cove being formed, the ribs may be covered with ftrong board-paper, both infide and out, which may either be japanned to match the fur- niture, or it may be covered with the furniture itfelf. The cir- cular part about the cove is nothing more than a ftraight board fixed on to the upper tefter. For the fake of eafy conveyance, the cove may be made in four parts, mitering at each corner, and the ornament intended to be at each miter on the outfide running entirely up to the feathers, will Jbdde the joint- The fwags of filk line that appear on the drapery fliould be fattened to the back part of the cornice, in order that they may. hang eafy. The pillars are to be japanned. The pannel that hides the fcrews is made to flip into a groove at the bottom, and when raifed up a little from their place, can be taken away to come at the fcrews. The valence and drapery both together flip on to a lath as in common. ( i6 ) Of the Sofa and Converfation Chairs. Plate X. With refpedt to this fofa, all that is neceffary to be ob- ferved is, that in the fpace between the divifions of the back part, it is meant that there fliould be a ground-work covered with filk, to fuit the reft of the fofa* Againft this ground the two columns and the ornament are fuppofed to reft. The converfation chairs are ufed in library or drawing- rooms. The parties who converfe with each other lit with their legs acrofs the feat, and reft their arms on the top rail, which, for this purpofe, is made about three inches and an half wide, ftuffed and covered. For the convenience of fitting in the manner juft men- tioned, the chair is made long between front and back, and very narrow at the back and front in proportion. The height of the chair to the fluffing is three feet ; at the back ten inches, fpreading out in width to the top rail, which is twenty inches in length. The front is fixteen inches, and the height of the feat as in common. Of 2 /» jPuMjhs/f at me. xlcr direct fa- F.Sfuralen April i6.iyg&. ( 17 ) X>f the Card "Tables. Plate XI. On tliefe tables it is fcarcely neceffary to fay any thing; efpecially as the quarter plans fliew how they muft be framed : and therefore I fhall only obferve, that the ornaments may be japanned on the frames and carved in the legs. As to the me- thod of managing the tops, I take it to be the beft to rip up dry deal, or faulty mahogany, into four inch widths, and joint them up. It matters not whether the pieces are whole lengths pro- vided the jump-joints be crofled. Some tongue the jump-joints for ftrength. After the tops are dry, hard mahogany is tongued into the ends of the deal, then flips are glued on the front and back, that the whole may appear folid mahogany, if a moulding is to be worked on the edge; but if the edge be crofs-banded there is in this cafe no need for tonguing in mahogany. Of the Library Table with a Writing Drawer. Plate XlL This table is intended either to fit or ftand and write at. The height of the fecretary-drawer is adjufted for fitting, and B the ( i8 ) the top of the table is high enough to ftand and write on, efpe- cially if the middle top be raifed by a horfe, as fhewn in the de- fign. This table will alfo prove very ufeful to draw on ; for when the middle part is up for drawing upon, there remains fufficient room at each end of the table on which to place the ; neceffary impliments for drawing ; befides, the drawers at each- end may be fitted up to hold colours of various kinds ; ' I mean the two upper ones,, for there are drawers, quite down to the plinth. The drawers under the fecretary will hold the large flieets of drawing-paper, together with the tee fquares ; and as it will not be neceffary to make the drawers under the fecretary the entire width of the table, the oppofite front, being made fham to have the fame appearance, the whole of it may be hinged at bottom and locked at the top, and the infide will al- low depth for books. This fham front being, a confiderable width, it would hazard the hinges to let it reft wholly on them, when turned down, and therefore there fhould be iron ride- joints at each end as flays. To thefe conveniences there are alfo four cupboards in* clofed with doors, as fhewn in the defign, and the whole finifh- ed in this manner, I venture to affirm, will prove as ufeful a table as has ever been devifed or publiflied. In ( 19 ) In refpedl to the manufacturing part, it will be beft to make it in two parts. The upper part containing the fecretary, and two drawers at each end; and the lower part, four drawers -under the feeretary, a book-cafe behind, and four drawers at each end, the kwermoft of which is fhewn in the defign. The top fhould be framed of inch and. quarter wainfcot (as der- fcribed in page 373), containing, a well for the deik part, which may be made to rife on the front as well as at the back, by forming a double horfe ; but in this defign it is only intended; to rife at the back by a fingle horfe, and hinged to the crofs* band at the front. The cupboard doors may either be framed and pannelled, or glued up to their fweep in narrow flips of inch mahogany, and clamped; not by tonguing, but by a fquare joint, and pins driven through the clamps. The management of the circular. bafe-moulding and plinth may be learned in page 375. Of the Fire Screens. Plate XI1L The lyre fcreen is conftru&ed upon an entire new plan, it being defigned to turn upon a fwivel, which fixes to the vafe and ( 20 ) and pafles through the bottom rail, fo that the fcreen may be turned to any pofition without moving the ftand. The fcreen part, which rifes between the ftandards or pil- lars, is fufpended by a weight in the taflels, which aire commu- nicated to the fcreen by a line palling through the pillars and over a pulley fixed to their top. There muft be a dovetail groove in each ftandard, and the fcreen made to fit into thefe; fo that the ftandards may keep their proper place, and not fly open at the top. Obferve, that the ornament on the tops of the pillars or ftandards rife up with the fcreen, being fixed to it, and detached from the pillars. It is intended that the lyre ornament be carved in bas relief,* gilt and burnifhed; which, when planted on to a blue filk or fatin ground, cannot fail to produce a fine efFedt. The other fcreen being common, needs no explanation, only that it is fufpended by little fprings fixed in the dovetail grooves of the ftandards. In ( 21 ) In refpedt to the general fize of horfe fire-fcreens, about eighteen inches or nineteen may be allowed for the breadth, and three feet fix or feven inches for their height. Of the Cabinet. Plate XIV. This cabinet, I prefume, is as new as the fire-fcreen, and will have a better effedt in the execution than in the defign. The front of the cabinet is hinged to a Aiding piece which runs in a groove, upon the fame principle as the writing-table page 408. The front being turned down to a horizontal pofi- tion, it may then be flipped in till it flops. To fupport the front thus turned down, there are two Aiders which come out of the plinth on which the cabinet refts. Thefe Aiders come out by relieving a fpring which is fixed in their fide, and having a common fpring behind, they are forced out fo that the fingers may lay hold to draw them quite out. They are lined with green cloth both at top and bottom to prevent fcratching. The infide of the front is alfo lined with green cloth to write on. The infide of the cabinet is fitted up in the manner Ihewn in the cabinet Plate XVI. F Above ( 22 ) Above the falling front is a drawer, to the under fide of which the front locks, fo that the drawer and front are either locked or opened at one time. Above the drawer is an ornamented freeze, japanned; and round the top, which is marble, is a brafs edging. The flower-pot at the top is fuppofed to be real, not carved; but that on the ftretcher is carved. The columns ftand clear, as fhewn by the plan ; and they are intended to have brafs bafes and capitals, with wooden fliafts fluted. The candle branches turn to any form in a focket, and the whole may be taken away, as they are only fcrewed into a nut fixed into the lees of the table. There is a brafs fret fixed at each end, which finifhes at the ftandards of the candle-branches. The lower frame contains a drawer in front, and the legs being o£tagon, are intended to be veneered croflways as far as to the carving, which may be gilt to fuit the bafes and caps of the columns. of ( *3 ) Of the Duffing Chefls. Plate XV. These chefls are alfo on a new plan, particularly as the common Aider for merely writing on is turned into a fliallow drawer, which contains a little writing flap which rifes behind by a horfe, and places for ink, fand, and pens, and alfo dreffing- boxes. When the drawer is in, it appears like a common Aider, with a partition above and below, as that with the convex front. There is therefore no ilip under the top, as the drawer fides rauft run clofe up to it. The drawer below of courfe muft lock up into the under edge of the drefling-drawer, and the dreffing drawer into the top, which is done at one time, by the bolt of the under lock forcing up that of the upper one. The height of thefe chefls are always governed by the Aider, which runs thirty-two or thirty-three inches from the floor. The fcale fhews their length, and their breadth is twenty-two or twenty-three inches. Of the Lady's Cabinet. Plate XVI. The cabinet in Plate XIV. is made in two parts, but this is entirely in one. The legs and columns are therefore all in one piece ( 24 ) piece. The infide of the cabinet is made feparate, and flips in between the legs, and a piece of narrow wood, as a band, is fit- ted to fill the fpace up to the column, as the defign fhews. The marble fti elves, with frets at each end, are for a tea equipage. Above and below thefe fhelyes are drawers which turn out by a hinge. Above and below the front are alfo draw- ers. The drawer below may be made to fupport the front when turned down to write on, or it may be fupported by brafs joints, as fhewn in the defign for the infide of the cabinet. * % The fcales and plans of each cabinet fliew their length and breadth ; it remains only to mention their height, which is four feet, and four feet two. Of the Horfe Dreffing Glqffes. Plate XVII. The dreffmg-glafs on the left rifes to any height, by lead weights inclofed in the ftandards. The weights are fufpended fometimes to tambour glued on to webbing, which paffes over a brafs roller at the top, and fixes to a piece of thin wood, tam- boured to match it. Through this piece of thin wood is put an iron pin, with a thin plate to it to fere w it faft ; which pin goes through the fide of the glafs, and fattens by a nut at the infide, 5 % ( *S\ ) fo that when the glafs is raifed, it may be turned to any direc- tion. But fome ufe a kind of coloured ftrong webbing, without the tambour, which makes it lefs troublefome, and lefs liable to injury, though it does not look fo neat. Thofe unacquaint- ed with the manner of gluing up the flandards, may fee a fec- tion of them in Plate XXX. Fig. C. There is a brafs handle behind the ornamented top to raife the glafs by. The boxes on each fide are intended to hold conveniences for dreffing. On thefe, there is a comb-tray on the left fide, and a pin-cufhion on the right. When the drefling-boxes are not in ufe, they are intended to turn behind the glafs. For this purpofe they are fixed to a brafs focket, which turns upon a fhort brafs rod, and by a fcrew they may be raifed up or low- ered at pleafure. See Fig. D. Plate XXX. The other dreffing-glafs has a convenience for w r riting as well as for dreffing, which convenience rifes by a little horfe. The dreffing-boxes are made with clofe covers, and a Aider in- clofes the whole, fo that when the w 7 hole is turned up nothing can come out of its place. The glafs does not rife as the other, but fixes in centers, fo as to move in any pofition either back or forward. G And ( 26 ) And obferve, that when the dreffing-flap is turned up it locks into the top rail, and the glafs of courfe falls to its own place. The under fide of the flap being the front when turned up, it may be japanned and banded. The lower parts of the ftandards are fhaped like a lyre ; and to form the firings, brafs wire is let in, which has a pretty effedt. Of the Chafe Longus. Plate XVIII. These have their name from the French, which imports a long chair. Their ufe is to reft or loll upon after dinner, and in fome cafes the lower one will ferve for a fofa* The drapery under the rail is tacked to a rabbet left on purpofe. The upper one is framed firft in two parts. The end, or chair part, is made to receive the ftool part within its fides ; and the fides of the ftool part fcrew in againft the infide of the chair. As to any other particular, the deligns themfelves are fufficient to point them out. Of the EngUfh State Bed. Plate XIX. In giving a defign for an Englilh ftate-bed, or fuch an one as is fuitable to the dignity of a prince, and worthy the notice of a king, I conceived it necefiary to cultivate as much as I could the Chaise Lomxnes . ////(?. ( *7 ) the molt exalted ideas, unfettered and unreftrained with the thoughts of expenfivenefs, which naturally produces meannefs of compolition, and in many cafes injures the ingenious in their defigns. For ornament to a bed of this kind, it ftruck me that no- thing could be more fuitable and chara&eriftic than fuch as ex- preffed fymbolically the different parts of our government, to- gether with thofe virtues and principles which ought to be the fupport of regal authority, and the ruling maxims of every good government of whatever kind, whether monarchical, ariftocrati- cal, or democratical. Emblems of war have been avoided as much as poffible, being inconfiftent ornaments for a bed, and becaufe good kings ought not to delight in war, but in peace, unity, and the love of men and their fubje6ls. As our government is compofed of three diftindt branches, the figure on the right hand bed-pillar is intended to reprefent the democratic part of it, or the power of the people invefted in their reprefentatives in parliament In iconoTogy*, democracy f is reprefented by the figure of * Iconology, from wxwj efkoti, an image ; and Uya^ lego, I fpeak. The interpretation of ancient images, monuments, and emblems. f Democracy, from hy.^, demos, people; and x^arsiv, krateln, to command or govern ; is when the fovereign power is lodged in the body of the people, a woman ( *s ) a woman drafted in a homely garment, and crowned with vine leaves. In her right hand fhe holds a pomegranate, which de- notes aflemblies of the people on matters of importance. In her left hand is a clufter of ferpents, which exprefles the winding and flow progrefiion of democratic ftates, owing to the inability of the common people to govern. Her ftanding on the two facks of corn which reft on the pedeftal, ftgniftes that democratic go- vernment is more attentive to the obtaining of neceflary pro- viiions, than the increafe of fame, or the acquifition of honours. If this be a juft reprefentation, and founded on fadt, the reader will, no doubt, conftder the democratic branch a very important one, and for which reafon it is here placed near the ground- work. The figure, oppofite, on the left pillar, reprefents the ari- ftocratic branch. Ariftocracy * is defcribed by the figure of an elderly lady, in a fumptuous drefs, with a crown of gold upon her head. Painters reprefent her fitting on a throne ; which is a pofition confonant to lawgivers, but which I could not make fuitable to this fituation. In her right hand fhe holds the con- fular fafces, that is, a number of elm rods tied in a bundle, with a hatchet in the middle, which, originally, were the enfigns of * Ariftocracy, from anJlos> the beft ; and *£*t»&;, kratio, I command or govern ; i> when the fupreme power is lodged in a fenate, compofed of the principal perfons of a ftate, either for their nobility, capacity, or probity. 5 fovereign C *9 ) fovereign dignity, but in after times the hatchet was taken out, and they were carried before the confute or magiftrates of Rome, to denote their authority. Thefe rods are entwined with a crown of laurels, a fymbol of reward due to thofe who have maintained the public welfare, and have performed great ac- tions for the good of the ftate. In her left hand is a fteel cap, at her feet a hatchet, a plate, and purfe with money, all which denote that arms and finances are neceflary fupports of ftates. And I would here obferve, that it is not abfolutely neceflary to confider the fteel cap and hatchet as fymbols of war, but of the executive power requifite in all governments for the mainte- nance of peace, and the punifliment of evil doers. The figure in the center of the upper cornice is intended to reprefent the monarchical branch of our government. Monarchy * is characterized by the figure of a young wo- man of grave countenance, feated on a terreftrial globe, holding four fcepters, to denote dominion and power. The other hand being uplifted, denotes her authority in giving command. The rays of light furrounding her head, denote luftre, and the re- fpe6t due to her greatnefs. The lion on each fide fymbolizes the * Monarchy, from ,ao»o ? , monos> alone; and agpis, arche, government; is when the Cupreme power is in veiled in one perfon, commonly termed the King, H power ( 3° ) power which ihe poffeffes and requires of others in order to her fupport. Painters, however, defcribe her with trophies of war, and a crowned head chained down as a captive at her feet, which I have here omitted, hoping that conqueft and war are not the prominent features in our government. Thefe three figures in their fituation to each other form a triangle, whofe bafe is democracy and ariftocracy, and whole fummit is monarchy; denoting that monarchical power and ho- nour are originally derived from the people, and that without their fupport, monarchy in its moft exalted ftate muft fall. The lions which fupport the bed, with oak foliage and leaves on the bed-frame and round the ftiafts of each pillar, are emblems of the ftrength and permanent nature of our govern- ment. The acorns being the fruit of the oak, denote, that by long progreffive improvements it is arrived to a good degree of maturity. The ferpents in the cornice, which mutually entwine them- felves round Mercury's rod, denote the unity, prudence, and wifdom, requifite to monarchs in the exercife of their impor- tant charge. The trumpets and laural crown are expreffive of the fame which the Englifh ftate has acquired through the mildnefs of its government. The beads under the cornice de- note ( 3i ) note its riches. The balkets of fruit on each capital, and in the quadrantal pannels, fymbolize the profperous ftate of the na- tion, and the plenty we enjoy. In the arch of each quadrant are marked the degrees, to denote that navigation has contri- buted greatly to our riches and fafety. The lyre and trumpets on the pedeftal above the cap, fignify the flour ilhing ftate of the arts ; and the fpreading oak leaves and rofes, are meant to exprefs the designer's wiih and hopes, that the ufeful arts may long continue to grow and fpread themfelves under the muni- ficence of our government. The coronets round the dome are thofe of the immediate fons and daughters of the king of Great Britain, of which there are thirteen ; but the dome being divided into fixteen compart- ments, ftill leaves room for an increafe of the royal family, to denote that the fubje&s of Great Britain ftiould hope for a long fueceffion of a mild and good government. The feftoons of flowers denote that happinefs and profperity are wifhed to fur- round each branch of the royal offspring. The crown of England is fupported on the top of the dome by three figures, intended to reprefent Juftice, Clemency, and Liberty; for notwithstanding thefe may, in fome inftances, be fullied in our government, yet fcarcely any nation can boaft of more than that which we tiave long enjoyed. 3 Juftice, ( 32 ) Juftice, which ought to be the moving principle of civil government, is by painters defcribed by the figure of a woman dreffed in white robes ; holding in her left hand a fword, to pu- nifh criminals ; and in her right a pair of fcales, to give that which is due to everyone without partiality; which imparti- ality is denoted by a bandage over her eyes. In this fituation the fword and fcales may be fuppofed to lie on the other fide of the dome ready for ufe. Clemency is a neceffary quality or principle in government, by which thofe in authority are enabled to take into conlidera- tion, and to effe£l the relief of the miferies of: the helplefs and infolvent. In the exercife of this virtue, he who is ready to be cut afunder by the uplifted hand of juftice can be faved, and the rotting infolvent prifoner can be abfolved and releafed. Such anions beget gratitude in the minds of the fubje£ts, and are as a pillar to the crown ; while cruelty and tyranny have of- ten proved fatal to princes. Painters defcribe this virtue by the figure of a woman crowned with olives, as a mark of her peaceful and gentle tem- j er ; and dreffed in a purple robe, which denotes her eminence. She is chara£terifed by the mildnefs of her countenance, and fitting on a lion (which I could not here introduce.) She alfb holds a laurel branch of honour and*refpe£t in her right hand. She ( 33 ) She is faid to have a fpear by her fide, fo that when her mercy is abufed fhe may in juftice revenge it. The other figure, Liberty, on the other fide of the dome, is an effential principle to good government. It fuppofes a difpo- fition in thofe poffeffing fupreme authority to allow fubjecSts to enjoy their natural, moral, and religious rights. In the poffef- fion of thefe we are delivered from flavery ; the yoke is broken. Therefore painters reprefent liberty by the figure of a woman, with a broken yoke-ftick in her left hand, and trampling upon it as a mark of refentment. She is drefled in white robes, to denote the bleflings which flie confers on mankind ; and in her right hand Ihe holds a fceptre as a fign of independence. She has alfo a cap of liberty on her head, in allufion to the cuftom of the Romans, in fetting their Haves free ; who alfo fhaved their heads, and permitted them to be covered in the prefence of thofe who gave them liberty *. The figures on the other fide, and at the end of the bed may be the fame, not merely for uniformity's fake, but to convey the fentiment expreffed by the allegory with more weight, as it is well known that repetition is fome- * Richardfon's Iconology, from whofe work I am indebted for feveral ideas on this fubjedl. I times ( 34 ) times introduced to give force and energy to a fubjedt. How- ever, if any fhould think it neceflary to vary the figures on the different fides, there are plenty of fubjedts fuitable enough. Fortitude may be placed on the center of the cornice, oppo- lite to monarchy ; to denote a quality of mind fo highly necef- fary in thofe who rule. The emblem of this quality is a wo- man refting on the fhaft of a column and its bafe, having a brown robe and part of a military drefs, with a lion on one fide of her ; but fhe may have one at each fide, to make the outline more agreeable to the figure of monarchy; Her military drefs conveys the idea of courage ; and refting on a column, fteadinefs and firmnefs ; and the lion, ftrength of mind. On the bed-pillar, oppofite to the figure which reprefents the ariftocratic branch of our government, fhould be Counfel, to denote the wifdom and ability neceflary in thofe who make up that branch., Counfel is reprefented by the figure of a grave old man, having a long beard, dreffed in long robes of violate colour. His age denotes that experience requires length of time, and that wifdom is the refult of experience. His long robes denote his ( 35 ) his high chara£ler, and their colour his gravity. He is repre- fented fitting, to fhe w his authority ; and with a chain of gold round his neck, to which is fufpended a human heart, to denote his integrity. In his right hand is a book, to fhew he has re- gard to law, and that from literature he obtains his knowledge. He may, however, in this fituation be Handing, as the bed-pillar will not fo well admit of a fitting attitude ; and in this attitude he may have a mirror in his left hand, furrounded with fer- pents, to denote prudence and {peculation, as neceffary to good eounfeL On the other pillar, oppofite to the figure which reprefents the democratic branch of our government, there may be the emblem of Law, to denote that the members of parliament, as the reprefentatives of the people, ought to be acquainted with the rights and interefts of their conftituents ; and alfo, that in their debates on thefe fubjedts, they ought to regard the laws of the conftitutiom Law is reprefented by the figure of a refpe6lable elderly lady, fitting on a tribunal chair. Her age denotes that law is an ancient fubjeft ; fhe is feated to denote eminence, and holds a fceptre in her right hand to denote authority. In her left hand Ihe holds an imperial crown, allufive to the law of nations, 4 importing ( 36 ) importing that no nation can exift without laws. Her head is adorned with diamonds, to fignify that law is moft precious, and that its origin was from God. At the end of the bed, and next to law, Obedience or Sub- jection may be introduced, to denote the duty and refpeil which the people owe to their reprefentatives whom they have ap- pointed, and particularly to fignify that fubjeits ought not to rebel againft government. Obedience is defcribed by the figure of a humble woman, in an upright pofition, with her eyes towards heaven, to denote her regard to its commands as the Appointer of government. Her upright pofition not only fhews her willingnefs to obey, but that government was never appointed to opprefs or bow down the backs of thofe who are willing to obey juft laws. She is dreffed in white robes, denoting innocence ; and acrofs her fhoulders is a yoke, the emblem of patience and obedience. By her fide may be reprefented a dog, which is a fymbol of obedi- ence and faithfulnefs. On the center of the cornice maybe reprefented Authority, to denote that without its influence law is rejected and con- temned, — obedience is without foundation, and therefore govern- ment could not exift. Authority ( 37 ) Authority is reprefented by the figure of a matron, or old lady, to fhew that the inftitution of authority which gives ef- fedt to laws is ancient as law itfelf. She is feated on a regal chair, becaule princes and magiftrates generally perform their office fitting, indicating tranquillity of mind. She holds a fcep- tre in her left hand, denoting regal power and authority ; and by her fide are arms, to fignify her power to punifh the licen- tious, and protedt the obedient. In her right hand is a book, refting on her knee, to denote that civil authority is of divine origin *« On the other pillar may be the reprefentation of Tyranny chained down, with her back bowed, to fignify that thofe in authority ought to fupprefs rather than cherifli it ; and to fhew that tyranny ought, in all good governments, to be at the foot of power, to prevent its baneful effects in a ftate. The em- blem of this noxious quality is a pale, proud, and cruel-looking woman, drefTed in armour, and purple drapery, to denote her readinefs to fhed blood in the defence of her arbitrary meafures. In her left hand is a yoke, and in her right an uplifted fword, to fhew that fhe is ready to enflave mankind, and puniih them if they will not put on the yoke. She wears an iron crown, to fhew that the authority which tyrants feek is for bafe purpofes and cruelty. * See Rom. xiii. I. K To ( 38 ) To make thefe three figures harmonize — Authority, at the top of the cornice, may be reprefented as looking towards Obe- dience with an eye of approbation ; and the book lying on her lap, with the right hand flie may hold a dart pointed dire£tly to Tyranny below. And to reprefent Tyranny in the molt wretched ftate, her iron crown may appear to tumble off her head, her yoke broken, and her fword pointed to her own breaft, to fhew that in the end tyranny is her own executioner. Thus, I think, the end of the bed will exhibit emblematically the end of civil government, which is to proteil the innocent and obedient, to fupprefs cruelty and oppreffion, which are the life and foul of tyranny. The front fide fhews the nature of our government, the dome the principles which fupport it, and the back fide the way in which government is managed. The ornaments on the head-board are emblems of love and continency, expreffed by the figure of Cupid, Chaftity, and a trophy below. Cupid is reprefented as drawing his bow to guard Chaftity from the violent attempts of Impurity, whofe figure, partly a woman and partly a monkey, is behind the cur- tain, to denote that fuch as pradtife it lurk in fecret. The emblem of Chaftity is the figure of a young woman in white robes, to denote purity and innocence. Her head is crowned with a garland of cinnamon, a pleafant and coftly plant, 5 to ( 39 ) to fignify that Chaftity is a virtue both pleafant and valuable. She is veiled, to exprefs her modefiy; and in her right hand holds a fcepter, as a fign of her conqueft over luft. In her left fhe holds a turtle dove, which is an emblem of continence. With refpeil to the manufacturing part of this bed, it fhould be obferved, that the curtains draw up by a pulley at the feveral corners, detached from the drapery valence which is fix- ed to the cornice. The tefter on which the dome refls, is made perfectly ftraight, and forms an even furface on both fides ; which, in the infide, is pannelled out with gilt moulding at each angle. The quadrantal pannels recede back from the cornice, and are framed into the top of the pillars, which are left fquare. The ground of thefe pannels being continued the whole length, from pillar to pillar, ferves as a facia on which to fix the cor- nice. Then obferve, that the bafket of fruit and the lyre being in one piece, they are fixed to the pillar, and meet in a miter with the other fide. The oak foliage is in one entire piece, and fcrewed up to the bed-fides, after the drapery valence is tacked to a rabbet made for that purpofe. Every ( 40 ) Every other particular muft naturally occur to the work^ man, after what has already been faid on the other beds in this work. Upon the whole, though a bed of this kind is not likely to be executed according to this defign, except under the mu- nificence of a royal order, yet I am not without hopes that ufe- ful ideas may be gathered from it, and applied to beds of a more general kind. Of the Dreffing Commode. Plate XX. With refpeil to the dreffing part of this commode, it may be made either fixed faft, or to be brought forward in the man- ner of a drawer, with leapers to keep it to its place. If it is made to be fixed faft, the doors may be opened to form the knee hole. The top which covers and enclofes the dreffing part, Hides down behind, in the manner defcribed in page 407, to which I refer the reader ; only obferve, that in this .top there are miters to fit the ftraight moulding in front when the top is put down. A bottle of water, and a pot to receive it when dirty, can both be kept in the cupboard part. The dreffing-table below can require no explanation, ex- cept what relates to the lize, which from front to back is eighteen m; \V( to ni: fu b€ m m ki dc re to A be ALu\ionr^ JDirje Commode. ( 4i ) eighteen inches, thirty-four the whole height, and two feet four the length of the front. Of the Sideboard, with Vafe Knife-cafes. Plate XXL The pedeftal parts of this fideboard may he made feparate, and then fcrewed to the fideboard. The top extends the whole length, in one entire piece, and is fcrewed down to the pedeftals. The hollow plinths of the vafes are worked in one length, and mitered round. The top of the plinth is then blocked on at the under fide, and the vafe part is made to fcrew into it, fo that the vafes may occafionally be taken off. A crofs band is meant to be mitered all round the hollow plinths, coming forward to the edge of the top ; fo that if the top be veneered, it will only require the length between the two plinths. Within the front is a tambour cupboard, which is both ufeful, and has a good effe£t in its appearance ; almoft any workman will know how to manage this, fo that I need not explain it. The ornament behind is brafs, intended as a ftay to lilver plate, and has branches for three lights. The circle in the center may have a glafs luftre hung within it, as an ornament. For any other particular relative to fideboards in general, fee page 363, where the com- mon principles of this ufeful piece of furniture are explained. L Of ( 4* ) Of the Library Steps. Plajte XXII. These fteps are confiderably more fimple than thofe al- ready defcribed ; and though not fo generally ufeful, will come vaftly cheaper. The upper flight of fteps turn down upon the under ones, both of which rife up and Aide in as a drawer ; af- ter which a flap, which is fhewn in the defign, is turned up, and has the appearance of a drawer front. Obferve, that the refting poft at the top folds down to the fide of the fteps by means of an iron joint. The horfe has green cloth under its feet, to prevent its fcratching the top. The defign fliews that the two fteps are connected together by hinges, fo made as to clear the edge of the table-top ; and alfo, that there is a Aiding board to which the under flight is hinged, which fliding-board runs in a groove. The length of the table is three feet fix inches, its width twenty-two inches. The table is thirty inches high, the upper flight is thirty perpendicular, and the refting-poft thirty-three. This, and the other defign for library fteps, have obtained a patent ; yet any part being materially altered, will evade the a£t, though the whole be nearly the fame. Thofe matters, how- ever, who do not think it worth their while to be at the trouble 8 of ( 43 ) of introducing any effential alteration in them may have thefe fleps from Mr. Robert Campbell and Son, Mary-le-bone Street, London, with a fufficient allowance for felling them again. Of the Chamber Horfe. . The upper figure fhews the infide when the leather is off, which confifts of five wainfcoat inch boards, clamped at the ends; to which are fixed ftrong wire twifted round a block in regular gradation, fo that when the wire is compreffed by the weight of thofe who exercife, each turn of it may clear itfelf and falL within each other. The top board is fluffed with hair as a chair feat, and the leather is fixed to each board with brafs nails, tacked all round. The leather at each end is cut in llits to give vent to the air, which would other wife refill, the motion down- wards. The workman fliould alfo obferve, that a wooden or iron pin is fixed at each end of the middle board, for the purpofe of guiding the whole feat as it plays up and down. This pin runs between the two upright pieces which are framed into the arms at each end, as the defign fhews. The ( 44 ) The length of the horfe is twenty-nine inches, the width twenty, its height thirty-two. To the top of the foot board is eight inches, and to the board whereon the feat is fixed is thir- > teen. Of the Corner Night Tables. Plate XXIIL That on the right requires no explanation, except that the doors may be hinged to turn in, if it is thought moft con- venient. The table on the left is intended to anfwer the purpofe of a wafh-hand ftand occafionally. To anfwer this end the top part is framed together of itfelf, and fixed by an iron or ftrong wooden pin, into the back corner of the lower part, which con- tains a focket, fo that the top part can be turned to one fide, as fhewn in the defign, or as much further as is neceflary to clear the hole. Obferve alfo, that on the front is worked a groove, in which a pin paffes that is fixed to the front of the bottom of the upper part, and prevents the top part from turning quite off from the 1 bottom, which would endanger the pin on which the top part turns; it fliould have caftors at the brackets, that when the night ( 45 ) night table is wanted, it may be drawn a little forward from the corner of the room to give place for turning round the upper part. It fhould be about thirty-four inches to the top of the bafon fhelf. The height of the feat fixteen inches and a half, and its other dimenfions are known from the plan. The bottom drawer may be made neat, and drawn out by means of a dovetail groove in the middle of the drawer, and a piece to fit it fixed acrofs the bottom of the carcafe. 0/ the Pulpit. Plate XXIV. The defign of introducing a pulpit into this work was to afford fome affiftance to the cabinet-maker, who in the country is generally employed on fuch occafions. In ere&ing a pulpit of this kind, three particulars ought principally to be regarded. Firft, the plan ; fecondly, the manner of conducing the fteps and hand-rail round the column; and, laftly, to fix the whole firm, fo that it may not by fhaking produce a difagreeable fenfation to the preacher. The plan of this pulpit is a regular hexagon, which to me is the mofl beautiful and compact of any. One of its fides is occupied by the door, and one for the back of the preacher, another to reft his arm, and the remaining three for the cufliion. M The ( 46 ) The plan of the fteps is a circle, which is raoft convenient where there is a want of room. The plan ftiould be divided according to the number of iteps neceffary for attaining to a proper height, which in this cafe is twelve, as one> two, three, Sec. in the plan; A fection fhould then be drawn, and the height of the rifers adj ufted to the number of the fteps, as in, the fe£lion a, Draw the femi plan P, and divide the' circumference into eight equal parts, as i, 2, 3, 4, &c. becaufe, that in the. plan there are fo many fteps contained in its femi. Draw from. i f 2, 3, 4, &x. lines perpendicular, and continue them to the uppermoft ftep. From a, the firft ftep, draw a line to a on the plan P. Do the fame from b to b, c to c r and fo of all the others, which will defcribe the fteps and rifers as they re- volve on a cylinder. The face mould for the hand-rail, when it is cut out of the folid, is found as follows. See Plate XXX. Draw a quarter plan as there defcribed, divide the chord line into any number of equal parts, as 1, 3, 5; from which raife perpendiculars to interfedt the circumference; draw next the rake or pitch-board of the fteps at Fig. R, by taking the breadth of the ftep on the plan, and repeating it i 5 2, 3, 4; then take the C 47 ) the height of four rifers, as from x toy, and draw the line y 4, which line will be the chord for the face mould; therefore takejy 4, and divide it into fix, as in the. plan of the hand-rail. Take the perpendicular heights as 1 2, 3 4, and 5 6, of the plan, and transfer them to the correfpondent perpendiculars on the face mould, which will give points through which the curve is to pafs, to form the face mould, as the figure fhews. Three of thefe lengths will be wanted, to complete the handr rail, including the ramp and knee, Thefe hand-rails are however fometimes glued up in thin pieces round a cylinder in one entire length, after which a crofs- banding is put* on the top, and rounded off. In this cafe a cy- linder is formed in deal, and the line of the fteps is traced out as defcribed Plate XXIV. which is the guide for the thin mahor gany to be bent round. In fixing the fteps, I prefume it will be found the beft method to mortice and dovetail the. rifers of each ftep into the pillar : this may be done by making the mor- tice as much wider than the breadth of the rifer as the dovetail is intended to be in depth, fo that when the rifer is put into the mortice, it may be forced up to its place by a wedge driven in at the under edge of the rifer. By this means it will, be impof- fible that the fteps fhould work when they are tongued and blocked together. The foffits of the fteps are in the form of an ogee, ( 4« ) ogee, anfwerable to the brackets, and are fitted up feparately af- terwards. In fixing the pillar it muft be noticed, that it is firft te- noned into tranfverfe pieces of oak timber, which are funk a good depth into the ground, fo that when the clay is beat in folidly about the pillar it cannot work ; yet it is eafy to conceive, that in the pulpit it will be liable to fpring when the preacher is in it; to prevent which I have introduced a light fmall co- lumn, fituated in the center of the pulpit, and comieiled with it by a cove, on which the pulpit refts. The found board is made as light as jpoffible, which finifhes in an odlave cove at the top, and is fixed to the pillar by a ftrong fcrew and nut, together with a tenon, which is funk into the found board. The bannif- ters of the hand-rail may be ftraight bars of brafs, made very light, dovetailed into the ends of the fteps, and let into a plate of thin iron at top, which is fcrewed to the under fide of the hand-rail. Obferve, that on the left fide of the plate is a fcale of feet and inches, from which the various meafurements may be taken. N. B. Plates 25 and 27, 28 and 29, require no explanations ; they are therefore omitted, 8 Of ( 49 ) Of the Ladies" Work "Tables. Plate XXVI. The table on the left is intended to afford conveniences for writing, by having a part of the top hinged in front to rife up. This riling top when it is let down locks into the frame, and fecures the bag where the work is. The ftandards on which the table frame refts have tranfverfe pieces tenoned on, which fcrew to the under fide of the frame. The drapery which hides the work-bag is tacked to a rabbet at the under edge of the frame all round. The defign on the right is fimply a work table ; the upper frame, to which the top is hinged, is about two inches broad, made feparate. The pillar is fixed to the bottom of the bag, which is a round frame made of wainfcot, with a ftretcher acrofs each way, for the purpofe of fixing the pillar to it, and to ftrengthen the frame. The upper frame, already mentioned, is connected with the lower one by fmall upright pieces tenoned in, after which the bag is formed of lilk, and tacked to each frame, and ornamented on the outfide with drapery. Of the Drawing Table. Plate XXX. This table will be found highly ufeful to fuch as draw, it being deligned from my own experience of what is neceflary N for ( 50 ) for thofe who pradtife this art. The top of this table is made to rife by a double horfe, that the defigner may Hand if he pleafe, or he may fit, and have the top raifed to any dire&ion. As it is fometimes neceflary to copy from models or flower-pots, See. a fmall flap is made to draw out of the top, which may be raifed by a little horfe to fuit any direction that the top may be in, fo that the model or flower-pot may ftand level. The Aiders at each end are neceflary for the inftruments of drawing, and for a light to ftand on. The long drawer holds paper, fquare and broad, and thofe drawers which form the knee hole are fitted up for colours. Of the Drawing Room. Plate XXXI. and XXXII. With refpeil to the fedtion, it is only neceflary to obferve, that the pier table under the glafs is richly ornamented in gold. The top is marble, and alfo the fhelf at each end; the back of it is compofed of three pannels of glafs, the Chinefe figure fitting on a culhion is metal and painted. The candle branches are gilt metal, the pannels painted in the ftyle of the Chinefe ; the whol£ producing a brilliant efFedt. The view, Plate XXXII. contains an otomon, or long feat, ex- tending the whole width of the room, and returning at each 5 end a Drawtng Table < her a! on Del. 7. CaJdwa/iM Tubli/Iied as the Act Directs btt LXheraCcn MZA ijo'- PI. 30. ( 51 ) end about five feet. The Chinefe columns are on the front of this feat, and mark out its boundaries. The upholftery work is very richly executed in figured fatin, with extremely rich borders, all worked to fuit the ftyle of the room. Within this otomon are two grand tripod candle-flands, with heating urns at the top, that the feat may be kept in a proper temperature in cold weather. On the front of the otomon before the columns are two cenfers containing perfumes, by which an agreeable fmell may be diffufed to every part of the room, preventing that of a contrary nature, which is the confequence of lighting a num- ber of candles. The chimney-piece is rich, adorned with a valuable time- piece, and two lights fupported by two Chinefe figures ; on each fide of the fire-place is alfo a Chinefe figure, anfwerable to thofe which fupport a table on the oppofite fide, under which is feated a Chinefe figure. Over each table, the fire-place, and in the center of the otomon, is a glafs, which by their reflections greatly enliven the whole. The fubjedts painted on the pannels of each wall are Chinefe views, and little fcenes. The carpet is worked in one entire piece, with a border round it, and the whole in efFeft, though it may appear extravagant to a vulgar eye, is but fuitable to the dignity of the proprietor. N. B. In ( 5* ) N. B. Ia addition to what has been faid on perfpe£tive in the firft work, I would here annex a few remarks on taking the geometrical or original raeafurements of a piece of furniture drawn in perfpe£tive, fuppofed to be deftitute of any lines or fcales. In Plate XXX. is therefore inferted a view of a bookcafe, figure K, which the reader muft imagine to be without any lines except thofe which form the outline of the piece. It muft, however, be premifed, that a workman is acquainted with the proportion of fome one or other of its parts, without which nothing can be done or afcertained. He muft alfo be acquainted with fo much of perfpe£live as to know that a line paffing through the diagonal of any fquare, if produced, cuts the horizontal line in the point of diftance. Thefe being known, proceed firft to find the horizontal or vanifhing line by producing c d, the top of, and/ r, the bottom of the under part, till they meet in a point, as at s, which will be the point of fight ; through s draw a line parallel to the front of the bookcafe, which will be the horizontal line fought for. From the point of fight draw at random lines forward from />, and e, or any other point that may be neceflary. Next find out the point of diftance, without which the depth of the ends cannot be known: in or- der to this, the workman muft recollect that the brackets are always A^iiew of the South Emd of the Fkwc Z. ' S/us-aJon ctt2in . 7hl7i/7i6d as Z/ieActclirtct, \ ^JLTES'S CHIMSE DKAWIIG ROOM, 1*1.32, T.JheraloTt Nov, ^ifz/g3 . I ( 53 ) always as long at the ends as on the front, and that therefore they form a fquare block ; wherefore take 4 /, and place it from / to g\ and from g to h, the end bracket will be the dia- gonal of a fquare, whole fide is 4/; produce the line g h, which will cut the horizon at D ; the diftance, as the line on the leg of the gouty ftool, paffes to the diftance which is out of the plate. Laftly; from D draw lines forward through rand 10, or any other part, till they cut the front line, as at t w, by which will be difcovered the proportion that the ends bear with the front, and how much the lower part projects before the bookcafe. Now if there be a fcale of the front already to the defign, then the whole can be determined ; for by taking the compaffes extended to a foot, and repeating it on the perpendicular line from a to /, the height of the doors are known, and by the fame rule the height of the pediment from / to m. Then if the fame compafs be applied from / to w 9 the depth of the lower part, it will be found vaftly out of proportion with the front, which I have done on purpofe, to fliew that by a comp&rifon of this fort the errors of a defign in point of perfpe6tive may be difcovered. If, however, there be no fcale to the defign, then it will be necef- fary to affign a certain portion for a foot, as near as we can judge, by confidering the common ength of a bracket, from / to 4, which in general is about four and a half or four inches, which repeated three times, finds a foot, as in this cafe, and then O it ( 54 ) it appears that the front is four feet long, and better than four feet high, that the doors are five feet nine high, and fo of the reft. But if there be no bracket, any other part may be taken whofe meafure is known, as the partition of a drawer, which is generally feven eighths thick, the height of a Aider, about thirty- two inches, or the depth of a fecretary drawer, about ten inches. The ufefulnefs of this method is not confined to pieces of furniture, but may be applied to any kind of regular perfpec- tive. END OF THE APPENDIX, A N ACCOMPANIMENT TO THE CABINET-MAKER AND UPHOLSTERER'S DRAWING-BOOK. CONTAINING A VARIETY OF ORNAMENTS USEFUL FOR LEARNERS TO COPY FROM, BUT PARTICULARLY ADAPTED TO THE CABINET AND CHAIR BRANCHES: EXHIBITING ORIGINAL AND NEW DESIGNS O F CHAIR LEGS, BED PILLARS, WINDOW CORNICES, CHAIR SPLADS, AND OTHER ORNAMENTS, CALCULATED TO ASSIST IN THE DECORATIONS OF THE ABOVE BRANCHES ; TOGETHER WITH INSTRUCTIONS IN LETTER-PRESS. By THOMAS SHERATON, CABINET-MAKER. LONDON: PRINTED BY T. BENSLEY, FOR THE AUTHOR, N° 106, WARDOUR-STREET, SOHO. Qf whom may be had, feparate, in Forty- two Numbers, price 2/. 3 s. 6d. The Cabinet- maker and Upholsterer's Drawing-Book, containing a great Variety of New Defigns in Houfehold Furniture. AN ACCOMPANIMENT, &c. mil Hii Inftru&ions for Drawing Ornaments. Asa proficiency in the art of drawing ornaments depends chiefly on the habit of copying and the natural turn of genius in this way, a few hints only are neceffary for the affiftance of the learner. Some inftrudiions, however., are certainly neceflary, as ap- pears from the frequent applications that are made to matters for their information. And though no written inftructions can fully fupply all that may be derived from a mafter*, yet fuch directions may be given, in letter-prefs, as greatly to facilitate the attainment of this ufeful branch of drawing without a mas- ter's help, The principal art of every branch of drawing is included in the difpofition of a few limple lines of but two different fpecies, * One very material advantage derived from a mafter is, that the pupil fees how he praclifes, by which he may acquire his manner and ftyle. A 2 the ( 4 ) the right line and the curve. Of thefe two are compofed all that infinite variety of fhapes that we are able to fee and con- ceive. I will, therefore, propofe to the learner, firft to begin with drawing, by the hand, right lines a tolerable length parallel to each other in all directions ; firft, inclined to the right, as ap- proaching neareft to the art of writing ; fecondly, perpendicu- lar ; thirdly, inclined to the left ; and laftly, horizontal and at right angles with thofe perpendiculars, and paffing through their center. A proficiency in this is certainly the firft ftep in draw- ing, and is not fo eafily attained as may be imagined*. Secondly, let the learner then proceed to draw by the hand a circle, as large as poffibly he can without moving the wrift. And it will be proper for the learner to obferve, that in being able to draw a circle by the hand and eye he thereby draws curve lines in all poffible pofitions, as perpendicular, inclined to the right and left, and horizontal. In addition to this practice it will be necefiary to draw one circle concentric with another ; that is, as when two or more circles of different diameters are drawn from one center. This becomes ufeful when any thing is to be defcribed in the fhape of volutes, as the running foliage frequently introduced in friezes and pilafters. What has here been faid of the circle will alfo apply to the practice of drawing aa dlipfis ( 5 ) ellipfis by hand. An ellipfis may be confidered as a curve con- fiding of a number of fegments of circles compound, whofe radii differ in length. Of this kind of curve are many of the turns in ornament, and therefore the practice of drawing them will be found worthy the attention of the learner. To pracSlife as has been defcribed I confider as indifpenfably requifite to a ready and perfedt attainment in the art of drawing ornaments ; and ought particularly to be recommended to youth, as a help to their writing any kind of hand, or drawing the Roman letters. The learner who is advanced in years will not, perhaps, fubmit to this kind of teaching : but if he cannot already draw right lines, of fome length, parallel in all pofitions, and a circle tolerably near by the eye, he ought not to be above learning it, becaufe the time that is fpent in this, will be deduced in future by a more fpeedy progrefs in the art of drawing orna- ments. And however this may be thought of by fome as a thing of no merit, yet we will venture to affirm, that the hand of a real mafter may be certainly diftinguiflied by the manner of drawing thefe*. Of ( 6 ) Of Copying Ornaments. Plate I. Suppose C to be the example to copy from. Take a black- lead pencil, and draw at B the principal curve-line at the bottom very faint - . Then proceed to form a rude flcetch of the out- line, obferving carefully each projecting part of C, that a fuf- ficient breadth or fpace may be taken within the out-line, in which may be formed all the diftinft parts of B, without re- ducing their proportion. Upon this procefs corredtnefs and difpatch very much de- pend. Therefore, if upon the firft attempt of this there fhould appear any defedt, it will be belt to take out the lines with the India rubber, and make them perfect. A carver or fculptor proceeds upon this principle until merely the maffive parts are made out ; and it is well known that thofe of the greateft fkill in thefe profeffions are always employed in this part of carving and fculpture. After having done this, proceed to give the diftindt forms of each leaf and rofe in faint touches, that if there fhould be any caufe for alteration it may be more eafily elected. The * To handle a pencil is, in many cafes of drawing, different from the manner of hold- ing a pen. In handling a pen, the ends of the fourth and fifth fingers reft on the paper; but in managing a pencil, the hand is turned over more to the right, and refts on the knuckles of the little finger. 8 learner ( 7 ) learner fhould, in doing this, carefully obferve and touch the fibres of each leaf, and give the proper lead to each ftem, fo that they do not cut each other. Laftly, take a view of the whole, and confider in what point the light is to ftrike on the ornament ; and on that edge of the leaves and rofes oppofite to it, retouch and ftrengthen the outline in fuch a way as to give relief and effedt to the whole, even upon fuppofition that the drawing is to remain a mere outline. Of Shading Ornaments. If the ornament is to be fhaded with Indian ink, mix fome of it thin and clear, and take a crow-quill pen, or fine camel- hair pencil, and touch the outlines very faintly, fo as fcarcely to be feen on the light edges of the ornament ; becaufe in na- ture there is, in reality, no outline on the light fides of obje6ts, efpecially if the fun is fuppofed to fliine on them. After this, touch the ftronger parts of each ftem and fibre, that they may not be loft when the pencil marks are expunged. Having cleaned your drawing, take a large camel-hair pen- cil, and dip it till it flow freely with Indian ink very thin and clear. And obferve, that if the ink do not work with freedom on a piece of wafte paper, which fhould be kept for the pur- pofe ( 8 ) pofe of trying the pencils, the brufh in this ftate ought not to be applied, but fhould again be well worked in the thin Indian ink, fo that it work eafy, without leaving white fpots on the paper. In this ftate apply the pencil to the ornament, and give a general tint to thofe parts fuppofed to be all in fhadow ; at the fame time a partial tint may be given to the objedts partly in the light. This firft courfe of fhadowing is the great balls of all real effect ; for if the maffes of light and fhadow are not pro- perly parted, but confounded, the drawing will look heavy, in- telligible, and boyifh. When the drawing is properly dry, the laft tints are to be given with great delicacy and care, left the whole be over done, and, as it were, tormented with harfh dabs. The intention of this laft tint is only to give reflected lights to thofe parts which lie in the mafs of fhadow, and fharpnefs to the partial fhadows direftly oppofed to the light. It is natural for the learner, in giving the laft tint, to think of thickening his ink; but this muft be avoided, as dangerous to the effedt of ornament ; for if the ink at firft ufed be again repeated on the former tint, it will give fuffici- ent colour, except the openings of the fibres, which may be touched with ftronger ink. EfFed ( 9 ) Effe6t to ornament may alfo be given by a pen, in imita- tion of etching; which, if well executed, is more pleafing in ornament than Indian ink. Italian chalk is fometimes ufed along with a black-lead pencil, which may be done with extremely good effedt. The learner, being furnifhed with thefe inftru£tions, may proceed in the fame way with the reft of the fpecimens in foli- age, the principal variety of which is here exhibited* K, is the thiftle leaf, fharply pointed and irregular. G, is the Roman-leaf, round and maffy. F, the parfley leaf, light and rather fliarp pointed. E, the rofe leaf, formed into groups. D, The oak-leaf, broad and mafly, fcolloped on the edge, with fmall partings. A, Is a fancy leaf, rather fliarp, with large partings. C, rofes and leaves alternately. B With ( io ) With thefe fpecimens the learner ought to be well acquaint- ed, before he proceed to draw running ornaments, that he may give fufficient variety in each turn. The regular leaves, in Plate XI, ftiould alfo be copied, as they are much in ufe in carving and japanning. Next proceed with the borders in Plate III, which are in- tended for japanning or inlaying; and fo on with any other of the Plates, as Plate V. VII. and IV. as they may appear raoft fuit- able to his abilities in drawing; obferving in all cafes to make a very light pencil-fketch of the whole defign, before any thing is attempted to be finifhed. Of Qualifications necejjary for Compojition. To qualify the learner for compofition, he ought, in fome meafure, to be acquainted with the proportions of human figures, efpecially thofe taken from the antiques. My very li- mited plan in publifhing thefe ornaments affords me no oppor- tunity of doing any thing in this way by example. I will, how- ever, give a few hints refpe£ting their proportions, for the af- fiftance of thofe who have no opportunity of confulting the beft matters. The ( II ) The proportion of the male figure, according to Mr. Bris- bane's Anatomy, from Albums, will be near enough, as follows : If the perpendicular height of the intended figure be divided into ten equal parts, and one of thefe parts into four, the proportions will run thus with refpedt to length : the head, from the crown to the chin, one tenth and one fourth ; the neck rather more than one third of the head; from the fummit of the fhoulders to the bottom of the belly, three tenths ; from the bottom of the belty to the center of the knee-joints, two tenths and one half ; and the fame from the center of the knee-joints to the bottom of the feet. Obferve, the height of the hips are fix tenths and one third from the ground, and the length of the arm four tenths and rather more than one half. In thicknefs as follows. — Over the flioulders, two tenths and one fourth; over the hips, one tenth and rather more than three fourths ; over the thick part of the thigh, one tenth ; the fmall part, near two thirds. Thefe principal parts being at- tended to, the reft will follow of courfe, by pradtifing a little upon the different parts of the body from examples. When the proportion of any male figure is to be proved, take the thick- nefs of the thigh as one tenth of its height, and by remember- ing the above proportions any figure may be examined. By thefe proportions I have examined a figure engraved from the famous Raphael, an Italian painter, and found them to agree B 2 exactly. ( 12 ) exadtly. In refpe6t to the female figure there is fome difference in the proportions ; the whole is more {lender and elegant; the Ihoulders are not fo broad ; the trunk or body is fhorter ; the hips broader, and in proportion higher from the ground ; and the mufcular parts are not fo ftrong and prominent. As female figures are frequently interfperfed in the compofing of orna- ments, it is proper to obferve, that much depends on the ma- nagement of the drapery with which they are clothed. It ought to hang with freedom and eafe, and in fome parts to lie clofe, fo as to difcover fome of the principal fhapes. To effe£t this, it is beft, firft, to draw the figure by the pencil as if entirely def- titute of drapery, and afterwards to lay the drapery gently over with Indian ink, or colour, as may be required; fo that the lines which marked out the parts of the body, now covered, may be expunged. This method gives true effect to the dra- pery, by enabling us to determine where there ought to be ftrong, where flight, and where no folds at all. On the pro- minent parts of the body there are no folds in the drapery ; but after "having juft pafled over thefe, the folds commence in ten- der marks, and increafe into ftrong folds where the drapery is detached from the body. In examining Cipriani's figures, I find, that if the affigned height of the female figure be divided into ten equal parts, from the ground to the waift, where the drapery is fometimes tied round. ( 13 ) round, is feven tenths ; from the waift to the top of the fhoulders, one tenth and an half; the neck a quarter, the head one tenth and a quarter, and over the Ihoulders rather more than two tenths. As boys or cupids are frequently introduced in ornaments, it is proper that the learner fliould take notice of their propor- tions and general appearance, as different from thofe already defcribed. Cipriani's boys are of the following proportions : — If the affigned height be, as before, divided into ten equal parts, the head will be full two tenths in height ; the neck very fhort ; from the top of the Ihoulders to the bottom of the belly, four tenths ; from the bottom of the belly to the knee-joint, full two tenths ; and from the knee to the ground, bare two tenths ; the arms, when hanging perpendicular, come not quite to the middle of the thigh ; the breadth of the Ihoulders not quite three tenths ; and, laftly, the thick part of the thigh, one tenth and an half, which will of courfe give the proportion of the leg. The learner fliould obferve the general caft of thefe figures ; the head is large and round ; the neck fcarcely diftinguiftiable between the head and Ihoulders ; no joints appearing in the arms or legs fcarcely; the ankle covered with flefh, and the whole leg thick and maffy. But, belide the human figures, there are others of an ima- ginary ( 14 ) ginary kind employed by the antiques in their decorations. Thefe are ftill, and ever will be retained in ornaments lefs or more. The moft tafty of thefe were feleiled by Raphael, and painted by his pupils on the walls and ceilings of the Vatican Library at Rome, and which are handed down to us, by the, Italians, in mafterly engravings ; which, in the courfe of this work, I have confulted, and from which I have extracted fome of my ideas, as well as from fome French works. In the Vatican are figures whofe upper part is female, and the lower of foliage entwifting round. Other female figures have their lower part of a fifh, and fome of a greyhound. Others fhew only a human head, with foliage fpringing from it in different forms, anfwering for wings, and for a covering of the lower parts. In it, we fee fometimes a dolphin fifh with an orna- mented tail ; a lion's head and an eagle's leg and talons brought into a fmooth outline by the help of foliage: at other times a tiger's head and paw formed in the fame manner. Some, again, are partly a horfe with wings and two fore legs, and partly the tail of a fifti ; all which are now a namelefs generation, but once the offspring, I prefume, of the ancient metamorphofes, either what they termed real or apparent. Befides thefe, are to be feen, in the above work, the fphinx, a figure of much fame amongft the ancients, whofe upper part is ( 15 ) is a woman's head and breafts, and the wings of a bird ; the lower part the body of a dog, and the claws of a lion. 'This monfter is faid to be the production of two deities, and fent as a fcourge to the Thebans. Its bufinefs, on a mountain at Thebes, was to propofe dark queftions to paffengers, and if not anfwered to devour them. It is faid that the Egyptians ufed the fphinx as a fymbol of religion, on account of the myfteries which it was capable of interpreting. The Romans therefore placed it on the porches of their temples. The centaur, partly a man, and partly a horfe, ufed as one of the figns of the zodiac, in which the man part is reprefented fhooting with a bow. This being is alfo faid to be the offspring of a deity in con- junction with a cloud. They inhabited Theffaly ; and, engaging in hoftilities with the bow, were vanquifhed by Thefeus. As they feem to have been a rebellious race, they may be intro- duced into fuch fubjeCts as are intended to fliew the odium of fuch condu6t. The griffon is another fabulous being, exifting only in the vain imaginations of the ancient heathen poets, as do the two former. They reprefent it partly an eagle, and partly a lion ; that is, the lower part of it. They fuppofe it to watch over golden ( 16 ) golden mines and hid treafures. It was confecrated to the fun, whofe chariot was drawn by a number of them. And thefe, if you pleafe, may be introduced into fubje£ts intended to reprefent covetoufnefs ; or they may be placed over cabinets where trea- fure is kept. » It will be proper that the learner fhould ftudy to compofe thefe, if he intends being a proficient in ornaments. In ftiort, to be fully qualified for ornamental decorations, is to be ac- quainted with every branch of drawing. And, further, to compofe to much purpofe, it requires to have a general infight into works of this nature, and particular- ly to fee the painted walls in noblemen's houfes, in many of which the art is exhibited to its utmoft perfection ; and in none more fo than in the printed and painted filks executed of late by Mr. Eckhardt, at his manufa6tury at Chelfea, adapted for the purpofe of ornamenting pannels, and the walls of the moft ele- gant and noble houfes. Of Compofition. After the ideas of the pupil are extenfively furnifhed in the manner now defcribed, it will be proper to begin with fome fmall ground to compofe on, fuch as the frieze of a cornice ; and ( 17 ) and to confider its lituation with the eye, whether it be intended to be much above it, fo that the parts of the ornaments may fuit the fuppofed diftance of the eye from it. It is of no effe£l to put a number of fmall ornaments in, to be viewed at a great diftance. In this cafe the parts fhould be fimple, entire, and rather maffy, to produce a proper effedt. If the frieze be near the eye, it may then be divided into fmaller parts ; but to crowd it in any cafe ought ftudioufly to be avoided. And obferve, the tablets of friezes ought to be diverfe to the other ornaments in it. I would then recommend to compofe on the ground-work of a pilafter not very broad ; for it is to be obferved, that the difficulty increafes in proportion to the width, more than in the height of a ground-work. The ornaments in a pilafter or pan- nel is coniidered as growing upwards, and therefore it ought to take its rife from fomething principal at the bafe, and grow rather lighter towards the top, as in every inftance is fhewn in nature. But this does not confine the compofer to fuppofe that every thing is to be fattened or tied to each other as in ftridt nature, for this would fometimes be the fource of heavinefs in ornaments ; nor do I fee it pradtifed in the Vatican, or by any of the beft artifts in this way. But certain it is, that the beft compofitions are thofe which keep the parts moft connected in one entire piece. The more we attain to this, whilft we avoid a C heavy ( is ) heavy repetition of the fame parts, the nearer do we arrive at perfection in this art. The ornaments of a pilafter ought to fill regularly on each fide, and not to leave much naked ground. And efpecially we ought to ohferve, not to have the ground alternately crowded and naked. If we begin in an open flyle, leaving much naked ground, this fliould be continued uniformly all the way up, and, if any thing, only to grow more open at the fummit. The laws of harmony in every art, where time, motion, and fpace are ob- ferved, require this. If the furface to be ornamented be horizontal^ and is liable to be viewed alike in all points, as in a ceiling, the fubje£t fhould be regular, and formed into pannels and groups, fur- rounded with foliage of the fame kind and form on all fides. Nature exemplifies a regularity in moft flowers, and in. other things that grow horizontal.. Laftly, to compofe ornaments for a large upright pannel, as in rooms, is by far the moft difficult tafk in this art. Here it is required that the artift colle£t and arrange all his ideas ; and thofe fcattered fragments which exift in his mind through long and repeated obfervation on the works of the beft mafters, muft now be colle&ed to form an entire whole, by a general concourfe t or C 19 ) or aftemblage of every branch of drawing. In this large field, archite£ture, perfpe£tive, figures, landfcape, foliage, and fruit, may vie with each other, and ftiew the niafter's fie ill. Attempts of this nature may be made by the learner, and with fuccefs, though he fall vaftly fhort of a perfect difplay of all thefe different branches of drawing ; for it is to be obferved, that the rule forjudging in works of this nature is not to look for eminence in each and every diftindfc branch, but to difcern fine tafte and juftnefs of compofition in the whole. In compofitions of this nature fomething fpreading and xnafly ought to be at the bottom of the pannel, except the orna* ment be only intended to occupy the center, in which cafe the principal part of the ornament flioukl be in the middle ; but where the entire pannel is to be filled up, we Ihould begin as above, that there may be an opportunity of giving breadth to the foliage, for the purpofe of filling up the ground regularly from one beginning only, for two defigns muft not be entwined ^vith each other in the manner of cyphers* This deftroys the beauty of fimplicity, which confifts in fewnefs of parts, and en- tirenefs of forms, without which all is a jumble. This obfervation will teach Us to avoid that kind of croffing and cutting each other, fomething like the rigging of a fhip, C 2 which ( 20 ) which may be obferved in fome ornaments, even of French production as well as Englifh. A practice this, which always denotes bad compofition, and a barrennefs of thought. It is done with a defign to enrich, but it only turns out to be a fill- ing up to the prejudice of the whole. The learner muft there- fore ftudy to enrich by a variety of thought fp ringing from fomething, yet without interfering with each other. He lhould alfo be careful in avoiding the appearance of ftraight lines continued from bottom to top, which is formal and bad. Some continuance of a right line is beautiful ; but it ought quickly to be broken in thefe compofitions, whether per- pendicular or horizontal. Obferve breadth in the parts, ftiun niggling and meannefs, and ftick at nothing that will have a comely and pleafant ap- pearanceo An Explanation of the Plates. Plate II. are chair legs. That on the left is intended for japanning, and is formed fquare. The other two on the right are turned, carved, and gilt. Obferve, ( 21 ) Obferve, the plinth of the center foot is left fquare, and pannelled out. If the leg on the right he thought to have too much work, the hufks in the flutes and the drapery on the plinth may be omitted. Plate III. Borders for japanning or inlaying. Plate IV. Ornament for a pannel. The whole fprings from a fpreading leaf at the bottom, from which a ferpent attempts to come at the doves on the fruit. In the center is a temple not dedicated to the interefts of the cupids, for which reafon they are burning it with their torches. The figure on the top of the column, in refentment, means to pelt them with ftones; and the geniufes above are pouring down water to quench the flames. The owls are emblematic of the night, at which feafon thefe mifchiefs are generally carried on. The other defigns in this plate require no remark. Plate V. Ornament for a tablet, intended for painting on a grey or blue ground, as beft calculated to throw forward the figure and fruit. In the cornices, the acorns in one, and hulk in the other, are ( 22 ) are turned with a pin; by which they are fixed into the large projecting fquare. I would advife to work the upper part of the cornice fepa- rate, by which means the acorns will be more eafily fixed. The frieze may be carved, painted, or inlaid, Plate VI. Defigns for Bed-pillars, No. i and 2 are to be painted; No. 3 carved in mahogany; and No. 4 and 5 are intended for rich ftate-beds, carved in white and gold. The fcale of feet and inches at the bottom will give the heights, and other proportions. The pateras which cover the fcrew heads are on loofe pan- nels let into the pillars, and which fettle down into a groove at the bottom, by which means they are kept in their place, and eafily taken out. Plate VII. Ornaments for the center of a pembroke and pier table needs no explanation. Plate VIII, Of chair fplads. No. 1, 2, 3, and 6, are intended for parlour chairs, carved in mahogany. No. C 23 ) No. 3 and 4 are for painted chairs, Obferve, the curve lines which come from the top rail at No. 2 and 6 are intended to fhew where the outfide fplads in a complete back will come in, anfwerable to No. 4. Plate IX. Of toes and knees for pier and card tables- No. 1, 3, 5, are meant for pier tables, the ornaments of which are intended to be carved and gilt. No. 2, 4, 6„ are for card tables, with ftringing and pannels let in. Plate X. Of chair elbows, with part of the feat, together with fplads for chair backs. The fplads are all intended for japanning, except No* 4, which may be worked in mahogany. The elbows are meant chiefly to be carved and gilt ; but the mere outlines of any of them will ferve as patterns either for painted or mahogany chairs, by leaving out the ornaments for the mahogany, and retaining fome of them, or even all of them may be adapted for painting. It ( *4 ) It may be proper to obferve, that as high as the Huffing of the feat a rabbet fhould be left on the flump to fluff againfl; which is eafily done, as the flump is made fmailer above the rail. The cufhions on the arms are formed by cutting a rabbet in the arm, or leaving the wood a little above the furface. Some, however, bring the rabbet fquare down at each end, covering the wood entirely, except a fillet, which is left at the bottom and continues round the eufhion. Plate XI. Ornament for a tablet intended for a painting, but which might be enlarged very well. The fubje6l is a faint moonlight fcene, reprefenting Diana in a vifit to Endymion ; who, as the flory goes, having offended Juno, was condemned by Jupiter to a thirty years fleep. It may not be improper to advertife fome, that thefe, with a thou- fand other of the fame kind of ftories, are merely the fabrica- tions of ancient poets and idolaters, forming to themfelves in- numerable gods, according to their vain imaginations, and which now, only ferve to try the painter's fkill in decorating our walls. And in oppofition to thefe vanities, I cannot well omit whifpering into the ear of the reader, that " To us there is but one God, the Father, of whom are all things." i Cor. viii. 6. Plate ( *5 ) Plate XII. Cornices for Windows. The one acrofs the plate is intended for japanning, the iipper one for carving and gilding, and the two under ones may be either carved or japanned. The circular ends of this cornice are fometimes formed of a faintifh curve, and fometimes of a quick one. When they are of a faint fweep, they ought to be made fomewhat longer at each end than the outfide of the architraves, to give place to the curtain rods, fo that they may be brought fufliciently for- ward on the lath, and not leave too great a vacancy between the rod and cornice leaves, otherwife the lath will be feen when there is no drapery. In making thefe cornices, it is beft to plough and tongue in the leaves to the under fide of the facia of the cornice. The ends may be formed by gluing blocks of deal one on another till they come nearly to the fweep ; and after having formed the oiitfide curve, I would then advife to gage on fpr the plough-groove for the leaves, before the wood in the infide is brought to its form, that the pieces for the leaves may- be put in without fplitting off the groove. After thefe are well dried, then the ftiperfluoiis wood on the infide can be taken away. When ( 26 ) When the cornices are made at each end with a quick curve, the whole is firft worked in ftraight mouldings, and mitered together at each end, the fame as if intended to be fquare, according to the old fafhioti. When they are glued in the miters, get out blocks of deal, about two inches and an half fquare, and cut them down anglewife, and let their length be equal to the width of the cornice and length of the leaves. After thefe blockings are dry, cut off as much of the old miter as is fufficient to form the curve, and work the mouldings again by hand ; and obferve, that as the block was left long enough, the curved leaf is intended to reft againft it, by which it will be much ftrengthened. The cornices made thus, with a quick curve, needs not be made longer than ufual, becaufe the quick curve admits the rod to come forward more eafily than the other. Plate XIII. Pilafters for Commodes. Thefe may be painted, inlaid, or gilt in gold behind glafs, and the glafs being then beded in the pilafter, it is fecure, and has a good effe£l. 7 Plate ( 2 7 } Plate XIV. Chair Legs. The center leg is worked fquare ; that on the right is octa- gon, except the vafe at the knee ; and that on the left, round. Thefe may, in the view of fome, be thought too full of work ; but the lkilful workman will eafily fee how to reduce their richnefs, and accommodate them to his purpofe. FIN I SL An Account of the Plates in the Appendix, and the Pages they face. PLATES. I. The Elliptic Bed » v ' • m m Faces Page 6 2. The Ducheffie »■««'*''« ibid. 3- Library Cafe - - • 8 4. Pier Tables - - - - », ibid. 5- Library Steps • 12 6. Drawing Room Chairs » - « - ibid. 7- Bidet Dreffing Table - - ibid. 8. A Wardrobe - 14 9- A Bed 16 10. A Sofa and Converfation Chairs ■» - Painted Chair Backs - - ibid. 26. Ladies' Work Tables - - 50 27. Book-cafe Doors - - „ ibid. 28. Back for painted Chairs ... - ibid. 29. Clockcafes - - „ - ibid. 3°- A Drawing Table - ibid. 3°- A Gouty Stool and Sundries * - - ibid. 3 1 - A Section - 52 * - ibid, 3 2 - A View of the Prince of Wales's Drawing Room SUBSCRIBERS NAMES SINCE THE BEGINNING OF THE APPENDIX, EXCLUSIVE OF THOSE SOLD BY THE BOOKSELLERS. A. Mr. Ahair, Cabinet-mailer, Briftol B. Barry, Cabinet-maker, London Batter, Cabinet-maker, ditto r Bellard, Cabinet-maker, ditto, Belchar, Cabinet-maker, Briflol Birch, Fringe-maker, Little JSartholomaw Clofe^ London Brown,.. Twickenham Barnard, Upholfterer and Appraifer, Lea- ther Lane, London C. Cock, Cabinet-maker, Briflol Curtis, Stationer, Ludgate Hill, London Caldwall, Engraver, ditto Curtis, Cabinet-maker, Wifbich Campbell John, Efq. Edinburgh D. Duevart, Cabinet-maker, Briflol Dixon, Wine-merchant, No. 9, St. Mar- garet's Hill, London De Michael, Dealer in Prints, at Bafil, Switzerland E. Eckhardt, Proprietor of the Printed Silk Manufactory, Chelfea, London H. Hodgeland, Cabinet-maker, Briflol Howell, Cabinet-maker, ditto Mr. Hicks, Cabinet-maker, London L. - " • 2 Lewis, Cabinet-maker, ditto Livefay*; Houfe-buikler, Ship-joiner, and " Cabinet-maker, Church-row, Limehoufe, London N. North, Joiner, Briflol G. Okeley, Upholfterer, St. Paul's Church* yard, London R. Reid, H, and J. Cabinet-makers, Glafgow Richardfon, Architect, Titchfield Street, London Richards, William, Mimfler, Lynn 5. Stafford, Cabinet-maker, Briflol Stribland, Cabinet-maker, ditto T. Toiputt, Cabinet-maker and Upholfterer, Long-acre, London Thomas, Cabinet-maker, Briflol W. Waddle, Cabinet-maker, Glafgow Walker, Hampton Wick Williams, Cabinet-maker, London Watts, Cabinet-maker, ditto Y. Yoe, Bookfeller, Briflol. Borders for Pier tables Ft,: J, \ \ a , i A < Subscribers Names lince the publication of the Ornaments, exclufive of thofe fold by the Bookfellers. Meflrs. Colnaghi and Co. Print-fellers, Pall-mall. Mr. Eyer, Upholflerer, near the Pantheon, Oxford-road. Meflrs-. Folgham and Son, Cabinet-makers, No. 81, Fleet-ftreet. Mr. Peter Groupner, Cabinet-maker and Inlayer, No. 43, Grcek-flreet, Soho» Meflrs. Gueft and Son, Upaolfterers, Bury St. Edmunds. Meflrs. Jenks and Co. Jamaica Wharf, Blackfriars. Mr. Powell, Cabinet-maker, No. ]8o> St. John's-ftreet. — Procer, Japanner, High Holborn. — Serfons, Cabinet-maker, Stamford. — « John Smith, Wholefale Upholflerer, Eaft-cheap. Meflrs. Stanton and Co. No. 58, Lombard-fbeet, . N. B. Such of the Subfcribers as are difpofed to bind the Work in Two Volumes, are here prefented with a fecond Title Page, gratis, to face the End of Part Second It is hoped they will recollect, that only a double and a fingle Plate was promifed in each Number ; therefore in this lafl Number, as good as a Quarto Plate is delivered gratis alfo. It is recommended to the Subfcribers to have all the Double Plates bound in with a Guard in the Middle, V 7