' 2 f E“ 3.! i4 ."""7.i‘""" . fl 1 «\i" ”Sn 1"“! y X. m mfli‘k' t , , ~. ~; ‘1 ~ #3 ifigr‘iww‘: L WWW . ‘ " ~ ,, ‘%}0F.sfl&-< ”N W‘ “duh-‘3 \ w ' (fig-M V. L ~w -.- . . g .. J , . b 'u - . K I °' \ \ ‘ i ‘ x ‘ f» , . w ‘ ’— _ ‘ . . '\ . ‘ V x V” 4 v ‘I "a ." \ CARPENTER’S NEW GUIDE: COMPLETE E right ones, as Q. 34. A rhombus is an equilateral parallelogram, whofi: angles are oblique, asU. 35. A 2homboi'd 2s an obli-que an (fled pa2 allelogram, as V. 36. A trapezium is a quadrilateral whzch has neither pair of itsfides parellel, as T. 37. A trapezoid hath only one pair of its oppofitefides parallel, as S. 38. Plane figures having more than four fides, are in general called polygons, and receive other particular names according to the number of their jz'cles or angles- 39. A pentagon is a polygon offivefules, a hexagon has fix fides, a heptagonfeven, an oé't'a- gon eight, a nonagon nine, a decagon ten, an undecagon eleven, and a dodecagon twelve fides. -40. A regular polygon has all itsfitles and its angles equal; and 2f the J are not equal, the polygon 2's 2'.2‘regular 41. A22 equilateral triangle 2's al/b a regular figure of three fides, and a fiuare is one qffour; t/lc’former being called a trigon, and the latter a tetz‘agon. 42. A ci2 cle 2's (2 plane figure bounded by a curve line called the circunference, which 2's eve2y .vheie equzd ftant from a certain point within, called 2ts centre. 4-3 The radius of a ci2 cle is a right line drawn f2 am the cent2 e to the ci2 cumference, as a b at W. 44. A diameter of a ci2 ele is a right line drawn through the centre, termi'natzng on bothfides of the circumference, as c d at W. 4-5,. 4- ‘ ‘ PRACTICAL GEOMETRY. 45. An arch of a circle is any part of the circumference. 46. A chord is a right line joining the extrenu‘ties of an arch, a.“ a bat X 47. dje 0mm is any part (1" a circle bounded: b} an arch and its C/IOId, as X. 48. 11 fennczrcle is half the Circle, or a fegment cut of by the diameter, as Y. 49. A /eé‘t'or is any part if a. Circle bounded by an arch and two radii, drawn to its ertremitzes, as Z. 50. A quadrant, or auartcr of a circle, is a feflor having a quarter of the circumference for its arch, and the two radii are perpendicular to each other, as A l. .The height or altitude of any figure is a perpendi'culaz let fall f) am an angle, or its adertex, to the applyitefide, called the baje, as a. b at B0 .. 52. When an angle is denoted by three letters, the middle one is the place of the angle, and the other twodenote the Jides containing that angle ,- thus let a b c be the angle at C ‘ 3, b is the angular point, and a b and b c are the two fidescontaining that angle. 53. The meafure of any right—lined angle is an arch of any circle contained between the two lines which form the angle, and the angular point being in the centre, as D 4. PLATE II. PROBLEMS. FIGURE 1. To draw a Perpendicular to a given Point in a Line. A B is a line, and c a given point; take a and b, two equal difiances on each tide of c, and with your. compafl'es in a and b make an interfeétion d, and draw (I c, which is the perpendicular. F IG. 2. To make a Perpendicular with a Ten Foot Rod. Let a b be fix feet, then take eight feet, and make an arch at c in the point b, and in the point a with the difiance ten feet crofs at c, then draw e b, which 15 the perpendicular. F10. 3. To letfall a Perpendicularfrom a given Point to a Line. In the given point c make an arch to crofs the line in a and b, and in a and b make an interfeétion at a’, and draw c d, the perpendicular. ‘ FIG. 4. T o draw a~Perpendicular upon the End of a Line. I Take any point at pleaiuie aboxc the line, and with the dillance d b make an arch a b c, and draw a line a d to crofs it at c, and draw c b the perpendicular F IG. Plate 2, ‘.“i/ L ,I“~.‘ gt: 0. , 129.2. 17" .7. . ’ j "0," 8 x / a; c 5 ab‘T—ZE ‘ t V Fly/l. ‘ a” ‘ 129.3. , 4‘ i '5 (2 , 3 ’ [ill/1.”:Lv/flr/Il-f (/z'rn-[v . 7/)”4‘ 0:179; 1" JL‘ [Er/plum” . P242? 3 ‘ PRACTICAL GEOMETRY. 0! FIG. 5. To divide a Line in two Parts by a Perpendicular In the points a and b defcrib'e two arches to interfeét at c and d, and draw 0 d, which div ides the line 1n two. F10. 6. To divide any given Angle into two equal Angles. Take two equal distances b and c on each fide of the angular point a, and with the fame opening of the compafs or any other, place the foot of your compafs in b and e, make an interfeétion at d, and draw d a, which will divide the angle into two equal parts. FIG. ’7 and 8. An Angle being given, to make another equal to it, from a given Point, in a right Line. Let b a c be the angle given, and c d a right line, e the given point; on a make an arch b c with any radius, and on c with the fame radius defcribe an arch d e, take the opening of b e, fet it from d to e, and draw e": then the angle e c d will be equal to e a b, PLATE III. F10. ]. Upon a 7ig 'fht Line to make an equzlateial T2 iangle Take a b the given fide with your compafs, place one foot 1n a and b, make an intex- feétion at e, and draw c a and c b. FIG. 2. Upon (1 mg “ht line to make a geometr ical Square. With the given fide a b, and in the points a b, defcribe two arches to interfeé‘t at e, divide b e into two equal parts at f, make e d and e c each equal to ef, draw a. d, do, and c b. Fm. 3. PROPOSITION. If through the point e in the extreme of the diameter c d, is drawn a tangent line e c 8, and if on this point c with any radius a femicn‘cle be dcfcribed and divided into equal parts, and from the centre c lines be drawn through thefepointa to terminate in the circumference, it will be divided into equal parts. FIG. 4-, 5, 6. The Side of any Polygon being given, to defcribe the Polygon to any Number of Sides whatever. On one extreme of the given fide make a femicircle of any radius, but it will be molt convenient to make it equal to the fide of the polygon, then divide the femicircle into the fame number of equal parts as you would have tides in the polygon, and draw lines 2 . from s q ‘ PRACTICAL GEOMETRY. from'the centre through the equal divifions in'the femicircle, always omitting the two lalt, and run the given fide round each way upon thefe lines, join each fide, and it will be completed. Example in a Pentagon, Fig. 4. Let a b be the given tide, and continue it out to e,- on a, as the centre and the given tide, defcribc a femicircle, divide it into five equal parts; through 2, 3, 4, draw a 2, a d, a e; make I) e equal to a I), 2 (1 equal to 2 a or a b; join 2 d, d e, and e (I In the fame manner may any' other polygon be defcribed. FIG. ’7. T lzrongr/z a given Point :1 to draw a Tangent to a given Circle. From a draw it o to the centre, then through a draw I) c perpendicular to a o, it will be the tangent. FIG. 8.- A tangent Line being given, lofind the Point where it [catches the Circle. From any point a in the tangent line I) a, draw a line to the centre 0, and divide a a into two equal parts at m, and with a radius m a, or m o, defcribe an arch, cutting the given circle in n, which is the point required. ‘ FIG. 9. T 700 rig/it Lines being given, tofind a mean Proportion. Join a b and (I c in one liraight line, divide it into two equal parts at the point 0, with the radius 0 a or o c defcribe a femicircle, and ereél; the perpendicular b (1, then is a b to bdasbdistobc. FIG. 10. T lzrmlglz any three Points to defiribe t/ze Circumference of a Circle. From the middle point I) draw chords 1) a and b e to the two other points a and e, divide the chords a b and b c into two equal parts by perpendiculars meeting at 0, which will be the centre. FIG. 11. .Tofirzd a rig/1t line equal to any given Arc/I. of a Circle. Divide the chord a. 1) into four equal parts, fet one part I) c on the arch from a (0 (I, and draw (1c, which will be nearly equal to half the arch. ‘ Arnie. This method ihould not be ul‘ed above a quarter of a circle; to that if you would find the circumference of a whole circle by this method, the fourth part mutt Only be ul'ed, which will give one eighth part of the whole exceedingly near. PLATE IV. FIG. 1. dny z/Iree Lines being given, to nan/re a. Triangle. Take one of the given {ides a. I), and make it the hnfe of the triangle; take the other tide (I C, 171m, 4 . \ J71};_2. If}. I z {3 Elk/.8. .11 7}, ................. .. (1 0 d (. B a I z 1, c ( 0 ,AL 1‘ — A C 1), K h \, W "A \ . .> 1 “él‘ww'fu; .1315; PRACTICAL GEOMETR‘r. '1 a e, and put the foot of the compafs in a, and make an arch at c; then take the third tide b e, and put the foot of the compafs 1n 1), and crofs the other arch at c, join the sides Note: That any two lines muft he greatei than a third. ' FIG. 2, 3. T 0 make a Quadrangle equal to a given Quadrangle. D11 1de the given quadrangle, fig 2, in two t1 1angles, make the triangle 6 g f equal to a b c, and e g 12 equal to a c d, and it is done FIG. 4, 5. Anyz'i regular Polygon bemg given, to male another qfthefizme Dz'men/ions. Divide the given polygon into triangles, and 111 fig. 5, make triangles 1n the fame poi- fition, refpeétively equal to thofe infig. 4; then will the irregular polygon f, g, 12., 2', It; be equal and fimilar to a b c d e: in the fame manner may any other polygon be made equal and limilar to another. F IG. 6. To make a Reaangle equal to a given Triangle. Draw a perpendicular c d, divide it into two equal parts at e, through 6 draw f g, pa- rallel to the bafe a b, draw a f, 6 g, perpendicular; then will the reétangle a 6 gf be equal to the triangle a b c. FIG. '7. To make a Square equal to a given Beflangle. Let a b c d be the given parallelogram; continue one of its (ides as a 6 out to It, make 6 6 equal to the other fide I) e, divide a e in two equal parts at 2', with the radius ie or in. make a femicircle a f e, and draw bf perpendicular to a b ; make the fquare l f g ll, which is equal to the parallelogram a ('1 e .a’. i ' FIG. 8. To make (1 Square equal to two given Squares; Make the perpendicular {ides a c and a b of the right-angled triangle a b c equal to the fides of the given fquares A and B ,- draw the hypotenufe c b, which is the fide of the fquare C, equal to the two fquares A and B. In the fame manner may a femicircle he made equal to two given femicircles, or any fimilar figures whatever. FIG. 9. To make a Squaw equal to flu ee given Squares. Let A B C be the three fquares; make a b equal to the fide of B, a 5 equal to the tide of A, at right angles to a bjoin [1 c, then make a (1 equal to b c, make a c equal to the fide of C, join (1 e, which will be the fide of the fquare 1) equal to the fquares A B C. c ' ' ' PLATE s PRACTICAL GEOMETRY. PLATE v. p, i FIG. 1. To draw a Segmmi of (2' Circle to any Length and Hag/it. a b is the length, 2'11, the height;. divide the length a 6 into two parts by a perpendicular, divide a I; by the fame method, then their meeting at‘g will be the centre ; fix the foot of the compafl‘es in g, extend the other leg to 1:, make the arch a Ii 1), which is the fegment. ~ FIG. 2'. To draw a Segment by Rods, to any Length and H'ez'g'lu‘. Get two rods c e and cf, each equal to a b the opening; place them to the height at :,-. and to the ends a b put a piece ,acrofs them to keep them tight, then move your lath round the points a b, and it will defcribe the fegment at the point c; F 1G. 3. To daycribe a Segment of a Circle at twice, upon true Principles, by a flat Triangle. Let the extent of the fegment be a 6, its height 6 (1,, from the extreme b'to the top d draw I) (1, through the point (I draw e d parallel to the hafe a 1), equal in length to d b, defcribe one half, as you fee at G ;. then move your nail, or- pin, out of a, {tick him the- point 6, and; defer-ibe the other half. FIG. 4. The tranfveifi and conjugate Axis (f an Ellz'pfis being given, to draw in Reprtfcntatzbn. » Draw Ltd parallel andequal to 77 c, bifeét in it e; draw 6 c and-(lg cutting each other at“ m, join m c, bifeét it by a perpendicular meeting cg, produced at It; draw It (1, cutting 15 a at lc, and make 72 z'equgtl to 72 (c; n lequal to n 1;,- through the points 2,1, A), 1;, draw- the lines It 2', k l, and i l, It It, then defc’ribe the four fe&ors by help‘of the centres ilk II, and it will be the reprefentation required. FIG. 5. To defcribe rm Elliy/is by 0rzlz'naies.. Make a7 7777 or CARPENTRY. ,9 PLATE XXIV. There will be no occafion- for explaining the lines of this groin, as they are of the fame natu1e as thofe in the 12111 plate; but it will be pioper to take notice, as this is a bevel groin, the ribs molt lie in the fame direétion as the plan of the groin, which will make them longer than their correfponding‘ given arches at the top, but of the fame height, they are ceiifequently ellipfes, being the feétions of cylinders, therefore to make a 1ib over lm, acrofs the two piers,~take the extent of the bafe l m, and the height of the given arch'no, and defcribe an ellipfis; and to del‘cribe the tide arches between any two piers, as from a to I), take the extent a b, and the height of the given arch, p g, at A, andfdea 'fcribe an ellipiis, it will give the proper form of the rib to {land over a b ,- the interfe&~ ing ribs will require two moulds C and» D, owing to the groins being bevel upon the plan. Note. The letters are marked the fame upon D and C as they are upon E, to {how they are traced f1 om it. , PLATE XXV. T0 dfifcrilie the interfefiing or Angle Ribs (f 0 Grain flandz'ng upon an ofiagorz Plan, the Side and Body Bibs being given bol/z to the fimzc Height. ‘ FIG.1. E is a gii en body rib, which may be eithera femicircle ora femi ellipfis, and A Is a fide rib given of the fame height; I) IS a rib ac1 ofs the angles: t1 ace f1 om E, the bafis of both- being divided intoa like number of equal pai ts, divide the bafe of the given. rib A, into the fame number of parts; from thefe‘ points draw lines acrofs the groin to its centre at m, and from the di'vifrons of the bafe of the other rib D, draw lines parallel to the fide of the groin, then trace the angle lines through thefe fquares, will be the place of the interfeéting ribs; draw the chords (1 b‘, and b c, then prick the moulds B and C from E or D, but take care not to prick them from the crooked line at the bafe, but from the {iraight chords (1 b, and b c. To dcfcribe and back the Angle Ribs qf a Groin circular upon t/ze Plan, be Side and . Body Arches being given, as in the [(1/2 Groin. The ribs are defcribed. in the fame manner as in the lafi example for the octagon groin, or in the fame manner as the Welih gnoin, plate 23, and the backing or bevelling is found in the fame manner as is defcribed in that plate. Note. E and F are the fame moulds as are fliown at B and I), PLATE 5 30 ' " THE THEORY AND PRACTICE PLATE XXVI. T he Side Bib A, and the Angles, being gzven flrazfiht upon the Plan, to find the An rrlc Bl!) C, and the Body 1215 C. 1F IG. 1. The rib A is fuppofed to be placed over the {traight line a b, and its bafe divided into any number of equal parts, as 8; from the divifions draw lines to the centre of the groin, to interfeét the angles at the points a b c (I e f g; place the foot of your compal‘s in the centre of the groin, and from the points a b c d, &c. draw lines to the bafe of C, and make the ordinates of C equal to thofe of A, then C is the body rib ; draw lines at right angles‘from the points a I) c d, &c. and prick the moulds G and B from A, will be the angle ribs required; this wants no mould to bend under the angle rib, as in the others that are crooked upon the plan. How to dcfcrzbe the Bibs of a Gram om Stabs upon a czrcular Plan, the Body B1!) bemg gzven FIG. 2. Take the tread of as many {teps as you pleafe, fuppofe nine, from E, and the heights correfponding to them, which lay down at F ; draw the plan of the angles as in the other groins, and take the firetch round the middle of the {teps at E, and lay it from a to I) at F; make d e perpendicular to b c at B, equal to d e at F, draw the hypotenufe e c, draw perpendimilars from dc up to B, and prick B from A, as the figures direct, thenB is the mould to Rand over a b; draw the chords (1 4 and 4 m at the angles, make a 9, 4- II, perpendicular to them, each equal to half the height tie, at B or F, draw the hypotenufe g,4 and It 772, draw the perpendicular ordinates from the chords through the interfeé‘tion of the other lines that meet at the angles, then trace the moulds D and C, from the given Ill.) A, will form the moulds for the angle or interfeéting ribs. Note. The reafon that the angle ribs D and C are laid contrary ways, is only to avoid confufion. PLATE Plate} 26. " “WW 1‘ ' ’ ’ ‘ ”(w/,4 ‘ ,w I" I ‘ . ‘ J UK" In ‘ “L‘AR'x‘J‘W WW?! \ “me 13%").Hl/n' .Ir/ ‘1'}-u.‘/.'I.I1//,"-/,I197.Anl‘A'r'n/ml-uw ‘ / . or CARPENTRY. _ 3; ' PLATE XXVII. As the fin face 9f a globe ts every where of the fizme cur with e, confequently the fur/ace of anyfegment 7y” a globe, or pent, 77777/2/27117 ctaz'n the fame curve as before it was cut,- amlfor this rea/bn z't appeats that the curves of the back 7 ibs of a mche mufl he the fame fwcep at the groundplan 7'tjelf; and the front rib is afemicz'rcle. See Aximn the 3d, page 14, and figme 1, plate 10. If a flz777i-globc is cut by a plane'at right angles to the plane (3f 7ts baje, then the [66717077 is aje7n7'.mele The practice ‘of this 7's eafy. To get out the 1776st the Head. From the centre c draw the ground-plan of the ribs as at figure A, and fet out as many ribs upon the plan as you intend to have in the head of the niche, and draw them all out towards the centre at e. PlaCe the foot of your compafs in the centre c, and from the ends of each rib, at e and c, draw the fmall concentric dotted circles round to‘the centre rib at m and 77; then draw 777' g and 77 2', parallel to r k, the face of the wall; then from g round to e upon the plan, is the length and fweep of the centre rib, to fiand over a b ,- and from 2' round to e, the length and fweep of the rib that {lands from c to (1 upon the plan; and from g round to e is the fweep of the fhortell: rib, that {lands from c tof upon the plan. 117770 to have! the Ends of the Back Ribs agat'w the Front Bib. The back ribs are laid down diftinét by themfelves at C D and E, from the plan. Takec l, in figme A, and fet it from 7: to l in I), will give the bevel of the top of the rib I). And fromfigme A take from c to 2 upon the plan, and fet from e to 0 in the rib E, will give the bevel of- the top. ~ To find the Places of the Bach Itz'hs where they arefixed upon the Front. From the points a e and e, at the ends of the ribs, in the plan, figure A, draw. the dotted lines up to the front rib, to d f and 77), which will (ho-w where they are to be fixed upon the front rib. The double circle upon the front rib {hows the backing. E . PLATE A m THE THEORY AND PRACTICE \ PLATE xxvm. To find 1/19 Cur :11: (f the szs qf a globular Nw/ze, the Plan and Elevatwn being gwcn Segments qf Cchlcs. In fzg‘. A is the elevation of the niche, being the fegment of ‘ a circle whol'e centre is t';. ntB is the plan of the fame width, andmay be made to any depth, according to the place it is intendedfor, and its centre is c,- on the plan B, lay out as many ribs as you think , itgwill take, drawlthem all tending tothe centre at c, they will cut the plan of the front ‘ rib in g f e (I; through the centre Kc, draw the line. m 71, parallel to a b, the plan of the front rib, put the foot of your compafs 1n the centre at c, draw the circular lines from a g f e d, to the line In 72, and make c .5“ equal to u t, that 1s, make the difiance from the middle of the chord line 921 n to s, the centre of the arch at _,C equal to the” diltan‘ce from the middle of the chord at the top at fig . 11, to its centre at t, then place the foot of yioul c'om‘pafs 1n 3, as a centre, and f1 0111 the extremities m or 72, defcribe the arch at: C; with the fame centre drawtianotherline parallel to it, to any breadth as you intend- your ribs {hall be; then C is the true {weep of all the back ribs in the niche. / Note... The phintsl kin/L, [how what length of each rib will be fuflicienti'rom the point II} ,- from [Z to _m is the rib that will (tend over (I .z', from i to m is the rib that will ' ltand over 3 u from kto 121 over f1), .andvfrom l to In over g 112: the other half is the” lame The t1 uth of this IS cal}; to be conceived by thol'e who have previoufly {ludied the Sec- tions of a Globe, 111 plate 10 of this book i . Through the centre t, draw D 1:, parallel to a b, complete the {weep of the top, 0 F, ; to the line D B, then 1) 12 is the diameter; through 72 draw 72 A parallel to u d, in the‘ centre t; with the dii’cance t A defcribe another femicircle, whofe diameter 15 c (I; then will the femicircle c 1‘ G A B, be equal to 3 Vertical feétion of the globe, fianding on K, patling through its centre at c, which is the fame fweep as the rib at C, becaufe u A isequal to c 71 and c s,- bifeéting m n at right angles, is equal to t u, bifeéting 1-: a at right angles; therefore the hypotenufe t A, that 15, the radius of the circle B A o 1: c," is equal to s It, the radius of the circle or rib at C. , PLATE or CARPENir'ui'. 3's PLATE 'erx. The Plan (3/ a Niche being given,flanding in a cz'rcuilai I” all, tafiiid the F1 ant Rib. B IS the plan given, which 1s a femicircle whofe diameter IS a b, and a, z, 1:, 1,721, It, the front of the circular wall; fuppbl‘e the femichcle 1)’ to be tuined reund its diameter a b, To that the point 7) may {land pe1 pendicular over h 111 the front of the wall, the feat of the femircircle {landing in this pofition upon the plan‘will be an ellipfis; therefore divide half the arch B upon the plan into any number of equal parts, as 5 , d1aw the per-a pendiculais 1d, 2e, 3f, 4g ,5/1, upon the centre 0 with the radius c It, defcribe the quadrant ofka fmalle1 circle, which divide into the fame number Of equal parts as are round B,- through the points 1,2, 3, 4, 5, draw pa1allel lines to a I), to interfeEt the othe1s or the points d, e, f, g, 11; through thefe pOints draw a curve, it will be an elliplis , then take the firetch-out of the rib B, round 1,2, 3, 4, 5, and lay the divilions double at F, firetched out; take the fame difiances d z, e Ir f l, g m, from the plan, and at F make (1 1, e 1:, fl, equal to them, which will give a mould to bend under the front rib, {0 that the edge of the front rib will be perpendicular to a, z', k, l, 171. Note. The {weep of the front rib is a femicircle, the fame as the ground-plan, and the back ribs at C D and E are likewil'e of the fame fweep. The reafon .of this is eafy, the niche being part of a globe, the curvature mufi; be every iWhere of the fame fweep, and confequently the ribs fit upon that curvature. Note. The curve of the mould F will not be exaétly true, as the difiances d i, c 11", f, 1, 8w. are rather too lhort for the fame correfponding diliances upon the foffit at F, but in praétice it will be fuificiently near for platter work; but thofe who would will) to fee a method more exact, may examine plate 15, fig A, where C is the exaét foflit that will bend over its plan at B. In applying: the mould F when bent round the under edge of the front rib, the firaight tide of the mould quIt be kept clofe to the back edge of the front rib, and the rib being drawn by the other edge of the mould, will give its place over the plan: ' t? ’3 I’LA'I‘E st "‘ ' Tm: THEORY AND PRACTICE. PLATE XXX. T be Plan and Elevation of am cllz'ptz'c‘Nz‘c-lze being given, toflnd t/zc Sweep of the Ribs, FIG. A. Defcr-oe every rib with a trammel, byitaking the extent of each bafe from- the plan whereon the ribs ftand‘ to its centre, and the height of each rib to. the height of. the top of the niche, it will: give the true fiveep of each rib. To back me Ribs if we Nz'c/z’e. There will he no occafinn fer making any moulds for thefe ribs, but make the ribs themfelves; then there will be two ribs of each kind; take the {mall diftances l e, 2 (1,. from the plan at B, and put it to the hottomof the ribs 1) and E, from (l'to 2, and e to ; then the backing may be (liawn of? by the other co1refponding rib, or the backing may be drau n of}p with the trammel, as for example at the rib E, by moving the centre of the t1 ammel towards e, upon the line ( c, from the centre c, equal to the diflance 1 c, the trammel 10d remaining the fame as when the infide of the curve was itruek. Given one of the common It’zbs If a. Cove Brae/w,“ tofind t/zc Angle Bma/sctfor a/quarc _ or rcEZangulm Room. 1310.11. Let H be the common bracket, (1 c its bafe; draw I) a perpendicular to b c, and equal to it draw the hypotenufe a c, which will be the place of the mitre; take any number of ordinates in H, perpendicular to b c, its bafe, and continue them to meet the'mitre line‘ a c‘, that is, the hate of the bracket at I; draw the ordinates of [at right angles to its- bafe, then the bracket at I, being pricked' from H; as may be-feen by the figures, will» be the form of the angle rib required. Able. The angle rib mufi be backed either externally or internally, according to the angle of the room. Having given a common B)‘d€/C€fK~, feeflg. G, for qu/Zer, to find the M z'tre Bracket,.L- Proceed as invthe laft'exarnple,. andfyouwill have (the bracket required. PLATE [$31034 ’ L WHHHWIHINW I . ,.mlllmflml as ‘ THE THEORY AND PRACTICE; PLATE XXXII. LINES FOR ROOFING. G The lines for roofing we found 1n the fame manne1 as the fky lights 1n the laft plate; the length and backing of the hip mutt be found in the fame manner as diieéted for the {ky lights; and if it is 1eq11i1ed to find the end of a horizontal bar, ['0 that it {hall fit againit the hip, it will be found in the fame manner as finding the form of the end of a purline, to as to fit againit the tide of a hip rafte1, which method will be defmibed below. the fame may be [aid of the jack bars to be fitted againft the hip of a tky «light as in a roof. In this plate one end of the roof is {hown 111 order to (how two cafes: the 'firft is when the purline lies level, or having two fides parallel to the horizon .; the fquare at B, and the bevel at C, will {how howto draw the end of the purline in this eafy’ cafe; but the following method is univerfal in all politions of the purline. Note. There will be no occafion to draw this at large; as the bevels Will be the fame if done to ever fo {mall a fcale, and the fides may be meafured from a fcale. Let a b be the width of a fquare roof, make bf 01' a c one half of the width, and make c d perpendicular in the middle of cf, the height of the roof, which is here one third, and draw d e, and d f, which are each the length of a'common rafter. T 0 find the Revels of a Purlz'ne ab (177/2 the H117 Rafm. Let the purline be 1n any place of the rafter, as at I, and 1n its 'mofi common petition, that is, to “fraud fqu’are, or at right angles to the rafter; and frOm the point/z, as a centre, with any radius defcribe a circle. Draw two lines 9 l, and p 72, to touch the circle in p and q, parallel tof l7,- and at the points 3 and 7', Where the circle and Wm ‘fides of the Apurline interfeét, draw two parallel lines to the former, to cut the diagonal in m and Ir,- and draw m 71 and k l perpendicular to f m and 7‘ 1c, and join the points 72 2' and Ir 2'; then G is the down bevel, and F the fide beVel of a purline: thel‘e two bevels, when applied to the end of the purline, and when cut by them, will exactly fit the tide hip rafter. Tofind the Bevels 9/ a Jack quter again/Z theffz'p. By turning the {took of the tide bevel of the purline, at F, from a round to the line ii, will give the fide bevel of thejack rafter. And the bevel at 44, that is, the top of a com- mon rafter, is the down bevel of the jack rafter. At the bottom is {hown the manner of cocking down the tie beam upon the wall plate, the prope1 fize of the cocking is figured at a PLATE or eAaeENTRY. _ 35 PLATE XXXI. S K KL 1 G H T S To find the Length of the H zps Qf‘ a swag Iztflandzgn upon a Aware Plan, the Height bezng given. Infig. A, draw the diagonals a b, and c (1; they will bifeEt each other at right angles 4 at 6; take a e for, the bale of any hip; from emake ef equal to the height of the lky- light; from a tof draw a line (If, it will be the length of the hip required. ‘ T o‘find f/ze backing of the flip. Draw any line It 1', at right angles to a He, the bale of the hip rafter, cut it in any point ll, put the foot of yourcompafs in 11, as a centre, and with the other defcribe a circle to touch (If, the hip rafter, to cut the halo line a e, at g; then drawg 2' and g A; then the angle Ir g 2' will be the backing of the hip, as is lhown by the bevel at B; but the bvfl Way to work the hips is to apply a bevel to the parallel {ides of the hips, as is lhown at C, by making the other fide of the bevel parallel to a c, the bale of the hip. Note. The fame lines will extend to any lky-light, whatever may be the form of its plan; if it be any polygon, to find the length of the hip rafter, draw a line throngh any point in its bale at right angles to it, ('0 as to cut the two contiguous (ides to that bale, and on the laid point as a centre deferibe a circle to touch the hip rafter from the point. where this circle cuts the ball: line, draw two lines to meet theends of the perpendicular line i at the tides of the polygon; then the angle formed by theft: two lines will be the backing required: but perhaps a few more examples will make it plainer than: many words can. FI-G. Bis a iky-light, ftanding upon a refitangular bafe, having a ridge in the middle ;. i‘ make c d upon the ridge line equal to half the width of a b; 'then the angle-1) d a will be a right angle; every other requiiite is the fame as directed forfig. 11.. If thefe hips are to be mitred, the bevel at C lhows the mitre. FIG. Cis another lkydight, {ianding alfo upon a_re&angular bafe; but the hips all; meet over the centre of the plan at e, and conibquently. the diagonals do not bifeét each. other at right angles; therefore take any bafe line asra e or e g, and make efperpendicu- lar to a e, from c, and equal to the height of the thy-light; and drawfa, orfg, for the length of the hip, by drawing the line [m at right angles to (1 en. The backing will be found in the fame manner as the others above. This lky-light will require two tlilferent bevels I) and E, to be applied to theparullel fules of the hip, which are both‘fouud from. the backing, by drawing the liocks of the bevel parallel to a e, the bale of the hip. But if the hips are to be mitred together, Fand G {how the two bowels for the mitring each half, f0 that when put together (hall form the proper backing. FIG. D is a lky -light {landing upon an oéi‘angular plan, as is dei'cribed in! fig. 8, plate 6, of the Geometry , the lengths of the hips and backing of the anwle are found in the fame manner as directed for others FIG. E is a lky-light whole plan is a trapezoid; upon each end as a diameter defcribe a. lemicircle to cut the ridge line; from these points draw lines to the extremities of their refpeétive diameters, which will form a right angle for the halo of the hips to Rand upon; the backing or mitring of the hips will be found as is defcribcd infig. A- aod B. PLATE. mati. *3 n... i ‘ _ H mm «hr-b- ‘~l /)////I (32. u" ‘1 E\ ,. s» 0,, (.7! 1: ”a, I \~ F), (I \ \ ”M," t n\ 1: > \ //(. H ~ \‘\ 4 “f 3‘» k: /’ o a G9 6” , b \ I: \ ‘5 ’3\. \‘ \ 1' ; G s ; n 5 ‘\\ 8 \= ‘ \1 \ \\ “t \ f 4‘ ‘7‘ l D a , . ,/ \ ' I / / ’ / . _ r , j ‘ [VI/”'24" (1/, 1M- f/Im/r / 1/”,K/j ///’/ ’/(//// N 1:) in L2 I” a, ’ , 1/ // )///// /J///( - W. .\ ‘ Pia/r .38.. cf r“- ' II runllunll.b..llli 1---.-4.. IILIIIIII : gjt'JTJI'I/IP/dtw . 1/79 t ; I)!I/’?‘ cu rfv'jirl‘ (/1): y K. 7;! m1}, xv . . .., & ._ z. .f . y Y. . . . ., ‘ , v ;, _ . . :. v.2. £732.“ fifdwwgifat: , a » 4. , . 1%... ,. . , , V. . «5:4 s. 1‘711.. :n. A ‘,:..1‘i| olfuo oi; .Lvfi..\,_ ,“é‘vn :1: : \x ' »;TW.I.JV.I.AI . - I \ \ K 1 I \. l , « . \. . \.\ n u . “I . I. ‘ i , . _ \ ._ . _.. \ .\M k r A \1 5% (u .r III.TI!.‘.WH..F:0... \ nvu “$5 ~ R K?» , ' , 3F. x w . . ._ , , . \ .. . . x . .‘ . .. _A O , . . . . . ‘ I x . . . .z‘ x \ \ .uaW, afiu. :v. . .. 9 . \K. .\.. r. . . _ J 4! . . z. . .n.u.;...la1,.$u. .2, x..._..\. , , . A .. , , f . . , \ v . . . r ,V a. - . 0.. , . » . I ‘, . . x _ 1.. n r 7 . l .A .. A , .l ”Iva/«54 ; ‘ , L or. CARPENTRY. 37 PLATE XXXIII'. This plate (hows the manner of framing a roof in ledgment; but as roofs are feldom executed in this manner, I {hall not be very particular in defcribin-g its lines. The fol. lowing defcription for winding will ferye for any. PLATE XXXIV. How to lay out an tr 7 egu‘lar roof in Ledgmem, wit/1 all its Beams lying bevel upon the Plan, fl) that the [ledge may be level when f mflzed the Plan and IIezg/zt (3f tlze Room bemg given. The lengths of the common and hip rafters are found'as ufual. From each fide in the broadefi end of the roof, through c and (I, draw two lines parallel to the ridge line; draw lines from the centres and ends of the beams perpendicular to the ridge line, and lay out the two fides of the roof D and E, by making e d at E equal to .z' n in A, the length of the longefi; common rafter, andc a in E equal to u vat A, and 1'0 011 with all the other rafters. To find the Windzhg qf t/u's Rory". T ake y 1), half the bafe of the lhortefi: rafter; and apply this to the bafe of the longeft rafter from a to l , then the difiance from 1 to 2 {hows the quantity of winding. How to lay the Sides m thdz'ng. Lay a firaight beam along the top ends of the rafters at E that IS, from c to e, and lay another beam along the line a 6, parallel to it, to take the ends of the hip rafters of m and l, and. the beams to be made out of winding at firfi. Raife the beam that lies from a to b, at the point 1), to the 'diflance l 2 above the level; which beam, being thus raifed, will raife all the ends of the rafters gradually, the fame as they would be when in their pl-.aces‘ The fame 1s to be underflood of the other fide 1);- the ends are laid down 1n the fame manner as making a triangle of any three dimenfions. To fatisfy the curious, I have given the lines of this roof; but in praaice there is not the leafi- occafion for framing the [ides in winding ; for, infiead of the ridge line, the top made level at the wideft end of the roof, from the narrowefi end, which begins at a point; and by this means the (ides may be framed quite out of winding, which will have a. much better efl‘eét than any winding roof can have. . 2 PLATE 38 ‘ ‘5 THE THEORY AND PRACTICE PLATE xxxv. POLYGON ROOFS The methods of confiruéting regular polygons upon any given tide, are fhown at fig 4, 5, and 6, in the Geometry. . The 14¢an a polygon Barf being gram, and one (f the common 121113 flandmg upon that Plan, to find the dngle R111, and the Form of the Boards that wzll cover 2t when the [libs are fitted 2111., Inf 5 A let B be the given rib;_divide the curve into any number of equal parts, as four, and lay them at I) from a to 4, which bifeEts h b, the tide of the polygon, at right angles; through thefe points draw lines parallel to the tide b b of the polygon; at B and 1) make 1 c at D equal to c c, between B and C 2 (1 equal to d d, and 3 c equal to e e, &c. and through the points I), c, d, e, f, draw a curve line, which will be the form of the boarding , from the pointsg 0',f, c, d, c, draw lines at 1ight angles to g b, the bafe of the angle rib, and prick the rib C from D as they are marked by the letters, which is plain. N 16. The mete parts there are in this opeiation, the truer will it he, or any other of this nature. In the fame manner may the covering and angle ribs of any other polygon be found, whatever may be the form of the ribs, as is lhown at figures B and C. 70 find the Covt’rmg of afl1he1 Ical Dome. F10. D. Make a ci1cle z c h f, of the plan of the dome, and if it is a femi globe take, the fiieteh out of one quartet f01 the length of a board; make the length of K from a to 4 eqn‘al to it, and let the width 6 c, at the bottom, be any thing that the board will admit of; on the bafe c c, as a diameter, make a- femicircle; divide half the arch line into anv number of equal parts; draw the little lines 1 I, 2 2, 3 3, parallel to c c the bafe of the board, and divide the height into the fame number of equal parts; draw the ordinates acrofs; make 1 _l, 2 2, 3 3, upon .thefc ordinates, equal to l l, 2 2, 3 3, in the femi- circle at the bottom; acurve being drawn through thefe points, will be the mould K for the covering. . \ To covm a [phe1 ual Dome ahon the 1011 does not 1'Jofl1 1125 h as a Senzzczmle, but only a Sc frmmt. Si1ppofe l d to be the height of the dome at F, and the width of of the dome as befo1e, upon the cl1o1d Cf, with the pe1pendieular height I (l (lefcribe a fegment, which will be the fame as a ve1tical fcétiou {landing upon of; here is only one half of the fegment, which is fulliei-ent: draw the chord c (l; take c (1 equal to half the width of a board, whatever it 11 ill admit of; draw a (1 pm pendicular to cut the chord c d at I); take the firetch or circumference of the arch c d, and make the length of 1 f10111 a to 4 equal to take the double of a c, at F and make it the bal‘e of the board at I; take a: h from 1' , and let it upon the hate of 1, upon the middle of c c, from a to h,- and with the chord r c, and the height a. b, defciibe a t'egment upon the bottom of the board at I,- divide one half into any number of equal parts; likewife divide the height of the board I mto the fame number of equal parts, draw ordinates 111 both, and the board I will be completed, as in the fame manner is that of II, defcribed before PLATE w. a . ‘ ‘nmrs... ., Alli "m § OF CARI’EN'FRY. ~ 33 PLATE XXXVI. DOr’lIES. As the common method of finding the centres for defcribing the boards to cover a ho. rizontal dome will be found in praétice very inconvenient, for thofe boards which come near to the bottom; I {hall in this place (how how to remedy that inconvenience. To find (/16 Sweep (3f the, Boards at the Top. Fig. A. Divide round the circumference of the dome into equal parts at 1, 2, 3, 4, 5, 6, 8m. each divifion to the width of a board, making proper allowance for the camber of each hoard; draw a line through the points 1, 2, to meet the axis of the dome at x; on x, as a centre, with the radii .r l and x 2 defcribe the two concentric circles, , it Will form the board G; in the fame manner continue a line through the points 2 and 3 at C, to meet the axis in w; then‘w is the centre for the board C; proceed in the fame manner for the boards I), E, and F. , Now fuppofe F to be the laft board that you can conveniently find a centre, for want of room; on t its centre, and the radius t 5, make from t on the axis of the dome ta, equal to t5; through the points 5 and a draw the dotted line 5 b,‘ to cut the other fide of the circumference of the dome at b; from the points 6, 7, 8, 9, 10, ll, draw radial lines to b, to cut the axis of the dome at i, k, l, m, 71, o; alfo through the points 6, 7, 8, '9, 10, ll, draw the parallels 6 r, 7 d, 8 e, &c. then will each of thefe parallel lines be half the length of a chord line for each board; then take c 6 fromfig‘. A, which transfer to No. I, from c to 6 and 6 ; make the height ci, at No. 1, equal to 02', at fig. A; and draw the chords i6 and i6; then upon either point 6, as a centre with any radius, de- fcribe an arch ofa circle 0 l 2; divide it into two equal parts at l, and through the points 6 and I draw 6 g; bifeét i 6 in p; draw p q perpendicular; then i 6 is the length, and p q the height of the board G, which may be dcfcribed as infig. 4, plate 5, of the Geome— try. The reader mufi obferve, that the length of a board is of no confequence ('0 as the true fweep is got, which is all that is required. Proceed in the fame mamier with No. 2, by taking (1y fromfig. A, and place it at No. 2, on each tide of d at 7 and ’7, and take (1k, fromfig. A, and make d It" at‘No. '2, equal to It; draw the chords It 7 and Ir 7, and bifeét k ’7 at n; draw 7; a. perpendicular; upon the other extremity at '7, as a centre, de- fcribe an arch 0 l 2, and bifet‘l it atl, and through the points '7 and I draw the line 7 a, to cut the perpendicular na at a; but if the difiauce Ir 7 is too long for the length of a board, bifeét the arch 0 l at 6; through '1' and I) draw '7 t, and draw the little chord a ’7, and bifea; it at i; draw in perpendicular to interfe& ’7 4 at u; and with the chord 7 a and the height t u, delcribe the fegment H. In the fame manner may the next board I be found, and by this means you may bring the {weep of your board into the i'malleft compafs, without having any recourl'e to the centre. Suppofc it were required to draw a Tangent from 8 at 1V0. 3, wit/tout having recourfi: to the Centre.- Bifeét the arch 81 8 at l on 8, as a centre; with a radius 8 l, defcribe an arch e It; make 1 t equal to le; draw the tangent t8. Given three Points in the Circumference qf a Circle, to find (my Number of cguidi/iant Points beg/0nd (liq/i: that will be in the flmze Circumference. FIG. K. Suppofe the three points a, b, C, to be given to one of the extreme points a; join the other two points I) and c by the lines a I), and a c; with a radius a b, and the centre a, defcribe the arch of a circle 1) l 2 3; then take I) 1, and fet it from 1 to ‘2, and from 2 to 3; through the points 2 and 3, draw ad and a 6; then take I) c, put the foot of your compafs in c, and with the other foot crofs the line a d at (I; with the fame extent put the foot of your compafs in d, and Wltll the other foot crofs the line a c at e; in the fame manner you may proceed for any number of pomts whatever. PI \T o ,1 E 4o " THE THEORY AND enhance PLATE xxxvn. F10. A is the plan of an elliptiCal dome; B is the longeft feé‘tion, C the {hortel‘t fec- tion; at 1117, in B, and I7 [7 in C, \Ihows how to fquare the purlines, ('0 that one tide may be fair with the furface of the dome; 'the dotted lines from a 11 in B, and b [7 in C", {how how to get the length and Widthof the purline'infig. A ; but if the fides of the purline were made to {tand perpendicular over the plan, the {weep of it would be found in the fame manner as before, then it would require no more t‘ 1an half the {tufi' that the other would, and take only half the time in doing, which is a confidei able advantage. How to p717po7tzo7zate the 27 311116 Car [1 fo7 the Sky- [lg/1t, fl7 as 1t/11all anfwer to the Sur- face of the Dome. Draw the diagonal 1 l and k 777 In fit, A, and let It 1? or d f be the width, then kg or e f will be the t1 ue length of the cuib; becaul'e every feé‘cion parallel to the bafe will be Rioportional to the bafe of the dome : To jiml tlze Ribs fr17 tlzz's Dome. The ribs 111 this are got 111 the fame manne1 as the ribs for a niche, asdireéted 1n page - 34-, and it the reader underftands that, he mutt know this. 7 0 f 7111 1/11. Form 1yr a Board 10/7117er 171 any Place (f 7111's Dome, to be bent up to the C7 own. Suppole you would find a board over a I) c in the plan; divide D into three parts round 11,17, 1:, 11, and draw (11', b 1', c c, and (l c, to the centre at c; 'then take the triangle ado in I), and lay it down at a b c in G; then. draw the line 1: 1 l 1, &c. at right angles to a 6, and defcribe a rib G to the height of the dome, and the length to the perpendicular of the triangle (1 [7 1', and divide it into five equal. parts; lay them along the line 1 1 1, &c. in'II, and prick the mould H from the triangle a b 1-,. as the letters are marked. The board K will be found in the fame manner. Nola. In the prafiice, you are to divide one quarter of this dome into as many parts as you think the breadth of a board will contain, and the boards, when got out by this method, will lit to a 1 ery great exa&nefs: this 15 only into three, that the parts may be cleanly feeu to learne1s If the boards me got out f01 one quarter of this dome to the lines here laid down, the l)0a1(lS that me in the other thiee quarters will not require any other lines, for every boaide in. the firit quaiter will be a mould i01 three more boaids. 2 PLATE 17(er ‘37. p—.‘ Illniu‘h|.Anl.ItI.I¢ft 12/4 .n Ml, .I.-r,/r}~,»,/z-.7/IW,/- 7,2 /,,1117;:/,.,z.~m A Fm, .............................................. Plalzjé, FyB MN\ , 1, ., 3‘ ”INK“ or 'c \RPFN‘TRY. '41 PLATE XXXVIII. ' 0F DOMES WHL'Z‘ 7 PLACE!) OI’ER T1" E OPENINGS 0F SIX/1117‘- Ca SES. *— 0277: 7f the Ribs 7f 77 Dome being 3277227, 772171 7176 Plan of 1126‘ 01126222223 7f 72 Sf7772‘c77/7 70/777212 7's flame, and 7727 067a ,7027 Curb. 772‘ 7176 T7212 fo2 77 Sky- 113177; to find (126 Ribs and 2176 C772 77 on 677712 Side 73* 7116 0226211273 0]" 1177' Stair cafe, 77112627: 2177‘ Foot 73f 7176 12112.1 co'més, jb 212727 P7727 75f t/ze Domefnall be 7722 oetagon F inf/1’7, 77326677b16 to 2176 C772 b. FIG. A. Let B be the given rib; take anV number of perpendiculzn ordinates to its'bafc atpleaf111e;fromthe points 77, c, 6, .'3,2, I, where they 111te1fe8t its bal'e, d1aw parallel lines to the Iides of the 0111b, 1eturni11rr round each diagonal, if there' 15 1110173 than one till it cut the bafe of the angle 1ib I), at the points a, 7‘, 6, 3,1,1, d1a11 the ordinates oI' I), and p1ick it 110111 13,11ill be the angle1ib; and at the points 72,0 b, 2', 1, at C, upon the fide of the opening of the Itai1cafe, than the perpendiculai ordinates, and prick C from 12’, agreeable to the letters; then the curve ‘C will be the t1 117, place for the foot of the 1ibs upon the fide of the ftahcafe, and the 11a1t that lies in the middle is a I't1aight line parallel to the horizon. »T/2c 7732776771 Seéiw'n 7f 77 fe2227'c2'2'c771772‘1)o2276 7172 7277312 its Centre being given, 7126 Open- 7'27g of £126 S7777'2 7377/6 being 77 S7177772 e as bquc, to find 7127: Curve D on 7177: S1716 7y” 717: Stuil c77j6fo2 the Foot 73f the [137725, jb t/zat 27/]27721 flm'j/z to a cz'rcnlm Curb at 71273 Top. 011 the Iide of the {Iaircafe 1222, as a diametei, defcribe a femieircle; D will be the true place for the foot of the ribs; this is evident, for every I'eé’tion of a femi— globe, at right angles to its bafe, is a femiciicle, and this' IS the fame thing if t1 1111 confidered. N 7277’. All the ribs of this dome a1e cut by the rib at C, as explained by the perpen- dicular lines , draw round the cent1e 72, from the points of each bracket, at c 71 6 2", to the points 17' 2 12 3; f1 om thefe points draw ue1pend1cular dotted lines, and thefe will Ihow‘ what length each bracket mul't ban 6 according to its place. T126 7262 727721 Seéh'on q, 77 Segment Dome 1277/“ 273 71227277317 its C622!) 6 being given, the Plan Qf [/26 Opening 72f t/76 Staz'rcajé being 721177 S711777272, as bque, 2'0 f 2271 7176 Sec-- t7'on 77127227 6776/2 Side of 2176 Sta2'2‘7‘77 6 for {/16 Foot qf the 112173, to fini/b v to 77 circular Curb at the Top. Let the feé'tion I) acrol's the angle be gi1e11, whoI'e centre is 1, and the difiauce of the centre from the chord 1c 1,- bil'cét the Iide of the Itaircafe by the line b 12, at 1ight angles at the point 7'; from 7' make 7' b equal to 117; with a radius b g, or b 7', dcferibe the fegn ment 7‘; mg will be the true place of the foot of the ribs; all the other lefl'er ribs are cut' from the angle rib I): all this is evident from the I'eé'tions of a globe, which is already defcribed in the Geometry. FIG. D is of the fame nature as the others, having an ogee top; the feaion I" is traced from E. G 2 PLATE 42 THE THEORY AND PRACTICE or CARPENTRY. PLATE XXXlX. _ FIG. A is the plan of an elliptical domical fky-light over a fialrcafe; B and C are the fe&ions, which {hows how to place your ribs. How to proportionate the Length of the zit/hie Curb to any Width given. I Proceed as directed in page 40 for-an elliptical dome, that will determine the true length to the width. How to- proportionate the cz'rczmzfcrihz’ng E [Mg/1’s, to pq/s through the zlngles at a, b, c, and d, to have the fame Proportion as a b, and b c, the Sides of the Staz‘rcufi’. Proceed asidireaed in fig. 5, plate 6, in the Geometry. To dcfcrz'he the Iii/is. The rib over n to the centre of the trammel in fig A , is a given quarter of a circle, as is them: at I", and of courfe all the other ribs mutt come to the fame height with it. Sup'pofe it was required to find a rib over (I p, you‘mufi take the full extent from (I to the centre, and det'cribe the quarter of an ellipfis D; then the part over‘dp will be as much of it as is wanted: in the fame manner E will be defuriherl, and the part over to is what is wanted of this rib; the fame lettcrs‘are marked upon the bales of I) and E, as they are in the plan, fig. A. Every other rib is defcribed in the fame manner; To find the Seflz'onson each Side q” the Stairca/e for the Foot of the Bibs toflandupom Defcribe‘the femicircle C, to c b, the width of the opening of the fiaircafe, which will give the bottom of the ribs on that tide; and defcribe a quarter of the el-lipfis B, for the bottom of the ribs on the other tide, to the fame height as C. This method depends on this principle, that all the parallel feé‘tions of a fpheroid are fimilar figures: therefore a vertical feetion {tan-ding upon a b, will be limilar to a vertical feétion pafling through its centre; both will be fimilar ellipfes: but a b is an ordinate to the conjugate axis, and be is an ordinate to the tranfverfe of the circumfcribing ellipfis; j" by conflrué‘tion half the length of the parallelogram is to half the length of the cllipfis, as half the width of the parallelogram is to half the width of the ellipfis, and a fpheroid may be {uppofed to be generated by the revolution of a femi-ellipfis about its axis; hence it follows, that all feétions of a fpheroid parallel to the axis are fimilar figures, confen quentl-y the feaion B is fimilar to the circumfcribing ellipfis of the ground plan, INTRO« 1’1/5904' l/n’Jrf nibvv-f: J/rresglznguj'fl ZVn/vm . INTRODUCTION TO PRACTICAL CARPENTRY. OF THE COMPARATIVE STRENGTH 0F TIMBER. PROPOSITION I. THE {trengths of the different pieces of timber, each of the fame length and thicknefs, are in proportion to the fquare of the depth; but if the thicknefs is to be confidered along with the depth, then the firengths will be in proportion to the fquare of the depth, multiplied into the thicknefs ; and if all the three are taken jointly, then the weights that will break each will be in proportion to the fquare of the depth, multiplied into the thick- nefs, and divided by the length: this is proved by the'doétrine of mechanics. Hence a true rule will appear for proportioning the {trength of timbers to one another. RULE. 31110sz the fquare of the depth (J each piece into its thichnefs; and each produ'c? being divided by their refireflive lengths, will give the proportional flrength If 6’40”- EXAMPLE. Suppofe three pieces of timber,‘of the following dimenfions: The firfl, 6 inches deep, 3 inches thick, and 12 feet long. ‘7 The fecond, 5 inches deep, 4 inches thick, and 8 feet long, » The third, 9 inches deep, 8 inches thick, and 15 feet long. The comparative weight that will break each piece is required, OPERATIONS, 144 . INTRODUCTION TO ' * OPERATIONS. 1111-11. , Second. , Third: 6 deep \ ‘ 5 deep 9 deep 6 ~ 5 9 30 25 81 3 thick _4- thick 8 thick Length 12)1os Length 8)1oo Length ‘15)643013 and a. fifth “—- —- _. _ 50 ' 9 12' and a half -—-—— 43 45 3 Therefore the weights thet will b1ea11 each are nearly in proportion to the numbersQ 12, and 43, leaving out the fiaétions, in which you will obferve, that the number 43 is almofl: 5 times the numbe1 9, therefore the thud piece of timbe1 will almoft bear 5 times as much 11e1ght as the firlt; and the lccond piece nearly once and a. third the weight of the firft piece, becaufe the number 12 is once and a thiid greate1 than the number 9. The timber is fixppofed to be every where of the {time texture, otherwife thefe calcu- lations cannot hold true. PROPOSITION II. Given the length, bieadth, and depth of a piece of timber, to find the depth of ano— ther piece whole length and breadth 9.1 e gi1 cu, ft) that it (hall been the fame weight as the firit piece, or any number of times more. RULE. Multiply the fquare of the depth of the firil piece into its breadth, and divide that pro- duct by its length: multiply, the quotient by’the number of times as you would have the other piece to carry more weight than the firf’r, and multiply that by the length of the laft piece, and divide it by its width; out of this left quotient extract the fquare root, which is the depth required. EXAMPLE I. Suppofe a piece of timber 12 feet long, 6 inches deep, 4 incl es thick; another piece 9.0 feet long, 5 inches thick, requireth Its depth, 11) that it lhall hem twice the 11e10ht of the firlt piece. 6 d eep PRACTICAL 6 deep 6 36- 4t r2)144 12 2 times- 24- 20 length 5)480 CARPENTRY. Proof. ‘9.7 9.7 45‘ 67.9 873 94.09 1.9 1 remainder added 96.00 5 —-—- 20)480 ‘ 2:12 96(9.7, or 9.8,. nearly for the depth 81 187)1500 1309 19!. EXAMPLE II. Suppofe a piece of timber 14 feet long, 8 inches deep, 3 inches thick; requireth the depth of another piece 18 feet long, 4 inches thick, f0 that the laft piece {hall bear: five times as much weight as the firfi. 8. 64 , 3, hflf’UlQZ 27.4, &c. 5 times ] 3"! 9 half the length 4)1233 308.25(17.5 the depth nearly 1 27)208( J89 345L1925, &c. As the length of both pieces of timber is divifible by the number 2, therefore half the length of each is ufed inftead of the whole; the anfwer will be the fame. PROPOSITION- 45 . INTRODUCTION TO PROPOSITIGN III. Given the length, breadth, and depth of a piece of timber; to find the breadth of ano- ther piece whofe length and depth is given, fo that the left piece fhall bear the fame weight as the firfl; piece, or any number of times mere. RU LE ' Multiply the fquare of the depth of the firl’c piece into its thicknefs; that divided by its length, multiply the quotient by the number of times as you would have the laft piece hear more than the firlt; that being multiplied by the length of the lalt piece, and divided by the fquare of its depth, this lafi quotient will be the breadth required. EXAMPLE I. Given a piece of timber 12 feet long, 6 inches deep, 4 inches thick; and another piece 16 feet long, 8 inches deep, requireth the thicknefs, f0 that it {hall bear mice as much weight as the firlt piece. Or this, at full length. ' 6 6 depth of_ the firlt piece 6 6 36 36 , 4 4 thickncfs of the firft piece 3) 144 Length 12)144 48 l 2 2 2 by the number of times firongcr 96 24 '4 16 length of the lal‘t piece 8)384- 144 ‘24- 8) 48 8)384 6 thicknefs. ’ -—-——— ‘ s) 48 6 thicknefs. EXAMPLE PRACTICAL CARPENTRY. 47 EXAMPLE II. Given a piece of timber 12 feet long, 5 inches deep, 3 inches thick; and another piece 14 feet long, 6 inches deep , requireth the thicknefs, [0 that the Ialt piece may bear four times as much weight as the firft piece. 25.00 14 25 6)350 e) 58 266 9788 PROPOSITION IV. If the {trefs does not lie in the middleof the timber, but nearer to one end than therothcr, the firength in the middle will be to the {trength in any other part of the tim- ber, as 1 divided by the fquare of half the length is to 1 divided by the rectangle of the two fegments, which are parted by the weight. EXAMPLE I. Suppofe a piece of timber 20 feet long, the depth and width is immaterial; ifuppofe the {trefs or Weight to lie five feet difiant from one of its ends, confequently from the other . . l 1 , l 1 end 15 feet, then the abete proportwn Will be————— 10x 10 "ml-(36 3321-51.. E as the ftrength 100 100 1, at five feet from the end IS to the {hength at the middle, or 10 feet, or 215—100 = 1' .75 ~—-= 1 3—, Hence it appears, that a piece of timber 20 feet long 1s one third fironger at 5 feet dif« tance from the bearing, than it is in the middle, which is. 10 feet, when cut in the above proportion , 1! EXAMPLE :58 INTRODUCTION TO EXAMPLE 1!. Suppofe a piece of timber 30 feet long , let the weight be applied 4 feet difiant from one end, or more propedy f1 om the place where it takes its bearing, then f1 cm the other end 1 1 . l l i 225 y 1. - 5 ° t ——-’——. = -—-— -——-——- = __._1 ‘ o—. it “ill be 26 feet, and the middle 1s 1 feet, hen 15x 15 2%. 4x26 104 01 as 225. .1 ' 9'25 ° 17 or near] 26 I ' i " '161" ‘ 104 y ' Hence it appears, that a piece of timber 30 feet long will bear double the weight, and one fixth meie, at four feet distance fiom one end, than it will do 1n the middle, which is 15 feet diitant. EXAMPLE III. Allowing that 266 pounds will break a beam 26 inches long, reqn-ireth the weight that will break the fame beam when it lies at 5 inches from either end; then the diltance- to the other end is 21 inches; 21 x 5: 105, the half of 26 inches is I3.'.13x‘13) =169; therefore the {trength at the middle of the piece is to the {trength at 5 inches 169 169196 I O . rt, . from the end, as —169 , , ——-5 or as 1,—— 105 the propo ion is Rated thus 1b. 169 . . 1 :55 ': 266 : to the we1ght required, 169 ' 9394 1596 266 105)44954(428 420 295 210 854 840 .14 From this calculation it appears, that rather more than 428 pounds will break the beam at 5 inches difiance from one of its ends, if 266 pounds will break the fame beam in the middle. By limilar piopolitions the fcantlings of any timber may be computed, fo that they {hall l'ultaiii any given weight; for if the weight one piece will fufiain be known, with its a PRACTICAL CARPENTRY. 49 its dimenfions, the weight that another piece will ‘fufiain, of any given dimenfions, may alfo be computed. The reader muft obferve, that although the foregoing rules are ma. . thematically true, yet it is impoflible to account for knots, crofs-grained wood, 8L0. fuch pieces being not {0 firong asthofe which are ftraight in the grain; and if care is. not taken in choofing the timber for a building, {0 that the grain of the timbers run nearly equal to one another, all rules which can'be laid down will be baffled, and confequently all rules » for jufi; proportion will be ufelefs in refpeét to its firength. It will be impoliible, how- ever, to efiimate the {trength of timbei fit for any building, or to have any true know. ledge of its proportions, without fome rule; as without a 1ule every thing mnft be done by me1e conjecture. ~ Timber is much weakened by its own weight, except it {land perpendicular, which will be fliown in the following problems; if a mortice is to be cut in the fide of a piece of timber, it will be much lefs weakened ’when out near‘ thevtop, than it will be if out at the bottom, provided the tenon is drove hard in to fill up the mortice. The bending of timber will be nearly in proportion to the weight that is laid 011 it; no beam ought to he trufied for any long time with-above one-third or one—fourth part of the weight it will abfolutely carry; for experiment moves, that a far lel's weight will break a piece of timber when hung to it fo1 any confiderable time, than what IS fufiis eicnt‘ to break it when firi’c applied. PROBLEM I. 1 Having the length and weight of a beam that can juft fupport a given weight, to find the length of another beam of the fame fcantling, that [halljult break with its own weight: Let Z =' the length of the firl‘t beam, L =the length of the fecond ; a =the weight of the firl’c beam, w:the additional weight that will break it. And becaufe the weights that will break beams of the fame fcantling are reciprocally as their lengths, ~ w+a x l therefore—:— : 3L- :2 w + g- : IV: the weight that will break the greater beam; , because w + g is the whole weight that will break the lesser beam. But the weights of beams of the fame fcantling are to one another as their lengths: Whence, l: L: :g— 1%: W half the weight of the g1eater beam ~ Now the beam can-not break by its own weight, unlefs the weight of the beam be equal to the weight that will break it: w+a x l . La 7; __ 2w+axl W'herefore, 22-5— : T” .5717“ L2a==°w+ax I? '. a : 2w+a :: l2 :L‘, confcquently ¢L= =L=the length of the beam that , 'uft fufiain its ewn weinht. m“ D a 2 ' PROBLEM \ so INTRODUCTION TO PROBLEM II. ' Having the Weight of a beam that can jufi fupport a given weightin the middle, to find the depth of another beam fimilar to the lonuer, to that it lhall jutt fupport 1ts own weight Let d~ _. the depth of the hilt beam, - 2 = the depth of the second, a— .. the weight of the tint beam , w = the additional \\ eight that will b1eal; the firft beam; 21v +a 2 then will w +— or := the whole weight that will break the leiTer beam. And becaule the weights that will break fimilar beams are as the fquares of their lengths}, A ~i~+Il 2172 xw+m2 a ' 2 : . ‘- z: : -—-——~ = l . . d z 2 g d" V the weights of limilar beams are as the cubes of their correfponding‘fides :1 3 . 3 .. 2 . (Leis. Henced .3: “2 . 2‘13 ——W _ a x3 __ 2x2w+xzm —‘ 2d: a x: 2m -. a : a+2w :: d : .7: = the depth required. As the weight of the lefi‘er‘beam is to the weight of the lefl'er beam together with the‘ additional weight; fo is the depth of the lefl'er beam, to the depth of the greater beam. JVote. Any other correfponding fides will anfwer the fame purpofe, for they are all; proportional to one another.‘ N) EXAMPLE. Suppofe a beam whole weight is one pound, and its length IO‘feet, to carry a weight of 399.5- pounds, requireth the length of a beam fimilar to the former, of the fame matter, f0 that it {hall break with its own-weight: then a = l and a+2w=800> d: 10‘ Then by the lalt problem it will be 1 :' 800 :: IO 10- 8000 = x'for the length of a. beam that will‘break by its own weight;— PROBLEM‘ PRACTICAL CARPENTRY. 1 ‘W 51 PROBLEM III. . (I The Weight and length of a piece of timber being given, and the additional weight that will break it, to find the length of a piece of timber fimilar to the formei, fo that this hit piece of timber {hall be the {trongeft polfible: Put 1 2 the length of the piece given, 71) :: half its weight, 7V__ — the weight that will break it ; - _the length required. Then, becaufe the weights that will break fimilar pieces of timber are in proportion to the fquares of their lengths, l“ : x"‘. :: W'+w: and becaufe the weights of fimil'ar beams are as the cubes of ' their lengths, or any other , eorrefponding (ides,- 2 2 W : the whole weight that breaks the beam; , 3 then [3 : x3 : :w : ”If the weight of’ the beam ;' W w” tax” wx" confequently-——-——;——-— 7—3 is the weight that bieaks the beam: a max-a imam- 5 therefore its fluxion is- nothing, 3 w .13" a: l that is, 2 _W x i1 + 2 71) xi— :: nothing, 27114220251331; 2 W+ 2111 3:11 Hence it appears from the foregoing problems, that large timber 1s weakened in a. _ much g1 eater proportion than fmall timber, even in fimilar pieces, therefore a. proper allowance mutt be made for the weight of the pieces, as I {hall here {how by an’example.‘ Suppofe a beam 12 feet long and a foot fquare, whofe weight is 3 hundred weight, to be capable of fupporting 20 hundred weight, what weight will a- beam. 20 feet long, 15 inches deep, and 12 thick, be able to fupport? hence,:r x21 X l 2 inches fquare 1 5 l 2 1 5 144. '75 12 1 5 1 2) 1728 - 225 ._._. 12' 1‘44- 2.0)270.o 135» But 52 INTRODUC'DION; To. But the weights ‘of both beams areas their folid contents: therefore, 12 inches fquare 15 deep 12 ‘ V 12- wide 5 izi4 * 186i 144- inches_:_12 feet long 24-0 length in inches 5'76 - 7200. . 5'76 ‘ l 360 14-4- - . . 4.3200 folid contents of the 2d beam . 20736-folid—eontents of‘ the lit beam . ‘ 20736:43200:: 3 144::135_::21.5 liyprop; i. 3 , 21.5 » ' . --—- cwt. lb. _.__... 20736)129600(6. . 28:the weight of G7. 5 1 24416 the 2d’beam 135 . 270 . . 5184 ——-— 112 i2)2902.5 10368; 12)241.875 5184- —~ 5184 20315625.. .5 . - 112 20736)580608(28 41472 31250 —- 15525- 165888 . 15625 165888 --—-- —-———-—- 17,50000 . . . . .. 16. 30 5 --I-n~ 8,0 21’ cwt. '56 lb. is the weight that will break the full: beam, and 20 cwt._17 lb. 8 02. the weight that will break the fecond beam; dedué}. out of thefe half their own weight. 20::17::8 3:14:20 half 1 7 3..8 Now 20 cwt. is the additional weight that will break the firfl: beam; and 17 cwt. 3 lb. 8 oz. the weight that will break the fecond: in which the reader will obfcrve, that 17::3::8 has a much lefs proportion to 20, than 20 cwt. 17 lb. 8 oz. has to 21 2: 56. From thefe examples the reader may feethata proper allowance ought to he made for all horizon— tal beams; that is, half the weights of beams ought to be deduéted out of the whole weight that they will carry, and that will give the weight that each piece will bear. 2 If' PRACTICAL ‘CARPENTRY. 5:; If feveral pieces of timber of the fame fcantling and length are applied One above another, and fupportcd by props at each end, they will be no {troiiger than if they were laid fide by fide; or this, which is the fame thing, the pieces that are applied one above another are no {tronger than one fingle piece whofe width is the width of the feveral pieces colleEted into one, and its‘depth the depth of one of the pieces; it is therefore ufelefs to cut a piece of timber lengthways, and apply the pieces fo cut one above another, for thefe pieces are not to firong as before, even if bolted. , - EXAMPLE. . Suppofe a girder 16 inches. deep, 12 inches thick, the length isii'nmaterial, and let the depth be cut lengthways in two equal pieces; then will each piece be 8 inches deep», and 12 inches thick. Now, according to the rule of preportioniiig timber, the fquare of 16 inches, that is, the depth before it was cut, is 256, and the fquare of 8 inches is 64, but twice 64 is only 128, therefore it appears that the two pieces applied one above another is but half the {trengthof the folid piece, becaufe 256 is double 128.. If a girder be cut le‘ngthways ina perpendiculardireétion, the ends turned contrary, and then bolted together, it will be but very little flronger than before it was cut; for although the ends being turned give to the girder an equal firength throughout, yet wherever a bolt is, there the girder will be weaker, and I am very doubtful whether it will be any fironger for this pi ocefs of fawing and bolting; and I fay this from expeiience. If there are two pieces of timber of an equal feantling (Pl. 52, “73511), the one lying horizontal, and the other inclined, the horizontal piece being fupported at the points 6 aiidf, and the inclined piece at c and (I, perpendicularly over 6 and f, according to the principles of mechanics, thefe pieces will be equally fireng. But, to reafon a little on this matter, let it be confidered, that although the inclined piece D is longer, yet the weight has lefs efi‘eét upon it when placed in the middle, than the weight at It has upon the hori- zontal piece C, the weights being the fame; it is therefore rcafonable to. conclude, that in thefe petitions the one “ill bear equal to the other. The foregoing iules will be found of excellent ufe when timbei is wanted to fuppmt a great weight, for, by knowing the fuperincumbent weight, the iiiength may be computed to a great degree of exaétnefs, 10 that it {hall be able to iupport the weight required. The confequence is as bad when there is too much timber, as when there is too lltilt , for nothing is more requilite than a jult proportion throughout the whole building, {'0 that the ftrength of eveiy pait {hall always be in preporiion to the ltrefs , {01 when tlieie is more {tiength given to fume pieces than others, it cucumbers the building, and confe— quently the foundations are lefs capable of l‘upporting the fiiperftruéture. No judicious perfon, who has the care of conducting buildings, fiiould rely on tables of fcaiitiings, fucli as are commonly in books; for example, in fiery pofts the i'caiitlings, according to feveral authors, are as follows: For 9 feet high 6 inches fquare. 8 12-”- l5-—-— 10 New, 51 ‘ INTRODUCTION TO PRACTICAL CARPENTRY. New, according to this table, the {headings are increafed in proportion to the height; but there is no propriety in this, for each of thefe will bear weight in proportion to the numbers ‘9, 16, 25, and 36,,that is, in proportion to the fquare of their heights, 36 being 4 times .9 ; therefore the piece that is 18 feet long, will bear four times as much weight as that piece which is 9 feet long; but the 9 feet piece may have a much greater weight to carry than an 18 feet piece, fuppofe double: in this cafe it mutt be near 12 inches fquare infiead of 6. The fame is alfo to be obferved in breafi-fummers, and in floors where they are wanted to fnpport a great weight ; but in common buildings, where there are onlv cnfiomary weights to fupport, the common tables for floors will be near enough for praétice. To conclude the fubieét, it may be proper to notice the following obfervations which feveial authors havejudiciouflv made, viz. that 1n all timber there IS moiftuie, wherefore all bearing timber ought to have a moderate camber or roundnefs on the upper (Me, for till that moiltme is dried out the timber will fwag with its own weight. But then oblerve, that it is belt to trufs girde1s when they are f1ell1 fawn out, for by their d1ying and thinking, the t1 ufl'es become more and more tight. That all beams or ties be cut, or in framing forced to a roundnefs, fuch as an inch in twenty feet in length, and that principal rafters alfo be cut or forced in framing, as before; becaufe all joifts, though ever ('0 well framed, by the {hrinking of the timber and weight of the covering will fwag, fometimes f0 much as not only to be vifible, but to offend the eye: by this precaution the trufs will always appear well. > Likewife oblei ve, that all cafe bays either 1n floors 01 roofs do not exceed twelve feet if poliible, that 15, do not .let yourjoifts 1n floors exceed twelve feet, nor your pnrlinq. in roofs, 810. but rather let their hearing be eight, nine, or ten feet: this fhould be re- ;garded in forming the plan. Alfo, in bridging floors, do not place your binding or {trong joifis above three, four, or five feet apart, and that your bridging or common joifis are not above ten or twelve inches apart, that is, between one joifl and another. Alfo, in fitting down tie beams upon the wall plates, never to make your cooking too large, nor yet too near the outfide of the wall plate, for the grain of the wood being cut acrofs 111 the tie beam, the piece that remains upon its end will be apt to lplit off, but keeping it near the infide will tend to fecure it. See plate 32, at the bottom, where the dimenfions are figured. Likewife obferve, never tomake double tenons for hearing ufes, fuch as binding joifis, common ioifis, or pnrlines; for, in the firft place, it very much 11 eakens whatever you home it into, and 111 the fecond place it is a rarity to have a diaug ht 111 both tenons, that is, to diaw both joints clofe; for the pin in pafling through both tenons, if there IS a draught in each, will bend 11') much, that, unlefs it be as tough as wire, it muft needs bieak 1n d1iving, and conlequently do more hurt than good. Roofs will be much {ironger if the purlines are notched above the pi 111c1pal rafters, than if they aie hamed into the tide of the principals; f01 by this means, when any weight is applied in the middle of the purline it cannot bend, being confined by the other rollers; and if it do, the (ides of the other rafters mutt needs bend along with it, confe. quenily it has the ftrength of all the other rafters lideways added to it. PRACTICAL f; ., ,. v: ‘ ;. ' t . ' Mlfivflai ‘3 3332:“! \ ' : P7512? ~40. ' \ 11,494.- m Arm)“ Jun-mpg gyzwamm . f’lm‘t 41. 1°11? a; My Art (In-M; Jinn-fl 1/192 é’l’fl’tflwl‘m - PRACTICAL CARPENTRY. PLATE XL. A“ and B {hows the method of trufiing girders, as is ufed by the greateft matters at 'thisitimc. , ~ Cis a horizontal i'eétion of B. I) is a feétion of the butment, by cutting acrofs a 3 in A. E and F {hows the two fides of the 'king-bolt,- at c in A, which is made with a wedge. way upon the top, to that it may force out the trufl‘es upon the butments. To tighten the Gz'rders. Your trufl'es ought to he let clofe in to the fides of the girder, about an inch and ahalf rm each fide, and the head of your king—bolt ought to be greafed, [0 that it may flide freely paft the ends of the trufl'es‘; firft [crew your girder clofe fideways, then proceed to turn the nut of the king-bolt, and another perfon to hit the-head at c of the king, with a mallet, which will make it {tart every time it is hit, and give freih eafe at every turn-9 ing of the nut, fo that you may camber the girder to any degree that you {hall have occafiou for, but generally not above an inch in twenty feet. _ 1Vote. The feétions I), E, and F, are to one eighth part of the real fize. PLATE XLL This contains the melt fimple confirué‘tion of roofs. FIG. A is calculated for a {mall building; at one end of the collar-beam is the Car. penters’ boafi, what they term a dove—tail tenon; but I think rather a rule joint, as it is Worked out to a‘centrc. This roof will do for an extent .of 20 or 25 feet. FIG. B is a trufs for a roof, the purlines to be notched upon the principal rafters, as will he dcfcribed in the following plates of ledgment roofs: this roof may- be well calcu.~ lzited for an extent of 30 or 35 feet, the height one fourth of the fpan for flate cover- ing. I . Fm. C is a fimple confiruétion of a roof, for the fegment finiih of a dome, which will nnfwer to any of the above extents. I PLATE, 56 r PRACTICAL CARPENTRY. PLATE. XLH. - FIG. .4 is a roof for the purlines to be framed in, and the common rafters to come fair with the principals. FIG. B. is a 1oof calculated for a gleater extent than any of the foregoing roofs, and may well extend :30 01 60 feet. Here likewifeis 11101111 the connexion. of the roof 1n the walls. - _ FIG. C is a roof filpported by two queens, inflead of a king, to give room for a puf- fage or any' other conveniency in the roof. ' PLATE. XLIII. i r This roof is‘ calculated for a fpan of {eventy or eighty feet. You will obfeive in this, and the foregoing roofs, that the t1 miles are the fame in num- ber as the pmlines which they have to fupport; fo1 how abfuul it is to give a roof more ftien'gth than neceflary! but, on the other hand, the confequences will be dangerous 1f ‘ too weak. FIG: A is a defign of a roof for a theatre, which may extend from 80 to 90 feet. As it happens frequently in building thatwalls run acrofs the roof, in fuch cafes there will be little Oceafion for trulfing the roof, then the purlines maybe trnfl'ed, which will fave one or two pair of principals, which is a confiderable advantage; FIG. B 15 a roof of this kind, which {hows the ends of the p111lines,‘ and C fhows 11011: to trufs the purline. D, E, and F, am the methods of fearfing timber. PLATE XLIV. is explained on the Plate. PLATE XLV. FIG. 11 is a curb roof, with a door in the middle of the partition; the beam (1 I) to run quite ac1ofs the pole plate, to be tenoned into the beam at a and b,- the fiery poft a c and b d likewife to be let In with a {mall tenon to the beam, as it fhould projeét about an inch on each fide of the beam, to take the {honlder ot the pole plate, 11 inch 11 ill dif. charge the weight from the tenon. FIG. B 18 a roof calculated f01 two rooms. FIG. C' [hows the method of framing a bridge floor, PLATE . _..... ... -m Plate 42 . Fay. A. J’z/éldas Mr Arr M§rzdufln¢29 1.792 ét'EWf‘llt’A‘LI/z . . ‘. '\v. \ _ ' f ', ‘ ‘ - ‘, MW at Kw‘fi‘beh'Aa >«“~««V“~‘1““i‘ I ’ ' | ~ ~ Plate 48. \ ‘ ¥ , 1:4! 1% “N; R 3 L_' L' 124D “4 ‘u’ 1 W531}. ‘ £ 4H, .—1 ‘ ' WRQE i U V fin. ’ 4 fi//?/n‘ flair/L 47/1777? lIdfl€9~7 02 {1 P41 71/10/30” . s; I . \ ' ' t. L. xv .,-_.¢...- Hwy-bm\ q ‘ ’\ « ~ _‘ ' I ‘.._"‘ ‘ ‘v * L “v ~ n,;-a\..,-.'.....‘, .. . 4“,: ““me- ~ .1 . ‘ ' ”M‘s... {‘r‘ ’i‘ .~' \v ,....«.,'. ”H‘. AQ‘gV: ‘ \ L \‘\ \‘ _ pfi.u¢\nmy;h ‘ u “5,.” - ‘ wfi‘ ‘ ‘ ‘ 1 \ . I. , l _ . , .. . . lye/1:44.. . , la" a “.‘t ()1 /(*Z111!a'/1 ll‘l/ll f/Iw/uuw/u’f'n/nw (‘t‘l'I’lY’l/lfl,’/II’ (’w‘nz/ /}‘mu 137’ /i '1(’ /;v/‘ ,5 ‘ 41 1300]“ /})2‘_ a TZH’ah-w f/IL' (”(‘fl’li/ 13;.01n 70!?) JO (:Lff 11 {/m/q/z .J(,'/‘ a I’tu'é‘z'flo” Hr L _ ‘ K 1 ME H” 1*) 4 fi\\ /§¢? §\\\\//C; 1/ X X »/ \x v?“ N f’ \‘ fl ' W x . ‘_ , __ ‘47 awn/gun; {/1/ 1147‘ (/(‘/'('(/.1 ( ’1'/.r'_!.2,//'./2./1 /,’.l:';'//M/u)// /'r" u nuaww- 10%." “a” 3M it \3“ V": ‘1‘." ‘ Play 457. >7 w/i .1511: £59. Izqe (fa/1W2 #1261»; . s‘Mt’Afl' (It rjya/Z’: 6‘0“ l‘ «S? 2. 448.1%». .'.§«9 _ Mm -/7 ‘ ‘ (‘\'/;‘/l/fl 77v” fl e 7 ffl (W) /(’I/’“ Jr? 73 . I ‘ Ply??? 48. ‘ 29/16,? ac daft! 1/1}?i’S-tl.ln€9-llz¢2 fvPJF’r/m/npu . _/)/(I/(‘ [V A _ 142/ A .; 1-7;, 1; 1%!” (17/ //(c [v.1 ‘e/v PRACTICAL CARPEN'I‘ltY. , 57 PLATE XLVI. FIG. {I is the defign of an M roof, which is ul‘eful in fome cafes where the {pan is great, and no wall between, and the roof is required not to/appear of a great height; but this fe-ldom happens in practice, for if there is any wall between the external walls, thereof}; are in general made double, as is lhown at figures 8, C, and D. PLATE XLVII. FIG. A. is a defign for a church roof, the extent marked on the plate. FIG. B. is a defign of the fame kind, but may be applied to an extent much greater.‘ Thefe two roofs, when finilhed, will be the fame in every refpeét withthe Welfh groin dcfcribed in plate 23: as the manner there fhown of fixing the ribs will not be different in this, I refer the reader to the defCIiption of that plate. P‘.IG C' 18 another delign for a church roof, where the ceiling over the galleries is to? finilh level. PLATE XLVIII. FIG. A is a ilefign for adomical roof; B {hows the manner of framing the curb for it to {land upon, the feétion of the curb being alfo fhown upon the bottom offig A PLATE XLIX. FIG. A is another delign for a domical roof; the bottom of it is nude into a very nar. row compafs, in order to gain room within the dome. FIGURES B and C are deligns for circular and elliptical trufl‘es for bridges, &c. Thefe’ {rull‘es may alfo be applied to roofs where there is no cavity wanting within. PLATE L. FIG. A is a delign for :1 Rory pelt and breal’c-fummers. FIG. B is a delign for a bridge. C is a feé’tion across. I) is part of the plan, which alto {hows the manner of fixing the piles. E {hows half the plan of the bridgings. I 2 PART PART, II. Of the Theory and. Practice of Joinery; ~. PRINCIPLES - 0F HAND—RAILS FOR STAIRCAiS'ES. AM now going to enter upon a fubjeét, which wants more particularly to be laid down by new methods, than any of the others which I have before touched upon; as the me- thods laid down hyall authors on the {object are grounded upon'errone'ous principles, with- out any proper foundation, and not confideriug it truly according to its nature. For it is evident, that if a cylinder is any how cut, but not parallel to the bafe, that fefiion will he an ellipfis; and if the Cylinder is perpendicular, the fcétion will alfohe perpendicular to the hate, or plumb from every point in it to every correfpondiug point in the bafe or plan: and likewil'e, if you ‘fuppole auv other ihéfion to be out under the former, and parallel to it, then‘ the ellipfis under will be the fame as that abqve; and therefore I fay, if a. mould is made to this elliptis, let it be drawn upon the upper lide of a plain piece of wood, of a pa1allel thickueiIs , then it the bevel where the ellipfis cuts the cylinder be~ applied to either of the extremes upon the edge, and the fame mould being. applied‘fr'omv the rake of that line to the under tide, theulet the plank be cut out between the rake. of the upper and under lines; and' if this is taken into confideration, it will appear that hand-mils are the feétions of cylinders, and confequently the rules for drawing them will he the fame as thofe for finding the feétion of a cylinder, which has been explained ‘In —tl1e Geometry, fee plate 9 and: its explanation; or if they are made in fev eral different pieces, they will ltill be tome po1tion of a cylinder, which are. all explained 1n the plate {hefow mentioned. PLATE LIZ To draw the Formof a IIand-raz’l. I 11 fig. A make an cquilateml triangle :2 wt upon its width, and divide it into five equal parts, and from one part on each tide draw ~ 3 and yrs , then tor and m me the centres, l m being made equal to lg; the centres are’found the fame for the upper fide. . The Form (f tile Rail being given, to draw the 11112173 Cap. Let the projeEtion of the cap be three inches and a half, and make the diflance of the infide circle from the outfide circle the projection of the nofe on each tide of the rail, and- draw the mitre no and 110; then continue parallel lines down to the mitre 1211, put the foot of your compafs in the centre of the cap,.a.nd circle the parallel lines round to a c c g" and i, and draw the ordinates a b, c d, of, &c. and then prick the cap to the rail ac;- cording to the letters. Ifow to draw the Form of the Cup for the 111 fire to come to the Centre. It is only drawing the parallel lines from the rail to the mitre wherever it is, and cirz' cling them round to the ordinates ,- and f0 pricked from the rail, and the thing is done. PLATE,» .- ) C‘ . ~ 1115.011: flu: A (‘f (/1 I‘IY‘A' 11:9 :19 1/:01 full] 7,,”/’¢’/J"” ‘ “ v. -o~"04 a...“ » o .. , , V ‘ ‘\ .. _.. ‘ ~ ‘- _- x. \ ~ '.' , . I y I ; l . . s . -. } n \ x \ macaw-m.— .n v- raw- G... .u..- - -n.m-».... "6" - M. .. . “a...“ uv—a—o-w m...“ w... -.-.. 9‘“ MN M‘th‘fi LEW l ‘ wv‘ on“- r\ _-.... ‘ r- . ' I r ‘ A» .__J ' .Y . , ‘ . .. c. . l D I, ‘~ A . I d a ‘. ‘ ~ \ I . u _ ‘5 , . x ' ‘3. , ‘\ '1 . d . V \ ‘ a ; 2 \ a - ,‘ .‘ u . ‘ f ; .." \ ' C n . . v n .\ 4. ‘~ .' ; , .. ,. u . ._'~ ." ,x j - .~ . . 1' . - u ' » t' . . “ \ ‘ ‘ {u :- : . \ w I ‘ ‘ y, a : ' ‘ ' ’ I . ' 1 ‘ . _. 4~ _ r A. ‘1 l .. . L‘ J ' . . . "" \\ \ V ‘ ' ~ ‘ - . ’ -\ v’: 'r.'- ' ‘ > .‘.‘ \'\ « 4" “ . 1% M ~. '<..-4&flv\ys|\‘:‘\ “k“. \ 3a .y~~\y~\\, . .\\\..\.» . k, _. k. . , - \ , .I ~ . ’, a . A I ‘ \ . , . , ‘ _ . I 1‘ I \ . ‘n | _ ‘ n u i ' . . ‘1. ..—...,.... ~ ,4... 13A”? 52. _ . V ‘ . . .70 (I’l‘ufl-IZII' }‘(lIlI/( u/‘l/NJ afau'. Afar/:0 (I I cynn/ f0 (Lat/aw draw [20’ ‘af I'{'q/zf (Ufa/ca 2‘0 f/zc [Calf/41nd (in: fltl'lll f/n' /'r/l . fizr-a//c’//v f/m Away, f/aw (J , f ______ 1;: .t/Lé. (cufcayf‘6/{C 31’! 1’ ’/f ._ H _V ..-----._----.-..~-. h---..---_--_.--..__-_ .--_---..-....‘_---- 0--.---— 1 Elflytlu/An’jlflf (/I‘I'I'I'fl/ ()/‘/./.,4.);)‘ /;’ ()2 [y/L171.}//(’/1(U( . h_.tk00u.iio,vui x‘ when" “am“ ])/(I/i' .53 y/(y J’fiu'r Pct. .f/Z' 7/7720/(721 IC’ (6'! L w r . jjfléy 61:} [/Il’lh‘f (/l '7'{’/‘/'}A‘ )m/H /x '/‘)/VL}4.‘/(/'/ 117/.' A do 21% \\\\\.\<\ ‘ / - [74(654. ' —. ‘ ‘ . \ — - --—-1r-1 u‘n .; n I I A n l . .Pltf/l I)mn-n/ ' ' ' Pitch Board dz“ fizIZz'ny 312ml? r. fi—‘y v 8 -g. ..__.....EL'.-..-......_;-...l‘ u 1 l w I’z'fr/I 19 on n/ \ Agra/K 0/}. ‘- I fl J } x x l f I x 3 fi](‘/((‘{': A ’II/t.":I-I f/n' . Ivl‘ u’ir. :'/4. luv.“ 1 *1); firflV/Elm/mvl . ‘ . I / ‘ ‘ THE THEORY AND PRACTICE OF JOINERY. 5! PLATE LIV. To (1’; aw tlzc Scroll (3f 11 [Lind-1111‘]. ‘ In_11g .11 make a ei1cle three inches and a half diamete1, divide the diamete1 into th1ec equal pa1 ts, and make a Tqua1e 1n the centle of the eye to one of thol'e pa1 ts, and divide each fide oi the fquaie into {ix equal parts; this i'qua1e' )S lhown' 111 E, at the bottom,' in full fize fox practice, and laid in the fame petition as the little fquare above, fo that the centres may be mo1e 1eadily found, which we all mmked 1n a legular petition; the centre at 1 draws fiom z iound to l, the ceut1e at 2 draws from k to Z, and the centre at 3 draws from Z to m, &c. which will complete the outlide 1evolution at a,1\ith the centre c,- then fet the thicknefs of the 1ail f1om‘ a to f, and go the reverfe way to d1aw the infide , then the fcroll will be completed. To draw l/ze Curtaz'l Slap. Set the ballifiers in their proper places on each quarter of, the fcroll in fig. A ,- the firl't ballil'ter lhows the return of the nofing round the ftep, the fecond balliller is placed at the beginning of the twilt, and the third ballilter a quarter (lil'tant, and {traight with the front of the lad ril'er: then fet the projection of your noting without, and draw it all round equal dil'tant from the fcroll, which will give the form of the curtail. To draw flu: Face 1110111defl/uuring 25/16 T1117? Par! if the Scroll. You will ebferve here, that theiomt is made at 3, 6, jult to clear the fide of the feroll ;, draw ordinates nerol's the feroll at difcretion, to cut therline d (7, a I) c being the pitch- board; take notice that lines be drawn from 3 and 6 to meet (I [2, 1'0 that you may have the [aid points exaét at 3 and 6 in your face mould; then take the line (l I), and mark the places of the ordinates upon a rod, and transfer the divifions tord b in B, then. trace 1}, from fig A , according to- the marks. ; T 0 find (/11: falling Jllould C.1 In C, a b c is the pitch—board; the height is divided into fix parts“, to give the level of the feroll; the diftance (& d is from the face of the rifer to the beginning of the twift; and the difianee from d to It in C, is the fireteh-out from a, the beginning of the twilt round to I; infig.A; each beingxany point taken at difcretion, more than the firlt quarter; divide the level of the feroll, and the rake of the pitch-board, into a like number of parts, and complete the top edge of the mould by interfeéting lines, and the under edge parallel te it to the depth of the rail. 110w tofind the pm (1116! T/11c/mcfc of S1197 fo; the Taifl and 5'1”.)011 Take the eompals round a b c d e, to 6, infig . .4, and firetch it out upon the bafe of the pitch-board from d to g,- d'rawg lz perpendicular to interfcét with the top of the mould; then draw the dottedline 11 f, parallel to the level of the feroll both ways; then take the diftanee 6 1 , infig. A, that is, the length of the plan, for the twill part, and fet it from d to e in C, and draw cf perpendicular, to cut the parallelf h; then draw a dotted line thronghf, parallel to c [1, the longefi tide of the pitclnboard, which gives the thicknel's of fluff for the twill, about three inches and a half; and the parallel line fromf to the hate, {hows the thicknefs of the fcroll. Nole. The falling mould I), for the outlide, is found” in the fame manner as the other falling mould C. 2 PLATE 60 ~ THE THEbRY AND PRACTICEOF JOINERY. PLATE LV. As the method of getting a fcroll out of a folid piece of wood, having the grain of the V1 oocl to run in the fame direé‘tion with the rail, is fa1 preferable to any of the othei methods, withjoints in them, being much fironger than any othe1 feroll with one or two joints, and much more beautiful when executed, as nojoint can be feen, and confequently no diffeience in the grain of the wood at the fame place; I (hall here giVe y on a fpecimen, the method f01 defc1ibing a fetoll being already given in the lalt plate, and likewife the falling mould 110w tqfind t/ze Baking or Face Mould. Place your pitclnboard, a I) c, in-fig. I), as in the laft plate; then draw ordinates acrofs the croll at dilcietio11, and take the length of the line (I b, with its divifions on the longelt fide of the pitch board, and lay it on d b 1n E: then the ordinates being diawn in E, it will be traced from fig 1), as the letteis direét Hon" tofiml t/ze parallel T ltz'cknefs qf Stzgf. Let a b c be the pitch-board in F, and let the level of the fcroll rife one fixth, as in the lait plate; and from the end of the pitch-board at 6, fet from b to (1 half the thicknefs of the ballifter, to the infide; then fet from d to 6 half the width of the rail, and draw the form of the rail‘on the end at e, the point 5 being where the front of the rifer comes, then the point 6 will be the projection of the rail before it; then draw a dotted line to touch the nofe of the feroll, parallel with c l), the longefi fide of the pitch-board; then will the dil‘tanee between this dotted line and the under tip of the fcroll {how the true thicknefs of fluff, which is nearly five inches and a half: but there is no occafion for the thicknefs -to come quite to the under fide; if it comes to the under fide of the'hollow, it will be quite fufhcient, as a little bit glued under the hollow could not be difcernable, and can be no hurt to the feroll, therefore a piece about four inches and a half will do. FIG. 44/ is a fcroll of a fmaller fize, drawn in the fame manner and with the fame centres as the others are, but with a centre lefs. The method of finding the raking would and tlricknefs of fiutl' is the fame asvfig. D mm; Plate 5.5: Tél‘s LIZOM'J‘ évu‘ ‘tl .Vz‘l‘fl// ('4‘ f0 fll‘ 'll‘f (VI/P)" ./%(’ J’n/AI/ _ - t Q 12;. D. | x l I | 2 ,‘J 1\ . , ‘3 I‘m? MVMz/fa/ - :3 .3 ' ‘ :4 To”. , 6‘. Farq'47I0/1/11JL>I‘ r fizz/41 ' ‘ a fa:- Ij'zé/ 41 ZY/JzMzg/y' 3f d’z‘gfltnfm' If; D 1"" 6 ”’-' A" ("I- "'rr40115¢7/J/yz éVJ’fl7r/u-luwz . T 512/: N €73: (5/1) 71/17:: 3. \ \ \ ~ .» .u .f \ . a a» _ “‘3 \ J \, \ \ ‘ \ \ . \ Q _“ A \W v. . - v u . _, ...\ ‘rr _ . ism ,J.‘ I « .x. AW .u0 4 ~51} ‘ x Sh \. 1%. v“ nix“. ‘ ‘ .‘W‘. ‘1‘ A ‘ Wen»: \ L. . i 5".» $116?“ N . ,H ._ A. . a \ ‘ _ , «I 3 , .Li‘AYIOIICt! .\ l . . i ‘ ‘ A . F_ a , \ _ . ‘4 ¥ ., \ \ L b , k < .\ x ‘ A». . _ .r . 41.. x 5 ‘ . « . I - . \ . ‘ F 7 r1, _ . .. . u i — . ~. \ n . . p . ‘x .. ‘~ ~ I . \ ‘L-‘k. -. ‘ \n‘\ V»; c \m ‘5‘»; \ \ N \ \ ~ J jyti/r .56: Plan and SIT/1.011 #2147111} raw "1175 a 517/, [anti/(WV fu'r m: é'narmw f/m Ift’-Q‘f1)/(lfil . I t / ‘ Hay“ Rod. I JM& 7‘: i i : ‘—£ Eat. I’llfigjrw Mud/f 09.177'411/14 t 6' 17y: 6/771’2V/0K11W ‘N‘ . £44 a! \n Y x... _.... ~ A 3‘ ‘1‘ M‘s THE-THEORY ANDiPRACTICE or JOINERY. 61 PLATE LVII. T 0 find the Face Mould qf a Staz'rcafc, fly that when fét to its proper Rake z't'wz'll be perpendicular thze Plan w/tereon itflandsfor a level Landing, as is/lzewn in the [a]! Plate. ' 7 f ’ Iufig. A draw the central line b q, parallel to the {ides of the rail; on the right line ,b 9 apply the pitch-board of a common Peep ; fromq to a draw ordinates n (l; m e, l f, kg, and. 2' Ir, at difcretion, taking care’ that one of the lines, as k g, touch the infide of the rail at the point g, {'0 that you may obtain the fame point exactly in the face mould; then take the divifions g It g f e d, from g', and apply them at B from g h g f e d ; from thefe points draw the ordinates of B, and prick them from the plan, as. the letters explain; then B will be the mould required. To find t/ze falling 211021111. Divide the radius of the circle into four equal parts, and felt three of thefe parts from- 4 to I); through 71 and *0, the extremities of the diameter of the rail, draw I) n and b v, to cut the tangent line at the points c and g; then will 6 d be the circumference of the rail, which is applied from c to d, at C, as a bafe line; make 0 e the height of a Rep; draw the hypotenufe ed, at the point e and d; apply the pitch-board of a common {tep at each end of their bafes, parallel to c (I, make (If equal to d e, if it will admit of it, and by thefe lengths eafe oh“ the corners by the common method of interfeéting lines; then draw a line parallel to it, for the upper edge of the mould. T 0 find Use parallel leicknefs (f Stafli The fame falling mould is again fhown difiinétly at D; bifeét the line d c, at a; divide a 0 into any number of parts, as 6; on c, as a centre, defcribe a quarter of a circle to the radius of the rail; divide the arch alfo into fix equal parts; from the points 0 g 2'! n, draw the parallel lines ef, g [1, 27¢, lm, 72 0,- from the equal divifions in the arch draw the perpendiculars of 1 it, 2 Ir, 3 m, 4- 0, and 5 q, to interfeét the parallel lines at f it It m o q; through the points draw a curve line; draw a right line 7' m, parallel to f f, to touch the curve; then is the diftance from 7' to s the parallel thiéknefs of fluff. PLATE 62 THE THEORY .AND PRACTICE or JOINERY. PLATE LVIII. Tofind a Face 1110M!!! of a Rail-fora large Opém'ng on a level Landing. ' Letflg. A be the plan of the rail; through the centre C draw the diameter 3 z, and pro- duce it to A; alfo produce the fide of the rail out to 2; then take the diameter z .9, put. the foot of your compafs inky, and crofs the line A z at A ; through A andy draw the line A 2, cutting the tide of. the rail produced at 2;, then the diflance from z to 2 is half dietarch line-of the rail 3 take the difiance z 2, and place it on the right line'v v at 'G, on each tide of w, to u and v; draw 11 B and v c, each perpendicular to the right line :2 v, and. equal to-the heightgof a fiep; make c E and B 1-) parallel to r) 12, each equal to the tread of a fiep; draw the hypotenufe v c, and the common pi-tclbboards 12 B D and ’c ‘E r, at eacheud; make H equal to '0 D, and c G equal to c F; and cafe 03' the angles 6 c F and .D u H by the common method of interfeé‘ting lines, which will give the curve of the under edge of the falling mould; draw a line parallel to it, equal to the thicknefs of the rail, will give the upper edge"; produce the line 71 :2 out "boy, from the middle w 'of the line ’07}, at G; make my equal to ray at the planfig. I),- y being the place of the. joint upon the plan, draw the line y ‘2 1 perpendicular to 72 1), cutting the upper tide of the falling mould .at 2, and the under .fide at 1.; from I draw the line 1 6, parallel to v 1', cutting the line 8. w, produced to 6; draw the tangent line M L; parallel to the chord a‘b, at the plan B, to the chord a I) draw any number of indefinite perpendiculars, obferving to draw a perpendicular through every joint, as from the joint d g and ,1, ‘y; then take the diiiance 1 2 from your falling mould at G, and let it from M to o of the plan at If; allo from L make L 'N 0 equal to 6 7 8 at G; then the {haded parts at N o and M o are feétions of the rail; then draw a line 0 b, to-touch-the corners of the feé‘tious at o and l 17; at the points a, a, d, c,_f, g, II, b, andp, draw perpendiculars to o b; then C'being pricked from the plan at B, as the letters direét, ,will be the trueface mould. F is. I) isa plan of the‘fame fize, {herring the face mould at F, when fprung, which will be a .very great faving of Quit, and not much more trouble in laying it down when properly under-flood. This method will be clearly explained in the following pages. PLATE ])/(,f‘(, tad) \ . é \\\\ \\ ._:\\\\\\.\\N.m \\ ~,~//, 6 § \\ i .\ a. E \\\\\_\ E? E \\‘§§\\\\V\M§=W ..: . RA .., K I . $§¥FK> .g _ ¥ .6 .1 1, H #3.? ' 1mm ~‘ ' ‘ \ Plan fffir mu? I‘ull":u/fl.u[.~/ llz'nxn‘bg/ ’0}; :éL‘IHZH/IU/Jpn . THE THEORY AND PRACTICE OF JOINERY. 63 PLATE nx. To draw thefdrllz'ng' dIowld of la Bail having a Quarter Space in it; theme wfind {fire v Face Moulds of the circular Part. At the planfig. A, d c is the firetchaout of half the circular partof the rail, found 'by the fame method as in'the foregoing plates; or it may be found more ex’afilythus: divide the radius into four equal parts, and let three of the divifions out to 3, and draw a line from 3 to b, cutting the fide‘df the rail produced at (1*; from the point f in the right line h g at B, makeflt, and-jg, éa‘ch equal to the firetchout of half the fail, that is, equal to a c, jg. A; draw the pet‘pendicularsfi 0, f l, and g t ; at B apply the pitcliaboard of a common Rep at F; through the point i draw it 1:, parallel to g In, cutting the linefl, at 16; from k to I fet up the height of the four winders; through I draw I 71, parallel to g [2, Cutting theline 11. a, at n ,- from 72 make 12 0, equal to the height of a Rep, for the. quarter {pace Upon the landing which only rifes one ltep; draw the hypotenufe l 0; (again, draw a p parallel to g It, and p q; perpendicular to o p, draw g o ; then a p y is the pitch-board of another common Rep above the winders: then ”161?: angles being eafed Off by the method of interfeéting lines, the falling mould will be completed, as in the lalt plate; make f u andftr, from f, equal to a (1, fig. A, that is, the firetch-out from the middle “of the arch at b, to the joint; draw 70 x and u 2 parallel to f l ; then take the heights from I to .y and ,z, and fet them from A to B and c, will give the feétion B C; then take m l from the falling mould, and from D make D 1-: equal to it, will gii'e the feaion D t ; then take 10 x from 1)’, and make F G, at E, equal to it 5 from w draw '10 7‘, parallel to g 11., cuttingf m at r; from 1‘ take the heights from m and l, and fet up thefe heights from H, to I and K at E, it will give the feétion I K 3 then the face moulds upon I) and .E will be traced as directed in the laft plate. PLATE LX. wants no explanation. * The line a c is nearly equal to the semi-circumference, and is the most exact of any that ever has yet theen shown by a geometrical method; it may be depended on in practice: it is absolutely impossible to find a right line exactly equal to the circumference bf a circle; this has exercised the attention of the greatest mathematicians in every age. it PLATE 64 T111: THEORY- AND 1111110110150? moment. PLATE LXI. deratv a falling ilfouldfoa' a Rail having a, Winder all‘romzd the circular ‘24,.5’:,,5 ,3, flown in the [4/2 Plate, thence zo/ind the Face [Vow/d ~ To dcfcribe every particular 1n this, would almolt be repeating what has been already defcribed 1n the lafi plate, the heights are marked the fame upon the falling mould at D, as they are at the face mould, which will give the heights of the leétions of the rail; and the face mould at C is traced from the plan B, according to the letters; in plate 60 is ihown the fame thing, only with this difference, that the face mould is partly firaight at lone end, becaufe the joint mufi have been weaker, had it been made where the circular part of the rail begins, as is {hown in this plate, but the method of tracing this is nothing dill'erent {mm the othei 1n the lalt plate: only I would have the maxim to obferve, in plate 60, that ordinates a1e drawnthrough the places wheie the circulai part begins, which will give the fame points on the face mould; for, by this means, you will be ‘able to determine what. part. of the face mould is exaé‘tly firaight, and where the crooked place of your mould begins. I 110110 the reader will underfland the fame thing in the following plates, without being told a fecond time. G {hows the application Of the mould to the plank ; take the bevel at 11, and apply it to the edge of the plank at 1), and draw the line b c ;then apply your mould to the top of the plank, keeping one co1 nei of it to the point B, and the othei comer clofe to the fame edge of the plank; then draw the top fate of the plank by your mould ; then take your mould, and apply it to the under fide at c, in thefame manner. ‘ ’ PLATE ). (1/17 ,‘ .02 J )/ (1/? , _.. Q» m// ,, \ ‘ ,PZaie 6'2... ¥ A): r/I/fi'rrr/I’lam :1 and/2w 17"” J‘fzrl}-zui(:1’c-r M; l’z’ln’w are ”re. next Plate A , ‘ ‘ A { 11¢th Bod C ,y K \/(()/(/;I ‘1" \ \ 21/5; (LI ///(' 4 lrf 1/1 'n-r/J Alf/Ll): 792 . évl’jW‘r/mé c 72 . ’1 1 1 ;\ \\ C §\\‘ c) // L ‘~ k‘ ' \ Mil/WW THE' THEORYAND PRACTICE OF KJOINERY. 65 PLATE LXIII. ' ' " 110w to draw 't/zc Face filoulds of an elliptic Stair. The plan and feetion being laid down as in plate 62, the reader will ehfer ve, that the ends of the Reps are equally divided at each end; that 1s, they are equally divided round the elliptic wall and alfo at the rail. In this plate, the rail is laid down to a larger fize than that in the Ian; plate: the plan of this rail mull: be divided round, into as many equal par ts as there are Reps; then take the treads of as many {leps as you pleafe, fuppol‘e 8, and let [1 I: at fig. H be the tread of 8 {teps frOm 1!; 011 the perpendiculai 11 m fet up the height of as many Reps, that is, 8; and draw the hypotenufe m 11, which will give the undei edge of the falling mould. The reader will obfeive, that this falling mould will be a l‘tria ght line, excepting a little turn at the landing and at the fcr,oll where the rail mutt have a little bend at thefe places, 111 order to b1ing it level to the landing and to the Torch; then mark the plan of your rail in as many places as you would have pieces in your rail (inthis plan arethree); then draw a chord line for each piece to the joints; alfo draw lines parallel to the chords, to touch the convex tide of the plan of the rail; from everyjoint draw perpendiculars to their refpeétive chords. Now the tread of the middle piece at C being juft 8 fieps, the height of the feétion from /L to m is 8 Reps; and the feétion m n is the fame as m 72 on the falling mould. and the. fixation 12 z' is the fame height as It 2' upon the Falling mould; then draw a line to touch the feé‘tions, and complete your face linould as in the foregoing plates, each of the other pieces at Fand G, the treads, being 6 fteps; therefore, from your falling mould fet the firetch of 6 Reps, from I) to H draw H 1, parallel to la n, then H It [will give the heights of the feé‘tions at D and E; every thing elfe agreeable to the letters. JVote. The firetch- out of 3 Reps, or any other number, is not reckoned on the chord; but it is the firetch-out round the convex fide of the rail, or what fome people call the infide. .1; 2 PL '3'; so rim THEORY AND exterior: casement: ' ' PLATE aniu" T/zc Tread of a winding Stair being given, round the .5113sz and-’15:: Plan of the Rail,- to dz’mz‘mfla (In: Ends «f the Slaps at this Raid/031m:- the Ballyiera/hall be all regular, or Of an equal Ifcig/zt’ whenfimflzed. ' Let the firf’c winder beginabout the firft fie before the'circle of the rail, at D ;‘ from: a to e, in the plan/17g. A, is thefiretcbout of ialf the circular part of the rail; the method» of finding it has already been explained in the foregoing plates; from c draw e H, perpen- diculai‘ to the fide of the rail; by reckoning round the dotted line, from 5‘ to 10, you? ‘will find there are five treads, or five winders ;.'therefore_ from g to 5 fet up the height of 5 fieps; produce the longefi: fide (1 [ref the pitch-b‘oa’rd=D, to c,- bife& b c, at 2; draw a line from 2 to 5; then divide 2 b and 2 5, each into the fame number of equal parts; and interfeét the angle by the common method of interfeéting lines, will ire the under edge of the falling mOuld'; then alline being drawn arallel to it, the thic nefs of the rail will give the upper‘edge, which is the fallinO‘ mould) for half the rail; draw the lines ll, 21‘, 31', and 4h, parallel to 6 g, to interfeét the falling mould at thepoints h, i, k, I; from thefe pointsidraw the parallel dotted lines to q H, down to the rail at]: to u ;‘ fromc draw cs, 0 t, c v, and. c u, cutting‘the arch line of the rail m, 71, o, 17, will give the ends of the Reps at the" rail; then drawl’ines- from m, n, o, 1), through 6, 7 ,. 8, 9, will be the plan of the flaps. Tofind the Face Ilf‘ould of a Rail, f0 that it may be got out of the Iw/Z Tide/(mfg qf S'tufl' pqflible. Lay down the plan of the rail at any convenient place, as No. 3; draw the chords .of the rail N o and o. P', fromthe’centre K draw K E, erpendicular to the chord N 0, cutting the outfide of the rail at e; in the lame manner raw the chord w 1,-at theplamfig. A; from the centre g draw g f perpendicular to it, cutting the outfide of the rail atf; from c draw a line cf, to cut the tangent line at 1’,- draw a line '0 1:, parallel to g H: fromthe‘ joint of the rail at I). draw [I B, alfo parallel to q 1-1, interfeEting the under fide of the rail. at A, and. the-topfide at B; draw from A a line A 1-" parallel to b q from-:I', at No. 3 ;, make r G r-r equal to F o H, at No. l g from C, at No. 3, make c 13‘ E, equal to c p a, at No. I; and make A I)’, at No. 3, from A, equal to A B, at No. I; draw a lineBR, for the chord of the mould to touch the fhaded l'eétions, perpendicular to N o and A r; from E draw 1-: M, perpendicular to B R; maker 2', at N9. 2, equal to} c, at No. 3; make z' e perpendicular to c 2', equal to E 'L, at No. 3; make L M equal to c c, at No. 2; from E draw E ’1’, parallel to A F', cutting the chord line B R, at '1‘; from the points If and M draw the line T M, then T M will be one of the ordinates; all the other ordinates- are draWn at dil‘cretion, parallel to it', andcompleted in thefame manner as is {hown in: plate 9, for the feétions of a cylinder. The reader will take notice, before the face mould at No. 3 can be applied, the edge' of the plank mufl be firfi bevelled according to No. 2; then the plumb-line will be drawn- on the bevelled edge of the plank, by the bevel that is drawn at No. 3. JVule. By this method of proceeding, 3. three inch plank will almofi be fuflicient for any rail of this kind however it ramp; whereas in many cafes, by the common method, it may require a plank five or fix inches thick. Many other advantages will attend the manner of fetting out this plan; I (hall mention one or two: in: fixing the banniiters, they will be all regular, and the firingboard will be as eafy as the rail itlelf; the lkirting will alfo be quite regular, for the ends of the fieps are wider and wider as they go round to the middle of the femicircle; laltly, a blackimith may put up an iron rail with very little trouble, the bannifters being all regular; whereas no other plan will admit of it, unlcfs it is {et out in this manner.» . PLATE g "I "mum"! a‘fllfluv «ME . 9 , m a «W m U, y b / B m ...A.... n W .N w r N. ...v......... .u ..... ................................. .. \ x / r .. w had m a ....... m....... N ........ m. ...... 3e ........ R. ...... k ....... $ ....... S. ....... mu.» ...... Wax. ...... 3 ........ x 81.x...» ...... W (V‘ r .P . a // .1 )5 .1 a ...................................................................................................... .................................................................................. THE THEORY AND PRACTICE OF JOINEYIY. 67 , PLATE va. To ‘(lz'mt'nf/ia ‘tlze Step of a Stair winding round one of the Quarters to a level Landing. Find the ltretch-out round half the circular part of the rail, as directed for the foregoing plates, and complete the falling mould as direéted in the laft plate, for the winding part of the rail, which is fix Reps from t to w; in order to bring the rail withan eafy turn round to the landing, fet off the height of another fiep from u to 7 , and let the under edge of the rail be half the height of a Rep above that to c; or it may be more, according to the dif- cretion of the workman; then the rail will be half the height of a Peep more upon the land— ‘ ing than it is upon the winders; through c draw c f, parallel to the bafe, and continue the line 2 u, that forms the interfeétion below for the winders up to D, and eafe off the angle u D c by interfeéting lines, will give the under edge of the mould turning up to the landing: in order that the lafi ficp beyond the quarter fhould alfo follow the mould, draw a line through '7, the height of the lafi fiep, parallel to u b, or c 0, cutting the under fide of the falling mould at A; through A draw A B, parallel to o t,- then u 3 is the tread of the laft Rep of the rail, which is fet from g to E. The face moulds at D and Fare completed in the fame manner as direéted in the hit plate, and the moulds in plate 58, at fig. D, is alfo laid down by the fame method, the height of the feétions being taken from the falling mould that. correfponds to that place of the rail which the face mould is made for; and the bevels that are laid down above each face ‘mould will {how how much you mufl bevel the edge of your plank, before you can apply the face moulds to the plank; then draw the plumb of your rail, upon the bevelled edge, by the other bevels that are {hown at the feétions; then apply your mould to each fide of the plank,- keeping it fair with the bevelled edge, the fame as in other cafes before mentioned, PLATE THE THEORY AND PRACTICE OF“JOINERY. PLATE LX’VI. , This plate {hows the method of capping an iron rail, Upon much the fame principles ,as the others, but with let’s trouble. How tojind the Thicil‘mfs {if flufl for capping of an Iron Bail. Lay a thin broad piece of wood , as 5, upon the top of the iron, upon the place that is to be capped, and turn it round upon the iron, till you fee the greateft fpace between the non and vood to be as little as poflible: then the open fpace will {how what thicknefs mutt be added to the thicknef's of the rail. ’ 110w tofind the Plumb ry’ the Piece, for the Applicatibn Qf‘l your filould. After having found what thicknefs of ftufl‘ will do, apply the folid piece itfelf, b, to its place, then let one of the ends, as d c, be cut plumb. How to trace‘ the under Side of the Plank to the 17071, 2'Mead (f the Face M'oulrl. Make a pricker, as c, with a heel point in the upper end, and let it be notched out, fo that when it is applied on each tide of the ballifier, it may juft leave the thicknefs of the rail between each point; then take yOur picker 0, and prick your piece 6, at every ballifler; always keeping your prickei clofe to every balliiter. This being done both outfide and infide, if you infpeti C, it will make it plain, wheie you fee the tides of the plank flatted out, which {hows upon the under tide at the black dots; ftrike a plumb— line (I 9, upon the end of your plank b, and this plumb line will (how how the top is to be pricked OH f1 om the bottom, which you fee at C; the under fide 1s fquared over to the edge, from your pricked points, and from thence drawn acrofs the edge to the rake, which 1s formed by the plumb upon the edge, then fquared over the top tide, and then it is to be pricked oil from a line drawn from the point (1, in the end feétion D, which the plumb—line gives upon the end, along the top face of the plank, parallel to the edge, and not from theifquare edge of the plank. PLATE PM)?» 66; ; 17!! 21y O. ‘U ('a/N V ‘1”! 171(7 (Ill. 7/ \ iK/f' 3‘1:on //m turf/(20’ of d" 125?,“ 2/” Art m‘madlyzbfwagvr (Mum): Aw , «a»? . *V Mm 57.. ' ,_ , T 1/1.? LJYMWU‘ flaw fa (/fl/r (I [WI/7 I}; IZ/é'Al/n/F . ' . t. Q \\\\ .\\ ‘ \ \\\‘\\ ~ ‘ \\\\\\VQ\\§ \i‘u‘ ‘ \'\\ \ ' “‘2 . \ \ \\ - \\\\ ‘\ \\ I , c \ \\\\ e \\ \\ \ THE THEORY AND PRACTICE 'OF-"JOINERYI 69-: ‘ , PLATE L‘XVII. This plate {hows the method of gluing a rail in thicknefl‘es; but if I mutt give my opinion, a rail got out of the folid is much preferable, although you are obliged to have more end joints in it; but if your joints are well fcrewed together, a folid rail has” a more beautiful appearance than a rail glued up, having fo many different t'hicknefl'es of' glue, which makes it have a black and gnafty look with it; if a perfon'is ever fo careful, the joints wilHtill (how, and this rail'in itfelf having a natural tendency to fprin , the leatt dampnefs will make it give way in time; but as this is held by fome a very valuable acquifition, I {hall proceed to lay down the moulds for it. To f/zow the Application of the our/Ede and infide falling Moulds to the upper and under ’aces «yr the Plan/c, :0 give it the Form of the Twyi. ‘ a b is the firetch-out of the greatest circle in B, and a c the height of the fieps; again, (1 c is the compafs ofthe lefl‘er circle, fet in the middle between a b and df, the height of the fieps, the fame with a c: therefore the triangle a b c is the pitch-board of thekinfide falling mould; and b m 0 at the bottom, and 2' h c at the top, are the pitch-boarls of two common Preps; which lines, when interfeéted, will give the under line of the infide falling mould. In the fame manner rife, with the two common {tops k gf at the top, and e l n at the. bottom, will give the under line of the outfide falling mould. {The top lines are only drawn parallel to the under lines to the thicknefs of the rail. flow to apply [liq/c ZlIoulds 2'0 l/zc Plan/c. 5 Draw a line (p, to touch the moulds fo laid down in two places, andgas both moulds in~ terfeét together at q; then draw a fquare line 1) q, upon the top of your plank, at the’fame diltance as p q is from the bottom ends ofyonr moulds, and this line being fquared acrotl the edge, and from thence acrofs the under tide; then fet the, difiance p q on beth lides of your plank, from the fame edge, and likewife fquare over '1 s '7", at the diltance p f on your plank, on both fides, then fet the diftanceof r from iupon the t0p tide of yourplank, and jet the diliance of s t upon the under fide; you will obfcrve to mark the point 9 upon both your moulds, then apply your outfide falling mould to the top of your'plank, making the point (I to coincide with the fame pomt q in the plank, and make the front of the falling mould to come to 7', and with thlSmOUld, placed in this pofition, draw the upper face of your plank with it , and in like manner apply your infide falling mould, that is, by applying the point q to the fame point q in the plank, on the under tide, and let the front edge be to s in the plank; then draw the under fide; your plank being fuppofed of a fullicient thicknefs, making allowance for the law cuts, and plaining up your veneers: this plank, ‘ when out our. twified to thofe lines, will be the true form of your veneers: the piece being thus formed, you are to cut your veneers the other way into thicknefl'es as you think they will bend eafy, and foI {hall leave you to complete the rail. ~ There is one thing‘that I would have you take notice of here, the general cufiom among workmen to keep the hand-rail highe‘ft Upon the winding part of the Hairs, on the fuppo- fition of a perfon coming down fiairs being liable to fall over the rail, when the defcent is very rapid; and therefbre to remedythat inconveniencefl have all along made the under fidc of the falling mould, or the under tide of the rail, which is the fame thing, to be eq‘ui- . diftant upon the rake from the face of the rifers, which will caufc the upper tide of the rail ‘to run higher on the rake, than the height of the rail above the common fieps, and the quickerthe afcent is, the difference will be greater. In laying down this, the diiiance v w {hows how much the winding part rifes above the common» fieps, which is about five inches and a half; this is done by continuing the top line of the rail upon the winding part. to w, and by continuing the top of the {iraight part to meet at 1', then the tki’iance of v a; will always be according to the pitch of the Winders. PLATE to rm: Tamer AND PRACTICE or Jomsen s7. PLATE LXVIII. This plate (hows the method of fitting doivn the lkirting, upon any fort of haircare whateVer; whether firaight, circular, regular, or irregular; if the treads are ever fo crock-ed, and the rifers out of an upright. Infig. A, is {hovm a beVel, made to the take of the Ikirting, and the other perpendicular to the fiair,~and a flitting piece to be applied to the perpendicular fide of the bevel With a hooked point of iron or Reel, to {land forward at the bottbm fo much, that the {liding piece may clear the nofin'g of the {tepi _ I {hall preceed to [how its application. , Hm iofit down the Skirting. , Lay the fkirting over the top of the iteps, and let a very fine notch he made on the front edge of your Hiding piece, to the height of a Rep, or rather higher; then apply the point of the Hiding piece to the internal corner of a flap, and prick your fltirting in the notch at 5,‘ the bevel being fuppofed .to be brought clofe to the flider: again, fuppofing you want to take a point at the nofing, where you fee the bevel applied under, apply the point of your fliding piece to the nofing at c; then prick your {kirting in the notch at d, that will give the point d, which is to correfpond with c, &c. and byrthis means you may take as many pricks as will be fufficient, till the whole is completed. COROLLARY. Hence it is evident by the fame method, that one thing may be fitted into another, whether confidered as a fiaircafe or not, {landing either raking, horizontal, or perpendicular. ' If the fteps of a fiaircafe be very true, two pricks from each rifcr and a tread will be fufiicient, as it. is only joining thefe pricks by lines, which will form the rife and tread of each Rep,- and three pricks in each nofe, becaufe a- cirele may be eafily drawn through the three points. If the nofings are all exa8c, let a mould be made to fit one of them, and your nofings on the fltirtings be drawn by this mould, which will likewife be exact. FIG. E {hows the method of laying down a raking fided flair, which is clear in itfelf, the height of the fieps being the fame on each fide. C and 1) draws the method of tracing one bracket from another, in a fiaircafe: C' being the bracket for the common Rep, D a bracket for one of the winders. ’There is {hown a method in the lad: plate, at E and D, for doing the fame thing by moans of a triangle, which is performed thus: let the other bracket at fig. 1) be given, whofe length is A B; and if you want a bracket for the winders, whofe length is B c, draw B C, making any angle at the point B join A c; take as many ordinates as you pleafe, to touch all the principal lines of the given bracket; then draw lines parallel to A c, from thefe ordinates; and complete the other bracket as you fee by the letters. PLATE 2 13/1777 04(5). \ l ‘ 1:65;? Aféoua‘ [5‘66 JM’KJW/ 0/1“ {Vt/>‘/l}zl}?y 413W J'fqfir C’mw 67; 2/521 [3’ 771(- (’ZL 151/117. n, .Onulwfl 0}. a 2/... lav/(7, l ‘92 {IV PREV/(Maw ' . . / 1 - ~ _ 3 4 . 1.4.anndn‘lnx.. 7.7} u/unn . In!“ I .71‘7 2 / /'¢ ‘Ir/ “/01 '4 Kg [Ill] - 101$} ’vm ///. 4 THE? THEORY AND PRACTICE OF J'OINERY. '71 PLATE LXIX.’ ,Ilow to dim inf/71 (be quft (f a Column, by the ancient blqtbod. In F1; . A, defL-1ibe a lcmicircle at the bottom , let a line be drawn through the diameter at the top, parallel with the axis of the column, till it interfe&s the femicircle at l, at the bottom; then 1 1 at the bottom will be equal to 1 1 at the tOp; divide the arch into four cpml parts, and throunh thele points draw lines paiallel to the bafe, the height of the col11. 1111 being alfo divide 1:] into the fame numbe1 of pal ts and lines diawn parallel to the bale, then the column 18 to be tiaced f1om the {e micircle, according to the figures. [[0121 to dimmf/k t/ze Column by Lines drawn from a Cc anr e at a. DyZancc. Pro. C. Take the diameter a b, at the bottom, fet the foot of your compal‘s in c at the top, and crol‘s the axis in the point (1, continue 6 a' at the top, and a b at the bottom, to meet at c; then draw from e as many lines acrol‘s the column as you pleafe, and take the diameter a b at the bottom, and prick each line upon the axis equal to b a, which will give the {well of the column. T o diminiflz a Column by Lat/ts, upon tbc fame Principle. Invxg‘. I), the point e being found, as in fig. C, take and plow a rod d b, and lay the groove upon the axis of the column, and plow the defcribing rod upon the under fide, and lay the groove e upon a pin fixed at e, and fix a pin atrJP a , to run in the groove upon the axis of the column, and the difiance of the pencil at f, equal to b a, then move the pencil at f, it will defmibe the diminifhing. How to defcribe t/zc Column by «not/tor Met/10d. Take the diameter a b at bottom, and fet the foot of your compafs in the top at c, and crofs the axis at 8, and draw the line a 8011 the outfide, parallel to b 8 on the axis, and divide each of thefe lines into eight equal parts, and fet the diameter a b at the bottom along the Hunt lines 1 l, 2 2, 73 3, 8:0. from the axis; this will alfo give the diminilhing of the column. _ flow to make a dimim'jln'ng Bide. Divide the height of your rule into any number of equal parts, as 6; draw lines at right angles from thefe points acrol's the rule, and divide the projection of the rule at the top; that is, half of what the column diminilhes; into the fame number of equal parts put a pin or brad—aw]; lay a ruler from u to 5; mark the croTs line atf; then lay a ruler from 4 to a, and mark the next crofs line at c; then lay the ruler from 3 to a, mark the next at d, and {0 on to the bottom; bend a flip round thefe points, and draw the curve by it, will give a proper curve for the fide of the column. Note. This is the readies: method, and gives the-best curve of any that I have tried. . 1. PLATE 1;: ’ THE s'I‘HiL'QRY AND' PRACTICE OF" JOINEItY. PLATE LXX. 3/15 Plan and Elevatzmz (f a czrcular Sa/It, in a C21 cular W 11/, bemg g1: m, to find the lilouldfor t/ze 7ac12al Bars, fl) that t/zeyflzall be pcspenduula) to tire Plan. Draw perpendiculars from the points 1 l l 1, 8w. atA and B, in the radial bars, either equally divided, or taken at dil‘cretion, down upon the plan, to 1 2 3 4 5 6 ’7, at Cand I); and draw a line f1 om the firfl: divifion upon the back fide parallel to the bafe, then draw ordinates from 1 1 I 1, 8:0. at right angles to the 1adial bars, at A and B, which being pricked from the plans at Band C, will give amould fo1 each bar , and the bevels upon the end will {how the application of the moulds. T 0 find the Veneer cf a circular Bar. To avoid confufion, I have laid down the plan and elevation for the head of the falh um der. The {tretch-out of the veneer. is got round 1 2 3 4- 5 6, on the circular bar, which being ‘pricked from the fmall diltance on the plan at Ill, will give the veneer above, at E. To find the Face-mould fir the Sq/lz-lzead. Divide the lath-head round, into any number of equal parts, at G, and draw them per- pendicular to the bafe at H; draw the cord (if one. half of the plan at II, and draw a line parallel to it to touch the plan upon the back (ide; then the diflance between thefe lines at H, will {how what thicknefs of l‘tufi' the head is to be made out of; and from the interfeéting points on the back fide, draw perpendiculars from the bafe of the face-mould, which being pricked from the elevation, as the figures direct, will give the face-mould. To find the fifaulds for gziuz'ng the Form Qf the Head, perpendicular to the Plan. The bafe of L is got round the arch l 2 3 4- 5 6, at F, and the bafe of K is got round a b c d e f g, alfo at F, and the heights of the ordinates of each are pricked either from H or I, which will give both moulds. By the fame method, a circular a1 ch1trave, in a circular wall, may be got out of the folid. .5 Alote. The face—mould at G mull be applied in the fame manner as in grains; fo that the falh-head muft be bevelled by lhifting the mOuld G, on each fide, before you can apply the moulds, If and L ,- the black lines at K and L are pricked from the plan at H,- thel‘e black lines will exactly coincide with the front of the rib when bent round, a line being drawn by the other edge of the moulds, will be perpendicular dver its plan, "and the thicknefs of the fafh frame tovsards the infide will be found near enough by gauging f1om the outfide. ' prim f/(I/fl 70. 7&1/5) (l-l //I4'JL'/' (11.1‘1T217JV2’1'9217‘92 [IVPAQ'rfir/uvll «as; : \y\\\.\ ; '<_ \ \ A} ‘ _ /)/(lf(fl71.‘ , ( 41(‘0/1’f/‘(1l'1' (3). JIFF/ill‘tl/{/(‘,/‘ (l (;.Iv4([/(]/' Zfi)/€fl))y (‘1’ (I a'rril/ar Wa/l \\\\\\\§\ I \\ . \\\\ / i/l L/KJ". m A m \ VZKJJcH/k/r J’f/ (’/('/z 0 I/' 164/1219! (tr/«ic/QKTV | " 4 a :2 1 0 JL 9. J Z716. y/zau/ (77317? /n [c //ar_//}’ 0sz 0111' Inf’l‘flr {12/1 ;/ ' Arcfi/[nuw . .1Q/(Il /‘ a.) /I I. (l ;l([.A',/I(’II (711% .JI;{(',/("'/-Ul}l ,ZI w/f/zr 111/;14/%%I’/;?’ /[u/ (you w/imvw Avl.(I/1z//t,/“//ll(’/Z jf/‘fla/c Mi'f;'(///' lm //; lL/h’7h'1l‘l’ w’ua'z' //zn/’1.IIJ/’/nw'n //>,6 (/1/(/ 1/2 H .or G .1. (£31m ‘ I A: _/-\ 5‘ C. 1)"??qu //4' ,L‘l‘ (/I}‘V(‘1£1JW7VI7("',// Eli/ylfl ”(x/(01‘0” , [Yak (v2. . , Izl.At/Q'ré('(/‘(’f‘(/Ilf(;’t/ (wf any/w [1111? WP A/Zu/I 1372013“: . 17/17/13 (7" (I I ’n/NI/u/t‘ - ,—>~< \ I‘K‘:w t/u‘Jrf I/(l'n 7531/1111 2‘ 1-9.} ~111‘|:}-/I‘)11‘i’( ' 1‘ . THE THEORY AND PRACTICE OF JOINERY. 13 ‘ PLATE LXXII. To defcv (be the Angle Bars for Size]; onnts. in fig. 11, fl is a common bar, and C Is the angle bar of the fame thiclmefs; take the raking projection l l, in C, and let the‘foot of your compafs in l at 12’, and crofs the middle of the bar at the other 1 ; then draw the lines 2 2, 3 3, &c. parallel to 1‘ 1; then prick your bar at C from the ordinates f0 drawn at B, which being traced will give the angle bar. How to draw the Mitre Angle of a Commode Fiio'nt for a Shop. In E divide the projeé‘tion each way in a like numbe1 of equal parts, then the parallel lines continued each way will give the mitre. 11011) to find the railing filouldings (if a Pedz'mem'. In fig F, let the cimareé'ta on the under fide he the given moulding, and let lines be drawn upon the rake at difcretion ; but if you pleafe, let them be equally divided upon the cimareéta, and then drawn parallel to the rake; then the mould at the middle being pricked off from thefe level lines at the bottom, will give the fo1m of the face. The return moulding at the top muft be pricked upon the rake, according to the letters. The cavetto, fig . C, is drawn 1n the fame manner. N. B. If the middle moulding, jig. F, is given, perpendiculars mull be drawn to the top of the middle moulding; then horizontal lines mull be drawn over the mouldings at each end, with the fame div ifions as me 0v er the middle moulding ;and lines being drawn perpendiculaily down, as above, will ihow how to t1 ace the end mouldings. PLATE LXXIII. Figures B and A {how how to trace bafe mouldings for fltirting to fiairs, upon the fame principle as Ihown 1n the laft plate, at the bottom are given two methods of mitring mouldings of different projections togethe1. - 1 2 PLAT‘E '14 THE THEORY AND PRACTICE or .JOINERY. PLATE LXXIV. ' Gi~ en the F0 mm of a Cornice, to draw It to a greatei Propmu'on. Infig. 21, let the given height of the comice he a b,- fet one feet of your compafs in a, and crofs the under fide at b with that height, and f1 om the point 0 draw the line L d at right angles to a b,- then the height of all your mouldings will be on a b, and the pro, jeétions on c (1' 1n proportion to a b. ’ 7\ ofc, u f ihows another height, 6 c its projeétion in proportion to that height. Ifow to dz'minzfl a Cornice in the Proportion (f a. greater; Defcribe equilateral triangles on the bafe and projeé‘tion as at D, and make if and 2' 5:“ equal to the intended height, and draw the line f g acrofs thetriangle, which will give the heights in proportion to a I); put the foot of your compafs in [9 as a centre, and circle I) c round to b 11, and draw the dotted line It 2', cuttingfg in A; then fet of? i e and id, each (qual to g/c; draw de; then take the divifions of c d, and fet them f1 omf to m,- in the fame order diaw perpendiculars: it will give the diminiflied comice at D. Another Zlfct/lOd. At E, let the given height be a b, and draw the hypotenufe a g, and lines being fquared up to a b, from the divifions of ag D, will give the heights; and if you draw the lineg d at a right angle with a g, then d a will give the projection 1n proportion, when returned upon (1 0. FIG. C is Me .Mct/zod for hangmg (1 J26 Door. Let a c be the projeétion of the furbafe or bafe moulding, and c the centre of the hinge; make a 11 equal to a c, and in the centre at c deferibe the arch bde; then the arch 1; dc will be the properjoint for the furbafe to 11 ork in. The joint of the furbafe or the bafe may alfo be flraight, as you fee by the dotted line touching the circle at the point I), as the tangent to it. m i PLATE LXXV. To find the Sweep of a Moulding to be bcnt upon tlze Spring round a circular Cylinder. In fig. .4, which {tands upon a femieircular plan, fet a c to the height of your mould- ing, and make a b the projection; draw the form of your moulding, and draw a dotted: line to touch the face of your moulding , then draw the line 6 d to meet in the centre of the body at d, f0 as to keep y our moulding to a. fufiicient parallel thicknefs; then in your centre d defcribe your moulding. ‘ How to find the Sweep (f your fllouldz'ng when the Plan is a Segment. Complete the femicircle as in plate 1, fig. 1, then proceed as deferibed in fig. A FIGURES C and D {how the method for bending a moulding round the infide, which is performed the fame as above. The demonitration may eafily be conceived from the covering of a cone. CON. . ~ 17412274. 77;” .vlmuao f/w HIM/.200]. (1/ (w/in-q/"zu/ z'urnlrm‘. EyA. ‘ ‘ ' ‘ 7 _ 5“, f. . d \ ‘ . 7711} y/um'y flu’ luff/HM, (Tf‘z/IM/ I/Iivlu‘l/z/ I'nzwza’x ,, ___£Y,_ > '. ,_ . T142 ‘- ,____, J ‘ ‘ , {4. B. - Tl'l's mlmuu‘ f/Jt‘ ”Hf/rod ofbalu/uzq 1! fl/ u/mrr ‘ _ I, e. n.’ U NE} a. ’ l r/Z/r 77:1/13/(‘11’1‘3 _._.,w”// (ll/V I//}%(7> )//////(’/ \ w < J’uéf "a mum-4 (lb-at; [Lax/fanyzflqJ’J’VJAo/Jw: "H '> 1" E} fi‘fiwfih '~\_ ‘5 1“} §’\ 15“.»... ‘3» «as. i.“ f .9? \ . -2..3 .v. ,m. , ‘ .uv’ g "‘ [741K 75. ~ - ' \ . 6 n . . . . u ‘ I I I \ o u C' \ | I l . a ‘ l | / . z . V 5 ' 3 I ‘. dd : I I . u 1 , . A . '. A | - . I . . . > I 1_ V-_,_._ _.V__._+ .......... ,...J 1 1 ", k V x \ . l \ I \_' I r \ , w x . \ / / \_ I § Tl) (SAP/aft .s‘lmu'y flu: c/z/fl’nnf NIH/[MH/J‘ (y fir/M/nu] (‘U/‘II/(‘t‘J‘ \;,'c/(f (‘7‘ f/Jt’ wild, l‘\ 9.. . . _ ~ . x in will/(M I‘v (1431» J/J/vnr/ * \ I \ l l I t | I’ll/1.9.1.; f/nulr/L M)? 276' 111/1] W. 1/1112 {,yjlifi/méuu . . v.1, m». .n xx, ~ . ~\. pu‘ . [‘5- ,gzw, ‘ i ‘vi- \lmfiwfiwnw .. , .0 ”f. n.»- fl.¢- :— fizz/f1 1., .24 lw/ l/U'n'rfo r ?‘/.'.‘."_’ If”) Affl'n/n'flhw CONCLUSION“ In which are examined, by way of preventive Caution to the Student, feveral prevailing Methods, which are founded on wrong Principles, and better ones are here propofed. 0f the Elam. PLATE ImXVI. THE old manner forinterfeéting all kinds of lines, applied to Gothic andelliptical figures, to this day is exceedingly ufefnl in forming the ramps of fiairs, or eating of? any angle, as at G,- but when this is applied to elliptical figures; It is far from forming a true ellipfis, being too full at the ends, as at fig. 1) and E.- and this is no certain rule for drawing an ellipiis, for the more diviiions there are, the worfc is the ellipfis; as for example, jig. F is divided into double the number of parts as D ,- it is plain that neither D nor F is an agree- able ellipfis, and F is much worfe than I), which is contrary to general opinion; for I have been frequently told, the more parts it is divided into, the tru’er it is; but by this it appears the more parts it is divided into, the worfe it is: if this is doubted, try. F 23‘. A is an ellipfis drawn on true principles, as laid down in plate 7, at C, of this book, and is here repeated to be compared with the others. F z'gm'es B, C, and E, are ellipfes drawn with a compafs: I may call them reprefentations, as it is impoflible to draw them true with a compafs; there is no part of the curvature of an ellipfis that will exaé’cly agree with any part of a circle, for in every quarter of an ellipfis, from the extremity of the , tranfverl‘e, the curvature in every fucceeding part is continually flatter towards the ex- tremity of the conjugate axis , but yet there is a method to reprefent an ellipfis, which will differ very little from the truth, as is {hown atfigur es B and E, which are both drawn by the fame method, jig. E or B Is the nearel’t to the lhape offig. A- , -fig. C, the method ufed by almoft every author who has written upon the fubjeét, is full at the ends, but not in f0 great a degree asfig. I) and E. - 0f raking Alouldz'ngs. PLATE LXXVII. In plate 77, fig. A , let the moulding at the bottom be given, and let the perpendicular height be divided into any number of equal parts as fix; likewife divide the perpendi- '* cular height of the top moulding into fix, and the face moulding into fix, at right angles to the rake; and let the ordinates of each be drawn through the equal divifions of each rcfpeétive perpendicular, and pricked from the bottom, as the figures direct. It is evident, that if the under moulding is compofed of two quarters of a circle, the upper mouldings will be compoi‘cd of two quarters of an ellipfis; confeqnently the return moulding at the tap will be too quick upon the round, and likewifc in the hollow. B 5 tit s ' ‘ CONCLUSION. But if this dem011firation {hould not be fuflicient, let a dotted line he continued from 1, in the given moulding, paiallel to the who, then it will be evidently feen, that this dot. ted line correfponds with neither the faCe nm the return moulding; for 1n the face mould- ing it falls between the points 1 and 2; and In the top moulding it falls almofi: at the point 2; whe1eas it lhould only come to the point 1 in each; but the horizontal pro- jeé‘tion firm 2 to 2, at the top, ought to be equal to 1 l at the bottom , but it is much greater: therefore this method is fall'e, and they will not mitr-e together. I {hall alfo notice another method ured by fome authors, feefigure B, at I) and E, where they are pricked perpendicular to their chords, in the middle, which is alfo falfe , but if they are pricked as at B and C, on the 1ake, will be exceedingly nea1 , if deferibed with a compafs through three points. 0/ Wining/[1mg Qf Columns. PLATE LXXVIII. The method for drawing a column, defcribed by fome authors, and which is properly called a conchoid column, is not only very inconvenient on account of the cumberlbme infirument which is necefl'ary to find the curve for praétice, hut alfo the appearance is, I think, lcfs graceful'than when produced by other methods. The conchoid curve, or co- lumn, is concave towards the bottom, and convex towards the top; and if this curve was infinitely extended, it would never meet the axis; which {hows it to be different from the elliptic curve or colhmn, as fome have called it. The column called hyperbolic, plate '78, is not fo named from the general properties of the conic hype1bola (becaufe there may be an infinite number of hyperbolas [tending upon the fame bafe, having one common vertex, which will all be contained between a triangle and a. parabola, according as its axis is longer or {horter), but becaufe it will nearly coincide with fome of thefe hyperbolas. This curve has been known among work- men, and by them has been mifiaken for an elliptic curve; to refute which I' have, on the fame plate, {hown a true elliptic column for comparifon; the lines of their curva- ture are continued only to fhow their true figure; either of thefe is a more commodious method than the conchoid. The method which I recommend as eafieit in practice for diminifhing of columns is al— ready defcribed on plate 69, by means of a dimiuifhing rule, which is infinitely more con- venient than the trammel, and which, to my eye, alfo produces a pleafanter contour; but as this will depend on the fancy of the architeét, the workman will find fome of the methods fhown will anfwei his purpol‘e for any curve. The conchoid is flattefi at the top, the hyperbolic is a little quicker, the parabolic is {till more 1’0, and the elliptic is the melt quick. FINI'S. * -—-—-7 . \V. Stratford, Printer, Crown-Court, Templediur. _A i ,____.__.__._ w .w .w a .u a/ / ,_ 1/ / / . g ,,.. ../ ,a; a d a / Hr 1, ,, . \ . \\\.3§ i {M2 xx} .: ,_( I ; [\mk \.\‘ .\_\¥\II' \\\ _ II . u|.|| 1. I IIJIW/n I t « . .. ‘ ‘ ‘ I ‘ (l‘ Gnanuhu. “NIKKI ». III .79: -‘y 11.1 .................... 1U ............. l \ l -3131-.. - .......... x f 1.---.. .- -. . \\\\\\\ ~¥ .\\ 5 \ . , \\\\ .\‘\\.\\ \ x \ i\\\3 / _ // I k H _ I _ o _/. _ ..... fl I r N 6... 4 - 3 , ; z i ...... , \\\\\,\\ \ LN \\ . \w ,. \ .on %\\\ , / ‘ . x ,, _ I _ l /r I. . _V . f4 . \\\\\\ \.\\\ xxxx > J . ..\. . n. O ,/ L d L .u \\ \\\\ - v \\\.\ x ) l ‘ . I . \x\-_\..\.\1\\ ~\\ . z. 1/ _/J/.’//. (I. 1%. 'A / ,/m-. M5 MM ’.///-—( a Ar/ewt-nz/wx L r xv, I \ 52.34.. % '. ' A; CA‘TA Cs OF MODERsBOOKs ON ARCH]? E C T UR E, THEORETICAL, PRACTICAL, AND ORNAMENTAL; V13. BOOKS OF PLANS AND ELEVATIONS FO COTTAGES, FARhI-HOUSES, MANSIONS, Sac, TEMPLE, BRIDGES, 8w. , OF ORNAMENTS FOR INTERNAL DICORATIONS, FOLIAGE FOR CARVERS, 8cc. 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The New Vitruqsias Britannicus, consisting of Plans and Elevations of modern Buildings, public and private, erected in Great Britain by the most celebrated Architects, engraved on r47. Plates, from original Drawings. By 6. Richardson, Architect. Two Vols. Imperial Folio, half bound, Ill. Ins. Sketches for Cottages, lillas, '&c. with their Plans and appropriate Scenery, by yam Soane; to which is added six Designs for improving and emhellishing Grounds, with Explanations, by an zlmaleur, on 54. Plates, elegantly engraved in Aquatinta. Folio. 21. 125. 6d. half bound. Plans, Elevations, and Sections of Buildings, executed in the Counties of Norfolh, Sufi'olh, Torhshire, ll/iltshire, lVarwichshire, Stafora’shire So/nersetshire, CVC. by iahn Soane, Architect, on 47 Folio Plates 21. 125. 6d. Plans, Elevations, and Sections, of Noblemen‘s and Gentlemen’l OOUF ‘*’ ‘ Houses, Stabling, Bridges public and private, Temples, and . other Garden Building, executed in the Counties of Derby, Durham, Middlesex, Northumberland, Nottingham, York, Essex, Wilts, Hertford, Suffolk, Salop, and Surrey; by fans“ Paine Architect. TwogVols. with 176 very large Folio Plates, 61. 16s. 6d. half bound. The Designs of Inigo 7ones, consisting of Plans and Elevations for Public and Private Buildings; including the Detail of the intended Palace at Whitehall; published by W. Kent. with some additional Designs. 2 Vols. Imperial Folio, 41. 4s. in Sheets; or half bound, 4l. 14s. 6d. Plans, Elevations, and Sections of Hot-Houses Green—Houses, an zlqzmriunz, Conservatories, &c. recently built in different Parts of England for various Noblemen and Gentlemen, by ‘G. Toll, Sur- vevor and Hot-House Builder; including a Hut-House and a Green-House in her Majesty’s Gardens at Frogmore, on 27 Plates, elegantly coloured, with proper Descriptions. Folio, 21. ms. 6d. in Boards. ' Designs for Villa; and other Rural Buildings, by Edmund Aihin, Architeft; with Hans and Explanations. ’I‘ogethe'rwnh an Intro— ductory Essay, containing Remarks on the prevailing Defects of Modern Architet‘ture, and an Investigation of the Style best adapted to the Dwellings of the present Times; engraved on 31 Plates large Quarto, Price 11 us. 6d. in Bonds. A Series of I);_cigns for Villas and Country Houses. Adapted with Economy to the Comforts and to the Elegancies of Modern Life; ' uith Plans hid Explanations to each. To which is prefixed, an Essay on Modern Architcé‘tural Taste. By C. A. Bush}, Architefl. Engraved in Aqumtinta, on 24 Plates, large Qrarto, in Boards, ll. 53. . Architectural- b: ~ I. Architectural Desig'nskfor Rustic Cottages, Picturesque Dwellings; Villas, &c. with appropriate Scenery, Plans and Descriptions; to which are pr‘e'fijted some critical Observations on their Style and Charac- ter; and also of Castles, Abbies, and ancient English Houses.— Concluding With Practical Remarks on Building, and the Causes of the Dry Rot. By W. F. Pococh, Architedt. Elegantly en- graved on 33 Plates, Royal Quarto, Price ii. 115. 6d. in Boards. Sketches in Architecture, consisting of original Designs for Cottages and Rural Dwellings, suitable to Persons of moderate Fortune, and for convenient Retirement; with Plans and apprOpriate ' Scenery to each; also some general Observations. B ‘I'. D. W. Dearn, Architect to his Royal Highness the Duke 0 Clarence. glegaintly engraved on so Plates, large anrto, Price il. 7s. in oar s. Architectural Sketches for Cottages, Rural Dwellings, and Villas: with Plans, suitable to Persoris of enteel Life‘and moderate Fortune: proper for Picturesque Buildings, by R. Lugar, Architect and Land Surveyor; elegantly engraved in Aquatinta, on 38 Plates Boards, il. us. 6d. T he Country Gentleman’s Architect, containing a variety of Designs for Farm Houses and Farm Yards of Difl'erent M agnitudes, arranged on the most approved Principles for Arable, Grazing, Feeding and Dairy Farms, with Plans and Sections, shewing at large the Construc- tion of Cottages, Barns, Stables, Feeding Houses, Dairies, Brew- liouse, &c. with Plans for Stables and Dog-kennels, and some De- signs for Labourers Cottages and small Villas. The whole adapted to the Use of Country Gentlemen about to build or to alter. Eii- graved on zi Plates, With some General Observations, and full Expla- nations to each. By R. Lugor, (marto, il. 58. in Boards. Designs for Small Picturesque Cottages, Hunting Boxes, Purl: Entrances, &c. by E. Gyfloro’, Architect. Part I. Engraved in Aquatinta, on 2.0 Plates, (Mano, 11. is. Boards. Designs for Elegant Cottages, and small Villas, calculated for the com- fort and Convenience of Persons of moderate and of ample For- tune, carelully studied and thrown into Perspective, with General Estimates, by E. Qyflord, ArcliiteEt Part II, Engraved in Aqua- tinta on 26 Plates, (Mano 11. us. 6d. boards. Hints for Dwellings, consisting of Original Designs for Cottages Fami-ho‘uses, Villas, 85c. plain and ornamental; with Plans to each, in which strict Attention is paid to unite Convenience and Elegance with Economy. Including some Designs for Town- houses. By D. Laing, Architect, and Surveyor. Elegantly en- graved on 34 Plates in Aquatinta, with appropriate Scenery. QEK'UTO, il. 55. in boards. Sketches for Country Houses, Villas, 471;, Rural Dwellings; calculated for Persons of moderate Income, and for comfortable Retirement. Also some Designs for Cottages, which maybe constructed of the simplest Materials; with Plans and general Estimates. By john Plow. Elegantly engraved in Aquatinta on 4.2 Plates, (marto, ii. I 15. 6d. in Boards. Prrme Orne’e, or Rural Improvements, 3 Series of Domestic and Orna- mental Designs, suited to Parks, Plantations, Rides, Walks, Rivers, Farms, (Sec. consisting of Fences, Paddock House, a Bath, Dog kennels, Pavilions, Farm-yards, Fishing-houses, Sporting-Boxes, Shooting-lodges, Single and Double Cottages, &c. calculated for Landscape and Picturesque Effects. By john Plow, Architect. Engraved in Aquatintaon 38 Plates, with appropriate Scenery, Plans, and Explanations. (mane. In Boards, :1. us. Get. Rural Architecture, or Designs from the Simple Cottage to the decorated Villa, including some which have been executed. By john Plow. On 62 Plates, with Scenery, in Aquatinta. Half Bound, 2b as. . An Essay on British Cottage Architecture, exemplified by fourteen Designs, with their Plans, &c. on 23 Plates, designed and cxe- cured by james Illa/ton. The Second Edition, with two additional Plates, large uarto, Boards, 11. 115. 6d. The same elegantly coloured, zl. 125. 6d. A Collection of ArchitecturalDesigns, for Villas, Casinos, Mansions, Lodges, and Cottages, from original Drawings, by james Randall, Architect, engraved in Aquutnita, on 3+ Plates, Folio, 2i. 123. 6d. ' The same on Imperial Folio Paper, 3l. i35. 6d. The Arrhitect and Builder": ll/Iiscellanv, or Pocket Library; containing original Picturesque Designs in Architecture, for Cottages, Farm, Country, and Town Houses, Public Buildings, Temples, Green. Houses, Bridges, Lodges and Gates for Entrances to Parks and Pleasure Grounds, Stables, Monumental Tombs, Garden Seats, &c. By (.‘hm-les M1.l.lleton, Architect. On 60 Plates; coloured. il. is. bound. Etmih'ar Architecture: consisting of Original Designs of Houses for Gentlemen :ind Tradesmen, Parsonages, and Summer Retreats; with Backd'ronts, Sections, Sec. together with Banqueting Rooms, and Churches. To which is added, The Masonry of the Semicir- cular and Elliptical Arches, with Practical Remarks. By the late Thomas Rawlins, Architect. On 51 Plates, Royal O‘uurto, ii. is. (,‘rundw‘s Convenient and Ornamental Ar.-hitecture; consisting of Origi- nal Designs for Plans, Elevations and Sections, beginning with the Farm-house, and regularly ascending to the most grand and magni— ficent Villa; calculated both for Town and Country. with Expla- nation in Letter—press, and exact Scales. Engraved on 7o (50;)- per-plates, 16$. Boards 44 Series of Plans, for Cottages or l-Iahitationsfir the Laliastrcr, either in Husbandry or the Mechanic Arts, adapted as well to Towns as to the Country. To which is added, an Introduction, containing many useful Observations on this Clas! of building, tending to the Comfort of the Poor, and Advantage of the Builder ; with Calcula- tions of Expeuces, By the late Mr. :7. Wood, of Bath, Architect. A new Edition, corrected to the present Time, with 30 Plates, large 4to. ii. is. The Country Gentleman‘s Architect, in a great Variety of New Designs for Cottages, Farmhouses, Country-houses, Villas, Lodges for Park or Garden Entrances, and ornamental wooden Gates, with Plans of theOli‘ices belonging to each Design; distributed with a strict Attention to Convenience, Elegance and Economy. On 3: Oparto Plates. By :7. Miller. Architect. Scwed, 105. 6d. assays of the London Architectural Society. Octave, 4 Plates. 73. Boards. \ iew of Rome, on i2. Sheets, 3]. 3s. . u u u \ us Britanntcus, 3 Vols. Tl ontinuation to ditto, 2 Vols. Ch er‘s (Sir William) Treatise on Civil Architecture, i3d. Edit. bound, 4.1. 4.9. ‘ Ch r's Buildings and Views of Kew'Gardens. Half bound, 09. Ch s‘s Designs for Chinese Buildings, Sec. Half bound, ll. its. 6d: CM rs‘s Dissertation on Oriental Gardening, 4to. 98. 1771}, ones’s Designs, by Kent, 2 vols. folio. Wa irArches, and their abutment Piers, octavo, 19 Plates. W4 emarks’on Theatres, octavo, 3 Plates. 73. Ma, (fumes) Perspective, (matte il. 15. ”/00 ectures on Perspective, with an Apparatus. 11. 155. Pain lam, Elevations, &c. of Noblemen’s Seats, Soc. folio, 2 vols. H ound, 6|. 16s. 6d. The hitectural Antiquities of Athens, by Stuart, 3 vols. of Rome, Ba , Palmyra, Pcestum, Ionia, de la Grece, par Le Roy. &c. &c. Rich on on the Five Orders, folio. Boards, il. :15. 6d. ‘ Plans fir Houses, octavo. Boards, 5s. New ' Translation qfl/itruvius, 1. vols. folio. Nicho 's Principles of Architecture, 3 vols. 8vo. 3i. 3s. boards. A ‘Tr se on Theatres, including some Experiments on Sound, by C. S ers, Architect, with Plates, 4to. boards, 105. 6d. 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Du nd Lecons a Ar:hitecture, Quarto. Dwnd Recueil et Parallel: des Eclifices Anciens et Mcdernes, avec un te historique. 92 very large folio Plates. Dr. roolt Taylor‘s Method of Perspective made “'9’ both in Theory and . ac‘lice; in two Books: being an Attempt to make the Art of Perspective easy and familiar, to. adapt it entirely to the Arts ot Design, and to make it an entertaining Study to any Gentleman who shall choose so Polite an Amusement. By joshua Kirhy. Illus- tinted~ with 35 Copper-plates. The third Edition, With several Addit us and -lni rovements. Elegantly printed on Imperial Paper“. Half Bonn , :l. 125. 6d. ‘ The Perspective of Architecture, :1 Work entirely new ; deduced from the Principles of Dr. Brook Taylor, and performed by two Rules of universal Application. Illustrated with 73 Plates. Begun by COIIHDIntl of his present Majesty when Prince of W'ales. By joshua. Kirlgy. Elegantly printed on Imperial Paper. 3l. 3s. lialfbouiid. The Description and Use ofa new Instrument cal/rd the Architectonic Sec- tor, bywhich any Part of Architectureinay be drawn wlth Facility and Etactness. By joslrna Kit-hf. Illustrated with 25 Plates; elegaiity printed on imperial Paper. Half bound, 11. 165. The two Frontispieces, by Hogarth, to Kirby‘s Perspective, may be ‘ had sepirate. each 55. Thirty Cipitals ofColumns, with six Frises, from the Antique. Eu- 3' gravedin Aquatiiita by G. Richardson, on 18 Plates. ato. 153. ° 18:. des Hotels, 51 Folio, no Designs br Shop Fronts and Door Cases, on 27 Plat-es. am. 103. 6d. Designs pr Monuments, including Grave-stones, (.‘ompartments, ll'all- ' pieces, .md rTombs. Elegantly engraved on 4.0 quarto Plates. Half bound 165. Designs hr Chimney-Pieces, with Mouldings and Buses at large on 24. . quartoPlntes, ios. 6d. The Studnt‘s Instructor, in drawing and working the Five Orders 0* Arclii'ecture; fully explaining the best Methods of_strilting regular ' and qiirked h‘louldings, for diminishing and glueiiig of Columns and C:pit:ils, for finding the true Diameter of an Order to any given Heigh, for striking the ionic Volute circular and elliptical, with finishcl Examples, on 11 large Scale, of the Orders, their Plunceers, ,,: &c. aid some Designs for Door Cases, by Peter Air/J.» 15w, engraved 1 on 41Pllites octavo. 105. 6d. hound. A new Edition corrected , and much enlarged. The C(lflr’flMI"! New Guide, being a complete Book of Lines for Car. pentr' and Joinery, treating fully on Practical. Geometry, Selim,- . Lincsfor Roofs and Domes, with :i great Variety of Dcs‘igns {grit Roofi. Trussed Girders, Floors, Domes, Bridges, C\‘c. Staii‘—C;ises‘~' and laud-rails of various Constructions. Angle-Burs for Shop ‘ Frons, and Raking Mouldings, with many other Things entirely new : the Whole founded on true Geometrical Principles, the The ory aid Practice well explained and fully exemplified on 73 Copper Plate; including some Practical Observations and Calculations oi ~ . the Sreiigth of Timber, by P. Nicholson, am. I 55. tThe Ctr-Mn,” and joiner": Assistant, containing Practical Rules fo ,. inakiig :ill Kinds of Joints. and varioush‘letliods of lluigcing thei ,. ‘ togetier; for hanging of Doors on strait or Cerlllle‘ Plans; frrtitfi 1131 c.» ting up Window's and Shutters to answer various Erpose‘s, with Rules for hanging them a for the Construction of Floos, Partitions, Sofiits, Groins, Arches for Masonry : for construcmg Roots in the best. Manner from a given Qi'antity of Timber; or placing of Bond-Timbers ; with various Methods for adjusting taking Pedi- ments, enlarging and diminishing of Mouldings, takh; Dimensions for Joinery, and for setting out Shot) Fronts; with new Scheme for constructing Stairs and Hand-rails, and for Stairs aving a coni- cal WellJiole, 85c. Sic. To which are added, Examrles of Various Roofs executed, with the Scantlings from actual heasuremeuts, with Rules for Mortices and Tenons, and for fixing Inn Straps, &c. Also Extracts from M. Belidor, M. du Hamel, M. d Bufl‘on, See. on the Strength of Timber, with practical ()bservatirns. Illustra- ted with 79 Plates, and copious Explanations. By liter ,Nicbolson. (first to 185. bound. The Carpenter and yoiner‘s Reporitory: or, a new Systert of Lines and Proportions for Doors, Windows, Chimneys, Comics and Mould- ings, for finishing of Rooms, Sic. Sec. A great Varietyof Stair-Cases, on a Plan entirely new, and easy to he understood. Circular—cir- cular Sollits, flewing and winding in strait and (ircular Walls, Grains, Angle Brackets, Circular and Elliptical Skylights, and the Method of squaring and preparing their Circular Ban, Shop Fronts, 85c. By 1!". Pain, Joiner. Engraved on 69 folio Copperxplatcs. Bound, i6s. Painfs British I’allaa’io, or Builder‘s general Assistant ; demonstrating in the most easy and practical Method, all the prircipal Rules of Architecture, from the Ground Plan to the Ornanental Finish. Illustrated with several new and useful Designs of Horses, with their Plans, Elevations, and Sections. Also clear and amrle Instructions annexed to each subiect in Letter-press; with a Lit of Prices for Materials and Labour, and Labour only. 7bis Il’rrk will be uni- pom-o:)omg ‘saasluui-aauiqeg ‘saaueg o: [ngssn Alternopiaa 'Jsisew u mouumguiumai .10} suoiz -:m.nsu1 qzrm ‘saleld 91 no ‘sfiuimmq 30 uogimiui] ur psnrtigug ‘329 ‘a‘s‘enog ‘5);an ‘snoms ‘slmrdno ‘sfiurplnow .10} sanea'I 30 ”[dtuexa’ .19de [q ‘Asna opstu rituuwtuo Farm-mp fa ”N’WF‘J at“; '59 ‘pamag ‘onog 'rtwqquog 'J :(q "parrots pun umer ‘ssitrd :1 no =saoaid-Aauuqu) J03 sufdrssq er :3er any]: 'yeugfiiio 9111 se uoguodmd sures sip filllllltwl ups ‘ulsqi aseuoap .10 aseaaaui o; M011 frnrzuag pup #:2ng ‘qmnlvg fa {ram/1 y ‘p9 ~s£ ‘paiuss 'oue% 'guqun/og H Aq patrols pun umua ~suit) fl {ridpuiid fiUlJBJODGG urpasn pun ‘Sugiutnd JO ‘poom ‘oosnig u! paiuosxs Kluounuoa ‘slauuad lUQpOlu .10} suflgsaq Juefiap 30 A'JagwA e Eugureiuoo Enusuzmuo flqaog ow” y '55: pastas would onog 9319‘ 28 no ‘8)“qu 30 Jauuuw sq: u! panesfiua K111123919 ‘saztid pun aSuuog so saldurexg ominous 30 AnarntAefiuiugmuoo '329 ‘smiuiud ‘SJSA 423 “a .103 Jadmd ‘Eupliom .103 DZES "u; e uo ‘pa.(v[-Ir_lq mummuo 's'h 1+ -paqsruy uaqm swoox sq; JO Joana um} sq; Mons sSuimuq [eurfiiao sq; o; Suipioaae pamoloa sardog owes 's‘! 1: aronuoaaq pus usmsymg ‘udoog '9 .(q poring pun umcaq ‘saield our); oz uo '93481 n: sszgsg pue smseua 1mm quauulsgnaquig unpum 30 591513 SI‘lOlJBA sq; “E swoon Jo uopuxoaaq an; .10} sufirsaq ‘ ‘ ‘pg '5“ '[1 an.“ 'ounlfi) 33.181 Spainomo fillucgals are qagqm 30 h ‘santld in no panmfius (new ngq;.ry ‘(qmg 7' '3 My '32? ‘SJled ‘sr:pumuA ‘ssasrd Kauluiqa ‘s‘Jooq .‘Eulplog ‘swoou fiurmwa pue Sunnq ‘smol «ma 0; alqenns siuatuusmoqulg uiapow .103 surging fa «0359qu y '97? ‘SLNHWV HO :10 83008 . “V . ,P‘ I . » seem, Heads, B} F. Rigaud, Esq. R. A. Illustrated . , _ Plates and . er Figures. To which is prefixed, a névfim , I. Author, dr n up from authentic Materials till now inaccessible,- by :7. S. Hvkiw, Esq. F. A. S. Octavo; 9s. 6d. Boards; on Royal Paper :33. 6d. Boards. ‘ @bservations the Theory and Practice of Landrcape Gardening, including s: e Remarks on Grecian and Gothic Architecture; collected fr various Manuscripts in the Possession of the dif- ferent Noble en and Gentlemen for whose Use they were originally written. T whole tending to establish fixed Principles in the re- speé'tive Art By H. Repton, Esq. Elegantly printed in large (Mano and illustrat with many Plates 51. 5s. Boards. An Enquiry ltO tlr‘e Changes of Taste in Landscape Gardening, to which are dded some Observations on its Theory and Practice including a efence of the Art. By H. Repton, Esq. Octavo 55. Hints for Pict esque Improvements in Ornamented Cottages and their Scener . including some Observations on the Labourer and _ _ ... . ..J r... exam.“ 1-." 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