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Les diagrammes suivants illustrent la mAthoda. 1 2 3 1 2 3 4 5 6 ^^K MICROCOPY RESOLUTION TEST CHART (*NSI and ISO TEST CHART No. 2) 1.0 I.I |50 ""•■ 114.0 L25 iu 2.5 2.2 2£ 1.8 1.6 _J APPLIED IIVMGE I ^^ '653 East Main stteel ST.a Rochester, New York U609 USA '-^ (716) «82 - 0300 - Phone ^5S (716) 288 - 5989 - Fax -#• ;r»f3e£V:T7aL' m Modem Carocntry A TKAC ; K AI, M AM AL A MW ,\Mi iiiMIIIIK (,111'K (-..MVIMN,. IHMiKII-, "I Ilk Mlllllii lilU 1 KiaRAI, W.m.I.WoKK, W KI l l tN IS II, I VI kS HAY *\\\\r. THAI' l>(>H Mir IllWIIhll; iVilKklSl.MAN, IIII^IKMHi Ullll IHMikll'S ill |ilM,k\\H Will. 11 AKK Kfll'H lAI.I.V M\|i|; -i . IIIAI ANWINK CAS 1.111. ,U rillM Wlnidl 1' LIllHlllV I'KKI) T. 11()I)(,S()\, Ar.liiiirt Ijili.ri.t llic NaII.isai. l;illli|n, Aiiili,.r I t "i ;iiriiii,.,M Stiise H.iiiJr.uhn^'." •i'r.uin.il l\.i i,f iln; Sm I Sui.ir.., " t-t. . if./.i SI h\i //■:/> k^^rrnu The Radford Architectural Co. Riverside, III., IJ. S. A. Chicago New YorK "% Special! WITHOUT extra cost to our readers we have added to this vohime the perspective views and floor plans of twenty-five houses. The complete working plans and specifications of any of those houses will be mailed the same day the order is received. Send all ordors to THE RADFORD ARCHITECTURAL CO. IlIVKKSIDE, ILL., U. S. A. M COPTRHiHIED. 190S BT FREDERICK J. DRAKE ft CO. Ik M- BT FKEPEKICK d PREFACE "Good wine," says Shakespeare, "needs no bush," which of course means that when a thing is good in itself, praise makes it no better. So with a book, if it is good, it needs no preface to make it better. The author of this book flatters himself that the work he has done on it, both as author and compiler, is good; therefore, from his standpoint a preface to it is some- what a work of supererogation. His opinion regard- ing the quality of the book may be questioned, but after forty years' experience as a writer of books for builders, all of which have met with success, and during that time over thirty years editor of one of the most popular building journals in America, he feels his opinion, reinforced as it is by thousands of builders and woodworkers throughout the country, should be entitled to some weight. Be that as it may, however, this little book is sent out with a certainty that the one and a half million of men and boys who earn their living by working wood, and fashioning it for useful or ornamental purposes, will appreciate it, because of its main object, which is to lessen their labors by placing before them the quickest and most approved methods of construction. To say more in this preface is unnecessary and a waste of time for both reader and author. FRED T. HODGSON. COLLINGWOOD, ONTARIO, July, I9O2, : ,M I CONTENTS 3 PART I I carpenter's geometry 1 he Circle g Tangents 1 1 Degrees ' ,' 14 Circular Ornamentation -8 Finding Centers 20 Polygons 22 Bisecting Angles 28 Octagons 30 Straight Line Solutions 32 Bisecting Angles with Steel Square 34 Solutions of Problems with Steel Square 38 Ellipses, Spirals and Other Curves 41 Describing Elliptical Curves 46 Flexible Radial Guide 49 Ovals 50 Spirals 52 Parabola and Its Uses, The 56 Cycloidal Curves 57 PART II PRACTICAL EXAMPLES Segmental Arches 61 Flat Arches " ' '. 62 Horseshoe Arches 62 Lintel Arches 63 Elliptical Arches 63 Lancet Arches " . 64 Four Centered Arches 65 Ogee Arches 66 Mouldings g^ Balusters and Turned-work 68 Steel Square, Description of 70 Lumber Rule " 71 Brace Rule 73 b 6 CONTENTS PAO» Table of Braces 75 Octagon Rule on Steel Square 76 Rafter Rule hy Steel Square 76 Cutting Bridging 78 Dividing Lines 79 Laying off Pitches 81 Cuts and Bevels for Rafters 83 Bevels for Hips, Jack Rafters and Purlins 85 Framing Sills, etc 8/ Trimming Stairs, Chimneys, etc 89 Framing Corners, etc 91 Roofs and Roofing Generally 06 Lines for Hip Roofs S Octagon Hip Roofs yg Lengths of Jack Rafters 102 Trussed Roofs 103 Sisser Roofs 104 Domical Roofs 105 Spires and Spire Framing 108 Triangular Framing 109 Timber Scarfing in Various Ways no Mortise a.id Tenon in Timber in Reinforcing Timber n3 Strapping Timber 112 Trussing and Strengthening Timber n4 PART HI joi:;er's work Laying out Kerfs nS Bending Kerfed Stuff ng Kerfing for an Ellipse 120 Kerfing on a Rake 121 Mitering Circular Mouldings 121 Mitering Circular and Straight Mouldiujjs 122 Mitering Curved Mouldings in Panels 122 Laying out Curved Hips 123 Laying out Ogee Hips and Rafters 124 Laying out Curved Hip? and Jack Rafters 125 Raking Mouldings 126 Raking Mouldings for Pediments 128 Laying out Faking Mouldings for Circular Pedi- ments 129 CONTENTS 7 rAGB Cutting R?king Mouldings in M'tcr-box 130 Angle Bits at Different Angles 13 » Inside Cornices on a Rake 132 Cluster Columns ^33 Bases and Capitals of Cluster Columns 133 Hoppers, Regular *34 Miter Cuts for Hoppers 135 Butt Cuts for Hoppers l3o Housed Hopper Cuts ^3'* Corner Blocks for Hoppers, etc 139 Corner Blocks for Acute Hoppers 140 Miters for Square Hoppers Mi Miters for Acute Hoppers Ml Miters for Obtuse Hoppers 142 Compound Hopper Lmes 143 Covering a Conical Roof 149 Gore f-'r Conical Roof 15° Covering Domical Roofs 150 Incli.ied Domical Roof 15* Circular Door Entrances 'S^ Bending Block for Splayed Heads I53 Splayed Soffits 154 Gothic Soffits 155 Dovetailing ^S^ Common Dovetailing 157 Lapped Dovetailing 158 BFnd Dovetailii. ■ 159 Splayed Dovetai ing 1 59 Stairbui'ding 159 Pitch-board and Strings loO Treads, Risers and Strings 161 Dog-legged Stairs 102 Table of Treads and Risers 163 Winding Stairs 163 Open String Stairs 164 Setting ' -"il and Newel Post 104 Metho< Forming Step 165 Brackettu Steps 165 Joiner's Work Generally 107 Various Styles of Stairs 168 St}'les of Doors 169 Description of Doors • I/O ■ '4: 5 CONTENTS Window Frames and Sections V?? Miscellaneous Illustrations jli Description of Balloon Framing...'.." .1, Sections of Bay Window Frames.. ,7^ Turned Mouldings and Carved Newels." ". 17^ Shingling, Different Methods ,7? Shingling liip Rafters ,^1 Shingling Valleys 'y Illustrations of Shingling /J Flashings for Valleys ".V;.'.". ". ; '. ". '. ; ; ; • ' ' J7° BUILDERS PART IV USEFUL TABLES AND MEMO.RANDA FOR Lumber Measurement '^able. . ,0, Strength of Materials Jo: Table of Superficial or Flat Measure." ,8, Round and Equal-sided Timber Measure ... " " " iS* Shingling '°'* Table for Estimating Shingles . . . ." .ol Siding, Flooring and Laths .0^ Excavations g'* Number of Nails Required in Carpentry "v'-ork." ." " igc Sizes of Boxes for Different Measure- " is? Masonry r^ Brick Work ."..".""; J°S Slating :::::::;.": \li To Compute the Number of Slates of a Give"n Size Required per Square ,00 Approximate Weight of Materials for Roofs .' ." .' .* " i8q Snow and Vvind Loads " o^ United i .ates Weights and Measures." .".".' to? Land Measure , rl Cubic or So'id Measure. ..! .X? Linear Measure ' .^. Square Measure .- . Miscellaneous Measures and Weights. .' inr Safe-bearing Loads .^ Capacity of Cisterns for Each " "fen' Inches ' in Depth Number of Nails and Tacks'per'Pound.". Jq, Wind Pressure on Roofs ..... J^j :.3L. ■1 MODERN CARPENTRY n 1 m 3 PART I CARPENTER'S GEOMETRY CHAPTER I THE CIRCLE While it is not absolutely necessary that, to become a gO(^ ' mechanic, a man must need be a good scholar or be well advanced in mathematics or geometry, yet, if a man be proficient in these sciences they will be a great help to him in aiding him to accomplish his work with greater speed and more exactness than if he did not know anything about them. This, I think, all will admit. It may be added, however, that a man, the moment he begins active operations in any of the con- structional trades, commences, without knowing it, to learn the science of geometry in its rudimentary stages. He wishes to square over a board and employs a steel or other square for this purpose, and, when he ccratches or pencils a line across the board, using the edge or the tongue of the square as a guide, while the edge of th'' blade is against the edge of the board or parallel with it, he thus solves his first geometrical problem, that is, he makes a right angle with the edge of the board. Thia Is one step forward in the path of geometrical science. He desires to describe a circle, say of eight inches diameter. He knows instinctively that if he opens his 9 nP 10 MODERN CARPENTRY compasses until the points of the legs are four inches apart,— or making the radius four inches— he can, by keeping one point fixed, called a "center," describe a circle with the other leg, the diameter of which will be eight inches. By this process he has solved a second geometrical problem, or at least he has solved It so far that it suits his present purposes. These examples, of course, do not convey to the operator the more subtle qualities of the right angle or the circle, yet they serve, in a practical manner, as assistants in every-day work. When a man becomes a good workman, it go'.-s with- out saying that he has also become possessor of a fair amount of practical geometrical knowledge, though he may not be aware of the fact. The workman who can construct a roof, hipped, gabled, or otherwise, cutting all his material on the ground, has attained an advanced practical knowledge of geometry, though he may never have heard of Euclid or opened a book relating to the science. Some of the best workmen I have met were men who knew nothing of geometry as taught in the books, yet It was no trouble for them to lay out a circular or elliDtical stairway, or construct a rail over them, a feai that requires a knowledge of geometry of a high order to properly accomplish. These few introductory remarks are made with the hope that the reader of this little volume will not be disheartened at the threshold of his trade, because of his lack of knowledge in any branch thereof. To become a good carpenter or a good joiner, a young man must begin at the bottom, and first learn his A, B, C's, and the difficuItiLs that beset him will disap- pear one after another as his lessons are learned. It CARPENTERS GEOMETRY II must always be borne in mind, however, that the young fellow who enters a shop, fully equipped with a knowl- edge of general mathematics and geometry, is in a much better position to solve the work problems that crop up daily, than the one who starts work without such equipment. If, however, the latter fellow be a boy possessed of courage and perseverance, there is no reason why he should not "catch up" — even over- take — the boy with the initial advantages, for what is then learned will be more apt to be better understood, and more readily applied to the requirements of his work. To assist him in "catching up" with his more favored shopmate, I propose to submit for his benefit a brief description and explanation of what may be termed "Carpenter's Geometry," which will be quite la MODERN CARPENTR " sufficient ,f he learn it well, to enable him to execute any work that he may be called upon to perform al Iw.I. do so a- clearly and plainly as possible^nd n as few words as the instructions can beVamcd so as o make them intelligible to the student The crcle shown in Fig. , is drawn from th.^ center 2. as shown, and may be said to be a plain BaJie w.thm a continual curved line, every part of the line bemg equally distant from the center .. I ^ he Tsir d c^mf'""^^^ '' '''^- ^'^ "- ^^ ^^ Hne l^t.^"^'^"'"f"^"^<-^ •« called the diameter, and ^he 1 ne DE .s denommated a chord, and the \re-i on aZiT'^^t' '7'' '■■-' -^ ^'^ chord i;^;::rd the In e". tl , h "\' ''''^' '' ' ""^ ^^^^^ '^on^ h.lf L . . '' circumference C. and is always one- half the length of the diameter, no matter what Zt d.ametermaybe. A tangent is a line which toJe the crcumference at some point and is at right a gle wuh a rad.al l.„e drawn to that point as shown Tc they win '\f^'""',"""'"'^^ ^'^'^ ^^'fi--^'-^ as they w,ll be frequently used when explanations of learner should memorize both the terms and their sig! n.ficat.ons m order that he may the more reld fv understand the problems submitted for solutLn "^ t frequently happens that the center of a circle is the 2^ '"; ""' '^' ^^""^ '■" -^'- to compL Thecen eVof "'P' ^''' °' '''' circumference. BHC I i, . K '' '""l'' T"" ^' ^°""d ^- f-"«^vs: let BTA -, ^H ^ V'^'"'^ ^^ '^^ ^^-g'^-'nt II; and BJA a chord enclosing the segment. Bisect or divide m equal parts, the chord BC at H -, n I down from this point to D Do 7hf ^"^.^^^are chord ATT> '"^ ^ame with the -hord AJL. squaring over trom J to D, then the CARPENTERS GEOMETRY >S point where JD and HD inteisect, will be the center of the circle. This is one of the most important problems for the carpenter in the whole range of g' 'omctry as it enables the workman to local-; any center, and to draw curves he could not othcrwlsr describe without this or other similar methods. It is by aid of this problem that through any three points not in a straight line, a circle can be drawn that will pass through • oh of . ,€ three points. Its usefulness will be shown further as applied to laying out segmental or curved t.-p window, door and other frames and sashes, and 'he learner should thoroughly master this problem bcfor. stepping further, as a full knowledge of it will assist him very materially in understanding other problems. The circumference of every circle is measured by being supposed to he divided into 360 equal parts, called degrees; each degree containing 60 minutes, a ■I I ; 14 MODERN CARPENTRY smaller division and each minute into 60 steonds, a still imaller division. Degrees, minutes, and seconds are written thus: 45° 15' 30", which is read, forty-five degrees, fifteen minutes, and thirty seconds. This, I think, will be quite clear to the reader. Arcs are meas- ured by the number of degrees which they contain: thus, in Fig. 3, the arc AE, which contains 90°, is called a quadrant, or the quarter of a circumference, because ^^i -/!• r^ u /a 1 ^y-^- v^^\ /so* i V 90° is one quartei cf 360°, and the arc ABC whici* .v^i CARPENTER'S GEOMETRY «5 the number it contains, as will be teen by counting off the spaces as shown by the divisions on the curved line *D. These rules hold good, no matter what may be the diameter of the circle. If large, the divisions are large; if small, the divisions are small, but the manner of reckoning is always the same. One of the qualities of the circle is, that when divided in two by a diameter, making two semicircles, any chord starting at the extremity of such a diameter, as at A or B, Fig. 4 -"'d c.;tting the circumference at any point, as at C. >t E, a line drawn from this point to the other extremity of the diameter, will form a right angle — or be square with the first chord, as is shown by the dotted lines BCA, BDA, and BEA. This is something to be remembered, as the problem will be found useful on many occasions. The diagram shown at Fig. 5 represents a hexagon within a circle. This is obtained by stepping around the circumference, with the radius of the circle on the compasses, six times, which divides the circumference into six equal parts; then draw lines to each point, which, when completed, will form a hexagon, a six- sided figure. By drawirj lines from the points obtained in the circumference to the center, we get a i6 MODERN CARPENTRY three-sided figure, which is called an equilateral trl angle, that ,s, a triangle having all its srer:;t,t Iength; as AB, ACand BC. ThedottOfllln. U U The diagram shown at Fig. 6 illustrates the method of trisecting a right angle or quadrant >nto three equal parts. Let A be a center, and with the same radius intersect at E, thus the quadrant or right anirle is divided into three equal parts. CARPENTER'S GEOMETRY »7 If we wish to get the length of a straight line that shall equal the circumference of a circle or part of circle or quadrant, we can do so by proceeding as fol- lows: Suppose Fig. 7 to represent half of the circle, as at ABC; then draw the chord BC, divide it at P, join it at A; then four times PA is equ-' *o the cir- cumference of a circle whose diameter is xtC, or equal to the curve CB. To divide the quadrant AB into any number of equal parts, say thirteen, we simply lay on a rule and make the distance from A to R measure three and one- fourth mches, which are thirteen quarters or parts on the rule; make R2 equal one-fourth of an inch; join KP; draw from 2 parallel with RP, cutting at V; now take PV in the dividers and set off from A on the circle thirteen parts, which end at B, each part being equal to PV, and the problem is solved. The "stretchout" or length of any curved line in the circle can then be obtained by breaking it into segments bv chords. a<= shown at BN. 1 have shown in Fig. 5, how to construct an equi- lateral triangle by the use of the compasses. I give at i8 MODERN CARPENTRY Fig 8 a practical example of how this figure, in con- nection with circles, may be employed in describing a figure known as the trefoil, a figure made much use of in the construction of church or other Gothic work and for windows and carvings on doors and panelings. Each corner of the triangle, as ABC, is a center from which are described the curves shown within the outer circles. The latter curves are struck from the center O, which is found by dividing the sides of the equi- lateral triangle and squaring down until the lines cross at O. The joint lines shown are the proper ones to be made use of by the carpenter when executing his work. The construction of this figure is quite simple and easy to understand, so that any one knowing how to handle a rule and compass should be able to construct it after a few minutes' thought. This figure is the key to most Gothic ornamentation, and is worth mastering. CARPENTER'S GEOMETRY »9 There is another method of finding the length or "stretchout" of the circumference of a circle, which I show herewith at Fig. 9. Draw the semicircle SZT, and parallel to the diameter ST draw the tangent UZV; upon S and T as centers, with ST as radius, mark the arcs TR and SR; from R, the intersection of the arcs, draw RS and continue to U; also draw RT, and con- tinue to V; then the line VU will nearly equal in length the circumference of the semicircle. The length of any portion of a circle may be found as fol- loA's: Through X draw RW, then VVU will be the ' stretchout" or length of that portion of the circle marked SX. There are several other ways of deter- mining by lines a near approach to the length of the circumference or a portion thereof; but, theoretically, the exact "stretchout" of a circumference has not been found by any of the known methods, either arith- 30 MODERN CARPENTRY ■■-^ No. ethod. however. th?t-;-:„^:,--^;;^ sample so convenient and so accurate as the a th metical one, which I mve hcrewifh Tf f . the diameter of a circle bvJi^" H ""' ."""'^'P'^ Eive the lenath f Ik ■ ^^ ^ ^' *''"-' Product will I ve ine length of the c.rcumference, very nearlv These figures are base ' on the fact fh./ , whose diameter is i « tne tact that a circle With ihe exception of the formation of mouldings, and orna- mentation where the circle and its parts take a prominent part, 1 have sub- mitted nearly all con- cerning the figure, the everyday carpen- ter will be called to use Ti,A:rT 7 '•"" ""■ ' "■'" "y -^-i ^t>'»v ho„ lo use the knowledge now given Before leaving the subject, however, it n . as well to show how a curve, havin,. any n abt Tots'inTe'^ obtained-practicalV-if bu. th points ,n the circumference are available; as referred to in the explanation given of Fifr r I , f '^^^^'^'^^^ there are three points 'given i^t^^- ircur^ e^rj-n^r^: ^an bc^^^'T; ^'^- "• ^'^" ^h— ^-of such .IM by strlht"r ' "k"'''*"^ ^'^' P°'"^^ ^« -nd BC by straight lines as shown, and by dividing these lines ^./^? CARPENTER'S GEOMETRY »i ^3 and squaring down as shown until the lin-f, intersect at O ?.i shown. This point O is the center of the circle. It frequently happens that it is not possible to find a place to locate a center, because of the didmeter being so great, as in segmental windows and doc-s of large dimensions. To overcome this difficulty a method has been devised by which the curve may be correctly drawn by nailing three wooden strips together so as to form a triangle, as shown in Fig. ii. Suppose NO to be the chord or width of frame, ' nd QP the height of segment, measuring from the springin'; lines N and O; dsive nails or pins at O and N, keep Lhe triangle close against the nails, and place a pencil at P, then slide the triangle against the pins or nails whii., sliding, and the pencil will describe the necessary curve. The arms of the triangle should be several inches long'^-- than the line NO, so that when the pencil P arrives at N c J, the arms will still rest against the pins. CHAPTER II POLYGONS A polygon is a figure that is bounded by any number b etnf J'"'' '''''•'"" '^'"^ *h^ least'^that can be employed ,n surrounding any figure, as a triangle. A polygon having three sides is called a trigon; it is st« i calf "a ?r''^"'' •*^'.^"^'^- ^ P°'^^- -i ^oar sides IS call a tetragon; it is also called a square and an equilateral rect- angle. A polygon of five sides is a pentagon. A poly- gon of six sides is a hexagon. A poly- gon of seven sides is called a heptagon. _^ A polygon of eight ^. . , sides is called an octagon. A polygon of nine sides is called a nonagon A polygon of ten sides is called a decagon. A polygon of eleven sides .s called an undecagon. And a poly- gon of twelve sides is called a dodecagon There are regular and irregular polygons. Those having equal sides are regular; those having unequal sides are irregular. Polygons having more than twelve sides are known among carpenters by being denom- inated as a polygon having "so many sides." as a polygon with fourteen sides," and so on. 23 CARPENTERS GEOMETRY •J Polygons are often made ie of in carpenter work, particularly in the formation of bay-windows, oriels, towers, spires, and similar work; particularly is this the case with the hexagon and the octagon; but the most used is the equilateral rectangle, or square; therefore it is essential that the carpenter should know considerable regarding these figures, both as to their qualities and their construction. The polygon having the least lines is the trigon, a three-sided figure. This is constructed as follows: Let CD, Fig. i, be any given line, and the dis- tance CD the length of the side required. Then with one leg of the compass on D as a center, and the other on C, describe the arc shown at P. Then with C as a center, describe an- other arc at P, cutting the fir-^t arc. From this point of intersection draw the lines PD and PC, and the figure is complete. To get the miter joint of this figure, divide one sic", into two equal parts, and from the point obtained draw a line through opposite angle as shown by the dotted line, and this line will be the line of joint a; C, or foi any of the other angles. The square, or equilateral rectangle, Fig. 2, may be obtained by a number of methods, many of which will suggest themselves to the reader. I give <^'- ethod that may prove suggestive. Suppose tw( .des of a square are given, LHN, the other sides are found by taking HL as radius, and with LN for centers make the intersection in P, draw LP and NP, which com- f I »4 MODERN CARPENTRY The do.«d line skoJLunl mV """'" "" ure regular miter, or miter. leng^;t?ii.v«4^ :^ CARPENTER'S GEOMETRY 31 etry the figures are given with all their qualities. If the solution of any of the problems offered in this work requires a description and explanation of poly- gons with a greater number of sides than eight, such explanation will be given. I 'i & I CHAPTER III SOME STRAIGHT LINE SOLUTIONS The greatest number of difficult problems in carpen- Tn^llTT''^ of solution by ?he use of strl^'t i'nes and a proper application of the steel square, and JT in this chapter I will endeavor to show the reader how some of the problems may be jr- y ( solved, though it is ^ ^- I not intended to offer a treatise on the subject of the utility of the steel square, as that subject has been treated at works, and another and exnaustlj^^o!;;::::^-; preparat.on; but it is thought no work on arp^nt y can be complete without, at least, showing some of the solutions that may be accomplished by the p7ope use tTo::t'''' ■■""^""^^"- ^"^ ^^''-•" '-5:^- - us to make a perpendicular line on any given straiL^h' oiro::^'tt^'rK ''p^^ ^ -r-- ^''^ ^^ ^^^^^^^ and r.'l. p -^ ' '^- '• ^" '^"^ ^'■^•^'" straight line, and make F any point in the .sn„an. or nerncndi-„'. 1-e required. From F with a,^ radius, ^trt^i^ 12 j:^i^mimm^mg^M^^ CARPENTER'S GEOMETRY 33 I cutting in JK; with these points as centers, and any radius greater than half JK, make intersection as shown, and from this point draw a line to F, and this line is the perpendicular required. Foundations, and other works on a large scale are often "squared" or laid out by this method, or by another, which I will submit later. In a previous illustration I showed how to bisect an angle by using the compasses and straight lines, so as to obtain the proper joints or miters for the angles. At Fig. 2, 1 show how this may be done by the aid of the steel square alone, as follows: The angle is ob- tuse, and may be that of an octagon or pentagon o r other polygon. Mark any two points on the angle, as DN, equally distant from the point of angle L; apply the steel square as shown, keeping the distance EM and ED the same, then a line running through the angle L and the point of the square E will be the line sought. To bisect an acute angle by the same method, pro- ceed as follows: Mark any two points AC, Fig 3, equally distant from B; apply the steel square as shown, keeping its sides on AC; then the distance on each side of the square being equal from the corner gives it for a point, through which draw a line from B, and the angle is divided. Both angles shown are divided by the same method, making the intersection i (I 34 MODL/ I CARPENTRY i>S '■ in P the center of the trianeJe Th^ ,« • .l- considered l„^,u -iu.iontio L'^e"^'" J^r^s^' " ^ and C equal from the point B>" also an equal distance from the point or toe of the square to the points of con- tact C and A on the boun- dary lines. A repetition method of bisectiniT an«i«. j of the same shown at Fig 4 The o!l?; " • "" °'''^ ^^"ditions. is S- 4. 1 he process is just the same, and the iXuoiTre^es:!';.'''^ --•---'-'.- CARPENTER'S GEOMETRY iS To get a correct miter cut, or, in other words, an anple of 45°, on a board, make either cf the points A or C, Fig. 5, the starting point for the miter, on the edge of the board, then ap- ply the square as shown, keep- ing the figure 12" at A or C, as the case may be, with the fig- ure 12" on the other blade of the square on the edge of the board as shown; then the slopes on the edge of the square from A to B and C to B, will form angles of 45° with the base line AC. This problem is useful from many points of view, and will often suggest itself to the workman in his daily labor. To construct a figure showing on one sid ,> an angle of 30" and on the other an angle of 60°, by the use of the steel square, we go to work as follows: Mark on the edge of a board two equal spaces as AB, BC, Fig. 6, apply the square, keeping its blade on AC and making \\ 36 MODERN CARPENTRY h AD equal AB; then the angles 30° and 60° a'^ formed as shown. If we make a templet cut exactly as shown in Fig. 5, also a templet cut as shown in this last figure, and these templets are made of some hard wood, we get a pair of set sqi .res for drawing puri OSes, by which a large number of geometrical problems and drawing kinks may be wrought out. The diameter of any circle within the range of the steel square may be determi.ied by the instrument as follows: The corner of the square touching any part of the circumference A, Fig. 7, and the blade cutting in points C, B, gives the diameter of the circle as i shown. Another application of this principle is, that the diameter of a circle being known, the square may be employed to describe the circumference. Suppose CB to be the known diameter; then put in two nails as shown, one at B and the other at C, apply the square, keeping its edges firmly against the nails, con- tinually sliding it around, then the point of the square A wi'l describe half the circumference. Apply the I CARPENTER'S GEOMETRY S7 square to the other side of the nails, and repeat the process, when the whole circle will be described. This problem may be appl-ed to the solution of many others of a similar nature. At Fig. 8, I show how an equilateral triangle may be obtained by the use of a square. Draw the line DC; take 12 on the blade and 7 on the tongue; mark on the tongue for one side of the figure. Make the dis- tance from D to A equal to the desired length of one side of the figure. Reverse the square, placing it as shown by the dotted lines in the sketch, bringing 7 of the tongue against the point A. Scribe along the tongue, pro- ducing the line until it intersects the first line drawn in the point E, then AEB will be an equilateral tri- angle. A method of describing a hexagon by the square, is shown at Fig. 9, which is quite simple. Draw the line GH; lay off the required length of one side on this line, as DE. Place the square as before, with 12 of the blade and 7 of the tongue against the line GH; placing 7 of the tongue against the point D, scribe along the tongue for the side DC. Place the square as shown by the dotted lines; bringing 7 of the tongue against the point E, scribe the side EF. Con- :i: i 1 iSb i9W**ii ki jl MODERN CARPENTRY tinue in this way until the other half of the figure is dravn. All is shown by FAHC. Ine manner of biscctiuff angles has been shown in Figs. 2, 3 and 4 of the present chapter, so that it is not :>^cessary to repeat the process at this time. The method of describing an octagon by using the square, ir shown at Fig. 10. Lay off a square section with any length of sides, as AB. Bisect this side and place the s(]uare as shown on the side AB, with the length bisected on the blade and tongue; then the tongue cuts the side at the point to gauge for the piece to be removed. To find the size of square required for an octagonal prism, when the side is given: Let CD equal the given side; place the square on the CARPENTER'S GEOMETRY 39 line of the side, with one-half of the side on the blade and tongue; then the tongue cuts the line at the point B, which determines the size of the square, and the piece to be removed. A near approxima- tion to the length or stretch-out of a cir- cumference of a cir- cle may be obtained by the aid of the steel square and a straight line, as fol- lows: Take three diameters of the circle and measure up the side of the blade of the sfjuare, as shown at Fig. 1 1, and fifteen-sixteenths of one diameter on the tongue. From these two points ^.f^ 24 U ihllllllll j^.l.i.i.i.i.T.l.i.i.i.M- I DlAMETEfl* draw a diagonal, aud the length of this diagonal will be the length or stretch-out of the circumference nearly. If it is desired to divide a board or other substance into any given number of equal parts, without going through the process of calculation, it may readily be done by the aid of the square or even a pocket rule. AC, BD, ^i" A2, be the width of the board or I F ^glweryVt^^f -■T-i^".' 4« MODERN CARPENTRY I other material, and this width is seven and one-quarter inches, and we wish to divide it into eight equal parts. Lay on the board diagonally, witi. furthermost point of the square fair with one edge, and the mark 8 on the square on the other edge; then prick off the inches, I, 2, 3, 4, 5, 6 and 7 as shown, and these points will be the gauge points from which to draw the parallel lines. These lines, of course, will be some- thing less than one inch apart. If the board should be more than eight inch*^ i wide, then a greater length of the square may be jsed, as for instance, if the board is ten inches wide, and we wish to divide it into eight equal parts, we simply make use of the figure 12 on the square instead of 8, and prick off the spaces every one and a half inches on the square. If the board is more than 12 inches wide, and we require the same number of divisions: we make use of figure 16 on the square, and prick off at every two inches. Any other divisions of the board may be obtained in a like manner, varying only the use of the figures, on the square to get the number of divisions required. As a number of problems in connection with actual work, will be wrought out on similar lines to the fore- going, further on in this book, I will close this chapter in order to give as much space as possible in describ- ing the ellipse and the higher curves. _ ■-o that while the inside or outside lines of an ellipse can be obtained by any of the metho'^l>; I have given, the parallel line must be obtained either by gauging the width of the material or space required, or must be obtained by "pricking off" with compasses or other aid. I thought it best to mention this as many a young mail has spent hours in trying to solve the unsolvable problem when using the pins, pencil ?r-J string. There are a number of oth(;r curves the carpenter will sometimes meet in daily work, chief among these being the scroll or spiral, so it wii! be well for him to have some little knowledge of its structure. A true spiral can be drawn by unwinding a piece of string that r/^./j. 51 MODERN CARPENTRY V ■ has been wrapped around a cone, and this is probably the method adopted by the ancients in the formation of the beautiful Ionic spirals they producer* A spiral drawn by this method is shown at Fig. 14. This was formed by using two lead-pencils which had been sharpened by one of those patent sharpen- ers and which gave them the shape seen in Fig. 15. A *^* * ^'**^— — '"^ was then tied tightly around the pencil, and one end was wound round the conical end, so as to lie in notches made in one of the pencils; the point of a second pencil was pierced through the string at a convenient point near the first pencil, completing the arrange- ment shown in Fig. 15. To draw the spiral the pencils must be kept vertical, the point of the first being held firmly ya. the hole of the spiral, and the second pencil must then be carried around the first, the distance between the two increasing regularly, of course, as the string unwinds. This is a r«ugh-and-ready apparatus, but a true Fi^J5. CARPENTER'S GEOMETRY 53 spiral can be described by it in a very few minutes. By means of a larger cone, spirals of any size can, of course, be drawn, and that portion of the spiral can be used which conforms to the required height. Another similar method is shown in Fig. i6, only in this case the string unwinds from a spool on a fixed center A, D, B. Make loop E in the end of the thread, in which place a pencil as shown. Hold the spool firmly and move the pencil around it, unwinding the thread. A curve will be described, as shown in the lines. It is evident that the proportions of the figure are determined by the size of the spool. Hence a larger or smaller spool is to be used, as circum- stances require. A simple method of forming a figure that corre- sponds to the spiral somewhat, is shown in Fig. 17. This is drawn from two centers only, a and e, and if the distance between these centers is not too great, a fairly smooth appearance will be given to the figure. The method 54 MODERN CARPENTRY of describing is simple. Take ai as radius and describe a semi-circle; then take el and describe semi-circle 12 on the lower side of the line AB. Then with a2 as radius describe semi-circle above the line; again, with e3 as radius, describe semi-circle below the line AB; lastly with 33 as radius describe semi- circle above the line. In the spiral shown at Fig. 18 we have one drawn in a scientific manner, and which can be formed to dimensions. T o draw it, proceed as follows: Let BA be the given breadth, and the number of revolu- tions, say one and three-fourths; now multiply one and three- fourths by four, which equals seven; to which add three, the number of times a side of a square is contained in the diameter of the eye, making ten in all. Now divide AB into ten equal parts and set one from A to D, making eleven parts. Divide DB into two equal parts at O, then OB will be the radius of the first quarter OF, FE; make the side of the square, as shown at GF, equal to one of the eleven parts, and divide the number of parts obtained by multiplying the revolutions by four, which is seven; make the CARPENTER'S GEOMETRY SS diameter of the eye, 12, equal to three of the eleven parts. With F as a center and E as a radius make the quarter EO; then, with G as a center, and GO as a radius, mark the quar- ter OJ. Take the next center at H and HJL in the quarter; so keep on for centers, drop- ping one part each time as shown by the dotted angles. Let EK be any width de- sired, and carry it around on the same centers. Another method of obtaining a spiral by arcs of circles is shown at Fig. 19, which may be confined to given dimensions. Proceed as follows: Draw SM and LK at right angles; at the intersection of these lines bisect the angles by the lines NO and QP; and on NO and QP from the intersection each way set off three equal parts as shown. On i as center and iH as radius, describe the arc HK, on 2 describe the arc KM, on 3 describe the arc ML, on 4 describe the arc LR. The fifth center to describe the arc RT is under i on the line QP; and so proceed to complete the curve. There are a few other curves that may occasionally prove useful to the workman, and I submit an example or two of each in order that, should occasion arise where such a curve or curves are required, they may be met with a certain amount of knowledge of the subject. s« MODERN CARPENTRY I ^: ■ The first is the parabola, a curve sometimes used in bridge work or similar construction. Two examples of the curve are shown at Fig. 20, and the methods of describing them. The upper one is drawn as follows: I. Draw C8 per- pendicular to AB, and make it equal to AD Next join A8 anil B8, and divide bo; 1 line into the same number of equal parts, say 8; number th m as in the figure; draw i, 1-2, .'-3, 3, etc., then these lines will be tangents to the curve; trace the curve to touch the center of * ach of tho ■ lines between the points of intersection. The lower example is described thus: I. Divide AT) and BE, into any number of equal parts; CD and CE into a simila' number. 2. Draw I, 1-2, 2, etc.. parallel to AD, rnd from the points of division in AD and BE, draw lines to C. Th< points of intersection of the respective lines are po' its in the curve. The curves found, as in these figu s, ar^ quicker at the crown than a true circular segment; but, where me rise of the arch is not mon than one-tenth of th*- span, the variation cannot be perceived. A raking example of thih cur\ e .^ shown in Fig. 21 and the method of describing it: Let AC be the • -di- nate or vertical line, and Dl the axis, and B its cuex; produce the axis to E. and make I'E equal to DB; j ;in EC, EA, and divide them each into the same r ^sabtr CARPENTER'S GEOMETRY S7 of equal parts, and number the diviiions as shown on the figures. Join th- corresponding divisions by the lines II, 22, etc., and their intersections will produte the contour of the curve. The hyper- bola is some- what similar in appear iHce t o the parabola but it has properties peculiar to it- self. It is a dg rt not much used in carpcn- 4 fry, but it may \ well to refer to it br efly: Suppose there be two rij^ht equal cones. Fig. 22, hav- .^ — ^' --ji^ ing tiic same axis, and cut by a ^ A J plane Mn , Nm, parallel to that V- — [ ^A- jv axis, the sections MAN, rana, \ \y which result, are hyperbolas. In \ 1 7& place < f two cones opposite to each other, geometricians some- times suppose ioi. cones, which join on thp lines EH, GB, Fig. 23. and of which axis form two right lines, Ff, FT, crossing the center C in the same plane. To describe a cych id: The cycloid is the curve describ-'d by a point i'- ■' Vcumfer^n of a circle and ' I . 58 MODERN CARPENTRY 1. Let GH, Fig. 24, be the edge of a straight ruler, and C the center of the generating circle. 2. Through C draw the diameter AB perpendicular to GH, and EF" parallel to GH; then AB is the height of the curve, and EF is the place of the center of the generating circle at every point of its progress. 3. Divide the semi-cir- cumference from B to A into any number of equal parts, say 8, and from A draw chords to the points of division. 4. From C, with a space in the dividers equal to one of the divi';' ins on the circle, step off on each side the same number of spaces as the semi-circumference is divided into, and through the points draw perpendiculars to GH; number them as in the diagram. 5. From the points of division in EF with the Fig. 2 4. radius of the generating :ircle, describe indefinite arcs as shown by the dotted lines. 6. Take the chord Ai in the dividers, and with the foot at I and i on the line GH, cut the indefinite arcs CARPENTER'S GEOMETRY 59 described from i and i respectively at D and D', then D and D' are points in the curve. 7 With the chord A2, from 2 and 2 in GH, cut the indefinite arcs in J and J', with the chord A3, from 3 and 3, cut the arcs in K and K' and apply the other chords in the same manner, cutting the arcs in LM, etc. 8. Through the points so found trace the curve. F{g.2S. Each of the indefinite arcs in the diagram represents the circle at that point of its revolution, and the points D.J.K, etc., the position of the generating point B at each place. This curve is frequently used for the arches of bridges, its proportions are always constant, viz.: the span is equal to the circumference of the generating circle and the rise equal to the diameter. Cycloidal arches are frequently constructed which ar< 6o MODERN CARPENTRY not true cycloids, but approach that curve in a greater or less degree. The epicycloidal curve is formed by the revolution of a circle round a circle, either within or without its circumference, and described by a point B, Fig. 25, in the circumference of the revolving circle, and Q of the stationary circle. The method of finding the points in the curve is here given: 1. Draw the diameter 8, 8 and from Q the center, draw QB at right angles to 8, 8. 2. With the distance QP from Q, describe an arc O, O representing the position of the center P throughout its entire progress. 3. Divide the semi-circle BD and the quadrants D8 into the same number of equal parts, draw chords from D to 1, 2, 3, etc., and from Q draw lines through the divisions in D8 to intersect the curve OO in 1, 2, 3, etc. 4. With the radius of P from I, 2, 3, etc., in 00, describe indefinite arcs; apply the chords Dl, D2, etc. from I, 2, 3, etc., in the circumference of Q, cutting the indefinite arcs in A,C,E,F, etc., which are points in the curve. We are now in a position to undertake actual work, and in the next chapter, I will endeavor to apply a part of what has preceded to practical examples, such as are required for every-day u?e. Enough geometry has been given to enable the workman, when he has mas- tered it all, to lay out any geometrical figure h«^ may be called upon to execute; and with, perhaps, the excep- tion of circular and elliptical stairs and hand-railings, which require a separate study, by what has been for- mulated and what will follow, he should be able to exe- cute almost any work in a scientific manner, that may be placed under his control.. ^3 PART II PRACTICAL EXAMPLES CHAPTER I We are now in a position to undertake the solution of practical examples, and I will commence this department by offering a few practical solutions that will bring into use some of the work already known to the student, if he has followed closely what has been presented. It is a part of the carpenter's duty to lay out and construct all the wooden centers required by the brick- layer and mason for turning arches over openings of all kinds; therefore, it is essential he should know as much concerning arches as will enable him to attack the problems with intelligence. I have said some- thing of arches, in Part I. but not sufficient to satisfy all the needs of the carpenter, so I supplement with the following on the same subject: Arches used in building are named according to their curves, — cir- cular, elliptic, cycloid, parabolic, hyperbolic, etc. Arches are also known as three or four centered arches. Pointed arches are called lancet, equilateral and depressed. Voussoirs is the name given to the stones forming the arch; the central stone is called the key- stone. The highest point in an arch is called the crown, the lowest the springing line, and the spaces between the crown and springing line on either side, the haunches or flanks. The under, or concave, sur- 6i 6a MODERN CARPENTRY face of an arch is called the intrados or soflfit, the upper or convex surface is called the extrados. The span of an di :h is the width of the opening. The supports of an arch are called abutments, piers, or springing walls. This applies to the centers of wood, as well as to brick, stone or cement. The following six illustrations show the manner ri getting the curves, as well as obtaining the radiating lines, which, as a rule, the carpenter will be asked to prepare for the mason. We take them in the following order: Fig. 1. A Semi-circular Arch.— RQ is the span, and the line RQ is the springing line; S is the center from Fig. 3. Fig.4- which the arch is described, and to which all joints of the voussoirs tend. T is the keystone of the arch. Fig. 2. A Segment Arch.— U is the center from which the arch is described, and from U radiate all PRACTICAL EXAMPLES «3 the joints of the arch stones. The bed line of the arch OP or MN is called by mason builders a skew- back. OM is the span, and VW is the height or versed sine of the segment arf-h. Figs. 3 and 4. Moorish c/ Saracenic Arches, one of which is pointed. Fig 3 is sometimes called the _^_^_^_^_^_^^.^ horseshoe arch. The springing ,\\\\in I 1/777 lines DC and ZX of both arches are below the centers BA and Y. Fig. 5. A Form of Lintel Called a Platband, built in this form as a substitute for a segment arch over the opening of doors or windows, generally of brick, wedge-shaped. Fig. 8. The Elliptic Arch.— This arch is most per- fect when described with the trammel, and in that case 1 rig. K the joints of the arch stones are found as follows: Let ZZ be the foci, and B a point on the intrados where a joint is required; from ZZ draw lines to B, bisect the angle at B by a line drawn through the intersecting arcs D produced for the joint to F. Joints at I and 3 MODERN CARPENTRY arc found in the same manner. The joints for the opposite side of the arch may be transferred as shown. The semi-axes of the ellipse, HG, GK, are in the same ratio as GE to GA. The voussoirs near the springing 8 — I line of the arch are thus increased in size for greater strength. I gave a very good description of this latter arch in Part I, which see. Another series of arches, known as Gothic arches, are shown as follows, with all the centers of the curve given, so that their formation is rendered quite simple. The arch shown at Fig. ; is equilateral and its out- lines have been shown before. I repeat, however, let AB be the g-ven span; on A and B as centers with AB as radius, describe the arcs AC and BC. The lancet arch. Fig. 8, is drawn as follows: DE is the given span; bisect DE in J, make DF and EG equal DJ; on Fas center with FE as radius describe Tig. 9 ' I Fig. 10 the arc EH, and on G as center describe the arc DH. A lancet arch, not so acute as the previous one, is PRACTICAL EXAMPLES <5 shown at Fig. 9. Let KL be the given span; bisect KL in M, make MP at right angles to KL and of the required height; connect LP, bisect LP by a line through the arcs R, Q produced to N; make MO equal MN; with N and O as centers, with NL for radius describe the arcs KP and LP. Fig. 10 shows a low or drop arch, and is obtained as follows: Let ST be the given span, bisect ST in W; let WX be the required height at right angles to TS; connect TX, bisect TX by a line through the arcs YZ produced to V, make TU equal SV; on V and U as centers with VT as radius describe the arcs TX and SX. Another Gothic irch with a still less height is shown at Fig. II. Suppose AB to be the given span; then divide AB into four equal parts; make AF and BG equal AB, connect FE and produce to D; with CA as radius, on C and E, describe the arcs AD and BK; on F and G as centers, describe the arcs JK and DK. Another four-centered arch of less height is shown at Fig. 12. Let SI be the given span, divide into six equal parts; on R and Q as centers with RQ as radius describe the arcs QV and RV, connect QV and RV and produce to L and M; on R and Q as centers with QT as 66 MODERN CARPENTRY radius describe the arcs TP and SO; on L and M as centers describe the arcs PN and ON. To describe an equilateral Ogee arch, like Fig. 13, proceed as follows: Make YZ the given span; make YX equal YZ, bisect YZ in A; on A as center with AY as radius describe the arcs YB and ZC; on B and X as centers describe the arcs BD and XD, and on C and X as centers describe the arcs CE and XE, on E and D as centers describe the arcs BX and CX. Fig. 14 shows the method of obtaining the lines for an Ogee arch, having a height equal to half the span Suppose FH to be the span, divide into four equal parts, and at each of the points of division draw lines LN, KG and JO at right angles to FH; with LF for radius on L and J describe the quarter circles FM and HP; and with the same radius on O and N describe the quarter circles PG and MG. These examples-all or any of them— can be made use of in a great number of instances. Half of the Ogee curve is often e^nployed for veranda rafters, as for the roofs of bay-windows, for tower roois and for bell bases, for oriel and bay-windows, and many other pieces of work the carpenter will be confronted with from tunc to time. They aiso have value as aids in forming mouldings and other ornamental work, as for i.'iasj''!i»ffiiir*?awBffBi».v,at-.--i*jlte!.- "'' J •TTTi^Kw^S^rfre^^TT^ PRACTICAL EXAMPLES 67 example Fig. 15, which shows a moulding for a base or other like purpose. It is described as follows: Draw AB; divide it into five equal parts; make CD equal to four of these. Through D draw DF parallel with AB. From D, with DC as radius, draw the arc CE. Make EF equal to DE; di- vide EF into five parts; make the line above F equal to one of these; draw FG equal to six of these. From G, with radius DE, describe the arc; bisect GF, and lay the distance to H. It is the center of the curve, meeting the semi-circle described from M. Join NO, OS, and the moulding is complete. The two illustrations shown at Figs. 16 and 17 will give the stu- dent an idea of the manner in which he can apply the knowledge he has now obtained, and -'t may not be out of place to say that with a little ingenuity he can form almost any sort of an ornament he wishes by using this knowledge. The two illustra- tions require no explanation as their formation is self- evident. Newel posts, balusters, pedestals and other turned or wrought ornaments, maybe designed easily if a little thought be brought to bear on the subject. The steel square is a great aid in working out prob- lems in carpentry, and I will endeavor to show, as briefly as possible, how the square can be applied to some difficult problems, and insure correct solutions. It is unnecessary to give a full and complete descrip- tion of the steel square. Every carpenter and joiner is • f 68 MODERN CARPENTRY supposed to be the possessor of one of these useful tools, and to have some knowledge of using it. It is not everyone, however, who thoroughly understands its powers or knows how to employ it in solving all : I li- the difficulties of framing, or to take advantage of its capabilities in laying out work. Whi'e it is not my intention to go deeply into this subject in this vol- ume, as that would lengthen it out to unreasonable limits, so it must be left for a separate work, yet there are some simple things connected with the steel square, that I think every carpenter and joiner should know, no matter whether he intends to go deeper into the study of the steel square or not. One of these things is the learning to read the tool. Strange as it may PRACTICAL EXAMPLES <9 appear, not over one in fifty of those who ivse the square are able to read it, or in other words, able to explain the meaning and uses of the figuies stamped on its two sides. The following will assist the young fellows who want to master the subject. The square consists of two arms, at right angles to each other, one of which is called the blade and which is two feet long, and generally two inches wide. The other arm is called the tongue, and may be any length from twelve to eighteen inches, and i^ to 2 inches in width. The best square has always a blade 2 inches wide. Squares made by firms of repute are generally perfect and require no adjusting or "squaring." The lines and figures formed on squares of different make sometimes vary, both as to their position on the square and their mode of application, but a thorough understanding of the application of the scales and lines shown on any first-class tool, will enable the stu- dent to comprehend the use of the lines and figures exhibited on any good square. It is supposed the reader understands the ordinary divisions and subdivisions of the foot and inch into twelfths, inches, halves, quarters, eighths and six- teenths, and that he also understands how to use that part of the square that is subdivided into twelfths of an inch. This being conceded, we now proceed to describe the various rules as shown on all good squares. Sometimes the inch is subdivided into thirty-seconds, in which the subdivision is very fine, but this scale will be found very convenient in the measure- ment ot drawings which are made to a scale of half, quarter, one-eighth or one-sixteenth of an inch to a foot. 7« MODERN CARPENTRY In the illustration Fig. iS, will )C noticed a series of lin<-s extending irom the junction of the blade and tongue to the fnur- inch limit. From the figures 2 to 3 tht'^'- lines are crossed by diatjonal lines. This figure, i ach- ing from 2 to 4. is c.nlled a diagonal cale, and i=; intended for takmp off hundredths of an inch The vn s.i.i Fig. 19 iJilllltilllillll ;;»ii ^am ( I lengths of the lines between the diagonal and the perpr iicular aremarkedon the latter. Primary divisions are tenths, and the junc- tion of the diagonal lines wf^h the longitudinal parallel lines enables the operator to obtain divisions of one-hundredth part of an inch; as for example, if we wish to obtain twenty-four hundredths we operate on the seventh line, taking five ^r'Tiaries and the fraction of the jt sixth where the diagonal inter- sects me parallel line, as shown mm PRACTICAL EXAMPLES 7« by the "dots" on the compasses, and this gives us tht distance required. The ISO ot the scale is obvious, nnd needs no further explanation, as the dots or points an. shown. Thu lines of figures running across the b'ade of the square, as shown in Fig. 19, forms what is . very con- venient rule for det'^- fining the amov.u. of n^itt . iai m length or wid'h .)i it tfi To use ir proc< as fol- lows: If we examine we will find under the figure 12, on he outer cdsf..- of the blade ,vhere the lerp'h of .he boards, plank (ir scantling to be measup'f .s given, and the an-.ver in feet and inches is founc under the inches ir width that the board, etc., n casures. For examp! , take a b *.. ')) • : etc., etc. If the stuff is longer than any fip.ii shown on the square it can be measured as above and doubling the result. This rule is calcu- lated, as its name indicates, for board measure, or for surfaces i inch in thickness. It may be advantageously used, however, upon timber by multiplying the result rf the face measure of one side of a piece by its depth in inches. To illustrate, suppose it be required to measure a piece 25 feet long, 10x14 inches in size. For the length we will take 12 and 13 feet. For the width we will take 10 inches, and multiply the result by 14. By the rule a board 12 feet long and 10 inches wide contains 10 feet, and one 13 feet long and 10 inches wide, lo feet 10 inches. Therefore, a board 25 teet long and 10 inches wide must contain 20 feet and 7a MODERN CARPENTRY f 10 inches. In the timber above described, however, we have what is equivalent to 14 such boards, and therefore we multiply this result by 14, which gives 291 feet and 8 inches the-board measure. Along the tongue of the square following the diag- onal scale is the brae* rule, which is a very simple and very convenient method of determining the length of any brace of regular run. The le.igth of any brace simply represents the hypothenuse. of a right-angled triangle. To find the hypothenuse extract the square root of the sum of the squares of the perpendicular and horizontal runs. For instance, if 6 feet is the horizontal run and 8 feet the perpendicular, 6 squared equals 36, 8 squared equals 64; 36 plus 64 equals 100, the square root of which is 10. These are the rules generally used for squaring the frame of a building. If the run is 42 inches, 42 squared is 1764, double that amount, both sides being equal, gives 3528, the square root of which is, in feet and inches, 4 feet 11.40 inches. In cutting braces always allow in length from a six- teenth to an eighth of an inch more than the exact measurement calls for. DirecMy under the half-inch marks on the outer edge of the back of the tongue, Fig. 19, will be noticed two figures, one above the other. These represent the run of the brace, or the length of two sides of a right- angled triangle; the figures immediately to the right represent the length of the brace or the hypothenuse. For instance, the figures I], and 80.61 show that the run on the post and beam is 57 inches, and the length of the brace is 8o.6l inches. Upon some squares will be found brace measure- ments given, where the run is not equal, as JJ.30. It will be noticed that the last set of figures are each just PRACTICAL EXAMPLES 73 three times those mentioned in the set that are usually used in squaring a building. So if the student or mechanic will fix in his mind the measurements of a few runs, wich the length of braces, he can readily work almost any length required. Take a run, for instance, of 9 inches on the beam and 12 inches on the post. The 1 e n gt h of brace is 15 inches. In a run, therefore, of 12, 16, 20, or any number of times above the figures, the length of the brace will bear the same proportion to the run as the multiple used. Thu-^ if you multiply all the fig- ures by 3 you will have 36 and 48 inches for the run, and 60 inches for the brace, or to remember still more easily, 3, 4 and 5 feet. There is still another and an easier method of obtain- ing the lengths of braces by aid of the square, also the bevels as may be seen in Fig. 20, where the lun is 3 feet, or 36 inches, as marked. The length and bevels of the brace are found by applying the square three times in the position as shown; placing 12 and 12 on the edge of the timber each time. By this method both length and bevel are obtained with the least amount of labor. Braces having irregular runs may be ooerated in the same manner. For instance, sup- pose we wish to set in a brace where the run is 4 feet and 3 feet; we simply take g inches on the 74 MODERN CARPENTRY tong^ue and 12 inches on the blade and apply the square four times, as shown in Fig. 21, where the brace is given in position. Here we get both the proper length and the exact bevels. It is evident from this tha* braces, regular or irregular, and of any length, may be obtained with bevels for same by this method, only care Pmust be taken in adopting the figures for the purpose. If we want a brace with a two- foot run and a four-foot run, it must be evident that as two is the half of four, so on the square take 12 inches on the tongue, and 6 inches on the blade, apply four times and we have the length and the bevels of a brace for this run. For a three-by-four foot run take 12 inches on the tongue and g inches on the blade, and apply four times, because as 3 feet is ^ of four feet, so 9 inches is ^ of 12 inches. While on the subject of braces I submit the follow- ing table for determining the length of braces for any run from six inches to fourteen feet. This table has been carefully prepared and may be depended upon as giving correct measurements. Where the runs are regular or equal the bevel will always be a miter or angle of 45°, providing always the angle which the brace is to occupy is a right angle — a "square." If the run is not equal, or the angle not a right angle, then the bevels or "cuts" will not be miters, and will have to be obtained either by taking figures on the square or by a scaled di.igram. PRACTICAL EXAMPLES 75 TABLE LENCTH OF Length or LBNOTR or Lkncth or KUN BllACB Run BUACB n. In. ft. In. ft. In. ft. In. ft. In. ft. In. 6 X 6 = 8.48 4 3 X 4 3 = 6 0.12 6 X 9 = 10.81 4 3 X 46 = 6 2.27 9 X 9 a I 0.72 4 3 X 4 9 = 6 4.49 I X I = I 4-97 4 3 X 5 = 6 6.74 1 X I 3 = I 7.20 4 6 X 46 = 6 4.36 I 3 X I 3 = 1 9-23 4 6 X 4 9 = 6 6.51 1 3 X I 6 = I 11.43 4 6 X 5 = 6 8.72 I 6 X I 6 =s 2 1.45 4 9 X 4 9 = 6 8.61 I 6 X I 9 = 2 3.65 4 9 X 5 = 6 10.75 I 9 X I -) = 2 5.69 5 X 5 S3 7 0.85 I 9 X 2 = 2 7.89 5 3 X 5 1 S3 7 509 2 X 2 = 2 9.94 5 6 X 56 a 7 9-33 2 X 2 3 =: 3 0.12 5 9 X 5 9 8 1.58 2 X 2 6 Z3 3 2.41 6 X 6 8 5.82 2 3 X 2 6 = 3 4.36 6 3 X 63 8 10.06 2 6 X 2 6 = 3 6.42 6 6 X 6 6 9 2.30 2 6 X 2 9 = 3 8.59 6 9 X 69 9 6.55 2 9 X 2 9 = 3 10.66 7 X 7 9 10.79 2 9 X 3 =3 4 0.83 7 3 X 7 3 10 3.03 3 X 3 = 4 2.91 7 6 X 76 10 7.28 3 X 3 3 B 4 5.02 7 9 X 7 9 s 10 11.52 3 X 36 =: 4 7-31 8 X 8 = II 376 3 X 3 9 = 4 9.62 8 3 X 8 3 = II 8.00 3 3 X 3 3 B3 4 7.15 8 6 X 8 6 = 12 0.24 3 3 X 36 = 4 9.31 8 9 X 89 = 12 4.49 3 3 X 3 9 = 4 11.54 9 X 9 = 12 8.73 3 3 X 4 = 5 1.84 9 6 X 96 = 13 5-22 3 6 X 36 = 4 11-39 10 X 10 - 14 1.70 3 6 X 3 9 = 5 1-55 10 6 X 10 6 s: 14 10.19 3 6 X 4 = 5 3-78 11 X II = 15 6.67 3 9 X 3 9 = 5 3.63 II 6 X II 6 ES 16 3.16 3 9 X 4 = 5 5 79 12 X 12 =5 16 11.64 4 X 4 = 5 7.88 12 6 X 12 6 C3 17 8.13 4 X 4 3 = 5 10.03 13 X 13 = 18 4.61 4 X 46 as 6 0.25 13 6 X 13 6 = 19 I. 10 4 X 4 9 » 6 2.51 14 X 14 = 19 9.58 4 X 5 = 6 4.83 76 MODERN CARPENTRY IT n rrr c? JJX *r 1 1 1 m.M 1 1 rrrn Fig. 22; There is on the tongue of the square a scale called the "octagonal scale." This is generally on the opposite side to Fig. 22 exhibits a por- Itis the scales shown on Fig. 19. tion of the tongue on which this scale is shown the central division on which the number 10 is seen along with a number of divisions. It is used in this way: If you have a stick 10 inches square which you wish to dress up octagonal, make a center mark on each face, then with the compasses, take 10 of the spaces marked by the short cross-lines in the middle of the scale, and layoff this distance each side of the center lines, do the same at the other end of the stick, and strike a chalk line through these marks. Dress off the cor- ners to the lines, and the stick will be octag- onal. If the stick is not straight it must be gauged, and not marked with the chalk line. Always take a number of spaces equal to the square width of the octagon in inches. This scale can be used for large octagons by doubling or trebling the measurements. On some squares, there are other scales, but I do not advise the use of squares that are surcharged with too many scales and fig- ures, as they lead toconfusion and lossof time. It will now be in order to offer a few things that can be done with the steel square, in a shorter time than by applying any other methods. If we wish to get the ^ <<^ \. <-. \ h Fig. 23. PRACTICAL EXAMPLES 77 length and bevels for any common rafter it can be done on short notice by using the square as shown in Fig. 23. The pitch of the roof will, of course, gov- ern the figures to be employed en the blade and tongue. For a quarter pitch, the figures must be 6 and 12. For half pitch, 12 and 12 must be used. For a steeper pitch, 12 and a larger figure must be used according to the pitch required. For the lower pitches, 8 and 12 gives a one-third pitch and 9 and 12 a still steeper pitch; and from this the workman can obtain any pitch he requires. If the span is 24 feet, the square must be applied 12 times, as 12 is half of 24. And so with any other span: The square must be applied half as many times as there are feet in the width. This is self-evident. The bevels and lengths of hip and val- ley rafters may be obtained in a similar manner, by first taking the length of the diagonal line between 12 and 12, on the square, which is 17 inches in round numbers. Use this figure on the blade, and the "rise" whatever that may be, on the tongue. Suppose we have a roof of one -third pitch, which has a span of 24 feet; then 8, which is one-third of 24, will be the height of the roof at the point or ridge, from the base of the roof on a line with the plates. For example, always use 8, which is one-third of 24, on tongue fcr altitude; 12, half the width of 24, on blade for base. This cuts common rafter. Next is the hip rafter. It must be understood that the diagonal of 12 and 12 is 17 in framing, as before stated, and the hip is the diagonal of a square added to the rise of roof; therefore we take 8 on tongue and 17 on blade; run the same number of times as common rafter. To cut jack rafters, divide the number of openings for com- mon rafter. Suppose wc have 5 jacks, with six open- J^ J « * 7« MODERN CARPENTRY ings, our common rafter 12 feet long, each jack would be 2 feet shorter, first 10 feet, second 8 feet, third 6 feet, and so on. The top down cut the same as cut of common rafter; foot also the same. To cut miter to fit hip: Take half the width of building on tongue and length of common rafter on blade; blade gives cut. Now find the diagonal o 8 and 12, which is M^^V. take 12 on tongue, 14^^ on blade; blade gives cut. The hip rafter must be beveled to suit; height of hip on tongue, length of hip on blade; tongue gives bevel. Then we take 8 on tongue, 8ji on blade; tongue gives the bevel. Those figures will span all cuts in putting on cornice or sheathing. To cut bed moulds for gable to fit under cornice, take half width of building on ^^ tongue, length of common rafter on blade; blade gives cut; machine mould- ings will not mem- ber, but this gives a solid joint; and to member properly it is necessary to make moulding by hand, the diagonal plumb cut differences. To cut planceer to run up valley, take height of rafter on tongue, length of rafter or. blade; tongue gives cut. The plumb cut takes the height of hip rafter on tongue, length of hip rafter on blade; tongue gives cut. These figures give the cuts for one-third pitch only, regardless of width of build- ing. The construction of roofs generally will be taken up in another chapter. A ready way of finding the length and cuts for cross- bridging is shown at Fig. 24. If the joists are 8 inches wide and 16 inches centers, there will be 14 inches ^iVL Bb^ PRACTICAL EXAMPLES 79 til Fig. 25, between. Place the square on 8 and 14, and cut on 8, and you have it. The only point to observe is that the 8 is on the lower side of the piece of bridging, while the 14 is on the upper, and not both on same side of tim- ber, as in nearly all work. Bridging for any depth of joists, to any rea- sonable distance of joists apart, may be obtained by this method. A quick way of finding the joists for laying out timber to be worked from the square to an octagon sec- tion is shown at Fig. 25. Lay your square diagonally across your timber and mark at 7 and 17, which gives corner of octagon. The figures 7 and 17, on either a square or two-foot pocket rule, when laid on a board or piece of timber as shown, always define the points where the octagonal angle or arris should be. Fig. 26 shows A rapid method of dividing anything into several equal parts. If the board is io>4 inches wide, lay the square from heel to 12, and mark at 3, 6 and g, and you have it divided into four equal parts. Any width of board or any number of parts may be worked with accuracy under the same method. A method for obtaining the "cuts" for octagon and hexagon joints is shown at Fig. 27. Lay off a quarter circle XA, with C as a center; then along the hori- zontal line AB the square is laid with 12" on the blade Fig. 26 jfiiStt' So MODERN CARPENTRY at the center C, from which the quadrant was struck. If we divide this quadrant into halves, we get the point E, and a line drawn from 12" on the blade of the square and through the point E, we cut the tongue of the square at 12" and through to O, and the line thus drawn makes an angle of 45°, a true miter. If we divide the quadrant between E and X, and then draw a line from C, and 12" on the blade of the square, cut- ting the dividing point D, we get the octagon cut, which is the line DC. Again, if we divide the space W^ between E and X into three equal parts, making GC one of these parts, and draw a line from C to G cutting the tongue of the square at 7", we get a cut that will give us a miter for a hexagon; therefore, we see from this that if we set a steel square on any straight edge or straight line, 12" and 12" on blade and tongue on the line or edge, we get a true miter by marking along the edge of the blade. For an octagon miter, we set the blade on the line at 12", and the tongue at 5'', and we get the angle on the line of the blade — nearly; and, for a hexagon cut, we place the blade at 12" on the L-»#*- PRACTICAL EXAMPLES 8i line, and the tongue at j", and the line of the blade gives the angle of cut — nearly. The actual figure for octagon is 45 J, but 5" is close enough; and for a hexa- gon cui, the exact figures are 12" and b\\, but 12" and 7" is as near as most workmen will require, unless the cut is a very long one. Ti e diagram shown at Fig. 28 illustrates a method of defining the pitches of roofs, and also gives the fig- ures on the square for laying out the rafters for such pitches. By a very common usage among carpenters and builders, the pitct. of a roof is described by indicating what fraction the rise is of the span If, for example, the span is 24 feet (and here it chould be remarked that the dia- gram shows only one-half the span), then 6 feet rise would be called quarter pitch, because 6 is one-quarter of .?4. The rule, somewhat arbitrarily ex- pressed, that is applicable 1 1 1 n I I . I * a i* iV 1 in such cases in roof framing where the roof is one. quarter pitch, is as follows: Use 12 of the blade, and 6 of the tongue. For other pitches use the figures .'ippropriate thereto in the sane general manner. The d' i:;ram indicates the figures for sixth pitch, quarter pitch, third pitch and half nitch. Tne first three of these are in viry comm-in uc, although the latter is somewhat exceptional. It will take but a moment's reflectir 5 upon the part MODERN CARPENTRY of a practical man, with this diagram before him, to perceive that no changes are necessary in the rule where the span is more or less than 24 feet. The cuts are the same for quarter pitch irrespective of the actual dimensions of the building. The square in all such cases is used on the basis of similar triangles. The broad rule is simply this: To construct with the square such a triangle as will proportionately and cor- rectly represent the full size, the blade becomes the base, the tongue the altitude or rise, while the hypoth- enuse that results rep- resents the rafter. The necessary cuts are shown by the tongue and blade respectively. In order to give a gen- eral idea of the use of the square I herewith ap- pend a few illustrations of its application in framing a roof of, say, one-third pitch, which will be supposed to consist of common rafters, hips, valleys, jack rafters and ridges. Let it be assumed that the building to be dealt with measures 30 feet from outside to outside of wall plates; the toe of the rafters to be fair with the outside of the wall plates, the pitch being one-third (that is the roof rises from the top of the wall plate to the top of the ridge, one-third of the width of the building, or 10 feet), the half width of the building being 15 feet. Thus, the figures for working on the square are obtained; if other figures are used, they must bear the same relative proportion to each other. To get the required lengths of the stuff, measure across the corner of the square, fruni the lo-inch mark PRACTICAL EXAMPLES 83 on the tongue to the 15-Inch mark on the blade, Fig. 29. This gives 18 feet as the length of the common rafter. To get the bottom bevel or cut to fit on the wall plate, lay the square flat on the side of the rafter. Start, say, at the right-hand end, with the blade of the square to the right, the point or ant,'U; of the square away from you, and the rafter, with its back (or what will be the top edge of it when it is fixed) towards you. Now place the 15-inch mark of the blade and the lo-inch mark of the tongue on the corner of the rafter— that is, towards you— still keeping the square laid flat, and mark along the side of the blade. This gives the bottom cut, and will fit the wall plate. Now move the square to the other end of the rafter, place it in the same position as before to the 18-foot mark on the rafter and to the 10-inch mark on the tongue, and the 15-inch mark on ihe blade; then mark alongside the tongue. This gives the top cut to fit against the ridge. To get the lens^rth of the hip rafter, take 15 inches on the blade and 15 inches on the tongue of the sqtiare, and measure across the corner. This gives 21^% inches. Now take this figure on the blade and 10 inches on the tongue, then measuring across the corner gives the length of the hip rafter. Another method is to take the 17-inch mark on the blade and the 8-inch mark on the tongue and begin as with the common rafter, as at Fig. 30. Mark along MICROCOPY RESOLUTION TEST CHART (ANSI and ISO TEST CHART No. 2) ^ >IPPLIED IM/1GE 1653 Easl Mam Street Rochester, New York 146O9 iji^ l"6) «82-030O-Phone (716) 288 - 5989 -Fox "f^m^ 84 MODERN CARPENTRY the side of the blade for the bottom cut. Move the square to the left as many times as there are feet in the half of the width of the building (in the present case, as we have seen, 15 feet is half the width), keep- ing the above mentioned figures 17 and 8 in line with the top edge of the hip rafter; step it along just the same as when applying a pitch board on a stair-string, and after moving it along 15 steps, mark along- side the tongue. This gives the top cut or bevel and the length. The reason 17 and 8 are taken on the square is that I2and 8 rep- resent the rise and run of the common rafter to i foot on plan, while 17 and 8 correspond with the plan of the hips. To get the length of the jack rafters, proceed in the same manner as for common or hip rafters; or alter- nately space the jacks and divide the length of the com- mon rafter into the same number of spaces. This gives the length of each jack rafter. To get the bevel of the top edge of the jack rafter, Fig. 31, take the length, 14^ of the common rafter on the blade and the run of the common rafter on the tongue, apply the square to the jack rafter, and mark along the side of the blade; this gives the bevel or cut. The down bevel and the bevel at the bottom end are the same as for the common rafter. To get the bevel for the side of the purlin to fit PRACTICAL EXAMPLES 8S aj^^iinst the hip rafter, place the square flat against the side of the purlin, with 8 inches on the tongue and 143/8 inches on the blade. Fig. 32. Mark alongside of the tongue. This gives the side cut or bevel. The 14^ inches is the length of the common rafter to the l-foot run, and the 8 inches represent the rise. For the edge bevel of puiiui, lay the square flat against the edge of purlin with 12 inches on the tongue and 141^ inches on the blade, as at Fig. 33, and mark along the side of the tongue. This gives the bevel or cut for the edge of the purlin. The rafter patterns must be cut half the thickness of ridge ■shorter; and half the thickness of the hip rafter allowed off the jack rafters. These examples of what may be achieved by the aid of the square are only a few of the hundreds that can be solved by an intelligent use of that wonderful instru- ment, but it is impossible in a work of this kind to illustrate more than are here presented. The subject will be dealt with at length in a separate volume. CHAPTER II GENERAL FRAMING AND ROOFING Heavy framing i. now almost a dead science in this country unless it be in the far west or south, a& steel and iron have displaced the heavy timber structures that thirty or forty years ago were so plentiful in roofs, bridges and trestle-work. As it will not be ^u[ffiin |f][ljjl_jiij|iLr necessary to go deeply into i.eavy-timber framing, therefore I will confine myself more particularly to the framing of ballon buildings generally. A ballon frame consists chiefly of a frame-work of scantling. The scantling may be 2 x 4 inches, or any other size that may be determined. The scantlings are spiked to the sills, or are nailed to the sides of the joist which rests on the sills, or, as is sometimes the case, a rough floor may be nailer! on the joists 36 PRACTICAL EXAMPLES 87 and on this, ribbon pieces of 2 X 4-inch stuff are spiked around to the outer edge of the foundation, and onto these ribbon pieces the scantling is placed and "toe-nailed" to them. The doors and windows are spaced off as shown in Fig. 34, which represents a ballon frame and roof in skeleton condition. These frames are generally boarded on both sides, always on the out- side Sometimes the boarding on the outside is nailed on diagonally, but more frequeHtly horizontally, which, in my opinion, is the better way, providing always the boarding is dry and the joints laid close. The joists are laid on "rolling," that is, there are no gains or tenons em- ployed, unless in trimmers or similar work. The joists are simply "toe- nailed" onto sill plates, or ribbon pieces, as shown in the illustration. Sometimes the joists are made to rest on the sills, as shown in Fig. 35, the sill being no more than a 2 X 4-inch scantling laid in mortar on the foundation, the — >,^ outside joists forming a sill for S- 37 the side studs. A better plan is .,o».3''«'"« W^^M^aW 88 MODERN CARPENTRY shown in Fig. 36, which gives a met^'od known as a "box-sill." The manner of construction is very simple. All joists in a building of this kind must be bridged similar to the manner shown in Fig. 37, about every eight feet of their length; in spans less than sixteen feet, nd more than eight feet, a row of bridging should always be put in midway in the span. Bridg- ing should not be less than I to 1^2 inches in section. In trimming around a chimney or a stair weil-hole, several methods are em- ployed. Sometimes the headers and trimmers are made from material twice as thick and the same depth as the ordinary joists, and the intermediate joists are tenoned into the header, as showr in Fig. 38. Here we have T, T, for header, and T, J, T, J, for trimmers, and b,j, for the ordinary joists. In the western, and also some of the central States, the trimmers and headers are made up of two thicknesses, the header being mortised to secure the ends of the joists. The PRACTICAL liXAMPLES 89 two thicknesses are well nailed together. This method is exhib- ited at Fig. 39., which also shows one way to trim around a hearth; C shows the header with trimmer Joists with tusk tenons, keyed solid in place. Frequently it hap- pens that a chimney rises in a building from its own foundation, disconnected from the walls, in which case the chimney shaft will require to 1: trimmed all around, as showh .ii Fig. 42. -'^ Fig. 40. In cases of th J kind the trim- mers A, A, should be made of stuff very much thicker than the joists, as they have to bear a double burden; B, B shovvs thj heading, and C, C, C, C the tail joists. E. B, should have a thickness double that of C, C, etc., and A, A should at least be 90 MODERN CARPENTRY three times as stout as C, C. This will to some extent equalize the strength of the whole floor, which is a matter to be considered in laying down floor timbers, for a floor is no stronger than its weakest part. There are a number of devices for trimming around stairs, fire-places and chimney-stacks by which the cutting or mortising of the timbers is avoided. One method is to cut the timbers the exact length, square in the ends, and then insert iron dowels — two or more — in the ends of the joists, and then bore holes in the trimmers and headers to suit, and drive the whole solid together. The dowels are made from J:^-inch or i-inch round iron. Another and a better device is the "bridle iron," which may be hooked over the trimmer or header, as the case may be, the stir- rup carrying the abutting timber, as shown in Fig. 41 These bridle irons" are made of wrought iron — 2 X 2Y2 inches, or larger dimensions if the work require such; for ordinary jobs, however, the size given wiL be found plenty heavy for carrying the tail joists, and a little heavier may be employed to carry the header. This style of connecting the trimmings does not hold the frame-work together, and in places where there is any tendency to thrust the work apart, some provision must be made to prevent the work from spreading. In trimming for a chimney in a roof, the "headers," "stretchers" or "trimmers," and "tail rafters," may be simply nailed in place, as there is no great weight PRACTICAL EXAMPLES 9« beyond snow and wind pressure to carry, therefore the same precautions for strength are not necessary. The sketch shown at Fig. 42 explains how the chimney openint,^s in the roof may be trimmed, the parts being only spiked together. A shows a hip rafter against which the cripples on both sides are spiked. The chimney-stack is shown in the center of the roof isolated— trimmed on the four sides. The sketch is F«44. self-explanatory in a measure, and should be easily understood. An example or two showing how the rafters may be connected with the plates at the eaves and finished for cornice and gutters, may not be out of place. A sim- ple method is shown at Fig. 43, where the cornice is complete and consists of a few members only. The gutter is attached to the crown moulding, as shown. Another method is shown at Fig. 44, this one being intended for a brick wall having sailing courses over cornice. The gutter is built in of wood, and is 9> MODERN CARPENTRY lined throughout with galvanized iron This makes a substantial job and may be used to good purpose on brick or stone warehouses, factories or similar build- in cfs. Another style of rafter finish is shown at Fig 45, which also shows scheme of co/'nice. A similar fin- ish is shown at Fig. 46, the cor- nice being a little differ- ent. In both the3'» e> im- ples, the gutters are of wood, which should be lined with sheet metal of some sort in order to pre- vent their t o rapio de- cay. At Fig. 47 a rafter finish is shown which n intended for a veranda or porch. Here the construction is very simple. The rafters are dressed and cut on projecting end to represent brackets and form a finish From these examples the workman ''1 ^et sufficient ideas for working his rafters to suit almost any condi- tion Though there are many hundreds of styles which might be presented, the foregoing are ample for our purpose. It will now be in order to take up the construc- tion of roofs, and describe the methods by which such construction is obtained. The method of obtaining the lengths and bevels of PRACTICAL EXAMPLES 93 rafters for ordinary roofs, such as that shown in Fig 48, has already been given in the chapter on the steel square. Something has also bet^n saiu regarding hip and vall( y roofs; but not enough, I think, to satisfy th.. full requirements of ihe workman, so I will endeavor to give a clearer idea of the construction of these roofs by employing the graphic system, instead of depending altogether on the steel square, though I earnestly advise the workman to "stick to the square." It never makes a mistake, though the owner may in its application. A "hip rcof," pure and simple, has .10 gables, and is oftt:n called a "cottage nof," because of its being best adapted for cottages ha. ing only one, or one and a half, stories. The chief difficulty in its construction is getting the lengths and bevels of the hip or angle rafter and the jack or cripple rafter. To the expert workman, this is an easy matter, as he can ieadily obtain both length? and bevels by aid of the square, or by lines such as I am about to produce. 94 MODERN CARPENiRY w The illustration shown at Fig. 49 shows the simplest form of .» hip roof. Here the four hips or diagonal rafters meet in the center of the plan. Another style of hip roof, having a gable and a ridge in the center of the building, is shown at Fig. 50. This is quite a common style of roof, and under almost every condi- ig. *\)t **on 't looks well and has a good effect. The plan shows lines of hips, valleys and ridges. The simplest form of roof is that known as the "lean-to" roof. This is formed by causing one side wall to be raised higher than the opposite side wall, so that when rafters or joists are laid from the high to the low wall a sloping roof is the re- sult. This style of a roof is sometimes called a "shed roof" or a "pent roof." The shape is shown at Fig. 51, the upper sketch showing i an end view and the j lower one a plan of the roof. The method of framing this roof, or adjusting the timbers It, is quite obvious and needs no explanation. This style of roof is in general use where an annex or shed is built up against a superior building, hence its name of "lean-to," as it usually "leans" against the main building, the wall of which is utilized for the t^ ^ r- -'.JT^^j^^ 'V\- '■.,'■1 PRACTICAL EXAMPLES 9S high part of [ho shed or annrx, thiib saving the co^t of the most important wall of the structure. Next to the "lean-to" or "shrcl roof" in simplicity comes the "saddle" or "double roof." This roof ib shown at Fig. 52 by the end view on the top of the fig- ure, and the plan r the bottom. It will be seen that this roof has a ( u^le slope, the planes forming the slopes are equal' .nclined to *he horizor* 'Iic meet- ing of their highest sides makes an -" '-hich is called the ridge of the roof, and the triangular spacy tiormers, as shown in the sketch, and the top is • -^vered either by a "deck roof" or a very h, 'nip root, is shown. Sometimes the sloping sitles ot these roofs are curved, which give them a graceful appearance, but add- materially to their cost. Another style of roof is shown at Fig. 54. This is a gambrel roof, and was very much in evidence in pre- revolutionary tunes, particularly among our Knicker- bocker ancestors. In conjunction with appropriate dormers, this style of roof figures prominently in what is known as early "colonial style." It has some Fig. 52, It is pene- MODERN CARPENTRY advantages over the mansard. Besides these there are many other kinds of roofs, but it is not my purpose to enter largely into the matter of styles of roofs, but simply to arm the workman with such rules and prac- tical equipment that he will be able to tackle with success almost anj' kind of a roof that he maybe called upon to construct. When dealing with the steel square I ex- plained how the lengths and bevels for common rafters could be obtained by the use of the steel square alone; also hips, purlins, valleys and jack rafters might be obtained by the use of the square, but, in order to fully equip the workman, I deem it necessary to present for his benefit a graphic method of obtaining the lengths, cuts and backing of rafters and purlins required for a hip roof. At Fig. 55, I show the plans of a simple hip roof having a ridge. The hips on the plan form an angle of 45^ or a miter, as it were. The plan being rectangular leaves the ridge the length of the difference between the length and the width of the building. Make cd on the ridge-line as shown, half the width of ab, and the angle bda will be a right angle. Then if we e.xtend bd to c, making ^/<- the rise of the foof, ae will be the length of the hip rafter, and the « PRACTICAL EXAMPLES 97 angle at x will be the plumb cut at point of hip and the angle at a will be the cut at the foot of the rafter. The angle at v shows the backing of the hip. This bevel is obtained as follows: Make /t^ and ah equal distances — any distance will serve— then draw a line //^across the angle of the building, then with a center on ad aX p, touching the line ae at j, describe a circle as shown by the dotted line, then draw the lines kh and ,^l 1 1 1 1 PTk kg^ and that angle, as shown by the bevel v, will be the backing or bevel for the top of the hip, beveling each way from a center line of the hip. This rule for backing a hip holds good in all kinds of hips, also for guttering a valley rafter, if the bevel is reversed. A hip roof where all the hips abut each other in the cen- ter is shown in Fig. 56. This style of roof is generally called a "pyramidal roof" because it has the appear- ance of a low flattened pyramid. The same rules governing Fig. 55 apply to this example. The bevels C and B show the backing of the hip, B showing the 98 MODERN CARPENTRY '4 top from the center line ae\ and C showing the bevel as placed against the side of the hip, which is always the better way to work the hip. A por- tion of the hip backed is shown at C. The rise of the roof is shown at O. At Fig. 57 a plan of a roof is shown where the seats of the hips are not on an angle of 45° and where the ends and sides of the roof are of different pitches. Take the base line of the hip, ac or eg, and make ^perpendicular to ae, from ^, and equal to the rise at/; make fa ox fg for the length of the hip, by drawing the line Im at right angles to ae. This gives the length of the hip rafter. The backing of the hip is obtained in a like manner to former examples, only, in cases of this kind, there are two bevels for the backing, one side of the hip being more acute than the other, as shown at D and E. If the hips are to be mitered, as is sometimes the case in roofs of this kind, then PRACTICAL EXAMPLES 99 the back of the hip will assume the shape as shown by the two bevels at F. A hip roof having an irregular plan is shown at Fig. 58. This requires no ex- planation, as the hips and bevels are obtained in the same manner as in previous examples. The backing of the hips is shown at FG. An octagon roof is shown at Fig. 59, with all the lines necessary for getting the lengths, bevels, and back- ing for the hips. The \i n e ax shows the seat of the hip, xe the rise of roof, and ae the length of hip and plumb cut, and the bevel at E shows the backing of the hips These exam- ples will be quite sufficient to enable the workman to understand the general theory of laying out hip roofs. I lOO MODERN CARPENTRY 1^ 1 ; may also state that to save a repetition of drawing and explaining the rules that govern the construction of hip roofs, such as I have presented serve equally well for skylights or similar work. Indeed, the clever workman will find hundreds of instances in his work where the rules given will prove useful. "m^^lo^^l^M^ There are a number of methods for getting the lengths and bevels for purlins. I give one here which I think is equal to any other, and perhaps as simple. Suppose Fig. 60 -hows one end of a hip roof, also the rise and length of common rafters. Let the purlin be in any place on the rafter, as I, and in its most com- mon position, that is, standing square with the rafter; then with the point ^ as a center with any radius, describe a circle. Draw two lines, ^/and pn, to touch \: 5^: f PRACTICAL EXAMPLES 101 the circle/ and q parallel \.o fb and at the points s and r, where the two sides of the purlin intersect, draw two parallel lines to the forrT^r, to cut the diagonal in m and k\ then G is the down bevel and F the side bevel of the purlin; these t.vo bevels, when applied to the end of the purlin, and when cut by them, will exactly fit the side of the hip rafters. To find the cuts of a purlin where two sides are parallel to horizon: The square at B and the bevel at C will show how to draw the end of the purlin in this easy case. Th following is universal in all posi- tions of the pur.a: Let , which will give the side bevel of the jack rafter The bevel at A, which .« the iop of the common rafter, is the down bevel of the jack rafter. At D the method of getting the backing of a hip rafter is shown the same as explained in other figures. There are other methods of obtaining bevels for purlins, but the one offered h-^re will suffice for all practical purposes. 1 gc've a method of finding the back cu or jack rafter! by the steel square, in a previous ciicipter. I give another rule herewith for the steel square: Take the length of the common rafter on the blade and the run of the same rafter on the tongue, and the blade of the square will give the bevel for the cut on the back W^ toa MODERN CARPENTRY of the jack rafter. For example, suppos': the rise to be 6 feet and the run 8 feet, the leng'.h of the _ommon rafter will be lo feet. Then take lO fi ct on the blade of he square, and 8 feet on the tonjrue, and the blade will give the back bevel for the cut of the jack rafters. To obtain the length of jack rafters is a ver^' simple process, and may be obtained easily by a diagram, as shown in Fig. 6l, which is a very common method: First lay off half the width of the building to scale, as from A to B, the length of the common rafter B to C, and the length of the hip rafter from A to C. Space off the widths from jack rafter to jack rafter as shown by the lines I, 2, 3, and measure them accurately. Then the lines i, 2, and 3 will be the exact lengths of the jack rafters in those divisions. Any number of jack rafters may be laid off this way, and the result will be the length of each rafter, no matter whc may be the pi*ch of the roof or the distance the rafters are apart. A table for determining the length of jack rafters is given below, which shows the lengths required for different spacing in three pitches: One-quarter pitch roof: They cut 13.5 inches shorter each time when spaced 12 inches. They cut 18 inches shorter each time when spaced 16 inches. PRACTICAL EXAMPLES 103 They cut 27 inches shorter each time when spaced 24 inches. One-third pitch roof: They cut 14.4 inches shorter each time when spaced 12 inches. They cut 19.2 inches shorter each time when spaced 16 inches. They cut 28.8 inches shorter each time when spaced 24 inchcj. One-half pitch roof; " They cut 17 inches shorter each time when spaced J2 inches. They cut 22.6 inches shorter each time when spaced 16 inches. They cut 34 inches shorter each time when spaced 24 inches. It is not my intention to enter deeply into a discus- sion of the proper methods of constructing roofs of all shapes, though a few hints and diagrams of octagonal, domical and other roofs and spires will dou'jtless be of service to ihe general workman. One of the most useful methods of trussing a roof is that known as a lattice "built-up" truss roof, similar to that shown at Fig. 62. The rafters, tie beams and the two main braces A, A, must be of one thickness — say. 2 x 4 or 2x6 inches, according to the length of the span — while the mine *»"Aces are made of i-inch stuff and 104 MODERN CARPENTRY about 10 or 12 inches wide. These minor braces are well nailed to the tie beams, main braces and rafters. The main braces must be halved over each other at their juncture, and bolted. Sometimes the main braces are left only half the thickness of the rafters, then no halving will be necessary, but this method has the disadvantage of having the minor braces nailed to one side only. To obviate this, blocks maybe nailed to the inside of the main braces to make up the thickness required, as shown, and the minor braces can be nailed oj bolted to the main brace. The rafters and tie beams are held together at the foot of the rafter by an iron bolt, the rafter having a crow-foot joint at the bottom, which is let into the tie beam. The main braces also are framed into the rafter with a square toe-joint and held in place with an iron bolt, and the foot of the brace is crow-footed into the tic beam over the wall. This truss is easily made, maybe put together on the ground, and, as it is light, may be hoisted in place with blocks and tackle, with but little trouble. This truss can be made sufficiently strong to span a roof from 40 to 75 feet. Where the span inclines to the PRACTICAL EXAMPLES greater length, the tic beams and raft- ers may be made of built-up timbers, but in such a case the tie beams should not be less than 6 X 10 inches, nor the rafters less than 6x6 inches. Another style of roof altoi^ether is shown at Fig. 63. This is a self-sup- porting roof, but is somewhat expensive if intended for a building having a span of 30 feet or less. If: is fairly well adapted for halls or for country churches, where a high ceiling is re- quired and the span anywhere from 30 to 50 feet over all. It would not be safe to risk a roof of this kind on a building having a span more than 50 feet. The main features of this roof are: (i) having io6 MODERN CARPENTRY :!'i collar beams, (2) truss bolts, and (3) iron straps at the joints and triple bolts at the feet. I show a dome and the manner of its construction at Fig. 64. This is a fine example of French timber framing. The main carlins are shown at <7, b, c, d and e, Nos. i and 2, and the horizontal ribs are also shown in the same numbers, with the curve of the outer edge described on them. These ribs are cut in between the carlins or rafters and beveled 0.'' to suit. This dome may be boarded over either horizontally or with boards made into "gores" and laid on in line with the rafters or carlins. The manner of framing is well illustrated in Nos. 3 and 4 in two ways. No. 3 being intended to form the two principal trusses which stretch over the whole diameter, while No. 4 may be built in between the main trusses. The illustrations are simple and clear, and quite sufficient without further explanation. Fig. 65 exiiibits a portion of the dome of St. Paul's Cathedral, London, which was designed by Sir Chris- topher Wren The system of the framing of the external dome of this roof is given. The internal cupola, AAl, is of brick-work, two bricks in thickness, with a course of bricks 18 inches in length at every five feet of rise. These serve as a firm bond. This dome was turned upon a wooden center, whose only support was the projections at the springing of the dome, which is said to have been unique. Outside the brick cupola, which is only alluded to in order that the PRACTICAL EXAMPLES 107 description may be the more intelligible, rises a brick* work cone B. A portion of this can be seen, by a spectator on the floor of the cathedral, through the central opening at A. The timbers which carry the externa! dome rest '.pon this conical brickwork. The horizontal hammer beams, C, D, E, F, are curiously tied to the corbels, G, H, I, K, by iron cramps, well ^ bedded with lead into the corbels and bolted to the ham- mer beams. The stairs, or lad- ders, by which the ascent to the Golden Gallery or the summit Fig. 66. of the dome is made, pass among the roof trusses. The dome has a planking from the base upwards, and hence the principals are secured horizontally at a little distance from each other. The contour of this roof is that of a pointed dome or arch, the principals being segments of circles; but the central opening for the lantern, of course, hinders these arches from meeting at a point. The scantling of the curved principals is 10 X ll}4 inches at the base, decreasing to 6 x 6 inches io8 MOI AN CARPENTRY II J at thf top. A lantern of Portland ston crowns the summit of the dome. The method of framing will be clearly seen in the diagram. It is in every respect an excellent specimen of roof construction, and is worthy of the genius and mathematical skill of a great work- man. With the rules offered herewith for the construction of an octagonal spire, I close the subject of roofs: To obtain bevels and lengths of braces for an octagonal spire, or for a spire of any number of sides, let AB, Fig. 66, be one of the sides. Let AC and BC be the seat line of hip. Let AN be the seat of brace. Now, to find the posi- tion of the tie beam on the hips so as to be square with the boardinr. draw a line through C, square with AB, indefinitely. From C, and square with EC, draw CM, making it equal to the height. Join EM. .-:, X . Let OF be the height of the tic beam. Il FiffcW ^^ ^ ^^^ ' ^^"^""^ ^'^*^ E^^ ^ ''"^» which ^ ■ '"^' produce until it cuts EC prolonged at G. Draw CL square with BC. Make CL in length equal to EM. Join BL, and make NH equal to OF. From G draw the line GS parallel with AB, cut- ting BC prolonged, at the point S; then the angle at H is the bevel on the hip for the tie beam. For a bevel to miter the tie beam, make FV equal ON. Join VX; then the bevel at V is the bevel on the face. For the down bevel see V, in Fig. 67. To find the length of brace, make AB, Fig. 67. equal to AB, Fig. 66. Make AL and BL equal to BL, Fig. 66. Make BP equal to BH. Join AP and BC, which will be the length of the brace. The bevels numbered i, 3, 5 and 7 are all to be PRACTICAL EXAMPLES 109 used, as shown on the edge of the brace. No. I is to be used at the top above No. 5. For the bevel on the face to miter on the hip, draw AG, Fig. 66, cutting BS at J. Join JH. Next, in Fig. 68, make A' ^qual AP, Fig. 67, and make AJ equal to AJ, Fig. 66. Make rj equal to J! I, Fig. 66, and make PI equal to HI. Join AI; then the bevel marked No. 5 will be correct for the beam iiext to the hip, and the bevel marked No. 6 will be correct for the top. Bevel No. 2 in this figure will be correct for the beam next to the plate. The edge of the brace is to correspond with the boarding. A few examples of scarfing tim- ber are presented at Figs. 69, 70, 71 and "jz. The example shown at Fig. 69 exhibits a mechod by which the two ends of the timber arc joined together with a step- splice and spur or tenon on end, it being drawn tight together by the keys, as shown in th j shaded part. Fig. 70 is a similar joint though simpler, -^nd therefore a better one; A, A are generally joggle A hardwood, and not wedged keys, but the latter are preferable, as they allow of tightening up. TIic shearing used along BF should be pine, and be not less than six and a half times BC; and BC shou'd be equal to at least twice the depth of the key. The shear in the keys being at right angles to the grain of the wood, a greater stress per square inch of shearing area can be put upon them than along BF, but their shearing area should be equal in strength to the othei parts of the joint; oak is the best word for thcui, as its shearing is from four to five times that of pine. no MODERN CARPENTRY m : I Scarfed joints with bolts and indents, such as that shown at Fig. 71, are about the strongest of the kind. From this it will be seen that the strongest and most economical method in every way, in lengthening ties, is by adoption of the common scarf joint, as shown at Fig. 71, and finishing the scarf as there represented. The carpenter meets with many conditions when timbers of various kinds have to be lengthened out "ri£'.65 rs D tti u iu- ? Fiff. 70.' ^ig. 72. t^ wW and spliced, as in the case of wail plates, etc., where there is not much tensile stress. In such cases the timbers may simply be halved together and secured with nails, spikes, bolts, screws or pins, or they may PRACTICAL EXAMPLES lit be halved or beveled as shown in Fig. 72, which, when boarded above, as in the case of wall plates built in the wall, or as stringers on which partitions are set, or joint beams on which the lower edges of the joists rest, will hold good together. Treadgold gives the following rules, based upon the relative resistance to tension, crushing and shearing of different woods, for the proportion which the length or overlap of a scarf should bear to the depth of the tie: without bolis 6 With bolU 3 6 With bolts and indents 2 Oak, ash, elm, etc. . Pine and similar woods . 12 o 4 There are many other kinds of scarfs that will occur to the workman, but it is thought the foregoing may be found useful on special li occasions. A few examples of odd joints in timber work will not be out of place. It sometimes happens that cross-beams are required to be fitted in between girders in position, as in renewing a defective one, and when this has done, and a mortise and tenon joint is used, a Fig.,73.! M\ to be chase has to be cut leading into the mortise, as shown in the horizontal section. Fig. 73. By inserting the tenon at the other end of the beams into a mortise cut so as to allow of fitting it in at an angle, the tenon can be slid along the chase d into its proper position. It is better in this case to dispense with the long tenon, and, if necessary, to substitute a bolt, as shown in the sketch. A mortise of this kind is called a chase mortise, but an 112 MODERN CARPENTRY m i w^ Fig 74. fe ^WA iron shoe made fast to the girder forms a better means of carrying the end of a cross-beam. The beams can be secured to the shoe with bolts or other fastenings. To support the end of a horizontal beam or girt on tjie side of a post, the joint shown in Fig. 74 may be used where the mortise for the long tenon is placed, to weaken the post as little as possible, and the tenon made about one-third the thickness of the beam on which it is cut. The amount of bearing the beam has on the post must greatly depend on the work it has to do. A hardwood pin can be passed through the cheeks of the mortise and the tenon as shown to keep the latter in position, the holes being draw-bored n\ order to bring the shoulders of the tenon tight home against the post, but care must be taken not to overdo the draw-boring or the wood at the end of the tenon will be forced out by the pin. The usual rule for draw-boring is to allow a quarter of an inch draw in soft woods and one-eighth of an inch for hard woods. These allowances may seem rather large, but it must be remembered that both holes in tenon and mortise will give a little, so also will the draw pin itself unless it is of iron, an uncommon circumstance. Instead of a mortise and tenon, an iron strap or a screw bolt or nut may be used, similiar to that shown in Fig. 75. [se*Vi5,*iiS'pj„ ,_ m PRACTICAL EXAMPLES 113 1 /M The end of the beam may also be supported on a block which should be of hardwood, spiked or bolted ^ on to the side of the •At*! post, as at A and B, Fig. 76. The end of the beam may either be tenoned into the post as shown, or it may have a shoulder, with the end of the beam beveled, as shown at A. Heavy roof tim- bers are rapidly giv- ing place to steel, but there yet remain many cases where timbers will remain employed and the old method of framing continued. The use of iron straps and bolts in fastening timbers together or for trussing purposes will never perhaps become obsolete, therefore a knowl- edge of the proper use of these will always rei-,: n valuable. Heel straps are used to secure the joints between inclined struts and hori- zontal beams, such as the joints between rafters and beams. They may be placed either so as merely to hold the beams close together at the joints, as in Fig. "JT, or so as to directly resist the thrust of the inclined strut and prevent it from shearing off the portion of the horizontal beam against which it presses. Str?ps u tl4 MODERN CARPENTRY P of the former kind are sometimes called kicking-straps. The example shown at Fig. yj is a good form of strap for holding a principal rafter down at the foot of the tie beam. The screws and nuts are prevented from sinking into the wood by the bearing plate B, which acts as a washer on which the nuts r'de when tighten- ing is done. A check plate is also provided under- neath to prevent the strap cutting into the tie beam. At Fig. 78 I show a form of joint often used, but it repress its a diffi- culty in getting the two parallel abutments to take their fair share of the work, both from want of accu- racy in workman- ship as we!' as from the disturb- ing influence of shrinkage. In making a joint of this sort, care must be taken that sufficient wood is left between the abutments and the end of the tie beam to prevent shearing. A little judgment in using straps will often save both time and money and yet be sufficient for all purposes. I show a few examples of strengthening and trussing joints, girders, and timbers at Fig 79. The diagrams need no explanation, as they are splf-evident. It would expand this book far beyond the dimensions PRACTICAL EXAMPLES "5 awarded me, to even touch on all matter:^ pertaining to carpentry, including bridges, trestle?, trussed gird- ers and trusses generally, so I must content mvself W \r''^^^^^^ ■^ •^r^ ^^sx with wha« s already been given or -.ne subject of carpentr\ ough, as the reader is aware, the subject is only sun cd. :ii iii f1 PART III JOINER'S WORK \ CHAPTER I KERFINC, RAKING MOULDINGS, HOPPERS AND SPLAYS This department could be extended indefinitely, as the problems in joinery are much more numerous than in carpentry, but as the limits of this book will not permit me to cover the whole range of the art, even if I were competent, I must be contented with dealing with / those problems the fij- 1. /' workman will most ^^ likely be confronted - X with in his daily oc- cupation. First of all, I give several methods of "keriing," for few things puzzle the novice more than this litlie problem. Let us suppose any circle around which it IS desired to bend a piece of stuff to be 2 inches larger on the outside than on the inside, or in other words, the veneer is to be i inch thick, then take out as many saw kerfs as will measure 2 inches. Thus, if a saw cuts a kerf one thiity-second of an inch in width, then it will take 64 kerfs :n the half circle to allow for the "7 i^*^ H ii8 MODERN CARPENTRY veneer to bend around neatly. The piece being placed in position and bent, the kerfs will exactly close. Another way is to saw one kerf near the center of the piece to be bent, then place it on the plan of the frame, as indicated in the sketch and bend it until the kerf closes. The distance, DC, Fig. I, on the line DB, will be the space between the kerfs neceS' sary to complete the bending. In kerfing the workman should be care- ful to use the same saw throughout, and to cut exactly the same depth every time, and the spaces must be of equal distance. In diagram Fig. i, DA shows the piece to be bent, ami at O the thickness of the stuff is shown, also path of the inside and outside of the circle. Another, and a safe method of kerfing is shown at Fig. 2, in which it is desired to bend a piece as shown, a n d which is in- tended to be secured at the ends. Up to A is the piece to be t r e a t e tl . First gauge a line on about one-eighth inch back from the face edges, and try how far it will yield when the first cut is made up to the gauge line, being cut perleclly straight through from side to side, then place the work JOINER'S WORK 119 »t r on a flat board and try it pontly until the kerf closes, and it goes as far as is shown at A, which is the first cut, R rcprcsentinjT the second. Those are the dis- tances the kerfs require to be placed apart to complete the curve. Try the work :■< it progresses. This eases the back of it and makes ■ much easier done when the whole cuts arc finished. Now make certain that the job will fold to the curve, th. n fill them all with hot glue and proceed to fix. The plan shown here is a half semi, and may be in excess of what is wanted, but the principle holds good. Another method is shown at Fig. 3 for determining the number and distances apart of the saw kerfs required to bend a board round a corner. The board is first drawn in position and a half of it divided into any rumber of equal parts by radii, as I, 2, 3, 4, 5, 6.' A straight piece is then marked off to correspond with the divi- sions on the circular one. By this it is seen that the part XX must be cut away by saw kerfs in order to let the board turn round. It therefore depends upon the thickness of the saw for the number of kerfs, and when that is known the distances apart can be determined as shown on the right in the figure. Here eight kerfs are assumed to be requisite. To make a kerf for bending round an ellipse, such as that shown at Fig. 4, proceed as shown, CC and GO being the distances for the kerfs; 2 to 2 and 2 103 are the lengths of the points EF, w^hile BB is the length of the Ipt I30 MODERN CARPENTRY points EE, making the whole head piece in one. In case it is necessary to joint D, leave the ends about inches longer than is necessary, as shown by N in the IZS sketch, so that should a breakage occur this extra length may be utilized. It is sometimes necessary to bend thick stuff around work that is on a rake, and when th s is required, all that is necessary is to run in the kerfs the angle of the rake whatever that may be, as shown at Fig. 5. This rule holds good for all pitches or rakes. Fig. 6 shows a very common way of obtaining the distance to place the kerfs. The piece to be kerfed is shown at C; now make one at E; hold firm the lower part of C and bend pi^g^ ^^ n JOINER'S WORK iti the upper end on the circle F until the kerf is closed. The line started at E and cutting the circumference of the circle indicates at the circumference the distance the saw kerfs will be apart. Set the dividers to this space, and be- ginning at the center cut, space the piece to be kerfed both ways. Use the same saw in a'l cuts and let it be clean and keen, with all dust well cleaned out. To miter mouldings, where straight lines must merge into lines having a curvature as in Figs. 7 and 8: In all cases, where a straij^ht moulding is intersected with a curved mould- ing,' of the same profile at whatever angle, the miter is ♦necessarily other than a straight line. The miter line is found by the intersec- tion of lines from the several points of the pro- file as they occur respect- ively in the straight and the curved mouldings. In order to find the miter between two such mould- . , in;Ts first project lines '. }^ from all of the poir.*^? of laa MODERN CARPENTRY •m< the profile indefinitely to the right, a« shown in the elevation of the sketch. Now. upon the center line of the curved portion, or un.^n any line radiating from the c Now lay off cny number of lines parallel with the seat from the rise, to and beyond the curve AB, as shown, and for each i.nrh in length of these lines (between rise and curve), add A of an inch to the same line to the left of the curve, and check. After ,84 MODERN CARPENTRY all lines have thus been measured, run an off-hand curve through the checks, and the curve will represent the corresponding hip at the center of its back. To find the bevel "7 or backing of the hip to coincide with the plane of the common rafter, measure back on the parallel lines to the right of the curve one-half the thickness of the hip and draw another curve, which will be the lines on the side to trim to from the center of the back. A like amount must be added to the plumb cut to fit the corner of deck. Pro- ceed in like manner for the octagon hip, but instead of adding A, add ,1^ of an inch as before described. [While this is worked out on a giv- en rise and run for the rafter, the rule is applicable to any rise or run, as the workman will readily understand.] A more elaborate system for obtaining the curve of a hip rafter, where the common rafters have an ogee or concave and convex shape, is shown at Fig. I2J^. This ■^.'^■'-^■^isfc ^vn C!i!}> j.>.T ". ^«?^.-:^^:^^ripf. JOINER'S WORK I as i is a very old method, and is shown — with slight varia- tions—in nearly all the old works on carpentry and winery. Draw the seat of the common rafter, AB, and r'.^ m gable, the moulding D shown at the right hand must be worker, out for the upper side, 'ihe manner in which this is done is self-evident upon examination of the drav'ng, and therc^fore needs no special description. A good example of a raking moulding and its appli- cations to actual work is shown in Fig. 15, on a differ- ent scale. The ogee moulding at the lower end is the regular moulding, while the middle line, ax, shows the shape of the raking moulding, and the curve on the top end, cdo, shows the face of a moulding that would be required to return horizontally at that point. The manner of pricking off these curves is shown by the letters and figures. At Fig. 16 a finished piece of work is shown, where this manner of work w'l! be required, on the returns. Fig. 17 shows the same moulding applied to a curved window or door head. The manner of pricking the curve is given in Fig. 18. At No. 2 draw any line, AD, to the center of the 1 7 v:- •f^.i JOINER'S WORK 129 pediment, meeting the upper edge of the upper fillet ia D, and intersecting the lines AAA, aa :, bbb, ccc, BBB in A, o, b, c, B, E. From these points draw lines aa, bb, cc, BB, EE, tangents to their respective arcs; 130 MODERN CARPENTRY ^ ^ig. 19. 7 1 A V on the tangent line DE, from D, make Y)d, D^, D/ DE, respectively equal to the listances D ^ and are bev- eled on the back at the bottom in such a man- ner that the top portion of the mem- ber hangs over, which gives it the appearance of being solid. ^ ■ of tills kmd are called "spring mouldings," and much care is required in mitering them. This should always be done in a miter box, which must be made for the purpose; often two boxes are required, as shown in Figs. 19-22. The cuts across the box are regular miters, while the angles down the side are the same as the down cut of the rafter, or plumb cut of the moulding. When the box is ready, place the mouldings in it upside down, keep- ing the moulded side to the front, as seen in Fig. 20, \A m T JOINER'S WORK 131 making sure that the level of the moulding at c fits close to the side of the box. To miter the rake mouldings together at the top, the box shown in Fig. 21 is used. The angles on the top of the box are the same as the down bevel at the top of the rafter, the sides being sawed down square. Put the moulding in the box, as shown in Fig. 22, keeping the bevel at c flat on the bottom of the box, and having the moulded side to the front, and the miter for the top is cut, which completes the moulding for one side of the gable. The miter for the top of the moulding for the other side of the gable may then be cut. When the rake moulding is made of the proper form these boxes are very con- venient; but a great deal of the machine- made mouldings are I'' L'l r ill ,3a MODERN CARPENTRY not of the proper form to fit. In such cases the moulding should be made to suit, o they come bad; although many use the mouldings as they come from the factory, and trim the miters so as to make them do. The instructions given, however, m hif,'s. 13, 14, 15 and 18 will enable the workman to make patterns for what he retjuires. While the "anslL' bar" is not J much in vogue at " the present time, the methods by which it is ob- tained, maybe ap- plied to many pur- poses, so it is but proiHT the method should be em- bodied in this work. In Fig. 23, R is a common sash bar, and C is the angle bar of t h e same thick- ness. Take the raking projection, 11, in C, and set the foot of your compass in i at 1?, and cross the middle of the bar at the other i ; then draw the pomts 2, 2, 3, 3, etc., parallel to li, then prick your bar at C from the ordinates su drawn at B, which, when traced, wdl give the angle bar ,• j * This is a simple operation, and may be applied to Fig.2i, i^ JOINER'S WORK »33 -i many other cases, and for enlarging or diminishing mouldings or other work. The next fi'_[ure, 24, gives the lines for a raking moulding, such as a cornice in a room with a sloping ceiling. As may be seen from the diagram the three sections shown are drawn equal in thickness to miter at the angles of the room. The construction should be easily under- stood. When a straight moulding is mitered with a curved one the line of miter is some- times straight and sometimes curved, as seen at Fig. 18, and when the mouldings are all curved the miters are also straight and curved, as shown in previous examples. If it is desired to make a cluster column of wood, it is first necessary to make a standard or core, which must have as many sides as there are to be faces of columns. Fig. 25 shows how the work is done. This shows a cluster of four columns, which are nailed to a square standard or core. Fig. 26 shows the base of a clustered column. These are blocks turned in the lathe, requiring four of them for each base, which are cut and mitered as shown in Fig. 25. The cap, or capital, is, of course, cut in the same manner. Fig. ^6. S.._=.-".c. »34 MODERN CARPENTRY i I* ■')■ Laying out lines for hopper cuts is often puzzling, and on this account 1 will devote more space to this subject than to those requiring less explanations. Fig. 27 shows an isometric view of three sides of a hopper. The fourth side, or end, is purposely left out, in order to show the exact build of the hopper. It will be noticed that AC and EC) show the end of the work as squared up from the bot- tom, and that HC shows the gain of the splay or flare. This gives the idea of what a hopper is, though the width of side and amount of flare may be any meas- urement that may be decided upon. The difficuUy in this work is to get the proper lines for the miter and for a butt cut. Let us suppose the flare of the sides and ends to be as shown at Fig. 28, though any flare or inclination will answer equally well. This diagram and the plan exhibit the method to be employed, where the sides and ends are to be mitered together. To obtain the bevel to apply for the side cut, use A' as center, B' as radius, and CDF para. lei to BF. Project from B to D oarallel to XY. Join AD, which gives the bevel required, as shown. If the top edge of the stuff is to be horizontal, as shown at B'G', the bevel to apply to the edge will be simply as shown in plan by BG; but if . ( -;:' .5«?*« :i5MRL. JOINER'S .'ORK '35 the edge of the stuff is to be square to the side, as shown at WC, Fig. 29, the bevel must be obtained as follows: Produce EB' to D', as indicated. Fig. 29. With B as center, describe the arc from C, which gives the point D. Project down from D, makin^j DF parallel to CC, as shown. Project from C parallel to XY. This will give the point D. Join BD, and this will give the bevel line required. At A, Tig. 31, is shown the application of the bevel to the side of the stuff, and at B the application of the bevel to the edge of the stuff. When the ends butt to the sides, as indi- cated at H, Fig. 30, the bevel, it will he noticed, is obtained in a similar manner to that shown at Fig 28. It is not often that simply a butt joint is used between IITT^' •.n 136 MODERN CARPENTRY I U if the ends and sides, but the ends are usually housed into the sides, as indicated by the dotted lines shown at H, Fig. 30. Another system, which was first taught by the cele- brated Peter Nicholson, and afterwards by Robert Riddeil, o^ P h i 1 a d e 1 • I)hia, is ex- plained in t h e follow- i n g : T h t' illustra- tion shown at I'^ig. 32 is in- tended to show how to find the lines for cutting butt joints for a hopper Construct a right angle, as A, B, C, Fig. 32, con- tinue A, H pastK. From K, B make the inclination of the sides of the hopper, 2, 3. Draw 3, 4 at right angles with 3, 2; take 3 as center, and strike an arc touching the lower line, cutting in 4. Draw from 4, cutting the miter line in 5; from 5 square draw a line cutting in 6. join it and B; this gives bevel W, as the direction of cut on the surface of sides. To find the butt joint, take any two points, A, C, on the JOINICkS WORK '37 rijiht anj,'it . equally distant from H, make the anglr H. K. L. ..qual that of 3. K. L. shown on the k-ft; from H tlraw through point I.; now take C as a center, and strike an arc, tnuchinf,' line BL. From A draw a line touching thr arc at II, and cuttinjj the extended line throujih H in N, thus fixing,' N as a point. Then by draw- i n g from C throuK'h N, \vc get the bevel X for the butt joint. Joints on the ends of timbers running horizontally in tapered framed structures, when the plan is square and the inclinations equal, may be found by this method. The backing of a hip rafter may also be obtained by this method, as shown at J, where the pitch line is used as at 2, 3, which would be the inclination of the roof. The solution just rendered is intended only for hop- pers having right angles and equal pitches or splays, as hoppers having acute or obtuse angles, must be treated in a slightly different way. Let us suppose a butt joint for a hopper having an 138 MODERN CARPENTRY acute angle, such as shown at A, B, C, Fig. 33, and with an inclination as shown at 2, 3. Take any two points, A, C, equally distant from B. Join A, C, bisect this line in P, draw through P, indefinitely. Find a bevel for the side cut by drawing 3, 4, square with 2, 3; take 3 as a center, and strike an arc, touch- ing the lower line cutting in 4; draw from 4, cutting I: • 1 !l the miter line in 5, and from it square draw a line cutting in 6. Join 6, B, this gives bevel W, for direc- tion of cut on the surface of inclined sides. The bevel for a butt joint is found by drawing C, 8, square with A, B; make the angle 8, K, L, equal that of 3, K, L, shown on the left. Draw from 8 through point L; take C as a center and strike an arc touching the line 8, L; draw from A, touching the arc at D, cutting JOINER'S WORK 139 the line from P, in D, making it a point, then by drawing from C, thro ^^h D, we get the bevel X for the butt joint. As stated regarding the previous illustration, the backing for a hip in a roof having the pitch as shown at 2, 3, may be found at the bevel J. The same rule also applies to end joints on timbers placed in a hori- zontal double inclined frame, having an acute angle same as described. Having described the methods for finding the butt joints in right-angled and acute-angled hoppers, it will be proper now to define a method for describing an obtuse-angled hopper having butt joints. Let the inclination of the sides of the hopper be "i U t • (' ] \' ' '* li li J 1 '. : ' i! : . i 1 : I; i (IP I' 140 MODERN CARPENTRY exhibited at the line 2, 3, and the angle of the obtuse corner of the hopper at A, B, C, then to find the joint, take any two points, A, C, equally distant from B, join these points, and divide the line at P. Draw through P and B, indefinitely. At any distance below the side A, B, draw the line 2, 6; make 3, 4, square with the inclination. From 3, as a center, describe an arc, touching the lower line and cutting in 4; from 4 draw to cut the miter line in 5, and from it square down a line cutting in 6, join 6, B, and we get the bevel W for cut on surface sides. The bevel for the butt joint is found by drawing C, D, square with B, A, and making the angle D, K, L equal to that of 3, K, L on the left. From C, as a center, strike an arc, touching the line D, L; then from A draw a line touching the arc H. This line having cut through P, in N, fixes N as a point, so that by drawing C through N an angle is determined, in which is bevel X for the butt joint. JOINER'S WORK 141 To obtain the bevels or miters is a simple matter to one who has mastered the foregoing, as evidenced by the following: Fig. 34 shows a right-angled hopper; its sides may stand on any inclination, as AB. The miter line. 2, W, on the p.un. being fixed, draw B, C square with the inclination. Then from B, as center, strike an arc, touching the base line and cutting in CD. From CD draw parallel with the base line, cutting the miters in F and E; and from these points square down the lines, cutting in 3 and 4. From 2 draw through 3; this gives oevel W for the direction of cut on the surface sides. Now join 2, 4, this gives bevel X to niiter the edges, which in all cases must be square, in order that bevels may be properly applied. Fig. 35 shows a plan forming an acute-angled hop- kI i!f 14s MODERN CARPENTRY per, the miter line being 2, W. The sides of this plan are to stand on the inclination AH. Draw BC square with the inclination, and from B, as center, strike an arc, touching the base line and cutting in CD. Draw from CD, cutting the miter line at E and F; from these points square down the lines, cutting in 3 and 4. From 2 draw through 4, which will give bevel W to miter the edges of sides. Now join 2, 3, which gives bevel X for the direction of cut on the surface of sides. Fig. 36 shows an obt'ise anj,dcd hopper, its miter line on the plan being 2 W, and the inclination of sides I AB. Draw BC square with the inclination, and from B as center strike an arc, touching the base line and cutting CD. Draw from CD, cutting the miter in F and E. From these points square down the lines, cut- ting the base; then by drawing from 2 through the point below E, we get bevel W for the direction of ci.<^- on the surface of sides, and in like manner the point below F being joined with 2, gives bevel X to miter the edges. It will be noticed that the cuts for the three differ- ent angles are obtained on exactly the same principle, without the slightest variation, and so perfectly sim- ple as to be understood by a glance at the drawing. The workman will notice that in each of the angles a JOINER'S WORK M3 »44 MODERN CARPENTRY line from C, cutting the miter, invariably gives a direc- tion for the surface of sides, and the line from D directs the miter on their edges. Unlike many other systems employed, this one meets all and every condition, and is the system that has been employed by high class workmen and millwrights for ages. One more example on hopper work and I am done with the subject: Suppose it is desired to build a hopper similar to the one shown at Fig. 37, several new conditions \ %. 38. will be met with, as will be seen by an examination of the obtuse and acute angles, L and P. In order to work this out right make a diagram like that shown at Fig. 38, where the line AD is the given base line on which the slanting side of hopper or box rises at any angle to the base line, as CB, and the total height of the work is represented by the line B, E. By this diagram it will be seen that the hori- zontal lines or bevels of the slanting sides are indi- cated by the bevel Z. Having got this diagram, which of course is not drawn to scale, well in hand, the ground plan of the hopper may be laid down in such a shape as desired, with the sides, of course, having the slant as given in Fig. 38. Take T2, 3S, Fig. 37, as a part of the plan, then set off the width of sides equal to C, B, as shown in Fig. 38. JOINER'S WORK 145 These are shown to intersect at P, L above; then draw lines from P, L through 2, 3, until they intersect at C, as the dotted lines show. Take C as a center, and with the radius A, describe the semi-circle A, A, and with the same radius transferred to C, Fig. 38, describe the arc A, 13, as shown. Again, with the same radius, set off A, B, A, B on Fig. 37, cutting the semi-circle at B, as shown. Now draw through B, on the right, parallel with S, 3, cutting at J and F; square over F, H and J, K, and join H, C; this gives bevel X, as the cut for face of sides, which come together at the angle shown at 3. The miters on the edge of stuff are parallel with the dotted line, L, 3. This is the acute corner of the hopper, and as the edges are worked off to the bevel 2, as shown in Fig. 38, the miter must be correct. Having mastered the details of the acute corner, the square corner at S will be next in order The first step is to join K, V, which gives the bevel V, for the cut on the face of sides on the ends, which form the square corners. The method of obtaining these lines is the same as that explained for obtaining them for the acute-angled corner, as shown by the dotted lines, Fig- 35. As the angles, S, T, are both square, being right and left, the same operation answers both, that \s, the bevel Y does for both corners. Coming to the obtuse angle, P, 2, we draw a line B, E, on the left, parallel with A, 2, cutting at E, as shown by dotted line. Square over at E, cutting T, A, 2 at N; join N, C, which will give the bevel \V, which is the angle of cut for face of sides. The miters on edges are found by drawing a line parallel with P, 2. In this problem, like Fig. 34, every line necessary to the cutting of a iiopper after the plan as shown by 146 MODERN CARPENTRY mi the boundary lines 2, 3, T, S. is complete and exhaust- ive, but it must be understood that in actual work the spreading out of the sides, as here exhibited, will not be necessary, as the angles will find themselves when the work is put together. When the plan of the base — which is the small end of the hopper in this case— is given, and the slant or inclination of the sides known, the rest may be easily obtained. In order to become thoroughly conversant with the problem, I would advise the workman to have the drawing made on cardboard, so as to cut out all the outer lines, in- cluding the open corners, which form the miter?, leaving the whole piece loose. Then make slight cuts in the back of the cardboard, opposite the lints 2, 3, S, T, just deep enough to admit of the cardboard being bent upwards on the cut lines without breaking. Then run the k life along the lines, which indicates the edges of the hopper sides. This cut must be made on the face side of the drawing, so as to admit of the edge ■ -ig turned downwards. After all cuts are made raise the sides until the corners come closely together, and let the edges fall level, or in such a position that the miters come closely together. If the lines have been drawn accurately and the cuts made on the lines in a proper manner, the work will adjust itself nicely, and the sides will have the exact inclina- tion shown at Fig. 38, and a perfect model of the work will be the result. This is a very interesting problem, and the working out of it, as suggested, cannot but afford both profit and pleasure to the young workman. From what has preceded, it must be evident to the workman that the lines giving proper angles and bevels for the corner post of a hopper must of neces- rr JOINER'S WORK »47 sity give the proper lines for the corner post for a pyr- a..iidai building, such as a railway tank frame, or any similar structure. True, the position of the post is inverted, as in the hopper, its top falls outward, while in the timber structure the top inclines inward; but this makes no difference in the theory, all the operator has to bear in mind is that the hopper in this case is reversed —inverted. Once the proper shape of the corner post has been obtained, all other bevels can readily be found, as the side cuts for joists and braces can be taken from them. A study of these two figures in this direction will lead the student up to a correct know! edge of tapered framing. p\ CHAPTER II COVERING SOLIDS, CIRCULAR WORK, DOVETAILING AND STAIRS There are several ways to cover a circular tower roof. Some arc covered by bending the boarding around them, while others have the joints of the coverii g ver- tical, or inclined. In either case, the boarding has to be cut to shape. In the first instance, where tht joints 148 JOINER'S WORK 149 are horizontal, the covering must be curved on both edges. At Fig. 39 I show a part plan, elevation, and develop- ment of a conical tower roof. ABC shows half the plan; DO and EO show the inclination and height of the tower, while EH and EI show the development of the lower course of covering. This is obtained by using O as a center, with OE as radius, and striking the curve EI, which is the lower edge of the board, and corre- sponds to DE in the elevation. From the same center O, with radius OF, describe the curve FH, which is the joint GF on the elevation. The board, EFHI, may be any convenient width, as may also the other boards used for covering, but whatever the width de- cided upon, that same width must be continued throughout that course. The remaining tiers of covering must be obtained in the same way. The joints are radial lines from the center O. Any convenient length of stuff over the distance of three ribs, or raft- ers, will answer. This solution is ap- plicable to many kinds of work. The rafters in this case are simply straight scantlings; the bevels for feet and points may be obtained from the diagram. The shape of a "gore," when such is required, is shown at Fig. 40, IJK showing the base, and L the top or apex. The method of getting it out will be easily understood by examining the diagram. When "gores" are used for covering it will be necessary Fig. 40. JBb 150 MODERN CARPENTRY ♦',) 1 to have cross-ribs n.uied in between the rnfters, ana these must be cut to the sweep uf the cir ic, where they are nailed in, so that i rib place cover this dome hori- zontally. Bisect th( base i i the point D. and draw DBE perpendicular to AC, cutting thi circumference in B. Now divide the arc, BC, into equal parts, that each part will be rather less than th<' width of a board and io!n th--' no'.nts r>f division Hv ^itr^icfht lines, which will form a. inscribed polygon of so many sides; and through thesv points draw lines parallel to JOINER'S WORK «5» the l)ase AC, m«'etinf( the opposite sides of the circum- ference. The trapezoids formed by the sides of the polygon and the horizontal lines may then be regarded as the sections of so many frustrums of cones; whence results thf foHuwinj^ mofie of procedure: Produce, until tht.y mtn t the line DE, the lines FG, etc., form- infi the sides of the polygon. Then to describe a lioard whicii corresponds to the surface of one of the zones, as FG, of which the trapezoid is a section from F>g.^^'^ the 1 oir }., whe the line FG prodi eu meets DE, with radi' EF, EG describe two arcs and cut off the t the boaid K on the line of a radius EK. 'i '^e her boards are described in the same manner. T'-^cre r-' many other solids, some oT which it is p ssible the workman may be called uj n to cover, but 15 space will not admit o.f us H.iscussinji them a!!, H' will illustrate one example, which includes within itself the (uinciples by !iich almost .uiy other so'' »5> MODERN CARPENTRY P^! may be dealt with. Let us suppose a tower, having a domical roof, rising from another roof having an incll nation as shown at BC, Fig. 42, and we wish to board it with the joints of the boards on the same inclination as that of the roof through which the tower rises. To accomplish this, let A, B, C, D, Fig. 42, be the seat of the generating section; from A draw AG perpendicular to AB, and produce CD to meet it in E; on A, E describe the semi -circle, and transfer its perim- eter to E, G by dividing it into equal parts, and setting off corre- sponding divisions on E, G. Through the divisions of the semi -circle draw lines at right angles to AE, producing them to meet the lines A, D and B, C in i, k, I, m, etc. Through the divisions on E, G, draw lines perpendicular to them; then through the intersections of the ordinates of the JOINER'S WORK 153 semi-circle, with the line AD draw the lines «, a, k, z, /, jr, etc., parallel to AG, and where these intersect the perpendiculars from EG, in points a, e, _y, ;r, w, v, «, etc., trace a curved line, GD, and draw parallel to it the curved line HC; then will DC, HG be the development of the covering required. Almost any description of dome, cone, ogee or other solid may be developed, or so dealt with under the principle as shown in the foregoing, that the workman, it is hoped, will ex- perience but little difficulty in laying out lines for cutting mate- rial to cover any form of curved roof he may be confronted with. Another class of covering is that of making soffits for splayed doors or windows having circular or segmental heads, such as shown in Fig, 43, which exhib- its a door with a circular head and splayed jambs. The head or soffit is also splayed and is paneled as shown. In order to obtain the curved soffit, to show the same splay or angle, from the vertical lines of the door, proceed as follows: Layout the width of the doorway, showing the splay of the jambs, as at C, B and L, P; extend the angle lines, as shown by the dotted lines, to A, which gives A, B as the radius of the w 1^ / Jfc "V 1 \FigA4,. /J IJ 154 MODERN CARPENTRY inside curve, and A, C as radius of the outside curve. These radii correspond to the radii A, B and A, C in Fig- 43; the figure showing the flat plan of the pan- eled soffit complete. To find the development, Fig. 43, get the stretch-out of the quarter circle 2 and 3, shown in the elevation at the top of the doorway, and «--< make 2, 3 and 3B, Fig. 43. equal to it, and the rest of the work is very simple. If the soffit is to be laid off into panels, as shown at Fig. 44, it is best to prepare a veneer, having its edges curved similar to those of Fig. 43, making the veneer of some flexible wood, such as basswood, elm or the like, that will easily bend over a form, such as is shown at Fig. 44, The shape of this form is a portion of a cone, the circle L being less in diameter than the JOINER'S WORK 155 circle P. The whole is covered with staves, which, of course, will be tapered to meet the situation. The veneer, x, x, etc., Fig. 43, may then be bent over the form and finished to suit the conditions. If the mouldings used in the panel work are bolection mould- ings, they cannot be planted in place until after the veneer is taken off the form. This method of dealing with splayed work is appli- cable to windows as well as doors, to circular pews in churches and many other places where splayed work is required. A simple method of finding the veneer for a soffit of the form shown in Fig. 43 is shown at Fig. 45. The splay is seen at C, from which a line is drawn on the angle of the splay to B through which the vertical line A passes. B forms the center from which the veneer tt1 ■ J 11 m -I li 1 156 MODERN CARPENTRY is descriDed. A is the center of the circular head, for both inside and outside curves, as shown at D. The radial linos centering at B show how to kerf the stuff when necessary for bending. The line E is at right angles with the line CB, and the veneer CE is the proper length to run half way around the soffit. The jtiints are radial lines just as shown. A method for ob- taining the correct shape of a veneer for a gothic splayed window or door- head, is shown at Fig. 46; E shows the sill, and line BA the angle of splay. BC shows the outside of the splay; erect the in- side line F to A, and this point will form the center from which to de- cribe the curve or ^'g- *7. veneer G. This veneer will be the proper shape to bend in the soffit on either side of the window head. The art of dovetailing is almost obsolete among carpenters, as most of this kind of work is now done by cabinet-makers, or by a few special workmen iu the factories. It will be well, however, to preserve the art, and every young workman should not rest until he can do a good job of work in dovetailing; he wiii not find it a difficult operation. JOINER'S WORK 157 There are three kinds of dovetailing, i.e., the com- mon dovetail, Fijj. 47; the lapped dovetail, Fig. 48, and the secret, or mitered dovetail, Fig. 49. These may be subdivided into other kinds of dovetailing, but there will be but little difference. The common dovetail is the strongest, but shows the ends of the dovetails on both faces of the angles, Fig. 48. and 's, therefore, only used in -^ h places as that of a drawer, where the extei A angle is not seen. The lapped dovetail, where the ends of the dovetails show on one side of the angle only, is used in such places as the front of a drawer, the side being only seen when opened. In the miter or secret dovetail, the dovetails are not seen at all. It is the weakest of the three kinds. i.'U 158 MODERN CARPENTRY At Figs. 50 and 51 I show two methods of dovetail- ing hoppers, trays and other splayed work. The reference letters A and B show that when the work is together A will stand directly over B. Care must be 11 ^ !■ Fig. 50. taken when preparing the ends of stuff for dovetailing for hoppers, trays, etc., that the right bevels and angles are obtained, according to the rules explained Fig. 51 for finding the cuts and bevels for hoppers and work of a similar kind, in the examples given previously. All stuff for hopper work intending to be dovetailed JOINER'S WORK «S9 must be prepared with butt joints before the dovetails are laid out. Joints of this kind may be made com- mon, lapped or mitered. In making the latter much skill and labor will be required. Stair building and handrailing combined is a science in itself, and one that taxes the best skill in the mar- ket, and it will be impossible for me to do more than touch the subject, and that in such a manner as to enable the workman to lay out an ordinary straight flight of stairs. For further instructions in stair building I would refer my readers to some one or two of the many works on the subject that can be obtained from any dealer in mechanical or scientific books. The first thing the stair builder has to ascertain is the dimension of the space the stairs are to occupy; then he must get the height, or the risers, and the width of the treads, and, as architects generally draw the plan of the stairs, showing the space they are to occupy and the number of treads, the stair builder has only to measure the height from floor to floor and divide by the number of risers and the distance from first to last riser, and divide by the number of treads. (This refers only to straight stairs.) Let us take an exam- ple: Say that we have ten feet of height and fifteen feet ten inches of run, and we have nineteen treads; thus fifteen feet ten inches divided by nineteen gives us ten inches for the width of the tread, and we have ten feet rise divided by twenty (observe here that there is always one more riser than tread), which gives us six inches for the height of the riser. The pitch- board must now be made, and as all the work has to be set out from it, care must be taken to make it exactly right. Take a piece of board, same as shown i6o MODERN CARPENTRY F "^ in Fig. 52, about half an inch thick, dress it and square the side and end, A, B, C; set off the heij^ht of the rise from A to B, and the width of the trend from B toC; now cut the line AC, and the pitch-board is com- plete, as shown in Fig. 53. This may be done by the steel square as shown at Fig. 54. To get the width of string-boards draw the line AB, Fig. 53; add to the len},fth of this line about half an inch more at A, the margin to be allowed, and the total will be the width of string-boards. Thus, say that we allow three inches for margin, one-half inch to be left on the under side of string-board, will make the width of string-boards in this case about nine inches. Now get a plank, siiy one and a half inches, of any thickness that may be ag'ced upon, the length may be obtained by multiply- ing the longest side of the pitch-boards, AC. Fig. 52, by the number of riser**: but as this is the only class of stairs that the length > Jring-boards can be obtained in this way I would rer-, .mend tb.c her^inner to prac- tice the sure plan of taking the pitch-hoard and apply- ing it as at I, 2. 3, 19, Fig. 55. Drawing all the steps JOINER'S WORK i6i this way will prevent a mistake that sometimes occurs, viz. the string-boards being cut too short. Cut the foot at the line AB, and the top, as at CD. This will give about one and a half inches more than the extreme length. Now cut out the treads and risers; the width of stair is, say, three feet, and we have one and a half inches on each side for string-boards. Allow three-eights of an inch for housing on each side. This will make the length of tread and risers two and one-fourth inches less than the full width of stairs; and as the treads must project their own thick- ness over rise, which is, say, one and a half inches, the full size of tread will be two feet by eleven and one- half inches, and of the risers two feet nine and three- fourths inches by six inches; and observe that the first riser will be the thickness of the tread less than the others; it will be only four and one-half inches wide. The reason of this riser being less than the others is because it has a tread thickness extra. I will now leave the beginner to prepare all his work. Dress the risers on one face and one edge; dress the treads on one face and both edges, making them all of equal width; gauge the ends and the face edge to the required thickness, and round off the nosings; dress the string-boards to one face and edge to match each other. A plan of a stair having 13 risers and three winders below is :hown at Fig. 56. This shows how the whole stair may be laid out. It is inclosed between two walls. The beginner in stair-work had better resort to the old method of using a story-rod for getting the num- ber of risers. Take a rod and mark on it the exact height from top of lower floor to top of next floor, then i6a MODERN CARPENTRY l\ J i divide up and mark off the number of risers required. There is always one more riser than trea.l in every flight of stairs. The first risrr must be cut the thick- ness of the tread less than the others. When there are winders, special treatment will be JifflMJ LANOINC , Fig. 6()< I* i IS IB II 10 9 i 7 6 s 4- im^HBi ^m l« PL AM required, as shown in Fig. 56, for the treads, but the riser must always be the same width for each separate flight. When the stair is straight and without winders, a rod may be used for laying off the steps. The width of the steps, or treads, will be governed somewhat by the space allotted for the run of the stairs. There is a certain proportion existing between the tread and riser of a stair, that should be kept to as close as possible when laying out the work Architects JOINER'S WORK 163 say that the exact measurement for a tread and riser should be sixteen incli(-s. or thereabouts. That is, if a riser is made six inch(ts, the tread should be ten inches wide, and so on. I give a table herewith, showing the rule generally made use of by stair builders for deter- mining the widths of risers and treads: 7>tads Kitert 7>eads /fistrs Inche* iDcheit Inches laches 5 9 12 5>4 6 8^ 13 5 , 7 8 14 4>i 8 9 7'A 7 \l 4 3H 10 6% 17 3 II 6 18 2}i It is seldom, however that the proportion of the riser and step is exactly a matter of choice — the room i64 MODERN CARPENTRY allotted to the stairs usually dctermin«'s this propor- tion; but the above will be found a useful standard, to which it is desirable to approximate. In better class I uldingi the number of steps is con- sidered in the plan, which it is the business of the architect to arrange, and in such cases the height of the story-rod is simply divided to the number required. An elevation of a stair with winders is sho^'n at Fig. 57, where the story-rod is in evidence with the number of risers figured off. Fig. 58 shows a portion of an open string stair, with a part of the rail laid on it at AB, CD, and the newel cap with the projection at A. This shows how the cap should stand over the lower step. Fig. 59 shows the manner of constructing the step; S represents the string, R the risers, T the tread, O the nosing and cove moulding, and B is a block glued or otherwise fastened to both riser and tread to render ^ JOINERS WORK '65 them strong and firm. It will be seen the riser is let in the trea'i and has a shoulder on the insid*-. The bottom of th riser is nailed to the back of the next !i wer tread, which binds the whoi lower part to- gether. The nosing of the stair is ^-^cn- c r a 1 ' y re- turned i the (\)cn end of the tread, and this ■ ov- ers the ' nd wo. (I of *he tread anu the joints of the balusters, as shown at Fif,'. CiO. When a stair is bracketed, as shown at B, Fig. 60, I lie point of the riser on its strin-,' r?nd should be left vE;. ifng past the string the thickness of the bracket, and the end of the bracket miters against it, thus avoid- ing the necessity of showing end wood or joint. The cove should finish inside the length of the bracket, and the nosing should fin- ish just outside the When brackets are employed Fig. 60. length of the bracket. i66 MODERN CARPENTRY they should continue along the cylinder and al) around the well -hole trimmers, though they may be varied to suit conditions when continuously run- ning on a straight horizontal facia. ill ^ 1 3 J ^ CHAPTER III joiner's work— useful miscellaneous examples I am well aware that workmen are always on the lookout for details of work, and welcome everything in this line that is new. While styles and shapes change from year to year, like fashion in women's dress, the principles of construction never change, and styles of finish in woodwork that may be in vogue to-day, may be old-fashioned and discarded next year, therefore it may not be wise to load these pages with many examples of finish as made use of to-day. A few examples, however, may not be out of place, so I close this section by offering a few pages of such details as I feel assured will be found useful for a long time to com'. full page illustration of three exam- and newels in modern styles. The colonial stairway with a square newel, A baluster is also shown, so that the whole may be copied if required. The second exam- ple shows two newels and balusters, and paneled string and spandril AB, also section of paneled work on end of short flight. The third shows a plain open stair, with baluster and newel, the latter starting from first step. At Fig. 2, which is also a full page, seven of the latest designs for doors are shown. Those marked 167 Fig. I is a pies of stairs upper one is a as shown at A. i i68 MODERN CARPENTRY JOINER'S WORK 169 'I Hi 170 MODERN CARPENTRY ABCD are more particularly employed for inside work, while F and G may be used on outside work; the five- paneled door being the more popular. There are ten different illustrations, shown at Fig. 3, of various details. The five upper ones show the gen- eral method of constructing and finishing a window frame for weighted sash. The section A shows a part of a wall intended for brick veneering, the upper story being shingled or clapboarded. The position of windows and method of finishing bottom of frame, both inside and out, are shown in this section, also manner of cutting joists for sill. The same method — on a larger scale — is shown at C, only the latter is intended for a balloon frame, which is to be boarded and sided on the outside. At B another method for cutting joists for sill is shown, where the frame is a balloon one. This frame is supposed to be boarded inside and out, and grounds are planted on for finish, as shown at the base. There is also shown a carpet strip, or quarter-round. The outside is finished with siding. The two smaller sections show foundation walls, heights of stories, position of windows, cornices and gutters, and methods of cornecting sills to joists. A number of examples are shown in Fig. 4 that will prove useful. One is an oval window with keys. This is often employed to light vestibules, back stairs or narrow hr.llways. Another one, without keys, is shown on the lower part of the page. There are three examples of eyebrow dormers shown. These arc different in style, and will, of course, require different construction. The dormer window, shown at the foot of the page, JOINER'S WORK i7> I ■f| ) m h i L„.: i B S 17a MODERN CARPENTRY ill fii^ JOINER'S WORK 173 is designed for a house built in colonial style, but may be adapted to other styles. The four first examples in Fig. 5 show the sections of various parts of a bay window for a balloon frame. The manner of constructing the angle is shown, also the sill and head of window, the various parts and manner of working thorn being given. A part of the section of the top of the window is shown at E, the inside finish being purposely left off. At F is shown an angle of greater length, which is sometimes the case in bay windows. The manner of construction is quite simple. The lower portion of the page shows some fine e.xnmplcs of turned and carved work. These will often be found useful in giving ideas for turned work for a variety of purposes. Six examples of shingling are shown in Fig. 6. The first sketch, A, is intended for a hip, and is a fairly good example, and if well done will insure a water-tight roof at that point. In laying out the shingles for this plan the courses are managed as fol- lows: No. I is laid all the way out to the line of the hip, the edge of the shingle being planed off, so that course No. 2, on the adjacent side will line per- fectly tight down upon it. Next No. 3 is laid and is dressed down in the sa ne manner as the first, after which No. 4 is brought a'ong the same as No. 2. The work proceeds in this manner, first right and then left. In the second sketch, B, the shingles are laid on the hip in a way to bring the grain of the shingles more nearly parallel with the line of the hip. This method overcomes the projection of cross-grained points. Another mctiiod of shingling hips is shown at C and D. In putting on shingles by this method a line is snapped four inches from angle of hip on both sides h^fic^- »74 MODERN CARPENTRY rv>^ m i2i^ i.^iram5ii'««&^^^^ JOINER'S WORK «TS of the ridge, as indicated by the dotted lints in C, then bring the corner of the shingles of each course to the line as shown. VVht n all through with the plain shin- gling, make a pattern to suit, and only cut the top to shape, as the bottoms or butts will break joints every time, and the hip line will lay square with the hip line, as shown at D; th-.is makin,^ a first-class water- tight job, and one on which tlse shingles will not curl up, and it will have a good appearance as well. At E a method is shown for shinglii.g a valley, where nc. tin or metil is employed. The maiv.ier of doing this work is as follov.s: P'irst take a stiip 4 inches wide and chamfer it on the rdges on i\\'-t out- side, so that It will lay down s.nooth to tlu; sheeting, and nail it into the valley Take a shin^de about 4 inches w-de to start with and lay lengthwise of the valley, fitting the shingle on each side. The first course, which is always doable, would then start with the narrow shingle, marked B, ant! carried up the val- ley, as shown in the sketch. Half way between each course lay a shingle, A. about 4 or 5 inches wide, as the case requires, chamferin j underneath on each side, so that the ntxt course will lie smooth over it. If tin or zinc can be obtained, it is better it should be laid in the valley, whether this method be adopted or not. The sketch shown at F is intended to illustrate the manner in which a valley should be laid with tin, zinc or galvanized iron. The dotted line--: show the width of the meta'i, which &;:ouUi never ', less than four- teen inches to insure a tight roof. The shingles should lap o\er as shown, and not less than four inches of the valley, H, should be clear of shingic". m 176 MODERN CARPENTRY In ■' *• "^- JOINER'S WORK »77 in order to insure plenty of space for the water to flow during a heavy rain storm. A great deai of care should \>c taken in shingling and finishing a valley, as it is always a weak spot in the roof. MICROCOPY RESOLUTION TEST CHART (ANSI and ISO TEST CHART No 2) 1.0 I.I 1.25 14.0 1.4 2.5 2.2 2.0 1.8 1.6 ^ /IPPLIED IfVMGE Inc ^Sr. 1653 East Mam Street ~— Rochester, New York 14609 USA ,JS (716) 482 - 0300 ■■ Pttore 5^ (716) 288 - 5989 - Fox *4Ial iWIii 1 f 'J I I PART IV i USEFUL TABLES AND MEMORANDA FOR BUILDERS Table showing quantity of material in every four lineal feet of exterior wall in a balloon frame build- ing, height of wall being given: o 5. 5 26 78 26 35 26 52 26 69 26 78 6xS 8x8 8x10 KIXIO 10X12 12X12 12 48 12 64 12 bu 12 100 12 120 12 144 14 56 14 75 14 93 14 117 14 140 '4 168 16 64 16 «5 16 107 16 133 16 160 16 192 18 72 IS 96 18 120 iS 150 18 180 18 216 20 80 20 10- 20 133 20 167 20 200 20 240 22 88 22 "7 22 147 22 1S3 22 220 22 264 24 96 24 128 24 160 24 200 24 240 24 288 26 104 26 ,130 26 173 26 217 26 260 26 312 Strength of Materials Resistance to extension and compression, in pounds per square inch section of some materials. Name of the Resistance Resistance Teiieile Stre'th Comp.StrenHh Material. to Extension. to Compression in Practice. in Practice White pine... 10,000 6,000 2,000 1,200 White oak.... 15,000 7,500 3, 000 1,500 Rock elm 16,000 8,011 3.200 1,602 Wroughtiron 60,000 50,000 12,000 10,000 Cast iron 20,000 100,000 4,000 20,000 In practice, from one-fifth to one-sixth of the strength is all that should be depended upon USEFUL TABLES 183 Table of Superficial or Flat Measure By which the contents in Superficial Feet, of Boards, Plank, Pav- ing, etc., of any Length and Breadth, can be obtained, by multiplying the decimal expressed in the Utble by the length of the board, etc. Breadth Ar«a of a lin- i^raailth Area of a liri- Braadtn Ar«,- 'alin- 8rt...'th Arttof a lin- Inchat. eal loot. ir,che». a al foot. Inchea. ., foot. inc'iea. eal foot. ■ .0208 3 2708 61 .5208 9i .7708 .0417 3 2Ql6 b\ • 5416 9 .7917 i .0625 3 3125 6f .5625 9 .8135 I .0834 4 3334 7 •5833 10 .8334 I ■ .1042 4 3542 71 .6042 10 .8542 I .125 4 375 71 .62r 10 .875 ' • 1459 4 3953 7i .6458 10 •8959 2 .1667 5 4167 8 .6667 I .9167 2i .1S75 51 4375 «i .6875 "1 •9375 H .2084 5i 45S3 «i .7084 I'i .958- n .2292 5S 4792 bl .7292 "S •9 3 •25 6 5 9 •75 12 T Round and Equal-Sided Timber Measure Table for ascertaining the number of Cubical Feet, or solid con- \. tents, in a Stick of Round or Equal-Sided Timber, Tree, etc. Mgirt Area In Mgirt Area in ygirt Area in '^Rit A-er in H gi't Area in in in. feet. in in. feet. in in. feet. In If). feet. in in. feet. 6 •25 loj .803 I5i 1.668 20 1 2.898 25 4.34 bi .272 II .84 »5J 1.722 2o| 2.917 25} 4.428 64 .294 III .878 10 1.777 20 1 2.99 25i 4.516 6J .317 Il| .9IS I6i 1-833 21 1 "^7 25? 4.605 7 •34 II» .959 161 1.89 2li 26 4.694 7 •3f4 12 I. 165 1.948 214 ^.-uq 26 4.785 7 •39 12 1.042 17 2.005 213 3285 26 4.876 r •417 12 1.085 I /I 2.066 22 3.362 26 4-969 8 •444 12 1. 129 I7i 2. I 26 22J 3-438 27 5-062 8 .472 13 I.I74 I7i 2.187 22| 3-516 271 5-158 8 .501 I3i 1219 18 2.25 22} 3-598 27i 5- 252 8i .531 I3J 1.265 isi £•313 23 3.673 271 5-348 9 .562 I3l 1-313 78f 2.376 231 3-754 28 5-444 9l .594 14 1361 l^ 2.442 23i r835 28i 5-542 9^ .626 I4i I.4T 19 2.506 23J 3917 28. 5.64 93 .6^9 I4i l.4>' I9l 2-574 24 4 285 5-74 10 .'n» m| ^ 5'I '9i 2 64 "41 40R4 29 5.84 lOl •73 15 1-562 193 2.709 24!' 4.168 294 29J 5.94 s 104 .766 I5> 1. 615 20 2-777 241 4.254 6.044 Ill 184 MODERN CARPENTRY Shingling To find the niimberof shingles required to cover ICX) square feet deduct 3 inches from the length, divide the remainder by 3, the result will be the exposed length of a shingle; multiplying this with the average width of a shingle, the product will be the exposed area. Dividing 14,400, the number of square inches in a square, by the exposed area of a shingle will give the number required to cover 100 square feet of roof. In estimating the number of shingles required, an allowance should always be made for waste. Estimates on cost of shingle roofs are usually given per 1,000 shingles. Table for Estimating Shingles Length of SLiagles. Bxposure to Weather, Inches. No. of Sq. Ft. of Roof Cov- ered by lUOO Shingles. No of Shingles Required for 100 Sq. Ft. of Roof. 4 In. Wide. 6 In. Wide. 4 In. Wide. 6 In. Wide. 15 in. 18 31 24 27 4 5 6 7 8 Ill 139 167 194 222 167 208 250 291 3.33 900 720 600 514 450 600 480 400 343 300 Siding, Flooring, and Laths One-fifth more siding and flooring is needed than the number of square feet of surface to be covered, because of the lap in the siding matching. 1,000 laths will cover 70 yards of surface, and 11 pounds of lath nails will nail them on. Eight bushels of good lime, 16 bushels of sand, and i bushel of hair, will make enough good mortar to plaster 100 square yards. Excavations Excavations are measured by the yard {2^ cubic feet) and irregular depths or surfaces are generally averaged in practice. USEFUL TABLES 185 Number of Nails Required in Carpentry Work To case and hanj^ one door, i pound. To case and hang one window, ^ pound. Base, 100 lineal feet, I pound. To put on rafters, joists, etc., 3 pounds to 1,000 feet To put up studding, same. To lay a 6-inch pine fluor, 15 pounds to 1,000 feet. I Sizes of Boxes for Different Measures A box 24 inches long by 16 inches wide, and 28 inches deep will contain a barrel, or 3 bushels. A box 24 inches long by 16 inches wide, and 14 inches deep will contain half a barrel. A box 16 inches square and 8f inches deep, will contain i bushel. A box 16 inches by 8| inches wide and 8 inches deep, will contain half a bushel. A box 8 inches by 8| inches square and 8 inches f^cc >, will contain I peck. jox 8 inches by 8 inches square and 4| inches wi 1 contain I gallon. .V be 8 inches by 4 inches square and 4^ inches deep, wi.l contain half a gallon. A box 4 inches by 4 inches square and 4J inches deep, will contain i quart. A box 4 feet long, 3 feet 5 inches wide, and 2 feet 8 inches deep, will contain i ton of coal. Masonry Stone masonry is measured by two systems, quarry- man's and mason's measurements. wm •HI il 'H ti 1 J. 1 86 MODERN CARPENTRY By the quarryman's measurements the actual con- tents aie measured -that is, all openings are taken out and all corners .u.- measured single. V.y the mason's measurements, corners and piers are doubled, and no allovvance made for openings less than 3'o"x5'o" and only half the amount of openings larger than 3'o"x5'o". Range work and cut work is measured superficially and in addition to wall measurement. An average of six bushels of sand and cement per perch of rubble masonry. Stone walls are measured by the perrh (243/^ cubic feet, or by the cord of 128 feelj. Openings I -ss than 3 feet wide arc counted solid; over 3 feet deducted, but 18 inches are added to the running measure for each jamb built. Arches are counted solid from their spring. Corners of buildings are measured twice. Pillars less than 3 feet are counted on 3 sides as lineal, multiplied by fourth side and depth. It is customary to measure all foundation and dimen- sion stone by the cubic foot. Water tables and base courses by lineal feet. All sills and lintels or ashlar by superficial feet, and no wall less than 18 inches thick. The height of brick or stone piers should not exceed 12 times their thickness at the base. Masonry is usually measured by the perch (contain- ing 24.75 cubic feet), but in practice 25 cubic feet are considered a perch of masonry. Concreting is usuallv measured by the cubic yard (27 cubic feet). ir f ..'-'-^ . ■'I rOdi ,■"'■■•♦■ «■ IT I ''I USEFUL TABLES 187 A cord of stone, 3 bushels of lime and a cubic yard of sand, will lay 100 cubic feet of wall. Cement, l bu^ihel, and sand, 2 bushels, will cover il4 square yards i nch thick, 4'yi square yards }i inch thick, and 6^ square yards "^ inch thick; i bushel of cement and I of sand will cover 2^ square yards 1 inch thick, 3 square yards J^ inch thick and 4J.- square yards }4 inch thick. Brick Work Brick work is generally measured by 1,000 bricks laid in the wall. In consequence of variations in size of bricks, no rule for volume of laid brick can he exact. The following scale is, however, a fair average' 7 com. bricks to a super, ft. 4 in. wall. I^ •• •! •• << •• „ ■• •• 21 ** ** (« *t n jn tl II a8 " " " " " 18 " " «r ** ** 't I* ** 22 *' ** Corners are not measured twice, as in stone work. O 'ings over 2 feet square are deducted. Arches are co> .fvl from the spring. Fancy work counted i^ bricks for i. Pillars are measured on their face only. A cubic yard of mortar requires I cubic yard of sand and 9 bushels of lime, and will fill 30 hods. One thousand bricks closely stacked occupy about 56 cubic feet. One thousand old bricks, cleaned and loosely stacked, occupy about 72 cubic feet. One superficial foot of gauged arches requires 10 bricks. Pavements, according to f ize of bricks, take 38 brick on fiat and 60 brick on edge per square yard, on aa average. t. nr^ 'U ' i I n II ' :|| 1 88 MODERN CARPENTRY Five courses of brick will lay i foot in height on a chimney, 6 bricks in a course will make a flue .\ inches wide and 12 inches long, and 8 bricks in a course will make a flue 8 inches wide and 16 inches long. Slating A square of slate or slating is 100 superficial feet. In measuring', the width of eaves is allowed at the widest part. Hips, vali. ys and cuttings are to be measured lineal, and 6 inches extra is allowed. The thickness of slates required is from {g to ^'j of at. =nch. and their weight varies when lapped from j| to bf4 pounds per square foot. The "laps" of slates vary from 2 to 4 inches, the standard assumed to be 3 inches. I.'t To Compute the Number of Slates of a Given Size Required per Square Subtract 3 inches from the length of the slate, mul- tiply the remainder by the width and divide by 2. Divide 14,400 by the number so found and the result will be the number of slates required. Tablr. showing number of slates and pounds 01 nails required to cover 100 square feet of roof. Size* of Slate li.ength of Expof-r;. 14 ill. X 28 in. 13 X 24 II X 33 10 X 30 g X 18 v X 16 7 t M 6 X 12 i '-vwr '^"^^^wmmss^m^limx^ USEFUL TABLES ,89 Approximate Weight of Material! for Roofe Material CorniKatefl Ralvanized iron. No. 20, unboarfltd. fi'plifr, 16 i)z. starniing scam I> t and asphalt, witho'it sheathing niass. J^ in, thick UenilfM i; sheathing, i in. tliick I.ead, atmut 'i a 4 to 10 4 % H 18 4 Saow and Wind L^ -^s Data in regard to snow and wind loads are nf '>sary in connection with the design of roof trii'ise^ . Snow Load. — When the slope of p roof is over 12 inches rise per foot of h ontal ru . a snow and accidental load of 8 pounds p^.. square foot is ample. When the slope is under 12 inches rise per foot of run a snow and accidental load of 12 pounds per square foot should be used. The snow load acts vertically, and therefore should be added to the dead lead in designing roof trusses. The snow load may be neglected when a high wind pressure has been consid- ered, as .T great wind storm would very likely remove all the snow frotr. the roof. .^'•'^vl'.l I90 MODERN CARPENTRY Wind Load.— The wind is considered as blowing in a horizontal direction, but the resulting pressure upon the roof is always taken normal (at right angles) to the slope. The wind pressure against a vertical plane depends on the velocity of the wind, and, as ascer- tained by the United States Signal Service at Mount Washington, N. H., is as follows: Velocity. Pressure. (Mi. per Hr.) (I,b. per Sq. Ft.) '° 0.4 Fresh breeze. "o I <^ Stiff breeze. 30 3 <> Strong wind. 40 6.4 High wind. 50 lo.o Storm. °° 14-4 Violent stonn. ^° 25.6 Hurricane. ^°° 40.0 Violent hurricane. The wind pressure upon a cylindrical surface is one- half that upon a flat surface of the same height and width. Since the wind is considered as traveling in a hori- zontal direction, it is evident that the more nearly vertical the slope of the roof, the greater will be the pressure, and the more nearly horizontal the slope, the less will be the pressure. The following tabic gives the pressure exerted upon roofs of different slopes, by a wind pressure of 40 pounds per square foot on a vertical plane, which is equivalent in intensity to a violent hurricane. UNITED STATES WEIGHTS AND MEASURES Land Measure I sq. acre = 10 sq. chains = 100,000 sq. links = 6,272,640 sq. in. I " " = 160 sq. rods = 4,840 sq. yds. = 43,560 sq. ft, AW^.— 2oS. 7103 feet square, or 69. 5701 yards square, or 220 feet by 198 feet Bquare=i acre. USEFUL TABLES 191 Cubic or Solid Measure 1 cubic yard = 27 cubic feet 1 cubic foot = 1,728 cubic inches. I cubic foot = 2,200 cylindrical inches. I cubic foot = 3,300 spherical inches. I cubic foot = 6,600 conical inches. t2 Linear Measure inches (in.) = i foot ft. 3 feet = I yard yd. 5. 5 yards = i rod rd. 40 rods = I furlong fur. 8 furlongs = i mile mi. in. ft. yd. 36= 3 = I 198 = 16.5 = 5- 7,920 = 660 = 220 rd. fur. mi. 5 = I = 40 = I 63,360=5,280 =1,760 = 320 = i Square Measure 144 square inches (sq. in.) := i square fix)t sq. ft. 9 square feet =: I stiuare yard sq. yd. 30J square yards = i square rod sq. rd. 160 square rods = i acre A. 640 acres = i square mile sq. mi. Sq. mi. A. Sq. rd. Sq. yd. Sq. ft. Sq. in. I = 640 = 102,400 = 3.097,600 = 27,878,400 = 4,014,489,600 M ¥. Miscellaneous Measures and Weights I perch of stone = i ft. X i ft. 6 in. X 16 ft. 6 in. = 24. 75 ft. cubic. I cord of wood, clay, etc., = 4 ft. X 4 ft. X 8 ft. = 128 ft. cubic. I chaldron = 36 bushels or 57.25 ft. cv.bic. I cubit foot of sand, solid, weighs 112J lbs. I cubic foot of sand, loose, weighs 95 lbs. I cubic foot of earth, loose, weighs 93} lbs. I cubic foot of common soil weighs 1 24 lbs. I cubic foot of strong soil weighs 127 lbs. I cubic foot of clay weighs 120 to 135 lbs. I cubic foot of clay and stone weighs 160 lbs. I cubic foot of common stone weighs 160 lbs. I cubic foot of brick weighs 95 to 1 20 lbs. I cubic foot of granite weighs 169 to 180 lbs. I cubic foot of marble weighs 166 to 170 lbs. I cubic yard of .sand weighs 3,037 lbs. I cubic yard of common soil weighs 3,429 lbs. «9« MODERN CARPENTRY Safe Bearing Loads m \ :> Brick and Stone Masonry. Bricks, hard, laid in lime mortar Hard, laid in Portland cement mortar Hard, laid in Rosendale cement mortar...!., _, . Masonry. Granite, capstone Squared stonework Sandstone, capstone !."!!!."!!!!!!!]!] Squared stonework ."!.......'.... Rubble stonework, laidin'iime'morta'r Kubble stonework, laid in cement mortar"" 1-imestone, capstone Squared stonework !.".".".."!......""] Rubble, laid in lime mortar!!.."!!!!... Rubble, laid in cement mortar Concrete, i Portland. 2 sand. 5 broken"stone! Lb. per Sq. III. Foundation Soils Rock, hardest in native bed Equal to best ashlar masonr\' Equal to best brick Clay, drj', in thick beds...!!! Moderately dry, in thick" beds Soft Gravel and course sand,"wen"ceniented' band, compact and well cemented Clean, dry Quicksand, alluvial' soir'etr 100 200 150 700 3ro 350 175 80 150 500 250 80 150 150 Tons per Sq. Ft. 100 — 25-40 15-20 4- 6 2- 4 1- 2 8-10 4- 6 2- 4 .5- I Capacity of Cisterns for Each 10 Inches in Depth Twenty-five feet in diameter holds ,„ „ Twenty feet in diameter holds...... f^Q Ra ons Fifteen feet in diameter holds ^^8 ga ons Fourteen feet in diameter holds noigaLons Thirteen feet in diameter holds 950 ga ons Twelve feet in diameter holds ^^ g^ Ions Eleven feet in diameter holds "°5 ^ ' Ten feet in diameter holds ^92 g Nine feet in diameter holvis "^ ? ^"m Eight feet in diameter holds 396 gail-ns Seven feet in diameter hoMs ^i gallons Six and one-half feet in diameVer"holV's "^"^1 gallons Six feet in diameter holds 206 gallons Five feet in di.unetLr ho]!]" >76 gallons Four and one-half feet in diameter Isolds!!!!!!!!!!!!!!!!!!!! '^^ gl|^^^ ons Ions 'ons USEFUL TABLES »93 Poor feet in diamet ;r holds 78 gallons Three feet in diameter holds 44 gallons Two and one-faalf feet in diameter holds 30 gallons Two feet in diameter holds ig gallons Number of Nails and Tacks per Psund NAILS. No. Name. Size. per lb. 3 penny, fine i J^ inch 760 nails 3 4 5 6 7 8 9 10 12 16 20 30 40 50 6 8 10 12 '• i>^ " ^H " 2hi " aX " 2/2 " 2^ " 3 " 3H " 3K " 4 " 4'X " 5 " s'A ' ' fence 3 " " 3 " " 3H 480 300 200 160 12S Q2 72 60 44 32 24 iS 14 12 80 50 34 29 Name. 1 oz., 1/2". 2 ". TACKS. Length. .^ inch., .316 " ■ 3 4 6 8 10 12 14 16 18 20 22 24 .5-1') ■■y» .7-16 .q-l6 ■H .11-16 .13-16 ■H .15-16 .1 .1 1-16 No. per lb. I6,ooi) 10,666 8,(x>o 6,400 5.333 4,000 2,666 2,000 1,600 1.333 1. 143 1,000 888 800 727 666 Wind Pressures on Roofs (Pounds per Square Foot.) Rite, lnch*> per Foot of Run, 4 6 8 13 16 18 24 Angle with Horizontal. 1 8'^ 26' 33" 45" 53° 56° 63° 25' 33' 41' o' 7' 20' 27' Pitch. Proportion of Ri«e to Span. Wind Preieure, Normal to Slop*. 16.8 23-7 29.1 36.1 38.7 39-3 40.0 In addition to wind and snow loads upon roofs, the weight of the principals or roof trusses, including the other features of the construction, should be figured in the estimate. For light roofs, having a span of not over 50 feet, and not required to support any ceiling, the weight of the steel construction may be taken at 5 pounds per square foot; for greater spans, i pound per square fool should be added for each 10 feet increase in the span. HOUSE PLAN ST^PPLEMENT PERSPKCTIVK VIKWS AND FLOOR PLANS OF Twenty-Five Low and Medium Priced Houses Full a, ! Cmple; ■ W.irking Plans and Sprcirications of anv „t thrse hi.u.is will l,e mailed at th^ l.,w priirs named, .m the ^ame day the order is r-ieised. OTHER PLANS W. illustrate in 'Modern Carpentry;" "Practical I'ses of the Steel Square, Vol. II; an,: "Common Sense Hand Raiiing;" -J other plans, -,- in each book, none of which .-re duplicates of tnosc we illi:,.trate herein, Kor further information, address The PlHLISHF.RS S,na All Ordtii for Plans to RADFORD ARCHITECTURAL COMPANY CHIC.iGn, n./.I.XolS: n^j ff,. livery plan illustrate,! wtll show l,v the complete workinj: pi ms ami sper,«ication. . .t we -ive you de- si.M.s that will work out to -he 1, est aavant,..e ami wilUue you tl|e most f,;; your .m.tiey; l.esnles. every Lit of sp xe has l-eeu ufh/cl to the hest advaiitane. ,. , , , This supi.letnent. as well as all other Looks pul.hshe.l l>y t.us co.n- p.,nv has for its foundation the l.est equipped ar<'hitectural estahhsh- n.ent ever maintaine.l for the purpose of furni.hins 'I'e l>u!."c \vith complete workinc plans and specdira- tioiis at the remarkably low jiriceof oidy §•> III) per set. Mvery i)lan is :ned hy a license.l architect, who stamls at -vrx^ / ^^ > the head of his |.rofessi(in in thi- particu- r-* ^ '^^ lar class of work. The Kadfonl Houses are now heinii erected in every .•omitry „f the worUl where frame houses are built . whi.'h bespeaks f„r our plans more than anythins we can say. What We Give You The first .piestion vou will ask is, •■What do we pet in ;hese con>plete w,.rki..s; l.latis and specilicat ions' Of what do tliey con.s.st ? .Me they the cheap, printed plans on tissue paper without delad.. or speci- ''\vedonot blame vou for wishing to know what you will ilri for vour tnonev. The plans we sen.l out are the regtilar blue-printed plans drawn one-iuarter inch scale to the foot, showing all the elevations, floor plans and =iece^s;,ry inu-rior details We use the very best quality heavv (lalha Blue Print I'aper. number lODO-X. using great care ni the blue-printing to have every line ami hgure perfect ami distinct. /-*>-! -jT ;■ ■: i4'/4."; I What We Furnish In Blue Prints Foundation and Cellar Plan Tllis MM...( .shows th.- si,.,,,,, ,,„„| ,i^,. „f ,,|| „..,||^ |,j,.^^^ f,„,ti„j;s. ,,„s,.s, elc, and of wlial niMtc n.'.s ||„.y .„■,. ,.oi,>tiiic|,.,l; sl,, ash |,i,s. partitions and .|„. like Th.- d.ff.T..nt wall s,.,.tio,.s ... niv,.,,. s|,..wi,t« th.-ir .'-.nst nation and liipasurcinpiits from all the dilTcicit points Floor Plans These pl,,„s show the .shape and si.e o. all roo,„s, halls, and closets- the loeat.on and size ,>f all .loors an,| windows; , he position of all phind,. inK fixtures, ^as lights, retfiMers. pa.ury work, elc, ai.d all Ihe nieas,„e. nients that are necess.aiy are f;iv«'n. Elevr>tions .V front, riKht. left an,l rear elevation ate fnrnished with all the plans Ihese .Irawtn^rs are eotnple.e and a.rnra' i„ everv respert Thev show the shape, s,ze an.l location of all doors and window^ vlu- rorn.ees, towers, l..,ys a.id the like, at.d. in faet. «,.,e von an exaet seale I'letnre of the h.ni.se as it shonid he .t eon,plet,o„. r„|l ,..,|1 sertion- are pven. s1,owh.« tl,e ■•onstrueiio,, on, foundation to ro, the Lei-dit of -stones between the joists. l,ei;;ht of plates. p,„.h of r.,of, ,!,.. Roof Plan This plan is fnrnisher<.of paper, making a handsome ami dur- able covering and prolectiMii for the i)lans. 3 Specifications llic s|(»'cilicnliiiii.s arc typfAiitlfii (in I,ak«'jiii|p lii>tiil l.iiiiMi Paper ami arc Ixiiiiul ill lliP saiiH- artistic iiiamicr asllic pla.is, the same {■\n\U ami «:itcrpr(">f papci liciisMry are ii\\vn in the clearest atid must explicit iiiMiiiier. so that there can lie no pussilnlitN of a misiiiuler- siaridimi. \: Basis of Contract These .\orkiii« plans ami speciticalions cati lie made the liasis ot contract lietween the home Kuilder and the contracior. They will prevent mistakes which cost money, and thev will pfcxcnl disputes which are unfore- seen and ncMM- settled satisfactorily to tiolh parties Ulicti no plans are used, t he coii- tractoi is often oliliireii(> man in ten llmusand who will pi rnissifi); situ.iiion. You cmu rail to mind inslan^e^ in your own locality where seillc:iierils lnv( del:. insurance nunp.inies wauled some pronf which c ml I d I lecause tlie ( inch (• Kill not he furnished. I'hcy demand proof of loss hefor" paying insurame money, and t hey are en I il led to it, \\c have pi .vided for this and have inaiiitu- r.'iled I he follow inn plan, which cannot hut meet with f.iv(u- hy whoever !)uilds i house from our plans: Imiiieili.itely upon receipt of information from you ihal your house ha- '■, mi dcMrovcd liv liic. • i.iier -—J totally (U- parli.ally. we u ill forward you. free of cost, m duplicate set of plans and specificaiions. and inaildition we will fiiriiisli an a.lidavil i,'ivinj: llie niimhcr of ilic (i.'.Mi,'ii and f.|ct,iry adiuslmcnl . This miv he liie means of savinu' y.u liuudreds ,,f dillars l>e,i li>^ miiCi time and worrv. Our Liberal Prices Many have imirveled at our ahility to furiii h such evcellent and coMi|ilcle worki'if; phi ■■ and specilicalions at such low prices. U e do not wonder at this, hecaiise we ch.irfie hul five dollars foi- ;i moro complete ■set of working' |iians .ami spei'ificaiioiis t han you would receive if ordtu'ed in the rej;ul;'r manner, .-iiid wiieji d",iw!i espci-inlly for yr,u, at a cost of from fifty to .«eventy-five dol- lars. On .account of our large litisiness and unusual equipment. .-iMd owimr to the fact that we divide theexjiense of iIh'sc |plan^ milium so iniiiiy, it i.-', imim.miMp for us to sell them at thCM low prices. Tin' iniirKiii of jirofit is very el ■se. Init it eimliles us to sell tliousaiiils of sets of plans, \vhir!i save many times tlieir cost to iMith the owner and the contractor in erecting even the smallest ilwellin|{. Our Reliability Our relialiilily is Kfvonil ipiestion. U'e have Ikh'u in the liusiness for many years, haviim (i""'!"'!! from a small institution to our present iarjce capacity, pulilishini; many hooks ami furnishing plans and s|)eci- ticalions for 'iiy thousands of houses in all parts of the I'liited States, Canada, lluropc. A'lstralia, and South Africa. We presume this lK)ok may fall into the hands of some one who does not know us; therefore, if you ha\e never heard of us and are not familiar with our reliahility i'ntl liusiness methods, imiuire of your lumlier dealer or hanker. This artii'lc is uuneiessary to those who have had previous dealings with us. If you are afr.'ti >iaudiug al tin- ii<'.ir.)- fession, and the slamlant of their work is the very highest. (i risk that / W'f iiiill.l mil .ilTiinl 111 in.ik'' llu-. yi|:ii:iiilfi" if ui' Hfit- nut |>ii>l- ll\i> that \\i' VM'ic riirni'liniu tlir ln'«l |il:iiis piii mit in iln« ciiiinlry even I liinnjh mir |in(i' !■• nut iiimic I hiiii iiiM'-»i'\fnlli tn uih'-Ii'IiI h ul ' tit |nirt' ii-iiiiliy rliMriifil Lumber Bill Uc liii nut liiiiu-h M I iniiiiT lull W- -i:iic ilii> licv |i:ii'nciil:irly , M.'> siiiMf |><>ii|ilc liMM- :in 1 li>:i iIkiI .'I I nilici' liiil iliiiillil .'ii riiin|i:inv iMi'li -ct uf |il III- .•ml >|i«M'iticMliiiii>. Ill lilt- lir>t |ilari our |i1mii- .•ire iroltt'ii \\\> in .1 xcrv ciiiiii !rlii\<' 11. iiiin'f. Ml liiiil iiiiy r:ir|it'ii- li'i- iMii ;lit t'liriii.-li wuiilil not !«' apiilicalilf in all sfcliunn ul' the cuiiiil i\-. We filiiiisli plan-- ainl :.jit'(i- lic:ii lull* t'ur liiin-cs wliifli ai'c Imill as far mnlli as I'.c llinlsun Itay ami a- far suiitli as llic I iiilf uf Mrxii'u. Tlicy art' linil; ijiuii I he Allaiili" ami I'aritii' coasts, and yuii cin alsii timi tlicniiii Aiist ., ilia ami Sunt li Africa. Ivicli cuimlrv anil scdiuii uf a cuiintry lias it- I iiliarilifs as to si/t's ami i|nalili<'s, I liiTi'furc 1, wuiilil lie ux'lcss fur lis to make a li-i tliat wuiilil nut lie iiniver-al. • >!ir liiiuses ulicn cunipleteil may iuuk tlies.anie. wlietlier they are Imiit in < aiiaila ur in II iriila. Imt the same materials will nut he iiseil. fur the reasun that the ciistuiiis uf t he peuple anil t lie clirnatic ciinditiuiis will ilic- tate the kind and aniuuiit uf materials tu he used in theii cunstrucl i"n. Estimated Cost Ir is itiipus>ilile fur any uiie tu esiim.ate the cu>i uf a Imildiii}.' ami lia\e the titrnres liuld };uud in all -ectiuns uf t!i. iiiitry. 'A e ilu nut claim tu he ahle |u du it. The est imated cuM <>{ the houses we ilhislrate i< l.:!sed on. the mu^t f:i\ur:r' Ic i-undiliuiis i.'i all respects, ami dues nut include pliiinhin;; and heating. We du nut knuw ymir lucal conditions, and should we cl.aitn to k'luw the exact cu.-l uf a Imildint; in your localitv, a child would know that mir stalbtneiit was false. We advise X r k. ^^ I , .■>—■' / II Mr l;li '. r r..n.ult«.i..n with your l.M-al rp«,HmMl.le nmiermi a^iil-rH „„,| r,.lml.lp .■ .Mtn„.|or., f.,r tl...y, an,l li.ey „|,.,„., kM„w y,.„r Inral ron.l.lionM Wo U.4. to 1h. frank with y.,„, „„.l th.-rH-r.. ,„„kp „.. .lut..;,>,.nt that «.. '•'"not HulwiMt.iuu.. ill every re.|K.rt. If ■ uy ,.hii, in tl.i. I„„,k, or in «nv other lK,ok we pul.liMh. pleas,., >ou; if the arran^je-nen, ,.f ,1,^ r „s i". MitiHfttelory. and if the exterior i, ,.leasi„« an,i at.raeiive. then we -Make this Hain, -that it ran !«■ l.mlt as e:,ea|.ly as if anv other Hrehiteel cles,«ne.| ,t, an.l we l«.lieve ,.hea,K.r. We have stu.lied eronon.v in .•.n.H.nu-tl.m, an.l our knowle.lae of all the material Cat u-k-s into" the h..use .|uah,'ies us to ^jve you the i.est f„r y.,ur inonev. We ^ive you :i P M t!iiit plea.s.-s you. ou- that is altrariive. an.l one where everv fool of spare in utili/e,| at , he h-ast p:,s,il,|e ,-:,m. fan anv arehite.^t • lo more, even at seven I,, ten times the pri.e we rharRe vou for plans' Reversing Plans We re.eive many re.p.ests from our patrons for plans ..x:„-,lv a.vonl- ir.K to the .lesions illustrate.l, with the ,.ne exreption of h-iviuK lh.-m reverse.l or face 1 in l! ,.p,,site ilire.'ti.ui. It is im|H.ssil.|e f,.r us t.. make this rhantte and draw new plans. e\.ept at a ro>' „f ahoul eidht tiriL's „ur regular prices. We see no reason why our renular plans wi.l n,.t answer your purpose. V.,ur rariwuiter can fai'P the hou.se e\ icily as you wish it. and the jilans will w.iri,- ..ut as well facing in one •lire.-ii.m a.s in am.ther. "V can, however, if you wish, and .so in.Mruci us, make y..u a reversed l.lue print ami furnish it a; .,ur >c«ul:ir jirice. hut in that ca.se all th< figures ami letlers will U- reverse.l, and theref.,re liahle to cause as much confusi..n .-is if y,„ir •arpenter reverse.l the plan himself while .■oust met iiiK the li.,u.se. We w.ml.l a.lvise, \1. iK.wever, in all cases where the |)lan is t.) he reversed and there is the le..st .,., ahout the cmtractor not l.ein« ahle to work from the plans as we have them, that two .sets of Mue prints he ,.ur,.hase.l. ..ne regular an.l the other rever.se.l, an.l in such -•ases we will fi.rmsh tw.. .sets of |.I,.e prints a, ne .se, of specifica- •■ons for .miy ftfty ,„.r cent, a 1 ,., .,ur re,ml;.r ...,st . making the .*.. (K) plan cost .>nly iT.M). Special Department He have es-ahlishe.! a spe..ial .lepartment un.ler the supervisi.m of u license,! architect, .., luui.lle all s,K...ial plans which our patrons may like t.i liiivi- ilriiwii, Wf rt'alur ih.it ..flcii «mi«« H|wiial or nnitiiial iilca i.i wi.-.ln'.l .■arricl (.iil, aii for this «,■ has.- mir ar.lut.Tl.s iiticl iliaiUjlil'iMt'ii. I'lii' prirc \\v rliuricr i" very ica^ntialilt'. Slimilil ymi \vi«li the wr- vircr* iif ihiM ,|,.|.artiui'iit, ii vMiiiM !«• nc,c»- -ary fnr y.m i,. ,..|i.| u- as full aiiij r(iiii|.|rli> iiiforti.aliini as j...>sil,|,.. aci'iitii|iaiiii» voii ran yi'nr iilcas ati.l r<-i|i|irt iiis. Iiiitiiciliali'ly il|">M iiint out your own idras, Mtid if our price iiiovcs to lie satisfactory . «<■ will suliiuit iM-ncil skffc'li .sulijfi't to your rorrccliipiis ami adilitiotis licfori' |iriMcci|itii: In coMiph-lf the |i|,iri> W .■ iihim, lioWfVfr, liavi' an uii(liM>l;.!iiliiu{ that we an- uiidrr I'otitrait to ill) this work, for we cantioi aifi nl to do all the |ircliiiiii,ary Work without soiiir cuaraiilfcthat it Wlli lie aircplcd after we ha\t> acrcfil to make the plans entirely .satisfaitory toy,,.. We " II. however, make / esiim.'ite on the .-..-i of any >piTi;il uurk. >o that you will know e\.iiil\- \\|i;ii n \vill rost you hefore we proi'erd with the pliin^.. How to Send Money HemitlaiH'es can lie made l>v l'o>t ' iid. ,• \|,,ne\ Order, JApres.s Money Order, Mank KraftJ'niled .. Take irreal care to write yoiu- addre» ,il,iinly, atid he . jr' ■■>iil'«' anil write your nauje and addres.s on "^ ,.' flu' upper left-hatid corner of the envelope. 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X o' TJ rj C «> m ^ c ^ "H. ^ t£ a> c ^ .a; :r o i t/j u u u •- c >— U- U 58 —' ■' ■ - -^ y it / in" C -j — / 3 1 1 ■J _i 5? « " r 15 ■< '53 S - S « iX 1 * L. s ^ 1 1 ? .- J 'r' 2 \ 7) •H \ s • o ^^^~. m.-j:rmm \ 2 I — -^ U o w ^ *^ ' u t^ tn ■— ^ X r (I) •~ tj ■C 'Z, O - ? : I c — b ^ f ^ ": 5 '5 O - /, -. ^ 1/ > yj - ^" > -^j tn 2 "^ '1 Z ■ "* ^ *J r: >_, < ^ - 5 f- •/! J ou o ■ 3 •^ X f.* i ! ~ '3 J' O H f-^n 1 jl-r 1^1 '"" .— ^ p- ■ .^ * T- =^ ' ^^ y [ ^= \ 1 \ n If »! _i c o u \ Am - ^ u- = 3i « \ z " - c £ '3 * f ^ i2 = B in ? "^ ,T 'C t; u 1 *• 5 \ o ^^ o « -U^- -=. - »: ij ^ .2 ■/". o 59 Common-Sense Stairbuilding and Handrailing illustrated By FRED T. HODGSON ri'^llIS new volume contains three (lintinrt treatiseHon tlie siilijert, ^ each of wh'K'h is complete in itself. The system of forming the lilies fur ohtaininc the viirioiis curves, wreaths, ramps and face mouhls for handrails are the simplest in use and those employed by the most successful haiidrailers. Mr. Ilodftson has placed this' unusually intricate sul>ject hefore his readers in a very plain and easilv understooil manner, and any workman haviii): a fair knowledge of "lines" and who can construct an ordimny straight stairway can readily grasp the whole system of '•handrailing" after a sin;ill st\idy of this W'ork. The liuilding of stairs and |>roi)e;ly making and ])lacing over them a graceful handrail and suitable balusters and newel |)osts is one of the greatest achievements of the joiner's art and skill, yet it is an art that is the least understood of ;my of the constructive processes the cari)enter or joiner is called upon to accomplish. In but very few of the plans jiiade by an architect are the stairs pro|)erly laid down or divided off; indeed, tnost of the stairs as laid out and piatuied liy the architect are impo.ssible ones, owing to the fact that the circumsiances that govern the formation of the rail are either not understood or not noticed by the designer, and the expert handrailer often finds it difhcult to con", foriii the stairs and rail to the jilan. (lenerally,however, he gets so close to it that the character of the design is sehlom changed. The stairs are the great feature of a building as they are the first object that meets the visitor and claims his attention, and it is es.scniial, therefore, that tlie stair and its adjuncts should have a neat and graceful appearance, and this can oidy be accomplished by having the rail jirop- ; rly made and set up. This little book gives such instructions in the art of handrailing as will enable the young workman to l>uild a rail .so that it will a.s.-ume a handsome appe:irMiicc wlien .set in pl;ice. There are eleven distinct styles of stairs shown, but the same principle that go\erns the making of the simplest rail, governs the construction of the most difficult, .so, once having mastered I he simple problems in this system, progress iti (lie art will become easy, and a little study anil -ractice will enable the Workman to construct a rail for the most tortui.iis stairway. The book is copiously illustrated with nearly one hundred working di;ii;rams together with full descriptive text. Price, $1.00. Address all orders to THE RADF^flD ARCHITECTURAL CO. Chicago Office: 190 W. 22d St. RIVERSIDE, ILL., U.S.A. New Yorii Office: 822-824 Broadway 60 PRACTICAL USES OF THE STEEL SQUARE AMODKHX TIJKATlSi; ).y 1 n-