CARPENTRY FOR BOYS IN A SIMPLE LANGUAGE, INCLUDING CHAPTERS ON DRAWING, LAYING OUT WORK, DESIGNING AND ARCHITECTURE WITH 250 ORIGINAL ILLUSTRATIONS TEXT

line is at right angles to some other line. Suppose you put a square upon a roof so that one leg of the square extends up and down on the roof, and the other leg projects outwardly from the roof. In this case the projecting leg is _perpendicular_ to the roof. Never use the word _vertical_ in this connection. SIGNS TO INDICATE MEASUREMENTS.--The small circle (°) is always used to designate _degree_. Thus 10° means ten degrees. Feet are indicated by the single mark '; and two closely allied marks " are for inches. Thus five feet ten inches should be written 5' 10". A large cross (×) indicates the word "by," and in expressing the term six feet by three feet two inches, it should be written 6' × 3'2". The foregoing figures give some of the fundamentals necessary to be acquired, and it may be said that if the boy will learn the principles involved in the drawings he will have no difficulty in producing intelligible work; but as this is not a treatise on drawing we cannot go into the more refined phases of the subject. DEFINITIONS.--The following figures show the various geometrical forms and their definitions: [Illustration: _Fig. 151.-Fig. 165._] 151. _Abscissa._--The point in a curve, A, which is referred to by certain lines, such as B, which extend out from an axis, X, or the ordinate line Z. 152. _Angle._--The inclosed space near the point where two lines meet. 153. _Apothegm._--The perpendicular line A from the center to one side of a regular polygon. It represents the radial line of a polygon the same as the radius represents half the diameter of a circle. 154. _Apsides_ or _Apsis_.--One of two points, A, A, of an orbit, oval or ellipse farthest from the axis, or the two small dots. 155. _Chord._--A right line, as A, uniting the extremities of the arc of a circle or a curve. 156. _Convolute_ (see also _Involute_).--Usually employed to designate a wave or folds in opposite directions. A double involute. 157. _Conic Section._--Having the form of or resembling a cone. Formed by cutting off a cone at any angle. See line A. 158. _Conoid._--Anything that has a form resembling that of a cone. 159. _Cycloid._--A curve, A, generated by a point, B, in the plane of a circle or wheel, C, when the wheel is rolled along a straight line. 160. _Ellipsoid._--A solid, all plane sections of which are ellipses or circles. 161. _Epicycloid._--A curve, A, traced by a point, B, in the circumference of a wheel, C, which rolls on the convex side of a fixed circle, D. 162. _Evolute._--A curve, A, from which another curve, like B, on each of the inner ends of the lines C is made. D is a spool, and the lines C represent a thread at different positions. The thread has a marker, E, so that when the thread is wound on the spool the marker E makes the evolute line A. 163. _Focus._--The center, A, of a circle; also one of the two centering points, B, of an ellipse or an oval. 164. _Gnome._--The space included between the boundary lines of two similar parallelograms, the one within the other, with an angle in common. 165. _Hyperbola._--A curve, A, formed by the section of a cone. If the cone is cut off vertically on the dotted line, A, the curve is a hyperbola. See _Parabola_. [Illustration: _Fig. 167.-Fig. 184._] 167. _Hypothenuse._--The side, A, of a right-angled triangle which is opposite to the right angle B, C. A, regular triangle; C, irregular triangle. 168. _Incidence._--The angle, A, which is the same angle as, for instance, a ray of light, B, which falls on a mirror, C. The line D is the perpendicular. 169. _Isosceles Triangle._--Having two sides or legs, A, A, that are equal. 170. _Parabola._--One of the conic sections formed by cutting of a cone so that the cut line, A, is not vertical. See _Hyperbola_ where the cut line is vertical. 171. _Parallelogram._--A right-lined quadrilateral figure, whose opposite sides, A, A, or B, B, are parallel and consequently equal. 172. _Pelecoid._--A figure, somewhat hatchet-shaped, bounded by a semicircle, A, and two inverted quadrants, and equal to a square, C. 173. _Polygons._--Many-sided and many with angles. 174. _Pyramid._--A solid structure generally with a square base and having its sides meeting in an apex or peak. The peak is the vertex. 175. _Quadrant._--The quarter of a circle or of the circumference of a circle. A horizontal line, A, and a vertical line, B, make the four quadrants, like C. 176. _Quadrilateral._--A plane figure having four sides, and consequently four angles. Any figure formed by four lines. 177. _Rhomb._--An equilateral parallelogram or a quadrilateral figure whose sides are equal and the opposite sides, B, B, parallel. 178. _Sector._--A part, A, of a circle formed by two radial lines, B, B, and bounded at the end by a curve. 179. _Segment._--A part, A, cut from a circle by a straight line, B. The straight line, B, is the chord or the _segmental line_. 180. _Sinusoid._--A wave-like form. It may be regular or irregular. 181. _Tangent._--A line, A, running out from the curve at right angles from a radial line. 182. _Tetrahedron._--A solid figure enclosed or bounded by four triangles, like A or B. A plain pyramid is bounded by five triangles. 183. _Vertex._--The meeting point, A, of two or more lines. 184. _Volute._--A spiral scroll, used largely in architecture, which forms one of the chief features of the Ionic capital. CHAPTER IX MOLDINGS, WITH PRACTICAL ILLUSTRATIONS IN EMBELLISHING WORK MOLDINGS.--The use of moldings was early resorted to by the nations of antiquity, and we marvel to-day at many of the beautiful designs which the Ph[oe]necians, the Greeks and the Romans produced. If you analyze the lines used you will be surprised to learn how few are the designs which go to make up the wonderful columns, spires, minarets and domes which are represented in the various types of architecture. THE BASIS OF MOLDINGS.--Suppose we take the base type of moldings, and see how simple they are and then, by using these forms, try to build up or ornament some article of furniture, as an example of their utility. THE SIMPLEST MOLDING.--In Fig. 185 we show a molding of the most elementary character known, being simply in the form of a band (A) placed below the cap. Such a molding gives to the article on which it is placed three distinct lines, C, D and E. If you stop to consider you will note that the molding, while it may add to the strength of the article, is primarily of service because the lines and surfaces produce shadows, and therefore become valuable in an artistic sense. THE ASTRAGAL.--Fig. 186 shows the ankle-bone molding, technically called the _Astragal_. This form is round, and properly placed produces a good effect, as it throws the darkest shadow of any form of molding. [Illustration: _Fig. 185. Band._] [Illustration: _Fig. 186. Astragal or Ankle Bone._] [Illustration: _Fig. 187. Cavetto. Concave._] [Illustration: _Fig. 188. Ovolo. Quarter round._] THE CAVETTO.--Fig. 187 is the cavetto, or round type. Its proper use gives a delicate outline, but it is principally applied with some other form of molding. THE OVOLO.--Fig. 188, called the ovolo, is a quarter round molding with the lobe (A) projecting downwardly. It is distinguished from the astragal because it casts less of a shadow above and below. THE TORUS.--Fig. 189, known as the torus, is a modified form of the ovolo, but the lobe (A) projects out horizontally instead of downwardly. THE APOPHYGES (Pronounced apof-i-ges).--Fig. 190 is also called the _scape_, and is a concaved type of molding, being a hollowed curvature used on columns where its form causes a merging of the shaft with the fillet. [Illustration: _Fig. 189. Torus._] [Illustration: _Fig. 190. Apophyge._] [Illustration: _Fig. 191. Cymatium._] [Illustration: _Fig. 192. Ogee-Recta._] THE CYMATIUM.--Fig. 191 is the cymatium (derived from the word cyme), meaning wave-like. This form must be in two curves, one inwardly and one outwardly. THE OGEE.--Fig. 192, called the ogee, is the most useful of all moldings, for two reasons: First, it may have the concaved surface uppermost, in which form it is called ogee recta--that is, right side up; or it may be inverted, as in Fig. 193, with the concaved surface below, and is then called ogee reversa. Contrast these two views and you will note what a difference the mere inversion of the strip makes in the appearance. Second, because the ogee has in it, in a combined form, the outlines of nearly all the other types. The only advantage there is in using the other types is because you may thereby build up and space your work better than by using only one simple form. [Illustration: _Fig. 193. Ogee-Reversa._] [Illustration: _Fig. 194. Bead or Reedy._] You will notice that the ogee is somewhat like the cymatium, the difference being that the concaved part is not so pronounced as in the ogee, and the convexed portion bulges much further than in the ogee. It is capable of use with other moldings, and may be reversed with just as good effect as the ogee. THE REEDY.--Fig. 194 represents the reedy, or the bead--that is, it is made up of reeds. It is a type of molding which should not be used with any other pronounced type of molding. THE CASEMENT (Fig. 195).--In this we have a form of molding used almost exclusively at the base of structures, such as columns, porticoes and like work. [Illustration:_ Fig. 195. Casement._] Now, before proceeding to use these moldings, let us examine a Roman-Doric column, one of the most famous types of architecture produced. We shall see how the ancients combined moldings to produce grace, lights and shadows and artistic effects. THE ROMAN-DORIC COLUMN.--In Fig. 196 is shown a Roman-Doric column, in which the cymatium, the ovolo, cavetto, astragal and the ogee are used, together with the fillets, bases and caps, and it is interesting to study this because of its beautiful proportions. [Illustration: _Fig. 196._] The pedestal and base are equal in vertical dimensions to the entablature and capital. The entablature is but slightly narrower than the pedestal; and the length of the column is, approximately, four times the height of the pedestal. The base of the shaft, while larger diametrically than the capital, is really shorter measured vertically. There is a reason for this. The eye must travel a greater distance to reach the upper end of the shaft, and is also at a greater angle to that part of the shaft, hence it appears shorter, while it is in reality longer. For this reason a capital must be longer or taller than the base of a shaft, and it is also smaller in diameter. It will be well to study the column not only on account of the wonderful blending of the various forms of moldings, but because it will impress you with a sense of proportions, and give you an idea of how simple lines may be employed to great advantage in all your work. LESSONS FROM THE DORIC COLUMN.--As an example, suppose we take a plain cabinet, and endeavor to embellish it with the types of molding described, and you will see to what elaboration the operation may be carried. APPLYING MOLDING.--Let Fig. 197 represent the front, top and bottom of our cabinet; and the first thing we shall do is to add a base (A) and a cap (B). Now, commencing at the top, suppose we utilize the simplest form of molding, the band. This we may make of any desired width, as shown in Fig. 198. On this band we can apply the ogee type (Fig. 199) right side up. But for variation we may decide to use the ogee reversed, as in Fig. 200. This will afford us something else to think about and will call upon our powers of initiative in order to finish off the lower margin or edge of the ogee reversa. [Illustration: _Fig. 197._] [Illustration: _Fig. 198._] [Illustration: _Fig. 199._] If we take the ogee recta, as shown in Fig. 201, we may use the cavetto, or the ovolo (Fig. 202); but if we use the ogee reversa we must use a convex molding like the cavetto at one base, and a convex molding, like the torus or the ovolo, at the other base. In the latter (Fig. 202) four different moldings are used with the ogee as the principal structure. BASE EMBELLISHMENTS.--In like manner (Fig. 204) the base may have the casement type first attached in the corner, and then the ovolo, or the astragal added, as in Fig. 203. [Illustration: _Fig. 200._] [Illustration: _Fig. 201._] [Illustration: _Fig. 202._] STRAIGHT-FACED MOLDINGS.--Now let us carry the principle still further, and, instead of using various type of moldings, we will employ nothing but straight strips of wood. This treatment will soon indicate to you that the true mechanic or artisan is he who can take advantage of whatever he finds at hand. Let us take the same cabinet front (Fig. 205), and below the cap (A) place a narrow strip (B), the lower corner of which has been chamfered off, as at C. Below the strip B is a thinner strip (D), vertically disposed, and about two-thirds its width. The lower corner of this is also chamfered, as at F. To finish, apply a small strip (G) in the corner, and you have an embellished top that has the appearance, from a short distance, of being made up of molding. PLAIN MOLDED BASE.--The base may be treated in the same manner. The main strip (4) has its upper corner chamfered off, as at I, and on this is nailed a thin, narrow finishing strip (J). The upper part or molded top, in this case, has eleven distinct lines, and the base has six lines. By experimenting you may soon put together the most available kinds of molding strips. [Illustration: _Fig. 203._] [Illustration: _Fig. 204._] DIVERSIFIED USES.--For a great overhang you may use the cavetto, or the apophyges, and below that the astragal or the torus; and for the base the casement is the most serviceable molding, and it may be finished off with the ovolo or the cymatium. Pages of examples might be cited to show the variety and the diversification available with different types. SHADOWS CAST BY MOLDINGS.--Always bear in mind that a curved surface makes a blended shadow. A straight, flat or plain surface does not, and it is for that reason the concaved and the convexed surfaces, brought out by moldings, become so important. [Illustration: _Fig. 205._] A little study and experimenting will soon teach you how a convex, a concave or a flat surface, and a corner or corners should be arranged relatively to each other; how much one should project beyond the other; and what the proportional widths of the different molding bands should be. An entire volume would scarcely exhaust this subject. CHAPTER X AN ANALYSIS OF TENONING, MORTISING, RABBETING AND BEADING In the chapter on How Work is Laid Out, an example was given of the particular manner pursued in laying out mortises and tenons, and also dovetailed work. I deem it advisable to add some details to the subject, as well as to direct attention to some features which do not properly belong to the laying out of work. WHERE MORTISES SHOULD BE USED.--Most important of all is a general idea of places and conditions under which mortises should be resorted to. There are four ways in which different members may be secured to each other. First, by mortises and tenons; second, by a lap-and-butt; third, by scarfing; and, fourth, by tonguing and grooving. DEPTH OF MORTISES.--When a certain article is to be made, the first consideration is, how the joint or joints shall be made. The general rule for using the tenon and mortise is where two parts are joined wherein the grains of the two members run at right angles to each other, as in the following figure. RULE FOR MORTISES.--Fig. 206 shows such an example. You will notice this in doors particularly, as an example of work. [Illustration: _Fig. 206._] [Illustration: _Fig. 207._] The next consideration is, shall the mortises be cut entirely through the piece? This is answered by the query as to whether or not the end of the tenon will be exposed; and usually, if a smooth finish is required, the mortise should not go through the member. In a door, however, the tenons are exposed at the edges of the door, and are, therefore, seen, so that we must apply some other rule. The one universally adopted is, that where, as in a door stile, it is broad and comparatively thin, or where the member having the mortise in its edge is much thinner than its width, the mortise should go through from edge to edge. The reason for this lies in the inability to sink the mortises through the stile (A, Fig. 207) perfectly true, and usually the job is turned out something like the illustration shows. The side of the rail (B) must be straight with the side of the stile. If the work is done by machinery it results in accuracy unattainable in hand work. [Illustration: _Fig. 208._] TRUE MORTISE WORK.--The essense of good joining work is the ability to sink the chisel true with the side of the member. More uneven work is produced by haste than by inability. The tendency of all beginners is to strike the chisel too hard, in order the more quickly to get down to the bottom of the mortise. Hence, bad work follows. STEPS IN CUTTING MORTISES.--Examine Fig. 208, which, for convenience, gives six successive steps in making the mortise. The marks _a_, _b_ designate the limits, or the length, of the mortise. The chisel (C) is not started at the marking line (A), but at least an eighth of an inch from it. The first cut, as at B, gives a starting point for the next cut or placement of the chisel. When the second cut (B) has thus been made, the chisel should be turned around, as in dotted line _d_, position C, thereby making a finish cut down to the bottom of the mortise, line _e_, so that when the fourth cut has been made along line _f_, we are ready for the fifth cut, position C; then the sixth cut, position D, which leaves the mortise as shown at E. Then turn the chisel to the position shown at F, and cut down the last end of the mortise square, as shown in G, and clean out the mortise well before making the finishing cuts on the marking lines (_a_, _b_). The particular reason for cleaning out the mortise before making the finish cuts is, that the corners of the mortise are used as fulcrums for the chisels, and the eighth of an inch stock still remaining protects the corners. THINGS TO AVOID IN MORTISING.--You must be careful to refrain from undercutting as your chisel goes down at the lines _a_, _b_, because if you commit this error you will make a bad joint. As much care should be exercised in producing the tenon, although the most common error is apt to occur in making the shoulder. This should be a trifle undercut. [Illustration: _Fig. 209._] See the lines (A, Fig. 209), which illustrate this. LAP-AND-BUTT JOINT.--The lap-and-butt is the form of uniting members which is most generally used to splice together timbers, where they join each other end to end. [Illustration: _Fig. 210._] Bolts are used to secure the laps. But the lap-and-butt form is also used in doors and in other cabinet work. It is of great service in paneling. A rabbet is formed to receive the edge of the panel, and a molding is then secured to the other side on the panel, to hold the latter in place. SCARFING.--This method of securing members together is the most rigid, and when properly performed makes the joint the strongest part of the timber. Each member (A, Fig. 212) has a step diagonally cut (B), the two steps being on different planes, so they form a hook joint, as at C, and as each point or terminal has a blunt end, the members are so constructed as to withstand a longitudinal strain in either direction. The overlapping plates (D) and the bolts (E) hold the joint rigidly. [Illustration: _Fig. 211._] [Illustration: _Fig. 212._] THE TONGUE AND GROOVE.--This form of uniting members has only a limited application. It is serviceable for floors, table tops, paneling, etc.